198 MINERALOGY 



of refraction will lie between a and -y as limiting values. Similarly 

 along the two directions OX and OZ. 



In general all plane sections of the indicatrix passing through O 

 are ellipses, except in two directions when they are circular. Light 

 passing perpendicular to all elliptical sections, as at any point p in 

 the direction pO, will be transmitted as two plane polarized rays 

 vibrating in planes at 90 to each other, the traces of which are 

 the major and minor diameters of the elliptical section of the indi- 

 catrix, cut by the plane at 90 to the direction of the entering ray. 

 The extremities of these two diameters are the conjugate points, 

 from which normals to the surface determine the velocity, the di- 

 rection of transmission, and vibration planes of the two rays. The 

 major and minor diameters of the elliptical section perpendicular 

 to the direction of the ray are the traces of the planes of vibrations of 

 the resulting rays in the crystal. These two diameters always bisect 

 the angle included between the traces on the same plane, of the 

 planes containing the ray and the optic axes, as the two planes pOA 

 and POA'. The directions AA" and A' A'" are the optic axes, and 

 sections of the indicatrix at right angles to these two directions are 

 circular, as yey'e' and ycyV, and there is no double refraction, as 

 there is no definite plane of vibration, as many or all planes are 

 possible ; and light is transmitted along A' A'" and AA" without 

 polarization or double refraction. Each section of a biaxial 

 crystal, not perpendicular to an optic axis, will transmit two rays 

 vibrating in planes and polarized in planes at 90, and when the 

 section is revolved on the stage between cross nicols, light will be 

 extinguished four times in 360, as in uniaxial crystals. 



In the orthorhqmbic system, where the planes of symmetry of 

 the indicatrix are parallel to the crystallographical axes, the pina- 

 coidal zones will show straight or parallel extinction ; any other 

 section will show symmetrical extinction as in uniaxial crystals. 

 There are three possible positions for the plane of the optic axes, 

 parallel to each of the three pinacoids in turn. In the monoclinic 

 system, where one plane of symmetry of the indicatrix must coin- 

 cide with the plane of symmetry of the system, one axis of the 

 indicatrix will be fixed parallel to the orthoaxis of the crystal. 

 There will be parallel extinction in one zone only, that in which 

 the orthoaxis is the zonal axis. In all other directions there will be 

 an extinction angle, reaching a maximum in the plane of symmetry. 



In the monoclinic system, the extinction angles in particular 

 zones or on fixed planes are characteristic, particularly that of the 



