Murthy 



A correction is similarly to be made for only the first term in the 

 integral of (V. 16). This takes the form of a line integral 



icrtJ - 



oce I (z 



001 



*XnJ 



f = 



^G(x,y,z; fj g | o') |"[ d*' 

 bv ' |J 



dG(x, y, z; £', V, ) 



r? = b 



V-b 



As we have defined ^, as the time -independent part of 4> , 

 we may suppress the factor e a in (V. 16), (V. 17) and the correction 

 terms. This factor arose from the expansion of the Green's function 

 and in deriving the correction terms, but may be suppressed for the 

 time being so long as it is understood that we use this factor always 

 along with oc when we derive the time- dependent potential <{> 



Combining (V. 16) with (V. 17) and taking into account the 

 correction terms we have, after simplification 



V S 2 



(g|* 



*-|^) dS =//*V-|j. G(x,y, z;f,b,r') + G(x, y, z; *', -b, f')l 



+ ^|(-ooi °tp + r ooi It } (i ; + ^ > (G b + G -b| 



* 



be 



3G 



an' 



T?'=b 



+ 



r)'z-b 



a | r ooi 



/ a g_ 

 k Spa,- 



ai'oV 



) + 



r,=b 



+ r' 



3 E G 



001 S,'Sf 



3 2 G 



rj = -b 

 ) 



«/*001 



[*] 



>>'=b 

 f'=0 



1 - b i? = - b 



3 G(x, y, z; £, 77 , o ) 



df'df 



a,' 



dG(x 



,y, z^'.^o ) "I 



~~ ^~ \ V 



or) J 



r? = b 



»? = -b 



(V. 18) 



238 



