Le Sage's Theory of Gravitation

by James Croll

LE SAGE'S theory of gravitation is at present exciting a good deal of attention among physicists. This is perhaps to a considerable extent owing to the fact that some of the conditions arbitrarily assumed by Le Sage in his hypothesis have been proved, from the kinetic theory of gases, to follow as necessary consequences.

A clear and able account of this theory has been given by Mr. Preston in the Philosophical Magazine for September and November last. Mr. Preston has endeavoured to answer all the objections which have been urged against the theory.^[1] There is one objection, however, which appears to me not to [46] have been fully met. It is a necessary condition of Le Sage's theory, in order that gravity may be proportional to mass, that the total volume of the free spaces in a substance in the form of interstices between the molecules must be great compared with the total volume of matter contained in the molecules themselves. This condition of free interstices Mr. Preston considers to be satisfied by assuming the molecules to be small relative to their mean distances.

Were we at liberty to make any assumptions we choose in reference to the smallness of the molecules of matter and their distance apart, we might be able to satisfy the conditions of Le Sage's theory as to mass ; but this we are not at liberty to do. Modern physics has enabled us to determine, at least roughly, the size of the ultimate molecules of matter and also their distance apart. This subject has recently been investigated by Sir William Thomson, the details of which will be found in a remarkable paper in ' Nature,' vol. i. p. 551. Sir William says the diameter of the molecule cannot be less than 1/500.000.000 a centimetre. The number of molecules in a cubic centimetre of a liquid or a solid may, he says, be from 3x10²⁴ to 3x10²⁶. This gives the distance from centre to centre of two consecutive molecules to be from 1/140.000.000 to 1/460.000.000 of a centimetre. Now, if we take the mean of these two values, we have 1/300.000.000 of a centimetre for the distance between the centres. The mean spaces between the molecules are therefore less than the diameter of the molecules themselves. Under this condition of things, it must be absolutely impossible that a gravific particle, even though it were infinitely small, could penetrate to the extent of a thousandth part of a centimetre into the interior of a body without having its motion stopped by coining into collision with a molecule. Le Sage's theory appears therefore to be utterly irreconcilable with Sir William's conclusions regarding the size of the material molecule. But even supposing we were to assume, what we are hardly warranted to do, that the molecules are 10.000 times smaller, and their distance apart 10.000 times greater than Sir William Thomson concludes, still this would not assist the theory. The gravific particles would then, no doubt, penetrate a little further into the interior of a body ; but beyond a few feet, or perhaps a few inches, no particle could go.

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1. Mr. W. B. Taylor, in an interesting article on Kinetic Theories of Gravitation, published in the Smithsonian Report for 1876, lays down six fundamental characteristics of gravitation, with which every theory, he says, must agree. Of these six requirements, Le Sage's theory, he maintains, satisfies but two — namely (1) that the direction of gravity is radial towards the acting mass, and (2) that its intensity diminishes as the square of the distance. But some of Mr. Taylor's objections have already been met by Mr. Preston in his memoir ; beside, one or two of Mr. Taylor's fundamental postulates seem doubtful.