Bessho 



4. Problem to reduce the wave resistance. This is also a practical prob- 

 lem, that is, how and how much the wave resistance can be reduced by the ade- 

 quate combination of the elementary distributions, keeping the practical restric- 

 tions of the actual ship. 



There is another case which has a unique solution, that is, a symmetric dis- 

 tribution about the origin over a circular disc, but it is nearly equal to case 3 

 for large velocity (1). 



TRANSVERSAL LINE DISTRIBUTION 



Case 3 above will now be studied, namely, a transversal line distribution 

 (1,5,7-9). Suppose the wave-source doublet is along the segment |y| < l, of 

 which the total is given as Eq. (25). Introducing a normalized distribution H as 



H(y) = ^Jp(x,y) dx , 



this is written as 



1 



1 



H(y) dy = 2 

 1 



(28) 



(29) 



The wave resistance (Eq. (22)) can be written as 



K|-^Uk/('^U2 



H(y) G(y) dy , 



(30) 



where 



and also 



r. ^ ^' fi 2 dM (31) 



G(y)=-(^l-^^JG(y) 



G*(y) = ^ H(y') P.JO, g(y-y'), 0] dy ' 



(32) 



or 



(33) 



G*(y) = -^ r H(y') K^ ^-|- | y - y ' |^ dy ' , 



where B is the breadth in the usual unit system and K^ is a modified Bessel 

 function. 



Equation (31) can be deduced from the following relations. Since the func- 

 tion P. J has an expansion (13) 



782 



