History Of Science

"In classical science, it was strange to find that action... should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time. Designating a volume of space-time by d\omega, we haved\omega = dxdydzdt,so that our principle of action, \partial A = 0, becomes\partial \int\,L\,d\omega = 0.Now there is a perfect symmetry between the rôles of space and time."

"When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible... This work was carried out by the pure mathematicians—by Klein and Hilbert in particular. It was then found that a principle of action differing but slightly from the classical one could be obtained."

"From the expression for the atom of energy or quantum hv, where h is a constant and v is the frequency of the radiation, it is obvious that there exist as many different types of quanta of energy as there exist different frequencies of radiation. There is no unique type of quantum of energy in nature. That which is universal is not the quantum of energy hv, but the constant h. It can be shown that Planck's constant h is not a mere number; it represents some definite abstract mathematical entity, and that entity is action. We must assume, therefore, that there exist atoms of action in nature, just as there exist atoms of matter. ...we must possess a fairly thorough understanding of what is meant by action, as also of the part this important entity plays in science. ...the atomicity of action ...suggests that change is always discontinuous ...a series of jerks or jumps."

"When Maxwell had proved that his equations of electromagnetics could be thrown into a form compatible with the principle of action, and when he succeeded in amalgamating electricity, magnetism and optics into one science, the universal validity of the principle was accepted. Inasmuch as this principle includes that of the conservation of energy, we can understand why the principle of action was often referred to as the supreme principle of physical science. ...when the principle of action is satisfied by a phenomenon, an indefinite of different mechanical interpretations of the phenomenon are theoretically possible. In the case of electrodynamic phenomena, however, in view of the complicated hypotheses which he was compelled to postulate, Maxwell abandoned all attempts to discover the precise mechanical interpretation which would correspond to reality."

"The principle... imposes the condition that the natural evolution of any system must be such as to render the action a maximum or a minimum. Could we but express this condition in terms of the usual physical magnitudes, we should be enabled to map out in advance the series of intermediary states through which the phenomenon would pass. From this knowledge we should derive the expression of the laws which governed the evolution of the phenomenon. Here... a twofold problem presents itself. First, we must succeed in finding the correct mathematical expression for the action; and, secondly, we must be in a position to solve the purely mathematical problem of determining under what conditions the action will be a maximum or a minimum. Now all problems of maxima and minima are solve by means of the calculus of variations, a form of calculus we owe chiefly to Lagrange. According to the methods of this calculus, we establish under what conditions a magnitude is a maximum or minimum by discovering under what conditions it will be stationary. ... When a stone is thrown into the air, it ascends with decreasing speed, then seems to hesitate for a brief period of time as it hovers near the point of maximum height before it starts to fall back again towards the earth. During this brief period of hesitation at the apex of its trajectory, the stone is said to remain "stationary." We can recognize a stationary state by observing that when it is reached no perceptible changes take place over a short period of time. In this way, we understand the connection which exists between the stationary condition and the presence of a maximum or a minimum. In mathematics small variations are represented by the letter δ; hence the stationary condition of the action, or again, the principle of action, is expressed by\partial A = 0,~ ~i.e.,~\partial \iiiint\,L\,dx\,dy\,dz\,dt = 0....Lamor applied this method to the phenomena of electricity and magnetism and showed how Maxwell's laws of electrodynamics could be deduced from a suitable mathematical expression L defining the electromagnetic function of action."

"History of science"

"Besides Lagrange's early printed works, his correspondence with Euler allows us to form some impression of the stimulating effect which the principle of least action had on Lagrange's mind at the beginning of his career. Lagrange's correspondence with Euler extends from 1754... to 1775... Already in 1754 Lagrange announces that he has made "some observations about the maxima and minima which are in the actions of nature." In a letter of August 12, 1755 Lagrange informs Euler that he had a new and simpler method of solving isoperimetrical problems and gives a full statement of it. This discovery of what was afterwards called "the calculus of variations" certainly gave the principle of least action an additional attractiveness to Lagrange; he speaks in a letter of May 19, 1756, of his meditations "on the application of the principle of least action to the whole of dynamics." Lagrange's interest in the principle of least action seems to have evaporated when he observed that, when developed, the integrand is the variational form of d'Alembert's principle, and that it is simpler and equally effective to start with the equations of motion divorced from the integration. This is Lagrange's point of view in 1788. The earliest date at which this change in point of view is... 1764. In a letter of Sept 15, 1782, to Laplace, Lagrange says that he has almost finished a mechanical treatise uniquely founded on "the principle or formula" given in... his memoir of 1780 on the libration of the moon."

