1877.] 



seen through a Crystalline Plate. 



399 



had been supposed, from the observations of those who had specially exa- 

 mined the question, that in biaxal crystals one of the rays obeyed the 

 ordinary law of refraction ; and Iresnel proved by two methods, both 

 requiring skill on the part of the optician who cut the crystals, that the 

 anticipation that his theory led him to entertain that that would not prove 

 to be the case was verified. It is interesting to find that the extraor- 

 dinary character of the refraction of both rays in a biaxal crystal admits 

 of being established by such a comparatively simple mode of observation 

 as that of Mr. Sorby. 



The theory of Eresnel is confessedly wanting in rigour ; and though 

 the observations of Huyghens, of TVollaston, and of Mains proved that 

 in Iceland spar Huyghens's construction, if not rigorously true, was at 

 least a very close approximation to the truth, it seemed desirable to put 

 it to a sharper observational test, more especially as different theories 

 might lead to Huyghens's construction as a near approximation. For 

 instance, in a paper read before the Cambridge Philosophical Society in 

 1849, I obtained a formula* which led me to perceive that double refrac- 

 tion would be simply accounted for by attributing it to a difference of 

 inertia in different directions, such as would be produced if a fluid had to 

 make its way among a number of bodies on the average regularly 

 arranged, that arrangement being different in different directions, and 

 that the wave- velocity on this theory would be related to the direction of 

 the wave normal just as in the theory of Fresnel, with the exception that 

 the reciprocals of wave-velocities would take the place of the velocities 

 themselves. I refrained, however, from putting forward that theory 

 either in the memoir referred to or elsewhere (though I have incidentally 

 alluded to it in my report on double refraction t), because, on calculating 

 the difference of refraction of the extraordinary ray on this theory and 

 according to Huyghens's construction, at about 45° from the axis, where 

 the difference would be greatest, I found it barely small enough, as seemed 

 to me, to have escaped detection. Still this theory, which has occurred 

 independently, in the same or a similar shape, to others +, led me to wish 

 for a more exact verification; and in the report referred to I have pro- 

 posed a method which seemed to me well calculated to lead to the desired 

 result. This method I carried out some years later in the case of Iceland 

 spar, though I did not publish the results ; and I found that, to the limit 

 of error of my observations (about 0*0001 in the index), Huyghens's con- 

 struction was fully confirmed, while the error of the other was nearly a 

 hundred times as great as the limit of error of the observations §. The 



* Cambridge Philosophical Transactions, vol. viii. p. 111. 

 t Eeport of the British Association for 1862, part i. p. 269. 



\ See papers by the late Professor Rankin in the Philosophical Magazine, vol. i. 

 (1851), p. 441, and by Lord Rayleigh in the same, vol. xli. (1871) p. 519. 



§ This result is briefly mentioned in the Proceedings of the Royal Society, vol. xx. 

 p. 443. 



VOL. XXVI. 2 E 



