1:39 1.40 1.20 1:53 1:36



For example, taking the following observations:-
B с D E F

G Quartz 1 millim. 15.50° 17.22° 21.67° 2746° 32-69°

42:37° Sugar

[a] 1 decim. + 47.56° 52.70°66.41° 84.56°101:18° 131.96° Cholalic Acid [a]

+ 28.2°

30.1° 33.9° 44.7° 52.7° 67.7° Cholesterin


20.63° 25.54°31:59° 39.91° 48.65° 62:37° Oil of Turpentine


23.4° 29.3° 36.8° 43.6° 55.9° Oil of Lemon + 34:0° 37.9° 48.5° 63.3° 77.5°

106.0° and calculating the ratios of rotation experienced by rays C, D, E, F, G, as compared with that by ray B, we get the following results :


G Quartz 1 1.11

1.77 2:10 2:72 Sugar 1 1:11

2:13 2.77 Cholalic Acid



1.87 2.40 Cholesterin 1 1.24

3:02 Oil of Turpentine


2.60 Oil of Lemon 1 1:11 1:43

3.12 It will be seen that the ratios in the case of


and quartz agree very closely. These two substances have thus equal powers of rotatory dispersion, while the others have either less or more than quartz. This fact has been turned to account in the construction of the Soleil (and Ventzke-Scheibler) saccharimeter, the principle of which supposes the rotatory dispersion of the active substance to be equal to that of quartz. But, so far as we know, this is only the case with cane-sugar, so that other substances cannot be properly examined with instruments of this description.

In the majority of cases, the determination of the rotation for several rays would be too troublesome, and it is considered sufficient to determine it for a single ray. In Wild's polariscope, and in the so-called "half-shade" instruments of Jellett, Cornu, and Laurent, the light is supplied by a sodium flame, thus giving the angle of rotation for ray D of the solar spectrum. If a polariscope consisting simply of two Nicol prisms be used, it is requisite to employ monochromatic light (sodium flame) in order to get reliable results. With Soleil's saccharimeter, as well as those of Ventzke, Scheibler, and Hoppe-Seyler, which are all made on the same optical principle, white (gas-lamp) light is used, and the rotation given is for the so-called transition tint—that is to say, the colour complementary

1 The values for oils of turpentine and lemon (given by Wiedemann, Pogg. Ann. 82, 222) are the angles of rotation a, directly determined with a layer 1 decimetre in depth ; whilst those for cane-sugar (Stefan, Sitzungsber. der Wiener Acad., 52, 486, II“ Abth.), anhydrous cholalic acid (Hoppe-Seyler, Journ. für prakt. Chem. 89, 257), and cholesterin (Lindenmeyer, Journ. für prakt. Chem. 90, 323), express the specific rotation [a]. For cholesterin the solvent used was alcohol ; for sugar and cholalic acid, water.

Aj =


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1: 1.131
1: 1.129
1: 1.198
1: 1.243

to mean yellow light—the wave-length of which may be taken at about 0.00055 millimetre. The angle of rotation and the specific rotation thus obtained are indicated by a; and [a] (jaune moyen) respectively, as proposed by Biot.

Now the wave-length of this mean yellow light is less than that of the ray D, which lies on the border between orange and yellow, so that the value of a; is always less than that of ap! For example, with quartz, according to Broch, ap = 21.67°, and a; = 24.5°, so that, to express the one in terms of the other, we have


ap= 1.1306ap, or approximately = / ap; 21:67

21.67 ap

a; = 0.8845aj, or approximately 8/9

24.5 The proportion, however, between a; and ap varies in different

; substances, according to their different rotatory dispersions. J. de Montgolfier" has determined it in the following

Quartz (according to Broch)
Aqueous solutions of Sugar
Alcoholic solutions of Camphor

Oil of Turpentine According to L. Weiss, in aqueous solutions of sugar containing 5 to 19 grammes in 100 cubic centimetres, the proportion is ap: aj

1 : 1:034. In any other substance, the rotation for one ray can be estimated from that for the other only approximately, by assuming that the rotatory dispersion of the substance agrees with that of some one of the preceding. As the transition tint corresponds to no sharply-defined ray, its use

, is attended with inconvenience, and latterly has been mostly abandoned.

Many older observations are in existence, made by Biot with red light, obtained by transmission through glass coloured by suboxide of copper, with a refrangibility about equal to that of Fraunhofer's line C. Assuming that, on passing through a quartz plate 1 millimetre thick, it experienced rotation through an angle of 18·414°, Wild4 calculates its wave-length to be 0.000635 millimetre. The ratio between this red ray and the transition tint Biotó gives as 23 : 30. By many observers the values of


and have been taken as equal, a confusion which has been remarked upon by J. Montgolfier, Bull. Soc. Chim. 22, 487, and Riban, idem, 22, 492.



? Montgolfer: Bull. Soc. Chim. 22, 489. 3 Weiss : Sitzungsber. der Wiener Acad. 69, 157, IIIte Abth. 4 Wild : Polaristrobometer,

5 Biot: Mém. de l'Acad. 3, 177.


p. 35.




