Kinetic Theories of Gravitation/General Conclusions

by William Bower Taylor

In this résumé of kinetic theories, doubtless other names, well deserving notice, have been overlooked from want of more extended research; but it is believed that the foregoing survey comprises essentially all the forms of the hypothesis of primeval motion which have been propounded. The general tenor of this line of speculation has been well set forth in an able review of " The Atomic Theory of Lucretius," which appeared in the North British Review for 1868.

"The most plausible suggestion yet made by this school is that a single omnipresent fluid aether fills the universe; that by various motions of the nature of eddies, the qualities of cohesion, elasticity, hardness, weight, mass or other universal properties of matter are given to small portions of the fluid which constitute the chemical atoms; that these, by modifications in their combination, form, and motion, produce all the accidental phenomena of gross matter ; that the primary fluid by other motions, transmits light, radiant heat, magnetism, and gravitation; that in certain ways, the portions of the fluid transmuted into gross matter can be acted upon by the primary fluid which remains imponderable or very light, but that these ways differ very much from those in which one part of gross matter acts upon another ; that the transmutation of the primary fluid into gross matter, or of gross matter into primary fluid, is a creative action wholly denied to us; the sum of each remaining constant."^[1] The hypothesis of the transmutation of aether, or of the evolution of " matter," is not however necessarily involved in that of referring all conditions, properties, and powers of matter to "a mode of motion."

General Conclusions

In the conception of a statical pressure of aether constantly acting inwardly on concentric spherical surfaces, there is the obvious irrationality of a stable non-equilibrium. Nor is there any real difference in the conception of an aether having concentric increments of density outward, in which ordinary matter is buoyed, as it were, toward the center: a scheme in which every particle of matter finds itself in the midst of its own little spheres of rarefaction, and in which such center of aetherial rarity is supposed to blindly follow the flying stone in whatever direction hurled at the caprice of an idle boy. Entirely too much importance has beoi attached to this conception as a speculation of Newton, when it was evidently an unconsidered and merely obiter dictum suggestion, utterly repudiated by him in later years.

Omitting then any further consideration of the statical method of explaining gravitation by pressure, we find that kinetic systems are essentially of two classes, the hypotheses of emissions or corpuscles, and the hypotheses of fluid undulations. It is proposed to show that no form of either hypothesis can satisfy the two Newtonian conditions of a scientific theory — verity and sufficiency. [275]

The corpuscular hypothesis is clearly invented pro hac vice. Nor can even an analogue of the invention be found in the corpuscular theory of gases ; for in the latter case, the free path of the particle is assumed to extend only for the short distance between neighboring molecules, and by reason of incessant collision and deflection among the elements the hydro-dynamic pressure of the medium is equal in all directions, quite irrespective of the number or character of intervening obstructions: while the gravific or ultramundane corpuscle must ex hypothesi travel from infinity in a perfectly straight and undisturbed path to fulfill its appointed mission. It is therefore a special creation, neither ascertained nor suggested by any other consideration.

Secondly, even if a vera causa, it is wholly insufficient. The first great triumph of the corpuscular assumption was its supposed happy expression of the distance-ratio of gravitative intensity : and this appears to have been admitted by all the mathematicians who have referred to the problem. But a very brief consideration will show that while this may be approximately true for small masses, there is a limit of magnitude as well as of number in the masses of gross matter, beyond which no assignable number of corpuscles is capable of acting. Let us suppose for definiteness (not as even suggesting a higher limit) that normal to a plane whose area is d² (d representing the distance between two adjacent molecules of ice or of water,) a million million corpuscles are passing simultaneously with any desired frequency. This neglects for the moment the far greater number passing through the same area at all other angles. The molecule of ice or water being a very small though appreciable fraction of the value of d, (a not improbable estimate of which value may be the five hundred millionth of an inch,) it is obvious that with an equable distribution of the material molecules in a continued right prism having d² for its base, no very great depth is required for a million million of such molecules to lie each in the line of motion of one of the parallel moving corpuscles. Beyond this depth or distance, of any number of molecules continued, no one will receive an impact, or in other words, will have any gravitation.^[2] This reasoning remains true, whatever be the number and direction of the prisms chosen, and whatever be the number of corpuscles passing through its base d². If it be said that this number is infinite, this is simply an unconditional surrender of the hypothesis. It is proved then that the number of corpuscles passing through a large mass must be very much less than the number impinging on its exposed strata or passing through a small mass; and that if the mass be large enough, the side presented toward another mass will receive no gravitative impulse thereto ; and a tidal [276] attraction between the bodies would be impossible ! The scheme therefore fails not only to satisfy the second condition, (as formerly stated,) but it equally fails to satisfy "indefinitely" the third condition. And this objection lies equally against every variety of the corpuscular hypothesis, from that of Bernouilli to that of Leray.

