Kinetic Theories of Gravitation/Waterston, 1858

In an essay "On the integral of gravitation, and its consequents with reference to the measure and transfer, or communication of force, by J. J. Waterston," of Edinburgh, published in the Philosophical Magazine, the writer commences with the general consideration : "Modern ideas with relation to heat and the active condition of the molecular element naturally incline us to estimate every force with regard to its work-producing capacity. In the following paper I have considered gravitation under this aspect, and in doing so, have been led to discuss some points relating to dynamical sequence in the abstract."

After referring to the fact that neither Newton nor Laplace recognized the principle of the conservation of force in their grand researches, Waterston continues : " Even at the present day, mathematicians have been so long accustomed to and brought up in the statical method of [244] creating molecular physics initiated by those great leaders, that the inefficiency and inconsistency of this mode of inquiry with the mechanical theory of heat seems as yet not to be fully appreciated by some even of the most zealous upholders of that theory. With this impression, it seems desirable that every effort should be made to arrive at a clear understanding of fundamental points, and the principle of physical causation, which the mechanical theory supplies."

As this is the usual point of departure with kinematics, (not " brought up in the statical method,") it may be well here to affirm with some positiveness that without the ceaseless co-operation of two antagonizing or reciprocating statical tensions, a " mechanical theory of heat " is rationally impossible. Matter possessing only inertia and motion (whose product is momentum) would very speedily arrive at a state of stable and inert equilibrium, without having ever exhibited a single phenomenon of force, and without the possibility of any dynamic potential. An abstract system of kinematics, under any geometrical arrangement or conception, is indeed quite irreconcilable with the actual system of dynamics found in nature and subject to our observation. All gases would under the operation of the first law of motion, tend to infinite and equable diffusion ; and liquids and solids would quickly follow in their wake. Heat, whether considered as a vibration or a revolution, (or preferably as both a rectilinear and an orbital movement,) could of course have no existence, since there could be neither recoil nor constraining bond ; and the very first step toward an oscillation would also be the last one. Even the principle itself of "conservation of force is absolutely dependent on the existence of primordial static potentiality. So much for a " clear understanding of fundamental points."

" Section 1. The integral of gravitation is a function of space. Suppose a central homogeneous globe to augment in bulk by the descent of similar matter from an infinite distance in radial directions all around ; each descending element, on arriving at the surface of the globe, presents itself charged with a certain amount of mechanical force equivalent to the square velocity with which it impinges. If we confine our attention to the centripetal influence of the original central globe only, the square velocity of the descending element diminishes in the inverse ratio of the radius of th e augmenting globular mass ; for it is upon the surface of this that impact takes place, and the matter that has been added to the original globe is assumed not to augment the centripetal force acting upon the descending matter." This established ratio of final velocity does not appear in any way to substantiate the general proposition ; nor is it seen to receive support from any of the succeeding illustrations. Gravitation, as a fact of observation, is always found to be rigorously relative to two posited elements ; and its integral is by such observation a function of the distance between these elements. If [245] the distance is infinite, the integral is negatively infinite. But how it is a function of " space" in any more general sense, is certainly not obvious. As Professor Brücke, of Vienna, has forcibly said in his response to Faraday : " So far as my consciousness reaches, so far as 1 am capable of distinguishing true from false, and like from unlike, all known facts are brought into complete harmony with our laws of thought, when we suppose forces as the causes of phenomena to reside in the masses, the spaces between these masses being traversed by the forces. If the forces could be imagined as existing in space, it must also be conceivable that matter may be annihilated without changing the sum of the forces, and this, at least by me, is not conceivable".

