Notes on some Points in the Theory of Light. 2 1 1 



tions agree, in a general way, with those of Fresnel, there is 

 yet, in one particular, an important difference between them ; 

 for, according to Fresnel, the vibrations are always exactly in 

 the surface of the wave, while, according to M. Cauchy (in his 

 old theory as well as the new), they are only so in ordinary 

 media. In a biaxal crystal he finds and!" this is one of the 

 ways in which the " invisible ray " manifests its influence that 

 the direction of vibration, in each of the two rays that are 

 visible, is inclined at a certain angle to the wave-plane ; but 

 this angle, though small, is by no means inconsiderable, as 

 M. Cauchy seems to intimate, overlooking the fact, which ap- 

 pears from his own equations, that it is of the same order of 

 magnitude as the quantities on which the double refraction 

 depends. It is true, the deviation measured by this angle can- 

 not, if it exists, be directly observed in the refracted light ; but 

 its indirect effects on reflected light ought to be very great, 

 since the action of the crystal on a ray reflected at its surface 

 differs from that of an ordinary medium by a quantity of the 

 same order merely as the aforesaid angle ; and as the problem 

 of crystalline reflexion has been already solved * on the suppo- 

 sition (which is an essential one in the solution) that the 

 vibrations are exactly in the plane of the wave, it is highly 

 improbable, considering the complex nature of the question, 

 that it will be solved, in any satisfactory way, on a supposition 

 so different as that which is required by the theory of M. Cauchy. 

 However, as the laws of such reflexion are now well known, by 

 means of the solution alluded to, it is possible that M. Cauchy 

 may, as in the case of double refraction, succeed in deducing the 

 same laws, or, if not the same, what may seem to be more exact 

 laws, from certain principles f of his own, helped out, if need be, 



* Transactions, Royal Irish Academy, VOL. xvin., p. 31 (supra, p. 87). 



t In applying these principles to the question of reflexion and refraction at the 

 surface of an ordinary medium (Compt.es Rendus, torn. ii. p. 348), M. Cauchy has 

 arrived at the singular conclusion, that light may he greatly increased hy refraction 

 through a prism, at the same time that it is almost totally reflected within it. Sup- 

 posing the refracting angle of the prism to be very little less than the angle of 



