160 Mr. J. Walker on Cauchy's Theory of 



Using Green's* method of separating the distortional and 

 condensational parts of the solution, and assuming 



fc—^i^ _^ dip 

 * ~~ dx dy ' dy dx ' 



the equations of motion become 



dt 2 y \dx 2 ^ dy 2 )' dt 2 ~ 7 \dx 2 "*" dy 2 P 

 where 



g 2 z=z(m + n)/p, 7 2 = njp . 



Similar equations apply to the second medium. 

 The principle of continuity gives for the interfacial con- 

 ditions that for x = 0, 



# &ty_d$_ dV 

 dx dy dx dy 



d(j> dty_ d<j>' dty' 

 dy dx dy dx ' 



dQ dfy = d 2 £ d 2 ty ' 



dx 2 dxdy dx 2 dxdy 



f^_d 2 ty_d^___dSy J 

 dxdy dx 2 ~ dxdy dx 2 J 



(8) 



(9) 



Since these equations are true for all values of y, we may 

 differentiate with respect to it, and hence, by means of the 

 equations of motion, replace (9) by 



i d 2 ^>_ i ay i^d 2 ty_] L d 2 ty^ 



g 2 dt 2 " g' 2 dt 2 ' 7 2 dt 2 ~ 7 /2 dt 2 * ' * " ^ 



It may here be noted, that if we take the general equations 

 of condition (7) and assume the equality of the rigidities of the 

 aether in the two media with no assumption respecting the 

 compressibilities, we get, instead of (9a), 



d 2 cj> ,#$ d?ty ,d?ty' 

 P-a¥=P^> P^=P-J ( 9 »> 



±f _-g// e (a"x+by-<ot)\f~l 

 if __ e (a'x+by—o>t)\f~l^ 



* Collected Works, p. 261. 



Assume 



