Murthy 



-= has ^ as a factor and these terms will therefore become of a 



much higher order. We may therefore ignore the terms containing 

 6 and write simply 



be 



dS = £ 



*-&♦•< 



ah 



1 dG 



ah 



ac 



a*' as 



ar 1 ar 



d^'df 



It should be noted that the derivatives of G on the actual hull surface 

 should be used although we have reduced the domain of integration 

 to the longitudinal plane of the hulls. We will therefore have to expand 

 the derivatives from the hull surface to the longitudinal plane. 



Let 



G = G + 



r r 



where G is the regular part of G and 



(x -u 2 + (y - v) 2 + (z -r ) 2 



1/2 



Then, using Taylor's theorem for the expansion of regular functions 



ac 



a n 



a G r 



h.b^d'n a^ 



rah aG 



+ 5 



n=b 



La*' a* 



ah 

 i 



af 



aG 



■> b + 



+ 5 



vH-'-i? 



f Sh i 

 | as' 



asa*? 



ac 

 ~a7 



ah. 



ar' 



a h i * G r 



a 2 G 



* h i 



ar,ar) J 



^ G r 



L^' a* 



a r ar 



a 2 G 

 V^'>"a 





+ 0(5") 



2 30 



