358 



of the sphere. Prora equation (4.4) and this result we 

 find that 



(4.6) 



E = 2TrpA^A^(^ + $'(0)) 

 = 2TrpA^A^(l + A$'(0)) 



so that f , = $ (0) . 



Solution of the Electrostatic Problem 



This shows that we need the value of $ only at the 

 center of the sphere. It will be found by considering 

 the infinite set of images produced by reflecting the 

 original source at the center and its images in the bot- 

 tom and free surface . 



For convenience of representation we shall draw the 

 surfaces vertically. The situation is as follows: 



-4 



^-3 ^-2 



'-1 



^1^2 



S3 S4 



Here, S is the soxirce of strength one at the center 



of the bubble. 



denote the image 



>1' •='_i' "^2' "^-2* 

 30\irces and sinks. They are obtained as follows: 



