B.—CHEMISTRY 43 
the equations of Kuhn and Braun. ‘Thus, in the fascinating case of 
tetra-acetyl-u-arabinose, where the positive and negative maxima are 
equal in magnitude, the equation of Kuhn and Braun gives a difference of 
200° between the observed and calculated values ; but this was reduced 
to only 30° by using Hudson’s own equation (56). 
This sugar-derivative provides ideal material for an experimental 
study of the form of the curves of rotatory dispersion in the region of 
absorption, since the partial rotation associated with the carbonyl-radical 
has been isolated automatically by a fortunate process of cancellation 
of the partial rotations of the asymmetric carbon atoms. A similar 
cancellation has been observed more recently by Baldwin in a specimen 
of penta-acetyl--fructose, also supplied by Dr. Wolfrom. Although 
the simple aldehydic radical —CO.H has now been replaced by the 
radical —CO.CH,.0.CO.CH3, this compound again gives rise to equal 
maxima on either side of the axis; but, since the configuration of the 
three asymmetric carbon atoms is reversed, these maxima are of oppo- 
site sign to those observed in the arabinose-derivative. Moreover, the 
absorption curves have not the same ideal symmetry, and the mathe- 
matical analysis of the dispersion curves has therefore not yet been 
completed. 
THE ORIGIN OF OpTicaL RoTaTOoRY POWER. 
Attempts to simplify the structure of an optically active molecule for 
the purpose of numerical calculations have been made by Drude (59), 
who used a model consisting of a vibrator moving in a spiral orbit, whilst 
Kuhn (62) has used a model consisting of two dissymmetrically coupled 
electrons. Each of these models includes a /ength, namely, the pitch of 
the spiral or the distance between the coupled electrons, and it is perhaps 
not surprising that they have led to equations which differ only in the 
meaning assigned to the arbitrary constants ; but in certain cases at least 
the length deduced from Kuhn’s model appeared to bear no relation to 
the linear dimensions of the molecule. Fortunately the formule which 
express the rotatory dispersion of a medium do not depend on the nature 
of the model used to deduce them, although new integrals are required to 
correspond with each new distribution of densities in the optically active 
absorption band. ‘This distribution depends on the intensities of the 
sub-levels associated with a given electronic jump, and cannot yet be 
_ predicted. In these circumstances it is remarkable that the absorption 
curve should be symmetrical even in the few cases studied by Hudson ; 
but this result may perhaps be interpreted as the effect of some limiting 
condition, which prevents the appearance even of curves which are 
symmetrical on a scale of frequencies instead of wave-lengths. 
The real theory of optical rotatory power may be found by the 
mathematician, but is concealed from the chemist, in the papers of 
Born (63), who recognised that four coupled electrons are required to 
produce optical rotatory power. Further advances appear to depend on 
reverting to this basis, in place of Drude’s single spirally controlled 
vibrator, or Kuhn’s two dissymmetrically coupled electrons, since neither 
of these conceptions can be realised except in a complicated field of force, 
