It should be recalled that the theory consists in applying the 

 rigorous theory of diffraction of light, or of sound, behind a 

 semi-infinite screen to the diffraction of a water wave in constant 

 depth behind a semi-infinite jetty; if the application is limited to 

 the terms of the first order for this latter problem the equations 

 and the limiting conditions are in effect the same for the two cases, 



The ratio of the amplitude of the diffracted wave at a polar 

 coordinate point (r, 9) to the amplitude of the incident wave is 

 given by the modulus of the following complex function: 



— / -£f£- cos(0 o -e) 

 F (r,9) = f(u-L)e L 



-l £f*- cos(e o +e) 



where 



V2 e ( U e civ 



c/ — °o 



L being the length of the wave and 



f(u)- -L e ' 7 ,r. _, 4L« . (1) 



Ut = A / dL s/n &° Q. 



x 2 



u, = — "\ / Sr sin Msl±A 



Note that F(r,9) may also be written in the form 

 F(r,0) = ?(r, 9)fi l '*fliO) 



where 



(J (r,9) is the modulus of the function F and determines the re- 

 lative height of the wave and 



^(r,9), the argument of the function F, determines the plan of 

 the wave distribution, or in other words, <j> (r,9) = const, is, in 



(1) Putnam and Arthur: Diffraction of water waves by breakwaters. 

 Trans. Am. Geophy. Union, Aug 48). Note that this method of calcula- 

 tion was proposed previously by Mr. Larras in the French publication 

 "Travaux" for June 194-2. 



16 