"The present investigations are concerned with the history of the Principle of Least Action in the hands of Maupertuis, Euler, and others. The subject is of great importance in the history of mechanics, both because the principle of least action became, in the hands of Lagrange, "the mother," as Jacobi expressed it, "of our analytical mechanics," and because the animistic tendency displayed in the search for a maximum or a minimum principle in physics undoubtedly had a great influence on such moulders of mechanical theory as Euler, Lagrange (in his early work), Hamilton, Gauss, and in our own times, Willard Gibbs. ...much in this chapter of the evolution of mechanics—one may even say, of thought in general—has been misquoted or misunderstood by even eminent authorities."

"Maupertuis's first enunciation of the law of the least quantity of action was in a memoir read to the French Academy on April 15th, 1744, entitled "Accord de différentes Loix de la Nature qui avoient jusqu'ici paru incompatibles." The laws in question appear to be those of the reflection and of the refraction of light. When a ray of light in a uniform medium travels from one point to another, either without meeting an obstacle or with meeting a reflecting surface, nature leads it by the shortest path and in the shortest time. But when a ray is refracted by passing from a uniform medium to one of different density, the ray neither describes the shortest space nor does it take the shortest time about it. As Fermat showed, the time would be the shortest if light moved more quickly in rarer media, but Newton proved that, as Descartes had believed, light moves more quickly in denser media. Maupertuis's discovery was that light neither takes always the shortest path nor always that path which it describes in the shortest time, but "that for which the quantity of action is the least.""

"In order to understand the significance of Action, let us consider any mechanical system passing from an initial configuration P to a final configuration Q. Classical science defined the action A of this system as the difference between its total kinetic energy... and its total potential energy... taken at every instant and then summated over the entire period of time during which the system passed from the initial state P to the final state Q. Now the total kinetic and potential energies of the system at any instant are given by\iiint\,T\,dx\,dy\,dz~ ~and~ \iiint\,V\,dx\,dy\,dz,where T and V represent the densities of the kinetic and potential energies of every point throughout the space occupied by the system. Accordingly, the expression of the action will be given byA = \iiiint\,(T-V)\,dx\,dy\,dz\,dt~ ~or~ \iiiint\,L\,dx\,dy\,dz\,dt....we have merely replaced (T - V) by a single letter L... referred to as the function of action (also called Lagrangian function). Roughly speaking, action was thus in the nature of the product of a duration by an energy contained in a volume of space. On no account may this action be confused with the action dealt with in Newton's law of action and reaction, also expressible as the principle of conservation of momentum. Still less may it be confused with the term "action" which appears in philosophical writings. ...the laws of mechanics can be expressed in a highly condensed form when the concept of action is introduced. Various forms may be given to the principle of Action; here we consider only the form... called Hamilton's Principle of Stationary Action. If we restrict our attention to the very simplest case, we may state Hamilton's principle as follows: If we consider all the varied paths along which a conservative system may be guided, so that it will pass in a given time from a definite initial configuration P to a definite configuration Q, we shall find that the course the system actually follows, of its own accord, is always such that along it the action is a minimum (or a maximum). ...the principle of action issues ...from the laws of classical mechanics ...A priori, we have no means of deciding whether the laws governing physical phenomena of a non-mechanical nature—those of electromagnetics, for example—would issue from the same principle of action."

"Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution."

"Classical mechanics"

"It [science] has as its highest principle and most coveted aim the solution of the problem to condense all natural phenomena which have been observed and are still to be observed into one simple principle, that allows the computation of past and more especially of future processes from present ones. ...Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regards form and content, may claim to come nearest to that ideal final aim of theoretical research."

"When a change occurs in Nature, the quantity of action necessary for that change is as small as possible. The quantity of action is the product of the mass of the bodies times their speed and the distance they travel. When a body is transported from one place to another, the action is proportional to the mass of the body, to its speed and to the distance over which it is transported."

