182" Astronomical and Nautical Collections, 



always affords the same intensity of light, whatever may be 

 the difference in the routes of the two systems of undulations 

 which interfere. 



Another remarkable circumstance is this ; that when they 

 have once been polarised in rectangular directions, it is no 

 longer sufficient that they be brought back to a common 

 plane of polarisation, in order to exhibit appearances of in- 

 fluencing each other. In fact^ if in Mr. Arago's experi- 

 ment, or in that which I have described after it, we cause the 

 rays which have been transmitted by the slit, and which are 

 polarised at right angles, to pass through a pile of inclined 

 plates, we perceive no fringes, in whatever direction we turn 

 the plane of incidence. In place of such a pile, we may em- 

 ploy a rhomboid of calcarious spar : and if we incline its 

 principal section in an angle of 45° to the planes of polarisa- 

 tion of the incident pencils, so that it may divide the right 

 angles v/hich they form into two equal parts, each image will 

 contain the half of each pencil ; and these two halves, having 

 the same polarisation in the same image, ought to produce 

 fringes, if it were sufficient to restore the plane of polarisa- 

 tion in order to renew the mutual influence of the pencils. 

 But it is impossible to obtain fringes in this manner, except 

 when the light has been polarised in some one plane, before 

 it is divided into two pencils polarised at right angles. 



When, however, the light has undergone the preliminary 

 polarisation, on the contrary, the interposition of the rhom- 

 boid restores the fringes. The most advantageous direction, 

 that can be given to the primitive plane of polarisation, is 

 that which divides into two equal parts the angle of the 

 orthogonal planes, in which the light is at last polarised, be- 

 cause, in this case, the light is equally divided between them. 

 We may suppose, to assist the imagination, that the plane of 

 the primitive polarisation is horizontal, the planes of the two 

 polarisations which follow being inclined to it in angles of 

 45°, the one upwards, the other downwards, so that they 

 may be perpendicular to each other. We may obtain this 

 orthogonal polarisation either by means of the two small piles 

 employed in the experiment of Mr. Arago, or by two plates, 

 with their axes in orthogonal directions, or with a single cry- 



