112 REPORT ON PHYSICAL OPTICS. 



degree upon rays polarized in intermediate planes. Now a ray 

 of common light, in the theory of emission, is composed of mole- 

 cules whose planes of polarization are turned in all azimuths ; and 

 these molecules, consequently, should feel the influence of the ex- 

 traordinary force in every possible degree. Instead, therefore, of 

 two refracted rays, such a ray should be divided into an infinite 

 number, inclined in every possible angle between the limiting 

 directions of the ordinary and extraordinary rays. 



It had been hitherto assumed, that no crystal had more than 

 one optic axis. While examining the rings which surround these 

 axes in polarized light, Sir David Brewster made the important 

 discovery that the greater number of crystals possess two optic 

 axes; and he soon after discovered the connexion between these 

 diversities of optical character and the crystalline form.* 



The optic axes, however, as Sir David Brewster has shown, 

 cannot be regarded in general as the fundamental axes of the 

 double-refracting medium. He calls them apparent axes; and 

 considers them as the resultants of others, which he denominates 

 true or polarizing axes, and from which the forces which produce 

 the phenomena of polarization and double refraction are conceived 

 to emanate. The polarizing force proceeding from a single axis 

 is measured by the difference of the squares of the velocities of the 

 ordinary and extraordinary rays, and is supposed to vary as the 

 square of the sine of the angle which the direction of the ray 

 within the crystal contains with it; and when two such axes 

 cooperate, it is assumed that the increment of the square of the 

 velocity, arising from their joint action, is equal to the diagonal 

 of a parallelogram whose sides are the increments of the squares of 

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

 of that formed by the two planes passing through the ray and the 

 axes.f From this hypothesis it followed that two rectangular 

 polarizing axes of equal intensity, and both positive or both 

 negative, compound a single resultant axis at right angles to both. 

 This axis is of the same intensity as the component axes, but of an 

 opposite character ; and, accordingly, three equal rectangular axes 

 of the same character balance each other's effects, and have no 



* The important relations here alluded to have heen already brought under the 

 attention of the Association, in the able Report on Mineralogy, by Mr. Whewell. 



t " On the laws of Polarization and Double Refraction in regularly crystallized 

 Bodies." Phil. Trans. 1818. 



