Works about the history of science

"Some of the Pythagoreans, if not Pythagoras himself, held that the earth is a sphere, and that the apparent daily revolution of the sun and stars is really due to a motion of the earth, though at first this motion of the earth was not supposed to be one of rotation about an axis."

"Eudoxus of Cnidus, endeavouring to account for the fact that the planets, during every apparent revolution round the earth, come to rest twice, and in the shorter interval between these “stationary points,” move in the opposite direction, found that he could represent the phenomena fairly well by a system of concentric spheres, each rotating with its own velocity, and carrying its own particular planet round its own equator, the outermost sphere carrying the fixed stars. ...the total number required by Aristotle reaching fifty-five."

"It may be regarded as counting in Aristotle’s favour that he did consider the earth to be a sphere and not a flat disc, but he seems to have thought that the mathematical spheres of Eudoxus had a real solid existence, and that not only meteors, shooting stars and aurora, but also comets and the milky way belong to the atmosphere."

"Aristarchus of Samos seems to have been the first to suggest that the planets revolved not about the earth but about the sun, but the idea seemed so improbable that it was hardly noticed, especially as Aristarchus himself did not expand it into a treatise."

"Hipparchus... noted the irregular motion of the sun, and, to explain it, assumed that it revolved uniformly not exactly about the earth but about a point some distance away, called the “excentric”. The same result he could obtain by assuming that the sun moved round a small circle, whose center described a larger circle about the earth; this larger circle carrying the other was called the “deferent”: so that the actual motion of the sun was in an epicycle. He... discovered the Precession of the Equinoxes."

"No advance was made in theoretical astronomy for 260 years, the interval between Hipparchus and Ptolemy of Alexandria."

"In his [ Ptolemy's ] planetary theory... in general the agreement between theory and observation was spoilt by the necessity of making all the orbital planes pass through the center of the earth, instead of the sun, thus making a good accordance practically impossible."

"After Ptolemy’s time very little was heard for many centuries of any fresh planetary theory, though advances in some points of detail were made, notably by some of the Arab philosophers, who obtained improved values for some of the elements by using better instruments. From time to time various modifications of Ptolemy’s theory were suggested, but none of any real value."

"In Spain... in the thirteenth century Alphonso of Castile, with the assistance of Jewish and Christian computers, compiled the Alphonsine tables, completed in 1252."

"Reviewing the suggestions of the ancient Greeks, he [ Copernicus ] was struck by the simplification that would be introduced by reviving the idea that the annual motion should be attributed to the earth itself instead of having a separate annual epicycle for each planet and for the sun. Of the seventy odd circles or epicycles required by the latest form of the Ptolemaic system, Copernicus succeeded in dispensing with rather more than half, but he still required thirty-four, which was the exact number assumed before the time of Aristotle."

"His [ Copernicus' ] considerations were almost entirely mathematical, his only invasion into physics being in defense of the “moving earth” against the stock objection that if the earth moved, loose objects would fly off, and towers fall. He did not break sufficiently away from the old tradition of uniform circular motion. ...he would not sacrifice the old fetish, and so, the orbit of the earth being clearly not circular with respect to the sun, he made all his planetary planes pass through the center of the earth’s orbit, instead of through the sun, thus handicapping himself in the same way though not in the same degree as Ptolemy. His thirty-four circles or epicycles comprised four for the earth, three for the moon, seven for Mercury (on account of his highly eccentric orbit) and five each for the other planets."

"It is rather an exaggeration to call the present accepted system the Copernican system, as it is really due to Kepler, half a century after the death of Copernicus, but much credit is due to the latter for his successful attempt to provide a real alternative for the Ptolemaic system, instead of tinkering with it."

"The old geocentric system once shaken, the way was gradually smoothed for the heliocentric system, which Copernicus, still hampered by tradition, did not quite reach. He was hardly a practical astronomer in the observational sense. His first recorded observation, of an occultation of Aldebaran, was made in 1497, and he is not known to have made as many as fifty astronomical observations, while, of the few he did make and use, at least one was more than half a degree in error, which would have been intolerable to such an observer as Hipparchus."

"Luther, with his obstinate conviction of the verbal accuracy of the Scriptures, rejected as mere folly the idea of a moving earth, and Melanchthon thought such opinions should be prohibited, but Rheticus, a professor at the Protestant University of Wittenberg and an enthusiastic pupil of Copernicus, urged publication, and undertook to see the work through the press. This, however, he was unable to complete and another Lutheran, Osiander, to whom he entrusted it, wrote a preface, with the apparent intention of disarming opposition, in which he stated that the principles laid down were only abstract hypotheses convenient for purposes of calculation. This unauthorized interpolation may have had its share in postponing the prohibition of the book by the Church of Rome."

"According to Copernicus the earth is only a planet like the others, and not even the biggest one, while the sun is the most important body in the system, and the stars probably too far away for any motion of the earth to affect their apparent places. ...He shows that the revolution of the earth will account for the seasons, and for the stationary points and retrograde motions of the planets. He corrects definitely the order of the planets outwards from the sun, a matter which had been in dispute. A notable defect is due to the idea that a body can only revolve about another body or a point, as if rigidly connected with it, so that, in order to keep the earth’s axis in a constant direction in space, he has to invent a third motion."

"With all its defects, partly due to reliance on bad observations, the work [ De revolutionibus orbium coelestium ] showed a great advance in the interpretation of the motions of the planets; and his determinations of the periods both in relation to the earth and to the stars were adopted by Reinhold, Professor of Astronomy at Wittenberg, for the new Prutenic or Prussian Tables, which were to supersede the obsolete Alphonsine Tables of the thirteenth century."

"In comparison with the question of the motion of the earth, no other astronomical detail of the time seems to be of much consequence. Comets, such as from time to time appeared, bright enough for naked eye observation, were still regarded as atmospheric phenomena, and their principal interest, as well as that of eclipses and planetary conjunctions, was in relation to astrology."

"The doctrine of Copernicus was destined very soon to divide others besides the Lutheran leaders. The leaven of inquiry was working, and not long after the death of Copernicus real advances were to come, first in the accuracy of observations, and, as a necessary result of these, in the planetary theory itself."

"On 21st December, 1571, at Weil in the Duchy of Wurtemberg, was born a weak and sickly seven-months’ child, to whom his parents Henry and Catherine Kepler gave the name of John. Henry Kepler was a petty officer in the service of the reigning Duke, and in 1576 joined the army serving in the Netherlands. His wife followed him, leaving her young son in his grandfather’s care at Leonberg, where he barely recovered from a severe attack of smallpox. It was from this place that John derived the Latinised name of Leonmontanus."

"His astronomical tutor, Maestlin, encouraged him to devote himself to his newly adopted science, and the first result of this advice appeared before very long in Kepler’s “Mysterium Cosmographicum”. The bent of his mind was towards philosophical speculation, to which he had been attracted in his youthful studies of Scaliger’s “Exoteric Exercises” (Exotericarum exercitationum). He says he devoted much time “to the examination of the nature of heaven, of souls, of genii, of the elements, of the essence of fire, of the cause of fountains, the ebb and flow of the tides, the shape of the continents and inland seas, and things of this sort.”"

"Following his tutor in his admiration for the Copernican theory, he [ Kepler ] wrote an essay on the primary motion, attributing it to the rotation of the earth, and this not for the mathematical reasons brought forward by Copernicus, but, as he himself says, on physical or metaphysical grounds."

"He was nevertheless unwilling to adopt the opinion of Rheticus that the number six was sacred, maintaining that the “sacredness” of the number was of much more recent date than the creation of the worlds, and could not therefore account for it."

"The actual planets moreover were not even six but only five, so far as he knew, so he next pondered the question of what sort of things these could be of which only five different figures were possible and suddenly thought of the five regular solids. He immediately pounced upon this idea and ultimately evolved the following scheme. “The earth is the sphere, the measure of all; round it describe a dodecahedron; the sphere including this will be Mars. Round Mars describe a tetrahedron; the sphere including this will be Jupiter. Describe a cube round Jupiter; the sphere including this will be Saturn. Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury.” With this result Kepler was inordinately pleased, and regretted not a moment of the time spent in obtaining it, though to us this “Mysterium Cosmographicum” can only appear useless, even without the more recent additions to the known planets."

"He admitted that a certain thickness must be assigned to the intervening spheres to cover the greatest and least distances of the several planets from the sun, but even then some of the numbers obtained are not a very close fit for the corresponding planetary orbits. Kepler’s own suggested explanation of the discordances was that they must be due to erroneous measures of the planetary distances, and this, in those days of crude and infrequent observations, could not easily be disproved."

"The next subject... dealt with the relation between the distances of the planets and their times of revolution round the sun. It was obvious that the period was not simply proportional to the distance, as the outer planets were all too slow for this, and he concluded “either that the moving intelligences of the planets are weakest in those that are farthest from the sun, or that there is one moving intelligence in the sun, the common centre, forcing them all round, but those most violently which are nearest, and that it languishes in some sort and grows weaker at the most distant, because of the remoteness and the attenuation of the virtue”. This is not so near a guess at the theory of gravitation as might be supposed, for Kepler imagined that a repulsive force was necessary to account for the planets being sometimes further from the sun, and so laid aside the idea of a constant attractive force."

"He sent copies of his book [Mysterium Cosmographicum] to several leading astronomers, of whom Galileo praised his ingenuity and good faith, while Tycho Brahe was evidently much struck with the work and advised him to adapt something similar to the Tychonic system instead of the Copernican. He also intimated that his Uraniborg observations would provide more accurate determinations of the planetary orbits, and thus made Kepler eager to visit him."

"Another copy of the book Kepler sent to Reymers the Imperial astronomer with a most fulsome letter, which Tycho, who asserted that Reymers had simply plagiarised his work, very strongly resented, thus drawing from Kepler a long letter of apology."

"About the same time Kepler had married a lady already twice widowed, and become involved in difficulties with her relatives on financial grounds, and with the Styrian authorities in connection with the religious disputes then coming to a head. On account of these latter he thought it expedient, the year after his marriage, to withdraw to Hungary, from whence he sent short treatises to Tübingen, “On the magnet” (following the ideas of Gilbert of Colchester), “On the cause of the obliquity of the ecliptic” and “On the Divine wisdom as shown in the Creation”."

"The age following that of Copernicus produced three outstanding figures associated with the science of astronomy, then reaching the close of what Professor Forbes so aptly styles the geometrical period. These three Sir David Brewster has termed “Martyrs of Science”; Galileo, the great Italian philosopher, has his own place among the “Pioneers of Science”; and invaluable though Tycho Brahe’s work was, the latter can hardly be claimed as a pioneer in the same sense as the other two. Nevertheless, Kepler, the third member of the trio, could not have made his most valuable discoveries without Tycho’s observations."

"Of noble family, born a twin on 14th December, 1546, at Knudstrup in Scania (the southernmost part of Sweden, then forming part of the kingdom of Denmark), Tycho was kidnapped a year later by a childless uncle. This uncle brought him up as his own son, provided him at the age of seven with a tutor, and sent him in 1559 to the University of Copenhagen, to study for a political career by taking courses in rhetoric and philosophy."

"On 21st August, 1560, however, a solar eclipse took place, total in Portugal, and therefore of small proportions in Denmark, and Tycho’s keen interest was awakened, not so much by the phenomenon, as by the fact that it had occurred according to prediction. Soon afterwards he purchased an edition of Ptolemy in order to read up the subject of astronomy, to which, and to mathematics, he devoted most of the remainder of his three years’ course at Copenhagen."

"He obtained the Alphonsine and the new Prutenic Tables, but soon found that the latter, though more accurate than the former, failed to represent the true positions of the planets, and grasped the fact that continuous observation was essential in order to determine the true motions."

"He provided himself with a cross-staff for determining the angular distance between stars or other objects, and, finding the divisions of the scale inaccurate, constructed a table of corrections, an improvement that seems to have been a decided innovation, the previous practice having been to use the best available instrument and ignore its errors."

"He matriculated at Rostock, where he found little astronomy but a good deal of astrology. While there he fought a duel in the dark and lost part of his nose, which he replaced by a composition of gold and silver."

"In 1568 Tycho left Rostock, and matriculated at Basle, but soon moved on to Augsburg, where he found more enthusiasm for astronomy, and induced one of his new friends to order the construction of a large 19-foot quadrant of heavy oak beams. This was the first of the series of great instruments associated with Tycho’s name, and it remained in use for five years, being destroyed by a great storm in 1574."

"On 11th November, 1572, Tycho noticed an unfamiliar bright star in the constellation of Cassiopeia, and continued to observe it with a sextant. It was a very brilliant object, equal to Venus at its brightest for the rest of November, not falling below the first magnitude for another four months, and remaining visible for more than a year afterwards."

"Tycho wrote a little book [On the New Star or De nova stella] on the new star, maintaining that it had practically no parallax, and therefore could not be, as some supposed, a comet. Deeming authorship beneath the dignity of a noble he was very reluctant to publish, but he was convinced of the importance of increasing the number and accuracy of observations, though he was by no means free from all the erroneous ideas of his time. The little book contained a certain amount of astrology, but Tycho evidently did not regard this as of very great importance. He adopted the view that the very rarity of the phenomenon of a new star must prevent the formulation and adoption of definite rules for determining its significance."

"We gather from lectures which he was persuaded to deliver at the University of Copenhagen that, though in agreement with the accepted canons of astrology as to the influence of planetary conjunctions and such phenomena on the course of human events, he did not consider the fate predicted by anyone’s horoscope to be unavoidable, but thought the great value of astrology lay in the warnings derived from such computations, which should enable the believer to avoid threatened calamities."

"In 1575 he left Denmark once more and made his way to Cassel, where he found a kindred spirit in the studious Landgrave, William IV of Hesse, whose astronomical pursuits had been interrupted by his accession to the government of Hesse, in 1567. Tycho observed with him for some time, the two forming a firm friendship, and then visited successively Frankfort, Basle, and Venice, returning by way of Augsburg, Ratisbon, and Saalfeld to Wittenberg; on the way he acquired various astronomical manuscripts, made friends among practical astronomers, and examined new instruments."

"On his return to Denmark to fetch his family with the object of transferring them to Basle, he found that his friend the Landgrave had written to King Frederick on his behalf."

"Tycho accepted from the king a grant of the small island of Hveen, in the Sound, with a guaranteed income... Here Tycho built his celebrated observatory of Uraniborg and began observations in December, 1576, using the large instruments then found necessary in order to attain the accuracy of observation which within the next half-century was to be so greatly facilitated by the invention of the telescope. ...For more than twenty years he continued his observations at Uraniborg, surrounded by his family, and attracting numerous pupils."

"His [Tycho's] constant aim was to accumulate a large store of observations of a high order of accuracy, and thus to provide data for the complete reform of astronomy."

"Few of the Danish nobles had any sympathy with Tycho’s pursuits, and most of them strongly resented the continual expense borne by the King’s treasury. Tycho moreover was so absorbed in his scientific pursuits that he would not take the trouble to be a good landlord, nor to carry out all the duties laid upon him in return for certain of his grants of income."

"His buildings included a chemical laboratory, and he was in the habit of making up elixirs for various medical purposes; these were quite popular, particularly as he made no charge for them. He seems to have been something of a homœopathist, for he recommends sulphur to cure infectious diseases “brought on by the sulphurous vapours of the Aurora Borealis”!"

"In November, 1577, appeared a bright comet, which Tycho carefully observed with his sextant, proving that it had no perceptible parallax, and must therefore be further off than the moon. He thus definitely overthrew the common belief in the atmospheric origin of comets, which he had himself hitherto shared. With increasing accuracy he observed several other comets, notably one in 1585, when he had a full equipment of instruments and a large staff of assistants."

"The year 1588, which saw the death of his royal benefactor, saw also the publication of a volume of Tycho’s great work “Introduction to the New Astronomy”. The first volume, devoted to the new star of 1572, was not ready, because the reduction of the observations involved so much research to correct the star places for refraction, precession, etc.; it was not completed in fact until Tycho’s death, but the second volume, dealing with the comet of 1577, was printed at Uraniborg and some copies were issued in 1588. Besides the comet observations it included an account of Tycho’s system of the world."

"He [Tycho] would not accept the Copernican system, as he considered the earth too heavy and sluggish to move, and also that the authority of Scripture was against such an hypothesis. He therefore assumed that the other planets revolved about the sun, while the sun, moon, and stars revolved about the earth as a center. Geometrically this is much the same as the Copernican system, but physically it involves the grotesque demand that the whole system of stars revolves round our insignificant little earth every twenty-four hours."

"Since his previous small book on the comet, Tycho had evidently considered more fully its possible astrological significance, for he foretold a religious war, giving the date of its commencement, and also the rising of a great Protestant champion. These predictions were apparently fulfilled almost to the letter by the great religious wars that broke out towards the end of the sixteenth century, and in the person of Gustavus Adolphus."

"He [Tycho]... reached Prague in June, 1599. Rudolph granted him a salary of at least 3000 florins, promising also to settle on him the first hereditary estate that should lapse to the Crown."

"Kepler, who had been in correspondence with Tycho, consented to join him as an assistant. Another assistant, Longomontanus, who had been with Tycho at Uraniborg, was finding difficulty with the long series of Mars observations, and it was arranged that he should transfer his energies to the lunar observations, leaving those of Mars for Kepler. Before very much could be done with them, however, Tycho died at the end of October, 1601"

"It was at Uraniborg that the mass of observations was produced upon which the fame of Tycho Brahe rests. His own discoveries, though in themselves the most important made in astronomy for many centuries, are far less valuable than those for which his observations furnished the material."

"He [Tycho] discovered the third and fourth inequalities of the moon in longitude, called respectively the variation and the annual equation, also the variability of the motion of the moon’s nodes and the inclination of its orbit to the ecliptic. He obtained an improved value of the constant of precession, and did good service by rejecting the idea that it was variable, an idea which, under the name of trepidation, had for many centuries been accepted. He discovered the effect of refraction, though only approximately its amount, and determined improved values of many other astronomical constants, but singularly enough made no determination of the distance of the sun, adopting instead the ancient and erroneous value given by Hipparchus."

"His [Tycho's] magnificent Observatory of Uraniborg, the finest building for astronomical purposes that the world had hitherto seen, was allowed to fall into decay, and scarcely more than mere indications of the site may now be seen."

"Kepler was delayed by illness on the way, but ultimately reached Prague, accompanied by his wife, and for some time lived entirely at Tycho’s expense, writing by way of return essays against Reymers and another man, who had claimed the credit of the Tychonic system."

"In September, 1601, Tycho presented him [Kepler] to the Emperor, who gave him the title of Imperial Mathematician, on condition of assisting Tycho in his calculations, the very thing Kepler was most anxious to be allowed to do: for nowhere else in the world was there such a collection of good observations sufficient for his purpose of reforming the whole theory of astronomy."

"Tycho... died of acute distemper; Kepler began to prepare the mass of manuscripts for publication, but, as everything was claimed by the Brahe family, he was not allowed to finish the work. He succeeded to Tycho’s post of principal mathematician to the Emperor, at a reduced official salary. In order to meet his expenses he had recourse to the casting of nativities, for which he gained considerable reputation and received very good pay. He worked by the conventional rules of astrology, and was quite prepared to take fees for so doing, although he had very little faith in them, preferring his own fanciful ideas."

"In 1604 the constellation of Cassiopeia was once more temporarily enriched by the appearance of a new star... Kepler at once wrote a short account of it... He made no secret of his views on conventional astrology, as to which he claimed to speak with the authority of one fully conversant with its principles, but he nevertheless expressed his sincere conviction that the conjunctions and aspects of the planets certainly did affect things on the earth, maintaining that he was driven to this belief against his will by “most unfailing experiences”."

"In 1604 he [Kepler] published “A Supplement to Vitellion,” containing the earliest known reasonable theory of optics, and especially of dioptrics or vision through lenses. He compared the mechanism of the eye with that of Porta’s “Camera Obscura,” but made no attempt to explain how the image formed on the retina is understood by the brain. He went carefully into the question of refraction, the importance of which Tycho had been the first astronomer to recognize, though he only applied it at low altitudes, and had not arrived at a true theory or accurate values."

"Kepler wasted a good deal of time and ingenuity on trial theories. He would invariably start with some hypothesis, and work out the effect. He would then test it by experiment, and when it failed would at once recognize that his hypothesis was a priori bound to fail. He rarely seems to have noticed the fatal objections in time to save himself trouble. He would then at once start again on a new hypothesis, equally gratuitous and equally unfounded. It never seems to have occurred to him that there might be a better way of approaching a problem."

"Not many years later Snell discovered the true law of refraction, but Kepler’s contribution to the subject, though he failed to discover the actual law, includes several of the adopted “by-laws”. He noted that atmospheric refraction would alter with the height of the atmosphere and with temperature, and also recognized the fact that rainbow colors depend on the angle of refraction, whether seen in the rainbow itself, or in dew, glass, water, or any similar medium. He thus came near to anticipating Newton."

"After hearing of Galileo’s telescope, Kepler suggested that for astronomical purposes two convex lenses should be used, so that there should be a real image where measuring wires could be placed for reference. He did not carry out the idea himself, and it was left to the Englishman Gascoigne to produce the first instrument on this “Keplerian” principle, universally known as the Astronomical Telescope."

"In 1606 came a second treatise on the new star... This was followed in 1607 by a treatise on comets, suggested by the comet appearing that year, known as Halley’s comet after its next return. He regarded comets as “planets” moving in straight lines, never having examined sufficient observations of any comet to convince himself that their paths are curved."

"Another suggestive remark of his [Kepler's] was to the effect that the planets must be self-luminous, as otherwise Mercury and Venus, at any rate, ought to show phases. This was put to the test not long afterwards by means of Galileo’s telescope."

"In 1607 Kepler rushed into print with an alleged observation of Mercury crossing the sun, but after Galileo’s discovery of sun-spots, Kepler at once cheerfully retracted his observation of “Mercury,” and... warmly adopted Galileo’s side... Maestlin and others of Kepler’s friends took the opposite view."

"When Gilbert of Colchester, in his “New Philosophy,” founded on his researches in magnetism, was dealing with tides, he did not suggest that the moon attracted the water, but that “subterranean spirits and humours, rising in sympathy with the moon, cause the sea also to rise and flow to the shores and up rivers”. It appears that an idea, presented in some such way as this, was more readily received than a plain statement. This so-called philosophical method was, in fact, very generally applied, and Kepler, who shared Galileo’s admiration for Gilbert’s work, adopted it in his own attempt to extend the idea of magnetic attraction to the planets."

"The general idea of “gravity” opposed the hypothesis of the rotation of the earth on the ground that loose objects would fly off: moreover, the latest refinements of the old system of planetary motions necessitated their orbits being described about a mere empty point. Kepler very strongly combated these notions, pointing out the absurdity of the conclusions to which they tended, and proceeded in set terms to describe his own theory."

"“Every corporeal substance, so far forth as it is corporeal, has a natural fitness for resting in every place where it may be situated by itself beyond the sphere of influence of a body cognate with it. Gravity is a mutual affection between cognate bodies towards union or conjunction (similar in kind to the magnetic virtue), so that the earth attracts a stone much rather than the stone seeks the earth. ...wheresoever the earth may be placed, or whithersoever it may be carried by its animal faculty, heavy bodies will always be carried towards it. If the earth were not round, heavy bodies would not tend from every side in a straight line towards the centre of the earth, but to different points from different sides. If two stones were placed... near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other. If the moon and earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon fall towards the earth through the other fifty-three parts, and they would there meet, assuming, however, that the substance of both is of the same density. If the earth should cease to attract its waters to itself all the waters of the sea would he raised and would flow to the body of the moon. The sphere of the attractive virtue which is in the moon extends as far as the earth, and entices up the waters; but as the moon flies rapidly across the zenith, and the waters cannot follow so quickly, a flow of the ocean is occasioned in the torrid zone towards the westward. If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue. Nothing which consists of corporeal matter is absolutely light, but that is comparatively lighter which is rarer, either by its own nature, or by accidental heat. And it is not to be thought that light bodies are escaping to the surface of the universe while they are carried upwards, or that they are not attracted by the earth. They are attracted, but in a less degree, and so are driven outwards by the heavy bodies; which being done, they stop, and are kept by the earth in their own place. But although the attractive virtue of the earth extends upwards, as has been said, so very far, yet if any stone should be at a distance great enough to become sensible compared with the earth’s diameter, it is true that on the motion of the earth such a stone would not follow altogether; its own force of resistance would be combined with the attractive force of the earth, and thus it would extricate itself in some degree from the motion of the earth.” The above passage from the Introduction to Kepler’s “Commentaries on the Motion of Mars,” always regarded as his most valuable work, must have been known to Newton, so that no such incident as the fall of an apple was required to provide a necessary and sufficient explanation of the genesis of his Theory of Universal Gravitation. Kepler’s glimpse at such a theory could have been no more than a glimpse, for he went no further with it. This seems a pity, as it is far less fanciful than many of his [Kepler's] ideas, though not free from the “virtues” and “animal faculties,” that correspond to Gilbert’s “spirits and humours”."

"When I began the study my object was to bring forward the many strong and true features of pre-Darwinian Evolution which are so generally passed over or misunderstood."

"In the growth of the numerous lesser ideas which have converged into the central idea of the history of life by Evolution, we find ancient pedigrees for all that we are apt to consider modern."

"Darwin owes more even to the Greeks than we have ever recognized."

"The Evolution law was reached not by any decided leap, but by the progressive development of every subordinate idea connected with it until it was recognized as a whole by Lamarck, and later by Darwin."

"I endeavor to trace back some of these lesser ideas to their sources, and to bring the comparatively little known early evolutionists into their true relief as original thinkers and contributors, or mere borrowers and imitators."

"The greatest defects I find in the historical literature of this subject are the lack of sense of proportion as to the original merits of different writers, and the non-appreciation of the continuity of evolution thought."

"We meet with many remarkable coincidences in the lines of independent and even simultaneous discovery, notably those between Erasmus Darwin and Lamarck, between Lamarck and Treviranus, before we reach the crowning and most exceptional case of Darwin and Wallace."

"At different periods similar facts were leading men to similar conclusions, and we gather many fine illustrations of the force of unconscious induction. Means of intercommunication were slow, and we should advance cautiously before concluding that any of the greater evolutionists were dealing with borrowed ideas."

"When we study single passages, we are often led widely afield. Haeckel, for example, appears to have far overstated the relative merits of Oken... Krause has placed Erasmus Darwin over Lamarck without sufficient consideration. Huxley has treated Treviranus and Lamarck with almost equal respect; they are really found to be most unequal."

"We must inquire into the sources or grounds of the conclusions advanced by each writer, how far derived from others how far from observation of Nature, and consider the soundness of each as well as his suggestiveness and originality, before we can judge fairly what permanent links he may have added or welded into the chain of thought."

"We are now taking our uncertain steps in search of the separate factors of this law, and cannot foresee when these will be completed. 'Before and after Darwin' will always be the ante et post urbem conditam [before and after the founding of the city] of biological history. Before Darwin, the theory; after Darwin, the factors."

"Lamarck has lately risen in popular knowledge as having propounded Evolution, but among his contemporaries and predecessors in France, Germany, and England, we find Buffon, Erasmus Darwin, Goethe, Treviranus, and searching for their inspiration, we are led back to the natural philosophers, beginning with Bacon, and ending with Herder. Among these men we find the second birth or renaissance of the idea, and among the Greeks its first birth."

"We know that Greek philosophy tinctured early Christian theology; it is not so generally realized that the Aristotelian notion of the development of life led to the true interpretation of the Mosaic account of the Creation."

"As late as the seventeenth century, the Jesuit Suarez and others contended that the Book of Genesis contained a literal account of the mode of Creation, and thereby Special Creation acquired a firm status as a theory in the contemporary philosophy. Singularly enough, Milton's epics appeared shortly afterwards, exerting an equally profound influence upon English Protestant thought, so that Huxley has aptly termed Special Creation, 'the Miltonic hypothesis.' Thus the opportunity of a free unchecked development out of natural science was lost."

"The contemplation of the various steps by which mankind has come into possession of the vast stock of mathematical knowledge can hardly fail to interest the mathematician. He takes pride in the fact that his science, more than any other, is an exact science and that hardly anything ever done in mathematics has proved to be useless."

"The chemist smiles at the childish efforts of alchemists but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of today."

"[Mathematics] warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialisation on the part of investigators, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken in other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoitre and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken."

"An untold amount of intellectual energy has been expended on the quadrature of the circle, yet no conquest has been made by direct assault. The circle-squarers have existed in crowds ever since the period of Archimedes. After innumerable failures to solve the problem at a time, even when investigators possessed that most powerful tool, the differential calculus, persons versed in mathematics dropped the subject, while those who still persisted were completely ignorant of its history and generally misunderstood the conditions of the problem. ...But progress was made on this problem by approaching it from a different direction and by newly discovered paths. Lambert proved in 1761 that the ratio of the circumference of a circle to its diameter is incommensurable. Some years ago, Lindemann demonstrated that this ratio is also transcendental and that the quadrature of the circle, by means of the ruler and compass only, is impossible. He thus showed by actual proof that which keen minded mathematicians had long suspected; namely, that the great army of circle-squarers have, for two thousand years, been assaulting a fortification which is as indestructible as the firmament of heaven."

"Another reason for the desirability of historical study is the value of historical knowledge to the teacher of mathematics."

"The interest which pupils take in their studies may be greatly increased if the solution of problems and the cold logic of geometrical demonstrations are interspersed with historical remarks and anecdotes."

"A class in arithmetic will be pleased to hear about the Hindoos and their invention of the "Arabic notation;" they will marvel at the thousands of years which elapsed before people had even thought of introducing into the numeral notation that Columbus-egg -- the zero; they will find it astounding that it should have taken so long to invent a notation which they themselves can now learn in a month."

"After the pupils have learned how to bisect a given angle, surprise them by telling of the many futile attempts which have been made to solve, by elementary geometry, the apparently very simple problem of the trisection of an angle."

"When they [students] know how to construct a square whose area is double the area of a given square, tell them about the duplication of the cube -- how the wrath of Apollo could be appeased only by the construction of a cubical altar double the given altar, and how mathematicians long wrestled with this problem."

"After the class have exhausted their energies on the theorem of the right triangle, tell them something about its discoverer -- how Pythagoras, jubilant over his great accomplishment, sacrificed a hecatomb to the Muses who inspired him."

"When the value of mathematical training is called in question, quote the inscription over the entrance into the academy of Plato, the philosopher: "Let no one who is unacquainted with geometry enter here.""

"Students in analytical geometry should know something of Descartes, and, after taking up the differential and integral calculus, they should become familiar with the parts that Newton, Leibniz, and Lagrange played in creating that science."

"In his historical talk it is possible for the teacher to make it plain to the student that mathematics is not a dead science, but a living one in which steady progress is made."

"The history of mathematics is important also as a valuable contribution to the history of civilisation. Human progress is closely identified with scientific thought. Mathematical and physical researches are a reliable record of intellectual progress. The history of mathematics is one of the large windows through which the philosophic eye looks into past ages and traces the line of intellectual development."

"Of the largest numbers written in cuneiform symbols, which have hitherto been found, none go as high as a million."

"Most surprising... is the fact that Sumerian inscriptions disclose the use, not only of the... decimal system but also of a sexagesimal one. ...We possess two Babylonian tablets which exhibit its use. One... contains a table of square numbers up to 602. The numbers 1, 4, 9, 16, 25, 36, 49, are given as the squares of the first seven integers respectively. We have next 1.4=82 1.21=92 1.40=102 2.1=112, etc. This remains unintelligible unless we assume the sexagesimal scale, which makes 1.4=60+4 1.21=60+21 2.1=2*60+1."

"The second [Babylonian] tablet records the magnitude of the illuminated portion of the moon's disc for every day from new to full moon, the whole disc being assumed to consist of 240 parts. ...This table not only exhibits the use of the sexagesimal system but also indicates the acquaintance of the Babylonians with [ geometric and arithmetic ] progressions."

"Not to be overlooked is the fact that in the [Babylonian] sexagesimal notation of integers the "principle of position" was employed. Thus in 1.4 (=64)... The introduction of this principle at so early a date is the more remarkable, because in the decimal notation it was not introduced till about the fifth or sixth century after Christ."

"The principle of position, in its general and systematic application, requires a symbol for zero. We ask, Did the Babylonians possess one? Neither of the above tables answers this question for they... contain no number in which there was occasion to use a zero."

"The sexagesimal system was used also in fractions. Thus, in the Babylonian inscriptions, 1/2 and 1/3 are designated by 30 and 20, the reader being expected, in his mind, to supply the word "sixtieths." The Greek geometer Hypsicles and the Alexandrian astronomer Ptolemæus borrowed the sexagesimal notation of fractions from the Babylonians and introduced it into Greece. From that time sexagesimal fractions held almost full sway in astronomical and mathematical calculations until the sixteenth century, when they finally yielded their place to the decimal fractions."

"It may be asked, What led to the invention of the sexagesimal system? Why was it that 60 parts were selected? ...Cantor offers the following theory: At first the Babylonians reckoned the year at 360 days. This led to the division of the circle into 360 degrees, each degree representing the daily amount of the supposed yearly revolution of the sun around the earth. Now they were, very probably, familiar with the fact that the radius can be applied to its circumference as a chord 6 times, and that each of these chords subtends an arc measuring exactly 60 degrees. Fixing their attention upon these degrees, the division into 60 parts may have suggested itself to them. Thus, when greater precision necessitated a subdivision of the degree, it was partitioned into 60 minutes."

"The division of the day into 24 hours, and of the hour into minutes and seconds on the scale of 60, is due to the Babylonians."

"Iamblichus attributes to them [the people in the Tigro-Euphrates basin] also a knowledge of proportion, and even the invention of the so called musical proportion. Though we possess no conclusive proof, we have nevertheless reason to believe that in practical calculation they used the abacus. ...Now, Babylon was once a great commercial centre,—the metropolis of many nations,—and it is therefore not unreasonable to suppose that her merchants employed this most improved aid to calculation."

"In geometry the Babylonians accomplished almost nothing. Besides the division of the circumference [of the circle] into 6 parts by its radius, and into 360 degrees, they had some knowledge of geometrical figures, such as the triangle and quadrangle, which they used in their auguries. Like the Hebrews (1 Kin. 7:23), they took π=3. Of geometrical demonstrations, there is, of course no trace. "As a rule, in the Oriental mind the intuitive powers eclipse the severely rational and logical.""

"When Alexander the Great, after the battle of Arbela (331 B.C.), took possession of Babylon, Callisthenes found there on burned brick astronomical records reaching back as far as 2234 B.C. Porphyrius says that these were sent to Aristotle. Ptolemy, the Alexandrian astronomer, possessed a Babylonian record of eclipses going back to 747 BC. Recently, Epping and [Johann Nepomuk] Strassmaier threw considerable light on Babylonian chronology and astronomy by explaining two calendars of the years 123 B.C. and 111 B.C. ...These scholars have succeeded in giving an account of the Babylonian calculation of the new and full moon and have identified by calculations the Babylonian names of the planets and of the twelve zodiacal signs and twenty-eight normal stars which correspond to some extent with the twenty eight nakshatras of the Hindoos."

"Though there is great difference of opinion regarding the antiquity of Egyptian civilisation, yet all authorities agree in the statement that, however far back they go, they find no uncivilised state of society."

"All Greek writers are unanimous in ascribing, without envy, to Egypt the priority of invention in the mathematical sciences. Geometry, in particular, is said by Herodotus, Diodorus, Diogenes Laertius, Iamblichus, and other ancient writers to have originated in Egypt."

"A hieratic papyrus, included in the Rhind collection of the British Museum, was deciphered by Eisenlohr in 1877, and found to be a mathematical manual containing problems in arithmetic and geometry. It was written by Ahmes some time before 1700 B.C., and was founded on an older work believed by Birch to date back as far as 3400 B.C.! This curious papyrus -- the most ancient mathematical handbook known to us -- puts us at once in contact with the mathematical thought in Egypt of three or five thousand years ago. It is entitled "Directions for obtaining the Knowledge of all Dark Things." We see from it that the Egyptians cared but little for theoretical results. Theorems are not found in it at all. It contains "hardly any general rules of procedure, but chiefly mere statements of results intended possibly to be explained by a teacher to his pupils.""

"In geometry the forte of the Egyptians lay in making constructions and determining areas. The area of an isosceles triangle, of which the sides measure 10 ruths and the base 4 ruths, was erroneously given as 20 square ruths, or half the product of the base by one side. The area of an isosceles trapezoid is found, similarly by multiplying half the sum of the parallel sides by one of the non-parallel sides. The area of a circle is found by deducting from the diameter 1/2 of its length and squaring the remainder. Here π is taken=(16/9)2=3.1604..., a very fair approximation. The papyrus explains also such problems as these,—To mark out in the field a right triangle whose sides are 10 and 4 units; or a trapezoid whose parallel sides are 6 and 4, and the non-parallel sides each 20 units."

"Some problems in this [Rhind] papyrus seem to imply a rudimentary knowledge of proportion."

"The base lines of the pyramids run north, and south and east and west, but probably only the lines running north and south were determined by astronomical observations. This, coupled with the fact that the word harpedonaptæ, applied to Egyptian geometers, means "rope-stretchers," would point to the conclusion that the Egyptian, like the Indian and Chinese geometers, constructed a right triangle upon a given line, by stretching around three pegs a rope consisting of three parts in the ratios 3:4:5, and thus forming a right triangle. If this explanation is correct, then the Egyptians were familiar, 2000 years B.C., with the well-known property of the right triangle, for the special case at least when the sides are in the ratio 3:4:5."

"On the walls of the celebrated temple of Horus at Edfu have been found hieroglyphics, written about 100 B.C., which enumerate the pieces of land owned by the priesthood, and give their areas. The area of any quadrilateral, however irregular, is there found by the formula (a+b)/2*(c+d)/2. ...The incorrect formulae of Ahmes of 3000 years B.C. yield generally closer approximations than those of the Edfu inscriptions, written 200 years after Euclid!"

"The Egyptians failed in two essential points without which a science of geometry, in the true sense of the word, cannot exist. In the first place, they failed to construct a rigorously logical system of geometry, resting upon a few axioms and postulates. A great many of their rules, especially those in solid geometry, had probably not been proved at all, but were known to be true merely from observation or as matters of fact. The second great defect was their inability to bring the numerous special cases under a more general view, and thereby to arrive at broader and more fundamental theorems. Some of the simplest geometrical truths were divided into numberless special cases of which each was supposed to require separate treatment."

"An insight into Egyptian methods of numeration was obtained through the ingenious deciphering of the hieroglyphics by Champollion, Young, and their successors. ...The symbol for 1 represents a vertical staff, that for 10,000 a pointing finger, that for 100,000 a burbot, that for 1,000,000 a man in astonishment."

"Fractions were a subject of very great difficulty with the ancients. Simultaneous changes in both numerator and denominator were usually avoided. In manipulating fractions the Babylonians kept the denominators (60) constant. The Romans likewise kept them constant, but equal to 12. The Egyptians and Greeks, on the other hand, kept the numerators constant, and dealt with variable denominators."

"Ahmes used the term "fraction" in a restricted sense, for he applied it only to unit-fractions, or fractions having unity for the numerator. It was designated by writing the denominator and then placing over it a dot. Fractional values which could not be expressed by any one unit-fraction were expressed as the sum of two or more of them. ...The first important problem naturally arising was, how to represent any fractional value as the sum of unit-fractions. This was solved by aid of a table, given in the [Rhind] papyrus, in which all fractions of the form 2/(2n+1) (where n designates successively all the numbers up to 49) are reduced to the sum of unit fractions."

"Having finished the subject of fractions, Ahmes proceeds to the solution of equations of one unknown quantity. The unknown quantity is called 'hau' or heap. ...It thus appears that the beginnings of algebra are as ancient as those of geometry."

"The principal defect of Egyptian arithmetic was the lack of a simple comprehensive symbolism, a defect which not even the Greeks were able to remove."

"The Ahmes papyrus doubtless represents the most advanced attainments of the Egyptians in arithmetic and geometry. It is remarkable that they should have reached so great proficiency in mathematics at so remote a period of antiquity. But strange, indeed, is the fact that during the next two thousand years, they should have made no progress whatsoever in it. ...All the knowledge of geometry which they possessed when Greek scholars visited them, six centuries B.C., was doubtless known to them two thousand years earlier, when they built those stupendous and gigantic structures—the pyramids. An explanation for this stagnation of learning has been sought in the fact that their early discoveries in mathematics and medicine had the misfortune of being entered upon their sacred books and that, in after ages, it was considered heretical to augment or modify anything therein. Thus the books themselves closed the gates to progress."

"About the seventh century B.C. an active commercial intercourse sprang up between Greece and Egypt. Naturally there arose an interchange of ideas as well as of merchandise. Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, Œnopides, Plato, Democritus, Eudoxus, all visited the land of the pyramids."

"The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the other hand, had within them a strong speculative tendency. They felt a craving to discover the reasons for things. They found pleasure in the contemplation of ideal relations and loved science as science."

"The early mathematicians, Thales and Pythagoras, left behind no written records of their discoveries. A full history of Greek geometry and astronomy during this period, written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abstract constitutes our most reliable information. We shall quote it frequently under the name of Eudemian Summary."

"To Thales of Miletus (640-546 B.C.), one of the "seven wise men," and the founder of the Ionic school, falls the honour of having introduced the study of geometry into Greece. During middle life he engaged in commercial pursuits which took him to Egypt. He is said to have resided there and to have studied the physical sciences and mathematics with the Egyptian priests."

"Plutarch declares that Thales soon excelled his masters and amazed King Amasis by measuring the heights of the pyramids from their shadows. ...by considering that the shadow cast by a vertical staff of known length bears the same ratio to the shadow of the pyramid as the height of the staff bears to the height of the pyramid. This solution presupposes a knowledge of proportion, and the Ahmes papyrus actually shows that the rudiments of proportion were known to the Egyptians. According to Diogenes Laertius the pyramids were measured by Thales in a different way; viz. by finding the length of the shadow of the pyramid at the moment when the shadow of a staff was equal to its own length."

"The Eudemian Summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the angles at the base of an isosceles triangle, the bisection of a circle by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. The last theorem he applied to the measurement of the distances of ships from the shore. Thus Thales was the first to apply theoretical geometry to practical uses."

"The theorem that all angles inscribed in a semicircle are right angles is attributed by some ancient writers to Thales, by others to Pythagoras."

"Thales was doubtless familiar with other theorems, not recorded by the ancients. It has been inferred that he knew the sum of the three angles of a triangle to be equal to two right angles, and the sides of equiangular triangles to be proportional."

"The Egyptians must have made use of the above theorems on the straight line, in some of their constructions found in the Ahmes papyrus, but it was left for the Greek philosopher to give these truths, which others saw, but did not formulate into words, an explicit abstract expression, and to put into scientific language and subject to proof that which others merely felt to be true."

"Thales may be said to have created the geometry of lines, essentially abstract in its character, while the Egyptians studied only the geometry of surfaces and the rudiments of solid geometry, empirical in their character."

"With Thales begins also the study of scientific astronomy. He acquired great celebrity by the prediction of a solar eclipse in 585 B.C. Whether he predicted the day of the occurrence, or simply the year, is not known."

"It is told of him [Thales] that while contemplating the stars during an evening walk, he fell into a ditch. The good old woman attending him exclaimed, "How canst thou know what is doing in the heavens when thou seest not what is at thy feet?""

"The two most prominent pupils of Thales were Anaximander (b. 611 B.C.) and Anaximenes (b. 570 B.C.). They studied chiefly astronomy and physical philosophy."

"Of Anaxagoras, a pupil of Anaximenes, and the last philosopher of the Ionic school, we know little, except that while in prison, he passed his time attempting to square the circle. This is the first time, in the history of mathematics, that we find mention of the famous problem of the quadrature of the circle, that rock upon which so many reputations have been destroyed. It turns upon the determination of the exact value of π. Approximations to π had been made by the Chinese, Babylonians, Hebrews, and Egyptians. But the invention of a method to find its exact value, is the knotty problem which has engaged the attention of many minds from the time of Anaxagoras down to our own. Anaxagoras did not offer any solution of it, and seems to have luckily escaped paralogisms."

"About the time of Anaxagoras, but isolated from the Ionic school, flourished Œnopides of Chios. Proclus ascribes to him the solution of the following problems: From a point without, to draw a perpendicular to a given line, and to draw an angle on a line equal to a given angle. That a man could gain a reputation by solving problems so elementary as these, indicates that geometry was still in its infancy, and that the Greeks had not yet gotten far beyond the Egyptian constructions."

"The Ionic school lasted over one hundred years. The progress of mathematics during that period was slow, as compared with its growth in a later epoch of Greek history. A new impetus to its progress was given by Pythagoras."

"Pythagoras (580?-500? B.C.). was one of those figures which impressed the imagination of succeeding times to such an extent that their real histories have become difficult to be discerned through the mythical haze that envelops them. The following account of Pythagoras excludes the most doubtful statements."

"He [Pythagoras] ...visited the ancient Thales, who incited him to study in Egypt. ...He settled at Croton, and founded the famous Pythagorean school. This was not merely an academy for the teaching of philosophy, mathematics, and natural science, but it was a brotherhood, the members of which were united for life. This brotherhood had observances approaching masonic peculiarity. They were forbidden to divulge the discoveries and doctrines of their school."

"We are obliged to speak of the Pythagoreans as a body, and find it difficult to determine to whom each particular discovery is to be ascribed. The Pythagoreans themselves were in the habit of referring every discovery back to the great founder of the sect."

"Pythagoras raised mathematics to the rank of a science. Arithmetic was courted by him as fervently as geometry. In fact, arithmetic is the foundation of his philosophic system."

"The Eudemian Summary says that "Pythagoras changed the study of geometry into the form of a liberal education, for he examined its principles to the bottom, and investigated its theorems in an immaterial and intellectual manner." His geometry was connected closely with his arithmetic. He was especially fond of those geometrical relations which admitted of arithmetical expression."

"Like Egyptian geometry, the geometry of the Pythagoreans is much concerned with areas."

"To Pythagoras is ascribed the important theorem that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. He had probably learned from the Egyptians the truth of the theorem in the special case when the sides are 3, 4, 5, respectively. The story goes, that Pythagoras was so jubilant over this discovery that he sacrificed a hecatomb. Its authenticity is doubted, because the Pythagoreans believed in the transmigration of the soul and opposed, therefore, the shedding of blood. In the later traditions of the Neo-Pythagoreans this objection is removed by replacing this bloody sacrifice by that of "an ox made of flour."! The proof of the law of three squares, given in Euclid's Elements, I. 47, is due to Euclid himself, and not to the Pythagoreans."

"What the Pythagorean method of proof was has been a favourite topic for conjecture."

"The theorem on the sum of the three angles of a triangle, presumably known to Thales, was proved by the Pythagoreans after the manner of Euclid. They demonstrated also that the plane about a point is completely filled by six equilateral triangles, four squares, or three regular hexagons, so that it is possible to divide up a plane into figures of either kind."

"From the equilateral triangle and the square arise the solids, namely the tetraedron, octaedron, icosaedron, and the cube. These solids were, in all probability, known to the Egyptians, excepting perhaps the icosaedron. In Pythagorean philosophy, they represent respectively the four elements of the physical world; namely fire, air, water, and earth. Later another regular solid was discovered, namely the dodecaedron, which, in absence of a fifth element, was made to represent the universe itself."

"Iamblichus states that Hippasus, a Pythagorean, perished in the sea, because he boasted that he first divulged "the sphere with the twelve pentagons.""

"The star-shaped pentagram was used as a symbol of recognition by the Pythagoreans, and was called by them Health."

"Pythagoras called the sphere the most beautiful of all solids, and the circle the most beautiful of all plane figures."

"According to Eudemus, the Pythagoreans invented the problems concerning the application of areas, including the cases of defect and excess, as in Euclid, VI. 28, 29."

"The Pythagoreans were... familiar with the construction of a polygon equal in area to a given polygon and similar to another given polygon. This problem depends upon several important and somewhat advanced theorems, and testifies to the fact that the Pythagoreans made no mean progress in geometry."

"Of the theorems generally ascribed to the Italian school, some cannot be attributed to Pythagoras himself, nor to his earliest successors. The progress from empirical to reasoned solutions must, of necessity, have been slow. It is worth noticing that on the circle no theorem of any importance was discovered by this school."

"Among the later Pythagoreans, Philolaus and Archytas are the most prominent."

"Philolaus wrote a book on the Pythagorean doctrines. By him were first given to the world the teachings of the Italian school, which had been kept secret for a whole century."

"The brilliant Archytas of Tarentum (428-347 B.C.), known as a great statesman and general, and universally admired for his virtues, was the only great geometer among the Greeks when Plato opened his school. Archytas was the first to apply geometry to mechanics and to treat the latter subject methodically. He also found a very ingenious mechanical solution to the problem of the duplication of the cube. His solution involves clear notions on the generation of cones and cylinders. This problem reduces itself to finding two mean proportionals between two given lines. These mean proportionals were obtained by Archytas from the section of a half-cylinder. The doctrine of proportion was advanced through him."

"There is every reason to believe that the later Pythagoreans exercised a strong influence on the study and development of mathematics at Athens. The Sophists acquired geometry from Pythagorean sources. Plato bought the works of Philolaus and had a warm friend in Archytas."

"Athens... became the richest and most beautiful city of antiquity. All menial work was performed by slaves. ...The citizen of Athens was well to do and enjoyed a large amount of leisure. The government being purely democratic, every citizen was a politician. To make his influence felt among his fellow-men he must, first of all, be educated. Thus there arose a demand for teachers. The supply came principally from Sicily, where Pythagorean doctrines had spread. These teachers were called Sophists, or "wise men." Unlike the Pythagoreans, they accepted pay for their teaching. Although rhetoric was the principal feature of their instruction, they also taught geometry, astronomy, and philosophy."

"Athens soon became the headquarters of Grecian men of letters, and of mathematicians in particular. The home of mathematics among the Greeks was first in the Ionian Islands, then in Lower Italy, and during the time now under consideration, at Athens."

"The geometry of the circle, which had been entirely neglected by the Pythagoreans, was taken up by the Sophists. Nearly all their discoveries were made in connection with their innumerable attempts to solve the following three famous problems:—(1) To trisect an arc or an angle. (2) To "double the cube," i.e. to find a cube whose volume is double that of a given cube. (3) To "square the circle," i.e. to find a square or some other rectilinear figure exactly equal in area to a given circle. These problems have probably been the subject of more discussion and research than any other problems in mathematics."

"The bisection of an angle was one of the easiest problems in geometry. The trisection of an angle, on the other hand, presented unexpected difficulties. A right angle had been divided into three equal parts by the Pythagoreans. But the general problem, though easy in appearance, transcended the power of elementary geometry. Among the first to wrestle with it was Hippias of Elis, a contemporary of Socrates, and born about 460 B.C. Like all the later geometers, he failed in effecting the trisection by means of a ruler and compass only. Proclus mentions a man, Hippias, presumably Hippias of Elis, as the inventor of a transcendental curve which served to divide an angle not only into three, but into any number of equal parts. This same curve was used later by Deinostratus and others for the quadrature of the circle. On this account it is called the quadratrix."

"The Pythagoreans had shown that the diagonal of a square is the side of another square having double the area of the original one. This probably suggested the problem of the duplication of the cube, i.e. to find the edge of a cube having double the volume of a given cube. Eratosthenes ascribes to this problem a different origin. The Delians were once suffering from a pestilence and were ordered by the oracle to double a certain cubical altar. Thoughtless workmen simply constructed a cube with edges twice as long, but this did not pacify the gods. The error being discovered, Plato was consulted on the matter. He and his disciples searched eagerly for a solution to this "Delian Problem.""

"Hippocrates of Chios (about 430 B.C.), a talented mathematician, but otherwise slow and stupid, was the first to show that the [duplication of the cube] problem could be reduced to finding two mean proportionals between a given line and another twice as long. For, in the proportion a:x=x:y=y:2a, since x2=ay and y2=2ax and x4=a2y2, we have x4=2 a3x and x3=2a3. But he failed to find the two mean proportionals. His attempt to square the circle was also a failure; for though he made himself celebrated by squaring a lune, he committed an error in attempting to apply this result to the squaring of the circle."

"In his study of the quadrature and duplication-problems, Hippocrates contributed much to the geometry of the circle."

"The subject of similar figures was studied and partly developed by Hippocrates. This involved the theory of proportion. Proportion had, thus far, been used by the Greeks only in numbers. They never succeeded in uniting the notions of numbers and magnitudes. The term "number" was used by them in a restricted sense. What we call irrational numbers was not included under this notion. Not even rational fractions were called numbers. They used the word in the same sense as we use "integers." Hence numbers were conceived as discontinuous, while magnitudes were continuous. The two notions appeared, therefore, entirely distinct. The chasm between them is exposed to full view in the statement of Euclid that "incommensurable magnitudes do not have the same ratio as numbers." In Euclid's Elements we find the theory of proportion of magnitudes developed and treated independent of that of numbers. The transfer of the theory of proportion from numbers to magnitudes (and to lengths in particular) was a difficult and important step."

"The Sophist Antiphon, a contemporary of Hippocrates, introduced the process of exhaustion for the purpose of solving the problem of the quadrature. He did himself credit by remarking that by inscribing in a circle a square, and on its sides erecting isosceles triangles with their vertices in the circumference, and on the sides of these triangles erecting new triangles, etc., one could obtain a succession of regular polygons of 8, 16, 32, 64 sides, and so on, of which each approaches nearer to the circle than the previous one, until the circle is finally exhausted. Thus is obtained an inscribed polygon whose sides coincide with the circumference. Since there can be found squares equal in area to any polygon, there also can be found a square equal to the last polygon inscribed, and therefore equal to the circle itself."

"Bryson of Heraclea, a contemporary of Antiphon, advanced the problem of the quadrature considerably by circumscribing polygons at the same time that he inscribed polygons. He erred, however, in assuming that the area of a circle was the arithmetical mean between circumscribed and inscribed polygons."

"Unlike Bryson and the rest of Greek geometers, Antiphon seems to have believed it possible, by continually doubling the sides of an inscribed polygon, to obtain a polygon coinciding with the circle. This question gave rise to lively disputes in Athens. If a polygon can coincide with the circle, then, says Simplicius, we must put aside the notion that magnitudes are divisible ad infinitum. Aristotle always supported the theory of the infinite divisibility, while Zeno, the Stoic, attempted to show its absurdity by proving that if magnitudes are infinitely divisible, motion is impossible. Zeno argues that Achilles could not overtake a tortoise; for while he hastened to the place where the tortoise had been when he started, the tortoise crept some distance ahead, and while Achilles reached that second spot, the tortoise again moved forward a little, and so on. Thus the tortoise was always in advance of Achilles. Such arguments greatly confounded Greek geometers. No wonder they were deterred by such paradoxes from introducing the idea of infinity into their geometry. It did not suit the rigour of their proofs."

"The process of Antiphon and Bryson gave rise to the cumbrous but perfectly rigorous "method of exhaustion." In determining the ratio of the areas between two curvilinear plane figures, say two circles, geometers first inscribed or circumscribed similar polygons, and then by increasing indefinitely the number of sides, nearly exhausted the spaces between the polygons and circumferences. From the theorem that similar polygons inscribed in circles are to each other as the squares on their diameters, geometers may have divined the theorem attributed to Hippocrates of Chios that the circles, which differ but little from the last drawn polygons, must be to each other as the squares on their diameters. But in order to exclude all vagueness and possibility of doubt, later Greek geometers applied reasoning like that in Euclid XII. 2..."

"Hankel refers this Method of Exhaustion back to Hippocrates of Chios but the reasons for assigning it to this early writer rather than to Eudoxus seem insufficient."

"During the Peloponnesian War (431-404 B.C.) the progress of geometry was checked. After the war, Athens sank into the background as a minor political power, but advanced more and more to the front as the leader in philosophy, literature, and science."

"Plato was born at Athens in 429 B.C., the year of the great plague, and died in 348. He was a pupil and near friend of Socrates, but it was not from him that he acquired his taste for mathematics. After the death of Socrates, Plato traveled extensively. In Cyrene he studied mathematics under Theodoras. He went to Egypt, then to Lower Italy and Sicily, where he came in contact with the Pythagoreans. Archytas of Tarentum and Timæus of Locri became his intimate friends. On his return to Athens, about 389 B.C., he founded his school in the groves of the Academia, and devoted the remainder of his life to teaching and writing."

"Plato's physical philosophy is partly based on that of the Pythagoreans. Like them, he sought in arithmetic and geometry the key to the universe. When questioned about the occupation of the Deity, Plato answered that "He geometrises continually." Accordingly, a knowledge of geometry is a necessary preparation for the study of philosophy. To show how great a value he put on mathematics and how necessary it is for higher speculation, Plato placed the inscription over his porch, "Let no one who is unacquainted with geometry enter here.""

"Plato observed that geometry trained the mind for correct and vigorous thinking. Hence it was that the Eudemian Summary says, "He filled his writings with mathematical discoveries, and exhibited on every occasion the remarkable connection between mathematics and philosophy.""

"With Plato as the head-master, we need not wonder that the Platonic school produced so large a number of mathematicians. Plato did little real original work, but he made valuable improvements in the logic and methods employed in geometry. It is true that the Sophist geometers of the previous century were rigorous in their proofs, but as a rule they did not reflect on the inward nature of their methods. They used the axioms without giving them explicit expression, and the geometrical concepts, such as the point, line, surface, etc., without assigning to them formal definitions. The Pythagoreans called a point "unity in position," but this is a statement of a philosophical theory rather than a definition. Plato objected to calling a point a "geometrical fiction." He defined a point as "the beginning of a line" or as "an indivisible line," and a line as "length without breadth." He called the point, line, surface, the 'boundaries' of the line, surface, solid, respectively. Many of the definitions in Euclid are to be ascribed to the Platonic school. The same is probably true of Euclid's axioms. Aristotle refers to Plato the axiom that "equals subtracted from equals leave equals.""

"One of the greatest achievements of Plato and his school is the invention of analysis as a method of proof. To be sure, this method had been used unconsciously by Hippocrates and others; but Plato, like a true philosopher, turned the instinctive logic into a conscious, legitimate method."

"The terms synthesis and analysis are used in mathematics in a more special sense than in logic. In ancient mathematics they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in Euclid, XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it.""

"The analytic method is not conclusive, unless all operations involved in it are known to be reversible. To remove all doubt, the Greeks, as a rule added to the analytic process a synthetic one, consisting of a reversion of all operations occurring in the analysis. Thus the aim of analysis was to aid in the discovery of synthetic proofs or solutions."

"Plato is said to have solved the problem of the duplication of the cube. But the solution is open to the very same objection which he made to the solutions by Archytas, Eudoxus, and Menæchmus. He called their solutions not geometrical, but mechanical for they required the use of other instruments than the ruler and compass. He said that thereby "the good of geometry is set aside and destroyed, for we again reduce it to the world of sense, instead of elevating and imbuing it with the eternal and incorporeal images of thought, even as it is employed by God, for which reason He always is God." These objections indicate either that the solution is wrongly attributed to Plato or that he wished to show how easily non-geometric solutions of that character can be found."

"It is now generally admitted that the duplication problem, as well as the trisection and quadrature problems, cannot be solved by means of the ruler and compass only."

"Plato gave a healthful stimulus to the study of stereometry [solid geometry], which until his time had been entirely neglected. The sphere and the regular solids had been studied to some extent, but the prism, pyramid, cylinder, and cone were hardly known to exist. All these solids became the subjects of investigation by the Platonic school."

"One result of these inquiries was epoch-making. Menæchmus, an associate of Plato and pupil of Eudoxus, invented the conic sections, which, in course of only a century, raised geometry to the loftiest height which it was destined to reach during antiquity. Menæchmus cut three kinds of cones, the 'right angled,' 'acute angled,' and 'obtuse angled,' by planes at right angles to a side of the cones, and thus obtained the three sections which we now call the parabola, ellipse, and hyperbola. Judging from the two very elegant solutions of the "Delian Problem" by means of intersections of these curves, Menæchmus must have succeeded well in investigating their properties."

"Another great geometer was Dinostratus, the brother of Menæchmus and pupil of Plato. Celebrated is his mechanical solution of the quadrature of the circle, by means of the quadratrix of Hippias."

"Perhaps the most brilliant mathematician of this period was Eudoxus. He was born at Cnidus about 408 B.C., studied under Archytas, and later, for two months, under Plato. He was imbued with a true spirit of scientific inquiry, and has been called the father of scientific astronomical observation. From the fragmentary notices of his astronomical researches, found in later writers, Ideler and Schiaparelli succeeded in reconstructing the system of Eudoxus with its celebrated representation of planetary motions by "concentric spheres." Eudoxus had a school at Cyzicus, went with his pupils to Athens, visiting Plato, and then returned to Cyzicus, where he died 355 B.C."

"The fame of the academy of Plato is to a large extent due to Eudoxus's pupils of the school at Cyzicus, among whom are Menaechmus, Dinostratus, Athenaeus, and Helicon."

"Diogenes Laertius describes Eudoxus as astronomer, physician, legislator, as well as geometer."

"The Eudemian Summary says that Eudoxus "first increased the number of general theorems, added to the three proportions three more, and raised to a considerable quantity the learning, begun by Plato, on the subject of the section, to which he applied the analytical method." By this 'section' is meant, no doubt, the "golden section" (sectio aurea), which cuts a line in extreme and mean ratio. The first five propositions in Euclid XIII. relate to lines cut by this section, and are generally attributed to Eudoxus."

"Eudoxus added much to the knowledge of solid geometry. He proved, says Archimedes, that a pyramid is exactly one-third of a prism, and a cone one-third of a cylinder, having equal base and altitude. The proof that spheres are to each other as the cubes of their radii is probably due to him. He made frequent and skilful use of the method of exhaustion, of which he was in all probability the inventor."

"A scholiast on Euclid, thought to be Proclus, says that Eudoxus practically invented the whole of Euclid's fifth book."

"Plato has been called a maker of mathematicians. Besides the pupils already named, the Eudemian Summary mentions the following: Theaetetus of Athens, a man of great natural gifts, to whom, no doubt, Euclid was greatly indebted in the composition of the 10th book, treating of incommensurables; Leodamas of Thasos; Neocleides and his pupil Leon, who added much to the work of their predecessors, for Leon wrote an Elements carefully designed, both in number and utility of its proofs; Theudius of Magnesia, who composed a very good book of Elements and generalised propositions, which had been confined to particular cases; Hermotimus of Colophon, who discovered many propositions of the Elements and composed some on loci; and finally the names of Amyclas of Heraclea, Cyzicenus of Athens, and Philippus of Mende."

"A skilful mathematician of whose life and works we have no details is Aristæus, the elder, probably a senior contemporary of Euclid. The fact that he wrote a work on conic sections tends to show that much progress had been made in their study during the time of Menæchmus. Aristaeus wrote also on regular solids and cultivated the analytic method. His works contained probably a summary of the researches of the Platonic school."

"Aristotle (384-322 B.C.), the systematiser of deductive logic, though not a professed mathematician, promoted the science of geometry by improving some of the most difficult definitions. His Physics contains passages with suggestive hints of the principle of virtual velocities. About this time there appeared a work called Mechanica, of which he is regarded by some as the author. Mechanics was totally neglected by the Platonic school."

"[There are] other works with texts more or less complete and generally attributed to Euclid. ...His treatise on Porisms is lost, but much learning has been expended by Robert Simson and M. Chasles in restoring it from numerous notes found in the writings of Pappus. The term "porism" is vague in meaning. According to Proclus the aim of a porism is not to state some property or truth, like a theorem, nor to effect a construction, like a problem, but to find and bring to view a thing which necessarily exists with given numbers or a given construction, as, to find the centre of a given circle, or to find the G.C.D. of two given numbers. Porisms, according to Chasles, are incomplete theorems, "expressing certain relations between things variable according to a common law.""

"We have seen the birth of geometry in Egypt, its transference to the Ionian Islands, thence to Lower Italy and to Athens. We have witnessed its growth in Greece from feeble childhood to vigorous manhood, and now we shall see it return to the land of its birth and there derive new vigour."

"In 338 B.C., at the battle of Chæronea, Athens was beaten by Philip of Macedon and her power was broken forever. Soon after, Alexander the Great, the son of Philip, started out to conquer the world. In eleven years he built up a great empire which broke to pieces in a day. Egypt fell to the lot of Ptolemy Soter. Alexander had founded the seaport of Alexandria, which soon became "the noblest of all cities." Ptolemy made Alexandria the capital. The history of Egypt during the next three centuries is mainly the history of Alexandria. Literature, philosophy, and art were diligently cultivated. Ptolemy created the university of Alexandria. He founded the great Library and built laboratories, museums, a zoological garden, and promenades. Alexandria soon became the great centre of learning."

"Demetrius Phalereus was invited from Athens to take charge of the Library, and it is probable, says Gow, that Euclid was invited with him to open the mathematical school."

"Euclid's greatest activity was during the time of the first Ptolemy, who reigned from 306 to 283 B.C. Of the life of Euclid, little is known, except what is added by Proclus to the Eudemian Summary."

"Euclid, says Proclus, was younger than Plato and older than Eratosthenes and Archimedes, the latter of whom mentions him. He was of the Platonic sect, and well read in its doctrines. He collected the Elements, put in order much that Eudoxus had prepared, completed many things of Theætetus, and was the first who reduced to unobjectionable demonstration the imperfect attempts of his predecessors."

"When Ptolemy once asked Euclid if geometry could not be mastered by an easier process than by studying the Elements, Euclid returned the answer, "There is no royal road to geometry.""

"Pappus states that Euclid was distinguished by the fairness and kindness of his disposition, particularly toward those who could do anything to advance the mathematical sciences. Pappus is evidently making a contrast to Apollonius, of whom he more than insinuates the opposite character."

"A pretty little story is related by Stobæus: "A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, 'What do I get by learning these things?' So Euclid called his slave and said, 'Give him threepence, since he must make gain out of what he learns.'""

"It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences."

"Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him. Allman conjectures that the substance of Books I., II., IV. comes from the Pythagoreans, that the substance of Book VI. is due to the Pythagoreans and Eudoxus, the latter contributing the doctrine of proportion as applicable to incommensurables and also the Method of Exhaustions (Book VII.), that Thætetus contributed much toward Books X. and XIII., that the principal part of the original work of Euclid himself is to be found in Book X."

"Euclid was the greatest systematiser of his time. By careful selection from the material before him, and by logical arrangement of the propositions selected, he built up, from a few definitions and axioms, a proud and lofty structure. It would be erroneous to believe that he incorporated into his Elements all the elementary theorems known at his time. Archimedes, Apollonius, and even he himself refer to theorems not included in his Elements, as being well-known truths."

"Among the manuscripts sent by Napoleon I. from the Vatican to Paris was found a copy of the Elements believed to be anterior to Theon's recension. Many variations from Theon's version were noticed therein, but they were not at all important, and showed that Theon generally made only verbal changes. The defects in the Elements for which Theon was blamed must, therefore, be due to Euclid himself."

"The Elements has been considered as offering models of scrupulously rigorous demonstrations. It is certainly true that in point of rigour it compares favourably with its modern rivals; but when examined in the light of strict mathematical logic, it has been pronounced by C.S. Peirce to be "riddled with fallacies." The results are correct only because the writer's experience keeps him on his guard."

"The term 'axiom' was used by Proclus, but not by Euclid. He speaks, instead, of 'common notions'—common either to all men or to all sciences."

"There has been much controversy among ancient and modern critics on the postulates and axioms. An immense preponderance of manuscripts and the testimony of Proclus place the 'axioms' about right angles and parallels (Axioms 11 and 12) among the postulates. This is indeed their proper place, for they are really assumptions, and not common notions or axioms."

"The postulate about parallels plays an important role in the history of non-Euclidean geometry."

"The only postulate which Euclid missed was the one of superposition, according to which figures can be moved about in space without any alteration in form or magnitude."

"The Elements contains thirteen books by Euclid, and two, of which it is supposed that Hypsicles and Damascius are the authors. The first four books are on plane geometry. The fifth book treats of the theory of proportion as applied to magnitudes in general. The sixth book develops the geometry of similar figures. The seventh, eighth, ninth books are on the theory of numbers, or on arithmetic. In the ninth book is found the proof to the theorem that the number of primes is infinite. The tenth book treats of the theory of incommensurables. The next three books are on stereometry. The eleventh contains its more elementary theorems; the twelfth, the metrical relations of the pyramid, prism, cone, cylinder, and sphere. The thirteenth treats of the regular polygons, especially of the triangle and pentagon, and then uses them as faces of the five regular solids; namely the tetraedron, octaedron, icosaedron, cube, and dodecaedron."

"The regular solids were studied so extensively by the Platonists that they received the name of "Platonic figures." The statement of Proclus that the whole aim of Euclid in writing the Elements was to arrive at the construction of the regular solids, is obviously wrong. The fourteenth and fifteenth books, treating of solid geometry, are apocryphal."

"A remarkable feature of Euclid's, and of all Greek geometry before Archimedes is that it eschews mensuration. Thus the theorem that the area of a triangle equals half the product of its base and its altitude is foreign to Euclid."

"Another extant book of Euclid is the Data. It seems to have been written for those who, having completed the Elements, wish to acquire the power of solving new problems proposed to them. The Data is a course of practice in analysis. It contains little or nothing that an intelligent student could not pick up from the Elements itself."

"The following are the other extant works generally attributed to Euclid: Phœnomena, a work on spherical geometry and astronomy; Optics, which develops the hypothesis that light proceeds from the eye, and not from the object seen; Catoptrica, containing propositions on reflections from mirrors; De Divisionibus, a treatise on the division of plane figures into parts having to one another a given ratio; Sectio Canonis, a work on musical intervals."

"His [Euclid's] treatise on Porisms is lost; but much learning has been expended by Robert Simson and M. Chasles in restoring it from numerous notes found in the writings of Pappus. The term porism is vague in meaning. The aim of a porism is not to state some property or truth, like a theorem, nor to effect a construction, like a problem, but to find and bring to view a thing which necessarily exists with given numbers or a given construction, as, to find the centre of a given circle, or to find the G.C.D. of two given numbers. His other lost works are Fallacies, containing exercises in detection of fallacies; Conic Sections, in four books, which are the foundation of a work on the same subject by Apollonius; and Loci on a Surface, the meaning of which title is not understood. Heiberg believes it to mean "loci which are surfaces.""

"The immediate successors of Euclid in the mathematical school at Alexandria were probably Conon, Dositheus, and Zeuxippus, but little is known of them."

"Archimedes was admired by his fellow-citizens chiefly for his mechanical inventions; he himself prized far more highly his discoveries in pure science. He declared that "every kind of art which was connected with daily needs was ignoble and vulgar." Some of his works have been lost. The following are the extant books, arranged approximately in chronological order: 1. Two books on Equiponderance of Planes or Centres of Plane Gravities, between which is inserted his treatise on the Quadrature of the Parabola; 2. Two books on the Sphere and Cylinder; 3. The Measurement of the Circle; 4. On Spirals; 5. Conoids and Spheroids; 6. The Sand-Counter; 7. Two books on Floating Bodies; 8. Fifteen Lemmas."

"In the book on the Measurement of the Circle, Archimedes proves first that the area of a circle is equal to that of a right triangle having the length of the circumference for its base, and the radius for its altitude. In this he assumes that there exists a straight line equal in length to the circumference -- an assumption objected to by some ancient critics, on the ground that it is not evident that a straight line can equal a curved one. The finding of such a line was the next problem. He first finds an upper limit to the ratio of the circumference to the diameter, or &pi;. To do this, he starts with an equilateral triangle of which the base is a tangent and the vertex is the centre of the circle. By successively bisecting the angle at the centre, by comparing ratios, and by taking the irrational square roots always a little too small, he finally arrived at the conclusion that &pi; < 3 1/7. Next he finds a lower limit by inscribing in the circle regular polygons of 6, 12, 24, 48, 96 sides, finding for each successive polygon its perimeter, which is, of course, always less than the circumference. Thus he finally concludes that "the circumference of a circle exceeds three times its diameter by a part which is less than 1/7 but more than 10/71 of the diameter." This approximation is exact enough for most purposes."

"The Quadrature of the Parabola contains two solutions to the problem -- one mechanical, the other geometrical. The method of exhaustion is used in both."

"Archimedes studied also the ellipse and accomplished its quadrature, but to the hyperbola he seems to have paid less attention. It is believed that he wrote a book on conic sections."

"Of all his discoveries Archimedes prized most highly those in his Sphere and Cylinder. In it are proved the new theorems, that the surface of a sphere is equal to four times a great circle; that the surface of a segment of a sphere is equal to a circle whose radius is the straight line drawn from the vertex of the segment to the circumference of its basal circle; that the volume and the surface of a sphere are 2/3 of the volume and surface, respectively, of the cylinder circumscribed about the sphere. Archimedes desired that the figure to the last proposition be inscribed on his tomb. This was ordered done by Marcellus."

"The spiral now called the "spiral of Archimedes," and described in the book On Spirals, was discovered by Archimedes, and not, as some believe, by his friend Conon. His treatise thereon is, perhaps the most wonderful of all his works. Nowadays, subjects of this kind are made easy by the use of the infinitesimal calculus. In its stead the ancients used the method of exhaustion. Nowhere is the fertility of his genius more grandly displayed than in his masterly use of this method. With Euclid and his predecessors the method of exhaustion was only the means of proving propositions which must have been seen and believed before they were proved. But in the hands of Archimedes it became an instrument of discovery."

"By the word 'conoid,' in his book on Conoids and Spheroids, is meant the solid produced by the revolution of a parabola or a hyperbola about its axis. Spheroids are produced by the revolution of an ellipse, and are long or flat, according as the ellipse revolves around the major or minor axis. The book leads up to the cubature of these solids."

"Archimedes is the author of the first sound knowledge on mechanics. Archytas, Aristotle, and others attempted to form the known mechanical truths into a science, but failed. Aristotle knew the property of the lever, but could not establish its true mathematical theory. The radical and fatal defect in the speculations of the Greeks, says Whewell, was "that though they had in their possession facts and ideas, the ideas were not distinct and appropriate to the facts." For instance, Aristotle asserted that when a body at the end of a lever is moving, it may be considered as having two motions; one in the direction of the tangent and one in the direction of the radius; the former motion is, he says, according to nature, the latter contrary to nature. These inappropriate notions of 'natural' and 'unnatural' motions, together with the habits of thought which dictated these speculations, made the perception of the true grounds of mechanical properties impossible. It seems strange that even after Archimedes had entered upon the right path, this science should have remained absolutely stationary till the time of Galileo -- a period of nearly two thousand years."

"The proof of the property of the lever, given in his Equiponderance of Planes, holds its place in text-books to this day. His [Archimedes'] estimate of the efficiency of the lever is expressed in the saying attributed to him, "Give me a fulcrum on which to rest, and I will move the earth.""

