Popular Science Monthly/Volume 4/December 1873/The Primary Concepts of Modern Physical Science III

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THE PRIMARY CONCEPTS OF MODERN PHYSICAL SCIENCE.
By J. B. STALLO.

III. — The Assumption of the Essential Solidity of Matter.

IT cannot have escaped the notice of the attentive reader of the passage quoted in my last paper from Prof. Tyndall's lecture on "The Use of the Scientific Imagination" that Tyndall urges the theory of the atomic constitution of matter as the only theory consistent with its objective reality. He takes it for granted that the alternative lies between the definite, tangible, solid atom on the one hand, and a shadowy abstraction—a "vibrating, multiple proportion, or a numerical ratio in a state of oscillation"—on the other. There is no doubt that the opinion thus expressed is shared by the great majority of physicists, as well as of ordinary untrained men. To the minds of most persons, as to the mind of Tyndall, the conception of matter involves the notion of definite, tangible, and indestructible solidity. It is the general tacit assumption that, of the three molecular states, or states of aggregation, in which matter presents itself to the senses — the solid, the liquid, and the gaseous — the last two are simply disguises of the first; that a gas, for instance, is in fact a group or cluster of solids, like a cloud of dust, differing from such a cloud only by the greater regularity in the forms and distances of the particles whereof it is composed, and by the fact that these particles are controlled in the case of a gas by their mutual attractions and repulsions, while in the case of the cloud of dust they are under the sway of extrinsic forces. And, while the transition of the three molecular states into each other in regular and invariable order is too obvious to be ignored, it is supposed that the solid is the primary, normal, and typical state of which the liquid and gaseous, or aëriform, states are simply derivatives, and that, if these states are considered as evolved the one from the other, the order of evolution is from the solid to the vapor or gas. In this view the solid form of matter is not only the basis and origin of all its further determinations—of all its evolutions and changes—but it is also the primary and typical element of its mental representation and conception.

While this view of the relation between the molecular states of matter is all but universally prevalent, it is not difficult to show that it is in irreconcilable conflict with the facts of scientific experience. All evolution proceeds from the relatively Indeterminate to the relatively Determinate, and from the comparatively Simple to the comparatively Complex. And (confining our attention, for the moment, to the two extreme terms of the evolution, the solid and the gas, and ignoring the intermediate liquid) a comparison of the gaseous with the solid state of matter at once shows that the former is, not the end, but the beginning of the evolution. The gas is not only comparatively indeterminate—without fixity of volume, without crystalline or other structure, etc.—but it also exhibits, in its functional manifestations, that simplicity and regularity which is characteristic of all types or primary forms. Looking, first, to the purely physical aspect of a gas—I speak, of course, only of gases which are approximately perfect, to the exclusion of vapors at low temperatures and of gases which are readily coercible: its volume expands and contracts inversely as the pressure to which it is subjected; its velocity of diffusion is inversely proportional to the square root of its density; its rate of expansion is uniform for equal increments of temperature; its specific heat is the same at all temperatures, and, in a given weight, for all densities and under all pressures; the specific heats of equal volumes of simple and incondensible gases, as well as of compound gases formed without condensation, are the same for all gases of whatever nature, and so on. In all these respects the contrast with both the liquid and solid forms, the relations of whose volumes, or structures, or both, to temperature and to mechanical pressure or other force are complicated in the extreme, is great and striking. But this contrast becomes still more signal, secondly, under the chemical aspect. We cannot, in any proper sense, assign the proportions of volume in which the combination of solids and liquids takes place—indeed, the combination of solids as such is impossible—and the numbers expressive of the proportions of the combining weights upon their face exhibit an appearance of inflation and irregularity which the most sustained endeavors of scientific men (such as Dumas, Strecker, Cooke, L. Meyer, Mendelejeff, and Baumhauer) have been unable to obliterate. In the combination of gases, on the contrary, all is simplicity and order. "The ratio of volumes, in which gases combine, is always simple, and the volume of the resulting gaseous product bears a simple ratio to the volumes of its constituents"—such is the law of the combination of gaseous volumes known as the law of Gay-Lussac. By weight, the ratio of combination between hydrogen and chlorine is 1 to 35.5; by volumes, one volume of hydrogen combines with one volume of chlorine (the volumes being taken, of course, at the same pressures and temperatures) so as to form two volumes of hydrochloric acid. Oxygen and hydrogen combine in the proportion of 16 to 2 by weight; but one volume of oxygen combines with two volumes of hydrogen, forming two volumes of watery vapor. Nitrogen and hydrogen, whose atomic weights, so called, are 14 and 1 respectively, combine in the simple ratio of one volume of nitrogen to three volumes of hydrogen, the combination resulting in two volumes of gaseous ammonia. And carbon, whose 'atomic weight' is 12, though it cannot be actually obtained in gaseous form, is assumed by all chemists (for reasons not necessary to state here) to combine with hydrogen in the ratio of one volume to four, so as to yield two volumes of marsh-gas.

