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XIV. Comparative Review of some Dynamical Theories of Gravitation. By Dr. S. TOLVER PRESTON*.



HE modes of accounting for natural phenomena have been very different at different times. The old philosophers had in general scarcely an idea of that which we now call a mechanical explanation; they figured to themselves rather the agencies working in nature as living beings. This applies also to Kepler, who banished from himself any idea of a mechanical explanation of the laws discovered by him. the basis of the researches of Galileo, Newton was the founder of the Mechanics of to-day; and on his principles the edifice of the action-at-a-distance theory has been founded. Until Newton's time the notion of a direct action at a distance was

completely unknown : on the contrary, many experiments exist by the Greek philosophers to account for the seeming action at a distance by the intervention of a medium; therefore Demokritos sought to explain natural phenomena by the motions of very fine bodies. First Boscovich, Mosotti, Wilhelm Weber, and many others developed the aspect of nature on the basis laid down by Newton, in accordance with which the universe consists of a number (if even very great)

*Being a Dissertation presented to the Philosophical Faculty of the University of Munich, for the attainment of the degree of Doctor of Philosophy (translated from the German). Communicated by the Author Phil. Mag. S. 5. Vol. 39. No. 237. Feb. 1895.


of material points, which, without anything intervening, act on each other directly at a distance, according to a mathematically exact formulated law. If the initial positions and velocities of all the atoms are given, then their motions can be calculated for any periods of time from the equations formulated by Newton, and so a clearly defined mathematical problem is presented.

It is, however, well to observe that Newton did not believe in such an action at a distance without the intervention of something, as appears from his third letter to Bentley, where he says:

"That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it" (Newton's third letter to Bentley, February 25, 1692-3).

In the same sense speak many subsequent important scientists. For instance Count Rumford remarks :

"Nobody surely in his sober senses has ever pretended to understand the mechanism of gravitation, and yet what sublime discoveries has our immortal Newton been enabled to make, merely by the investigation of the laws of its action" ("An Inquiry concerning the Source of the Heat which is excited by Friction," by Count Rumford, Phil. Trans. 1798).

These last scientists are therefore not satisfied with the

Boscovich-Mosotti explanation of natural phenomena; they demand rather an explanation (by the intervention of a medium) of the seeming action at a distance. To give such an explanation was never seriously attempted by Newton: the first attempt of that kind is to be found in the mechanical gravitation theory of Le Sage, born at Geneva in 1724. This theory is contained in a memoir published in the Transactions of the Royal Berlin Academy for 1782, under the title Lucrèce Newtonien. There is also a book, Deux Traités de Physique mécanique, edited by Pierre Prévost, Paris, 1818, which contains a full description of Le Sage's theory.

Le Sage lays emphasis on the probability of the existence of a mechanism of gravitation, and devoted his life to the development of his idea. The introductory paragraph of his memoir (entitled Lucrèce Newtonien) is as follows, translated from the French original, viz. :

"I propose to show that if the first Epicureans had had as healthy ideas of Cosmography as several of their contem

poraries (to whom they would not listen), and only a part of the knowledge of Geometry which was then prevalent, they would in all probability have discovered the laws of universal gravitation and its mechanical cause. Laws, the discovery and the demonstration of which constitute the fame of the most powerful genius that has ever existed; and Cause, which after having been the ambition for a long time of the greatest scientists, is at present the despair of their successors. So that, for example, the celebrated laws of Kepler, discovered somewhat less than 200 years ago, partly by gratuitous conjectures, and partly by repeated trial and error, would have been no more than inevitable corollaries which could have been arrived at by these ancient philosophers by investigating the mechanism of nature. The same conclusion applies also to the laws of Galileo upon the fall of bodies, the discovery of which took place still later, and which have been more contested, because the experiments upon which this discovery was based permitted a latitude in their results (necessarily rough), which would make them fit equally well with other laws, so that one did not fail to contest them : whereas the inferred consequences of the shock of atoms would have been unmistakably in favour of the only true principle, viz., equal accelerations in equal times." (Trans. of Royal Berlin Academy, 1782.)