"While the Equiponderance treats of solids, or the equilibrium of solids, the book on Floating Bodies treats of hydrostatics. His [Archimedes'] attention was first drawn to the subject of specific gravity when King Hieron asked him to test whether a crown, professed by the maker to be pure gold, was not alloyed with silver. The story goes that our philosopher was in a bath when the true method of solution flashed on his mind. He immediately ran home, naked, shouting, "I have found it." To solve the problem, he took a piece of gold and a piece of silver, each weighing the same as the crown. According to one author, he determined the volume of water displaced by the gold, silver, and crown respectively, and calculated from that the amount of gold and silver in the crown. According to another writer, he weighed separately the gold, silver, and crown, while immersed in water, thereby determining their loss of weight in water. From these data he easily found the solution. It is possible that Archimedes solved the problem by both methods."

"After examining the writings of Archimedes, one can well understand how, in ancient times, an 'Archimedean problem' came to mean a problem too deep for ordinary minds to solve, and how an 'Archimedean proof' came to be the synonym for unquestionable certainty. Archimedes wrote on a very wide range of subjects, and displayed great profundity in each. He is the Newton of antiquity."

"Eratosthenes, eleven years younger than Archimedes, was a native of Cyrene. He was educated in Alexandria under Callimachus the poet, whom he succeeded as custodian of the Alexandrian Library. His many-sided activity may be inferred from his works. He wrote on Good and Evil, Measurement of the Earth, Comedy, Geography, Chronology, Constellations, and the Duplication of the Cube. He was also a philologian and a poet. He measured the obliquity of the ecliptic and invented a device for finding prime numbers. Of his geometrical writings we possess only a letter to Ptolemy Euergetes, giving a history of the duplication problem and also the description of a very ingenious mechanical contrivance of his own to solve it. In his old age he lost his eyesight, and on that account is said to have committed suicide by voluntary starvation."

"About forty years after Archimedes flourished, Apollonius of Perga's genius nearly equalled that of his great predecessor. He incontestably occupies the second place in distinction among ancient mathematicians. Apollonius was born in the reign of Ptolemy Euergetes and died under Ptolemy Philopator, who reigned 222-205 B.C. He studied at Alexandria under the successors of Euclid, and for some time, also, at Pergamum, where he made the acquaintance of that Eudemus to whom he dedicated the first three books of his Conic Sections. The brilliancy of his great work brought him the title of the "Great Geometer." This is all that is known of his life."

"Apollonius' Conic Sections were in eight books, of which the first four only have come down to us in the original Greek. The next three books were unknown in Europe till the middle of the seventeenth century, when an Arabic translation, made about 1250, was discovered. The eighth book has never been found. In 1710 Halley of Oxford published the Greek text of the first four books and a Latin translation of the remaining three, together with his conjectural restoration of the eighth book, founded on the introductory lemmas of Pappus. The first four books contain little more than the substance of what earlier geometers had done."

"Eutocius tells us that Heraclides, in his life of Archimedes, accused Apollonius of having appropriated, in his Conic Sections, the unpublished discoveries of that great mathematician. It is difficult to believe that this charge rests upon good foundation. Eutocius quotes Geminus as replying that neither Archimedes nor Apollonius claimed to have invented the conic sections, but that Apollonius had introduced a real improvement. While the first three or four books were founded on the works of Menæchmus, Aristæus, Euclid, and Archimedes, the remaining ones consisted almost entirely of new matter."

"The preface of the second book [of Conic Sections] is interesting as showing the mode in which Greek books were 'published' at this time. It reads thus: "I have sent my son Apollonius to bring you (Eudemus) the second book of my Conics. Read it carefully and communicate it to such others as are worthy of it."

"The first book [of Conic Sections], says Apollonius in his preface to it, "contains the mode of producing the three sections and the conjugate hyperbolas and their principal characteristics, more fully and generally worked out than in the writings of other authors." We remember that Menæchmus, and all his successors down to Apollonius, considered only sections of right cones by a plane perpendicular to their sides, and that the three sections were obtained each from a different cone. Apollonius introduced an important generalisation. He produced all the sections from one and the same cone, whether right or scalene, and by sections which may or may not be perpendicular to its sides. The old names for the three curves were now no longer applicable. Instead of calling the three curves, sections of the 'acute angled,' 'right angled,' and 'obtuse angled' cone, he called them ellipse, parabola, and hyperbola, respectively. To be sure, we find the words 'parabola' and 'ellipse' in the works of Archimedes, but they are probably only interpolations. The word 'ellipse' was applied because y2 < px, p being the parameter; the word 'parabola' was introduced because y2 = px, and the term 'hyperbola' because y2 > px."

"The first book of the Conic Sections of Apollonius is almost wholly devoted to the generation of the three principal conic sections. The second book treats mainly of asymptotes, axes, and diameters. The third book treats of the equality or proportionality of triangles, rectangles, or squares, of which the component parts are determined by portions of transversals, chords, asymptotes, or tangents, which are frequently subject to a great number of conditions. It also touches the subject of foci of the ellipse and hyperbola. In the fourth book, Apollonius discusses the harmonic division of straight lines. He also examines a system of two conics, and shows that they cannot cut each other in more than four points. He investigates the various possible relative positions of two conics, as, for instance, when they have one or two points of contact with each other. The fifth book reveals better than any other the giant intellect of its author. Difficult questions of maxima and minima, of which few examples are found in earlier works, are here treated most exhaustively. The subject investigated is, to find the longest and shortest lines that can be drawn from a given point to a conic. Here are also found the germs of the subject of evolutes and centres of osculation. The sixth book is on the similarity of conies. The seventh book is on conjugate diameters. The eighth book, as restored by Halley, continues the subject of conjugate diameters."

"It is worthy of notice that Apollonius nowhere introduces the notion of directrix for a conic, and that, though he incidentally discovered the focus of an ellipse and hyperbola, he did not discover the focus of a parabola. Conspicuous in his geometry is also the absence of technical terms and symbols, which renders the proofs long and cumbrous."

"The discoveries of Archimedes and Apollonius, says M. Chasles, marked the most brilliant epoch of ancient geometry. Two questions which have occupied geometers of all periods may be regarded as having originated with them. The first of these is the quadrature of curvilinear figures, which gave birth to the infinitesimal calculus. The second is the theory of conic sections, which was the prelude to the theory of geometrical curves of all degrees, and to that portion of geometry which considers only the forms and situations of figures, and uses only the intersection of lines and surfaces and the ratios of rectilineal distances. These two great divisions of geometry may be designated by the names of Geometry of Measurements and Geometry of Forms and Situations, or, Geometry of Archimedes and of Apollonius."

"Besides the Conic Sections, Pappus ascribes to Apollonius the following works: On Contacts, Plane Loci, Inclinations, Section of an Area, Determinate Section, and gives lemmas from which attempts have been made to restore the lost originals. Two books on De Sectione Rationis have been found in the Arabic. The book on Contacts as restored by Vieta, contains the so-called "Apollonian Problem:" Given three circles, to find a fourth which shall touch the three."

"Euclid, Archimedes, and Apollonius brought geometry to as high a state of perfection as it perhaps could be brought without first introducing some more general and more powerful method than the old method of exhaustion. A briefer symbolism, a Cartesian geometry, an infinitesimal calculus, were needed. The Greek mind was not adapted to the invention of general methods. Instead of a climb to still loftier heights we observe, therefore, on the part of later Greek geometers, a descent during which they paused here and there to look around for details which had been passed by in the hasty ascent."

"Among the earliest successors of Apollonius was Nicomedes. Nothing definite is known of him, except that he invented the conchoid (mussel-like). He devised a little machine by which the curve could be easily described. With aid of the conchoid he duplicated the cube. The curve can also be used for trisecting angles in a way much resembling that in the eighth lemma of Archimedes. Proclus ascribes this mode of trisection to Nicomedes, but Pappus, on the other hand, claims it as his own. The conchoid was used by Newton in constructing curves of the third degree."

"About the time of Nicomedes, flourished also Diocles, the inventor of the cissoid (ivy-like). This curve he used for finding two mean proportionals between two given straight lines."

"Perseus... lived some time between 200 and 100 B.C. From Heron and Geminus we learn that he wrote a work on the spire, a sort of anchor-ring surface described by Heron as being produced by the revolution of a circle around one of its chords as an axis. The sections of this surface yield peculiar curves called spiral sections, which, according to Geminus, were thought out by Perseus. These curves appear to be the same as the Hippopede of Eudoxus."

"Probably somewhat later than Perseus lived Zenodorus. He wrote an interesting treatise on a new subject; namely, isoperimetrical figures. Fourteen propositions are preserved by Pappus and Theon. Here are a few of them: Of isoperimetrical regular polygons, the one having the largest number of angles has the greatest area; the circle has a greater area than any regular polygon of equal periphery; of all isoperimetrical polygons of n sides, the regular is the greatest; of all solids having surfaces equal in area, the sphere has the greatest volume."

"Hypsicles (between 200 and 100 B.C.) was supposed to be the author of both the fourteenth and fifteenth books of Euclid, but recent critics are of opinion that the fifteenth book was written by an author who lived several centuries after Christ. The fourteenth book contains seven elegant theorems on regular solids. A treatise of Hypsicles on Risings is of interest because it is the first Greek work giving the division of the circumference into 360 degrees after the fashion of the Babylonians."

"Hipparchus of Nicaea in Bithynia was the greatest astronomer of antiquity. He established inductively the famous theory of epicycles and eccentrics. As might be expected, he was interested in mathematics, not per se, but only as an aid to astronomical inquiry. No mathematical writings of his are extant, but Theon of Alexandria informs us that Hipparchus originated the science of trigonometry, and that he calculated a "table of chords" in twelve books. Such calculations must have required a ready knowledge of arithmetical and algebraical operations."

"About 155 B.C. flourished Heron the Elder of Alexandria. He was the pupil of Ctesibius, who was celebrated for his ingenious mechanical inventions, such as the hydraulic organ, the water clock, and catapult. It is believed by some that Heron was a son of Ctesibius. He exhibited talent of the same order as did his master by the invention of the eolipile and a curious mechanism known as "Heron's fountain." Great uncertainty exists concerning his writings. Most authorities believe him to be the author of an important Treatise on the Dioptra, of which there exist three manuscript copies, quite dissimilar. But M. Marie thinks that the Dioptra is the work of Heron the Younger, who lived in the seventh or eighth century after Christ, and that Geodesy, another book supposed to be by Heron, is only a corrupt and defective copy of the former work. Dioptra contains the important formula for finding the area of a triangle expressed in terms of its sides; its derivation is quite laborious and yet exceedingly ingenious. "It seems to me difficult to believe," says Chasles, "that so beautiful a theorem should be found in a work so ancient as that of Heron the Elder, without that some Greek geometer should have thought to cite it." Marie lays great stress on this silence of the ancient writers, and argues from it that the true author must be Heron the Younger or some writer much more recent than Heron the Elder. But no reliable evidence has been found that there actually existed a second mathematician by the name of Heron."

""Dioptra," says Venturi, were instruments which had great resemblance to our modern theodolites. The book Dioptra is a treatise on geodesy containing solutions, with aid of these instruments, of a large number of questions in geometry, such as to find the distance between two points, of which one only is accessible, or between two points, which are visible but both inaccessible; from a given point to draw a perpendicular to a line which cannot be approached; to find the difference of level between two points; to measure the area of a field without entering it."

"Heron was a practical surveyor. This may account for the fact that his writings bear so little resemblance to those of the Greek authors, who considered it degrading the science to apply geometry to surveying. The character of his geometry is not Grecian but decidedly Egyptian. ...There are ...points of resemblance between Heron's writings and the ancient Ahmes papyrus. Thus Ahmes used unit-fractions exclusively; Heron uses them oftener than other fractions. Like Ahmes and the priests at Edfu, Heron divides complicated figures into simpler ones by drawing auxiliary lines; like them, he shows, throughout, a special fondness for the isosceles trapezoid. The writings of Heron satisfied a practical want, and for that reason were borrowed extensively by other peoples. We find traces of them in Rome, in the Occident during the Middle Ages, and even in India."

"Geminus of Rhodes (about 70 B.C.) published an astronomical work still extant. He wrote also a book, now lost, on the Arrangement of Mathematics, which contained many valuable notices of the early history of Greek mathematics. Proclus and Eutocius quote it frequently."

"Dionysodorus of Amisus in Pontus applied the intersection of a parabola and hyperbola to the solution of a problem which Archimedes, in his Sphere and Cylinder, had left incomplete. The problem is "to cut a sphere so that its segments shall be in a given ratio.""

"The close of the dynasty of the Lagides which ruled Egypt from the time of Ptolemy Soter, the builder of Alexandria, for 300 years; the absorption of Egypt into the Roman Empire; the closer commercial relations between peoples of the East and of the West; the gradual decline of paganism and spread of Christianity,—these events were of far-reaching influence on the progress of the sciences, which then had their home in Alexandria. Alexandria became a commercial and intellectual emporium. Traders of all nations met in her busy streets, and in her magnificent Library, museums, lecture halls, scholars from the East mingled with those of the West; Greeks began to study older literatures and to compare them with their own. In consequence of this interchange of ideas the Greek philosophy became fused with Oriental philosophy. Neo-Pythagoreanism and Neo-Platonism were the names of the modified systems. These stood, for a time, in opposition to Christianity. The study of Platonism and Pythagorean mysticism led to the revival of the theory of numbers. Perhaps the dispersion of the Jews and their introduction to Greek learning helped in bringing about this revival. The theory of numbers became a favourite study. This new line of mathematical inquiry ushered in what we may call a new school. There is no doubt that even now geometry continued to be one of the most important studies in the Alexandrian course. This Second Alexandrian School may be said to begin with the Christian era. It was made famous by the names of Claudius Ptolemæus, Diophantus, Pappus, Theon of Smyrna, Theon of Alexandria, Iamblichus, Porphyrius, and others."

"Serenus of Antissa was connected more or less with this [Second Alexandrian] school. He wrote on sections of the cone and cylinder, in two books, one of which treated only of the triangular section of the cone through the apex. He solved the problem, "given a cone (cylinder), to find a cylinder (cone), so that the section of both by the same plane gives similar ellipses." Of particular interest is the following theorem [show figure], which is the foundation of the modern theory of harmonics: If from D we draw DF, cutting the triangle ABC, and choose H on it, so that DE:DF=EH:HF, and if we draw the line AH, then every transversal through D, such as DG will be divided by AH, so that DK:DG=KJ:JO."

"In letters which went between me and that most excellent geometer. G.G. Leibniz, ten years ago, when I signified that I was in the knowledge of a method of determining maxima and minima, of drawing tangents, and the like, and when I concealed it in transposed letters involving this sentence (Data æquatione, etc., above cited) that most distinguished man wrote back that he had also fallen upon a method of the same kind, and communicated his method, which hardly differed from mine, except in his forms of words and symbols."

"[Joseph Fourier] carried on his elaborate investigations on the propagation of heat in solid bodies, published in 1822 in his work entitled La Theorie Analytique de la Chaleur. This work marks an epoch in the history of mathematical physics. "Fourier's series" constitutes its gem. By this research a long controversy was brought to a close, and the fact established that any arbitrary function can be represented by a trigonometric series. The first announcement of this great discovery was made by Fourier in 1807 before the French Academy. The trigonometric series \sum_{n=0}^{n=\infty} (a_n\sin nx+b_n\cos nx) represents the function \phi(x) for every value of x if the coefficients a_n = \frac{1}{\pi}\int_{-\pi}^{\pi}\phi(x) \sin nx\,dx, and b_n be equal to a similar integral. The weak point in Fourier's analysis lies in his failure to prove generally that the trigonometric series actually converges to the value of the function."

"Most expositions of Aristotle's doctrines, when they have not been dictated by a spirit of virulent detraction, or unsympathetic indifference, have carefully suppressed all, or nearly all, the absurdities, and only retained what seemed plausible and consistent. But in this procedure their historical significance disappears. ...I have allowed the errors and the crudities to take their rightful place beside the plausibilities and truths; thus preserving, as far as may be, the historical colouring derived from the inherent weakness of early Science, and the individual weakness of Aristotle."

"It eminently desirable that the growing practice of secondhand citation should be discouraged; since our native infirmity renders us all sufficiently liable to error, without our taking on ourselves the responsibility of other men's carelessness or their misrepresentations."

"It is difficult to speak of Aristotle without exaggeration: he is felt to be so mighty, and is known to be so wrong."

"The splendour of his fame perpetuates the memory of his failure, and to be just we must appreciate both."

"His intellect was piercing and comprehensive; his attainments surpassed those of every known philosopher; his influence has only been exceeded by the great founders of Religions; nevertheless, if we now estimate the product of his labours in the discovery of positive truths, it appears insignificant, when not erroneous. None of the great germinal discoveries in science are due to him, or to his disciples."

"All ancient writers, except, perhaps, Thucydides, are uncritical in their reception of facts. Even in our own critical age, as it is rashly called, we find it extremely difficult to ascertain the truth respecting celebrated persons; so powerful is the mythical tendency, and so fungus-like the rapidity with which lies are propagated."

"The ancients had not risen to the conception of what constitutes evidence; they were as credulous as children; and accepted almost any marvel which was narrated gravely."

"Often in antagonism... he is never in hostility to Plato. Indeed, in the Ethics, he complains of the necessity of attacking doctrines held by "dear friends," adding—"It is our duty to slay our own flesh and blood where the cause of Truth is at stake, especially as we are philosophers; loving both, it is our sacred duty to give the preference to Truth." It is a timidity unworthy of a noble mind to shrink from intellectual opposition as an offence against friendship, and to suppress convictions for fear of misconstruction."

"His heart was kind, as was manifest in certain acts, and is expressed in this saying, "He who has many friends has no friends," which profoundly touches the very core of the subject, and may be paired off with this other saying of his, "A friend is one soul in two bodies." When asked how we should behave towards friends, he said, "As we should wish them to behave towards us.""

"Advancing age and development, no less than the decidedly scientific bias impressed upon his studies, necessarily caused him to take up an independent position with respect to Plato, who had little taste for physical science, and whose intellect naturally withdrew from those very subjects to which his young rival was, by nature and early bias, strongly determined."

"Had it not been for Alexander's princely aid, Aristotle's enormous collections could not have been made. ...Add to this the statement of Pliny, that Alexander gave orders to his hunters, gamekeepers, fishermen, and bird-catchers to furnish the philosopher with all the material he might desire—an order which at once placed several thousand men at his service. ...But at the same time remember it is Pliny who makes the statement, and for untrustworthiness of statement he cannot easily be surpassed; so that even here an immense exaggeration may be suspected; and to sum up remember that although Aristotle must have had a large collection of materials before he could have written his work on animals, Humboldt declares that there is no trace in that work of any acquaintance with animals first known through Alexander's expedition."

"After an absence of twelve years, B.C. 355, Aristotle reappeared in Athens. He found the Academy already occupied by his friend Xenocrates; so that some other place had to be sought where he might open a school. This he found at the Lyceum...But we must not suppose, as many suppose, that this establishment was placed under the direction of Aristotle, or that he had any voice in its affairs. He simply received permission to teach in the morning and evening at the peripatos, a permission which was the more acceptable because the shady walks offered facilities to his accustomed habit of walking to and fro during the delivery of lectures. ...Aristotle was by no means singular in this practice of promenading while he taught."

"As a foreigner, a philosopher, and a friend of Macedon, he was trebly odious to the political leaders; and a pretext for accusation was raised on a ground where such pretexts are always easily raised and are always dangerous—irreligion. He was accused of blasphemy, and of paying divine honours to mortals. And who were these mortals he had honoured? His friend and his wife. ...The blameless life and lofty soul of Socrates had been no defence against the charges of Melitus; and Aristotle quitted Athens, "not to give the Athenians a second opportunity of committing a sacrilege against philosophy." ...An idle sentence of death was passed; but nature had already written that sentence in terms that were not idle. He died in the sixty-third year of his age B.C. 322."

"His will, which may be read in Diogenes Laertius tells of his thoughtful kindness. His daughter Pythias, his son Nicomachus, his adopted son Nicanor, and his concubine Herpyllis, are all duly provided for, and some of his slaves are emancipated, others rewarded."

"He is admirable for the intense urgency of his mind in seeking scientific explanations of phenomena, at a period when such explanations were novelties; and for the dominant inductive tendency which led him on all subjects to collect the facts before reasoning on them."

"Plato was the most artistic of philosophers, and, among men of great eminence, one of the worst of investigators; not, assuredly, from deficient power, but from his disastrous misconception of Method. In spite of a certain loitering diffuseness of style, and an oppressive circumstantiality in refuting trivial considerations, no one before Plato, no one since, has managed the extremely difficult art of dramatic debate on philosophic topics with such commanding success; and in consequence of this fascinating art, aided by the union of dialectical subtlety with mystical yearnings, a subtlety which seems to give a hope to mysticism, and a warrant to transcendentalism, no one has exercised a more pernicious influence on culture. The charm of the artist has immortalized the vices of the thinker."

"With Aristotle... His Method although imperfect... was not utterly wrong, but wrong only in one important particular; in direction it was wholly right. It was a Method which required development, and was not like that of Plato, one upon which rational philosophy was impossible."

"As an artist, Aristotle is simply without rank and as a writer... he is many degrees removed from excellence. ...In works like the Politics, Poetics, Ethics, and Rhetoric... ...he is intelligible, and sometimes epigrammatic, although without charm. But where more severely tasked... his composition is rambling scattered and confused. There is little illustration, and no side-lights of suggestion. The want of artistic composition renders this absence of illustration a serious defect. When a writer's composition is good there is less need of illustration... But there are few writers who understand this art; and Aristotle understood it not at all."

"Whatever may be the excellencies of Aristotle's diction (and these few moderns can pretend to appreciate), the defects of his composition are not matters of opinion, but of demonstration."

"The history of Aristotle is for many centuries the history of learning."

"Hegel and Sir W. Hamilton have done their best to impress on fluctuating public opinion the conviction that not only was Aristotle a thinker of vast power, but of present worth: not only great in his own time, but anticipating the truths of all time."

"Cuvier, Isidore St. Hilaire, De Blainville, and Johannes Müller, drawing after them crowds of obedient disciples, have spoken of his scientific works as if they were on a level with the science of our day, claiming for him some of the most curious discoveries of modern research."

"Among his modern eulogists will be found biologists, politicians, and metaphysicians, but no astronomer, no physicist, no chemist. In other words, in those sciences which have advanced to the positive stage, and in which the rigour of proof reduces Authority to its just position, his opinions are altogether disregarded; whereas in those sciences in which, from their complexity and immaturity, the influence of Authority and the delusive promises of the Subjective Method still gain acceptance, his dicta are cited as those of a puissant investigator."

"Science... begins when the forces of Nature are appreciated in their relations to each other; and in its highest flights all personal relations are merged in a grand disinterestedness."

"To measure the ground; to measure the seasons and the length of days; to cure a disease or dress a wound; to plough the soil and garner the harvest; to guide a fragile bark along a perilous coast by the aid of the Pleiades; or "sailing stars;" to know that fire burns, liquids evaporate, and metals fuse—these are among the early experiences of the race, but they are not Science. They are the preparatory materials—items of that Common Knowledge which the energy of man, as he advances to maturity developes into Science."

"Science as we now understand the word is of later birth. If its germinal origin may be traced to the early period when Observation, Induction, and Deduction were first employed, its birth must be referred to that comparatively recent period when the mind,—rejecting the primitive tendency to seek in supernatural agencies for an explanation of all external phenomena,—endeavoured, by a systematic investigation of the phenomena themselves to discover their invariable order and connection."

"The separation of Science from Knowledge was effected step by step as the Subjective Method was replaced by the Objective Method: i.e., when in each inquiry the phenomena of external nature ceased to be interpreted on premisses suggested by the analogies of human nature."

"The history of human development shows that there are three modes by which we conceive phenomena... The first of these supposes that the order and succession observed in phenomena, is due to the influence of outlying agencies—powers which are super natural, above the objects, not belonging to them. ...The attitude of mind which is based on the first of these assumptions is that which is common to all primitive theories. It characterizes what Auguste Comte names the Theological Stage in human development. On this assumption, all phenomena not of the simplest and most familiar kind are referred to the agency of invisible powers, spirits, deities, or demons. ...As this idea of will originates in the analogies of human volitions influencing human actions, the same capriciousness and variability which characterize human actions are supposed to characterize external phenomena."

"Before men could refer the changes they observed to the influence of properties inherent in the objects, a strong conviction must have arisen that the order of succession in phenomena was not variable, but fixed. Invariableness would inevitably lead to the conception of all changes being due to the relations between the various properties of objects—first, by discrediting the interference of an external will, which is essentially incalculable; next, by disclosing that there was really no need of anything but the recognized or recognizable properties of objects to account for all changes."

"Causation is now assumed to lie within, and not without, the circle of phenomena. Science, withdrawing from all speculation where it can find no adequate evidence, and where its methods are inoperative, refrains from inquiry as to ultimate causes, and says nothing respecting the mystery of creation."

"The scientific mind replaces these gods and angels by laws of nature, according to which the planets move by forces similar, and under conditions similar to those observed in all other moving bodies. ...it gets rid of the presumed variability in the agency, and leads to the careful study of the inevitable order; instead of encouraging attempts, by prayers, supplications, invocations, or the sacrifices of animal life, to persuade the inevitable order to alter its course."

"The metaphysical explanation is an obstacle, because it withdraws attention from the close scrutiny of facts, and deludes the mind with unverified, unverifiable assumptions."

"So long as diseases were conceived to be the products of supernatural agency, their cure was properly sought in invocations, sacrifices, prayers, and charms, rather than in the study of the organism, and an accurate acquaintance with the properties of objects."

"The theological, metaphysical, and scientific explanations have three different criteria, or guarantees. The guarantee of the first is sacerdotal. ...The guarantee of the second is somewhat less absolute; it admits of question, because it is based on reason, not on faith; nevertheless, any conclusion which can be logically deduced from general doctrines accepted by metaphysicians is held by them to be demonstrated. To the theologian it is enough if he can adduce a text. To the metaphysician it is enough if he can deduce his proposition from "clear and distinct ideas." The guarantee of science is in the verification of experience, direct or indirect. It distrusts the validity of à priori conclusions, or of any explanations drawn solely from general ideas of Nature's order, unless those general ideas have themselves been rigorously demonstrated to be necessities of thought, or to represent the observed order. What must be or may be has to give place to what is."

"The general doctrines of Science are never, like those of Theology and Metaphysics, conceived to be final. However firmly fixed at present, they may be shaken tomorrow by a new discovery."

"In every case Science welcomes scrutiny and scepticism; its final guarantee is conformity with fact."

"While both the metaphysicist and the physicist draw conclusions from their general doctrines, the one is contented with logical symmetry, the other demands the confrontation with fact."

"The ancient astronomers believed in the uniformity of the celestial revolutions, and in the circularity of their orbit. ...performed in perfect freedom and in periods rigorously constant ...From this assumption of uniformity, the circularity of the orbit was a necessary conclusion. The logical chain was perfect. It so completely fettered the mind as almost to bar the way against the admission of the truth. Kepler had difficulty in accepting his own discovery... Thus nothing could be more plausible considered à priori, than the ancient theory; nevertheless, no sooner were adequate means of Verification applied to the theory than the whole fabric tumbled down like a house of cards."

"The Subjective Method claims direct knowledge of the nature of things and the ultimate causes of all changes. The Objective Method by looking at things, assuming the position of simple spectator, renounces all hope of ever penetrating the mysteries of existence, of ever knowing the intimate essence of things, and only hopes to detect the invariable order of co-existence and succession. The one claims a knowledge of "noumena," the other a knowledge of the laws of phenomena."

"The superior exactness and certainty of Mathematics are due to the fact that no hypothesis is allowed to stand for more than an hypothesis; no deduction takes its place as a datum until it has been demonstrated."

"Whenever the data and the deductions have been rigorously verified, the truths of Physics and Chemistry are as certain as those of Mathematics."

""Men who desire to learn," said Aristotle, "must first learn to doubt; for science is only the solution of doubts:" an aphorism, novel in those days, in our own a truism."

"It is their [the Greeks] immortal glory to have recognized the necessity of proof; and this recognition was itself consequent upon their ceasing to interpret phenomena as the direct results of supernatural agencies."

"The mysteriousness was not denied; it was simply set aside, removed from the sphere of scientific thought. The Greek had a free, independent spirit, adventurous, rebellious, curious; and boldly doubting, sought a solution of his doubts in his own way. He refused submission to established doctrines. He would accept neither priest nor philosopher as his oracle. Without directly contradicting the priest, he boldly erected his own Academy beside the Temple."

"It was a weakness in them that they had little sympathy with that sense of the Infinite which characterizes some other eminent nations. This is visible in their Art: an Art matchless in clearness and proportion, in the beauty of arrested lines, and the repose of symmetrical simplicity; but having none of those finer issues which escape into the sublimity of Christian Art. Greek Art is a lute not an organ."

"Aristotle... seems utterly destitute of any sense of the Ineffable. There is no quality more noticeable in him than his unhesitating confidence in the adequacy of the human mind to comprehend the universe... He never seems to be visited by misgivings as to the compass of human faculty, because his unhesitating mind is destitute of awe. He has no abiding consciousness of the fact deeply impressed on other minds, that the circle of the Knowable is extremely limited; and that beyond it lies a vast mystery... impenetrable. Hence the existence of Evil is no perplexity to his soul; it is accepted as a simple fact. Instead of being troubled by it, saddened by it, he quietly explains it as the consequence of Nature not having correctly written her meaning. This mystery which has darkened so many sensitive meditative minds with anguish he considered to be only bad orthography."

"Science acquires her dignity, and her supreme power, from her noble disinterestedness. ...Use is secondary and derivative; the primary object is elucidation of the Truth. All Truth is beneficent; but her seekers desire to behold the serene splendour of her face, and not themselves to reap the benefits which spring up on her track. This attitude was first assumed by the Greeks. Their philosophers were content to seek wisdom as the one great object, without directly subordinating their search to Religion or to Use."

"The attempt to explain Nature, without reference to the gods, very generally drew on philosophers the accusation of impiety. Nor was this prejudice confined to the vulgar and unthinking; it was shared and avowed by Socrates. ...The same thought has, in all ages, roused the bitter hostility of theologians, against the scientific attitude, as one essentially irreligious."

"Science can only destroy false explanations, which it is for our welfare to have destroyed. No single truth can be shaken by Science. If in her own path she detects certain truths, these must necessarily be harmonious with all other truths. We must learn to welcome all, and to prove all."

"Other peoples amassed details of knowledge, manifested intellectual activity, invented useful arts; but it is in the Greek writers that we must seek the inauguration of the scientific epoch. It is in them that, for the first time, appears the systematic effort to ascertain the relations of things objectively, to detect the causes of all changes as inherent in the things themselves, and to reject all supernatural or outlying agencies."

"The Greeks began, but only began, this revolution. They carried it but a little way. Their explanations were generally inaccurate... and the eclipse which for several centuries darkened the day that had thus brightly dawned, was owing chiefly to the energetic revival of that very theological spirit from which the illustrious Greeks had emancipated themselves."

"We have to consider how it was that the Greeks and Romans, in spite of the splendour of their genius, made such slight progress in the discovery of physical laws. In Art, Literature, and Philosophy they have legislated for the world. In Science they are without authority."

"The failure [of a Greek or Roman science] is generally assigned to a complete disregard of Observation and Experiment, together with a "fondness for abstract reasoning." ...A survey... detects the existence of two causes: a psychological and an historical cause. The first lies in the nature of the Method pursued; the second lies in the condition of knowledge at the period. On the Method pursued by the ancients, no satisfactory issues could have been reached, even had it been backed by the stored-up wealth of modern research... [The second,] there was no stored up material to form the basis of extensive discovery. Science is a growth. The future must issue from seeds sown in the past. The bare and herbless granite must first be covered with mosses and lichens, if from their decay is to be formed the nidus of a higher life."

"From the small beginnings and successive growths of knowledge there emerges a more comprehensive and more complex Science. The advance is not simply one of addition but of new development—a development rendered possible by the addition... The truth sought in one age as a goal becomes a starting-point to the age which follows; the discovery which was the passionate aim of one man, and conferred on him lasting glory, becomes to his successors a mere instrument of new research."

"No one who reflects on the actual condition of any science, will fail to notice the complicated connection of all the sciences. The perfection of one demands illumination from all. ...This connection of the sciences points to a simultaneous growth, and a slow growth. Therefore in the early ages before a large mass of established truth had been accumulated, before instruments had been invented, and when discoveries which were to be the instruments of research were still unsuspected, it almost was impossible for any mind, however great, to give a scientific explanation of any class of phenomena; all that could be done was to suggest some happy hypothesis, or to work out some small point of special value."

"The majority, especially of philosophers, were too impatient; and unable to rest without some explanation, trusted confidently to the Subjective Method, because the Objective Method could not then have been constantly applied so as to satisfy their intellectual cravings."

"Before we can explain the failure of the ancients we must rightly appreciate the influence of two different and concurrent causes, methodological and historical. Those writers who... have treated this subject ex professo have entirely overlooked the historical cause... Nor does it seem to me that they have been successful in very distinctly marking the sources of failure even with respect to Method. They have felt the defects rather than assigned a philosophical explanation of them. An exception must be made in favour of Dr.Whewell, who has brought his views on the philosophy of science to elucidate this very question."

"Experiment, by varying the circumstances which usually accompany the phenomena, endeavours to disengage the conditions which are coincident from the conditions which are causally related."

"Observation gives us the fact with great certainty, but without precision; Experiment adds nothing to the certainty, but renders the fact precise, and quantitatively appreciable."

"Experiment is an art, and demands an artist."

"Dr. Whewell... in the section on the "Cause of the failure of the Greek Philosophy" in his History... first points out the common error of supposing that this cause lay in neglect of facts. The Greeks, he assures us, did not disregard experience, did not spin their philosophy purely from their own minds. "The disregard of experience is a phrase which may be so interpreted as to express almost any defect of philosophic method, since coincidence with experience is requisite to all theory." He adds that Aristotle not only insisted on experience as the foundation of science, but "also stated in language much resembling the habitual phraseology of modern schools that particular facts must be collected; that from these, general principles must be obtained by induction; and that these principles, when of the most general kind, are axioms"...Dr. Whewell concludes that "the defect was that though they had in their possession Facts and Ideas, the Ideas were not distinct and appropriate to the Facts. ...he simply says that the Facts were wrongly interpreted, not why they were so."

"Answering this criticism [above], he [Dr. Whewell] affirms that his explanation, over and above the case of failure, points out the one special direction, out of several, in which the Greeks went wrong. "They did not fail because they neglected to observe facts; they did not fail because they had not ideas to reason from; but they failed because they had not the right ideas in each case. And as long as they were wrong in this point, no industry in collecting facts, or ingenuity in classing them and reasoning about them, could lead them to solid truth. ...the reason of Aristotle's failure in his attempts at mechanical science is that he did not refer the Facts to the appropriate Idea, namely Force, the Cause of Motion, but to relations of Space, and the like; that is he introduced geometrical instead of mechanical Ideas.""

"When the orbit of the planets was held to be circular, and their motion uniform, the appropriate and distinct Ideas of Space and Time were not less vividly present to the mind of Aristotle, than they were to the mind of Kepler, when he held the orbit to be elliptical, and the motion variable."

"Aristotle's failure in Biology is not less conspicuous than his failure in Mechanics; yet the ideas of Final Cause, Likeness, and Vitality, which are said to be the ideas appropriate to this science, were assuredly possessed by him with a distinctness unsurpassed in modern times."

"Many glaring errors of the Greeks will have to be noticed... few of them can be referred to the cause assigned by Dr. Whewell."

"The appropriate Ideas said to determine the progress of discovery are... themselves perfected—brought into distinctness—during the progress of discovery, and cannot properly be applied as Instruments until some progress has been achieved."

"It is true that they [the Greeks] observed; it is not true that they observed adequately. It is true that they invoked experience; it is not true that they invoked it sufficiently. They very imperfectly appreciated the nature of evidence; they were careless both as to the quantity and quality of the facts. ...They observed and reasoned, but observed badly, and reasoned precipitately."

"There are three modes of investigation: Observation, Induction, Deduction. To be fruitful these must all be rigorously subordinated to Verification. ...At any one of these stages error may creep in ...Imperfectly observed facts, imperfect inductions and deductions, constantly betray men of science in our own day; and more constantly betrayed the Greeks, because the Greeks were less alive to the dangers."

"Our sole superiority consists in this: we have an ampler basis of demonstrated and colligated truths, and a keener sense of the sources of error. They [the Greeks] were careless and credulous, where we are circumspect and sceptical. They were confident and precipitate in induction; and when an argument was verbally consistent it had an excellent chance of being accepted as an accurate representation of the order of nature."

"The true [Scientific] Method came into use only after the baffled ingenuity of many generations had disclosed the futility of every other, and partial success had cheered men on the difficult but certain path."

"The complexity of phenomena is that of a labyrinth, the paths of which cross and recross each other; one wrong turn causes the wanderer infinite perplexity. Verification is the Ariadne-thread by which the real issues may be found."

"Unhappily, the process of Verification is slow, tedious, often difficult and deceptive; and we are by nature lazy and impatient, hating labour, eager to obtain. Hence credulity."

"Science is the attempt to interpret the phenomena. ...But men ...will not await the tardy results of discovery; they will not sit down in avowed ignorance. Imagination supplies the deficiencies of Observation. A theoretic arch is thrown across the chasm, because men are unwilling to wait till a solid bridge be constructed."

"Newton, with all his genius, would not have detected the law of gravitation had not Kepler and Galileo preceded him; nor could they have made their discoveries had not Greek mathematicians supplied the means."

"The Subjective Method is co-extensive with our ignorance."

"It is the tendency of all positive knowledge of objects gradually to displace the subjective fictions by which the blank of ignorance was at first filled up."

"The amazing rapidity of scientific progress in the last half century, compared with the slowness of its progress in early times, is clearly due to the facilities afforded by what may be called the historical conditions—the state of knowledge out of which the progress issued."

"The false Method is still employed, and in certain inquiries preserves its supremacy; but the existence of a vast body of scientific doctrine, and the rapidly increasing extension of the scientific spirit, prove that the true Method is at length predominant."

"It is a great, though frequent error, to suppose that all metaphysical problems are beyond our power, and that many physical problems are not so. The vanity of Metaphysics lies in its Method, not in its aims."

"The fundamental ideas of modern science are as transcendental as any of the axioms in ancient philosophy. Who will say that the Law of Causation, or the Laws of Motion, although suggested by experience, and found to be conformable with it, do not transcend it?"

"The uniformity of undisturbed rectilinear motion is an abstraction. But it is gained objectively—it is abstracted from facts accurately observed, and is verified by undeviating conformity with facts."

"We are... brought round to the simple rule which Science inscribes on the pediment of her temple:—No formula admissible unless verifiable; none admitted, except as an hypothesis, until verified; the Verification having two different criteria: one, conformity with the positive laws of thought; the other, conformity with the observed order of phenomena."

"No question within the sphere of natural phenomena is too vast for human capacity, or too subtle for human ingenuity, if it can be brought within the range of Verification, direct or indirect; and all questions are insoluble so long as they remain outside this range."

"Facts are indissolubly ideal—the appearances of things to us, not the things per se, and... so far from any fact being the unadulterated image of its object, the conditions of our consciousness are necessarily mingled with it."

"A fact may be defined as a bundle of inferences tied together by one or more sensations."

"If.... Facts are inextricably mingled with Inferences, and if both Perception and Reasoning are processes of mental vision reinstating unapparent details, and liable to error in the inferences, it is clear that the radical antithesis is not between Fact and Theory, but between verified and unverified Inferences."

"The same statement may be either a fact or a theory, without any change in its evidence."

"Failing... to discover any valid antithesis between Fact and Theory, we must look upon the ordinary distinction as simply verbal. Shall we express it by the terms Description and Explanation, implying that a Fact describes the order of phenomena, and a Theory interprets that order? ...Yet on examination we shall find that an Explanation is only a fuller Description: more details are introduced, greater precision is given, the links in the chain which are unapparent to sense, are made apparent to reason; but the essential mystery is untouched; successions are enumerated, but causation escapes."

"What is termed the explanation of a phenomenon by the discovery of its cause, is simply the completion of its description by the disclosure of some intermediate details which had escaped observation. The phenomenon is viewed under new relations. It is classed. It is no longer isolated, but linked onto known facts."

"We learn that chlorine is a gas having a strong "tendency" to unite with hydrogen... But the tendency is only manifested in sunlight. The two gases may be mingled together in darkness, and will not there unite... Admit a ray of light, and the gases rush together with a loud explosion. So far we can describe. ...Shall we seek... a "repulsive force," which we assign to the darkness, and which would forcibly separate the two gases? On the Metaphysical Method this would be legitimate, and metaphysicists might accept the explanation. On the Scientific Method it would at once be condemned, because it does not bring the unknown into visible relation with the known, but into imaginary relation with an imagined fact. Darkness is itself a negation, and its repulsive force a fiction without basis."

""There is one basis of science," says Descartes, "one test and rule of truth, namely, that whatever is clearly and distinctly conceived is true." A profound psychological mistake. It is true only of formal logic, wherein the mind never quits the sphere of its first assumptions to pass out into the sphere of real existences; no sooner does the mind pass from the internal order to the external order, than the necessity of verifying the strict correspondence between the two becomes absolute. The Ideal Test must be supplemented by the Real Test, to suit the new conditions of the problem."

""Reason is the Absolute," says Schelling, "and all the objections against this proposition spring from our tendency to regard things, not as they are in Reason, but as they appear." Again: "It is a fundamental belief that not only do things exist independently of us, but that our Ideas so completely correspond with them that there is nothing in the things which is not in our Ideas."

"Hegel... scornfully characterizes Empiricism as seeking truth in Experience instead of in Thought. It is on such principles that the modern German Philosophy has reproduced the ambitious but inane attempts of Scholasticism."

"It is obvious that the truths of formal logic are unimpeachable. But they lose their guarantee in passing beyond their sphere. ...No sooner do we pass beyond the region of abstractions, than we must at every step assure ourselves of the truth of our inferences by the confirmation of reality. This necessity metaphysicians have overlooked. Logical dependence was the sole test they sought."

"The uniform velocity of the planets was involved in the idea of their circular orbit, which again was involved in the idea of the circle as the most perfect form. The variable velocity of the planets is equally involved in the idea of their orbit being elliptical; but this idea was not gained by deduction from the idea of perfection; it was gained by an abstraction from the observed order of phenomena: it was a verifiable and verified inference. The one conclusion was purely metaphysical, the other purely scientific."

"Unless we adopt the Platonic conception of Ideas, and suppose that our á priori notions are independent of experience, it is obvious that the Metaphysical Method violates the first principles of research. If experience is the basis of even abstract knowledge—the abstract notions being elicited from concrete facts—experience will be the test of all knowledge."

"This is not the place to re-open the discussion respecting the origin of knowledge. Those who hold that the mind is furnished with ideas derived from a source independent of experience, and not therefore amenable to it, must nevertheless confine themselves strictly within the sphere of such ideas, and not include in it the facts only given by experience."

"Descartes, who started from universal doubt, refusing to admit anything but what was demonstrably true, very soon wandered into error, because his criterion of truth was simply subjective... What he can easily conceive, he at once unsuspectingly accepts to be the truth; any confirmation of this view by the application of the Real Test he deems superfluous. Here, as throughout, he falls into the common mistake of metaphysicians."

"Kant truly says "it is the fate of human reason in speculation to build as rapidly as possible, and only when the edifice is completed to examine the solidity of its foundations." And the source of such carelessness he finds in this, that [from] knowledge often consisting in the analysis of our conceptions, we are led to pay exclusive attention to them, rather than to their origin."

"A theory may be transferred from Metaphysics to Science, or from Science to Metaphysics, simply by the addition or the withdrawal of its verifiable element."

"The law of universal attraction becomes pure Metaphysics if we withdraw from it the verifiable specification of its mode of operation. Withdraw the formula "inversely as the square of the distance and directly as the mass," and Attraction is left standing a mere "occult quality." Indeed the Cartesians reproached it with being such an occult quality and stigmatized it as a revival of Aristotelianism. On the other hand, add this verifiable formula to the "inherent virtue" of the old metaphysicists, and the result is a strictly scientific proposition."

"How is... transference from Metaphysics to Science effected? Obviously by the precision of our description, the intercalation of facts in their proper order, facts which previously had been unsuspected, or had not been seen in that order."

"It is a common mistake to suppose that Science deals solely with facts, and Metaphysics with ideas. Both deal largely with both. The difference lies in the authenticity of the Method by which the facts are collected, and coordinated."

"There is abundance of well authenticated facts which nevertheless form no Science because their co-ordination has not been effected; they are bricks awaiting the architect."

"The spontaneous tendency to invoke a Final Cause in explanation of every difficulty is characteristic of metaphysical philosophy. It arises from a general tendency towards the impersonation of abstractions which is visible throughout History."

"We animate Nature with intentions like our own... impersonate the causes as Deities; we next eliminate more and more of the personal elements, leaving only abstract Entities; we finally reduce these Entities to Forces, as the general expression of Properties or Relations, e.g., the Force of gravity is only the abstract expression of the fundamental relation which matter universally manifests."

"We can conceive that what we imagine to be a Vital Principle, anterior and independent in the organism, is really nothing but our generalized expression, abstracted from the mutually dependent facts. It is the same with all the other numerous impersonations of abstract ideas. They are collected from the observed order, and interpreted according to the analogies of our personality; then the facts from which they were abstracted are gradually dropped out of sight, until only the abstraction remains. When this has been done, we have great difficulty in not believing that they exist independently of the facts—that our subjective separation corresponds with an objective separation—and we therefore make them the starting-points of investigation without reference to the facts. This is the basis of Metaphysics."

"We may now glance at the influence of Language in abetting the spontaneous tendency... "...the method of real inquiry was the way to success, but the Greeks followed the... verbal or notional course, and failed." Not the Greeks alone, but all metaphysicians, metaphysicists, and metaphysiologists, have followed this course... when they have once adopted the belief that the order in ideas necessarily represents the order in external things. The pivot of Science is precisely the Verification of this assumed correspondence."

"Aiding and abetting this tendency in the mind to accept ideas as exact representations of things, there is the tendency to assume that distinct names represent distinct facts, so that to analyse the meaning of words is held equivalent to analysis of the things represented. Psychology has made a great advance when it has learned to question these primitive assumptions, an advance which was scarcely suspected in ancient philosophy. The theory of Language was little understood, and nations familiar with no language but their own could hardly have been on their guard against verbal fallacies."

"In passing from formal logic to physical inquiry, a new set of conditions is entered upon, and the test of conformity with fact becomes imperative."

"There has of late years arisen a desire to banish the word "cause" from inductive philosophy; but the word is useful, and it cannot be banished. All that can be done is to mark out clearly the meaning assigned to it in science, namely that of unconditional antecedence. The metaphysical conception of a cause, the producer of effect, needs limitation. We can know nothing of the final nexus."

"We must limit even the conception of necessary sequence, which is held to express all that is known of causation. There is no following of effects from causes; but as Sir John Herschel more truly says, the causes and effects are simultaneous."

"Bring a magnet within a certain distance of a needle and the needle rushes towards it. Here the magnet is said to produce motion. ...But however indispensable, such language is merely an artifice. No separation actually exists. There is not first attraction, and subsequently motion; the two are simultaneous. In like manner, we say the earth's attraction causes the weight of the apple; but the weight is the attraction: they are two aspects of one unknown reality."

"Science... recognizes the constant presence of the Unknowable, as something real though inaccessible; but while admitting the mystery it makes no effort to transcend the already vast limits of the Knowable."

"So readily does it [Science] restrict itself within the relative and phenomenal that it accepts hypotheses which are themselves unverifiable and which even seem absurd if in any way they facilitate the more accurate co-ordination of facts. This is a paradox but it is significant. The first person who grasped its significance I believe to be Copernicus. In the preface to his immortal work he says of the heliocentric hypothesis, "It is by no means necessary that hypotheses should be true, nor even seem true, it is enough if they reconcile calculation with observation.""

"So indifferent is Science to the absolute truth of ideas; so anxious about their relative truth! The reverse is the case with Metaphysics. It cannot be indifferent to absolute truth; if its ideas are false, all deductions drawn from them are vitiated."

"Metaphysics is the co-ordination of unverified facts. Science is the co-ordination of verified facts. That confirmation which the one sees in Logic, the other sees in Observation. The metaphysical tendency is the spontaneous tendency; the scientific caution is an acquired caution."

"No one who scrutinizes the science of our day can fail to perceive how ready men still are to accept phrases for explanations, and guesses for facts."

"I have thus endeavoured to make clear the characteristics and defects of the Metaphysical Method in contrast with the characteristics of the Scientific Method, and shall have frequent opportunities... of invoking and illustrating what may be called the supreme law of all research—the principle of Verification. ...The principles of Inductive and Syllogistic Logic have indeed been amply expounded [historically]; but the supreme law (with its two criteria, Ideal and Real) has been taken for granted rather than articulately expressed, and has very often been wholly overlooked."

"Respect often degenerates into servility because... the admiration of the few becomes the exaggeration of the many..."

"We have to consider him [ Plato ] solely with reference to Science; an aspect, it must be confessed, in which he is seen to great disadvantage."

"To his [Plato's] great disappointment, he found Anaxagoras adducing simple physical reasons, instead of the teleological reasons, which he had expected. Such a teacher could no longer allure him."

"In... frank avowal of the Subjective Method he [Plato] takes no precautions and offers no guarantee for the solidity of the grounds upon which he judges one reason to be stronger than another. Between the caprices of imagination and the rigours of demonstration he offers no criterion. And the disastrous consequences of this oversight are visible in every page of the Timeeus, where the idea of a Best, to which Nature is made to conform, leads him into extravagances such as would be incredible unless their origin were known."

"Even a great intellect may unsuspectingly wander into absurdities, when it quits the firm though laborious path of inductive inquiry."

"The dove cleaving the thin air," to use the happy illustration of Kant, "and feeling its resistance, might suppose that in airless space her movements would be more rapid. Precisely in this way Plato thought that by abandoning the sensuous world, because of the limits it placed to his understanding, he might more successfully venture into the void space of pure intellect."

"It is not in Science only that Plato is misled by his Method. The same confidence in deduction from unverified premisses vitiates his teaching in every other department of inquiry, moral and political; but in Science his errors are more patent, because his statements admit of a readier, and less equivocal, confrontation with fact."

"Aristotle may be truly styled the father of the Inductive Philosophy, since he first announced its leading principles; and announced them with a completeness and precision not surpassed by Bacon himself."

"Common to all the systematic expositions of Method that have yet been published... is the absence of the due recognition of Verification. All writers implicitly recognize Verification as the inseparable attendant of Observation, Induction, and Deduction; but they do not explicitly, and emphatically, assign to it the primary importance it should have; they do not trace in its neglect the cause of every failure. Overlooking this defect, men have expressed surprise at the unquestionable fact that Aristotle and Bacon failed egregiously in scientific research, in spite of their conception of scientific Method..."

"In direct opposition to Plato, who, denying the validity of the senses, made intuitions the ground of all true knowledge, Aristotle sought his basis in sensuous perception. Anticipating Bacon, he affirmed that it was wiser to dissect the complex phenomena of sense than to resolve them into abstractions."

"Plato held that the deceptions of sense justified scepticism of all sense-knowledge... Aristotle, more correctly, taught that error did not arise from the senses being false media, but from the wrong interpretations we put on their testimony. Manifold deceptions may thence arise; but each sense speaks truly so far as it speaks at all. It is from sense we gain the knowledge of particulars. It is from Induction we gain the knowledge of universals. Agreeing with Plato that Science is only concerned with universals, he affirmed that these could only be reached through Experience. This is the corner stone of the experience-philosophy or "Empiricism," so often urged as a reproach against Aristotle."

"Unhappily, even by Aristotle, experience was too frequently neglected and too carelessly interrogated. The vigilance of scientific scepticism was wanting. Yet at times he seems thoroughly impressed with the necessity of securing his basis before attempting to build. "Let us first understand the facts, and then we may seek for their causes.""

"The reason why men do not sufficiently attend to the facts is their want of experience. Hence those accustomed to physical inquiries are more competent to lay down the principles which have an extensive application; whereas others who have been accustomed to many assumptions without the confrontation of reality, easily lay down principles, because they take few things into consideration. It is easy to distinguish those who argue from facts and those who argue from notions."

"In indicating the way we are to arrive at general truths, he expresses himself with a precision unsurpassed by moderns. "We must not," he says, "accept a general principle from logic only, but must prove its application to each fact, for it is in facts that we must seek general principles, and these must always accord with the facts.""

"Since... it appears that Aristotle very distinctly recognized the cardinal principles of the Baconian philosophy, why... has the world credited Bacon with a great reform in the very attacks he made on Aristotle? The answer is simple. Bacon did not attack the Method which Aristotle taught; indeed, he was very imperfectly acquainted with it. He attacked the Method which the followers of Aristotle practised."

"Hypothesis, like everything else, must be proved, or held as a mere thread, which for convenience sake may tie the facts together until a better be discovered. It must never form a basis of deduction. This Aristotle did not distinctly understand, although he is said to have invented the theory of proof."

"If the question be asked why we must seek this proof of what has already been perceived, Aristotle answers: "Because only particulars can be perceived, and science is of universals." ...out of numerous particulars the universal becomes evident. But, he adds, the universal has the preference, because it makes evident the cause. We do not understand a phenomenon until we can demonstrate its cause by a syllogism, showing that it necessarily follows from some general principle. Hence syllogism is the true scientific instrument; and as the syllogism proceeds from the general to the particular, it must be better known in its nature than the particulars it has to prove."

"It is necessary to appreciate clearly this distinction between knowledge of universals and knowledge of particulars. He affirms that although sensation is the origin of all knowledge, the first ideas awakened in the soul consist of general ideas. Thus a man seeing a body at a distance has at first only the general idea of substance; on approaching nearer and... recognizing many of the particulars which distinguish it as kind... he thus gains a particular idea, in lieu of his first general idea. In this way the mind advances from the universal to the particular. The infant at first calls every man papa, and every woman mamma; afterwards it learns to discriminate individuals. The fallacy here is patent. It confounds an indefinite with a generalized conception. It is a fallacy which leavens ancient speculation."

"In spite of his recognition of the importance of observation and induction, he conceived universals as better known than particulars. It was therefore inevitable that he should practically rely on universals to the neglect of particulars, care more about syllogisms than observations; and whenever the universals (general ideas) happened to be true, the reliance was secure. Unfortunately these universals were very often false, still oftener irrelevant; and as no criterion of their truth or relevancy was furnished by the syllogism, the reliance proved disastrous."

"By his theory of proof he placed the Ideal Test above the Real Test: this is metaphysical. Hence in his writings we see little of the patient circumspection of Verification; we see only the impatient facility of Deduction from assumptions which have not been confronted with reality."

"It was this which led him and all the ancients to waste so much effort in the pursuit of causes. Science was supposed to be the knowledge of causes; not the knowledge of laws, or the order of succession and co-existence, but of causes which were knowable entities."

"The distinction between the essence of a thing and the essence of our conception of a thing had not then been admitted into philosophy."

"[Scholsticism:] Inasmuch as change is incessant, there must be some principle of change. Nature is not self-moved; we must, therefore, assume a Prime Mover, himself immoveable."

"[Scholsticism:] What is it which causes the harmony, regularity, and beauty of the world? Obviously a fourth cause:—The final cause... gives to every movement an aim, and a benevolent aim. The good of each and the good of all is the final cause of every change."

"It is apparent, on the most casual inspection, that no one of these [Four] causes can be verifiable; no one of them is susceptible of any stronger guarantee than that of a certain logical concordance in the assumptions we make respecting them; but inasmuch as they pass beyond the sphere of ideas, and claim to represent external realities, the Real Test is indispensable; yet it cannot be applied. Such conceptions are, therefore, utterly unscientific."

"Even in the present day there are not wanting men of eminence who firmly uphold the validity of final causes, and believe teleological argument to be an instrument of research. This is owing to the lingering influence of the Subjective Method."

"The Objective Method teaches that it is idle to assign a final cause, unless we believe that we have, or can have, authoritative knowledge of what actually were the Creator's intentions; and such knowledge Science modestly disclaims."

"It [Science] endeavours to co-ordinate facts; assumptions respecting the intentions of the Creator are not verifiable; if we accept them as we accept other transcendental conceptions, they can only be an unknown quantity in our calculation."

"The futility of the teleological argument may be seen in this, that until we have discovered the law of succession, until the facts are co-ordinated, the assumption of a final cause brings with it no illumination; and when the law has been discovered, the addition of the final cause brings no increase of knowledge."

"By the imperfection of his Method, no less than by the condition of culture at the time, Aristotle was, therefore, practically a metaphysician, assuming without misgiving, the validity of all principles that were clear and logically consistent, no matter if they were merely verbal propositions, wholly without correspondence in fact. He argued from these principles, and only scrutinized the logical dependence of his deduction, instead of scrutinizing the principles themselves, and the verification of his conclusions."

"Aristotle's claim to our veneration is that he produced an organon of science. It was a gigantic creation and for centuries was regarded as the perfect organon. This book it was which opened the subject, and which for centuries was thought to have closed it. We, instructed by a fuller wisdom, may point out its deficiencies, and perceive how they hampered as much as they aided true investigation."

"His noblest title is that of Father of the Inductive Method. He first made men aware of the paramount importance of Fact, and taught them to seek explanations of phenomena on the Objective Method."

"Roger Bacon expressed a feeling which afterwards moved many minds, when he said that if he had the power he would burn all the works of [Aristotle] the Stagirite, since the study of them was not simply loss of time, but multiplication of ignorance. Yet in spite of this outbreak every page is studded with citations from Aristotle, of whom he everywhere speaks in the highest admiration."

"Although modern Science includes ideas not less transcendental than those included in ancient Science... As abstract expressions of the observed order of nature they are liable at any moment to be displaced in favour of expressions more accurate. They serve as guides and starting-points in research. They are not believed in as absolute existences. In ancient science they were held to be absolute existences, which it was the primary object of research to find, and which, when disclosed to the imagination, required no confrontation with reality."

"The ancients studied phenomena to discover the realities underlying phenomena; the moderns study phenomena to detect the order of their co-existences and successions."

"It is also noticeable that, although the ancients had formed the conception of the Indestructibility of Matter, they failed to take the step which now seems so easy, the Indestructibility of Force. Ex nihilo nihil fit [Nothing comes from nothing] was an axiom applied only to Matter. ...every one believed that force could be produced where no force pre-existed."

"The conception of the Indestructibility of Force... is now so obvious that no physicist disputes it, whatever may be his views of the nature of Force—whether he believes it to be an Entity or a Relation."

"All we know of motion is change of position; such changes are necessarily relative; absolute motion is therefore unknown; and consequently Rest must be equally unknown."

"Herschel has noticed how the Stagirite obstructed the progress of astronomy by not identifying celestial with terrestrial mechanics, but laying down the principle that celestial motions were regulated by peculiar laws, thus placing them entirely without the pale of experimental research, while at the same time the progress of mechanics was impeded by the [his] assumption of natural and unnatural motions."

"In our day the principle [of Uniformity] is so familiar that we imagine it must have been an easy step to generalize from terrestrial to celestial mechanics. Yet neither Kepler, the bold, nor Galileo, the far seeing, had the courage to make such a generalization. Kepler assumed that there was some distinct force operating in planetary motions; and it was for the same purpose that Descartes invented his vortices. Even Newton... was very timid in extending terrestrial to celestial laws; and Auguste Comte goes so far as to consider the extension of gravitation beyond our solar system to be very rash, unless understood to be simply a conjecture founded on analogy."

"He who is ignorant of Motion, says Aristotle, is necessarily ignorant of all natural things. ...Not only was he entirely in the dark respecting the Laws, he was completely wrong in his conception of the nature of Motion. ...He thought that every body in motion naturally tends to rest."

"We have learned... that Rest is only Equilibrium, and that is the action of equal and opposing forces, i.e., tension."

"The ancients all conceived Rest as something essentially different from Motion, different in nature, not simply in quantitative amount. They believed the earth to be at rest; we... have learned to regard motion simply as a change of relation."

"The physical writings of Aristotle still extant are the eight books of Physics, the four books On the Heavens, the two books on Generation and Corruption, with the Meteorology, and the Mechanical Problems. The sciences which we class under the heads of Physics and Astronomy are in no sense represented in them. ...There is nothing beyond metaphysical disquisitions suggested by certain physical phenomena; wearisome disputes about motion, space, infinity, and the like; verbal distinctions, loose analogies, unhesitating assumptions, inexpressibly fatiguing and unfruitful. ...We cannot say that on every point he is altogether wrong; on some points he was assuredly right; but these are few, isolated, without bearing on the rest of his speculations, and without influence on research."

"In Book I., after briefly laying down the rules of Method, he examines the opinions of his predecessors. This has an historical interest, but science nowadays is somewhat indifferent to criticisms on Being, or the various meanings which may be attached to the word."

"There are, he says, three principles: Matter, Form, and Privation. In every phenomenon we can distinguish the substance and its form; but as the form can only be one of two Contraries, and as only one of these two can exist at each moment, we are forced to admit the existence of a third principle—Privation—to account for the contrary which is absent. Thus a man must be either a musician or a non-musician; he cannot be both at the same time; and that which prevents his being one of these is the privation of the form."

"Another conclusion reached, after some difficulty, is that Motion really exists."

"In Book II. he presents his definition of Nature. After some confused and vacillating explanation, he arrives at the conclusion that Nature is the principle of Motion and Rest."

"Those things are called natural which are self-moved. He then enters upon the four causes... These comprise Nature: for everything has substance, everything has form, everything has motion, everything has an end or aim."

"He... argues against those who hold Chance to be a cause of phenomena. "What, it has been said, is to prevent nature from acting without an aim, and without any reference to the Best? Why should not Zeus rain from necessity, and not to make the corn grow? Since the vapour, rising upwards, must become cold, and vapour chilled is water, which would descend as rain; and, because this has happened, the corn has grown. Again, if the corn in a granary is ruined by the rain, we cannot say that the final cause of the rain was the ruin of the corn, but that this ruin was accidental. ...What then prevents the organs of animals from being formed in a similar way [above]? Those things which happen to be constituted as if they were made for an express purpose persist, and are preserved because the conditions permit; but those of which this is not the case have perished, or will perish." ...he proceeds to answer it as follows:—"That this should be the case is impossible, and for this reason: these things and all things naturally generated, are always, or mostly, so generated. On the contrary, this is never seen in spontaneous or accidental cases."

""If it is impossible to say the phenomena are accidental, it is clear they must occur with some end in view. But since all things are thus in nature... there must necessarily be a final cause of these things which in nature exist, or are produced." Considering the reputation of Aristotle as a logician, this is, perhaps, one of the feeblest arguments ever put forth on this subject, which has elicited many."

"Nature is to be considered under two aspects—Matter and Form. Now form being an end, and all the rest being arranged with reference to it, we may call the form the final cause. Error, is however, possible both in Nature and in Art. A grammarian may be betrayed into an error of spelling, a physician into administering a wrong potion. Similar errors may exist in Nature."

"In Book III. we have his celebrated definition of Motion as the passage from potential existence to actual existence. "Motion is the energy of what exists in power, so far as existing. It is the act of a moveable which belongs to its power of moving.""

"Since motion is continuity, and as such infinitely divisible; therefore the Infinite must first be studied. Then again as Motion implies both Space and Time, these also must be studied. What Aristotle has to say on these transcendental questions... would occupy too much space and too unprofitably, to reproduce it here."

"I... call attention to the long persistence of the metaphysical fallacy which kept up discussions on such subjects as the existence of space as anything more than a relation. The fallacy is, that whenever man can form clear ideas, not in themselves contradictory, these ideas must of necessity represent truths of nature. Hence when we conceive body, we conceive it as existing in something, which contains it (i.e., body as filling space) we are led to believe that this all-container must itself have an objective existence. The idea will not withstand criticism. An equal necessity can be shown for something to contain the container. As we cannot pursue this reduction ad infinitum, we must stop somewhere; why not, therefore, stop at Substance, of which we know something, rather than go on to Space, of which we know nothing?"

"The argument of J. Bernouilli... is a specimen of metaphysical trifling quite worthy of Aristotle. "Before the creation of the world there was nothing existing, except God. If this universal vacuity was not repugnant to Creative Wisdom, we cannot suppose it repugnant to his Wisdom if there are now many vacant spaces between existing bodies." Out of similar "suppositions" and "clear ideas," metaphysicians have built many systems; systems, but no science."

"Instead of wearying the reader with discussions about Space, let me detach from Aristotle's fourth book the theory of projectiles, interesting in itself, and also because it gives us the first glimpse of a conception of Inertia."

"He argues that in vacuo, Motion is impossible. In a void there can be no difference of place; and motion implies difference of place. He then adds that projectiles continue moving after the original motor ceases to be in contact with them, "either, as some say, by reaction, or by the motion of the moved air, which is more rapid than that of the natural tendency of the body to its proper place.""

""Moreover," he adds, "no one can say why in vacuo a body once set in motion should ever stop; since why rather here than there? Consequently it must either remain in necessary rest, or—if in motion—in endless motion, unless some stronger interferes." ...He had by no means overlooked the fact of the resistance of air, since he compares it with the resistance of water. Yet the air is made to keep up rather than destroy the motion of a projectile. He had... got a glimpse of Inertia—at least, as regards bodies in vacuo. But it never occurred to him to connect the two ideas, and make inertia keep up the continuity of motion, and resistance of the air destroy the motion."

"He was forced to seek for some continuous external motor to account for continuous motion; "the pulses of the moved air" was the first cause which presented itself, and was accepted at once. Whereas had he (and succeeding philosophers) steadily conceived the so-called Law of Inertia—that is to say, the transcendental Law of Causation, that every change demands a cause,—he would have perceived that continuous motion was motion unchanged—would have perceived that no external cause was needed for such continuity, but was only needed to arrest, deflect, accelerate, in a word change the motion. The pulses of air might thus have been conceived as retarding the motion, deflecting it, or accelerating it—and by Verification he would have ascertained which of these conceptions was correct. But in no sense could the pulses of air have been conceived as causing the simple continuance of motion, since continuance implied that there was nothing to cause change."

"The succeeding Books (V. VIII.) are mainly devoted to Motion. It is divided into absolute, partial, and accidental motions—phrases much cherished by scholasticism, which fed on phrases as the fabled chamæleon fed on air."

"In the theory of motion five elements are involved: the motor, the moved, the direction of movement, the starting point, and the goal. It is from the last that motion receives its special designation. Thus the corruption of a body is its movement towards non-existence, although it must necessarily start from existence. In like manner the movement of generation is a movement towards existence, though starting from non-existence. ...how fertile such principles must have been in verbal disputation, how sterile in any other result. Yet this is the system which has been compared with Newton's!"

"There are three Categories of Motion laid down:—1. Quantity; 2. Quality; 3. Place. On these he rings the changes. When a body increases or diminishes, there is the motion of quantity. When the body changes its quality without changing its quantity—as in becoming hot or cold—there is the motion of quality. When a body merely changes its place, there is locomotion, or the "motion of place.""

"There are two great classes of movements—1st, the natural; and 2nd, the violent, or unnatural. ...Fire ascends, and a stone descends, by natural movement. A stone may be made to ascend, but this is owing to violence; some external motor causes it to ascend; by its natural movement the stone would never rise, but always fall. For a similar reason fire may be made to descend; but left to its natural movement it will only ascend."

"Translation being the first of movements, and being reducible to circular, linear, and mixed, the question arises: Which of these is the most perfect? which represents the infinite, continuous, uniform motion of the First Mover? Not the mixed, since that is a combination of the two others. Not the linear, since a straight line is necessarily finite, and if a body were to move eternally along it, there must be a return, which would produce contrary movements, and moments of repose, which would be solutions of continuity. The circular therefore alone remains: in the circle there is no solution of continuity: the motion may be eternal in it. This demonstration of circular movement as the most perfect, played a conspicuous part in peripatetic philosophy. Yet the reader sees at once how entirely it is removed from reality, how purely verbal its basis, how utterly unscientific. The same may be said of all the ideas expounded in the Physics; and we need bestow no more time upon them."

"This history is intended mainly for the use of students and teachers of physics. The writer is convinced that some attention to the history of a science helps to make it attractive, and that the general view of the development of the human intellect, obtained by reading the history of science, is in itself stimulating and liberalizing."

"In the announcement of Ostwald's Klassiker der Exakten Wissenschaften [Classics of the Exact Sciences] is the following significant statement: "While, by the present methods of teaching, a knowledge of science in its present state of advancement is imparted very successfully, eminent and far-sighted men have repeatedly been obliged to point out a defect which too often attaches to the present scientific education of our youth. It is the absence of the historical sense and the want of knowledge of the great researches upon which the edifice of science rests." It is hoped that the survey of the progress of physics here presented may assist in remedying this defect so clearly pointed out by Professor Ostwald."

"In mathematics, metaphysics, literature, and art the Greeks displayed wonderful creative genius, but in natural science they achieved comparatively little. ...it is true that, as a rule, they were ignorant of the art of experimentation, and that many of their physical speculations were vague, trifling, and worthless."

"As compared with the vast amount of theoretical deduction about nature, the number of experiments known to have been performed by the Greeks is surprisingly small. Little or no attempt was made to verify speculation by experimental evidence."

"Mechanical subjects are treated in the writings of Aristotle. The great peripatetic had grasped the notion of the parallelogram of forces for the special case of the rectangle. He attempted the theory of the lever, stating that a force at a greater distance from the fulcrum moves a weight more easily because it describes a greater circle. He resolved the motion of a weight at the end of the lever into tangential and normal components. The tangential motion he calls according to nature; the normal motion contrary to nature. ...the expression contrary to nature applied to a natural phenomenon is inappropriate and confusing."

"Aristotle's views of falling bodies are very far from the truth. ...He says "That body is heavier than another which, in an equal bulk, moves downward quicker." In another place he teaches that bodies fall quicker in exact proportion to their weight. No statement could be further from the truth. ...If it had only occurred to him, while walking up and down the paths near his school in Athens, to pick up two stones of unequal weight and drop them together, he could easily have seen that the one of, say, ten times the weight, did not descend ten times faster."

"Immeasurably superior to Aristotle as a student of mechanics is Archimedes. He is the true originator of mechanics as a science. To him we owe the theory of the centre of gravity (centroid) and of the lever. In his Equiponderance of Planes [On the Equilibrium of Planes] he starts with the axiom that equal weights acting at equal distances on opposite sides of a pivot are in equilibrium, and then endeavours to establish the principle that "in the lever unequal weights are in equilibrium only when they are inversely proportional to the arms from which they are suspended.""

"In his Floating Bodies Archimedes established the important principle, known by his name, that the loss of weight of a body submerged in water is equal to the weight of the water displaced, and that a floating body displaces its own weight of water. Since the days of Archimedes able minds have drawn erroneous conclusions on liquid pressure. The expression "hydrostatic paradox" indicates the slippery nature of the subject. All the more must we admire the clearness of conception and almost perfect logical rigour which characterize the investigations of Archimedes."

"It is reported that he astonished the court of Hieron by moving heavy ships by aid of a collection of pulleys. To him is ascribed the invention of war engines, and the endless screw ("screw of Archimedes") which was used to drain the holds of ships."

"The Greeks invented the hydrometer, probably in the fourth century AD. ...It was first used in medicine to determine the quality of drinking water, hard water being at that time considered unwholesome. According to Desaguliers it was used for this purpose as late as the eighteenth century."

"Optics is one of the oldest branches of physics. A converging lens of rock crystal is said to have been found in the ruins of Nineveh."

"In Greece burning glasses seem to have been manufactured at an early date. Aristophanes in the comedy of The Clouds... introduces a conversation about "fine transparent stone (glass) with which fires are kindled," and by which, standing in the sun, one can, "though at a distance, melt all the writing" traced on a surface of wax."

"The Platonic school taught the rectilinear propagation of light and the equality of the angle of incidence to that of reflection."

"The astronomer Claudius Ptolemy... measured angles of incidence and of refraction and arranged them in tables."

"Metallic mirrors seem to have been manufactured in remote antiquity. Looking glasses are referred to in Exodus 38:8, and in Job 37:18; they have been found in graves of Egyptian mummies."

"Spherical and parabolic mirrors were known to the Greeks. To Euclid... is attributed a work on Catoptrics, dealing with phenomena of reflection. In it is found the earliest reference to the focus of a spherical mirror. In Theorem 30 it is stated that concave mirrors turned toward the sun will cause ignition. In the "fragmentum Bobiense," a document written, perhaps, by Anthemius of Tralles, the focal property of parabolic reflectors is demonstrated. Several Greek authors appear to have written on concave mirrors."

"The Greeks elaborated several theories of vision. According to the Pythagoreans, Democritus, and others vision is caused by the projection of particles from the object seen, into the pupil of the eye. On the other hand Empedocles, the Platonists, and Euclid held the strange doctrine of ocular beams, according to which the eye itself sends out something which causes sight as soon as it meets something else emanated by the object."

"Thales of Miletus... one of the "seven wise men" of early Greece, is credited with the knowledge that amber, when rubbed, will attract light bodies, and that a certain mineral, now called magnetite, or loadstone, possesses the power of attracting iron."

"Amber—a mineralized yellowish resin—was used in antiquity for decoration. In common with the bright shining silver-gold alloys, and gold itself, it was called "electron"; hence the word "electricity.""

"Theophrastus, in his treatise On Gems mentions another mineral which becomes electrified by friction. We know now that all bodies can be thus electrified."

"The polarity of magnets and the phenomenon of repulsion which may exist between electric charges or magnetic poles were unknown to Greek antiquity."

"It is in Athens that we find the oldest contrivance for observing the direction of the wind. There, in its essential parts standing to this day, is the "tower of the winds," built about 100 B.C. Upon an octagon of marble was a roof, the highest part of which carried a weather-vane in form of a triton."

"Among the Greeks meteorology can hardly be said to have risen to the dignity of a science."

"Theophrastus of Eresus... wrote a book On Winds and on Weather Signs, but like most other Greek philosophers, he was hardly the man to adopt patient and exact observation in place of dogmatic assertion and the teaching of authority."

"Aristotle makes a good observation on the formation of dew; viz. dew is formed only on clear and quiet nights."

"Aratus of Soli... wrote a book of Prognostics, giving predictions of the weather from observation of astronomical phenomena, and various accounts of the effect of weather on animals."

"The founders of the schools of the Middle Ages included astronomy, along with geometry, arithmetic, and music, as one of the four branches of advanced education; and, in this respect, it is only just to them to observe that they were far in advance of those who sit in their seats. The schoolmen considered no one to be properly educated unless he were acquainted with, at any rate, one branch of physical science. We have not, even yet, reached that stage of enlightenment."

