It will now prove of interest to examine the effects produced by two plates of opposite varieties of quartz of half this thickness, namely, 3.75 mm. The phenomena are very similar to those just described, but the rings are a little wider, and the larger area within the innermost ring is now filled with yellow light instead of violet, when the analyser is exactly crossed to the polariser. It passes into a bright green when the analyser is rotated slightly on one side, and into orange when the Nicol is rotated in the reverse direction. But the most interesting thing of all is to observe what occurs when these two plates of 3.75 mm. thickness, one of right-handed quartz and the other of left-handed, are superposed and placed in contact together as one plate, of double the thickness, 7.5 mm., at the convergent focus. A beautiful spiral figure is produced on the screen, composed of the celebrated “Airy’s spirals” as if the black cross were being reproduced in the central part, but with each of its bars distorted into the shape of the letter S, as shown in Fig. 78 at the foot of Plate XV. The contrary effects of the two opposing rotations are thus extraordinarily indicated visually in the interference figure afforded by the composite plate.

Now, it is of great practical interest that certain quartz crystals are found in nature which show Airy’s spirals directly, on cutting a plate 7.5 mm. thick or thereabouts, perpendicular to the optic axis. For instance, one in the author’s collection of quartzes, a single plate of an apparently homogeneous and perfectly limpid crystal, shows the spirals exceedingly well and clearly defined. As a matter of fact, it is a twin, a right and a left-handed crystal being twinned together with an invisible plane of composition, which is only revealed on examining the crystal in polarised light, as will be demonstrated in the next chapter by the use of parallel polarised light. The fact of such a plate of quartz affording Airy’s spirals in convergent polarised light is, however, of itself an excellent proof of the twinning of two crystal individuals of the opposite varieties.

Now the very shape of these spiral figures suggests screw action of the molecular structure of the crystals on the waves of light passing through them, and moreover, of the action of two screws of opposite directions of winding, one clockwise and the other anti-clockwise, thus remarkably confirming the supposition that the point-systems of the structure of the right and left-handed varieties of quartz are of a helical nature and respectively of opposite modes of winding.

Another experiment, devised by Reusch, which still further enhances the probability that this supposition as to the structure of quartz crystals is correct, may next be introduced. A thin film of biaxial mica has been cut into twenty-four narrow strips, which have been laid over each other at angles of 60°, so that a screw-shaped pile has been formed of the central overlapping parts, consisting of four complete rotations; that is, there are four repetitions of the “pitch” of the screw, each composed of six films. On placing this composite plate of mica at the convergent focus of the lantern polariscope, so that the overhanging ends of any four identically superposed strips occupy the focus, the ordinary biaxial interference figure of mica—two sets of rings and hyperbolic brushes, very much like Fig. 52, Plate XII.—is observed on the screen. But when the plate is moved so that the central part comes into the focus, where all the twenty-four films overlap in their six different orientations 60° apart, and so that all the light rays have to traverse the whole helical pile of the twenty-four films, a uniaxial figure exactly like that of quartz is produced, namely, one composed of circular rings, with a black cross only visible, however, at the marginal part, and with the inner ring filled with brightly coloured light. Moreover, on slightly rotating the analysing Nicol the innermost ring moves outwards or inwards and the colour changes to blue or red, according to the direction in which the helix had been wound, in exact accordance with the rule stated above for quartz.

If now a second such helical pile of mica films, but one for which the opposite manner of winding has been adopted, anti-clockwise if the first had been clockwise, be examined at the convergent focus, precisely the same appearance will be observed with crossed Nicols, but the opposite changes will occur on rotating the analyser. Finally, to complete the interesting proof of the helical nature of quartz crystals, when these two oppositely wound composite mica plates are superposed—each being marked carefully to indicate the direction of the helix and the proper mode of superposition in order to effect precise oppositeness of arrangement, mirror-image symmetry, in fact, about the plane of contact—and placed in the convergent beam near its focus, there is at once seen on the screen a magnificent display of Airy’s spirals, as perfect as those afforded by the fine natural twin last experimented with. Hence, there can be no doubt whatever that the remarkable optical behaviour of quartz is due to its point-system being of a helical nature, a right or a left-handed screw structure being apparently produced in nature with equal facility. The circumstances of environment during the formation of the crystal probably determine which variety shall be produced, and when the nature of the environment becomes changed during the operation of formation either twins are produced of the two varieties, or separate individual crystals.

This may well conclude our experiments in convergent polarised light, which—including the beautiful Mitscherlich experiment described in Chapter VII., of exhibiting the crossing of the optic axial plane in the case of gypsum, and the production of all the types of interference figures in succession, as the crystal becomes warmed by the heat rays accompanying the beam of convergent light—will have introduced the reader to a typical series of such experiments, and such as were actually exhibited by the author to the British Association at Winnipeg. We may pass, therefore, in the next chapter to the consideration of an equally interesting series in which a parallel beam of polarised light will be used, which will still further elucidate the internal structure in the especially instructive case of quartz crystals, and that of crystals in general.

CHAPTER XIV
EXPERIMENTS WITH QUARTZ AND GYPSUM IN PARALLEL POLARISED LIGHT. GENERAL CONCLUSIONS FROM THE EXPERIMENTS WITH QUARTZ.

In order to rearrange the projection polariscope for experiments in parallel light, we simply remove the three lenses on separate stands (Fig. 71), and the convergent systems of lenses on their special adjustable stand with goniometrical crystal holder, from between the two Nicol prisms, and replace them by two other separately mounted lenses, acting together as an achromatic projecting objective, and a rotatable object stage. The whole arrangement as thus altered for experiments in parallel polarised light is shown in position in Fig. 79. The change is readily made, a gap in the plinth-bed guides near the analysing Nicol enabling it to be effected without removing either of the prisms, the analyser being simply drawn along a few inches nearer the end in order to expose the changing gap. The pair of lenses consists of a plano-convex lens of 5 inches focus and 2¼ inches diameter, and another plano-convex lens of 8½ inches focus and 2 inches aperture, with their convex faces turned towards each other. Together they produce on the screen an excellent image of the object on the stage, and the size of the image can be varied at will by regulating the relative positions of the two lenses with respect to each other and to the object stage. If found more suitable for the particular screen distance available, the 5–inch lens may be replaced by a 6–inch lens also provided as an alternative.

Fig. 79.—Projection Polariscope arranged for Parallel Light.