MICROSCOPICAL PETROGRAPHY 489 
measure, to the refractive indices. But in ordinary mounted, 
thin sections no satisfactory method has yet been devised for 
measuring the refractive indices directly and the microscopist 
is forced, in consequence, to make use of the other properties 
which can be ascertained under these conditions but which do not 
express, even in aggregate, all the information embodied in the 
simple statement of the refractive indices. It is for this reason — 
especially that so much emphasis is placed on methods for refract- 
ive index determination and in particular on the immersion 
method by means of which the refractive indices of minute, isolated 
mineral grains 0.or mm. and over in diameter can be readily 
measured with a fair degree of accuracy. 
For the complete description of the optical behavior of a mineral, 
it is essential to determine not only the lengths of the principal 
axes of the optic ellipsoid but also its position within the crystal. 
This is usually accomplished by means of extinction angles on 
crystal faces of known orientation. From the position of the 
optic ellipsoid within the crystal we are able to infer the system 
in which the mineral crystallizes, since this position depends, as 
Brewster was the first to show, on the symmetry of the crystal 
itself. By determining the principal refractive indices of a mineral - 
and its extinction angles on plates of known orientation, we can 
thus define its optic ellipsoid and its crystal system and from these 
in turn derive the optical behavior of any section cut from the 
crystal. 
Having given the optic ellipsoid of a mineral for a particular 
color of light, the directions of vibration (positions of extinction 
between crossed nicols) and the relative velocities of light waves 
entering normally to any given section of the mineral can be ascer- 
tained by considering the section to pass through the center of 
the optic ellipsoid and to cut out of the same an ellipse, along the 
major and minor axes of which the light vibrations take place and 
produce plane-polarized light waves, whose velocities of trans- 
mission are inversely proportional to the lengths of these axes. 
This ellipse may be called the optic ellipse of the section. The 
optic ellipse is completely defined when the length of its major and 
‘minor axes (refractive indices y’ and a’) and their positions with 