"Francis Bacon had essayed to sum up the past of physical science, and to indicate the path which it must follow if its great destinies were to be fulfilled. And though the attempt was just such a magnificent failure as might have been expected from a man of great endowments, who was so singularly devoid of scientific insight that he could not understand the value of the work already achieved by the true instaurators of physical science; yet the majestic eloquence and the fervid vaticinations of one who was conspicuous alike by the greatness of his rise and the depth of his fall, drew the attention of all the world to the 'new birth of Time.'"

"Descartes was an eminent mathematician, and it would seem that the bent of his mind led him to overestimate the value of deductive reasoning from general principles, as much as Bacon had underestimated it."

"The progress of physical science has been effected neither by Baconians nor by Cartesians, as such but by men like Galileo and Harvey, Boyle and Newton, who would have done their work just as well if neither Bacon nor Descartes had ever propounded their views respecting the manner in which scientific investigation should be pursued."

"That growth of knowledge beyond imaginable utilitarian ends, which is the condition precedent of its practical utility, began to produce some effect upon practical life; and the operation of that part of nature we call human upon the rest began to create, not 'new natures,' in Bacon's sense, but a new Nature, the existence of which is dependent upon men's efforts, which is subservient to their wants, and which would disappear if man's shaping and guiding hand were withdrawn. Every mechanical artifice, every chemically pure substance employed in manufacture, every abnormally fertile race of plants, or rapidly growing and fattening breed of animals, is a part of the new Nature created by science. ...During the last fifty years, this new birth of time, this new Nature begotten by science upon fact, has pressed itself daily and hourly upon our attention, and has worked miracles which have modified the whole fashion of our lives."

"The bare enumeration of the names of the men who were the great lights of science in the latter part of the eighteenth and the first decade of the nineteenth century, of Herschel, of Laplace, of Young, of Fresnel, of Oersted, of Cavendish, of Lavoisier, of Davy, of Lamarck, of Cuvier, of Jussieu, of Decandolle, of Werner, and of Hutton, suffices to indicate the strength of physical science in the age immediately preceding that of which I have to treat. But of which of these great men can it be said that their labors were directed to practical ends? I do not call to mind even an invention of practical utility which we owe to any of them, except the safety lamp of Davy."

"The history of physical science teaches (and we cannot too carefully take the lesson heart) that the practical advantages, attainable through its agency, never have been, and never will be, sufficiently attractive to men inspired by the inborn genius of the interpreter of nature, to give them courage to undergo the toils and make the sacrifices which that calling requires from its votaries. That which stirs their pulses is the love of knowledge and the joy of the discovery of the causes of things sung by the old poets—the supreme delight of extending the realm of law and order ever farther towards the unattainable goals of the infinitely great and the infinitely small, between which our little race of life is run."

"Far be it from me to depreciate the value of the gifts of science to practical life, or to cast a doubt upon the propriety of the course of action of those who follow science in the hope of finding wealth alongside truth, or even wealth alone. Such a profession is as respectable as any other. And quite as little do I desire to ignore the fact that, if industry owes a heavy debt to science, it has largely repaid the loan by the important aid which it has, in its turn, rendered to the advancement of science."

"In considering the causes which considering hindered the progress of physical knowledge in the schools of Athens and of Alexandria, it has often struck me that where the Greeks did wonders was in just those branches of science, such as geometry, astronomy, and anatomy, which are susceptible of very considerable development without any, or any but the simplest, appliances."

"It is a curious speculation to think what would have become of modern physical science if glass and alcohol had not been easily obtainable; and if the gradual perfection of mechanical skill for industrial ends had not enabled investigators to obtain, at comparatively little cost, microscopes, telescopes, and all the exquisitely delicate apparatus for determining weight and measure and for estimating the lapse of time with exactness, which they now command."

"It has become obvious that the interests of science and of industry are identical; that science cannot make a step forward without, sooner or later, opening up new channels for industry; and, on the other hand, that every advance of industry facilitates those experimental investigations, upon which the growth of science depends."

"We may hope that, at last, the weary misunderstanding between the practical men who professed to despise science, and the high and dry philosophers who professed to despise practical results, is at an end."

"The great steps in its [science's] progress have been made, are made, and will be made, by men who seek knowledge simply because they crave for it."

"Nothing great in science has ever been done by men, whatever their powers, in whom the divine afflatus of the truth-seeker was wanting. Men of moderate capacity have done great things because it animated them; and men of great natural gifts have failed, absolutely or relatively, because they lacked this one thing needful."

"In science, as in art, and, as I believe, in every other sphere of human activity, there may be wisdom in a multitude of counsellors, but it is only in one or two of them. And, in scientific inquiry, at any rate, it is to that one or two that we must look for light and guidance."

"Newton said that he made his discoveries by 'intending' his mind on the subject; no doubt truly. But to equal his success one must have the mind which he 'intended.' Forty lesser men might have intended their minds till they cracked, without any like result. It would be idle either to affirm or to deny that the last half-century has produced men of science of the calibre of Newton. It is sufficient that it can show a few capacities of the first rank, competent not only to deal profitably with the inheritance bequeathed by their scientific forefathers, but to pass on to their successors physical truths of a higher order than any yet reached by the human race. And if they have succeeded as Newton succeeded, it is because they have sought truth as he sought it, with no other object than the finding it."

"So far as physical science is concerned, the days of Admirable Crichtons have long been over, and the most indefatigable of hard workers may think he has done well if he has mastered one of its minor subdivisions. Nevertheless, it is possible for anyone, who has familiarised himself with the operations of science in one department, to comprehend the significance, and even to form a general estimate of the value, of the achievements of specialists in other departments."

"By a happy chance, the first edition of Whewell's 'History of the Inductive Sciences' was published in 1837, and it affords a very useful view of the state of things at the commencement of the Victorian epoch."

"I may hope... that my chance of escaping serious errors is as good as that of anyone else, who might have been persuaded to undertake the somewhat perilous enterprise in which I find myself engaged."

"Physical science is one and indivisible. ...the method of investigation and the ultimate object of the physical inquirer are everywhere the same. The object is the discovery of the rational order which pervades the universe; the method consists of observation and experiment (which is observation under artificial conditions) for the determination of the facts of nature; of inductive and deductive reasoning for the discovery of their mutual relations and connection."

"The various branches of physical science differ in the extent to which, at any given moment of their history, observation on the one hand, or ratiocination on the other, is their more obvious feature, but in no other way; and nothing can be more incorrect than the assumption one sometimes meets with, that physics has one method, chemistry another, and biology a third."

"All physical science starts from certain postulates. One of them is the objective existence of a material world. It is assumed that the phenomena which are comprehended under this name have a 'substratum' of extended, impenetrable, mobile substance which exhibits the quality known as inertia and is termed matter. Another postulate is the universality of the law of causation; that nothing happens without a cause (that is a necessary precedent condition), and that the state of the physical universe, at any given moment, is the consequence of its state at any preceding moment. Another is that any of the rules, or so called 'laws of nature,' by which the relation of phenomena is truly defined, is true for all time."

"The validity of these postulates [of science] is a problem of metaphysics; they are neither self-evident nor are they, strictly speaking, demonstrable. The justification of their employment, as axioms of physical philosophy, lies in the circumstance that expectations logically based upon them are verified, or at any rate, not contradicted, whenever they can be tested by experience."

"Physical science... rests on verified or uncontradicted hypotheses; and, such being the case, it is not surprising that a great condition of its progress has been the invention of verifiable hypotheses."

"It is a favorite popular delusion that the scientific inquirer is under a sort of moral obligation to abstain from going beyond that generalisation of observed facts which is absurdly called 'Baconian' induction. But anyone who is practically acquainted with scientific work is aware that those who refuse to go beyond fact, rarely get as far as fact; and anyone who has studied the history of science knows that almost every great step therein has been made by the 'anticipation of Nature,' that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with; and, not unfrequently, in spite of a long career of usefulness, turned out to be wholly erroneous in the long run."

"The geocentric system of astronomy, with its eccentrics and its epicycles, was an hypothesis utterly at variance with fact, which nevertheless did great things for the advancement of astronomical knowledge."

"Kepler was the wildest of guessers."

"Newton's corpuscular theory of light was of much temporary use in optics, though nobody now believes in it; and the undulatory theory, which has superseded the corpuscular theory and has proved one of the most fertile of instruments of research, is based on the hypothesis of the existence of an 'ether,' the properties of which are defined in propositions, some of which, to ordinary apprehension, seem physical antinomies."

"It sounds paradoxical to say that the attainment of scientific truth has been effected, to a great extent, by the help of scientific errors. But the subject-matter of physical science is furnished by observation, which cannot extend beyond the limits of our faculties; while, even within those limits, we cannot be certain that any observation is absolutely exact and exhaustive. Hence it follows that any given generalisation from observation may be true, within the limits of our powers of observation at a given time, and yet turn out to be untrue, when those powers of observation are directly or indirectly enlarged. Or, to put the matter in another way, a doctrine which is untrue absolutely, may, to a very great extent, be susceptible of an interpretation in accordance with the truth."

"At a certain period in the history of astronomical science, the assumption that the planets move in circles was true enough to serve the purpose of correlating such observations as were then possible; after Kepler, the assumption that they move in ellipses became true enough in regard to the state of observational astronomy at that time. We say still that the orbits of the planets are ellipses, because, for all ordinary purposes, that is a sufficiently near approximation to the truth; but, as a matter of fact, the centre of gravity of a planet describes neither an ellipse or any other simple curve, but an immensely complicated undulating line."

"It may fairly be doubted whether any generalisation, or hypothesis, based upon physical data is absolutely true, in the sense that a mathematical proposition is so; but, if its errors can become apparent only outside the limits of practicable observation, it may be just as usefully adopted for one of the symbols of that algebra by which we interpret nature, as if it were absolutely true."

"The development of every branch of physical knowledge presents three stages which, in their logical relation, are successive."

"The first [stage of physical knowledge] is the determination of the sensible character and order of the phenomena. This is Natural History, in the original sense of the term, and here nothing but observation and experiment avail us."

"The second [stage of physical knowledge] is the determination of the constant relations of the phenomena thus defined [above] and their expression in rules or laws. The third is the explication of these particular laws by deduction from the most general laws of matter and motion. The last two stages constitute Natural Philosophy in its original sense. In this region the invention of verifiable hypotheses is not only permissible but is one of the conditions of progress."

"From the dawn of exact knowledge to the present day, observation, experiment, and speculation have gone hand in hand; and, whenever science has halted or strayed from the right path, it has been, either because its votaries have been content with mere unverified or unverifiable speculation (and this is the commonest case, because observation and experiment are hard work, while speculation is amusing); or it has been, because the accumulation of details of observation has for a time excluded speculation."

"The progress of physical science, since the revival of learning, is largely due to the fact that men have gradually learned to lay aside the consideration of unverifiable hypotheses; to guide observation and experiment by verifiable hypotheses; and to consider the latter, not as ideal truths, the real entities of an intelligible world behind phenomena, but as a symbolical language, by the aid of which nature can be interpreted in terms apprehensible by our intellect."

"If physical science, during the last fifty years, has attained dimensions beyond all former precedent, and can exhibit achievements of greater importance than any former such period can show, it is because able men, animated by the true scientific spirit, carefully trained in the method of science, and having at their disposal immensely improved appliances, have devoted themselves to the enlargement of the boundaries of natural knowledge in greater number than during any previous half-century of the world's history."

"I think that there are three great products of our time... One of these is that doctrine concerning the constitution of matter which, for want of a better name, I will call 'molecular;' the second is the doctrine of conservation of energy; the third is the doctrine of evolution."

"Each of these [above doctrines] was foreshadowed more or less distinctly in former periods of the history of science... The peculiar merit of our epoch is that it has shown how these hypotheses connect a vast number of seemingly independent partial generalisations; that it has given them that precision of expression which is necessary for their exact verification; and that it has practically proved their value as guides to the discovery of new truth."

"All three doctrines are intimately connected, and each is applicable to the whole physical cosmos. But... the first two grew mainly out of the consideration of physico-chemical phenomena; while the third, in great measure, owes its rehabilitation, if not its origin, to the study of biological phenomena."

"The laws of motion of visible and tangible, or molar, matter had been worked out to a great degree of refinement and embodied in the branches of science known as Mechanics, Hydrostatics, and Pneumatics. These laws had been shown to hold good... throughout the universe on the assumption that all such masses of matter possessed inertia and were susceptible of acquiring motion, in two ways, firstly by impact, or impulse from without; and, secondly, by the operation of certain hypothetical causes of motion termed 'forces,' which were usually supposed to be resident in the particles of the masses themselves, and to operate at a distance, in such a way as to tend to draw any two such masses together, or to separate them more widely."

"With respect to the ultimate constitution of... masses, the same two antagonistic opinions which had existed since the time of Democritus and of Aristotle were still face to face. According to the one, matter was discontinuous and consisted of minute indivisible particles or atoms, separated by a universal vacuum; according to the other, it was continuous, and the finest distinguishable, or imaginable, particles were scattered through the attenuated general substance of the plenum. A rough analogy to the latter case would be afforded by granules of ice diffused through water; to the former, such granules diffused through absolutely empty space."

"In the latter part of the eighteenth century, the chemists had arrived at several very important generalisations... However plainly ponderable matter seemed to be originated and destroyed in their operations, they proved that, as mass or body, it remained indestructible and ingenerable... a certain number of the chemically separable kinds of matter were unalterable by any known means (except in so far as they might be made to change their state from solid to fluid, or vice versâ)... and that the properties of these several kinds of matter were always the same, whatever their origin. All other bodies were found to consist of two or more of these, which thus took the place of the four 'elements' of the ancient philosophers. Further, it was proved that, in forming chemical compounds, bodies always unite in a definite proportion by weight, or in simple multiples of that proportion, and that, if any one body were taken as a standard, every other could have a number assigned to it as its proportional combining weight. It was on this foundation of fact that Dalton based his re-establishment of the old atomic hypothesis on a new empirical foundation."

"The gradual reception of the undulatory theory of light necessitated the assumption of the existence of an 'ether' filling all space. But whether this ether was to be regarded as a strictly material and continuous substance was an undecided point, and hence the revived atomism escaped strangling in its birth. For it is clear, that if the ether is admitted to be a continuous material substance, Democritic atomism is at an end and Cartesian continuity takes its place."

"The real value of the new atomic hypothesis... did not lie in the two points which Democritus and his followers would have considered essential—namely, the indivisibility of the 'atoms' and the presence of an interatomic vacuum—but in the assumption that, to the extent to which our means of analysis take us, material bodies consist of definite minute masses, each of which, so far as physical and chemical processes of division go, may be regarded as a unit—having a practically permanent individuality. ...that smallest material particle which under any given circumstances acts as a whole."

"The doctrine of specific heat originated in the eighteenth century. It means that the same mass of a body, under the same circumstances, always requires the same quantity of heat to raise it to a given temperature, but that equal masses of different bodies require different quantities."

"Ultimately, it was found that the quantities of heat required to raise equal masses of the more perfect gases, through equal ranges of temperature, were inversely proportional to their combining weights. Thus a definite relation was established between the hypothetical units and heat. The phenomena of electrolytic decomposition showed that there was a like close relation between these units and electricity. The quantity of electricity generated by the combination of any two units is sufficient to separate any other two which are susceptible of such decomposition. The phenomena of isomorphism showed a relation between the units and crystalline forms; certain units are thus able to replace others in a crystalline body without altering its form and others are not."

"The laws of the effect of pressure and heat on gaseous bodies, the fact that they combine in definite proportions by volume, and that such proportion bears a simple relation to their combining weights, all harmonised with the Daltonian hypothesis and led to the bold speculation known as the law of Avogadro—that all gaseous bodies, under the same physical conditions, contain the same number of units. In the form in which it was first enunciated, this hypothesis was incorrect—perhaps it is not exactly true in any form; but it is hardly too much to say that chemistry and molecular physics would never have advanced to their present condition unless it had been assumed to be true."

"Another immense service rendered by Dalton, as a corollary of the new atomic doctrine, was the creation of a system of symbolic notation, which not only made the nature of chemical compounds and processes easily intelligible and easy of recollection, but, by its very form, suggested new lines of inquiry. The atomic notation was as serviceable to chemistry as the binomial nomenclature and the classificatory schematism of Linnæus were to zoölogy and botany."

"The class of neutral salts... includes a great number of bodies in many ways similar, in which the basic molecules, or the acid molecules, may be replaced by other basic and other acid molecules without altering the neutrality of the salt; just as a cube of bricks remains a cube, so long as any brick that is taken out is replaced by another of the same shape and dimensions, whatever its weight or other properties may be. Facts of this kind gave rise to the conception of 'types' of molecular structure, just as the recognition of the unity in diversity of the structure of the species of plants and animals gave rise to the notion of biological 'types.'"

"The notation of chemistry enabled these ideas to be represented with precision; and they acquired an immense importance, when the improvement of methods of analysis, which took place about the beginning of our period enabled the composition of the so called 'organic' bodies to be determined with rapidity and precision. A large proportion of these compounds contain not more than three or four elements, of which carbon is the chief; but their number is very great, and the diversity of their physical and chemical properties is astonishing. The ascertainment of the proportion of each element in these compounds affords little or no help towards accounting for their diversities; widely different bodies being often very similar, or even identical, in that respect. And in the last case, that of isomeric compounds, the appeal to diversity of arrangement of the identical component units was the only obvious way out of the difficulty."

"Here, again, hypothesis proved to be of great value; not only was the search for evidence of diversity of molecular structure successful, but the study of the process of taking to pieces led to the discovery of the way to put together; and vast numbers of compounds, some of them previously known only as products of the living economy, have thus been artificially constructed."

"It is largely because the chemical theory and practice of our epoch have passed into this deductive and synthetic stage, that they are entitled to the name of the 'New Chemistry' which they commonly receive."

"This new chemistry has grown up by the help of hypotheses, such as those of Dalton and of Avogadro, and that singular conception of 'bonds' invented to colligate the facts of 'valency' or 'atomicity,' the first of which took some time to make its way; while the second fell into oblivion, for many years after it was propounded, for lack of empirical justification. As for the third it may be doubted if anyone regards it as more than a temporary contrivance."

"Combining them [chemical hypotheses] with the mechanical theory of heat and the doctrine of the conservation of energy, which are also products of our time, physicists have arrived at an entirely new conception of the nature of gaseous bodies and of the relation of the physico-chemical units of matter to the different forms of energy. The conduct of gases under varying pressure and temperature, their diffusibility, their relation to radiant heat and to light, the evolution of heat when bodies combine, the absorption of heat when they are dissociated, and a host of other molecular phenomena, have been shown to be deducible from the dynamical and statical principles which apply to molar motion and rest; and the tendency of physico-chemical science is clearly towards the reduction of the problems of the world of the infinitely little, as it already has reduced those of the infinitely great world, to questions of mechanics."

"The primitive atomic theory, which has served as the scaffolding for the edifice of modern physics and chemistry, has been quietly dismissed. I cannot discover that any contemporary physicist or chemist believes in the real indivisibility of atoms, or in an interatomic matterless vacuum. Atoms appear to be used as mere names for physico-chemical units which have not yet been subdivided, and 'molecules' for physico-chemical units which are aggregates of the former. And these individualised particles are supposed to move in an endless ocean of a vastly more subtle matter—the ether."

"If this ether is a continuous substance... we have got back from the hypothesis of Dalton to that of Descartes. But there is much reason to believe that science is going to make a still further journey, and, in form, if not altogether in substance, to return to the point of view of Aristotle."

"The greater number of the so-called 'elementary' bodies, now known, had been discovered before the commencement of our epoch; and it had become apparent that they were by no means equally similar or dissimilar, but that some of them, at any rate, constituted groups, the several members of which were as much like one another as they were unlike the rest. Chlorine, iodine, bromine, and fluorine thus formed a very distinct group; sulphur and selenium another; boron and silicon another; potassium, sodium and lithium another; and so on. In some cases, the atomic weights of such allied bodies... could be arranged in series, with like differences between the several terms. In fact, the elements afforded indications that they were susceptible of a classification in natural groups, such as those into which animals and plants fall."

"Recently this subject [periodicity of the chemical elements] has been taken up afresh with a result which may be stated... so that it is said to express a periodic law of recurrent similarities. ...This is a conception with which biologists are very familiar, animal and plant groups constantly appearing as series of parallel modifications of similar and yet different primary forms. In the living world, facts of this kind are now understood to mean evolution from a common prototype. It is difficult to imagine that in the not-living world they are devoid of significance. Is it not possible, nay probable, that they may mean the evolution of our 'elements' from a primary undifferentiated form of matter? Fifty years ago, such a suggestion would have been scouted as a revival of the dreams of the alchemists. At present, it may be said to be the burning question of physico-chemical science."

"The so called 'vortex-ring' hypothesis is a very serious and remarkable attempt to deal with material units from a point of view which is consistent with the doctrine of evolution. It supposes the ether to be a uniform substance, and that the 'elementary' units are, broadly speaking, permanent whirlpools, or vortices, of this ether, the properties of which depend on their actual and potential modes of motion. It is curious and highly interesting to remark that this hypothesis reminds us not only of the speculations of Descartes, but of those of Aristotle."

"The resemblance of the 'vortex rings' to the 'tourbillons' of Descartes is little more than nominal; but the correspondence between the modern and the ancient notion of a distinction between primary and derivative matter is, to a certain extent, real. For this ethereal 'Urstoff' of the modern corresponds very closely with the &pi;&rho;&#974;&tau;&eta; &#944;&lambda;&eta; of Aristotle, the materia prima of his mediæval followers; while matter, differentiated into our elements, is the equivalent of the first stage of progress towards the &#941;&sigma;&chi;&#940;&tau;&eta; &#944;&lambda;&eta;, or finished matter, of the ancient philosophy."

"If the material units of the existing order of nature are specialised portions of a relatively homogeneous materia prima—which were originated under conditions that have long ceased to exist and which remain unchanged and unchangeable under all conditions, whether natural or artificial, hitherto known to us—it follows that the speculation that they may be indefinitely altered, or that new units may be generated under conditions yet to be discovered, is perfectly legitimate."

"Theoretically, at any rate, the transmutability of the elements is a verifiable scientific hypothesis; and such inquiries as those which have been set afoot, into the possible dissociative action of the great heat of the sun upon our elements, are not only legitimate, but are likely to yield results which, whether affirmative or negative, will be of great importance."

"The idea that atoms are absolutely ingenerable and immutable 'manufactured articles' stands on the same sort of foundation as the idea that biological species are 'manufactured articles' stood thirty years ago; and the supposed constancy of the elementary atoms, during the enormous lapse of time measured by the existence of our universe, is of no more weight against the possibility of change in them, in the infinity of antecedent time, than the constancy of species in Egypt, since the days of Rameses or Cheops, is evidence of their immutability during all past epochs of the earth's history."

"It seems safe to prophesy that the hypothesis of the evolution of the elements from a primitive matter will, in future, play no less a part in the history of science than the atomic hypothesis, which, to begin with, had no greater, if so great, an empirical foundation."

"The connotation of these terms, in the mind of the modern, is almost infinitely different from that which they possessed in the mind of the ancient philosopher. In antiquity, they meant little more than vague speculation; at the present day, they indicate definite physical conceptions, susceptible of mathematical treatment, and giving rise to innumerable deductions, the value of which can be experimentally tested. The old notions produced little more than floods of dialectics; the new are powerful aids towards the increase of solid knowledge."

"In the old philosophy, a curious conjunction of ethical and physical prejudices had led to the notion that there was something ethically bad and physically obstructive about matter. Aristotle attributes all irregularities and apparent dysteleologies in nature to the disobedience, or sluggish yielding, of matter to the shaping and guiding influence of those reasons and causes which were hypostatised in his ideal 'Forms.'"

"Given a cause of motion of a certain value, the amount of motion, measured by distance travelled in a certain time, which it will produce in a given quantity of matter, say a cubic inch, is not always the same, but depends on what that matter is—a cubic inch of iron will go faster than a cubic inch of gold. Hence, it appears, that since equal amounts of motion have, ex hypothesi, been produced, the amount of motion in a body does not depend on its speed alone, but on some property of the body. To this the name of 'mass' has been given. And since it seems reasonable to suppose that a large quantity of matter, moving slowly, possesses as much motion as a small quantity moving faster, 'mass' has been held to express 'quantity of matter.' It is further demonstrable that, at any given time and place, the relative mass of any two bodies is expressed by the ratio of their weights."

"When all these great truths respecting molar motion, or the movements of visible and tangible masses, had been shown to hold good not only of terrestrial bodies, but of all those which constitute the visible universe, and the movements of the macrocosm had thus been expressed by a general mechanical theory, there remained a vast number of phenomena, such as those of light, heat, electricity, magnetism, and those of the physical and chemical changes, which do not involve molar motion, Newton's corpuscular theory of light was an attempt to deal with one great series of these phenomena on mechanical principles, and it maintained its ground until, at the beginning of the nineteenth century, the undulatory theory proved itself to be a much better working hypothesis."

"Heat up to that time [early nineteenth century] and indeed much later, was regarded as an imponderable substance, caloric; as a thing which was absorbed by bodies when they were warmed, and was given out as they cooled; and which, moreover, was capable of entering into a sort of chemical combination with them, and so becoming latent. Rumford and Davy had given a great blow to this view of heat by proving that the quantity of heat which two portions of the same body could be made to give out, by rubbing them together, was practically illimitable. This result brought philosophers face to face with the contradiction of supposing that a finite body contain an infinite quantity of another body..."

"It was not until 1843, that clear and unquestionable experimental proof was given of the fact that there is a definite relation between mechanical work and heat; that so much work always gives rise, under the same conditions, to so much heat, and so much heat to so much mechanical work. Thus originated the mechanical theory of heat, which became the starting-point of the modern doctrine of the conservation of energy."

"Molar motion had appeared to be destroyed by friction. It was proved that no destruction took place, but that an exact equivalent of the energy of the lost molar motion appears as that of the molecular motion, or motion of the smallest particles of a body, which constitutes heat."

"Before 1843... the doctrine of conservation of energy had been approached. Bacon's chief contribution to positive science is the happy guess... that heat may be a mode of motion; Descartes affirmed the quantity of motion in the world to be constant; Newton nearly gave expression to the complete theorem; while Rumford's and Davy's experiments suggested, though they did not prove, the equivalency of mechanical and thermal energy."

"The discovery of voltaic electricity, and the marvellous development of knowledge, in that field, effected by such men as Davy, Faraday, Oersted, Ampere, and Melloni, had brought to light a number of facts which tended to show that the so-called 'forces' at work in light, heat, electricity, and magnetism, in chemical and in mechanical operations, were intimately, and in various cases, quantitatively related. It was demonstrated that any one could be obtained at the expense of any other; and apparatus was devised which exhibited the evolution of all these kinds of action from one source of energy. Hence the idea of the 'correlation of forces' which was the immediate forerunner of the doctrine of the conservation of energy."

"Even the second edition of the 'History of the Inductive Sciences,' which was published in 1846, contains no allusion either to the general view of the 'Correlation of Forces' published in England in 1842, or to the publication in 1843 of the first of the series of experiments by which the mechanical equivalent of heat was correctly ascertained. Such a failure on the part of a contemporary, of great acquirements and remarkable intellectual powers, to read the signs of the times, is a lesson and a warning worthy of being deeply pondered by anyone who attempts to prognosticate the course of scientific progress."

"In so far as matter may be conceived to exist in a purely passive state, it is, imaginably, older than motion."

"Let it be conceived that the [or a] particle acquires a tendency to move, and that nevertheless it does not move. It is then in a condition totally different from that in which it was at first. A cause competent to produce motion is operating upon it, but for some reason or other, is unable to give rise to motion. If the obstacle is removed, the energy which was there, but could not manifest itself, at once gives rise to motion. While the restraint lasts, the energy of the particle is merely potential; and the case supposed illustrates what is meant by potential energy. In this contrast of the potential with the actual, modern physics is turning to account the most familiar of Aristotelian distinctions—that between &delta;&#973;&nu;&alpha;&mu;&iota;&zeta; [potential] and &#941;&nu;&#941;&rho;&gamma;&epsilon;&iota;&alpha; [action, effect, entelechy, power or energy]."

"If a stone is picked up and held, say, six feet above the ground, it has potential energy, because, if let go, it will immediately begin to move towards the earth; and this energy may be said to be energy of position, because it depends upon the relative position of the earth and the stone. The stone is solicited to move but cannot, so long as the muscular strength of the holder prevents the solicitation from taking effect. The stone, therefore, has potential energy, which becomes kinetic if it is let go, and the amount of that kinetic energy which will be developed before it strikes the earth depends on its position—on the fact that it is, say, six feet off the earth, neither more nor less. Moreover, it can be proved that the raiser of the stone had to exert as much energy in order to place it in its position, as it will develop in falling. Hence the energy which was exerted, and apparently exhausted, in raising the stone, is potentially in the stone, in its raised position, and will manifest itself when the stone is set free. Thus the energy, withdrawn from the general stock to raise the stone, is returned when it falls, and there is no change in the total amount. Energy as a whole is conserved."

"In the currently accepted language of science, the cause of motion... when bodies tend to move towards or away from one or another, without any discernible impact of other bodies, is termed a 'force,' which is called 'attractive' in the one case, and 'repulsive' in the other. And such attractive or repulsive forces are often spoken of as if they were real things, capable of exerting a pull, or a push, upon the particles of matter concerned. Thus the potential energy of the stone is commonly said to be due to the 'force' of gravity which is continually operating upon it."

"The bob of a pendulum swings first to one side and then to the other of the centre of the arc which it describes. Suppose it to have just reached the summit of its right-hand half-swing. It is said that the 'attractive forces' of the bob for the earth, and of the earth for the bob, set the former in motion; and as these 'forces' are continually in operation, they confer an accelerated velocity on the bob; until, when it reaches the centre of its swing, it is, so to speak, fully charged with kinetic energy. If, at this moment, the whole material universe, except the bob, were abolished, it would move for ever in the direction of a tangent to the middle of the arc described. As a matter of fact, it is compelled to travel through its left-hand half-swing, and thus virtually to go up hill. Consequently, the 'attractive forces' of the bob and the earth are now acting against it, and constitute a resistance which the charge of kinetic energy has to overcome. But, as this charge represents the operation of the attractive forces during the passage of the bob through the right-hand half-swing down to the centre of the arc, so it must needs be used up by the passage of the bob upwards from the centre of the arc to the summit of the left-hand half-swing. Hence, at this point, the bob comes to a momentary rest. The last fraction of kinetic energy is just neutralised by the action of the attractive forces, and the bob has only potential energy equal to that with which it started. So that the sum of the phenomena may be stated thus: At the summit of either half-arc of its swing, the bob has a certain amount of potential energy; as it descends it gradually exchanges this for kinetic energy, until at the centre it possesses an equivalent amount of kinetic energy; from this point onwards, it gradually loses kinetic energy as it ascends, until, at the summit of the other half-arc, it has acquired an exactly similar amount of potential energy. Thus, on the whole transaction, nothing is either lost or gained; the quantity of energy is always the same, but it passes from one form into the other."

"To all appearance, the phenomena exhibited by the pendulum are not to be accounted for by impact: in fact, it is usually assumed that corresponding phenomena would take place if the earth and the pendulum were situated in an absolute vacuum, and at any conceivable distance from one another. If this be so, it follows that there must be two totally different kinds of causes of motion: the one impact—a vera causa [true cause], of which, to all appearance, we have constant experience; the other, attractive or repulsive 'force'—a metaphysical entity which is physically inconceivable."

"Newton expressly repudiated the notion of the existence of attractive forces, in the sense in which that term is ordinarily understood; and he refused to put forward any hypothesis as to the physical cause of the so-called 'attraction of gravitation.'"

"As a general rule, his [Newton's] successors have been content to accept the doctrine of attractive and repulsive forces, without troubling themselves about the philosophical difficulties which it involves. But this has not always been the case; and the attempt of Le Sage, in the last century, to show that the phenomena of attraction and repulsion are susceptible of explanation by his hypothesis of bombardment by ultra-mundane particles, whether tenable or not, has the great merit of being an attempt to get rid of the dual conception of the causes of motion which has hitherto prevailed. On this hypothesis, the hammering of the ultra-mundane corpuscles on the bob confers its kinetic energy, on the one hand, and takes it away on the other; and the state of potential energy means the condition of the bob during the instant at which the energy, conferred by the hammering during the one half-arc, has just been exhausted by the hammering during the other half-arc."

"It seems safe to look forward to the time when the conception of attractive and repulsive forces, having served its purpose as a useful piece of scientific scaffolding, will be replaced by the deduction of the phenomena known as attraction and repulsion, from the general laws of motion."

"The doctrine of the conservation of energy which I have endeavored to illustrate is thus defined by the late Clerk Maxwell: 'The total energy of any body or system of bodies is a quantity which can neither be increased nor diminished by any mutual action of such bodies, though it may be transformed into any one of the forms of which energy is susceptible.'"

"Energy, like matter, is indestructible and ingenerable in nature."

"The phenomenal world, so far as it is material, expresses the evolution and involution of energy, its passage from the kinetic to the potential condition and back again."

"Wherever motion of matter takes place, that motion is effected at the expense of part of the total store of energy."

"As the phenomena exhibited by living beings, in so far as they are material, are all molar or molecular motions, these are included under the general law [of the conservation of energy]."

"That a particular molecular motion does give rise to a state of consciousness is experimentally certain; but the how and why of the process are just as inexplicable as in the case of the communication of kinetic energy by impact."

"When dealing with the doctrine of the ultimate constitution of matter, we found a certain resemblance between the oldest speculations and the newest doctrines of physical philosophers. But there is no such resemblance between the ancient and modern views of motion and its causes, except in so far as the conception of attractive and repulsive forces may be regarded as the modified descendant of the Aristotelian conception of forms."

"The essential and fundamental difference between ancient and modern physical science lies in the ascertainment of the true laws of statics and dynamics in the course of the last three centuries; and in the invention of mathematical methods of dealing with all the consequences of these laws. The ultimate aim of modern physical science is the deduction of the phenomena exhibited by material bodies from physico-mathematical first principles. Whether the human intellect is strong enough to attain the goal set before it may be a question, but thither will it surely strive."

"The emanistic theories which played so great a part in Neoplatonic philosophy and Gnostic theology are forms of evolution. In the seventeenth century, Descartes propounded a scheme of evolution, as an hypothesis of what might have been the mode of origin of the world, while professing to accept the ecclesiastical scheme of creation, as an account of that which actually was its manner of coming into existence. In the eighteenth century, Kant put forth a remarkable speculation as to the origin of the solar system, closely similar to that subsequently adopted by Laplace and destined to become famous under the title of the 'nebular hypothesis.'"

"The careful observations and the acute reasonings of the Italian geologists of the seventeenth and eighteenth centuries; the speculations of Leibnitz in the 'Protogæa' and of Buffon in his 'Théorie de la Terre;' the sober and profound reasonings of Hutton, in the latter part of the eighteenth century; all these tended to show that the fabric of the earth itself implied the continuance of processes of natural causation for a period of time as great, in relation to human history, as the distances of the heavenly bodies from us are, in relation to terrestrial standards of measurement. The abyss of time began to loom as large as the abyss of space. And this revelation to sight and touch, of a link here and a link there of a practically infinite chain of natural causes and effects, prepared the way, as perhaps nothing else has done, for the modern form of the ancient theory of evolution."

"In the beginning of the eighteenth century, De Maillet made the first serious attempt to apply the doctrine [of evolution] to the living world. In the latter part of it, Erasmus Darwin, Goethe, Treviranus, and Lamarck took up the work more vigorously and with better qualifications. The question of special creation, or evolution, lay at the bottom of the fierce disputes which broke out in the French Academy between Cuvier and St.-Hilaire; and, for a time, the supporters of biological evolution were silenced, if not answered, by the alliance of the greatest naturalist of the age [Cuvier] with their ecclesiastical opponents. Catastrophism, a short-sighted teleology, and a still more short-sighted orthodoxy, joined forces to crush evolution."

"Lyell and Poulett Scrope, in this country, resumed the work of the Italians and of Hutton; and the former, aided by a marvellous power of clear exposition, placed upon an irrefragable basis the truth that natural causes are competent to account for all events, which can be proved to have occurred, in the course of the secular changes which have taken place during the deposition of the stratified rocks."

"The publication of 'The Principles of Geology,' in 1830, constituted an epoch in geological science. But it also constituted an epoch in the modern history of the doctrines of evolution, by raising in the mind of every intelligent reader this question: If natural causation is competent to account for the not-living part of our globe, why should it not account for the living part? By keeping this question before the public for some thirty years, Lyell, though the keenest and most formidable of the opponents of the transmutation theory, as it was formulated by Lamarck, was of the greatest possible service in facilitating the reception of the sounder doctrines of a later day."

"Agassiz... was doomed to help the cause he hated. Agassiz not only maintained the fact of the progressive advance in organisation of the inhabitants of the earth at each successive geological epoch, but he insisted upon the analogy of the steps of this progression with those by which the embryo advances to the adult condition, among the highest forms of each group. In fact, in endeavoring to support these views he went a good way beyond the limits of any cautious interpretation of the facts then known."

"Although little acquainted with biological science, Whewell seems to have taken particular pains with that part of his work which deals with the history of geological and biological speculation; and several chapters of his seventeenth and eighteenth books, which comprise the history of physiology, of comparative anatomy, and of the palsetiological sciences, vividly reproduce the controversies of the early days of the Victorian epoch. But here, as in the case of the doctrine of the conservation of energy, the historian of the inductive sciences has no prophetic insight; not even a suspicion of that which the near future was to bring forth."

"Those who still repeat the once favorible objection that Darwin's 'Origin of Species' is nothing but a new version of the 'Philosophie zoologique' will find that so late as 1844, Whewell had not the slightest suspicion of Darwin's main theorem, even as a logical possibility. In fact, the publication of that theorem by Darwin and Wallace, in 1859, took all the biological world by surprise."

"Neither those who were inclined towards the 'progressive transmutation' or 'development' doctrine, as it was then called, nor those who were opposed to it, had the slightest suspicion that the tendency to variation in living beings, which all admitted as a matter of fact; the selective influence of conditions, which no one could deny to be a matter of fact, when his attention was drawn to the evidence; and the occurrence of great geological changes which also was matter of fact; could be used as the only necessary postulates of a theory of the evolution of plants and animals which, even if not, at once, competent to explain all the known facts of biological science, could not be shown to be inconsistent with any."

"So far as biology is concerned, the publication of the 'Origin of Species,' for the first time, put the doctrine of evolution, in its application to living things, upon a sound scientific foundation. It became an instrument of investigation, and in no hands did it prove more brilliantly profitable than in those of Darwin himself. His publications on the effects of domestication in plants and animals, on the influence of cross-fertilisation, on flowers as organs for effecting such fertilisation, on insectivorous plants, on the motions of plants, pointed out the routes of exploration which have since been followed by hosts of inquirers, to the great profit of science."

"It is only within the present epoch, that physiology and chemistry have reached the point at which they could offer a scientific foundation to agriculture; and it is only within the present epoch, that zoology and physiology have yielded any very great aid to pathology and hygiene. But within that time, they have already rendered highly important services by the exploration of the phenomena of parasitism. Not only have the history of the animal parasites, such as the tapeworms and the trichina, which infest men and animals, with deadly results, been cleared up by means of experimental investigations... but the terrible agency of the parasitic fungi and of the infinitesimally minute microbes, which work far greater havoc among plants and animals, has been brought to light."

"The 'particulate' or 'germ' theory of disease... has obtained a firm foundation, in so far as it has been proved to be true in respect of sundry epidemic disorders. Moreover, it has theoretically justified prophylactic measures, such as vaccination, which formerly rested on a merely empirical basis; and it has been extended to other diseases with excellent results. ...the progress of experimental physiology and pathology will, indubitably, in course of time place medicine and hygiene upon a rational basis."

"Two centuries ago England was devastated by the plague; cleanliness and common sense were enough to free us from its ravages. One century since, small-pox was almost as great a scourge; science, though working empirically, and almost in the dark, has reduced that evil to relative insignificance. ...sooner or later it will deal in the same way with diphtheria, typhoid and scarlet fever."

"There is no reasonable ground for believing that the oldest remains yet obtained carry us even near the beginnings of life. The impressive warnings of Lyell against hasty speculations, based upon negative evidence, have been fully justified; time after time, highly organised types have been discovered in formations of an age in which the existence of such forms of life had been confidently declared to be impossible."

"Certain forms persist with very little change, from the oldest to the newest fossiliferous formations; and thus show that progressive development is a contingent, and not a necessary result, of the nature of living matter."

"Geology is, as it were, the biology of our planet as a whole. In so far as it comprises the surface configuration and the inner structure of the earth, it answers to morphology; in so far as it studies changes of condition and their causes, it corresponds with physiology; in so far as it deals with the causes which have effected the progress of the earth from its earliest to its present state, it forms part of the general doctrine of evolution."

"It should never be forgotten that what we call 'catastrophes,' are, in relation to the earth, changes, the equivalents of which would be well represented by the development of a few pimples, or the scratch of a pin on a man's head."

"There is no study better fitted than that of geology to impress upon men of general culture that conviction of the unbroken sequence of the order of natural phenomena, throughout the duration of the universe, which is the great, and perhaps the most important, effect of the increase of natural knowledge."

"There appeared in December 1921, just before this reprint was struck off, Sir T. L. Heath's work in 2 volumes on the History of Greek Mathematics. This may now be taken as the standard authority for this [first] period."

"The subject-matter of this book... primarily it is intended to give a short and popular account of those leading facts in the history of mathematics which many who are unwilling, or have not the time, to study it systematically may yet desire to know."

"The first edition was substantially a transcript of some lectures which I delivered in the year 1888 with the object of giving a sketch of the history, previous to the nineteenth century, that should be intelligible to any one acquainted with the elements of mathematics."

"Doubtless an exaggerated view of the discoveries of those mathematicians who are mentioned may be caused by the non-allusion to minor writers who preceded and prepared the way for them, but in all historical sketches this is to some extent inevitable, and I have done my best to guard against it by interpolating remarks on the progress of the science at different times."

"Generally I have not referred to the results obtained by practical astronomers and physicists unless there was some mathematical interest in them."

"In quoting results I have commonly made use of modern notation; the reader must therefore recollect that, while the matter is the same as that of any writer to whom allusion is made, his proof is sometimes translated into a more convenient and familiar language."

"For the history previous to 1758, I need only refer, once for all, to the closely printed pages of M. Cantor's monumental Vorlesungen über die Geschichte der Mathematik (hereafter alluded to as Cantor), which may be regarded as the standard treatise on the subject."

"Although the history of mathematics commences with that of the Ionian schools, there is no doubt that those Greeks who first paid attention to the subject were largely indebted to the previous investigations of the Egyptians and Phoenicians. Our knowledge of the mathematical attainments of those races is imperfect and partly conjectural..."

"The history of mathematics cannot with certainty be traced back to any school or period before that of the…Greeks…."

"Though all early races which have left records behind them knew something of numeration and mechanics, and though the majority were also acquainted with the elements of land-surveying, yet the rules which they possessed were in general founded only on the results of observation and experiment, and were neither deduced from nor did they form part of any science."

"The fact... that various nations in the vicinity of Greece had reached a high state of civilisation does not justify us in assuming that they had studied mathematics."

"Greek tradition uniformly assigned the special development of geometry to the Egyptians, and that of the science of numbers either to the Egyptians or to the Phoenicians."

"The magnitude of the commercial transactions of Tyre and Sidon necessitated a considerable development of arithmetic, to which it is probable the name of science might be properly applied."

"A Babylonian table of the numerical value of the squares of a series of consecutive integers has been found, and this would seem to indicate that properties of numbers were studied."

"According to Strabo the Tyrians paid particular attention to the sciences of numbers, navigation, and astronomy; they had, we know, considerable commerce with their neighbours and kinsmen the Chaldaeans."

"Whatever was the extent of their [the Chaldaeans] attainments in arithmetic, it is almost certain that the Phoenicians were equally proficient."

"It seems probable that the early Greeks were largely indebted to the Phoenicians for their knowledge of practical arithmetic or the art of calculation, and perhaps also learnt from them a few properties of numbers. It may be worthy of note that Pythagoras was a Phoenician; and according to Herodotus, but this is more doubtful, Thales was also of that race."

"The almost universal use of the abacus or swanpan rendered it easy for the ancients to add and subtract without any knowledge of theoretical arithmetic. These instruments... afford a concrete way of representing a number in the decimal scale, and enable the results of addition and subtraction to be obtained by a merely mechanical process."

"About forty years ago a hieratic papyrus, forming part of the Rhind collection in the British Museum, was deciphered... The manuscript was written by a scribe named Ahmes... The work is called "directions for knowing all dark things," and consists of a collection of problems in arithmetic and geometry; the answers are given, but in general not the processes by which they are obtained. It appears to be a summary of rules and questions familiar to the priests."

"The first part [of the Rhind Papyrus] deals with the reduction of fractions of the form 2/(2n + 1) to a sum of fractions each of whose numerators is unity... Probably he had no rule for forming the component fractions, and the answers given represent the accumulated experiences of previous writers: in one solitary case, however, he has indicated his method, for, after having asserted that 2/3 is the sum of 1/2 and 1/6, he adds that therefore two-thirds of one-fifth is equal to the sum of a half of a fifth and a sixth of a fifth, that is, to 1/10 + 1/30."

"That so much attention was paid to fractions is explained by the fact that in early times their treatment was found difficult. The Egyptians and Greeks simplified the problem by reducing a fraction to the sum of several fractions, in each of which the numerator was unity, the sole exception to this rule being the fraction 2/3. This remained the Greek practice until the sixth century of our era. The Romans, on the other hand, generally kept the denominator constant and equal to twelve, expressing the fraction (approximately) as so many twelfths. The Babylonians did the same in astronomy, except that they used sixty as the constant denominator; and from them through the Greeks the modern division of a degree into sixty equal parts is derived. Thus in one way or the other the difficulty of having to consider changes in both numerator and denominator was evaded. To-day when using decimals we often keep a fixed denominator, thus reverting to the Roman practice."

"In multiplication he [Ahmes] seems to have relied on repeated additions. Thus in one numerical example, where he requires to multiply a certain number, say a, by 13, he first multiplies by 2 and gets 2a, then he doubles the results and gets 4a, then he again doubles the result and gets 8a, and lastly he adds together a, 4a, and 8a. Probably division was also performed by repeated subtractions, but, as he rarely explains the process by which he arrived at a result, this is not certain."

"Ahmes goes on to the solution of some simple numerical equations. For example, he says "heap, its seventh, its whole, it makes nineteen," by which he means that the object is to find a number such that the sum of it and one-seventh of it shall be together equal to 19; and he gives as the answer 16 + 1/2 + 1/8, which is correct."

"The arithmetical part of the [Rhind] papyrus indicates that he had some idea of algebraic symbols. The unknown quantity is always represented by the symbol which means a heap; addition is sometimes represented by a pair of legs walking forwards, subtraction by a pair of legs walking backwards or by a flight of arrows; and equality..."

"He [Ahmes] concludes the work with some arithmetico-algebraical questions, two of which deal with arithmetical progressions and seem to indicate that he knew how to sum such series."

"Some methods of land-surveying must have been practised from very early times, but the universal tradition of antiquity asserted that the origin of geometry was to be sought in Egypt. ...Herodotus states that the periodical inundations of the Nile (which swept away the landmarks in the valley of the river, and by altering its course increased or decreased the taxable value of the adjoining lands) rendered a tolerably accurate system of surveying indispensable, and thus led to a systematic study of the subject by the priests."

"We have no reason to think that any special attention was paid to geometry by the Phoenicians, or other neighbours of the Egyptians. A small piece of evidence which tends to show that the Jews had not paid much attention to it is to be found in the mistake made in their sacred books, where it is stated that the circumference of a circle is three times its diameter: the Babylonians also reckoned that was equal to 3."

"That some geometrical results were known at a date anterior to Ahmes's work seems clear if we admit... that, centuries before it was written, the following method of obtaining a right angle was used in laying out the ground-plan of certain buildings. The Egyptians were very particular about the exact orientation of their temples; and they had therefore to obtain with accuracy a north and south line, as also an east and west line. By observing the points on the horizon where a star rose and set, and taking a plane midway between them, they could obtain a north and south line. To get an east and west line, which had to be drawn at right angles to this, certain professional "rope-fasteners" were employed. These men used a rope... divided by knots or marks... in the ratio 3 : 4 : 5. ...A similar method is constantly used at the present time by practical engineers for measuring a right angle. ...But though these are interesting facts in the history of the Egyptian arts we must not press them too far as showing that geometry was then studied as a science. Our real knowledge of the nature of Egyptian geometry depends mainly on the Rhind papyrus."

"Ahmes then goes on to find the area of a circular field … and gives the result as (d - 1/9d)2, where d is the diameter of the circle: this is equivalent to taking 3.1604 as the value of π, the actual value being very approximately 3.1416."

"Ahmes gives some problems on pyramids. ...Ahmes was attempting to find, by means of data obtained from the measurement of the external dimensions of a building, the ratio of certain other dimensions which could not be directly measured: his process is equivalent to determining the trigonometrical ratios of certain angles. The data and the results given agree closely with the dimensions of some of the existing pyramids. Perhaps all Ahmes's geometrical results were intended only as approximations correct enough for practical purposes."

"All the specimens of Egyptian geometry which we possess deal only with particular numerical problems and not with general theorems; and even if a result be stated as universally true, it was probably proved to be so only by a wide induction. ...Greek geometry was from its commencement deductive. There are reasons for thinking that Egyptian geometry and arithmetic made little or no progress subsequent to the date of Ahmes's work; and though for nearly two hundred years after the time of Thales Egypt was recognised by the Greeks as an important school of mathematics, it would seem that, almost from the foundation of the Ionian school, the Greeks outstripped their former teachers."

"Ahmes's book gives us much that idea of Egyptian mathematics which we should have gathered from statements about it by various Greek and Latin authors, who lived centuries later. Previous to its translation it was commonly thought that these statements exaggerated the acquirements of the Egyptians, and its discovery must increase the weight to be attached to the testimony of these authorities."

"We know nothing of the applied mathematics (if there were any) of the Egyptians or Phoenicians. The astronomical attainments of the Egyptians and Chaldaeans were no doubt considerable, though they were chiefly the results of observation: the Phoenicians are said to have confined themselves to studying what was required for navigation."

"At a very early period the Chinese were acquainted with several geometrical or rather architectural implements, such as the rule, square, compasses, and level; with a few mechanical machines, such as the wheel and axle; that they knew of the characteristic property of the magnetic needle; and were aware that astronomical events occurred in cycles. But the careful investigations of L. A. Sédillot have shown that the Chinese made no serious attempt to classify or extend the few rules of arithmetic or geometry with which they were acquainted, or to explain the causes of the phenomena which they observed."

"The idea that the Chinese had made considerable progress in theoretical mathematics seems to have been due to a misapprehension of the Jesuit missionaries who went to China in the sixteenth century. ...they failed to distinguish between the original science of the Chinese and the views which they found prevalent on their arrival|the latter being founded on the work and teaching of Arab or Hindoo missionaries who had come to China in the course of the thirteenth century or later, and while there introduced a knowledge of spherical trigonometry."

"The only geometrical theorem with which we can be certain that the ancient Chinese were acquainted is that in certain cases (namely, when the ratio of the sides is 3 : 4 : 5, or 1 : 1 : √2) the area of the square described on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares described on the sides. It is barely possible that a few geometrical theorems which can be demonstrated in the quasi-experimental way of superposition were also known to them."

"Their [the ancient Chinese] arithmetic was decimal in notation, but their knowledge seems to have been confined to the art of calculation by means of the swan-pan."

"Our acquaintance with the early attainments of the Chinese... serves to illustrate the fact that a nation may possess considerable skill in the applied arts while they are ignorant of the sciences on which those arts are founded."

"Our knowledge of the mathematical attainments of those who preceded the Greeks is very limited; but... the early Greeks learned the use of the abacus for practical calculations, symbols for recording the results, and as much mathematics as is contained or implied in the Rhind papyrus. It is probable that this sums up their indebtedness..."

"Thales... must have had considerable reputation as a man of affairs and as a good engineer, since he was employed to construct an embankment so as to divert the river Halys in such a way as to permit of the construction of a ford."

"We cannot form any exact idea as to how Thales presented his geometrical teaching. We infer, however, from Proclus that it consisted of a number of isolated propositions which were not arranged in a logical sequence, but that the proofs were deductive, so that the theorems were not a mere statement of an induction from a large number of special instances, as probably was the case with the Egyptian geometricians. The deductive character which he thus gave to the science is his chief claim to distinction."

"The following comprise the chief propositions that can now with reasonable probability be attributed to him [Thales]...(i) The angles at the base of an isosceles triangle are equal (Euc. I, 5). Proclus seems to imply that this was proved by taking another exactly equal isosceles triangle, turning it over, and then superposing it on the first—a sort of experimental demonstration. (ii) If two straight lines cut one another, the vertically opposite angles are equal (Euc. I, 15). Thales may have regarded this as obvious, for Proclus adds that Euclid was the first to give a strict proof of it. (iii) A triangle is determined if its base and base angles be given (cf. Euc. I, 26). Apparently this was applied to find the distance of a ship at sea—the base being a tower, and the base angles being obtained by observation. (iv) The sides of equiangular triangles are proportionals (Euc. VI, 4, or perhaps rather Euc. VI, 2). This is said to have been used by Thales when in Egypt to find the height of a pyramid. "...the pyramid [height] was to the stick [height] as the shadow of the pyramid to the shadow of the stick." …we are told that the king Amasis, who was present, was astonished at this application of abstract science. (v) A circle is bisected by any diameter. This may have been enunciated by Thales, but it must have been recognised as an obvious fact from the earliest times. (vi) The angle subtended by a diameter of a circle at any point in the circumference is a right angle (Euc. III, 31). This appears to have been regarded as the most remarkable of the geometrical achievements of Thales... It has been conjectured that he may have come to this conclusion by noting that the diagonals of a rectangle are equal and bisect one another, and that therefore a rectangle can be inscribed in a circle. If so, and if he went on to apply proposition (i), he would have discovered that the sum of the angles of a right-angled triangle is equal to two right angles, a fact with which it is believed that he was acquainted. It has been remarked that the shape of the tiles used in paving floors may have suggested these results."

"I was influenced by my experience of the limited acquaintance with the historical development of the science which has often been shown, even by those who have done good service in enlarging its boundaries. English-speaking geologists have for the most part contented themselves with the excellent, but necessarily brief, summary of the subject given by Lyell in the introductory chapters of his classic Principles, no fuller digest of geological history having been published in their language."

"It appeared to me that it might be useful to recount the story of a few of the great pioneers during the momentous period... and to show, from their struggles, their failures, and their successes, how geological ideas and theories arose, and were step by step worked out into the forms they now wear."

"In order to trace the history of... petrographical resuscitation we must... transport ourselves to the workshop of an ingenious and inventive mechanician, William Nicol... Among his inventions was the famous prism of Iceland spar that bears his name. Every petrographer will acknowledge how indispensable this little piece of apparatus is in his microscopic investigations. ...it was the same skillful hands that devised the process of making thin slices of minerals and rocks, whereby the microscopic examination of these substances has become possible."

"Nicol hit upon the plan of cutting sections of fossil wood, so as to reveal its minutest vegetable structures. He took a slice from the specimen to be studied, ground it perfectly flat, polished it, and cemented it by means of Canada balsam to a piece of plate-glass. The exposed surface of the slice was then ground down, until the piece of stone was reduced to a thin pellicle adhering to the glass, and the requisite degree of transparency was obtained. Many of these were described by Henry Witham in his Observations of Fossil Vegetables (1831)."

"I am afraid that the geologists are about as difficult to move as their own erratic blocks. They took no notice of the possibilities put in their way by William Nicol."

"When Nicol died, his instruments and preparations passed into the hands of the late Mr. Alexander Bryson of Edinburgh, who... made many additions to the collections which he had acquired. In particluar, he made numerous thin slices of minerals and rocks for the purpose of exhibiting the cavities containing fluid, which had been described long before by David Brewster and Nicol."

"At last Mr. Henry Clifton Sorby came to Edinburgh, and...was particularly struck with the series of slices illustrating "fluid cavities," and at once saw that the subject was one of which the further prosecution could not fail to "lead to important conclusions in geological theory." He soon... made sections of mica-schist, and... threw his whole energy into the investigation for several years, and produced at last in 1858 the well-known memoir, On the Microscopical Structure of Crystals, which marks one of the most prominent epochs of modern geology."

"William Nicol was never adequately recognised in his lifetime."

"Sorby... for the first time, showed how, by means of a microscope, it was possible to discover the minute structure and composition of rocks, and to learn much regarding their mode of origin. He took us... into the depths of a volcanic focus, and revealed the manner in which lavas acquire their characters. He carried us still deeper into the terrestrial crust, and laid open the secrets of those profound abysses in which granitic rocks have been prepared."

"The reproach that it was impossible to look at a mountain through a microscope was brought forward in opposition to the new departure which he [Sorby] advocated. Well did he reply by anticipation to this objection. "Some geologists, only to examine large masses in the field, may perhaps be disposed to question the value of the facts I have described, and to think the objects so minute as to be quite beneath their notice, and that all attempts at accurate calculations from such small data are quite inadmissible. What other science, however, has prospered by proposing such a creed? ...I ague that there is no necessary connection between the size of an object and the value of the fact, and that, though the objects I describe are minute, the conclusions to be derived from the facts are great.""

"From the beginning of its career, geology has owed its foundation and its advance to no select and privileged class. ...No branch of natural knowledge lies more invitingly open to every student who, loving the fresh face of Nature, is willing to train his faculty of observation in the field, and to discipline his mind by the patient correlation of facts and the fearless dissection of theories."

"The history of geological science presents some conspicuous examples of the length of time that may elapse before a fecund idea comes to germinate and bear fruit. Consider for a moment how many years passed before the stratigraphical conceptions of [G.C.] Füchsel, Lehmann, and [the Abbé, Jean-Louis] Giraud-Soulavie took more definite shape in the detailed investigations of Cuvier, Brongniart and Smith, and how many more years were needed before the Secondary and Tertiary formations were definitely arranged and subdivided as they now stand in out tables. ...even after the principles of stratigraphy had been settled, a quarter of a century had slipped away before they were successfully applied to the Transition rocks, and a still longer time before the system of zonal classification was elaborated."

"Note how long the controversy lasted over the origin of basalt, and how slowly came the recognition of volcanic action as a normal part of terrestrial energy... Mark also, in the history of physiographical geology, that though the principles of this branch of science were in large measure grasped by Desmarest, De Saussure and Hutton in the eighteenth century, their work was neglected and forgotten until the whole subject has been revived amd marvellously extended in our own day."

"How slowly the key that now unlocks the innermost mysteries of rock-structure was made use of. Five and twenty years after William Nicol had shown how stony substances could be investigated by means of the microscope, before Mr. Sorby called the attention of geologists to the enormous value of the method thus put into their hands."

"We are warned to be on the lookout for the unrecognized meanings and applications in the work of our own day and in that of older date. We are taught the necessity not only of keeping ourselves abreast of the progress of science at the present time, but also of making ourselves acquainted as far as we possibly can with the labours of our predecessors."

"...the permanent vitality of truth. The seed may be long in showing signs of life, but these signs come at last."

"In the case of geological literature, a large mass of the writing of the present time is of little or no value for any of the higher purposes of the science, and... it may quite safely and profitably, both as regards time and temper, be left unread."

"If geologists... could only be brought to realise that the addition of another paper to the swollen flood of our scientific literature involves a serious responsibility; that no man should publish what is not of real consequence, and that his statements should be as clear and condensed as he can make them, what a blessed change would come over the faces of their readers, and how greatly would they conduce to the real advance of science which they wish to serve!"

"It seems to me that one important lesson to be learnt from a review of the successive stages in the foundation and development of geology is the absolute necessity of avoiding dogmatism. Let us remember how often geological theory has altered. The Catastrophists had it all their own way until the Uniformitarians got the upper hand, only to be in turn displaced by the Evolutionists."

"The Wernerians were as certain of the origin and sequence of rocks as if they been present at the formation of the earth's crust. Yet in a few years their notions and overweening confidence became a laughing-stock."

"What seems to be a well-established deduction in one age may be seen to be more or less erroneous in the next."

"Each of us has it in his power to add to this accumulation of knowledge. Careful and accurate observation is always welcome, and may eventually prove of signal importance."

"While availing ourselves freely of the use of hypothesis as an aid in ascertaining the connection and significance of facts, we must be ever on our guard against premature speculation and theory, clearly distinguishing between what is fact and what may be our own gloss or interpretation of it."

"Let us hold high the torch of science, and pass it on bright and burning to those who shall receive it from our hands."

"This History has been written because of a conviction, from my own experience and experience with my students, that one of the best aids to an intelligent comprehension of the science of chemistry is the study of the long struggle, the failures, and the triumphs of the men who have made this science for us."

"Free use has been made of all the chief authorities; the historical works of Kopp, Berthelot, Hoefer, Thomson, Ernst [von] Meyer, Ladenburg, [George Farrer] Rodwell, Muir, Wurtz, Hartmann, [Johann Friedrich] Gmelin, [Karl] Karmarsch, and Siebert, besides the original works of nearly all the chemists mentioned for the past century and a half, have been consulted."

"The ovum from which chemistry has... slowly evolved seems to have been sorcery and magic."

"The word χημεία occurs first in the writings of Suidas, a Greek lexicographer of the eleventh century. It is there defined as the "preparing of gold and silver." This is manifestly a Greek rendering of the name Chema or Chemi, which is of Egyptian origin, and all attempts at deriving it from χεω, to fuse, or χνμα a liquid, are without import."

"Plutarch tells us that Chemia was a name given Egypt on account of the black soil, and that this term further meant the black of the eye, symbolizing that which was obscure and hidden."

"The Coptic word khems or chems is closely related to this, and also signifies obscure, occult, and with this is connected the Arabic word chema, to hide."

"It [chemistry] is therefore the occult or hidden science, the black art."

"Two difficulties meet one in studying the early history of the science. One is... mysticism... and the other is the custom among the early writers of ascribing their discoveries, books, etc., to fabulous names or ancient heroes and gods. This latter had two objects, the first being to shield the true author in time of persecution, and the second to gain a certain amount of credit and reputation... by the use of the names of such celebrities as Moses, Solomon, Alexander, or Cleopatra. This tendency is especially noticeable among the writers of the Middle Ages, and also the early Greek authors, and is not peculiar to authors of alchemical treatises."

"No original manuscript of the earliest writers on chemistry or alchemy has been discovered. Our knowledge must be gleaned from the pages of those writing upon other subjects, or must come from fragments handed down to us through several copyists."

"The reason generally assigned for this absence of early records is that burned all writings of the Egyptians bearing upon alchemy, because, as he said, these taught the art of making gold and silver; and, by destroying them, he took away... the power of enriching themselves and rebelling against the Romans."

"[T]he Chinese... had... knowledge of metals, alloys, colors, and salts for a long time, and that they manufactured gun powder and before they were known in Europe."

"In... India... knowledge of the extraction of metals, the making of steel, the preparation of colors, and similar technical operations, dates back to the most remote antiquity. They also theorized as to the elements and their number. Their synonym for death was, "man returns to the five elements.""

"The almost universal tradition among alchemists is that their art was first cultivated among the Egyptians, and that , the Egyptian god of arts and sciences, was its founder. The finding of papyri of a chemical nature in the tombs... lead us to give credence to this tradition... Clement of Alexandria tells us that the knowledge... was restricted to the priests, who were forbidden to communicate it... Plutarch also mentions the strict secrecy observed, and the cloaking... under the guise of fables."

"[T]here is a similarity easily detected between the hieroglyphics and the alchemical signs."

"The phraseology in the early treatises is similar to that in the priestly writings."

"[N]ote the important part played by the number four with the alchemists as well as with the Egyptian priests. There are the four bases or elements, the tetrasomy of ; the four zones, four funeral deities, four cardinal points, four winds, four colors, etc."

"The ns, as masters of occult sciences, played an important part at Rome. In much earlier times, the Bible mentions them as the depositaries of all wisdom and science... They were rivals of the Egyptians in knowledge, and were especially famous as astrologers. Many industrial arts were brought to as high perfection in as in Egypt; for instance, the processes of glass-making, of dyeing, and of working in metals. Those Chaldeans who settled in Rome in later years came from Syria and . Tacitus makes mention of them. They were much sought after by the fashionable as the representatives of Eastern religions and mystic doctrines."

"Ostanes, the Mede, was one of the celebrated early alchemists. Several writers have recorded for us the existence of a book called The Book of the Divine Prescriptions, which seems to have been the most famous writing of these Persian sages."

"The belief in some wonderful connection between planets and metals is due to these ns. The signs of the heavenly bodies became the symbols for the metals. These planets influenced a supposed growth of the metals, and were esteemed all-powerful in regulating human life and fate. Many of these notions are to be attributed to the Alexandrian epoch."

"The idea of the macrocosm, or outer world, and the microcosm, or little inner world of a man's own nature, which is so often referred to and utilized in alchemical writings, originated also at ."

"In many of the treatises on alchemy we meet with Jewish names, and some of these writings have been ascribed to Jewish authors. ...[T]he Jews ...were often superstitious, and believers in magic and demons. They were very learned; and at Alexandria, where Greek culture came in contact with the culture of Egypt and of the Chaldeans, the Jews... at the time of the birth of Christianity, were at the head of science and philosophy, and played a very important part in the fusion of Greek doctrines, scientific and religious, with those of the Orient."

"[A]part from mysticism and magic... the practical and useful came first before all theory."

"[A]t Babylon and in Egypt, the industrial arts were practised with a high degree of skill; but... all was empirical, and... slow of development. There is little evidence of any attempt at finding out the causes of the changes observed or brought about."

"... is by some supposed to be identical with Canaan, the son of Ham. The name is synonymous with Toth, the god of intellect, the patron of arts and sciences in ancient Egypt. The adepts in alchemy were unanimous in writing of him as the founder of their art. [P]robably... as the god of letters, all books were dedicated to him and he was in one sense their author. Clement of Alexandria describes the solemn procession in which these books were borne in the great ceremonies. Tin and mercury were set apart as metals sacred to him. During the Middle Ages the science was often known under the name of the Hermetic Art."

"Albertus Magnus, in a treatise attributed to him, tells us that Alexander the Great found in the sepulchre of Hermes (or in the tomb of ) certain tables inscribed with the secrets of his wisdom. This famous inscription is constantly quoted in books on alchemy. It consisted of thirteen parts or sayings. They are sufficiently obscure to receive almost any interpretation. ...[T]hey refer to the universal medicine or the . Two quotations will suffice... No. 7. Separate the whole earth from the fire, the subtle from the gross, acting prudently and with judgment. No. 8. Ascend with the greatest sagacity from the earth to heaven, and then again descend to the earth, and unite together the powers of things superior and things inferior. Thus you will possess the glory of the whole world, and all obscurity will fly far from you."

"To most this seems a meaningless forgery of the early alchemists. Still, this mystical personage [] had great influence... through many centuries. We find various axioms ascribed to Hermes, also a mystic hymn, and a so-called instrument or table of figures for predicting the outcome of disease, a life's fate, etc. Such tables were used in very ancient times in Egypt."

"The alchemists called themselves the Hermetic Philosophers, and followed the Hermetic Art or Hermetics. To close anything very securely, as, for instance, to seal it in a glass tube, is called to this day sealing it hermetically."

"In old times the symbol of Hermes was affixed to the article, and it was thus sealed with "Hermes, his seal.""

"The earliest historical personage connected with alchemy is Demokritos of Abdera... the founder of the atomistic school, extending and developing the theory of Leukippos. His definition of the atom is almost as absolute and precise as that found in modern treatises. His chief work was entitled "Physica et Mystica.""

"Aristotle frequently cites from the writings of Demokritos. Many works have been ascribed to him which were undoubtedly the productions of later centuries. As was customary for men of learning in early times, Demokritos visited Egypt, , and various parts of the East, in the search of knowledge, and doubtless owes much to the wise men of those regions."

"The works of Demokritos and his school formed a sort of encyclopaedia of philosophy and science. These books are unfortunately lost, with the exception of a few fragments."

"Pliny tells us that Demokritos was instructed in magic by Ostanes the Mede."

"[T]he Sphere of Demokritos, for foretelling death or recovery from a malady ...was similar to the table of Hermes..."

"It is impossible to tell how much of the magical and alchemical should justly be accredited to Demokritos]."

"The observation and experiments necessary for the pursuit of alchemy did not comport with the Greek idea of philosophy. This is shown by the saying of Socrates, that the nature of external objects could be discovered by thought without observation, and by the renunciation of all natural sciences by the Cynics. This came largely from the fact that they saw in the nature around them the mutable only. Plato separated logic, as the knowledge of the immutable, from physics, the knowledge of the mutable. That which was subject to indefinite change would not repay observing nor recording, therefore they could not conceive of astronomy and physics as serious objects of mental occupation. There was nothing to be learned from fields and trees and stones."

"One of the [Ancient Greek] philosophers is said to have gone to the length of putting out his eyes, in order that his mind might not be influenced by external objects, but might wholly give itself to pure contemplation. The intellectual power and grasp of these philosophers were wonderful, but faulty and misleading, since the real and practical was left out."

"The Egyptians and other ancient peoples held the same idea of the mutability of all external objects, and the absence of law in their changes. ...The investigation of nature was ...considered impious. The phenomena of nature were brought about by the gods, and their actions should not be inquired into too closely by men. This manner of thinking is not yet extinct."

"The theories of the early Greek philosophers, then, were not based upon close observation and a multitude of facts experimentally learned... [George Farrer] Rodwell gives a most interesting resume of the theories of these philosophers with regard to the formation of the world and the primal elements. These elements were not the chemical elements of the present day, but rather principles. They meant more the characteristic and essential properties of matter than matter itself."

"Thales of Miletus... the "first of the natural philosophers," affirmed that water was the first principle of all things. This theory had its supporters even during the Middle Ages, philosophers who got water from air and solids by evaporating water, and carefully proved that plants would grow when fed with water only. The theory was not completely disproved until a little more than a century ago."

"Anaximenes regarded air as the primal element... According to Anaximenes, clouds are caused by the condensation of air, and rain by the condensation of clouds."

"Archelaus said that air, when rarefied, became fire; when condensed, water; and water, when boiled, became air."

"Empedokles introduced the idea of four distinct elements, — earth, air, fire, and water, — which were not interchangeable, but formed all things by mixing."

"Anaxagoras of Klazomene (500 b.c) seems to have been the first of the Greeks to formulate a theory approaching the atomic. This was more clearly expressed by Leukippos and extended by Demokritos. Long before the time of any of these, however, the idea seems to have been conceived in India."

"The views of Aristotle ...held undisputed sway for nearly twenty centuries. He introduced... a fifth element, the quintaessentia, which he called ether, more subtle and divine than the other elements. From this comes the word quintessence, so much used by the alchemists... We have to assume the existence of a rarefied ether in the theories of the present day."

"Aristotle added much to the theory of the four elements, assigning properties to each, and elaborating the changes caused by their mingling, and also dwelling on their inter-convertibility. This was often cited as justifying the idea of the transmutation of the metals. The four elements — earth, air, fire, and water — became known as the Aristotelian elements, and from them various names were derived in the early chemical books. Thus there were earths, alkaline earths, rare earths, etc.; [airs,] fixed airs, inflammable airs, dephlogisticated air, and others; and a number of different waters, — aqua fortis, , aqua ammonia, etc."

"The motive principle causing combination and change was, in the philosophy of Anaxagoras. the νους; in that of Demokritos, ἀνἁγκη; of Herakleitos, fire; of Aristotle, the moving ether. In our day we call it affinity, but we are still a long way off from solving the mystery of its nature."

"Zosimus, the Panopolite... is the most ancient of the alchemists whose works we possess. ...Suidas, the Greek lexicographer, tells us that he wrote twenty-eight books on alchemy entitled "Manipulations." ...they give us a good idea of the learning... of his times. They contain descriptions of apparatus, of furnaces, studies of minerals, of alloys, of glass-making, of mineral waters, and much that is mystical, besides a good deal referring to the transmutation of metals. He is cited as the author of the saying that like begets like, and is often quoted by the alchemists... spoken of... as a great and learned master of the science."

"Africanus, another of these alchemists, was a Syrian of the time of Heliogabalus. He is said to have written on medical, agricultural, and chemical subjects. Certain geographical and military works are also attributed to him."

"... was named Bishop of Ptolemais, and was an astronomer, physician, agriculturist, and embassador. His works... are mostly philosophical and commentaries on Zosimus."

"Olympiodorus... wrote a history of his times. He was not so obscure in his language as Zosimus. ...He seems to have been the first to divide matter into the fixed and the volatile, a distinction depending upon the combustibility."

"These few names serve to give some idea of the character of the Greek alchemists. ... had been, during this period, the centre of science and philosophy. ...Under Roman rule and depredations it gradually declined, until by the fourth century no buildings of importance were left in it except the Temple of Serapis... the great bulwark of Greek culture and of medical and alchemical study. ...[T]his also was destroyed in the reign of Theodosius... The Serapeum of Memphis and the Temple of Ptah, where the medical laboratories and the workshops of the alchemists were probably to be found, were destroyed at the same time. And thus the learned men of Greece and Egypt were dispersed, suffering a political and a religious persecution."

"The light of science was transferred to , communicated in the sixth and seventh centuries to the Arabians, and by them in turn to their brothers of and Spain."

"The name alchemy, al-embic, al-cohol, etc., are of Greek origin, with the Arabic article prefixed; and they point to the source of the knowledge possessed by the Arabians when Europe was in darkness."

"[T]he ancients... had a sort of practical or technical chemistry. In certain branches of metallurgy, in glass-making, dyeing, and tanning, they attained decided proficiency."

"[A]s to the apparatus used in the work shops... processes used were those requiring the aid of fire; s, furnaces... [T]he treatise of Zosimus, "On Instruments and Furnaces,"... claims to describe the various appliances he saw in the temple at Memphis. These... apparatus were made of gold or bronze or clay-ware. The was a crude form of distilling apparatus, and comes from the Alexandrian period. The water-bath, or '... was said to have been invented by ... The blow-pipe and are both figured among these drawings, as well as on very early Egyptian and other monuments."

"Six metals were well known, — gold, silver, tin, , copper, and . Homer mentions these six, and the Bible does also; so they seem to have been in use from a very early antiquity. Mercury was afterwards added to the list."

"The derivation of the word metal is from the Greek word μεραλλάω, "to search after," and the noun first meant or referred to mines."

"The ancients, especially the Egyptians, were very skilful workers in metals. They made gold wire and leaf, and fine inlaid work, and very beautiful ornaments."

"Gold was the first known of the metals apparently. Its color, lustre, and malleability attracted the attention of the early peoples. Its occurrence free in nature and in a bright pure state would doubtless account for its being utilized first of the metals. Early vessels were made of it; and it was used for coating, or plating, over wood and other materials."

