4 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



medium : the rest is a mere matter of integration ; and whatever difficulties the solution of 

 the problem may present for particular forms of aperture, they are purely mathematical. 



In the investigation, the incident light is supposed to be plane-polarized, and the follow- 

 ing results are arrived at. Each diffracted ray is plane-polarized, and the plane of polari- 

 zation is determined by this law ; The plane of vibration of the diffracted ray is parallel to 

 the direction of vibration of the incident ray. The expression plane of vibration is here 

 used to denote the plane passing through the ray and the direction of vibration. The direction 

 of vibration in any diffracted ray being determined by the law above mentioned, the phase 

 and coefficient of vibration at that part of a secondary wave are given by the formulae of 

 Art. 33. 



The law just enunciated seems to lead to a crucial experiment for deciding between the 

 two rival theories respecting the directions of vibration in plane-polarized light. Suppose 

 the plane of polarization, and consequently the plane of vibration, of the incident light to be 

 turned round through equal angles of say 5° at a time. Then, according to theory, the planes 

 of vibration of the diffracted ray will not be distributed uniformly, but will be crowded 

 towards the plane perpendicular to the plane of diffraction, or that which contains the incident 

 and diffracted rays. The law and amount of the crowding will in fact be just the same as 

 if the planes of vibration of the incident ray were represented in section on a plane perpen- 

 dicular to that ray, and then projected on a plane perpendicular to the diffracted ray. Now 

 experiment will enable us to decide whether the planes of polarization of the diffracted ray 

 are crowded towards the plane of diffraction or towards the plane perpendicular to the plane 

 of diffraction, and we shall accordingly be led to conclude, either that the direction of vibration 

 is perpendicular, or that it is parallel to the plane of polarization. 



In ordinary cases of diffraction, the light is insensible at such a small distance from the 

 direction of the incident ray produced that the crowding indicated by theory is too small 

 to be detected by experiment. It is only by means of a fine grating that we can obtain light 

 of considerable intensity which has been diffracted at a large angle. 



On mentioning to my friend, Professor Miller, the result at which I had arrived, and 

 making some inquiries about the fineness, &c. of gratings, he urged me to perform the 

 experiment myself, and kindly lent me for the purpose a fine glass grating, which he has in his 

 possession. For the use of two graduated instruments employed in determining the positions 

 of the planes of polarization of the incident and diffracted rays I am indebted to the kindness 

 of my friend Professor O'Brien. 



The description of the experiments, and the discussion of the results, occupies Part II. of 

 this Paper. Since in a glass grating the diffraction takes place at the common surface of two 

 different media, namely, air and glass, the theory of Part I. does not quite meet the case. 

 Nevertheless it does not fail to point out whereabouts the plane of polarization of the diffracted 

 ray ought to lie, according as we adopt one or other of the hypotheses respecting the direction 

 of vibration. For theory assigns exact results on the two extreme suppositions, first, that the 

 diffraction takes place before the light reaches the grooves; secondly, that it takes place 

 after the light has passed between them ; and these results are very different, according as we 

 suppose the vibrations to be perpendicular or parallel to the plane of polarization. Most of 



