﻿of the Optical Constants of a Crystal. 31 



where (/> is the angle which the wave-front in the crystal 

 makes with the plane bisecting the acute angle of the prism. 



The angles i and D can be found by observation with a 

 goniometer, and the values of n and <f> may be calculated 

 from equations (5) and (1) or (2). Thus we can completely 

 determine the velocity (?. e. the inverse of the refractive 

 index, n) of any plane-wave within the crystal and its orien- 

 tation with regard to the crystallographic axes. 



Suppose we are able to take a series of observations round 

 a zone, i. e. through pairs of faces with parallel edges, we 

 should obtain a series of values for the velocity of propa- 

 gation and the corresponding direction within the crystal, and 

 can plot out curves with the former as ordinates and the 

 latter as abscissae. In the case of a doubly-refracting sub- 

 stance there will be two curves, the nature of which we will 

 now proceed to determine. 



Let us take the most general case in which the indica- 

 trix * is an ellipsoid. Let R be any point on the surface, 



RN the normal at that point, and the centre of the 

 ellipsoid. Through draw ON at right angles to RN and 



produce it backwards to r so that Or = pr^ . In the plane 



ROr, Of is drawn at i\ght angles to OR to meet rf drawn 



parallel to OR, in /. Then Q/ = q]^ • We know that 0/ 



is the normal corresponding to a ray Or, and the plane 

 through fr at right angles to 0/ is the wave-front, which 



* The notation is the same as that employed by Mr. L. Fletcher, F.R.S., 

 "The Optical Indicatrix and the Transmission of Light in Crystals," 

 Mineralogical Magazine, 1891, vol. ix. pp. 278-388 ; published separately, 

 London, Henry Frowde, 1892. The diagram above is his fig. 12, the 

 block of which Vas courteously lent to the Author. 



