42 SECTIONAL ADDRESSES 
ratios which are either higher or lower than this value, according as 
they are of the same or of opposite sign as the partial rotations associated 
with absorption bands in the Schumann region. In the remarkable case 
of tetra-acetyl-u-arabinose, H[CHOAc],.CHO, however, the partial 
rotations associated with the three asymmetric carbon atoms cancel 
out (56). The whole of the rotatory power is therefore due to the partial 
rotation associated with the carbonyl group. ‘This gives rise to a simple 
rotatory dispersion in the region of transparency. In the region of 
absorption it gives a symmetrical loop, with equal and opposite maxima 
[«] = + 1200° on either side of a zero rotation at 2909 A.U. Camphor- 
quinone is a less precise example of the same phenomenon, since its 
rotation in a narrow region of transparency in the red, yellow, and green 
is dominated by an absorption band in the blue. ‘The influence of the 
Schumann terms is therefore so small that the rotatory dispersion can be 
expressed by a single term of Drude’s equation (54). 
Simple rotatory dispersion then does not imply the existence of only 
a single partial rotation, but merely indicates that the partial rotations of 
the molecule can in practice be covered by one term of Drude’s equation. 
It provides, however, the most practical way of classifying rotations, since 
no real physical meaning can be assigned to a rotation which is not 
‘simple,’ until the various partial rotations, which make the rotatory 
dispersion ‘ complex,’ have been unravelled. For this purpose, however, 
a precise algebraic analysis must be made of the observed rotations for a 
large number of wave-lengths ; and no sanction can be given to the use 
of graphical methods, except for the rough preliminary tests for which 
alone they are suitable (57). 
RoOTATORY DISPERSION IN ABSORBING MEDIA. 
A formula for rotatory dispersion in a region of absorption was developed 
by Natanson (58) in 1909, by reintroducing a ‘ damping factor ’ which 
Drude had discarded in his final simplified equation for rotatory dispersion 
in transparent media (59). No basic change has been made in the funda- 
mental relation thus developed between absorption and rotation; but 
Kuhn and Braun (60) found that, since the form of the absorption bands 
cannot be expressed by means of a damping factor, the form of the 
corresponding curves of rotatory dispersion is also incorrect. They 
therefore introduced a new series of equations on the supposition that 
‘the form of the absorption band can be expressed by an exponential 
equation representing a Maxwellian probability-distribution of fre- 
quencies. ‘Their equations are an improvement on those of Ketteler, 
Helmholtz and Natanson ; but absorption curves of the form postulated 
by them are so uncommon that, in the course of a long experience of 
absorption spectroscopy, I have not yet discovered a single example of 
this type. On the other hand, several absorption curves have been studied 
which are rigidly symmetrical on a scale of wave-lengths, and many more 
are known which shade off more slowly at higher frequencies. Hudson (61) 
has therefore developed a modified series of equations for substances 
which give rise to these symmetrical absorption curves. His equations 
express his own very exact measurements with far greater precision than 