"Silver seems to have been known at very nearly the same time as gold. It also occurs free, and was easily prepared ready for use. Then follow copper, , tin, and ."

"The purification of gold and silver by the process was known before the Christian era, but there was no means of separating gold from silver. The alloy of the two metals, as they are often found together in nature, was regarded as a peculiar metal itself, and was called . The oldest coins we have are made of this electron, or pale gold. This alloy was made artificially out of three parts of gold and one of silver."

"Copper was in use before iron, and was called χαλκός by Homer. From this we get the word and others. The Romans got it first from the Island of Cyprus, and called it aes cyprium; and from this it became cuprum, and in English copper. It was used mainly in alloys."

"Aurichalcum, or golden copper, they called the alloy made from copper and an ore of zinc; and this is known now as brass."

"They were ignorant of the metal in the free state."

"was an alloy of copper and tin, and was known also before metallic tin. This was very strong, and much easier to work into shape than iron, and hence was a substitute for it. Weapons and many utensils were made from it."

"was known in very early times; Lepsius maintaining that the Egyptians used it five thousand years ago in the preparation of the harder instruments which they required for... work, as in building the pyramids, and engraving precious stones. Iron was coined by the Greeks, and in the time of Homer they used it for axes and ploughshares. As it rusts so easily very few early implements have come down to us. The early Egyptians understood how to harden or temper iron."

"Steel was made in India at a very early period. The difficulty of reducing iron from its ores, and the fact that it does not occur free, would account for its not being used more largely and at an earlier time."

"Tin was obtained from India and Spain and afterwards from Britain. It was one of the articles of commerce used in trade by the ns. Mirrors were made of it, and copper vessels were coated over with it. and tin seem to have been regarded as varieties of the same metal, and were called plumbum nigrum and plumbum candidum. Pliny speaks of conveying water in leaden pipes, and Homer makes much earlier mention of the metal. It came mainly from Britain and Spain; and from this latter country mercury was also gotten, and was used, as now, in extracting gold from its ores. The first mention of it was in 300 B.C. Native mercury was called argentum vivum (quicksilver), and mercury distilled from was known as hydrargyrum (ὔδωρ). Various compounds of these metals were known and used."

"The two oxides cuprous oxide & cupric oxide of copper were used in glass-making; was manufactured and put to several uses; was used as a cosmetic by the Athenian ladies, and found further use as a medicine; red lead was used as a paint; stibium, or native antimony sulphide, was used as a paint for the eyelashes, and is still used for that purpose in the East under the name of kohl; black oxide of manganese was used in glass-making, especially for clearing up darkened masses, and so got its name of ; the native carbonate of zinc was also known and used; the sulphides of , and , were well-known pigments."

"According to Sir Humphry Davy, the ancient Greeks and Romans had almost the same colors as those employed by the great Italian masters at the period of the revival of arts in Italy."

"Soda and were both used in washing and whitening clothes, in glass-making, and in saponifying the fats for soap and s."

"Lime was burned and mortar made from it, though the earliest cementing material was bitumen."

"Bitumen and were also used for torches and embalming."

"The art of glass-making is exceedingly old, and apparently originated with the Egyptians. They reached a high degree of proficiency in its preparation, knowing how to color it, and also how to prepare imitation precious stones from it. Clear, transparent, colorless glass was not known by them, however."

"[The Egyptians] were... skilful in the production of clay-wares and pottery. The Egyptians decorated these wares with colored enamels. The Etruscans showed great skill in the ceramic art. From the earliest ruins have been unearthed specimens of pottery. The Chinese, alone of early nations, knew how to make ."

"Dyeing was carried to great perfection. Many vegetable and animal coloring matters were known. s were used, and the effects produced were very beautiful. Paints were also prepared, and applied with brushes. The following mineral colors were known at the time of Pliny : , , , smalt, , , lampblack, , , and ."

"Leather was tanned, at first by means of oil, and later with bark, very much after the manner in use now. The hair was removed by means of lime, as is still done. Some leather, said to have been tanned at the time of Solomon, has been found in modern times fairly well preserved."

"Soap was made by mixing wood ashes with animal fats, thus saponifying them. It was used as a kind of pomatum; s, oils, etc., were rubbed upon the body in the place of soap as used in modern times. Both hard and soft soap were known. Burnt lime was often added in the manufacture."

"Many substances were used as medicaments; some of these might be called chemical preparations, showing an early union between chemistry and pharmacy. Lead plasters were made from and oil, iron rust was used, also alum, soda, and bluestone. The use of sulphur as a disinfectant is mentioned in the well-known passage in Homer, in which he speaks of its being burnt to drive away the evil spirits from a home. It was also used for bleaching purposes. The only acid known was , or vinegar; and its solvent power seems to have been greatly over-estimated."

"About the middle of the eighth century the caliph Al-Mansour... founded the city of Bagdad. ...He founded an academy or university at Bagdad, which became very celebrated. Pupils and professors flocked to it from all quarters, and they numbered at one time as many as six thousand. Hospitals and laboratories were erected, and experimental science began to be properly recognized. ...the successors of Al-Mansour continued his work. Ancient books were collected, and... their store of learning was eagerly saved. For several centuries this great institution of learning flourished."

"At Fez and Morocco academies were founded, but Spain was still more favored. The caliphate of Cordova was probably the most prosperous and splendid of the Moorish possessions, and the University of Cordova became the most celebrated in the world. It was attended by Christian students from all Western Europe, as well as by Moors. Its library contained two hundred and eighty thousand volumes, the catalogue filling forty-four volumes. The university produced one hundred and fifty authors. Other universities and libraries were scattered through Spain during this, its golden age."

"Islamism prohibited magic and all arts of divination, and also all dissection of the human body after death. In the hands of the Arabians, therefore, alchemy was chiefly applied to the preparation of medicines. During this period there were two especially famous authors and workers, Geber and Avicenna."

"Geber (eighth century) was a Sabean of Mesopotamia, of Greek parentage, but a convert to Islam. His name in full was Abou-Moussah-Dschafer-al-Sofi. ...He gathered together all the chemical knowledge attainable, systematized it in a measure, and sought to apply it to medicine."

"Several manuscripts are to be found in the libraries of Europe, purporting to contain his writings. From what source he derived his knowledge we do not know... His works were translated into Latin in 1529, and into English in 1678. There are four treatises : 1. "Of the Search for Perfection;" 2. "Of the Sum of Perfection;" 3. "Of the Invention of Verity;" 4. "Of Furnaces." ...The object of his work seems to have been the discovery of the ...He was especially interested in finding out the properties of substances, and experimenting upon the possibility of putting them to use as medicines. In his works we find various additions ...to the chemical knowledge ...possessed by the ancients."

"He considered all metals as compounds of mercury and sulphur in varying proportions, an opinion which he says he derived from the ancients... Gold and silver were the perfect metals, the others imperfect."

"He frequently made use of sulphur, and knew many of its properties. Geber writes... " Sulphur is a substance, homogeneous, and of a very strong composition. Although it is a fatty substance, it is not possible to distil its oil from it. It is lost on calcining. It is volatile, like a spirit. Every metal calcined with sulphur augments its weight in a palpable manner. All the metals can be combined with this body except gold, which combines with it with difficulty. Mercury produces with sulphur, by way of sublimation, Uzufur or . Sulphur generally blackens the metals. It does not change mercury into gold nor into silver, as has been imagined by some philosophers.""

"As to , [Geber] says: "Arsenic is composed of a subtile matter, and of a nature analogous to that of sulphur. It is fixed by the metals as sulphur; and one prepares it, like the last, by the calcination of minerals.""

"As a proof of the possibility of transmutation, he gives an example of copper being changed into gold. " In copper mines we see a certain water which flows out and carries with it thin scales of copper, which (by a continued and long-continued course) it washes and cleanses. But after such water ceases to flow... in three years' time... digested with the heat of the sun; and among these scales the purest gold is found..." Very plausible reasoning from defective premises, as Thomson observes."

"He understood the purification of bodies by crystallization, solution, and filtration, calling the latter process distillation through a filter. The majority of the chemical processes in use up to the eighteenth century were known to Geber."

"The alkaline carbonates were known to [Geber], and he prepared caustic soda. He knew also saltpetre and sal ammoniac, and evidently made use of the mineral acids, nitric, sulphuric, and . He made use of these as solvents, and thus the wet processes of modern chemistry began to substitute the furnaces of the old."

"Various s or sulphates were spoken of by [Geber], and also and purified common . Certain compounds of mercury were prepared by him; among others, the chloride or corrosive sublimate and the red oxide."

"[Geber's] method of preparing , which he discovered. "Dissolve silver calcined in solutive water (nitric acid)... which being done, coct it in a phial with a long neck, the orifice of which must be left unstopped, for one day only, until a third part of the water be consumed. This being effected, set it with its vessel in a cold place, and then it is converted into small fusible stones, like crystal.""

"His [Geber's] philosophy was not very advanced, as he ascribed the various phenomena he observed to occult causes."

"Avicenna... [exerted] the same influence over medicine that Geber did over chemistry. He was called the Prince of Physicians, and as an authority ranked next to Aristotle and Galen. ...He was the author of the "Canones Medieincœ," a work which was translated into many languages, and was the standard medical authority for several centuries. ...He divided minerals (chemical compounds) into: 1. Infusible minerals; 2. Fusible and malleable (metals); 3. Sulphurous minerals; 4. Salts. There was little that was original in the canons of Avicenna, the matter coming mainly from the works of Galen and Aristotle, but there was a clear and orderly arrangement..."

"Avenzoar (eleventh century), a Spanish physician, is quoted as making some additions to the knowledge of medicinal preparations."

"In the beginning of the twelfth century Averrhoes attained prominence as a physician and chemist."

"From the thirteenth to the fifteenth centuries... decadence of the Moorish power in Europe was... rapid. ...The Arabs... were driven from Spain, and Bagdad was conquered by the Mongols. There was a decline, and then almost complete cessation from literary work. Still, for some centuries... [t]heir writings were translated into Latin and other languages, and formed the chief treasures of medical and scientific men. Their modes of thought and work were often imitated by their monkish successors."

"The characteristics of the age were a shameful mental imprisonment and caging of the human reason. Free striving for higher light, or criticism of accepted authorities, was looked upon as high treason to the Holy Church, and punished by the Inquisition. Those who dared to think clearly for themselves, wrote mysteriously for their fellows as a measure of safety."

"Albertus Magnus... was the first eminent German chemist. ...He and his pupil, Thomas Aquinas, are said to have constructed a brazen statue which he animated with his elixir vitœ. It was capable of walking, talking, etc., like a living being, and was very useful as a servant. It was unfortunately very talkative and noisy. It one day so enraged Thomas Aquinas, by constantly interrupting him while he was deeply engaged with mathematical problems, that he took a hammer and broke it in pieces. Of course this is a fanciful account of a noisily creaking automaton, made by these two..."

"Albertus Magnus lectured in , and great numbers of students flocked to hear him. He skilfully managed to escape the persecution which befell so many of his brother monks who dabbled in the occult art, and was high in the odor of sanctity. His principal writings were the following: "De Rebus Metallicis et Mineralibus;" "De Alchymia;" "Secretorum Tractatus;" "Breve Compendium de Ortu Metallorum;" "Concordantia;" "Philosophorum de Lapide." ...He was the first to use the term "affinitas" to designate the cause of the combination of the metals with sulphur and other elements. The term "" was also first used by him. He regarded the transmutation of the metals as an assured possibility. He did not regard the metals as distinctly differing substances, but varieties of the same species. "The metals are all essentially identical; they differ only in form. Now, the form brings out accidental causes, which the experimenter must try to discover and remove, as far as possible. Accidental causes impede the regular union of sulphur and mercury; for every metal is a combination of sulphur and mercury. A diseased womb may give birth to a weakly, leprous child, although the seed was good; the same is true of the metals which are generated in the bowels of the earth, which is a womb for them; any cause whatever, or local trouble, may produce an imperfect metal. When pure sulphur comes in contact with pure mercury, after more or less time, and by the permanent action of nature, gold is produced." His views are in the main those of Geber, though he adds water to mercury and sulphur as one of the constituents of the metals."

"[Magnus] was a diligent and successful worker, and added many chemical facts to those known by Geber, as, for instance, the purification of gold, the preparation of arsenic, etc."

"Thomas Aquinas... was a favorite pupil of Albertus Magnus... He was devoted to mathematics and at the same time was a great alchemist. He... wrote several books on alchemy, all of which are obscure and unintelligible. His chief treatise was the "Most Secret Treasure of Alchemy." He wrote on the making of artificial gems, and, according to some, was the first to make use of the term amalgam for alloys containing mercury."

"Roger Bacon['s]... success... brought with it the reputation of being in league with the devil, and he was severely persecuted while at Oxford. He did not in this have the good fortune of Albertus Magnus, or lacked his skill and tact. He replied to his accusers by a strong tract, "De Nullitate Magice" in which he showed that no such thing as magic could exist, and that what his accusers thought were the work of spirits were but ordinary operations of nature. Still, in spite of his arguments, he was imprisoned ten years. ...His chief writings were : — 1. "'." In this his high appreciation is shown of the experimental method and the inductive philosophy, afterwards advocated by his namesake, Francis Bacon. 2. "Speculum Alchymim." 3. "Breve Breviarium de Dono Dei.""

"He [Roger Bacon] collected the facts known to the alchemists before his time, and followed Geber closely in many things. He knew of gun powder, but speaks of it obscurely. According to some he mentions saltpetre and sulphur by name as two constituents, and the third constituent under the anagram luru mone capubre, which is convertible into carbonum pulvere. He probably got this knowledge from some Arabic source. ...Gunpowder was first used by the English at the battle of Crecy, more than fifty years after the death of Bacon."

"Roger Bacon... subjected organic substances to , and noticed that inflammable gases were produced; and he showed that air was necessary for the burning of a lamp. He was an ardent supporter of the belief in the transmutation of the metals, and related some very wonderful things as to the power of the philosopher's stone. ...he drew direct from Albertus Magnus and the Arabians."

"The following quotation from [Roger Bacon's] treatise "Speculum Secretorum" will serve to give his ideas as to the transmutation of the metals : "To wish to transform one kind into the other, as to make silver out of lead, or gold out of copper, is as absurd as to pretend to create anything out of nothing. The true alchemists never held such a pretence. What is the real problem? The problem is, first, by means of art, to remove from a rough, earthy mineral a bright metallic substance, like lead, tin, or copper. But that is only the first step towards perfection; and the chemist's work must not stop there, for, besides that, he must look for some means of getting the other metals, which are always present in the bowels of the earth in an adulterated condition. For example, the most perfect is gold, which one always finds in the native state. Gold is perfect, because in it nature finished her work. It is necessary, then, to imitate nature; but here a grave difficulty presents itself. Nature does not count the cycles which she takes for her work, to which the term of life of a man is but as an hour. It is, then, important to find some means which will permit one to do in a little time that which nature does in a very much longer time. It is this means which the alchemists call, indifferently, the elixir, the philosopher's stone, etc.""

"It is not enough for a wise man to study nature and truth; he should dare state truth for the benefit of the few who are willing and able to think. As for the rest, who are voluntarily slaves of prejudice, they can no more attain truth, than frogs can fly."

"I reduce to two the systems of philosophy which deal with man's soul. The first and older system is materialism; the second is spiritualism."

"In truth, to ask whether matter can think, without considering it otherwise than in itself, is like asking whether matter can tell time. It may be foreseen that we shall avoid this reef upon which Locke had the bad luck to shipwreck."

"The Leibnizians with their monads have set up an unintelligible hypothesis. They have rather spiritualized matter than materialized the soul. How can we define a being whose nature is absolutely unknown to us? Descartes and all the Cartesians, among whom the followers of Malebranche have long been numbered, have made the same mistake. They have taken for granted two distinct substances in man, as if they had seen them, and positively counted them."

"To distrust the knowledge that can be drawn from the study of animated bodies, is to regard nature and revelation as two contraries which destroy each other, and consequently to dare uphold the absurd doctrine, that God contradicts Himself in His various works and deceives us."

"If there is a revelation, it can not then contradict nature."

"[M]an, even though he should come from an apparently still more lowly source, would yet be the most perfect of all beings, so whatever the origin of his soul, if it is pure, noble, and lofty, it is a beautiful soul which dignifies the man endowed with it."

"[E]ither everything is illusion, nature as well as revelation, or experience alone can explain faith."

"Experience and observation should therefore be our only guides here. Both are to be found throughout the records of the physicians who were philosophers, and not in the works of philosophers who were not physicians. The former have traveled through and illuminated the labyrinth of man; they alone have laid bare to us those springs [of life] hidden under the external integument which conceals so many wonders from our eyes. What could the others, especially the theologians, have to say? Is it not ridiculous to hear them shamelessly coming to conclusions about a subject concerning which they have had no means of knowing anything, and from which on the contrary they have been completely turned aside by obscure studies that have led them to a thousand prejudiced opinions,—in a word, to fanaticism, which adds yet more to their ignorance of the mechanism of the body?"

"Man is so complicated a machine that it is impossible to get a clear idea of the machine beforehand, and hence impossible to define it. For this reason, all the investigations have been vain, which the greatest philosophers have made à priori, that is to say, in so far as they use, as it were, the wings of the spirit. Thus it is only à posteriori or by trying to disentangle the soul from the organs of the body, so to speak, that one can reach the highest probability concerning man's own nature, even though one can not discover with certainty what his nature is."

"Let us then take in our hands the staff of experience... To be blind and to think that one can do without this staff is the worst kind of blindness."

"One can and one even ought to admire all these fine geniuses in their most useless works, such men as Descartes, Malebranche, Leibniz, Wolff and the rest, but what profit, I ask, has any one gained from their profound meditations, and from all their works? Let us start out then to discover not what has been thought, but what must be thought for the sake of repose in life."

"Even Galen knew this truth which Descartes carried so far as to claim that medicine alone can change minds and morals, along with bodies. ...[E]ach man different from another. In disease the soul is sometimes hidden, showing no sign of life; sometimes it is so inflamed by fury that it seems to be doubled; sometimes, imbecility vanishes and the convalescence of an idiot produces a wise man. Sometimes, again, the greatest genius becomes imbecile and loses the sense of self. Adieu then to all that fine knowledge... This man cries like a child at death's approach, while this other jests. What was needed to change the bravery of Caius Julius, Seneca, or Petronius into cowardice or faintheartedness? Merely an obstruction in the an impediment in the portal vein? Why? Because the imagination is obstructed along with the viscera, and this gives rise to all the singular phenomena of hysteria and hypochondria."

"[T]his man who is devoured by jealousy, hatred, avarice, or ambition, can never find any rest. The most peaceful spot, the freshest and most calming drinks are alike useless to one who has not freed his heart from the torment of passion."

"The soul and the body fall asleep together. ...the soul can no longer bear the burden of thought; it is in sleep as if it were not."

"Opium is too closely related to the sleep it produces... This drug intoxicates, like wine, coffee, etc., each in its own measure and according to the dose. It makes a man happy in a state which would seemingly be the tomb of feeling, as it is the image of death."

"The human body is a machine which winds its own springs. It is the living image of perpetual movement. Without food, the soul pines away, goes mad, and dies exhausted. ...[H]eavy food makes a dull and heavy mind whose usual traits are laziness and indolence. ...We think we are, and in fact we are, good men, only as we are gay or brave; everything depends on the way our machine is running."

"One is sometimes inclined to say that the soul is situated in the stomach, and that Van Helmont, who said that the seat of the soul was in the , made only the mistake of taking the part for the whole."

"One needs only eyes to see the necessary influence of old age on reason."

"The soul follows the progress of the body, as it does the progress of education."

"The mind, like the body, has its contagious diseases and its scurvy. ...[W]e catch everything from those with whom we come in contact; their gestures, their accent, etc... the body of the spectator mechanically imitates, in spite of himself, all the motions of a good mimic."

"[A] brilliant man is his own best company, unless he can find other company of the same sort. In the society of the unintelligent, the mind grows rusty for lack of exercise..."

"I should prefer an intelligent man without an education, if he were still young enough, to a man badly educated. A badly trained mind is like an actor whom the provinces have spoiled."

"Thus the diverse states of the soul are always correlative with those of the body."

"In general, the form and the structure of the brains of quadrupeds are almost the same as those of the brain of man... with this essential difference, that of all the animals man is the one whose brain is largest, and, in proportion to its mass, more convoluted... then come the monkey, the beaver, the elephant, the dog, the fox, the cat. These animals are most like man, for among them, too, one notes the same progressive analogy in relation to the ' in which Lancisi—anticipating the late M. de la Peyronie—established the seat of the soul. The latter, however, illustrated the theory by innumerable experiments."

"I shall draw the conclusions... 1st, that the fiercer animals are, the less brain they have; 2d, that this organ seems to increase in size in proportion to the gentleness of the animal; 3d, that nature seems here eternally to impose a singular condition, that the more one gains in intelligence the more one loses in instinct. Does this bring gain or loss? Do not think, however, that I wish to infer by that, that the size alone of the brain, is enough to indicate the degree of tameness in animals..."

"A mere nothing, a tiny fibre, something that could never be found by the most delicate anatomy, would have made of Erasmus and Fontenelle two idiots, and Fontenelle himself speaks of this very fact in one of his best dialogues."

"Willis has noticed in addition to the softness of the brain-substance in children, puppies, and birds, that the corpora striata are obliterated and discolored in all these animals, and that the striations are as imperfectly formed as in paralytics..."

"[S]o many different varieties can not be the gratuitous play of nature. They prove at least the necessity for a good and vigorous physical organization, since throughout the animal kingdom the soul gains force with the body and acquires keenness, as the body gains strength."

"Among animals, some learn to speak and sing; they remember tunes, and strike the notes as exactly as a musician. Others, for instance the ape, show more intelligence, and yet can not learn music. What is the reason for this... would it be absolutely impossible to teach the ape a language? I do not think so. ...I should take it in the condition of the pupils of Amman, that is to say, I should not want it to be too young or too old... Would not Amman too have passed for mad if he had boasted that he could instruct scholars like his in so short a time, before he had happily accomplished the feat? ...Amman's discoveries are certainly of a much greater value; he has freed men from the instinct to which they seemed to be condemned, and has given them ideas, intelligence, or in a word, a soul which they would never have had. What greater power than this!"

"Locke, who was certainly never suspected of credulity, found no difficulty in believing the story told by Sir William Temple in his memoirs, about a parrot which could answer rationally, and which had learned to carry on a kind of connected conversation, as we do."

"Whoever owes the miracles that he works to his own genius surpasses... the man who owes his to chance. He who has discovered the art of adorning the most beautiful of the kingdoms [of nature], and of giving it perfections that it did not have, should be rated above an idle creator of frivolous systems, or a painstaking author of sterile discoveries."

"Let us not limit the resources of nature; they are infinite, especially when reinforced by great art."

"What was man before the invention of words and the knowledge of language? An animal of his own species with much less instinct than the others. ...the same, old as young, child at all ages, he lisped out his sensations and his needs, as a dog ...asks for something to eat, or for a walk."

"Words, languages, laws, sciences, and the fine arts have come, and by them finally the rough diamond of our mind has been polished. Man has been trained in the same way as animals. He has become an author, as they became beasts of burden."

"A geometrician has learned to perform the most difficult demonstrations and calculations, as a monkey has learned to take his little hat off and on... All has been accomplished through signs, every species has learned what it could understand, and in this way men have acquired symbolic knowledge..."

"But who was the first to speak? Who was the first teacher of the human race? ...[T]he names of these first splendid geniuses have been lost in the night of time. But art is the child of nature, so nature must have long preceded it."

"As a violin string or a harpsichord key vibrates and gives forth sound, so the cerebral fibres, struck by waves of sound, are stimulated to render or repeat the words that strike them."

"[T]he sciences that are expressed by numbers or by other small signs, are easily learned; and... this facility rather than its demonstrability is what has made the fortune of algebra."

"[I]t is comparatively rare to imagine a thing without the name or sign that is attached to it."

"[E]verything is the work of imagination, and that all the faculties of the soul can be correctly reduced to pure imagination in which they all consist. Thus judgment, reason, and memory are not absolute parts of the soul, but merely modifications of this kind of medullary screen upon which images of the objects painted in the eye are projected as by a ."

"[W]hy should we divide the sensitive principle which thinks in man? Is not this a clear inconsistency in the partisans of the simplicity of the mind? For a thing that is divided can no longer without absurdity be regarded as indivisible. See to what one is brought by the abuse of language and by those fine words (spirituality, immateriality, etc.) used haphazard and not understood even by the most brilliant."

"[I]magination is the soul, since it plays all the roles of the soul."

"By the imagination, by its flattering brush, the cold skeleton of reason takes on living and ruddy flesh, by the imagination the sciences flourish, the arts are adorned, the wood speaks, the echoes sigh, the rocks weep, marble breathes, and all inanimate objects gain life. It is imagination again which adds the piquant charm of voluptuousness to the tenderness of an amorous heart; which makes tenderness bud in the study of the philosopher and of the dusty pedant, which, in a word, creates scholars as well as orators and poets. ...it can not reflect on what it has mechanically conceived, without thus being judgment itself."

"The more the imagination or the poorest talent is exercised, the more it gains in embonpoint... and the larger it grows. It becomes sensitive, robust, broad, and capable of thinking. The best of organisms has need of this exercise."

"Man's preeminent advantage is his organism. ...Only through nature do we have any good qualities; to her we owe all that we are."

"Whatever the virtue may be, from whatever source it may come, it is worthy of esteem... Mind, beauty, wealth, nobility, although the children of chance, all have their own value, as skill, learning and virtue have theirs."

"If one's organism is an advantage, and the preeminent advantage, and the source of all others, education is the second. The best made brain would be a total loss without it... But if the brain is at the same time well organized and well educated, it is a fertile soil, well sown, that brings forth a hundredfold what it has received... and takes in easily an astounding number of objects, in order to deduce from them a long chain of consequences, which are again but new relations, produced by a comparison with the first, to which the soul finds a perfect resemblance. Such is... the generation of intelligence."

"I say of truth in general what M. de Fontenelle says of certain truths in particular, that we must sacrifice it in order to remain on good terms with society. ...The Cartesians would here in vain make an onset upon me with their innate ideas. I certainly would not give myself a quarter of the trouble that M. Locke took, to attack such chimeras. In truth, what is the use of writing a ponderous volume to prove a doctrine which became an axiom three thousand years ago?"

"According to the principles which we have laid down, and which we consider true; he who has the most imagination should be regarded as having the most intelligence or genius, for all these words are synonymous; and again, only by a shameful abuse [of terms] do we think that we are saying different things, when we are merely using different words, different sounds, to which no idea or real distinction is attached."

"[T]he finest, greatest, or strongest imagination is... the most suited to the sciences as well as to the arts."

"If one is known as having little judgment and much imagination, this means that the imagination has been left too much alone, has... occupied most of the time in looking at itself in the mirror of its sensations... more impressed by images than by their truth or their likeness."

"[I]f attention, that key or mother of the sciences, does not do its part, imagination can do little more than run over and skim its objects."

"See that bird on the bough: it seems always ready to fly away. Imagination is like the bird... [T]he soul pursues it, often in vain: it must expect to regret the loss of that which it has not quickly enough seized and fixed. Thus, imagination, the true image of time, is being ceaselessly destroyed and renewed."

"Such is the chaos and the continuous quick succession of our ideas: they drive each other away even as one wave yields to another. Therefore, if imagination does not... maintain a kind of equilibrium... to keep its attention for a while... and to prevent itself from contemplating prematurely another object—[unless the imagination does all this], it will never be worthy of the fine name of judgment. ...it will create orators, musicians, painters, poets, but never a single philosopher."

"[W]hat is there absurd in thinking that beings, almost as perfect machines as our selves, are, like us, made to understand and to feel nature? ...Man is not moulded from a costlier clay; nature has used but one dough, and has merely varied the leaven."

"[T]here are a thousand hereditary vices and virtues which are transmitted from parents to children..."

"[T]here is so much pleasure in doing good, in recognizing and appreciating what one receives, so much satisfaction in practising virtue, in being gentle, humane, kind, charitable, compassionate and generous (for this one word includes all the virtues), that I consider as sufficiently punished any one who is unfortunate enough not to have been born virtuous."

"Nature has created us solely to be happy—yes, all of us from the crawling worm to the eagle lost in the clouds."

"I do not mean to call in question the existence of a supreme being; on the contrary it seems to me that the greatest degree of probability is in favor of this belief. But since the existence of this being goes no further than that of any other toward proving the need of worship, it is a theoretic truth with very little practical value."

"[S]ince... religion does not imply exact honesty, we are authorized by the same reasons to think that atheism does not exclude it."

"[W]ho can be sure that the reason for man's existence is not simply the fact that he exists? Perhaps... simply that he must live and die, like the mushrooms which appear from day to day, or like those flowers which border the ditches and cover the walls."

"Let us not lose ourselves in the infinite, for we are not made to have the least idea thereof, and are absolutely unable to get back to the origin of things."

"[I]t does not matter for our peace of mind, whether matter be eternal or have been created, whether there be or be not a God. How foolish to torment ourselves so much about things which we can not know, and which would not make us any happier even were we to gain knowledge about them!"

"[T]o destroy chance is not to prove the existence of a supreme being, since there may be some other thing which is neither chance nor God—I mean, nature."

"The weight of the universe therefore far from crushing a real atheist does not even shake him. All these evidences of a creator, repeated thousands and thousands of times... Such is the pro and the con, and the summary of those fine arguments that will eternally divide the philosophers. I do not take either side."Non nostrum inter vos tantas componere lites." [It is not for us to settle such weighty disputes among you. --from Virgil--]"

"[S]ince all the faculties of the soul depend to such a degree on the proper organization of the brain and of the whole body, that apparently they are but this organization itself, the soul is clearly an enlightened machine."

"[E]ven if man alone had received a share of natural law, would he be any less a machine for that? A few more wheels, a few more springs than in the most perfect animals... a number of unknown causes might always produce this delicate conscience so easily wounded, this remorse which is no more foreign to matter than to thought, and in a word all the differences that are supposed... Could the organism then suffice for everything? ...[Y]es; since thought visibly develops with our organs, why should not the matter of which they are composed be susceptible of remorse also, when once it has acquired, with time, the faculty of feeling?"

"The soul is therefore but an empty word, of which no one has any idea, and which an enlightened man should use only to signify the part in us that thinks."

"If now any one ask me where is this innate force in our bodies... it... resides in what the ancients called the parenchyma... in the very substance of the organs not including the veins, that arteries, the nerves, in a word, it resides in the organization of the whole body... consequently each organ contains within itself forces more or less active according to the need of them."

"I wish to speak of this impetuous principle that Hippocrates calls ἐνορμὤν (soul). This principle exists and has its seat in the brain at the origin of the nerves, by which it exercises its control over all the rest of the body. By this fact is explained all that can be explained, even to the surprising effects of maladies of the imagination."

"[I]f what thinks in my brain is not a part of this organ and therefore of the whole body, why does my blood boil, and the fever of my mind pass into my veins, when lying quietly in bed... forming the plan of some work or carrying on an abstract calculation? Put this question to men of imagination... by what they will tell you they have experienced, you will judge the cause by its effects; by that harmony which Borelli, a mere anatomist, understood better than all the Leibnizians, you will comprehend the material unity of man."

"[I]f the nerve-tension which causes pain occasions also the fever by which the distracted mind loses its will-power, and if, conversely, the mind too much excited, disturbs the body... if an agitation rouses my desire and my ardent wish for what, a moment ago, I cared nothing about, and if in their turn certain brain impressions excite the same longing and the same desires, then why should we regard as double what is manifestly one being? In vain you fall back on the power of the will, since for one order that the will gives, it bows a hundred times to the yoke. ...[A]s the power of the will is exercised by means of the nerves, it is likewise limited by them"

"Should we... be astonished that philosophers have always had in mind the health of the body, to preserve the health of the soul, that Pythagoras gave rules for the diet as carefully. as Plato forbade wine? The regime suited to the body is always the one with which sane physicians think they must begin, when it is a question of forming the mind, and of instructing it in the knowledge of truth and virtue; but these are vain words in the disorder of illness, and in the tumult of the senses."

"Without the precepts of hygiene, Epictetus, Socrates, Plato, and the rest preach in vain: all ethics is fruitless for one who lacks his share of temperance; it is the source of all virtues, as intemperance is the source of all vices."

"[T]he soul is but a principle of motion or a material and sensible part of the brain, which can be regarded, without fear of error, as the mainspring of the whole machine, having, a visible influence on all the parts."

"Stahl... has wished to persuade us that the soul is the sole cause of all our movements. But this is to speak as a fanatic and not as a philosopher."

"One need only read the "Institutions of Medicine" by Boerhaave to see what laborious and enticing systems this great man was obliged to invent, by the labor of his mighty genius, through failure to admit that there is so wonderful a force in all bodies."

"Willis and Perrault, minds of a more feeble stamp, but careful observers of nature seem to have preferred to suppose a soul generally extended over the whole body, instead of the principle which we are describing."

"[H]ow many excellent philosophers have shown that thought is but a faculty of feeling, and that the reasonable soul is but the feeling soul engaged in contemplating its ideas and in reasoning! This would be proved by the fact alone that when feeling is stifled, thought also is checked, for instance in , in lethargy, in catalepsis, etc. For it is ridiculous to suggest that, during these stupors, the soul keeps on thinking, even though it does not remember the ideas that it has had."

"The nature of motion is as unknown to us as that of matter. I am... quite as content not to know how inert and simple matter becomes active and highly organized, as not to be able to look at the sun without red glasses..."

"It appears that there is but one [type of organization] in the universe, and that man is the most perfect [example]. ...He is to the ape, and to the most intelligent animals, as the planetary pendulum of Huyghens is to a watch of Julien Leroy."

"[O]f two physicians, the better one and the one who deserves more confidence is always, in my opinion, the one who is more versed in the physique or mechanism of the human body, and who, leaving aside the soul and all the anxieties which this chimera gives to fools and to ignorant men, is seriously occupied only in pure naturalism."

"[L]et the pretended M. Charp deride philosophers who have regarded animals as machines. How different is my view! I believe that Descartes would be a man in every way worthy of respect, if, born in a century that he had not been obliged to enlighten, he had known the value of experiment and observation, and the danger of cutting loose from them. But it is none the less just for me to make an authentic reparation to this great man for all the insignificant philosophers—poor jesters, and poor imitators of Locke—who instead of laughing impudently at Descartes, might better realize that without him the field of philosophy, like the field of science without Newton, might perhaps be still uncultivated. This celebrated philosopher, it is true, was much deceived, and no one denies that. But at any rate he understood animal nature, he was the first to prove completely that animals are pure machines. And after a discovery of this importance demanding so much sagacity, how can we without ingratitude fail to pardon all his errors! In my eyes, they are all atoned for by that great confession. For after all, although he extols the distinctness of the two substances, this is plainly but a trick of skill, a ruse of style, to make theologians swallow a poison, hidden in the shade of an analogy which strikes everybody else and which they alone fail to notice. For it is this, this strong analogy, which forces all scholars and wise judges to confess that these proud and vain beings... are at bottom only animals and machines which, though upright, go on all fours."

"I believe that thought is so little incompatible with organized matter, that it seems to be one of its properties on a par with electricity, the faculty of motion, impenetrability, extentension, etc."

"We are veritable moles in the field of nature; we achieve little more than the mole's journey and it is our pride which prescribes limits to the limitless."

"[W]e disdain, ungrateful wretches that we are, this common mother of all kingdoms... We imagine, or rather we infer, a cause superior to that to which we owe all, and which truly has wrought all things in an inconceivable fashion."

"[M]atter contains nothing base, except to the vulgar eyes which do not recognize her in her most splendid works... Her power shines forth equally in creating the lowliest insect and in creating the most highly developed man; the animal kingdom costs her no more than the vegetable, and the most splendid genius no more than a blade of wheat."

"Let us observe the ape, the beaver, the elephant, etc., in their operations. If it is clear that these activities can not be performed without intelligence, why refuse intelligence to these animals?"

"[W]ho does not see that the soul of an animal must be either mortal or immortal, whichever ours [is]... and that thus [in admitting that animals have souls], you fall into in the effort to avoid ?"

"Break the chain of your prejudices, arm yourselves with the torch of experience, and you will render to nature the honor she deserves... Only open wide your eyes, only disregard what you can not understand, and you will see that the ploughman whose intelligence and ideas extend no further than the bounds of his furrow, does not differ essentially from the greatest genius,—a truth which the dissection of Descartes's and of Newton's brains would have proved; you will be persuaded that the imbecile and the fool are animals with human faces, as the intelligent ape is a little man in another shape..."

"Let us not say that every machine or every animal perishes altogether or assumes another form after death, for we know absolutely nothing about the subject."

"[T]o assert that an immortal machine is a chimera or a logical fiction, is to reason as absurdly as caterpillars would reason if, seeing the cast-off skins of their fellow-caterpillars, they should bitterly deplore the fate of their species, which to them would seem to come to nothing."

"What more do we know of our destiny than of our origin? Let us then submit to an invincible ignorance on which our happiness depends."

"He who so thinks will be wise, just, tranquil about his fate, and therefore happy. He will await death without either fear or desire, and will cherish life... filled with reverence, gratitude, affection, and tenderness for nature, in proportion to his feeling of the benefits he has received from nature; he will be happy, in short, in feeling nature, and in being present at the enchanting spectacle of the universe, and he will surely never destroy nature either in himself or in others."

"Full of humanity, this man will love human character even in his enemies. He will pity the wicked without hating them... [as] mis-made men. ...[T]he materialist, convinced, in spite of the protests of his vanity, that he is but a machine or an animal, will not maltreat his kind... he will not wish to do to others what he would not want them to do to him."

"[M]an is a machine... in the whole universe there is but a single Substance differently modified. ...Experience has thus spoken to me in behalf of reason; and in this way I have combined the two. ...Against so strong and solid an oak, what could the weak reeds of theology, of metaphysics, and of the schools, avail... Need I say that I refer to the empty and trivial notions, to the pitiable and trite arguments that will be urged (as long as the shadow of prejudice or of superstition remains on earth) for the supposed incompatibility of two substances which meet and move each other unceasingly?"

"Such is my system, or rather the truth, unless I am much deceived. It is short and simple. Dispute it now who will."

"In very different fashion does the book set to work that already in its very title declares that man is a machine. While the 'Natural History of the Soul' was cautious, cunningly arranged, and only gradually surprising us with its results, here, on the contrary,the final conclusion is expressed at the outset of the work. While the 'Natural History of the Soul' allied itself with the whole Aristotelian metaphysics only in order to prove by degrees that the soul is but an empty form, into which we may pour a materialistic content, here we no longer deal in all those fine distinctions."

"Yet the doctrine that man is a machine was argued most forcefully in 1751, long before the theory of evolution became generally accepted, by de La Mettrie; and the theory of evolution gave the problem an even sharper edge, by suggesting there may be no clear distinction between living matter and dead matter. And, in spite of the victory of the new quantum theory and the conversion of so many physicists to indeterminism, de La Mettrie's doctrine that man is a machine has perhaps more defenders than before among physicists, biologists and philosophers; especially in the form of the thesis that man is a computer."

"[T]ake note of those cases in which men not only solved a problem but had to alter their mentality in the process, or... discovered afterwards that the solution involved a change in their mental approach."

"It has proved almost more useful to learn something of the misfires and the mistaken hypotheses of early scientists... particular intellectual hurdles that seemed insurmountable... to pursues courses... that ran into a blind alley, but... had their effect on the progress of science..."

"It is not sufficient to read Galileo with the eyes of the twentieth century... we can only understand his work if we know something of the system which he was attacking... apart from the things which were said about it by his enemies."

"Little progress can be made if we think of the older... as merely a case of bad science or... imagine that only the achievements of... recent times are worthy of serious attention..."

"[I]n... celestial and terrestrial physics... change is brought about... by transpositions... inside the minds of the scientists... [H]andling the same bundle of data... in a new system of relations... a different framework..."

"Even the greatest geniuses who broke through the ancient views in some special field... would remain stranded in... medievalism... outside their chosen field."

"It required... combined efforts to clear up... simple things which we now regard as obvious..."

"Perhaps the lack of mathematics, or... mathematical ways of formulating... was partly responsible for... verbal subtleties and... straining of language... to find the way to... modern... mechanics."

"[T]he peculiar character of that Aristotelian universe... things... in motion had to be accompanied by a mover all of the time. A universe... [that] had the door half-way open for spirits...unseen hands had to be in constant operation... sublime Intelligences had to roll the planetary spheres... Alternatively, bodies had to be endowed with souls and aspirations... [M]atter itself seemed to possess mystical qualities."

"In... 1277 a council in Paris condemned a large number of Aristotelian theses... as... even God could not create a void, or an infinite universe, or a plurality of worlds... apparently extended by the ..."

"[F]ourteenth-century writers, first... a group at , and after these, , Albert of Saxony and Nicholas of Oresme... [were] teaching on the subject of impetus. ...[I]n the sixteenth century, when the world was looking for a formula to represent the uniform acceleration of falling bodies ...the solution ...at their disposal ...the medieval formula for ...uniformly difform motion."

"Even the apostles of the new ... regarded a projectile as moving in a straight line until the impetus had exhausted itself... then quickly curving... to make a direct vertical drop... [I]mpetus... gradually weakened and wore itself out... as a poker grows cold... Or, said Galileo, like the reverberations... in a bell... which gradually fades away."

"It is possible that the men of the Renaissance were less capable of seeing history as the ascent of the human race, or... the successive centuries as... advancing, than even their medieval predecessors... What they saw behind them... were the peaks of classical antiquity... the summit of human reason... reached by the Greeks and since lost, the ideal for the return of which they... were engaging their finest endeavors. ...[T]hey were governed by... a static outlook... and... a theory of decadence... under a [cyclic] system. ...{T]ime and the course of history were not considered to be... generative of anything. ...[N]o conception of a world expanding to ever grander things, to an expanding future ..."

"It has been suggested that the modern idea of progress owes something to the fact that Christianity had provided a meaning for history and a grand purpose to which the whole of creation moved. ...[S]ecularisation of an attitude, initially religious ...a fine fulfilment ...leading to something."

"Previously... there had been an idea that a scientific revolution was necessary... that it would occur and complete itself as a great historical episode, putting a new view of the universe in place of the Aristotelian... Bacon had imagined that the work... could be achieved in a limited period, while Descartes had thought... the revolution should be carried out by a single mind. A cataclysmic view... was still prevalent... rather than as a growth..."

"In the latter... seventeenth century... men have a vision of science as a young affair with... an ever expanding future—and Fontenelle points out that the sciences are still in their cradle."

"For those of us attempting to inaugurate teaching of the history of science after the war, Herbert Butterfield’s Origins of Modern Science, 1300-1800 was literally a godsend. He began the cultivation of a largely untilled field like a ' bestriding, albeit unpretentiously, the discipline of history proper. ...[H]e also wrote a book we could give undergraduates to read. ..The current generation can scarcely imagine the conceptual and stylistic poverty of what passed for the literature half a century ago... none of which was properly historical, the pickings were thin and thorny. ...[H]e popularized, or better publicized, an analysis developed by Burtt and more deeply by Alexandre Koyré... Thanks to them... the very concept of a scientific revolution was of crucial importance to our thinking."

"Forty years ago the British historian Herbert Butterfield proclaimed that the "so called 'scientific revolution,' popularly associated with the sixteenth and seventeenth centuries... outshines everything since the rise of Christianity and reduces the Renaissance and Reformation to the rank of mere episodes, mere internal displacements, within the system of medieval Christendom." It was a remarkable claim. But in the generation following Butterfield's classic survey... much was written to extend and enrich the vision. And there are good reasons. Because the Scientific Revolution is the acknowledged birthplace of the history of science... But ironically, while Europeanists... have come to accept the legitimacy of the Scientific Revolution, there is a growing sense among specialists that... the once proud periodization has been lost in a wave of "New ." ...I reduce the problem to a simple question: Is the Scientific Revolution a 'paradigm lost'?"

"The Scientific Revolution... roughly... from Copernicus to Newton, is now so deeply entrenched... that it is hard to believe that it was only given broad currency in Herbert Butterfield’s The Origins of Modern Science in 1949. Whereas 19th-century historians claimed that the great changes that catapulted Europe into the modern age were the Reformation and the Renaissance, Butterfield saw the major breakthrough in the twin advance of scientific conceptualization and factual discovery that began in the 16th century. ...Butterfield captured a major aspect of the historical shift that took place at this time, and I will stress... some of the reasons why his thesis still holds. We need only reread the famous aphorisms at the beginning of Bacon’s Novum Organum [Book I, Aphorisms 1-3] to be reminded that our way of viewing the world changed in the 17th century... The shift is clear: knowledge has become power to be used not to contemplate nature, but to improve it."

"Chemistry, as an art, was practised thousands of years before the Christian era; as a science, it dates no further back than the middle of the seventeenth century."

"The monumental records of Egypt and the accounts left us by Herodotus and other writers show that the ancient Egyptians... had a considerable knowledge of processes essentially chemical in their nature. ...The operations of chemistry as performed by them were of the nature of manufacturing processes, empirical in character and utilitarian in result."

"China, India, Chaldæa have each in turn been regarded as the birthplace of the various technical processes from which chemistry may be said to have taken its rise. Nevertheless, it is mainly from Egyptian records, or from writings avowedly based on... Egyptian sources, that such knowledge... is derived."

"[T]he word "chemistry" has its origin in chêmi, "the black land," the ancient name for Egypt. The art... was constantly spoken of as the "Egyptian art.""

"Boerhaave gathers that chemistry was... originally denominated because it was considered of old as "not fit to be divulged to the populace, but treasured up as a religious secret""

"[The] legend of the " feministic" origin of chemistry is... much older than the fifth century of our era, and is but a variant of that which, according to Jewish writers, led to the expulsion of man from Paradise. A similar myth was current among the Phoenicians, Persians, Greeks, and Magi. ...Some of the ecclesiastics who elaborated these myths included the use of charms, a knowledge of gold and silver and precious stones, the art of dyeing, of painting the eyebrows, etc. the kind of arcana, in fact, which women in all ages were presumably most keen to know."

"[H]owever, in all allusions to chemia, even after the translation of the seat of the Roman Empire to Constantinople, it is implied that a knowledge of it was a sacred mystery, to be known only to the priesthood, and jealously guarded by them. It was characteristic of writers who had affixed an eternal stigma on Eve to make the sex in general answerable for an illicit knowledge of "things unfit for men to know.""

"[C]hemistry originated with men, and it was not so much in the love of women as of wine that it took its rise."

"The manufacture of alcohol by processes of is probably the oldest of the chemical arts. The word vine means, in fact, a product of . ...[T]he ancient Egyptians ascribed the origin of wine to . It was a sacrificial offering even in the earliest times, as was bread. Wine seems to have been prepared by the Chinese as far back as the time of the Emperor Yü, circa 2220 B.C. Beer was manufactured in Egypt in the time of Senwosret III... B.C. 1880."

"The Egyptians were skilled in dyeing and in the manufacture of leather, and in the production and working of metals and alloys. They were familiar with the methods of tempering iron. They made glass, artificial gems, and enamels."

"[I]t is through [the Jews] and the ns, who were among the earliest of traders, that Europe was gradually made acquainted with many technical products of Eastern origin."

"Gold was undoubtedly one of the earliest metals to be made use of by men, as it probably was one of the first to be discovered. It occurs free in nature, and is met with in many rocks and in the sands of rivers. Its colour, lustre, and density would early attract attention... its malleability and ductility and the ease with which it could be fashioned, together with its unalterability, would render it valuable."

"Ethiopian and n gold were known from the earliest times, and crushing and gold washing were practised by the Egyptians. Representations of these processes have been found on Egyptian tombs dating from 2500 B.C. Gold-wire was used by the Egyptians for embroidery, and they practised plating, , and ing as far back as 2000 B.C."

"Silver... like gold, to have been coined into money. It was originally known as "white gold." Some of the oldest coins in existence are alloys of silver and gold, obtained probably by the fusion of naturally occurring argentiferous gold, such as the pale gold of the . Such an alloy was termed , from its resemblance in colour to ."

"Copper is also found to a limited extent in the metallic state, but probably the greater part of that used by the ancients was obtained from its ores, which are comparatively abundant and readily smelted. It was also used for coinage by the Egyptians, and was fashioned by them into a variety of utensils and implements. The older writers drew no clear distinction between copper, , and ..."

"Pure copper is too soft a metal to be used for swords and cutting instruments, but copper ores frequently contain associated metals, as, for example, tin, which would confer upon the copper the necessary hardness to enable it to be fashioned into weapons. Such copper would be of the character of , and it was known to the early workers that the nature of the metal was greatly modified by the selection of ores from particular localities."

"It was comparatively late in the metallurgical history of copper that was produced by knowingly adding tin to the metal."

"Aurichalcum, or golden copper that is, was well known to the early workers in copper, and was made in Pliny's time by heating together copper, cadmia (calamine), and charcoal."

"was employed by the Assyrians, and was cast by the Egyptians for the manufacture of mirrors, vases, shields, etc., as far back as 2000 B.C."

"Tin... known to the early Egyptians, would appear to have been first obtained from the , and to have been known under the Sanskrit name of Kastîra (Kâs, to shine), whence... the Arabic word for tin, Kàsdir, and the Greek κασσιτερος, used by Homer and Hesiod."

"Tin ores are found in Britain (Cornwall), and were brought thence by the Phoenicians."

"The Latin word for tin was stannum; it was also known as plumbum album, in contradistinction to lead, which was called plumbum nigrum. Tin was used by the Romans for covering the inside of copper vessels, and was also occasionally employed in the construction of mirrors."

"Lead was well known to the Egyptians. In Pliny's time it was mainly procured from Spain and from Britain ()."

"Leaden pipes were used by the Romans for the conveyance of water, and sheet lead was employed by them for roofing purposes. Argentarium was composed of equal parts of lead and tin; tertiarium, used as a solder, consisted of two parts of lead and one part of tin."

"Iron, although now the most important of the common metals, was not in general use until long after the discovery of gold, silver, and copper. ...[A]lthough its ores are relatively abundant and widely distributed, its extraction as a metal demanded greater skill and more appliances... Metallic iron was, however, well known to the Egyptians, who employed it in the manufacture of swords, knives, axes, and stone-chisels, both as malleable iron and as steel."

"Steel was... known to the Chinese as far back as 2220 B.C., and they were acquainted with the methods of tempering it. The good quality of Chinese steel caused it to be highly prized by Western nations."

"Mercury was familiar to Aristotle, and its mode of manufacture from is described by Theophrastus (320 B.C.), who terms it "liquid silver." Processes of amalgamation were known to Pliny, who notes the readiness with which mercury dissolves gold. Pliny appears to distinguish the native metal found in Spain, which he terms argentum vivum (quicksilver), from that obtained by sublimation or from , which he calls hydrargyrum, from which we get the chemical symbol for mercury Hg."

"[M]etallic compounds were known to the ancients, and were employed by them as medicines and as pigments. The oxides of copper, known as flos œris, and scoria œris, obtained by heating copper bars to redness and exposing them to air, were used as escharotics. , or œrugo, was made by the same methods as now. Blue vitriol, or chalcantum, is described by Pliny, who says that the blue transparent crystals are formed on strings suspended in its solution."

"', malachite, or copper carbonate, was used as a green pigment. The blue κύανος of the Greeks, or cœruleum of the Romans, was obtained by ting together alkali, sand, and oxide of copper. Botryitis, placitis, onychitis, ostracitis, were varieties of ' or oxide of zinc, obtained by calcining calamine, and were used in the treatment of ulcers, etc."

"Molybdena, which was the Latin name for , was employed externally as an and in the manufacture of plaster. The lead plaster employed by Roman surgeons was practically identical... with that in use to-day."

"Cerussa, or , was made as now by exposing sheets of lead to the fumes of . It was used in medicine, as a pigment, and in the preparation of cosmetics."

"Cerussa usta was probably red lead. Its present name of minium was originally applied to , the red sulphide of mercury, which was frequently adulterated with red lead."

"', formerly obtained from Africa, and, by the Romans, from Spain, was also used externally in medicine, and was a highly prized pigment, whose value was known to the Chinese from very early times."

"The black sulphide of antimony, the stimmi and stibium of Dioscorides and Pliny, was employed by women in Asia, Greece, and latterly in Western Europe, and is still so used in the East, for blackening their eyelashes. Preparations of were used in medicine."

"', the scarlet sulphide of arsenic, the sandarach of Aristotle, and the arrenichon of Theophrastus, was employed as a pigment, and also in medicine, both internally and externally. The yellow sulphide of arsenic, or auri pigmentum (), was... used for the same purposes."

"A variety of yellow and red s, in addition to the pigments above... were used by painters, such as rubrica, an iron ochre of a dark red colour, and sinopis, or reddle, obtained from Egypt, , and the Balearic Isles."

"Oxides of manganese were used as brown pigments."

"The white pigment, paratonium, was probably meerschaum. Melinum was a variety of chalk found in ."

"The ancients were well acquainted with indigo and madder, and with the mode of manufacturing lakes, which were employed by Grecian artists."

"The famous purpurissum was chalk or clay stained by immersion in a solution of ."

"' was lamp-black: ivory-black was used by , and was known as elephantinum. The ink of the ancients consisted of lamp-black suspended in a solution of gum or glue. The atramentum indicum, imported from the East, was identical with China ink."

"The ancients were well skilled in the art of dyeing, and even of printing. The Tyrians produced their famous purple dye as far back as 1500 B.C. It was obtained from shell-fish, mainly species of , inhabiting the Mediterranean. Tyrian purple has been shown to be dibrom-indigo, and to have been produced by the action of air and light upon the juices exuded from the shell-fish."

"[T]he Egyptians were acquainted with the use of s ... [Pliny] accurately describes the process of madder dyeing on cotton, whereby a variety of fast colours—reds, browns, and purples—can be obtained from the same vat by the employment of different mordants, such as alumina, oxide of iron, or oxide of tin, etc."

"[L]arge quantities of glass were exported to Greece and Rome from Egypt, mainly by Phoenicians. Aristophanes mentions it as hyalos, and speaks of it as the beautiful transparent stone used for kindling fire."

"The Egyptians made use of various metallic oxides in colouring glass. The hœmatinon of Pliny was a red glass coloured with cuprous oxide. Cupric oxide was used to colour glass green; and ancient blue glass has been found to contain cobalt. The costly vasa murrhina of the Romans, obtained from Egypt, probably consisted of fluorspar, identical with the Blue John of the mines."

"Soap (sapo) is mentioned by Pliny, but its detergent properties were apparently unknown to him. It appears to have been first made by the , who prepared it from the ashes of the beech and the fat of goats, and used it as a pomatum, as did the jeunesse d'oreé of Rome. Wood ashes, as well as natron, were, however, used by the ancients for their cleansing properties."

"Starch, acetic acid, sulphur, alumen or crude sulphate of alumina, beeswax, , bitumen, naphtha, asphalt, nitrum (carbonate of soda), common salt, and lime, were all well known to the Egyptians, and were used by them for many of the purposes in which they are employed to-day."

"[T]he ancients possessed a considerable acquaintance with many operations of technical chemistry... Their methods were probably jealously guarded and handed down by successive members of the crafts as precious secrets. ...[T]he scientific spirit was not free to develop, for science depends essentially upon free inter-communication of facts ...Moreover, the great intellects of antiquity, for the most part, had little sympathy with the operations of artisans, who, at least among the Greeks and Romans, were, for the most part, slaves. Philosophers taught that industrial work tended to lower the standard of thought."

"The priests, in most ages, have looked more or less askance at attempts, on the part of the laity, to inquire too closely into the causes of natural phenomena. The investigation of nature in early times was impossible for religious reasons."

"The educated Greeks had no interest in observing or in explaining the phenomena of technical processes. However prone they might be to speculation, they had no inclination to experiment or to engage in the patient accumulation of the knowledge of physical facts. ...The influence of a spurious , which lasted through many centuries and even beyond the time of Boyle, was wholly opposed to the true methods of science, and it was only when philosophy had shaken itself free from that chemistry, as a science, was able to develop."

"Speculations as to the origin and nature of matter, and as to the conditions and forces which affect it, are to be found... in the oldest systems of philosophy... These speculations are not based... upon the systematic observation of natural phenomena. Still, as they appealed to human reason, they must be... founded upon experience, or at least not... consciously inconsistent with it."

"All the oldest cosmogonies regarded water as the fundamental principle of things: from Okeanos sprang the gods—themselves deified personifications of the "elements" or principles of which the world was made. ...[T]his doctrine of the origin and essential nature of matter came to be... associated with the name of Thales of Miletus... who, according to Tertullian, is to be regarded as the first of the race of the natural philosophers—that is, the first of those who made it their business to inquire after natural causes and phenomena. Thales... may have been influenced by the Egyptian teaching in the formulation of his cosmological theories."

"[T]he teaching of Thales... survived through the space of twenty-four centuries. It can be shown to have affected the course of chemical inquiry down to the close of the eighteenth century. It influenced the experimental labours of philosophers so diverse in character as Van Helmont, Boyle, Boerhaave, Priestley, and Lavoisier all of whom made attempts to prove or disprove its adequacy."

"Van Helmont... was one of the most strenuous supporters of the doctrine of Thales, and sought to establish it by observations which, in the absence of all knowledge of the true nature of air and water, seemed at the time irrefutable. ...[H]e planted a willow weighing 5 lbs. in 200 lbs. of earth previously dried in an oven. ...[A]t the end of five years it was found to weigh 169 lbs. 3oz., whereas the earth, after redrying, had lost only 2 oz... Hence, 164 lbs. ...had been produced seemingly from water alone. More than a century had to elapse before any clue to the true interpretation... was first furnished by the observations of Ingenhousz and Priestley."

"Although the idea of a primal "element" or common principle is to be found in every old-world philosophical system, the ancient philosophers were by no means in agreement as to its character. Anaximenes... taught that it was air, Herakleitos of Ephesus that it was fire, and Pherekides that it was earth."

"It was a comparatively simple evolutionary step to regard these principles or "elements" as mutually convertible. Anaximenes' theory of the formation of rain was an implicit admission of such convertibility. This philosopher taught that rain came by the condensation of clouds, which in their turn were formed by the condensation of air. Everything comes from air, and everything returns to air. That water might be converted by fire into air was surmised from the earliest times."

"[W]ater was everywhere recognised to disappear or to pass into the air under the influence of fire or solar heat. The supposition had grown into a fixed belief in the Middle Ages. Even Priestley, as late as the end of the eighteenth century, imagined for a time that he had obtained proof of such a mutual conversion."

"The possibility of the transmutation of water into earth was a belief current through twenty centuries, and was only definitely and finally disproved by Lavoisier in 1770."

"The conception of fire as the primal principle has its germ in the fire- or sun-worship of the ns, , Persians, Parsees, and Hindus; and it is not difficult to trace, therefore, how heat came to be regarded either as antecedent to, or as associated with, the other primal principles."

"Empedokles... was the first whose name has come down to us to reintroduce the definite conception of four primal elements—fire, air, water, and earth. These he regarded as distinct, and incapable of being transmuted, but as forming all varieties of matter by intermixture in various proportions. These principles he deified, Zeus being the personification of the element of fire, Here of air, Nestis of water, and Aidoneous of earth."

"The doctrine of the four elements was also adopted by Plato and amplified by Aristotle... [who] exercised an authority almost supreme in Europe during nearly twenty centuries. His influence is to be traced throughout the literature of chemistry long after the time of Boyle. It may be detected even now. ...His theory of the nature of matter is contained in his treatise on Generation and Destruction. It mainly differed from that of Empedokles in regarding the four "elements" as mutually convertible. Each "element" or principle was regarded as being possessed of two qualities, one of which was shared by another element or principle.Thus: Fire is hot and dry; air is hot and wet; water is cold and wet; earth is cold and dry. In each primal "element" one quality prevails. Fire is more hot than dry; air is more wet than hot; water is more cold than wet; earth is more dry than cold. ...[I]f the dryness of fire is overcome by the moisture of water, air is produced; if the heat of air is overcome by the coldness of earth, water is formed; if the moisture of water is overcome by the dryness of fire, earth results. Ancient chemical literature contains many illustrations or diagrams symbolising the convertibility or mutual relations...."

"[[Aristotle|[T]he founder]] of [the Peripatetic school], a descendant of Esculapius, and undoubtedly one of the greatest and most enlightened thinkers of antiquity, was an ideal man of science. ...Much of what is called is entirely foreign to the spirit of the teaching of Aristotle. The Aristotelians of the Middle Ages were mainly s, and almost wholly concerned with the formulae of syllogistic inference, and without real sympathy with, or knowledge of, his system. Much... that was attributed to him, and which was venerated accordingly, is undoubtedly spurious. The fame of the Master has consequently suffered at the hands of those who, calling themselves Peripatetics, were in no proper sense followers of his method or interpreters of his dogma."

"Aristotle affirmed that natural science can only be founded upon a knowledge of facts, and facts can only be ascertained through observation and experiment."

"It is erroneous and unjust... to suppose that Aristotle's philosophy, as he taught it, is opposed to the true methods of science."

"A knowledge of Aristotle's works was transferred by Byzantine writers to Egypt; and, when that land was overrun by the Arabs in the seventh century, they adopted his system, spreading it abroad wherever their conquests extended. In the eighth century they carried it into Spain, where it flourished throughout their occupation of that country."

"From the ninth to the eleventh century the greater part of Europe was in a state of barbarism. The Moslem caliphate in Spain, under the beneficent rule of emirs] Jusuf and Jaküb, alone preserved science from extinction. Cordova, Seville, Grenada, and Toledo were the chief seats of learning in Western Europe; and it was mainly through "the perfect and most glorious physicist," the Moslem Ibn-Roshd—better known as Averroes... that Christian scholiasts like Roger Bacon acquired their knowledge of the philosophical system of Aristotle, and mainly through the Moslems Geber and Avicenna that they gained acquaintance with the science of the East."

"The conception that matter is made up of particles or atoms, and that these particles are in a state of ceaseless motion, is to be met with in Hindu and n philosophy. It was taught by Anaxagoras, Leukippos, and Demokritos to the Greeks, and by Lucretius to the Romans."

"Leukippos and Demokritos explained the creation of the world as due solely to physical agencies without the intervention of a creative intelligence. According to their theories, the atoms are variable not only in size, but in weight. The smallest atoms are also the lightest. Atoms are impenetrable; no two atoms can simultaneously occupy the same place. The collision of the atoms gives them an oscillatory movement, which is communicated to adjacent atoms, and these, in their turn, transmit it to the most distant ones."

"Anaxagoras taught that every atom is a world in miniature, and that the living body is a congeries of atoms derived from the aliments which sustain it. Plants are living things, endowed like animals with respiratory functions, and, like them, atomically constituted. This philosopher was so far in advance of his age that his countrymen accused him of sacrilege, and he only escaped death by flight."

"[T]he assumption that these atoms exert mutual attractions and repulsions is probably as old as the fundamental conception itself. ...[S]o far as can be traced, the conceptions of atoms and atomic motion are indissolubly connected."

"[We cannot] now concern ourselves with the old metaphysical quibble of its divisibility or indivisibility. It may be, as Lucretius said, that the original atom is very far down."

"It may be that the physical atom is something which is not divided, not something that cannot be divided. This theory, dimly perceived in the mists of antiquity, has grown and strengthened with the ages, and in its modern application to the facts of chemistry has acquired a precision and harmony unimagined even by the poets and thinkers of old. ...[T]he whole course of the science has been controlled, illumined, and vivified by it. [T]he chemistry of to-day is one vast elaboration of this primeval doctrine."

"The latter half of the seventeenth century was a remarkable period... [N]early every department of human knowledge seemed to have become permeated by an eager spirit of scepticism, inquiry, and reform. The foundation of the of London for Improving Natural Knowledge, the of Florence, the Academie Royale at Paris, the Berlin Academy, all within a few years of each other, was significant of the times. Chemistry was no longer to be a sacred mystery, to be known only to priests, and its secrets jealously guarded by them."

"[P]urely deductive methods of the Peripatetics gradually gave place to the only sound method of advancing natural knowledge."

"The supremacy of the old philosophy may be said to have been first distinctly challenged by Robert Boyle. The appearance in 1661 of his book, The Sceptical Chemist, marks a turning-point in the history of chemistry."

"The "Chemico-physical Doubts and Paradoxes" raised by Boyle "touching the experiments whereby vulgar Spagyrists are wont to endeavour to evince their Salt, Sulphur, and Mercury to be the true Principles of Things," eventually sealed the fate of the doctrine of the tria prima, and of the tenets of the school of Paracelsus."

"In this treatise Boyle sets out to prove that the number of the peripatetic elements or principles hitherto assumed by chemists is, to say the least, doubtful."

"The words "element" and "principle" are used by him as equivalent terms, and signify those primitive and simple bodies of which compounds may be said to be composed, and into which these compounds are ultimately resolvable."

"He concludes... that the Paracelsian elements—their "salt," "sulphur," and "mercury"—are not the first and most simple principles of bodies; but that these consist, at most, of concretions of corpuscles or particles more simple than they, and possessing the radical and universal properties of volume, shape, and motion."

"He became a member of what was known as the , a small association of men interested in the new philosophy, who met at each other's houses in London, and occasionally at Gresham College, "to discourse and consider of philosophical inquiries and such as related thereunto." The meetings were subsequently held in , and Boyle took up his residence there in 1654. Here—in association with Wilkins; John Wallis and Seth Ward, the two Savilian Professors of Geometry and Astronomy; , the physician, then student of Christ Church; Christopher Wren, then Fellow of All Souls' College; Goddard, Warden of Merton; and , Fellow of Trinity, and afterwards its President—they sought to cultivate the new philosophy, "being satisfied that there was no certain way of arriving at any competent knowledge unless they made a variety of experiments upon natural bodies. In order to discover what phenomena they would produce, they pursued that method by themselves with great industry, and then communicated their discoveries to each other." The Invisible College eventually grew into the ..."

"He introduced the air-pump into England, and his "pneumatical engine" enabled him to discover many of the fundamental properties of a gas, notably the relation of its volume to pressure."

"He... discovered the dependence of the of a liquid upon , explained the action of the , the effect of the air on the vibration of a pendulum and on the propagation of sound, and made experiments on the nature of , and on the relation of air to and ."

"In his History of Fluidity he seeks to show that a body seems to be by consisting of corpuscles touching one another only in some parts of their surfaces; whence, by reason of the numerous spaces between them, they easily glide along each other till they meet with some resisting body to whose internal surface they exquisitely accommodate themselves. He considers the requisites of fluidity to be chiefly these: The smallness of the component particles, their determinate figure, the vacant spaces between them, and the fact of their being agitated variously and apart by their own innate motion or by some thinner substance which tosses them about in its passage through them."

"His published works contain many well-authenticated chemical facts, which are commonly held to be the discovery of a later time."

"He prepared by the distillation of the s of lead and lime; and he isolated methyl alcohol from the products of the of wood."

"He was one of the earliest to insist on the necessity of studying the forms of crystals. He saw in their formation proof that the internal motions, configuration, and position of the integral parts are all that is necessary to account for alterations and diversities in outward character."

"Some of the stock illustrations of our lecture-rooms were of his contrivance. Thus he illustrated the expansive power of freezing water by bursting a plugged gun-barrel filled with water by solidifying the water by means of a mixture of snow and salt a freezing mixture which he first introduced."

"Boyle was the first to formulate our present conception of an element in contradistinction to that of the Greeks and the schoolmen who influenced the theories of the iatro-chemists. In the sense understood by him, the Aristotelian elements were not true elements, nor were the salt, sulphur, and mercury of the school of Paracelsus."

"He was... the first to define the relation of an element to a compound, and to draw the distinction we still make between compounds and s."

"He revived the atomic hypothesis, and explained chemical combination on the basis of affinity."

"He contended that one of the main objects of the chemist was to ascertain the nature of compounds; and thereby he stimulated the application of analysis to chemistry. Boyle discovered a number of qualitative reactions, and applied them to the detection of substances, either free or in combination."

"Boyle's greatest service to learning consisted in the new spirit he introduced into chemistry. Henceforward chemistry was no longer the mere helpmeet of medicine. She became an independent science, the principles of which were to be ascertained by experiment; a science to be studied with the object of discovering the laws regulating the phenomena with which it is concerned and hence elucidating truth for truth's sake."

"The old philosophy of the Greeks had, as we have seen, become merged into the doctrine of the iatro-chemists; and this was now to be purified from the theosophical mysticism with which Paracelsus and his followers had enshrouded it. "The ical subtleties of the schoolmen much more," says Boyle, "declare the wit of him that uses them than increase the knowledge or remove the doubts of sober lovers of truth... For in such speculative inquiries where the naked knowledge of the truth is the thing principally aimed at, what does he teach me worth thanks, that does not, if he can, make his notion intelligible to me, but by mystical terms and ambiguous phrases darkens what he should clear up, and makes me add the trouble of guessing at the sense of what he equivocally expresses, to that of learning the truth of what he seems to deliver.""

"The influence of the new spirit... infused into the science by Boyle is seen in the general style of chemical literature at the end of the seventeenth century, when compared with that of the close of the sixteenth. The mysticism and obscurity of the alchemists were no longer tolerated."

"Kunkel did much to liberate chemical literature from the mysticism and obscurity of alchemy. He was scornful of the theories of the adepts, and contemptuous of their tria prima."

"Kunkel discovered the secret of the manufacture of aventurine glass and of ruby glass by means of the a product from gold first obtained by a doctor of medicine of that name in Hamburg."

"He made observations on fermentation and putrefaction recognised that was a (sal duplicatum); described the present method of preparing pure silver, and of parting gold and silver by means of sulphuric acid. He also described the mode of preparing a number of essential oils, detected the presence of stearopten in oils, and discovered nitrous ether."

"Becher's name is remembered mainly in connection with his theory of combustion, which... was subsequently developed by Stahl into the theory of Phlogiston—a generalisation which dominated chemistry until near the close of the eighteenth century."

"John Mayow... was a practising physician, whose name chiefly lives by virtue of his clear recognition of the substance or principle in the air which is concerned in combustion, the of metals, respiration, and the conversion of venous into . This substance, which he found to be contained in saltpetre, he called spiritus igno-aëreus or nitro aëreus."

"Had he been able to follow up his observations, he might have influenced very materially the development of . As it was, he was practically overlooked by his contemporaries, and the real significance of his work was not appreciated until long afterwards."

"Nicolas Lemery... wrote a Cours de Chimie, one of the best text-books of the time... and was translated into English, German, Latin, Italian, and Spanish. In this book he strove... to express himself clearly, and to avoid the obscurities which were to be found in the authors who had preceded him."

"Nicolas Lemery... made a considerable number of contributions to pharmaceutical chemistry; and his Pharmacopée Universelle, Dictionnaire Universel des Drogues Simples, and Traité de l'Antimoine were standard works in their day."

"In 1682 he was invited to Paris by Colbert, and in 1691 was made a member of the Academy and was placed by the Duke of Orleans in charge of his laboratory—then one of the finest in Europe."

"Homberg married the daughter of Dodart, the physician. She became an expert preparateur, and was of great assistance to him in his experimental inquiries."

"He first made known the existence of in France, discovered by Brand, of Hamburg, and he described the phosphorescent salt [Homberg's phosphorus] associated with his name."

"He made important observations on the saturation of s by s, and was aware that they combined in different proportions."

"Next to Boyle, perhaps the most active agent in emancipating chemistry from the yoke of alchemy was Boerhaave..."

"As a chemist Boerhaave is chiefly known by his Elementa Chemia,... the most complete and most luminous chemical treatise of its time, translations of which appeared in the chief European languages. ...The first [part] is concerned with the origin and progress of the art, and with the personal history of its most distinguished cultivators. The second... part deals with the attempt to form a system of chemistry based on such observational matter as seemed well established. The third consists of a collection of chemical processes relating to the analysis or decomposition of bodies, grouped under the heads of "vegetables," "animals," and "fossils"—the beginnings... of a sub-division of the science into organic and ."

"As regards his belief in alchemy, Boerhaave was an agnostic: he neither affirmed nor denied the possibility of transmutation. In this respect he resembled Newton and Boyle."

"Boyle, indeed, was singularly cautious and reticent in his references to alchemistic matters. As was said of him by Shaw, he was too wise to set any bounds to nature: he was not prone to say that every strange thing must needs be impossible, for he saw strange things every day, and was well aware that there are powerful forces in the world of whose laws and modes of action he knew nothing. With that wariness which was habitual to him, he was wont to say that "those who had seen them might better believe them than those who had not"; and he was modest enough to suppose that Paracelsus or Helmont might conceivably know of agents of which he was ignorant."

"Boerhaave unquestionably spent much time in the study of alchemical works, particularly those of Paracelsus and Helmont, which he repeatedly read."

"The ' contain the results of a laborious but fruitless investigation by him on quicksilver, which he undertook in the hope of discovering the seminal or engendering matter which, on the old theory of the generation of metals, was supposed to be contained in mercury. But although... he tortured it by "conquassation, , digestion, and by , either alone or amalgamated with , tin, or gold, repeating this operation to 511 or even to 877 distillations, "the mercury appeared only" rather more bright and liquid, without any other variation in its form or virtues, and acquired very little, if any, increase of its .""

"Stephen Hales... distinguished as a physiologist and inventor, occupied himself in chemical pursuits, and made a number of observations on the production of gaseous substances. His results were communicated to the and subsequently republished, in a collected form, under the title of Statical Essays. In these experiments he used methods very similar in principle to those subsequently employed by Priestley."

"[H]e must have prepared a considerable number of gaseous substances—, , carbonic oxide, sulphur dioxide, , etc.—but he seems to have made no systematic attempt to study their properties, as he considered that they were simply air, modified or "tinctured" by the presence of substances which he regarded as more or less fortuitous."

"Prior to the time of Black all forms of gaseous substance were regarded as substantially identical in fact, as being air, as understood by the Ancients a simple elementary substance. It was Black's study of which first clearly established that there were essentially distinct varieties of gaseous matter."

"The first year of the nineteenth century is further memorable on account of the invention of the , and by reason of its application by William Nicholson and Sir to the electrolytic decomposition of water. This mode of resolving water into its constituents made a great sensation at the time, mainly because of the extraordinary method by which it was effected. It afforded an independent and unlooked-for proof of the compound nature of water by a method altogether differing in principle from that by which its composition had been previously ascertained."

"The formation of water by the combustion of hydrogen brought no conviction of its real nature to a confirmed phlogistian like Priestley; and it is even doubtful whether Cavendish ever fully realised the true significance of his great discovery. But the fact that the quantitative results of the analysis thus effected were identical with those of its synthesis, as made by Cavendish and Lavoisier, admitted of only one interpretation."

"This cardinal discovery may be said to have completed the downfall of phlogiston."

"The value of the as an analytical agent was... quickly appreciated... In the hands of Humphry Davy its application to the analysis of the alkalis and alkaline earths led to discoveries of the greatest magnitude."