It seems to be evident, then, that the typical and primary state of matter is, not the solid, but the gas. And, this being so, it follows that the molecular evolution of matter conforms to the law of all evolution in proceeding from the indeterminate to the determinate, from the simple to the complex, from the gaseous to the solid form. This is no longer a mere presumption; if the nebular hypothesis, so called, after being stripped of its non-essential features, is recognized as a true theory—as it is by all the prominent physicists of the day since the recent revelations of the spectroscope—the gaseous form of matter, in fact, precedes the liquid and solid forms in the order of Nature, and the solid is not the initial, but the concluding term of material evolution. Inasmuch, therefore, as the explanation of any phenomenon consists in the exhibition of its genesis from its simplest beginnings, or from its earliest forms, the gaseous form of matter is the true basis for the explanation of the solid form, and not conversely the solid for the explanation of the gas.

From the foregoing considerations I take it to be evident that the true relation between the molecular states of matter is the exact reverse of that universally assumed. The universality of this assumption, however, indicates that it is not due to a mere chance error of speculation, but to some natural bias of the mind. The question arises, therefore: What is the origin of this prevalent delusion respecting the constitution of matter? I believe the answer to this question to be exceedingly simple, and important in proportion to its simplicity. There are certain fallacies to which the human intellect is liable by reason of the laws of its growth which I propose to call structural fallacies, one of which is that the intellect tends to confound the order of the genesis of its ideas respecting material objects with the order of the genesis of these objects themselves. It is well known that the progress of our knowledge depends upon analogy—upon a reduction of the Strange and Unknown to the terms of the Familiar and Known. In a certain sense it is true, what has been often said, that all cognition is recognition. "Man constantly institutes comparisons," says Pott (" Etymologische Forschungen," ii., 139), "between the new which presents itself to him, and the old which he already knows." That this is so is shown by the development of language. The great agent in the evolution of language is metaphor—the transference of a word from its ordinary and received meaning to an analogous one. This transference of the name descriptive of a known and familiar thing to the designation of an unknown and unfamiliar thing typifies the proceeding of the intellect in all cases where it deals with new and strange phenomena. It assimilates these phenomena to those which are known; it identifies the Strange, as far as possible, with the Familiar; it apprehends that which is extraordinary and uncommon in terms of that which is ordinary and common. But that which is most obvious to the senses is both the earliest and most persistent presence in consciousness, and thus receives the stamp of the greatest familiarity. Now, the most obtrusive form of matter is the solid, and for this reason it is that form which is first cognized by the infant intellect of mankind, and thus serves as the basis for the subsequent recognition of other forms. Accordingly we find that, on the early stages of human history, the solid alone was apprehended as material. It was long before even atmospheric air, obtrusive as it was in wind and storm, came to be known as a form of matter. To this day words signifying wind or breath—animus, spiritus, geist, ghost, etc.—are the terms denoting that which is the fundamental correlate of matter, even in the languages of civilized nations. And it is very questionable whether either the ancient philosophers or the mediæval alchemists distinctly apprehended any aëriform substance, other than atmospheric air, as material. It is certain that up to the time of Van Helmont, in the latter part of the sixteenth and the first decades of the seventeenth century, aëriform matter was not the subject of sustained scientific investigation.

