162 MR. GEORGE W. WALKER ON THE INITIAL ACCELERATED 



In these x> which is independent of t, satisfies 



and (f> satisfies 



(* /.r 



( K; A 1^ - - --- , 



\d day \9a; 2 P?/ 2 3z 2 / 



while x and < are both small of the same order as f. ' 



Vibrations may be supposed to arise and subside rapidly. It is clearly not possible 

 to determine these in a simple form since the question corresponds now to vibrations 

 on a spheroid at rest. 



Such vibrations do not lend themselves to analysis in the same way as vibrations 

 on a sphere, and only approximate treatment has been found possible. 



Our object, however, is the determination of the motion after vibrations have 

 subsided, and with this limitation it has been found possible to complete the solution. 



The determination of < and ^ to satisfy the surface conditions proved an exceed- 

 ingly difficult problem. The process was in great measure tentative, and does not 

 possess much intrinsic interest. When obtained the solutions can be verified in a 

 straightforward although slightly tedious manner. 



If 



/'= \f/?, where f () is constant, 

 then 



where 



, i./o 2,r J _ e \ 



r2 2 ~r\2- TTi - T5\ 1 rO 1 i f 



C A:(l A"*) I kacoshr)} 



and 



where 



These expressions substituted in the equations satisfy the condition that (X', Y', Z') 

 should be entirely radial at r = a. 



