[V(x')A (x')-V(x)A (x)] N'(K|x-x' |)dx' (172) 



( (x) = V(x) A Q (x) Tl- | KA (x){N(K|£+x|)+N(K|il-x|)}l 

 W(x) = y K V(x) A n (x) {N(K|Jl+x|)+N(K|£-x|)} 



♦1*J 







I 



[V(x , )A (x')-V(x)A (x)] N'CKlx-x'Ddx' (173) 



where 



N'(K|x-x'|) = --f^j + fH (K|x-x'|) + yY (K|x-x'|) 



+ iri J (K|x-x'|) (174) 



The vertical component of the force acting on the ship by the fluid 

 pressure is given by 



-J/fe 



F z = ~ J I "^ P ds < 175 > 



" S 



and the moment about the y-axis is 



M 



y 



■ IS (n - 1 ') ? ds <i76) 



The second term in the parentheses can be omitted because of the slender 

 body assumption. Then the vertical force and the pitching moment on the 

 slender ship are given by 



63 