"While in the capacity of assistant and operator in Beddoes's Pneumatical Institute, Davy discovered the intoxicating properties of (so called laughing gas), which brought him into prominence and led to his engagement by the managers of the newly-created in London as lecturer in chemistry in succession to Garnett."

"He early began to experiment on , and soon succeeded in developing the fundamental laws of electro-chemistry; and in 1807 he effected the decomposition of [[w:Potassium hydroxide|[caustic] potash]] and [[w:Sodium hydroxide|[caustic] soda]] by the application of voltaic electricity thereby establishing... that the alkalis are compound substances. He subsequently proved that this was also the case with the alkaline earths. Davy thus added some five or six metallic elements to those already known."

"These discoveries, perhaps the most brilliant of their time, afforded additional evidence of the invalidity of Lavoisier's assumption that oxygen, as the name implies, was the "principle of acidity." The surmise, in fact, was already disproved by the case of water—a neutral substance [containing oxygen yet] devoid of all the recognised attributes of an acid. It was still further disproved by the cases of [caustic] potash and [caustic] soda—strongly alkaline compounds [yet both containing oxygen]."

"Additional evidence was adduced by Davy in demonstrating, in 1810, that the so-called oxymuriatic acid, [i.e.,] the dephlogisticated marine acid discovered by Scheele, contained no oxygen, but was a simple, indivisible substance."

"For the old designation, which connoted a compound body, he substituted the name , in allusion to the characteristic colour of the element."

"In the course of his investigation on this substance he discovered the penta- and trichloride of phosphorus, chlorophosphamide, and . He was also the discoverer of telluretted hydrogen and an independent discoverer of nitrosulphonic acid."

"He worked on and the s, on the diamond, on the so-called fuming liquor of Cadet, on nitrogen chloride, and on the s of the ancients. Lastly, he invented the miner's safety lamp..."

"In the preceding volume an attempt was made to outline the significant features in the development of chemistry, as an art and as a science, from the earliest times down to about the middle of the last century. Since that time chemistry has progressed at a rate and to an extent unparalleled at any period of its history."

"Not only have the number and variety of chemical products inorganic and organic been enormously increased, but the study of their modes of origin, properties, and relations has greatly extended our means of gaining an insight into the internal structure and constitution of bodies."

"This extraordinary development has carried the science beyond the limits of its own special field of inquiry, and has influenced every department of natural knowledge. Concurrently there has been a no less striking extension of its applications to the prosperity and material welfare of mankind."

"With the death of Davy the era of brilliant discovery in chemistry, wrote Edward Turner, appeared for the moment to have terminated."

"Although the number of workers in the science steadily increased, the output of chemical literature in England actually diminished for some years; and, as regards inorganic chemistry, few first-rate discoveries were made during the two decades prior to 1850."

"Chemists seemed to be of Turner's opinion that the time had arrived for reviewing their stock of information, and for submitting the principal facts and fundamental doctrines to the severest scrutiny. Their activity was employed not so much in searching for new compounds or new elements as in examining those already discovered. The foundations of the atomic theory were being securely laid. The ratios in which the elements of known compounds are united were being more exactly ascertained. The efforts of workers, Graham excepted, seemed to be spent more on points of detail, on the filling-in of little gaps in the chemical structure, as it then existed, than in attempts at new developments."

"For a time—during the early 'thirties—chemists struggled with the claims of rival methods of notation, and it was only gradually that the system of Berzelius gained general acceptance. At none of the British universities was there anything in the nature of practical tuition in chemistry."

"Thomson, at Glasgow, occasionally permitted a student to work under him, but no systematic instruction was ever attempted. The first impulses came from Graham in 1837, when he took charge of the chemical teaching at the , and when, in 1841, he assisted to create the Chemical Society of London."

"It was largely through the influence of [the following] master-minds that chemistry took a new departure. Prior to their time organic chemistry hardly existed as a branch of science: organic products, as a rule, were interesting only to the pharmacist mainly by reason of their technical or medicinal importance. But by the middle of the nineteenth century the richness of this hitherto untilled field became manifest, and scores of workers hastened to sow and to reap in it. The most striking feature, indeed, of the history of chemistry during the past sixty years has been the extraordinary expansion of the organic section of the science. The chemical literature relating to the compounds of now exceeds in volume that devoted to all the rest of the elements."

"In the middle of the nineteenth century chemists began to concern themselves with the systematisation of the results of the study of organic compounds, and something like a theory of organic chemistry gradually took shape. From this period we may date the attempts at expressing the internal nature, constitution, and relations of substances which, step by step, have culminated in our present representations of the structure and spatial arrangement of molecules."

"In 1850 the dualistic conceptions of Berzelius ceased to influence the doctrines of organic chemistry. The enunciation by Dumas of the principle of substitution, and its logical outcome in the nucleus theory and in the theory of types, had not only effected the overthrow of dualism, but was undermining the position of the of Liebig and Wöhler."

"The teaching of Gerhardt and Laurent had spread over Europe, and was influencing those younger chemists who, while renouncing dualism, were not wholly satisfied with a belief in compound radicals."

"Other representative men of the middle period of the nineteenth century, in addition to Williamson, were Graham and Bunsen. The three men were investigators of very different type, and their work had little in common. But each was indentified with discoveries of a fundamental character, constituting turning-points in the history of chemical progress, valuable either as regards their bearing on chemical doctrine or as regards their influence on operative chemistry."

"[In 1845 the] in London was founded and placed under the direction of August Wilhelm Hofmann—one of the most distinguished pupils of Liebig."

"Under his inspiration the study of practical chemistry made extraordinary progress, and discovery succeeded discovery in rapid succession. In bringing Hofmann to England we had, in fact, imported something of the spirit and power of his master, Liebig."

"Among the pupils and co-workers of Hofmann were , Abel, Nicholson, Mansfield, [Henry] Medlock, Crookes, [Arthur S.] Church, Griess, Martius, Sell, Divers, and Perkin."

"Whilst at Giessen he had begun the study of the s in coal-tar with a view more especially of establishing the identity of Fritzsche's ' with the benzidam of Zinin and the krystallin of Unverdorben."

"With Muspratt he discovered paratoluidine and nitraniline; with Cahours, '."

"His pupil Mansfield worked out, at the cost of his life, the methods for the technical extraction of benzene and toluene from coal-tar, and thereby made the coal-tar colour-industry possible."

"It was in attempting to synthesise by the oxidation of aniline that Perkin, then an assistant at the college, obtained, in 1856, aniline purple or mauve, as it came to be called by the French, the first of the so-called coal-tar colouring matters."

"In 1859 this was followed by the discovery of magenta, or ', by [François-Emmanuel] Verquin. For its manufacture [Henry] Medlock, one of Hofmann's pupils, in 1860 devised a process by which for a time it was almost exclusively made. Hofmann studied the products thus obtained, and showed that they were derivatives of a base he called rosaniline; and he demonstrated that the colouring matters were only produced through the concurrent presence of and . He also proved that the base of the dye, known as aniline blue, was triphenylrosaniline. As the result of these inquiries he obtained the violet or purple colouring matters known by his name [Hofmann's violets]."

"[A]ll his classical work on the amines, compounds, and the analogous derivatives was done at the ."

"Prior to the establishment by Liebig, in 1826, of the Giessen laboratory, the state of chemistry in Germany was not much... better than [England's.] The creation of the Giessen school initiated a movement which has culminated in the pre-eminent position [of] Germany... in the chemical world. Students from every civilised country came to study and to work under its leader..."

"Justus von Liebig... after graduating at Erlangen, where he worked on the s, ...entered the [] laboratory of Gay Lussac, with whom he continued his inquiries."

"Returning to Germany, he was appointed Professor of Chemistry at Giessen in 1826, and began those remarkable series of scientific contributions upon which the superstructure of organic chemistry largely rests."

"He investigated the s, s, s, s, and their derivatives."

"In conjunction with Wöhler he discovered the group of the benzoic compounds and created the ."

"With Wöhler... he investigated and its derivatives. He discovered , fulminuric acid, , , , thialdine, , and elucidated the constitution of the s and the amides."

"He greatly improved the methods of organic analysis, and was thereby enabled to determine the empirical formulae of a number of carbon compounds of which the composition was imperfectly known."

"He practically laid the foundations of modern , and to his teaching is due the establishment of an important branch of technology the manufacture of chemical fertilisers."

"He worked on physiological chemistry, especially on the elaboration of , on the nature of blood, , and on the juice of flesh."

"He studied the processes of , and of the decay of organised matter."

"He was a most prolific writer. The 's Catalogue of Scientific Papers enumerates... 317 contributions... He was the founder of the Annalen der Chemie... and of the Jahresbericht; he published an Encyclopedia of Pure and Applied Chemistry and a Handbook of Organic Chemistry. His Familiar Letters on Chemistry was translated into every modern language, and exercised a powerful influence in developing popular appreciation of the value and utility of science."

"With the name of Liebig that of Wöhler is indissolubly connected. Although the greater part of their work was not published in conjunction, what they did together exercised a profound influence on the development of chemical theory."

"After studying at Marburg, where he discovered, independently of Davy, , and worked on mercuric thiocyanate, he went to Heidelberg and investigated cyanic acid and its compounds, under the direction of Gmelin."

"In 1823 he worked with Berzelius at Stockholm, where he prepared some new tungsten compounds and practised analysis."

"In 1825 he became a teacher of chemistry in the Berlin Trade School. Here he succeeded for the first time in preparing the metal ' and in effecting the synthesis of —one of the first organic compounds to be prepared from inorganic materials."

"Jointly with Liebig he worked upon mellitic and cyanic and s."

"In 1832 Wöhler, now appointed to the Polytechnic at Cassel, began with Liebig their memorable investigation on bitter almond oil."

"In 1836 he was called to the Chair of Chemistry in the , and with Liebig attacked the constitution of and its derivatives the last great investigation the friends did in common."

"Wöhler subsequently devoted himself mainly to . He isolated crystalline boron, and prepared its nitrides, discovered the spontaneously inflammable silicon hydride, , and analysed great numbers of minerals and meteorites and compounds of the rarer metals."

"He made Gottingen famous as a school of chemistry. ...[U]pwards of 8000 students had listened to his lectures or worked in his laboratory."

"If Liebig could reckon among his pupils Redtenbacher, [Johann Conrad] Bromeis, [Franz] Varrentrapp, Gregory, Playfair, Williamson, Gilbert, Brodie, Anderson, Gladstone, Hofmann, [Heinrich] Will, and Fresenius; Dumas could point to [Félix-Polydore] Boullay, Piria, Stas, Melsens, Wurtz, and [Félix] Leblanc all of whom did yeoman service in developing the rapidly expanding branch of organic chemistry."

"Jean Baptiste André Dumas was born on July 14, 1800, at Alais, where he was apprenticed to an . In his sixteenth year he went to Geneva and entered the pharmaceutical laboratory of [Elie] Le Royer. Without, apparently, having received any systematic instruction in chemistry, he commenced the work of investigation."

"With Coindet he established the therapeutic value of iodine in the treatment of goître; with Prevost he attempted to isolate the active principle of ' [foxgloves], and studied the chemical changes in the development of the chick in the egg."

"In his twenty-fourth year Dumas went to Paris and became Répétiteur de Chimie at the . He joined Audouin and Brongniart in founding the ', and began his great work on Chemistry Applied to the Arts... [published 1828]. At about this time he devised his method of determining vapour densities, and published the results of a number of estimations made by means of it."

"With [Félix-Polydore] Boullay he began an inquiry on the compound ethers, out of which grew the etherin theory, which served as a stepping-stone to the theory of compound radicals subsequently elaborated by Liebig and Wöhler."

"Dumas discovered the nature of ' and of ethyl oxamate [C4H7NO3], isolated methyl alcohol, and established the generic connection of groups of similarly constituted organic substances, or, in a word, the doctrine of homology."

"His work on the metaleptic action of upon organic substances eventually effected the overthrow of the electro-chemical theory of Berzelius and led to the theory of types, which, in the hands of Williamson, Laurent, Gerhardt, and Odling, was of great service in explaining the analogies and relationships of whole groups of organic compounds."

"He worked in every field of chemistry. He invented many analytical processes, established the gravimetric composition of water and of air, and revised the atomic weights of the greater number of the elements then known."

"Dumas exercised great influence in scientific and academic circles in France. He was an admirable speaker, and had rare literary gifts. On the creation of the Empire he was made a Senator, and was elected a member of the Municipal Council of Paris, of which he became president in 1859."

"Thomas Graham... after studying under Thomas Thomson at the University of [Glasgow], attended the lectures of Hope and Leslie in Edinburgh."

"In 1830 he succeeded Ure as teacher of chemistry at Anderson's College in Glasgow, and in 1837 was called to the Chair of Chemistry in the newly-founded , in succession to Edward Turner. In 1854 he was made ."

"Graham's work was mainly devoted to... ."

"His contributions to pure chemistry are few in number. By far the most important is his discovery of metaphosphoric acid and its relations to the other modifications of . Ortho- or ordinary phosphoric acid was known to Boyle; was discovered by Clark."

"Graham's work is noteworthy as first definitely indicating the inherent property of the acids to combine with variable but definite amounts of basic substances by successive replacement of hydroxyl groups the property we now term basicity, and was of fundamental importance in regard to its bearing on the constitution of s and salts."

"Graham's fame chiefly rests upon his discovery of the law of gaseous diffusion (1829-1831), upon his work on the diffusion of liquids, and upon his recognition of the condensed [metallic] form of hydrogen he termed hydrogenium. Questions involving the conception of molecular mobility... constituted the main feature of his inquiries."

"We owe to him, among others, the terms , , dialysis, atmolysis, occlusion—all of which have taken a permanent place in the terminology of science."

"Williamson's discovery, in 1850, of the true nature of ether and of its relation to alcohol, and his subsequent preparation of mixed ethers, served not only to reconcile conflicting interpretations of the process of etherification, but also to reconcile the theory of types with that of radicals."

"[H]is method of representing the constitution of the ethers and their mode of origin gave a powerful stimulus to the use of type-formulas in expressing the nature and relations of organic compounds."

"In 1840... Williamson entered the University of Heidelberg with the intention of studying medicine; but, under the influence of , he turned to chemistry."

"In 1844 he went to Giessen, to work under Liebig, and there [he] made his first contributions to chemical science viz., on the decomposition of s and salts by ; on ; and on the blue compounds of and iron."

"After graduating at Giessen he went, in 1846, to Paris, where he came under the influence of Comte, with whom he studied mathematics."

"In 1850, at Graham's solicitation, he was appointed to the Chair of Practical Chemistry at University College, vacant by the death of Fownes. He at once embarked upon those researches which constitute his main contribution to science. In the attempt to build up the homologous series of the aliphatic alcohols from ordinary alcohol he succeeded in demonstrating the real nature of ether and its genetic relation to alcohol, and in explaining the process of etherification. The memoirs (1850-52) in which he embodied the facts had an immediate influence on the development of chemical theory. His explanation of the process of etherification familiarised chemists with the idea of the essentially dynamical nature of chemical change."

"He imported the conception of molecular mobility not only into the explanation of such metathetical reactions as the formation of the ethers, but into the interpretation of the phenomena of chemical change in general."

"In these papers, as also in one on the constitution of salts, published in 1851, he attempted to systematise the representation of the constitution and relations of oxidised substances—organic and inorganic—by showing how they may be regarded as built up upon the type of water considered as ^{H}_{H}O, in which the hydrogen atoms are replaced, wholly or in part, by other chemically equivalent atoms. This idea was immediately adopted by Gerhardt, was further elaborated by Odling and Kekulé, and was eventually developed into a theory of chemistry."

"[A]fter studying chemistry under Stromeyer, the discoverer of , [he] went to Paris and worked with Gay Lussac."

"In In 1836 he succeeded Wöhler as teacher of chemistry in the Polytechnic School of Cassel, and in 1842 became Professor of Chemistry in the . In 1852 he was called to Heidelberg, and occupied the Chair of Chemistry there until his retirement in 1889."

"Bunsen first distinguished himself by his classical work on the compounds, obtained as the result of an inquiry into the nature of the so-called "fuming liquor of Cadet," an evil-smelling, highly poisonous, inflammable liquid formed by heating arsenious oxide with an alkaline . The investigation (1837-1845) is noteworthy, not only for the skill it exhibits in dealing with a difficult and highly dangerous manipulative problem, but also for the remarkable nature of its results and on account of their influence on contemporary chemical theory. The research, in the words of Berzelius, was the foundation-stone of the theory of compound radicals. The name cacodyl or kakodyl was suggested by Berzelius in allusion to the nauseous smell of the compounds of the new radical arsinedimethyl, As(CH3)2, as it was subsequently termed by Kolbe."

"Bunsen greatly improved the methods of gasometric analysis; these he applied, in conjunction with Playfair, to an examination of the gaseous products of the in the manufacture of iron, and thereby demonstrated the enormous waste of energy occasioned by allowing the gases to escape unused into the air, as was then the universal practice. This inquiry effected a revolution in the manufacture of iron as important, indeed, as that due to the introduction of the ."

"Bunsen devised methods for determining the solubility of gases in liquids, for ascertaining the specific gravity of gases, their rates of diffusion, and of combination or inflammation."

"In 1841 he invented the carbon-zinc battery, and applied it to the electrolytic production of metals, notably of , the properties of which he first accurately described."

"In 1844 he contrived the grease-spot photo-meter, which was long in general use for ascertaining the photometric value of illuminating gas."

"His methods of ascertaining the specific heats of solids and liquids were simple, ingenious, and accurate."

"In 1855-1863 he carried out, in conjunction with Roscoe, a long series of investigations on the chemical action of light."

"In 1859, in association with Kirchhoff, he devised the first methods of spectrum analysis, and explained this origin and significance of the in the solar spectrum, thus laying the foundations of solar and . The application of the spectroscope to analytical chemistry almost immediately resulted in his discovery of cœsium and ."

"Bunsen worked on problems of chemical geology, and made a long series of analyses of volcanic products."

"With [Leon] Schischkoff, he examined, in 1857, the products of fired ."

"He effected many improvements in analytical chemistry; devised the iodiometric method of volumetric analysis, and systematised the processes of water analysis."

"[H]e invented the gas-burner... with which his name is inseparably associated, and which has been of inestimable service to operative chemistry and in the arts."

"Bunsen was no theorist, and purely speculative questions had little or no interest for him."

"[H]e was a great teacher, and made the chemical school of Heidelberg no less famous than the schools of Giessen and Gottingen."

"Thorpe's observation... that "Organic chemistry has been largely developed by the discovery from time to time of special reagents and special types of reactions which have shown themselves to be capable of extensive application" continues to be true to this day."

"A transient view of the progress of chemical philosophy will prove that the most brilliant discoveries, and the happiest theoretical arrangements belonging to it are of very recent origin; and a few historical details and general observations upon the progress and effects of the science will form, perhaps, no improper introduction to the elements of this branch of knowledge."

"The only processes which can be called chemical, known to the civilized nations of antiquity, belonged to certain arts, such as metallurgy, dyeing, and the manufacture of glass or porcelain; but these processes appear to have been independent of each other, pursued in the workshop alone, and unconnected with general knowledge."

"The inhabitants of Lower Egypt, where the overflowing of the Nile covered a sandy desert with vegetation and life, might easily adopt the notion, that water, in different modifications, produced all the varieties of inanimate and organized matter; and this dogma characterized the earliest school of Greece."

"In the beginning of the Macedonian dynasty, the school of Aristotle gave a transient attention to the objects of natural science, but the great founder attempted too many subjects to be able to offer correct views of any one series.—And his erroneous practice, that of advancing general principles, and applying them to particular instances, so fatal to truth in all sciences, more particularly opposed itself to the progress of one [chemistry] founded upon a minute examination of obscure and hidden properties of natural bodies."

"Theophrastus, the successor of Aristotle, ...says, in the beginning of his book on fossils, 'stones are produced from earth, metals from water.' ...Theophrastus is perhaps the best observer among the ancients, whose works are in our possession, and [his] theories... cannot be considered as an unfavourable specimen of the theoretical physics of the age."

"[T]he Greeks... possessed, as if instinctively, the perception of everything beautiful, grand, and decorous. As philosophers, they failed not from a want of genius, or even of application, but merely because they pursued a false path,—because they reasoned more upon an imaginary system of nature, than upon the visible and tangible universe."

"Democritus is quoted by Laertius as having employed himself in processes for imitating gems, and for softening and working ivory. Caligula is said to have made experiments with the view of extracting gold from .—Dioscorides... has described the process of subliming mercury from its ores.—Even Cleopatra... might be considered as an experimenter, because... she dissolved a pearl in vinegar... but it is idle to relate such circumstances as indications of science."

"[N]ot even distillation is noticed in the works of Hippocrates or Galen; and... Dioscorides... who probably possessed whatever knowledge was at that time extant in Egypt, recommends the use of a fleece of wool or a sponge, for collecting the products from boiling or burning substances."

"The origin of chemistry, as a science of experiment, cannot be dated farther back than the seventh or eighth century of the Christian era, and it seems to have been coeval with the short period in which cultivation and improvements were promoted by the Arabians."

"The early nomenclature of chemistry demonstrates how much it owes to the Arabians.—The words alcohol, , , , , require no comment."

"The first Arabian systematic works on chemistry are said to have been composed by Geber... The preparation of medicines seems to have been the primary object in this study; and Rhases, Avicenna, and Avenzoar, who have described various chemical operations in their works, were the celebrated physicians of the age."

"[E]early chemical discoveries led to the pursuit of alchemy, the objects of which were to produce a substance capable of converting all other metals into gold: and an universal remedy calculated indefinitely to prolong the period of human life."

"The processes supposed to relate to the transmutation of metals, and the , were probably first made known to the Europeans during the time of the ..."

"The public spirit in the West, was calculated to assist the progress of all pursuits that carried with them an air of mysticism. Warm with the ardour of an extending and exalted religion, men were much more disposed to believe than to reason;—the love of knowledge and power is instinctive in the human mind; in darkness it desires light, and follows it with enthusiasm even when appearing merely in delusive glimmerings."

"The records of the middle ages contain a great variety of anecdotes relating to... pretensions of persons considered as adepts in alchemy... Some of the alchemists were low impostors, whose object was to delude the credulous and the ignorant; others seemed to have deceived themselves with vain hopes; but all followed the pursuit as a secret and mysterious study. The processes were communicated only to chosen disciples, and being veiled in the most enigmatic and obscure language, their importance was enhanced by the concealment."

"In all times men are governed more by what they desire or fear, than by what they know; and in [the middle ages] it was peculiarly easy to deceive, but difficult to enlighten, the public mind; truths were discovered but they were blended with the false and marvellous; and another era was required to separate them from absurdities, and to demonstrate their importance and uses."

"Arnald of Villa Nova... was one of the earliest European inquirers who attended to chemical operations. ...[H]e firmly believed in the transmutation of metals; the same opinions are attributed to him and to Geber; and he seems to have followed the study with no other views than those of preparing medicines, and attempting the composition of the philosopher's stone."

"That the delusions of alchemy were ardently pursued... may be learned from a reference to the public acts... ... openly condemned the alchemists as impostors, and the bull begins by stating, that "they promise what they do not perform;" and in England an act of Parliament was passed in the fifth year of the reign of Henry IV. prohibiting the attempts at transmutation, and making them felonious."

"In the beginning of the thirteenth century, Roger Bacon of Oxford applied himself to experiment, and his works offer proofs of talents, industry, and sagacity. He was a man of a truly philosophical turn desirous of investigating nature... but neither his labours nor those of Albert of Cologne, his contemporary, who appears to have been a genius of a kindred character, had any considerable influence on the improvement of their age."

"The wonders performed by the experimental art were attributed by the vulgar to magic; and at a time when knowledge belonged only to the cloister, any new philosophy was... regarded even by the learned with a jealous eye."

"of deserves [attention] on account of the novelty and variety of his experiments on metallic preparations, particularly : in his Currus triumphalis Antimonii https://books.google.com/books?id=J66EAAAAIAAJ&pg=PA11 The triumphal chariot of Antimony he has described a number of the combinations of this metal. He used the s for solutions, and seems to have been one of the first persons who observed the production of ether from alcohol."

"Cornelius Agrippa... was born at Cologne in 1486, openly professed magic and endeavoured to connect... , the hermetic art, and metaphysical philosophy; and he was followed by Paracelsus, in Switzerland and Digby, Kelly, and Dee, in England."

"The first Arabian Alchemists seem to have adopted the idea that the elements were under the dominion of spiritual beings who might be submitted to human power..."

"The speculative ideas of the Arabians were more or less adopted by their European disciples. The Rosicrucian philosophy in which gnomes, s, salamanders, and s were the spiritual agents, supposed capable of being governed or enslaved by man, seems to have originated with the alchemists of this period; and Agrippa, Paracelsus, and their followers... professed to believe in supernatural powers, in an art above experiment, in a system of knowledge not derived from the senses."

"Paracelsus... deserves... notice from the circumstance of his being the first public lecturer on chemistry in Europe, and from... his application of mercurial preparations to the cure of diseases. The magistrates of Basle established a professor's chair for their countryman, but he soon quitted an occupation in which regularity was necessary, and spent his days in wandering from place to place, searching for, and revealing secrets. He pretended to confer immortality, by his medicines, and yet died at the age of 49..."

"The enthusiasm [of Paracelsus] almost supplied his want of genius. He formed a number of new preparations of the metals, which were studied and applied by his disciples; his exaggerated censure of the methods of the ancients, and of the systems of his day, had an effect in diminishing their popularity; one error was expelled by another; and it is a great step towards improvement, that men should know they have been in delusion."

"Van Helmont of ... was formed in the school of Alchemy, and his mind was tinctured with its prejudices: but his views concerning nature and the elements were distinguished by much more philosophical acuteness, and more sagacity, than those of any former writer. He is the first person who seems to have had any idea respecting elastic fluids, different from the air of the atmosphere; and he has distinctly mentioned three of these substances, to which he applied the term es: namely aqueous gas or steam, unctuous or inflammable gas, and gas from wood or carbonic acid gas. Van Helmont developed some accurate views respecting the permanent elasticity of air, and the operation of heat upon it; and a sketch of a curious instrument very similar to the differential thermometer, is to be found in his works."

"Van Helmont has used a term not so applicable or intelligible as gas, namely, Blas; which he supposed to be an influence derived from the heavenly bodies, of a most subtile and etherial nature; and on the idea of its operations in our terrestrial system, he has endeavoured to found the vindication of astrology."

"At this period there was no taste in the public mind to restrain vain imaginations. There were no severe critics to correct the wanderings of genius. The systems of logic, adopted in the schools, were founded rather upon the analogies of words than upon the relations of things; and they were more calculated to conceal error, than to discover truth."

"Till the revival of literature in Europe, there was no attempt at philosophical discussion in any of the sciences; the diffusion of letters gradually brought the opinions of men to the standard of nature and truth; failures in the experimental arts produced caution, and the detection of imposture created rational scepticism."

"The delusions of Alchemy were exposed by Guibert, Gassendi, and Kepler. Libavius answered Guibert in a tone which demonstrated the weakness of his cause. This person was the last active experimentalist who believed that transmutation had actually been performed; and in the beginning of the 17th century the processes of rational chemistry were pursued by a number of enlightened persons..."

"George Agricola published, in 1542, his twelve books, '... on the methods of extracting and purifying the useful metals; and he was followed by Lazarus Erckern, Assay-Master General of the Empire of Germany, whose works, brought forward in 1574, contain a number of useful practices detailed in a simple and perspicuous manner."

"Lord Bacon happily described the Alchemists as similar to those husbandmen who in searching for a treasure supposed to be hidden in their land, by turning up and pulverising the soil, rendered it fertile; in seeking for brilliant impossibilities, they sometimes discovered useful realities; and in speaking of the chemistry of his time, he says, a new philosophy has arisen from the furnaces, which has confounded all the reasonings of the ancients. This illustrious man himself pointed out many important objects of chemical inquiry; but he was a still greater benefactor to the science, by his development of the general system for improving natural knowledge. Till his time there had been no distinct views concerning the art of experiment and observation."

"Lord Bacon demonstrated how little could be effected by the unassisted human powers, and the weakness of the strongest intellect... without artificial resources. He directed the attention of inquirers to instruments for assisting the senses, and for examining bodies under new relations. He taught that Man was but the servant and interpreter of Nature; capable of discovering truth in no other way but by observing and imitating her operations; that facts were to be collected and not speculations formed; and that the materials for the foundations of true systems of knowledge were to be discovered, not in the books of the ancients, not in metaphysical theories, not in the fancies of men, but in the visible and tangible external world."

"Though Van Helmont had formed some just notions respecting the properties of air, yet his views were blended with obscure and vague speculations; and it is to the disciples of Galileo that the true knowledge of the mechanical qualities and agencies of elastic fluids is owing. After Torricelli and Pascal had shewn the pressure and weight of the atmosphere, the investigation of its effects in chemical operations became an obvious problem."

"John Rey is generally quoted as the first person who shewed by experiments that air is fixed in bodies during ; but it appears from the work of this acute and learned man that he reasoned upon the processes of others rather than upon his own observations. He quotes [Modestinus] Fachsius, Libavius, Cesalpin, and Cardan, as having ascertained the increase of weight of during its conversion into a , and he mentions an experiment of Hammerus Poppius, who found that calcined by a burning-glass, notwithstanding the loss of vapours, yet was heavier after the process.."

"Rey ridicules the various notions of the Alchemists on the cause of this phenomenon; and ascribes it to the union of air with the metal; he supposes that air is miscible with other bodies besides metals, and states distinctly that it may be expelled from water."

"The observations of John Rey seem to have excited no attention amongst his contemporaries. The philosophical spirit was only beginning to animate chemistry, and the labourers in this science, occupied by their own peculiar processes, were little disposed to listen to the reasonings of an inquirer in general science; yet, though the most active of the forms of matter were neglected in the processes of the operative chemists of this day, and consequently no just views formed by them, still they discovered a number of important facts respecting the combinations and agencies of solid and fluid bodies."

"Glauber at Amsterdam, about 1640, made known several neutral salts, and several compounds of metallic and vegetable substances."

"Kunckel in Saxony and Sweden, pursued technical chemistry with very great success, and was the first person who made any philosophical experiments upon , which was accidentally discovered by Brandt in 1669."

"[Jacob] Barner in Poland, and Glaser in France, published elementary books on the science, and Borichius in Denmark, Bohn at Leipzic, and Hoffman at Halle pursued... scientific investigations with much zeal and success; and Hoffman was the first person who attempted the philosophical analysis of s."

"About the middle of this [17th] century... mathematical and physical investigations were pursued in every part of the civilized world with an enthusiasm before unknown. The new mode of improving knowledge by collecting facts, associated a number labourers in the same pursuit. It was felt that the whole of nature was yet to be investigated... distinct subjects connected with utility... sufficient to employ all enquirers, yet tending to the common end of promoting the progress of the human mind. Learned bodies were formed in Italy, England, and France, for the purpose of the interchange of opinions, the combination of labour and division of expense in performing new experiments, and the accumulation and diffusion of knowledge. The Academy del Cimento was established in 1651 under the patronage of the Duke of Tuscany; the of London, in 1660; the Royal Academy of Sciences of Paris, in 1666."

"The ardour of scientific investigation was excited and kept alive by sympathy: taste was improved by discussion, and by a comparison of opinions. The conviction that useful discoveries would be appreciated and rewarded, was a constant stimulus to industry, and every field of enquiry was open for the free and unbiassed exercise of the powers of genius."

"Boyle, Hooke, and Slare, were the principal early chemical investigators attached to the of London. Homberg, Geoffroy, and the two Lemerys Nicolas & Louis], a few years later, distinguished themselves in France."

"Otto de Guericke of invented the air pump; and this instrument, improved by Boyle and Hooke, was made an important apparatus for investigating the properties of air."

"Boyle and Hooke, from their experiments, concluded that air was absolutely necessary to combustion and respiration, and that one part of it only was employed in these processes. And Hooke formed the sagacious conclusion, that this principle is the same as the substance fixed in nitre and that is a chemical process, the solution of the burning body in elastic fluid, or its union with this matter."

"Mayow of Oxford, in 1674, published his treatises on the nitro-ærial spirit, in which he advanced opinions similar to those of Boyle and Hooke, and supported them by a number of original and curious experiments; but his work, though marked by strong ingenuity, abounds in vague hypotheses. He attempted to apply the imperfect chemistry of his day to physiology; his failure was complete, but it was the failure of a man of genius."

"Boyle was one of the most active experimenters, and certainly the greatest chemist of his age. He introduced the use of tests or s, active substances for detecting the presence of other bodies: he overturned the [prevalent] ideas... that the results of operations by fire were the real elements of things, and he ascertained... important facts respecting inflammable bodies, s, es, and the phænomena of combination; but neither he nor any of his contemporaries endeavoured to account for the changes of bodies by any fixed principles."

"The solutions of the phænomena were attempted either on rude mechanical notions, or by occult qualities, or peculiar subtile spirits or ethers supposed to exist in the different bodies.—And it is to the same great genius who developed the laws that regulate the motions of the heavenly bodies, that chemistry owes the first distinct philosophical elucidations of the powers which produce the changes and apparent transmutations of the substances belonging to the earth."

"dissolves in water, es unite with s, s dissolve in acids. Is not this, says Newton, on account of an attraction between their particles? Copper dissolved in aquafortis is thrown down by . Is not this because the particles of the iron have a stronger attraction for the particles of the acid, than those of copper: and do not different bodies attract each other with different degrees of force?"

"A few years after Newton had brought forwards these sagacious views, the elder Geoffroy endeavoured to ascertain the relative attractive powers of bodies for each other and to arrange them in an order in which these forces which he named affinities were expresed."

"Chemistry had scarcely begun to assume the form of a science, when the attention of the most powerful minds were directed to other objects of research;—the same great man who bestowed on it its first accurate principles, in some measure impeded its immediate progress, by his more important discoveries in optics, mechanics, and astronomy."

"These objects of the Newtonian philosophy were calculated by their grandeur, their simplicity, and their importance, to become the study of the men of most distinguished talents; the effect that they occasioned on the scientific mind may be compared to that which the new sensations of vision produce on the blind receiving sight;—they awakened the highest interest, the most enthusiastic admiration, and for nearly half a century, absorbed the attention of the most eminent philosophers of Britain and France."

"Germany still continued the great school of practical chemistry, and at this period it gained an ascendancy of no mean character over the rest of Europe in the philosophy of the science."

"Beccher, ...after having studied with minute attention, the operations of , and the phænomena of the kingdom, formed the bold idea of explaining the whole system of the earth by the mutual agency and changes of a few elements. And by supposing the existence of a vitrifiable, a metallic, and an inflammable earth, he attempted to account for the various productions of rocks, crystalline bodies, and metallic veins, assuming a continued interchange of principles between the atmosphere, the ocean, and the solid surface of the globe, and considering the operations of nature as all capable of being imitated by art."

"Beccher's] Physica subterranea and... Oedipus chemicus... are... extraordinary productions. They display the efforts of a vigorous mind, the conceptions of a most fertile imagination, but the conclusions are too rapidly formed; there is a want of logical precision in his reasonings; the objects he attempted were grand, but his means of execution comparatively feeble. He endeavoured to raise a perfect and lasting edifice upon foundations too weak, from materials too scanty and not sufficiently solid; and the work, though magnificent in design, was rude unfinished and feeble, and rapidly fell into decay."

"Beccher added very little to the collection of chemical experiments, but he improved the instruments of research, simplified the manipulations, and by the novelty and boldness of his speculations, excited enquiry amongst his disciples."

"Beccher's] most distinguished follower was George Ernest Stahl... who soon attained a reputation superior to that of his master, and developed doctrines which for nearly a century constituted the theory of chemistry of the whole of Europe."

"Albertus Magnus had advanced the idea that the metals were earthy substances impregnated with a certain inflammable principle. Beccher supported the idea of this principle, not only as the cause of metallization, but likewise of combustibility: and Stahl endeavoured, by a number of ingenious and elaborate experiments, to prove the existence of phlogiston... and to explain its agencies in the phænomena of nature and art."

"Glauber, about fifty years before Stahl.., had discovered Glauber's salt,] the combination of fossil alkali and sulphuric acid, which still bears his name."

"Stahl, in operating upon [Glauber's salt], thought he had discovered the proof, that the inflammability not only of metals, but likewise of all other substances, was owing to the same principle phlogiston]. is entirely dissipated or consumed in combustion, therefore, says this philosopher, it must be phlogiston nearly pure; by heating charcoal with metallic earths, they become metals; therefore they are compounds of metallic earths and phlogiston: by heating Glauber's salt, which consists of sulphuric acid and fossil alkali, with charcoal, a compound of sulphur and is obtained; therefore sulphur is an acid combined with phlogiston."

"Stahl entirely neglected the chemical influence of air on these phenomena; and though Boyle had proved that and sulphur would not burn without air, and had stated that sulphur was contained in sulphuric acid, and not the acid in sulphur, yet the ideas of the Prussian school were received without controversy."

"Similar opinions were adopted in France by Homberg and Geoffroy, who... opposed them to the more correct and sagacious views of the English school of chemistry."

"Though misled in his general notions, few men have done more than Stahl for the progress of chemical science.—His processes were, many of them, of the most beautiful and satisfactory kind: he discovered a number of properties of the caustic es and metallic calces, and the nature of sulphureous acid; he reasoned upon all the operations of chemistry in which gaseous bodies were not concerned, with admirable precision. He gave an axiomatic form to the science, banishing from it vague details, circumlocutions and enigmatic descriptions, in which even Beccher had too much indulged; he laboured in the spirit of the Baconian school, multiplying instances, and cautiously making inductions, and appealing in all cases to experiments which, though not of the most refined kind, were more perfect than any which preceded them."

"Dr. Hales... resumed the investigations commenced with so much success by Boyle, Hooke, and Mayow; and endeavoured to ascertain the chemical relations of air to other substances, and to ascertain by statical experiments the cases in nature, in which it is absorbed or emitted. ...[B]ut, misled by the notion of one elementary principle constituting elastic matter... he formed few inferences connected with the refined philosophy of the subject..."

"In 1756 Dr. Black published his admirable researches on , magnesian, and alkaline substances, by which he proved the existence of a gaseous body, perfectly distinct from the air of the atmosphere. He shewed that quicklime differed from and by containing this substance, and that it was a weak acid capable of being expelled from alkaline and earthy substances by strong acids. Ideas so new and important... were not received without opposition; several German enquirers endeavoured to controvert them."

"[Johann Friedrich von] Meyer attempted to shew that limestones became caustic, not by the emission of elastic matter, but by combining with a peculiar substance in the fire; but the loss of weight was perfectly inconsistent with this view..."

"Bergman at Upsal, Macbride in Ireland, Keir at Birmingham, and Cavendish in London, demonstrated the correctness of the opinions of Black; and a few years were sufficient to establish his theory upon immutable foundations."

"The knowledge of one elastic fluid different from air, immediately led to the enquiry whether there might not be others."

"The processes of which had been observed by the ancient chemists, and those [processes] by which Hales had disengaged and collected elastic substances, were now regarded under a novel point of view; and the consequence was, that a number of new bodies, possessed of very extraordinary properties, were discovered."

"Mr. Cavendish, about 1765, invented an apparatus for examining elastic fluids confined by water, which has been since called the hydro-pneumatic apparatus. He discovered inflammable air, and described its properties; he ascertained the relative weights of fixed air, inflammable air, and common air, and made... beautiful and accurate experiments on the properties of these elastic substances."

"Dr. Priestley, in 1771, entered the same interesting path of enquiry; and principally by repeating the processes of Hales, added a number of most important facts to this department of chemical philosophy. He discovered nitrous air, , and dephlogisticated air; and by substituting mercury for water in the pneumatic apparatus, ascertained the existence of several æriform substances, which are rapidly absorbable by water, muriatic acid air, sulphurous acid air, and ."

"Whilst a new branch of the science was making this rapid progress in Britain, the chemistry of solid and fluid substances was pursued with considerable zeal and success in France and Germany; and Macquer, Rouelle, Margraff, and [John Henry] Pott, added considerably to the knowledge of fossile bodies, and the properties of the metals."

"Bergman, in Sweden, developed refined ideas on the powers of chemical attraction, and reasoned in a happy spirit of generalization on many of the new phænomena of the science; and in the same country Scheele, independently of Priestley, discovered several of the same æriform substances; he ascertained the composition of the atmosphere; he brought to light fluoric acid, prussic acid, and the substance which has been improperly called oxymuriatic gas."

"Black, Cavendish, Priestley, and Scheele, were undoubtedly the greatest chemical discoverers of the eighteenth century; and their merits are distinct, peculiar, and of the most exalted kind. Black made a smaller number of original experiments than either of the other philosophers; but being the first labourer in this new department of the science, he had greater difficulties to overcome."

"[Black's] methods are distinguished for their simplicity, his reasonings are admirable for their precision; and his modest, clear, and unaffected manner, is well calculated to impress upon the mind a conviction of the accuracy of his processes, and the truth and candour of his narrations."

"Cavendish was possessed of a minute knowledge of most of the departments of Natural Philosophy: he carried into his chemical researches a delicacy and precision, which have never been exceeded; possessing depth and extent of mathematical knowledge, he reasoned with the caution of a geometer upon the results of his experiments; and it may be said of him, what, perhaps, can scarcely be said of any other person, that whatever he accomplished, was perfect at the moment of its production."

"[Cavendish's] processes were all of a finished nature; executed by the hand of a master, they required no correction; the accuracy and beauty of his earliest labours even, have remained unimpaired amidst the progress of discovery, and their merits have been illustrated by discussion, and exalted by time."

"Dr. Priestley began his career of discovery without any general knowledge of chemistry, and with a very imperfect apparatus. His characteristics were ardent zeal and the most unwearied industry. He exposed all the substances he could procure to chemical agencies, and brought forward his results as they occurred, without attempting logical method or scientific arrangement."

"[Priestley's] hypotheses were usually founded upon a few loose analogies; but he changed them with facility; and being framed without much effort, they were relinquished with little regret."

"[Priestley] possessed in the highest degree ingenuousness and the love of truth. His manipulations, though never very refined, were always simple, and often ingenious. Chemistry owes to him some of her most important instruments of research, and many of her most useful combinations; and no single person ever discovered so many new and curious substances."

"Scheele possessed in the highest degree the faculty of invention; all his labours were instituted with an object in view, and after happy or bold analogies. He owed little to fortune or to accidental circumstances; born in an obscure situation, occupied in the duties of an irksome employment, nothing could damp the ardour of his mind or chill the fire of his genius: with very small means he accomplished very great things. No difficulties deterred him from submitting his ideas to the test of experiment. Occasionally misled in his views, in consequence of the imperfection of his apparatus, or the infant state of the inquiry, he never hesitated to give up his opinions the moment they were contradicted by facts."

"[Scheele] was eminently endowed with that candour which is characteristic of great minds, and which induces them to rejoice as well in the detection of their own errors, as in the discovery of truth. His papers are admirable models of the manner in which experimental research ought to be pursued; and they contain details on some of the most important and brilliant phænomena of chemical philosophy."

"The discovery of the ses, of a new class of bodies, more active than any others in most of the phænomena of nature and art, could not fail to modify the whole theory of chemistry. The ancient doctrines were revised; new modifications of them were formed by some philosophers; whilst others discarded entirely all the former hypotheses and endeavoured to establish new generalizations."

"The idea of a peculiar principle of inflamability was so firmly established in the chemical schools, that even the knowledge of the composition of the atmosphere for a long while was not supposed to interfere with it; and the part of the atmosphere which is absorbed by bodies in burning, was conceived to owe its powers to its attraction for phlogiston."

"All the modern chemists who made experiments upon combustion, found that bodies increased in weight by burning, and that there was no loss of ponderable matter. It was necessary therefore to suppose, contrary to the ideas of Stahl, that phlogiston was not emitted in combustion, but that it remained in the inflammable body after absorbing gaseous matter from the air."

"But what is phlogiston? was a question constantly agitated. Inflammable air had been obtained during the dissolution of certain metals, and during the distillation of a number of combustible bodies. This light and subtile matter, therefore, was fixed upon as the principle of inflammability, and Cavendish, Kirwan, Priestley, and Fontana, were the illustrious advocates of this very ingenious hypothesis."

"In 1774 Bayen shewed that mercury converted into a or earth, by the absorption of air, could be revived without the addition of any inflammable substance; and hence he concluded, that there was no necessity for supposing the existence of any peculiar principle of inflammability, in accounting for the calcination of metals."

"The subject, nearly about the same time was taken up by Lavoisier, who had been for some time engaged in repeating the experiments of the British philosophers. Bayen formed no opinion respecting the nature of the air produced from the calx of mercury. Lavoisier, in 1775, shewed that it was an air which supported flame and respiration better than common air, which he afterwards named oxygene; the same substance that Priestley and Scheele had procured from other metallic substances the year before, and had particularly described."

"Lavoisier discovered that the same air is produced during the revivification of metallic calces by , as that which is emitted during the calcination of limestone; hence he concluded that this elastic fluid is composed of oxygene and charcoal []; and from his experiments on and oil of vitriol he concluded that this gas entered into the composition of these substances."

"Dr. Black had demonstrated by a series of beautiful experiments, that when gases are condensed, or when fluids are converted into solids, heat is produced. In combustion gaseous matter usually assumes the solid or the fluid form."

"Oxygene gas, said Lavoisier, seems to be [a] compound of the matter of heat and a basis. In the act of burning, this basis is united to the combustible body, and the heat is evolved. There is no necessity, said this acute philosopher, to suppose any phlogiston, any peculiar principle of inflammability; for all the phænomena may be accounted for without this imaginary existence."

"Lavoisier must be regarded as one of the most sagacious of the chemical philosophers of the last century; indeed, except Cavendish, there is no other inquirer who can be compared to him for precision of logic, extent of view, and sagacity of induction. His discoveries were few, but he reasoned with extraordinary correctness upon the labours of others. He introduced weight and measure, and strict accuracy of manipulation into all chemical processes. His mind was unbiassed by prejudice; his combinations were of the most philosophical nature; and in his investigations upon ponderable substances, he has entered the true path of experiment with cautious steps, following just analogies, and measuring hypotheses by their simple relations to facts."

"The doctrine of Lavoisier, soon after it was framed, received some important confirmations from the two grand discoveries of Mr. Cavendish, respecting the composition of water, and ; and the elaborate and beautiful investigations of Berthollet respecting the nature of ; in which phænomena, before anomalous, were shewn to depend upon combinations of æriform matter."

"The notion of phlogiston, was however defended for nearly 20 years, by some philosophers in Germany, Sweden, Britain, and Ireland. Mr. Cavendish, in 1784, drew a parallel between the hypothesis, that all inflammable bodies contain inflammable air, and the doctrine in which they are considered as simple substances, in a paper equally remarkable for the precision of the views displayed in it, and for the accuracy and minuteness of the experiments it contains. To this great man, the assumption of M. Lavoisier, of the matter of heat, appeared more hypothetical than that of a principle of inflammability. He states, that the phænomena may be explained on either doctrine; but he prefers the earlier view, as accounting, in a happier manner, for some of the operations of nature."

"De Morveau, Berthollet, and Fourcroy, in France, and William Higgins and Dr. Hope, in Britain, were the first advocates for the anti-phlogistic chemistry. Sooner or later, that doctrine which is an expression of facts, must prevail over that which is an expression of opinion."

"The most important part of the theory of Lavoisier was merely an arrangement of the facts relating to the combinations of oxygene: the principle of reasoning which the French school professed to adopt was, that every body which was not yet decompounded, should be considered as simple; and though mistakes were made with respect to the results of experiments on the nature of bodies, yet this logical and truly philosophical principle was not violated; and the systematic manner in which it was enforced, was of the greatest use in promoting the progress of the science."

"Till 1786, there had been no attempt to reform the nomenclature of chemistry; the names applied by discoverers to the substances which they made known, were still employed. Some of these names, which originated amongst the alchymists, were of the most barbarous kind; few of them were sufficiently definite or precise, and most of them were founded upon loose analogies, or upon false theoretical views."

"It was felt by many philosophers, particularly by the illustrious Bergman, that an improvement in chemical nomenclature was necessary, and in 1787, Messrs. Lavoisier, Morveau, Berthollet, and Fourcroy, presented to the world a plan for an almost entire change in the denomination of chemical substances, founded upon the idea of calling simple bodies by some names characteristic of their most striking qualities, and of naming compound bodies from the elements which composed them."

"The new nomenclature was speedily adopted in France; under some modifications it was received in Germany; and after much discussion and opposition, it became the language of a new and rising generation of chemists in England. It materially assisted the diffusion of the antiphlogistic doctrine, and even facilitated the general acquisition of the science; and many of its details were contrived with much address, and were worthy of its celebrated authors: but a very slight reference to the philosophical principles of language will evince that its foundations were imperfect, and that the plan adopted was not calculated for a progressive branch of knowledge."

"Simplicity and precision ought to be the characteristics of a scientific nomenclature: words should signify things, or the analogies of things, and not opinions. If all the elements were certainly known, the principle adopted by Lavoisier would have possessed an admirable application; but a substance in one age supposed to be simple, in another is proved to be compound; and vice versa. A theoretical nomenclature is liable to continued alterations; oxygenated muriatic acid is as improper a name as dephlogisticated marine acid."

"Every school believes itself in the right; and if every school assumes to itself the liberty of altering the names of chemical substances, in consequence of new ideas of their composition, or decomposition, there can be no permanency in the language of the science, it must always be confused and uncertain."

"Bodies which are similar to each other should always be classed together; and there is a presumption that their composition is analogous."

"Metals, earths, alkalies, are appropriate names for the bodies they represent, and independant of all speculative views; whereas oxides, sulphurets, and muriates, are terms founded upon opinions of the composition of bodies, some of which have been already found erroneous."

"The least dangerous mode of giving a systematic form to a language, seems to be, to signify the analogies of substances by some common sign affixed to the beginning or the termination of the word. Thus, as the metals have been distinguished by a termination in um, as aurum, so their calciform or oxidated state, might have been denoted by a termination in a, as aura; and no progress, however great, in the science, could render it necessary that such a mode of appellation should be changed."

"Moreover, the principle of a composite nomenclature must always be very limited. It is scarcely possible to represent bodies consisting of five or six elements in this way, and yet it is in such difficult cases that a name implying a chemical truth would be most useful."

"The new doctrines of chemistry, before 1795, were embraced by almost all the active experimental enquirers in Europe; and the adoption of a precise mode of reasoning, and more refined forms of experiment, led not only to the discovery of new substances, but likewise to a more accurate acquaintance with the properties and composition of bodies that had long been known."

"New investigations were instituted with respect to all the productions of nature, and the immense variety of substances in the mineral, vegetable, and animal kingdom, submitted to chemical experiments."

"The analysis of mineral bodies first attempted by Pott in experiments principally on their igneous fusion, and afterwards refined by the application of acid and alkaline menstrua, by Margraaf, Bergman, Bayen, and Achard, received still greater improvements from the labours of Klaprothk, Vauquelin, and Hatchett."

"Hoffman, in the beginning of the 18th century, pointed out magnesia as a peculiar substance. Margraaf, about fifty years later, distinguished accurately between the silicious, , and aluminous earths. Scheele, in 1774, discovered s. Klaproth, in 1788, made known zircone. Dr. Hope, strontites in 791. Gadolin, ittria in 1794; and Vauquelin, glucine in 1798."

"Seven metals only had been accurately known to the ancients, gold, silver, mercury, copper, tin, and . , , , and , though mentioned by the Greek and Roman authors, yet were employed only in certain combinations, and the production of them in the form of reguli or pure metals, was owing to the Alchemists."

"had been used to tinge glass in in the sixteenth century; but the metal was unknown till the time of Brandt, and this celebrated Swedish chemist discovered it in 1733."

"was procured by Cronstedt in 1751."

"The properties of , which was announced as a peculiar metal by Kaim in 1770, were minutely investigated by Scheele and Bergman a few years after."

"was discovered by Scheele in 1778, and a metal procured from it by Hielm in 1782, the same year that tellurium was made known by Muller."

"Scheele discovered in 1781; and soon after a metal was extracted from it by Messrs. Fausto & Juan José] D' Elhuyars."

"Klaproth discovered uranium in 1789."

"The first description of the properties of the oxide of titanium was given by Gregor in 1791."

"Vauquelin made known chromium in 1797; Hatchett columbium in 1801; and shortly after, the same substance was noticed by Ekeberg, and named by him tantalium."

"Cerium was discovered in 1804, by Hissinger and Berzelius."

"Platina had been brought into Europe and examined by Lewis in 1749 and in 1803, Descotils, Fourcroy, and Vauquelin announced a new metallic substance in it; but the complete investigation of the properties of this extraordinary body was reserved for Messrs. Tennant and Wollaston, who in 1803 and 1804 discovered in it no less than four new metallic substances, besides the body which exists in it in the largest proportion, namely, iridium, osmium, palladium, and rhodium."

"The attempts made to analyse vegetable substances previous to 1720, merely produced their resolution into the supposed elements of the chemists of those days, namely, salts, Earths, phlegm, and sulphur. Boerhaave and Newmann attempted an examination by fluid menstrua, which was pursued with some success by Rouelle, Macquer and Lewis. Scheele, between 1770 and 1780, pointed out several new vegetable acids."

"Fourcroy, Vauquelin, Deyeux, Seguin, Proust, Jacquin, and Hermbstadt, between 1780 and 1790, in various interesting series of experiments, distinguished between different secondary elements of vegetable matter, particularly extract, , gums, and resinous substances; and investigations of this kind have been pursued with great success by Hatchett, Pearson, Shraeder, Chenevix, Gehlen, Thomson, Thenard, Chevreul, Kind, Brande, Bostock and Duncan. The chemistry of animal substances has received great elucidations from several of the same enquirers; and Berzelius has examined most of their results, and has added several new ones, in a comprehensive work expressly devoted to the subject, published in 1808."

"Mr. Howard, by an accurate examination of the testimonies... and by a minute analysis of the substances said to have fallen in different parts of the globe... shewed that... meteoric productions differed from any substances belonging to our earth."

"The philosophy of heat, the foundations of which were laid between 1757 and 1785, by Dr. Black, Wilcke, Crawford, Irvine, and Lavoisier, since that period has received some new and very important additions, from the inquiries of Pictet, Rumford, Herschel, Leslie, Dalton, and Gay Lussac."

"The circurmstances under which bodies absorb and communicate heat, have been minutely investigated; and the important discoveries of the different physical and chemical powers of the different solar rays, and of a property analogous to polarity in light, bear immediate relation to the most refined doctrines of corpuscular science, and promise to connect by close analogies, the chemical and mechanical laws of matter."

"A general view of the philosophy of chemistry was published under the name of Chemical Statics, in 1803, by the celebrated Berthollet. It is a work remarkable for the new views that it contains on the doctrines of attraction; views which are still objects of discussion, and which bear an immediate relation to some of the conclusions depending upon very recent discoveries."

"At the time when the antiphlogistic theory was established, electricity had little or no relation to chemistry. The grand results of Franklin, respecting the cause of lightning, had led many philosophers to conjecture, that certain chemical changes in the atmosphere, might be connected with electrical phænomena;—and electrical discharges had been employed by Cavendish, Priestley, and Vanmarum, for decomposing and igniting bodies; but it was not till the era of the wonderful discovery of Volta, in 1860, of a new electrical apparatus, that any great progress was made in chemical investigation by means of electrical combinations."

"Nothing tends so much to the advancement of knowledge as the application of a new instrument. The native intellectual powers of men in different times, are not so much the causes of the different success of their labours, as the peculiar nature of the means and artificial resources in their possession. Independent of vessels of glass, there could have been no accurate manipulations in common chemistry: the air pump, was necessary for the investigation of the properties of gaseous matter; and without the Voltaic apparatus, there was no possibility of examining the relations of electrical polarities to chemical attractions."

"By researches, the commencement of which is owing to Messrs. Nicholson and Carlisle, in 1800, which were continued by Cruickshank, Henry, Wollaston, Children, Pepys, Pfaff, Desormes, Biot, Thenard, Hissinger, and Berzelius, it appeared that various compound bodies were capable of decomposition by electricity; and experiments, which it was my good fortune to institute, proved that several substances which had never been separated into any other forms of matter in the common processes of experiment, were susceptible of analysis by electrical powers; in consequence of these circumstances, the fixed es and several of the earths have been shewn to be metals combined with oxygene; various new agents have been furnished to chemistry, and many novel results obtained by their application, which at the same time that they have strengthened some of the doctrines of the school of Lavoisier, have overturned others, and have proved that the generalizations of the Antiphlogistic philosophers were far from having anticipated the whole progress of discovery."

"Certain bodies which attract each other chemically, and combine when their particles have freedom of motion, when brought into contact, still preserving their aggregation, exhibit what may be called electrical polarities; and by certain combinations these polarities may be highly exalted; and in this case they become subservient to chemical decompositions; and by means of electrical arrangements the constituent parts of bodies are separated in an uniform order, and in definite proportions."

"Bodies combine with a force, which in many cases is correspondent to their power of exhibiting electrical polarity by contact; and heat, or heat and light, are produced in proportion to the energy of their combination. Vivid inflammation occurs in a number of cases in which gaseous matter is not fixed; and this phenomenon happens in various instances without the interierence of free or combined oxygene."

"Experiments made by Richter and Morveau had shewn that, when there is an interchange of elements between two neutral salts, there is never an excess of or basis; and the same law seems to apply generally to double decompositions."

"When one body combines with another in more than one proportion, the second proportion appears to be some multiple or divisor of the first; and this circumstance, observed and ingeniously illustrated by Mr. Dalton, led him to adopt the atomic hypothesis of chemical changes, which had been ably defended by Mr. Higgins in 1789, namely, that the chemical elements consist of certain indestructible particles which unite one and one, or one and two, or in some definite [] numbers."

"Whether matter consists of indivisible corpuscles, or physical points endowed with attraction and repulsion, still the same conclusions may be formed concerning the powers by which they act, and the quantities in which they combine; and the powers seem capable of being measured by their electrical relations, and the quantities on which they act of being expressed by numbers."

"In combination certain bodies form regular solids; and all the varieties of crystalline aggregrates have been resolved by the genius of Haüy into a few primary forms."

"The laws of crystallization, of definite proportions, and of the electrical polarities of bodies, seem to be intimately related; and the complete illustration of their connection, probably will constitute the mature age of chemistry."

"The just fame of those who have enlightened the science by new and accurate experiments, cannot fail to be universally acknowledged; and concerning the publication of novel facts there can be but one judgment; for facts are independent of fashion, taste, and caprice, and are subject to no code of criticism; they are more useful perhaps even when they contradict, than when they support received doctrines, for our theories are only imperfect approximations to the real knowledge of things; and in physical research, doubt is usually of excellent effect, for it is a principal motive for new labours, and tends continually to the developement of truth."

"From the first discovery of the production of metals from rude ores, to the knowledge of the bleaching liquor, chemistry has been continually subservient to cultivation and improvement."

"In the manufacture of porcelain and glass, in the arts of dying and tanning, it has added to the elegancies, refinement, and comforts of life; in its application to medicine it has removed the most formidable of diseases; and in leading to the discovery of gunpowder, it has changed the institutions of society..."

"It is... a double source of interest in this science, that whilst it is connected with the grand operations of nature, it is likewise subservient to the common processes as well as the most refined arts of life. New laws cannot be discovered in it, without increasing our admiration of the beauty and order of the system of the universe; and no new substances can be made known which are not sooner or later subservient to some purpose of utility."

"When the great progress made in chemistry within the last few years is considered, and the number of able labourers who are at present actively employed in cultivating the science, it is impossible not to augur well concerning its rapid advancement and future applications. The most important truths belonging to it are capable of extremely simple numerical expressions, which may be acquired with facility by students; and the apparatus for pursuing original researches is daily improved, the use of it rendered more easy, and the acquisition less expensive."

"Complexity almost always belongs to the early epochs of every science; and the grandest results are usually obtained by the most simple means."

"A great part of the phaenomena of chemistry may be already submitted to calculation; and there is great reason to believe, that at no very distant period the whole science will be capable of elucidation by mathematical principles."

"The relations of the common metals to the bases of the alkalies and earths, and the gradations of resemblance between the bases of the earths and acids, point out as probable a similarity in the constitution of all inflammable bodies; and there are not wanting experiments, which render their possible decomposition far from a chimerical idea."

"It is contrary to the usual order of things, that events so harmonious as those of the system of the earth, should depend on such diversified agents, as are supposed to exist in our artificial arrangements; and there is reason to anticipate a great reduction in the number of the undecompounded bodies, and to expect that the analogies of nature will be found conformable to the refined operations of art."

"The more the phaenomena of the universe are studied, the more distinct their connection appears, the more simple their causes, the more magnificent their design, and the more wonderful the wisdom and power of their Author."

"Humphry Davy's objection to Bacon has not been found. In "Historical View of the Progress of Chemistry" in Elements of Chemical Philosophy (1812) Davy cited Bacon's Preface in Instauratio magna in support of his own rejection of Aristotle's "erroneous practice" of advancing general principles for application to particular instances, "so fatal to truth in all sciences". ...In his works Davy typically praised Bacon for his knowledge and novelty..."

"This historical sketch has no pretensions to originality. It is compiled from the best authors, and from the Introduction to Sir H. Davy's Elements of Chemical Philosophy."

"The late Dr. Campbell Brown was accustomed, as part of his Chemical Course at Liverpool University, to deliver a series of Lectures on the History of Chemistry. These lectures were to him a labour of love, and were prepared after much research... It was his intention... to revise the lectures and to put them into shape for publication. But death put a sudden term to his labours... and the lectures were left in the form of manuscript notes, more or less complete, but not in that perfect shape which Dr. Campbell Brown would have wished... to be published."

"Mrs. Campbell Brown and the friends of the Author considered that it would be matter for deep regret if his... History were not carried into effect, and... made available to students and others interested in the subject."

"[I]t seemed good to Mrs. Campbell Brown to entrust the writer with the duty of editing... and passing the work through the press."

"[The editor] has endeavoured to present the substance of the lectures as nearly as possible in the shape in which Dr. Campbell Brown used to deliver them, subject to... changing them... to the form of a book... [I]t may be that in some instances the notes of Dr. Campbell Brown have been misunderstood. ...[T]he Editor, knowing the extreme accuracy of the Professor, requests that such slips may be attributed, not to the Author, but to himself."

"James Campbell Brown was born at , on January 31st, 1843. His father... soon removed to London as principal partner of the Bow Common Alum Works."

"[I]n 1863 he proceeded to the Royal College of Chemistry at London, where he studied under Tyndall and Hofmann, at the same time matriculating at London University. ...in 1870... obtaining the degree of Doctor of Science."

"With a elear perception of whatever object he had for the time being set before him, with indomitable courage to fight against a delicate constitution and indifferent health, and with a determination which would be satisfied with no half-measures, but would insist that whatever was done should be rightly done, he was a true representative of [his] family..."

"One of my earliest recollections of my cousin, who was my senior by thirteen years, is of wandering with him in a field searching for a bulbous crowfoot... [A]t a later date it was on his initiative, and with his assistance and encouragement, that I began the amateur study of chemistry from which I acquired a knowledge of its practice and principles sufficient to enable me to undertake the editing of the present work."

"Educational and scientific matters... provided for him a field of usefulness in which he was occupied for the greater part of his life, and to which he devoted all his gifts of organisation, hard work, and self-denial."

"In the new College he occupied the Chair of Chemistry, and found a fresh field of work in organising the duties of the Chair, and planning and equipping the classrooms and laboratories which were essential for their performance. The Chemical Laboratories were built in 1884 and extended two years later, while in 1896-7 the Wilham Gossage Laboratory was opened and rooms were added for Metallurgy, Electro-Chemistry, and Gas Analysis. The whole forms one of the most perfect installations for the teaching of chemistry, which is to be found in this country."

"He was in 1872 appointed’Public Analyst for Liverpool under the Adulteration of Food Act, and received a similar appointment for Lancashire in 1875. ...In addition, he was analyst to the Water Committee for the City of Liverpool, and to all the Local Authorities in the administrative county of Lancashire, and was frequently consulted in reference to large schemes of public water supply, both at home and abroad."

"How his services were appreciated by those who were associated with him in the Water Undertaking, may be estimated from the following extract from the Report of Mr. Joseph Parry, the Water Engineer, for the year 1910:—"He was a rigid guardian of the purity of the supply, and it was an enormous advantage to the Corporation to have the professional assistance of one who had attained to such eminence and influence as a chemist.""

"He was skilled in forensic chemistry, and was engaged in a number of criminal cases involving the use of poisons. His experience in the matter of arsenic poisoning was unique."

"He was one of the original members of the Society of Chemical Industry, and as the result of a long series of experiments in the analysis of soils and examination of tea-plants, devised a fertiliser for use in tea plantations in India. Where it was adopted, this fertiliser raised the tea production from 397 to 494 pounds per acre, and it is characteristic of him that he refused... pecuniary return from its very extensive use."

"His "Practical Chemistry" is now in its sixth edition."

"He made several ingenious inventions. An apparatus for the direct determination of the latent heat of evaporation was awarded two gold medals at the Franco-British Exhibition at London in 1908. ...[T]his apparatus was exhibited at the Japan-British Exhibition in 1910, and along with it another invention—an apparatus for fractional distillation of fats and fatty acids in the vacuum of the cathode light. Both of these exhibits were again shown in 1911 at the Coronation Exhibition in London."

"The University of Aberdeen in 1907 conferred upon him the Degree of Doctor of Laws. In 1908 he was elected Vice-President of the Chemical Society of London, an office which he held at the time of his death. The Council of the Institute of Civil Engineers awarded to him in 1904 the Mamby Premium for a paper on "Deposits in Pipes and other Channels conveying notable water." He was a member or an honorary member of numerous scientific bodies..."

"He had suffered from an attack of influenza... [H]eart failure ensued and he died... March 14th, 1910. ...[H]e was called away without the trial of a lingering illness. He died in harness, for he was giving instructions to his secretary about examinations, and signing certificates, till within ten minutes of the end."

"I have failed in my purpose, if I have not made plain two points—his devotion to duty, and his thoroughness. He took life at a gallop; he never spared himself when duty was to be done; and he was not satisfied with any attainment short of absolute precision and completeness. In that single sentence his biography is comprised."

"The art of alchemy was now to receive an impulse in a new direction."

"In the hands of the fourteenth century alchemists and their immediate successors, its main object had become the discovery of that mysterious powder or elixir, which was to bring about universal perfection, to raise the baser metals to the perfect gold, and to endow human beings with eternal youth."

"At this stage a great, though erratic, genius appeared on the scene, and opened up a fresh channel, into which students of chemical science might thenceforth direct their energies."

"Paracelsus (1493—1541), who gave his name as Philippus Aureolus Theophrastus Paracelsus Bombastes ab Hohenheim, created in his day more stir than any other alchemist, for he shook the faith of the world in Galen and Avicenna, and was thus the means of introducing a new era."

"[A]lthough there is no reason to doubt that he was gifted with original genius... he was on the whole a vain and self-seeking quack, who neither understood the nature of chemical science, nor undertook any regular or successful investigation. But he condemned loudly and boldly all medical knowledge and all medical practitioners, except himself, and his own methods. By these means, and by some cures which he effected, partly by bold treatment, partly by good luck, he made such a reputation for himself that he freed the medical world from old trammels."

"He roused the mental energy of medical men by calling their attention to the importance of chemical medicines and chemical investigations, and in consequence, workers arose who studied the preparations and reactions of those metals which were most likely to be useful in medicine, and by their efforts the store of chemical knowledge was rapidly increased."

"His father, Wilhelm von Hohenheim, was a physician and taught him alchemy, astrology, and medicine."

"After a short period spent at the University of Basle, [Paracelsus] became a wandering scholar, practising medicine and picking up knowledge over the greater part of Europe, Egypt, and ."

"He had little university training, but worked long and earnestly with the wealthy Sigismond Fuggerus of Schwartz, trying to make the philosopher’s stone."

"Loud advertisement of the successful cures he had wrought by the use of mercury and raised him to such a pitch of fame that the magistrates of Basle in 1526 appointed him to the Chair of Medicine in that University."

"At his first lecture he ostentatiously burned the works of Galen and Avicenna, the great medical authorities of the age. In this spirit he lectured for two years, but his vanity and bombast disgusted and drove away his students, and his greed made him quarrel with the magistrates over his fees. In the end he suddenly quitted the town, and resumed his wandering life through and Germany."

"During the latter part of his career he effected many cures, the reputation of which concealed his many failures, but his private life was disfigured by intemperance, which he indulged in the lowest company."

"Finally, he announced that he had discovered the Elixir Vitæ, and could extend human life for an indefinite term. [H]owever, he was unable to conform to the maxim "physician, heal thyself," for he was seized with a fever and died at in 1541, at the early age of 48. His property was bequeathed to the poor."

"Paracelsus did little by actual discovery to advance either science or medicine."

"His great work was effecting a breach with tradition, and setting physicians and alchemists free from the bondage in which they were held by convention."

"He borrowed his medical treatment from others—barber-surgeons, old women and quacks—and his fearless nature made him employ the powerful and dangerous medicines prepared from mercury, , and more boldly than any before him had ventured to do."

"His alchemical doctrine, that everything consisted of three elements—mercury, sulphur, and salt—is adapted from old authors, but he was the first to use the word "alcahest" to indicate the universal menstruum or , which at that time was a special object of research. He describes this liquor, alcahest, as having great power over the , comforting and confirming it, and preserving it from dropsy and other diseases that take their origin within it. ...Unhappily, he does not give precise directions for the preparation of this invaluable remedy."

"The great debt which chemistry owes Paracelsus is the influence... in discarding the ideas of the ancients, and even of the more modern alchemists, and in teaching that the object of chemistry was not to make gold but to ameliorate disease."

"The art of making drugs was one of the original branches of alchemy, but for many centuries this had been obscured by endeavours to effect the transmutation of metals. Paracelsus reinstated it in its prominent position."

"He used preparations not only of , but of mercury, , , blue vitriol, and (for external use) . He said that the most energetic poisons might become precious medicines, and endeavoured to concentrate in essences, extracts, and mixtures the active principles of various drugs."

"He arranged the several parts of man, his own universal elements, and the Aristotelian elements in triplets, thus :—"

"Having adopted the Cabala and its doctrines, he was grossly pantheistic."

"As a rule his writings are full of mysticism, although there are a few grains of wheat among the chaff."

"He repudiates the view of Galen that fire is dry and hot, air moist and hot, earth dry and cold, and water moist and cold. He says that each of these elements is capable of admitting all qualities, so that there is a dry water and a cold fire."

"[According to Paracelsus,] [t]here is in the stomach a demon named Archæus, who presides over the chemical operations which take place in that organ, changing bread into blood, and separating the poisonous from the nutritive. Tartar is the leading principle of the maladies which arise from the thickening of the humours. Stone in the abdominal organs is only part of it, and as tartar is deposited in wine casks, so tartar is deposited on the teeth. When tartar is increased by certain kinds of food, renal calculi are engendered. In this connection he thought it necessary to subject to chemical analysis."

"All remedies, according to Paracelsus, are subject to the will of the stars and are directed by them, but chemistry is indispensable in the preparation of medicines. After his time the old disgusting decoctions gave place to tinctures, essences, and extracts. He even recommended quintessences, and described how they were to be made."

"[H]e ascertained that contains an earth united to an acid."

"He mentions metallic , and , but did not regard them as true metals, to which he considered malleability and ductility as essential characters."

"[H]is reputation as a chemist depends not so much upon discoveries made, as on the importance which he attached to a knowledge of the science."

"In consequence of his teaching chemistry became an indispensable part of the education of a medical man, and it was perceived that the true object of the science was not the discovery of the philosopher’s stone, but the preparation of new medicines. He thus introduced the next period in the history of chemistry, when many medicinal and other substances were discovered in the laboratories of the chemical physicians, or Iatrochemists..."

"As might be expected the protest of Paracelsus against ancient tradition led to a vast amount of discussion among contemporary alchemists. One of these named Gerhardt Dorn (circa 1550—1600), a pupil of Paracelsus, in his Clavis Totius Philosophiae Chymisticae (1561), Artificii Chymistici {circa 1568), and In Aurorum Paracelsi (1583) attempted to explain and comment upon his master. ...[H]e only rendered obscurity more obscure."

"Thomas Erastus (1523-83)... adopted the reasoning of scholastic philosophy and thus weakened the force of his attack, but he pointed out many contradictions in the writings of Paracelsus and his followers, denied the existence of the philosopher's stone, and combated the idea that mercury, sulphur, and salt are the elements of living bodies."

"He charged Paracelsus with bad faith."

"Erastus... wrote an apology for hermetic science, and treatises on the philosopher's stone and the triple preparation of gold."

"Leonhardt Thurneisser or Thurneysser zum Thurn (1530-96), a native of Basle and a friend and pupil of Paracelsus... had not the penetration of his master, and lived most of his life by his wits."

"His chief experimental work was a very incomplete investigation of the residues got by evaporating mineral waters."

"He wrote many books, of which may be named Quinta Essentia (1574) and Magna Alchymia (1583)."

"His father was a goldsmith, who, having need of money, sold a quantity of gilded lead as gold. This was the son’s introduction to alchemy, as his father understood the art."

"After a visit to Germany, France, England, and the Scottish lead mines, Thurneysser started mining and sulphur-extracting in 1558..."

"[L]ater... he studied under Paracelsus, and so far associated himself with the Paracelsian system that he acquired a great reputation for a time, which was heightened by his curing the wife of the Elector of Brandenburg. He was thereupon made court physician, and amassed a considerable fortune by medical practice with tincture of gold and similar medicines, but was exposed by Gaspard Hoffmann, lost his repute, and fled to Italy."

"His last years were devoted to transmutation of metals, and he died at Cologne."

"His character is well summed up by Ferguson: "He was endowed with quickness and a powerful memory, but he tried to pass as a man of science, a learned physician, and an accurate scholar, when in reality he was a man of action with a gift for organising and commercial advertising. At the present day he might have been a successful manufacturing chemist, able to turn his raw material into gold without the red elixir.""

"Pantheus was an instance of a churchman devoting himself to alchemy. His full name was Giovanni Agostino Pantheo (circa 1510-60), and he was a priest at Venice."

"[H]is books—Ars et Theoria Transnmutationis Metallicae cum Voarchadumia (1550) and Voarchadumia contra Alchimiam (1530). He opposed the spurious alchemy current in his day, and treated of the purification and assaying of gold, the manufacture of , and the preparation of an alloy used for making mirrors."

"Bernardus Georgius Penotus (1520—1618)... studied at Basle, and first admired Paracelsus and then abused him as a plagiarist."

"He wrote several books dealing with medicine and chemistry, of no great importance, squandered his means in the search for the philosopher’s stone, and died in the poor-house..."

