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which only differs from that obtained by Tollens by 0.26°.1 Tollens has attempted, as Biot3 had already done, to determine the rotatory power of anhydrous sugar directly, by employing plates cast from the melted substance. In this way he obtained a value considerably below that of the calculated specific rotation, viz., [a] = 46.9°. This is not surprising, as under the influence of heat sugar undergoes various important changes, as indicated by the assumption of a yellow coloration, as well as a strong reducing action on cupric salts. Even after solution in water, such a sugar exhibits a notably smaller rotatory power than before fusion, and the decrease is greater in proportion to the length of time during which it was kept fused (Hesse1). Probably, in such cases a formation of inactive glucose takes place.
§ 38. The true specific rotation of right-handed glucose (grapesugar) has been determined by Tollens both for the hydrate C, H12 O + H2O, and the anhydrous substance.
In the subjoined table are given the solutions employed (with p per cent. by weight of glucose), along with the values of [a]D observed in each case, and side by side the values calculated from the interpolation-formulæ given below.
1 This trifling difference is partly explained by Tollens having taken the specific gravity of the sugar solutions at a temperature of 17.5 Cent., whilst Schmitz took it at 20° Cent. The angles of rotation were observed by both at a temperature of 20° Cent. 2 Tollens: Ber. der deutsch. chem. Gesell. 1877, 1413.
3 Biot Mém. de l'Acad. 13, 130.
4 Hesse: Liebig's Ann. 192, 167.
5 Tollens: Ber. der deutsch. chem. Gesell. 1876, 1531.
(As the molecular weights of C H12 О6 + H2 O and C ̧ H12 06, and, therefore, also the corresponding values of p for the two substances, are in the ratio 198: 180, or 11: 10, the specific rotation of the hydrate and the anhydride must stand to each other in the inverse ratio 10: 11.)
As will be seen, the specific rotation increases with increase of concentration, or, conversely, decreases with increased dilution. Glucose thus exhibits a behaviour the reverse of that of cane-sugar. For glucose hydrate, the experiments gave the formula [a]D = 47.925 +0.015534 p + 0.0003883 p2;
or, with reference to q, the percentage of water present in the solution : [a]D = 53.362 0.093194 g + 0·0003883 q2.
For anhydrous glucose, by raising the preceding values by onetenth, we get the equations
[a]D = 52-718+ 0.017087 p + 0.0004271 p2,
[a]D =58-698-0.10251 q +0.0004271 qo.
Lastly, from the foregoing formulæ we get, as the true values of the rotation-constants,
$39. Camphor, cane-sugar, and glucose1 are the only solids, up to the present time, the direct specific rotations of which have been accurately determined. Numerous investigations, indeed, have been published as to the variation of the specific rotation in a large number of substances, but the observers have, as a rule, employed only solutions containing small percentages of active substance, so that only a few points have been determined, and that at the outer end of the respective curves, where the variation of rotatory power is at its maximum. From results of this kind the value for A cannot be determined. But, indeed, this were impossible at any rate, from the fact that neither the percentage composition by weight nor the density of the solutions is stated, but merely their concentration, i.e., the number of grammes of substance in 100 cubic centimetres. For the determination of individual values of [a] this is enough; but, as before explained (§ 25), it is altogether insufficient for determining the value of A.
Nevertheless, in chemical writings we still find many specific
1 Arndtsen (see § 19) has determined for tartaric acid the relation between specific rotation and percentage of water, and hence deduced the formula [a]=1·95+0·1303 q, which gives the value for the pure substance ДD=1.95. However, as the number of solutions observed was but small, a verification of the constants given is desirable.
rotation-data based on the old view that the value is constant, and may be obtained by observation of a single solution of any optically-active substance. Accordingly, neither the weight-percentage of active substance nor the concentration is stated, and in most cases no reference is made to the ray with which the observations were made. For example, in many text-books the specific rotation of tartaric acid is given briefly thus: [a] = +9.6°; whereas, as we have seen from the table already given (§ 19), the specific rotation in solutions containing 10 to 90 per cent. of this substance varies for the yellow ray D from 3.25° to 13.68°; for the green ray b, from 1·08° to 16·40°; and for the blue ray e, as much as from 6.51° to +18 64°. Again, we find the specific rotation of cane-sugar given as [a] = + 73° to 74°, without mention of the fact that this is the value for the transition tint, although for the neighbouring yellow ray D the value for solutions holding, say 25 per cent. of sugar, is, as shown in § 37, only [a]D = 66.44°, and the value ranges, moreover, for the same ray from 64° to 67°, according to the degree of concentration of the solutions employed. That data of this sort, as remarked in § 23, are utterly worthless, must now be obvious after what has been said.
