all the phenomena of quartz as further described in the next chapter (§ 178). Professor Reusch's films were actually built up as described, of oblong slips; but such is not the best way of making them in practice. The long slips consume so much mica, that it is difficult to get all the films exactly equal, which is essential. But this object can be easily obtained by another method of construction, which is that adopted by Mr. C. J. Fox, in making the finest preparations of the kind which have ever come under my notice. A largish slab of mica must be procured, from which can be split even films as thin and large as possible—say nine or ten inches long by five or six inches wide. On this must be carefully found by experiment, and scratched, a line to show the principal polarising planes. Then all the films for the same preparation are to be cut from one and the same sheet. As good a plan as any is to draw on a sheet of paper squares at the proper angles, and laying the mica upon it, scratch over the For instance, supposing the preparation is to be built up of films at 45°, half the sheet will be covered by squares like Fig. 177, with sides parallel to the polarising planes, and half by squares at an angle of 45° with them, as Fig. 178. These may be cut with scissors; but special care must be taken that none are inverted or turned round, else all will be disarranged and all labour lost; hence it is best to scratch some mark in one given corner of every square, by which the position of that corner can be distinguished. Then if we take first a square from Fig. 177, and superpose on it a square from Fig. 178, turned round 45°, say to the left, so as to coincide; next another from Fig. 177, turned round 90° to the left; and next a second from Fig. 178, turned round 90° to the left; we shall have gone accurately round the circle, and the whole preparation can be built up in this manner. If 60° be the angle adopted, equilateral X triangles may be similarly treated, and the alternate triangles with apex inverted may be used for a preparation of contrary rotation. The best effects are obtained with not less than about 24 films, as near wave thick as possible; but Mr. Fox has made fine preparations consisting of as many as 42 films; and on the other hand, moderately good results may be got from as few as a dozen films a quarter-wave thick, arranged in four ternary sets. The one main thing is absolute uniformity in thickness, which can only be obtained by using the same sheet for all the successive films. FIG. 177.-Mica Squares. FIG. 178.-Mica Squares. 158. Quartz in Circularly-Polarised Light.-Con versely to these phenomena, if the quartz or bi-quartz be placed in the optical stage, and the quarter-wave plate introduced between it and the analyser (in this case in its normal position, as the plane of polarisation to which it is related is that of the polariser), this will be found to behave nearly like a film of mica, giving in the main two complementary colours and scarcely any intermediate colours. This slight qualification is necessary, because of the fact that all the colours, as we have before seen, cannot be quite circularly polarised by a plate of mica. 159. Further Chromatic Phenomena of Thin Films. Still further, we know that if we rotate a film between the polariser and analyser, whenever its planes are at 45°, it exhibits its colours; but when the planes correspond with those of polariser and analyser, there is no colour-in fact no effect at all is produced, for obvious reasons already explained. But now place first in the stage the large quarter-wave plate in its normal position; insert in the stage also a second quarter-wave plate with its principal plane at right angles to that of the first;1 and between them, or after the first plate in the stage, the double mica-film (Fig. 173), or the geometrical figure described in the foot-note. The circularly-polarised ray from the first plate, after being doubly-refracted by the film, is now again converted into a circularly-polarised ray. It has, therefore, lost all trace of sides or plane polarity; and when the analyser is crossed, if the double film is also in a rotating frame, this can now be rotated without the colours changing in the least. The best way is to adjust it first at an angle of 45° with the usual position for a coloured film (a position which would show no colour at all but for the first quarter-wave plate). Then the crossed position of analyser may be found by the two tints being equalised; and if then the bi-mica or compound selenite be rotated, the uniform colour will be preserved in all positions. If then again brought to the unusual position just indicated, and the analyser is rotated, we get the same successive, or bi-quartz phenomena, already described. 1 The most convenient plan is to have a second smaller quarter-wave plate fitted in the crystal stage described further on (Fig. 181). CHAPTER XV. OPTICAL PHENOMENA OF CRYSTALS IN PLANE-POLARISED LIGHT. Rings in Uni-axial Crystals-Cause of the Black Cross-Apparatus for Projection or Observation - Preparation of Crystals — Artificial Crystals-Anomalous Dispersion in Apophyllite Rings-Quartz— Bi-axial Crystals-Apparatus for Wide-angled Bi-axials-Anomalous Dispersion in Bi-axials-Fresnel's Theory of Bi-axials-Deductions from it-Mitscherlich's Experiment-Conical and Cylindrical Refraction-Relations of the Axes in Uni-axials and Bi-axials-Composite, Irregular, and Hemitrope Crystals - Mica and Selenite Combinations-Crossed Crystals-Norremberg's Uni-axial Mica Combinations-Airy's Spirals-Savart's Bands. 160. Rings in Uni-axial Crystals.-To some extent we have found proofs already of the close connection between the form and other physical characteristics of crystals, and the optical phenomena they present. But seeing we have found polarised light such a delicate analyser of the inner constitution of bodies, acting as a sure revealer of any state of unequal tension, however caused; of invisible sonorous vibrations; and even of electro-magnetic stress; it is natural to inquire if it will not yield us further evidence of the molecular constitution of the crystals themselves, or the plan on which they are, as it were, built up. This line of inquiry takes us into a new and magnificent range of optical phenomena, to enter which we have simply to abandon the nearly parallel beam of light we have hitherto employed, bringing to bear upon our crystals pencils of rays distinctly convergent. Provide a plate of Iceland spar, cut across the axis, and about inch thick. It need not be large; and for the lantern polariscope it may be conveniently mounted between two thin glass circles, like Fig. 179, in the centre of a wooden slide 4 inches long by 1 inches wide. Placed in the centre of the optical stage, so as to get the parallel beam of polarised light, we have already discovered (§ 121) that it acts as a plate of glass would do, producing no effect; its image is dark or light, according as the analyser is crossed or parallel. But now imagine converging or O FIG. 179.-Calcite Plate in Slider. diverging rays, or a conical beam of plane-polarised rays, such as are given by a lens, passing through the slice; it is evident that only the central rays can pass exactly along the optic axis; and hence inclined rays must be more or less doubly refracted. At equal distances all round the centre, therefore, the slice must act as a thin film, and give colour arranged in symmetrical circles. But this is not all. We have already learnt the two directions into which the original polarised plane of vibration must be resolved in the crystal, and that one of the new planes must pass through the axis, while the other of course is at right angles to it (§ 122). Taking therefore Fig. 180 as a diagram of our slice, and supposing A B to be the original plane of vibration from the polariser, the plate of calcite resolves that, everywhere, into |