Physicists From Scotland

"28 Proposition. The image of the Beast, is these degenerate Princes, that in name onely were called Roman Emporours, and were neither Romans of blood, nor Emperours of Magnanimitie."

"29 Proposition. The name of the beast expressed by the number 666. (cap. 13.) is the name λαγεινος onely."

"30 Proposition. The marke of the Romane beast, is that invisible profession of servitude and obedience, that his subjects hath professed to his Empire, since the first beginning thereof, noted afterward by the Pope, with divers visible markes."

"31 Proposition. The visible marks of the Beast, are the abused characters, of λρς and crosses of all kindes, taken out of the number of the first beasts name."

"32 Proposition. Gog is the Pope, and Magog is the Turkes and Mahometanes."

"33 Proposition. The armies of Gog and Magog (cap. 20) are all one with the armies of the sixt Trumpet and sixt Viall."

"34 Proposition. The thousand yeares that Sathan was bound (Revel. 20.) began in Anno Christi 300. or thereabout."

"35 Proposition. The Devils bondage a thousand yeares (cap. 20) is no waies els, but from stirring up of universall warres among nations."

"36 Proposition. The 1260 years of the Antichrists universal raign over Christians, begins about the year of Christ 300. or 316. at the farthest."

"So ends this demonstratiue resolution of all difficulties of the Revelation, first of all dates and times, and last of the principall termes and matters, as to the meaner termes and smaller matters, they are interpreted in the notes of the principall treatise."

"Conclusion. Then for conclusion, by these interpretative propositions, followeth foure thinges marvelous and notable. First, that the interpretation of every parte of the Revelation, is accessorie or consectarie to other: that is to say, it is so chained and linked together, that every mysterie opens other to the discoverie of the whole. Secondly, that the first halfe of the book is orderly, that is to say, it containeth in order of time the most notable accidents that concerneth Gods Church, from the time of Christs Baptisme successively to the latter day. Thirdly, that every historie prophecied, is limited or dated with his own nŭber of years. Fourthly and last of all, that whatsoever historie is more orderlie and summarlie, than plainly set downe in the first orderlie parte of the booke, the same is repeated, interpreted, or amplified in the last part of the booke: deviding the whole Revelation according to the table following, before we proceed to the principall matter."

"Seeing there is nothing, (right well beloved students of mathematics,) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculations, that the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expence of time, are for the most part subject to many slippery errors, I began, therefore, to consider in my mind, by what certain and ready art I might remove these hindrances. And having thought upon many things to this purpose, I found at length some excellent brief rules to be treated of perhaps hereafter: But amongst all, none more profitable than this, which together with the hard and tedious multiplications, divisions, and extractions of roots, doth also cast away even the very numbers themselves that are to be multiplied, divided, and resolved into roots, and putteth other numbers in their place which perform as much as they can do, only by addition and substraction, division by two, or division by three. Which secret invention being, (as all other good things are,) so much the better as it shall be the more common, I thought good heretofore, to set forth in Latin for the public use of mathematicians."

"But now, some of our countrymen in this island, well affected to these studies, and the more public good, procured a most learned mathematician to translate the same into our vulgar English tongue, who after he had finished it, sent a copy of it to me, to be seen and considered on by myself. I having most willingly and gladly done the same, find it to be most exact and precisely conformable to my mind and the original. Therefore it may please you who are inclined to these studies, to receive it from me and the translator, with as much good will as we recommend it unto you.—Fare thee well."

"A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions."

"It is picked out from numbers progressing in continuous proportion. Of continuous progressions, an arithmetical is one which proceeds by equal intervals; a geometrical one which advances by unequal and proportionally increasing or decreasing intervals. Arithmetical progressions: 1, 2, 3, 4, 5, 6, 7, &c.; or 2, 4, 6, 8, 10, 12, 14, 16, &c, Geometrical progressions: 1, 2, 4, 8, 16, 32, 64, &c.; or 243, 81, 27, 9, 3, 1."