"Fermat making use of the argument that Nature could not be wasteful, and was bound for this reason to cause the rays of light to travel between two points in the shortest time possible, was able to deduce from this proposition the laws of reflexion and refraction. Though we do not now attach any weight to the premise, we accept the conclusion."

"I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light."

"After so many great men have worked on this subject, I almost do not dare to say that I have discovered the universal principle upon which all these laws are based, a principle that covers both elastic and inelastic collisions and describes the motion and equilibrium of all material bodies. This is the principle of least action, a principle so wise and so worthy of the supreme Being, and intrinsic to all natural phenomena; one observes it at work not only in every change, but also in every constancy that Nature exhibits. In the collision of bodies, motion is distributed such that the quantity of action is as small as possible, given that the collision occurs. At equilibrium, the bodies are arranged such that, if they were to undergo a small movement, the quantity of action would be smallest. The laws of motion and equilibrium derived from this principle are exactly those observed in Nature. We may admire the applications of this principle in all phenomena: the movement of animals, the growth of plants, the revolutions of the planets, all are consequences of this principle. The spectacle of the universe seems all the more grand and beautiful and worthy of its Author, when one considers that it is all derived from a small number of laws laid down most wisely. Only thus can we gain a fitting idea of the power and wisdom of the supreme Being, not from some small part of creation for which we know neither the construction, usage, nor its relationship to other parts. What satisfaction for the human spirit in contemplating these laws of motion and equilibrium for all bodies in the universe, and in finding within them proof of the existence of Him who governs the universe!"

"There are certain general principles or theorems in mechanics, such as Lagrange's equations, Hamilton's principle, the principle of least work, and Gauss' principle of least constraint, which afford general solutions of certain types of problems. Such general principles have therefore the advantage over ordinary methods in that once having found the general solution, any particular problem may be solved by merely routine processes."

"Euler's view is, that the purposes of the phenomena of nature afford as good a basis of explanation as their causes. If this position is taken, it will be presumed a priori that all natural phenomena present a maximum or a minimum. ...in the solution of mechanical problems... it is possible... to find the expression which in all cases is made maximum or minimum. Euler is thus not led astray... and proceeds much more scientifically than Maupertuis. He seeks an expression whose variation put = 0 gives the ordinary equations of mechanics. For a single body moving under the action of forces Euler finds the requisite expression in the formula ∫vds, where ds denotes the element of the path and v the corresponding velocity. This expression is smaller for the path actually taken... therefore, by seeking the path that makes ∫vds a minimum, we can also determine the path. ...In the simplest cases Euler's principle is easily verified. ... The consideration of the motion of a projectile... will also show that the quantity ∫vds is smaller for the parabola than for any other neighboring curve; smaller, even, than for the straight line... between the same terminal points. ... Jacobi pointed out that we cannot assert that ∫vds for the actual motion is a minimum, but simply that the variation of this expression, in its passage to an infinitely adjacent neighboring path, is = 0. ...unquestionably various other integral expressions may be devised that give by variation the ordinary equations of motion, without its following that the integral expressions in question must possess... any particular physical significance. The striking fact remains, however, that so simple and expression as ∫vds does possess the property mentioned."

"We find... that Mie's Electrodynamics exists in a compressed form in Hamilton's Principle—analogously to the manner in which the development of mechanics attains its zenith in the principle of action. Whereas in mechanics, however, a definite function L of action corresponds to every given mechanical system and has to be deducted from the constitution of the system, we are here concerned with a single system, the world. This is where the real problem of matter takes its beginning: we have to determine the "function of action," the world-function L, belonging to the world. For the present it leaves us in perplexity. If we choose an arbitrary L, we get a "possible" world governed by this function of action, which will be perfectly intelligible to us—more so than the actual world—provided that our mathematical analysis does not fail us. We are, of course, then concerned in discovering the only existing world, the real world for us. Judging from what we know of physical laws, we may expect the L which belongs to it to be distinguished by having simple mathematical properties. Physics, this time as a physics of fields, is again pursuing the object of reducing the totality of natural phenomena to a single physical law: it was believed that this goal was almost within reach once before when Newton's Principia, founded on the physics of mechanical point-masses was celebrating its triumphs. But the treasures of knowledge are not like ripe fruits that may be plucked from a tree."

