386 FOUllTH REPORT — 18.S4. 



double-itfracting media, in which the elasticity is different in dif- 

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

 elasticities should vary in the same proportion in the direction of 

 the three axes of elasticity, it will follow that in general each re- 

 fractive index \vill have its appropriate dispersive ratio. Sir 

 David Brewster 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 dispersion in double- refracting media with much care, 

 following the accurate method of Fraunhofer. He has in this 

 manner determined the greatest and least refractive index cor- 

 responding 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 x'atio of these indices 

 increiised with the refrangibility of the light f. The experiments 

 of M. Rudberg 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 Ro- 

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

 rays amounts to 10^ Generally the position of the three axes 

 of elasticity is invariable, and the optic axes for all colours are 

 confined to one plane ; but Sir John Herschel has lately observed, 

 that in borax the optic axes belonging to different colours lie in 

 different planes; and we are compelled to conclude that the 

 direction of the axes of elasticity in this, and probably in many 

 other crystals, varies with the colour. 



The first addition to the theory of Fresnel was made by 



* Treatise on New Philosophical Instruments, Edin. 1813. 



t Annales dn Chimie, 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 

 rnys whose vibrations 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 these data have been directly determined. It is true that if we know the 

 greatest and least index, and the angle contained by the optic axes, the mean 

 index can be deduced. But the inclination of the optic axes cannot be deter- 

 mined experimentally with the same precision as the other elements. 



t Phil Trans. 1820. 



