Popular Science Monthly/Volume 4/January 1874/The Primary Concepts of Modern Physical Science IV
By J. B. Stallo.
IV. Inertia and Force.
IF we look for the speculative background of modern physical theories, we find something like this: Originally there was created, or somehow came to be, an indefinite number of absolutely hard and unchangeable particles of matter. There was also created, or somehow came to be, a number of forces, equally unchangeable—the force of attraction, the force of cohesion, heat, electric and magnetic forces, and boon. The forces began to act and continue to act upon the particles of matter, producing inorganic as well as organic forms. These particles and forces are ultimate facts of experience as well as of thought; and the action of the forces upon the material particles is likewise an ultimate empirical datum, and therefore inexplicable. Force and matter, though presupposing each other in action, are fundamentally disparate; they are essentially distinct, and mutually irreducible entities. Matter, as such, is passive, dead; all motion or life is caused by force; and the only possible solution of the problems of physiology, no less than of physics and chemistry, consists in the enumeration of the forces acting upon the material particles, and in the exact quantitative determination of the effects produced by their action.
This statement of the tenets of the prevailing physical philosophy, to be exact, requires at most two qualifications. In the first place, the recent doctrine of the correlation and mutual convertibility of the physical forces, as a part of the theory of the conservation of energy, has shaken, if not destroyed, the conception of a multiplicity of independent original forces. And, in the second place, physiologists, like Du Bois-Reymond, recognize force as the invariable concomitant, if not the essential attribute of matter, and assume that to every constant primordial mass belongs a constant primordial quantity of force, so that the problem of physics, chemistry, and physiology, resolves itself into the quantitative determination of the mechanical interactions of material constants primarily endowed with forces acting equally in all directions, or, as they express it, constant central forces.
I have endeavored, thus far, to show that there are no absolute constants of mass; that both the hypothesis of corpuscular "atoms" and that of "centres of force" are growths of a confusion of the intellect which mistakes conceptual elements of matter for real elements; that these elements—force and mass, or force and inertia—are not only inseparable, as is conceded by the more thoughtful among modern physicists (or, as they usually, but inaccurately express it, that there is no force without matter, and no matter without force), but that neither of these elements has any reality as such, each of them being simply the conceptual correlate of the other, and thus the condition both of its realization in thought and of its objectivation to sense. The tendency to deal with these elements as separate and separately real entities is so irrepressible, however, that it is necessary to subject them to still further discussion, in order to clear up the prevalent confusion in regard to them.
Newton's original definition of inertia was in terms of force. According to him ("Principia," Definitio III.), "there is inherent in matter a force, a power of resistance, in virtue of which every body, as far as in it lies, perseveres in a state of rest, or of uniform rectilinear motion." In the definitions since Newton's time, the term "force" has usually been avoided. Thus Young ("Mechanics," p. 117) defines inertia as "the incapability of matter of altering the state into which it is put by any external cause, whether that state be rest or motion;" and similarly Whewell ("Mechanics," p. 245), as "the quantity of matter considered as resisting the communication of motion." As is readily seen, all these definitions imply, nevertheless, that matter can be moved or changed only from without, by forces external to matter itself. Newton expressly ("Principia," Definitio IV.) speaks of force as "impressed upon a body, and as exerted upon it to change its state of rest or uniform motion in a straight line."
