iu)t f + „, N a 2 ex P[a 2 z+ia R cos(a-9)] 



+ 2 1 e H(a 2 ,a) da 



Q-tt/2 /l-4ft cos a 



+ 0(R *) (257) 



where 



g 1 - 2 ft cos a ± /l-4ft cos a 



2 2 



U 2 cos a 



(258) 



The interval - a Q < a < a Q must be omitted from the integral where 



a = for ft £ 1/4 



a Q = cos -1 (l/4ft) for ft > 1/4 



The function H(a.,a) is the Kochin function which is determined by singu- 

 larities representing the hull. Inserting the above expressions for the 

 velocity potential in the integral giving the force in x-direction, and 

 taking the time average of the lowest order term, we obtain an expression 

 for the mean resistance to the forward motion. It is composed of the wave 

 resistance in the calm water and the added resistance due to incident 

 waves. Let us define the latter by AR. The derivation of the final 

 formula is rather lengthy and will not be reproduced here. Only the result 

 is shown as follows. 



AR = 2 tt p 



/•/-/ 



*— -tt/2 



2Tr-a 



„ a, (a., cos 6-K cos a) 



H(a 9)p d9 



/l-4ft cos e 



r 9 a ?( a 9 cos ®~ K cos a ) 



+ 2 up |H(a„,9)r ~ d0 (259) 



J „ /l-4ft cos 



92 