It is obvious, then, that, while the progress of evolution in Nature is from the aëriform to the solid state of matter, the progress of the evolution of knowledge in the minds of men was conversely from the solid to the aëriform; and, as a consequence, the aëriform or gaseous state came to be apprehended as a mere modification of solidity. For the same reason, the first form of material action which was apprehended by the dawning intellect of man was the interaction between solids—mechanical interaction—and from this, again, it followed that the difference between the solid and the gas was apprehended as a mere difference of distance between the solid particles, as produced by mechanical motion.

Again: familiarity, in the minds of ordinary men, is universally confounded with simplicity. And, the explanation of a phenomenon consisting, as we have seen, in an exhibition of its genesis from its simplest beginnings, the mind, in its attempts to explain the gaseous form, naturally retraces the steps in the evolution of its ideas concerning matter—of its concepts of matter—back to the earliest, most familiar, and therefore apparently simplest form in which matter was and is apprehended, and assumes the solid particle, the atom, as the ultimate fact, as the primary element for all representation and conception of material existence.

This is not the place to develop the important consequences which flow from the total subversion of the prevailing concepts respecting the constitution of matter that, in my judgment, is inevitable. When it comes to be fully realized that an aëriform body is not a group of absolute solids, but is elastic to the core; that a gas is a gas throughout, and in its very essence; that in the simplest states of matter there is no absolute residuum which is exempt from all change and remains constant amid all variation—when the relation of primordial matter to its structural, or rather formative, agencies is properly understood—the whole science of molecular statics and dynamics will press at once for thorough reorganization.

It may be proper, in this connection, before I proceed to the discussion of another topic, to say a few words about the ordinary mechanical explanation of the molecular states of matter, or states of aggregation, on the basis of the atomic theory. This explanation proceeds on the assumption that the molecular states are produced by the conflict of antagonistic central forces—molecular attraction and repulsion—the preponderance of the one or the other of which gives rise to the solid and gaseous forms, while their balance or equilibrium results in the liquid state. The utter futility of this explanation is apparent at a glance. Even waiving the considerations presented by Herbert Spencer ("First Principles," p. 60, et seq.) that, in view of the necessary variation of the attractive and repulsive forces in the inverse ratio of the squares of the distances, the constituent atoms of a body, if they are in equilibrio at any particular distance, must be equally in equilibrio at all other distances, and that their density or state, therefore, must be invariable; and, admitting that the increase or diminution of the repulsive force, heat, may render the preponderance of either force, and thus the change of density or state of aggregation, possible: what becomes of the liquid state as corresponding to the exact balance of these two forces in the absence of external coercion? The exact balance of the two opposing forces is a mere mathematical limit which must be passed with the slightest preponderance of either force over the other. All bodies being subject to continual changes of temperature, the equilibrium can at best be but momentary; it must of necessity be of the most labile kind. If the mechanical explanation of the molecular states were valid, all bodies would present the phenomena exhibited by arsenic under the action of heat—they would at once pass from the solid into the gaseous form, the intervening liquid state vanishing after the manner of all limits.

The notion of the essential solidity of matter of necessity leads to—indeed, at bottom, is identical with—the assumption of its absolute hardness or unchangeability of volume, and thus involves the theory of the atomic constitution of matter in its ordinary form. This assumption is connected with another fallacious bias of the mind, which results from the inability of the mind to consider phenomena otherwise than singly, and under some one definite aspect—the tendency to assign absolute limits to every series of material phenomena. It has been a favorite tenet, not only of metaphysicians but of physicists as well, that reality is cognizable only as absolute, permanent, and invariable, or, as the metaphysicians of the sixteenth and seventeenth centuries expressed it, sub specie œterni et absoluti. This proposition, like so many others which have served as pillars of imposing metaphysical structures, is the precise opposite of the truth. All material reality is, in its nature, not absolute, but essentially relative. All material reality depends upon determination; and determination is essentially limitation, as even Spinoza well knew. A "thing in and by itself" is an impossibility. And I may add here (without dwelling upon it further, a discussion of this subject being foreign to my theme), the "thing per se" is not only impossible, according to the criteria of our intellect, but it is not the object of knowledge, in any sense, and cannot, therefore, be the legitimate subject of speculation. As Ferrier would say, we can neither know it nor be ignorant of it. I do not speak here merely of objects without relation to the intellect, in the sense of Ferrier's "Theory of Ignorance," but of objects without relation to each other. "We only know anything," justly says John Stuart Mill ("Examination of Sir W. Hamilton's Philosophy," i., 14), "by knowing it as distinguished from something else; all consciousness is of difference; two objects is the smallest number required to constitute consciousness; a thing is only seen to be what it is by contrast with what it is not." Here, again, the doctrines of psychology are corroborated by the teachings of the science of language. "Words," says Rev. Richard Garnett ("Philological Essays," p. 282), "express the relations of things; and this, it is believed, is strictly applicable to every word in every language, and under every possible modification."

