rt£c 



Fi'gure 



Figure 2 



and which causes a movement at P of amplitude 



cos 6 + cos oc l_ 



2 "V7" 



Eq. 1 



that is to say proportional to the inverse of the square root of 

 the distance MP multiplied by the term cos 9 + cos tx f and whose 

 phase at P is equal to that existing at M retarded by 2.7rr 

 measuring r in terms of wave length as unity. For normal incidence 

 cc « 0. One then has ' - J or • j= which is the mean of the two 



solutions that we have considered (1), and which are quite similar 

 especially in the neighborhood of the limit of the geometrical 

 shadow. 



The Approximations Made 



To this point the sole approximations that have bean made are 

 due to the fact that the variation of amplitude in r~t is only ap- 

 proximate and that in order to obtain equation 1, one has neglected 

 a new term in r""3/2 But how does one apply practically the result 

 acquired according to Kirchoff, to the diffraction through a very 

 large opening in a breakwater. It is here that new aoproximations 

 must be ma.de . 



Inferring to Figure 2 S let A and B be the arms of the break- 

 water and AB the opening, CC is again the crest of a wave. We will 

 choose a surface S where the velocity potential and its normal 

 derivative are supposed known. This surface is the contour formed 

 by the opening AB- the part X'A and BX of the supposed infinitely 

 long breakwater and a dotted line traced very far from AB toward 

 the interior of the port and on which the agitation is ccnsidered 

 to be negligible . 



?Je suppose further that: 



1. On X'A and BX the velocity potential is zero (its 

 normal derivative is necessarily so); 



2. Between A and B the movement is the same as though 

 the jetty did not exist. 



16 



