+ 0.20823 = + 0.19203 = 8.664 7.917 = 1 The rise in specific rotation here observed in ethyl tartrate on the addition of increasing volumes of water, is almost proportional to the amounts added. Adopting, therefore, the formula [a] = A + Bq, we have, From Mixtures I. and II. А 7.689 B = + 0.20070 and taking the means, [a]] = 8:090 + 0·20032 9. The departure here shown by constant A from the specific rotation of pure ethyl tartrate (8:31) is explicable by the fact that water causes a gradual decomposition of the substance, and thereby reduces the rotatory power. This effect was apparent in the marked decrease in the angles of rotation when the same solutions were again observed after standing for forty-eight hours. Solution I. now showed a decrease of 0.028°, II. a decrease of 0.113, and III. a decrease of 0.166o. But even smaller differences would affect the calculation of the formulæ very considerably. Fig. 18 is a graphic representation of the foregoing results. Fig. 18. The extent to which the observational results agree with the results furnished by the interpolation formulæ of the three solvents viz. : : 0.00034786 y For Alcohol [a], = 8.409 + 0.018667 9 Wood-Spirit [a]ı = 8.418 + 0.062466 Water [a] = 8:090 + 0.20032 9 is shown in the table annexed : a $ 34. The results of the investigations detailed in the previous sections may be stated as follows :1. The Rate of Change in the Specific Rotation of an Active Substance, when progressively diluted with some Inactive Liquid, is gradual throughout. — The nature of the change,whether an increase or decrease, will depend on the nature of the active substance: thus, oil of turpentine and ethyl tartrate, in whatever liquids dissolved, always exhibit an increase, whilst nicotine and camphor (for which see § 36), on the other hand, exhibit a decrease in the amount of their specific rotation. Moreover, the rates of variation produced by increasing quantities of different solvents with the same active substance are very different, so that if we represent them graphically we shall have a series of curves radiating from the common point which represents the rotation of the pure substance. Thus the more dilute any solution of an active substance, the more will its specific rotation differ from that of the absolute substance; and the total amount of possible variation may be shown by putting in the interpolation-formulæ the limiting values q = 0) (absolute sub ( stance), and q = 100 (maximum of dilution). Taking the substances we have been investigating and applying this process, we obtain the following results : From this it will be seen that the amounts of variation of the specific rotation of an active substance differ widely for different solvent media. 2. The True Rotatory Power of an Active Substance can be calculated from Observations on a Number ofits Solutions.—The degree of exactitude attainable varies for each substance, and is dependent on the following conditions :—a) On the general extent of the variation produced by the inactive liquid upon the rotation of the substance. The larger the scale, the more unfavourable will be the elements of the calculation (as in the case of nicotine). (6) On the law of dependence of the variations on the increasing percentages of the solvent present, in accordance with which such variations must be represented by a straight or a more or less curved line. (c) On the strength of the solutions employed. The higher the degree of concentration, the greater the possible exactitude of the calculation. The above examples show that where the formula [a] = A+B q applies, the constant A approximates with sufficient closeness (.e., within a few tenths of a degree) to the true specific rotation of the absolute substance even if the most concentrated solution a contains only about 50 per cent. of the active substance. On the other hand, in cases where it is necessary to use the formula [a]=A+B 9 +Cq, divergences of over 1° will occur whenever solutions containing less than about 80 per cent. of the active substance are employed. 3. In calculating the True Specific Rotation of a Substance, the same Value is obtained, whatever Inactive Liquid may have been used as Solvent. -Collecting the various values obtained for A in the substances we have already had under investigation, they appear as follows :I. Left-handed Oil of Turpentine : Divergence. By direct observation [a]! 37.01° Calculated from mixtures with Alcohol [a] 36.97° - 0.04° Benzene [a]. 36.97° - 0.12° Acetic Acid [a 36.89° - 0:12° II. Right-handed Oil of Turpentine : By direct observation [a] 14:15° Calculated from mixtures with Alcohol [a]] 14:17° + 0.02° III. Nicotine (left-rotating) By direct observation [a] = 161.55° Calculated from mixtures with Alcohol [a]}} 160.83° - 0.72° Water [a]] 161.29° - 0.26° IV. Ethyl tartrate (right-rotating) By direct observation [a]p 8.31° Calculated from mixtures with Alcohol [a]] 8.27° - 0.04° Wood-spirit [a]D 8.42° +0.11° Water [a]D 8.09° - 0.22° The differences between the values are so small as to be clearly within the limits of experimental error. 4. In making Comparisons between Solid Bodies, in respect to their Rotatory Powers, only those Values should be used which hold good for the Absolute Substances, that is, only the Constants A.-If we employ the modified values obtained from solutions in inactive liquids, we shall find that any relations will become less apparent the more dilute the solutions are from which the values have been derived. $ 35. The foregoing results point to the method to be employed in determining the true specific rotation of active solids. The most important point to be observed in the process is the employment of the most concentrated solutions attainable, so that, since it is of no consequence otherwise what inactive liquid be employed as solvent, we ought to select that one which best satisfies this condition. Having fixed upon the proper liquid, we must then prepare at least three solutions of different strengths and ascertain their respective rotatory powers. If we now proceed to represent graphically the relation between the values obtained for specific = = rotation [a], and the percentage of solvent present q, we shall obtain either a straight line or a curve. In the former case, where the three points, representing the three observations, lie in a straight line, [a] being simply proportional to q, the equation [a] = A + B q applies, and the value of the constant A calculated from this equation, will be the specific rotation of the absolute substance. Should the middle one of the three points, however, diverge to either side of the line joining the other two, we have then to deal with a curve, and in this case must proceed to extend our observations over a whole series of solutions, so as to make the data for the construction of the curve as full as possible, using some appropriate interpolation-formula ([a] = A + Bq + Cqʻ, or some other such) for calculation. By the graphic method alone, indeed, an approximate value for the specific rotation of the absolute substance may be arrived at, by simply prolonging the straight or curved line so obtained till the abscissa q = 0. That values obtained by such extrapolations must be used with caution is self-evident. For greater accuracy, we should never omit to repeat the experiments with other solvents, and, should the values obtained for constant A agree sufficiently well, the mean of the whole may then be taken as the true value of the specific rotation; if otherwise, the results should be rejected altogether. The imperfect solubility of many active substances is a serious obstacle to the determination of their true specific rotation. As the foregoing experiments show, it is only in cases where solutions containing at least 50 per cent. of active substance can be prepared, and where the rotation-curve does not depart too considerably from a straight line, that anything like trustworthy numbers can be obtained ; so that when we have to do with sparingly soluble bodies, we can have no hope of arriving at any knowledge of the rotatory wer of the absolute substances. $36. By the method above described, the author has endeavoured to determine the rotatory power of a solid substance, choosing for the purpose common camphor. The camphor employed for this purpose was first purified by distillation from a retort with short, wide neck. In this way, on the first application of heat, oily drops, which did not solidify, separated out, and were put aside. The melting-point of the purified material was 175° Cent., the boiling-point 204° Cent. As solvents, a number of liquids in the purest possible condition were employed, viz., acetic |