There is little difficulty in understanding how this language, in connection with the etymological import of the word "inertia," led to the assumption that matter is essentially passive, or, as it is commonly expressed, dead. There are other reasons for this assumption, connected with the evolution, not only of scientific concepts, properly so called, but of cosmological ideas, to which I shall have occasion, perhaps, to recur in the sequel; indeed, Newton's definitions which I have just cited are simply instances of the intellectual postulates of his time. And the mathematical treatment of mechanical problems, from the nature of its methods, necessitates the fiction that force and mass are separate and distinct terms. In general, it may be said that the assumption of the absolute passivity of matter is one of those errors which are inevitable in the progress of knowledge—one of the "clay moulds in which the bells of scientific truth are cast." But the perpetuation of this error is one of the most fatal impediments to real scientific progress in our day, and is fruitful of vagaries which are wholly incommensurable with the real state of modern scientific knowledge. Thus, Prof. Philip Spiller, the author of a very serviceable manual of physics, and a prolific writer on scientific subjects, has recently published a cosmological treatise, whose theorems are founded upon the express proposition (op. cit., p. 4) that "no material constituent of a body, no atom, is in itself originally endowed with force, but that every such atom is absolutely dead, and without any inherent power to act at a distance." It appears from the further contents of Spiller's treatise, that he not only denies force to the atoms taken singly, but that he also denies the possibility of their mutual action. He is driven, therefore, to the assertion of the independent substantiality of force; and, accordingly, he assumes force to be an all-pervading quasi-material presence—as he terms it, an "incorporeal matter" (unkoerperlicher Stoff). In utter disregard of the fundamental correlation of force and mass, Spiller identifies his force-substance with the ordinary luminiferous ether, so that this phantom, which, in the view of other physicists, is not only imponderable, but destitute of cohesive, chemical, thermal, electric, and magnetic forces (which, indeed, must be destitute of them if it is to serve as the mere substratum of these various modes of motion)—which therefore is, if possible, still more "dead" than ordinary ponderable matter—now suddenly, without changing its name, and without ceasing to be the substratum of luminar and other undulations, comes to be the very quintessence of all possible energy.
It may be said here, parenthetically, that all these recent attempts (to one of which, by Prof. Challis, I had occasion to refer in my second paper) to construe the apparent attractions of bodies as cases of ethereal pressure and propulsion are simply returns to the state of scientific anarchy which prevailed in celestial mechanics before Newton's time. Prof. Spiller is evidently unaware that his theory—according to which, force is an "incorporeal matter"—is nothing but a reproduction of Kepler's speculations (not to speak of the Cartesian and Leibnitian theories to which I have already alluded), in which the vortices supposed to carry the planets along with them were asserted to be an "immaterial species," capable of overcoming the inertia of bodies. It is plain that this "immaterial species" is the same wooden iron which Spiller exhibits under the name of "incorporeal matter," the only difference being that the absurdity of Kepler's chimera was less glaring in the hazy dawn of the mechanical notions of his time, than the extravagance of Spiller's conceit in the light of the scientific atmosphere of our day.
It is almost superfluous to say to the intelligent reader of these papers that Spiller's "dead matter" is a nonentity, inasmuch as we know nothing of material reality except through its action. And it is hardly worth while to point out in detail that the hypothesis of dead atoms is not only inadmissible, but wholly useless. Unchangeable particles destitute of gravity and all other force, even if the action of force upon them were conceivable, must be equally acted upon from all sides by the omnipresent ether, and could, therefore, in no wise help to establish differences of density, or other differences not contained in or evolvable from the ether itself. They could not even add to the extension of a body, much less to its hardness, being wholly without the power of resistance; but, waiving this, and granting for a moment that extension without resistance is possible, they would simply be bubbles of void space encysted in the universal ether, and to the differentiation of this ether alone all the phenomena of the material world would be due.
The truth is, that absolutely passive, dead matter is as unknown in experience as it is inconceivable in thought. Every particle of matter of which we have any knowledge attracts every other particle in conformity to the law of gravitation; and every material element exerts chemical, electrical, magnetic, thermic, and similar forces upon other elements which in respect to these forces are its correlates. The whole presence of matter to the senses consists in the manifestation of power, in the exhibition of force. All this has been very clearly seen and very explicitly stated by numerous physicists; but, unfortunately, by most of them it has been speedily lost sight of in their ulterior speculations.
