ISIS.] 



Imperial InstUule of Fra?ice. 



231 



The preceding laws extend likewise to rock crystal cut parallel 

 to the axis of the crystals : but they do not apply to mica ; and 

 we shall see afterwards the cause of this exception. 



Nothing now remains but to give the manner of finding the 

 two colours O and E, or rather to find one of them^ the colour 

 E for example, since the colour O is its complement. The law 

 by which the colours may be found is as follows ; — 



The inclination of the polarized ray upon the plate leing give??9 

 and likewise the direction of the plane of incidence^ if we turn 

 ihe plate upon its plane iv hen its axis approaches the plane of 

 hicidence, the colours of the ray which it polarizes ivill appear In 

 ihe order of the coloured rings, as if the plate lecame thinner ; 

 und on the contrary, when the axis removes from this plane the 

 colours of the extraordinary ray will appear in the order of the 

 rings, as if the plate became thicker. Finally, the colours will 

 lecome the same as under a perpendicular incidence, whenever the 

 axis of the plate makes with the plane of incidence an angle of 

 45°. 



Thus, calling this last colour E''^ and denoting by 6 the inci- 

 dence of the rav, we shall liave, under all incidences^ 



E' = E 4- (A COS. 2i + B cos.^ 2 i) sin.^ Q 

 A and B being two constant co-efficients. This formula, deduced 

 from experiment, is only an approximation with respect to the 

 incidence L It is sufficient for sulphate of liine, where the 

 changes of colour by the variation of incidence are inconsider- 

 able. By studying the same phenomena in other substances, 

 where the changes are much more considerable, M. Biot has 

 discovered another law, much more general, of which this is 

 only a reduction. 



The preceding formula? apply-likewise to rock crystal, but not 

 to mica. The reason of this is, that the constitution of mica as 

 a crystallized body is difl-erent, as we shall see afterwards. In 

 general, when these experiments are repeated, nothing is more 

 striking than the well-defined separation w^hich exists between 

 the laws of the intensities and of the colours. If we calculate 

 beforehand the succession of these colours for all the values of ?*, 

 from 10° to 10°, that is to say, for all the positions of the axis 

 of tiie plate upon its plane, we shall perceive, not without sur- 

 prise, the ditlerent colours extend in the different azimuths, in 

 proportion as the values of F become null for the different 

 values of I, of a, and of A. 



On the 15th June, 11612, M. Biot read to the Class a second 

 memoir, in which he announced that he had found in the polari- 

 zation of light a new law analogous to the preservation of the vii 

 viva in mechanics. That law consists in this, that the colour o 

 the ray polarized by a plate, or by a system of plates whose axes 

 are parallel, depends entirely upon the thickness of the crystallizftd 

 matter tliat the light passes through. It is of no consequence la 



