When the prism of quartz or calcite, or of any hexagonal, tetragonal, or trigonal substance, is cut so that the rays of light are transmitted through it perpendicularly to the axis, and so that the refracting edge is parallel to the axis, the light is broken up into two rays, one of which is composed of light vibrating parallel to the edge and therefore to the axis, and the other of light vibrating perpendicularly to the axis. Such a prism consequently affords the two principal extreme refractive indices of the crystal, ω and ε, the latter letter being always assigned to the refractive index of a uniaxial crystal corresponding to vibrations parallel to the axis. A uniaxial crystal, one belonging to the hexagonal, tetragonal, or trigonal systems, has thus two principal refractive indices, ω and ε, while a biaxial crystal, one belonging to the rhombic, monoclinic, or triclinic systems of symmetry, has three, α, β, γ, corresponding to vibrations respectively parallel to the three rectangular axial directions of the optical ellipsoid, which are also the crystallographic axial directions in the case of a rhombic crystal. The index α is the minimum, and γ the maximum refractive index,the β index being intermediate; when the latter lies nearer to α in value, the crystal is said to be a positive one, but when nearer to γ the crystal is conventionally supposed to be negative. Similarly, when in a uniaxial crystal ε is the greater, as it is in the case of quartz, the crystal is termed positive, but if ω be the greater index, as happens in the case of calcite, then the crystal is by convention considered negative. Just as in the case of gypsum, which is a positive biaxial crystal (the reason for the term biaxial will presently be more fully explained), when the two spectra afforded by a prism of calcite or quartz cut to afford both ε and ω are examined in plane polarised light, by introducing a Nicol prism somewhere in the path of the light, the two images corresponding respectively to ε and ω will be found to be produced by light polarised in two planes at right angles to each other. For when the Nicol is at its 0° position one will be extinguished, and when it is at 90° the other will be quenched. At the 45° position of the Nicol both images will be visible with their partial intensities, as happens also in the cases of biaxial prisms.