The former represents the longitudinal disturbance such as heaving and 

 pitching, and the latter represents the lateral disturbance such as sway- 

 ing, yawing, and rolling. Now let us designate densities of these wave 

 sources and wave dipoles by m(x)e and y(x)e . Then the Kochin 

 function is expressed as 



r i a. x cos 9 



H(a ± ,0) = {m(x)+ia i sin 0y(x)} e 1 dx 



(264) 



Then we put 



f 

 H 1 (a i ,6) =1 m(x) e 1 



r i a. 



H 2 (a ± ,e) = y(x) e 1 



i a. x cos 



x a. x cos 



dx 



dx 



(265) 



On integrating with respect to the integrals in Equation (264), odd 



9 



functions of vanish. Therefore, we can replace |H(a.,0)| by 



! H i Ca ±' e) ! 2 + 4 sin2 e l H 2 (a i' e) 



Changing the integration variable from to m, we obtain 

 -K„ 



AR = 4 it p 





(m+K.fi) (m-K cos a) A „ 



1 . |H (m)| dm (266) 



/(m+K Q) 4 -KQm 2 



where 



|H*(m)| = |H*(m)| 2 + 



4 2 2 

 (m+K.fi) - K^ m 



|H 2 (m) 



(267) 



and 



94 



