Bessho 



(^\y^ = on L 

 <j>ly = - Xy on S 



^2 = ?2 = C20» given on L 

 ^Sv~ on S 



(4.21) 



(4, 22) 



The corresponding functionals are of the form (4,10) for ^\, 

 and of the form (4,14), without the third term, on the right-hand side, 

 for <^2* 



For the present case, ^gQ must be equal to l/g by (4.19); 

 however, in general, it will be arbitrary and, perhaps, a constcint 

 of the form (4.18). ^^ ^^ called the honnogeneous solution. [18,22^ 

 26] 



Finally, it should be noticed that the Lagranglan is closely 

 related to the far-field potential. For a submerged body, we have, 

 from the boundary conditions, (A. 9), (A. 11), and (4.3), 



B = - \ \ xXydS + 2L(<1),<|)) 



'S 

 = 2L(<j>,(|>) +V, (4.23) 



where V is the displaced volume. For a surface-piercing body, 

 intesrpreting condition (A. 10) as a correction for the reed wetted 

 surface, we have 



yy x(j)^dS + |j x<t), dy=V, (4.24) 



where V is the displacement volume under the still waterline. 

 Therefore, we can write (A. 11) as 



B =V + 2L*((}),^, +'$2)» (4.25) 



where <{>| and <j>2 are defined by (4.21) and (4.22), with ^20" ^/s* 

 For a pressure distribution, we have, from (A, 18) and (4.8), 



B = 2p£*(p,5J, (4.26) 



560 



