where the metrics h, and h^ (defined by i =h,d(t) and !Lr,=^r,dQ) are evaluated 

 at the point (({) +iA(j), jA6) . Rearranging the terms of Equation (38) 

 yields the equation 



= C''-^ = D^^ W^^ + h^ A(}) C^^ (39a) 



where 



''^2^'^'' (39b) 



The values of w"-" for j = 0, 1,...,M are specified initial conditions; 

 they may be obtained from experimental data. Along the symmetry lines 

 j = (6=0) and j = M (6 =" y) . the crossflow angle 3 is zero, so that 

 W„ = t = 0, the equation W_ H replaces the second momentum Equation (36) 

 along the two lines of symmetry, the load water line and the keel. Moreover, 



a = on these lines, so that g-, o » Sot' §9?' ^o' ^?2' ^' *^f ' 2' ^ gu 



9 

 are identically zero. Thus, along the symmetry lines, the momentum integral 



Equation (3a) reduces to the equation 



^ii + e..^|^ = ^c. ^,f.-^^] (40) 



3Ji, 11 3t 9£„ 2 f^ 11 \ (|) U 9Jl 



and the auxiliary Equation (7) reduces to the equation 



'llH-6,.4il?-+e„^l^-F(H)-9„ G(i|^-KJ (41) 



dl, 11 dH 9£, 11 3t 8£o ' ' 11 \U 9£ 



22 



