ON OPTICAL ROTATORY DISPERSION. 
273 
dispersion-constants. This may be regarded as substantially correct for the whole of 
the series, since, in case after case, independent calculations have given numbers lying 
within a narrow range on either side of this average value. 
Having thus established a fixed value for the smaller dispersion-constant, the magni¬ 
tude of the larger dispersion-constant \ 2 2 may be deduced with a very fair degree of 
accuracy. Thus in the case of methyl and ethyl tartrates the values were as follows — 
Methyl ester. Ethyl ester. 
Pure ester. 0-054 0-056 
In ethylene chloride or bromide .... 0-058 0-061 
In formaldehyde. 0-070 0-070 
The concordance in the values for the two esters when examined under similar condi¬ 
tions is a very fair indication of the accuracy of the dispersion-constants deduced in 
this way. 
In the case of the two concentrated solutions of tartaric acid, the values of the second 
dispersion-constant deduced independently were 0-074 and 0*073. With these values, 
a close agreement was found between the observed and calculated rotations as set out 
in Table III., both in the visual and in the photographic regions. This agreement, 
following upon a similar concordance in 12 long series of observations of methyl and 
ethyl tartrate, is sufficient to establish the general validity of the two-term equation as 
an expression of the complex rotatory dispersion both of tartaric acid and of its esters.* 
It is then a simple problem to study the variations of the four constants of this equation 
as the concentration of the solution is increased or diminished. Preliminary observations 
indicated that the dispersion-constant \.f for tartaric acid in aqueous solutions might, 
with advantage, be reduced from 0-074 for solutions containing 70 grams of acid in 
100 c.c. to 0-065 for solutions containing 5 grams in 100 c.c. ; but this diminution could 
not be confirmed in the more exact, though rather less extensive, observations set out 
in Table I. We have, therefore, preferred to make use of constant values, Ai 2 = 0-030, 
A/ = 0-074, for the two dispersion-constants of this series of solutions rather than to 
introduce small variations which would merely have led to irregularities in the values 
of the “ rotation-constants ” ^ and k 2 . The observed and calculated values of the 
molecular rotatory powers at eleven different concentrations are set out in Table IV. 
Table V. shows, for the 13 solutions for which data are given in Tables III. and IV., 
the magnitude of the four constants of the two-term equation, together with the wave¬ 
lengths at which the principal anomalies are found, namely, the inflection of the curve 
at A,,, the maximum at A^ and the reversal of sign at A p . These latter have been 
calculated from the equations, as a convenient method of interpolation ; wave-lengths 
* In the case of the acid there are indications of a predominance of negative errors between the green 
and violet mercury lines ; this is, perhaps, an effect of ionisation, since nothing of the sort has been noticed 
in the case of the esters. 
2 Q 
VOL. CCXXII.—A. 
