PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 41 



light which has been once diffracted and once reflected, the externally diffracted light being 

 considered as both diffracted and reflected, namely, one has been diffracted internally, and then 

 regularly reflected and refracted, a second in which the light has been regularly refracted and 

 reflected, and then diffracted at emergence, and a third in which the light has been diffracted 

 externally. Any other light which enters the eye must have been at least twice diffracted, or 

 once diffracted and at least three times reflected, and therefore will be comparatively weak, 

 except perhaps when the angle of incidence, or else the angle of diffraction, is very large. 

 Now when the grating is perpendicular to the incident light the second and third of the 

 principal images are necessarily superposed ; and as they might be expected to be very dif- 

 ferently polarized, it was likely enough that the light arising from the mixture of the two 

 should prove to be very imperfectly polarized. 



To separate these images, I placed a narrow vertical slit in front of the grating, between 

 it and the polarizer, and inclined the grating by turning it round a vertical axis so that the 

 normal fell between the polarizer and the analyzer. As soon as the grating was inclined, the 

 image which had been previously observed separated into two, and at a certain inclination the 

 three principal images were seen equidistant. The middle image, which was the second of 

 those above described, was evidently the brightest of the three. The three images were found 

 to be nearly if not perfectly plane-polarized, but polarized in different planes. The third 

 image, and perhaps also the first, did not wholly vanish at the minimum. This might have 

 been due to some subordinate image which then appeared, but it was more probably due to 

 a real defect of polarization. 



The planes of polarization of the side images, especially the first, were greatly crowded 

 towards the plane of diffraction, or, which is the same, the plane of incidence. Those of the 

 middle image were decidedly crowded in the same direction, though much less so than those 

 of the side images. The light of the first and second images underwent one regular refraction 

 and one regular reflection besides the diffraction and the accompanying irregular refraction. 

 The crowding of the planes of polarization in one direction or the other produced by the 

 regular refraction and the regular reflection can readily be calculated from the known formula;*, 

 and thus the crowding due to diffraction and the accompanying irregular refraction can be 

 deduced from the observed result. 



The crowding of the planes of polarization of the third image is due solely to diffraction 

 and the accompanying irregular reflection. The crowding in one direction or the contrary, 

 according as one or other hypothesis respecting the direction of vibrations is adopted, is readily 

 calculated from the dynamical theory, and thus is obtained the crowding which is left to be 

 attributed to the irregular reflection. In the absence of an exact theory little or no use can 

 be made of the result in the way of confirming either hypothesis ; but it is sufficient to destroy 

 the vague analogy which might have been formed between the effects of diffraction and of 

 irregular scattering. 



The crowding of the planes of polarization of the middle image, after the observations had 



* It is here supposed that the regularly reflected or re- I ing to a system of spectra is affected as to its polarization in 

 fracted light which forms the central colourless image belong- ' the same way as if the surface were free from grooves. 



Vol. IX. Part I. 6 