"To decrease geometrically is this, that in equal times, first the whole quantity then each of its successive remainders is diminished, always by a like proportional part."

"Whence a geometrically moving point approaching a fixed one has its velocities proportionate to its distances from the fixed one."

"From the Radical table completed in this way, you will find with great exactness the logarithms of all sines between radius and the sine 45 degrees; from the arc of 45 degrees doubled, you will find the logarithm of half radius; having obtained all these, you will find the other logarithms. Arrange all these results as described, and you will produce a Table, certainly the most excellent of all Mathematical tables, and prepared for the most important uses."

"If a first sine be multiplied into a second producing a third, the Logarithm of the first added to the Logarithm of the second produces the Logarithm of the third. So in division, the Logarithm of the divisor subtracted from the Logarithm of the dividend leaves the Logarithm of the quotient."

"And if any number of equals to a first sine be multiplied together producing a second, just so many equals to the Logarithm of the first added together produce the Logarithm of the second."

"Any desired geometrical mean between two sines has for its Logarithm the corresponding arithmetical mean between the Logarithms of the sines."

"In the early part of my chymical studies, the author whose works made the most agreeable impression on my mind was Markgraaf of Berlin; he contrived and executed his experiments with so much chymical skill that they were uncommonly instructive and satisfactory; and he described them with so much modesty and simplicity, avoiding entirely the parade of erudition and self-importance, with which many other authors encumber their works, that I was quite charmed... and said to Dr. Cullen I would rather be the author of Markgraaf's Essays than of all the Chymical works in the library. The celebrated Reaumur's method of writing appeared to me also uncommonly pleasing. After 3 years spent with Dr. Cullen, I came to Edinburgh to finish my education in medicine. Here I attended the lectures of Dr. Munro, senr. and the other medical Professors, until the summer of the year 1754, when I received the degree of Doctor of Medicine, and printed my inaugural Dissertation De Humere Acido a Cibis Orto et Magnesia Alba."

"When I am well instructed in a method of Practice here, a very short time of London will be sufficient; for then I need only observe the different manner of doing the same thing there, which I shall soon be master of."

"These, sir, are the chief of the reasons which have been urged to me for staying here some time longer & which I thought so good that I determined to acquaint you with them & in the meanwhile [I] will employ my time to the best advantage till I have your opinion of them. I am Dr Sir Your most affecte & Dutyfull Son,"

"The quantitative investigations of Black on the burning of lime and magnesia alba, in which the balance (previously characterized by the French chemist Jean Rey as "an instrument for clowns") was applied at every turn, led to the rejection of a hypothetical "principle of causticity," and replaced it by a "sensible ingredient of a sensible body," fixed air."

"The extension of Black's method by the physicist Lavoisier led to the downfall of the purely qualitative theory of phlogiston, and gave to chemistry the true methods of investigation, and its first great quantitative law—the law of conservation of matter."

"He had discovered that a cubic inch of marble consisted of about half its weight of pure lime, and as much air as would fill a vessel holding six wine gallons. ...What could be more singular than to find so subtle a substance as air existing in the form of a hard stone, and its presence accompanied by such a change in the properties of that stone? … It is surely a dull mind that will not be animated by such a prospect."

"Black discovered the difference between weak and strong s, i.e. between the alkali s and s. The work... is essentially quantitative, and... leads into... gas analysis, which was to play a very important role in providing a new chemical theory. ...Black ...first showed that and were two different substances. Although both effervesce when treated with s... [m]agnesium carbonate does not form common lime when heated strongly, and on cooling, the residue is insoluble in water. This product of ignition (oxide) however forms the same salts with acids as does the original salt (carbonate) with the difference that no effervescence occurs. Black also observed that during ignition "air" () is lost, and supposed that to be responsible for the loss of weight as well as for the effervescence... [H]e dissolved the magnesium oxide in sulphuric acid and then precipitated the magnesium with . ...[T]he composition of the precipitate was identical with that... before the ignition... He... concluded that alkali carbonates were not elemental substances, as had been originally thought, because they give "air" to the... oxide... [the] same "air"... responsible for the effervescence... Black then [examined] lime and limestone and applied similar experiments. He established that the air was not identical with atmospheric air... only a component... called by Black "fixed air"... that part... absorbed by lime and the alkali hyroxides. ...[T]he relationship... is similar to that between alkalis and acids... alkalis are "in some measure neutralized" by the fixed air. However, the relation between acids and alkalis is stronger as the acid drives out the fixed air."

