heated, the angle between the optic axes diminishes until the crystal appears uni-axal; with a further increase of temperature the axes again open out, but in a direction at right angles to the former. When the crystal is cooled, the axes generally resume their original directions. Sometimes, however, when the heating has been carried to a great degree, or has been continued for a long time, the axes never completely return to their normal condition; and in such a case the crystal may appear permanently uni-axal. Such an appearance, when permanent, has been considered a test of former heating; and this phenomenon, when presented by crystals found in a state of nature, may be taken as evidence that the rocks in which they have been formed have been subject to high temperatures.

In the production and examination of the rings hitherto described, we have used light which has been plane-polarised and plane-analysed; but there is nothing to prevent our polarising the light or analysing it circularly, or indeed doing both.

If a quarter-undulation plate be placed betweenthe polariser and the crystal to be examined, with its axis inclined at 45° to the plane of original vibration, the light will fall upon the crystal in a state of circular polarisation; and as the polarisation will then have no reference to any particular plane of vibration, the black cross will disappear. A system of rings will be produced, but they will be discontinuous. At each quadrant, depending upon the position of the analyser, the rings will be broken, the portions in opposite quadrants being contracted or expanded, so that in

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passing from one quadrant to the next the colours pass into their complementaries. If either the direction of the axis of the quarter-undulation plate be changed from 45° on one side to 45° on the other side of the plane of vibration of the polariser, or if the crystal be changed for another of an opposite character

(i.e. negative for 'positive, or vice versa), the quadrants which were first contracted will be expanded, and those which were first expanded will be contracted. Hence for a given position of the quarter-undulation plate the appearance of the rings will furnish a means of determining the character of the crystal under examination.

Similar effects are produced if the quarter-undulation plate be placed between the crystal and the analyser; that is, if the light be analysed circularly.

In the case of bi-axal crystals under the action of light polarised or analysed circularly, the black brushes. are wanting, but they are replaced by lines of the same

form, marking where the segments of the lemniscatas pass from given colours into their complementaries.

If the light be both polarised and analysed circularly, all trace of direction will have disappeared. In uni-axal crystals the rings will take the form of perfect circles without break of any kind; and in bi-axal they will exhibit complete lemniscatas..

To pursue this matter one step further, suppose that, the arrangements remaining otherwise as before (viz. first, the polariser; secondly, a quarter-undulation plate with its axis at 45° to the principal plane of the polariser; thirdly, a uni-axal crystal; fourthly, a quarter-undulation plate with its axis parallel or perpendicular to the first; and, lastly, the analyser), the analyser be turned round; then in any position intermediate to o° and 90° the rings will be contracted and extended in opposite quadrants until at 45° they are divided by two diagonals, on each side of which the colours are complementary. Beyond 45° the rings begin to coalesce, until at 90° the four quadrants coincide again. During this movement the centre has changed from bright to dark. If the motion of the analyser be reversed, the quadrants which before contracted now expand, and vice versa. Again, if the crystal be replaced by another of an opposite character -say positive for negative-the effect on the quadrants of the rings will be reversed. This method of examination, therefore, affords a test of the character of a crystal.

A similar process applies to bi-axal crystals; but in this case the diagonals interrupting the rings are replaced by a pair of rectangular hyperbolas, on either

side of which the rings expand or contract, and the effect is reversed by reversing the motion of the analyser, or by replacing a positive by a negative crystal. The test experiment may then be made by turning the analyser slightly to the right or left, and observing whether the rings appear to advance to, or recede from, one another in the centre of the field. In particular if, the polariser and analyser being parallel, the first plate have its axis in a N.E. direction to a person looking through the analyser, the second plate with its axis at right angles to the former, and the crystal be so placed that the line joining the optic axes by N.S., then on turning the analyser to the right the rings will advance towards one another if the crystal be negative, and recede if it be positive.

It was explained in a former chapter that the coloured bands and rings shown by white light, when polarised and transmitted through crystals, fade, and cease to be visible when the retardation of the rays, due to the thickness of crystal traversed, is large. The feebleness of tint and confusion of definition arises from the overlapping of figures of different colours. But when monochromatic light is used no mixture of colour can take place, and the bands and rings remain perfectly defined, even when the thickness of the crystal is considerable. The more complicated figures produced by two plates of crystal are still more liable to obliteration; and the use of monochromatic light is in this case even more important for maintaining the integrity of the phenomena.

One essential requisite for bringing out the figures in question is purity of colour in the light employed.

On this account the ordinary method of absorption by coloured media fails; and it is only by the use of a monochromatic source of light that a satisfactory result can be obtained. For eye observations, a spirit lamp, sometimes with the addition of a little salt, suffices; but the illumination from this source is insufficient for projection on a screen. If, however, the lime in an oxy-hydrogen lamp be replaced by a mixture formed by melting borax, with the addition of some small pieces of hard Gernian glass, and a bead of this substance be placed in a small platinum cup, so fixed that the jet of mixed gases could play upon it at a distance of about three-sixteenths of an inch, a good monochromatic light is obtained. This arrangement serves perfectly for laboratory and experimental work; but for projection on a large scale a still more powerful source of light is required. The only burner adapted to lecture purposes is due to a suggestion of Professor Dewar. The burner consists of an oxyhydrogen jet, with the addition to the hydrogen tube of a chamber containing metallic sodiuin. The metal is volatilised by a Bunsen's burner placed below it; so that the hydrogen emerges charged with sodium vapour. The result is a bright monochromatic light.

If convergent or divergent light is used, uniaxal crystals (with which alone we are here concerned), when cut perpendicularly to their axes, show the wellknown systems of isochromatic rings and dark brushes. When cut at other angles, they show portions of the same systems. But when two such plates are used in combination, theory indicates the presence of some