174 



MINERALOGY 



section is a circle, and the ellipsoid is one of revolution, with z as 

 the axis of revolution, analogous to the prolate ellipsoid in quartz. 

 In such cases, where z is the acute bisectrix and the value of p is 

 nearer to a than to "y, the crystal is said to be optically (+). On the 

 other hand, when the point c moves up toward z, the value of P will 

 increase, and the angle 2 V will increase constantly until it is greater 

 than 90, when the line oz will be the obtuse bisectrix and ox the 

 acute bisectrix ; when c reaches z, the ellipse will be an oblate ellip- 

 soid of revolution, analogous to that of calcite, and the crystal is 

 said to be optically negative ( ). 



The three axes of the ellipsoid are usually written X = a = a, 



The relations of the axes of the ellipsoid to the crystallographical 

 axes in the prthorhombic, monoclinic, and . triclinic systems vary 



with the possible conditions, de- 

 pending upon the symmetry of 

 the system and the relation of the 

 axial plane of the ellipsoid to the 

 planes of symmetry in the system. 

 In the orthorhombic system, 

 where the three crystallographical 

 axes are at right angles to each 

 other, these correspond in direc- 

 tion to the axes of the ellipsoid, 

 and the position of the planes of 

 symmetry of the ellipsoid is fixed 

 parallel to the planes of symmetry 

 of the system. The axes X, Y, or 

 Z may correspond with any one of 

 the crystallographic axes, but for 

 any one species this relation is definite, as is shown in Fig. 320, 

 a diagram of the optical conditions in the mineral aragonite, where 

 the plane of the optic axis is parallel to the macropinacoid (Ax. PI. 

 = 100). The acute bisectrix is X = 6, the crystal is therefore ( ) ; 

 b = Z, a = Y; 2V= 18 11'. 



In the monoclinic system, the plane of symmetry of the system is 

 parallel with one of the planes of the ellipsoid and the orthoaxis b 

 is parallel to one of the axes of the ellipsoid, this axis is therefore 

 fixed ; the other two must lie in the plane of symmetry of the sys- 

 tem; but their relation to the a or c crystallographical axes will 

 vary with the mineral species, and their relation is characteristic 



FIG. 320. Diagram of the Optical 

 Properties of Aragonite. 