"His most valuable contribution to philosophy was the bitter remark that if he had an enemy whom he dared not attack by force, but yet to whom he wished to do the greatest possible injury, he would urge him by every means in his power to study alchemy."

"[A] a mysterious body, the Rosicrucian Order... seems to have owed its origin to a determination to uphold the ancient alchemy in opposition to Paracelsus and all innovators."

"The cult is involved in mystery and doubt, and has for centuries exercised an attraction, and retained a prestige, of which it was hardly worthy."

"The extreme caution which was observed by its members in preserving their secrets, if they had any, and the unintelligible symbolism in which they contrived in their published writings to wrap up their meaning, have combined to render the study of Rosicrucianism extremely difficult and confusing."

"The Rosicrucians seem to have existed for about one hundred years, practically coeval with the seventeenth century."

"They devoted themselves to the study of science, astrology, necromancy, and, it is said, some of the most debasing forms of Oriental superstition."

"Their energy was due to the impulse imparted to human thought by the three great events of the Middle Ages; the discovery of America, the invention of printing, and the reformation of religion."

"To them the Cabala was the touchstone of wisdom."

"To them the Cabala was the touchstone of wisdom. They mixed the spiritual with the material, aiming at the perfection of the human body and soul, as well as at the transmutation of the baser metals into gold."

"Incidentally, they discovered scientific facts, but directly they sought to impress the truths that men ought to subordinate their appetites and desires to nobler aspirations, and that by the subjugation of our lower nature we actually prolong our lives."

"[T]he writings and labours of the alchemists were both extensive and important. ...[T]heir studies, although misdirected, were not... haphazard. The alchemists had a definite, and... logical, system of philosophy... [T]hey recognised—(1) the unity of matter; (2) the three principles—philosophical mercury, sulphur, and salt; (3) the four elements—fire, air, water, and earth; and (4) the seven metals—gold, silver, mercury, copper, , tin, and ."

"This was the fundamental theory of alchemy, and goes back to remote ages. [T]he smaragdite tablet attributed to Hermes Trismegistus [states] "As all things were produced by the one word of one Being, so all things were produced from this one thing by adaptation," and we again find it in the "one is all" of the Chrysopoeia of Cleopatra..."

"The alchemists held that matter is one, but can take a variety of forms, and under these different forms can be combined and re-combined ad infinitum."

"The original matter, or ', was called by various names—universal substance, seed, chaos. Although matter changes its form, it cannot be destroyed."

"As Hermes is alleged to have said. "Nothing in the world dies, but all things pass and change.""

"In its nature the ' was assumed to be a liquid, containing everything in posse, but nothing in esse."

"All metals and minerals consist of certain principles. These were at first called "mercury" and "sulphur," not the ordinary substances... but a philosophical mercury and a philosophical sulphur."

"At a later period the alchemists added a philosophical salt, or a philosophical arsenic, but they never ascribed to these the importance they attached to the other two principles."

"Traces of these ancient conceptions are still to be recognised in the word "quick-silver," that is living silver, a literal translation of argentum vivum. A term "quick-sulphur" (sulphur vivum) was also in use, but it has long since disappeared."

"The mercury of a metal... represented its lustre, volatility, fusibility, and malleability; the sulphur of the metal, its colour, combustibility, affinity, and hardness."

"The salt of the was merely a means of union between the mercury and the sulphur, just as the vital spirit in man unites soul and body. It was doubtless devised to impart a triple form to the idea, in conformity with the method of the theological schoolmen."

"Mercury, sulphur, and salt were not three matters, but one, derived from the '."

"[W]hen an alchemist converted a metal into its oxide, or, as they expressed it, "made a " of it, he thought he had volatilised its mercury and fixed its sulphur. When he distilled ordinary mercury and found a solid residue in the , he called it the "sulphur" of mercury; when he found a sublimed product in the receiver (mercury bichloride), he termed it the "mercury" of mercury or "corrosive sublimate.""

"The more logical mind of Artephius Longaevus introduced a modification of this theory. He distinguished two properties in a metal—the visible and the occult. The former, comprehending its colour, lustre, extension, and other properties visible to the eye, he called its "sulphur"; the latter, comprehending its fusibility, malleability, volatility, and other properties not visible until after... special treatment, he called its "mercury.""

"Practically... there was little difference in the application of these diverse theories regarding the three principles."

"Aristotle... taught that all things consisted of four elements, or rather four elemental properties:— 1. Fire, the property of dryness and heat; 2. Air, the property of wetness and heat, or of gaseousness; 3. Water, the property of wetness and cold; 4. Earth, the property of dryness and cold, or of solidity."

"The alchemists adopted these four states of matter, and sought them in all substances. Everything hot was called "fire"; cold and subtle, "air"; moist and fluid, "water"; or dry and solid, "earth.""

"But, as heat changes liquids to vapour, and consumes solids, they reduced the number of visible elements to two—earth and water, which contained within themselves the invisible elements, fire and air."

"They were thus able to apply the conception of the three principles to that of the four elements. Earth corresponded to philosophical sulphur, and water to philosophical mercury. Later, when they conceived philosophical salt, they devised a fifth element called "quintessence" or "ether." which corresponded to the third principle. Thus, if an alchemist distilled wood and obtained an inflammable gas, a liquid oil and a solid residue, he said that he had decomposed the wood into its elements—fire, water, and earth."

"[T]he n star-gazers of Harran came to fix the number of metals at seven, and to associate them with the sun, moon, and five planets in the following manner:— Gold, corresponding to the sun. Silver, corresponding to the moon. Mercury, corresponding to the planet Mercury. Copper, corresponding to the planet Venus. , corresponding to the planet Mars. Tin. corresponding to the planet Jupiter. , corresponding to the planet Saturn. Each metal acted under the influence of the planet with which it was associated..."

"[T]hey regarded gold and silver as being perfect, because they were unalterable... The other five were deemed imperfect, as each could be formed into a or oxide, was readily attacked by s, and could be consumed by fire; but they deemed it possible to purify and modify the imperfect metals, so as to transmute them into the perfect."

"The seven metals were... derived like other substances from the ' or universal substance. They were the same in essence and differed only in form."

"The sulphur of a metal was its active principle; the mercury its passive; the salt was the link which united the other two."

"The sulphur, the property of dryness and heat, ultimately overcame the mercury, the property of wetness and cold, and thus changes were effected. ...[S]ulphur was the father, mercury the mother, and metals were conceived between them. In this expression the philosophical principles are meant, not the ordinary substances called sulphur and mercury."

"[A]lchemists accounted for the diversity of metals by five causes:— 1. Variation in the proportion of the principles, mercury and sulphur. 2. Variation in the purity of these principles. 3. Variation in the duration of the period of concoction to which the compound was subjected in the bowels of the earth. 4. Variation in planetary influences. 5. Variation in accidental influences."

"Nature always sought to attain perfection, but was checked by these diverse causes, and instead of producing the perfect metals, gold and silver, produced imperfect metals, mercury, copper, , tin, or ."

"The later alchemists, who were mostly astrologers as well, laid special stress upon the influence of the heavenly bodies. ...Paracelsus even pretended to be able to calculate when and how this planetary influence took effect."

"In the fifteenth and sixteenth centuries alchemy was affected by two external systems, magic and religion, both to its detriment. To astrology the alchemists added necromancy and the Cabala. The latter had really no connection with alchemy. It was a purely speculative system of numbers."

"At a still later date it was argued that exact and natural sciences proceed by induction and deduction, and occult and spiritual sciences by analogy. Following out this line of thought the alchemists produced the following remarkable :—"

"Each of these was a trinity in unity, and a unity in trinity. In each world was a distinct design,—in the material, the perfection of the metals; in the human, the perfection of the soul; in the divine, the contemplation of the Deity in His splendour."

"These mystic alchemists interpreted the three principles in their own fashion. Mercury, the passive and female principle, was matter; sulphur, the active and male principle, was force; and salt, the middle term in the proposition, was movement, which applied force to matter. Or, expressed in another shape, mercury was the subject: sulphur, the cause; and salt, the effect. Symbolically, the theory was represented by an equilateral triangle, in one angle of which was the sign of sulphur or force; in the second, the sign of mercury or matter; and in the third, the sign of salt or movement."

"[T]he philosophy of the alchemists... when fully considered... is by no means despicable. The knowledge which was at that period available did not permit of the practical application of this philosophy, and the sages did not rightly understand their own theories. Yet... while there is much that seems absurd and nonsensical, there is much which is not inconsistent with recent researches and discoveries of science."

"The Modern History of Chemistry may be said to have begun when the alchemists... applied their minds to the search for knowledge instead of the search for gold."

"The peculiarity of the Iatrochemical Period is the tendency of chemistry towards investigating and producing new medicinal preparations by chemical means, and forming other chemical compounds in the search for new medicines, in place of a tendency towards searching for the philosopher's stone, which was the peculiarity of the Alchemical Period."

"The iatrochemists, chemist-physicians, or chemist-apothecaries, devoted themselves mainly to the attempt to discover the Elixir Vitœ or universal medicine, a quest as hopeless as that of their predecessors, yet they did not altogether give up the older quest, and the search for the red elixir or philosopher's stone continued to engage the attention of chemists during the whole Iatrochemical Period, which endured from the first quarter of the sixteenth century till the middle of the seventeenth, or a little later."

"[P]eculiarities assigned to each period are not to be regarded as being anything more than general characteristics. Thus, alchemical ideas extended far down into the Iatrochemical Period, so that we find Van Helmont declaring that he believed in the transmutation of metals, and that he possessed a small portion of the philosopher's stone. This attitude was characteristic of those chemist-physicians of the seventeenth century who practised medicine according to the old traditions."

"On the other hand, those who followed Roger Bacon in the study of theoretical chemistry for its own sake, or who made technical applications of it, tended rather in the direction of our modern views, even prior to the close of what we term for convenience the Iatrochemical Period."

"The iatrochemists carried to excess their efforts to give an explanation of everything which happened in the human body and in Nature; but their explanations were fanciful and founded either upon complete ignorance or entire neglect of facts. Their contributions to the philosophy of chemistry were meagre; their additions to our knowledge were the fruits of their practical research."

"[T]he period is in marked contrast to the next, the Phlogiston Period, which is memorable for the development of a rational theory of chemistry, which, although wrong, is not so far wrong as may appear... at first sight..."

"[S]everal men whom we have included in the Alchemical Period were iatrochemists as well as alchemists. Of these we may mention Paracelsus... Erastus... who although he opposed Paracelsus was an advocate of chemical medicines, Thurneysser... Ulstadt... Sir Kenelm Digby... and ..."

"[W]e mention... one who might have been included among the alchemists—Basil Valentine (circa 1394—1450). We... deferred consideration... partly because his reputation rests upon his advocacy of the medicinal virtues of , and partly because he is a mythical personage, and there is reason to believe that the writings attributed to him are the work of an anonymous author of the Iatrochemical Period."

"His biography is made up of several more or less improbable legends."

"[T]he works were not published till 1602, or nearly two hundred years after Valentine's death, but whether they were only then discovered, or... only then written... is now impossible to answer with confidence."

"About two dozen books stand in the name of Basil Valentine. Of these the most important is Currus Triumphalus Antimonii (The Triumphal Chariot of Antimony), and one of the best English editions is the translation of the work and of the notes by Theodore Kirkringuis or Kerckringuis, made by Edward Russell, in 1678. It is an excellent book, far too good... for the time of its reputed author. In clear and precise terms it sets down all that was known about antimony prior to the discoveries of the nineteenth century."

"The writer of these books, whoever he was, had a wide knowledge of chemical compounds. He understood the preparation of , which he called spirit of salt, by the distillation of common salt with . He knew and its sulphide, ; in its compound, if not its metallic, state; , which he sometimes termed marcasite; the red oxide, nitrate, and bichloride of mercury (corrosive sublimate); and its compounds; the acetate, yellow oxide, and white carbonate of lead; and of the salts, ferrous sulphate (green vitriol) and the double chloride of iron and ammonium. He obtained metallic mercury by distilling corrosive sublimate with . He discovered . He precipitated metallic solutions by ; copper by ; and gold by mercury. Lastly, he experimented with spirits of wine, which he combined with nitric or s, and used for dissolving the caustic alkalis."

"[H]e was as bitter against the physicians of his day as Paracelsus. He believed that there is an analogy between the purification of gold and the cure of disease, and maintained that is sovereign for both."

"He asserted that the metals are composed of the mercury and sulphur of the philosophers, to which he added philosophical salt. The philosopher's stone, he said, is composed of the same materials."

"[H]is works do not merit the deference they received, and... the knowledge imputed to him is almost certainly not his, but belongs to a far later period... [R]eceive with caution all that is said about Basil Valentine in text-books and histories."

"Francis Anthony or Antonio (1550—1623) was an unlicensed practitioner, who advocated chemical medicines, and sold a panacea aurea after the fashion of Paracelsus."

"He strongly maintained the virtues of aurum potabile (liquid gold), and wrote a book entitled Medicinae Chymicae et Veri Potabilis Auri Assertio (1610). Another tract, De Lapide philosophorum et Lapide Rebis, related to the older alchemy. ...[I]n alchemical symbolism "Rebis" was the name given to the hermaphrodite figure representing the union of the great philosophical principles, sulphur and mercury, in the operation of making the philosopher's stone..."

"It is refreshing, among the many vain theorists and dreamers of those days, to come upon a man who was a theorist... but also an acute observer and accurate experimenter."

"Andreas Libavius (1540—1610) was one of the pioneers of chemical science, and the first author who wrote a really valuable text-book of chemistry."

"As a physician he was an unflinching opponent of Paracelsus; as a chemist he was an earnest seeker after truth."

"He was so far the child of his age that he believed in the possibility of the transmutation of metals and in the virtue of aurum potabile, but he was so far in advance of it that he was able to distinguish between the mystical and the practical, and to make discoveries which enriched the science."

"Much of his time was wasted in useless controversy. He thought it his duty to expose the quackery of his contemporaries, and as the quacks were numerous and vindictive, the struggle was continuous and bitter."

"His System of Chemistry, published... in folio in 1585, and in quarto in 1597, has the... title: "Alchymia e Dispersis passim Optimorum Auctorum..." was for long the leading textbook on the science, and contained a collection of all the chemical facts then known. He also wrote Ars Probandi Mineralia (1597), De Judicio Aquarum Mineralium (1597), Praxis Alchymiae (1604), Alchymia Triumphans (1607). They were ultimately collected as Opera Omnia Medico-Chemica."

"Libavius was mainly interested in the preparation of chemical medicines, but some passages in his writings bear on the transmutation of metals."

"He observed that the fumes of blacken ; he purified by means of arsenic and ; he made artificial rubies and other precious stones by tinting glass with metallic oxides; he described fluor spar as a flux for metals and their oxides; he oxidised sulphur with ; he knew that alcohol is obtained by distilling the fermented juice of sweet fruits; he proved that the acid extracted from and from ferrous sulphate (green vitriol) is the same as that obtained by burning sulphur with saltpetre, that is to say, it is sulphuric acid; and he discovered tin tetrachloride (stannic chloride), which is sometimes called Liquor fumans Libavii. It is a truly remarkable record of practical work, considering the age in which Libavius lived."

"One of the most original thinkers of his day was Angelo or Angelus Sala (1575—1640)."

"His Opera Medico-Chemica were published in 1647. He scouted the idea of the philosopher's stone, or of a universal medicine, and rejected aurum potabile for medicinal purposes. He administered gold only in the form of the fulminate."

"Sala showed that sal ammoniac is obtained by treating with ; he described in wonderfully clear terms; he observed the formation of by the action of upon saltpetre; and he recognised that in the deposition of copper upon , when the latter is dipped in a solution of cupric sulphate (blue vitriol), there is no change of metal, but that the blue vitriol already contained copper."

"In the words of Conring.... he was "primus chemicorum qui desiniit ineptire" (the first chemist who ceased from trifling)."

"Whether as a critic of the old theories, or as an exponent of the new, Sala merits a distinguished place amongst the founders of chemistry."

"[T]he greatest name of this period is... Van Helmont."

"Paracelsus had discarded the disgusting decoctions of Galen and introduced chemical medicines, while Libavius and Sala had dismissed the fanatical conceptions which disfigured and almost nullified the teachings of both Paracelsians and Rosicrucians, but chemists still adhered either to the Aristotelian doctrine of the four elements, or to the later theory of the three principles (mercury, sulphur, and salt). John Baptist van Helmont (1577—1644) was the first to deny these propositions, and to begin a revolution in the philosophy of chemistry."

"Continuing his philosophical studies under the auspices of the Jesuits, he was taught necromancy, but was soon disappointed with such useless learning. He then turned to mysticism, reading the works of Thomas à Kempis and John Tauler. ...[H]e resigned his titles, and gave up his property to his sister."

"Desiring now to practise medicine, he read Hippocrates and Galen, but detected the futility of their methods of treatment. This led him to become a disciple of Paracelsus, but having much greater knowledge than that writer, he speedily discovered the ignorance and egotism which mar his writings."

"In 1599 he took his degree as Doctor of Medicine, and for a time travelled and practised his profession in various countries. At last he married... and passed the closing years of his life on his own estates at Vilvorde, chiefly in his laboratory."

"Van Helmont absolutely discarded the doctrines of Aristotle and Paracelsus in regard to the four elements and the three principles. He denied the elemental character of fire, air, and earth. He disputed the material existence of fire, and asserted that earth cannot be an element, because it can be converted into liquid."

"He admitted the elemental nature of water, which he deemed the fundamental principle of everything that exists. All metals and even rocks, he affirmed, may be resolved into water, and from water all animal and vegetable substances may be produced. The former proposition he based upon the fact that fish live in water; the latter he proved by a curious, but faulty, experiment."

"He took a willow weighing five pounds, and planted it in two hundred pounds’ weight of earth carefully dried in an oven. All dust was excluded, and the plant was frequently watered. At the end of five years he weighed the plant. Its weight was one hundred and sixty-nine pounds, an increase of one hundred and sixty-four. He again dried the earth, and weighed it, when he ascertained that it had lost only two ounces. Hence, he concluded that the increase of one hundred and sixty-four pounds in the weight of the willow was derived from water alone. He was not aware that in addition to the water, the plant had absorbed a great store of carbon from the carbonic acid gas (carbon dioxide) existing in the air."

"Van Helmont was the first to perceive that when a metal is dissolved in an it is not destroyed, but may be recovered from the solution in the metallic state by the use of suitable means."

"[H]is outstanding discovery was the discrimination of various kinds of air, which he thus proved to be no elementary substance. In this connection he introduced the term "gas." Of these gases he mentions several, but the most important were "gas silvestre" (i.e., the gas that is wild and dwells in out-of-the-way places) and "gas pingue.""

"Gas silvestre was evolved from alcoholic liquor during fermentation, from burning charcoal, from marble or {{w|chalk} when acidulated, and from the Grotto del Cane near Naples. It was, in fact, gas, or (CO2)."

"[T]his discovery... was entirely forgotten by chemists, and... carbonic acid gas was rediscovered by Dr. Black in the middle of the eighteenth century under the name of "fixed air.""

"Gas pingue was an inflammable air evolved from dung, and was probably impure gaseous ."

"He held strange notions respecting the vital functions. From his sensations on swallowing aconite he thought that the stomach was the seat of the sentient soul, which he named Archeus. ...[H]e founded his physiological system on the operation of Archeus and of various ferments, all mainly imaginary."

"Van Helmont believed in the philosopher’s stone and in transmutation, but did not waste much time upon that part of alchemy. He asserted that he had actually witnessed the transmutation of a base metal into gold..."

"His chief aim, however, was the discovery of the alcahest or universal , another of the alchemical problems, and in this line he was followed by Glauber... It seems to have been thought that the alcahest would be a universal medicine as well as solvent. It is a curious reflection that it never seems to have occurred to Van Helmont and others to consider how they were to retain the alcahest, when they found it. ...[I]t would dissolve the vessel ...so would be lost as soon as found!"

"The writings of Van Helmont were collected in 1648 under the title of Ortus Medicinae vel Opera et Opuscula Omnia."

"All honour is due to his name. In addition to his great discovery of the diversity of gases, and the distinction between gas and vapour, he was the first to point out the imperative necessity for the use of the balance in chemical operations, and to adopt the melting point of ice and the boiling point of water as standards for the measurement of temperature. It is in his writings that the term "saturation" in its chemical sense first occurs. Altogether he was a great chemist, undoubtedly the greatest prior to Lavoisier."

"Daniel Sennert (circa 1575—1625) is... notable as a professor of medicine at Wittenberg, who devoted himself to the advocacy of chemical medicines."

"He was held... by the erroneous doctrines of Paracelsus, especially... the three principles, but he did good service to chemistry by protesting against the possibility of a universal medicine."

"His chief work was Epitome Naturalis Scientiae, which was published at Oxford in 1664."

"Oswald Croll (1580—1609)... won distinction as a pharmacist."

"His Basilica Chemica, published at Frankfort in 1608... is a treatise of some value. The English edition was entitled "Philosophy Reformed and Improved in Four Profound Tractates" (1657)."

"He discovered, or brought into use, a number of new medicines: for example, volatile salt of amber (); potassium sulphate; antimonic acid; ; fused [luna cornea), and silver chloride prepared by precipitation. Of course, he did not use the modern names of these substances, which are adopted here..."

"Croll was a practical chemist, rather than a theorist, although the Basilica contains a critical study of the Paracelsian doctrines, and discusses at length both pharmacy and therapeutics, as they were understood in his day."

"Much of his time was wasted in writing polemical tracts against those who still followed Galen. His anger was specially kindled against one Earner, who had worked in his laboratory, to whom he had communicated secrets, and who had not only broken his promise not to divulge these, but had boasted of them as his own discovery, and added insult to injury by decrying the skill of Glauber."

"The collected works of Glauber were translated into English in 1689 by Christopher Packe."

"Glauber was an alchemist and a believer in the universal medicine, but he was also an iatrochemist, and applied chemical processes to the improvement of both medicine and art."

"His first treatise related to philosophical furnaces, Furni Novi Philosophici (1648)... showed how he made chemical preparations with these; for example, muriatic acid by distilling salt (), ferrous sulphate (green vitriol), and ."

"The name "muriatic" acid, derived from "muria," brine, was invented by him. He made solutions of metals in this acid, calling them "oils" of the metals. The s of gold, iron, Mercury chloride|mercury]], and antimony, thus prepared, he praised as medicines."

"Sulphuric acid he made by distilling green vitriol (ferrous sulphate), and by distilling nitre (potassium nitrate), and (double sulphate of potassium and aluminium). he prepared, but said it was of little use as a medicine."

"In... "The Mineral Work" he explains how to separate gold from clay and other earthy substances by means of spirit of salt (hydrochloric acid). He further describes a panacea or universal antimonial medicine, consisting of a solution of oxide of antimony in pyro-tartaric acid, which he eulogised as being specially good for cutaneous eruptions."

"The salt which still bears his name, , and which he called Sal Mirabile, is the subject of a long disquisition in his "Miraculum Mundi." We recognise it as a useful purgative, but Glauber maintained that it was a universal medicine and partook of the nature of the alcahest."

"Secret sal ammoniac () is recommended in the "Spagyrical Pharmacopoeia or Dispensatory" as a substance used by Paracelsus and as the alcahest of Van Helmont. He gives a clear description of its preparation and of its conversion into ordinary sal ammoniac () by distillation or sublimation with common salt ()."

"He knew , which he termed "nitrum flammans.""

"In 1648 he demonstrated the possibility of making blue vitriol () by boiling copper with sulphuric acid."

"He prepared a , which he called acetum lignorum, by the of wood. It was what we now term . He said that by re-distillation it could be made as "virtuous" as acetum vini, or "common wine vinegar," a fact not unknown to those artful persons of the present day who adulterate malt vinegar. The preservative effect of wood tar did not escape his observation."

"Glauber was a keen observer, a persevering experimenter, and an original genius, and he had the modesty of genius, for he says... "Nevertheless, I easily persuade myself that this discourse of mine will not be credited by many, which I cannot help. It contenteth me that I have written the truth, and lighted a candle to my neighbour.""

"Werner or Guerner Rolfinck (1599—1673)... has been called "the first professor of chemistry in Germany.""

"Alchemy he determinedly opposed, and his treatise "Chymia in Artis Formam Eedacta" (1661) methodised the science, and according to Stahl (1766), "brought chemistry into shape, deduced its operations from causes conformed to Nature and reason, and laid a foundation on which many subsequently built.""

"So keen an anatomist was he that the verb "to Rolfinck" became a popular equivalent for "to dissect"..."

"The author of the book Aurum Superius (1675), Christopher A. Baldwin (1600—1682) is memorable for a single discovery. He prepared a hygroscopic salt by treating with . This substance took up water from the atmosphere, which he distilled off, and sold under the name of "Spiritus Mundi" using the title of an old alchemic conception. The calcined salt (anhydrous ), being phosphorescent in the dark, he named "phosphorus." It thus became known as Baldwin’s Phosphorus, and created much interest, ultimately leading to the researches which enabled Brandt and Kunckel to discover the element which we now call ".""

"Francois de la Boe or Bois, in Latin Franciscus Sylvius (1614—1672), was... [a] disciple of Van Helmont and Descartes... led to the study of those chemical compounds which we now term "salts.""

"The first chemical laboratory in Europe was on his persuasion erected by the University of Leyden, where he became Professor of the Theory and Practice of Chemistry."

"He was one of the most eminent iatrochemists, was the first to prove the presence of volatile alkali in plants, and regarded all phenomena from a purely chemical standpoint, but he had wild notions of ."

"While he agreed with Van Helmont in attributing many of the operations of the human body to fermentation, he entertained a totally different idea of what fermentation was, and sometimes used the word "effervescence" to denote the process."

"Van Helmont recognised the acid of the gastric juice and the alkali of , but Sylvius appreciated the importance of the salivary secretion and the . Many of the digestive processes were, he maintained, due to the swallowed with the food, rather than to the ferment secreted by the stomach and other organs. Saliva caused the first stage of fermentation, but the second was due to the bile and the pancreatic juice. He identified physiological fermentation with chemical effervescence. He discarded such agencies as the demon Archaeus of Paracelsus, and contended that although he could not explain the various processes, physiological operations were due to chemical principles, and that air inhaled in respiration acted upon and altered the blood. Illness was due to abnormal chemical reactions in the body, and could therefore be counteracted by other reactions. These theories, connecting as they did chemistry with medicine, had a great influence on the development of the former science."

"He taught the use of various chemical medicines, such as , , , corrosive sublimate, and other salts of mercury. Nevertheless, he retained the old alchemical superstitions regarding the transmutation of metals."

"One of the best-known followers of Sylvius was Otto Tachenius (circa 1620—1690). He was one of the first to give quantitative data in chemistry, and greatly improved qualitative analysis."

"He observed the difference of colour when corrosive sublimate is precipitated by a fixed or by a volatile alkali, and noted the use of gallic acid as a test for other metals than iron."

"[A]fter the close of the eighteenth century the... science was intimately connected with manufactures, commerce, and all the varied departments of human work and enterprise. To-day, no technical art or craft is independent of it."

"The importance of the theory of phlogiston... [I]t was... the first successful attempt to give a rational explanation of a number of different phenomena, and to correlate a number of isolated facts and observations, and assign... a common cause. It gave an intelligible account of... combustion, and led to the discovery of , oxygen, and many other elements and compounds."

"If... we define phlogiston as "the property of combustibility,"...their ideas were not so far removed from our own, and... their knowledge was very considerable..."

"[S]o soon as the balance was applied to the investigation of chemical processes, the phlogiston hypothesis had to make way for another... more correct explanation."

"[T]he first seven leaders of the Quantitative Period were in the main phlogistonists. Cullen, Black, Cavendish, Priestley, Bergman, Scheele, and Kirwan were, during the greater part of their lives, and in some cases till their death, believers in the phlogiston hypothesis. But they also, by insisting on the necessity of accurate estimation of weight and measure, laid the foundation of quantitative determinations..."

"William Cullen (1710—1790), was celebrated rather as a physician than as a chemist, and owes his place in the history of the science mainly to his having been the teacher of Joseph Black."

"After being for a time Professor of Chemistry in Glasgow University, he went in the same capacity to Edinburgh, where he filled the chair for ten years... appointed Professor of the Institutes of Medicine."

"[D]etails of his life will be found in the biography by Dr. John Thomson, published in 1832."

"His Lectures on the Elements of Chemistry were published in 1803."

"An investigation into the means of dissolving urinary calculi led Black to study the action of quick lime in rendering alkalis caustic."

"At that time the causticity of these substances was held to be dependent on phlogiston."

"He showed in 1754 that causticisation meant not the gain, but the loss, of something. This he found to be a gas which he called "fixed air," and which was in 1781 named by Lavoisier "carbonic acid gas" ()."

"In this manner [he] re-discovered the gas silvestre of Van Helmont... [from] more than a hundred years before, but which had entirely escaped the memory of chemists. Black’s great thesis, "De Humore Acido a Cibis orto et Magnesia Alba" [On the Acid Humour Arising from Food, and Magnesia Alba] (1754), shook the phlogiston theory."

"[H]e demonstrated that magnesia alba when heated lost weight; that this loss was due to the escape of "fixed air"; and that its weight was regained when the calcined mass was made to re-absorb fixed air."

"Before Black’s time s, such as magnesia alba (), were considered to be simple substances. When limestone was burned, chemists supposed that it took up "fire-stuff" and became caustic, and this "fire-stuff" passed on to potash and soda, when they were causticised by lime."

"His experiments on magnesia alba, quick lime, and other alkaline substances proved that "fixed air" is given off when limestone is burned, and that the same loss is incurred when it is dissolved in muriatic acid ()."

"[M]ild alkalis, instead of taking up an acidum pingue, or fire-stuff, when they become caustic by the addition of quick lime, give up something to the lime, which then [returns to] its original weight, and capable of once more evolving fixed air. Therefore, it has received fixed air from the mild alkali. It now effervesces when treated with an , which quick lime will not do."

"Prior to Black, the action by which in combination with slaked lime () produces caustic potash () and carbonate of lime, and which we express by the following equation:— K2CO3 + Ca(OH)2 = 2KOH + CaCO3 was expressed thus:— Mild Alkali+(Mild lime+Phlogiston)=(Mild alkali+Phlogiston)+Mild lime. The bracketed terms, "mild lime plus phlogiston" and "mild alkali plus phlogiston," in this equation stand respectively for caustic lime and caustic alkali."

"Black found that by heating magnesia alba in a crucible, weight was lost, due in part to the loss of a little water, but chiefly to the loss of an "air." The product [had become] caustic, and on treatment with mild alkali gave the same weight as the original magnesia [alba], and acquired the property of effervescing with s, which it had lost by the ignition."

"He... concluded that the effervescence was due to fixed air, and that caustic alkali in combination with fixed air became mild alkali. A similar treatment of produced similar results."

"Black then neutralised some limestone with acid, and also a like amount of caustic lime obtained from the same quantity of limestone, and found that the amount of acid required to neutralise the substances was in both cases identical."

"Some confusion existed at that time between magnesia and limestone, but Black distinguished the one from the other by observing that when both were treated with oil of vitriol () fixed air was in each case given off, but the lime product formed a sediment in water, which the magnesia product did not."

"[H]e noted the great heat produced when water is added to quick lime, and attributed this to a strong affinity subsisting between the two."

"He inferred that an alkali, destitute of fixed air, became acrid and caustic, not because it had taken up phlogiston or an acidum pingue, but because of its powerful affinity."

"In the course of these experiments he was the first to distinguish, in 1756, from ."

"Black's success in research work was largely due to his constant appeal to the balance... [I]t has been said that he laid the foundation of quantitative analysis."

"He... made many discoveries in physics. One of the most important... his doctrine of "latent heat,"... discovered in 1760... When ice melts it takes up a quantity of heat without undergoing any change in temperature. Black argued... this absorbed heat... combined with the particles of the ice, and become latent in its substance. He determined the latent heat of water... and... of steam... Watt, who was a personal friend of Black, made use of these... in his work on the steam-engine."

"Black further observed that different bodies in equal masses require different degrees of heat to raise them to the same temperature, and hence derived his theory of "specific heat.""

"Lavoisier learned much from his correspondence [with Black]; but [Lavoisier] does not appear to have recognised fully his correspondent's important services."

"Black's work was... followed up... by the Honourable Henry Cavendish (1731—1810). He led a most retired life, devoted to scientific pursuits, chiefly in chemistry, but also in electricity, meteorology, and other departments of science. His quiet manner of life afforded no opportunity for spending his fortune..."

"The scientific work of Cavendish is remarkable for its width of range, and its extreme accuracy."

"Eighteen papers by him were published in the Philosophical Transactions, of which ten were on chemical subjects."

"In 1766 Cavendish published his Experiments on [[wikt:factitious#Pronunciation|F[a]ctitious]] Air... [which] showed that an inflammable air () was evolved when sulphuric or , diluted with water, was poured upon , , or tin. He concluded that this [inflammable air] was the unaltered phlogiston of the metals. He was mistaken... but determined with fair accuracy the properties of the gas."

"Following up Black's experiment, he obtained "fixed air" from marble acidulated with , examined its properties, and measured the quantity of it contained in different alkaline s, in marble, and in the products of fermentation and decay. He demonstrated, as Van Helmont had done a century before, that the gas from these different sources was the same."

"[In] the work of the chemists of this period... the four most important gases were..."

"Other papers by Cavendish were: ....1767 on the salts found in water, particularly s, and on the in water of bicarbonate of lime and magnesia; another on eudiometric experiments to determine the quantity of dephlogisticated air in the atmosphere; one to determine the freezing point of mercury... and one on freezing, in which he considered heat to be a rapid internal motion of the particles of a hot body."

"[T]he most valuable work of Cavendish was contained in the two papers "Experiments on Air" (1784-5)... to determine the phlogistication of air... [i.e.,] the change in air when s are calcined in contact with it, and when , , or similar substances, are burned in it."

"The following are his principal conclusions:— 1. That fixed air is only produced when some animal or vegetable substance is present. 2. That inflammable air, when mixed with common air and exploded, produces water, the relation of the volumes... 1 to 2. 3. That nitrous gas gives . 4. That when electric sparks are passed through a mixture of dephlogisticated air and phlogisticated air, the gases combine and produce ."

"In his experiments with fixed air Cavendish... dried the gas by passing it over or through ignited pearl ashes... so, he was able to fix the specific gravity of the gas and of inflammable air. He also investigated their degree of absorption by liquids."

"Having... fired a mixture of inflammable air and an excess of dephlogisticated air, mixed with common air, he found in the water produced. From this he assumed that an inert gas must be present. He called this gas "phlogisticated air.""

"He... proceeded to inquire whether the whole of the phlogisticated air in a given quantity of common air could be reduced to . He found that only 1/120th resisted change. ...[T]his small irreducible residue was probably and other analogous gases... not identified until more than a century later.."

"Cavendish bestowed much attention upon heat, and might have anticipated Black's doctrines of latent and specific heal."

"In his own day, the part of his work which created the greatest sensation was his attempt to measure the density of the earth."

"[T]he discovery of voltaic electricity by Galvani and Volta, and the controversy between these two pioneers of electric science in 1790, began to influence chemical research."

"Nicholson, the editor of Nicholson's s Philosophical Magazine, and Carlisle in 1800 repeated Volta’s experiments with the voltaic pile, performed , distinguished the positive and negative poles, and established the connection between electricity and chemistry. ...They ...found that at the end of one wire was evolved, while at the end of the other oxygen appeared, provided the metal of which the wire was made was not oxidisable. When the current was passed through tincture of , they... noticed that the latter was coloured red in the neighbourhood of the positive pole, as if by an acid."

"Between 1803 and 1807 Berzelius and Hisinger in Sweden reported... [t]hat neutral salts are decomposed by the electric current; that, in general, chemical compounds are decomposed by the current, and their constituents collect at the poles; and that combustible substances, alkalis, and earths migrate to the negative pole; while oxygen, s, and oxidised compounds migrate to the positive pole."

"Gay-Lussac also worked on electro-decomposition, but the first to investigate completely electro-chemical decompositions, and to explain the laws which regulate them, was Sir Humphry Davy (1778—1829). ...An interesting narrative of his parentage and early years will be found in A History and Account of Penzance...the ancient town... chiefly devoted to mining, and... those who in early times came into contact with the Romans, and with traders from Europe and Africa, seeking tin from the famed ."

"On the death of his father, Davy was apprenticed to Mr. Borlase, a surgeon and apothecary in , in whose house he began to show his interest in chemistry... While in the service of Mr. Borlase, Davy made the acquaintance of two visitors to Penzance, Gregory Watt, a son of the great engineer, and . The latter recommended him to Dr. Beddoes, Professor of Chemistry at Oxford. The doctor had established at a Medical for investigating the medicinal properties of various gases, and in 1798 he made Davy superintendent..."

"There [Davy] set to work upon original research, and amongst other things discovered that was perfectly respirable, but produced absolute intoxication. In 1800 he published... "Researches, Chemical and Philosophical, chiefly concerning Nitrous Oxide or Dephlogisticated Nitrous Gas, and its Respiration." This treatise was the beginning of the use of nitrous oxide as an anæsthetic and intoxicant, and at once gave Davy a high reputation."

"Shortly before this Count Rumford had established the of London, and the first Professor of Chemistry, Dr. Garnet, having resigned, Davy was appointed in 1801 lecturer, and next year professor... As a lecturer he was extremely popular, his audience at the Royal Institution sometimes numbering a thousand."

"In 1802, at the request of the Board of Agriculture, he delivered a course of lectures, which he continued for ten years, and then published as Elements of Agricultural Chemistry (1813)."

"Davy was elected a member of the in 1803, and delivered under its auspices his celebrated Bakerian Lectures. In the first of these, in 1806, "On some Chemical Agencies of Electricity," described by Berzelius as one of the most remarkable memoirs in the history of chemical theory, he demonstrated that , alkaline substances, s, and some metallic oxides are attracted by negatively electrified, and repelled by positively electrified, metallic surfaces; while, on the contrary, oxygen and substances are attracted by positively electrified, and repelled by negatively electrified, metallic surfaces."

"His great discovery, the production of metallic and by ... was made in 1807. Next year in his third Bakerian Lecture he dealt with this subject, and disproved the idea of Gay-Lussac that potassium is not a simple substance, but a compound of and . At the same time he described the preparation of , which he then thought a metal."

"The study of next occupied his attention, and formed the subject of his fifth Bakerian Lecture in 1810. Discussing the nature of what was called oxymuriatic acid, he demonstrated that it was not a compound, but a simple substance, for which he proposed the name "," by which it has since been known."

"Trinity College, Dublin, in 1811 conferred upon him the degree of Doctor of Laws, the only honorary degree he received. He was knighted by the Prince Regent in 1812, and created a in 1818."

"In 1812 his Elements of Chemical Philosophy was published, and next year he travelled on the Continent. During this journey, while in Paris, he examined , and declared it to be an element..."

"The numerous accidents in mines caused by explosions of fire-damp led him to study the principles of the ignition of explosive gases. After an investigation on the spot, he invented the safety-lamp, which bears his name... declined to patent his idea [and] left it free for the benefit of all miners."

"Davy commenced his researches with the newly discovered Voltaic electricity, especially its chemical effects. ...It had previously been observed that when two wires from a battery are plunged into water, an appears round the positive, and an round the negative wire, but both... had been variously explained. Davy proved that in all cases these are derived from the decomposition of some salt dissolved in the water. On this observation he founded the Electro-chemical Theory of Affinity. He asserted that all substances which have chemical affinity for each other are in different states of electricity, one positive, the other negative; and that the degree of affinity is proportional to the intensity of these opposite states. When a compound is placed in contact with the poles of a galvanic battery, the positive pole attracts the electro-negative and repels the electro-positive, while the negative pole acts in the opposite way."

"He noticed that when copper and sulphur are mixed, they exhibit an , which increases with increasing temperature until finally they combine, and all traces of electricity disappear. Hence, he inferred that the same forces which, acting on masses at a distance, produce electric phenomena, when acting on atoms at small distances, produce chemical combination, the positive electricity of the one atom attracting and holding the negative of the other. In electrolysis the positive charge is on one and the negative on the other, but these two charges have to be discharged through the electrode before the elements are set free. This is the reverse of what takes place in combination. Davy in this view differed from the electro-chemical theory of Berzelius."

"Davy held that if the battery is strong enough any compound may be decomposed, and that chemical affinity is merely a form of electric attraction. He vigorously put his theory into practice, and by means of a powerful battery of 500 cells decomposed in 1807 [[w:Potassium hydroxide|[caustic] potash]] and [[w:Sodium hydroxide|[caustic] soda]], and in 1808 [[w:Calcium oxide|[quick]lime]], magnesia, strontia, baryta, and lithia, yielding the metals , , , , , , and ."

"The method he adopted was to pass a current from the through a solution of caustic potash or soda, which was then believed to be an element, and thus obtain metallic or , as the case might be, at the negative pole. He inferred that these caustic alkalis are s, and guessed that the alkaline earths have a similar constitution."

"Gay-Lussac and Thenard... prepared by heating (caustic potash) with red-hot filings. On passing gaseous (NH3) over the metal thus obtained, they evolved , and consequently refused to believe the simple nature of potassium, declaring it to be a compound of potash and hydrogen. Davy met this by maintaining that potassamide (the substance they obtained) is a potassium-substitution compound of ammonia."

"Another far-reaching result of Davy’s research was the proof of the elemental nature of . Berthollet’s conclusion that chlorine is oxymuriatic acid was universally accepted until Gay-Lussac and Thenard in 1809 endeavoured to decompose the gas and failed. They concluded that it contained water, because it yielded water when passed over . Their researches read to the Institute in 1809 led Davy to investigate muriatic acid () gas, which in 1808 he had shown to be decomposed by , with evolution of ."

"In 1810 he proved that is an element, and that muriatic acid gas is a compound of chlorine and . He thus overturned the oxygen-acid theory [of Antoine Lavoisier], and demonstrated that muriates are compounds of metals with chlorine. He pointed to the fact that some acids, such as sulphuretted hydrogen, contain no , and argued that muriatic acid gas was one of these, chlorine in it taking the place of oxygen."

"He used the following arguments to show that there is no in muriatic acid gas:—"

"The conclusions of Davy were at first doubted, but when and were also discovered, Gay-Lussac and his followers adopted Davy’s views. The latter worked out , and proved that (HF) contains no ."

"Berzelius also opposed Davy until the discovery of , but embraced the latter’s opinion in 1820."

"One of the greatest contemporaries of Davy and Dalton was the Swedish chemist Jons Jakob Berzelius (1779—1848). He... studied medicine at the University of Upsala, especially chemistry under Afzelius. His first chemical research was an analysis of s in 1799."

"Graduating as Doctor of Medicine in 1802, his thesis was "On the Action of Galvanism on Organic Bodies," in which he made use of the discovery in 1800 by Volta of the battery known by his name."

"Next year, in an essay "On the Division of Salts through Galvanism," he propounded a theory of electro-chemistry."

"Berzelius spent ten years in ascertaining with unprecedented care and accuracy the atomic or molecular weights of over two thousand simple and compound bodies. The results were published in 1818, and revised in 1826. In making these calculations he regarded oxygen as the pivot round which chemistry revolves, and therefore took it as the basis of reference for atomic weights. The greater part of his figures bear comparison with the most accurate determinations of more modern date."

"In 1815 he applied the Atomic Theory to the mineral kingdom, and made a new arrangement of minerals, founded on their being definite chemical compounds."

"As the outcome of his study of voltaic electricity, he proposed a theory based upon the supposition that the atoms of elements are electrically polarised, the positive charge predominating in some, and the negative in others."

"He also put forward a dualistic hypothesis that chemical compounds are composed of two electrically different components. In extending this hypothesis to organic chemistry, he regarded organic compounds as containing a group or groups of atoms forming compound radicles, in place of simple substances or elements. Although his views never commanded full assent from other chemists, he is... one of the founders of the Radicle Theory."

"One of his most useful services to chemistry was the invention of a system of symbols and notation, which with modification is still used in stating chemical formulæ."

"He indicated each simple substance or element by the initial letter (or, where more than one had the same initial, by two letters) of its Latin or Greek name. In the case of compound bodies he added a small subscript figure to show the number of atoms of each element present in the compound when these atoms exceeded unity. Thus:— Oxygen was represented by the letter O. Hydrogen was represented by the letter H. Mercury was represented by the letters Hg (Hydrargyrum). Lead was represented by the letters Pb (Plumbum). Water, a compound of two atoms of hydrogen and one of oxygen, was represented by H2O. Litharge, a compound of one atom each of lead and oxygen, was represented by PbO."

"He analysed many rare minerals; in 1818 discovered , , and its compounds; in 1822 studied the mineral waters of Carlsbad; in 1823 made experiments on , , and pure ; in 1824 and ; in 1826 thio acids and those salts in which was held to replace ; in 1828 examined , , , ; in 1833 and thio derivatives; and in 1834 ."

"Davy and Berzelius were chemists of the first rank in all branches of the science; but... [in] electro-chemistry... they were the leading pioneers."

"This volume is the outgrowth of a series of talks which the author had for several years given to his students at the Institute of Technology... The lectures have dealt in a direct informal way with the fundamental ideas of the science: their origin, their philosophical basis, the critical periods in their development, and the personalities of the great men whose efforts have contributed to that development."

"[T]he person addressed is the more mature student of chemistry, though it is believed that few portions of the book will present serious difficulties to the general reader."

"The aim has been to emphasize only those facts and influences which have contributed to make the science what it is today... [T]he claim of a topic for consideration has been not its practical but its historical importance... [i.e.,] did it contribute a new fundamental idea."

"Little attention has been paid to questions of priority. A great discovery is usually preceded by a multitude of earlier observations, the sum total of which may even include all the fundamental facts involved. ...[F]rom the historical standpoint the discoverer of a great truth is usually the one through whose efforts it first becomes available to the [human] race."

"The value of the historical method for studying every department of human thought is now so universally recognized that it requires no emphasis, but... by observing the errors and misunderstandings of the past, we learn to avoid errors in our own thinking; by acquaintance with the way in which great men have solved problems, we are assisted in solving problems of our own; by observing the different aspects presented by the same facts in the light of successive theories, we acquire an insight obtainable in no other way into the nature, limitations and proper function of all theories."

"[A]s we study how man's knowledge of nature has broadened and deepened with the years, we acquire a better understanding of the trend of thought in our own times, and of the exact bearing of each new discovery upon the old but ever recurring problems of the science."

"At no period has the development of chemistry been more rapid or more interesting than it is today, and the author indulges the hope that even this brief sketch of its history may assist the reader to follow that development with a fuller appreciation of its significance, for, after all, we study the past that we may understand the present and judge wisely of the future."

"With Joseph Black (1728-1799) we come to the eminent group of distinguished chemists whose work contributed so largely to the overthrow of the phlogiston theory... [T]hey themselves almost without exception remained blind to this, its most important significance."

"Black was long professor in Glasgow, and made some important discoveries in physics, developing independently the idea of specific heat and of , though his work was not formally published."

"He is best remembered... for his work on magnesia alba which he presented for the doctor's degree in 1754. In this investigation he took up the study of what we now call as a new substance... we may sum up Black's results in a series of propositions: I. Magnesia alba when strongly heated loses about half its weight and yields a new substance magnesia usta () II. With vitriolic acid magnesia alba yields epsom salt () with effervescence. III. Magnesia usta when similarly treated yields epsom salt without effervescence. IV. In a solution of epsom salt, mild alkali () precipitates magnesia alba and the solution on evaporation yields vitriolated tartar (). V. Mild alkali effervesces with acids while caustic does not. VI. Mild alkali is made caustic by addition of magnesia usta."

"[I]t is... easy to see what a handicap upon the chemists of that time was the use of a nomenclature necessarily incapable of expressing chemical relationships, and how impossible it then was to know whether all substances in a reaction were accounted for or not. Nevertheless, Black interpreted his results with perfect accuracy."

"From II and III he concluded that the difference between magnesia alba and magnesia usta was the gas ("fixed air") liberated from the former by acids, and that it was the expulsion of the same gas which accounted for the loss of weight when magnesia alba was heated (I)."

"II and IV showed that magnesia alba could be regenerated from magnesia usta by the aid of mild alkali, hence the latter must contain fixed air which it surrenders in the reaction. This is further confirmed by V which shows that mild alkali differs from caustic by its content of fixed air."

"VI completes the caustifying of the alkali by the action of magnesia."

"Black saw at once that these reactions were analogous to those involved in the ancient method of preparing caustic alkali from quicklime. He accordingly repeated his experiments using limestone instead of magnesia alba and so reached the correct conclusion that the 'burning' of lime consists essentially in the expulsion of fixed air."

"Such a result was utterly opposed to [previous] explanations... [i.e.,] when lime was heated in the kiln phlogiston entered into it making it fiery or caustic. Later when the quicklime was treated with mild alkali another transfer of phlogiston occurred and the latter became caustic in its turn."

"[I]n later years, when Lavoisier had once shown the way, Black was among the first to adopt the new views."

"[A]lthough in middle life he inherited a fortune which made him one of the richest men in England, this had no influence upon his regular and frugal habits."

"[H]is work was done with little thought of fame, and much of the best of it remained entirely unknown till long after his death."

"Cavendish was the first to make a thorough study of and he gave it the name of "inflammable air" in a paper published in 1766. The evolution of a combustible gas when a metal is dissolved in acids was observed much earlier. We are reasonably sure that it was known to Paracelsus and Van Helmont, and we know that it was isolated by Boyle."

"Cavendish identified with phlogiston, and this was entirely in the spirit of current views, for if a metal is a compound of a base with phlogiston then when the base unites with an acid to form a salt phlogiston must escape."

"About 1783, after the discovery of oxygen. Cavendish combined this gas with by means of the electric spark, and so established the composition of water."

"In 1785... he noticed that oxygen and when sparked... over water yielded ... He always found... a small inert residue whose volume... he estimated at about 1/120 of the whole. ...in spite of this valuable clue ... and the other rare gases of the atmosphere remained undiscovered for more than a hundred years."

"Cavendish... accounted for his results in terms of the phlogiston theory... on the assumption of Priestley that oxygen was "dephlogisticated air," that portion... which unites with phlogiston on combustion."

"He was not ignorant of the work of Lavoisier, and acknowledged frankly that the latter's views would explain the results of his experiments "nearly as well," but after weighing both opinions he clung to the old for what now seems a curious reason. He writes: "There is one circumstance also, which though it may appear to many not to have much force, I own has some weight with me; it is, that as plants seem to draw their nourishment almost entirely from water and fixed and phlogisticated air, and are restored back to those substances by burning, it seems reasonable to conclude, that notwithstanding their infinite variety they consist almost entirely of various combinations of water and fixed and phlogisticated air, united according to one of these opinions to phlogiston, and deprived according to the other of dephlogisticated air; so that, according to the latter opinion, the substance of a plant is less compounded than a mixture of those bodies into which it is resolved by burning; and it is more reasonable to look for great variety in the more compound than in the more simple substance.""

"F. J. Moore was born at Pittsfield, Mass., June 9, 1867. ...He ...went to the University of Heidelberg, where he studied with Victor Meyer and with Gatterman ...and was awarded the degree of doctor of philosophy in 1893. ...In ... 1894 he came to the Massachusetts Institute of Technology ...The condition of his health caused him to retire from active teaching in 1925 ...All American students of the history of chemistry are familiar with Moore's book on the subject. Many owe to it their first interest in the history of their science. ...He published "Outlines of Organic Chemistry (1910), "Experiments in Organic Chemistry" (1911), and "A History of Chemistry (1918). The last book shows the character of the man—widely read, witty, and lucid. It is entertainingly written and can be recommended to chemist and non-chemist alike. The writer has found it excellent medicine for the student who thinks that organic chemistry is difficult, for it gives him an interest which removes difficulties and makes intricacies appealing. As an undergraduate at Amherst, F.J. Moore was interested in chemistry and in philosophy... Although he decided to pursue the chemistry, his "History of Chemistry" makes it clear that he never abandoned the philosophy."

"During the enforced leisure of a long illness, I commenced, in 1842, to collect materials for a projected work on the lives of the Chemists of Great Britain, in which Cavendish should occupy a prominent place; and I had made some progress in my task when the Cavendish Society was founded."

"When... at the call of the Society, I... turned my attention solely to the works and character of the Honourable Henry Cavendish, circumstances had occurred which gave him an importance in the eyes of the lettered public, such as no other chemist at the time possessed. He prosecuted zealously and successfully so many branches of knowledge, that the students of nearly all the physical sciences may consider him as an illustrious brother..."

"[H]is memory has been specially honoured by chemists, among whom Sir Humphry Davy, Faraday, and Thomas Thomson have been foremost."

"I have written this volume as a student of chemistry... I have dwelt less upon Cavendish's purely physical researches, than I should have done had I been free to expatiate upon his merits as a natural philosopher. His physical researches, however, especially those on electricity and on the density of the earth, have not been overlooked in the succeeding pages; and the value of these memoirs is... fully appreciated by men of science..."

"I have given prominence, accordingly, to his discoveries in chemistry, and in the science of heat, but especially to the former. It has been impossible to do otherwise. ...Cavendish has been the occasion of the keenest controversy that has interested chemists for a long time, and much of this volume is occupied with... Who discovered the composition of water,—Cavendish, Watt, or Lavoisier?"

"[C]harges of plagiarism, and of unfair dealing towards each other, have been brought against the rivals, nor have their friends and acquaintances escaped reproach, including the entire ..."

"I have undertaken... a delicate and difficult task, in writing a work which compels me to pass under review the judgments of men of such note in science and letters as Arago, Dumas, Brougham, Brewster, Jeffrey, Harcourt, Whewell, and Peacock, at whose feet I have been accustomed to sit as a humble disciple."

"The reputation of Lavoisier, and of Watt, is as sacred a thing in my eyes as that of Cavendish; and I should be the first to regret if the tone of this work should seem at variance with the catholic spirit of esteem for all great philosophers..."

"Whilst... I have endeavoured to be impartial, and to make the biography a faithful sketch, not a eulogy, I have deemed it an essential part of my duty as a biographer to vindicate the moral character of Cavendish from even the shadow of suspicion. It has been impossible to do this, without censuring those who have called his good name in question."

"If in uttering censure I have forgotten what is due to great authorities in literature and in science, even when they are in error, I shall deserve and bow to reproof; but if I have only reluctantly fulfilled an imperative though invidious duty, and have justified my censures by showing that they are deserved, I shall hope to be vindicated at the hands of my readers."

"In 1845, Mr. Muirhead, the able editor of "the Correspondence of the late James Watt on his discovery of the theory of the Composition of Water,"... and by that gentleman, the most zealous of Watt's defenders, and the most unhesitating of Cavendish's assailants, I had everything that could be said in favour of Watt urged upon me in the strongest terms."

"The publication, also, of the Watt Correspondence in 1846, led to my obtaining the friendship of the late lamented Lord Jeffrey. He had known and esteemed Watt, and he welcomed the publication of the Watt Correspondence, as furnishing a becoming occasion for exalting the honour of his old friend."

"Before his Lordship published his judgment on the rival claims of Cavendish and Watt in the ' for 1848, I had many conversations with him... Chemistry was a science in which he had always taken great interest... With his estimate of the relative merits of Cavendish and Watt I could not concur, and he listened to my earnest defence... with all the frank courtesy and love of fair dealing which so eminently characterized him."

"Against Cavendish he entertained no animosity or prejudice, and he was most willing to praise him; but he thought that Watt had been wronged... so that he pressed me with all the arguments which... might be urged in favour of his great client... and I defended Cavendish in the strongest terms which courtesy sanctioned."

"My zeal in Cavendish's cause made no difference in Lord Jeffrey's kindly dealings towards me, and he was the first in whose hands I purposed to place this volume, in which many of his conclusions are called in question."

"After Lord Jeffrey's decease, the Rev. William Vernon Harcourt, the ablest of Cavendish's defenders... furnished me with his estimate of the position in which Cavendish's claims were placed by the publications in favour of Watt... since 1846. ...I owe to him an introduction to the Earl of Burlington, who placed at my disposal the whole of Cavendish's papers in his possession, and obtained for me much information concerning his illustrious ancestor's personal history."

"The papers on Electricity which Cavendish left behind him, are at present in the hands of that accomplished Electrician, Sir W. Snow Harris, who, in the kindest manner, drew up for me an abstract of them, accompanied by a commentary."

"I have thus had access to many unpublished documents, which are fitted to throw light on Cavendish's merits and his personality..."

"[T]he Rev. Dr. Vaughan, of , has permitted me to make any use I pleased of papers contributed to the ', in which I published, in 1845, a short biographical sketch of Cavendish."

"[S]ince the publication of the Watt Correspondence, in 1846, the only lengthened notices... in reference to Cavendish, have been Sir David Brewster's Article in the ' for 1847, and Lord Jeffrey's Paper in the ' for 1848. Both of these writers pronounce against Cavendish, and refer to the Watt Correspondence as decisive of the merits of Watt; but... from the following pages... the admirers of Cavendish have every reason to congratulate themselves on the publication of the "Correspondence;"... for... it furnishes the most decisive evidence in favour of Cavendish, and as such I have constantly quoted from it."

"He was an excellent mathematician, electrician, astronomer, meteorologist, and geologist, and a chemist equally learned and original. In the fullest sense of the term, indeed, he was a natural philosopher, and had he published during his lifetime all the researches which he completed, his reputation would have been much wider and more varied even than it was."

"Cavendish... dealt with his discoveries as with his great wealth, and allowed the larger part of them to lie unused in his repositories."

"His published papers, accordingly, give but an imperfect notion of the great extent of ground over which he travelled in the course of his investigations, and of the success with which he explored it."

"[A]s chemistry is concerned, Mr. Harcourt has left little to be done in this matter by his analyses of the Cavendish MSS."

"[H]e could, with the greatest ease, change his subject of study, and that he was in the constant practice of carrying on together, widely dissimilar enquiries."

"Cavendish's life is so barren of incident, that with the solitary exception of the Controversy concerning the discovery of the composition of Water, almost no connexion can be traced between the events of his history and the researches which he prosecuted."

"Cavendish did not give to the world his earliest researches. He probably kept many back. Two lengthened investigations, at least, the one chemical, the other physical, were completed and laid aside, in a condition ready for publication, before he commenced contributing to the Transactions of the Royal Society of London, in which all his papers were published."

"Experiments on Arsenic... experiments... are as early... as 1764... [T]he paper... contains an elaborate enquiry into the differences between regulus of Arsenic (Metallic ), white Arsenic (Arsenious Acid, AsO3), and Arsenical Acid (Arsenic Acid, AsO5). The properties... are described with no little accuracy. ...Cavendish ...held arsenic acid to be "more thoroughly deprived of its phlogiston" than arsenious acid; and the latter to bear a similar relation to metallic arsenic. ...[Equivalently] arsenic acid contains more oxygen than arsenious acid, and the latter more than metallic arsenic, which we know to be the case. The paper, is otherwise remarkable for its speculations on the nature of the "red fumes," (, produced by the action of the air on ) which attended the action of nitric acid on arsenious acid, and for its discussion of the theory of the solution of metals in acids, and the reduction of the former by heat and inflammable matter."

"Cavendish engaged in an extensive series of Experiments on Heat... [W]e must go back... into 1764, for the commencement of the researches... They were written out for a friend... but were not publicly referred to till some nineteen years after... when certain of the results were quoted in a paper published in 1783, on the Congelation of Quicksilver."

"[H]ad [these researches] been made public in 1764 or 1765, they would have given Cavendish chronological precedence to Black in some of his discoveries, and equality of merit in others. They would have entitled him... to rank above Black's pupils and imitators... as Irvine, Crawford, and Wilcke."

"Cavendish discovered for himself, and announced with admirable clearness, the fundamental laws of specific heat; and collected, probably before any one else, tables of the specific heats of various bodies."

"With scarcely any knowledge... of what Black had done towards the exposition of the laws of Latent Heat, and guiding himself by a totally different theory, as to its relation to solidity and liquidity, Cavendish investigated... the evolution of heat which attends the solidification of Liquids, and the condensation of Gases or Vapours, and the converse "generation of Cold," as he styled it, which accompanies the liquefaction of Solids and the Vaporisation of Liquids."

"Cavendish's earliest public contribution to science was... his paper on Factitious Airs, published in the Transactions of the Royal Society for 1766. It consisted of three parts: a fourth, which was not published, remains in a state of perfect completion, ready for the press, among his papers. It was evidently intended to be read to the Royal Society, for it contains a reference to the "Former Experiments read to this Society." ...since ...published by the Rev. W. V. Harcourt."

"Those four papers... are occupied with the discussion of the properties of , , and the gases evolved during the , putrefaction, and of vegetable and animal matters. They contain the first distinct exposition of the properties of hydrogen, and the first full account of those of carbonic acid, besides investigations into the combining proportion of the latter, and the properties of s. They recount also the first successful attempt to determine the differences in which characterise the gases, and suggest the probability of there being more kinds than one of inflammable air."

"A paper which was published by Cavendish in the Philosophical Transactions for 1767, may be considered as an extension of the research into the properties of . It is occupied with an account of the Analysis of one of the London pump waters (... of ), which was remarkable for the quantity of calcareous earth which it deposited when boiled."

"Cavendish showed that the earth was originally retained in solution by carbonic acid, which the boiling dissipated, so as to allow the earth to precipitate. The other constituents of the water were determined also, and the whole research is curious as one of the earliest tolerably successful attempts to analyse a natural water."

"Abstracts of [the above] papers are given in the sequel... I refer to them... as showing the prominent position which Cavendish took... as a discoverer in chemistry."

"He may be counted the third in order of time among the four great English pneumatic chemists of the eighteenth century, the other three being Hales, Black, and Priestley."

"Hales was the earliest enquirer into the properties of elastic fluids, and, without injustice to his illustrious predecessors, the immediate disciples of Bacon, and early contemporaries of Newton, who had made some progress in investigating the properties of the gases, he may be called the father of in England."

"His great merit was to point out that elastic fluids may be obtained from an immense variety of organic and inorganic substances, of which they are as important constituents as the solids or liquids which may be separated from them."

"Hales did not recognise, unless very imperfectly, that those elastic fluids were chemically unlike, and specifically distinct, so that he spoke of them as if essentially identical with each other and with the atmosphere; and had no other name for them than simply air. His writings belong to the first third of the preceding century."

"Black, appeared a little after the middle of the century, and by his celebrated essay on Magnesia Alba, demonstrated that there existed at least one gas totally distinct from the atmosphere, and able by its addition to bodies, or its removal from them, to alter immensely their physical and chemical properties."

"Black thus rose to a higher discovery than that reached by Hales. The latter had shown that the most solid stone might owe half or more of its weight to the presence of an imprisoned or solidified air; but he had paid little or no attention to the effect which the removal of this air had in altering the chemical properties of the substance from which it had been extracted."

"Black demonstrated that the fixed or solidified air did not merely increase the bulk and weight of the solid, but determined in a most striking manner its chemical properties, so that a substance which, when saturated with a peculiar air, was a bland, innocuous insoluble powder, or crystalline solid, became by the expulsion of this air soluble, caustic, and corrosive; and the difference between or on the one hand, and quicklime on the other, was shown to be entirely dependent on the presence or absence of the gas, which Black named fixed air, and we name '."

"Twelve years after the publication of Black's paper, namely in 1766, Cavendish published the first of the essays we have been considering. He took up the investigation of fixed air where Black and his pupils had left it, and examined in particular its properties when free, on which Black had published scarcely anything."

"Thus far Cavendish appears rather as the follower of Black than as an independent observer, although... his investigation of the properties of free was equally original and accurate. He struck out, however... a new path... and added to the solitary fixed air, a second gas equally distinct from it and from atmospheric air in properties. This was , of which Cavendish cannot be called the discoverer, for many of his predecessors, Boyle among others, had encountered it; but no chemist had carefully examined its properties, or at least had described them."

"His predecessors... knew only as much about the gas as a navigator who merely touches at a strange island, knows of its geography and various products, to whom we cannot deny the merit of being its discoverer, although we often assign much more credit to some later visitor who surveys and describes the new territory."

"The mere discovery of was no great feat; for the most random experimenter, who, with or without purpose, handled the more powerful reagents, was likely to encounter a phenomenon of which the conditions are so simple as the evolution of hydrogen from the contact of and an ; and the ready and explosive of the gas when it meets flame could not fail to attract the attention of the most heedless observer."

"[A]mong Cavendish's predecessors backwards through several centuries, there were many who could assert equally good claims to be called the discoverers of hydrogen, of which, nevertheless, they knew exceedingly little. Cavendish did not claim to be one of them, but he could claim a merit which was much greater."

"Boyle, Mayow, and Brownrigg had preceded him in showing how gases may be collected, but no one had given an example of the mode of examining them."

"Cavendish's examination, accordingly, of the properties of and , has all the interest that attaches to the first demonstration of a method of pursuing a novel investigation. It is easy to look back from our thoroughly appointed laboratories, filled with the apparatus which some ninety years have added to the chemist's instruments... and to criticise and depreciate the methods and results it records; and this has been done largely and unreasonably."

"[I]f we consider how much more genius is requisite for the devising of an apparatus or method of research which is quite new than is needed for its indefinite extension and improvement, and if we further judge the experimenter of 1766, not by his successors of 1840 or 1850, but by his contemporaries, we shall not hesitate to assign a very high rank to Cavendish, as one of the earliest investigators of the chemical properties of the gases."

"We find him... collecting the elastic fluids on which he experimented, with various precautions to secure their purity, observing carefully from how many different sources they could be procured with identical properties, and determining with numerical precision the relative volumes yielded by different processes. The questions of their permanent elasticity, their in different liquids, their combustibility or power to support combustion, their specific gravity, and likewise their combining equivalent, were all carefully enquired into."

"The apparatus employed, though deficient in delicacy according to modern standards, was unexceptionable in principle, and wherever... possible, was made to yield quantitative results, so that this earliest analyst of the gases introduced the principle of rendering all descriptions of phenomena as precise as possible, and endeavoured... to attach a numerical value to each. We... have done little more in later times than extend, improve, and... perfect Cavendish's processes for the analysis of gases, and that we differ from him more in our mode of interpreting certain of the phenomena... than we do in our methods..."

"[H]e mistook... the source of the ... procured... from the solution of , , and , in sulphuric and muriatic acids, and referred it to the metals in which he supposed it to exist in a peculiar state of combination."

"Water at this time... was supposed to be an element, and the composition of all the acids was unknown. No gas had been certainly traced to a liquid as its source, otherwise than as dissolved in it like in a ; whilst Hales and Black had shown that the most fixed and solid bodies might yield from their very substance large volumes of elastic fluid."

"[T]his may have been one reason which induced Cavendish to suppose that the came out of the rather than out of the . ...[T]he belief common to him with the majority of his contemporaries, [was] that the metals contained a peculiar combustible principle named phlogiston. This Cavendish supposed to abandon the metal, and, assuming the form of an elastic fluid, to show itself as the inflammable air."

"was... the first of the combustible gases examined, and for many years... great confusion existed in the mind of chemists as to the number and nature of the different inflammable elastic fluids; nor did this begin to cease till the composition of water and of was ascertained."

"Cavendish... had clearer views on this... than most of his fellow chemists. He ascertained that vegetable and animal matters, by putrefaction and , yielded inflammable air. He was not aware of its exact nature, but he satisfied himself by the test of specific gravity, and the volume of common air required for its combustion, that it was not identical with Hydrogen, which accordingly he distinguished as the "inflammable air from metals." He further observed that "the nature of the inflammable air was not quite the same" from animal as from vegetable substances. [H]e turned these observations to excellent account in the researches which led him to the discovery of the composition of water."

"Between the years 1767 and 1783, Cavendish did not appear before the public as an author on any subject directly connected with chemistry, but... he continued to prosecute chemical enquiries."

"Among his papers is one on which he himself has written, "communicated to Dr. Priestley," the contents of which are referred to by the latter in his account of Experiments and Observations made in and before the year 1772... The paper... has been printed by Mr. Harcourt, and is... one of the earliest distinct accounts of . Cavendish prepared it by passing atmospheric air repeatedly through red hot , and removing the produced, by caustic potash."

"He gives the following description of it: "The specific gravity of this air was found to differ very little from that of common air; of the two, it seemed rather lighter. It extinguished flame, and rendered common air unfit for making bodies burn in the same manner as fixed air, but in a less degree, as a candle which burnt about 80” in pure common air, and which went out immediately in common air mixed with 6/55 of fixed air, burnt about 26” in common air mixed with the same portion of this burnt air.""

"Cavendish gave no special name to nitrogen, which he referred to generally as mephitic air. It was afterwards minutely described by Lavoisier and Scheele, and was distinguished by Priestley and his contemporaries, by the name phlogisticated air."

"The quotation adduced above, shows incontestably that Cavendish discovered for himself, and had ascertained with great precision its chief properties; but in the absence of precise dates, I hesitate to adopt Mr. Harcourt's conclusions, that the paper from which I have quoted contains "the first clear description of nitrogen as a distinct gas.""

"Dr. Rutherford, of Edinburgh, the reputed discoverer of , published his Thesis De Aere Mephitico, in 1772. His process for procuring the gas, for which he had the same general term as Cavendish, viz., mephitic air, resembled that of the latter chemist, except that he employed atmospheric air vitiated by respiration, not by combustion. This he passed through caustic potash, and tested by lime-water, which it did not precipitate, whilst it possessed the power of extinguishing life and flame."

"The dates of publication, or announcement, of Cavendish and Rutherford's observations, are thus the same, whilst the dates of their experiments are uncertain. We cannot in these circumstances give precedence to the former, but it is certain that he was an independent discoverer of ."

"In 1771 he published the elaborate paper on the theory of the principle phenomena of electricity, which appears in the Philosophical Transactions for that year. In 1776 appeared... his Attempts to imitate the effects of the Torpedo. ...[T]he singular power which the torpedo possesses, of benumbing those that touch it, had been referred with great ingenuity and force of argument, by Walsh and others, to its possessing the means of discharging electricity at will. Cavendish... tried whether he could not successfully imitate the effects of the living fish, by a piece of apparatus constructed in imitation of it, and placed in connection with a friction electrical machine and a Leyden battery. He succeeded... all doubts as to the identity of the torpedinal benumbing power, with common electricity, were removed."

"Faraday, among others, have borne testimony to the light which was thrown upon every department of electrical enquiry, by Cavendish's demonstration... Faraday found the theory which Cavendish suggested, sufficient to explain the curious and apparently contradictory voltaic phenomena which he observed so late as 1833. ...In none of his essays does Cavendish appear to greater advantage than in this."

"[T]he Royal Society... selected... [Cavendish] in 1776 to describe the meteorological instruments which were made use of... The Society had commenced in 1773 recording their observations with the thermometer, barometer, rain-guage, , variation-compass, and dipping needle, and Cavendish was applied to, to give an account of these. His father, , had devoted himself to , and had paid special attention to the improvement of the thermometer and barometer... That [Henry] had paid great attention... to the thermometer... is certain from his unpublished papers on heat of 1764 and 1765... The most important part of this paper is his description of the best method of accurately graduating thermometers... found specially referred to in the abstract of his papers on Heat."

"1777 or perhaps... 1778, marks the period when he commenced his most important chemical researches... Experiments on Air... carried on with frequent, and sometimes long interruptions till 1788, and no part... was published till 1783. They led to the discovery of the constant quantitative composition of the atmosphere, the compound nature of water, and the composition of ."

"In 1783... Cavendish published his first paper on heat, embodying some of the results he obtained in 1764 in reference to the freezing or solidifying point of liquids. [T]he papers on heat... are three... 1783, 1786, and 1788. All of them refer to ; the first to that of quicksilver, the second and third to... mineral acids and... alcohol [respectively]. ...They are all... commentaries upon observations made in North America by officers of the Hudson Bay Company on the effect of great natural cold, assisted by powerful freezing mixtures in congealing mercury, , oil of vitriol, and spirits of wine. These observations were made under Cavendish's directions, and at his cost..."

"The most important of these papers was that on the freezing of quicksilver. This metal... was frozen in a thermometer in 1759... by Professor Braun, of Petersburgh, who observed that its congelation was accompanied by a descent of the mercury, through many hundred degrees, and came to the conclusion that the freezing point of the metal was some 300° or 400° below Farhenheit's zero, but was unable to determine the exact point of congelation."

"Braun confounded two phenomena. The one of these was the contraction which accompanies the cooling of liquid mercury; the other the further contraction which attends its solidification. The contraction due to both these causes [was] exaggerated by the peculiarities which attend the freezing of mercury in capillary tubes... To his conclusion the majority of the natural philosophers of Europe assented, but... Cavendish and Black... by independent researches, suggested the same way of ascertaining the true freezing point of mercury... This method... was put in practice by Governor Hutchins at Albany Fort, Hudson Bay... The result was, that the freezing point of mercury is not more than 39° or 40° below Fahrenheit's zero... Mr. Hutchins's observations were not made till 1782, but the directions by which he was guided had been laid down by Cavendish in 1764 and 1765."

"The experiments on air... supplied materials for four papers, besides leading to the observation of many phenomena which were never made public. ...In the interval which elapsed between the publication of Cavendish's first chemical papers and [these]... Priestley, the fourth of the great English pneumatic chemists, had appeared... while Scheele... and Lavoisier... besides other less distinguished observers had effected the discovery of nearly all the gases known to... the present... and their study engrossed the attention of every chemist."

"[T]he relation of the atmosphere to combustion demanded explanation, and the nature of the change which the air underwent when inflammables, burned within confined portions of it, deprived it of the power of further supporting combustion. At this problem all the active chemists of Europe were now working, but with very unequal success, owing to the false theory of combustion which the majority espoused, and the erroneous opinions which were current concerning the constitution of atmospheric air."

"Boyle, Hooke and Mayow in England, and Rey in France, besides other early disciples of the school of Bacon, understood the true nature of combustion in air much better than the immediate predecessors of Lavoisier. The former held as we do, that a burning body is literally fed by the air, and they apprehended with considerable clearness, that burning combustibles add something to themselves from the atmosphere. Some of these observers were also well aware that combustibles are converted by combustion into substances possessing greater weight than the original inflammable."

"In an evil day... Beccher and Stahl, two men of unquestionable genius, devised a theory of combustion which led all chemistry astray for half a century. According to their view combustion consisted in the emission from the combustible of a peculiar fiery principle, to which the name phlogiston was given. It was present in all inflammables, however different their appearance and properties. When they burned, it passed out of them into the air which surrounded them, and by its loss they became changed in character and quite incombustible; but if phlogiston was restored to them, they recovered their original appearance and properties, among the rest, their combustibility."

"Much has been said by the historians of chemistry in praise of this theory as having served, in spite of its inaccuracy, to guide chemistry to great results, at a time when the science was not ripe for a juster theory. From this statement I must totally dissent. Its devisers assuredly were men of rare gifts, and their theory, welcomed by their fellows and immediate successors as a great boon to the science, exerted for some forty or fifty years a strange fascination over all the chemists of Europe. These forty years, however, were like those spent by the Israelites in the wilderness, after their glimpse of the Promised Land."