§ 40. The Specific Rotation exhibited by an Active Substance in a Solution of given Composition is Constant, and hence can be employed as a Distinguishing Characteristic of the Substance. But that it may possess this value, it is indispensably necessary that, along with the value of [a], the following data should be stated :—
1. The ray with which the observations have been made-the index-letter being placed after the bracket.
2. The description of solvent used (as water, alcohol, &c.; in the case of the latter, either the per cent. composition or specific gravity being stated).
3. The proportion of active substance in 100 parts by weight of solution (per cent. composition p), or else the number of grammes in 100 cubic centimetres of solution (the concentration c).
4. The temperature t, of the solution when the angle of rotation was observed. The determination of the specific gravity of the solution, or the adjustment of the volume in a graduated measure, must be done at this same temperature.
5. The direction of rotation (dextro-rotatory +, lævo-rotatory -).
These data may be recorded as follows:-
16.993, t = 20°), [a]D
Ordinary camphor (solution in alcohol of specific gravity 0·796, at 20°, p = 15.092, t = 20°), [a]D + 43.66°.
Santonin (solution in alcohol of 97 per cent. by volume, c = 2, 15°), [a]D = - 174.00.
Quinine hydrate, C20 H24 N2 O2 + 3 H2O (solution in alcohol of 80 per cent. by volume, c = 1, t = 15°), [a]D = - 158.63°.
(solution in alcohol of 80 per cent. by volume, c = 6, t = 15°), [a]p
(solution in a mixture of 2 volumes chloroform + 1 volume alcohol of 97 per cent. by volume, c = 5, t = 15°), [a]D = · 140.50°.
In this way Hessel has estimated the specific rotation of a great number of optically-active substances dissolved in different liquids, thus supplying data which, as constant marks of the several substances, are of great value in determining the identity or purity of different preparations.
In all cases it is advisable to record the per cent. composition p, rather than the concentration c of the solutions, and so to calculate the specific rotation by the formula [a] which, moreover,
renders it necessary to determine the specific gravity of the solutions. The resulting values, at least in cases where several solutions have been observed, can then be used in determining the specific rotation of the absolute substance. This, as frequently already mentioned, is not the case when only the concentration is determined by means of a graduated vessel, and the specific rotation calculated by the otherwise a. 100 more convenient formula [a]
§ 41. Molecular Rotation.-Specific rotation [a] is frequently referred to by Biot under the name of molecular rotation, indicating, as observed (§ 10), that the rotatory power of liquids is a property resident in the molecules.
1 Hesse: Liebig's Ann.176, 89, 189; 178, 260; 182, 128. Hesse indicates the number of grammes of active substance in 100 cubic centimetres solution by p. It is, however, much better to employ e for this purpose (concentration) and let p denote the true per cent. composition (or number of parts by weight of active substance in 100 parts by weight of solution).
But this expression has been applied by Wilhelmy,1 HoppeSeyler, and more recently by Krecke,3 to a different value, viz., to the number obtained by multiplying the specific rotation of any substance into its molecular weight P. The values thus obtained being inconveniently large, Krecke has proposed to divide them uniformly by 100. The molecular rotation [M] of a given substance then appears as
P [a] 100
which expresses the angles of rotation produced by passage of the ray through layers 1 millimetre thick of substances when the unitvolumes contain the same number of molecules.
It has been attempted, by means of this formula, to discover relations between an active substance and its derivatives in respect to rotatory power, and the existence of certain multiple relations has been supposed to have been detected (Krecke,3 Landolt1). But the observations on which these comparisons were based were made, as was formerly the practice, with a single solution of each substance, whereas we have seen (§ 34) that the constant A of the pure substance should alone have been employed. Before, therefore, the hypothetical so-called law of multiple rotation is ripe for discussion a much more extensive series of experiments is necessary.
1 Wilhelmy: Pogg. Ann. 81, 527.
2 Hoppe-Seyler: Journ. für prakt. Chem. , 89, 273.
3 Krecke: Journ. für prakt. Chem.  5, 6.
4 Landolt: Ber. der deutsch, chem. Gesell. 1873, 1073.