In what sense, then, can inertia be truly predicated of matter? The answer to this question will suggest itself at once to those who have properly apprehended the principle of the essential relativity of all material existence. A material object is, in every one of its aspects, but one term of a relation; its whole being is a presupposition of correlates without; all things are, figuratively speaking (if I may resort to such a figure without incurring the charge of illustrating obscurum per obscurius) shadows of each other. Every change of a body, therefore, presupposes a corresponding change in its correlates. If the state of any material object could be changed without a corresponding change of state in other objects without, this object would, to that extent, become absolute. But this is utterly unthinkable, and therefore utterly impossible, as we have already seen. At the same time it is also evident that, while every change of a body is thus conditioned by changes without, these latter changes are equally conditioned by it; that all material action, therefore, is mutual; that reaction is invariably equal to action. A corollary from, or rather an application of this is the well-known theorem that the forces within a body or conservative system can alter only the positions of its constituent parts, but cannot change the position of the body as a whole; and that, whenever such an internal change takes place, the momentum accruing in one direction has its counterpart in an equal momentum accruing in the opposite direction. If we apply this theorem to the universe as a whole, i. e., as a single dynamical system, and if we bear in mind that, mechanically speaking, all force properly so called, i. e., all potential energy, is energy of position, we see at once that whatever energy is spent in actual motion is gained in position—that the system, therefore, is absolutely conservative; and we are thus led, by a very simple approach, to the principle of the conservation of energy.
After this summary discussion of the first conceptual element of matter, inertia, I proceed to the consideration of the other element, force. In the canonical text-books on physics, force is defined as the cause of motion. "Any cause," says Whewell ("Mechanics," p. 1), "which moves or tends to move a body, or which changes or tends to change its motion, is called force." Similarly Clerk Maxwell ("Theory of Heat," p. 83): "Force is whatever changes or tends to change the motion of a body by altering either its direction or its magnitude." Taking either of these definitions as correctly representing the received theories of physical science respecting the nature of force, it is manifest, irrespective of the considerations which I have presented in this and the preceding essays, that force is not an individual thing or distinct entity which presents itself directly either to observation or to thought, but that, so far as it is taken as a definite and unital term in the operations of thought, it is purely a fiction of the intellect. The cause of motion, or change of motion, in a body is simply the condition or group of conditions upon which this motion depends; and this condition, or group of conditions, as we have already seen, is always a corresponding motion, or change of motion, in the bodies, outside of the moving body, which are its correlates. Otherwise expressed, force is a mere inference from the motion itself under the universal conditions of reality, and its measure, therefore, is simply the effect for which it is postulated as a cause; it has no other existence. The only reality of force and of its action is the correspondence between physical phenomena in conformity to the principle of the essential relativity of all material existence.
That force has no independent reality is so plain and obvious that it has been proposed by some thinkers to abolish the term force, like the term cause, altogether. However desirable this might be in some respects, it is impossible, for the reason that the concept "force," when properly interpreted in terms of experience, is valid, and, if its name were abolished, it would instantly reappear under another name. There is hardly any concept which has not, in science as well as in metaphysics, given rise to the same confusion which prevails in regard to "force" and "cause;" and the blow leveled at these would demolish all concepts whatever. Nevertheless, it is of the greatest moment, in all speculations concerning the interdependence of physical phenomena, never to lose sight of the fact that the reality of force is purely conceptual, and that it is not a distinct and individual tangible or intangible entity.
How imperfectly all this is understood by the physicists of our time appears at once upon an examination of elementary treatises as well as original disquisitions on physical science. Thus the relation of force to mechanical motion is constantly spoken of as a "fact" ascertained by experience and verified experimentally beyond the possibility of question. In a learned article by J. Croll, published in the July number, 1872, of the Philosophical Magazine ("What determines Molecular Motion," etc., Phil. Mag., fourth series, vol. xl., p. 37), it is said: "In regard to the first question (what produces motion) there is no diversity of opinion. All agree that what produces change or causes motion is force." The obvious meaning of this is that it might possibly admit of question whether material change or motion is produced by force or something else, and that physicists, on the whole, have come to the conclusion that it is produced by force. Such a question ought, indeed, to be solemnly pondered by grave philosophers! It is like the question which Simon Sachs, in his despair, propounded to the gods: 'Who will assure us that the star, which the astronomers regard as Uranus, is Uranus in fact?'"
