Chapter 54: MECHANICS

INTRODUCTION

MECHANICS, taken as the name for just one of the physical sciences, would merit no place on a small list of basic, focal terms. But the word “mechanics” means more than that. In the tradition of western thought it signifies a whole philosophy of nature, and it connotes a set of fundamental principles under which, it has been thought, all the physical sciences can be unified.

The principles of mechanics have been applied not only in statics and dynamics, which are concerned with the action and reaction of bodies at rest or in motion, but also in acoustics and optics and the sciences of heat, magnetism, and electricity. They have been extended to astronomical phenomena to constitute what is called “celestial mechanics.” They have been thought to govern the action or motion of invisible particles or waves as well as the familiar bodies of ordinary experience. In the range and variety of the phenomena it covers, mechanics would seem to be co-extensive with physics. Such at least appears to be its scope at one stage in the development of natural science.

We shall presently consider the dissatisfaction with the mechanical point of view which causes scientists in our own day to hail the replacement of “classical mechanics” by the “new physics” as a great advance in science. The intellectual significance of this change can be compared with that earlier revolution in the 17th century when the new natural science founded on the achievements of Galileo, Huygens, and Newton replaced the physics of Aristotle which had long reigned as the traditional philosophy of nature. What Einstein calls “the rise and decline of the mechanical point of view” thus seems to provide an apt title for the story of three stages in the history of science, in only one of which does the whole of physics appear to be dominated by mechanics.

One way, then, of understanding the importance of mechanics is in terms of that story. Other chapters, such as ASTRONOMY, CHANGE, ELEMENT, MATTER, PHYSICS, SPACE, and TIME—and perhaps also CAUSE and HYPOTHESIS—tell part of that story, especially the part which turns on the differences between Aristotle’s physics (which is neither experimental nor mathematical) and modern physics (which is both). This chapter focuses on issues which fall largely within modern physics—issues belonging to that part of the story which, in the great books, begins with Galileo, Huygens, and Newton and runs to Fourier and Faraday. The story itself does not end there, but the point to which Faraday carries it suggests the sequel in Clerk Maxwell and Einstein, just as Galileo’s point of departure reflects antecedents in Aristotle. The great books state the issues sufficiently well, though they do not tell the whole story. That can be fully documented only by a host of supplementary scientific classics in various fields, such as the works listed in the Additional Readings.

IN MODERN TIMES it is accepted that physics should be both experimental and mathematical. No one questions the ideal of unifying the physical sciences and finding the unity in nature’s laws. But the question is whether that unification can be achieved under the aegis of mechanics; and the issue is whether physics should gather its experimental findings together under purely mathematical formulations or should also try to give those mathematical formulae a mechanical interpretation.

The issue involves more than a question of scientific method. It concerns the ultimate aim of natural science and the kind of concepts it should employ to fulfill this aim. Should the scientist seek to do no more than describe the phenomena of nature in terms of the simplest and most universal mathematical relations? Or should he go beyond description to an explanation of the phenomena in terms of their causes?

When the issue is thus stated as a choice between being content with description or striving for explanation, it appears to be broader than the question whether physics should or should not be mechanical. Even granted that explanation is desirable, does it necessarily follow that physical explanation must employ the principles and concepts of mechanics? Aristotle’s physics, it can be argued, provides a negative answer. His various physical treatises represent a natural science which tries to explain the phenomena without doing so mechanically, just as it tries to describe the phenomena without doing so mathematically.

That the connection of these two features of Aristotle’s physics is not accidental seems to be indicated by the conjunction of their opposites in modern physics. When in the 17th century the physicist describes natural phenomena in mathematical terms, he explains them—if he tries to explain them at all—in mechanical terms. “The laws of Mechanics,” writes Descartes, “are the laws of Nature.” Huygens opens his Treatise on Light by referring to optics as the kind of science “in which Geometry is applied to matter”; but he at once expresses the desire to advance this branch of mathematical physics by investigating “the origin and the causes” of the truths already known, in order to provide “better and more satisfactory explanations.” Such explanations, he thinks, will be found only if we conceive “the causes of all natural effects in terms of mechanical motions.” He declares it his opinion that “we must necessarily do this, or else renounce all hopes of ever comprehending anything in Physics.”

Galileo and Newton, as will be noted, do not unqualifiedly share Huygens’ view that it is proper for the mathematical physicist to inquire about causes. But they would agree that if any explanation is to be given for laws of nature expressed in mathematical form, one or another type of mechanical hypothesis would be required to state the causes. Postponing for the moment the consideration of whether the investigation of causes belongs to mathematical physics, let us examine what is involved in giving a mechanical explanation of anything and why this type of explanation tends to occur in the causal interpretation of mathematically formulated laws of nature.

Two points seem to constitute the essence of mechanical theory. Both are fundamental notions and both are philosophical in the sense that they do not seem to result from the findings of experimental research. The first point is an exclusive emphasis upon efficient causes, which means the exclusion of other types of causes, especially final and formal causes, from mechanical explanation. As the chapter on CAUSE indicates, efficient causality consists in one thing acting on another. But not every sort of action by which one thing affects another is mechanical. According to the doctrine, an efficient cause is mechanical only if it consists in a moving body acting on another by impact, or if it consists in a force exerted by one body to cause motion in another or to change its quantity or direction. The notion of a force which does not work through the impact of one moving thing upon another raises the problem of action-at-a-distance to which we shall return subsequently.

The second fundamental point is an exclusive emphasis upon quantities. Mechanical explanation makes no references to qualities or other attributes of things. Paradoxically this point is sometimes expressed in terms of a distinction between primary and secondary qualities; but, as the chapters on QUANTITY and QUALITY point out, the primary qualities are all quantities. According to Locke, they are “solidity, extension, figure, motion or rest, and number”; according to Newton, “the universal qualities of all bodies whatsoever” are “extension, hardness, impenetrability, mobility, and inertia.” Others, like Galileo and Descartes, give still different enumerations, but the point remains that the only attributes of bodies which have mechanical significance are measurable quantities. Such secondary qualities, for example, as colors and tones belong to the physical world (as it is mechanically conceived) only by reduction to the local motion of particles or waves having certain velocities, lengths, or other quantitative attributes.

We need not be concerned here with what sort of reality is assigned to secondary qualities, or how their presence in experience is accounted for. These problems are discussed in other chapters, such as QUALITY and SENSE. However they are solved, the philosophy of mechanism excludes from the physical world whatever does not consist in, or cannot be reduced to, quantities of matter (or mass), motion, or force, and such related quantities as those of time and space (or distance).

The two points of mechanical theory are obviously connected, for the kind of cause which mechanical explanation employs to the exclusion of all others consists in a quantity of motion or of force. Just as obviously, mechanical explanation, dealing only in quantities and in causes which are quantitatively measurable, is precisely the type of explanation which would seem to be appropriate if one felt called upon to give an interpretation of the mathematical relationships which the mathematical physicist formulates as laws of nature. These mathematical laws are after all statements of the relations among physical quantities which have been subjected to experimental determination or measurement.

AS A PHILOSOPHICAL theory the mechanical view of nature antedates modern physical science. The atomistic conception of the world, which Lucretius expounds, contains both of the fundamental points of mechanism—the doctrine of primary and secondary qualities and the doctrine that all effects in nature are produced by efficient moving causes.

The controversy over mechanism is also ancient. Aristotle denies both points of doctrine in his criticism of the Greek atomists, Democritus and Leucippus; and in the exposition of his own physical theories he states an opposite view. To qualities and qualitative change he assigns physical reality. He explains change in terms of four types of causes, not one. He does not exclude the mechanical type of cause in his explanation of local motion. On the contrary, with respect to local motion his theory that a body in motion must be directly acted upon by a moving cause throughout the period of its motion, seems to be more mechanical than the modern theory that no cause need be assigned for the continuing uniform motion of a body along a straight line but only for a change in its direction or velocity.

What is new in modern times is not the philosophical doctrine of mechanism, but the introduction of mechanical explanation into experimental and mathematical physics, and the controversy about whether it belongs there or can be defended as useful. The so-called rise and decline of the mechanical view in modern physics is connected with experimental discoveries and mathematical formulations. It is not an alternation between success and failure on the level of philosophical argument concerning the ultimate truth of mechanical conceptions. When these conceptions are rejected, it is not for the sake of returning to opposite notions in physical theory, such as those of Aristotle, but rather because, as Einstein says, “science did not succeed in carrying out the mechanical program convincingly, and today no physicist believes in the possibility of its fulfillment.”

There is a touch of prophecy in the conversation Swift imagines taking place between Aristotle and the physicists of the 17th century. According to Swift, when Aristotle was confronted with Descartes and Gassendi, he “freely acknowledged his own mistakes in natural philosophy, because he proceeded in many things upon conjecture, as all men must do; and he found that Gassendi, who had made the doctrine of Epicurus as palatable as he could, and the vortices of Descartes, were equally exploded. He predicted the same fate to attraction, whereof the present learned are such zealous asserters. He said that new systems of nature were but new fashions, which would vary in every age; and even those who pretend to demonstrate them from mathematical principles, would flourish but a short period of time, and be out of vogue when that was determined.”

BOTH GALILEO AND DESCARTES re-state the philosophical doctrine which first appears in ancient atomism, but both re-state it in a way that suggests its utility for an experimental investigation of nature. It is significant that Galileo’s statement occurs in the context of his concern with the nature and causes of heat. He wishes to explain, he writes in Il Saggiatore, why he thinks that “motion is the cause of heat.” To do this he finds it necessary to question a prevalent notion “which is very remote from the truth”—the belief that “there is a true accident, affection, or quality, really inherent in the substance by which we feel ourselves heated.” He denies the physical reality of heat as an inherent quality of bodies on the same ground that he denies the physical reality of other qualities. “I do not believe,” he declares, “that there exists anything in external bodies for exciting tastes, smells, and sounds, but size, shape, quantity, and motion, swift or slow; and if ears, tongues, and noses were removed, I am of the opinion that shape, quantity, and motion would remain, but there would be an end of smells, tastes, and sounds, which, apart from the living creature, I regard as mere words.”

Descartes’ statement of the doctrine is bolder, perhaps, in its suggestion of a mechanical program for physical research. “Colors, odors, savors, and the rest of such things,” he writes, are “merely sensations existing in my thought.” They differ from the real properties of bodies just as much as “pain differs from the shape and motion of the instrument which inflicts it.” The true physical properties, such as “gravity, hardness, the power of heating, of attracting and purging” consist, in Descartes’ opinion, “solely in motion or its absence, and in the configuration and situation of [bodily] parts.”

As a philosophical doctrine, the mechanical view is not necessarily tied to atomism. Descartes opposes atomism as plainly as does Aristotle. Furthermore, Newton, who is an atomist, disagrees with both Descartes and the Greek atomists on one fundamental point in mechanical theory. The ancient atomists make the actual motion of one particle in collision with another the indispensable cause of a change of motion in the latter. Descartes likewise requires one motion to be the cause of another and explains gravity in terms of actual bodily motions. Newton rejects Descartes’ mechanical hypothesis of material vortices as the cause of gravitation. He seems to have this in mind, and to put Descartes in the same class with Aristotle, when he says that “hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”

The force of gravity, according to Newton, is a power of attraction which one body exercises on another without the first being in motion or coming into contact with the second. Newton acknowledges the problem of action-at-a-distance which his theory raises. For the most part he lets it stand as a problem which does not affect the mathematical results of his work. But in the Queries he attaches to his Optics he suggests, by way of solution, the hypothesis of an ether as the continuous medium through which gravitational force is exerted. In the opinion of later physicists, Newton’s hypothesis is no less mechanical than Descartes’. Nor does there seem to be any philosophical grounds for preferring one hypothesis to the other.

But Newton’s quarrel with Descartes is not on a philosophical issue. It turns on which mechanical conception, if any at all is to be offered, fits best with the mathematical laws of terrestrial and celestial motion which Newton had succeeded in formulating as universal laws of nature. Those mathematical laws, moreover, had the merit of fitting the observed phenomena and so, of realizing the scientific ideal of accurate description stated in the most generalized form. Newton’s triumph over Descartes, then, is a triumph in mathematical and experimental physics, not a triumph in philosophy.

Pope’s couplet

Nature and Nature’s Laws lay hid in Night, God said, Let Newton be, and all was light records that triumph, and celebrates the illumination of nature by the mechanical as well as the mathematical principles of Newton’s physics. Newton’s picture of the world dominates the mind of a century and controls its science. Locke speaks of “the incomparable Mr. Newton” and of “his never enough to be admired book”; Hume refers to him as the philosopher who, “from the happiest reasoning … determined the laws and forces, by which the revolutions of the planets are governed and directed”; and even Berkeley, who challenges his theories of space, time, and attraction, regrets that he must take issue with “the authority of so great a man,” a man “whom all the world admires” as the author of “a treatise on Mechanics, demonstrated and applied to nature.”

NEWTON’S ACHIEVEMENT is to have accomplished an extraordinary synthesis of all that was good in previous scientific work, and a sweeping criticism of all that was considered stultifying. That so many and such varied phenomena should be organized mathematically by a theory as simple as Newton’s, is altogether impressive. Equally astonishing is the predictive power of Newton’s laws and the explanatory power of his mechanics, not to mention the technological fruits of the latter in mechanical engineering and the invention of machinery of all sorts. Whatever difficulties are implicit in the Newtonian mechanics—subsequently to become, with new discoveries, more and more perplexing—the scope and grandeur of Newton’s book gives mechanics a commanding position with respect to the future of science for at least two centuries.

In the century between the publication of Newton’s Mathematical Principles and the publication in 1787 of Lagrange’s Mécanique analytique, “the notion of the mechanical explanation of all the processes of nature,” writes Whitehead, “finally hardened into a dogma of science.” In the next century, the mechanical dogma spreads from physics and chemistry throughout the whole domain of natural science—into biology and psychology—and even beyond that, into economics and sociology. Books bear such titles as The Mechanistic Conception of Life, The Mechanism of Human Behavior, Social Statics, Social Dynamics. At the end of the 19th century, James notes the conquests which are being made on all sides by the mechanical idea. “Once the possibility of some kind of mechanical interpretation is established,” he writes, “Mechanical Science, in her present mood, will not hesitate to set her brand of ownership upon the matter.”

James himself testifies to the persuasiveness and success of the mechanical dogma, though not without some resentment. “The modern mechanico-physical philosophy, of which we are so proud,” he says, “because it includes the nebular cosmogony, the conservation of energy, the kinetic theory of heat and gases, etc., etc., begins by saying that the only facts are collocations and motions of primordial solids, and the only laws the changes in motion which changes in collocation bring. The ideal which this philosophy strives after,” he continues, “is a mathematical world-formula, by which, if all the collocations and motions at a given moment were known, it would be possible to reckon those of any wished-for future moment, by simply considering the necessary geometrical, arithmetical, and logical implications.”

Laplace had in fact pictured a lightning calculator who, given the total configuration of the world at one instant, would be able to bring the whole future “present to his eyes.” And James quotes Helmholtz to the effect that the whole problem of physical science is “to refer natural phenomena back to unchangeable attractive and repulsive forces whose intensity depends wholly upon distance. The solubility of this problem is the condition of the complete comprehensibility of nature.”

In commenting on this, James admits that “the world grows more orderly and rational to the mind, which passes from one feature of it to another by deductive necessity, as soon as it conceives it as made up of so few and so simple phenomena as bodies with no properties but number and movement to and fro.” But he also insists that it is “a world with a very minimum of rational stuff. The sentimental facts and relations,” he complains, “are butchered at a blow. But the rationality yielded is so superbly complete in form that to many minds this atones for the loss, and reconciles the thinker to the notion of a purposeless universe, in which all the things and qualities men love … are but illusions of our fancy attached to accidental clouds of dust which will be dissipated by the eternal cosmic weather as careless as they were formed.”

WITH THE 20TH CENTURY a change occurs. The dogma of mechanism may continue to spread in other sciences and gain even wider acceptance as a popular philosophical creed, but within the domain of the physical sciences, certain mechanical conceptions become suspect and a wholesale rejection of classical mechanics (which becomes identified with Newtonian physics) is called for.

Einstein, for example, quotes the passage from Helmholtz that James had cited, in which Helmholtz goes on to say that the vocation of physics “will be ended as soon as the reduction of natural phenomena to simple forces is complete.” This “mechanical view, most clearly formulated by Helmholtz,” Einstein concedes, “played an important role in its time”; but, he adds, it “appears dull and naive to a twentieth century physicist.”