"The atheist who affects to reason, and the fanatic who rejects reason, plunge themselves alike into inextricable difficulties. The one perverts the sublime and enlightening study of natural philosophy into a deformity of absurdities by not reasoning to the end. The other loses himself in the obscurity of metaphysical theories, and dishonours the Creator, by treating the study of his works with contempt. The one is a half-rational of whom there is some hope, the other a visionary to whom we must be charitable. When at first thought we think of a creator our ideas appear to us undefined and confused; but if we reason philosophically, those ideas can be easily arranged and simplified. It is a Being, whose power is equal to his will."

"History of science"

"Contemplating the universe, the whole system of creation, in this point of light, we shall discover, that all that which is called natural philosophy is properly a divine study— It is the study of God through his works — It is the best study, by which we can arrive at a knowledge of the existence, and the only one by which we can gain a glimpse of his perfection."

"It has been the error of schools to teach astronomy, and all the other sciences and subjects of natural philosophy, as accomplishments only; whereas they should be taught theologically, or with reference to the Being who is the Author of them: for all the principles of science are of divine origin. Man cannot make, or invent, or contrive principles; he can only discover them, and he ought to look through the discovery to the Author. When we examine an extraordinary piece of machinery, an astonishing pile of architecture, a well-executed statue, or a highly-finished painting where life and action are imitated, and habit only prevents our mistaking a surface of light and shade for cubical solidity, our ideas are naturally led to think of the extensive genius and talent of the artist. When we study the elements of geometry, we think of Euclid. When we speak of gravitation, we think of Newton. How, then, is it that when we study the works of God in creation, we stop short and do not think of God? It is from the error of the schools in having taught those subjects as accomplishments only and thereby separated the study of them from the Being who is the Author of them."

"Religion has two principal enemies, fanaticism and infidelity, or that which is called atheism. The first requires to be combated by reason and morality, the other by natural philosophy."

"Philosophy"

"The evil that has resulted from the error of the schools in teaching natural philosophy as an accomplishment only has been that of generating in the pupils a species of atheism. Instead of looking through the works of creation to the Creator Himself, they stop short and employ the knowledge they acquire to create doubts of His existence. They labor with studied ingenuity to ascribe everything they behold to innate properties of matter and jump over all the rest by saying that matter is eternal."

"It is certain that either the earth is becoming on the whole cooler from age to age, or the heat conducted out is generated in the interior by temporary dynamical (that is, in this case, chemical) action. To suppose, as Lyell, adopting the chemical hypothesis, has done, that the substances, combining together, may be again separated electrolytically by thermo-electric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfil the expectations of its ingenious inventor by going for ever."

"About the year 1645 while, I lived in London (at a time, when, by our Civil Wars, Academical Studies were much interrupted in both our Universities:) beside the Conversation of divers eminent Divines, as to matters Theological; I had the opportunity of being acquainted with divers worthy Persons, inquisitive into Natural Philosophy, and other parts of Humane Learning; And particularly of what hath been called the New Philosophy or Experimental Philosophy. We did by agreement, divers of us, meet weekly in London on a certain day, to treat and discourse of such affairs. ...The meetings we held sometimes at Dr. Goddard's lodgings...on occasion of his keeping an Operator in his house, for grinding Glasses for Telescopes and Microscopes... and sometime... at ' or some place near adjoyning. Our business was (precluding matters of Theology and State Affairs) to discourse and consider of Philosophical Enquiries, and such as related thereunto, as Physick, Anatomy, Geometry, Astronomy, Navigation, Staticks, Magneticks, Chymicks, Mechanicks, and Natural Experiments; with the state of these studies, as then cultivated, at home and abroad. We there discoursed of the Circulation of the Blood, the Valves in the Veins, the Venæ Lecteæ, the Lymphatick Vessels, the Copernican Hypothesis, the Nature of Comets, and New stars, the Satellites of Jupiter, the Oval Shape (as it then appeared) of Saturn, the Spots in the Sun, and it's turning on it's own Axis, the Inequalities and Selenography of the Moon, the several phases of Venus and Mercury, the improvement of Telescopes and grinding of Glasses for that purpose, the Weight of Air, the Possibility or Impossibility of Vacuities, and Nature's Abhorrence thereof, the Torricellian Experiment in Quicksilver, the Descent of heavy Bodies, and the degrees of acceleration therein; and divers other things of like nature. Some of which were then but New Discoveries, and others not so generally known and imbraced, as now they are, with other things appertaining to what hath been called The New Philosophy; which, from the times of Galileo at Florence, and Sr. Francis Bacon (Lord Verulam) in England, hath been much cultivated in Italy, France, Germany, and other Parts abroad, as well as with us in England. About the year 1648, 1649, some of our company being removed to Oxford (first Dr. Wilkins, then I, and soon after Dr. Goddard) our company divided. Those in London continued to meet there as before... Those meetings in London continued, and (after the King's Return in 1660) were increased with the accession of divers worthy and Honorable Persons; and were afterwards incorporated by the name of the , &c. and so continue to this day."