Among those who have had occasion of late to insist upon the relativity of all objective reality is Prof. Helmholtz. Speaking of the inveterate prejudice according to which the qualities of things must be analogous to, or identical with, our perceptions of them, he says ("Die neueren Fortschritte in der Theorie des Sehens," Pop. wiss. Vortraege II., 55, et seq.): "Every property or quality of a thing is in reality nothing else than its capability of producing certain effects on other things. The effect occurs either between connatural parts of the same body, so as to produce differences of aggregation, or it proceeds from one body to another, as in the case of chemical reactions; or the effects are upon our organs of sense and manifest themselves as sensations such as those with which we are here concerned (the sensations of sight). Such an effect we call a 'property,' its reagent being understood without being expressly mentioned. Thus we speak of the 'solubility' of a substance, meaning its behavior toward water; we speak of its 'weight,' meaning its attraction to the earth; and we may justly call a substance 'blue,' under the tacit assumption that we are only speaking of its action upon a normal eye. But, if what we call a property always implies a relation between two things, then a property or quality can never depend upon the nature of one agent alone, but exists only in relation to and dependence on the nature of some second object acted upon. Hence, there is really no sense in talking of properties of light which belong to it absolutely, independently of all other objects, and which are supposed to be representable in the sensations of the human eye. The notion of such properties is a contradiction in itself. They cannot possibly exist, and therefore we cannot expect to find any coincidence of our sensations of color with qualities of light."

The fundamental truth which is implied in these sentences is of such transcendent importance that it is hardly possible to be too emphatic in its statement, or too profuse in its illustration. All quality is relation; all action is reaction; all force is antagonism; all measure is a ratio between terms neither of which is absolute; every objectively real thing is a term in numberless series of mutual implications, and its reality outside of these series is utterly inconceivable. A material entity, absolute in any of its aspects, would be nothing less than a finite infinitude. There is no absolute material quality, no absolute material substance, no absolute physical unit, no absolutely simple physical entity, no absolute constant, no absolute standard either of quantity or quality, no absolute motion, no absolute rest, no absolute time, no absolute space. There is no physical thing, nor is there a real or conceptual element of such a thing, which is either its own support or its own measure, and which abides either quantitatively, or qualitatively, otherwise than in perpetual change, in an unceasing flow of mutations. An object is large only as compared with another which, as a term of this comparison, is small, but which, as a term in a comparison with a third object, may be indefinitely large; and the comparison which determines the magnitude of objects is between its terms alone, and not between any or all of these terms, and an absolute standard. An object is hard as compared with another which is soft, but which, in turn, may be contrasted with a third still softer; and, again, there is no standard object which is either absolutely hard or absolutely soft. A body is simple as compared with the compound into which it enters as a constituent; but there is, and can be no physically real thing which is absolutely simple. Similarly, all changes of position or distance between two bodies are wholly relative, and it is a matter of purely arbitrary determination, which of them is taken as being at rest, and which as in motion. It is equally true to say that the earth falls toward the apple, and that the apple falls toward the earth.

I may observe, in this connection, that not only the law of causality, the persistence of force, and the indestructibility of matter, have their root in the relativity of all objective reality—being, indeed, simply different aspects of this relativity—but that Newton's first and third laws of motion, as well as all laws of least action, so called, in mechanics (including Gauss's law of movement under least coercion), are but corollaries from the same principle. And the fact that every thing is, in its manifest existence, but a group of relations and reactions, at once accounts for Nature's inherent teleology.