Einstein reviews the assumptions which physicists had to make in order to construct a mechanical theory of light, gravitation, and electricity. “The artificial character of all these assumptions,” he says, “and the necessity for introducing so many of them all quite independent of each other, was enough to shatter the belief in the mechanical point of view. … In the attempt to understand the phenomena of nature from the mechanical point of view,” he continues, “throughout the whole development of science up to the twentieth century, it was necessary to introduce artificial substances like electric and magnetic fluids, light corpuscles, or ether.” According to Einstein, “attempts to construct an ether in some simple way” have been “fruitless”; but what is more important in his opinion, such failures “indicate that the fault lies in the fundamental assumption that it is possible to explain all events in nature from a mechanical point of view.”

Does this mean that the contemporary physicist has found another and better way of explaining nature? Is there a non-mechanical way of explaining the phenomena, which fits the mathematical laws of experimental physics; or does discarding mechanics mean relinquishing all efforts to explain nature?

Eddington suggests an answer. “One of the greatest changes in physics between the nineteenth century and the present day,” he writes, “has been the change in our ideal of scientific explanation. It was the boast of the Victorian scientist that he would not claim to understand a thing until he could make a model of it; and by a model he meant something constructed of levers, geared wheels, squirts, and other appliances familiar to the engineer. Nature in building the universe was supposed to be dependent on just the same kind of resources as any human mechanic. … The man who could make gravitation out of cogwheels would have been a hero in the Victorian age.” Today, however, Eddington continues, “we do not encourage the engineer to build the world for us out of his material, but we turn to the mathematician to build it out of his material.”

We may turn to the mathematician’s construction of the world in his terms; but in the tradition of western thought, mathematically formulated laws of nature are not, with the single exception perhaps of the Pythagoreans, regarded as explanations of why things behave as they do or how they work. The change from the 19th to the 20th century with respect to “our ideal of scientific explanation” cannot, then, be the substitution of the mathematical for the mechanical account of why and how. The shift from mechanics to mathematics is rather a shift from explanation as the scientific ideal to the statement of laws which, while having maximum generality, remain purely descriptive. What Eddington means by building the world out of the material of mathematics seems to be the same as what Galileo means, four centuries earlier, when he says that the book of nature “is written in mathematical language.” The materials are such symbols as “triangles, circles, and other geometrical figures.” Without the help of these, Galileo writes to Kepler, nature “is impossible to comprehend.”

But does the mathematical comprehension of nature mean a causal explanation of it? More explicitly than Eddington, Galileo insists that explanation—at least in the sense of stating the causes—is not the business of the mathematical physicist. In a passage which cannot be read too often or examined too closely, he names three opinions which the philosophers have expressed about “the cause of the acceleration of natural motion.” Some, he says, “explain it by attraction to the center, others to repulsion between the very small parts of the body, while still others attribute it to a certain stress in the surrounding medium which closes in behind the falling body and drives it from one of its positions to another. Now all of these fantasies,” he continues, “and others too, ought to be examined, but it is not really worthwhile.”

They ought to be examined by philosophers, perhaps, but debating them is not worthwhile in “those sciences where mathematical demonstrations are applied to natural phenomena.” Perfectly defining the program of mathematical physics, Galileo sets himself a limited task: “merely to investigate and to demonstrate some of the properties of accelerated motion (whatever the cause of this acceleration may be).” It should be noted that of the three opinions about causes which Galileo mentions, the first, which anticipates Newtonian attraction, is no less summarily dismissed than the third, which summarizes the Aristotelian theory.

“What I call Attraction,” Newton later writes, “may be performed by impulse or by some other means unknown to me. I use that word here to signify only in general any force by which bodies tend towards one another, whatsoever be the cause.” It is well known, he asserts in the same passage of the Optics, “that bodies act one upon another by the attractions of gravity, magnetism, and electricity”; but, he goes on, “how these attractions may be performed I do not here consider.”

Newton’s attitude toward causes and explanation would seem to be identical with Galileo’s. Galileo calls opinions about causes “fantasies” and dismisses them; Newton calls them “hypotheses” and seems to banish them as resolutely. “Hypotheses are not to be regarded in experimental philosophy,” he declares in one place; and in another, having just referred to predecessors who feigned hypotheses “for explaining all things mechanically,” he says that, on the contrary, “the main business of natural philosophy is to argue from phenomena without feigning hypotheses.”

The task of the physicist who is both experimental and mathematical in his method, Newton plainly states, is “to derive two or three general principles of motion from phenomena, and afterwards to tell us how the properties and actions of all corporeal things follow from those manifest principles. [This] would be a very great step in philosophy, though the causes of those principles were not yet discovered. And therefore,” he says of his own work, “I scruple not to propose the principles of motion above mentioned, they being of very general extent, and leave their causes to be found out.”

The two or three principles of motion mentioned in this passage from the Optics are the foundation of Newton’s other great work, the Mathematical Principles of Natural Philosophy. Its title indicates the clearly conceived intention of its author to limit himself to the program of mathematical physics on which both he and Galileo seem to agree. He will not try to define “the species or physical qualities of forces”; he will only investigate “the quantities and mathematical proportions of them.” In the General Scholium with which the Mathematical Principles concludes, Newton disavows once more any knowledge of the cause of gravity. “To us it is enough,” he says, “that gravity does really exist, and acts according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.” Admitting that he has “not been able to discover the causes… of gravity from phenomena,” Newton flatly reiterates his policy: “I frame no hypotheses.”

IN VIEW OF THIS policy, how does the name of Newton come to be associated with the triumph of the mechanical point of view in physics? Why do contemporary scientists like Einstein identify Newtonian physics with classical mechanics? If a mathematical physicist, like Newton or Galileo, refrains from guessing at or asserting causes, how can he be charged with having indulged in the impurity of a mechanical explanation of the phenomena, and with having foisted a mechanical conception of the universe upon mankind?

The answer to these questions, so far as Newton is concerned, may be partly found in his own writings. He did not, it seems, entirely disavow an inquiry into the cause of attractive force, as in itself either misguided or irrelevant to science. “We must learn from the phenomena of nature,” he tells us, “what bodies attract one another, and what are the laws and properties of the attraction, before we enquire the cause by which the attraction is performed.” This statement postpones, but does not exclude, an inquiry into causes. In another statement, Newton even gives us a reason for the postponement. “In mathematics,” he says, “we are to investigate the quantities of force with their proportions consequent upon any conditions supposed; then, when we enter upon physics, we compare those proportions with the phenomena of nature, that we may know the several kinds of attractive bodies. And this preparation being made, we argue more safely concerning the physical species, causes, and proportions of the forces.”

These remarks of Newton do not give the whole answer. For the other and perhaps more important part of it, we must go to the actual development of physical science in the 17th century. The steps in this development—largely discoveries and formulations made by Galileo, Huygens, and Newton—lead to crises from which the scientists could not extricate themselves without discussing causes—the causes of gravity and of the propagation of light. We may thus be able to understand why Newton could not abandon the search for causes; and why, in the Queries he appended to the Optics, he proposes a mechanical hypothesis in order to explain how the attractive force of gravity exerts itself across great distances, and also defends his mechanical theory of light against the equally mechanical but different hypothesis of Huygens.

It might well be argued that, though Galileo’s pure position initiated modern mathematical physics, it was the persistence of impurity in the worrying about causes, or even the inescapability of such concern, which caused great scientific advances to be made. The concern about causes seems to provide, time and time again, the pivot for new discoveries. The causes are not found, but new hypotheses are made, and these, when employed, lead to wider, more general results in the form of more inclusive, unifying laws. We see this happen not only in the study of gravitation and light, but also in the investigation of heat and electricity. The concern of Faraday, for example, to explain electrical attraction and repulsion in terms of the action of contiguous particles, and to establish the existence of physical lines of force, leads to Maxwell’s theory of the electro-magnetic field; and his field equations, combined with Faraday’s speculations concerning the relation between electrical and gravitational attraction, lead to the attempt, on the part of contemporary physics, to construct a unified field theory covering all physical phenomena.

Physics may return in the 20th century to the purely mathematical character it had at the beginning of its modern development. But as may be seen in any introduction to recent physics written for the layman, it is necessary to mark the influence of mechanical conceptions upon scientific discovery and thought, in order to understand the difference between the unifying mathematical laws of the 17th and the 20th centuries. As we retrace the steps we see how fertile is the interplay between mathematical insights and mechanical hypotheses.

AS FOURIER TELLS the story of “rational mechanics,” the “discoveries of Archimedes” begin the science. “This great geometer,” he says, “explained the mathematical principles of the equilibrium of solids and fluids. About eighteen centuries elapsed before Galileo, the originator of dynamical theories, discovered the laws of motion of heavy bodies.” Statics and dynamics are related as the two parts of mechanics when that is conceived narrowly as the science which treats of the local motions of inert or inanimate bodies. The rest or equilibrium of bodies, which is the subject of statics, can be thought of as a limiting case of their motions, to which the principles of dynamics apply.

In the eighteen centuries between Archimedes and Galileo, little progress is made in mechanics. So far as statics is concerned, Archimedes, according to Galileo, by the “rigor of his demonstration” established the science in all its essentials; “since upon a single proposition in his book on Equilibrium depends not only the law of the lever but also those of most other mechanical devices.” Pascal may later enlarge statics, by showing in his treatise On the Equilibrium of Liquids that “a vessel full of water is a new principle of Mechanics, a new machine which will multiply force to any degree we choose”; in other works Pascal extends these conceptions further, as in his treatment of the pressure of air. But at the time of Galileo, it could be said that although Archimedes had offered an exemplary model of mathematical physics, no progress was made until the work of Galileo’s immediate predecessors.

Not without assistance from certain predecessors like Stevin, Galileo founds the science of dynamics. It may be wondered why, with the start made by Archimedes, no earlier application of his principles and method had been made. The answer may be found in the physics of Aristotle. His theory of the four elements carried with it a doctrine of natural motions to different natural places, drawn from the observation of fire rising, stones dropping, air bubbling up through water. Such a doctrine would prevent the search for laws of motion applicable to all bodies; and the general character of Aristotle’s physics, treating qualities as well as quantities, seems to have discouraged the application of mathematics even to the study of local motions.

The mathematical expression of the laws of motion is Galileo’s objective. His interest in the new astronomy which affirmed the motion of the earth led him, he told Hobbes, to the careful study of movements on the earth. His aim is simply to describe with precision the motions to be found in a child’s play—stones dropped and stones thrown, the one the natural motion of free fall, the other the violent motion of a projectile. It is clear to observation that the motion of a freely falling body is accelerated. But though, as a mathematical physicist, Galileo refrains from asking why this is so, he is not satisfied to know simply that it is so. He wants to know the properties of such acceleration. What is the relation of the rate of increase in velocity to the durations and distances of the fall? How much increase in velocity is acquired and how fast? What is the body’s velocity at any given point in the fall? Similarly, when Galileo turns to projectiles, he wants to know, not merely that their trajectory is consistently curvilinear, but precisely what curve the path of the projectile describes.

Galileo succeeds in answering all these questions without being perturbed by any of the philosophical perplexities connected with space and time; nor does he allow questions about the forces involved in these motions to distract him from his purpose to “demonstrate everything by mathematical methods.” With mathematical demonstration he combines observation and experiment and uses the latter to determine which mathematical conclusions can be applied to nature—which principles can be empirically verified as well as mathematically deduced.

ONE OF GALILEO’S principles, however, seems to outrun ordinary experience and to defy experimental verification. In the interpretation of his experiments on inclined planes, Galileo expresses an insight which Newton later formulates as the first law of motion, sometimes called the “law of inertia.” It declares that “every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.”

Though Newton describes his method as one of “making experiments and observations, and in drawing general conclusions from them by induction,” the law of inertia seems to be an exception; for it is difficult to say, as Hume does, that “we find by experience that a body at rest or in motion continues forever in its present state”—that is, unless it is acted on by some new force.

The condition introduced by “unless” raises Poincaré’s question: “Have there ever been experiments on bodies acted on by no forces?” If not, and if they are impossible, then James may be right in saying that “the elementary laws of mechanics” are “never matters of experience at all, but have to be disengaged from under experience by a process of elimination, that is, by ignoring conditions which are always present.” Because “the idealized experiment [which it calls for] can never be performed,” the law of inertia, according to Einstein, can be derived “only by speculative thinking consistent with observation.”

In any case, the first law of motion initiates a new departure in physics. So far as local motion is concerned, Aristotle and his followers look for the cause which keeps a moving body in motion or a stationary body at rest. According to Galileo and Newton, uniform motion continues naturally without cause. Only a change in the velocity or direction of that motion requires a cause, such as a force impressed upon it.

How radical this innovation is may be judged from its consequences in celestial mechanics, which in turn lead to a completely unified dynamics for both celestial and terrestrial motions. These advances are the work of Newton’s mathematical genius, but the ground for them had been laid by the investigations of Galileo. Galileo had resolved the curvilinear motion of a projectile into the imparted rectilinear motion and the deflecting pull of gravity. This composition of forces—sometimes called the “parallelogram law”—explains why the path of the projectile is a parabola. The path of the planets in their orbits, Kepler had previously shown, is another conical curve—an ellipse. But Kepler, lacking the first law of motion, could theorize physically about the cause of the planetary orbits only by looking for a force, projected outward from the sun, which would sweep around to keep the planets moving in their paths. On the other hand, a follower of Galileo, as Whitehead points out, would seek “for normal forces to deflect the direction of motion along the curved orbit.” He would look for a force pulling the planet off its own rectilinear course inward toward the sun.

That is precisely what Newton did. When the problem, which others had been able to formulate, was put to Newton, he simply went to his study for the solution. He had solved that problem some years before. He had found the law of the force which, attracting the planets to the sun, would produce their elliptical paths and the other proportionalities stated in Kepler’s purely descriptive laws.

With that single discovery, Galileo’s terrestrial dynamics becomes a celestial one, too; and the traditional separation of the heavens from the earth is overcome. Newton goes even further. He guesses, and then shows by arithmetic, that the force deflecting the planets around the sun and the moon around the earth, is the same force which makes apples fall and stones heavy in the hand. He generalizes this insight in his famous inverse-square law: “Every particle of matter attracts every other particle of matter with a force proportional to the mass of each and to the inverse square of the distance between them.”

Accordingly, the world can be pictured as one in which material particles each have position in absolute space and a determinate velocity. The velocity of each particle causes the change of its position, and changes in velocity are caused by forces, the amounts of which are determined by positions. From his laws of motion and this simple law of force Newton is able, by mathematical deduction, to account for the perturbations of the moon, the oblateness of the earth, the precession of the equinoxes, the solar and lunar tides, and the paths of the comets.

But is Newton’s law of force as simple as it appears to be at first? Its mathematical meaning is plain enough, and its application to measured phenomena reveals its descriptive scope. When we ask, however, about its physical significance, we raise difficult questions concerning the nature of this attractive force and how it operates. To call it the “force of gravity” and to point out that this is a familiar force which everyone experiences in his own person hardly answers the question.

GALILEO WOULD NOT have tried to answer it. In his Dialogues Concerning the Two Great Systems of the World, one of the characters, Simplicio, refers to that manifest cause which “everyone knows is gravity.” To this Salviati replies: “You should say that everyone knows it is called gravity. I do not question you about the name,” he continues, “but about the essence of the thing”; and that, he concludes, is precisely what cannot be defined.

A physicist like Huygens, who expects the explanation of natural effects to be expressed in the familiar mechanical terms of bodily impact, has other objections. “I am not at all pleased,” he writes to Leibnitz about Newton, “with any theories which he builds on his principle of attraction, which seems to me absurd.” What shocks Huygens is a scandal that Newton himself cannot avoid facing. It is the scandal of action-at-a-distance—of the force of gravity being propagated instantaneously across great distances and producing effects at some remote place but no effects along the way. Newton recognizes the strangeness of such a force. In a letter to Bentley, he echoes Huygens’ protest to Leibnitz. “That gravity should be innate, inherent and essential to matter,” he says, “so that one body may act on another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.”

The absurdity of action-at-a-distance seems to be recognized by common sense and philosophy alike. “No action of an agent,” Aquinas remarks, “however powerful it may be, acts at a distance except through a medium”; and Kant, who regards Newtonian physics as the model of a rational science of nature, speaks of “a force of attraction without contact” as a “chimerical fancy” which “we have no right to assume.” How can Newton avoid this absurdity without violating his rule of method in mathematical physics—not to frame hypotheses?

