REPORT ON PHYSICAL OPTICS. 397 



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 repre- 

 sent 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 isochromatic lines, in biaxal crystals, will be lemniscateSj 

 whose poles are in the apparent direction of the optic axesj. 

 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 con- 

 stant parameter, or the product of the radii-vectores drawn from 

 any point to the two poles, varies inversely as the thickness of 

 the plate, for different plates of the same substance, and increases 

 from one curve to another in the same plate, in the ratio of the 

 numbers of the natural series. 



To account for these varied phenomena in the hypothesis of 

 emission, M. Biot has imagined his ingenious and beautiful theory 

 of moveable polarization. When a polarized ray of any simple 

 colour enters a crystalline plate, the component molecules are 

 supposed, in this theory, to penetrate at first to a certain depth 

 without losing their primitive polarization ; and then to com- 

 mence a series of regular oscillations round their centres of 



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

 lized Bodies,"P/«7. 'frans. 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, was inferred. 



X M. Biot has observed an apparent exception to this law in the diopside 

 of 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 crystalline plate is turned in its own plane. These dis- 

 tortions 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 unsym- 

 metrically placed with respect to the crystalline form, Mem. Inst, tom. x. 