"Had Stahl and Beccher carried out the conclusions which the early disciples of Bacon had imperfectly announced, we should not have waited till the close of the eighteenth century, and the advent of Lavoisier, for the true interpretation of the nature of combustion. A Joshua would have been found some half a century sooner, and the goodly land which the chemists cultivate, would exhibit a much wider extent of fertile territory than it does at the present day."

"[N]o service can be rendered to the cause of truth by affecting to deny that, especially in the early history of the sciences, we find long periods of total stagnation, and the tide even ebbing, when by our calculations it should have overflowed."

"Stahl's theory of phlogiston was not a refined speculation. It scarcely deserves to be called a scientific hypothesis. It really amounted to nothing more than the assertion, that a body was combustible because it contained something combustible; which was equivalent to the identical proposition that a body burned because it burned. This declaration instead of being a refinement of philosophy, to which only a man of science could reach, was but the reduction to terms, of a vulgar belief. It was a poetical, rather than a scientific thought; for the natural tendency of every untrained imaginative mind, as we see in children, and in the early history of all nations, is to impute every manifestation of power, to the presence in the body manifesting it, of some inner principle more or less self-sustaining, and resembling a living or vital agent."

"The same spirit, which made the Greeks people the winds and the waves, the rivers and the trees, with gods; which makes the savage regard the compass needle as animated; and the child demand to see in some visible shape, the motive principle of a watch or moving toy; led the Chemists of the seventeenth and eighteenth centuries to declare that a candle burned because it contained a burning principle."

"I have sometimes thought that this theory was in part occasioned by the spectacle of the sun and other heavenly bodies unceasingly emitting heat and light. I have found, however, no reference to this striking phenomenon in the writings of the phlogistians; and however much the unbroken radiance of the sun might justify a popular belief in the power of combustibles simply to emit light, it could never justify the assertion of this even as a probable truth, for this would have been to explain one mystery by another."

"Whilst poetry might have welcomed the doctrine that a blazing body throws off light and heat, as a bell utters a sound, or a flower exhales an odour, that science could only accept it as an hypothesis of no great likelihood or high value, and which at all events required at once to be tested, as to its utility as an interpreter of known phenomena, and a guide to the discovery of new ones."

"The doctrine of phlogiston... [i]nstead of being treated as a doubtful hypothesis... was employed as a perfect theory; and phenomena at variance with it were either wilfully overlooked, or compelled to adjust themselves to its Procrustean bed."

"A true hypothesis, or one in the main, true, is always found capable of explaining more than it professed or expected to explain. But the phlogiston hypothesis transgressed its own self-imposed conditions, and failed to explain the most simple and essential phenomena of combustion. Thus its presence in bodies was held to confer upon them combustibility, yet when transferred from a blazing combustible to air, instead of rendering the latter inflammable, and changing it into a gas which could be kindled, it changed it into one which was totally incombustible and at once extinguished flame; for phlogisticated air in its simplest form was our ."

"[P]hlogiston was held to be a material and therefore ponderable substance, so that its escape from a combustible should have caused the latter to diminish in weight; yet the metals and phosphorus were known to increase in weight by combustion. Thus the lameness of the phlogiston hypothesis was betrayed at its first step, and it had to be furnished with a crutch, in the shape of an assumption that it was a principle of levity, so that a body containing it weighed less than if it were absent, before it could move a step further. Many of the Phlogistians... did not adopt this assumption... but they ignored the phenomenon of increased weight... and stood in the anomalous position of professors of a Quantitative Science, who should weigh and measure... and yet had put aside the balance as a useless thing."

"That a burning body changed the quality of the air around it, whilst itself undergoing a complete change of properties, had not escaped the attention of the phlogistians. Beccher and Stahl, although they made no investigation into the nature of the change which air underwent when it supported combustion, were aware that a limited quantity of air in which a combustible had burned till it was extinguished, could not a second time support combustion, a fact... of universal belief from the earliest times."

"Such, then, was the crude and clumsy hypothesis which was recognised as a fundamental law of all chemistry, at the period when Cavendish commenced his Experiments on Air. Their object was to ascertain what Beccher and Stahl should have ascertained before they promulgated their hypothesis, viz., what change does combustion effect upon air."

"The discovery of oxygen, of , and of other gases, and the experiments which Priestley, Scheele, and Lavoisier had been assiduously making for some years, had directed... attention... to the fact, that air not only became irrespirable and unable to support combustion when exposed to the action of burning inflammables, but... underwent a diminution in volume, so that a portion of it was to appearance lost."

"To discover what became of the lost air was a question which, in 1777, greatly interested... chemists... and Cavendish's attention was specially directed to the problem, by the researches of Scheele on this point... Priestley and Lavoisier had, contemporaneously with Scheele, investigated the same subject; and all three had made some progress, especially Lavoisier, in explaining the problem."

"When those researches commenced, air was universally reputed to be a simple or elementary body. It was liable, according to the phlogistians, to vitiation, by the addition to it of phlogiston, so that it was referred to as being more or less phlogisticated, according to the degree of its power to support respiration and combustion."

"When oxygen was discovered by Priestley and Scheele, it was regarded by them as air altogether respirable, and exhibiting a maximum power of supporting combustion, because it was quite free from phlogiston. It was named accordingly de-phlogisticated air, and for a season the atmosphere was referred to as consisting of two parts, a "dephlogisticated part" and a "phlogisticated part," which differed... only in degree. By-and-by those parts were regarded as differing in kind, not merely in degree; the dephlogisticated part, or dephlogisticated air, being our oxygen, and the phlogisticated part or air, our . Cavendish's enquiry began before this later view became general."

"He had proceeded but a short way in his attempt to discover what became of the air apparently lost during combustion, when he was arrested in his researches by the necessity... of ascertaining the quantitative composition of atmospheric air."

"The problem which originally interested him... If any combustible, such as , , or a candle, was allowed to burn till it went out, in a portion of air confined over water, the volume of the air was observed to diminish as the combustion proceeded, and at its close the water was found to have risen through about a fifth of the space originally occupied by the air."

"[[[Henry Cavendish|H]e]] published in 1783, and, like all his other papers, the modest title... An Account of a New , conveyed a very imperfect idea of its contents. ...[I]t is ostensibly devoted to the explanation of an instrument for determining the proportion of oxygen in air, by observing the contraction which followed its mixture with a given volume of . Priestley, the first investigator of the properties of nitric oxide, had devised this process, but was too inaccurate a manipulator to make good use of it."

"[N]itrous gas... can combine with oxygen in various proportions, according to the mode in which it is mixed with air... Priestley... and the great majority of his contemporaries were either ignorant or heedless of this fact... travelling from place to place, analysing what they called the good air and the bad air of different localities, and coming to the most extravagant conclusions as to the relative purity of specimens... in which... modern analysis would fail to detect any difference."

"The instruments... ', or measurers of the goodness of the air; the object of the analyst being to determine the freedom of the air from phlogiston, which rendered it bad in proportion to the amount of it present."

"By the performance of an immense number of elaborate experiments, Cavendish succeeded in perfecting a process, by means of which he could employ so as to occasion a constant amount of contraction, when mixed with different portions of the same specimen of air. Having certified this, he applied his method to the determination of the two important questions: Is the atmosphere constant in composition? And if so, what is its composition?"

"He came to the conclusion which all subsequent observations have confirmed, that no sensible difference can be detected by Eudiometrical analysis between the purity of different specimens of atmospheric air. It was universally such "that the quantity of pure air in common air is 10/48" or... the per centage by volume of oxygen in air is 20.83. This... is remarkable... accuracy, when we consider how totally the great majority, not only of Cavendish's contemporaries, but also his successors, even among living philosophers, failed to obtain any constant results with nitric oxide eudiometers."

"Cavendish is... the discoverer of the constant composition of the atmosphere, and its first accurate analyst."

"[T]he atmosphere had long occupied his attention. So far back as 1766 he had imperfectly analysed it, by observing the loudness... which it gave when detonated with . This device might be called an Acoustic Eudiometer."

"Whilst engaged also in the enquiry... we have been discussing, he checked the results obtained with , by observing the diminution which air underwent when exposed to dissolved in water, and when exploded with in a shut vessel by means of the electric spark. The apparatus last referred to is... Cavendish's Eudiometer, and... in connexion with the discovery of the composition of water, has been selected by the Cavendish Society as their emblem, and placed on the title-page of their publications."

"Cavendish... never named this instrument a Eudiometer, nor was it his device, but Volta's. The Society's emblem represents the instrument as it is constructed at the present day, not as it was used by Cavendish."

"He concludes this paper with an estimate of... the information which the eudiometer supplies, which he shows to be very much smaller than the majority of his contemporaries imagined. His views in this respect... are another monument to the caution and sagacity with which he kept himself free from the prejudices of his time, and anticipated conclusions which were not generally accepted till a recent period."

"The protracted eudiometrical enquiry... taught Cavendish... the maximum amount of diminution... one-fifth of the original volume of the air... was the dephlogisticated part, or pure air (oxygen), of the atmosphere, which disappeared during combustion, so that he was now fully prepared to enquire what had become of the lost oxygen. His account... forms the first series of his Experiments on Air... read to the Royal Society in January 1784... a year after the paper on the New Eudiometer..."

"When he commenced... researches, he found an opinion prevailing, that the production of fixed air, or , is the invariable result of what he called the phlogistication, and we should call the deoxidation, of atmospheric air. He readily disproved... this view, and also of another notion, that nitric, or sulphuric acid was produced in those circumstances; and having disposed of these erroneous opinions, he proceeded to observe with great care, what was the product of the combustion of in air and in ."

"Priestley, and... Mr. [John] Warltire, had already experimented on this... with a detonating globe of the same kind as... Cavendish's Eudiometer. Their experiments were made partly in metallic, partly in glass vessels, and when employing the latter, they observed a deposition of moisture follow each explosion, but Priestley paid no attention to this... and Warltire referred it to the condensation of water which had been diffused in the state of vapour through the gases. ...Cavendish ...from the first appears to have anticipated that in the deposited water would be found the oxygen, which disappeared during the combustion of hydrogen in air, and the explanation of the diminution in volume which attended the vitiation of air."

"[I]n his paper on , of 1766, he had represented this gas as itself phlogiston. He now experimented accordingly upon it, not as an individual combustible which would yield a certain product, but as the phlogiston... in all combustibles, and the product of whose combustion would represent the universal product of combustion."

"He first employed and air, varying their relative proportion, till he ascertained that ratio in which, after their explosion in a shut vessel, the air was found diminished one-fifth, whilst the residual air was free from oxygen, and possessed the properties of ."

"In place of the oxygen which had thus disappeared, and a volume of hydrogen twice as great which had burned along with it, there was found a certain amount of liquid. The globe, moreover, had remained shut during the experiment, so that nothing had been allowed to escape, and nothing ponderable had been lost, for the vessel was found to weigh the same after the electric spark had passed, as before the explosion."

"[T]here was exactly the same weight of matter in the globe after the explosion as before, but the oxygen originally present in the air, and twice its volume of the hydrogen which had been mixed with it, had disappeared as gases, and were replaced by a volume of liquid, which... exactly equalled them in weight."

"Cavendish... unhesitatingly concluded, that in the circumstances described, "almost all the inflammable air, and about one-fifth part of the common air, lose their elasticity and are condensed into the dew which lines the glass.""

"Having demonstrated... that the lost gas was accounted for, and remained in the produced liquid, he proceeded to investigate the nature of the latter. The globe explosions yielded too small a quantity of liquid for a full analysis. He burned together, accordingly, by direct combustion, a large volume of hydrogen with 2 1/2 times that quantity of common air within a glass cylinder, and collected the liquid produced. This he found to be without taste, or smell, or action on colouring matter, and to leave no sediment on evaporation; in short... "it seemed pure water," and his... conclusion... "that this dew is plain water, and consequently, that almost all the inflammable air, and about one-fifth of the common air, are turned into pure water.""

"The proceeding quotation contains the account of the first conclusion that was drawn concerning the compound nature of water, and the possibility of producing it out of hydrogen, and the oxygen contained in air."

"Cavendish proceeded to try whether free oxygen, if detonated with hydrogen, would in like manner yield water. ... [I]t was only necessary to fill the globe with a mixture of one volume of oxygen and two of hydrogen, and to explode it by the electric spark, to secure the entire conversion of the contents of the globe into water. Cavendish came as near this result, as a slight mistake in the adjustment of the combining volumes of hydrogen and oxygen, and the limits of error in such an experiment, at the period when it was made... permitted."

"[A]n unexpected and perplexing phenomenon showed itself. The liquid instead of being pure water, was found in certain cases to consist in addition of an acid, which analysis proved to be the nitric, and a long and difficult investigation had to be prosecuted into the source of this acid, the composition of which... was totally unknown in 1784."

"This startling phenomenon, on which the chemistry of the period could throw no light... led not only Priestley, but even La Place astray; and it was probably ignorance of the phenomenon on the part of Watt and Lavoisier, which saved them from being entangled in difficulties in their investigation into the nature of water."

"Cavendish solved the problem... and whilst he avoided the confusion in which it involved others, he built upon it an additional great discovery. After ascertaining that the appearance of nitric acid was not dependent on the source from which the oxygen was prepared, and that the acid did not show itself unless more than a combining measure of oxygen was detonated with the hydrogen, he traced its production to the presence in the [eudiometer] of a little nitrogen, derived from the atmospheric air which had originally filled it, or had become mingled with the hydrogen and oxygen during their preparation or collection. He... verified this conclusion, by showing that the artificial addition of nitrogen to hydrogen, mixed with more than one-half its volume of oxygen, increased the amount of nitric acid produced at each detonation, and on the other hand, that if the hydrogen instead of the oxygen was in excess, no nitric acid appeared, although nitrogen was present."

"In this way he demonstrated that the only product of the combustion of pure hydrogen and oxygen is pure water; but he was further led to a view of the composition of nitric acid, which he carried out in the second series of his experiments on air, and which secures to him the honour of being the discoverer of the composition of nitric acid, as well as of that of water."

"The general conclusion to which Cavendish came concerning the nature of water, was in his own words, "that water consists of dephlogisticated air united with phlogiston;" and as dephlogisticated air was his term for oxygen, and phlogiston his term for , this... corresponds to the modern view of the nature of water introduced by Lavoisier. The two views cannot be considered identical, yet this is certain, that Cavendish was the first who consciously converted hydrogen and oxygen into water, and taught that it consisted of them."

"His identification, however, of and phlogiston, and his inheritance of the prejudices of the early phlogiston school, led him to the erroneous conclusion that every combustible contains hydrogen, and that the deoxidation of air and the oxidation of combustibles, are invariably accompanied by the production of water. In this respect he erred, but we may forgive the discoverer of so great a truth as that of the composition of water, for over-estimating its importance. To this, and to the other points glanced at in this sketch of the first series of experiments on air, I have referred fully in the abstract of the paper, and in the chapters devoted to the discussion of the Water Controversy."

"It only remains that I offer very briefly my own estimate of the character of the Philosopher. Morally it was a blank, and can be described only by a series of negations. He did not love; he did not hate; he did not hope; he did not fear; he did not worship as others do. He separated himself from his fellow men, and apparently from God. There was nothing earnest, enthusiastic, heroic, or chivalrous in his nature, and as little was there anything mean, grovelling, or ignoble. He was almost passionless."

"All that needed for its apprehension, more than the pure intellect, or required the exercise of fancy, imagination, affection, or faith, was distasteful to Cavendish. An intellectual head thinking, a pair of wonderfully acute eyes observing, and a pair of very skilful hands experimenting or recording, are all that I realise in reading his memorials."

"His brain seems to have been but a calculating engine; his eyes inlets of vision, not fountains of tears; his hands instruments of manipulation which never trembled with emotion, or were clasped together in adoration, thanksgiving, or despair; his heart only an anatomical organ, necessary for of the circulation of the blood."

"Yet, if such a being, who reversed the maxim nihil humani me alienum puto [nothing human is foreign to me], cannot be loved, as little can he be abhorred or despised. He was, in spite of the atrophy or non development of many of the faculties which are found in those in whom the "elements are kindly mixed," as truly a genius as the mere poets, painters, and musicians, with small intellects, and hearts and large imaginations, to whom the world is so willing to bend the knee."

"He is more to be wondered at than blamed."

"Cavendish did not stand aloof from other men in a proud or supercilious spirit, refusing to count them his fellows. He felt himself separated from them by a great gulf, which neither they nor he could bridge over, and across which it was vain to stretch hands or exchange greetings. A sense of isolation from his brethren, made him shrink from their society and avoid their presence, but he did so as one conscious of an infirmity, not boasting of an excellence."

"He was like a deaf mute sitting apart from a circle, whose looks and gestures show that they are uttering and listening to music and eloquence, in producing or welcoming which he can be no sharer. Wisely, therefore, he dwelt apart, and bidding the world farewell, took the self imposed vows of a Scientific Anchorite, and, like the Monks of old, shut himself up within his cell. It was a kingdom sufficient for him, and from its narrow window he saw as much of the Universe as he cared to see. It had a throne also, and from it he dispensed royal gifts to his brethren."

"He was one of the unthanked benefactors of his race, who was patiently teaching and serving mankind, whilst they were shrinking from his coldness, or mocking his peculiarities."

"He could not sing for them a sweet song, or create a "thing of beauty" which should be "a joy for ever," or touch their hearts, or fire their spirits, or deepen their reverence or their fervour. He was not a Poet, a Priest, or a Prophet, but only a cold, clear, Intelligence, raying down pure white light, which brightened everything on which it fell, but warmed nothing—a Star of at least the second, if not of the first magnitude, in the Intellectual Firmament."

"Comparatively little is known concerning the personal history of [Cavendish]. Nor is there much hope now that more may be gleaned. It may be doubted, indeed, whether there is much more to learn, for apart from his scientific achievements, his life was singularly uneventful. He lived a solitary, secluded existence, and, despite his rank, and, in his later years, his great wealth, he deliberately refrained from any attempts to exercise the slightest social influence. He left no personal records, and few of his letters seem to have been preserved, possibly because few were written. Such as are known relate almost exclusively to matters of science and are otherwise of very slight human interest. All the knowledge of him we possess is based upon the fragmentary notices of a few contemporaries, principally Thomas Young, Thomas Thomson of Glasgow, Sir Humphry Davy, and Lord Brougham. Their accounts, together with the reminiscences of others who had a certain small measure of personal acquaintance with him, or were able to communicate hearsay information concerning his character, habits and mode of life, have been brought together by the late Dr George Wilson, of Edinburgh, whose Life of the Honble Henry Cavendish, written at the request of the Cavendish Society, and published in 1851, still remains the only authoritative biography of the philosopher."

"In order to understand the true value and character of the Positive Philosophy, we must take a brief general view of the progressive course of the human mind, regarded as a whole; for no conception can be understood otherwise than through its history."

"In the final... positive state, the mind has given over the vain search after Absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study of their laws,—that is, their invariable relations of succession and resemblance."

"Reasoning and observation, duly combined, are the means of this knowledge."

"What is now understood when we speak of an explanation of facts is simply the establishment of a connection between single phenomena and some general facts, the number of which continually diminishes with the progress of science."

"There is no science which, having attained the positive stage, does not bear marks of having passed through the others. Some time since it was... composed... of metaphysical abstractions; and, further back... it took its form from theological conceptions. ...[O]ur most advanced sciences still bear very evident marks of the two earlier periods ..."

"The progress of the individual mind is not only an illustration, but an indirect evidence of that of the general mind. The point of departure of the individual and of the race being the same, the phases of the mind of a man correspond to the epochs of the mind of the race. Now, each of us is aware, if he looks back upon his own history, that he was a theologian in his childhood, a metaphysician in his youth, and a natural philosopher in his manhood. All men who are up to their age can verify this for themselves."

"[I]t is to the chimeras of astrology and alchemy that we owe the long series of observations and experiments on which our positive science is based. Kepler felt this on behalf of astronomy, and Berthollet on behalf of chemistry. Thus was a spontaneous philosophy, the theological, the only possible beginning, method, and provisional system, out of which the Positive philosophy could grow."

"M. Fourier, in his fine series of researches on , has given us all the most important and precise laws of the phenomena... and many large and new truths, without once inquiring into its nature, as his predecessors had done when they disputed about calorific matter and the action of an universal ether. In treating his subject in the Positive method, he finds inexhaustible material for all his activity of research, without betaking himself to insoluble questions."

"[I]f we must fix upon some marked period, to serve as a rallying point, it must be that,—about two centuries ago,—when the human mind was astir under the precepts of Bacon, the conceptions of Descartes, and the discoveries of Galileo. Then it was that the spirit of the Positive philosophy rose up in opposition to that of the superstitious and scholastic systems which had hitherto obscured the true character of all science. Since that date, the progress of the Positive philosophy, and the decline of the other two, have been so marked that no rational mind now doubts that the revolution is destined to go on to its completion,—every branch of knowledge being, sooner or later, brought within the operation of Positive philosophy."

"Now that the human mind has grasped celestial and terrestrial physics,—mechanical and chemical; organic physics, both vegetable and animal,—there remains one science, to fill up the series of sciences of observation,—Social physics. This is... the principal aim of the present work to establish."

"The purpose of this work is not to give an account of the Natural Sciences. Besides that it would be endless, and that it would require a scientific preparation such as no one man possesses, it would be apart from our object, which is to go through a course of not Positive Science, but Positive Philosophy. We have only to consider each fundamental science in its relation to the whole positive system... with regard to its methods and its chief results."

"In the primitive state of human knowledge there is no regular division of intellectual labour. Every student cultivates all the sciences. As knowledge accrues, the sciences part off; and students devote themselves each to some one branch. It is owing to this division... and concentration of whole minds upon a single department, that science has made so prodigious an advance... But... we cannot be blind to the eminent disadvantages which arise from... limitation... to a particular study. It is inevitable that each should be possessed with exclusive notions, and be therefore incapable of the general superiority of ancient students, who... owed that general superiority to the inferiority of their knowledge. ...[T]his is the weak side of the positive philosophy, by which it may yet be attacked, with some hope of success, by the adherents of the theological and metaphysical systems."

"As to the remedy... It lies in perfecting the division of employments itself,—in carrying it one degree higher,—in constituting one more speciality from the study of scientific generalities."

"Let us have a new class of students... to take the respective sciences... determine the spirit of each, ascertain their relations and mutual connection, and reduce their respective principles to the smallest number of general principles..."

"[L]et other students be prepared for their special pursuit... so as to profit by the labours of the students of generalities, and so as to correct reciprocally, under that guidance, the results obtained by each."

"[R]efer to a saying of M. de Blainille, in his work on Comparative Anatomy, that every active... being, may be regarded under two relations—the Statical and the Dynamical... apply this classification to the intellectual functions."

"After two thousand years of psychological pursuit, no one proposition is established to the satisfaction of its followers. ...This interior observation gives birth to almost as many theories as there are observers."

"The Positive Method can be judged of only in action. ...the work on which it is employed."

"[[Psychology|[P]sychologists]], by dint of reading the precepts of Bacon and the discourses of Descartes, have mistaken their own dreams for science."

"This... is the first great result of the Positive Philosophy—the manifestation by experiment of the laws which rule the Intellect in the investigation of truth; and, as a consequence the knowledge of the general rules suitable for that object."

"The second effect of the Positive Philosophy... regenerate Education. [O]ur... education, still essentially theological, metaphysical, and literary, must be superseded by a Positive training... [E]verything yet done is inadequate to the object."

"The present exclusive speciality of our pursuits, and the consequent isolation of the sciences, spoil our teaching."

"If any student desires to form an idea of natural philosophy as a whole, he is compelled to go through each department as it is now taught, as if he were to be only an astronomer, or only a chemist... his training must remain very imperfect. And yet... he should obtain general positive conceptions of all the classes of natural phenomena."

"In order to [attain] this regeneration of our intellectual system, it is necessary that the sciences, considered as branches from one trunk, should yield us, as a whole, their chief methods and their most important results."

"The subject of our researches is one: we divide it for our convenience... to deal... more easily with its difficulties. But... sometimes... especially with the most important doctrines of each science... we need what we cannot obtain under the present isolation... a combination of several special points of view; and for want of this, very important problems wait for their solution much longer..."

"Descartes' grand conception with regard to analytical geometry... changed the whole aspect of mathematical science, and... it issued from the union of two sciences which had always before been separately regarded and pursued."

"The case of pending questions is yet more impressive; as... in Chemistry, the doctrine of Definite Proportions. ...[I]n order to determine whether it is a law of nature that atoms should necessarily combine in fixed numbers... the chemical point of view should be united with the physiological. ...[P]hysiology must unite with chemistry to inform us whether azote is simple or compound, and to institute a new series of researches upon the relation between the composition of living bodies and their mode of alimentation."

"The Positive Philosophy offers the only solid basis for that Social Reorganization which must succeed the critical condition in which the most civilized nations are now living."

"Ideas govern the world, or throw it into chaos... [i.e.,] all social mechanism rests upon Opinions. The great political and moral crisis that societies are now undergoing... arise out of intellectual anarchy. ...[W]e are suffering under an utter disagreement which may be called universal."

"Till a certain number of general ideas can be acknowledged as a rallying-point of social doctrine, the nations will remain in a revolutionary state..."

"[W]henever the necessary agreement on first principles can be obtained, appropriate institutions will issue from them, without shock or resistance; for the causes of disorder will have been arrested by the mere fact of the agreement."

"[T]he existing disorder is... accounted for by the existence... of three incompatible philosophies,—the theological, the metaphysical, and the positive. Any one of these might alone secure... social order; but while the three co-exist, it is impossible... to understand one another..."

"[W]e have only to ascertain which of the philosophies must, in the nature of things, prevail..."

"[A]ll considerations... point to the Positive Philosophy as the one destined to prevail. It alone has been advancing during a course of centuries, throughout which the others have been declining. The fact is incontestable."

"This general revolution of the human mind is nearly accomplished. We have only to complete the Positive Philosophy by bringing Social phenomena within its comprehension..."

"The marked preference which almost all minds, from the highest to the commonest, accord to positive knowledge over vague and mystical conceptions, is a pledge of what the reception of this philosophy will be..."

"When it has become complete, its supremacy will take place spontaneously, and will re-establish order throughout society."

"It is time to complete the vast intellectual operation begun by Bacon, Descartes, and Galileo, by constructing the system of general ideas which must henceforth prevail among the human race. This is the way to put an end to the revolutionary crisis which is tormenting the civilized nations of the world."

"[I]t must not be supposed that we are going to study this vast variety as proceeding from a single principle, and as subjected to a single law. There is something... chimerical in attempts at universal explanation by a single law..."

"Our intellectual resources are too narrow, and the universe is too complex, to leave any hope that it will ever be within our power to carry scientific perfection to its last degree of simplicity."

"The only necessary unity is that of Method, which is already in great part established."

"As for the doctrine, it need not be one; it is enough that it should be homogeneous."

"While pursuing the philosophical aim of all science, the lessening of the number of general laws requisite for the explanation of natural phenomena, we shall regard as presumptuous every attempt, in all future time, to reduce them rigorously to one."

"Classification of the Sciences... have failed, through one fault or another, to command assent: so that there are almost as many schemes as there are individuals to propose them."

"[T]he distribution of the sciences, having become a somewhat discredited task, has of late been undertaken chiefly by persons who have no sound knowledge of any science at all."

"A... reason... is, the want of homogeneousness in the different parts of the intellectual system,—some having successively become positive, while others remain theological or metaphysical."

"Every attempt at a distribution has failed from this cause... the enterprise was premature; and... it was useless to undertake it till our principal scientific conceptions should all have become positive."

"[T]he time has arrived for laying down a sound and durable system of scientific order."

"We may derive encouragement from the example set by... botanists and zoologists... viz. that the classification must proceed from the study of the things to be classified, and must by no means be determined by à priori considerations."

"[T]he mutual dependence of the sciences... resulting from that of the corresponding phenomena,—must determine the arrangement of the system of human knowledge."

"Before proceeding to investigate this mutual dependence, we have only to determine the real bounds of the classification... [i.e.,] to settle what we mean by human knowledge..."

"The field of human knowledge is either speculation or action: and thus, we are accustomed to divide our knowledge into the theoretical and the practical. ...[I]n this inquiry, we have to do only with the theoretical."

"[S]peculation is our material, and not the application of it,—except... to throw back light on its speculative origin."

"This is probably what Bacon meant by that First Philosophy which he declared to be an extract from the whole of Science... so differently and... strangely interpreted by his metaphysical commentators."

"Man's study of nature must furnish the only basis of his action upon nature; for it is only by knowing the laws of phenomena, and thus being able to foresee them, that we can, in active life, set them to modify one another for our advantage."

"Our direct natural power over everything about us is extremely weak, and altogether disproportioned to our needs."

"Whenever we effect anything great it is through a knowledge of natural laws..."

"The relation of science to art may be summed up in a brief expression: From Science comes Prevision: from Prevision comes Action."

"We must not... fall into the error of our time, of regarding Science chiefly as a basis of Art."

"However great may be the services rendered to Industry by science, however true may be the saying that Knowledge is Power, we must never forget that the sciences have a higher destination... [and] more direct;—that of satisfying the craving of our understanding to know the laws of phenomena."

"This need of disposing facts in a comprehensible order (...the proper object of all scientific theories) is so inherent in our organization, that if we could not satisfy it by positive conceptions, we must inevitably return to those theological and metaphysical explanations which had their origin in this very fact of human nature.—It is this original tendency which acts as a preservative, in the minds of men of science, against the narrowness and incompleteness which the practical habits of our age are apt to produce. It is through this that we are able to maintain just and noble ideas of the importance and destination of the sciences; and if it were not thus, the human understanding would soon, as Condorcet has observed, come to a stand, even as to the practical applications for the sake of which higher things had been sacrificed; for..."

"[I]f the arts flow from science, the neglect of science must destroy the consequent arts."

"Some of the most important arts are derived from speculations pursued during long ages with a purely scientific intention."

"[T]he ancient Greek geometers delighted themselves with beautiful speculations on Conic Sections; those speculations wrought, after... generations, the renovation of astronomy; and out of this has the art of navigation attained a perfection which it never could have reached otherwise than through the speculative labours of Archimedes and Apollonius..."

"[T]o use Condorcet's illustration, "the sailor who is preserved from shipwreck by the exact observation of the longitude, owes his life to a theory conceived two thousand years before by men of genius who had in view simply geometrical speculations.""

"[A]n intermediate class is rising up, whose particular destination is to organize the relations of theory and practice; such as the engineers, who do not labour in the advancement of science, but who study it in its existing state, to apply it to practical purposes. Such classes are furnishing us with the elements of a future body of doctrine on the theories of the different arts."

"Monge, in his view of , has given us a general theory of the arts of . But we have as yet only a few scattered instances of this nature."

"If we remember that several sciences are implicated in every important art,—that...[e.g.,] a true theory of Agriculture requires a combination of physiological, chemical, mechanical, and even astronomical and mathematical science,—it will be evident that true theories of the arts must wait for a large and equable development of these constituent sciences."

"We must distinguish between the two classes of ;—the abstract or general, which have for their object the discovery of the laws which regulate phenomena in all conceivable cases: and the concrete, particular, or descriptive, which are sometimes called Natural sciences in a restricted sense, whose function it is to apply these laws to the actual history of existing beings."

"The first are fundamental; and our business is with them alone, as the second are derived, and however important, not rising into the rank of our subjects of contemplation."

"We shall treat of , but not of botany and zoology, which are derived from it."

"We shall treat of chemistry, but not of ... secondary to it."

"We may say of Concrete Physics, as these secondary sciences are called, the same thing that we said of theories of the arts,—that they require a preliminary knowledge of several sciences, and an advance of those sciences not yet achieved..."

"At a future time Concrete Physics will have made progress, according to the development of Abstract Physics, and will afford a mass of less incoherent materials than those which it now presents."

"At present, too few of the students of these secondary sciences appear... aware that a due acquaintance with the primary sciences is requisite..."

"We have now considered, First, that science being composed of speculative knowledge and of practical knowledge, we have to deal only with the first; and Second, that theoretical knowledge, or science properly so called, being divided into general and particular, or abstract and concrete science, we have again to deal only with the first."

"The classification of the sciences is not so easy a matter... However natural it may be, it will always involve something, if not arbitrary, at least artificial; and in so far, it will always involve imperfection."

"It is impossible to fulfil... rigorously, the object of presenting the sciences in their natural connection, and according to their mutual dependence, so as to avoid... a vicious circle."

"Every science may be exhibited under two methods or procedures, the Historical and the Dogmatic."

"These are wholly distinct from each other, and any other method can be nothing but some combination of these two."

"By the first method knowledge is presented in the same order in which it was actually obtained... together with the way in which it was obtained."

"By the second, the system of ideas is presented as it might be conceived of at this day, by a mind which, duly prepared and placed at the right point of view, should begin to reconstitute the science as a whole."

"A new science must be pursued historically, the only thing to be done being to study in chronological order the different works which have contributed to the progress..."

"But when such materials have become recast to form a general system, to meet the demand for a more natural logical order, it is because the science is too far advanced for the historical order to be practicable or suitable."

"The more discoveries are made, the greater becomes the labour of the historical method of study, and the more effectual the dogmatic, because the new conceptions bring forward the earlier ones in a fresh light."

"Thus, the education of an ancient geometer consisted simply in the study, in their due order, of the very small number of original treatises then existing on the different parts of geometry. The writings of Archimedes and Apollonius were, in fact, about all."

"On the contrary, a modern geometer commonly finishes his education without having read a single original work dating further back than the most recent discoveries, which cannot be known by any other means."

"Thus the Dogmatic Method is for ever superseding the Historical, as we advance to a higher position in science."

"If every mind had to pass through all the stages that every predecessor in the study had gone through... however easy it is to learn rather than invent, it would be impossible to effect the purpose of education,—to place the student on the vantage-ground gained by the labours of all the men who have gone before. By the dogmatic method this is done, even though the living student may have only an ordinary intellect, and the dead may have been men of lofty genius."

"By the dogmatic method, therefore, must every advanced science be attained, with so much of the historical combined with it as is rendered necessary..."

"The only objection to the preference of the Dogmatic method is that it does not show how the science was attained; but... this is the case also with the Historical method."

"To pursue a science historically is quite a different thing from learning the history of its progress. This last pertains to the study of human history..."

"[A] science cannot be completely understood without a knowledge of how it arose; and... a dogmatic knowledge of any science is necessary to an understanding of its history; and therefore we shall notice, in treating of the fundamental sciences, the incidents of their origin, when distinct and illustrative; and we shall use their history, in a scientific sense, in our treatment of Social Physics; but the historical study, important, even essential, as it is, remains entirely distinct from the proper dogmatic study of science."

"Great confusion would arise from any attempt to adhere strictly to historical order in our exposition of the sciences, for they have not all advanced at the same rate; and we must be for ever borrowing from each some fact to illustrate another, without regard to priority of origin."

"Thus... in the system of the sciences, astronomy must come before physics, properly so called: and yet, several branches of physics, above all, optics, are indispensable to the complete exposition of astronomy."

"In the main... our classification agrees with the history of science; the more general and simple sciences actually occurring first and advancing best... being followed by the more complex and restricted, though all were, since the earliest times, enlarging simultaneously."

"Our problem is, then, to find the one rational order, among a host of possible systems. ...This order is determined by the degree of simplicity, or... [i.e.,] generality of their phenomena. Hence results their successive dependence, and the greater or lesser facility for being studied. ...à priori... the most simple phenomena must be the most general; for whatever is observed in the greatest number of cases is of course the most disengaged from the incidents of particular cases."

"We must begin then with the study of the most general or simple phenomena, going on successively to the more particular or complex."

"[T]he most general and simple phenomena are the furthest removed from Man's ordinary sphere, and must thereby be studied in a calmer and more rational frame of mind than those in which he is more nearly implicated; and this constitutes a new ground for the corresponding sciences being developed more rapidly."

"We are first struck by the clear division of all natural phenomena into two classes—of inorganic and of organic bodies. The organized are evidently, in fact, more complex and less general than the inorganic, and depend upon them..."

"Therefore... physiological study should begin with inorganic phenomena..."

"We have not to investigate the nature of either; for the positive philosophy does not inquire into natures."

"[T]he general laws of inorganic physics must be established before we can proceed with success to the examination of a dependent class..."

"Each of these great halves of natural philosophy has subdivisions. Inorganic physics must... be divided into two sections—of celestial and terrestrial phenomena. Thus we have Astronomy, geometrical and mechanical, and Terrestrial Physics."

"Astronomical phenomena are the most general, simple, and abstract of all; and therefore the study of natural philosophy must... begin with them. ...[T]he laws to which they are subject influence all others whatsoever."

"The general effects of gravitation preponderate, in all terrestrial phenomena, over all effects which may be peculiar to them, and modify the original ones."

"It follows that the analysis of the simplest terrestrial phenomenon, not only chemical, but even purely mechanical, presents a greater complication than the most compound astronomical phenomenon."

"The most difficult astronomical question involves less intricacy than the simple movement of even a solid body, when the determining circumstances are to be computed."

"[W]e find a natural division of Terrestrial Physics into two, according as we regard bodies in their mechanical or their chemical character. Hence we have Physics... and Chemistry. Again, the second class must be studied through the first."

"Chemical phenomena are more complicated than mechanical, and depend upon them, without influencing them in return. [A]ll chemical action is first submitted to the influence of weight, heat, electricity, etc., and presents moreover something which modifies all these. Thus, while it follows Physics, it presents itself as a distinct science."

"An analogous division arises in the other half of Natural Philosophy—the science of organized bodies."

"Here we find ourselves presented with two orders of phenomena; those which relate to the individual, and those which relate to the species, especially when it is gregarious. With regard to Man, especially, this distinction is fundamental."

"[W]e have two great sections in organic physics—Physiology... and Social Physics, which is dependent on it."

"In all Social phenomena we perceive the working of the physiological laws of the individual; and moreover something which modifies their effects, and which belongs to the influence of individuals over each other—singularly complicated in the case of the human race by the influence of generations on their successors."

"[O]ur social science must issue from that which relates to the life of the individual. On the other hand, there is no occasion to suppose, as some eminent physiologists have done, that Social Physics is only an appendage to physiology. The phenomena of the two are not identical, though they are homogeneous; and it is of high importance to hold the two sciences separate."

"As social conditions modify the operation of physiological laws, Social Physics must have a set of observations of its own."

"It would be easy to make the divisions of the Organic... by dividing physiology into vegetable and animal, according to popular custom. But this distinction... hardly extends into those Abstract Physics... Vegetables and animals come alike... when our object is to learn the general laws of life— ...[i.e.,]to study physiology. ...[T]he distinction grows ever fainter and more dubious with new discoveries, it bears no relation to our plan of research..."

"Thus we have before us Five fundamental Sciences in successive dependence,—Astronomy, Physics, Chemistry, Physiology, and... Social Physics."

"The first considers the most general, simple, abstract, and remote phenomena known to us, and those which affect all others without being affected by them. The last considers the most particular, compound, concrete phenomena, and those which are the most interesting to Man."

"Between these two, the degrees of speciality, of complexity, and individuality are in regular proportion to the place of the respective sciences in the scale exhibited."

"This—casting out everything arbitrary—we must regard as the true filiation of the sciences; and in it we find the plan of this work."

"[W]e shall find that the same principle which gives this order to the whole body of science arranges the parts of each science; and its soundness will therefore be freshly attested us often as it presents itself afresh."

"There is no refusing a principle which distributes the interior of each science after the same method with the aggregate sciences."

"This gradation is in essential conformity with the order which has spontaneously taken place among the branches of natural philosophy, when pursued separately, and without any purpose of establishing such order."

"Such an accordance is a strong presumption that the arrangement is natural. ...[I]t coincides with the actual development of natural philosophy."

"If no leading science can be effectually pursued otherwise than through those which precede it in the scale, it is evident that no vast development of any science could take place prior to the great astronomical discoveries to which we owe the impulse given to the whole. The progression may since have been simultaneous; but it has taken place in the order we have recognized."

"This consideration is so important that it is difficult to understand without it the history of the human mind. The general law which governs this history... cannot be verified, unless we combine it with the scientific gradation just laid down: for it is according to this gradation that the different human theories have attained in succession the theological state, the metaphysical, and finally the positive."

"If we do not bear in mind the law which governs progression, we shall encounter insurmountable difficulties: for it is clear that the theological or metaphysical state of some fundamental theories must have temporarily coincided with the positive state of others which precede them in our established gradation, and actually have at times coincided with them; and this must involve the law itself in an obscurity which can be cleared up only by the classification we have proposed."

"[T]his classification marks, with precision, the relative perfection of the different sciences, which consists in the degree of precision of knowledge, and in the relation of its different branches."

"[T]he more general, simple, and abstract any phenomena are, the less they depend on others, and the more precise they are in themselves, and the more clear in their relations with each other."

"Thus, organic phenomena are less exact and systematic than inorganic; and of these again terrestrial are less exact and systematic than those of astronomy."

"This fact is completely accounted for by the gradation we have laid down; and we shall see... that the possibility of applying mathematical analysis to the study of phenomena is exactly in proportion to the rank which they hold in the scale of the whole."

"We must beware of confounding the degree of precision which we are able to attain in regard to any science, with the certainty of the science itself."

"The certainty of science, and our precision in the knowledge of it, are two very different things, which have been too often confounded; and are so still..."

"A very absurd proposition may be very precise; as if we should say, for instance, that the sum of the angles of a triangle is equal to three right angles; and a very certain proposition may be wanting in precision in our statement of it; as, for instance, when we assert that every man will die."

"If the different sciences offer to us a varying degree of precision, it is from no want of certainty in themselves, but of our mastery of their phenomena."

"The most interesting property of our formula of gradation is its effect on education, both general and scientific. This is its direct and unquestionable result."

"[N]o science can be effectually pursued without the preparation of a competent knowledge of the anterior sciences on which it depends."

"Physical philosophers cannot understand Physics without at least a general knowledge of Astronomy; nor Chemists, without Physics and Astronomy; nor Physiologists, without Chemistry, Physics, and Astronomy; nor, above all, the students of , without a general knowledge of all the anterior sciences."

"As such conditions are, as yet, rarely fulfilled, and as no organization exists for their fulfilment, there is amongst us, in fact, no rational scientific education."

"To this may be attributed, in great part, the imperfection of even the most important sciences at this day."

"If the fact is so in regard to scientific education, it is no less striking in regard to general education."

"Our intellectual system cannot be renovated till the natural sciences are studied in their proper order."

"Even the highest understandings are apt to associate their ideas according to the order in which they were received: and it is only an intellect here and there, in any age, which in its utmost vigour can, like Bacon, Descartes, and Leibnitz, make a clearance in their field of knowledge, so as to reconstruct from the foundation their system of ideas."

"Such is the operation of our great law upon scientific education through its effect on Doctrine. We cannot appreciate it duly without seeing how it affects Method."

"As the phenomena which are homogeneous have been classed under one science, while those which belong to other sciences are heterogeneous, it follows that the Positive Method must be constantly modified in an uniform manner in the Range of the same fundamental science, and will undergo modifications, different and more and more compound, in passing from one science to another."

"[I]f... we cannot understand the positive method in the abstract, but only by its application... we can have no adequate conception of it but by studying it in its varieties of application. No one science... could exhibit it. Though the Method is always the same, its procedure is varied."

"[I]t should be Observation with regard to one kind of phenomena, and Experiment with regard to another; and different kinds of experiment, according to the case. In the same way, a general precept, derived from one fundamental science, however applicable to another, must have its spirit preserved by a reference to its origin; as in the case of the theory of Classifications."

"The best idea of the Positive Method would... be obtained by the study of the most primitive and exalted of the sciences, if we were confined to one; but this isolated view would give no idea of its capacity of application to others in a modified form."

"Each science has its own proper advantages; and without some knowledge of them all, no conception can be formed of the power of the Method."

"It is necessary, not only to have a general knowledge of all the sciences, but to study them in their order. What can come of a study of complicated phenomena, if the student have not learned, by the contemplation of the simpler, what a Law is, what it is to Observe; what a Positive conception is; and even what a chain of reasoning is?"

"Yet this is the way our young physiologists proceed every day,—plunging into the study of living bodies, without any other preparation than a knowledge of a dead language or two, or... a superficial acquaintance with Physics and Chemistry, acquired without any philosophical method, or reference to any true point of departure in Natural philosophy."

"In the same way, with regard to Social phenomena, which are yet more complicated, what can be effected but by the rectification of the intellectual instrument, through an adequate study of the range of anterior phenomena? There are many who admit this: but they do not see how to set about the work, nor understand the Method itself, for want of the preparatory study; and thus, the admission remains barren, and social theories abide in the theological or metaphysical state, in spite of the efforts of those who believe themselves positive reformers."

"These, then, are the four points of view under which we have have recognized the importance of a Rational and Positive Classification."

"We have said nothing of Mathematical science. The omission was intentional; and the reason is no other than the vast importance of mathematics."

"In the present stage of our knowledge we must regard mathematics less as a constituent part of natural philosophy than as having been, since the time of Descartes and Newton, the true basis of the whole of natural philosophy; though it is... both the one and the other. To us it is of less value for the knowledge of which it consists, substantial and valuable as that knowledge is, than as being the most powerful instrument that the human mind can employ in the investigation of the laws of natural phenomena."

"Mathematics must be divided into two great sciences, quite distinct... Abstract Mathematics, or the Calculus (taking the word in its most extended sense), and Concrete Mathematics, which is composed of General Geometry and of Rational Mechanics."

"The Concrete part is necessarily founded on the Abstract, and it becomes in its turn the basis of all natural philosophy; all the phenomena of the universe being regarded, as far as possible, as geometrical or mechanical."

"The Abstract portion is the only one which is purely instrumental, it being simply an immense extension of natural logic to a certain order of deductions."

"Geometry and mechanics must, on the contrary, be regarded as true natural sciences, founded, like all others, on observation, though, by the extreme simplicity of their phenomena, they can be systematized to much greater perfection. It is this capacity which has caused the experimental character of their first principles to be too much lost sight of. But these two physical sciences have this peculiarity, that they are now, and will be more and more, employed rather as method than as doctrine."

"[I]n placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,—the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others."

"Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education, whether general or special."

"In an empirical way, this has hitherto been the custom,—a custom which arose from the great antiquity of mathematical science. We now see why it must be renewed on a rational foundation."

"We have now considered, in the form of a philosophical problem, the rational plan of the study of the Positive Philosophy. The order that results is this; an order which of all possible arrangements is the only one that accords with the natural manifestation of all phenomena. Mathematics, Astronomy, Physics, Chemistry, Physiology, Social Physics."

"[T]he direct measurement of a magnitude is often an impossible operation... We can rarely even measure a right line by another right line; and this is the simplest measurement of all."

"If there is difficulty about the measurement of lines, the embarrassment is much greater when we have to deal with surfaces, volumes, velocities, times, forces, etc., and in general with all other magnitudes susceptible of estimate, and, by their nature, difficult of direct measurement."

"[F]inding direct measurement so often impossible, we are compelled to devise means of doing it indirectly. Hence arose Mathematics."

"In observing a falling body, we are aware that two quantities are involved: the height from which the body falls, and the time occupied in its descent. ...In the language of mathematicians, they are functions of each other."

"We want to determine a distance not directly measurable. We shall conceive of it as making a part of some figure, or system of lines of some sort, of which the other parts are directly measurable; let us say a (for this is the simplest, and to it all others are reducible). ...The knowledge required is obtained by the mathematical labour of deducing the unknown distance from the observed elements, by means of the relation between them."

"Thus, when we once know the distance of any object, the observation, simple and always possible, of its apparent diameter, may disclose to us, with certainty, however indirectly, its real dimensions; and at length, by a series of analogous inquiries, its surface, its volume, even its weight, and a multitude of other qualities which might have seemed out of the reach of our knowledge for ever."

"It is by such labours that Man has learned to know, not only the distances of the planets from the earth and from each other, but their actual magnitude,—their true form, even to the inequalities on their surface, and... their respective masses, their mean densities ...etc."

"Through the power of mathematical theories, all this and very much more has been obtained by means of a very small number of straight lines, properly chosen, and a larger number of angles."

"We can... define Mathematical science... It has for its object the indirect measurement of magnitudes, and it proposes to determine magnitudes by each other, according to the precise relations which exist between them. Preceding definitions have given to Mathematics the character of an Art; this raises it at once to the rank of a true Science."

"[T]he spirit of Mathematics consists in regarding as mutually connected all the quantities which can be presented by any phenomenon whatsoever, in order to deduce all from each other."

"[T]here is evidently no phenomenon which may not be regarded as affording such considerations. Hence results the naturally indefinite extent, and the rigorous logical universality of Mathematical science. As for its actual practical extent, we shall see... hereafter."

"These explanations justify the name of Mathematics [from Greek: μάθημα, máthēma, 'knowledge, study, learning'] applied to the science we are considering. By itself it signifies Science [from Latin scientia 'knowledge']. The Greeks had no other, and we may call it the science; for its definition is neither more nor less (if we omit the specific notion of magnitudes) than the definition of all science whatsoever."

"All science consists in the co-ordination of facts; and no science could exist among isolated observations."

"It might even be said that Mathematics might enable us to dispense with all direct observation, by empowering us to deduce from the smallest possible number of immediate data the largest possible amount of results. Is not this the real use, both in speculation and in action, of the laws which we discover among natural phenomena?"

"If so, Mathematics merely urges to the ultimate degree, in its own way, researches which every real science pursues, in various inferior degrees, in its own sphere."

"Thus it is only through Mathematics that we can thoroughly understand what true science is. Here alone can we find in the highest degree simplicity and severity of scientific law, and such abstraction as the human mind can attain. Any scientific education setting forth from any other point, is faulty in its basis."

"Every mathematical solution spontaneously separates into two parts. The inquiry being... the determination of unknown magnitudes, through their relation to the known..."

"[T]he student must... first... ascertain what these relations are... This... is the Concrete part of the inquiry. When it is accomplished, what remains is... the determination of unknown numbers, when we know by what relation they are connected with known numbers. This second operation is the Abstract part of the inquiry."

"The primary division of Mathematics is therefore into two great sciences:—Abstract Mathematics, and Concrete Mathematics. This division exists in all complete mathematical questions whatever, whether more or less simple."

"Recurring to the simplest case of a falling body, we must begin by learning the relation between the height from which it falls and the time occupied in falling. As Geometers say, we must find the ' which exists between them. Till this is done, there is no basis for a computation. This ascertainment may be extremely difficult, and it is incomparably the superior part of the problem."

"The true scientific spirit is so modern, that as far as we know, no one before Galileo had remarked the of velocity in a falling body, the natural supposition having been that the height was in uniform proportion to the time. This first inquiry issued in the discovery of the law of Galileo."

"The mathematical law may be easy to ascertain, and difficult to work; or it may be difficult to ascertain, and easy to work. In importance, in extent, and in difficulty, these two great sections of Mathematical Science will be seen hereafter to be equivalent."

"The Concrete must depend on the character of the objects examined, and must vary when new phenomena present themselves: whereas, the Abstract is wholly independent of the nature of the objects, and is concerned only with their numerical relations."

"The character of the Concrete is experimental, physical, phenomenal: while the Abstract is purely logical, rational."

"The s being once found... it is for the understanding, without external aid, to educe the results which these equations contain."

"[T]here are as yet only two great categories of phenomena whose equations are constantly known:—Geometrical and Mechanical... Thus, the Concrete part of Mathematics consists of Geometry and Rational Mechanics."

"Abstract Mathematics... is composed of what is called the Calculus, taking this word in its widest extension, which reaches from the simplest numerical operations to the highest combinations of transcendental analysis. Its proper object is to resolve all questions of numbers. Its starting-point is that which is the limit of Concrete Mathematics,—the knowledge of the precise relations—that is, the equations—between different magnitudes... considered simultaneously."

"The object of the Calculus, however indirect or complicated the relations may be, is to discover unknown quantities by the known. This science, though more advanced than any other, is... only at its beginning... but it is necessary, in order to define the nature of any science, to suppose it perfect."

"From an historical point of view, Mathematical Analysis appears to have arisen out of the contemplation of geometrical and mechanical facts; but it is... independent of these sciences, logically speaking."

"Analytical ideas are, above all others, universal, abstract, and simple; and geometrical and mechanical conceptions are necessarily founded on them. Mathematical Analysis is therefore the true rational basis of the whole system of our positive knowledge."

"If a single analytical question, brought to an abstract solution, involves the implicit solution of a multitude of physical questions, the mind is enabled to perceive relations between phenomena apparently isolated, and to extract from them the quality which they have in common."

"To the wonder of the student, unsuspected relations arise between problems which, instead of being, as they appeared before, wholly unconnected, turn out to be identical."

"There appears to be no connection between the determination of the direction of a curve at each of its points and that of the velocity of a body at each moment of its variable motion; yet, in the eyes of the geometer, these questions are but one."

"The perfection [of Mathematical Analysis] consists in the simplicity of the ideas contemplated; and not, as Condillac and others have supposed, to the conciseness and generality of the signs used as instruments of reasoning. The signs are of admirable use to work out the ideas, when once obtained; but, in fact, all the great analytical conceptions were formed without any essential aid from the signs."

"Subjects which are by their nature inferior in simplicity and generality cannot be raised to logical perfection by any artifice of scientific language."

"There is no inquiry which is not finally reducible to a question of Numbers..."

"Nothing can appear less like a mathematical inquiry than the study of living bodies in a state of disease; yet, in studying the cure... we are endeavouring to ascertain the quantities of the different agents which are to modify the organism, in order to bring it to its natural state..."

"Kant has divided human ideas into the two categories of quantity and quality, which, if true, would destroy the universality of Mathematics; but Descartes' fundamental conception of the relation of the concrete to the abstract in Mathematics abolishes this division, and proves that all ideas of quality are reducible to ideas of quantity. He had in view geometrical phenomena... but his successors have included... first, mechanical phenomena, and, more recently, those of heat. There are now no geometers who do not consider it of universal application, and admit that every phenomenon may be as logically capable of being represented by an equation as a curve or a motion, if only we were always capable (which we are very far from being) of first discovering, and then resolving it."

"The limitations of Mathematical science are not, then, in its nature. The limitations are in our intelligence: and by these we find the domain of the science remarkably restricted, in proportion as phenomeua, in becoming special, become complex."

"[T]he reduction [to mathematics] cannot be made by us except in the case of the simplest and most general phenomena. ...[A]t the utmost, it is only the phenomena of the first three classes... of Inorganic Physics,—that we can even hope to subject to the process."

"By the rapidity of their changes, and their incessant numerical variations, vital phenomena are, practically, placed in opposition to mathematical processes."

"Social phenomena, being more complicated still, are even more out of the question, as subjects for mathematical analysis."

"It is not that a mathematical basis does not exist in these cases... but that our faculties are too limited for the working of problems so intricate."

"To the popular mind it may appear strange... that we know so much as we do about the planets. But... that class of phenomena is the most simple of all within our cognizance. The most complex problem... they present is the influence of a third body acting in the same way on two which are tending towards each other in virtue of gravitation; and this is a more simple question than any terrestrial problem... We have, however, attained only approximate solutions..."

"[T]he high perfection to which solar astronomy has been brought... is owing to our having profited by... facilities... accidental, which... our planetary system presents. The planets which compose it are few; their masses are very unequal, and much less than that of the sun; they are far distant from each other; their forms are nearly spherical; their orbits are nearly circular, and only slightly inclined in relation to each other; and so on."

"Their perturbations are, in consequence, inconsiderable... and all we have to do is usually to take into the account, together with the influence of the sun on each planet, the influence of one other planet, capable, by its size and its nearness, of occasioning perceptible derangements."

"If any of the conditions mentioned above had been different, though the law of gravitation had existed as it is, we might not... have discovered it."

"The most difficult sciences must remain, for an indefinite time, in that preliminary state which prepares for the others the time when they too may become capable of mathematical treatment. Our business is to study phenomena... abstaining from introducing considerations of quantities, and mathematical laws... beyond our power to apply."

"We owe to Mathematics both the origin of Positive Philosophy and its Method. When this method was introduced into the other sciences, it was natural that it should be urged too far. But each science modified the method by the operation of its own peculiar phenomena."

"We must next pass in review the three great sciences of which [Mathematical Science] is composed,—the Calculus, Geometry, and Rational Mechanics."

"The historical development of the Abstract portion of Mathematical science has, since the time of Descartes, been for the most part determined by that of the Concrete. Yet the Calculus in all its principal branches must be understood before passing on to Geometry and Mechanics."

"The Concrete portions of the science depend on the Abstract, which are wholly independent..."

"The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon... and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others."

"It is only by forming a true idea of an that we can lay down the real line of separation between the concrete and the abstract part of mathematics."

"[I]t almost impossible to explain the difficulty we find in establishing the relation of the concrete to the abstract which meets us in every great mathematical question..."

"[F]unctions must... be divided into Abstract and Concrete; the first of which alone can enter into true equations."

"Every is a relation of equality between two abstract functions of the magnitudes... including the primary magnitudes and all auxiliary magnitudes which may... facilitate the discovery of the equations..."

"This distinction may be established by both the à priori and à posteriori methods; by characterizing each kind of function, and by enumerating all the abstract functions yet known..."

"A priori; Abstract functions express a mode of dependence between magnitudes which may be conceived between numbers alone, without the need of pointing out any phenomena... while Concrete functions are those whose expression requires a specified... case of physics, geometry, mechanics, etc."

"Most functions were concrete in their origin,—even those which are at present the most purely abstract; and the ancients discovered... through geometrical definitions elementary algebraic properties of functions, to which a numerical value was not attached till long afterwards, rendering abstract to us what was concrete to the old geometers."

"[[w:Trigonometric functions|[C]ircular functions]], both direct and inverse... are still sometimes concrete, sometimes abstract, according to the point of view from which they are regarded."

"A posteriori; the distinguishing character, abstract or concrete, of a function having been established, the question of any determinate function being abstract, and therefore able to enter into true analytical equations, becomes a simple question of fact, as we are acquainted with the elements which compose all the abstract functions at present known. We say we know them all, though analytical functions are infinite in number, because we are here speaking, it must be remembered,— of the elements— of the simple, not of the compound."

"We have ten elementary formulas; and, few as they are, they may give rise to an infinite number of analytical combinations. There is no reason for supposing that there can never be more. We have more than Descartes had, and even Newton and Leibnitz; and our successors will doubtless introduce additions, though there is so much difficulty attending their augmentation, that we cannot hope that it will proceed very far."

"It is the insufficiency of this very small number of analytical elements which constitutes our difficulty in passing from the concrete to the abstract."

"In order to establish the equations of phenomena, we must conceive of their mathematical laws by the aid of functions composed of these few elements."

"[T]hese elements of our analysis have been supplied to us by the mathematical consideration of the simplest phenomena of a geometrical origin, which can afford us à priori no rational guarantee of their fitness to represent the mathematical laws of all other classes of phenomena."

"[W]e have considered the Calculus as a whole. We must now consider its divisions... the Algebraic Calculus, and the Arithmetical Calculus, or Arithmetic, taking care to give them the most extended logical sense, and not the restricted one... usually received."

"[E]very question of Mathematical Analysis presents two successive parts, perfectly distinct... The first stage is the transformation of the proposed equations, so as to exhibit the mode of formation of unknown quantities by the known. This constitutes the algebraic question. Then ensues the task of finding the values of the formulas thus obtained. ...this is the arithmetical question."

"Thus the algebraic and the arithmetical calculus differ in their object. They differ also in their view of quantities,—Algebra considering quantities in regard to their relations, and Arithmetic in regard to their values."

"In practice, it is not always possible... to separate the processes entirely in obtaining a solution; but the radical difference of the two operations should never be lost sight of."

"Algebra... is the Calculus of Functions, and Arithmetic the Calculus of Values."

"We have seen that the division of the Calculus is into two branches. It remains... to compare the two... to learn their respective extent, importance, and difficulty."

"Functions being divided into simple and compound... when we become able to determine the value of simple functions, there will be no difficulty with the compound."

"In the algebraic relation, a compound function plays a very different part from... the elementary functions which constitute it; and this is the source of our chief analytical difficulties. But it is quite otherwise with the Arithmetical Calculus."

"[T]here can be no new arithmetical operations otherwise than by the creation of new analytical elements, which must... for ever be extremely small."

"The domain of arithmetic then is, by its nature, narrowly restricted, while that of algebra is rigorously indefinite."

"Still, the domain of arithmetic is... extensive... for there are many questions treated as incidental in the midst of a body of analytical researches, which... are... arithmetical. Of this kind are the construction of a table of logarithms, and the calculation of trigonometrical tables, and some distinct and higher procedures; in short, every operation which has for its object the determination of the values of functions."

"[W]e must also include... the Theory of Numbers, the object of which is to discover the properties inherent in different numbers, in virtue of their values, independent of any particular system of numeration. It constitutes a sort of transcendental arithmetic."

"Though the domain of arithmetic is thus larger than is commonly supposed, this Calculus of values will yet never be more than a point, as it were, in comparison with the calculus of functions, of which mathematical science essentially consists."

"Determinations of values are, in fact, nothing else than real transformations of the functions to be valued. These transformations have a special end; but... are essentially of the same nature as all taught by analysis."

"[T]he calculus of values might be regarded as a particular application of the calculus of functions, arithmetic thereby disappearing, as a distinct section, from the domain of abstract mathematics."

"[W]e will now see how the establishment of the s of phenomena has been achieved."

"The first means of remedying the difficulty of the small number of analytical elements seems to be to create new ones. But... this resource is illusory."

"[T]he introduction of another elementary abstract function into analysis supposes the simultaneous creation of a new arithmetical operation; which is certainly extremely difficult. ...We have... no idea how to proceed to create new elementary abstract functions. Yet, we must not... conclude that we have reached the limit... Special improvements in mathematical analysis have yielded us some partial substitutes, which have increased our resources: but... the augmentation... cannot proceed but with extreme slowness. It is not in this direction, then, that the human mind has found its means of facilitating the establishment of equations."

"As it is impossible to find the equations directly, we must seek... corresponding ones between other auxiliary quantities, connected with the first according to a certain determinate law, and from the relation... ascend to that of the primitive magnitudes. This is the... transcendental analysis... our finest instrument for the mathematical exploration of natural phenomena."

"[T]he auxiliary quantities... might be derived, according to any law whatever, from the immediate elements of the question."

"[O]ur future improved analytical resources may perhaps be found in a new mode of derivation. But, at present, the only auxiliary quantities habitually substituted for the primitive quantities in transcendental analysis are what are called— 1st, infinitely small elements, the differentials of different orders of those quantities, if we conceive of this analysis in the manner of Leibnitz: or 2nd, the s, the limits of the ratios of the simultaneous increments of the primitive quantities, compared with one another; or, more briefly, the prime and ultimate ratios of these increments, if we adopt the conception of Newton: or 3rd, the derivatives... of these quantities; that is, the coefficients of the different terms of their respective increments, according to the conception of Lagrange. These conceptions, and all others that have been proposed, are by their nature identical."

"We now see that the Calculus of functions, or Algebra, must consist of two distinct branches."

"To ordinary analysis I... give the name of Calculus of Direct Functions. To transcendental analysis, (...Infinitesimal Calculus, Calculus of fluxions and of fluents, Calculus of Vanishing quantities, the Differential and Integral Calculus, etc...) I shall give the title of Calculus of Indirect Functions.... by generalizing and giving precision to the ideas of Lagrange, and employ them to indicate the exact character of the two forms of analysis."

"[A]nalysts first divide equations... into two principal classes, according as they contain functions of only the first three of the [five] couples, or as they include also either exponential or circular functions. Though the names of algebraic and s given to these principal groups are inapt, the division between the corresponding equations is real enough, insofar as that the resolution of equations containing the transcendental functions is more difficult than that of s. Hence the study of the first is extremely imperfect, and our analytical methods relate almost exclusively to the elaboration of the second."

"[W]e must observe that, though [Algebraic equations] may often contain irrational functions of the unknown quantities, as well as rational functions, the first case can always be brought under the second, by transformations more or less easy..."

"[T]he resolution of algebraic equations is as yet known to us only in the four first degrees. In this respect, algebra has advanced but little since the labours of Descartes and the Italian analysts of the sixteenth century..."

"The only question... of eminent importance... in its logical relations, would be the general resolution of algebraic equations of any degree whatever. But... we are led to suppose, with Lagrange, that it exceeds the scope of our understandings."

"[I]f we had obtained the resolution of algebraic equations of any degree whatever, we should still have treated only a very small part of algebra... that is, of the calculus of direct functions, comprehending the resolution of all the equations that can be formed by the s known to us..."

"[B]y a law of our nature, we shall always remain below the difficulty of science, our means of conceiving of new questions being always more powerful than our resources for resolving them... [i.e.,] the human mind being more apt at imagining than at reasoning."

"Thus, if we... resolved all the analytical equations now known, and if, to do this, we had found new analytical elements, these again would introduce classes of equations of which we now know nothing: and so, however great might be the increase of our knowledge, the imperfection of our algebraic science would be perpetually reproduced."

"The methods that we have are, the complete resolution of the equations of the first four degrees; of any binomial equations; of certain special equations of the superior degrees; and of a very small number of exponential, logarithmic, and circular equations. These elements are very limited; but geometers have succeeded in treating with them a great number of important questions in an admirable manner."

"The improvements introduced within a century into mathematical analysis have contributed more to render the little knowledge that we have immeasurably useful, than to increase it."

"To fill up the vast gap in the resolution of algebraic equations of the higher degrees, analysts have had recourse to a new order of questions,—to... the numerical resolution of equations. Not being able to obtain the real algebraic formula, they have sought to determine at least the value of each unknown quantity for such or such a designated system of particular values attributed to the given quantities."

"This operation is a mixture of algebraic with arithmetical questions; and it has been so cultivated as to be rendered possible in all cases, for equations of any degree and even of any form. The methods for this are now sufficiently general; and what remains is to simplify them so as to fit them for regular application."

"[T]his is very imperfect algebra; and it is only isolated, or truly final questions (which are very few), that can be brought finally to depend upon only the numerical resolution of equations."

"Most questions are only preparatory,—a first stage of the solution of other questions; and in these cases it is evidently not the value of the unknown quantity that we want to discover, but the formula which exhibits its derivation."

"Even in the most simple questions, when this numerical resolution is strictly sufficient, it is... a very imperfect method. Because we cannot abstract and treat separately the algebraic part of the question, which is common to all the cases which result from the mere variation of the given numbers, we are obliged to go over again the whole series of operations for the slightest change that may take place in any one of the quantities concerned."

"Thus is the calculus of direct functions at present divided into two parts, as it is employed for the algebraic or the numerical resolution of equations. The first, the only satisfactory one, is... very restricted, and there is little hope that it will ever be otherwise: the second, usually insufficient, has at least the advantage of a much greater generality. They must be carefully distinguished in our minds, on account of their different objects, and therefore of the different ways in which quantities are considered by them. Moreover, there is, in regard to their methods, an entirely different procedure in their rational distribution."

"In the first part, we have nothing to do with the values of the unknown quantities, and the division must take place according to the nature of the equations which we are able to resolve; whereas in the second, we have nothing to do with the degrees of the equations, as the methods are applicable to equations of any degree whatever; but the concern is with the numerical character of the values of the unknown quantities."

"These two parts, which constitute the immediate object of the Calculus of direct functions, are subordinated to a third, purely speculative, from which both derive their most effectual resources, ...designated by the general name of ', though it relates, as yet, only to algebraic equations. The numerical resolution of equations has, on account of its generality, special need of this rational foundation."

"Two orders of questions divide this important department of algebra between them; first, those which relate to the composition of equations, and then those that relate to their transformation; the business of these last being to modify the roots of an equation without knowing them..."

"One more theory... to complete our rapid exhibition of the different essential parts of the calculus of direct functions... relates to the transformation of functions into series by the aid of the Method of indeterminate Coefficients... one of the most fertile and important in algebra. This... is one of the most remarkable discoveries of Descartes."

"[I]nfinitesimal calculus, for which it might be... substituted in some respects, has... deprived it of some... importance; but the growing extension of the transcendental analysis has, while lessening its necessity, multiplied its applications and enlarged its resources; so by the useful combination of the two theories, the employment of the method of indeterminate coefficients has become much more extensive than... even before the formation of the calculus of indirect functions."

"We must next pass on to the more important and extensive branch... the Calculus of Indirect Functions."

"[T]he views of the transcendental analysis... by Leibnitz, Newton, and Lagrange... each... has advantages... all are finally equivalent, and... no method has yet been found which unites their respective characteristics."

"[I]t is only by the use of them all that an adequate idea of the analysis and its applications can be formed."

"The first germ of the infinitesimal method (which can be conceived of independently of the Calculus) may be recognized in the old Greek Method of Exhaustions, employed to pass from the properties of straight lines to those of curves. The method consisted in substituting for the curve the auxiliary consideration of a polygon, inscribed or circumscribed, by means of which the curve itself was reached... but there was in it no equivalent for our modern methods; for the ancients had no logical and general means for the determination of... limits, which was the chief difficulty of the question."

"The task remaining for modern geometers was to generalize the conception of the ancients, and, considering it in an abstract manner, to reduce it to a system of calculation..."

"Lagrange justly ascribes to... Fermat the first idea in this new direction. Fermat... initiated the direct formation of transcendental analysis by his method for the determination of ', and for the finding of s, in which process he introduced auxiliaries which he afterwards suppressed as null when the equations obtained had undergone... suitable transformations."

"After some modifications of the ideas of Format in the intermediate time, Leibnitz stripped the process of some complications, and formed the analysis into a general and distinct calculus, having his own notation: and... is thus the creator of transcendental analysis, as we employ it now."

"This pre-eminent discovery was so ripe, as all great conceptions are at the hour of their advent, that Newton had at the same time, or... earlier, discovered a method exactly equivalent, regarding the analysis from a different point of view, much more logical... but less adapted than that of Leibnitz to give all practicable extent and facility to the fundamental method."

"Lagrange... discarding the heterogeneous considerations which had guided Leibnitz and Newton, reduced the analysis to a purely algebraic system, which only wants more aptitude for application."

"The method of Leibnitz consists in introducing... in order to facilitate the establishment of equations, the infinitely small elements or differentials which are supposed to constitute the quantities whose relations we are seeking."

"There are relations between these differentials which are simpler and more discoverable than those of the primitive quantities; and by these we may afterwards (through a special calculus employed to eliminate these auxiliary infinitesimals) recur to the equations sought, which it would usually have been impossible to obtain directly."

"[W]hen there is too much difficulty in forming the equation between the differentials of the magnitudes under notice, a second application of the method is required, the differentials being now treated as new primitive quantities, and a relation being sought between their infinitely small elements, or second differentials, and so on... repeated any number of times..."

"[P]reliminary ideas being laid down, the spirit of the infinitesimal analysis consists in constantly neglecting the infinitely small quantities in comparison with finite quantities; and generally, the infinitely small quantities of any order whatever in comparison with all those of an inferior order."

"[I]t becomes possible in geometry to treat curved lines as composed of an infinity of rectilinear elements, and curved surfaces as formed of plane elements; and, in mechanics, varied motions as an infinite series of uniform motions, succeeding each other at infinitely small intervals of time."

"[T]he conception of transcendental analysis, as formed by Leibnitz... is... the loftiest idea ever yet attained by the human mind."

"[T]his conception was necessary to complete the basis of mathematical science, by enabling us to establish... the relation of the concrete to the abstract. In this respect, we must regard it as the necessary complement of the great fundamental idea of Descartes on the general analytical representation of natural phenomena; an idea which could not be duly estimated or put to use till after the formation of the infinitesimal analysis."

"The differential formulas exhibit an extreme generality, expressing in a single equation each determinate phenomenon, however varied may be the subjects to which it belongs."

"Thus, one... equation gives the tangents of all curves, another their rectifications, a third their quadratures; and, in the same way, one invariable formula expresses the mathematical law of all variable motion; and one single equation represents the distribution of heat in any body, and for any case."

"This remarkable generality is the basis of the loftiest views of the geometers."

"Thus this analysis has not only furnished a general method for forming equations indirectly which could not have been directly discovered, but it has introduced a new order of more natural laws for our use in the mathematical study of natural phenomena, enabling us to rise at times to a perception of positive approximations between classes of wholly different phenomena, through the analogies presented by the differential expressions of their mathematical laws."

"In virtue of this second property of the analysis, the entire system of an immense science, like geometry or mechanics, has submitted to a condensation into a small number of analytical formulas, from which the solution of all particular problems can be deduced, by invariable rules."

"This beautiful method is, however, imperfect in its logical basis."

"Leibnitz himself failed to justify his conception, giving, when urged, an answer which represented it as a mere approximative calculus, the successive operations of which might... admit an augmenting amount of error."

"Some of his successors were satisfied with showing that its results accorded with those obtained by ordinary algebra, or the geometry of the ancients, reproducing... some solutions..."

"Some... demonstrated the conformity of the new conception with others; that of Newton especially, which was unquestionably exact. This afforded a practical justification: but... a logical justification is also required,—a direct proof of the necessary rationality of the infinitesimal method."

"Carnot... furnished this at last, by showing that the method was founded on the principle of the necessary compensation of errors. We cannot say that all the logical scaffolding... may not have a merely provisional existence... but, in the present state of our knowledge, Carnot's principle... is of... importance, in legitimating the analysis of Leibnitz... His reasoning is founded on the conception of infinitesimal quantities indefinitely decreasing, while those from which they are derived are fixed. The infinitely small errors introduced with the auxiliaries cannot have occasioned other than infinitely small errors in all the equations... Carnot's theory is doubtless more subtle than solid; but it has no other radical logical vice than that of the infinitesimal method itself..."

"Newton offered his conception under several different forms in succession. That... most commonly adopted... was called by himself, sometimes the Method of prime and ultimate Ratios, sometimes the Method of Limits... [W]e find nearly the equivalent of the facilities offered by the analysis of Leibnitz, which are merely considered from another point of view."

"Thus, curves will be regarded as the limits of a series of rectilinear polygons, and variable motions as the limits of an aggregate of uniform motions of continually nearer approximation, etc., etc."

"Such is... Newton's conception; or rather, that which Maclaurin and d'Alembert have offered as the most rational basis of the transcendental analysis, in the endeavour to fix and arrange Newton's ideas on the subject."

"Newton had another view... the Calculus of s and of fluents, founded on the general notion of velocities."

"Conceive of every curve as generated by a point affected by a motion varying according to any law whatever. The different quantities presented by the curve, the abscissa, the ordinate, the arc, the area, etc.,... regarded as simultaneously produced by successive degrees during this motion. The velocity with which each one will have been described will be called the fluxion of that quantity, which inversely would have been called its fluent. Henceforth, the transcendental analysis... forming directly the equations between the fluxions of the proposed quantities, to deduce from them afterwards, by a special Calculus, the equations between the fluents... any magnitudes... by the help of a suitable image... being produced by the motion of others."