Physicists generally, however, are in still greater confusion as to the nature of force in another respect. Bodies are said to be endowed with a definite quantity of force, if not with a given number of forces; it is assumed that to every particular body or particle belongs, or in such body or particle in and by itself is inherent, an invariable measure of energy. This statement, besides involving the confusion just noted as to the reality of force, implies the assumption that force can be an attribute or concomitant of a single body or particle as such. This assumption ignores the fact, which is otherwise well known to physicists, that the very conception of force depends upon the relation between two terms at least. "Every force," says Clerk Maxwell ("Theory of Heat," p. 94), "acts between two bodies or parts of bodies." A "constant central force," therefore, as belonging to an individual atom in and by itself, is an impossibility.
We have now arrived at a point where it will be profitable to recur for a moment to the proposition of Du Bois-Reymond referred to at the beginning of my first paper, that the whole problem of physical science consists in "the resolution of all changes in the material world into motions of atoms caused by their constant central forces." The entire passage in Du Bois-Reymond's text, from which I extracted two sentences, reads as follows: "Natural science—more accurately expressed, scientific cognition of Nature, or cognition of the material world by the aid and in the sense of theoretical physical science—is a reduction of the changes in the material world to motions of atoms caused by central forces independent of time, or a resolution of the phenomena of Nature into atomic mechanics. It is a fact of psychological experience that, whenever such a reduction is successfully effected, our craving for causality is, for the nonce, wholly satisfied. The propositions of mechanics are mathematically representable, and carry in themselves the same apodictic certainty which belongs to the propositions of mathematics. When the changes in the material world have been reduced to a constant sum of potential and kinetic energy, inhering in a constant mass of matter, there is nothing left in these changes for explanation.
"The assertion of Kant in the preface to the 'Metaphysical Rudiments of Natural Science,' that 'in every department of physical science there is only so much science, properly so called, as there is mathematics,' is to be sharpened by substituting 'mechanics of atoms' for 'mathematics.' This was evidently his own meaning when he denied the name 'science' to chemistry. It is not a little remarkable that in our time chemistry, since it has been constrained, by the discovery of substitution, to abandon the old electro-chemical dualism, has seemingly taken a retrograde step in its advance toward science in this sense. The resolution of all changes in the material world into motions of atoms caused by their constant central forces would be the completion of natural science."
How do these sentences of one of the foremost physicists of the day now present themselves to our view in the light of the preceding discussion? Atoms are absolute physical constants, or constants of mass; and I have shown that there are, and can be, no absolute constants of mass. And it is evident now, I trust, that there are similarly no constant central forces belonging to, or inherent in, constants of mass as such. Both the constants of mass and the constant forces assumed to belong to them are simply parts of the scaffolding of the intellect, when it seeks to subject the phenomena of the material world to exact mathematical determination. They are, as I have already intimated, instrumental fictions which are, for the moment, indispensable by reason of the inability of the intellect to deal with phenomena otherwise than singly and under a definite aspect. In order to effect a quantitative determination of material action, the mathematician is constrained to insulate the conceptual elements of matter and to treat them as separate and distinct terms. He is constrained to represent as discrete what is continuous, and as absolute what is relative. In this, as he knows, or ought to know, very well, he is doing violence to the fact. But this violence is harmless, provided he does not forget that what appears in abstract insulation in his formulæ exists in concrete and indissoluble union in Nature, and what he exhibits as unconditioned in thought is essentially conditioned in objective reality. The steps to all scientific knowledge consist in a series of representative fictions. When the old Greek sought to determine