where a is replaced by G in a and a„. Note that this formula is valid 

 when the energy relation mentioned before holds. If there is another kind 

 of energy dissipation such as viscosity, the above relation needs some 

 alteration. In order to facilitate numerical work, the integration 

 variable is changed to 



1 - 2 jjj cos 6 ± A-4^ cos 9 

 2 cos 6 



(260) 



where K„ = g/U. Then we obtain 



AR = 4 it p 



-K, 



-J -I 



(m+K fi) (m-K cos a) A „ 



. |H (m)| dm (261) 



A 



4 2 2 

 (m+K fl) -KqIh 



where 



H (m) = H(a.,9) i = 1, 2 



(262) 



K l = \ K ( 1+2f2+,/l+4fi )» K 2 = \ K (l+2ft-/l+4fl) 

 If Q < 1/4, the interval 



(263) 



y K (l-2fi-/L-4n) < m < | K (l-2n+/l-4fi) 



must be omitted from the integral. 



Simplification of the Formula 



At a great distance from the ship, the disturbance by the ship, in- 

 cluding both radiation and diffraction, is represented by a combination of 

 wave sources and y-directed wave dipoles distributed along the x-axis. 



93 



