166 Dr. L. Silberstein on the recent Eclipse Results 



Miehelson-Morley experiment a pronounced positive effect. 

 But enough has now been said in illustration of the formula* 

 for the condensation and for the slip. 



5. Before passing to consider the Eclipse result it may be 

 well to generalize the condensation formula (3) for the case 

 in which Boyle's law is replaced by any relation between the 

 pressure and the density of the aether. The corresponding- 

 generalization of the slip-formula (2), not required for our 

 present purposes, may be postponed to a later opportunity. 



Let the pressure^ he any function of the density p alone, 

 and let there be any distribution of gravitating masses.. 

 Introduce the function, familiar from hydrodynamics, 



<S> = <t>(p)=\ d/ ' (5> 



Then, in the state of equilibrium, and with dm written for 

 any mass-element in astronomical units, 



<S> 



=f-> ....:. (6) 



where r is the distance of the contemplated point from dm, 

 and the integral, representing the total gravitational poten- 

 tial, extends over all material bodies. <1> being a known 

 function of p, formula (6) gives the required relation. It 

 will be seen from the definition (5) that the dimensions 

 of <E> (work per unit mass of aether) are those of a squared 

 velocity. In order to bring this into evidence, let us recall 

 that 



•=>/f •••••• e> 



is the velocity of propagation of longitudinal waves in any 

 compressible non-viscous fluid *. This velocity is, in general, 

 a function of p, and becomes a constant for the special case 

 of Boyle's law, namely, our previous 1/ v/«. Using (7) and 



writing, as bef ore, — = d log s, we have 



<P = \ V 2 ,dlogs, .... (5a] 



- 



the required form. The integral is to be extended from 



* This result, known as the formula of Laplace, holds also for the most 

 characteristic kind of waves — to wit, for a wave of longitudinal dis- 

 continuity (Hugoniot, Hadamard), for which it follows directly, without 

 integration, from the hydrodynamical equations of motion. See, for 

 instance, my 'Vectorial Mechanics/ p. 169. 



