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249

In quartz the more refrangible rays have their plane of polarization rotated to a greater extent than the less refrangible, and Biot found that the angles of rotation for particular rays are nearly proportional to the squares of the indices of refraction, or, what comes to the same thing, inversely proportional to the squares of the wave lengths. With the knowledge of the wave length at different parts of the spectrum, and the rotation of one of the rays, it is possible to calculate the rotations of the other rays; also the observed rotations multiplied by the square of the wave lengths should give a constant number. The following table in which the angles of rotation produced by a layer of quartz mm. in thickness, as observed by Broch, and the wave lengths determined by Angström, are employed, and it will be seen that Biot's law is approximately correct the angle of rotation for the line в is used as the basis for the calculation of the numbers in column 5.

The angles of rotation are proportional to the thickness of

the quartz, a piece 1

piece 1mm thick rotating the mean yellow 24°, it follows that a plate 3'75" 5mm. in thickness will produce a rotation

for the same colour of 90°.

Biot's law does not hold good for all bodies, for in some cases the rotatory dispersion varies very much from that observed in quartz. By an aqueous solution of tartaric acid, for example, the plane of polarization of the green ray is more rotated than that of the violet.

:

There are many liquids which produce rotatory polarization. Solution of sugar-candy, for example, gives a right-handed rotation; oil of lemons does so likewise. Certain varieties of oil of turpentin produce a left-handed rotation in some isomeric organic bodies, indeed, the action on polarized light. is one of the few important distinguishing properties they possess; hence the value of a proper investigation of their rotatory power when this method is capable of application. In all these cases the degree of the rotation effected by liquids is

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COLOURED ROTATORY POLARIZATION.

[126. much less than that produced by quartz; and, consequently, the light must traverse a much greater depth of the liquid to exhibit the effect. Oil of turpentin has a power not exceeding

of that of quartz. In some cases dilution with an inactive liquid does not destroy or even weaken the power, provided that the depth of the column be increased in proportion to the extent of the dilution; this is true with an aqueous solution of sugar when diluted with water. With rotating liquids, such as oil of turpentin, mixture with inactive liquids produces a marked change in the angle of rotation (1555). A mixture of two substances acting oppositely produces a result exactly equal to the difference between the two.

Biot, who discovered the phenomenon of coloured rotatory, or as it is often incorrectly termed, circular polarization,* has applied it to chemical purposes. It may be used, for example, to ascertain the purity of syrups; crystallizable cane-sugar causes a right-handed rotation, while the molasses, or uncrystallizable syrup, produces a rotation of the ray to the left. In order to measure the extent of the rotation, the solution for trial is placed in a long glass tube shown at o o (fig. 108), closed at the two ends by flat plates of glass. This tube is placed

FIG. 108.

חד

9

B

within a metallic tube, r s, for the purpose of excluding stray light. A beam of homogeneous light, obtained by transmission through red glass, is polarized by reflection from the mirror of black glass a b. A Nicol's prism,t or other pola

* Circular polarization was discovered by Fresnel, and is quite distinct from the phenomenon now under consideration.

The Nicol's prism affords a convenient means of obtaining a polarized beam, depending upon the principle of total reflection (102). It is prepared in the following manner: A long rhomboidal prism of Iceland spar, the base of which is equal to one-third of its length, is divided in half by a plane perpendicular to the plane of the longer diagonal of the base; the line of section

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COLOURED ROTATORY POLARIZATION.

251

rizing eye-piece, n, is so mounted as to admit of rotation around the line di; this eye-piece is provided with a vernier, m, which traverses a circle p 9, divided to degrees, for the purpose of measuring the angular rotation of the eye-piece. The eye-piece is then so adjusted that, when the polarized beam becomes no longer visible, the vernier stands at o°. Now, if the tube, o o, full of solution, be placed on the supports, A, B, so that it shall be traversed by the reflected ray, i d, light becomes visible to the observer at n, but on causing the eye-piece to rotate to the right or to the left (according to the nature of the solution), the image again disappears: the amount of the movement to the right or to the left expresses the amount of rotatory power exerted by the liquid under the cir

cumstances.

