29 
1918-19.] Researches in Optical Activity. 
recent communication (J.C.S., 1916, 109, 1183) that constancy can be 
expected only if the dispersion coefficients be calculated from what was 
called a rational zero. The rational zero (taking molecular rotations) for 
the Hg g and Hg v T-R curves — i.e. the rotation value at their point of 
intersection — for homogeneous ethyl tartrate was found to be 2 9 ‘4°, and 
when the dispersion ratio was calculated from this rotation value as zero 
the number 2*0989 was found {ibid., 1191). The rational zero for the 
green and violet lines for isobutyl dibenzoyltartrate cannot meantime 
be determined directly, but, assuming the dispersion ratio to remain 
constant over the requisite interval, the rational zero can obviously be 
calculated from the rotation data at 100° and 182°, which are as 
follows : — 
Iso butyl Dibenzoyltartrate. 
Temperature. 
100°. 
182°. 
[M] v . . . 
- 559° 
-463° 
[M] s . . . 
-271 
-223 
Since the dispersion coefficients at these two temperatures should, by 
hypothesis, be the same, we must have 
559° + aj° 463° + x° 
27V+x 0 ~223 0 + x 0 ’ 
where x° is the value of the rational zero. From this equation x° = l'7°, 
and setting this value in either of the above expressions, the dispersion 
coefficient 2*00 is obtained, very nearly the same as that of ethyl tartrate 
for these two colours of light. Again, taking the data for ethyl tartrate 
in ethylene bromide, we have in a similar manner 
81° + x° 58*06° +x° 
32*86° + a?° _ 20*53° +x° ’ 
from which x° = 18*7°, almost the same value as found for' isobutyl 
dibenzoyltartrate ; and, accepting this as the rational zero, the dispersion 
ratio is 1*96, again much the same as in homogeneous ethyl tartrate 
for the same two colours of light. 
[Experimental Data. 