The truth that all our knowledge of objective reality depends upon the establishment or recognition of relations, has been proclaimed by innumerable thinkers, but, nevertheless, is constantly lost sight of, or ignored. There is nothing more interesting and instructive, than a review of the errors and perplexities that have been entailed by the rejection or disregard of this truth both upon metaphysical speculation, and upon physical science. The ontological vagaries spun from the proposition that all reality is in its last elements absolute, do not, of course, concern us here; there is, however, one form of this proposition which is so intimately connected with the main subject under discussion, that it is, perhaps, well to indulge in a passing allusion to it.

Leibnitz places at the head of his "Monadology" the principle that there must be simple substances, because there are compound substances. "Necesse est," he says, "dari substantias simplices quia dantur compositœ." This enthymeme, though it has been long since exploded in metaphysics, is still regarded by many physicists as proof of the real existence of absolutely simple constituents of matter. Nevertheless, it is obvious that it is nothing but a vicious paralogism—a fallacy of the class known in logic as fallacies of suppressed relative. The existence of a compound substance certainly proves the existence of component parts which, relatively to this substance, are simple. But it proves nothing whatever as to the simplicity of these parts in themselves.

Among the most notable intellectual hobbles resulting from the attempt to deal with quantity as an absolute, self-determining entity are the various theories of infinitesimals in mathematics, and of the real basis of the differential and integral calculus. The consideration of these theories is beyond the limits of my task, which restricts me to the discussion of questions relating to physical science. But within these limits, it is by no means difficult to find conspicuous proof of the fact that the supposed physical constant of weight and volume, the "atom," is by no means the only absolute real term—the only finite infinitude—which is postulated by physical science in its most recent forms. How completely the minds of modern physicists are under the control of the conceit that physical entities, for purposes of their real apprehension, can be disentangled from the net-work of relations as a part of which they present themselves both to thought and to sense, is at once seen upon the most cursory examination of the remarkable speculative writings which have been published of late by eminent scientific men. I select from the many lectures and essays of this class which have fallen under my notice, a lecture delivered November 3, 1869, in the Aula of the University of Liepsic, by Dr. C. Neumann (Professor of Mathematics at the university, and well known as the author of several important contributions to the theory of Abel's Integrals), "On the Principles of the Galileo-Newtonian Theory."[1] The first part of this lecture is without special interest for us here; but the second part is of the greatest possible significance as an exhibition of the tendency of physicists to postulate determinate last elements, absolute spatial limits, and invariable physical standards in the construction of material phenomena. For this reason, I shall take the liberty of reproducing, as literally as is possible in a translation, the most important passages of this part of the lecture.

"The principles of the Galileo-Newtonian theories," says Prof. Neumann (loc. cit., p. 11), "consist in two laws—the law of inertia proclaimed by Galileo, and the law of attraction added by Newton. . . . A material point, when once set in motion, free from the action of an extraneous force, and wholly left to itself, continues to move in a straight line so as to describe equal spaces in equal times. Such is Galileo's law of inertia. It is impossible that this proposition should stand in its present form as the corner-stone of a scientific edifice, as the starting-point of mathematical deductions. For it is perfectly unintelligible, inasmuch as we do not know what is meant by "motion in a straight line," or, rather, inasmuch as we do not know that the words "motion in a straight line" are susceptible of various interpretations. A motion, for instance, which is rectilinear as seen from the earth, would be curvilinear as seen from the sun, and would be represented by a different curve as often as we change our point of observation to Jupiter, to Saturn, or another celestial body. In short, every motion which is rectilinear with reference to one celestial body, will appear curvilinear with reference to another celestial body. . . . . .

"The words of Galileo, according to which a material point left to itself proceeds in a straight line, appear to us, therefore, as words without meaning—as expressing a proposition which, to become intelligible, is in need of a definite background. There must be given in the universe some special body as the basis of our comparison, as the object in reference to which all motions are to be estimated; and only when such a body is given, shall we be able to attach to those words a definite meaning. Now, what body is it which is to occupy this eminent position? Or, are there several such bodies? Are the motions near the earth to be referred to the terrestrial globe, perhaps, and those near the sun, to the solar sphere? . . . .