An experienced observer usually substitutes the white light of day for that of the red glass. In this case the rotatory power is measured from a particular violet, the sensitive or transition tint, the teinte de passage of French writers, which, from the suddenness with which by a slight rotation it passes into red on the one side, or into blue on the other, is the most favourable for accurate observation. The tube, with its liquid contents, is interposed between the polarizing mirror and the eye-piece, previously adjusted to zero, and the rotation is estimated by the angular motion necessary to produce the violet tint.* This colour is complementary to the yellow of the spectrum, and is therefore produced when the latter colour is replaced by the black band; as we have seen above, this extinction of the yellow light is effected when the polariscope contains a plate of quartz 3.75 mm. thick, whilst the polarizer and analyser are parallel,

for the angle through which the analyser must be turned, in order to stop the yellow light, is 90° from the crossed position.

The most delicate method of employing the sensitive tint in the determination of the rotation produced by a liquid is to place in the instrument a biquartz, that is, a combination of two pieces of quartz, one right-handed and the other left-handed, and placed side by side, so that half of the light reaching the eyepiece passes through one and half through the other. If these pieces of quartz are 3'75 m. thick, they will both show the sensitive tint when polarizer and analyser are parallel. A movement of the analyser to the right will cause the colour of the right-handed quartz to appear red, while that of the left-handed quartz will change to blue. If, therefore, the analyser is so placed that the index points to o° when the sensitive tint is seen on both halves of the field of view, and a body producing right-handed rotation is introduced, an effect on the colour is produced identical with that which would occur by increasing the thickness of the right-handed and diminishing the thickness of the left-handed quartz-the right-handed would appear blue, showing that the analyser is not sufficiently turned to the right, and the left-handed would be red, showing that the analyser is too much turned to the left. On now rotating the analyser to

passing through the opposite obtuse solid angles of the prism, so as to divide it obliquely into two equal portions; the two halves of the prism are then re-united by means of Canada balsam. When light is transmitted through the prism parallel to its length, the incident light falls very obliquely upon the layer of Canada balsam; and, as the balsam has a smaller refractive index than the ordinary ray, this ray experiences total reflection, whilst the extraordinary ray alone is transmitted, because, the refractive index of the balsam being greater than that of the extraordinary ray, total reflection does not occur

in its case.

Full details of the most approved method of conducting the operation are given by Clerget, Ann. Chim. Phys. 1849 [3], xxvi. 175.

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COLOURED ROTATORY POLARIZATION.

[126.

the right, the sensitive tint is reproduced in both halves of the field of view. The angle through which the analyser must be rotated to produce this result is the power which the introduced body possesses of rotating the plane of polarization of yellow light. In Soleil's saccharimeter, which is employed for the determination of the quantity and kind of saccharine bodies present in a solution, the angle of rotation is not directly measured, the effect produced by the sugar solution being neutralized by the alteration of the thickness of a plate of quartz, by the introduction of two wedges of this material between the polarizer and analyser. As a figure and full description of this apparatus are given in Part III. of this work (1555), it will be merely necessary to describe in general terms the principle of the instrument. The light is polarized by means of a doubly refracting or by a Nicol's prism, and then passes through a biquartz, beyond this is placed the tube containing the saccharine liquid, and in front of the tube is a piece of left-handed quartz, followed by two wedges of right-handed quartz. These wedges are attached to slides, moveable in opposite directions by a pinion, so that when the wheel is turned in one direction the narrow ends of the wedges are introduced into the path of the rays, and the combined thickness of the plate increased; reversal of the motion of the pinion diminishes the thickness of the layer. One of the slides holding the wedges is provided with a scale, and the other with a pointer or vernier, and when this arrangement marks o°, the combined thickness of the two wedges is equal to that of the plate of quartz behind them, which being of opposite rotation, completely neutralizes their action. The eye-piece consists of a small Galilean telescope, focussed to give a clear definition of the division of the biquartz. The polarizer and analyser are so fixed that when the index points to o°, the transition tint is seen in both parts of the biquartz on the introduction of a tube containing a rotating liquid, the colours of the two halves of the field change, and must be brought back to their original appearance by a movement of the compensating wedges. The index then shows a number which indicates the increase or diminution of the thickness of the quartz in hundredths of a millimetre, which may be transformed into angles of rotation for any particular colour, by help of the table previously given, indicating the rotation produced by a plate of quartz of the thickness of Imm.. For the yellow light from a sodium flame, for example, each division will correspond to a rotation of 2166°, and for the mean yellow of 24°. When the sugar solutions are coloured, which not unfrequently happens, the colour of the transition tint is somewhat affected; this difficulty is overcome by placing another Nicol's prism and plate of quartz either between the source of light and the polarizer, or between the analyser and the eye-piece; by turning this combination, the colour of the whole field of view is altered, and the effect of the coloured liquid may be neutralized. Soleil's apparatus can be used only for those liquids which, like sugar solutions, rotate the planes of polarization of the more refrangible rays more powerfully than those of the less refrangible; for other bodies different instruments must be employed.

