April 8, 1922] 



NATURE 



449 



homogeneous liquids at different temperatures or in 

 a series of different solvents (Lowry and Dickson, 

 lYans. Chem. Soc, vol. 107, p. 1183, 1915 ; Lowry and 

 Abram, ibid., p. 1193). 

 Careful, mathematical analysis has shown that all 



these curves can be expressed by two terms of Drude's 

 equation, of opposite sign and with unequal dispersion- 

 constants — e.g. 



= -A - ^2 

 " A2-Aj2 A2-A22- 



The agreement is particularly good in the case of the/ 



esters. In the case of aqueous solutions of tartaric 



CO 0,0- «ote« acid the ionisation 



|5 2!55 g??* of the acid appears 



3 5 jj * j* 3 00 J* to introduce an 



additional factor 

 of complexity 

 giving rise to small 

 but systematic 

 deviations from 

 the values calcu- 

 lated by means of a 

 two-term formula. 

 In cases of 

 " simple " rota- 

 tory dispersion 

 Drude's formula 

 postulates a linear 

 relation between 

 I /a and A2^ but 

 gives a rectangular 

 hyperbola when a 

 is plotted against 

 A2. The corres- 

 ponding disper- 

 sion - curves for 

 methyl and ethyl 

 tartrates are made 

 up of the sum of two such rectangular hyperbolas, lying 

 on opposite sides of a common horizontal asymptote, but 

 working up to two different vertical asymptotes. These 

 simple hyperbolas lie beyond the curves for solutions in 

 formamide and in acetylene chloride, which are the 

 highest and lowest of the series shown in Fig. 2, but 

 every curve in this figure can be represented as a 

 weighted mean of two such hyperbolas. 



NO. 2 73 6, 'vol. 109] 



4300 3800 



It should be noted that in this series of compounds 

 the negative term always has a higher dispersion- 

 constant than the positive term, so that the asymptote 

 of the negative hyperbola is nearer to the visible region 

 of the spectium than that of the positive hyperbola. 

 All the positive rotations are therefore 

 drawn over towards the negative side as 

 the wave-length diminishes, as in the top 

 curve of Fig. 2, which shows a reversal of 

 curvature on the extreme right. The 

 curves in the upper part of Fig. 2 must 

 therefore show, not merely one, but all 

 of the features which are usually regarded 

 as characteristic of anomalous rotatory- 

 dispersion — namely, (i) an inflexion, (ii) 

 a maximum, (iii) a diminution of rotatory 

 power with decreasing wave-length, (iv) 

 a reversal of sign. 



On the other hand, the curves at the 

 bottom of Fig. 2 are negative through- 

 out, since the positive term is always 

 smaller than the negative term of the 

 equation. There is therefore no in- 

 flexion, maximum, or reversal of sign. 

 The curves obtained by plotting a against A^ are, 

 however, not rectangular hyperbolas, but the 

 weighted means of two hyperbolas, and require 

 two terms of the Drude formula to represent them. 

 Although, therefore, these curves are not anomalous, 

 they are not " simple," and must be classed with the 

 anomalous curves as " complex." 



It should be noted that a small alteration in the 

 numerical values of the constants of the equation for 

 a complex curve may suffice to introduce the whole 

 range of anomalies, or alternatively to remove them, 

 whereas, to render a complex curve simple, one of the 

 two terms in the complex equation must be made to 

 disappear altogether. The difference between simple 

 and complex dispersion is therefore probably of more 

 significance than that between normal and anomalous 

 dispersion, in spite of the more picturesque character 

 of the latter contrast. 



4.— The Origin of Anomalous Rotatory Dispersion. 



It has been shown above that the curves of rotatory 

 dispersion of organic compounds may be of three 

 types — (i) simple, as in the case of the vast majority 

 of the alcohols, acids, sugars, terpenes, etc., to which 

 reference has already been made ; (ii) complex, but 

 without anomalies, as in the case of the tartaric esters 

 when dissolved in solvents such as acetylene tetra- 

 chloride ; (iii) anomalous, as in the case of tartaric 

 acid and its esters. What, then, is the origin of the 

 complexities seen in classes (ii) and (iii) ? Mathe- 

 matically they depend on the same fundamental factor 

 — namely, the introduction into the equation of 

 rotatory dispersion of a second term of opposite sign, 

 which is absent in class (i). From the chemical point 

 of view it is difficult to avoid the conclusion that the 

 complexities expressed by the two-term formula are 

 due to the presence in these liquids of two kinds of 

 optically active molecules, differing in sign and in 

 dispersive power, but each characterised by a simple 

 rotatory dispersion corresponding with one term of the 

 equation. 



