mannitan, mannitan tetracetate, mannitan monochlorhydrin are rightrotating; whilst mannite dichlorhydrin, crystallizable mannitan, and mannitone are left-rotating (Vignon,' Bouchardat”). By oxidation of dextro-camphor with nitric acid we obtain, simultaneously with rightrotating camphoric and camphic acids, left-rotating camphoronic acid as well (Montgolfier).

Lastly, the remarkable fact must be mentioned that in certain cases active substances exhibit changes in the direction of their rotatory powers, when dissolved in various liquids or when certain substances are added to their solutions. Asparagin and aspartic acid are left-rotating in alkaline (i.e. sodic, or ammoniacal) solutions ; but in acid (i.e. hydrochloric or nitric acid) solutions, on the contrary, they are right-rotating (Pasteur“). The acid ammonium salt of lævo-rotatory malic acid exhibits left-handed rotation in aqueous and ammoniacal solutions; in nitric acid it forms a right-rotating solution (Pasteurt). The calcium salt of dextro-tartaric acid is dextrorotatory in aqueous and lævo-rotatory in hydrochloric acid solution ; whilst, on the other hand, lævo-tartrate of lime is dextro-rotatory in hydrochloric acid solution (Pasteur”). An aqueous solution of mannite, which, as such, manifests a very feeble left-handed rotation, becomes strongly lævo-rotatory, on addition to the solution of certain alkalies (as caustic potash, caustic soda, magnesia, lime, baryta), and dextro-rotatory, in presence of salts of the alkalies (as borax, chloride of sodium, sodium sulphate, potassium hydrarseniate). Ammonia renders it feebly dextro-rotatory, but acids have no effect upon it (Vignon, Bouchardat,” Müntz and Aubins).

Similar properties are exhibited to a remarkable extent by ordinary tartaric acid. In aqueous solution it is dextro-rotatory, whilst in the solid state it may assume a lævo-rotatory power (s 19). The rotatory power of its aqueous solutions is very considerably increased by the addition of even small quantities of boric acid, or borax; on the other hand, it is diminished by the addition of sulphuric, hydrochloric, or citric acid, and also of alcohol or wood-spirit (Biot').

1 Vignon: Jahresb. für Chem. 1874, 885. ? Bouchardat: Jahresb. für Chem. 1875, 790—792. 3 Montgolfier: Jahresb. für Chem. 1872, 569. 4 Pasteur : Ann. Chim. Phys. [3], 31, 67. Jahresb. für Chem. 1851, 176. 5 Pasteur: Ann. Chim. Phys. [3], 28, 56. Jahresb. für Chem. 1849, 128. 6 Vignon : Ann. Chim. Phys. [5], 2, 433. Jahresb. für Chem. 1874, 884. 7 Bouchardat: Comptes Rend. 80, 120. Jahresb. für Chem. 1875, 145. 8 Müntz and Aubin : Ann. Chim. Phys. [6], 10, 553. Jahresb. für Chem. 1876, 149. 9 Biot: Mém. de l'Acad. 16, 229.



If, moreover, tartaric acid is dissolved in acetic ether or acetone, the resulting solutions, which either are inactive or may exhibit a feeble lævo-rotation, become immediately dextro-rotatory, on the addition of a little water. Malic acid

Malic acid appears to possess similar peculiarities. Phenomena of this sort differ from those exhibited by derivatives, in that the changes in the direction of rotation are temporary only, and disappear with the removal of the substances which induce them.

The whole series of phenomena of this kind require, however, fuller investigation before the subject can be properly explained.



$ 17. Amount of Rotation dependent on the Thickness of the Medium.From experiments with quartz, Biot, in 1817, deduced the following laws:

1. The angle, through which the plane of polarization of a ray of given wave-length rotates, is directly proportional to the thickness of the quartz plate.

2. Dextro-rotatory and lævo-rotatory plates of quartz of equal thickness, cause the plane of polarization to deviate through equal angles. If the ray be transmitted through more plates than one, the final deviation is equal to the sum of the individual deviations if the plates all rotate in the same direction, and to their collective differences if they rotate in different directions.