Newton’s dilemma can perhaps be stated in the following alternatives: either the inverse-square law of gravitational attraction is to be treated as a purely mathematical, and hence a purely descriptive, proposition of great simplicity and generality; or it must be given physical meaning by a causal explanation of how gravitational force operates. On the first alternative, Newton can avoid framing hypotheses, but the physical meaning of the concepts he employs to state the mathematical law is then left dark. On the second alternative, he can solve the mechanical problem created by such words in his law as “attracts” and “force,” but only by going beyond mathematical physics into the realm of mechanical hypotheses.

Newton seems to take the first alternative in his Mathematical Principles of Natural Philosophy, and the second in his Optics. There he proposes the hypothesis of an ethereal medium to explain the attractive force of gravity. “Is not this medium,” he asks, “much rarer within the dense bodies of the sun, stars, planets, and comets, than in the empty celestial spaces between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavoring to go from the denser parts of the medium towards the rare? … And though this increase of density may at great distances be exceeding slow, yet if the elastic force of this medium be exceeding great, it may suffice to impel bodies from the denser parts of the medium towards the rarer, with all that power which we call gravity.”

The hypothesis fits the law of gravitation if, as Maxwell points out, “the diminution of pressure [in the ether] is inversely as the distance from the dense body.” Newton recognized, according to Maxwell, that it then becomes necessary “to account for this inequality of pressure in this medium; and as he was not able to do this, he left the explanation of the cause of gravity as a problem for succeeding ages. … The progress made towards the solution of the problem since the time of Newton,” Maxwell adds, “has been almost imperceptible.”

THE PROBLEM OF the mechanical properties of an ethereal medium occurs in another form in the field of optics. Here it is complicated by the rivalry between two theories of light—Newton’s corpuscular theory and Huygens’ undulatory or wave theory. Each involves a mechanical hypothesis—one concerning the motion of particles emitted from the light source, and one concerning the wave-like propagation of the light impulse through a medium. Both theories involve the motion of particles. In their explanation of the oar which appears bent in the water, both appeal to the action of the particles in the refracting medium on the light corpuscles or the light waves.

Both theories, furthermore, are expressed by their authors in a mathematical form which permits the deduction of quantitative facts like the equality of the angles of incidence and of reflexion, the bending of the light ray in refraction according to the law of sines, and the recently discovered fact of the finite velocity of light. Huygens’ book gives prominence to the explanation of the strange phenomena of double refraction found in “a certain kind of crystal brought from Iceland”—Iceland spar. But both theories seem to be equally competent in dealing with the established facts of reflexion and refraction, and the new facts about dispersion.

For a century at least, their rivalry resembles that between the Ptolemaic and Copernican theories at a time when they seemed equally tenable so far as accounting for the phenomena was concerned. Later, new discoveries, such as those by Young and Fresnel, tend to favor the wave theory of light; but the rivalry continues right down to the present day. It remains unresolved, at least to an extent which prompts Eddington, in reviewing contemporary controversy about the nature of light and electricity, to suggest the invention of the word “wavicle” to signify the complementary use of both particles and waves in the modern theory of radiation.

Unlike the rivalry between the Ptolemaic and Copernican systems, which seemed for a while to be entirely a matter of different mathematical descriptions of the same phenomena, the conflict between these two theories of light involves from the very beginning an issue between diverse mechanical hypotheses to explain the phenomena. That issue is argued not only with respect to the adequacy of either theory to explain such phenomena as the rectilinear propagation of light and its different behavior in different mediums; but it is also debated in terms of the underlying mechanical conceptions. As gravitational force acting at a distance raises a mechanical problem which Newton’s ether is not finally able to solve, so Huygens’ ether as the medium through which light is propagated in waves raises mechanical problems which, if insoluble (as they seem to be), contribute even more heavily to the general scientific scandal of mechanics.

The two authors take different attitudes toward hypotheses and mechanical explanation. Huygens, as we have seen, begins his book with the express intention to “investigate … the causes” and to express them “in terms of mechanical motions.” Newton, on the other hand, begins his with a reiteration of his disavowal of hypotheses. “My design in this book,” he writes, “is not to explain the properties of light by hypotheses, but to propose and prove them by reason and experiments.” Nevertheless, Newton’s explanation of how the prism produces from white light the band of colors in the spectrum seems to require the assumption of a distinct kind of light corpuscle for each color; and, in addition, the assumption that, although all light particles have the same velocity when they travel together making white light, separate particles for different colors are differently refrangible, that is, differently susceptible to the action of the particles in the refracting medium of the glass.

Perhaps only in Newton’s somewhat artificially restricted sense of the word “hypothesis” could these assumptions escape that denomination. In any case, the existence of Huygens’ rival theory prevented his escaping a controversy about hypotheses. In the Queries attached to his Optics, he engages in that controversy with an acumen which shows another side of his genius.

HUYGENS’ WAVE THEORY requires what anybody would have to call an hypothesis and requires it from the very start. “It is inconceivable,” he writes, “to doubt that light consists in the motion of some sort of matter.” He immediately rejects the notion that light rays consist in the “transport of matter coming to us from the [luminous] object, in the way in which a shot or an arrow traverse the air”—if for no other reason, because “the rays traverse one another without hindrance.” The similarity between the phenomena of light and the phenomena of sound suggests to him the “way that light spreads,” and causes him to extend the mechanics of sound—conceived as a wave motion—to light.

“We know that by means of air, which is an invisible and impalpable body,” Huygens argues, “sound spreads around the spot where it has been produced, by a movement which is passed on successively from one part of air to another; and that the spreading of this movement, taking place equally on all sides, ought to form spherical surfaces ever enlarging and which strike our ears. Now there is no doubt at all that light also comes from the luminous body to our eyes by some movement impressed on the matter which is between the two…. If, in addition, light takes time for its passage… it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as sound does, by spherical surfaces and waves; for I call them waves from their resemblance to those which are seen to be formed in water when a stone is thrown into it.”

Huygens is aware, however, that the analogy between light and sound is far from perfect. “If one examines,” he says, “what this matter may be in which the movement coming from the luminous body is propagated, one will see that it is not the same that serves for the propagation of sound. … This may be proved,” he goes on, “by shutting up a sounding body in a glass vessel from which the air is withdrawn.” An alarm clock beating its bell in a jar without air makes no sound, but a jar without air is no less transparent than one with air. Since when “the air is removed from the vessel the light does not cease to traverse it as before,” and since waves have to be waves of something, and light waves cannot be waves of air, there must be waves of a substance, says Huygens, “which I call ethereal matter.”

This ether, a transparent medium permeating the whole universe, proves to be what Einstein calls the enfant terrible in the family of hypothetical physical substances. Postulated by Huygens in order to explain light mechanically, it in turn calls for a mechanical account of its own extraordinary properties. Huygens does not avoid this new problem, but neither does he undertake to solve it completely.

Suppose “one takes a number of spheres of equal size, made of some very hard substance, and arranges them in a straight line, so that they touch one another.” Then, says Huygens, “one finds, on striking with a similar sphere against the first of these spheres, that the motion passes as in an instant to the last of them, which separates itself from the row, without one’s being able to perceive that the others have been stirred.” This type of motion in the ether would account for “the extreme velocity of light” and yet “this progression of motion is not instantaneous,” as the motion of light also is not.

“Now in applying this kind of movement to that which produces light,” Huygens continues, “there is nothing to hinder us from estimating the particles of the ether to be of a substance as nearly approaching to perfect hardness and possessing a springiness as prompt as we choose.” Beyond this Huygens does not go. “It is not necessary to examine here,” he says, “the causes of this hardness, or of that springiness…. Though we shall ignore the true cause of springiness we still see that there are many bodies which possess this property; and thus there is nothing strange in supposing that it exists also in little invisible bodies like the particles of the ether.”

But difficulties which Huygens did not foresee make his ether more than a strange supposition—almost a mechanical impossibility. Huygens had thought that light waves are transmitted in the ether in the way that sound waves are in the air, that is, longitudinally, the direction in which the individual particles vibrate being the same as the direction of the wave motion itself. But when, in the 19th century, it was found that the phenomena of the polarization of light could not be explained by the corpuscular theory, but only by the wave theory (thus shifting the scales decisively in favor of the latter), it was also found that the wave theory could explain polarization only on the assumption that the motion of the ether particles which produce the light waves is not longitudinal, but transverse, that is, in a direction perpendicular to the waves produced by the vibration of the particles.

As Fresnel pointed out at the time, “the supposition that the vibrations were transverse was contrary to the received ideas on the nature of the vibration of elastic fluids.” They had all involved, as in the case of air as the medium for sound, a longitudinal transmission. The character of the ether is changed by the requirement that its particles vibrate transversely. It ceases to be an air-like ether and must be imagined as a jelly-like ether.

The task which Huygens had postponed—that of giving a mechanical explanation of the ether he had posited in order to state the mechanics of light—becomes in consequence far more difficult, if not impossible. In their efforts to construct “the ether as a jelly-like mechanical substance, physicists,” according to Einstein, had to make so many “highly artificial and unnatural assumptions,” that they finally decided to abandon the whole program of mechanical explanation.

OF NEWTON’S two objections to the wave theory of light, the second by itself seems to create an insuperable difficulty for Huygens’ ether, even before the realization that it must be a jelly-like medium.

Newton’s first objection is that any wave theory is inconsistent with the fact of the rectilinear propagation of light. “If light consisted in pression or motion, propagated either in an instant or in time, it would bend into the shadow; for,” he points out, “pression or motion cannot be propagated in a fluid in right lines, beyond an obstacle which stops part of the motion, but will bend and spread every way into the quiescent medium which lies beyond the obstacle. … The waves, pulses or vibrations of the air, wherein sound consists, bend manifestly, even though not so much as the waves of water.”

This objection loses its force when, in the 19th century, light’s bending is experimentally discovered. But Newton’s other objection gains force when, two centuries after he made it, a jelly-like density is imposed upon the ether by the experimental facts of polarization. This second objection does not point to the inadequacy of the wave theory with respect to the phenomena which must be described, but rather calls attention to its inconsistency with celestial mechanics.

Light travels through inter-stellar space. But so also do the planets. Newton’s astronomy accounts for the motion of the planets with great precision, only on the supposition of no resistance from a medium. “To make way for the regular and lasting motions of the planets and comets,” he writes, “it is necessary to empty the heavens of all matter, except perhaps … such an exceedingly rare ethereal medium as we described above.” Here he refers to the ether he himself had posited as a possible cause of gravitational attraction. Its resistance, he thinks, is “so small as to be inconsiderable.” The “planets and comets and all gross bodies [can] perform their motions more freely in this ethereal medium than in any fluid, which fills all space adequately without leaving any pores.” Such “a dense fluid … serves only to disturb and retard the motions of those great bodies, and make the frame of nature languish.” Since it “hinders the operations of nature,” and since “there is no evidence for its existence,” Newton concludes that “it ought to be rejected.”

The next conclusion follows immediately. “If it be rejected, the hypotheses that light consists in pression or motion, propagated through such a medium, are rejected with it.” Newton would seem entitled to draw these conclusions because, no matter how slight the density of ethereal matter, the use of the ether in the wave theory of light involves some interaction between the particles of ether and the particles of matter. Unless such interaction takes place, no explanation can be given of the change in the velocity of light when it enters a medium like glass or water. Since in Newton’s universe there is no difference between terrestrial and celestial matter, Newton cannot accept an ether which interacts with the matter of glass or water, but does not interact with the matter of the planets.

This objection of Newton’s, pointing to an inconsistency between the kind of ether required by the wave theory of light and the unretarded motion of the heavenly bodies, appears not to have been answered, but only waived, at the time of the wave theory’s ascendancy. The famous Michelson-Morley experiment on ether drift later re-opens Newton’s penetrating query about the ether. But this occurs at a time when physicists are prepared to give up not only the ether, but also with it the mechanical explanations of gravity and light which it had brought into conflict with one another.

BEFORE THE MECHANICAL dogma runs its course, it has a career in other fields of physical inquiry. The phenomena of heat, magnetism, and electricity are explored and explained under its inspiration. The history of these subjects is marked by a very rash of hypotheses. Each time mechanical explanation is attempted for a new domain of phenomena, new substances are added.

The postulated entities—calorific, magnetical, and electric fluids—are unobservable and without weight. In Newton’s terms, they are “occult”; though, it must be added, they are no more occult than the ether Newton himself postulated to explain gravity or the ether Huygens postulated to explain light. In fact, each of these new substances seems to resemble the aeriform or fluid ether, just as each is conceived, as the gravitational or optical ether was earlier conceived, in the context of the issue of action-at-a-distance as opposed to action-by-contact. They would seem to be unavoidable in a mechanical account of the radiations of heat, magnetism, and electricity.

The phenomena of heat, Lavoisier writes, are “difficult to comprehend … without admitting them as the effects of a real and material substance, or very subtle fluid. …. Wherefore,” he continues, “we have distinguished the cause of heat, or that exquisitely elastic fluid which produces it, by the term of caloric.” Lavoisier declares himself “unable to determine whether light be a modification of caloric, or if caloric be, on the contrary, a modification of light.” But in terms of observed effects he does attribute ether-like properties to caloric. “This subtle matter,” he says, “penetrates through the pores of all known substances”; for “there are no vessels through which it cannot escape.”

The theory of caloric serves its purpose before it gives way to the theory of heat as molecular motion, a conception which can be integrated with the molecular, or kinetic, theory of gases. “The development of the kinetic theory of matter,” writes Einstein, “is one of the greatest achievements directly influenced by the mechanical view.” It is all the more striking, therefore, that in the opening pages of Fourier’s Analytical Theory of Heat—wherein he reviews the triumphs of explanation achieved by Newton and his successors—Fourier should so flatly assert: “But whatever may be the range of mechanical theories, they do not apply to the effects of heat. These make up a special order of phenomena which cannot be explained by the principles of motion and equilibrium.”

It is equally striking that Lavoisier seems to have anticipated not only the mechanical theory of heat, but the possibility of a purely mathematical treatment of the phenomena. “We are not obliged to suppose [caloric] to be a real substance,” he writes; it is sufficient “that it be considered as the repulsive cause, whatever that may be, which separates the particles of matter from each other, so that we are still at liberty to investigate its effects in an abstract and mathematical manner.”

The second of these two things is precisely what Fourier proposes to undertake, but he disavows any interest in the first, namely, the explanation of heat in terms of the mechanical separation of particles by repulsion. In language which resembles Newton’s disavowal of concern with the cause of attraction, Fourier declares that “primary causes are unknown to us, but are subject to simple and constant laws, which may be discovered by observation.”

In another place he writes: “Of the nature of heat only uncertain hypotheses could be formed, but the knowledge of the mathematical laws to which its effects are subject is independent of all hypothesis.” Fourier’s aim, therefore, with respect to “the very extensive class of phenomena, not produced by mechanical forces, but resulting simply from the presence and accumulation of heat,” is “to reduce the physical questions to problems of pure analysis” and “to express the most general conditions of the propagation of heat in differential equations.” He expresses his indebtedness to Descartes for “the analytical equations” which that mathematician “was the first to introduce into the study of curves and surfaces,” but “which are not restricted to the properties of figures, and those properties which are the object of rational mechanics.” These equations, he insists, “extend to all general phenomena,” and “from this point of view, mathematical analysis is as extensive as nature itself.”

This strongly worded statement affirms the mathematical character of nature as the support and justification for a purely mathematical physics. If Fourier’s remarks about causes and hypotheses are reminiscent of Newton in his mathematical mood, how much more is Fourier’s faith in pure mathematical analysis reminiscent of Galileo. Like Galileo, and unlike Newton, Fourier never deviates from his indifference to causes and never softens his judgment of the incompetence and irrelevance of mechanics to the subject he is investigating. His trust in mathematical analysis, which is able by itself to yield and organize physical discoveries, not only revives the spirit of Galileo, but also seems to have inspired Clerk Maxwell to turn from a mechanical to a mathematical theory of electricity.

Certain of Fourier’s mathematical achievements, such as his theory of dimensions, prove useful to Maxwell. More important, perhaps, is the fact that Maxwell’s predictions about the propagation of electro-magnetic waves, later experimentally verified by Hertz, are the result of mathematical analysis. With such a demonstration of the power of mathematics to work fruitfully with experiment, and without any aid from mechanical hypotheses, Maxwell gives up the attempt to formulate a mechanics for his equations describing the electro-magnetic field. He is quite content to let his field theory state the mathematical structure of the phenomena.

