136 F. E. Wright — Index Ellipsoid (Optical Indicatrix) 



ellipse, whose major and minor axes, 7 and a, furnish directly 

 the refractive indices and the directions of vibration of those 

 light waves whose front-normals, both before and after incidence, 

 coincide with the normal to the plate. For obliquely incident 

 waves a similar relation exists between the index ellipsoid and 

 the wave-front normals, but the refractions at the surfaces of 

 the plate have to be taken into account and the direction of the 

 resultant wave-front normals within the plate considered ; in 

 calculating these directions for rock minerals of medium or 

 weak birefringence it is permissible to use the average refractive 

 index of the mineral and to disregard the rotatory effects of the 

 boundary surfaces on the planes of vibration of the obliquely 

 transmitted waves. 



In short, it is possible by means of the index ellipsoid to 

 account, in a systematic and quantitative way, for the various 

 optical phenomena, such as refractive indices, positions of 

 extinction, birefringence, optic axial angle, optical character, 

 direction of elongation, etc., which are encountered by the 

 microscopist in work with mineral plates in monochromatic 

 light. The index ellipsoid is, moreover, different for differ- 

 ent wave lengths of light, both in shape and often in position, 

 within the crystal, and these differences find expression in the 

 various color phenomena, such as color, pleochroism, interfer- 

 ence colors, 'dispersion of the bisectrices, and dispersion of the 

 optic axes, which are observed on crystal plates and which are 

 also important diagnostic features. 



In view of these facts it would seem logical and feasible to 

 describe and to systematize, on the basis of the index ellipsoid, 

 the optical properties thus made use of in practical mineral 

 determination under the microscope. Thus for a given mineral, 

 the most important optical feature to be ascertained is obviously 

 the type of its index ellipsoid, whether a triaxial ellipsoid, an 

 ellipsoid of rotation or a sphere. In the first case the mineral 

 is biaxial (there are two optic axes, and two axial ratios are re- 

 quired to define the shape of its index ellipsoid) ; in the second, 

 uniaxial (there is only one optic axis, and one axial ratio is 

 sufficient to define the shape of its index ellipsoid) ; in the 

 third, isoaxial or isotropic (all axes are equal, and the index 

 ellipsoid is a sphere). This optical feature of the mineral, which 

 defines the shape of its index ellipsoid, has been called the 

 " optic ellipsoidity"* of the mineral and is the primary dis- 

 tinguishing characteristic on which the minerals are grouped 

 in the tables given in recent text-books on microscopical petrog- 

 raphy. 



The most direct method for determining the optic ellipsoid- 

 ity of a mineral is the measurement of its principal refractive 

 * F. E. Wright, Jour. Geology, xx, 488, 1912. 



