By taking as unit-density that of water at 4° Cent., we make density synonymous with weight in grammes of 1 cubic centimetre of the substance, and the specific rotation of any active substance may then be defined as the deviation produced by 1 gramme of the substance when occupying a space of 1 cubic centimetre, and forming a column of 1 decimetre in length for the ray to traverse. The diameter of the column is thus immaterial.

Moreover, since not only the density, but apart from that the rotatory power of an active liquid, is affected by changes of temperature, the specific rotation will vary with the temperature, and it therefore becomes necessary to record the readings of the thermometer when a and d are observed. At any given temperature, the specific rotation of an active liquid in a state of purity is always constant.

§ 21. For active solid substances brought into the liquid state by solution in optically inactive and chemically indifferent solvents, the specific rotation is determined as follows :-Let P grammes of the active substance be dissolved in E grammes of inactive liquid, and d be the density of the resulting solution. Then the latter will

Р contain in unit volume (cubic centimetre) P+El grammes of active substance.

If a solution of the above composition, in a tube 1 decimetres long, gives an angle of rotation a, then the deviation for a solution containing 1 gramme of active substance in 1 cubic centimetre of solution-i.e., the specific rotation [a]-is deducible from the proportion


d: ^ = 1: [a],

P + E whence,

a (P + E) [a]

1. P.d

If, with Biot, we indicate

that is, the amount of active

P + E' substance in the unit weight of solution, by e, then


1.6.d Lastly, if the proportion of active substance be stated for 100 parts by weight of solution, so as to make the numbers more con


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venient for reference, and this proportion be indicated by p, the formula becomes

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For the calculation of specific rotation by these formulæ, the percentage weight and the density of the solution must be known. But since pd = the concentration that is, the number of grammes of active substance in 100 cubic centimetres of the solution—we need not determine p and d separately. We have simply to dissolve a certain weight K (grammes) of the active substance in a graduated measure of known capacity V (cubic centimetres), and dilute the solution to the mark. Then we have

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100 a



lc The specific rotation of a large number of active substances has been thus determined, without regard to the densities of the solutions employed. But the method in many cases is insufficient. As will presently be seen, specific rotation calculated from solutions is not constant, but varies with the proportion of inactive substance present in each case; and although this can be allowed for when the weight per

; cent. composition of the solution is known, it is not possible to do so when only the concentration is stated. In preparing solutions, therefore, by means of a graduated flask, it is always necessary, for the sake of determining p and d, that the weight of the contents should be ascertained after the vessel has been filled up to the mark.

In cases where the length of tube is given in millimetres, indicated by L, the foregoing formulæ appear as below :

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$ 22. Influence of Temperature on Specific Rotation.-A decrease in the angle of rotation is observed in active substances when the temperature is increased. This is primarily a direct consequence of the decrease of density; whilst, on the other hand, there is a simultaneous increase in the length of the tube, producing an opposite effect, but in much feebler degree. In the calculation of specific

, rotation, this element of variation is eliminated when the density and length of tube’ are determined for the same temperature as the angle of rotation ; and were such the only element of variation the value [a] would be the same for all temperatures. Such, for example, is the case with aqueous solutions of cane-sugar according to Tuchschmid.3 In most substances, however, the angle of rotation and the density do not vary together equally when the temperature is raised, since increase of rotation is observed as a result in some substances as well as decrease. Hence there must be some other influence at work independently of altered density and consequent on intramolecular changes produced by the action of heat. So far as at present known, the most usual result is a decrease ; this has been observed in invert-sugar (Clerget, Tuchschmid), quinine, quinidine, cinchonine, cinchonidine, quinine disulphate, quinidine disulphate, thebain, santonate of soda (Hesse), gelatine (De Bary). The completest observations on the influence of increase of temperature are those of Gernezi on the specific rotation of certain ethereal oils, the decrease in which may be expressed for temperatures between 0° and 150° Cent., as follows:Oil of turpentine [a]!= 36.61 – 0.004437 t.

[a]}=115:31 – 0.1237 t-0.000016 to.

Bigarade essence [a]=118:55 – 0.11751 -0.00216 to.