Between Fourier and Maxwell comes Faraday. One of the greatest experimenters in the whole tradition of science, Faraday discovers the phenomena whose mathematical structure Maxwell later develops. He prepares the way for Maxwell’s application to electricity and magnetism of the method Fourier had practiced. His speculations concerning the relation of electrical and gravitational force point ahead, beyond Maxwell, to the possibility of a field theory which might unify all physical phenomena under a single set of mathematical laws.

Faraday sees no incompatibility between experimentation and speculation. On the contrary he says that “as an experimentalist I feel bound to let experiment guide me into any train of thought which it may justify; being satisfied that experiment, like analysis, must lead to strict truth, if rightly interpreted; and believing also that it is in its nature far more suggestive of new trains of thought and new conditions of natural power.” Faraday’s faith seems to have been amply justified. His experiments not only discovered a stunning number of new facts, but the speculations to which they led transformed the whole mode of thinking about electricity and magnetism, and, to some extent, the whole of physics.

The Elizabethan Gilbert, with his bold and brilliantly handled thesis that the earth is a magnet, had made magnetism appear something more than a random phenomenon occasionally met with in nature. But not until Faraday’s discovery of diamagnetism, announced in a memoir On the Magnetic Condition of All Matter, would anyone have dared to say that “all matter appears to be subject to the magnetic force as universally as it is to the gravitating, the electric and the chemical or cohesive forces.” Of electricity, he can only predict, as the result of his protracted experimental investigations, that “it is probable that every effect depending upon the powers of inorganic matter … will ultimately be found subordinate to it.”

These remarks indicate the controlling theme of Faraday’s researches, namely, the convertibility and unity of natural forces. It seems to have been suggested to him by the discovery that both electrical and magnetic forces obey the same simple inverse-square law as the force of gravitational attraction. The fact that certain forces obey the same law or that their action can be described by the same equations, would not of itself reveal whether one of these forces is primary or all are derivative from some other primary force. But it would suggest questions to be asked by experiment.

Gilbert compares magnetism and electricity but he is not able to convert one into the other. Oersted, before Faraday, is the first to establish one aspect of their convertibility. He shows that an electric current has a magnetic effect. Faraday succeeds in showing the reverse—that a magnetic current has electrical power. He expresses his fascination with such reversibilities in his remarks on the electrical torpedo fish. “Seebeck,” he writes, “taught us how to commute heat into electricity; and Peltier has more lately given us the strict converse of this, and shown us how to convert electricity into heat…. Oersted showed how we were to convert electric into magnetic forces, and I had the delight of adding the other member of the full relation, by reacting back again and converting magnetic into electric forces. So perhaps in these organs, where nature has provided the apparatus by means of which the fish can exert and convert nervous into electric force, we may be able, possessing in that point of view a power far beyond that of the fish itself, to reconvert the electric into the nervous force.”

Faraday demonstrates still another such reversibility in nature. The nature of his discovery is indicated by the titles of the papers in which he announces it: On the Magnetization of Light and the Illumination of Magnetic Lines of Force and The Action of Electric Currents on Light. These papers, in his opinion, “established for the first time, a true, direct relation and dependence between light and the magnetic and electric forces”; and he concludes them with an explicit statement of the central theme of all his researches and speculations.

“Thus a great addition is made,” he writes, “to the facts and considerations which tend to prove that all natural forces are tied together and have one common origin. It is no doubt difficult in the present state of our knowledge to express our expectation in exact terms; and, though I have said that another of the powers of nature is, in these experiments, directly related to the rest, I ought, perhaps, rather to say that another form of the great power is distinctly and directly related to the other forms.”

ONE FORM OF the “great power” remained to be connected with such “other forms” as those of light, heat, electricity, and magnetism. That was the power of gravitational force. Faraday comes to this last stage of his speculations concerning the unity of nature’s powers in terms of his conception of “lines of force” and of what later came to be called “the field of force.”

The earliest theories of electricity and magnetism, in an orthodox atomistic vein, had conceived them as exerting an influence by means of the effluvia which they emitted. Newton, for example, speculates on “how the effluvia of a magnet can be so rare and subtle, as to pass through a plate of glass without any resistance or diminution of their force, and yet so potent as to turn a magnetic needle beyond the glass.” When electrical conduction is later discovered, effluvia are replaced by fluids, on the analogy of caloric as the fluid conductor of heat. But when Faraday finds that he can induce from one current to another, he becomes interested in the dielectric, non-conducting medium around the circuits. He is strongly averse to any theory which involves action-at-a-distance, and so he argues that induction takes place by the action of contiguous particles. To support that argument he shows experimentally that electrical induction can “turn a corner.”

From his study of all the phenomena of magnetism, Faraday forms the conception of “lines of force” and concludes that there is “a center of power surrounded by lines of force which are physical lines essential both to the existence of force within the magnet and to its conveyance to, and exertion upon, magnetic bodies at a distance.” He says of this “idea of lines of force” that “all the points which are experimentally established with regard to [magnetic] action, i.e., all that is not hypothetical, appear to be well and truly represented by it”; and he adds: “Whatever idea we employ to represent the power ought ultimately to include electric forces, for the two are so related that one expression ought to serve for both.”

Subsequently Faraday satisfies himself as to the physical reality of electrical lines of force in addition to the magnetic lines. The compulsion of his interest in the unity of nature then drives him to speculate about gravitational force. He begins by admitting that, “in the case of gravitation, no effect sustaining the idea of an independent or physical line of force is presented to us; as far as we at present know, the line of gravitation is merely an ideal line representing the direction in which the power is exerted.” But encouraged, perhaps, by Newton’s repeated references to “the attractions of gravity, magnetism, and electricity,” and by Newton’s letter to Bentley which he interprets as showing Newton to be “an unhesitating believer in physical lines of gravitating force,” Faraday goes to work experimentally.

The report of these researches On the Possible Relation of Gravity to Electricity opens with the re-statement of Faraday’s central theme. “The long and constant persuasion that all the forces of nature are mutually dependent, having one origin, or rather being different manifestations of one fundamental power, has made me often think of establishing, by experiment, a connexion between gravity and electricity, and so introducing the former into the group, the chain of which, including also magnetism, chemical force and heat, binds so many and such varied exhibitions of force together by common relations.” His experiments, he tells us, unfortunately “produced only negative results,” but that does not shake his “strong feeling of the existence of a relation between gravity and electricity.”

THOUGH FARADAY FAILS to prove “that such a relation exists,” he does bequeath, as a legacy to 20th century physics, the problem of a field theory which would embrace both gravitational and electrical force. But whereas Faraday conceives the problem mechanically in terms of the physical reality, as well as unity, of all lines of force, in which contiguous particles act on one another, those who inherit the problem from him cease to concern themselves with the physical existence of “lines of force” and their mechanical basis in the action and reaction of bodies. Influenced by the amazing generality implicit in Maxwell’s field equations, they proceed to search for a purely mathematical statement of nature’s structure.

In the judgment of the 20th century physicist mathematics may at last succeed in doing precisely what mechanics, from Newton to Faraday, kept promising but forever failing to do. If the unity of nature can be expressed in a single set of laws, they will be, according to Einstein, laws of a type radically different from the laws of mechanics. Taking the form of Maxwell’s equations, a form which appears “in all other equations of modern physics,” they will be, he writes, “laws representing the structure of the field.”

In saying that “Maxwell’s equations are structure laws” and that they provide “a new pattern for the laws of nature,” Einstein means to emphasize their non-mechanical character. “In Maxwell’s theory,” he writes, “there are no material actors.” Whereas “Newton’s gravitational laws connect the motion of a body here and now with the action of a body at the same time in the far distance,” Maxwell’s equations “connect events which happen now and here with events which will happen a little later in the immediate vicinity.” Like the equations which describe “the changes of the electro-magnetic field, our new gravitational laws are,” according to Einstein, “also structure laws describing the changes of the gravitational field.”

The heart of the difference between a “structure law” and a mechanical law seems to be contained in Einstein’s statement that “all space is the scene of these laws and not, as for mechanical laws, only points in which matter or changes are present.” This contrast between matter and space brings to mind the difference between physics and geometry. Yet Einstein’s repeated reference to “changes” in these space-structures also reminds us that the electrical and gravitational fields are not purely geometrical, but physical as well.

The structure laws of the new physics may be geometrical in form, but if they are to have any physical meaning, can they entirely avoid some coloring by the mechanical conceptions which have been traditionally associated with the consideration of matter and motion? At least one contemporary physicist appears to think that mechanics survives to bury its undertakers. After describing the development in which geometry progressively “swallowed up the whole of mechanics,” Eddington observes that “mechanics in becoming geometry remains none the less mechanics. The partition between mechanics and geometry,” he continues, “has broken down and the nature of each of them has diffused through the whole”; so that “besides the geometrisation of mechanics, there has been a mechanisation of geometry.”

According to this view, it is not mechanics, but classical mechanics, which the new physics has abandoned. The character of the mechanics seems to have altered with the character of the mathematical formulations. Field theory, dealing with contiguous areas and successive events, avoids the problem of action-at-a-distance and also apparently that problem’s classical solution in terms of the action of contiguous particles. But another sort of mechanics may be implicit in the field equations which connect events in one area with events in the immediate vicinity. If those equations had been available to him, Newton might have expressed his theory of a variably dense ether—analogous to the modern conception of a variably filled or variably curved space—in terms of structure laws describing the gravitational field.

WE ARE LEFT with a number of questions. Is the story of mechanics the story of its rise and decline or the story of its changing role—now dominant, now subordinate; now more manifest, now more concealed—at all stages in the development of a physics which is committed to being both mathematical and experimental? Do the status and character of mechanical conceptions change with changes in the form of the mathematical laws which describe the phenomena? Can physics be totally devoid of mechanical insight and yet perform experiments which somehow require the scientist to act on bodies and to make them act on one another? Could a pure mathematical physics have yielded productive applications in mechanical engineering without the intermediation of mechanical notions of cause and effect?

Whichever way these questions are answered, we face alternatives that seem to be equally unsatisfactory. Either experimental physics is purely mathematical and proclaims its disinterest in as well as its ignorance of causes; or physics cannot be experimental and mathematical without also being mechanical, and without being involved in a search for causes which are never found.

To the layman there is something mysterious about all this. He stands in awe of the physicist’s practical mastery of matter and its motions, which he naively supposes to depend upon a scientific knowledge of the causes, while all the time the scientists protest that the causes remain unknown to an experimental and mathematical physics. Mechanical explanations may be offered from time to time, but the various “forces” they appeal to can be understood only from their effects, and are nothing more than verbal shorthand for the formulae or equations which express the mathematical laws. Yet they remain cause-names, and seem to stimulate advances in science—both experimental and mathematical—almost as a consequence of the exasperating elusiveness of these hidden causes.

Certain philosophers hold a view which suggests that the clue to the mystery may lie in the word “hidden.” Causes exist and we can control them to build machines and explode bombs, but we cannot with our senses catch them in the very act of causing, or perceive the inwardness of their operation. If the fact that they are thus unobservable means that they are occult, then all causes are occult—not least of all the mechanical type of cause which consists in the impact of one body upon another. In the century in which physicists tried to avoid the scandal of forces acting at a distance by postulating mechanical mediums through which one body acted directly on another, philosophers like Locke and Hume express their doubts that such causal action is any less occult than Newton had said Aristotle’s causes were.

“The passing of motion out of one body into another,” Locke thinks, “is as obscure and unconceivable, as how our minds move or stop our bodies by thought. … The increase of motion by impulse, which is observed or believed sometimes to happen, is yet harder to understand. We have by daily experience, clear evidence of motion produced both by impulse and by thought; but the manner how, hardly comes within our comprehension; we are equally at a loss in both.” In Locke’s judgment we will always remain “ignorant of the several powers, efficacies, and ways of operation, whereby the effects, which we daily see, are produced.” If scientific knowledge is knowledge of causes, then “how far soever human industry may advance useful and experimental philosophy in physical things, scientifical will still be out of our reach.”

When we try to observe efficient causes at work, what do we see? Hume answers that we only see one thing happening after another. “The impulse of one billiard-ball is attended with motion in the second. This is the whole that appears to the outward senses.” Nor can we form any “inward impression” of what takes place at the moment of impact. “We are ignorant,” he writes, “of the manner in which bodies operate on each other”; and we shall always remain so, for “their force or energy is entirely incomprehensible.”

As the chapter on CAUSE indicates, Aristotle holds an opposite view of the matter. What takes place in efficient causation may be imperceptible, but it is not incomprehensible. All causes may be occult so far as the senses are concerned, but they are not obscure to the intellect. But Aristotle would also insist that the action of efficient causes cannot be understood if they are totally isolated from other causes—material, formal, final. A purely mechanical physics, in his opinion, defeats itself by its basic philosophical tenets, which exclude all properties that are not quantitative and all causes except the efficient. Only a different metaphysics—one which conceives physical substances in terms of matter and form, or potentiality and actuality—can yield a physics which is able to deal with causes and explain the phenomena; but such an Aristotelian physics, from the modern point of view, stands condemned on other grounds. It is not experimental. It is not productive of useful applications. It is not mathematical; nor is it capable of comprehending all the phenomena of nature under a few simple, universal laws.

OUTLINE OF TOPICS

1. The foundations of mechanics

   • 1a. Matter, mass, and atoms: the primary qualities of bodies
   • 1b. The laws of motion: inertia; the measure of force; action and reaction
   • 1c. Space and time in the analysis of motion

2. The logic and method of mechanics

   • 2a. The role of experience, experiment, and induction in mechanics
   • 2b. The use of hypotheses in mechanics
   • 2c. Theories of causality in mechanics

3. The use of mathematics in mechanics: the dependence of progress in mechanics on mathematical discovery

   • 3a. Number and the continuum: the theory of measurement
   • 3b. The geometry of conics: the motion of planets and projectiles
   • 3c. Algebra and analytic geometry: the symbolic formulation of mechanical problems
   • 3d. Calculus: the measurement of irregular areas and variable motions

4. The place, scope, and ideal of the science of mechanics: its relation to the philosophy of nature and other sciences

   • 4a. Terrestrial and celestial mechanics: the mechanics of finite bodies and of particles or atoms
   • 4b. The explanation of qualities and qualitative change in terms of quantity and motion
   • 4c. The mechanistic account of the phenomena of life

5. The basic phenomena and problems of mechanics: statics and dynamics

   • 5a. Simple machines: the balance and the lever
   • 5b. The equilibrium and motion of fluids: buoyancy, the weight and pressure of air, the effects of a vacuum
   • 5c. Stress, strain, and elasticity: the strength of materials
   • 5d. Motion, void, and medium: resistance and friction
   • 5e. Rectilinear motion
     • (1) Uniform motion: its causes and laws
     • (2) Accelerated motion: free fall
   • 5f. Motion about a center: planets, projectiles, pendulum
     • (1) Determination of orbit, force, speed, time, and period
     • (2) Perturbation of motion: the two and three body problems

6. Basic concepts of mechanics

   • 6a. Center of gravity: its determination for one or several bodies
   • 6b. Weight and specific gravity: the relation of mass and weight
   • 6c. Velocity, acceleration, and momentum: angular or rectilinear, average or instantaneous
   • 6d. Force: its kinds and its effects
     • (1) The relation of mass and force: the law of universal gravitation
     • (2) Action-at-a-distance: the field and medium of force
     • (3) The parallelogram law: the composition of forces and the composition of velocities
   • 6e. Work and energy: their conservation; perpetual motion

7. The extension of mechanical principles to other phenomena: optics, acoustics, the theory of heat, magnetism, and electricity

   • 7a. Light: the corpuscular and the wave theory
     • (1) The laws of reflection and refraction
     • (2) The production of colors
     • (3) The speed of light
     • (4) The medium of light: the ether
   • 7b. Sound: the mechanical explanation of acoustic phenomena
   • 7c. The theory of heat
     • (1) The description and explanation of the phenomena of heat: the hypothesis of caloric
     • (2) The measurement and the mathematical analysis of the quantities of heat
   • 7d. Magnetism: the great magnet of the earth
     • (1) Magnetic phenomena: coition, verticity, variation, dip
     • (2) Magnetic force and magnetic fields
   • 7e. Electricity: electrostatics and electrodynamics
     • (1) The source of electricity: the relation of the kinds of electricity
     • (2) Electricity and matter: conduction, insulation, induction, electrochemical decomposition
     • (3) The relation of electricity and magnetism: the electromagnetic field
     • (4) The relation of electricity to heat and light: thermoelectricity
     • (5) The measurement of electric quantities

REFERENCES

To find the passages cited, use the numbers in heavy type, which are the volume and page numbers of the passages referred to. For example, in 4 Homer: Iliad, BK II [265-283] 12d, the number 4 is the number of the volume in the set; the number 12d indicates that the passage is in section d of page 12.

