Modified Theory of Gravitation. 89 



In virtue of our assumption that k is overwhelmingly 

 greater than any other elastic modulus of the aether, we have 

 for the square of the velocity of compressional waves 



n 2 \ 2 — K/p, 

 whence 



K = n 2 X 2 p (44) 



From (39), (43), (44), 



z-"jrVm <« 



1-WO- ■ (46) 



B 2 X 2 i 



R'D^^ <«> 



where E is the constitutive energy per cubic centimetre of 

 the aether. Thus the factor of E in the right-hand member 

 of (47) expresses the maximum potential energy per unit 

 volume due to the wave-motion as a proportion of the con- 

 stitutive energy of the medium. Moreover, this maximum 

 potential energy per unit volume corresponds to an increment 

 8F, equal to ?F, above the mean value F, and is thus, to our 

 order of approximation, proportional to f 2 . We may write, 

 then, 



which serves to define a numerical constant S now first 

 introduced. This constant might, not improbably, be unity, 

 or a number of that order of magnitude, and for illustrative 

 purposes it is later assumed that 



a=i (49) 



29. From (42), (48), 



■«£\/l£> <«» 



the velocity of compressional waves in free oether being 