In the next place, the hypothesis of undulations similarly fails. First, because the motion assumed is not a vera causa. If it be answered that an all-pervading aether and its system of undulations are otherwise established, by the large array of well-observed phenomena shown to be in exact accordance both in quantity and in quality with the mathematical deductions from such postulated undulations, the rejoinder is, that such undulations as have thus been established are demonstrably incapable of inducing anything in the slightest degree analogous to gravitation; and therefore the new undulations required have not been otherwise ascertained. And this is a radical defect in all the wave suppositions. We are not at liberty to assume unknown and undemonstrated actions, entirely different in character from anything which has been actually observed or necessarily inferred. Great as is the credit due to Professor Challis, for instance, for his dexterous, persevering, and laborious efforts to develop his theory by the stern logic of mathematics the whole demonstration is vitiated by the unwarranted preliminary assumption of qualities and modes of action in the aether analogous to those of gases; as for example, that the pressure and the density are proportional. Now as a matter of fact, the aether is a medium so wholly and so radically dissimilar to any known gas in structure and in properties, that the most characteristic features of its luminiferous undulations, — rectilinear propagation,with its special incident inflection; selective refraction or chromatic aberration ; birefraction ; and polarization in its various forms, — find no representative therein ; leading a Newton to the reluctant conviction that a gaseous aether could not be the vehicle of light.^[3] The denial therefore, of the verity of fluent undulations in the aether is based upon the skeptical affirmation that beyond experience and safe induction therefrom, we can tell nothing as to the behavior of an unknown agent.

But if the character of undulation required were established, secondly, it would as in the former case, be entirely insufficient for the purpose. The aether must have the elasticity and the mass or inertia [277] necessary to execute precisely its ascertained dynamic function.^[4] This specific and very limited inertia is manifestly inadequate to the indefinite accumulation of energy required to give the same proportional tendency between large masses as between small ones. The experiments of Guyot and of Guthrie quite conclusively show that neither in the law of quantity nor in the law of intensity can gaseous vibrations represent even approximately the ascertained facts of gravitation embodied in the second and third propositions.

But if in dynamic action a gaseous undulation of aether, with its existing co-efficient of inertia, is found to be so palpably inadequate to the known effect, on the other hand the elasticity must be assumed to be incomparably more active than the limit expressed by the actual velocity of a luminous undulation. If its rate of propagation be assumed to be very many millions of times more rapid than that of light, the inertia must be correspondingly reduced ; in short, must be practically nil; and the action must be really kinematic rather than dynamic.

Failing thus at every point, the hypothesis leaves still more inscrutable the origin of the undulation. The center of disturbance is supposed to be the vibrating material element; but the cause of the vibration is never stated. If innate tendency be the answer, never surely was a more mysterious " occult quality " attributed to matter in the history of human excogitations. Either misapprehending altogether, or quite ignoring the origin of thermal vibrations, the kinetic theorist not unfrequently appeals to the dynamical doctrine of heat as the type and the warrant of his assumptions. But in the case of heat, as in every other observed case, motion is a phenomenon to be accounted for; and no physical theory is complete, until in origin, in quantity, and in direction, it is accurately explained by a true and sufficient antecedent cause.

But granting a prime mover — the immediate operation of a Demiurgus, if necessary, — how is the initial impulse converted into vibration ? What is the resisting power deflecting the element in motion from that rectilinear direction, which is its first law of action? And by what opposing battledoors (for two are absolutely necessary) does the deflected particle become a shuttlecock I Upon these important questions there is a very remarkable reticence. We know that when a bell is struck with a hammer the moving impulse of a segment of the free edge is resisted by a molecular pressure which (for want of a better name) has been called repulsion ; and that this reaction is in turn resisted by a molecular tension which (for want of a better name) has been called attraction; and that this reciprocating play very rapidly declines as [278] the momentum of vibration is transferred to the elastic air. And these two qualities of the vibrating bell — cohesion and elasticity — as Sir John Herschel has well remarked, " we have no means of analyzing further, and must therefore regard them, till we see reasons to the contrary, as ultimate phenomena, and referable to the direct action of an attractive and a repulsive force."^[5] But in a kinetic system there is no room for such abstractions. How then are they to be displaced and superseded ? We wait in vain for an intelligent or an intelligible answer.

