160 ELEMENTS OF APPLIED MICROSCOPY. 
once to distinguish isometric crystals from those of other 
systems. Good crystals to compare in this respect are 
garnet and gypsum, the former being isotropic, the latter 
anisotropic. The same minerals furnish an instructive 
contrast in refractive index, the former showing high and 
the latter low relief. 
Tetragonal, hexagonal, and orthorhombic crystals may 
be separated from those of the monoclinic and _tri- 
clinic types by the fact that in them the directions of 
vibration (sometimes called axes of elasticity) are par- 
allel to the crystal axes of the crystal. The position of 
these vibration directions can be determined by noting 
the position in which the crystal becomes dark (position 
of extinction) with crossed Nicols, for it is then that 
the vibration directions coincide with the planes of the 
Nicols. A cross-wire placed in the eyepiece so as to 
coincide with the plane of vibration of the analyzer under 
these conditions coincides also with the axis of elasticity 
of the crystal. By now removing the analyzer, the 
cleavage lines and boundaries of the crystal may be 
seen and the stage rotated so that the cross-wire corre- 
sponds with them. The angle of rotation required to 
produce this effect as measured on the graduated edge of 
the stage, if o° or go°, on all the crystals examined, indi- 
cates a tetragonal, hexagonal, or orthorhombic crystal. 
Such substances are said to show no extinction angles 
or to be symmetrical. Quartz (hexagonal) illustrates this 
condition, while in Gypsum (monoclinic) all planes but 
one show large extinction angles. This, like other 
monoclinic minerals, exhibits in one plane phenomena 