the properties of the circle, he began by constructing a polygon whose sides he subdivided until they were supposed to become infinitely small; and in his view every line of definite extent and form, i. e., every line which could become the subject of mathematical investigation, was composed of an infinite number of infinitely small straight lines. But he speedily found that, while this fiction enabled him to deduce a rule for calculating the area of the circle and otherwise to determine a number of its properties, nevertheless the circle and its rectilinear diameter were fundamentally incommensurable, and the quadrature of the circle was impossible. The modern analyst similarly determines the "locus" of a curve by the relation of small increments of coordinates arbitrarily established; but he is well aware that the curve itself has nothing to do with this arbitrary representation, and he very emphatically asserts the continuity of the curve by differentiating, or passing to the "limit" of, his increments—at the same time transforming his coördinates by changing their origin or their inclination, or even their system, from bilinears to polars, whenever he finds it convenient, without ever dreaming that thereby he is in the least affecting the nature of the curve whose properties are under discussion. The astronomer, in calculating the attraction of a sphere upon a "material point," begins by assuming the atomic or molecular constitution of the attracting sphere, establishing a series of finite differences as one of the terms of his equation; but thereupon he takes the series to be infinite and the differences to be infinitely small, and very effectually dismantles the molecular scaffolding by integrating instead of effecting a summation of a series of finite differences. Observe: the astronomer begins with two fictions—the fiction of the "material point" (which is, in truth, a contradiction in terms), so as to insulate the attractive force and treat it as proceeding from the sphere alone, and the fiction of the finite differences representing the molecular constitution of the sphere; but the validity of his result depends upon the eventual rescission of these fictions and the rehabilitation of the fact. In like manner, the chemist represents the proportions of weight in which substances combine, as atoms of definite weight and figure, and the resulting compounds as definite groups of such atoms; and this mythical coinage has, no doubt, been serviceable in some ways. But, apart from the circumstance, avowed by thoughtful chemists themselves, that the symbols have become wholly inadequate to the proper representation of the facts, and that new representative fictions will have to be resorted to, it is important to bear in mind always that the symbol is not the fact, and that the fiction is very different from the reality. Newton derived many of the leading optical laws from his corpuscular theory of light and from the hypothesis of "fits of easy transmission and reflection." His theory for a time served a good purpose; but it proved, after all, to be but a convenient mode of symbolizing the phenomena with which he was familiar, and had to be discarded when the phenomenon of interference was observed. In 1824 Sady Carnot deduced the law of thermic action, which still bears his name, from an hypothesis respecting the nature of heat (supposed by him, as by nearly all the physicists of his time, to be imponderable matter), which is now known, or universally believed to be, erroneous. Since his time, Clausius, Rankine, Thomson, and Clerk Maxwell, have shown that thermic phenomena find a very convenient representation in the hypothesis that gaseous molecules are in a state of incessant motion; and Maxwell has even succeeded in predicting the phenomenon of the gradual cessation of the oscillatory movement of a disk, suspended between two other disks, in consequence of the friction of a gaseous medium, whatever be the degree of its tenuity, and this prediction has since been verified by experiment, just as Hamilton's prediction of conical refraction was verified by the experiments of Lloyd; but, of course, neither Clausius's and Rankine's formulæ, nor Maxwell's experiments, are conclusive as to the real nature of a gas. In all such cases science erects a scaffolding which is invariably kicked down as soon as its work has been accomplished. And, if the scientific architects are so captivated with the scaffolding that they insist upon maintaining it intact, its eventual demolition is none the less sure in the progress of observation and experiment. Facts supply the ictus calcis which the theorist refuses to administer.