"This method is... the same with that of limits complicated with the foreign idea of motion. ...[A] way of representing, by a comparison derived from mechanics, the method of prime and ultimate ratios, which alone is reducible to a calculus... without its being requisite for us to offer special proofs of this."

"Lagrange's conception consists, in its admirable simplicity, in considering the transcendental analysis to be a great algebraic artifice, by which... we must introduce, in the place of or with the primitive functions, their derived functions; that is... the coefficient of the first term of the increment of each function, arranged according to the ascending powers of the increment of its variable."

"The Calculus of indirect functions... is destined here, as well as in... Leibnitz and Newton, to eliminate these derivatives, employed as auxiliaries, to deduce from their relations the corresponding equations between the primitive magnitudes."

"The transcendental analysis is then only a simple, but very considerable extension of ordinary analysis."

"It has long been a common practice with geometers to introduce... in the place of the magnitudes in question, their different powers, or their logarithms, or their sines, etc., in order to simplify the equations, and even to obtain them more easily. Successive derivation is a general artifice of the same nature, only of greater extent, and commanding, in consequence, much more important resources for this common object."

"Other theories have been proposed, such as Euler's Calculus of vanishing quantities: but they are merely modifications of the three just exhibited."

"Considering the three methods in regard to their destination... they all consist in the same general logical artifice... the introduction of a certain system of auxiliary magnitudes being substituted for the express object of facilitating the analytical expression of the mathematical laws of phenomena..."

"Whether these indirect equations are differential equations, according to Leibnitz, or equations of limits, according to Newton, or derived equations, according to Lagrange, the general procedure is evidently always the same. ...[T]he auxiliaries introduced are really identical, being only regarded from different points of view."

"The transcendental analysis... examined abstractly and in its principle, is always the same, whatever conception... and the processes... are necessarily identical in these different methods, which must therefore, under any application whatever, lead to rigorously uniform results."

"The method of Leibnitz has... the advantage in the rapidity and ease with which it effects the formation of equations between auxiliary magnitudes. We owe to its use the high perfection attained by all the general theories of geometry and mechanics."

"Lagrange... after having reconstructed the analysis on a new basis, rendered a candid and decisive homage to the conception of Leibnitz, by employing it exclusively in the whole system of his "Analytical Mechanics.""

"Yet... we... admit, with Lagrange, that the conception of Leibnitz is radically vicious in its logical relations. He himself declared the notion of infinitely small quantities to be a false idea: and it is... impossible to conceive of them clearly..."

"This false idea bears... the characteristic impress of the metaphysical age of its birth and tendencies of its originator. By the ingenious principle of the compensation of errors, we may... explain the necessary exactness of the processes... but it is a radical inconvenience to be obliged to indicate, in Mathematics, two clashes of reasonings so unlike, as that the one order are perfectly rigorous, while by the others we designedly commit errors which have to be afterwards compensated."

"[T]he infinitesimal method exhibits the very serious defect of breaking the unity of abstract mathematics by creating a transcendental analysis founded upon principles widely different from those which serve as a basis to ordinary analysis."

"Newton's conception is free from the logical objections imputable to that of Leibnitz. The notion of limits is in fact remarkable for its distinctness and precision. The equations are... regarded as exact from their origin; and the general rules of reasoning are as constantly observed as in ordinary analysis. But it is weak in resources, and embarrassing in operation, compared with the method. In its applications, the relative inferiority of this theory is very strongly marked. It also separates the ordinary and transcendental analysis, though not so conspicuously as the theory of Leibnitz."

"As Lagrange remarked, the idea of limits, though clear and exact, is not the less a foreign idea, on which analytical theories ought not to be dependent."

"This perfect unity of analysis, and a purely abstract character in the fundamental ideas, are found in the conception of Lagrange... alone. It is therefore the most philosophical..."

"Discarding every heterogeneous consideration, Lagrange reduced the transcendental analysis to its proper character,—that of presenting a very extensive class of analytical transformations, which facilitate... the expression of the conditions of the various problems. This exhibits the conception as a simple extension of ordinary analysis. It is a superior algebra. This philosophical superiority marks it for adoption as the final theory of transcendental analysis; but it presents too many difficulties in its application..."

"Lagrange... had great difficulty in rediscovering, by his own method, the principal results already obtained by the infinitesimal method, on general questions in geometry and mechanics. ...Though Lagrange... obtained results in some cases which other men would have despaired of... his conception has thus far remained... essentially unsuited to applications."

"In all the other departments of mathematical science, the consideration of different methods for a single class of questions may be useful, apart from the historical interest... but it is not indispensable. Here... it is strictly indispensable. Without it there can be no philosophical judgment of this admirable creation of the human mind; nor any success and facility in the use of this powerful instrument."

"[A]lmost all geometers employ the terms Differential Calculus and Integral Calculus established by Leibnitz. Newton... called the first the Calculus of Fluxions, and the second the Calculus of Fluents... According to the theory of Lagrange, the one... the Calculus of Derived Functions, and the other the Calculus of Primitive Functions."

"The differential calculus is... the rational basis of the . ...[T]en simple functions constitute the elements of our analysis. We cannot know how to integrate directly any other differential expressions than those produced by the differentiation of those ten... The art of integration consists therefore in bringing all the other cases, as far as possible, to depend wholly on this small number of simple functions."

"The entire system of the differential calculus is simple and perfect, while the integral calculus remains extremely imperfect."

"I will sketch the great impending philosophical regeneration from the four points of view... the scientific, or rather rational; the moral; the political; and finally, the aesthetic."

"The positive state will... be one of entire intellectual consistency, such as has never yet existed in an equal degree, among the best organized and most advanced minds."

"The kind of speculative unity which existed under the polytheistic system, when all human conceptions presented a uniformly religious aspect, was liable to perpetual disturbance from a spontaneous positivity of ideas..."

"In the scholastic period, the nearest approach to harmony was a precarious and incomplete equilibrium: and the present transition involves such contradiction that the highest minds are perpetually subject to three incompatible systems."

"[W]hen we shall habitually restrict our inquiries to the simplest affairs in life; and... to accessible subjects, and understand... the relative character of all human knowledge, our approximation towards the truth, which can never be completely attained by human faculties, will be thorough and satisfactory... and it will proceed as far as the state of human progress will admit."

"We have never experienced, and can... only imperfectly imagine, the state of unmingled conviction with which men will regard that natural order when all disturbing intrusions, such as... from lingering theological influences, shall have been cast out by the spontaneous certainty of the invariableness of natural laws."

"[T]he absolute tendencies of the old philosophies prevent our forming any adequate conception of the privilege of intellectual liberty which is secured by positive philosophy."

"Our existing state is so unlike all this, that we cannot... estimate the importance and rapidity of progress which will be thus secured; our only measure being the ground gained during the last three centuries, under and imperfect and even vicious system, which has occasioned the waste of the greater part of our intellectual labour."

"In abstract science, men will be spared the preliminary labour which has hitherto involved vast and various error, scientific and logical, and will be set forward far and firmly by the full establishment of the rational method."

"When the ascendancy of the sociological spirit shall have driven out that of the scientific, there will be an end of the vain struggle to connect every order of phenomena with one set of laws, and the desired unity will be seen to consist in the agreement of various orders of laws,—each set governing and actuating its own province; and thus will the free expansion of each kind of knowledge be provided for, while all are analogous in their method of treatment, and identical in their destination."

"Then there will be an end to the efforts of the anterior sciences to absorb the more recent, and of the more recent to maintain their superiority by boasting of sanction from the old philosophies; and the positive spirit will decide the claims of each, without oppression or anarchy, and with the necessary assent of all."

"The same unquestionable order will be established in the interior of each science; and every proved conception will be secured from such attacks as all are now liable to from the irregular ambition or empiricism of unqualified minds."

"Though abstract science must hold the first place, as Bacon so plainly foresaw, the direct construction of concrete science is one of the chief offices of the new philosophical spirit, exercised under historical guidance, which can alone afford the necessary knowledge of the successive states of every thing that exists."

"[T]here will be another result... the fixing,—not yet possible, but then certainly practicable,—of the general duration assigned by the whole economy to each of the chief kinds of existence; and, among others, to the rising condition of the human race."

"[T]he collective organism is necessarily subject, like the individual, to a spontaneous decline, independently of changes in the medium. The one has no more tendency to rejuvenescence than the other; and the only difference in the two cases is in the immensity of duration and slow progression in the one, compared with the brief existence, so rapidly run through, of the other."

"There is no reason why, because we decline the metaphysical notion of indefinite perfectibility, we should be discouraged in our efforts to ameliorate the social state; as the health of individuals is ministered to when destruction is certainly near at hand."

"It is too soon in infancy to prepare for old age; and there would be less wisdom in such preparation in the collective than in the individual case."

"Morality must become more practical than it ever could be under religious influences, because personal morality will be seen in its true relations,—withdrawn from all influences of personal prudence, and recognized as the basis of all morality whatever, and therefore as a matter of general concern and public rule. The ancients had some sense of this, which they could not carry out; and Catholicism lost it by introducing a selfish and imaginary aim."

"[M]oral rules certainly hold the very first place, because they especially admit of the universal concurrence in which our chief power resides. If we are thus brought back from an immoderate regard to the future by a sense of the value of the present, this will equalize life by discouraging excessive economical preparation; while a sound appreciation of our nature, in which vicious or unregulated propensities originally abound, will render common and unanimous the obligation to discipline, and regulate our various inclinations."

"[T]he scientific and moral conception of Man as the chief of the economy of nature will be a steady stimulus to the cultivation of the noble qualities, affective as well as intellectual, which place him at the head of the living hierarchy."

"There can be no danger of apathy in a position like this,—with the genuine and just pride of such pre-eminence stirring within us; and above us the type of perfection, below which we must remain, but which will ever be inviting us upwards. The result will be a noble boldness in developing the greatness of Man in all directions, free from the oppression of any fear, and limited only by the conditions of life itself."

"[P]rogression will develop more and more the natural differences on which such an economy is based, so that each element will tend towards the mode of existence most suitable to itself, and consonant with the general welfare."

"The positive philosophy is the first that has ascertained the true point of view of social morality. The metaphysical philosophy sanctioned egotism; and the theological subordinated real life to an imaginary one; while the new philosophy takes social morality for the basis of its whole system."

"We have yet to witness the moral superiority of a philosophy which connects each of us with the whole of human existence, in all times and places."

"The restriction of our expectations to actual life must furnish new means of connecting our individual development with the universal progression, the growing regard to which will afford the only possible, and the utmost possible, satisfaction to our natural aspiration after eternity."

"[T]he scrupulous respect for human life, which has always increased with our social progression, must strengthen more and more as the chimerical hope dies out which disparages the present life as merely accessory to the one in prospect."

"The philosophical spirit being only an extension of good sense... it alone, in its spontaneous form, has for three centuries maintained any general agreement against the dogmatic disturbances occasioned or tolerated by the ancient philosophy, which would have overthrown the whole modern economy if popular wisdom had not restrained the social application of it."

"[P]ositive morality will tend more and more to exhibit the happiness of the individual as depending on the complete expansion of benevolent acts and sympathetic emotions towards the whole of our race; and even beyond our race, by a gradual extension to all sentient beings below us, in proportion to their animal rank and their social utility."

"Till the full rational establishment of positive morality has taken place, it is the business of true philosophers, ever the precursors of their race, to confirm it in the estimation of the world by the sustained superiority of their own conduct, personal, domestic, and social; giving the strongest conceivable evidence of the possibility of developing, on human grounds alone, a sense of general morality complete enough to inspire an invincible repugnance to moral offence, and an irresistible impulse to steady practical devotedness."

"I have only to glance at the growth and application of the division between the spiritual or theoretical organism and the temporal or practical..."

"Catholicism afforded the suggestion of a double government of this kind, and that the Catholic institution of it shared the discredit of the philosophy to which it was attached: and... the Greek Utopia of a Reign of Mind (well called by Mr. Mill a Pedantocracy), transmitted to the modern metaphysical philosophy, gained ground till its disturbing influence rendered it a fit subject for our judgment and sentence."

"The present state of things is that we have a deep and indestructible, though vague and imperfect, sense of the political requirements of existing civilization, which assigns a distinct province, in all affairs, to the material and the intellectual authority, the separation and co-ordination of which are reserved for the future."

"The Catholic division was instituted on the ground of a mystical opposition between heavenly and earthly interests... and when the terrestrial view prevailed over the celestial, the principle of separation was seriously endangered, from there being no longer any logical basis which could sustain it against the extravagances of the revolutionary spirit."

"The positive polity must... go back to the earliest period of the division, and re-establish it on evidence afforded by the whole human evolution; and, in its admission of the scientific and logical preponderance of the social point of view, it will not reject it in the case of morality, which must always allow its chief application, and in which everything must be referred, not to Man, but to Humanity."

"Moral laws, like the intellectual, are much more appreciable in the collective than in the individual case; and, though the individual nature is the type of the general, all human advancement is much more completely characterized in the general than in the individual case; and thus morality will always, on both grounds, be connected with polity. Their separation will arise from that distinction between theory and practice which is indispensable to the common destination of both."

"We may... sum up the ultimate conditions of positive polity by conceiving of its systematic wisdom as reconciling the opposing qualities of that spontaneous human wisdom successively manifested in antiquity and in the Middle Ages; for there was a social tendency involved in the ancient subordination of morality to policy, however carried to an extreme under polytheism; and the monotheistic system had the merit of asserting, though not very successfully, the legitimate independence, or rather, the superior dignity of morality."

"Antiquity alone offered a complete and homogeneous political system; and the Middle Ages exhibit an attempt to reconcile the opposite qualities of two heterogeneous systems, the one of which claimed supreme authority for theory, and the other for practice."

"Such a reconciliation will take place hereafter, on the ground of the systematic distinction between the claims of education and of action."

"If the whole experience of modern progress has sanctioned the independence, amidst co-operation, of theory and practice, in the simplest cases, we must admit its imperative necessity, on analogous grounds, in the most complex."

"Thus far, in complex affairs, practical wisdom has shown itself far superior to theoretical; but this is because much of the proudest theory has been ill-established. However, this evil may be diminished when social speculation becomes better founded, the general interest will always require the common preponderance of the practical or material authority, as long as it keeps within its proper limits, admitting the independence of the theoretical authority; and the necessity of including abstract indications among the elements of every concrete conclusion."

"We have still to reap some of the bitter fruits of our intellectual and moral anarchy: and especially, in the quarrels between capitalists and labourers first, and afterwards in the unsettled rivalship between town and country. In short, whatever is now systematized must be destroyed; and whatever is not systematized, and therefore has vitality, must occasion collisions which we are not yet able accurately to foresee or adequately to restrain. This will be the test of the positive philosophy, and at the same time the stimulus to its social ascendancy."

"The difficulties proper to the action of the new regime, the same in kind, will be far less in degree, and will disappear as the conditions of order and progress become more and more thoroughly reconciled."

"[T]he advent of the positive economy will have been owing to the affinity between philosophical tendencies and popular impulses: and if so... that affinity must become the most powerful permanent support of the system."

"For five centuries, society has been seeking an aesthetic constitution correspondent to its civilization. In the time to come... we may see how Art must eminently fulfil its chief service, of charming and improving the humblest and the loftiest minds, elevating the one, and soothing the other. For this service it must gain much by being fitly incorporated with the social economy, from which it has hitherto been essentially excluded."

"The public life and military existence of antiquity are exhausted; but the laborious and pacific activity proper to modern civilization is scarcely yet instituted, and has never yet been aesthetically regarded; so that modern art, like modern science and industry, is so far from being worn out, that it is as yet only half formed. The most original and popular species of modern art, which forms a preparation for that which is to ensue, has treated of private life, for want of material in public life. But public life will be such as will admit of idealization: for the sense of the good and the true cannot be actively conspicuous without eliciting a sense of the beautiful; and the action of the positive philosophy is in the highest degree favourable to all the three."

"The systematic regeneration of human conceptions must also furnish new philosophical means of aesthetic expansion, secure at once of a noble aim and a steady impulsion. There must certainly be an inexhaustible resource of poetic greatness in the positive conception of Man as the supreme head of the economy of Nature, which he modifies at will, in a spirit of boldness and freedom, within no other limits than those of natural law. This is yet an untouched wealth of idealization, as the action of Man upon Nature was hardly recognized as a subject of thought till art was declining from the exhaustion of the old philosophy."

"The marvellous wisdom of Nature has been sung, in imitation of the ancients, and with great occasional exaggeration; and the conquests of Man over nature, with science for his instrument, and sociality for his atmosphere, remains, promising much more interest and beauty than the representation of an economy in which he has no share, and in which magnitude was the original object of admiration, and material grandeur continues to be most dwelt upon."

"There is no anticipating what the popular enthusiasm will be when the representations of Art shall be in harmony with the noble instinct of human superiority, and with the collective rational convictions of the human mind."

"To the philosophical eye it is plain that the universal reorganization will assign to modern Art at once inexhaustible material in the spectacle of human power and achievement, and a noble social destination in illustrating and endearing the final economy of human life."

"What philosophy elaborates, Art will propagate and adapt for propagation, and will thus fulfil a higher social office than in its most glorious days of old."

"I have here spoken of the first of the arts only,—of Poetry, which by its superior amplitude and generality has always superintended and led the development of them all: but the conditions which are favourable to one mode of expression are propitious to all, in their natural succession."

"While the positive spirit remained in its first phase, the mathematical, it was reproached for its anti-aesthetic tendency: but we now see how, when it is systematized from a sociological centre, it becomes the basis of an aesthetic organization no less indispensable than the intellectual and social renovation from which it is inseparable."

"This summary estimate of the ultimate result of the Positive Philosophy brings me to the close of the long and arduous task... to carry forward the great impulse given to philosophy by Bacon and Descartes."

"Their work was essentially occupied with the first canons of the positive method: it was entirely powerless to found any final reconstruction of human society, the need for which was hardly apparent in their age, but which is now so urgently required by the prospect of social anarchy and revolutionary agitation."

"In the course of my labours... prolonged over twelve years, my own mind has spontaneously, but exactly, traversed the successive phases of our modern mental evolution."

"As the new science of Sociology had to be created, it was not planned with the same precision... But even here I hope that... readers will admit that each science has been treated in the degree of its true philosophical importance."

"Having thus worked through the... scale of the sciences... my mind has reached a.... positive condition, and has wholly disengaged itself from metaphysics as well as theology."

"There are four essential works required... Two of the four contemplated works would be occupied with the more complete elaboration of the new system of philosophy; the other two works relate to the application of it to practice."

"In the Treatise just completed, it was inevitable that each science in turn should be handled from the point of view of its actual condition... by a gradual and sure process of growth to the ultimate state which I had conceived from the first, but which I could only reach by passing through the successive stages of modern evolution in the same way as Descartes did in his famous formula."

"[W]hatever may have been the advantages of this method of systematizing the sciences à posteriori, and without it I must have failed in my object, the consequence was, that the philosophy of each science, on which the general positive philosophy was founded, could not be presented in its definitive form."

"This definitive form could only be secured by the reaction upon each science of the new philosophical synthesis."

"Such an effect, which, duly completed, will be for abstract purposes the final state of the positive systematization, would properly require as many special philosophical treatises, each infused with the sociological spirit, as there are different substantive sciences."

"It is... impossible that I could ever properly complete so vast a task... and I... restrict my... work to the first and the last of the sciences, which are the more decisive, and... those with which I am most familiar."

"I... limit myself to Mathematics and Sociology, and... leave it to my successors or... colleagues to deal with the philosophy of the four intermediate sciences—astronomy, physics, chemistry, and biology."

"When I composed the first part of this work twelve years ago, I... thought that the theories on the philosophy of mathematics there put forward would be sufficiently clear to be grasped. I underrated the extreme narrowness of the views now current in that science."

"I feel it necessary to attempt to lay down a true philosophy of mathematical science, the base... of the whole scientific series."

"The second work, on Sociology... will consist of... the methods of Sociology, the... Social Statics, the... Social Dynamics, the last... the practical application of the doctrine."

"The philosophy of the Social Polity is the most important task that awaits me."

"[T]he most direct mode of contributing to the general acceptance of the new positive philosophy must be found in promoting the normal completeness of the social science. ...[T]here are strong practical grounds for giving a special importance to Sociology."

"With regard to... the practical application of the new system of philosophy, I propose... a Treatise upon the principles of positive education..."

"[E]ducation must always be the first step towards a political regeneration. Thus the third work I propose is a sequel to the present Treatise. Its important duty would be the reorganization of Morals on a positive basis. This will... be the principal part of education; and this alone will effectively dispel that theological philosophy, which, in its decline, is still powerful enough to embarrass the course both of intellectual and social progress."

"I have already read the noble preface and the excellent table of contents, as well as some decisive chapters. And I am convinced that you have displayed clearness of thought, truth, and sagacity in your long and diflicult task."

"The important undertaking that you so happily conceived and have so worthily accomplished will give my 'Positive Philosophy' a competent audience greater than I could have hoped to find in my own lifetime."

"It is due to you, that the arduous study of my fundamental treatise is now indispensable only for the small number of those who purpose to become systematic students of philosophy. But the majority of readers, with whom theoretic training is only intended to provide them with practical good sense, may now prefer, and even ought to prefer for ordinary use, your admirable condensation... It realises a wish of mine that I formed ten years ago. And looking at it from the point of view of future generations, I feel sure that your name will be linked with mine, for you have executed the only one of those works that will survive amongst all those which my fundamental treatise has called forth."

"Not only is it extremely well done, but it could not be better done."

"Twelve years had passed... during which his life had been closed against any kind of distraction. No wish for premature publication was suffered to lead his mind off the conscientious completion of his task. No ambition of gaining popularity was allowed to modify a single line in conformity with the opinions of the time. With stern resolution, and deaf to all external distractions, he concentrated his whole soul upon his work. In the history of men who have devoted their lives to great thoughts, I know nothing nobler than that of these twelve years."

"Auguste Comte wrote a few pieces for various periodicals in Paris, to which he attached but little importance. His first great philosophical work was a pamphlet... published in May, 1822... entitled a "Prospectus of the scientific works required for the reorganization of Society, by Auguste Comte, former pupil of the Ecole Polytechnique." He republished his pamphlet with some small modifications and additions in 1824, under the title "System of Positive Polity," and this is reprinted in vol. iv. of the " Politique Positive," 1854. This essay of 1822 contains a statement of the classification of the sciences, of the law of the three states, and the suggestion of a science of sociology. It is... the prospectus of that which for thirty years Comte continued to elaborate... and has always been treated by Comte and by his adherents as the the first sketch of the "Positive Philosophy.""

"In April, 1826 (ætat. 28), he opened in his own rooms a course of public lectures [1826-1827] on the Positive Philosophy, which was to extend to seventy-two lectures.... Amongst his audience were such men as Broussais, Blainville, Poinsot, J. Fourier, Alexander von Humboldt, D'Eichthal, Montebello, Carnot, ...[Antoine] Cerclet, Montgéry, and other young students."

"At the fourth lecture the course was abruptly broken off. Intense mental strain, together with domestic misery, brought on an attack of insanity. He... was placed in an asylum by his friend Broussais.... [and] remained for seven months."

"The devotion of his mother and his wife, who took him from the care of Dr. Esquirol whilst still suffering from the disease, succeeded in gradually restoring his reason. An epoch of profound despair followed, during which he threw himself into the Seine, but was rescued; and thenceforth he resolved to devote himself with patience and resignation to the work of his life, supporting himself with private lessons."

"In January, 1829, he resumed his course of lectures on the Positive Philosophy, ...[with] the same eminent men amongst his audience, with the exception of Humboldt, who was no longer in France. On this occasion he completed the whole series of lectures, and in December, 1829, he repeated them in a public course at the Athénée."

"The work of which these three volumes are a condensation was published were published from 1830 to 1842. The first volume, containing the Introduction and the philosophy of Mathematics, was published separately... A brief note described it as the result of the author's labours from the year 1816, and as a development of the new ideas put forth in his early essay of 1822, entitled a "System of Positive Polity.""

"The second volume, comprising Astronomy and Physics, did not appear until 1835, owing to the commercial disasters of the Revolution of July."

"The third volume, comprising Chemistry and Biology, appeared in 1838."

"The new science of Sociology, which was intended to he comprised in a single volume, ultimately extended to three volumes, published in 1839, 1841, and 1842."

"The last volume... was introduced by a personal preface to explain the prolongation of the work over twelve years, and the grounds for devoting one half of the entire work to the new Social Science. And it contained in notes Comte's vehement repudiation of Saint-Simon, and his no less vehement condemnation of M. Arago and the official directors of the '."

"His courses of lectures were all delivered without writing. When he commenced to prepare them for the press, he simply wrote them down from memory with great rapidity... without altering the proofs. ...[I]t had the obvious disadvantages of a certain multiplicity of phrase, a monotony, and that repetition which is only proper to oral exposition. ...[H]abitually and on system, he... uniformly cast his philosophic thoughts into a very formal, artificial, and undoubtedly cumbrous style..."

"Tedious and even repulsive as it is to the average reader, to the serious student of Positivism this method of exposition has rare and paramount advantages. It is unerringly precise, lucid, qualified, and suggestive. ...[H]is long-drawn and over-elaborated sentences never leave the student in doubt for a moment as to his meaning, as to his whole meaning, as to all that he wishes to express, and all that he means to disclaim or exclude."

"The result is, that the general reader can hardly follow these crowded and closely welded paragraphs without the assistance of an expert, whilst the serious student of the Positive Philosophy finds some new light or some needful warning in everyone of these pregnant epithets and precise limitations."

"Comte saw this clearly himself; and hence, in his "Popular Library," embodied in his later works, he inserts—not his own "Positive Philosophy" in six volumes—but Miss Martineau's condensed English version. Unfortunately not only the general reader, but the professed critics of Positivism have too often adopted his generous suggestion."

"Sir David Brewster... a strong opponent of Positivism as a religious and social philosophy, reviewed the first two volumes in the "Edinburgh Review"... In this essay... Brewster pays homage to the depth and sagacity of Comte's mind, and he accepts in principle the law of the Three States, the Classification of the Sciences, and the ultimate extension of the methods of Science to Sociology."

"Mr. Mill... in his "System of Logic," 1843... spoke of Auguste Comte as amongst the first of European thinkers, and by his institution of a new social science, as in some respects, the first."

"In 1845-6, George Henry Lewes published his "Biographical History of Philosophy"... and... treated of Auguste Comte as "the greatest of modern thinkers," and as crowning the general history of philosophical evolution."

"In 1853, Lewes published Comte's "Philosophy of the Sciences," a volume in Bohn's Philosophical Library. And in the same year Miss Martineau published the condensed translation which at once made Comte familiar to all English students."

"It is a singular fact in literary history, and a striking testimony to the merit of Miss Martineau, that the work of a French philosopher should be studied in France in a French re-translation from his English translator—and that at his own formal desire and by his own special followers."

"When Miss Martineau translated the " Philosophy," more than forty years ago, the later works of Comte were not before her; and... the later works of Comte are not referred to in her book at all. She carried this decision to the very extreme point of suppressing... the last ten pages of the sixth and concluding volume of the "Philosophy.""

"Now, from the point of view of the unity of Comte's career these ten pages are crucial, for they contain the entire scheme of Comte's future philosophical labours as he designed them in 1842, and as they were ultimately carried out in the "Polity," "Catechism," "Synthesis," etc... These important pages have been added by the present writer, in the condensed form adopted by Miss Martineau."

"Miss Martineau seized the dominant idea of each sentence or rather paragraph—not without much sacrifice of the continuity of thought, no little loss in precision and accuracy of definition, sometimes a serious omission of important matter—but on the whole with an extraordinary gain to the freshness of impression on the general reader."

"For the details of Sir Humphry Davy's personal history, as set forth in this little book, I am mainly indebted to the well-known memoirs by Dr. Paris and Dr. John Davy. As biographies, these works are of very unequal value."

"Dr. Paris is not unfrequently inaccurate in his statements as to matters of fact, and disingenuous in his inferences as to matters of conduct and opinion. The very extravagance of his laudation suggests a doubt of his judgment or of his sincerity, and this is strengthened by the too evident relish with which he dwells upon the foibles and frailties of his subject. The insincerity is reflected in the literary style of the narrative, which is inflated and over-wrought."

"Sir Walter Scott, who knew Davy well and who admired his genius and his many social gifts, characterised [Paris'] book as "ungentlemanly" in tone; and there is no doubt that it gave pain to many of Davy's friends who, like Scott, believed that justice had not been done to his character."

"Dr. Davy's book... whilst perhaps too partial at times... is written with candour, and a sobriety of tone and a directness and simplicity of statement far more effective than the stilted euphuistic periods of Dr. Paris, even when he seeks to be most forcible."

"When... I have had to deal with conflicting or inconsistent statements in the two works on matters of fact, I have generally preferred to accept the version of Dr. Davy, on the ground that he had access to sources of information not available to Dr. Paris."

"Davy played such a considerable part in the social and intellectual world of London... that... his name frequently occurs in the personal memoirs and biographical literature... and a number of journals and diaries, such as those of Horner, Ticknor, , Lockhart, Maria Edgeworth, and others that might be mentioned, make reference to him and his work, and indicate what his contemporaries thought of his character and achievements. Some of these references will be found in the following pages."

"Londoners... owe the Zoological Gardens, in large measure, to a Professor of Chemistry in Albemarle Street, and that the magnificent establishment in the Cromwell Road, South Kensington, is the outcome of the representations, unsuccessful for a time, which he made to his brother trustees of the as to the place of natural history in the national collections. Davy had a leading share also in the foundation of the Athenæum Club, and was one of its first trustees."

"I am... indebted to Dr. Rollenston for the loan of a portrait representing Davy in Court dress and in the presidential chair of the Royal Society, which, reproduced in , forms the frontispiece to this book. The original is a small highly finished work by Jackson, and was painted about 1823. The picture originally belonged to Lady Davy, who refers to it in the letter to (quoted by Weld in his "History of the Royal Society"), in which she offers Lawrence's well-known portrait to the Society, and which... the Society nearly lost through the subsequent action of the painter."

"For the references to the early history of the I am mainly indebted to Dr. Bence Jones's book."

"It is not necessary to belittle Davy in order to exalt Faraday; and writers who, like Dr. Paris, unmindful of George Herbert's injunction, are prone to adopt an antithetical style in biographical narrative have, I am convinced, done Davy's memory much harm."

"With the exception of a rapid journey into Cornwall, for the sake of seeing his family, he spent the greater part of the summer and autumn of 1807 in town. He had been made Secretary of the in succession to Gray, and was obliged to be in or near London in order to see the Philosophical Transactions through the press. From the Laboratory Journal it would appear that he was occupied at this time on a variety of disconnected investigations such as the nature of Antwerp Blue, and the effect of electricity on flame. In a letter to , dated September 12th, he states that he has been a good deal engaged in experiments on distillation for revenue purposes."

"Towards the end of this month, or during the first week of October, he resumed his experiments with the voltaic battery, and he was led to study its action on the alkalis. There is some evidence that he had attacked the same question at Bristol."

"In a note-book of that period, under date August 6th, 1800, is the following sentence: "I cannot close this notice without feeling grateful to M. Volta, Mr. Nicholson, and Mr. Carlisle, whose experience has placed such a wonderful and important instrument of analysis in my power"..."

"This is immediately followed by "Query: Would not potash, dissolved in spirits of wine, become a conductor?" And he then gives an account of some experiments on the action of voltaic electricity on aqueous solutions of , caustic potash, and , which apparently led to the same result as that already obtained by Nicholson and Carlisle in the case of water."

"[H]e said of the alchemists that "even their failures developed some unsought-for object partaking of the marvellous"—and the statement in this case is even more true of himself."

"Each phase in the story of this discovery indeed partakes of the marvellous. Sometime during the first fortnight in October, 1807, he obtained his first decisive result; and on the 19th of November he delivered what is generally regarded as the most memorable of all his Bakerian lectures, "On some new Phenomena of chemical Changes produced by Electricity, particularly the Decomposition of the fixed Alkalies, and the Exhibition of the new substances which constitute their bases; and on the general Nature of alkaline Bodies.""

"Few discoveries of like magnitude have been made and perfected in so short a time, and few memoirs have been more momentous in result than that which Davy put together in a few hours, and in which he announced his results to the world."

"The whole work was done under conditions of great mental excitement. His cousin ,.. his assistant, relates that when he [Humphrey Davy] saw the minute globules of the quicksilver-like metal burst through the crust of potash and take fire, his joy knew no bounds; he actually danced about the room in ecstasy, and it was some time before he was sufficiently composed to continue his experiments. The rapidity with which he accumulated results after this first feeling of delirious delight had passed was extraordinary."

"Before the middle of November he had obtained most of the leading facts. In a letter dated November 13th he tells W. H. Pepys—"

"[H]e seldom entered the laboratory before ten or eleven in the morning, and rarely left it later than four, and he was scarcely ever known to visit it after he had dressed for dinner."

"Except when preparing a lecture, he seldom dined in his rooms at the Institution: his brother tells us that his invitations to dinner were so numerous that he was, or might have been, constantly engaged; and after dinner he was much in the habit of attending evening parties, and devoting the evening to amusement, "so that to the mere frequenters of such parties he must have appeared a votary of fashion rather than of science.""

"The Bakerian lecture in which Davy announces the discovery of the compound nature of the fixed alkalis opens with a reference to the concluding remarks of his lecture of the previous year, "that the new methods of investigation promised to lead to a more intimate knowledge than had hitherto been obtained concerning the true elements of bodies. This conjecture, then sanctioned only by strong analogies, I am now happy to be able to support by some conclusive facts.""

"In the first attempts he made to decompose the fixed alkalis he acted upon concentrated aqueous solutions of potash and soda with the highest electrical power he could then command at the Royal Institution—viz. from voltaic batteries containing 24 plates of copper and zinc of 12 inches square, 100 plates of 6 inches, and 150 of 4 inches, charged with solutions of alum and nitric acid; but although there was high intensity of action nothing but and oxygen was disengaged."

"He next tried potash in igneous fusion, and here the results were more encouraging: there were obvious and striking signs of decomposition; combustible matter was produced accompanied with flame and a most intense light."

"He had observed that although potash when dry is a nonconductor, it readily conducts when it becomes damp by exposure to air, and in this state "fuses and decomposes by strong electrical powers.""

"It is frequently stated that Davy was enabled to isolate the metals of the alkalis because of the large and powerful voltaic battery which he had at his disposal in the Royal Institution. This is not correct. The battery he employed was of very moderate dimensions, and not by any means extraordinary in power. It was the success he thus achieved that caused the large battery, which is probably referred to, to be constructed, by special subscription, in 1809."

"The platina... was, he found, in no way connected with the result: a substance of the same kind was produced when copper, silver, gold, plumbago, or even charcoal was employed for completing the circuit."

"It would seem from his description of its properties that the potassium he obtained was most probably alloyed with sodium derived from impure potash. Potassium is solid up to 143° F.; but, as Davy subsequently found, an alloy of potassium and sodium is fluid at ordinary temperatures."

"When the potassium was exposed to air its metallic lustre was immediately destroyed, and it was ultimately wholly reconverted into potash by absorption of oxygen and moisture."

"With the substance from soda the appearance and effects were analogous."

"When heated in oxygen to a sufficiently high temperature, both substances burnt with a brilliant white flame."

"On account of their alterability on exposure to air, Davy had considerable difficulty in preserving and confining them so as to examine the properties of the new substances. As he says, like the s imagined by the alchemists, they acted more or less upon almost every body to which they were exposed."

"He eventually found that they might be preserved in ."

"The "basis" of potash at 50° F. was a soft and malleable solid with the lustre of polished silver."

"It may be converted into vapour at a temperature approaching a red-heat, and may be distilled unchanged; it is a perfect conductor of electricity and an excellent conductor of heat. Its most marked difference from the common run of metals was its extraordinarily low specific gravity."

"Davy endeavoured to gain an approximation to its relative weight by comparing the weight of a globule with that of an equal-sized globule of mercury."

"Although no great stress can be laid on numbers so obtained, they serve to indicate that Davy had not yet obtained the pure metal."

"The "basis" of soda is described as a white opaque substance of the lustre and general appearance of silver. It is soft and malleable, and is a good conductor of heat and electricity. Its specific gravity was found by flotation in a mixture of oil of sassafras and naphtha... It was found to fuse at about 180° F. (the real melting point of sodium is 197.5°). Its action on a number of substances—oxygen, hydrogen, water, etc.—is then described, and its general behaviour contrasted with that of the "basis" of potash."

"Davy then attempted to determine the amount of the "metallic bases" in potash and soda respectively... the results are fairly accurate."

"He then enters upon some general observations on the relations of the "bases" of potash and soda to other bodies."

"[S]uch was his position in England at this period, that a Bakerian lecture seemed to be expected from him at each succeeding session of the as a matter of course, and he was always ready to respond to the expectation, even if he did not invariably satisfy it."

"On November 16th, 1809, he read his fourth Bakerian lecture. It was "On some new Electrochemical Researches on various Objects, particularly the metallic Bodies, from the Alkalies and Earths, and on some Combinations of Hydrogene.""

"He begins by again drawing attention to the various surmises which had been made respecting the true nature of potassium and sodium. Although these substances had been isolated, and in the hands of chemists for upwards of two years, their properties were so extraordinary when compared with those of the metals in general, that many philosophers hesitated to consider them as true metals."

"Gay Lussac and Thenard... regarded them as compounds of potash or soda with ; [F. R.] Curaudau as combinations of or carbon and hydrogen with the alkalis; whilst an ingenious inquirer in this country communicated to Nicholson's Journal his belief that they were really composed of oxygen and hydrogen!"

"Davy, in the light of the fuller knowledge he obtained from Gay Lussac and Thenard's paper in the "Mem. d’Arcueil"... had no difficulty in again proving "that by the operation of potassium upon , it is not a metallic body that is decompounded, but the volatile alkali, and that the hydrogen produced does not arise from the potassium, as is asserted by the French chemists, but from the ammonia.""

"M. Curaudau's hypothesis is shown to be based upon the accidental association of with the metals he employed."

"In repeating some experiments of Ritter's, designed to show that potassium contained hydrogen, Davy was led to the discovery of telluretted hydrogen, the properties of which he describes in some detail. at that time was regarded as a metal, but Davy points out its strong analogies to sulphur, with which element, indeed, it is now classed."

"The paper is noteworthy for the clear distinction which is drawn for the first time between potash hydrate ( of modern nomenclature) and , the product formed by heating the metal in ordinary oxygen."

"There is much in the rest of the paper that is ingenious and suggestive, and not a few isolated facts that seem to have been lost sight of, or rediscovered by subsequent observers, such... as the action of upon metallic —an action which has vitiated the attempts to determine the vapour density of that metal in iron vessels."

"Davy clings to the belief that will turn out to be a compound substance, and with what pertinacity he importunes it to give up its components. At times he thinks he is on the verge of proof. "I hope on Thursday,” he wrote to his friend Children, "to show you nitrogen as a complete wreck, torn to pieces in different ways." But still nitrogen, with that passive immutability which is characteristic of it, in spite of every form of torture, remained whole and indissoluble. On this point he wrote in the Laboratory Journal under date February 15th:—"Were a description... to be given of all the experiments I have made, of all the difficulties I have encountered, of the doubts that have occurred, and the hypotheses formed ——." But the sentence was not finished. The attack was renewed and continued throughout the whole of the spring and summer, until, fairly baffled, Davy confessed himself beaten, and turned his attention to other matters."

"Davy was perfectly reckless with apparatus; with him to think was to act, and he frequently had half a dozen experiments going on simultaneously, upon disconnected parts of the same inquiry."

"His usual method of erasure was by dipping his finger in the ink-pot; and... he was simply "Death on pens!""

"Dr. Thorpe has succeeded excellently in his endeavour to condense the somewhat diffuse biographies of Humphry Davy, written by Dr. Paris and Dr. John Davy, and to give us in moderate compass all the information concerning him that we need to remember. In doing this he has also been able to add much that is valuable, which now appears for the first time. The portrait of Davy, by Jackson, reproduced in photogravure, which forms the frontispiece to Dr. Thorpe's volume, greatly adds to the interest of Humphry Davy: Poet and Philosopher."

"So familiar are we with the numerals that bear the misleading name of Arabic, and so extensive is their use... that it is difficult... to realize that their general acceptance... is a matter of only the last four centuries."

"It seems strange that such a labor-saving device should have struggled for nearly a thousand years after its system of place value was perfected before it replaced such crude notations as the one that the Roman conqueror made substantially universal in Europe."

"This story has often been told in part, but it is a long time since any effort has been made to bring together the fragmentary narrations and to set forth the general problem of the origin and development of these numerals."

"In this little work we have attempted to state the history of these forms in small compass, to place before the student materials for the investigation of the problems involved, and to express as clearly as possible the results, of the labors of scholars who have studied the subject..."

"We have had no theory to exploit, for the history of mathematics has seen too much of this tendency... we have weighed the testimony and have set forth what seem to be the reasonable conclusions from the evidence..."

"If this work shall show more clearly the value of our number system, and shall make the study of mathematics seem more real to the teacher and student, and shall offer material for interesting some pupil more fully in his work... the considerable labor involved in its preparation has not been in vain."

"We... acknowledge our especial indebtedness to Professor Alexander Ziwet for reading all the proof, [and] for the digest of a Russian work, to Professor Clarence L. Meader for Sanskrit transliterations, and to Mr. for Arabic transliterations... and... to other scholars in Oriental learning..."

"It has long been recognized that the common numerals used in daily life are of comparatively recent origin."

"The number of systems of notation employed before the Christian era was about the same as the number of written languages, and in some cases a single language had several systems."

"The Egyptians... had three systems of writing, with a numerical notation for each; the Greeks had two... sets of numerals, and the Roman symbols... changed... from century to century."

"It will be well... to think of the numerals... we... call Arabic, as only one of many systems in use just before the Christian era. As it then existed the system was no better than many others, it was of late origin, it contained no zero, it was cumbersome and little used, and it had no particular promise."

"In Europe the invention of notation was generally assigned to the eastern shores of the Mediterranean until the critical period of about a century ago,—sometimes to the Hebrews, sometimes to the Egyptians, but more often to the early trading ns."

"The idea that our common numerals are Arabic in origin is not an old one. The mediaeval and Renaissance writers generally recognized them as Indian, and many of them expressly stated that they were of Hindu origin."

"Others argued that they were probably invented by the Chaldeans or the Jews because they increased in value from right to left, an argument... [also made by] England’s earliest arithmetical textbook-maker, Robert Recorde (c. 1542): "In that thinge all men do agree, that the Chaldays, whiche fyrste inuented thys arte, did set these figures as thei set all their letters, for they wryte backwarde as you tearme it, and so doo they reade. And that may appeare in all Hebrewe, Chaldaye and Arabike bookes .. . where as the Greekes, Latines, and all nations of Europe, do wryte and reade from the lefte hand towarde the ryghte.""

"Tartaglia in Italy and Köbel in Germany, asserted the Arabic origin of the numerals, while still others left the matter undecided or simply dismissed them as "barbaric.""

"[T]he Arabs... never laid claim to the invention, always recognizing their indebtedness to the Hindus both for the numeral forms and for the distinguishing feature of place value."

"Foremost among these writers was the great master of the golden age of Bagdad, one of the first of the Arab writers to collect the mathematical classics of both the East and the West, preserving them and finally passing them on to awakening Europe. This man was Mohammed the Son of Moses, from Khowarezm, or, more after the manner of the Arab, Mohammed ibn Mūsā al-Khowārazmī, a man of great learning and one to whom the world is much indebted for its present knowledge of algebra and of arithmetic. ...[I]n the arithmetic which he wrote, and of which Adelhard of Bath (c. 1130) may have made the translation or paraphrase, he stated distinctly that the numerals were due to the Hindus. This is as plainly asserted by later Arab writers, even to the present day. Indeed the phrase ilm hindī, "Indian science," is used by them for arithmetic, as [is] also the adjective hindī alone."

"Probably the most striking testimony from Arabic sources is that given by the Arabic traveler and scholar Mohammed ibn Ahmed, Abū ’l-Rīahān al-Bīrūnī (973-1048), who spent many years in Hindustan. He wrote... the “Book of the Ciphers,” unfortunately lost, which treated... of the Hindu art of calculating... being versed in Arabic, Persian, Sanskrit, Hebrew, and Syriac, as well as in astronomy, chronology, and mathematics. In his work on India he... states explicitly that the Hindus of his time did not use the letters of their alphabet for numerical notation, as the Arabs did. He also states that the numeral signs called aṅka had different shapes in various parts of India, as was the case with the letters. In his Chronology of Ancient Nations he gives the sum of a geometric progression... in three different systems..."

"Preceding Al-Bīrūnī... another Arabic writer of the tenth century, Motahhar ibn Tāhir, author of the Book of the Creation and of History... gave... in Indian (Nāgarī symbols), a large number asserted by the people of India to represent the duration of the world."

"Al-Mas'ūdī (885?-956), whose journeys carried him from Bagdad to Persia, India, Ceylon, and... across the China sea, and at other times to Madagascar, Syria, and Palestine... neglected no accessible sources of information, examining also the history of the Persians, the Hindus, and the Romans. ...[H]is ...Meadows of Gold ...states that the wise men of India, assembled by the king, composed the Sindhind...that by order of Al-Mansur many works of science and astrology were translated into Arabic, notably the Sindhind (Siddhanta). Concerning the meaning and spelling of this name... Colebrooke ascribes... the meaning "the revolving ages." Similar designations are collected by Sedillot... Casiri... refers to the work as the Sindum-Indum... meaning "perpetuum aeternumque [eternal perpetuity].""

"This Sindhind is the book, says Mas'ūdī, which gives all that the Hindus know of the spheres, the stars, arithmetic, and the other branches of science. He mentions... Al-Khowārazmī and Habash as translators of the tables of the Sindhind."

"The oldest work... complete, on the history of Arabic literature and history is the Kitah al-Fihrist, written in the year 987 a.d., by Ibn Abī Ya'qūb al-Nadīm. ...Of the ten chief divisions of the work, the [second subdivision of the] seventh... treats of mathematicians and astronomers. The first of the Arabic writers mentioned is Al-Kindī (800-870 A.D.), who wrote five books on arithmetic and four books on the use of the Indian method of reckoning. Sened ibn 'Alī... is also given as the author of a work on the Hindu method of reckoning. ...[T]here is a possibility that some of the works ascribed to Sened ibn 'Alī are really works of Al-Khowārazmī ...However, ...Casiri also mentions the same writer as the author of a most celebrated work on arithmetic. To Al-Sūfī... is also credited a large work... and similar treatises by other writers..."

"[T]herefore... the Arabs from the early ninth century on fully recognized the Hindu origin of the new numerals."

"Leonard of Pisa... wrote his Liber Abbaci in 1202. ...[H]e refers frequently to the nine Indian figures, thus showing again the general consensus of opinion in the Middle Ages that the numerals were of Hindu origin."

"One of the earliest treatises on algorism is... the Carmen de Algorismo [Poem about Arithmetic], written by Alexander de Villa Dei (Alexandre de Ville-Dieu), a Minorite monk of about 1240 a.d. The text of the first few lines is as follows: "Hee algorism’ ars p’sens dicit’ in qua Talib; indor\mathit{4} fruim bis quinq; figuris." "This boke is called the boke of algorim or augrym after lewder use. And this boke tretys of the Craft of Nombryng [arithmetic], the quych crafte is called also Algorym. Ther was a kyng of Inde the quich heyth Algor & he made this craft. . . . Algorisms, in the quych we use teen figurys of Inde.""

"While it is generally conceded that the scientific development of astronomy among the Hindus towards the beginning of the Christian era rested upon Greek or Chinese sources, yet their ancient literature testifies to a high state of civilization, and to a considerable advance in sciences, in philosophy, and along literary lines, long before the golden age of Greece."

"From the earliest times... to... present day the Hindu has been wont to put his thought into rhythmic form. The first of this poetry... being also worthy from a metaphysical point of view... consists of the Vedas, hymns of praise and poems of worship, collected during the ... from approximately 2000 B.C. to 1400 B.C. Following this work, or possibly contemporary... is the Brahmanic literature, which is partly ritualistic (the s), and partly philosophical (the Upanishads). Our... interest is in the s... which contain... geometric material used in connection with altar construction, and also numerous examples of... "Pythagorean numbers," although this was long before Pythagoras lived."

"Whitney places the whole of the Veda literature, including the Vedas, the Brahmanas, and the Sutras, between 1500 B.C. and 800 B.C., thus agreeing with [Albert] Bürk who holds that the knowledge of the Pythagorean theorem revealed in the Sütras goes back to the eighth century B.C."

"The importance of the Sutras as showing an independent origin of Hindu geometry, contrary to the opinion long held by Cantor of a Greek origin, has been repeatedly emphasized in recent literature, especially since... Von Schroeder."

"Further fundamental mathematical notions such as the conception of irrationals and the use of s, as well as the philosophical doctrine of the transmigration of souls, —all of these having long been attributed to the Greeks, —are shown in these works to be native to India."

"[W]e are not at all sure that the most ancient forms of the numerals commonly known as Arabic had their origin in India. ...[T]heir forms may have been suggested by those used in Egypt, or in Eastern Persia, or in China, or on the plains of Mesopotamia. We are... in the dark as to these early steps; but as to their development in India, the approximate period of the rise of their essential feature of place value, their introduction into the Arab civilization, and their spread to the West, we have more or less definite information."

"When... we consider the rise of the numerals in the land of the Sindhu... only the large movement... is meant, and that there must... be... numerous possible sources outside of India... and long anterior to the first prominent appearance of the number symbols."

"[I]n the history of ancient India... primary schools... existed in earliest times, and of the seventy-two recognized sciences writing and arithmetic were the most prized. In the Vedic period [~]2000 to 1400 B.C., there was the same attention to astronomy that was found in the earlier civilizations of Babylon, China, and Egypt... Such advance... presupposes a fair knowledge of calculation, but of the manner of calculating we are quite ignorant..."

"[T]he Lalitavistara, relates that when the Bödhisattva was of age to marry, the father of Gopa, his intended bride, demanded an examination of the five hundred suitors, the subjects including arithmetic, writing, the lute, and archery. Having vanquished his rivals in all else, he is matched against Arjuna the great arithmetician and is asked to express numbers greater than 100 kotis. In reply he gave a scheme of number names as high as 1053, adding that he could proceed as far as 10421... which suggests the system of Archimedes and the unsettled question of the indebtedness of the West to the East in the realm of ancient mathematics."

"Sir Edwin Arnold, in The Light of Asia... speaks of Buddha’s training at the hands of the learned : "And Viswamitra said, 'It is enough, Let us to numbers. After me repeat Your numeration till we reach the lakh, One, two, three, four, to ten, and then by tens To hundreds, thousands.’ After him the child Named digits, decads, centuries, nor paused, The round lakh reached, but softly murmured on, Then comes the koti, nahut, ninnahut, Khamba, viskhamba, abab, attata, To kumuds, gundhikas, and utpalas, By pundarikas into padumas, Which last is how you count the utmost grains Of Hastagiri ground to finest dust; But beyond that a numeration is, The Kātha, used to count the stars of night, The Kōti-Kātha, for the ocean drops; Ingga, the calculus of circulars; Sarvanikchepa, by the which you deal With all the sands of Gunga, till we come To Antah-Kalpas, where the unit is The sands of the ten crore Gungas. If one seeks More comprehensive scale, th’ arithmic mounts By the Asankya, which is the tale Of all the drops that in ten thousand years Would fall on all the worlds by daily rain; Thence unto Maha Kalpas, by thé which the gods compute their future and their past.'""

"Thereupon Ācārya expresses his approval... and asks to hear the "measure of the line" as far as yōjana, the longest measure bearing name. This given, Buddha adds: ..." 'And master! If it please, I shall recite how many sun-motes lie From end to end within a yōjana.’ Thereat, with instant skill, the little prince Pronounced the total of the atoms true. But Viswamitra heard it on his face Prostrate before the boy; 'For thou,' he cried, 'Art Teacher of thy teachers—thou, not I, Art Guru.' ""

"[T]his is far from being history. And yet it puts in charming rhythm only what the ancient Lalitavistara relates of the number-series of the Buddha’s time. ...[I]t reveals a condition that would have been impossible unless arithmetic had attained a considerable degree of advancement."

"[W]e are uncertain as to the time and place of [the] introduction [of these numeral forms] into Europe. There are two general theories... The first is that they were carried by the Moors to Spain in the eighth or ninth century, and thence were transmitted to Christian Europe... The second, advanced by Woepcke, is that they... were already in Spain when the Arabs arrived there, having reached the West through the Neo-Pythagoreans. There are two facts to support this second theory: (1) the forms of these numerals are characteristic, differing materially from those which were brought by Leonardo of Pisa from Northern Africa early in the thirteenth century (before 1202 a.d.); (2) they are essentially those which tradition has so persistently assigned to Boethius (c. 500 A.D.), and which he would naturally have received, if at all, from these same Neo-Pythagoreans or from the sources from which they derived them."

"Woepcke points out that the Arabs on entering Spain (711 A.D.) would naturally have followed their custom of adopting for the computation of taxes the numerical systems of the countries they conquered... The theory is that the Hindu system, without the zero, early reached Alexandria (say 450 a.d.), and that the Neo-Pythagorean love for the mysterious and... the Oriental led to its use... that it was then passed along the Mediterranean, reaching Boethius in Athens or in Rome, and to the schools of Spain, being discovered in Africa and Spain by the Arabs even before they themselves knew the improved system with the place value."

"Bubnov holds that the forms first found in Europe are derived from ancient symbols used on the abacus, but that the zero is of Hindu origin. This theory does not seem tenable..."

"The Spanish forms of the numerals were called the hurūf al-ģobār, the ģobār or dust numerals, as distinguished from the hurūf aljumal or alphabetic numerals. Probably the latter... were also used by the Arabs. ...[D]oubtless ...these numerals were written on the dust abacus, this plan being distinct from the counter method ...Al-Bīrūnī states that the Hindus often performed numerical computations in the sand. ...The system has nine characters, but no zero. A dot above a character indicates tens, two dots hundreds, and so on, \dot{5} meaning 50, and [\ddot{5} meaning 500]."

"When we consider... that the dot is found for zero in the Bakhsālī manuscript, and that it was used in subscript form in the Kitāb al-Fihrist in the tenth century... we are forced to believe that this form may also have been of Hindu origin."

"The Indian use of subscript dots to indicate the tens, hundreds, thousands, etc., is established by a passage in the Kitāb al-Fihrist (987 A.D.)... The numeral forms given are those which have usually been called Indian, in opposition to ģobār. In this document the dots are placed below the characters, instead of being superposed... The significance was the same."

"Anicius Manlius Severinus Boethius was born at Rome c. 475. Not many generations after his death, the period being one in which historical criticism was at its lowest ebb, the church found it profitable to look upon his execution as a martyrdom. He was accordingly looked upon as a saint, his bones were enshrined, and as a natural consequence his books were among the classics in the church schools for a thousand years. It is pathetic, however, to think of the medieval student trying to extract mental nourishment from a work so abstract, so meaningless, so unnecessarily complicated, as the arithmetic of Boethius."

"The numerals had existed, without the zero, for several centuries; they had been well known in India; there had been a continued interchange of thought between the East and West; and warriors, ambassadors, scholars, and the restless trader, all had gone back and forth, by land or more frequently by sea, between the Mediterranean lands and the centers of Indian commerce and culture. Boethius could very well have learned one or more forms of Hindu numerals from some traveler or merchant."

"[I]t is one of the mistakes of scholars to believe that they are the sole transmitters of knowledge. ...[T]he characters, the methods of calculating, the improvements that took place from time to time, the zero when it appeared, and the customs as to solving business problems, would all have been made known from generation to generation along... trade routes from the Orient to the Occident. [I]t was to the tradesman and the wandering scholar that the spread of such learning was due, rather than to the school man."

"Avicenna (980-1037 a.d.)... relates that when his people were living at Bokhara his father sent him to the house of a grocer to learn the Hindu art of reckoning, in which this grocer (oil dealer, possibly) was expert. Leonardo of Pisa, too, had a similar training."

"It could not have been at all unusual for the ancient Greeks to go to India, for Strabo lays down the route, saying that all who make the journey start from and traverse and before taking the direct road. The products of the East were always finding their way to the West, the Greeks getting their ginger from Malabar, as the Phoenicians had long before brought gold from Malacca."

"Greece must also have had early relations with China, for there is a notable similarity between the Greek and Chinese life, as is shown in their houses, their domestic customs, their marriage ceremonies, the public story tellers, the puppet shows which Herodotus says were introduced from Egypt, the street jugglers, the games of dice, the game of finger-guessing, the , the music system, the use of the , the calendars, and in many other ways."

"The Chinese historians tell us that about 200 B.C. their arms were successful in the far west, and that in 180 B.C. an ambassador went to , then a Greek city, and reported that Chinese products were on sale in the markets there. There is also a noteworthy resemblance between certain Greek and Chinese words, showing that in remote times there must have been more or less interchange of thought."

"The Romans also exchanged products with the East. Horace says, "A busy trader, you hasten to the farthest Indies, flying from poverty over sea, over crags, over fires." The products of the Orient, spices and jewels from India, from Persia, and silks from China, being more in demand than the exports from the Mediterranean lands, the balance of trade was against the West, and thus Roman coin found its way eastward."

"Augustus speaks of envoys received by him from India... and it is not improbable that he also received an embassy from China. ...In Pliny's time the trade of the Roman Empire with Asia amounted to a million and a quarter dollars a year, a sum far greater relatively then than now, while by the time of Constantine Europe was in direct communication with the Far East."

"In the fifth century the Persian medical school at Jondi-Sapur admitted both the Hindu and the Greek doctrines..."

"[N]ot far from the time of Boethius, in the sixth century, the Egyptian monk Cosmas, in his earlier years as a trader, made journeys to Abyssinia and even to India and Ceylon, receiving the name Indicopleustes (the Indian traveler). His map (547 a.d.) shows some knowledge of the earth from the Atlantic to India."

"Mohammedanism was to the world from the eighth to the thirteenth century what Rome and Athens and the Italo-Hellenic influence generally had been to the ancient civilization. ...The Arab empire was an ellipse of learning with its foci at Bagdad and Cordova, and its rulers not infrequently took pride in demanding intellectual rather than commercial treasure as the result of conquest."

"[T]he Hindu numerals found their way to the North... in the eighth century they were taken to Bagdad. It was early in that century that the Mohammedans obtained their first foothold in northern India, thus foreshadowing an epoch of supremacy that endured with varied fortunes until after the golden age of the Great (1542-1605) and Shah Jehan. They also conquered Khorassan and Afghanistan, so that the learning and the commercial customs of India at once found easy access to the newly-established schools and the bazaars of Mesopotamia and western Asia."

"It was just after the Sindhind was brought to Bagdad that Muhammad ibn Mūsā al-Khwārizmī... was called to that city. ...Appreciating at once the value of the position system so recently brought from India, he wrote an arithmetic based upon these numerals, and this was translated into Latin..."

"Contemporary with Al-Khowarazmi... Abū 'l-Teiyib, Sened ibn Allī... also wrote a work on Hindu arithmetic...[T]he struggle to have the Hindu numerals replace the Arabic did not cease for a long time thereafter."

"We thus have the numerals in Arabia, in two forms: one the form now used there, and the other the one used by Al-Khowarazmi. The question then remains, how did this second form find its way into Europe?"

"[T]he probability [is] that it was the trader rather than the scholar... [who] carried these numerals from their original habitat to various commercial centers... we shall never know when they first made their inconspicuous entrance into Europe."

"The power of the Goths, who had held Spain for three centuries, was shattered at the battle of Jerez de la Frontera in 711, and almost immediately the Moors became masters of Spain and so remained for five hundred years, and masters of Granada for a much longer period. Until 850 the Christians were... free as to religion and... holding political office, so that priests and monks were not infrequently skilled... in Latin and Arabic, acting as official translators... [W]hile it lasted the learning and the customs of the East must have be come more or less the property of Christian Spain. At thie time the ġobār numerals were probably in that country, and these may well have made their way into Europe from the schools of Cordova, Granada, and Toledo."

"This book gives in compact form a readable and carefully prepared account of the numerous researches... made in the endeavor to trace the origin and development of the Hindu-Arabic numerals. Teachers of mathematics will welcome it, while students specializing in the history of mathematics will derive great help... Like the arithmetician Tonstall the authors read everything in every language and spent much time in licking what they found into shape ad ursi exemplum, as the bear does her cubs."

"Samasya dwikaraṇi pramāṇam tṛtīyena vardhayettacca caturthenātmacatustriṃśonena saviśeṣaḥ."

"Like the crests on the heads of peacocks, like the gems on the hoods of the cobras, mathematics is at the top of the Vedanga s."

"Astronomers should not be granted excessive license to conceive anything they please without reason: on the contrary, it is also necessary for you to establish the probable causes of your Hypotheses which you recommend as the true causes of the Appearances. Hence you must first establish the principles of your Astronomy in a higher science, namely Physics and Metaphysics."

"It has been ten years since I published my Commentaries on the Movements of the Planet Mars. As only a few copies of the book were printed, and as it had so to speak hidden the teaching about celestial causes in thickets of calculations and the rest of the astronomical apparatus, and since the more delicate readers were frightened away by the price... too; it seemed... that I should be doing right and fulfilling my responsibilities, if I should write an epitome, wherein a summary of both the physical and astronomical teaching concerning the heavens would be set forth in plain and simple speech and with the boredom of the demonstrations alleviated."

"[A] comparison was undertaken between this book—or the related work On the Harmonies...—and Aristotle's books ' and Metaphysics... I have nothing to worry about in the case of Aristotle... His Most Serene Highness cannot dislike whatever is the more convincing, whether it be that the world was first made at a fixed beginning in time as was my work On the Harmonies, or will be destroyed at some time, or is merely liable to destruction, like the alterations of the ether and the celestial atmosphere; nor will he ever prefer the Master Aristotle to the truth of which Aristotle was ignorant."

"Aristotle is the man... who in On the Heavens... Chapter 9... asks: "Do the stars give forth sounds which are modulated harmonically? and answers no: ...I grant that no sounds are given forth but I affirm and demonstrate that the movements are modulated according to harmonic proportions."

"I... led on by... thirst for philosophy, first wiped away from the eyes of astronomy those mists of the multiplicity of movements in the single planets: then I gave a demonstration... that the movement of the planet is not uniform throughout its whole circuit—as Aristotle argued in Chapters 6 and 7; but that... the movement is increased and decreased at places in its period which are fixed and are opposite to one another; and I explained the efficient or instrumental causes... between the planet and the sun... as from what source..."

"Then, as in each and every planet there is a very fast movement and a very slow movement and in a fixed proportion... and... Saturn and Jupiter have middling eccentricities, Mars a great eccentricity, the Sun and Venus slight eccentricities, and Mercury a very great eccentricity... I also brought forward a solution... and I took my solution from the Archetype of the harmonic cosmos: whence it is established that this cosmos cannot be better... and that it is impossible that the world should not have been created at a fixed beginning in time. This attempt of mine... should have been brought forth into the light with strength of mind... the highest confidence in the visible works of God... or at the exhortation of Aristotle himself, who judged that in these questions you should not suppress or be silent about probabilities any more than... certainties."

"Aristotle... in the Metaphysics, Book XII, Chapter 8... built... the most sublime part of his philosophy... concerning the gods... who... sends his students to the astronomers and who defers to the astronomers in respect to their authority and... testitimony...[H]e would never have scorned or... myself, if... necessity... had made us contemporaries. For he orders his students "to read through both,"...[i.e.,] Eudoxus and , for the one had corrected the errors of the other; and today that would be to read both Ptolemy and Tycho: "but to follow" not, he says, the more ancient, but "the more accurate." And so... if the astronomer, using the arguments which modern times have put forward concerning the heavens, has indicated that creatures arose in the heavens and will disappear once more—in opposition to the opinion of him who alleges experience, but experience not sufficiently long."

"As regards the academies, they are... concerned not to have the program of teaching change very often... the things which have to be chosen are not those which are most true but those which are most easy."

"[T]he truth concerning the mutable nature of the heavens can be taught conveniently... [I]t is not without its use in explaining even those parts of the philosophy of Aristotle which are clearly false, as Book VIII of the Physics concerning celestial movement and Book II of On the Heavens concerning the eternity of the heavens—so... a comparison could be made between the philosophy of the gentiles and the truth of Christian dogma."

"Accordingly, if certain subtleties which are difficult to grasp should not be laid before beginners, or if they should not be preferred to the accepted and necessary teachings, it does not follow that... those things should neither be written nor read privately."

"You can count few academies in which it is a part of the program to explain the Metaphysics of Aristotle: yet Aristotle wrote the Metaphysics too, a very useful work..."

"[T]he philosophers speak of the visible heavens; and Christ of the invisible heavens, or, as the schools say, of the , or, as the simple Christians take it, of the blessed seats, which no corruption will ever touch: since not Tycho, not I, but Christ Himself pronounces concerning this visible world: "Heaven and Earth shall pass away," and the Psalmist, "they shall grow old like a garment"; and Peter, "They shall be destroyed root and all, and be consumed by burning in the fire.""

"And that will occur in order that the alterations in the heavens should not destroy their eternity, if there should be such an eternity, just as the terrestrial alterations, which are perrennial and return in a circle, destroy the Earth’s eternity which was equally believed by Aristotle."

"But this kind of argument against Aristotle will perhaps seem too contentious. Therefore let us use his own testimony... for he is not everywhere consistent: in the Metaphysics he attributes movement to the celestial bodies for its own sake and teaches "that they are moved in order that they may be moved"; but in On the Heavens, being admonished by the things themselves, he attributes something... like the terrestrial... multiplex and turbulent to the stars or... their movers, who by... these mechanisms and movements seek another end... in this way... he adduces the fewness of movements in the moon as... the inferior... closer kinship to the Earth."

"[I]t would be first in my program... to warn... of the distinction between the love—or thirst, to use the Aristotelian word—for the knowledge of natural things and the lust for contradicting and holding the opposite opinion. All philosophers... and all the poets... recognize a divine ravishment in investigating the works of God: and not merely in investigating them privately but even in teaching them publicly: and... the false charge of esoteric novelty-hunting cannot cling to this ravishment.There is God in us, and our warmth comes from His movements: This Spirit has descended from the heavenly seats."

"[T]he boundary posts of investigation should not be set up in the narrow minds of a few... "The world is a petty thing, unless everyone finds the whole world in that which he is seeking," as Seneca says. ...[T]he boundary posts of true speculation are the same as those of the fabric of the world; but the Christian religion has put up some fences around false speculation... in order that error may not rush headlong but may become... harmless..."

"Antiquity teaches us... how vainly man sets up boundary posts where God has not set them... how severely all the astronomers were blamed by the first Christians. ...Yet today we set up academies everywhere: we order that philosophy be taught, that astronomy be taught, that the antipodes be taught."

"I even in private free myself from the blame of seeking after novelty by suitable proofs: let my doctrines say whether there is love of truth in me or love of glory: for most of the ones I hold have been taken from other writers..."

"I build my whole astronomy upon Copernicus' hypotheses concerning the world, upon the observations of , and lastly upon the Englishman, William Gilbert's philosophy of magnetism."

"[F]or me there is so much importance in the true doctrine of others or even in correcting the doctrines which are not... well established, that my mind is never at leisure for the game of inventing new doctrines that are contrary to the true."

"[B]ecause certain people cannot grasp the subtleties of things, they lay the charge of novelty-hunting upon me."

"I now descend to the work... the Harmonies... [H]e who condemns the itch to devise new things and the presumption to profess new and grandiose things will find in the epilogue to the Fifth Book that which he will mark critically. For here the sun-spots and little flames are brought forward as evidence of there being exhalations from the sun which are analogous to exhalations from the Earth: here things corresponding to the generation of animals... in the planets—here the confines of the mysteries of Christian religion are touched: we knock at the doors of the science of the , of , of the idolatry of the Persians, and of those who worship the sun as god—as the interjection of frequent warnings does not dissimulate. ...[R]eason ...leads "from the Muses to Apollo": nevertheless, since the other parts of the work are established by means of their proper demonstrations, the chapter, or epilogue, can be considered as cut off from the rest."

"[T]he following thesis is upheld by incontrovertible demonstrations: that in the farthest movements of any two planets, the universe was stamped with the adornment of harmonic proportions; and, accordingly, in order that this adornment might be brought into concord with the movements, the eccentricities which fell to the lot of each planet had to be brought into concord. ...[H]ow great an addition this makes in illustrating the glory of the fabric of the world, and of God the Architect."

"[I]f... even this inquiry is accused of being esoteric... the head of astronomy is struck off. And since astronomy is studied either for its own sake as a philosophy or for the sake of making astronomical predictions... the taking away from me of the primary end slays this whole subtle astronomy and plainly makes it useless."

"[T]his work of mine, the Harmonies, is nothing except... a certain picture of the edifice of astronomy; and though it may be erased at the pleasure of him who spits upon it, nevertheless the house called astronomy stands by itself: and I know that astronomy is not condemned by His Most Serene Highness but is held of great value on account of its certitude in predicting movements: perhaps, therefore, he will judge its architect—who is almost the only renovator after the Master Tycho and who thought it worth while to devote his life to this work—to be not unworthy of his favour."

"These extracts from the letter, most of which have to do with the investigation of very hidden causes which is to be viewed in this little book, should be spoken and understood. And now it is time for the reader to pass on to the little book."

"What is the subject of the doctrine of the schemata? The proper movements of the planets; we call them the secondary movements; and the planets, the secondary movables."

"Why do you call them the proper movements of the planets? 1. Because the apparent daily movement—with which the doctrine on the sphere is concerned—and which is common to both the planets and the fixed stars, and so to the whole world, is seen to travel from the east to the west; but the far slower single movements of the single planets travel in the opposite direction from west to east; and therefore it is certain that these movements cannot depend upon that common movement of the world—which we have discussed so far—but should be assigned to the planets themselves, and thus they are generically proper to the planets."

"State the opinion of the ancient astronomers as to how the planets move. The ancients, Eudoxus and , and their follower Ptolemy did not advance beyond circles... for in Book XIII of the ', Chapter 2, Ptolemy writes as follows:"But let no one judge that these interweavings of circles which we postulate are difficult, on the ground that... manual imitation of these interweavings is... intricate. For it is not right for our human things to be compared on a basis of equality with the immortal gods, and for us to seek the evidence for very lofty things from examples of very unlike things. ...Indeed we must try hard to fit the most simple hypotheses to the celestial movements... but if that is not successful, whatever sort of hypotheses can be used. ...[W]e should not judge what is simple in celestial bodies by the examples of things which seem to us to be simple ...For ...he who wishes to judge celestial things in this way will not recognize as simple any of those movements which take place in the heavens, not even the invariable constancy of the first movement: because it is ...impossible to find among men this thing (namely, something which stays in the same state perpetually). Therefore we must not form our judgement upon terrestrial things, but upon the natures of the things which are in the heavens and upon the unchanging steadfastness of their movements. So... in this way all the movements are seen to be simple, and much more simple than those movements which seem to us to be simple. For we are unable to suspect them of any labor or any difficulty in their revolutions." So [says] Ptolemy."

"Why do you say that a celestial body, which is unchanging with respect to its matter, cannot be moved by assent alone? For if the celestial bodies are neither heavy nor light, but most suited for circular movement, then do they resist the motor mind? Even if a celestial globe is not heavy in the way in which a stone on the earth is... and is not light in the way in which among us fire is... nevertheless by reason of its matter it has a natural... powerlessness of crossing from place to place, and it has a natural inertia or rest whereby it rests... where it is placed alone. ...[I]n order that it may be moved out of its... rest, it has need of some power... stronger than its matter and its naked body, and which should overcome its natural inertia. For such a faculty is above the capacity of nature and is a sprout of form, or a sign of life."

"Then what is it which makes the planets move around the sun, each planet within the boundaries of its own region, if there are not any solid spheres, and if the globes themselves cannot be fastened to anything else and made to stick there, and if without solid spheres they cannot be moved from place to place by any soul? Even if things are very far removed from us and... are difficult to explain and give rise to... uncertain judgements... if we follow probability and... not to postulate anything... contrary to us, it will... be clear that no mind is to be introduced which should turn the planets by the dictation of reason and... that no soul is to be put in charge of this revolution, in order that it should impress something into the globes by the balanced contest of the forces, as takes place in the revolution around the axis; but that there is one only solar body, which is situated at the centre of the whole universe, and to which this movement of the primary planets around the body of the sun can be ascribed."

"By what reasons are you led to make the sun the moving cause or the source of movement for the planets? 1. Because it is apparent that in so far as any planet is more distant from the sun... it moves the more slowly—so that the ratio of the periodic times is the ratio of the 34th powers of the distances from the sun. Therefore we reason from this that the sun is the source of movement. 2. Below we shall hear the same... use in the case of the single planets—so that the closer any one planet approaches the sun during any time, it is borne with an increase of velocity in exactly the ratio of the square.3. Nor is the dignity or the fitness of the solar body opposed to this, because it is... beautiful... of a perfect roundness... very great and is the source of light and heat, whence all life flows out into the vegetables: to such an extent that heat and light can be judged to be... instruments fitted to the sun for causing movement in the planets. 4. But in especial... the sun’s rotation in its own space around its immobile axis, in the same direction in which all the planets proceed: and in a shorter period than Mercury, the nearest to the sun and fastest of all the planets."

"For... it is disclosed by the telescope... and can be seen... that the solar body is covered with spots, which cross the disk of the sun or its lower hemisphere within 12 or 13 or 14 days, slowly at the beginning and at the end, but rapidly in the middle, which argues that they are stuck to the surface of the sun and turn with it..."

"The most interesting person in this group of Pythagoreans was... Kepler... a technical astronomer well versed in the mathematical arcana of the subject, who knew how to construct an... argument on the basis of observations. ...[A] ...style of argument ...reveals an underlying view of the world similar to... Fludd and Kircher. Kepler recognized harmonies... as correspondences among the different parts of the universe. ...[I]n arguing for Copernican cosmology—the central sun, the outer sphere of the fixed stars, and the intermediate region of the planets—with the Trinity. Kepler... compare[d] the sun with the common sense of animals... in the head, the globes that surround the sun with... sense organs, and the fixed stars with sensible objects. He... compared the sun with the central fireplace... the heart of the world, the seat of reason and life... reminiscent of... Paracelsus and the chymical philosophers..."

"The Epitome Astronomiae Copernicanae, contains much of the material from Kepler's earlier works... It was written for a more general audience, and... gained a relatively wide readership. ...[Here] Kepler's mature physics, metaphysics, and astronomy were presented together for the first time. ...[I]t is an invaluable resource for exploring the evolution of Kepler's thought, fleshing out his conception of the relationship between physics, metaphysics, and astronomy, and—since... intended as a textbook—uncovering what Kepler believed he needed to do to promote his new astronomy."