3» We will suppose that we are able to apply Kirehoff ! s 

 reasoning, that is to say Green's formula s to the 

 surface S, although the velocity potential and its 

 derivatives are subject to discontinuity in A and Bo 

 There is no reason not to believe that one nay avoid 

 this discontinuity by taking a different path of 

 integration, avoiding A and B but passing vary close 

 thereto (e.g. the ends of the breakwater rounded). 



These are without doubt approximations whose effect is difficult 

 to appreciate; even more so since it appears that the second 

 hypotheses is hard to accept,, In view of the fact that it states 

 that diffraction does not exist at all cr at least does not alter 

 the movement at fche opening AB, which is certainly not correct . The 

 sole verification possible consists in comparing the results ob- 

 tained from the use of this method to the results obtained by the 

 exact hydrodynamic solution,, 



The Resultant Solution 



One deduces from Equation 1 the movement in P by an integra- 

 tion from A to Bo This movement is practically given by the 

 distance j measured on a spiral analogous to Gornu spirals of 

 optics^ between two points characterized by parameters which are 

 related simply to the position of point P in relation to the two 

 arms A and B. The lines of equal value of these parameters are 

 parabolas whose foci are the points A and B and which may be traced 

 in advance by supposing that all horizontal lengths are measured 

 in terms of wave length as the unit of length,, In fact if one 

 compares the results obtained thus to the simplified solution of 

 Putnam and Arthur (4) one finds an almost perfect coincidence , the 

 differences not exceeding one hundredth of the amplitude of the 

 incident wave „ This is the verification a posteriori of the validity 

 of the hypotheses that have been made. 



The form of solution obtained, which is quite similar to that 

 of Putnam and Arthur, leds, for the case of a semi-infirite break- 

 water (i.e. a very large opening) to a distribution of amplitudes 

 which is in some fashion rigidly bound to the direction of incidence 

 of the wave. If for example, in normal incidence one obtains at a 

 distance y behind the jetty (i.e. at a distance y from the wave 

 coinciding with the breakwater). A certain distribution of move- 

 ment, then one obtains the distribution in oblique incidence by 

 turning the normal incidence distribution around the breakwater 

 through an angle equal to the angle of incidence,, The homolog of 

 the line situated at the distance y from the breakwater in normal 

 incidence is then the line situated at the distance y beyond the 

 crest passing the jetty. The line of equal amplitude are essentially 

 parabolas whose focus is at the breakwater. 



17 