But after this long list of difficulties, supposing the vibrating particles set in motion, still by the Demiurgus, with his right and left propulsions, by what power (short of his incessant repercussion) is the vibrating particle enabled to transmit without decline or interruption, these aetherial waves of gravitation — let us say for a single year, we might as well have said for a single minute ? Here again we listen vainly for an answer !

And thus, step by step, have we been led to the culminating vice of every kinetic system ; its utterly reckless violation of any rational conception of the conservation of energy. And yet remarkably enough, the ostensible impulse and occasion of such creeds have usually been a strong veneration for this much-abused principle, and the consciousness of a special mission to restore and to vindicate its neglected authority ! Not unfrequently the vibrations communicated to the telegraphic aether by a trembling atom have been supposed to be transmitted unimpaired to that or to other atoms, and back again, in endless and magnificent cycles of "perpetual motion." And as "there is no limit to the vis viva which such a medium may conserve" within its boundless bosom, such projectors have the Bank of the Infinite on which to draw in every dynamic emergency, without the fear of a depleted treasury, and without any necessity being felt for inquiring too nicely into the balance of the depositor's account. And thus, as Leray has intimated, suns and stars are maintained for ever blazing on a borrowed capital of motion.

In opposition to all this ideal programme of an illimitable ocean of dynamic, with its treasures lying loose in space, to be absorbed by every projected ball or stone, it may be simply declared that from observation we have no reason whatever to believe the aether to be in any case a source of energy. We have absolutely no experience of any undulations originating in its broad expanse. It is never self-luminous; and even in the case of electricity there is always required the disturbance cf a material element. Nor is there any ascertained fact to warrant the supposition that the aether is a reservoir of force, — in any other sense than that without the possession of intrinsic tension it would be incapable of transmitting energy. So far therefore as sober experience is accepted as our guide, we only know that a mechanical impulse of suitable character being committed to the aether, it is a faithful vehicle of energy, never adding to, and never abstracting from its charge. [279]

Among the names presented in the foregoing selection from kinetic theorists are several eminent in the domains of physics and mathematics. Their labors, animated with the zeal, the diligence, and the persistency of purpose and conviction here displayed, might be expected to enlarge notably the boundaries of our knowledge to whatever department of natural law they were devoted. But when we look for any actual results from these elaborated speculations, how barren is the prospect. How wonderfully contrasted in character is the prime assumption with the fruitfulness of that generalization which it aims to subordinate and to comprehend. How striking its failure, not in the higher role of prophecy, but in the humbler one of mere interpretation. How clumsy the mechanism by which it vainly strives to accomplish its results.

But it is not simply in the negative aspects of an unsuccessful effort that these varied speculations, prompted by a common sentiment and motive, teach us their most suggestive lesson. Beyond the facts of constant and of signal failure, these restless, resolute probings by the human mind in all directions, serve as the cumulative bases of a new induction ; and by the very sharpness of the contrasts brought to view at every point between the tentative conjecture and the determinate experience, they enforce the assurance, that whatever else the principle of gravitation may be, it is not in its essence any form of motion. And that gravitation is not a resultant of pressure, appears to be very clearly made out by the inability of every scheme of such hypothesis, in the hands of its most skilfull adherents, to give any rational account of the semi-diurnal ocean-tides.

Another lesson no less striking, is the utter worthlessness of metaphysical axioms as a criterion of physical truth, or as a foundation for rational physical theory. Such propositions as "It is impossible to imagine an infinite attribute belonging to a finite entity," or " It is impossible to conceive anything to act where it is not," are not merely quite irrelevant to scientific verity, but if gravely accepted as physical postulates, prove only to be positive obstructions to scientific investigation. Professor Challis has well said, " I do not admit that any metaphysical argument can be adduced either in support of or against a physical hypothesis. Meta-physics come after physics."^[6] And Sir John Herschel, some thirty years ago, laid down as a rule of sound philosophy, " Experience once recognized as the fountain of all our knowledge of nature it follows that in the study of nature and its laws we ought at once to make up our minds to dismiss as idle prejudices, or at least suspend as premature, any preconceived notion of what might or what ought to be the order of nature in any proposed case, and content ourselves with observing, as a plain matter of fact, what is."^[7] And again, long before him, Newton condemned the "feigning hypothesis for explaining all things mechanically, and referring other causes to metaphysics. [280] Whereas the main business of natural philosophy is to argue from phenomena without feigning hypotheses, and to deduce causes from effects, till we come to the very first cause, which certainly is not mechanical."^[8]