"There are many properties of motion, displacement, and deformation, which may be considered altogether independently of such physical ideas as force, mass, elasticity, temperature, magnetism, electricity. The preliminary consideration of such properties in the abstract is of very great use for Natural Philosophy, and we devote to it, accordingly... the Geometry of our subject, embracing what can be observed or concluded with regard to actual motions, as long as the cause is not sought."

"That which is now called natural philosophy, embracing the whole circle of science, of which astronomy occupies the chief place, is the study of the works of God, and of the power and wisdom of God in his works, and is the true theology."

"The term Natural Philosophy was used by Newton, and is still used in British Universities, to denote the investigation of laws in the material world, and the deduction of results not directly observed. Observation, classification, and description of phenomena necessarily precede Natural Philosophy in every department of natural science. The earlier stage is in some branches commonly called Natural History; and it might with equal propriety be so called in all others."

"When we reflect on the magnificence of the great picture of the universe... we are lost in the contemplation of the immensity of the prospect, and returning to the comparatively diminutive proportions of our individual persons, and of all the objects with which we are most immediately connected, we cannot help feeling our own insignificance in the material world. The mind, notwithstanding, endeavours to raise itself above the restraints which nature has imposed on the body, and to penetrate the abyss of space in search of congenial existences. But in speculations of this kind, reason and argument must give way to conjecture and imagination; and thus, from natural philosophy, our imaginations wander into the regions of poetry; and it must be confessed that the union of poetical embellishment with natural philosophy is seldom very happy. ...his object is, to say a little, very elegantly, in very circuitous, and somewhat obscure terms. But the information, which the natural philosopher has to impart, is too copious to allow of prolixity in its detail; his subjects are too intricate to be compatible with digressions after amusement, which, besides interrupting, are too likely to enervate the mind; and if he is ever fortunate enough to entertain, it must be by gratifying the love of truth, and satisfying the thirst after knowledge."

"To make way for the regular and lasting Motions of the Planets and Comets, it's necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams or Effluvia, arising from the Atmospheres of the Earth, Planets and Comets, and from such an exceedingly rare Æthereal Medium … A dense Fluid can be of no use for explaining the Phænomena of Nature, the Motions of the Planets and Comets being better explain'd without it. It serves only to disturb and retard the Motions of those great Bodies, and make the frame of Nature languish: And in the Pores of Bodies, it serves only to stop the vibrating Motions of their Parts, wherein their Heat and Activity consists. And as it is of no use, and hinders the Operations of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected. And if it be rejected, the Hypotheses that Light consists in Pression or Motion propagated through such a Medium, are rejected with it. And for rejecting such a Medium, we have the authority of those the oldest and most celebrated philosophers of ancient Greece and Phoenicia, who made a vacuum and atoms and the gravity of atoms the first principles of their philosophy, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical."

"As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition."

"A true philosopher does not engage in vain disputes about the nature of motion; rather, he wishes to know the laws by which it is distributed, conserved or destroyed, knowing that such laws are the basis for all natural philosophy."