$ 19. Abnormal Rotatory Dispersion. - Although in ordinary cases the angle of rotation increases pari passu with the refrangibility of the ray, there are exceptions, as Biot,' and later Arndtsen, have noticed in aqueous solutions of dextro-tartaric acid. This acid exhibits, in a remarkable degree, the property that its specific rotation [a] ($ 24) increases with the diluteness of the solution from observation of which it is calculated. The increase is directly proportional to the dilution, and may be expressed by the formula [a] = A + B q, where q represents the percentage by weight of water in the tartaric acid solution. Arndtsen has determined by Broch's method the deviations for the Fraunhofer lines C, D, E, b, F, e, in a series of solutions of different degrees of concentration, at a temperature of 24° Cent., from which he deduces the subjoined values for the constants A and B in the preceding formula :

[a]c = + 2.748 + 0.09446 a
[a] + 1.950 + 0.13030 9
[a]E = + 0.153 + 0.17514 9
[a]o 0.832 + 0.19147 a
[a]F 3.598 + 0·23977 9

[a]e 9.657 + 0.31437 9 Computing from these formulæ the specific rotation for solutions containing from 10 to 90 per cent. of tartaric acid, we get the annexed results :


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1 Biot: Mém. de l'Acad., 15, 93. 2 Arndtsen : Ann. Chim. Phys. [3], 54, 403. Pogg. Ann. 105, 312.

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From this table it appears that every solution exhibits a maximum of rotatory power for some one particular colour (as will be seen from the bracketed figures). In the most dilute solutions, containing 10 per cent. only of tartaric acid, the maximum is found, in its normal position, under the most refrangible ray e; but as the concentration of the solution is increased it shifts towards the red end of the spectrum, and in the case of solutions containing 40 to 50 per cent. is found under the green rays. In 80 and 90 per cent. solutions the rotatory dispersion is entirely changed; dextro-rotation is there at its maximum for the red rays, and decreases as the refrangibility of the rays increases, until under the blue ray it passes into lævo

, rotation. Such is the case also with anhydrous tartaric acid. Now, according to the preceding formula of Arndtsen, this should be dextrorotatory for the rays C, D, E, lævo-rotatory for b, F, e, and inactive for light between E and b, and Biot 1 actually observed these phenomena in cast plates of tartaric acid ; moreover, Arndtsen ? observed that the left-handed rotation for highly refrangible rays occurs when concentrated alcoholic solutions of this acid are used.

The anomalies of rotatory dispersion in tartaric acid disappear when the solutions are exposed to higher temperatures (Krecke"), or when mixed with a small quantity of boracic acid (Biot); moreover, they do not occur in the tartrates.

Similar conditions may be produced artificially by mixing dextro- and lævo-rotatory solutions together in certain proportions. Biot* in this way obtained an achromatic compensation of the rotation

4 for certain rays.

Lastly, as regards the influence of temperature on rotatory dispersion, Gernez discovered that the application of heat, even to the extent of complete evaporation, produces no change in the dispersive powers of oils of turpentine, orange, bigaradia, and camphor.


1 Biot: Ann. Chim. Phys. [3], 28, 351. 2 Arndtsen : Ann. Chim. Phys. [3], 54, 415. 3 Krecke: Arch. Néerland, Bd. 7 (1872). 4 Biot: Ann. Chim. Phys. [3], 36, 405. 5 Gernez: Ann, de l'école norm. 1, 1,




A. Definition of Specific Rotation.


$ 20. In the discussions that follow certain abbreviations have been adopted viz. :

a, the observed angle of rotation for a given ray. l, the length of liquid column used, in decimetres. d, the density of the rotatory liquid. P, the weight of active substance in 100 parts by weight of solution (per cent.

composition). 9, the weight of inactive liquid in 100 parts by weight of solution. c = p d, the number of grammes of active substance per 100 cubic centimetres of

solution (concentration).

In comparisons of the rotatory powers of different substances it is not enough, as Biot? first showed, merely to take account of the angles of rotation observed in layers of a uniform length of 1 decimetre. It must be remembered that when different active substances, ordinarily liquids (as oil of turpentine, amylic alcohol, nicotine, &c.), are placed in turn in the tube of a polariscope, very different masses of molecules will be brought to bear upon the transmitted rays in accordance with the different densities of the liquids. Therefore, before any just comparison can be made, the observed angles of rotation must be calculated to some common standard of density. If the density 1 be taken, the angles of rotation a of the several liquids must be divided by their specific gravity d. The angle of rotation given by a length of 1 decimetre of any active liquid, corrected to the standard density 1, is denominated by Biot the specific rotation [a] of that substance, and may be found from the observed data a, l, and d, by the formula I.

7. d
| Biot: Mém. de l'Acad. 13, 116 (1835). Ann. Chim. Phys. [3], 10, 5.


[a] =



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