A convenient instrument is Wild's Polaristrobometer (Pogg. Ann. 1864, cxxii. 626, and Dingler's Pol. Journ. 1869, cxciv. 338), which depends on the principle of Savart's polariscope, and is more accurate and more easily used than Soleil's saccharimeter. The light entering the instrument is polarized by a Nicol's prism, and then passes into the body of which the rotatory power is to be determined, and afterwards through the Savart's arrangement. In the earlier forms of apparatus, two pieces of quartz 20′ mm. thick were used, cut with their surfaces at 45° to the axis of the crystal, and placed in a crossed position, with their principal sections making angles of 45° with the vibration plane of the analyser, which consists of a second Nicol's prism. In the more recent instruments, two pieces of Iceland spar 3mm. thick are employed instead of the quartz. The

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253

analyser is fixed, but the polarizer is attached to a graduated circle, turned by a milled head near the eye piece, the divisions being read by means of a microscope or by the help of a vernier. In using the instrument, it is most convenient to employ a Bunsen flame coloured yellow by means of a bead of sodic chloride or carbonate, supported on platinum wire. To adjust the apparatus, the graduated circle is turned until the o° of the scale coincides with the o° of the vernier, and the polarizing Nicol turned in its socket until the dark lines on the field of view have disappeared, which takes place when the vibration plane of the polarizer coincides with one of the vibration planes of the pieces of Iceland spar. A tube containing the solution to be examined is now introduced, when the dark lines again become visible; by turning the graduated circle until the lines again disappear, the rotation of the yellow ray is at once ascertained. A skilful observer can determine the rotation to one minute of arc.

Jellett (Proc. Roy. Irish Acad. 1860, vii. 348) described an analysing prism, which he subsequently (Proc. Roy. Irish Acad. 1864, viii. 279) applied to a saccharimeter, the readings of which are very accurate. The analyser is made by cutting a square prism from a rhombohedron of Iceland spar by planes perpendicular to the edges of the crystal, the ends of the prism are then cut at right angles to the sides. On looking longitudinally through such a prism a double image is seen, the line joining the two images being coincident with one of the diagonals of the end of the prism. The prism is now bisected longitudinally by a plane, making with one of the diagonals an angle of 2 or 3 degrees, and the halves are cemented together in a reversed position. On viewing a small circular aperture through the compound prisun a disk is seen in the centre consisting of the ordinary beams, and two half disks, separated from the central one, consisting of the two extraordinary beams. The disk in the centre is therefore composed of light, half of which has passed through one side of the prism, the other half having passed through the other side, and polarized in planes inclined to one another at an angle of 4 or 6 degrees; consequently, on examining the light by a Nicol's prism, it will not be possible to quench the light of both halves of the disk simultaneously; when the plane of vibration of the Nicol is equally inclined to the vibration planes of the two halves of the compound prism, the two halves of the disk will be equally illuminated. In the saccharimeter, the liquid to be examined is placed in a tube closed with glass plates, and capable of being raised or lowered in a wider vessel containing oil of turpentin, of a rotation opposite to that of the liquid under examination; the length of the column of turpentin necessary to neutralize the effect of the rotating liquid is measured by a vernier. Cornu (Bull. Soc. Chim. Paris, 1870, xiv. 140) has employed Jellett's prism, in conjunction with a Nicol, reading the rotation directly on a graduated circle.

It is remarkable that the vapours of oil of turpentin and of some other liquids which exhibit the power of coloured rotatory polarization, display the phenomenon when seen through very long tubes, though more feebly than the liquids themselves.

Sir Charles Wheatstone has discovered that when a ray of light is polarized by a plate of black glass, transmitted through a film of a crystal of quartz cut parallel to the optic axis, and then reflected from a plate of polished silver at an angle of 18°, it exhibits all the phenomena of circular polarization when examined by means of a Nicol's prism. A plate of quartz cut perpendicularly to the optic axis behaves when examined in this manner as it would when observed with rectilinear polarized light. (Proc. Roy. Soc. 1871, xix. 381.)

(127) Magnetic Polarization.-Faraday discovered another modification of coloured rotatory polarization, which homogeneous