where m(x) is the complex conjugate of m(x) . Here we write 



arg m(x) = &Ax) 



(271) 



Then we obtain 



A^ = - 8 T\ 2 p f jm(x)| 2 



d6 1 (x) 

 K cos a+ — 



(272) 



A similar reduction is applied to the portion by the lateral disturbance. 

 In consequence, the added resistance is given by 



AR = - 8 



^W 



I d6 1 (x) 

 m(x) I { K cos a+ 



dx 



a) 4 2 ( d6 2 (x) 



+ — £ |y(x) | JK COS a+ "j : | (!>: 



(273) 



where 



arg y(x) = § 2 (x) 



(274) 



It can be readily shown, that the expression for AR is valid in the case 



-1/2 

 of U = 0(1) and 0) = 0(e ) too, but the expression for the added 



resistance due to lateral disturbances takes another form which is more 



complicated and spoils the practical utility to some extent. A similar 



simplification can be applied to the lateral drift force, and the final 



result is 



, f r 4 

 D = 8 ir p I 2-^2 |m(x)||y(x)|sin{6 1 (x)-6 2 (x)} 



' i / \ 1 2 . w i,.i2 

 -K sin a \ |m(x) H y(x) 



dx 



(275) 



96 



