‘A 
B.—CHEMISTRY 41 
which are now attainable (52). Thus normal rotatory dispersion 
(defined by the fact that «, dx /di and d*x/di? are of constant sign through- 
out the region of transparency (50)) can often be expressed by a single 
term of the equation, with only two constants ; but this is by no means 
universally true, since the rotatory dispersion of quartz, which requires 
a five-constant equation, is nevertheless rigidly normal throughout the 
whole region of transparency. On the other hand, anomalous rotatory 
dispersions can only be expressed by using two terms of opposite sign. 
These two terms, however, are adequate to account for the presence in 
curves of anomalous rotatory dispersion of (i) a reversal of sign, where 
%=0, (ii) a maximum, where dx«/d\ =o, and (iii) an inflexion, where 
d*x/dd2 = 0 (50). 
Those normal rotations which cannot be expressed by a single term of 
Drude’s equation can usually be represented by equations with two 
terms, either of similar or of opposite signs. When the two terms are of 
opposite signs, the equation becomes identical in form with that which 
is used to represent anomalous rotatory dispersion. The distinction 
between normal and anomalous dispersion is indeed often almost a matter 
of accident. ‘Thus a wide range of dispersion-curves can be plotted for 
the tartaric esters in different solvents, and at different concentrations 
and temperatures (51). [hese curves all belong to one family, and can be 
expressed by the same equation, with small variations in the four arbitrary 
constants; but some of them cross the zero axis and are therefore 
anomalous, whilst others just fail to do so and are therefore normal (52). 
SIMPLE AND COMPLEX ROTATORY DISPERSION. 
An alternative method of classification is to describe as simple those 
rotatory dispersions which can be expressed by one term of Drude’s 
equation, and as complex those which cannot be so expressed (53). 
This classification lends itself very easily to practical use, since, for the 
purpose of complete verification, measurements need only be extended 
to a wave-length in the ultra-violet at which absorption first begins to be 
troublesome, in view of the fact that Drude’s equation is only valid in the 
region of complete transparency. On the other hand, the distinction 
between normal and anomalous rotatory dispersion depends on knowing 
whether the curve does or does not cross the zero axis in the infra-red ; 
and this cannot yet be determined with certainty with the apparatus now. 
commonly used in polarimetry. 
In general, simple rotatory dispersions are only observed when the 
characteristic frequencies of all the partial rotations lie close together 
in the Schumann region, giving a dispersion-ratio 4353/0546; = 1 °6 
approximately. ‘Thus, in the sugar series, the partial rotations associ- 
ated with the different asymmetric carbon atoms sometimes give rise to a 
simple dispersion, as in cane-sugar (54) ; but they do not necessarily do 
so (55), since even in a sugar the characteristic frequencies of the radicals 
may cover a wide range in the Schumann region, and the foot of the 
absorption bands often extends into the ordinary ultra-violet. 
Additional partial rotations of lower frequency give rise to dispersion- 
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