"Black... began a new epoch in Chemistry and Physics, by his fundamental work on Heat, and on the nature of chemical combination; and his name must ever remain associated with those of other illustrious Scotsmen of his day as one who led the way in chemical research and its technical applications."

"Black's celebrated thesis ...gained for him not merely the degree of Doctor of Medicine, but also brought his name before every "philosopher" in Europe and America as that of a man who had made a discovery of more fundamental influence on the progress of Chemistry than any which had previously been described."

"In the olden days it was considered quite as marvellous that a gas could be made to occupy a small volume, or that "air" could be produced in quantity from a stone, as that an Arabian "djinn" of enormous size and ferocious mien could issue from a bottle..."

"[I]n the middle of the seventeenth century Robert Boyle had enunciated his famous discovery, "Touching the Spring of the Air"; in which he proved that the greater the pressure to which a gas is exposed the smaller the volume it will occupy. But however great the pressure, Boyle's air remained air."

"It was Black's discovery of the production of carbonic-acid gas, or, as he named it, "fixed air," from , which first directed notice to this possibility of the production of a gas from a solid; and, further, the peculiar property of this gas its power of being fixed was one which completely differentiated it from ordinary air."

"Stephen Hales... had distilled many substances of vegetable, animal, and mineral origin ; among them he treated many which must have produced impure hydrogen, marsh-gas, carbonic-acid gas, and oxygen; but Hales contented himself with measuring the volume of gases obtained from a known weight of material, without concerning himself as to their properties. And, as the result of many experiments, he concluded that "our atmosphere is a chaos, consisting not only of elastick, but also of unelastick air-particles, which in plenty float in it, as well as the sulphureous, saline, watry, and earthy particles, which are no ways capable of being thrown off into a permanently elastick state, like those particles which constitute true permanent air." This was the current belief as regards the nature of air."

"[I]t was with the object of discovering a "milder alkali," and bringing it into the service of medicine, that Black began his experiments on magnesia. They are described in... "Experiments upon Magnesia Alba, Quicklime, and some other Alcaline Substances"... his thesis for the... M.D... at Edinburgh in 1754; he had been making the experiments since 1752. The actual thesis was in Latin: "De Humore Acido a Cibis orto, et Magnesia Alba"; the pamphlet was published in the following year."

"As Dr. Black had never anything for ostentation, he was at all times precisely what the occasion required, and no more. Never did anyone see Dr. Black hurried at one time to recover matter which had been improperly neglected on a former occasion. Everything being done in its proper season and place, he ever seemed to have leisure in store; and he was ready to receive his friend or acquaintance, and to take his part with cheerfulness in any conversation that occurred."

"As he advanced in years, his countenance continued to preserve that pleasing expression of inward satisfaction, which, by giving ease to the beholder, never fails to please. His manner was perfectly easy and unaffected, and graceful. He was of most easy approach, affable, and readily entered into conversation, whether serious or trivial. His mind being abundantly furnished with matter, his conversation was at all times pertinent and agreeable. He was a stranger to none of the elegant accomplishments of life."

"I do not imagine that Mr. Black's researches at this time (or perhaps at any time) have been keen or pertinacious. This could not accord with the native gentleness of his mind; but his conceptions being distinct, and his judgment sound, his progress in scientific research, if slow, was steady, and his acquisitions were solid. Perhaps this moderation and sobriety of thought was his happiest disposition, and the most conducive to his improvement."

