CALCULATION OF REFRACTIVE INDEX. 177 



THE CALCULATION OF REFRACTIVE INDEX IN 

 RANDOxM SECTIONS OF MINERALS. 



By Leo A. Cotton, m.a., d.Sc and Mary M. Peart, b.Sc. 



[Read before the Royal Society of N. S. Wales, November 3, 1920.~] 



Part I.— Principle of the Method. 

 By Dr. Cotton. 



A relatively simple formula has been established for 

 estimating the double refraction of minerals in random 

 sections, the said formula being 



y 1 — a 1 = (y - a) sin 6 sin 6 l 

 in which y 1 -** 1 is the double refraction sought, y — a is the 

 maximum double refraction of the mineral and 6 and 1 are 

 the angles which the particular direction of transmission 

 makes with the two optic axes. 



Such an equation does not, however, furnish the separate 

 values of y 1 and a 1 . As it is sometimes desirable to obtain 

 these values other methods must be employed. 



It is a well known proposition of analytical solid geometry 

 that if the equation of an ellipsoid referred to its principal 

 axes as co-ordinates be 



+ 152 +T¥= l 0) 



a 2 T /3 2 T y 2 



then the major and minor axes r x and r 2 of a given central 

 section of the ellipsoid are given by the roots of the equation 



1 1 /l 2 + m 2 l 2 + n 2 m 2 + n 2 \ l 2 a 2 + m 2 /3 2 + n 2 f . ._. 

 -^-A-f- + ^ + —a^-) + oTWf =0 - (2) 



where I, m, and n are the direction cosines of the normal to 

 the plane of the central section. 



L— November 3, 1920. 



