( 444 ) 



The problem becomes much simpler if, in the second equation, we 

 suppose the variations of the square of the velocity to be much 

 smaller than those of either of the first terms. We may then write 



const. , 



or, since 



». 3 

 Y ^ 



r 



log h — f.t (J — = const, 

 r 



If k^ be the density at the surface, and 



II (J r^" = «, 



the last equation becomes 



lo,jk-logh^-ix[---]=0 (3) 



As we see, our simplification consists in this, that the distribution 

 of the aether is independent of its motion, that is to say that it is 

 condensed to the same degree as if it were at rest. 



Substituting the value of h from (3) in (1), we find a ditterential 

 equation for the determination of q^. It can be satisfied by 



the form of the solution being chosen with a view to the remaining 

 conditions of the problem. These are 

 1'^. for r = 00 



dcp _ ^(p __ f. 'èf _ 

 9 -c di/ ds 



2". for r = u 



dr 



They give us the following relations between the constants of 

 integration a and h : 