To allow comparison to be made of the rotatory powers of different active crystals, Biot proposed to adopt as a standard the angle of rotation afforded by plates 1 millimetre (.039 in.) in thickness.

In active liquids (as, for example, oil of turpentine, or solutions of active solid substances in inactive liquids) the following laws have been observed :

1. The angle of rotation is directly proportional to the thickness of layer traversed by the ray.

2. When a ray is transmitted through several media, the observed rotation will be the algebraical sum of the individual rotations. As the rotatory power is generally much weaker in liquids

1 Biot: Mém. de l'Acad. 2, 41.

than in crystals, Biot proposed that the angle of rotation for thicknesses of 1 decimetre (3.9 in.) should be taken as the standard of comparison for the former.

§ 18. Amount of Rotation dependent on the Wave-length of Transmitted Ray. "Rotatory Dispersion.-If a series of polarized rays of different colours be transmitted successively through an active medium, it is found that the amount of rotation which the plane of polarization experiences, varies with the wave-length of the ray, being least for red, and greatest for violet.

From his experiments with quartz, Biot arrived at the conclusion, that the angle of rotation a varies inversely almost exactly as the square of the wave-length of ray d, but this has not been confirmed by

B later observers. The formula a

in which A and B are


A +

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a =

two constants, has also been found unsatisfactory; whereas the equation since proposed by Boltzmann,



1? 14' which, like the preceding, contains two constants only (B and C), and which is based upon the assumption that rotation in a ray of infinite wave-length 0, has been shown to agree very closely with the results of observation.

For a complete determination of the rotatory power of a given substance, it is necessary to take the angles of rotation for a number of different rays of known wave-lengths. This can only be fully accomplished with the aid of Fraunhofer's lines ; that is, by the use of solar light, the deviations being determined by the method of Broch (S$ 61, 62, 63). V. von Lang has lately employed artificial light, the lithium, sodium, and thallium rays, for the same purpose.

In the case of quartz, the angles of rotation for different lines have been accurately determined by Broch, Stefan,4 Soret and Sarasin, and von Lang. The table on page 44 contains the observations of Stefan and von Lang, along with the corresponding wave-lengths i, expressed in millimetres.

1 Boltzmann: Pogg. Ann. Jubelband, p. 128.

von Lang : Pogg. Ann. 156, 422.
3 Broch: Dove's Repert. d. Phys., 7, 115.
4 Stefan : Sitzungsber. der Wiener Acad. 50. Pogg. Ann. 122, 631.
5 Soret and Sarasin : Pogg. Ann. 157, 447.
von Lang : ut supra.




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a =


From the foregoing measurements Boltzman has deduced the dispersion-formula

7.07018 0.14983


106.12 101214 which does not differ from the results of actual observation by more than the hundredth part of a degree.

For ray D different observers have obtained the following values :-Biot, 20.98°; Broch, 21.67° + 0.11; Stefan, 21.67o; Wild, 21.67o ; von Lang, 21•64° at a temperature of 13.3o Cent.; Soret and Sarasin 21.80°, at about 35° Cent. According to Scheiblero, quartz from different places, and even from the same place, is not quite constant in its rotatory power.

As von Lang has shown, the rotatory power of quartz increases with rise of temperature, the relative alteration for different rays remaining the same. At 0° we have


21:597° and for any given temperature t,

Q= a, (1 + 0.000149 t). According to the later researches of Sohncke,

at = a. (1 + 0.0000999 t + 0.000000318 t?) expresses the value more accurately.

Extending the investigation to other substances, we find that not only do the absolute values of rotation in any one substance vary for different rays, but also in different substances the values vary by a different series of proportions—that is, different bodies have different powers of rotatory dispersion.


Th. 26.533°

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1 Wild : Ueber ein neues Polaristrobometer. Berne, 1865, p. 55. 2 Scheibler : Zeitsch. des Vereins für Rübenzuckerindustrie. 1869, p. 388. 3 Sohncke: Wied. Ann. 3, 516.

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