strength of the solution be half that in the former experiment, then also the angle of rotation will be the half only of that first observed. The vanishing points of the dark lines will then appear either at

15°

105°

195°

285°,

as in Fig. 34, in which case the substance is dextro-rotatory, or at

Accordingly, if observations with the shorter tube or weaker solution give lower readings than the original, the rotation is righthanded, whilst if the readings are higher than at first, the rotation is left-handed. The conditions are, of course, reversed when the graduation of the instrument is towards the left.

§ 53. In examining solutions of very high rotatory power it may happen that the angle of rotation exceeds 90°, so that the readings are always found in the quadrant beyond. In such cases, to avoid error, the observations should be made with two tubes of

different lengths.

For example, the following were, in round num bers, the values obtained with lavo-rotatory nicotine, in a 1

Apparently, therefore, a layer of nicotine 100 millimetres in depth rotates through an angle of 72°. A second observation was now taken with a tube 50 millimetres long, when the following results were obtained :

Here the angle, instead of being reduced to half, as we should expect, is larger even than that given by twice the thickness of medium. It 50 millimetres of nicotine rotate through 81°, 100 millimetres should rotate through 162°. Now this is found to be the case when the zeropoint of the observations with a tube of the last-named length is moved a quadrant to the right. We then get :

Angle of rotation

Quad. Quad. Quad. Quad.

II. 180° III. 270° IV. 360° I. 90°

I. 18° II. 108° III. 198° IV. +72°(=360-288

The foregoing conditions are shown in Figs. 35 and 36, the former

of which shows the rotation for a length of 50 millimetres, the latter for 100 millimetres.

§ 54. Wherever exactness is required, the observations should be repeated in each of the four quadrants of the circle. It will be found that appreciable differences exist between the angles of rotation. thus obtained, differences which van de Sande Bakhuyzen1 has shown originate in defective construction of the Nicol, as well as in improper placing of the two calc-spar plates of the Savart. These errors, however, disappear altogether when the mean of the four values for the angle of rotation is taken. When the observations are repeated in two opposite quadrants only, and the mean of the readings is taken, the compensation of errors is not indeed complete, but the degree of accuracy attained is usually enough for all ordinary purposes. The deviations from the true value do not exceed 0·03° at the most, and are generally less than 0.01°. To take observations in two adjoining quadrants has not, of course, the same compensatory effect.

To obtain very precise results, it is obviously requisite that a still larger number of observations should be taken. As a rule, five observations in each quadrant will be enough, so that allowing for the verification of the zero-points, which should be repeated at least once each day on taking observations, the angle of rotation finally obtained will be the result of forty readings. Where considerable differences are found in the readings, the number of observations must be increased. This will occur when the solutions are not absolutely clear; slight colorations, on the other hand, do not materially affect the observations.

The degree of accuracy attainable is shown in the two series of observations appended. These were taken with an instrument of Hermann and Pfister's manufacture, graduated to divisions of 5 minutes, and allowing of approximate reading to single minutes. The liquid employed was an aqueous solution of cane-sugar containing 19:45 grammes in 100 cubic centimetres. The length of tube was 219.79 millimetres.

1 van de Sande Bakhuyzen: Pogg. Ann. 145, 259.

2 Differences of 20 minutes in the readings may easily occur with unpractised observers, but with care these can soon be much reduced in amount, so that a hasty opinion should not be formed of a newly-purchased Wild polariscope. When the observer has become accustomed to the instrument, and the latter is properly constructed, the difference in the readings will seldom exceed 5 minutes.

0° 20.0' 28° 43.8′ 90° 19.0' 118° 40.0' 180° 13.8' 208° 38.6′ 270° 17.8′ 298° 40%

0° 20.4' 28° 44.6'

90° 18.0' 118° 38-8' 180° 14.4' 208°38.4' 270° 18.6′ 298° 47.2

(c) Half-Shade Instruments (Polarimètres à Pénombre) of Jellett, Cornu, and Laurent.

In these instruments the mechanism for sensitiveness is arranged to produce a circular field of vision divided into halves, which in certain positions of the analyzing Nicol are unequally illuminated, but in one particular position exhibit a uniformly faint shade. This position, which can be fixed with great accuracy, is taken as the point of reference. The use of monochromatic sodium light is pre-supposed.

§ 55. The earliest instrument of this kind was constructed by Jellett in 1860.1 In this, between the polarizing and analyzing Nicols, and close behind the former, is placed a prism of peculiar form. An elongated rhombohedron of calc-spar which, by grinding the ends, has been converted into a right prism, is divided longitudinally into halves by a plane nearly, but not quite, perpendicular to its principal section, and the two halves then reunited, but in reversed. positions. The prism is mounted in a case, furnished at the extremities with diaphragms having circular apertures. The circular field so obtained appears divided diametrically by the section into equal halves, in which the planes of polarization are slightly inclined to each other. A plane polarized ray passing through can, by turning the analyzer, be extinguished by either half of the prism, these points of extinction lying very close together, whilst between them lies the position of uniform shade. The appearance of uniform shade can also be made to vanish by the introduction of an active liquid, and, to bring it once more into view, the analyzer must be turned on its axis through a certain angle, which can be taken as measure of the deviation of the ray produced by the active substance.

§ 56. Cornu's instrument consists of an ordinary Nicol as analyzer, with a polarizer of peculiar construction. The latter is formed out of a Nicol prism, by bisecting it in the direction of the plane passing through the two shorter longitudinal diagonals, cutting down the sectional faces 210 and reuniting the halves. In this way we have a double Nicol prism, having its two principal sections forming an angle of 5° with each other. When, therefore, by turning 1 Jellett: Reports of the British Association, 1860, 2, 13.

2 Cornu: Bull. Soc. Chim. [2], 14, 140,