On Rotatory Polarization in Biaxial Crystals. 361 



direct incidence is here replaced by m — n sin 2 '« — cos 2 a. 

 Since m and n both represent the effect of the drag due to 

 the wall, they may be taken to be equal, and the quantity now 

 becomes (m — 1) cos" 2 a. Thus 



n — n Am—l) cos 2 a . 2irrj/A. . 



Consequently the wave will break if rj cos 2 "'a/X v - exceed a 

 certain value. For a given wave-length the critical amplitude 

 will vary as the square of the secant of the angle of incidence. 



XXXVI. On Rotatory Polarization in Biaxial Crystals. 

 By H. C. Pocklington, M.A., D.Sc* 



1. rilHE only doubly refracting crystals in which a rota- 

 JL tion of the plane of polarization of the transmitted 

 light has been observed are uniaxials, e. g. quartz. It is, 

 however, clearly possible for a biaxial crystal to produce this 

 rotation, for quartz subject to a uniform stress perpendicular 

 to the axis must act as a biaxial crystal without losing its 

 rotatory power, and a biaxial crystal must acquire rotatory 

 power in a magnetic field. The object of this paper is to 

 investigate from a theoretical standpoint the phenomena in 

 the second case, assuming that the action of the magnetic 

 field may be attributed to a Hall effect into the specification 

 of which the anisotropy of the crystal does not enter. The 

 formula? are afterwards (§ 7) extended to the more important 

 case of crystals wh«re the rotation is due to the mode of- 

 arrangement, or to the structure, of the molecules. The 

 general equations are found in § 2, and the equation of the 

 index-surface in § 3. The shape of the wave-surface near an 

 axis is discussed in § 4, together with the modifications pro- 

 duced by the rotatory power in the conical refraction. In 

 § 5 it is proved that the two waves propagated in any direc- 

 tion are elliptically polarized, and that the ellipses are similar 

 but with corresponding axes perpendicular. These ellipses 

 are completely determined, and also the relative retardation 

 of the two waves. 



The case of a plate in convergent polarized light, and also 

 that of a pair of such plates of opposite rotatory powers 

 (Airy's spirals) is investigated in § 0*. Finally, § $ contains 

 the results of some experiments made with plates cut from 

 sugar crystals, which confirm the mathematical investigation. 



2. Let the magnetic force be t + t , where t is the variable 

 force due to the light-waves, and t is the constant field in 

 which the crystal lies. Let the electric displacement be <r, 

 * Communicated by the Author. 