It has already been noticed that elasticity has proved a stumblingblock to every kinetic hypothesis. A system of molecular physics without this property would represent a chaos ; but a chaos destitute of energy. As Lam6 has well observed in his admirable treatise on the subject, " The role of Elasticity in nature is as important as that of Gravitation!" How then are we to formulate this prime and potent force? Evidently no phase or form of motion can simulate its action. Here all kinetic theory fails: and there is then something in the world beside " inertia and motion." Until some rational analysis be discovered, we must accept the fact (in the language of Sir John Herschel) as an "ultimate phenomenon." And as we find that the molecules of all material substance resist compression with a force proportional in some high ratio thereto, we can only conceive that they are separated by an interval through which this repellant resistance is exercised. Here then it seems, we are at once confronted with an "occult quality" or virtue, a force of repulsion, quite beyond the reach of any explanation or relegation. And worse than all, with a quality or virtue which proves to be that ever-dreaded and in fact "impossible" actio in distans! Are we then driven in the last resort to admit that devoid of all perception of propriety, the insignificant physical molecule does positively "act where it is not," and where it ought not ?

When we endeavor to penetrate into the secrets of molecular physics, again ate we borne on the waves of a large induction that the atoms of matter never are and never can be in contact : but that in Seguin's fine conception, they are really circulating iu perpetual orbits of varying magnitude, according to the resultants of impulsions received by mutual impacts on their dynaspheres, or on the mystic boundaries of their elastic repulsions: in orbits whose magnitude determines the character of their aggregation, and which notwithstanding constant perturbation, could be suppressed only by the total absorption of motion, in an absolute zero of temperature. And thus, whether we contemplate the infinitely small or the infinitely grand, in every case comes back upon us the wide induction, that the action of matter in atom, in molecule, or in mass, is ever at a distance! Of actual contact there is probably no instance afforded in nature, excepting in the intimate substance of the ultimate atom. And notwithstanding the petulant sneer of some distinguished physicists, there is nothing to forbid (on the contrary much to favor) the Newtonian conception of infinitely hard spherules of determinate magnitude, as the real substratum of the physical universe.

The assumption therefore of a material band or bar between bodies, to transmit energy from one to another, whether by a pull or by a push, is [281] still very far from establishing an action by contact or from sustaining the fond hypothesis that an atom " acts where it is!" Admitting a connecting rod for drawing the railway train of dynamic, as Professor Maxwell has remarked, " the action of the rod is explained by the existence of internal forces in its substance; and the internal forces are explained by means of forces assumed to act between the particles of which the rod is composed, that is between bodies at distances which, though small, must be finite. The observed action at a considerable distance is therefore explained by means of a great number of forces acting between bodies at very small distances, for which we are as little able to account as for the action at any distance, however great."^[9] To the wondering inquiry what possible explanation can be given of [282] such a theory or hypothesis of attraction, the obvious answer is, there is neither "theory" nor "• hypothesis" in the case. The observed fact that one body does actually induce approach in another body at a distance from it, if accepted as an "ultimate" one, is of course thereby excluded from all idea of "explanation." And as this observed fact, by the multiplicity of instances in which no intermediate agent has yet been detected, or rendered rationally plausible, is generalized into an " induction," the burden of proof lies entirely "on the shoulders of those who with a keener vision through nature's veil, are ready to proffer hypotheses "without assumptions," and endless motions without the aid of " occult qualities."

But this stern requirement of a demonstrated instance of material link, or mechanical connection, to impugn the large induction of an actio in distans, cannot be evaded by the logical artifice of designating such "induction" as a competing "hypothesis!" If by the scientific method of a carefully registered experience such theorists should ever be successful in physically justifying their ill-advised scruples, their mala fastidia, (to use the phrase of Horace,) none will be more heartily rejoiced at this new conquest over ignorance than the astronomers and physicists who hitherto have given themselves but small concern respecting the metaphysical paradoxes supposed to be involved in the more usual statement of the law of gravitative action.

But as yet this generalization, after two centuries of busy thought and daring speculation, still remains the largest, clearest, surest, yet attained by man ; and with each revolving year new demonstrations of -its absolute precision and of its universal domination serve only to fill the mind with added wonder and with added confidence in the stability and the supremacy of the power in which has been found no variableness, neither shadow of turning, but which, the same yesterday, to-day, and forever,

"Lives through all life, extends through all extent, Spreads undivided, operates — unspent!"

