﻿of the Optical Constants of a Crystal. 35 



of the prism. The plane of polarization of any wave is at 



right angles to the normal at the corresponding point on the 



indicatrix. The angles of extinction will be in the case of 



the principal axes cos~'A,, cos -1 /-*? cos —1 v, and for the fourth 



, . a 2 \ 2 + b 2 u 2 + c 2 v 2 



value cos -1 — . 



The values for the three principal axes must satisfy the 

 condition \ 2 + /j? + v' 2 = 1. 



It may be noted that the planes of polarization for the two 

 rays with parallel wave-fronts are in general not strictly at 

 right angles, since the normals at the extremities of the axes 

 of the central-section to which they are perpendicular are not 

 themselves in general at right angles. 



Another point that is worthy of notice is that the two curves 

 are in general not symmetrical about the critical positions. 

 The abscissae, as we have remarked above, represent the 

 angles which the wave-normal makes with some fixed direc- 

 tion; or, in other words, the angles which the central section 

 revolving round the diameter parallel to the edge of the prism 

 makes with some fixed plane. Supposing the upper curve 

 contains the greatest and the mean of the principal indices, 

 the angle between the corresponding positions of the central 

 section is 



cos L — - 

 VO* + v 2 )(v 2 + \ 2 ) 



which in general is not a right angle ; on the lower curve 

 the angle is 



_i \u(a 2 -b 2 ) 



cos l — v ' . 



^(^+/* 2 ){(^-c 2 )VV + {c 2 -a 2 ) 2 v 2 \ 2 + (a 2 -6 2 ) 2 \V } 



If the crystal be uniaxial the upper curve becomes a 

 straight line, and the lower curve, which is still undulating, 

 is now symmetrical, since a — b and the angle between the 

 critical positions is a right angle. 



Although the tilt of the refracted image, as was mentioned 

 above, is in general not sufficiently perceptible for purposes 

 of measurement, it may be indirectly of service, because its 

 existence signifies that the corresponding direction in the 

 crystal is not near one of the critical positions and, therefore, 

 no observations need be taken. The range inside the crystal 

 corresponding to a particular prism may be increased if the 

 observations are made on an inverted goniometer in some 

 liquid medium. In an instrument of this kind which is in 

 the British Museum light passes into and out of the liquid by 

 means of double-ended glass-prisms. As the angle of incidence 



D2 



