Yim 



Letting 



,1 e dt 



= -^ + i{(Z- Slkx,) cos kx, + Cikx, sinkx^} , 



and 



Ztt , Sir 1 // ir 



., -—coskx, -^ -k^W 



I, = 4^ COS kx, - 4? - i {( ■? - Sikx ) cos kx, 



+ Cikx, sin kx,} , in x, > 



Therefore, for X| < 



U =3^[4x,(log |x,| - 1) - 4j dxlog (Vx2 + bV4 + B/2) 

 + 1 {( I _ Sikx,) cos kx, + Cikx, sin kx,}] (52a) 



and for x, > 



;, = ^ [4x,(log X, - 1) - 4 ^ dx log (Vx2 + bV4 + B/2) 

 + -T^ cos kx, - -=- — IT ^ ( "T " Sikx,) cos kx, 



+ Cikx, sin kx,}] (52b) 



The wave height related to the second term of I can be approxi- 

 mated by the method of stationary phase, [ 5] neglecting the local 

 disturbance: 



^^ = . 4/^ I±^ (i - e^") cos (kx .1 ) (53) 



586 



