258 
MESSES. THOMAS MARTIN LOWRY AND PERCY CORLETT AUSTIN 
both the optical and the magnetic rotations* can be expressed by a single term of the 
general equation (Lowry and Dickson, c Trans. Chem. Soc.,’ 1913, vol. 103, pp. 1067- 
1075 ; Lowry and Abram, ‘ Trans. Chem. Soc.,’ 1919, vol. 115, p. 300 ; Rupe and 
Akermann, ‘ Ann. der Chem.,’ 1920, vol. 420, p. 4) ; liquids such as ethyl and methyl 
tartrates and aqueous solutions of tartaric acid, which show anomalous rotatory dis¬ 
persion, require two terms of opposite sign (Lowry and Dickson, ' Trans. Chem. Soc.,' 
1915, vol. 107, pp. 1173-1187 ; Lowry and Abram, ‘ Trans. Chem. Soc.,’ 1915, vol. 107, 
pp. 1187-1195) ; quartz, although showing no obvious anomalies, requires three terms 
of Drude’s equation in order to express the most recent measurements that have been 
made of its rotatory dispersion (Lowry, ‘ Phil. Trans.,’ A, 1912, vol. 212, p. 261). This 
determination of the exact form of the curves has led to an extremely easy and con¬ 
venient classification of rotatory dispersion, as simple when one term of Drude’s equation 
is sufficient and complex when two or more terms are required (Lowry and Dickson, 
‘ Trans. Faraday Soc.,’ 1914, vol. 10, p. 102). The complex curves are only anomalous 
when they cross the axis of rotations and exhibit a reversal of sign ; but a simple mathe¬ 
matical analysis has established the conditions under which a complex curve, expressed 
by two terms of Drude’s equation, ceases to be normal and becomes anomalous in the 
sense of the exact definition already referred to ( £ Trans. Chem. Soc.,’ 1915, vol. 107, 
p. 1198). 
3. The Origin of Anomalous Rotatory Dispersion. 
(a) Anomalous Rotatory Dispersion as a Problem in Chemical Mechanics. 
The present paper follows one on rotatory dispersion in quartz. It may be regarded 
as supplementing that paper by extending the new series of exact measurements from 
the first to the second of Biot’s types of rotatory dispersion. It also carries the work 
forward from optically active crystals to optically active liquids, and so opens up again 
the complex chemical problems which led Biot to describe most of his work on tartaric 
acid as a study in chemical mechanics rather than as an investigation of the physical 
properties of the acid. It is this underlying chemical interest that more especially 
* The magnetic rotatory dispersion in carbon disulphide can be expressed, at least as well by a simple 
two-constant equation a . ~ k/p 2 — 0-055), as by the four-constant equation used by Deuce. Thus the 
five lines quoted by Drude (‘ Theory of Optics,’ 1907, p. 431) give for k the values :— 
C. D. E. F. G. 
k = 0-2224 0-2221 0-2226 0-2236 0-2224 
whilst the observed and calculated dispersion-ratios compare as follows :— 
Observed.'. . 0-592 0-760 1-000 1-234 1-704 
Cal. (four constants). 0-592 0-762 0-999 1-232 1-704 
Cal. (two constants). 0-593 0-762 1-000 1-228 1-706 
Later measurements (‘ Trans. Chem. Soc.,’ 1913, vol. 103, p. 1074) agree still more closely with a simple 
constant equation. 
