As quartz possesses the symmetry of the trigonal system and is thus optically uniaxial, its optical properties are expressed, in common with those of all trigonal, tetragonal, and hexagonal crystals, by an ellipsoid of revolution, an ellipsoid the section of which perpendicular to the principal axis—that of revolution, the maximum or minimum diameter of the ellipsoid—is a circle. The optical properties are consequently the same in all directions round this axis, which has already been referred to by its common appellation of the “optic axis.” The optic axis is identical in direction with the trigonal axis of symmetry in the case of quartz or other trigonal crystal, and in the cases of hexagonal and tetragonal crystals with the axes of hexagonal and tetragonal symmetry, these three axes of specific symmetry being the distinctive property of these three respective systems, which are thus known in common as optically “uniaxial.” Consequently, no double refraction is suffered by a ray transmitted parallel to the optic axis, and the refractive index is equal in all directions perpendicular to the optic axis, that is, for all rays vibrating perpendicularly to the axis; hence the value of the refractive index obtained along any such direction is one extreme value for the whole crystal, and as already mentioned is distinguished by the letter ω. The refractive index along the direction of the axis itself is the other extreme value, and is labelled ε. It must be clearly appreciated, however, that it is not the direction of transmission but that of vibration perpendicular thereto, that is meant when it is said that, for instance, the direction of the axis corresponds to the index ε. That is to say, a ray the _vibrations_ of which occur parallel to the optic axis of a uniaxial crystal is refracted to an amount which corresponds to the refractive index ε, while a ray the vibrations of which occur perpendicularly to the axis affords ω. The difference between ε and ω is the measure of the double refraction of the crystal.