" Section 2, The force-generating faculty exists in space, and is directed centripetally. [?] This is proved by the following considerations. The integral force producing power of any body, however small, subject to the law of universal gravitation, is illimitable as space. It is impossible to imagine an infinite attribute belonging to a finite entity. It is therefore in space that the energy that contributes the power of gravitation exists, and the element of matter merely gives to it a centripetal direction. This, as a consequent of the law of gravitation, seems noteworthy from it probably being applicable to molecular forces generally. It favors the idea that the function of the material element is to give directions to a living force that pervades space." The first part of this proposition, (as an iteration of the previous one,) that gravitative force "exists in space," is derived as an inference from a metaphysical postulate, — " It is impossible to imagine" it as belonging to a finite body. But our powers of " imagining" can hardly be accepted as the measure of scientific verity. "It is impossible to imagine" the nature of electrical action, chemical affinity, luminiferous vibration, aether, atom, force, or space ! Who is able to formulate in thought the co-existence of an equal repulsive and attractive energy in either pole of a bar magnet, simultaneously discriminating by opposite action between the reversed ends of two magnetic needles? But when it is said that the sole function of the material element is to give centripetal direction to the circumambient ocean of force, wonderful indeed is the conception of virtue in the " finite entity" thus drawing to itself the centripetal tendency in all directions throughout illimitable space, and instantaneously readjusting these infinite lines of force with every momentary change of position! If difficulty of "imagining" were a criterion of error, surely it might be well applied to this hypothesis.

" Section 3. The law of gravitation with respect to the element of radial space, is usually defined with reference to a constant element of time; the increment of velocity generated being proportional to the increment of time, whatever the direction or velocity of the motion, and [246] inversely as the square of the central distance. If we view it with reference to a constant element of radial space, we find that the increment of square velocity generated by the force of gravitation is proportional to decrement of radial distance, and inversely as square of central distance. This holds whatever the velocity or direction of the motion, whatever the orbit of the projectile . . . ."

"Section 4. The mutual gravitation of two bodies develops mechanical force in each of them inversely proportional to its mass. Suppose two bodies to descend toward each other by their mutual gravitation, their common center of gravity being at rest. At any time before they meet, their acquired velocities being examined will be found inversely as their masses 5 which assume as one to ten. Suppose them removed to the earth's surface, and each projected up a vertical with their acquired velocities respectively : the smaller body rises 100 limes the height ascended by the larger, and thus in again descending would be able to perform ten times the work . . . ."

After some other propositions and discussions, not specially bearing on the present inquiry, Mr. Waterston gives a general statement of results as follows : " Even if we had not those proofs of the existence of a universal medium that the undulatory theory of light supplies, it would be well to admit the existence of media to which ordinary matter may be assumed to be entirely subordinate in all their potential relations, so as to give order to our ideas in tracing out the dynamical sequence of nature. It would be taking too narrow a view if we limited the function of the luminiferous aether to the conveying of physical pulses only. The atmosphere also conveys physical pulses, but that is the least important of its functions in the economy of nature. There is nothing that should hinder us attributing to the media concerned in the radiation of heat and light the higher functions of electric polarity and gravitation. The special dynamic arrangements by which this is effected may ever elude research, but as there is no limit to the vis viva which such media may conserve in their minutest parts, so there is no physical impossibility in that vis viva being suddenly transferred to the molecules of ordinary matter in the proportions and sequence required to carry out the order and system of nature. The fundamental principle of action in such media must be in accordance with elastic impact, for upon that the dynamic theory of heat and conservation of force rests as a foundation. The statical and dynamical characteristics of gravitation and transfusion of force have also been shown to conform to it, so that all the forces that hold the molecules of bodies together must also be in subjection to it."

From the above it would appear that the writer in previously affirming the integral of gravitation to be a function of space, intended rather the content of space, or the dynamic medium supposed to occupy it. The [247] whole suggestion is however, so indefinite that it must be accounted less a coherent hypothesis than a mere speculation, — a cast among the possibilities. To refer the great fact of gravitation to some unimagined and unimaginable aether-motion, the special arrangements of which for effecting the desired purpose " elude research," is not to proffer an explanation, but to indulge in an illusion ; and although Mr. Waterston has in terms recognized all of the six propositions (excepting the last one) announced as the necessary conditions of the problem, he has failed to show that one of these conditions can be satisfied by his speculations.