Muvthy 



and along the lower boundary 



h (x',z') = 



as the hull may be assumed to have a pointed keel. The line integrals 

 along C are therefore both zero and the surface integrals cancel 

 with each other so that the net result is zero. 



Now, on the strip SV the integral may be written 

 o 



2 8 p g / dx' / z K^-, co 



s6 + tt — , sin0 dz' 



z=o 



and expanding the integral about its value when z' = the inner 

 integral becomes 



2 5 f 



a z 



/ 



ZzO 



a 



^h a , ah 



< — - cos0 + ^ — . sin0 



dx' dz' 



dz' 



z'ro 



and since 



= cos0 = 1 + O(0 2 ) 



dz' 



the integral becomes 



cos + —z — ; 

 d z' 



-] [4 A 



z= r 



z'ro z-° 



on linearizing with respect to and noting that 



2 2 2 



z' = z + 0(0 ) . 



1_ _ah_ 

 2 ax- 



The surface integral over S'.j therefore becomes 



- 5pg 



/ 



&"(»■■ ■■> f 2 dx , 



ax 1 



192 



