176 Astronomical and Nautical Collections. 



plate of glass to the light, it be made to turn round the ray 

 as an axis, and to assume different azimuths, reckoning the 

 azimuth as the angle which the plane of incidence forms 

 with the primitive plane of polarisation, as the word is used 

 by astronomers : in these changes of azimuths it is observed 

 that the reflected light begins to appear the more sensibly as 

 the plane of reflection is further removed from that which is 

 perpendicular to the former plane of polarisation : there is a 

 maximum when it becomes parallel to this plane, and then 

 the reflection diminishes till it disappears entirely, after half 

 a revolution of the plate round the ray. 



These phenomena are evidently analogous to those which 

 have been observed in each of the two images produced by a 

 polarised pencil which passes through a rhomboid of calca- 

 rious spar, when it is turned round the ray. It is also by 

 the same formula that Malus has represented, in both cases, 

 the variations of intensity of the images and of the reflected 

 light. If we apply the character i to the angle formed by 

 the primitive plane with that of reflection, or with the prin- 

 cipal plane of the double refraction to be considered ; and 

 if we call the maximum of brightness unity, the brightness 

 of the image and of the reflected light will both be expressed 

 by cos H. 



We may examine this formula in the case of a polarised 

 pencil passing through a rhomboid of calcarious spar ; and 

 making i the angle which the plane of polarisation of the 

 ordinary image, that is, the principal section of the crystal^ 

 forms with the primitive plane, the angle formed with the 

 plane of polarization of the extraordinary image will be 

 90° — i; so that since cos'e represents the intensity of the 

 ordinary image, that of the extraordinary image will be 

 expressed by cos ^ (90° — z), or by sin ^i. When i =. 0, 

 sin*t = 0; that is to say, when the principal section coin- 

 cides with the primitive plane, the extraordinary image 

 vanishes, and all the light passes to the ordinary image, 

 because, in this case, cos*i= 1. When z == 45°, sinV and 

 cos ^i become equal each to | ; and the two images are of 

 equal intensity: lastly, when z = 90°, sin^'z— 1, and cos ^2 = 0, 

 >yhich implies that the ordinary image vanishes, and all the 



