9f o . 9f o . • df o 9<)) o 9f o 



9x o 9z o g 3z o 9x 9z o 



9f n a 9f n a 9 *o 



+ a-^ 4- (*i+4> ) + a-^ I - ^i^ > " U ST- * 



3x 3x 1 w dz dz 1 w dz 



,3f a\ a 2 * 



((J). +<|) ) + U(z -x*) I 3-^ — ^ - 3-5^ J = (100) 



3y ^ y l Y w' g r/ \3z Q 3z 2 3y3z 



If we assume U and to are both of the order of unity, (f> will be of the order 

 of 6 E. The term of the lowest order in the above equation has the order 

 of 6 and the equation of the same order is 



9f n • • 9f o 9f o 3 



- -5-^ (z -at*) + U -r-^ * + -5-^ |- ((f), +(J) ) 



3z Q g ry dz Q r 8z 3z Y l T w 



( 9f o d \ 9 \ 



3y 1 w g \3z Q 3z 2 3yd 



= (101) 



If we write the outward normal to the sectional form of the hull in the 

 plane perpendicular to the x axis by n' , the above equation takes the form 



^- = ( 8g -*MW ^ - U(z g --- 



f = (z -ttMJtiO ^r - u(z -*|» ^ I -^ i - ^r (102) 



The right-hand side is regarded as a known function provided that the 

 steady potential (J>_ is known. One can divide the periodical potential c|>, 

 into a part determined by the ship's oscillation and a part originated by 

 the diffraction of the ambient wave. The former is the radiation po- 

 tential ((> for which the boundary condition becomes 



42 



