238 Cambridge Philosophical Society. 



f{u) = sin u the line in ^ is replaced in ?' by a cosine. It may readily 

 be verified, that if the formula (a.) be applied to determine by inte- 

 gration the disturbance which corresponds- to the whole of the plane 

 P, the disturbance in front is the same as if the wave had not been 

 supposed broken up, and no disturbance is propagated backwards. 



The law obtained for determining the position of the plane of po- 

 larization of the diffracted ray seems to lead to a crucial experiment 

 for deciding between the two rival theories between the directions of 

 vibration in plane-polarized light. Suppose the incident light po- 

 larized by transmission through a Nicol's prism mounted in a gra- 

 duated instrument, and let the diffracted light be analysed in a similar 

 manner. By means of the graduation of the polarizer, we can turn 

 the plane of polarization of the incident ray, and consequently the 

 plane of vibration, which is either parallel or perpendicular to the 

 plane of polarization, round through equal angles of say b° or 10° 

 at a time. According to theory, the planes of vibration of the dif- 

 fracted ray will not be distributed uniformly, but will be crowded 

 towards the perpendicular to the plane of diffraction. But experi- 

 ment will enable us to decide whether the planes of polarization are 

 crowded towards the plane of diffraction or towards the perpendicular 

 to the plane of diffraction, and we shall accordingly be led to con- 

 clude, either that the vibrations are perpendicular, or that they are 

 parallel to the plane of polarization. 



In ordinary cases of diffraction, the illumination, in consequence 

 of interference, is insensible beyond a small angle of diffraction. It 

 is only by means of a fine grating that we can procure light of con- 

 siderable intensity that has been diffracted at a large angle. The 

 author has been enabled to perform the experiment, or rather a mo- 

 dification of it, by the kindness of his friends Professors Miller and 

 O'Brien; of whom the former lent him a fine glass-grating, con- 

 sisting of a glass plate on which parallel and equidistant lines had 

 been ruled with a diamond at the rate of 1300 to the inch, and the 

 latter lent him the graduated instruments required. The theory 

 does not quite meet the case of a glass -grating, in which the diffrac- 

 tion takes place at the common surface of two media, but it leads to 

 a definite result on each of the two extreme suppositions : — 1st, that 

 the diffraction takes place before the light reaches the grooves ; 2nd, 

 that it takes place after the light has passed them ; and the results are 

 very different according as one or other of the two rival theories is 

 adopted. In the principal experiments, the plane of the plate was 

 placed perpendicular to the incident light, and the light observed 

 was that which had been diffracted by transmission through the 

 plate. The angle of diffraction, by which is meant the angle mea- 

 sured in air, ranged in the different experiments from about 20° to 

 60°. The result obtained was, that when the grooved face was 

 turned towards the eye, there was a very sensible crowding of the 

 planes of polarization of the diffracted light towards the plane of 

 diffraction. When the grooved face was turned towards the incident 

 light, there was a considerable crowding in the same direction, much 

 more than in the other case. Since the effect of refraction, con- 



