by wave reflected from one part or another of the jetty. 



The General Rigorous Solution and Its Practical Complexity 



At a meeting of the Section on Fluvial and Maritime Hydraulics 

 of the Societe Hydrotechnique de France in June 1950 , Mr. Schoemacher 

 of the Hydraulic Laboratory of the University of Delft, stated that 

 the rigorous solution of the diffraction problem for any incidence 

 of wa-"e and for a limited opening in a breakwater had been discovered 

 for cylindrical raves and reported by P, M. Morse and p. J. Ruben- 

 stein (6) in 1938 . These latter studies refeired to a German study 

 made in 1902 and it is curious to note that neither Putnam and Arthur 

 nor Blue and Johnson apparently had any knowledge of these studies. 

 J. Larras (7) showed in 194-2 that the acoustic solution in two 

 dimension was applicable to ocean -waves and it followed that the ex- 

 pression given by Morse and Rubenstein entirely solved the problem 

 for swell, at least in theory! but for practical use these authors 

 referred to tables of Mathieu functions which were established by 

 themselves. 



The solution utilizes in effect cylindrical elliptic coordinate 

 and the ?.fethieu function which occurs in various elliptic or hyper- 

 bolic problems, noteably those of the vibration of an elliptic 

 membrane (8) and -the propagation of electro-magnetic waves in 

 elliptical guides (9). Batsman, (3) on pages 429, 430, and 490, 

 gives supplementary references and adds; "These elliptical 

 coordinates a re useful for the treatment of the problem of vibration 

 of an elliptic membrane and the diffusion of electro-magnetic waves 

 by an obstacle having the form of an elliptic or hyperbolic cylinder. 

 A screen containing a rectangular slot of constant width may be con- 

 sidered as the limit of an obstacle having the form of a hyperbolic 

 cylinder." The author did not discuss the solution in detail. 



It is a fact that this knowledge which has been unknown 

 theoretically for almost 50 years has not become of current usage. 

 Perhaps the reason may be found in the slight mention made of the 

 Mathieu functions in classical teaching and in the absence of or 

 very slight knowledge of the tables of these functions. 



Research Toward a Practical Approximate Solution Based on a 

 Generalization of Huyghen's Frinciple , Its Justification and Its 

 Expression 



Despite the slight theoretical interest of a solution founded 

 on Huyghen's principle, which is necessarily only approximate, we 

 have devised a solution of this type whose practical use is simple 

 and elementary. It is nevertheless necessary to assure oneself 

 that Huyghen's principle, or an adapted Huyghen's principle, is 

 applicable to oblique incidence of the wave. Its approximate 



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