Page Sections: When the text is printed in one column, the letters a and b refer to the upper and lower halves of the page. For example, in 53 James: Psychology, 116a-119b, the passage begins in the upper half of page 116 and ends in the lower half of page 119. When the text is printed in two columns, the letters a and b refer to the upper and lower halves of the left-hand side of the page, the letters c and d to the upper and lower halves of the right-hand side of the page. For example, in 7 PLATO: Symposium, 163b-164c, the passage begins in the lower half of the left-hand side of page 163 and ends in the upper half of the right-hand side of page 164.

Author’s Divisions: One or more of the main divisions of a work (such as PART, BK, CH, SECT) are sometimes included in the reference; line numbers, in brackets, are given in certain cases; e.g., Iliad, BK II [265-283] 12d.

Bible References: The references are to book, chapter, and verse. When the King James and Douay versions differ in title of books or in the numbering of chapters or verses, the King James version is cited first and the Douay, indicated by a (D), follows; e.g., OLD TESTAMENT: Nehemiah, 7:45—(D) II Esdras, 7:46.

Symbols: The abbreviation “esp” calls the reader’s attention to one or more especially relevant parts of a whole reference; “passim” signifies that the topic is discussed intermittently rather than continuously in the work or passage cited.

For additional information concerning the style of the references, see the Explanation of Reference Style; for general guidance in the use of The Great Ideas, consult the Preface.

1. The foundations of mechanics

1a. Matter, mass, and atoms: the primary qualities of bodies

• 8 ARISTOTLE: Heavens, BK III, CH 4 [303ª3-b8] 394b-d / Generation and Corruption, BK I, CH 2 410d-413c; CH 8 423b-425d
• 10 GALEN: Natural Faculties, BK I, CH 12, 173a-b
• 12 LUCRETIUS: Nature of Things, BK I [146-328] 2d-5a; [483-634] 7a-8d; BK II [333-568] 19b-22b
• 19 AQUINAS: Summa Theologica, PART I, Q 115, A 1, ANS and REP 3, 5 585d-587c
• 23 HOBBES: Leviathan, PART I, 72a-d; PART II, 172a-b; PART IV, 269d
• 28 GILBERT: Loadstone, BK II, 29c-34b esp 29c-30a
• 28 GALILEO: Two New Sciences, FIRST DAY, 134a-153a passim
• 30 BACON: Novum Organum, BK I, APH 66 114d-115c; BK II, APH 8 140b; APH 48 179d-188b
• 31 DESCARTES: Meditations, II, 78c-d / Objections and Replies, DEF VII 130c-d; 231a-232a
• 33 PASCAL: Vacuum, 367a-368b
• 34 NEWTON: Principles, PREF 1 5a; DEF III 5b; BK I, PROP 73, SCHOL 133b-134a; BK II, GENERAL SCHOL, 218a-219a; PROP 40, SCHOL, 246a-b; BK III, RULE III 270b-271a; PROP 6, COROL I-IV 281b; PROP 7 281b-282b / Optics, BK III, 479b-485b; BK III, 520a-522a; 528b; 531a-543a esp 537a-b, 541b-542a
• 34 HUYGENS: Light, CH I, 558b-560a; CH III, 566b-569b; CH V, 601b-603b
• 35 LOCKE: Human Understanding, BK II, CH IV 129b-131a; CH VIII, SECT 7-26 134b-138b passim; CH XI, SECT 11-27 150d-154d passim; CH XXI, SECT 2-4 178c-179c; CH XXIII, SECT 7-17 205d-209a passim; SECT 22-32 209d-212d; CH XXXII, SECT 2, 239d; BK III, CH X, SECT 15 295a-c
• 35 BERKELEY: Human Knowledge, SECT 9-18 414d-416c passim; SECT 50 422c; SECT 102 432d-433a
• 45 LAVOISIER: Elements of Chemistry, PREF, 3b-4a; PART I, 9a-15c passim, esp 9b-c, 13a-b; 16b-c; 41b-c
• 45 FOURIER: Theory of Heat, 169a-170a
• 45 FARADAY: Researches in Electricity, 685d-686c; 850b,d-855a,c
• 53 JAMES: Psychology, 68a-b
• 54 FREUD: Narcissism, 400d-401a

1b. The laws of motion: inertia; the measure of force; action and reaction

• 8 ARISTOTLE: Physics, BK VIII, CH 10 [266b27-267a21] 354b-d / Heavens, BK III, CH 2 [301b21-31] 392c-393b
• 9 ARISTOTLE: Motion of Animals, CH 2-4 233c-235c / Gait of Animals, CH 3 243d-244a / Generation of Animals, BK IV, CH 3 [768b16-24] 310b-c
• 12 LUCRETIUS: Nature of Things, BK II [80-99] 16a-b; [184-250] 17b-18b
• 16 KEPLER: Epitome, BK IV, 894a-895b; 899a-900a; 905a-906b; 933b-934b; 936a-937a; 938b-939a
• 20 AQUINAS: Summa Theologica, PART III, Q 84, A 3, REP 2 985d-989b
• 23 HOBBES: Leviathan, PART I, 50a; 72a-d; PART IV, 271d
• 28 GILBERT: Loadstone, BK II, 56b-c
• 28 GALILEO: Two New Sciences, THIRD DAY, 209a-210a; 224d-225d; FOURTH DAY, 240a-d
• 30 BACON: Novum Organum, BK II, APH 35-36 162a-168d passim; APH 48 179d-188b
• 34 NEWTON: Principles, DEF II 5b; LAWS OF MOTION 14a-24a; BK II, PROP 40, SCHOL, 246a-b / Optics, BK III, 541b-542a
• 35 LOCKE: Human Understanding, BK II, CH XXI, SECT 2-4 178c-179c; CH XXIII, SECT 17 209a
• 35 BERKELEY: Human Knowledge, SECT 111, 434d
• 35 HUME: Human Understanding, SECT IV, DIV 27, 460c; SECT VII, DIV 57, 475d-476b [fn 2]
• 38 MONTESQUIEU: Spirit of Laws, BK I, 1b
• 45 FOURIER: Theory of Heat, 169a-b
• 51 TOLSTOY: War and Peace, EPILOGUE I, 695a-c

1c. Space and time in the analysis of motion

• 8 ARISTOTLE: Physics, BK VI 312b,d-325d
• 28 GALILEO: Two New Sciences, THIRD DAY, 176a-179a; 201a-202a
• 33 PASCAL: Geometrical Demonstration, 434a-439b
• 34 NEWTON: Principles, DEFINITIONS, SCHOL 8b-13a; BK III, GENERAL SCHOL, 370a-371a / Optics, BK II, 528b-529a; 542a-543a
• 35 BERKELEY: Human Knowledge, SECT 110-117 434b-436a
• 42 KANT: Pure Reason, 24a-29d; 74b-76c; 160b-163a
• 45 FOURIER: Theory of Heat, 249a-251b
• 51 TOLSTOY: War and Peace, BK XI, 469a-d

2. The logic and method of mechanics

• 28 GALILEO: Two New Sciences, SECOND DAY, 179c-d; THIRD DAY, 200a-b; 202d-203a
• 30 BACON: Advancement of Learning, 34b / Novum Organum, PREF 105a-106d; BK I, APH 8 107c-d; APH 50 111b; APH 64 114b; APH 70 116b-117a; APH 82 120d-121b; APH 99-100 127b-c; APH 121 132b-d; BK II 137a-195d / New Atlantis, 210d-214d
• 31 DESCARTES: Rules, VIII, 12b-13a / Discourse, PART VI, 61d-62c
• 33 PASCAL: Vacuum, 355a-358b passim; 365b-366a
• 34 NEWTON: Principles, 1a-2a; BK I, PROP 69, SCHOL 130b-131a; BK III, 269a-b; RULES 270a-271b; GENERAL SCHOL, 371b-372a / Optics, BK III, 531b; 543a-b
• 34 HUYGENS: Light, PREF, 551b-552a; CH I, 553b-554a
• 35 LOCKE: Human Understanding, BK IV, CH III, SECT 16 317a-c; SECT 25-29 321a-323a passim; CH XII, SECT 9-13 360d-362d
• 35 BERKELEY: Human Knowledge, SECT 104 433a-b; SECT 107 433d-434a
• 35 HUME: Human Understanding, SECT IV, DIV 23-27 459a-460d esp DIV 26-27 460b-d; SECT VII, DIV 57, 475d-476b [fn 2]
• 42 KANT: Pure Reason, 6b-c; 17d-18d; 32a; 69c-72c esp 71b-72a
• 45 FOURIER: Theory of Heat, 169a-170a
• 45 FARADAY: Researches in Electricity, 440b,d; 758a-759c; 831a-d; 850b,d-855a,c esp 850b,d-851c
• 49 DARWIN: Origin of Species, 239c
• 53 JAMES: Psychology, 882a-884b
• 54 FREUD: Instincts, 412a-b

2a. The role of experience, experiment, and induction in mechanics

• 28 GILBERT: Loadstone, PREF, 1a-b; BK I, 6a-7a esp 6d-7a; BK II, 27b-c
• 28 GALILEO: Two New Sciences, THIRD DAY, 200a-b; 207d-208a
• 30 BACON: Advancement of Learning, 16a; 33d-34b; 42a-c
• 31 DESCARTES: Rules, VII, 12b-13a / Discourse, PART VI, 61d-62c
• 33 PASCAL: Vacuum, 356a-357a
• 34 NEWTON: Principles, BK I, PROP 69, SCHOL 130b-131a; BK III, RULE IV 271b; GENERAL SCHOL, 371b-372a / Optics, BK I, 379a; BK III, 542a; 543a-b
• 34 HUYGENS: Light, CH I, 553a
• 35 LOCKE: Human Understanding, BK IV, CH III, SECT 16 317a-c; SECT 25-29 321a-323a passim; CH XII, SECT 9-13 360d-362d
• 35 BERKELEY: Human Knowledge, SECT 58-59 424a-b; SECT 104 433a-b; SECT 107 433d-434a
• 35 HUME: Human Understanding, SECT IV, DIV 24-27 459b-460d esp DIV 26 460b-c; SECT VII, DIV 57, 475d-476b [fn 2]
• 42 KANT: Pure Reason, 6b-c; 227b-c
• 45 LAVOISIER: Elements of Chemistry, PREF, 1c-2b; PART I, 23c; PART III, 87b-c
• 45 FOURIER: Theory of Heat, 175b; 181b; 184a
• 45 FARADAY: Researches in Electricity, 385b-c; 440b,d; 467a-b; 607a,c; 659a; 774d-775a
• 53 JAMES: Psychology, 864a

2b. The use of hypotheses in mechanics

• 12 LUCRETIUS: Nature of Things, BK V [509-533] 67d-68a
• 28 GALILEO: Two New Sciences, FOURTH DAY, 240d-241c
• 33 PASCAL: Vacuum, 367a-370a
• 34 NEWTON: Principles, BK III, RULE IV 271b; GENERAL SCHOL, 371b-372a / Optics, BK I, 379a; BK III, 528b; 543a
• 34 HUYGENS: Light, PREF, 551b-552a
• 35 LOCKE: Human Understanding, BK IV, CH III, SECT 16 317a-c; CH XII, SECT 12-13 362a-d
• 35 BERKELEY: Human Knowledge, SECT 50 422c; SECT 105-106 433b-d
• 35 HUME: Human Understanding, SECT VII, DIV 57, 475d-476b [fn 2]
• 36 SWIFT: Gulliver, PART III, 118b-119a
• 42 KANT: Pure Reason, 227b-c
• 45 LAVOISIER: Elements of Chemistry, PART I, 9d-10b
• 45 FOURIER: Theory of Heat, 181b; 184a
• 45 FARADAY: Researches in Electricity, 467a-b; 607a,c; 758a-759c; 777d-778c; 850b,d-855a,c esp 850b,d-851c
• 49 DARWIN: Origin of Species, 239c
• 53 JAMES: Psychology, 884a-b
• 54 FREUD: Narcissism, 400d-401a

2c. Theories of causality in mechanics

• 12 LUCRETIUS: Nature of Things, BK V [509-533] 67d-68a
• 28 GALILEO: Two New Sciences, THIRD DAY, 202d-203a
• 31 DESCARTES: Discourse, PART V, 59a
• 34 NEWTON: Principles, DEF VIII, 7b-8a; BK I, PROP 69, SCHOL 130b-131a; BK III, RULE I-II 270a; GENERAL SCHOL, 369b-372a / Optics, BK III, 528b-529a; 531b; 541b-542a
• 34 HUYGENS: Light, CH I, 553b-554a
• 35 LOCKE: Human Understanding, BK II, CH XXI, SECT 1-4 178b-179c; BK IV, CH III, SECT 25-26 321a-c
• 35 BERKELEY: Human Knowledge, SECT 50-53 422c-423a passim; SECT 60-66 424b-426a; SECT 102-109 432d-434b
• 35 HUME: Human Understanding, SECT IV, DIV 24-27 459b-460d esp DIV 26 460b-c; SECT VI, DIV 55, 474c-d; DIV 56-57 475a-d esp DIV 57, 475d [fn 2]; SECT VIII, DIV 64, 478d
• 36 SWIFT: Gulliver, PART III, 118b-119a
• 45 FOURIER: Theory of Heat, 169a; 183a-b
• 51 TOLSTOY: War and Peace, EPILOGUE I, 687d; 695b-c
• 53 JAMES: Psychology, 885b-886a

3. The use of mathematics in mechanics: the dependence of progress in mechanics on mathematical discovery

• 8 ARISTOTLE: Posterior Analytics, BK I, CH 9 104b-d; CH 13 [78b31-79a16] 108b-c / Physics, BK II, CH 2 [194a7-11] 270b-c; BK VII, CH 5 333a-d / Metaphysics, BK XII, CH 3 [1078a5-17] 609b-c
• 11 ARCHIMEDES: Equilibrium of Planes 502a-519b / Floating Bodies 538a-560b / Method 569a-592a
• 14 PLUTARCH: Marcellus, 252a-255a
• 16 KEPLER: Epitome, BK V, 964b-965a
• 19 AQUINAS: Summa Theologica, PART I-II, Q 35; A 8, ANS 779c-780c
• 23 HOBBES: Leviathan, PART I, 72a-d; 73b; PART IV, 268c-d
• 28 GALILEO: Two New Sciences, FIRST DAY, 131b-132a; 133b; SECOND DAY-FOURTH DAY 178a-260a,c
• 30 BACON: Advancement of Learning, 46b-c
• 31 DESCARTES: Rules, IV, 7a; XIV, 31c-d / Discourse, PART I, 43b-c; PART II, 50d / Objections and Replies, 169c-170a / Geometry, BK II, 322b-331a
• 34 NEWTON: Principles, 1a-2a; DEF VIII 7b-8a; BK I, PROP 1-17 and SCHOL 32b-50a; PROP 30-98 and SCHOL 76a-157b esp PROP 69, SCHOL 130b-131a; BK II 159a-267a; BK III, 269a-b
• 35 HUME: Human Understanding, SECT IV, DIV 27 460c-d
• 36 SWIFT: Gulliver, PART III, 94b-103a
• 42 KANT: Judgement, 551a-552a
• 45 FOURIER: Theory of Heat, 169a-b; 172a-173b; 175b; 177a; 182b-184a; 249a-b
• 45 FARADAY: Researches in Electricity, 831a-d
• 50 MARX: Capital, 170a-c
• 51 TOLSTOY: War and Peace, BK XI, 469a-d
• 53 JAMES: Psychology, 675b; 876a-b; 882a-883a

