CALCULATION OF REFRACTIVE INDEX. 181 



The data required are given as follows: — 



The composition corresponded to Ab x An u The values of 

 the principal refractive indices are known to be 

 a = 1-554, p = 1'558, y = 1*562. 



The position of the acute bisectrix corresponding to a and 

 of the optic axial plane are given from text books of 

 mineralogy such as Idding's Rock Minerals. 



y lies in the optic axial plane at 90° from a; and the 

 direction of /? is given by the pole of the optic axial plane. 



An amount equal to V (where 2V is the optic axial angle 

 in the mineral) is marked off on each side of a and in the 

 optic axial plane, so that the two points A and B so 

 obtained represent the optic axes. 



Now according to the Biot-Fresnel law the planes of 

 polarisation bisect the angles between the two planes 

 passing through the direction of transmission and each of 

 the optic axes respectively. 



If a stereographic net be employed the positions of these 

 planes can be readily determined and hence the planes of 

 polarisation can be drawn. The directions^of vibration in 

 the plane of the mineral section are given by the lines of 

 intersection of the planes of polarisation P Z and P Z 1 with 

 the plane of the mineral section SCT. The [points Z and 

 Z 1 therefore represent the directions of the vibrations cor- 

 responding to the refractive indices r x and r 2 . They are, 

 therefore, the directions correspondingTto those radii of 

 the indicatrix which have for their lengths n and r 2 . 



Hence if we find the direction cosines of r 2 and r 2 we 

 may substitute these values in equations (6) and (7) and so 

 determine the required refractive indices. 



Here again the employment of a stereographic net will 

 enable the angular distance of Z from «, f3 and y to be 

 easily determined and the cosines of these angles are the 



