If a second prism be cut complementarily to the first, that is, so that the refracting edge is parallel to the third axis of the ellipsoid (the direction of transmission through the first prism) and the bisecting plane again parallel to one of the three axial planes of the ellipsoid, such a prism will also yield two refracted images corresponding to two indices; one of them, that particular image the vibrations of which are parallel to the refracting edge, will correspond to that one of the three principal indices which was not given by the first prism, while the other one will afford a duplicate determination of one of the two indices afforded by the first prism. Hence, a couple of such axially orientated prisms of a rhombic, monoclinic, or triclinic crystal will enable us to determine all three refractive indices, and one of them in duplicate, which latter fact will enable us to check the accuracy of our work. If the 60°-prism be cut from a crystal of the uniaxial group, that is, from a hexagonal, tetragonal, or trigonal crystal—quartz or calcite being admirable examples of the latter and particularly suitable for demonstration purposes—it will generally afford two spectra in the same manner as a crystal of the three birefringent systems of lower symmetry. But there is one special mode of cutting which results in the prism exhibiting only a single spectrum, namely, when the hexagonal, tetragonal, or trigonal axis of symmetry, which is also the unique “optic axis” of the crystal along which there is no double refraction, is arranged to be perpendicular to the bisecting plane of the 60°-prism. For then the light is transmitted along this unique axial direction when the prism is arranged for the minimum deviation of the refracted rays out of their original path, and as it may vibrate in any direction perpendicular thereto with equal velocity there is no separation into two rays, that is, no double refraction, and thus only a single spectrum is afforded by such a prism in white light, or a single image of the slit in monochromatic light, and this latter will at once yield the refractive index which is generally indicated conventionally by the letter ω, corresponding to light vibrations perpendicular to the axis. Spectroscopists take advantage of this interesting fact, when they employ a train of quartz prisms so cut in order to explore the violet and ultra-violet region of the spectrum; for quartz transmits many of the ultra-violet rays which glass absorbs. Each prism gives only a single image like glass, whereas if it were otherwise cut it would give two spectra, which would so complicate matters as to render quartz useless for the purpose.