3a. Number and the continuum: the theory of measurement

• 11 EUCLID: Elements, BK V 81a-98b esp DEFINITIONS, 5 81a; BK VII, DEFINITIONS, 20 127b; BK X, PROP 1-2 191b-193a; PROP 5-9 195a-198b
• 11 ARCHIMEDES: Measurement of a Circle, PROP 3 448b-451b / Conoids and Spheroids, PROP 3-6 458b-460b / Equilibrium of Planes, BK I, PROP 6-7 503b-504b
• 16 PTOLEMY: Almagest, BK I, 18b-20b
• 28 GALILEO: Two New Sciences, THIRD DAY, 197b-200a; 205b-206c
• 31 DESCARTES: Rules, XIV, 31b-33b / Geometry, BK I, 295a-296b
• 34 NEWTON: Principles, BK I, LEMMA 1 25a
• 42 KANT: Judgement, 551a-552a
• 45 FOURIER: Theory of Heat, 183a-b
• 51 TOLSTOY: War and Peace, BK XI, 469a-d

3b. The geometry of conics: the motion of planets and projectiles

• 11 ARCHIMEDES: Quadrature of the Parabola 527a-537b
• 11 APOLLONIUS: Conics 603a-804b
• 16 KEPLER: Epitome, BK V, 975a-979b
• 28 GALILEO: Two New Sciences, SECOND DAY 191c-195c; FOURTH DAY 238a-260a,c passim, esp 238b-240a
• 31 DESCARTES: Geometry, BK I-II, 298b-314b
• 34 NEWTON: Principles, BK I, PROP 11-29 and SCHOL 42b-75b esp PROP 11-13 42b-46a; BK III, PROP 13 286a-b; PROP 40 337b-338a
• 34 HUYGENS: Light, CH V, 583b-598a; 604b-606b; CH VI, 607b-611a
• 42 KANT: Judgement, 551a-552a

3c. Algebra and analytic geometry: the symbolic formulation of mechanical problems

• 31 DESCARTES: Rules, IV, 5c-d; XIV, 30d-33b; XVI 33d-35c; XVIII 36b-39d / Geometry 295a-353b esp BK I-II, 298b-314b, BK III, 322b-331a
• 34 NEWTON: Principles, BK I, LEMMA 19 57b-58b
• 34 HUYGENS: Light, CH VI, 610a-b
• 45 LAVOISIER: Elements of Chemistry, PREF, 1a
• 45 FOURIER: Theory of Heat, 172a-173b; 177a-251b

3d. Calculus: the measurement of irregular areas and variable motions

• 11 ARCHIMEDES: Equilibrium of Planes, BK I, PROP 7 504b / Quadrature of the Parabola 527a-537b
• 16 KEPLER: Epitome, BK V, 973a-975a; 979b-983b
• 28 GALILEO: Two New Sciences, SECOND DAY, 193b-194d; THIRD DAY, 205b-d; 224b-c
• 33 PASCAL: Equilibrium of Liquids, 395a-b / Geometrical Demonstration, 434b-435b
• 34 NEWTON: Principles, BK I, LEMMA I-II and SCHOL 25a-32a esp LEMMA II, SCHOL, 31a-b; BK II, LEMMA 2 and SCHOL 168a-170a
• 45 FOURIER: Theory of Heat, 172b; 177a; 181a-b; 183a-b; 221a-248b
• 51 TOLSTOY: War and Peace, BK XI, 469a-d; EPILOGUE II, 695b-c

4. The place, scope, and ideal of the science of mechanics: its relation to the philosophy of nature and other sciences

• 23 HOBBES: Leviathan, PART I, 72a-d
• 30 BACON: Advancement of Learning, 16a-b; 33d-34b / Novum Organum, BK I, APH 74 118b; BK II, APH 9 140b-c / New Atlantis, 210d-214d
• 31 DESCARTES: Rules, IV, 7a; V, 8a / Discourse, PART V, 54d-56a; 59a
• 34 NEWTON: Principles, 1b-2a; BK I, PROP 69, SCHOL 130b-131a / Optics, BK III, 541b-542a
• 34 HUYGENS: Light, CH I, 553b-554a
• 35 HUME: Human Understanding, SECT I, DIV 9, 454c-d
• 36 SWIFT: Gulliver, PART III, 94b-103a
• 42 KANT: Pure Reason, 32a; 69c-72c esp 71b-72a / Judgement, 563a-564c
• 45 FOURIER: Theory of Heat, 169a-b; 172a-173b; 182a-184a
• 45 FARADAY: Researches in Electricity, 468d-469a
• 53 JAMES: Psychology, 69b-70a; 882a-886a esp 883a-884b; 889a-890a

4a. Terrestrial and celestial mechanics: the mechanics of finite bodies and of particles or atoms

• 9 ARISTOTLE: Motion of Animals, CH 3 [699a11]-CH 4 [700a5] 234a-235a
• 16 KEPLER: Epitome, BK IV, 888b-905a passim; 919b; 929a-933a; 935b; 940b-941a; 959a-960a
• 28 GALILEO: Two New Sciences, FOURTH DAY, 245b-d
• 30 BACON: Novum Organum, BK II, APH 5 138b-139a; APH 35 162a-164a; APH 36, 165c-166c; APH 46, 178c; APH 48, 186c-d
• 34 NEWTON: Principles, BK III, RULES 270a-271b; PROP 7 281b-282b / Optics, BK III, 539a-542b
• 51 TOLSTOY: War and Peace, BK XIII, 563a-b; EPILOGUE II, 694d-696d

4b. The explanation of qualities and qualitative change in terms of quantity and motion

• 8 ARISTOTLE: Metaphysics, BK I, CH 4 [985b3-19] 503c-d / Sense and the Sensible, CH 4 [442a30-b24] 680a-c
• 10 GALEN: Natural Faculties, BK I, CH 2, 167b-168b
• 12 LUCRETIUS: Nature of Things, BK II [398-521] 20a-21c; [677-687] 23c-d; [730-1022] 24b-28a; BK IV [522-721] 51a-53d
• 23 HOBBES: Leviathan, PART I, 49b-d; PART III, 172b
• 31 DESCARTES: Objections and Replies, 231a-b
• 34 NEWTON: Optics, BK I, 431a-455a esp 450a-453a
• 34 HUYGENS: Light, CH I, 553b-554a
• 35 LOCKE: Human Understanding, BK II, CH VIII, SECT 4 133d; SECT 7-26 134b-138b; CH XXI, SECT 3 178d; SECT 75 200b-d; CH XXIII, SECT 8-9 206a-c; SECT 11 206d-207a; SECT 37 213d-214b; CH XXXI, SECT 2 239b-d esp 239d; BK III, CH IV, SECT 10 261b-d; BK IV, CH III, SECT 11-13 311c-312b; CH VI, SECT 6, 314b; SECT 12-14 316a-d; SECT 28 322a-c
• 35 BERKELEY: Human Knowledge, SECT 25 417d-418a; SECT 102 432d-433a
• 45 FOURIER: Theory of Heat, 169b; 182a-b

4c. The mechanistic account of the phenomena of life

• 7 PLATO: Phaedo, 240d-242b / Sophist, 567a-568a
• 8 ARISTOTLE: Sense and the Sensible, CH 4 [442a30-b24] 680a-c
• 9 ARISTOTLE: Parts of Animals, BK I, CH 1 [640b5-641a19] 163a-164a / Motion of Animals, CH 7 [701b1-30] 236d-237b; CH 8 [702a22]-CH 10 [703a1] 237c-239a / Gait of Animals 243a-252a,c / Generation of Animals, BK II, CH 1 [734b3-20] 275a-b; CH 5 [741b5-10] 282c
• 10 GALEN: Natural Faculties, BK I, CH 12-BK II, CH 8 172d-195c esp BK I, CH 12 172d-173c, BK II, CH 3, 185a, CH 6 188c-191a; BK III, CH 14-15, 213b-214c
• 12 LUCRETIUS: Nature of Things, BK II [865-1022] 26a-28a; BK III [94-869] 31b-41a; BK V [783-836] 71b-72a
• 23 HOBBES: Leviathan, INTRO, 47a-b
• 28 HARVEY: On Animal Generation, 355b-d; 495c-496d
• 31 DESCARTES: Discourse, PART V, 56a-60b
• 34 NEWTON: Optics, BK I, 384b-385b; 428a-b; BK III, 518b-519b; 522a
• 35 LOCKE: Human Understanding, BK II, CH IX, SECT 11 140b-c; CH X, SECT 10 143c-d; CH XI, SECT 11 145d-146a; CH XXVI, SECT 5 220b-c; BK IV, CH III, SECT 25 321a-b
• 38 ROUSSEAU: Inequality, 337d-338a / Political Economy, 368d-369a
• 42 KANT: Judgement, 571c-572a; 575b-578a; 578d-582c
• 45 LAVOISIER: Elements of Chemistry, PART I, 14a
• 45 FARADAY: Researches in Electricity, 440b,d; 540a-541a,c
• 49 DARWIN: Origin of Species, 89b-c
• 51 TOLSTOY: War and Peace, BK X, 449b-c; EPILOGUE II, 689c-690a
• 53 JAMES: Psychology, 5a-6b; 9a-17b; 44a-52a; 68a-71a; 95b-98a
• 54 FREUD: Instincts, 412c-414c / Beyond the Pleasure Principle, 651d-657d passim, esp 651d, 652d; 659d-661c esp 660a / Ego and Id, 708d-709b; 711c-d

5. The basic phenomena and problems of mechanics: statics and dynamics

5a. Simple machines: the balance and the lever

• 8 ARISTOTLE: Physics, BK VIII, CH 4 [255a20-22] 339d
• 10 HIPPOCRATES: Fractures, PAR 31, 87c
• 11 ARCHIMEDES: Equilibrium of Planes, BK I, POSTULATES, 1-3 502a; 6 502b; PROP 1-3 502b-503a; PROP 6-7 503b-504b
• 14 PLUTARCH: Marcellus, 252c-d
• 16 KEPLER: Epitome, BK IV, 933b-934b; BK V, 970b-972a
• 28 GALILEO: Two New Sciences, SECOND DAY, 178b-180c; THIRD DAY, 209a-210a; FOURTH DAY, 258c-d
• 33 PASCAL: Equilibrium of Liquids, 390a-394b
• 34 NEWTON: Principles, COROL II 15a-16b; LAWS OF MOTION, SCHOL, 23a-24a
• 35 HUME: Human Understanding, SECT IV, DIV 27, 460c
• 50 MARX: Capital, 181a

5b. The equilibrium and motion of fluids: buoyancy, the weight and pressure of air, the effects of a vacuum

• 8 ARISTOTLE: Heavens, BK IV, CH 6 404d-405a,c
• 10 GALEN: Natural Faculties, BK I, CH 16, 181a-d; BK II, CH 1-2, 183b,d-184c; CH 6 188c-191a; BK III, CH 14-15, 213b-214c
• 11 ARCHIMEDES: Floating Bodies 538a-560b
• 28 GALILEO: Two New Sciences, FIRST DAY, 135b-138b; 163a-166c
• 30 BACON: Novum Organum, BK II, APH 48, 180a
• 33 PASCAL: Vacuum, 359a-365b / Great Experiment 382a-389b / Equilibrium of Liquids 390a-403a / Weight of Air 403a-429a
• 34 NEWTON: Principles, BK II, PROP 19-23 and SCHOL 194b-203a; PROP 36 226a-231b; HYPOTHESIS-PROP 53 and SCHOL 259a-267a; BK III, PROP 41, 356b-357b / Optics, BK III, 518a-b
• 35 LOCKE: Human Understanding, BK II, CH XXIII, SECT 23-24 209d-210c
• 45 LAVOISIER: Elements of Chemistry, PART I, 10c-12d; 15c-16d; PART III, 88d-89d; 96b-99a

5c. Stress, strain, and elasticity: the strength of materials

• 28 GALILEO: Two New Sciences, FIRST DAY, 131a-139c; SECOND DAY 178a-196d passim
• 30 BACON: Novum Organum, BK II, APH 48, 180a-d; 187d
• 34 NEWTON: Principles, LAWS OF MOTION, SCHOL, 21b-22a; BK II, PROP 23 and SCHOL 201b-203a / Optics, BK III, 540b-541a
• 34 HUYGENS: Light, CH I, 558b-559b
• 35 LOCKE: Human Understanding, BK II, CH XXIII, SECT 23-27 209d-211b
• 45 LAVOISIER: Elements of Chemistry, PART I, 14c-15c; PART III, 96b-99a
• 45 FOURIER: Theory of Heat, 192a-b

5d. Motion, void, and medium: resistance and friction

• 7 PLATO: Timaeus, 460c-d
• 8 ARISTOTLE: Physics, BK IV, CH 6-9 292c-297c / Heavens, BK III, CH 2 [301b21-31] 392c-393b / Dreams, CH 2 [459b28-34] 703b
• 12 LUCRETIUS: Nature of Things, BK I [329-448] 5b-6c; [951-1051] 12d-14a; BK II [142-166] 16d-17a; [225-242] 17d-18a; BK VI [830-839] 91b-c
• 16 KEPLER: Epitome, BK IV, 857a-b
• 20 AQUINAS: Summa Theologica, PART II, Q 84, A 3, REP 2 985d-989b
• 28 GILBERT: Loadstone, BK VI, 110c
• 28 GALILEO: Two New Sciences, FIRST DAY, 134a-135b; 157b-171b; FOURTH DAY, 241d-243c
• 30 BACON: Novum Organum, BK II, APH 8 140b; APH 36, 167b-c; APH 48, 186a; 187a; 187c
• 34 NEWTON: Principles, BK II 159a-267a passim, esp GENERAL SCHOL 211b-219a; BK III, PROP 6, COROL III 281b; PROP 10 284a-285a / Optics, BK III, 521b-522a; 527a-528b
• 35 LOCKE: Human Understanding, BK II, CH XIII, SECT 22-23 153b-d; CH XVII, SECT 4 168b-d
• 42 KANT: Pure Reason, 71b-72a

5e. Rectilinear motion

• 8 ARISTOTLE: Physics, BK V, CH 4 [228b15-229a7] 309d-310a; BK VIII, CH 8 [261b27-263a3] 348b-349c / Heavens, BK I, CH 2 [268b15-24] 359d
• 28 GALILEO: Two New Sciences, FIRST DAY, 157b-171b; THIRD DAY 197a-237a,c
• 30 BACON: Novum Organum, BK II, APH 48, 186b-c
• 34 NEWTON: Principles, LAW I-II 14a-b; BK I, PROP 32-39 81a-88a; BK II, PROP I-14 159a-189a passim

5e(1) Uniform motion: its causes and laws

• 28 GALILEO: Two New Sciences, FIRST DAY, 162c-163a; THIRD DAY, 197b-200a
• 34 NEWTON: Principles, DEF III-IV 5b-6a; LAW I 14a; COROL IV-V 18a-19a; BK II, PROP I, COROL 159a; PROP 2 159b-160a; PROP 5-6 165a-167a; PROP 11-12 183a-184b

5e(2) Accelerated motion: free fall

• 8 ARISTOTLE: Physics, BK IV, CH 8 [215a24-216a21] 295a-d / Heavens, BK III, CH 2 [301b16-31] 393a-b
• 12 LUCRETIUS: Nature of Things, BK II [225-242] 17d-18a
• 16 PTOLEMY: Almagest, BK I, 10b-11b
• 19 AQUINAS: Summa Theologica, PART I, Q 115, A 1, REP 3 585d-587c
• 28 GALILEO: Two New Sciences, FIRST DAY, 157b-171b; THIRD DAY, 200a-237a,c
• 30 BACON: Novum Organum, BK II, APH 36, 166b-c; APH 48, 181d
• 34 NEWTON: Principles, DEF IV 6a; LAW II 14a-b; COROL VI 19b; BK I, PROP 32-39 81a-88a; BK II, PROP 3-4 160b-165a; PROP 8-10 170a-179a; PROP 13-14 184b-189a; PROP 32-40 and SCHOL 219a-246b esp PROP 40, SCHOL 239a-246b; PROP 41-50 and SCHOL 247a-259a

5f. Motion about a center: planets, projectiles, pendulum

• 8 ARISTOTLE: Physics, BK VIII, CH 8-10 348b-355d / Heavens, BK I, CH 2 359d-360d; CH 4 362a-c; BK II, CH 3-12 377c-384c / Metaphysics, BK XII, CH 8 603b-605a / Soul, BK I, CH 3 [406b26-407a13] 636b-637b
• 16 KEPLER: Epitome, BK IV, 895b-905a passim; 913a; 914b-915a; 918b-928a passim; 933a-946a esp 939a-940b; BK V, 965a-966a / Harmonies of the World, 1015b-1023a
• 28 GALILEO: Two New Sciences, FOURTH DAY, 240a-d
• 30 BACON: Novum Organum, BK II, APH 36, 167b-c; APH 46, 177c-178a; APH 48, 186b-d
• 34 NEWTON: Principles, DEF V 6a-7a; LAWS OF MOTION, SCHOL, 19b-20a; BK I, LEMMA I-II and SCHOL 25a-32a; PROP 1-3 and SCHOL 32b-35b esp PROP 3, SCHOL 35b; PROP 46 101a-b; BK II, PROP 51-53 and SCHOL 259a-267a esp PROP 53, SCHOL 266a-267a; BK III, PHENOMENA 272a-275a; PROP 13 286a-b

