9U 



Mr. G. H. Livens on some Further Problems 



negligible and Ave can leave them out o£ the discussion. 

 Thus the solution is obtained with 



A<*) 



es 



(>-S) 



. , an . 



cos id -\ sin nt 



e 



c' 2 n 2 1 a 2 u 2 a 4 ?^ 



The density on the sphere is just as before 

 1 /. 2/Wx 



and the force on the sphere in the direction of motion is 



This gives 



P = 





cos nt ^ sin ?i£ 



c 



3 a<; 2 



i- a ^ + 



This is the effective force resulting from the motion and 

 is the force which would be required to produce it. The 

 motion can be interpreted as a solution of the dynamical 

 equation 



wherein 



J C(6' w 



('-¥) 



1/ c 2 J + c 2 



£ = 



an 



V 1 <r J + c» 



and P is the force above investigated. If — is small this is 

 practically c 



2 e" 



m 



k = 



3 c 3 ' 