?. The decrease, as Gernez found, still goes on after the boilingpoint is exceeded and the substance takes the gaseous form. The dispersive powers, on the other hand, were not influenced by heat.

Oil of orange

For example, within ordinary temperatures, an increase of 1° Cent. causes a reduction of the angle of rotation in a tube 2 decimetres long, as follows:In Nicotine

by 0.1° Oil of turpentine

0.06° Oil of bitter orange


0.38° Aqueous solution of invert-sugar, with

0.22° 17 grammes per 100 cub. cent. solution The variations are, therefore, somewhat considerable in amount, and hence it is necessary that the solutions under observation should be kept at an uniform known temperature.

2 In glass tubes this may be found from the length as measured at ordinary temperatures, by means of the coefficient of linear expansion 0.0000085 for 1° Cent.

3 Tuchschmid : Journ. für prakt. Chem. [2], 2, 235, 4 Gernez : Ann, de l'école norm. 1, 1,

Oil of orange :


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In tartaric acid, on the contrary, solid as well as in solution (Biot, Tuchschmid) an increase of specific rotation is observed with increase of temperature for all rays of the spectrum, and in solutions of all degrees of concentration, but in unequal amounts. How variable the values obtained may become in this substance is shown by the observations of Krecke in the table annexed :

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Among tartrates, Krecke found that neutral sodium and sodiumpotassium tartrate showed a slight increase ; tartar emetic, on the contrary, a decrease. Lastly, in malic acid (Pasteur) and nicotine (see $ 32) an increase also of specific rotation with increase of temperature has been observed.

Hence in all specific rotation data the temperature at which the angle of rotation and the specific gravity (or concentration) of the solutions have been observed should be given.

B. Dependence of Specific Rotation on the Nature and

Amount of the Solvent.

$ 23. The first substance of which the specific rotation was determined by Biot+ (1819) was cane-sugar. He found that with tubes of 1 Biot: Mém. de l'Acad. 16, 229.

2 Tuchschmid : ut supra. 3 Krecke: Arch. Néerland, 7, 97 (1872). 4 Biot: Mém. de l'Acad. 2,41 (1819), 13, 39 (1832).


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equal length the angles of rotation were in direct proportion to the amounts of sugar in solution, so that the value for [a] was constant whatever the degree of concentration of the solution. The same result was obtained with mixtures of oil of turpentine and ether. Biot therefore assumed that the amount of deviation is simply proportional to the number of optically active molecules encountered by the ray in its passage through the solution, and thence formulated the following axiom :

“When an optically active substance is dissolved in an inactive liquid, which exerts no influence upon it chemically, the deviation is in direct proportion to the quantity of active substance in the unitvolume of solution, and thus specific rotation [a] is determinable from the equation [a] = Tema." (See $ 21.) a

) 1..d Subsequently (1838), from experiments with aqueous solutions of tartaric acid, Biotfound that the specific rotation of this substance increases in proportion as the solutions are more dilute. This was long regarded as an exceptional case, until (in 1852) Biot?, with the aid of improved polariscopic apparatus, found that similar phenomena are exhibited by other substances. Alcoholic and acetic solutions of camphor, for example, were found to show a decrease of specific rotation in proportion to the diluteness of the solutions. With oil of turpentine, on the contrary, an increase was observed on the addition of successive quantities of alcohol or olive-oil; and lastly, even in the case of sugar, a feeble increase with the amount of water in the solution could be detected. Moreover, the influence of the nature of the solvent medium was brought to light, as it was found that different values of [a] for camphor were obtained, according as solution was effected in alcohol or in equal weights of acetic acid. Hence Biot concluded generally that the values of specific rotation deduced from solutions are more or less variable; so that the phenomena cannot, as at one time, be regarded as the result of mere mechanical diffusion of active molecules in an optically indifferent medium.

This fuller and more correct view of specific rotation has, however, remained in a great measure unheeded. The fact that in solutions of cane-sugar the angle of rotation is almost exactly proportional to the degree of concentration, so that the saccharine strength of a solution can be deduced from the deviation observed therein, has

1 Biot: Mém. de l'Acad. 15, 93 ; Ann. Chim. Phys. [3], 10, 385.
2 Biot: Ann. Chim. Phys. [3],,36, 257.

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