vibrations passing through the axis, represented by the radii ; and others at right angles to them, represented by the circles. Further still, it is evident that all along the two radii, A B and C D, there will be no double refraction at all, since the planes of vibration in the crystal there coincide with that of the polariser, and that perpendicular to it. Along those lines, therefore, the slice can have no influence, and must appear black when the analyser is crossed, and white when it is parallel with the polariser (§ 136). B FIG. 180.-Vibration Planes in the Calcite. All this is justified to the letter; but to exhibit it on the screen, we must add to the polariscope what is called a "crystal stage," which will hold the plate in the converging cone of rays from the objective. Fig. 181 shows the construction of it. A tube, A B, fits on the nozzle of the objective, and has transversely cut through it a slit, s, through which the crystal sliders are passed, kept in place by a spiral spring as usual. The end, B, of the tube is of exactly the nozzle, so that the Nicol or other analyser fits and rotates on it, as on the nozzle. We place this addition on the nozzle, add the analyser, and insert our plate of calcite in the slit, s. We then get on the screen same size as the the beautiful figures represented at A and B, Plate V., according as the analyser is crossed, or parallel with the polariser. In the former position the beautiful coloured rings are traversed by the black cross we were led to expect; in the other position, we get the complementary rings traversed by a white cross. The centre, of course, shows no phenomena at all beyond white or black, as the rays there pass along the optic axis. 161. Apparatus for Observing the Rings. The objective described in Fig. 1 gives, in practical work, about the best average effects with these "crystal rings," unless an addition to be presently described is made to the apparatus. Much more convergence, unless extra lenses are added, causes a great deal of light not to get through the Nicol analyser; and much less gives fewer rings, unless a very thick slice be employed. For a moment's consideration will show that the amount of retardation in a plate of crystal thus cut, depends on both the thickness of the plate and the amount of convergence; and that the rings must become closer and more numerous as the plate increases in thickness. The private student will often find a simple tourmaline pincette (Fig. 182) the most convenient apparatus. A slice of tourmaline is mounted so as to be capable of rotation at each end of the spring tongs, and the crystal plate to be examined is held between them: the rays passing through this simple polariscope into the small pupil of the eye, are sufficiently convergent to exhibit the phenomena. Or a single loose tourmaline, such as the one used in the rotating frame, held close to the eye with the crystal close up to it, will show the rings well, if the whole, and the eye, are turned towards the plane-polarised light from a glass plate or any other polarising surface, or even towards certain portions of a bright sky (see Chapter XVII.). FIG. 182.-Tourmaline Pincette. 162. Preparation of Crystals. Many crystals can only be prepared, as a rule, by skilled workmen ; and the most immense variety, numbering over a hundred, of uniaxials and the bi-axials to be next considered, may be obtained from Dr. Steeg and Reuter, Homburg von der Höhe, who prepare this class of objects for almost the whole world. The rarer crystals can hardly, in fact, be obtained elsewhere; but Messrs. Darker and one or two |