DOUBLE REFRACTION. 119 



The phenomenon of dispersion, in singly-refracting substances, 

 proves that the elasticity of the vibrating medium varies with the 

 length of the wave. The same thing must take place in double- 

 refracting media, in which the elasticity is different in different 

 directions ; and as we have no reason for supposing that the elas- 

 ticities should vary in the same proportion in the direction of the 

 three axes of elasticity, it will follow that in general each refractive 

 index will have its appropriate dispersive ratio. Sir David Brew- 

 ster first showed that this was actually the case, and that Iceland 

 spar and other double-refracting substances had two dispersive 

 powers.* M. Rudberg has recently examined the laws of dis- 

 persion in double-refracting media with much care, following the 

 accurate method of Fraunhof er. He has in this manner determined 

 the greatest and least refractive index, corresponding to the seven 

 principal dark lines of the spectrum, in Iceland spar and rock 

 crystal, and the three principal indices in arragonite and topaz ; 

 and has found, in accordance with the discovery of Sir David 

 Brewster, that the ratio of these indices increased with the refran- 

 gibility of the light.f The experiments of M. Budberg confirm 

 also the fundamental position of Fresnel's theory- namely, that 

 the velocity of a ray in a given medium is the same as long as its 

 plane of polarization is unchanged. 



The angle contained by the optic axes, in biaxal crystals, is a 

 simple function of the three principal elasticities; and if their 

 ratio vary with the colour of the light, the inclination of the axes 

 must likewise vary. Such a variation has been established by the 

 observations of Sir John Herschel ; and it has been found that the 

 inclination of the axes is greater in red than in violet light for 

 some crystals, while in others it is less.J In the case of Rochelle 

 salt, the angle between the optic axes of the red and violet rays 



* Treatise on New Philosophical Instruments, Edin. 1813. 



t Annales de C/iimie, torn, xlviii. For the calculation of the phenomena of double 

 refraction in biaxal crystals, according to Fresnel's theory, it is necessary to know the 

 three principal refractive indices, or the velocities of propagation of rays whose vibra- 

 tions are parallel to the three axes of elasticity. Beside the researches of M. Rudberg, 

 I do not know that we possess any other in which all those data have been directly 

 determined. It is true that if we know the greatest and least index, and the an* 

 contained by the optic axes, the mean index can bo deduced. But the 11 

 of the optic axes cannot be determined experimentally with the same prec 

 other elements. 



J Phil. Trans. 1820. 



