Wright — Two Microscopic- Petrographical Methods. 389 



bolas of the interference figure of an optic normal in conver- 

 gent polarized light leave the field on a slight revolution from 

 position of darkness. Determine value of this ellipsoidal axis 

 (whether a or c) by means of quartz wedge in parallel polarized 

 light and with it the optical character of the mineral ; on the 

 same section the birefringence (7 — a) can also be ascertained; 

 and in monoclinic and triclinic crystals an angle of extinction 

 in general be measured. 



Proof. — In uniaxial minerals, the rays travelling parallel 

 to the principal axis suffer no double refraction. The height 

 of the birefringence increases with the angle which the incident 

 ray makes with the principal axis. On observing a section cut 

 parallel to the principal axis in convergent polarized light, the 

 center of the field will become bright for only a slight turn 

 of the stage from the position of darkness, while those rays 

 nearer the principal axis will become less bright for the same 

 angle of revolution. Hence, on rotating the stage from posi- 

 tion of darkness of mineral plate to light, the dark weak hyper- 

 bolas (less brightly lighted portion) appear to move out in the 

 direction of the least double refraction, i. e. direction of the 

 principal axis. 



In the biaxial minerals the acute bisectrix is, in general, 

 direction of lower birefringence than the obtuse. The faint 

 hyperbolas observed in convergent polarized light on a plate 

 parallel to the bisectrices (perpendicular to the b ellipsoidal 

 axis) will, therefore, leave the field in the direction of the 

 acute bisectrix. 



The statement that the acute bisectrix in biaxial minerals is 

 direction of less double refraction than the obtuse bisectrix 

 can be proved by elementary means as follows : 



Let Y be the angle which one optic binormal (optic axis) 

 makes with the least ellipsoidal axis c and a, ft, 7, the three 

 indices of refraction. 



The equation 



1 1 * 



CO s 2 V= £ ^. (1) 



a y 



which express the relation between the angle Y and the indices 

 of refraction, reduces, for Y — 45°, to the form 



cos 2 Y = -J-, or 

 1 1 



2 2 



a y 



*Kosenbusch-Iddings, " Microscopical Physiography of Kock-fo raring 

 Minerals," 1903, p. 38. 



