in which the superscript k + 1 denotes the (k + 1)' iteration and applies to the 

 improved estimates of a and H/L^. Once these estimates are known, the parameters with 

 the k subscripts on the right hand sides of Equations (11-8) and (11-9) are calculated and 

 improved estimates of a and H/L^ are determined, etc. The procedure was initiated in 

 deep water and the wave steepness and direction calculated at the remaining nine values of 

 relative depth advancing shoreward or until breaking was indicated. At each relative depth, 

 the iteration converged very rapidly with three or four iterations usually sufficient. For the 

 first iteration at a relative depth, the initial value for wave steepness was taken as the final 

 value for the preceding (greater) relative depth. 



The shoaUng-refraction results are presented in graphical form, for a^, "= 0°, 10°, 20°, 

 40°, and 60° in Figures 25, 26, 27, 28, and 29, respectively. A description of these tables is 

 presented in Section IV and two examples illustrating their application are given in 

 Section V. 



107 