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1. North British Review, March, 18GS, vol. xlviii, p. 127 of Am. edition.
2. This idea may be more popularly illustrated by supposing ou a plane of indefinite extent a grove of small, vertical trees, planted at irregular but equable intervals, at; any assignable distance apart. It is evident that it would require no indefinite extension of the woods to absolutely exclude a horizontal ray of light in any direction, even though suns or electric lights were blazing with unimaginable splendor.
3. Dr. Young, in referring to Fresnel's discussion of " polarization," says, " it might be inferred that the luminiferous aether pervading all space, and penetrating almost all substances, is not only highly elastic but absolutely solid." (Miscellaneous Works of Thomas Young, London, 3 vols. 8vo, vol. i, No. 18, p, 415.) And Sir John Herschel remarks : " Every phenomenon of light points strongly to the conception of a solid rather than a fluid constitution of the luminiferous aether, in this sense, — that none of its elementary molecules are to be supposed capable of interchanging places, or of bodily transfer to any measurable distance from their own special and assigned localities in the universe." (Familiar Lectures on Scientific Subjects, London, 1867, lect. vii, p. 285.) On the other hand, recent mathematical discussions have found some difficulties even in this hypothesis.
4. From the actual dynamic energy transmitted by the aether, Sir William Thomson, in 1855, estimated that a cubic foot should weigh not less than the quadrillionth (1-10²⁴) of a grain ; or that the inertia of tether had for its higher limit about one two-thousand-trillionth (½:10²¹) of that of ordinary air. (L. E. D. Phil. Mag., Jannary, 1855, vol. ix, p. 39.) Its lower limit may be one hundred times this amount, or one twenty-trillionth (½:10¹⁹) of the inertia of air.
5. Prelim. Discourse on the Study of Natural Philosophy, part ii, chap, ii, sec. 80.
6. L. E. D. Phil. Mag., 1861, vol. xxi, p. 505.
7. Discourse on Study of Natural Philosophy, part ii, chap, i, sec. 68.
8. Optics, Book iii, Query 28.
9. A Treatise on Electricity acd Magnetism : by James Clerk Maxwell. Oxford, 2 vols. 8vo, 1873. Part i, chap, v, sec. 105, vol. i, p. 123.
   If the attempts hitherto made by kinetic theorists to explain the tensile strength of a rope or of a chain by the pressure of a vis a tergo have been exceedingly lame and unsatisfactory, even the more direct examples of actual impact and propulsion are really as little serviceable to the hypothesis of contact action. If we have good reason to believe that the constituent molecules of a steel bar are actually separated by relatively large spaces of intense repulsion, — a fortiori must the physical impact of the most violent percussion be resolved into an action through a vacant space. Taking the case of a steel ball struck suddenly by a steel bat, the interval of distance between the first impression of the moving mall and its nearest approach to the ball, is sufficient to permit the acceleration of motion in the missile through every gradation, from zero to its full velocity.
   Perhaps no better " prerogative of instances" of a physical contact could be suggested than that of a thick glass plate resting on the convex surface of a large glass lens, since the perfectly-ground plane surface of the upper glass and the perfectly ground spherical surface of the lower one are best adapted to exclude a possible film of air. Such an arrangement represents the well-known experiment by which Newton determined from the measurable variation of distance between the glasses (when closely pressed together) the wave-length of light for different colors. On this very beautiful experiment Dr. Robison forcibly remarks in his excellent work on Natural Philosophy :
   "The conclusion seems unquestionable that we have no proof from the black spot between the glasses, that they are in mathematical contact in that place. We know by the first experiment that a very considerable force is necessary for producing the black spot. A greater pressure makes it broader, and in all probability this is partly by the mutual yielding of the glasses. I found that before a spot, whose surface is a square inch can be produced, a force exceeding one thousand pounds must be employed. When the experiment is made with thin glasses, they are often broken before any black spot is produced There is therefore an essential difference between mathematical and physical contact ; between the absolute annihilation of distance, and the actual pressure of adjoining bodies. We must grant that two pieces of glass are not in mathematical contact till they are exerting a mutual pressure not less than one thousand pounds per square inch. For we must not conclude that they are in contact till the black spot appears ; and even then we dare not positively affirm it. My own decided opinion is, that the glasses not only are not in mathematical contact in the black spot, but that the distance between them is vastly greater than the eighty-nine-thousandth part of an inch, the difference of the distances at two successive rings." — A System of Mechanical Philosophy : by John Robison. 4 vols. 8 vo., Edinburgh, 1822, vol. i, sec. 241, 242, pp. 250, 251.