"Plato introduced into philosophy a variety of imaginations, which resembled the fictions of poetry much more than the truths of science. He maintained, for example, that ideas existed independently of the human mind, and of the external world, and that they composed beings of different kinds, by their union with an imperfect matter. It is observed by Bacon, in his essay on the opinions of Parmenides, that the most ancient philosophers Empedocles, Anaxagoras, Anaximenes, Heraclitus and Democritus, submitted their minds to things as they found them; but that Plato made the world subject to ideas, and Aristotle made even ideas, as well as all other things, subservient to words; the minds of men beginning to be occupied, in those times, with idle discussions and verbal disputations, and the correct investigation of nature being wholly neglected. Plato entertained, however, some correct notions respecting the distinction of denser from rarer matter by its greater inertia; and it would be extremely unjust to deny a very high degree of merit to Aristotle's experimental researches, in various parts of natural philosophy, and in particular to the vast collection of real information contained in his works on natural history. Aristotle attributed absolute levity to fire, and gravity to the earth, considering air and water as of an intermediate nature. By gravity the ancients appear in general to have understood a tendency towards the centre of the earth, which they considered as identical with that of the universe; and as long as they entertained this opinion, it was almost impossible that they should suspect the operation of a mutual attraction in all matter, as a cause of gravitation. The first traces of this more correct opinion respecting it are found in the works of Plutarch."

"Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth. If one considers a series of objects of the same nature one perceives among them and in their changes ratios which manifest themselves more and more in proportion as the series is prolonged, and which, extending and generalizing continually, lead finally to the principle from which they were derived. But these ratios are enveloped by so many strange circumstances that it requires great sagacity to disentangle them and to recur to this principle: it is in this that the true genius of sciences consists. Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity. It is difficult to appreciate the probability of the results of induction, which is based upon this that the simplest ratios are the most common; this is verified in the formulae of analysis and is found again in natural phenomena, in crystallization, and in chemical combinations. This simplicity of ratios will not appear astonishing if we consider that all the effects of nature are only mathematical results of a small number of immutable laws. Yet induction, in leading to the discovery of the general principles of the sciences, does not suffice to establish them absolutely. It is always necessary to confirm them by demonstrations or by decisive experiences; for the history of the sciences shows us that induction has sometimes led to inexact results."

"And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy."

"If we examine the mere signification of the two words Natural Philosophy, we find that natural means something that is produced by nature; and philosophy, from the Greek, is literally "love of wisdom or knowledge." Thus, then, the words imply love of a knowledge of the productions of nature or God. Knowledge, in its true sense, is an accumulation of facts; these man carefully collects, and reasoning thereupon, is capable of penetrating many of the secret workings of nature, and turning such acquisition to his peculiar advantage. Natural Philosophy is also termed Physics, that is, a study of nature by means of the strictest modes of investigation the intellect of man has at command."

"Wide is the scope of Natural Philosophy. It leads to an acquaintance with the laws that keep the planets in their undeviating path; it treats of the phenomena of the earth, the air, and the ocean; of the simple principles of mechanism that man employs; of the falling of the silent dew or the rushing of the roaring cataract; of the heat of summer and the frost of winter; of the zephyr-breeze or the destructive tornado; of the swimming of fishes or the flying of birds; of the ripple of the placid lake or the mountain waves of the ocean; of the grace, motion, and powers of the human form; of the mechanism of the voice, the ear, and the eye. By an acquaintance with its first principles—the embellishments of a palace, the necessities of a cottage, the swinging of a carriage, and the management of a dray, are all better accomplished. The elasticity of air and steam, that drives the vessel despite of tide or wind, or sends tons of merchandise with surprising velocity to the extremes of a kingdom, are by its teaching comprehended. Knowing the cause of the awful voice of thunder, of the terrific destruction of lightning, and of the peaceful beauties of the rainbow, much ignorant teaching is dispelled. Man has so advanced in his comprehension of nature, that he chains one of the most fearful elements to his use, which he guides and directs as if it were possessed of the feebleness of a helpless babe; with it he sends his thoughts with a speed surpassing the rapid flight of time. No one can feel but abashed at not understanding the simple principles that produce such seemingly miraculous effects. Natural Philosophy aids, then, our commerce, wealth, happiness, luxuries, necessities, and civilisation."

"Neither in science itself, nor in that lower class of the arts which arise out of its practical application, has any individual work an enduring ultimate value, unless from its execution: and this would be altogether independent of its scientific value, and would belong to it solely as a work of art. In science its main worth is temporary, as a stepping-stone to something beyond. Even the Principia, as Newton, with characteristic modesty entitled his great work, is truly but the beginning of a natural philosophy, and no more an ultimate work than Watt's steam-engine, or Arkwright's spinning-machine. ...Thus in science there is a continual progress, a pushing onward: no ground is lost; and the lines keep on advancing. We know all that our ancestors knew, and more: the gain is clear, palpable, indisputable. The discoveries made by former ages have become a permanent portion of human knowledge, and serve as a stable groundwork to build fresh discoveries atop of them; as these in their turn will build up another story, and this again another."