"Unfortunately, neither Galileo nor Newton gives us a definite answer to this question. But, if we carefully examine the theoretical structure which they erected, and which has since been continually enlarged, its foundations can no longer remain hidden. We readily see that all actual or imaginable motions in the universe must be referred to one and the same body. Where this body is, and what are the reasons for assigning to it this eminent, and, as it were, sovereign position, these are questions to which there is no answer.

"It will be necessary, therefore, to establish the proposition, as the first principle of the Galileo-Newtonian theory, that in some unknown place of the universe there is an unknown body—a body absolutely rigid and unchangeable for all time in its figure and dimensions. I may be permitted to call this body "The body Alpha." It would then be necessary to add that the motion of a body would import, not its change of place in reference to the earth or sun, but its change of position in reference to the body Alpha.

"From this point of view the law of Galileo is seen to have a definite meaning. This meaning presents itself as a second principle, which is, that a material point left to itself progresses in a straight line proceeds, therefore, in a course which is rectilinear in reference to the body Alpha."

It will be observed that the assumption which underlies all this reasoning of Prof. Neumann is that, to conceive motion as real, it is necessary to conceive it as absolute—an assumption in every respect analogous to that of Prof. Tyndall, according to which the reality of matter implies its constitution from absolute, unvarying elements. The logical parentage of the body Alpha is precisely the same as that of the "atom." And I may add that the assumption of Prof. Neumann is the tacit assumption of almost all the physicists and philosophers of the day, although it is not usually developed to its last consequences. It is one of the tasks of Herbert Spencer, for instance, to exhibit the contradictions involved in the essential relativity of motion. "A body impelled by the hand," says Spencer ("First Principles," chap, iii., §17), "is clearly perceived to move, and to move in a definite direction: there seems at first sight no possibility of doubting that its motion is real, or that it is toward a given point. Yet it is easy to show that we not only may be, but usually are, quite wrong in both these judgments. Here, for instance, is a ship which, for simplicity's sake, we will suppose to be anchored at the equator, with her head to the west. When the captain walks from stem to stern, in what direction does he move? East is the obvious answer—an answer which for the moment may pass without criticism. But now the anchor is heaved, and the vessel sails to the west with a velocity equal to that at which the captain walks. In what direction does he now move when he goes from stem to stern? You cannot say east, for the vessel is carrying him as fast toward the west as he walks to the east; and you cannot say west, for the converse reason. In respect to surrounding space, he is stationary, though to all on board the ship he seems moving. But now are we quite sure of this conclusion? Is he really stationary? "When we take into account the earth's motion round its axis, we find that, instead of being stationary, he is traveling at the rate of 1,000 miles per hour to the east; so that neither the perception of one who looks at him, nor the inference of one who allows for the ship's motion, is anything like the truth. Nor, indeed, on further consideration, shall we find the revised conclusion much better. For we have forgotten to allow for the earth's motion in its orbit. This being some 68,000 miles per hour, it follows that, assuming the time to be mid-day, he is moving, not at the rate of 1,000 miles per hour to the east, but at the rate of 67,000 miles per hour to the west. Nay, not even now have we discovered the true rate and the true direction of his movement. With the earth's progress in its orbit, we have to join that of the whole solar system toward the constellation Hercules; and, when we do this, we perceive that he is moving neither east nor west, but in a line inclined to the plane of the ecliptic, and at a velocity greater or less (according to the time of the year) than that above named. To which let us add that, were the dynamic arrangements of our sidereal system fully known to us, we should probably discover the direction and rate of his actual movement to differ considerably even from these. How illusive are our ideas of motion is thus made sufficiently manifest. That which seems moving proves to be stationary; that which seems stationary proves to be moving; while that which we conclude to be going rapidly in one direction turns out to be going much more rapidly in the opposite direction. And so we are taught that what we are conscious of is not the real motion of any object, either in its rate or direction, but merely its motion as measured from an assigned position—either the position we ourselves occupy or some other. Yet in this very process of concluding that the motions we perceive are not the real motions, we tacitly assume that there are real motions. In revising our successive judgments concerning a body's course or velocity, we take for granted that there is an actual course or an actual velocity—we take for granted that there are fixed points in space with respect to which all motions are absolute; and we find it impossible to rid ourselves of this idea. Nevertheless, absolute motion cannot even be imagined, much less known. Motion, as taking place apart from those limitations of space which we habitually associate with it, is totally unthinkable. For motion is change of place; but, in unlimited space, change of place is inconceivable, because place itself is inconceivable. Place can be conceived only by reference to other places; and, in the absence of objects dispersed through space, a place could be conceived only in relation to the limits of space; whence it follows that in unlimited space place cannot be conceived—all places must be equidistant from boundaries that do not exist. Thus, while we are obliged to think that there is an absolute motion, we find absolute motion incomprehensible."

