Murthy 



47Tg 



j>] G^ - G O] +^-Mg| dv (V. 19) 



The potentials of various orders may now readily be written 

 down by equating terms of the same order on both sides of (V. 19) 

 with the assumption that the "jumps" in the potential relate only to 

 the cushion and not to the side hulls. This has been discussed above. 



We thus derive the following expressions for the potentials : 

 ° (5) *1000 (*>Y> Z ) = TT"i/|^ G(x,y, Z ;^b,r') + G(x, y, z; «'„ -b,f ') J 



d£df 



0(a«)4> i()io (x,y,z)= — 



W" ' " 



+h c ] *ooi|t1T + 



+ (z ooi ■ e W~r 



1* + v tf] K + G -b] 



d£ df 



0(0)4) (x,y, z) = - 



0100 y 4*Pg 



i 



*g O , 01 



L R+ L q L 



p G(x, y, z; I, tj ,o ) d£ dr; + 



00 



(M.o) 



G .(x, y, z; £, ?7 ,o ) - 



[ 



' |"ai"*0100^ ,7?, °M G (x>Y> z '>Z>V .°) dr, 



.JL//L ( «,b-,f)-*<*'- b+ - f '>l 



47r// 0100 v 0100 J 



1o 



[£G(x, y, z;£', tj', f) 



aG( x 



r?=b 



,;y,«i^',f)n d{ < df - 



d*7 |J 



7?Z-b 



°^ a )*oiio (x ' y ' z) = 



( "001 + VoOlY/T/.v W * \ 

 II (2Vp^ - i<rp^ ;G(x, y, z;£, iJ,o) 



^o 



Att p g 



'« 



$ 



+ Vp Q G (x,y, z;^,t, ,o) dHl 



240 



