COLOURS OF CRYSTALLINE PLATES. 131 



This phenomenon was observed, under different circumstances, by 

 Sir David Brewster, Dr. Wollaston, M. Biot, and M. Seebeck. 



The researches of M. Biot were followed by those of Sir David 

 Brewster. In investigating the law of the tints in biaxal crys- 

 tals, Sir David Brewster considers the optic axes as the re- 

 sultants of others which he denominates polarizing axes. The 

 tint developed by a single axis is taken as the measure of its 

 polarizing force, and is assumed to vary as the square of the sine 

 of the angle contained by the ray with it ; and when two such 

 axes cooperate, the tint resulting from their joint action is measured 

 by the diagonal of a parallelogram whose sides represent the tints 

 produced by each axis separately, and whose angle is double the 

 angle contained by the two planes passing through them and the 

 ray. This law Sir David Brewster has verified by comparison 

 with the observations of M. Biot on sulphate of lime, and its 

 agreement with phenomena was complete.* When analytically 

 developed by M. Biot, it was found to accord with the beautiful law 

 to which he was himself conducted by analogy namely, that the 

 tint is measured by the product of the sines of the angles which 

 the direction of the ray within the crystal makes with the optic 

 axes.f From this law it easily followed that the isochromatio 

 lines, in biaxal crystals, will be lemniscates, whose poles are in the 

 apparent direction of the optic axes.J This phenomenon was first 

 discovered by Sir David Brewster in topaz. The law has been 

 established in the most complete manner by Sir John Herschel ; 

 and he has found that the constant parameter, or the product of 



* " On the Laws of Polarization and Double Refraction in regularly crystallized 

 Bodies," Phil. Trans., 1818. 



t From the researches of M. Biot it appeared that the measure of the tint, in 

 uniaxal crystals, observed the same law as that attributed to the difference of the 

 squares of the velocities of the two rays in the theory of emission. The same relation 

 was assumed to hold generally ; and thus from the law of the tints in biaxal crystals 

 the relation of the velocities of the two pencils, noticed in the preceding section, waa 

 inferred. 



I M. Biot has observed an apparent exception to this law in the dioptiilr <>f the 

 Tyrol, in which the rings are in general unsymmetrical with respect to the two axes. 

 One of the axes presents the ordinary phenomena ; but in the neighbourhood of the 

 other there is a remarkable distortion of the rings near their centre, when the crystal- 

 line plate is turned in its own plane. These distortions seemed to observe a regular 

 law, and were the same in all the specimens examined. It may be remarked that the 

 optic axes of this crystal are unsymmetrically placed with respect to the crystalline 

 form, Mem. Inst., torn. x. 



K2 



