U. , = U. + 2C(N . , + N.) (193) 



.7+1 .7 .7+1 .7 



(194) 



3 +l 3 J+l 3 



2 



[A(b . , + b .)] 



L V .7 + 1 <T J 



J + l J 



Aw 2 

 (4g) 



D. = b .d. (196) 



3 3 3 



j = 1, 2, 3, . . . 



where b ? - and b-- +1 represent the distance between refracted wave 

 rays at stations j and jj+ 1, respectively, N the horizontal dis- 

 placement of a water particle, and A the horizontal distance between 

 stations j and j + 1. For an unrefracted wave, 



W - T C197) 



U = 1 at the shoreline (as in the case of Hidaka) and N = at the 

 shoreline. 



Looking at unrefracted waves on a constant shelf slope S 2 for the 

 same wave periods previously defined by equations (189) and (190), 



T = K —2- (198) 



n n W 



where Kj = 3.2417 and K 2 = 1.9254 as previously defined in equations 

 (189) and (190). From this 



2tt /gd 

 n 



and for the constant slope, from equation (186), 



d S d S S 2 S 2 



_i = §_i . = i_ (20 0) 



a (^2 - 1) d s Jl - 1 



96 