On this paragraph the following opinion is emitted by Lord Kelvin, viz. :—

"If Le Sage had but excepted Kepler's third law, it must be admitted that his case, as stated above, would have been thoroughly established by the arguments of his "mémoire"; for the Epicurean assumption of parallelism adopted to suit the false idea of the earth being flat, prevented the discovery of the law of the inverse square of the distance, which the mathematicians of that day were quite competent to make, if the hypothesis of atoms moving in all directions through space, and rarely coming into collision with one another, had been set before them, with the problem of determining the force with which the impacts would press together two spherical bodies, such as the earth and moon were held to be by some of the contemporary philosophers to whom the Epicureans "would not listen." But nothing less than direct observation, proving Kepler's third law-Galileo's experiment on bodies falling from the tower of Pisa, Boyle's guinea-and-feather experiment, and Newton's experiment of the vibrations of pendulums composed of different kinds of substance-could either give the idea that gravity is proportional to mass, or prove that it is so to a high degree of

accuracy for large bodies and small bodies, and for bodies of different kinds of substance" (Phil Mag. May 1873, p. 323).

Le Sage's Theory.

Le Sage based his theory on perfectly arbitrary assumptions. He assumed (Deux Traités de Physique mécanique, Paris 1818, edition Pierre Prévost) :

(1) That a number of streams of atoms, equally distributed in space, exist; of which each stream moves continually in one and the same direction.

(2) The length of these streams (at the centre of which the universe known to us is placed) is finite, but very great; therefore gravitation must have a correspondingly limited period for existence.

(3) That the streams must be everywhere equally dense. (4) That the mean velocity of the streams is everywhere the same.

The conditions above set forth depend manifestly on perfectly arbitrary assumptions, and it is not easy to see by what mechanism such streams should either originate or be kept up. As regards the behaviour of these streams of atoms towards gross matter, Le Sage assumes the following. Gross matter is chiefly freely penetrated by the streams of atoms, only a small part of their energy is absorbed by gross matter, which implies a continuous annihilation of energy. Whence it arises that every portion of gross matter opposes a certain shelter to every other neighbouring portion from the encounters of the streams of atoms; and from this the apparent attraction of the gross matter according to the Newtonian law of gravity is easily explained.

Lord Kelvin presupposes exactly the same streams of atoms as Le Sage; the mechanism which regulates or maintains these atom-streams therefore remains with him as obscure as with Le Sage. An important progress in Lord Kelvin's case consists, however, in the fact that he regards the atoms as elastic. In order to explain the elasticity, he proposes to regard the atoms as vortex rings in a perfect liquid. The elasticity of these is then explained by the laws which Helmholtz found to apply to the motions of such vortex rings.

The æther atoms then rebound from gross matter in accordance with the laws of elastic collision: instead of the absorption (annihilation) of energy assumed by Le Sage, Lord Kelvin supposes that the æther atoms, in addition to their translatory energy, also possess an energy of internal motion, just as Clausius assumes for the molecules of ordinary gases.

On account of the relatively very large dimensions and superior elastic rigidity of the gross molecule, it is scarcely disturbed by the collision of the very minute atom. On the other hand, the minute atom is thrown into strong vibration and rotation by the blow. This vibration or rotation ("internal motion") cannot evidently be generated out of nothing. The small atom therefore loses at impact a portion of its translatory motion, by converting the same into internal motion (vibration and rotation). The diminution of the translatory motion of the small gravity-atoms at their encounter with gross molecules is therefore rather to be looked upon as a necessary deduction than as an hypothesis. One might, indeed, easily illustrate this fact experimentally.

If an elementary example be excused, we can consider the case when any small elastic body such as a small polished steel key-ring is thrown against the surface of a polished steel anvil. A key-ring and an anvil (of the same metal) may be equally elastic, but on account of the considerable difference in their dimensions-therefore pliability-only the small ring will be thrown into perceptible vibration by the encounter (or into rotation, for the anvil cannot rotate on account of its mass). The ring rebounds with a diminution of its translatory motion, by converting the same into vibration and rotation.

The atom gains its full translatory motion gradually again by collisions against atoms of its own kind,-from the fact that the proportionality existing between the amount of translatory motion and the amount of internal motion of the atom continually strives to maintain itself constant; which is a known consequence of the kinetic theory of gases, demonstrated by Clausius.

So is explained how the æther atoms, in being sifted through gross matter, on the average lose a certain velocity of translatory motion, and that therefore a portion of gross matter "shelters" any other neighbouring portion from the impacts of the æther atoms.

The penetration of the two masses by the flying æther atoms brings about the fact that on the adjacent sides of the two masses the pressure of the medium is smaller than on the remote sides of the molecular surfaces of the two masses. The remote sides encounter the full or undiminished translatory velocity of the atoms. Therefore the two masses are naturally driven together, and with a force which obviously, from the nature of the case, must be proportional to the square of the distance of the masses. The further explanation of the gravitation effect is then exactly as by Le Sage's theory.

The present writer attempted in some papers, of which the

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