"Les causes primordiales ne nous sont point connues; mais elles sont assujetties à des lois simples et constantes, que l'on peut découvrir par l'observation, et dont l'étude est l'objet de la philosophie naturelle."

"Natural Philosophy is placed among those Parts of Mathematics, whose Object is Quantity in general. Mathematics are divided into pure and mixed. Pure Mathematics enquire into the general Properties of Figures and abstracted Ideas. Mixed Mathematics examine Things themselves, and will have our Notions and Deductions to agree both with Reason and Experience. Physics belong to mix'd Mathematics. The Properties of Bodies, and the Laws of Nature, are the foundations of mathematical Reasoning, as all that have examined the Scope of the Science will freely confess. But Philosophers do not equally agree upon what is to pass for a Law of Nature, and what Method is to be followed in quest of those Laws. I have therefore thought fit... to make good the Newtonian Method... Physics do not meddle with the first Foundation of Things. That the World was created by God, is a Position wherein Reason so perfectly agrees with Scripture, that the least Examination of Nature will shew plain Footsteps of supreme Wisdom. It is confounding and oversetting all our clearest Notions, to assert that the World may have taken its Rise from some general Laws of Motion, and that it imports not what is imagined concerning the first Division of Matter. And that there can hardly be anything supposed, from which the same Effect may not be deduced by the same Laws of Nature: and that for this Reason; That since Matter successively assumes all the Forms it is capable of by means of those Laws, if we consider all those Forms in order, we must at last come to that Form wherein this present World was framed; so that we have no Reason in this Case to fear any Error from a wrong Supposition. This Assertion, I say, overthrows all our clearest Notions, as has been fully proved by many learned Men; and is indeed so unreasonable, and so injurious to the Deity, that it will seem unworthy of an Answer to any one that does not know that it has been maintain'd by any antient and modern Philosophers, and some of them of the first Rank, and far removed from any Suspicion of Atheism. Then first laying it down as an undoubted Truth, that God has created all Things, we must afterwards explain by what Laws every thing is governed."

"Our imagination is struck only by what is great; but the lover of natural philosophy should reflect equally on little things. We have just seen that winged insects, collected in society, and concealing in their sucker a liquid that irritates the skin, are capable of rendering vast countries almost uninhabitable. Other insects equally small, the termites (comejen), create obstacles to the progress of civilization, in several hot and temperate parts of the equinoctial zone, that are difficult to be surmounted. They devour paper, pasteboard, and parchment with frightful rapidity, utterly destroying records and libraries. Whole provinces of Spanish America do not possess one written document that dates a hundred years back. What improvement can the civilization of nations acquire if nothing link the present with the past; if the depositaries of human knowledge must be repeatedly renewed; if the records of genius and reason cannot be transmitted to posterity?"

"Since the word "knowledge" occurs in my general title... I am going to be talking about epistemology, although I prefer to use the eighteenth-century, indeed, medieval phrase, "natural philosophy." ...that enterprise of the human mind which attempts to trace lawfulness to nature, dead and living, but which is not directed to specific inquiries into how this or that law works. Philosophy in the sense in which I practice it, natural philosophy, is concerned with lawfulness rather than with laws and the general nature of laws rather than with the specific structure of this or that law. Natural philosophy was one of the three topics (moral philosophy and metaphysical philosophy were the others) to which one graduated in medieval universities after having studied the seven liberal arts. I believe that we need to review the whole of our natural philosophy in the light of scientific knowledge that has arisen in the last fifty years."

