c d p r /2 



I — = / 2 cot a da (233) 



J& d J a, 



s 1 



which when integrated gives 



In d/ =2 £n(sin a) / (234) 



d 

 s 1 



£. 



which reduces to 



In d - In d = -2 & sin a. (235) 



Taking the antilogs 



d 

 d 



P sin 2 a. 



(236) 



But cL = d + Sx v where S is the bottom slope, so 



d d 

 s s , 



Xp = (237) 



p S sin 2 0]L S 



To compute the coordinate parallel to the shoreline of a point on the 

 wave ray, note that 



dy 



(238) 



(239) 



or, differentiating equation (240) with respect to a, 



2d sin a cos a da 



dx = — (240) 



S sin 2 a, 



substituting equation (240) into equation (238) , equation (238) becomes 



2 d 



dy = sin o cos a tan a da (241) 



S sin 2 a. 



111 



tan a = — 

 dx 





is given by 





d sin 2 a 

 s 

 x = ■ 



d 



s 



S sin 2 a. 



S 



