the double spiral shown in C, Plate VIII. The relation still holds good; each axis has its own spiral, and the two now mutually enwrap each other as in the calcite.

To examine crystals with wider angles, we must of course employ the convergent system. But a moment's reflection will show that we must also alter our other arrangements. In such strongly-convergent light the rings and spirals proper to the quartz itself, which have not appeared in the moderate convergence so far employed, would overpower and distort those belonging to the crystals under examination (a single experiment will show that they do). It is moreover well to demonstrate absolutely that the figures are in no way due to any effects of convergent rays traversing the quartz, but solely to selective action upon the right-handed and left-handed waves traversing it axially. We therefore reverse Our

arrangements, placing a large plate of quartz, say 7 mm. thick, next the polarising Nicol, in parallel light, and introducing the quarter-wave plate between the crystal to be examined and the analyser. Of course, as it is the analyser which is now related to the quarter-wave plate, the spirals only appear in opposite positions; while on the other hand, with analyser in those positions, they only move and change in colour as the polariser is rotated.1

First we take again the small angle of a nitre crystal, but which, for this strongly convergent light, to show conspicuous rings, must be cut much thinner than the former. The result is shown in D, Plate VIII.; where it is to be observed that we can hardly distinguish its spirals from those of the calcite (A, same plate). They are just a little drawn out into an oval form, precisely as we should expect ; and that is all. Arragonite, with a wider axial angle of about 181

1 This arrangement might have been adopted all along; but the experiments are given as first made, in order to show how each point was successively determined.

degrees, shows a spiral of several turns round each axis (E, Plate VIII.), but still mutually enwrapping each other at last; and finally mica, or sugar, or other crystal with an angle of say 45° to 60°, shows still more numerous convolutions, but still preserving the same mutual relation (F, Plate VIII.). Only crystals which, owing to peculiarities in their double refraction for various colours (§ 169), do not show in the ordinary manner tolerably complete lemniscates, for the same reason fail to show these figures.

That the spirals are due to selective action upon the coloured components of the two axial quartz waves, is shown by the fact that they are not seen at all in homogeneous or one-coloured light.

We next examine a crystal of selenite gradually heated, thus repeating Mitscherlich's beautiful experiment with this additional method of analysis. Care is required to produce equally perfect figures, the least excess of heat on any side of the crystal of course causing distortion. This can however be avoided. We first obtain two spirals exactly similar to those of F, Plate VIII. As the axes approach and coincide, the spirals also approach in their centres, until at the point of coincidence they exactly resemble those of the calcite (A, Plate VIII.). And finally they re-open in a direction at right angles to the former. All through we have a double spiral; and we can only get a single one by taking separately one of the axes of a bi-axial; the axis of a uniaxial always preserving what we may call its twin character. Thus we have the ocular proof sought, of the relation predicated by the theory of Fresnel between the axes of the two classes of crystals.

But the reason is also thus demonstrated of the spirals observed by Mr. Airy in quartz itself (F, Plate VII.), when examined in convergent circularly-polarised light. We see that the quartz, considered as an ordinary uni-axial crystal,

is able, owing to its peculiar and totally distinct effects upon plane-polarised light passing through it axially, to show its own spirals, which of course are double. These are not seen at all in parallel light; and on the other hand, if we employ extremely convergent circularly-polarised light, they become as numerous and distinct as those of the calcite.

A crucial test of this view of the case readily suggests itself. If it be well founded, we can represent our quartz artificially, as it were; since many fluids act similarly (§ 151) upon a plane-polarised ray. If therefore we take a column of such fluid of sufficient length, and any ordinary uniaxial crystal, the one will represent the axial properties, and the other the ordinary doubly-refractive properties of the quartz; and the two ought to give us double spirals; in fact an adequate column of fluid ought successfully to replace the quartz in all the foregoing experiments.1

The rotatory effect of fluids is so inferior to that of quartz, that it is not easy to transmit sufficient light to give good projections through a column of fluid of adequate length. By employing a tube 8 inches long and 2 inches in diameter with plane glass ends, filled with oil of lemons (1 lb. of which costs about 10s. 6d., and is just sufficient to fill such a tube) the object can however be effected. We introduce this next the polariser in lieu of the quartz. In the crystal stage we place the calcite or any other uni-axial crystal; and now introducing the quarter-wave plate between crystal and analyser, we obtain at once the double spirals. The fluid will also give the same phenomena as the quartz with

1 It is probable that a bar of heavy glass in the electro-magnetic field would give similar effects; but I have not as yet been able to test the matter experimentally, and there is the very interesting difference between the behaviour of such a bar and other rotary substances described in § 150. It seems scarcely probable that this difference would affect the above phenomena; but the settlement of that point would be interesting.

other crystals, its slightly yellow colour only slightly interfering with the effect, for the same reason that the figures fail to appear in homogeneous light. Spirit of turpentine is free from this defect, but requires a column of almost unmanageable length.

Finally, it may be mentioned that Reusch's artificial quartzes made of mica-films (§ 157) and Norremberg's artificial uni-axial crystals made of crossed micas (§ 177), give in each case similar results to the natural crystals. So also does a circular disc of unannealed glass in parallel light.

CHAPTER XVII.

POLARISATION AND COLOUR OF THE SKY.-POLARISATION BY SMALL PARTICLES.

Polarisation of the Sky-Light Polarised by all Small Particles-Blue Colour similarly Caused-Polarisation by Black Surfaces--Experimental Demonstration of the Phenomena-Multi-coloured Quartz Images-Identity of Heat, Light, and Actinism.

185. Polarisation of the Sky.-On a clear day, in morning or afternoon, almost any of the colour phenomena we have now reviewed may be tolerably seen, by using the tourmaline close to the eye as analyser, and looking through the selenite or other object to the sky as polariser, in any direction at a tolerably wide angle with the direction of the sun, the maximum effect being at 90°. For instance, if the sun were due east, the greatest polarisation will be found anywhere in an arc extending due north and south. In the most favourable positions the quantity of polarised light is about one-fourth of the whole, and the rings in crystals can be seen very plainly with the sky as polariser. The direction of greatest polarisation of course depends upon the place of the sun; and upon this fact Sir Charles Wheatstone based the construction of a "polar clock," which gives the astronomical time by the effects upon slips of selenite in certain positions.