"Those who have treated of natural philosophy may be nearly reduced to three classes. Of these, some have attributed to the several species of things specific and occult qualities, on which, in a manner unknown, they make the operations of the several bodies to depend. The sum of the doctrine of the schools derived from Aristotle and the Peripatetics is herein contained. They affirm that the several effects of bodies arise from the particular natures of those bodies; but whence it is that bodies derive those natures they do not tell us, and therefore they tell us nothing. And being entirely employed in giving names to things, and not in searching into things themselves, we may say, that they have invented a philosophical way of speaking, but not that they have made known to us true philosophy. Others, therefore, by laying aside that useless heap of words, thought to employ their pains to better purpose. These supposed all matter homogeneous, and that the variety of forms which is seen in bodies arises from some very plain and simple affections of the component particles; and by going on from simple things to those which are more compounded, they certainly proceed right, if they attribute no other properties to those primary affections of the particles than nature has done. But when they take a liberty of imagining at pleasure unknown figures and magnitudes, and uncertain situations and motions of the parts; and, moreover, of supposing occult fluids, freely pervading the pores of bodies, endued with an all-performing subtilty, and agitated with occult motions; they now run out into dreams and chimeras, and neglect the true constitution of things; which certainly is not to be expected from fallacious conjectures, when we can scarcely reach it by the most certain observations. Those who fetch from hypotheses the foundation on which they build their speculations, may form, indeed, an ingenious romance; but a romance it will still be. There is left, then, the third class, which profess experimental philosophy. These, indeed, derive the causes of all things from the most simple principles possible; but, then, they assume nothing as a principle that is not proved by phænomena. They frame no hypotheses, nor receive them into philosophy otherwise than as questions whose truth may be disputed. They proceed, therefore, in a twofold method, synthetical and analytical. From some select phænomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by synthesis shew the constitution of the rest. This is that incomparably best way of philosophizing which our renowned author most justly embraced before the rest, and thought alone worthy to be cultivated and adorned by his excellent labours. Of this he has given us a most illustrious example by the explication of the System of the World, most happily deduced from the theory of gravity. That the virtue of gravity was found in all bodies, others suspected or imagined before him; but he was the only and the first philosopher that could demonstrate it from appearances, and make it a solid foundation to the most noble speculations."

"It is the object of Natural Philosophy to make us acquainted with the various qualities or properties of matter, and the manner in which different masses of it affect each other."

"Epicurus appears to have reasoned as justly respecting many particular subjects of natural philosophy, as he did absurdly respecting the origin of the world, and of the animals which inhabit it. He adopted in great measure the principles of Democritus respecting atoms, but attributed to them an innate power of affecting each other's motions, and of declining, in such a manner, as to constitute, by the diversity of their spontaneous arrangements, all the varieties of natural bodies. He considered both heat and cold as material; the heat emitted by the sun he thought not absolutely identical with light, and even went so far as to conjecture that some of the sun's rays might possibly possess the power of heating bodies, and yet not affect the sense of vision. In order to explain the phenomena of magnetism, he supposed a current of atoms, passing, in certain directions, through the magnet and through iron, which produced all the effects by their interference with each other. Earthquakes and volcanos he derived from the violent explosions of imprisoned air."

"Since they are neither great mathematicians nor able experimenters, what are we to call such men as Maxwell, Lorentz and Einstein? If we concede that the name philosopher should apply to those who are concerned with a harmonisation of the whole than with individual facts, or, again, with a general view of things rather than with a restricted view, we must agree that the theoretical physicists must be called philosophers. They are, then, the philosophers of the inorganic world, just as the pure mathematicians might be called the philosophers of abstract relations. Now... the facts which these scientific philosophers are seeking to co-ordinate are of a restricted species; they are mathematical, physical and chemical in nature; hence it is clear that there is room for a more general type of philosopher—a super-philosopher, as it were—whose facts would comprise all the spheres of human knowledge, including consciousness, emotions and the relationships between mind and matter. The traditional philosophers—or shall we say lay philosophers, since we are discussing scientific matters?—aspire to be placed in this category of thinkers. It would appear, then, that theoretical scientists, and lay philosophers have much in common; they differ only in the scope of the facts they are seeking to co-ordinate. But here is where the first breach arises. The theoretical scientist proceeds with the utmost caution and considers himself at liberty to theorise only after a sufficient number of facts have been established by experiment and observation; till then he remains silent. ...It was not one, nor two, nor even three of the negative experiments in electromagnetics that drove Einstein towards his revolutionary theory; it was the whole body of electrodynamics. ... But when we examine the procedure of the lay philosopher who discusses scientific matters, we see that his procedure is entirely different."