36 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



amount of the crowding agree with theory as well as could reasonably be expected, some 

 allowance being made for the influence of modifying causes, (such as the direct action of the 

 edge of the diffracting body,) whose exact effect cannot be calculated, then we shall be led to 

 conclude that the vibrations in plane-polarized light are perpendicular or parallel to the plane 

 of polarization, according as the crowding takes place towards or from the plane of diffraction. 



In all ordinary cases of diffraction, the light becomes insensible at such a small angle from 

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

 to be sensible in experiment, except perhaps in the mean of a very great number of observa- 

 tions. It is only by means of a fine grating that we can obtain strong light which has been 

 diffracted at a large angle. I doubt whether a grating properly so called, that is, one consist- 

 ing of actual wires, or threads of silk, has ever been made which would be fine enough for the 

 purpose. The experiments about to be described have accordingly been performed with the 

 glass grating already mentioned, which consisted of a glass plate on which parallel and equi 

 distant lines had been ruled with a diamond at the rate of about 1300 to an inch. 



Although the law enunciated at the beginning of this section has been obtained for diffrac- 

 tion in vacuum, there is little doubt that the same law would apply to diffraction within a 

 homogeneous uncrystallized medium, at least to the degree of accuracy that we employ when 

 we speak of the refractive index of a substance, neglecting the dispersion. This is rendered 

 probable by the simplicity of the law itself, which merely asserts that the vibrations in the 

 diffracted light are rectilinear, and agree in direction with the vibrations in the incident light 

 as nearly as is consistent with the necessary condition of being perpendicular to the diffracted 

 ray. Moreover, when dispersion is neglected, the same equations of motion of the luminiferous 

 ether are obtained, on mechanical theories, for singly refracting media as for vacuum ; and if 

 these equations be assumed to be correct, the law under consideration, which is deduced from 

 the equations of motion, will continue to hold good. In the case of a glass grating however 

 the diffraction takes place neither in air nor in glass, but at the confines of the two media, and 

 thus theory fails to assign exact values to a. Nevertheless it does not fail to assign limits 

 within which, or at least not far beyond which, a must reasonably be supposed to lie; and as 

 the values comprised within these limits are very different according as one or other of the two 

 rival theories respecting the direction of vibration is adopted, experiments with a glass grating 

 may be nearly as satisfactory, so far as regards pointing to one or other of the two theories, as 

 experiments would be which were made with a true grating. 



The glass grating was mounted for me by Prof. Miller in a small frame fixed on a board 

 which rested on three screws, by means of which the plane of the plate and the direction of the 

 grooves could be rendered perpendicular to the plane of a table on which the whole rested. 



The graduated instruments lent to me by Prof. O'Brien consisted of small graduated 

 brass circles, mounted on brass stands, so that when they stood on a horizontal table the planes 

 of the circles were vertical, and the zeros of graduation vertically over the centres. The 

 circles were pierced at the centre to admit doubly refracting prisms, which were fixed in brass 

 collars which could be turned round within the circles, the axes of motion being perpendicular 

 to the planes of the circles, and passing through their centres. In one of the instruments, 

 which I used for the polarizer, the circle was graduated to degrees from 0° to 360°, and the 



