Silberstein L. The recent Eclipse Results and Stokes-Planck's s AEther. // Phil. Mag. S. 6. Vol. 39. No. 230. Feb. 1920. — Page 161

Silberstein L. The recent Eclipse Results and Stokes-Planck's s AEther. // Phil. Mag. S. 6. Vol. 39. No. 230. Feb. 1920.

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XV. The recent Eclipse Results and Stokes-Planck's s AEther. By L. Silberstein, Ph.D., Lecturer in Mathem. Physics at the University of Rome*.

1. IT is well known that, in 1845, Stokes proposed a theory of aberration (Phil. Mag. xxvii. p. 9), which was based on the assumption that the luminiferous aether surrounding our planet is dragged along in its annual motion so that the velocity of the aether relative to the Earth is nil at its surface, and, increasing continuously, becomes equal and opposite to the Earth's velocity at very large distances from the Earth or, to put it short, at infinity. The purpose of this hypothesis, as opposed to that of Fresnel's stagnant aether, was to give a rigorous independence of all purely terrestrial optical experiments from the Earth's annual motion (combined with that of the solar system). In order to account for the semi-terrestrial phenomenon known as astronomical aberration, Stokes had to assume that the motion of the aether, between the Earth and the stars in question, is purely irrotational. But, by a well-known theorem of hydrodynamics, this assumption was not compatible with the incompressibility of Stokes's aether and, at the same time, with the absence of slipping over the Earth’s surface.

2. In order to overcome this essential difficulty Max Planck lias suggested that the incompressibility could be

* Communicated by Sir Oliver Lodge.

Phil. Mag. S. 6. Vol. 39. No. 230. Feb. 1920.

162 Dr. L. Silberstein on the recent Eclipse Results

given up * and replaced by the assumption that the aether is condensed round the Earth, and other celestial bodies, as if it were subjected to the force of gravitation and behaved more or less like a perfect gas. Lorentz, in spite of his personal preference for a fixed rather, took up Planck's idea and worked out the problem under the special (but by no means the only possible) assumption that the aether density p and pressure p obey Boyle’s law, p = ap, where a = const. If M be the Earth’s mass, in astronomical units, this gives

where is the density at infinity and r the distance of any external point from the Earth’s centre. The maximum velocity of slip at the Earth's surface (r=H), in the direction opposite to that of its motion becomes t

where a = otM/R, and is the velocity of the aether, relative to the Earth, at infinity.

To account for the astronomical aberration within the limits of experimental error it is necessary and sufficient to make This gives, by (2), with sufficient approxi

mation (since the required a is manifestly so large as to make the second term of the denominator negligible],

so that the said requirement is amply satisfied by

This means, according to (1), a condensation J, of the aether amounting at the Earth’s surface to little less than

and gives at the same time for the (lower limit of the) coefficient a the value 10"2R/M, to which we may return

* Of. H. A. Lorentz’s paper on Stokes’s theory of aberration in A mster-dam Proc. for 1898-99, p. 443, reprinted in vol. i. of his Abhandlungen.

t A short deduction of this formula will be found in Lorentz’s 1 Theory of Electrons,’ 1909, p. 314.

J What is commonly called “condensation” would in our case be

--1. But it will be convenient to use this as a short name for p/p .


which will henceforth be denoted by s.