350 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



It is not then a matter of surprize, that modern writers should 

 in some cases confound the t^vo; and this particular formula has been 

 diflferently enunciated by different writers. 



Thus Mr M'CuUagb, in the Transactions of the Royal Irish 

 Academy, enunciates Fresnel's proposition as foUows: 



" The difference of the squares of the reciprocals of the velocities 

 of the two rays having a common direction in the crystal, is pro- 

 portional to the product of the sines of the angles which that direc- 

 tion makes with the optic axes." 



Mr Airy gives the following: 



" The difference between the reciprocals of the squares of the ve- 

 locities of the two rays is proportional to the product of the sines of 

 the two angles made by the front of the wave with the two circular 

 sections, or to the product of the sines of the angles made by the 

 normal to the front with the two optic axes." The latter is, I have 

 no doubt, incorrect. 



Having then, in some instances, contradictory statements of the 

 nature of the theory, I have, probably, here misled in some points. 

 With respect to the mechanical part to which 1 object, all statements, 

 which I have seen, coincide. 



26. I refrain from making any extended application of the subject, 

 but will only trouble you with one case, which T adduce on account of 

 its great importance. The explanation of the lemniscates in biaxal crys- 

 tals depends on the difference of the retardation of two vibrations which 

 have a common normal to their front. The usual method of proceeding 

 has been to find the retardation for uniaxal crystals, and from the cir- 

 cumstance of the retardation in that case being proportional to the 

 difference of the squares of the velocities of the two waves, the same is 

 true of the difference of the squares of the velocities of the two rays 

 in biaxal crystals, and then, finally, to assume the difference of the re- 

 ciprocals of the squares of the velocities of the rays to vary as the 

 product of the sines of the angle made by the normal with the optic 



