analysing Nicol, through which the quartz is viewed, is turned round. If the quartz be about 33 mm. in thickness, for one position of the Nicol it will appear of a peculiar neutral grey tint, known as the tint of passage. A slight rotation in one direction will make it red, in the other blue. After a little practice it is easier to determine, even by eye, when this tint appears, than to feel certain when the light is completely quenched by a Nicol. It can be readily shewn moreover that when the quartz gives the tint of passage, the most luminous rays, those near the Fraunhofer line E, are wanting from the emergent beam; and if the quartz have the thickness already mentioned, the plane of polarisation of these rays has been turned through 90°.

A still more accurate method of making the observation is afforded by the use of a bi-quartz. Some specimens of quartz produce a right-handed, others a left-handed rotation of the plane of polarisation of light traversing them. A biquartz consists of two semicircular plates of quartz placed so as to have a common diameter. The one is righthanded, the other left. The two plates are of the same thickness, and therefore produce the same rotation, though in opposite directions, in any given ray. If, then, planepolarised white light pass normally through the bi-quartz, the rays of different refrangibilities are differently rotated, and that too in opposite directions by the two halves, and if the emergent light be analysed by a Nicol, the two halves will appear differently coloured. If, however, we place the analysing Nicol so as to quench in each half of the bi-quartz the ray whose plane of polarisation is turned through 90°that is to say, with its principal plane parallel to that of the polariser-light of the same wave-length will be absent from both halves of the field, and the other rays will be present in the same proportions in the two; and if the thickness of the bi-quartz be about 3.3 mm. this common tint will be the tint of passage. A very slight rotation of the analyser in one direction renders one half red, the other blue, while if

the direction of rotation be reversed, the first half becomes blue, the second red. Hence the position of the plane of polarisation of the ray which is rotated by the bi-quartz through a certain definite angle can be very accurately determined.

A still better plan is to form the light after passing the analyser into a spectrum. If this be done in such a way as to keep the rays coming from the two halves of the bi-quartz distinct-e.g. by placing a lens between the bi-quartz and the slit and adjusting it to form a real image of the bi-quartz on the slit, while at the same time the slit is perpendicular to the line of separation of the two halves-two spectra will be seen, each crossed by a dark absorption band. As the analysing Nicol is rotated the bands move in opposite directions across the spectrum, and can be brought into coincidence one above the other. This can be done with great accuracy and forms a very delicate method. Or we may adopt another plan with the spectroscope: we may use a single piece of quartz and form the light which has passed through it into a spectrum, which will then be crossed by a dark band; this can be set to coincide with any part of the spectrum. This is best done by placing the telescope so that the cross-wire or needle-point may coincide with the part in question, and then moving the band, by turning the analyser, until its centre is under the cross-wire.

Fig. 40 gives the arrangement of the apparatus: Lis the lamp, A the slit, and c the collimating lens. The parallel rays fall on the polarising Nicol N and the biquartz B. They then traverse the tube T containing the active rotatory substance and the analysing Nicol N', falling

on the lens M which forms an image of the bi-quartz on the slit s of the small direct-vision spectroscope. If we wish to do without the spectroscope, we can remove both it and the lens M and view the bi-quartz either with the naked eye or with a lens or small telescope adjusted to see it distinctly. If we use the single quartz, we can substitute it for the bi-quartz, and focus the eye-piece of the telescope to see the first slit a distinctly, and thus observe the tint of passage.

The quartz plate may be put in both cases at either end of the tube T. If it be placed as in the figure, and the apparatus is to be used to measure the rotation produced by some active substance, the tube should in the first instance be filled with water, for this will prevent the necessity of any great alteration in the adjustment of the lens M or in the focussing of the telescope, if the lens be not used, between the two parts of the experiment.

The mode of adjusting the Nicols has been already described.

The light should traverse the quartz parallel to its axis, and this should be at right angles to its faces. This last adjustment can be made by the same method as was used for placing the axis of the Nicol in the right position, provided the maker has cut the quartz correctly. In practice it is most convenient to adjust the quartz by hand, until the bands formed are as sharp and clear as may be.

Care must be taken that each separate piece of the apparatus is securely fastened down to the table to prevent any shake or accidental disturbance.

If a lens is used at M, it is best to have it secured to the tube which carries the analysing Nicol, its centre being on the axis of this tube; by this means it is fixed relatively to the Nicol, and the light always comes through the same part of the lens. This is important, for almost all lenses exert a slight depolarising effect on light, which differs appreciably in different parts of the lens. For most purposes

this is not very material, so long as we can be sure that the effect remains the same throughout our observations. This assurance is given us, provided that the properties of the lens are not altered by variations of temperature, if the lens be fixed with reference to the principal plane of the analyser, so that both lens and analyser rotate together about a common axis.

One other point remains to be noticed. If equality of tint be established in any position, and the analyser be then turned through 180°, then, if the adjustments be perfect, there will still be equality of tint. To ensure accuracy we should take the readings of the analysing Nicol in both these positions. The difference between the two will probably not be exactly 180°; this arises mainly from the fact that the axis of rotation is not accurately parallel to the light. The mean of the two mean readings will give a result nearly free from the error, supposing it to be small, which would otherwise arise from this cause.

To attain accuracy in experiments of this kind needs considerable practice.

Experiments.

(1) Set up the apparatus and measure the rotation produced by the given plate of quartz.

(2) Make solutions of sugar of various strengths, and verify the law that the rotation for light of given wave-length varies as the quantity of sugar in a unit of volume of the solution. Enter results thus:

The theory of these, as has been stated, all turns on the fact that it is comparatively easy to determine when two objects placed side by side are equally illuminated, the illumination being faint.

Suppose, then, we view through a small telescope or eye-piece placed behind the analyser a circular hole divided. into two parts across a diameter, and arranged in such a way that the planes of polarisation of the light emerging from the two halves are inclined to each other at a small angle. For one position of the analyser one half of the field will be black, for another, not very different, the other half will be black, and for an intermediate position the two halves will have the same intensity. The analyser can be placed with the greatest nicety in the position to produce this. If now the planes of polarisation of the light from the two halves of the field be each rotated through any the same angle and the analyser turned until equality of shade is re-established, the angle through which the analyser turns measures the angle through which the plane of polarisation has been rotated.

Whatever method of producing the half-shadow field be adopted, the arrangement of apparatus will be similar to that shewn in fig. 40, only в will be the half-shadow piate,