I. On the Dynamical Theory of Diffraction. By G. G. Stokes, M.A., Fellow of 

 Pembroke College, and Lucasian Professor of Mathematics in the University 

 of Cambridge. 



[Read November 26, 1849.] 



When light is incident on a small aperture in a screen, the illumination at any point in front 

 of the screen is determined, on the undulatory theory, in the following manner. The incident 

 waves are conceived to be broken up on arriving at the aperture ; each element of the aperture is 

 considered as the centre of an elementary disturbance, which diverges spherically in all directions, 

 with an intensity which does not vary rapidly from one direction to another in the neighbourhood 

 of the normal to the primary wave ; and the disturbance at any point is found by taking the 

 aggregate of the disturbances due to all the secondary waves, the phase of vibration of each 

 being retarded by a quantity corresponding to the distance from its centre to the point where 

 the disturbance is sought. The square of the coefficient of vibration is then taken as a measure 

 of the intensity of illumination. Let us consider for a moment the hypotheses on which this 

 process rests. In the first place, it is no hypothesis that we may conceive the waves broken 

 up on arriving at the aperture : it is a necessary consequence of the dynamical principle of 

 the superposition of small motions ; and if this principle be inapplicable to light, the undula- 

 tory theory is upset from its very foundations. The mathematical resolution of a wave, or 

 any portion of a wave, into elementary disturbances must not be confounded with a physical 

 breaking up of the wave, with which it has no more to do than the division of a rod of 

 variable density into differential elements, for the purpose of finding its centre of gravity, has 

 to do with breaking the rod in pieces. It is an hypothesis that we may find the disturbance 

 in front of the aperture by merely taking the aggregate of the disturbances due to all the 

 secondary waves, each secondary wave proceeding as if the screen were away ; in other words, 

 that the effect of the screen is merely to stop a certain portion of the incident light. This 

 hypothesis, exceedingly probable a priori, when we are only concerned with points at no 

 great distance from the normal to the primary wave, is confirmed by experiment, which shews 

 that the same appearances are presented, with a given aperture, whatever be the nature of the 

 screen in which the aperture is pierced, whether, for example, it consist of paper or of foil, 

 whether a small aperture be divided by a hair or by a wire of equal thickness. It is an 

 hypothesis, again, that the intensity in a secondary wave is nearly constant, at a given distance 

 from the centre, in different directions very near the normal to the primary wave ; but it 

 seems to me almost impossible to conceive a mechanical theory which would not lead to this 

 result. It is evident that the difference of phase of the various secondary waves which agitate 

 a given point must be determined by the difference of their radii ; and if it should afterwards 

 be found necessary to add a constant to all the phases the results will not be at all affected. 

 Vol. IX. Part I. 1 