"During the period in which the theory of phlogiston reached its zenith, four names stand out in bold relief. They are those of Joseph Black (1728–99), Henry Cavendish (1731–1810), Karl Wilhelm Scheele (1742–86), and Joseph Priestley (1733–1804). Of these men the last three were steadfast adherents of the theory, while Black seems to have been indifferent, devoting himself to his researches and placing his own interpretation upon his results."

"Black was Professor of Chemistry at Glasgow and Edinburgh successively, and although he published only three papers on chemical subjects, these were models of accuracy and logic, and may still be read with profit by the novice—and indeed by the mature chemist. The most important of the three is entitled Experiments upon Magnesia Alba, Quicklime, and some other Alcaline Substances, published in 1756. A modern reprint of it was made by the Alembic Club..."

"In all essentials, Black's explanation is identical with our own, and the careful logic of his procedure makes his monograph conspicuous at once among the multitude of useful researches which were now beginning to bear witness to the new spirit in chemistry."

"His only other important discovery was that of the s, but he is nevertheless correctly regarded as one of the greatest chemists of one of the most fruitful periods of chemistry, and his fame rests upon impregnable foundations."

"Black's research began in an attempt to produce a milder [for medicinal use] from Epsom salts. ...He commenced by studying the different forms of lime. , when heated in a fire, became activated, and this quicklime, when placed in water, generated much heat, and was transformed into slaked lime. The limestone was supposed to have absorbed phlogiston from the fire and later to have lost it to the water. Black heated a weighed quantity of marble and found that in the process it lost weight, thus giving the first blow to the phlogiston theory. He next showed that if slaked lime be treated with a mild alkali, such as , it is changed again to chalk, while the mild alkali becomes caustic alkali."

"In modern nomenclature the changes are:"

"Black realized that when or was heated, a gas which he called fixed air was released. He was able to collect the gas, which we know as , and to study its properties. He was also able to show that carbon dioxide was a normal constituent of the air because quicklime was changed into ordinary chalk, albeit tardily, by exposure to air. This was the first atmospheric gas to be isolated and described. The discovery heralded the dawn of a new era in chemical investigation, and so Black is often given the title-Father of Pneumatic Chemistry."

"Much of Black's success was due to his accuracy in weighing. The experiments quoted are the first example of a reversible chemical reaction. A certain weight of chalk is taken in experiment 1 and the same weight is recovered at the end of experiment 3. In the words of Sir William Ramsay, "his proof that the change of a complex compound to simpler compounds, and the building up of a complex compound from simpler ones, can be followed successfully by the use of the balance, has had for its consequence the whole development of chemistry." On this score he has been called the Father of Quantitative Chemistry."

"I have the happiness to be lodged with a Gentleman who is justly esteemed by all his Brethren, who has extensive practice both as a Physician & Surgeon & tho no Doctor himself, yet the oldest of them are not ashamed to consult with him in private. Besides this he is my intimate & familiar Friend & is willing upon every occasion to teach me as far as he knows himself."

"If I go to London to acquire this part of medicine, I may see a good deal of Practice, but I am a stranger there, & have no acquaintance whom I can venture to trust so much or be so familiar with as to trouble him with all my questions and doubts.—On the contrary here, medicine is allowed on all hands to be in a very flourishing condition. It is practised in the most rational & simple manner."

"I have not had time this last winter to apply to it sufficiently; tho I had the opportunities, my attention was too much taken up with some of the Colleges, preparing my Thesis, & recalling to my mind everything I had learned, on account of the examinations."

"I should be thoroughly acquainted with the real Practice & this is a thing very different from what can be learned in a College; thus for instance we are taught by our Professors that if a sick person breaths with great difficulty, one thing must be done; if his respiration is yet more laborious, another. But how shall we judge of the nice degrees of laborious breathing unless from a dayly & familiar acquaintance with, & study of, the appearances and looks of Patients &c. Most young Physicians neglect this essential point of their art in their education & very often acquire it when they come to Practice at the expense of their patients' safety."