CALCULATION OF REFRACTIVE INDEX. 179 



Then r 2 and r 2 will be the major and minor axes of the 

 central section of the indicatrix parallel to the mineral 

 plate. 



Let the direction cosines of r x and r 2 be respectively k, 

 ■tWi, tii, and l 2 , m 2 , n 2 . 



Hence the co-ordinates x x y x z x of the extremity of the 

 diameter n are given by the equations 



fci = r ih 2/i =■■ r 1 m 1 z 1 = r x n, 



Since the point (#1 y x £1) lies on the surface of the indi- 

 catrix the co-ordinates x x y x z^ must satisfy the equation of 

 the ellipsoid and hence we have 



W ^ (rim,) 2 fa r h ) 2 _ . 



a 2 + f¥ ' f ~ { } 



which may be expressed in the form 



l\ m\ n\ 1 



Thus when \ m x Hi are known the value n is simply cal- 

 culated. Similarly from the equation 



J| m 2 n| _J._ 

 a 2 + (3 2 + f ~ r\ V> 



the value r 2 of the second refractive index can be calculated. 



The problem therefore, is now resolved into one of find- 

 ing the direction cosines k m^ rii and l z m 2 ti 2 . 



These values may be readily obtained by graphical means. 

 The stereographic projection is employed for this purpose. 

 The general method may be illustrated by a particular 

 case. 



It was desired to obtain the values for the two refractive 

 indices for a section of labradorite cut parallel to the 010 

 face. The plane of the stereographic projection is chosen 

 so that it is perpendicular to the direction of section in the 

 mineral plate. 



