If one nicol be placed above another and their corresponding principal planes be at right angles no light is transmitted through the pair. In the polarizing microscope one such nicol, called the polarizer, is placed below the stage, and the other, called the analyser, is either inserted in the body of the microscope or placed above the eyepiece, and the pair are usually set in the crossed position so that the field of the microscope is dark. If a piece of glass or a fragment of some singly refractive substance be placed on the stage the field still remains dark; but in case of a doubly refractive stone the field is no longer dark except in certain positions of the stone. On rotation of the plate, or, if possible, of the nicols together, the field passes from darkness to maximum brightness four times in a complete revolution, the relative angular intervals between these positions being right angles. These positions of darkness are known as the positions of extinction, and the plate is said to extinguish in them. This test is exceedingly delicate and reveals the double refraction even when the greatest difference in the refractive indices is too small to be measured directly. Doubly refractive substances are of two kinds: uniaxial, in which there is one direction of single refraction, and biaxial, in which there are two such directions. In the case of the former the direction of one, the ordinary ray, is precisely the same as if the refraction were single, but the refractive index of the other ray varies from that of the ordinary ray to a second limiting value, the extraordinary refractive index, which may be either greater or less. If the extraordinary is greater than the ordinary refractive index the double refraction is said to be positive; if less, to be negative. A biaxial substance is more complex. It possesses three principal directions, viz., the bisectrices of the directions of single refraction and the perpendicular to the plane containing them. The first two correspond to the greatest and least, and the last to the mean of the principal indices of refraction. If the acute bisectrix corresponds to the least refractive index, the double refraction is said to be positive, and if to the greatest, negative. The relation of the directions of single refraction, _s_, to the three principal directions, _a, b, c_, is illustrated in Fig. 27 for the case of topaz, a positive mineral. The refractive indices of the rays traversing one of the principal directions have the values corresponding to the other two. In the direction _a_ we should measure the greatest and the mean of the principal refractive indices, in the direction _b_ the greatest and the least, and in the direction _c_ the mean and the least. The maximum amount of double refraction is therefore in the direction _b_. [Illustration: FIG. 27.—Relation of the two Directions of single Refraction to the principal Optical Directions in a Biaxial Crystal.]