the analyzer, we bring its principal section exactly perpendicular to one of the two principal sections of the polarizer, perfect obscuration follows in the corresponding half of the field of vision, the other half remaining illumined. A rotation of 5° reverses these conditions, the dark half then becoming bright and vice versa, while midway between these two positions lies a point where the halves exhibit equal degrees of incipient shadow.

§ 57. The half-shade instrument, however, which has come into most general use is that of Laurent, of which a representation is given in Figs. 37, 38.

Laurent: Dingler's Polyt. Journ. 223, 608.

In this, the light from a sodium flame passes through the following optical apparatus:

1. A thin plate, a (Fig. 37), cut from a crystal of bichromate of potash, serving to free the yellow ray from intermixture of green, blue, and violet light. This is enclosed between a couple of glass plates and fixed in a movable diaphragm.

2. A double refracting calc-spar prism, b, as polarizer.

These two pieces are placed one at each end of the tube AB, Fig. 38, which is inserted in the fixed portion C C', of the instrument, within which it is capable of rotation through a small angle. The amount of this movement is regulated by means of the screw-stop B, passing through the slot at C.

3. A circular diaphragm c, containing a glass plate, to which is affixed a thin plate of quartz, cut parallel to the axis, and just large enough to cover exactly one half of the circle. The thickness of the quartz plate must be so regulated that the yellow rays polarized parallel and perpendicularly to the axis may in their transmission undergo a retardation of half a wave-length. (In an instrument manufactured by Dr. Hofmann, of Paris, the thickness of this quartz plate is 0:11 millimetre.)

4. The solution-tube d.

5. An analyzing Nicol e, furnished with rotatory movement.
6. The lenses ƒ and g, forming a small Galilean telescope.

The analyzer rotates in a piece with the divided disc E, within the stout ring, M. For this purpose, the back of the disc is furnished with a bevelled toothed wheel, driven by a small pinion worked by the milled-head F. The vernier is screwed firmly to the arm G, hanging down over the graduated edge of the disc. In reading, a magnifier, H, is used, which has a motion round the point 0, and is provided at the top with a metal reflector, J. The latter can be made to reflect light on the divisions either from the sodium flame or some other convenient source. The Nicol can be turned in its case slightly by means of the screw L, so as to alter the zero-point. The telescopic lenses are mounted in tubes, KN, the latter of which has a draw motion. The graduated circle, a front view of which, with the parts pertaining thereto, is given in the figure, has a diameter of 250 millimetres, and the vernier reads to single minutes. The optical

1 May be obtained of Dr. Hofmann, 29, Rue Bertrand, Paris; Schmidt and Haensch, Berlin; J. Duboscq, 21, Rue de l'Odéon, Paris; Bartels and Diederiche, mechanicians, Göttingen. Fig. 38 is drawn from one of Hofmann's instruments.

arrangements are fixed at the ends of a brass trough, of semi-circular section, D, resting on the stand P. The size of the trough should be such as easily to take tubes 3 decimetres long with their water jackets.

§ 58. The peculiar feature in Laurent's instrument is the thin plate of quartz PQ, cut parallel to the axis, Fig. 39. Let the polarizer

b

Fig. 39.
C' B C

Fig. 40.

Fig. 41.

Fig. 42.
B

be first so adjusted that the plane of polarization of the transmitted pencil of light is parallel to the axis of the plate—that is, lies in the direction AB-the two halves of the field of vision will then appear equally dark or equally bright in every position of the analyzer. But if the polarizer be inclined to A B, at an angle a, the plane of polarization of the rays passing through the quartz plate will undergo deviation through an equal angle, a', in the opposite direction. Therefore, when in the uncovered half the plane of polarization has the direction AC, in the covered half it will have the direction AC'. If now we turn the analyzer, then, according as its plane of polarization lies in the direction cc or c'e', so will either the rays polarized parallel to AC or to AC' be extinguished, and the corresponding half of the field of vision will appear completely dark, while the other half merely suffers a partial decrease of brightness (Figs. 40, 41). In the middle position, b b, Fig. 42, there is a uniform shading over the two halves, but a very slight movement to and fro of the analyzer will at once destroy the equality. These phenomena repeat themselves when the analyzer has been moved through an angle of 180°.1

The degree of uniform shade obtained by bringing the analyzer into the middle position will be greater, the smaller the angle a (Fig. 39), which the plane of the polarizer makes with the axis of the quartz plate. The parts are set by the instrument-maker so that these two

1 For the theory of the phenomena produced by polarized light with plates cut parallel to the axes of uni-axial crystals, see Wüllner's Lehrbuch der Physik, 3 Aufl. Bd. II. S. 568. Laurent, in his earlier instruments, employed a thin plate of gypsum instead of the quartz, which gave the same results (Comptes Rend. 78, 349).

directions are parallel to one another, but, as before observed, § 57, adjustment is arranged for by allowing the polarizer a slight amount of rotation, by means of the ring B, in the slot ß, Fig. 38, whereby the field of vision is brightened. In this way the sensitiveness of the instrument can be altered. This is always greater the smaller the departure from the parallel position, when, consequently, the less will be the amount of movement of the analyzer requisite to produce perfect obscurity of one or other half of the field of vision. The deepest shading suitable should therefore be chosen.

§ 59. In setting up the instrument it is directed towards a sodium flame, and the telescopic eye-piece so adjusted that the edge of the quartz plate appears to divide the diaphragm by a sharply defined vertical line. The analyzing prism must then be turned until both halves of the field of vision appear equally dark, and the polarizer adjusted to that position where the least displacement of the analyzer is required to produce an appreciable change in the appearance of the field.

In determining the zero-point, the analyzer is brought into the middle position, where the partition-line becomes invisible. Moreover, it is better to fill the experimental tube with water, so as to equalize the conditions in respect to absorption of light with those holding in observations of active liquids. One can then make the actual zero-position correspond as nearly as possible with the zeromark by means of the screw L (Fig. 38). Then, introducing the liquid, a rotation of the analyzer with its disc to the right will be necessary to restore the reference position if the substance be dextrorotatory, and to the left if it be lævo-rotatory.

If now, owing to colouring or any slight turbidity, the field of vision is too dark, greater brightness can be obtained by a slight movement of the polarizer on its axis (see § 58), but this entails the disadvantage that larger movements of the analyzer are then required before any alteration on the uniformity of shade is apparent, and the readings accordingly are more divergent. In clear solutions these do not differ by more than single minutes. For determining the direction of rotation in active substances of high rotatory power, the procedure given under the head of Mitscherlich's instrument (§ 46) is equally appropriate here.

A bright sodium flame is necessary, which is best obtained by using the lamp shown, § 46, Fig. 22. If tubes provided with water

jackets are employed, the complete arrangement of the instrument corresponds exactly with the description given § 50, Fig. 29. T eliminate errors in the Nicols, the observations should be made at tw: positions 180° apart, and the mean taken. The subjoined table contains, as an example, a series of observations with one of Hofmann's instruments, graduated from 0° both ways to 180°. The zero-point was approximately at 90° in each half circle. The active liquid was a solution of cane-sugar:

Exmparison of Mitscherlich's, Wild's, and Laurent's Instruments. 59, To determine the degree of concordance possible between