Du Bois-Reymond's proposition is nothing less than this, that natural science is constrained, by the law of all its methods, to exhibit the arbitrary scaffolding of the intellect as the real nature of the universe. He not only confounds the scaffolding of his intellect with its own structure, but he confounds this scaffolding with the structure of Nature. He mistakes the beams of his temporary platform for the rafters of the permanent edifice; the arbitrary masses of his mathematical calculations (the "atoms") for bricks of Nature's building; and the ropes of his scientific tackling (the "forces") for the ingenerate energy of the Universe. There are, it is true, passages in Du Bois-Reymond's lecture which may be construed as a virtual disclaimer of this, but his assumption that the limits of mathematical reasoning about atoms and their constant central forces are the irremovable bounds of all possible knowledge respecting physical phenomena, and the emphatic "Ignoramus—Ignorabimus" with which he concludes his lecture, utterly invalidate the disclaimer. He forgets that the framework on which he and his compeers have thus far been stationed is by no means the only scaffolding that can be devised. The spectroscope has convinced the chemist that a chemical analysis can be effected otherwise than by mixing substances in a testing-tube, and that he can react upon the gas of a distant comet as well as upon the hydrogen in the water which flows from a stop-cock in his laboratory. Modern analysis has shown that the limits of mathematical insight, which the synthetical geometrician supposed to be absolute, may be transcended indefinitely; and Gauss's and Hamilton's new conception which is now expanding into the calculus of operations, or calculus of quaternions, is opening theoretical vistas which, even to the analyst of modern times, seem next to illimitable. It is true that no mathematical wings will ever carry us into the regions of the "Absolute," and no spectroscopic vision will discern the indelible spectral bands of the "thing per se;" but, before we indulge in any lamentations over this fact, it may be well to examine the livery of the messenger who brings us the wonderful intelligence of the existence of these entities without all possible relation to the intellect, and to inquire of him how he became possessed of his message.
I must not be understood as asserting or intimating that our knowledge can ever be other than asymptotic to the endless and boundless fact of the universe. But there is a dogmatism of ignorance which is no less audacious than the dogmatism of sciolistic knowledge. The "Ignoramus—Ignorabimus" at the close of Du Bois-Reymond's lecture is at least as presumptuous as the pretended omniscience of a giddy metaphysician. One of the urgent needs of modern physical science is a thorough investigation of the nature, methods, and aids of scientific cognition, and thus of the nature of its real limits, chiefly in the light of the teachings of comparative philology and comparative psychology. Max Müller has happily designated the tendency to "reify" intellectual concepts (or, as Mill expresses it in nominalist phrase, to mistake names for things), as "modern mythology." But this mythology is not at all confined to ordinary language; it extends to all the formularies, including those employed in scientific research, which serve as the intellectual net-work for the delineation of physical phenomena and for the exact mathematical determination of the laws of their interdependence.
The most pressing need of modern physical science, however, is the disengagement of the facts of observation and induction from their present theoretical complications. Most of the scientific theories of our day have their root in the metaphysics of three centuries ago, and some of the materialistic speculations based upon them are redolent of the ancient culture of the Middle Kingdom. Both in physics and in chemistry (not to speak of the biological sciences), the facts have long since transcended the narrow bounds of the prevailing scientific hypotheses, and have thus been either ignored or misinterpreted. On the remaining pages of this paper I desire to direct attention to some of the facts connected with the main subject of my present inquiry—the concept force.
Physical forces are distributed by modern science into two classes, molecular and molar forces. Molecular forces are those which determine the internal changes of a body, while molar forces cause the motion of the entire mass. Molecular forces, therefore, are the agencies which determine the particular state of the body in its physical relations, considering it as an independent whole—or, as it is termed in modern mechanics, as an independent conservative system—while the molar forces determine the physical relations of the body to other bodies which, together with it, are integrant parts of a greater whole, i. e., of a more comprehensive conservative system.
Modern science teaches that all physical forces, molar as well as molecular, are mutually convertible. This fact is discussed and illustrated in scientific treatises without number, and its importance is duly appreciated. But there is another fact connected with it, equally well known, the significance of which is not, I think, at all realized: all force in its physical origin is molecular. The power which grinds the wheat in the mill on the stream, or which drives the steam-engines in a factory; the force which propels the cannon-ball on its path of destruction, or the vital juices in a vegetable or animal organism in their course of vital regeneration; the energy which causes the muscles of a man's arm or the vessels of his circulatory system to expand and contract—all are alike of helio-planetary origin, and are ultimately traceable to the "molecular" movements of the conservative system of which our planet is a part. It would be a work of supererogation to attempt to prove this, or to illustrate it in detail; it is sufficient to refer the reader to the eloquent exposition in Tyndall's "Heat as a Mode of Motion," p. 447, et seq. (Appletons' edition).
