Murthy 



and 



bG bG 



a* ar 



aG aG 



ar ar 



when terms of a higher order are neglected and , of course, 



o-G aG 



a*? a v' 



A similar result will hold for S_ with ( £', -b, f ') as the argument 

 of the Green's function. 



We therefore have 



//•!»-# M[ 



aG(x,y, z; £', V ,£') 



V S 2 



10 



a^ 



2 



aG(x,y, z; £', v , t) 



bv 



»7=b 



V--b 



icrt ( a G 



ae r ooi LaTav 



i=b 



a g 



77z-b 



+ r! 



001 



.2 



a G 



arj'ar I 



T7=b 



we have finally to evaluate 



a* 



n2 



a g 

 a vaf 



Tji-b 



d£df 

 (V. 16) 



// 



G , 



T^ 



dS 



a* s i +s 2 



Now, "5 — is given exactly by the linearized boundary condition (V. 8) 

 on the hull 



"ST.- SV ~W + '"j^'ooi - a — +r ioi ^r> + v V>i- 3 -J 



applicable to S., and S 2 _ with a similar expression for S^ and 

 S_ where h replaces h 1 . Inserting these expressions, using 



the expansion derived above for G and combining S and S ? 



u o o 



we have 



236 



