Eggers 





|_ [ [Erad^<-.];-,<-'[,X".4i']JJ(4"-*r""')-«dV. 

 "' " (51) 



In particular for a symmetrical hull, where Tq^z*^ ^'/'xx^ ^^ °^^ ^^<^ ^x'^'^x i^ 

 even, we have 



-T ^00 

 ( 3) 



[grad0^*^] 0x^\-X) dXdY = - [grad^^^)] ^jcx^"^)^^^ 



J-J J-O) J- J J- CD 



= 7" [grad 0^')] 4'^-X)dXdY. 



J-T J-co (52) 



K now for a symmetrical hull we have 



4'\X,Y,0) = 2^ a^(X) cos (U^7oY) , with a^ = a.^ 



(53a) 



00 



0y'\x,Y,O) = J^ /3^(X) sin (U,7oY) . with /3^ = /3_^ , (53b) 



V = - CD 



and 



CO 



4'\x,Y,0) = 2^ 7^(X) cos (U,7oY) ■ with y^ = y_^ , (53c) 



V=- CO 



where according to Eqs. (33) and (Al) the coefficients a^ , /3^, and y^ depend on 

 hull geometry given by Y= ±eF(X,Z) through the relations 



a^ = BHyBX , /3^ = V^y^H^ , \ = SHyBZ . (54) 



with the function H^(X,Y,Z) given by 



H^(X,Y,Z) = -^ ^^ [sign(X-^)- 1] e'^'^^'o^ F(^, O cos [W^7o(X-f)] d^dC 



,0' 



-0* -'v=o 



sign(X-^) F(^,Oe""''° '^' I V cos (\yA) 



- U^ sin (V7oO 



U dV 



J U'* + V^ 



and u^, M^, w^, K^, and u as given by Eq. (A4b); then we can express 



664 



d^d^ (55) 



