/ o ^ *^ 



PROCEEDINGS 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



November 26, 1849. 



On the Dynamical Theory of Diffraction. By Professor Stokes. 



The problem of diffraction is treated mathematically by conceiving 

 each wave of a series incident on a small aperture, or passing the 

 edge of a diffracting body, broken up on arriving at the aperture or 

 diffracting edge, regarding each element of the wave as the centre 

 of an elementary disturbance, which diverges spherically from that 

 element, and finding by integration the aggregate disturbance at any 

 point in front of the primary wave. With the exception of one case 

 of diffraction, which will be mentioned further on, the illumination 

 in front of an aperture is insensible except in the immediate neigh- 

 bourhood of a normal to the primary wave drawn through a point 

 in the aperture. Consequently we are only concerned with the law 

 of disturbance in that part of a secondary wave which lies very near 

 the normal to the primary wave ; the nature of the disturbance in 

 other directions does not affect the result, since the secondary waves 

 neutralize each other by interference. Now it has been shown by 

 others, by indirect methods, that if c be the coefficient of vibration 

 in the incident light, dS an element of the area of the aperture, r the 

 radius of a secondary wave diverging from dS, X the wave length, 



the coefficient of vibration in the secondary wave will be- — , and 



J Xr 



the phase of vibration must be accelerated by a quarter of an undula- 

 tion ; or in other words, - must be subtracted from the retardation 

 4 



due to the radius r. These results, however, according to what has 

 been already remarked, only apply to that portion of a secondary 

 wave which lies immediately about the normal to the primary. The 

 object of the author in this paper was to determine, on purely dyna- 

 mical principles, the law of disturbance in any direction in a se- 

 condary wave. 



The author has treated the aether as an elastic solid ; and as such 

 it must be treated in considering light, if the theory of transverse 

 vibrations be not rejected. The object which he had in view re- 

 quired the solution, in the first instance, of the following problem ; — ■ 

 to determine the disturbance at any point of an elastic medium, and 



No. VII. — Proceedings of the Cambridge Phil. Soc. 



