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 aether, 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 



p=p^ lr , (i) 



where p^ 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 = M), in the direction 

 opposite to that of its motion becomes f 



v ~ f V-(l + <r + ia 2 y ' ' ' ' (2) 



where a = ccM/R, and v m 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 t>== T J- <J v^ . 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 



cT-10-2 ..(E) 



This means, according to (1), a condensation J of the aether 

 amounting at the Earth's surface to little less than 



s=- p =27000, 



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 Amster- 

 dam Proc. for 1898-99, p. 443, reprinted in vol. i. of his Abhandlunyen. 



t A short deduction of this formula will be found in Lorentz's 

 < Theory of Electrons,' 1909, p. 314. 



% 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^, 



Pea 



which will henceforth be denoted by s. 



