62 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



of these observations the light was reflected at the ruled, and in two at the plane surface. 

 The accordance of the results bears out the supposition made in Part II, that the light 

 belonging to the central colourless image, which is reflected or refracted according to the 

 regular laws, is also affected as to its polarization in the same manner as if the surface were 

 free from grooves. The refractive index of the plate being now known for certain, the 

 experiments described in this paper render it probable that the crowding of the planes of 

 polarization which actually takes pjace is rather less than that which results from theory on 

 the supposition, (which is in a great measure empirical,) that the diffraction takes place before 

 the light reaches the grooves. The difference is however so small that more numerous 

 and more accurate experiments would be required before we could affirm with confidence 

 that such is actually the case. 



When a stream of light is incident obliquely on an aperture, it is sometimes necessary 

 to conceive each wave broken up as its elements arrive in succession at the plane of the aperture. 

 In applying the formula (46) to such a case, it will be sufficient to substitute for dS the 

 projection of an element of the aperture on the wave's front, 6 being measured as before from 

 the normal to the wave, which no longer coincides with the normal to the plane of the aperture. 



Before concluding, it will be right to say a few words respecting M. Cauchy's dynamical 

 investigation of the problem of diffraction, if it be only to shew that I have not been 

 anticipated in the results which I here lay before the Society. This investigation is referred 

 to in Moigno's Repertoire (TOptique moderne, p. 190, and will be found in the fifteenth Volume 

 of the Comptes Rendus, where two short memoirs of M. Cauchy's on the subject are printed, 

 the first of which begins at p. 605, and the second at p. 670. The first contains the analysis 

 which M. Cauchy had some years before applied to the problem. This solution he afterwards, 

 as it appears, saw reason to abandon, or at least greatly to restrict; and he has himself stated, 

 (p. 675), that it is only applicable when certain conditions are fulfilled, and when moreover 

 the nature of the medium is such that normal and transversal vibrations are propagated with 

 equal velocity. This latter condition, as Green has shewn, is incompatible with the stability 

 of the medium. In the second memoir M. Cauchy has explained the principles of a new 

 solution of the problem which he had obtained, without giving any of the analysis. The 

 principal result, it would appear, at which he has arrived is, that light incident on an aperture 

 in a screen is capable of being reflected, so to speak, by the aperture itself (p. 675) ; and he 

 proposes seeking, by the use of very black Weens, for these new rays which are reflected and 

 diffracted. But it follows from reasoning similar to that of Art. 34, or even from the general 

 formula (45) or (46), that such rays would be wholly insensible in all ordinary cases of dif- 

 fraction, even were the screen to reflect absolutely no light. The only way apparently of 

 rendering them sensible would be, to construct a grating of actual threads, so fine as to allow 

 of observations at a large angle of diffraction. Such a grating I believe has never been made; 

 and even if it could be made it would apparently be very difficult, if not impossible, to 

 separate the effect to be investigated from the effect of reflection at the threads of the 

 grating. 