5f(1) Determination of orbit, force, speed, time, and period

• 12 LUCRETIUS: Nature of Things, BK V [614-649] 69a-c
• 16 KEPLER: Epitome, BK IV, 905a-907a; BK V, 968a-985b esp 975a-979b
• 28 GALILEO: Two New Sciences, FIRST DAY, 166d-168a; 171b-172d; THIRD DAY, 203d-205b; 235b-d; FOURTH DAY 238a-260a,c
• 30 BACON: Novum Organum, BK II, APH 48, 186b-d
• 34 NEWTON: Principles, LAWS OF MOTION, SCHOL, 19b-22a; BK I, PROP 1-17 and SCHOL 32b-50a; PROP 30-31 and SCHOL 76a-81a; PROP 40-42 88b-92b; PROP 46-47 and SCHOL 101a-102a; PROP 51-56 105b-111a; BK II, PROP 4 161b-165a; PROP 10 and SCHOL 173b-183a; LEMMA 3-PROP 18 189b-194b; PROP 24-GENERAL SCHOL 203a-219a; BK III, PROP 1-5 and SCHOL 276a-279a; PROP 13 286a-b; PROP 20 291b-294b; LEMMA 4-PROP 42 333a-368b
• 35 LOCKE: Human Understanding, BK II, CH XIV, SECT 21 159a-d
• 35 BERKELEY: Human Knowledge, SECT 111, 434d

5f(2) Perturbation of motion: the two and three body problems

• 16 KEPLER: Epitome, BK IV, 920b-921b; 922b-926a; 957b-959a
• 28 GILBERT: Loadstone, BK I, 54c-d; 55c-56b
• 34 NEWTON: Principles, BK I, PROP 43-45 92b-101a; 111b; PROP 57-69 and SCHOL 111b-131a; BK III, PROP 5, COROL II 279a; PROP 12-14 and SCHOL 285a-287b; PROP 21-39 294b-333a
• 45 FARADAY: Researches in Electricity, 817a-b

6. Basic concepts of mechanics

6a. Center of gravity: its determination for one or several bodies

• 11 ARCHIMEDES: Equilibrium of Planes 502a-519b / Method, PROP 6 578a-579a; PROP 8-9 580b-582b
• 31 DESCARTES: Objections and Replies, 231c-d
• 33 PASCAL: Equilibrium of Liquids, 393b-394a
• 34 NEWTON: Principles, COROL IV 18a-19a; BK III, HYPOTHESIS I-PROP 12 285a-286a

6b. Weight and specific gravity: the relation of mass and weight

• 7 PLATO: Timaeus, 462d-463c
• 8 ARISTOTLE: Physics, BK IV, CH 8 [216a12-20] 295c-d / Heavens, BK I, CH 3 [269b18-270a12] 360d-361b; CH 6 [273b22-274a18] 364c-365b; BK III, CH 2 [301a21-32] 392c-393b; BK IV, CH 1-3 399a-402c
• 12 LUCRETIUS: Nature of Things, BK I [358-369] 5c; BK II [80-108] 16a-b; [294-296] 18d
• 16 COPERNICUS: Revolutions of the Heavenly Spheres, BK I, 521a
• 16 KEPLER: Epitome, BK V, 970b
• 19 AQUINAS: Summa Theologica, PART I-II, Q 26, A 2, ANS 734d-735c
• 23 HOBBES: Leviathan, PART IV, 271d
• 28 GILBERT: Loadstone, BK VI, 115d-116a
• 28 GALILEO: Two New Sciences, FIRST DAY, 158b-c; 160a-164a passim
• 30 BACON: Novum Organum, BK II, APH 24, 154d-155a; APH 35, 163c-d; APH 36, 166b-c; APH 40, 172a-b
• 31 DESCARTES: Objections and Replies, 231b-232a
• 34 NEWTON: Principles, DEF I 5a; BK II, PROP 24 203a-204a; BK III, PROP 6 279b-281b; PROP 8 282b-283b; PROP 20 291b-294b passim
• 45 LAVOISIER: Elements of Chemistry, PART III, 88d-89d
• 45 FOURIER: Theory of Heat, 249a-251b
• 45 FARADAY: Researches in Electricity, 632a

6c. Velocity, acceleration, and momentum: angular or rectilinear, average or instantaneous

• 8 ARISTOTLE: Physics, BK IV, CH 8 [215a24-216a21] 295a-d; BK V, CH 4 [228b20-229a7] 309b-310a; BK VI, CH 1-2 312b,d-315d; BK VII, CH 4 330d-333a
• 28 GALILEO: Two New Sciences, FIRST DAY, 166d-168a; THIRD DAY, 197b-c; 200a-207d; 209a-210a; 224b-225d; FOURTH DAY, 240a-d; 243d-249b
• 30 BACON: Novum Organum, BK II, APH 46, 177d-178d
• 34 NEWTON: Principles, DEF II 5b; DEF VII-VIII 7a-8a; LAW II 14a-b; COROL III 16b-17b; LAWS OF MOTION, SCHOL, 20a-22a; BK I, LEMMA 10 28b-29a; LEMMA II, SCHOL, 31b-32a; PROP I, COROL 1 33a / Optics, BK III, 540a-541b
• 35 HUME: Human Understanding, SECT IV, DIV 27, 460c
• 51 TOLSTOY: War and Peace, BK XI, 470d-471a; BK XIV, 589d

6d. Force: its kinds and its effects

• 8 ARISTOTLE: Physics, BK VII, CH 5 333a-d; BK VIII, CH 10 [266b25-267a20] 353c-354d / Heavens, BK III, CH 2 [301b2-32] 392d-393b
• 9 ARISTOTLE: Motion of Animals, CH 3 234a-c
• 16 KEPLER: Epitome, BK IV, 938b-939a; BK V, 969a-971b
• 19 AQUINAS: Summa Theologica, PART I, Q 105, A 4, REP 1 541c-542a; PART I-II, Q 23, A 4 726a-727a
• 20 AQUINAS: Summa Theologica, PART III, Q 84, A 3, REP 2 985d-989b
• 28 GILBERT: Loadstone, BK II, 26d-40b passim
• 31 DESCARTES: Rules, IX, 15c / Objections and Replies, 231c-232a
• 34 NEWTON: Principles, DEF III-VIII 5b-8a; DEFINITIONS, SCHOL, 11a-13a; LAW II 14a-b; BK I, LEMMA 10 28b-29a; PROP 6 37b-38b; BK III, PROP 6, COROL V 281b; GENERAL SCHOL, 371b-372a / Optics, BK III, 531b; 541b-542a
• 35 BERKELEY: Human Knowledge, SECT 103-106 433a-d
• 36 SWIFT: Gulliver, PART III, 118b-119a
• 45 FARADAY: Researches in Electricity, 338a-b; 514d-532a; 595a; 603d; 646b-655d; 670a-674a; 685d-686b; 817a-818d; 819b,d; 850b,d-855a,c esp 855a,c
• 54 FREUD: Narcissism, 400d-401a

6d(1) The relation of mass and force: the law of universal gravitation

• 16 KEPLER: Epitome, BK IV, 910b
• 28 GILBERT: Loadstone, BK II, 51c-52c
• 30 BACON: Novum Organum, BK II, APH 24, 154d-155a; APH 36, 166b-c; APH 40 170c-173d
• 31 DESCARTES: Objections and Replies, 231c-232a
• 34 NEWTON: Principles, BK I, PROP 69-93 and SCHOL 130a-152b esp PROP 75-76 134b-136a; BK III, PROP 1-7 276a-282b esp PROP 7 281b-282b; GENERAL SCHOL, 371b / Optics, BK III, 531b-543a esp 541b-542a
• 35 BERKELEY: Human Knowledge, SECT 103-106 433a-d
• 35 HUME: Human Understanding, SECT VII, DIV 57, 475d [fn 2]
• 45 FARADAY: Researches in Electricity, 850b,d-855a,c esp 855a,c
• 49 DARWIN: Origin of Species, 239c
• 51 TOLSTOY: War and Peace, EPILOGUE II, 695c
• 54 FREUD: Narcissism, 400d-401a

6d(2) Action-at-a-distance: the field and medium of force

• 8 ARISTOTLE: Physics, BK VIII, CH 10 [266b27-267a21] 354b-d / Heavens, BK III, CH 2 [301b16-31] 393a-b / Dreams, CH 2 [459b28-34] 703b
• 12 LUCRETIUS: Nature of Things, BK VI [906-1089] 92b-94c
• 16 KEPLER: Epitome, BK IV, 897b-905a esp 900b-901b; 906a-b; 922a-b; 934b
• 19 AQUINAS: Summa Theologica, PART I, Q 8, A 1, REP 3 34d-35c
• 28 GILBERT: Loadstone, BK I, 10a-c; BK II, 26d-40b esp 30a-32c; 42b-43c; 45d-47b; 51a-c; 54d-55c; BK V, 102d-104b; BK VI, 112d
• 28 GALILEO: Two New Sciences, THIRD DAY, 202d
• 30 BACON: Novum Organum, BK II, APH 37 168d-169c; APH 45 176a-177c; APH 48, 183a-c; 186a
• 31 DESCARTES: Rules, IX, 15c / Discourse, PART V, 55c
• 34 NEWTON: Principles, DEF V-VIII 6a-8a; BK I, PROP 69, SCHOL 130b-131a; BK III, GENERAL SCHOL, 371b-372a / Optics, BK III, 507a-516b; 520a-522a esp 521a-b; 531b-542a passim
• 35 HUME: Human Understanding, SECT VII, DIV 57, 475d [fn 2]
• 42 KANT: Pure Reason, 227b
• 45 LAVOISIER: Elements of Chemistry, PART I, 9b-c
• 45 FARADAY: Researches in Electricity, 441a-442b; 451a-454a; 463d-465d; 513d-514c; 521a-524a; 528c-532a; 604b-c; 631b-c; 648b-d; 685d-686c; 816b,d-819a,c; 819a-d; 824a-b; 832a-c; 840c-842c; 855a,c

6d(3) The parallelogram law: the composition of forces and the composition of velocities

• 16 KEPLER: Epitome, BK V, 969a-970a
• 28 GALILEO: Two New Sciences, THIRD DAY, 224d-225c; FOURTH DAY, 240a-d; 243d-249b passim
• 34 NEWTON: Principles, COROL I-II 15a-16b
• 45 FARADAY: Researches in Electricity, 691b-692a; 788c-793c; 817a-b
• 51 TOLSTOY: War and Peace, BK XIII, 570d
• 53 JAMES: Psychology, 105a

6e. Work and energy: their conservation; perpetual motion

• 28 GILBERT: Loadstone, BK II, 56b-c
• 31 DESCARTES: Rules, XIII, 27c
• 33 PASCAL: Equilibrium of Liquids, 392b-394b
• 34 NEWTON: Principles, COROL II 15a-16b; LAWS OF MOTION, SCHOL, 23a-24a
• 45 FARADAY: Researches in Electricity, 582b-584a; 837b-c; 837d-840c
• 53 JAMES: Psychology, 884a

7. The extension of mechanical principles to other phenomena: optics, acoustics, the theory of heat, magnetism, and electricity

7a. Light: the corpuscular and the wave theory

• 8 ARISTOTLE: Soul, BK II, CH 7 [418b26-419a24] 649b-650b
• 12 LUCRETIUS: Nature of Things, BK IV [364-378] 48d-49a
• 16 KEPLER: Epitome, BK IV, 896b; 901a-903a; 922b-926a passim
• 17 PLOTINUS: Fourth Ennead, TR V 183a-189b
• 19 AQUINAS: Summa Theologica, PART I, Q 53; A 3, ANS and REP 2 283b-284d; Q 67 349d-354a; Q 104, A 1, ANS and REP 1,4 534c-536c
• 20 AQUINAS: Summa Theologica, PART III SUPPL, Q 92, A 1, REP 15 1025c-1032b
• 28 GILBERT: Loadstone, BK II, 43a-b
• 30 BACON: Novum Organum, BK II, APH 36, 167a-b; APH 37, 169a-c; APH 48, 185a-c / New Atlantis, 212d-213a
• 31 DESCARTES: Discourse, PART V, 54d-55b
• 33 PASCAL: Vacuum, 366b-367a
• 34 NEWTON: Principles, BK I, PROP 94-98 and SCHOL 152b-157b; BK II, PROP 41-42 247a-249b; PROP 50, SCHOL, 257b / Optics 377a-544a passim, esp BK I, 379a, BK II, 492a-495b, BK III, 525b-531b
• 34 HUYGENS: Light 551a-619b passim, esp CH I 553a-563b
• 35 LOCKE: Human Understanding, BK III, CH IV, SECT 10 261b-d; BK IV, CH III, SECT 11-13 311c-312b
• 45 LAVOISIER: Elements of Chemistry, PART I, 10b-c
• 45 FARADAY: Researches in Electricity, 595a-607a,c; 817b-c
• 49 DARWIN: Origin of Species, 239c

7a(1) The laws of reflection and refraction

• 7 PLATO: Timaeus, 454c-455a
• 8 ARISTOTLE: Meteorology, BK III, CH 2-6 476b-482d / Soul, BK II, CH 8 [419b28-33] 651a
• 12 LUCRETIUS: Nature of Things, BK IV [269-323] 47d-48b; [436-442] 49d-50a
• 20 AQUINAS: Summa Theologica, PART III SUPPL, Q 82, A 4, REP 5 972d-974c
• 21 DANTE: Divine Comedy, PURGATORY, XV [16-24] 75c
• 31 DESCARTES: Rules, VIII, 12b-13a / Geometry, BK II, 322b-331a
• 34 NEWTON: Principles, BK I, PROP 94 152b-153b; PROP 96-98 and SCHOL 154b-157b / Optics, BK I, 379a-423b passim, esp 379a-386b, 409a-412a; BK II, 478b-479b; 485b-495b; BK III, 520b; 522b-530b passim
• 34 HUYGENS: Light, CH II-VI 563b-619b esp CH II-III 563b-575a

7a(2) The production of colors

• 7 PLATO: Meno, 177b-c / Timaeus, 465b-d
• 12 LUCRETIUS: Nature of Things, BK II [730-841] 24b-25c; BK VI [524-526] 87b
• 16 KEPLER: Epitome, BK IV, 901b
• 19 AQUINAS: Summa Theologica, PART I, Q 14, A 6, ANS 80a-81c
• 30 BACON: Novum Organum, BK II, APH 23, 154a-b
• 31 DESCARTES: Discourse, PART V, 55c-d / Objections and Replies, 231b
• 34 NEWTON: Optics, BK I-II 379a-506b passim, esp BK I, 424a-428b, 440a-441b, 453a-455a, BK II, 481a-482a; BK III, 519a-b
• 48 MELVILLE: Moby Dick, 144b-145a

7a(3) The speed of light

• 12 LUCRETIUS: Nature of Things, BK IV [176-208] 46c-47a; BK VI [164-172] 82b-c
• 28 GALILEO: Two New Sciences, FIRST DAY, 148b-149c
• 30 BACON: Novum Organum, BK II, APH 46, 178a-b
• 31 DESCARTES: Discourse, PART V, 55b
• 34 NEWTON: Principles, BK I, PROP 96, SCHOL, 155a / Optics, BK I, 379b; BK II, 488b-492a
• 34 HUYGENS: Light, CH I, 554b-557b; CH III, 570a-575a
• 45 FARADAY: Researches in Electricity, 817b