I have quoted this elaborate exposition from the text of Mr. Spencer, because it most clearly evinces the difficulty experienced even by those who habitually insist upon the relativity, not only of all our actual knowledge, but also of all our possible cognition, in freeing themselves from the prejudice that nothing can be real which is not absolute.

Prof. Neumann is not content with showing, or attempting to show, that the reality of motion necessitates its reference to a rigid body unchangeable in its position in space, but he seeks to verify this assumption by asking himself the question what consequences would ensue, on the hypothesis of the mere relativity of motion, if all bodies in space, except one, were annihilated. "Let us suppose," he says (loc. cit., p. 27), "that among the stars there is one which consists of fluid matter, and which, like our earth, is in rotary motion around an axis passing through its centre. In consequence of this motion, by virtue of the centrifugal forces developed by it, this star will have the form of an ellipsoid. What form, now, I ask, will this star assume if suddenly all other celestial bodies are annihilated?

"These centrifugal forces depend solely upon the state of the star itself; they are wholly independent of the other celestial bodies. These forces, therefore, as well as the ellipsoidal form, will persist, irrespective of the continued existence or disappearance of the other bodies. But, if motion is defined as something relative—as a relative change of place of two points—the answer is very different. If, on this assumption, we suppose all other celestial bodies to be annihilated, nothing remains but the material points of which the star in question itself consists. But, then, these points do not change their relative positions, and are therefore at rest. It follows that the star must be at rest at the moment when the annihilation of the other bodies takes place, and therefore must assume the spherical form taken by all bodies in a state of rest. A contradiction so intolerable can be avoided only by abandoning the assumption of the relativity of motion, and conceiving motion as absolute, so that thus we are again led to the principle of the body Alpha."

This reasoning of Prof. Neumann is irrefutable, if we concede the admissibility of his hypothesis of the destruction of all bodies in space but one. But the very principle of relativity forbids such an hypothesis. The annihilation of all bodies but one would not only destroy the motion of this one remaining body and bring it to rest, as Prof. Neumann sees, but it would also destroy its very existence and bring it to naught, as he does not see. A body cannot survive the system of relations in which alone it has its being; its presence or position in space is no more possible without reference to other bodies than its change of position or presence is possible without such reference; and, as I have abundantly shown, all properties of a body are in their nature relations, and imply terms beyond the body itself. The case put by Prof. Neumann is thus an attestation of the truth that the essential relativity of all physical reality implies the persistence both of force and of matter, so that his argument is a demonstration, not of the falsity, but of the truth of the principle of relativity.

As there is no Unconditional in subjective thought, so there is no Absolute in objective reality. There is no absolute system of coordinates in space to which the positions of bodies and their changes can be referred; and there is neither an absolute measure of quantity, nor an absolute standard of quality. There is no physical constant.

 
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  1. "Ueber die Principien der Galilei-Newton'schen Theorie. Akademische Antrittsvorlesung gehalten in der Aula der Universität, Leipzig, am 3. November, 1869. Von Dr. C. Neumann, ord. Professor der Mathematik an der Universität, Leipzig," etc. Leipzig, B. G. Teubner, 1870.