I need not say that I use the term "molecular force" simply because it is a generally-received term, and because I am constrained to use it in order to be intelligible, but that I do not intend to commit myself by this use to the theory of the constitution of matter which it implies. In like manner I use the term "force" with the reservation that it rightfully denotes, not a substantive entity distinct from matter, but the relation of at least two particular states of matter at a given moment.
The molecular character of molar motion is evinced in numerous ways, which are almost wholly neglected and ignored by the modern physicist. To take the simplest instance: when two solids impinge, so that an exchange or distribution of their motions takes place, they contract and immediately expand again, according to the degree of their elasticity. It is unnecessary to inquire whether or not a communication of motion between two absolutely rigid bodies is possible; all bodies, of which we know any thing, are more or less elastic, and therefore contract and expand at the instant of impact. And their contraction is accompanied by the evolution of heat, by the conversion of molar into molecular motion, while in the expansion we have a reconversion of molecular into molar motion. No transfer of molar motion ever takes place without this momentary transition through the molecular phase.
Since the establishment of the doctrine of the conservation of energy and the correlation and mutual convertibility of forces, physicists have repeatedly called attention to the fact that the old interpretation of the phenomenon of an apparent destruction of force is inaccurate, and that the true interpretation of this phenomenon consists in the tracing of the evanescent molar motion into resulting molecular motion. But they fail to observe that the old notions respecting the transfer of molar motion, when there is no loss, are in similar need of rectification.
Now, what is this molecular motion, in the light of the insight which, as I hope, has been gained in the foregoing discussion? Simply an exhibition of the struggle involved in the formation or constitution of a body as a distinct conservative system. All molecular energy is in its nature constitutive, formative, or structural. All kinetic energy, or actual motion, represents the progress of morphological action in periodical alternations of advancing and retrograde metamorphosis. And the main problem of physical science is, not to calculate the play of atomic motions, under the sway of their constant central forces, but to trace the differentiation and transformation of material forms as determined by the differentiation and transformation of the formative energy of the universe. In this connection, observation and experiment have brought to light a number of the most significant facts, to one of which I may be permitted to draw attention before the conclusion of this paper. Force, or, more correctly speaking, energy, is not only indestructible, like mass; it not only passes through a cycle of transformations corresponding to the metamorphic round of physical forms; it is not only specialized at even pace with the specialization of its corresponding material structures; but, just as the progressive specialization of these material structures is, on the whole, an advance in the direction of greater definiteness and more perfect concretion (in the case of inorganic bodies, generally accompanied by greater condensation): so, also, the specialization of formative energy is, on the whole, characterized by an ever-increasing intensification. Generally speaking, the more advanced the stage of material concretion, the greater the intensity of its constitutive force. Faraday has somewhere observed that the chemical force contained in a drop of water, if transformed into heat and light, would be sufficient to illuminate the heavens. Of course, this intensification of force, in proportion to the condensation, concretion, and differentiation of the forms produced by it, is not a thickening of a substantive entity, but is simply an increasing complication in the relations in the establishment of which all realization consists. The energy which forms and maintains the higher and more definite forms of material existence has to overcome and to hold its own against not only the inherent energy of the primary physical form, but against the specialized energy of the intermediate forms as well.
I ought, perhaps, to observe here that, whenever energy is seemingly destructive, if is in reality reconstitutive of a conservative system of a lower grade.
But I must not be led into discussions which belong to special science, and are in strictness foreign to my theme; and, so far as I am at liberty to enter upon these discussions, especially in the field of chemical science, they must be reserved for another article.