7a(4) The medium of light: the ether

• 8 ARISTOTLE: Soul, BK II, CH 7 [418b27-419a24] 649b-650b; BK III, CH 12 [434b22-435a11] 667c-668a / Sense and the Sensible, CH 3 676a-678b; CH 6 [446b20-447a12] 684c-685c
• 12 LUCRETIUS: Nature of Things, BK V [449-508] 67a-c
• 16 KEPLER: Epitome, BK IV, 857a-b; 901a-b
• 19 AQUINAS: Summa Theologica, PART I, Q 14, A 6, ANS 80a-81c
• 30 BACON: Novum Organum, BK II, APH 48, 186a
• 33 PASCAL: Vacuum, 366a-367a
• 34 NEWTON: Principles, BK III, GENERAL SCHOL, 372a / Optics, BK III, 520a-522b; 525b-529a
• 34 HUYGENS: Light, CH I, 553b-560b esp 557b-560b
• 45 FARADAY: Researches in Electricity, 595a [fn 2]

7b. Sound: the mechanical explanation of acoustic phenomena

• 7 PLATO: Meno, 177b-c / Timaeus, 471b
• 8 ARISTOTLE: Soul, BK II, CH 8 650c-652c
• 9 ARISTOTLE: Generation of Animals, BK V, CH 7 328c-330b
• 12 LUCRETIUS: Nature of Things, BK IV [524-614] 51a-52b
• 17 PLOTINUS: Fourth Ennead, TR V, CH 5 186b-d
• 28 GALILEO: Two New Sciences, FIRST DAY, 172b-177a,c
• 30 BACON: Novum Organum, BK II, APH 46, 178a; APH 48, 185a-c; 186a / New Atlantis, 213b
• 31 DESCARTES: Rules, XII, 25c
• 34 NEWTON: Principles, BK II, PROP 41-50 and SCHOL 247a-259a passim / Optics, BK III, 525b-526a
• 34 HUYGENS: Light, CH I, 554b-558b passim
• 45 FARADAY: Researches in Electricity, 485b-486b

7c. The theory of heat

7c(1) The description and explanation of the phenomena of heat: the hypothesis of caloric

• 7 PLATO: Timaeus, 462c-d / Theaetetus, 533b-c
• 8 ARISTOTLE: Heavens, BK II, CH 7 380c-d
• 12 LUCRETIUS: Nature of Things, BK V [592-613] 68d-69a; BK VI [132-322] 82a-84c; [848-905] 91c-92b
• 19 AQUINAS: Summa Theologica, PART I, Q 67, A 3, ANS and REP 1,3 351b-352a; Q 104, A 1, ANS 534c-536c
• 30 BACON: Novum Organum, BK II, APH 10-20 140c-153a; APH 24, 154c-d; APH 26, 157a; APH 33, 161c; APH 36, 168b-d; APH 48, 182b; 183d; 184d-185a; APH 50, 190b-192b
• 31 DESCARTES: Objections and Replies, 231a-b
• 34 NEWTON: Principles, BK III, GENERAL SCHOL, 372a / Optics, BK III, 516b-518b; 520a-b; 541a-b
• 42 KANT: Judgement, 545b-546b
• 45 LAVOISIER: Elements of Chemistry, PART I, 9a-16d
• 45 FOURIER: Theory of Heat 169a-251b passim
• 45 FARADAY: Researches in Electricity, 812b-c; 813b-815b; 857a-858d
• 51 TOLSTOY: War and Peace, BK XIII, 587b-c; EPILOGUE II, 687d

7c(2) The measurement and the mathematical analysis of the quantities of heat

• 33 PASCAL: Great Experiment, 388a
• 45 LAVOISIER: Elements of Chemistry, PART I, 14a-c; 33b-36a; PART III, 99d-103b
• 45 FOURIER: Theory of Heat, 184b-185b

7d. Magnetism: the great magnet of the earth

• 10 GALEN: Natural Faculties, BK I, CH 14, 177a-178c
• 12 LUCRETIUS: Nature of Things, BK VI [906-1089] 92b-94c
• 28 GILBERT: Loadstone, BK I, 23b-25d; BK VI 106a-121a,c
• 30 BACON: Novum Organum, BK II, APH 36, 166c-167a; APH 45, 176b-c; APH 48, 183b-c
• 36 SWIFT: Gulliver, PART III, 100a-102a
• 45 FARADAY: Researches in Electricity, 286a-294a; 697b-757d

7d(1) Magnetic phenomena: coition, verticity, variation, dip

• 7 PLATO: Ion, 144b / Timaeus, 471b-c
• 8 ARISTOTLE: Physics, BK VIII, CH 10 [266b30-267a2] 354b-c
• 16 KEPLER: Epitome, BK IV, 897b-898b; 935a-936a; 941b-942a
• 28 GILBERT: Loadstone, BK I-V 3a-105d passim
• 30 BACON: Novum Organum, BK II, APH 25, 155c-d; APH 35, 163c-d; APH 36, 166c-167a; APH 37, 169b-c; APH 42, 174b-c; APH 45, 176b-c; APH 48, 182c; 183b-c; 184a; 185a-d
• 45 FARADAY: Researches in Electricity, 595a-600a; 607a-669d; 673b,d-757d; 812b-c; 813b-815b; 855a-866a,c

7d(2) Magnetic force and magnetic fields

• 16 KEPLER: Epitome, BK IV, 897b-898b; 935a-936a; 941b-942a
• 28 GILBERT: Loadstone, BK II, 26d-43c esp 38a-39b; 45d-47b; 54d-55c; BK V, 102d-105d
• 30 BACON: Novum Organum, BK II, APH 37, 169b-c; APH 45, 176b-c
• 34 NEWTON: Principles, BK I, PROP 69, SCHOL, 130b; BK II, PROP 23, SCHOL 202b-203a; BK III, PROP 6, COROL V 281b; PROP 7, COROL I 282a / Optics, BK III, 531b
• 45 FARADAY: Researches in Electricity, 281c-282c; 298d-301a; 302a-d; 528c-532a; 603d-604c; 679a-b; 690a-697b; 758a-795d; 816b,d-824b; 830b-848a,c
• 48 MELVILLE: Moby Dick, 376b-379a

7e. Electricity: electrostatics and electrodynamics

• 28 GILBERT: Loadstone, BK II, 26d-34b
• 34 NEWTON: Principles, BK III, PROP 7, COROL I 282a; GENERAL SCHOL, 372a / Optics, BK III, 531b; 542a
• 45 FARADAY: Researches in Electricity, 514d-528c

7e(1) The source of electricity: the relation of the kinds of electricity

• 45 FARADAY: Researches in Electricity, 269a-273a; 277a-316a esp 281d-282c, 302a-d, 315d-316a; 386c-422a,c; 433a-440a,c; 532b-539b; 541b,d-594d; 813a-b; 824b-830b esp 826a-b, 829d-830a
• 49 DARWIN: Origin of Species, 89b-c

7e(2) Electricity and matter: conduction, insulation, induction, electrochemical decomposition

• 30 BACON: Novum Organum, BK II, APH 48, 181b-c
• 45 FARADAY: Researches in Electricity, 265a-269a; 273a-277a; 306a; 309a-312a; 312c-313d; 314b; 315a-b; 319b,d-345d; 361a-432d; 440b,d-514c; 515a-d; 522b,d-532d; 541b,d-584a,c; 824b-830b; 848b,d-855a,c

7e(3) The relation of electricity and magnetism: the electromagnetic field

• 28 GILBERT: Loadstone, BK II, 26d-34b
• 34 NEWTON: Principles, BK III, PROP 7, COROL I 282a
• 45 FARADAY: Researches in Electricity, 266b-d; 269a-302d; 305d-306a; 307a-309a; 313d-314c; 315a; 520b-521a; 528c-532a; 595a; 615a-619c; 658b,d-667c; 685d-686b; 759c-788c; 795b,d-813a; 816b,d-819a,c

7e(4) The relation of electricity to heat and light: thermoelectricity

• 34 NEWTON: Principles, BK III, GENERAL SCHOL, 372a / Optics, BK III, 516b-517a
• 45 FARADAY: Researches in Electricity, 305b-d; 306d-307a; 313d-314a; 314c-d; 315a; 404b-405a; 476a-506a; 515d-516a; 518a-d; 561b,d-569b; 580d-582b; 595a-607a,c
• 51 TOLSTOY: War and Peace, EPILOGUE II, 687d

7e(5) The measurement of electric quantities

• 45 FARADAY: Researches in Electricity, 277a-279a; 316b-318c; 366d-371d; 377d-390d; 444a-451a; 465d-467a,c; 768d-773d; 778b,d-788c

CROSS-REFERENCES

For:

• Considerations relevant to the basic concepts and laws of mechanics, see CHANGE 7d; QUANTITY 5a–5e; SPACE 2a; TIME I.
• Discussions of the role of experiment, induction, and hypotheses in physical science, see EXPERIENCE 5a-5c; HYPOTHESIS 4b-4d; INDUCTION 5; LOGIC 4b; PHYSICS 4a-4d; SCIENCE 5a-5e; and for the physicist’s treatment of causes, see CAUSE 2, 5b, 6; NATURE 3c(3); PHYSICS 2b; SCIENCE 4c.
• The general theory of applied mathematics or mathematical physics, see ASTRONOMY 2c; MATHEMATICS 5b; PHYSICS 1b, 3; SCIENCE 5c.
• Other discussions of the mathematical ideas or operations which are applied in mechanics, see MATHEMATICS 4a–4d; QUANTITY 3d(1), 4c, 6b.
• The relation of mechanics to the philosophy of nature and to other natural sciences, see PHILOSOPHY 1c; PHYSICS 2; SCIENCE 1c.
• Other treatments of the problem of qualitative change, see CHANGE 6a-6b; QUALITY 3a, 3c; QUANTITY 1a.
• Mechanism as a philosophy of nature, man, and history, see ANIMAL 1e; ELEMENT 5e-5f; HISTORY 4a(2); MAN 3c; MIND 2e; WILL 5c; WORLD 1b.
• Other discussions of motion and its laws, see ASTRONOMY 8c-8c(3); CHANGE 7–7d; MATTER 2b; and for the related consideration of the void and action-at-a-distance, see ASTRONOMY 3b; ELEMENT 5c; SPACE 2b(2)-2c.
• Another discussion of mass and weight, see QUANTITY 5d; for another discussion of velocity, acceleration, and momentum, see QUANTITY 5c; for another discussion of force, see QUANTITY 5e; and for another discussion of the composition of forces, see OPPOSITION 3d.

ADDITIONAL READINGS

Listed below are works not included in Great Books of the Western World, but relevant to the idea and topics with which this chapter deals. These works are divided into two groups:

I. Works by authors represented in this collection.

II. Works by authors not represented in this collection.

For the date, place, and other facts concerning the publication of the works cited, consult the Bibliography of Additional Readings which follows the last chapter of The Great Ideas.

I.

1. Kepler. Dioptrik
2. Descartes. The Principles of Philosophy, PART I, 6-7, 19, 24-27, 48-64; PART III, 48-102, 121-125; PART IV, 20-27, 133-187
3. Hobbes. Concerning Body, PART IV, CH 30
4. —. Examinatio et Emendatio Mathematicae Hodiernae
5. —. Dialogus Physicus
6. Huygens. Travaux divers de statique et de dynamique de 1659 a 1666
7. —. Percussion
8. —. L’horloge a pendule
9. —. Sur la cause de la pesanteur
10. —. Force centrifuge
11. —. Question de existence et de la perceptibilité du mouvement absolu
12. Berkeley. De Motu
13. Kant. Metaphysical Foundations of Natural Science
14. Goethe. Beitrage zur Optik
15. —. Theory of Colours
16. Hegel. Science of Logic, VOL II, SECT I, CH I
17. Faraday. The Various Forces of Matter and Their Relations to Each Other

II.

1. Epicurus. Letter to Pythocles
2. R. Bacon. Opus Majus, PART V
3. Nicolas of Cusa. The Idiot, BK IV
4. Stevin. L’art ponderaire, ou la statique
5. Boyle. New Experiments Physico-Mechanical
6. —. A Defence of the Doctrine Touching the Spring and Weight of the Air… Against the Objections of Franciscus Linus
7. Wallis. Mechanica: sive, De Motu
8. Guericke. Experimenta Nova
9. Leibniz. Discourse on Metaphysics, XV-XXII
10. —. Philosophical Works, CH 20 (On Nature in Itself)
11. —. New Essays Concerning Human Understanding, APPENDIX, CH 47-5
12. Voltaire. Letters on the English, XIV-XVII
13. Euler. Mechanik
14. D’Alembert. Traité de dynamique
15. Franklin. Experiments
16. J. Priestley. Experiments and Observations on Different Kinds of Air
17. —. Experiments and Observations Relating to Various Branches of Natural Philosophy
18. Carnot. Principes fondamentaux de l’équilibre et du mouvement
19. Lagrange. Mécanique analytique
20. Galvani. De Viribus Electricitatis in Motu Musculari Commentarius
21. Rumford. An Experimental Inquiry Concerning the Source of Heat
22. Laplace. Mécanique céleste (Celestial Mechanics)
23. Poinsot. Éléments de statique
24. T. Young. Miscellaneous Works, VOL I, NUMBER II, VII, IX-X, XVII-XVIII
25. Fresnel. Théorie de la lumière
26. Poncelet. Cours de mécanique
27. Airy. Gravitation
28. W. R. Hamilton. Dynamics
29. Whewell. The Philosophy of the Inductive Sciences, VOL I, BK III, CH 5-10
30. Joule. Scientific Papers
31. Helmholtz. Popular Lectures on Scientific Subjects, VII
32. W. Thomson and Tait. Treatise on Natural Philosophy
33. Tyndall. Light and Electricity
34. Reuleaux. The Kinematics of Machinery
35. Maxwell. Theory of Heat
36. —. A Treatise on Electricity and Magnetism
37. —. Matter and Motion
38. Rayleigh. The Theory of Sound
39. Stallo. Concepts and Theories of Modern Physics, CH 2-6, 9-12
40. Clifford. The Common Sense of the Exact Sciences, CH V
41. Ball. A Treatise on the Theory of Screws
42. Gibbs. Collected Works
43. C. S. Peirce. Collected Papers, VOL VI, PAR 35-87
44. Kelvin. Lectures on Molecular Dynamics and the Wave Theory of Light
45. —. Popular Lectures and Addresses
46. Pearson. The Grammar of Science
47. Appell. Traité de mécanique rationnelle
48. Hertz. The Principles of Mechanics
49. Mach. History and Root of the Principle of the Conservation of Energy
50. —. The Science of Mechanics
51. —. “On the Principle of the Conservation of Energy,” in Popular Scientific Lectures
52. Boltzmann. Prinzipien der Mechanik
53. B. Russell. Principles of Mathematics, CH 54, 56-59
54. Painlevé. Les axiomes de la mécanique
55. Santayana. Reason in Science, CH 3
56. Duhem. L’évolution de la mécanique
57. —. Les origines de la statique
58. —. Etudes sur Léonard de Vinci
59. Enriques. Problems of Science, CH 5-6
60. Heaviside. Electromagnetic Theory
61. Meyerson. Identity and Reality, CH 2-3, 10
62. Poincaré. Science and Hypothesis, PART III; PART IV, CH 12-13
63. —. Science and Method, BK II
64. Cassirer. Substance and Function, PART I, CH 4; SUP VII
65. Curie. Traité de radioactivité
66. E. T. Whittaker. A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
67. —. A History of the Theories of Aether and Electricity
68. Rutherford. Radio-active Substances and Their Radiations
69. Eddington. Space, Time, and Gravitation
70. Einstein. Relativity: The Special and the General Theory
71. —. Sidelights on Relativity
72. —. The Meaning of Relativity
73. Levi-Civita. Fragen der klassischen und relativistischen Mechanik
74. Planck. Das Prinzip der Erhaltung der Energie
75. —. Treatise on Thermodynamics
76. —. “The Place of Modern Physics in the Mechanical View of Nature,” in A Survey of Physics
77. Whitehead. Science and the Modern World, CH I-IV
78. Bridgman. The Logic of Modern Physics, CH 3
79. Schrödinger. Collected Papers on Wave Mechanics
80. —. Four Lectures on Wave Mechanics
81. Bohr. Atomic Theory and the Description of Nature
82. Broglie. An Introduction to the Study of Wave Mechanics
83. Dirac. The Principles of Quantum Mechanics
84. Heisenberg. The Physical Principles of the Quantum Theory
85. Nagel. On the Logic of Measurement
86. M. R. Cohen. Reason and Nature, BK II, CH 2-3
87. C. G. Darwin. The New Conceptions of Matter
88. Lenzen. The Nature of Physical Theory, PART I, II
89. Bergson. Time and Free Will
90. —. Creative Evolution, CH 1, 4
91. —. Two Sources of Morality and Religion, CH 4
92. Wiener. Cybernetics