312 



BELL SYSTEM TECHNICAL JOURNAL 



founder of the wave-theory of light invented in reality a novel language 

 for expressing the corpuscular theory! 



Fresnel however invested these wavelets of Huyghens with some of 

 the properties which entitle them to the name. He supposed that the 

 amplitude was distributed widely over each, not confined to the point 

 ^ = 0, though greatest at that point; he thought that it diminished 

 slowly with increase of 6, though he did not suggest the precise factor 

 (1 + cos 6) nor any other; and he thought that it varied inversely as 

 distance. Further, he endowed it with a periodicity. Thus far, he 

 was right. But naturally he supposed that the cause of the wavelet 

 was the cyclic variation of the wave-function s, and therefore he pre- 

 sumed that it started out in consonance of phase with the primary 

 wave; and he did not insert the factor m. However when he came to 

 test his ideas in somewhat the sameway as Kirchhoff's theorem has been 

 tested in these pages — by applying them to a case where the required 

 result was known a priori — he was unable to derive the proper answer, 

 except by introducing the factor m and the advance-in-phase; and 

 thenceforth they have figured in the theory of diffraction, indispensable 

 and until the day of Kirchhoff inexplicable. 



To return to the problem of determining the wave-motion beyond 

 the apertures: under the approximations stated, it is mathematically 

 quite definite. The solution is the value of the integral: 



^0 



rj^<7 



(1 -f cos 6) sin {nt — mr) 



(77) 



Fig. 2 



extended over the apertures; r standing for the length of the line join- 

 ing the field-point P with the element-of-wave-front dS, and B for the 

 angle between this line and the perpendicular dropped from P to the 

 plane of the screen. 



