p^/f. Sha//cwer ivai-er 



I 



Peeper waf^r 



Figure 



The basic theory of Johnson et al applies equally well however, re- 

 gardless of the direction of drawing the orthogoaal, but it must be 

 remembered that the measured angles are different in the two cases » As 

 may be seen from Figure 1^ 0C»= Oc-Aoc where OC/ is the measured angle 

 between the wave crest and the contour on the way out from shore , ^doc 

 is the change in angle of the direction of tte wave crest, and OC is 

 the angle between the contour and the wave crest beyond the point of turn- 

 ings OC would be the angle measured if the orthogonal were being drawn 

 into shore from deep water, and is the angle applicable to the equations 

 of Johnson et al<, This angle may be written in terms of CX| y however, 

 and substituted in these equations to obtain 



Aa:^-^-Y= sinoc ^-^4^ sin (a,+A<x) 



ian (oCi +Aoc) 



(1) 



(2) 



or for the general case, where r/j ~ sec OC 



where Z-,}/, is the average wave length between two adjacent contours and 

 /^L is the change in wave length between these two contours o 



A protractor may then be drawn on the basis of equation (2) to 

 determine Acc in terms of OC f and /L^^/. ^°^ drawing orthogonals directly 

 out from shore o Two such protractors are reproduced hereo That shown in 

 Figure 2 is for use at low values of A^/j_ and that in Figure 3 for 



