* 
B.—CHEMISTRY 45 
metric molecule, although Hermann has calculated the rotatory power of 
crystals of sodium chlorate and Hylleraas that of $-quartz from formulze 
developed by Born. For the purpose of predicting the magnitude of the 
rotatory power of a molecule it is convenient to deal, not with single 
electrons or pairs of electrons, or even groups of four, but with the 
complete octet which constitutes the valency-shell of the atom. From 
this point of view, the four different radicals which are required to give 
rise to an asymmetric carbon atom may be considered as ellipsoids, with 
three principal axes of polarisation, arranged at a definite distance 
from the central carbon atom and with a definite orientation relatively 
to one another ; but this system is too complex for easy computation 
and some simplification is needed before numerical data can be 
deduced. 
This simplification was attempted nearly ten years ago by de Malle- 
mann (65), who assumed that, for the purpose of computation, single 
atoms might be treated as isotropic spheres. A further simplification 
was made by assuming that the three halogens in CHCIBrI could be 
placed on the rectangular axes of x, y and z at distances depending on 
their atomic radii. On this basis he calculated (66) the rotatory power 
of the molecule in terms of the radii and refractivities of the radicals, and 
obtained a value, [«],, = + 32°, of the expected order of magnitude for 
_a compound of this type; but, since the compound has not yet been 
prepared, no direct comparison of observed and calculated rotations was 
possible. During the present year, however, S. F. Boys (67) has been 
able to make this comparison by extending the postulate of isotropic 
spheres from single atoms to radicals. Langmuir’s theory of isosterism 
can be cited as justification for extending this postulate from the halogens 
to the isosteric radicals, OH, NH,, CH; ; but it is certainly invalid when 
extended to radicals such as C,H; and CH,OH, which cannot be either 
spherical or isotropic. Nevertheless Boys has been able to deduce, for 
four of the simplest alcohols and amines, rotations which are of very 
similar magnitude to those observed experimentally. This coincidence 
is limited to dissymmetric molecules of the simplest possible type, con- 
taining only one asymmetric carbon atom and no unsaturated or chromo- 
phoric group ; but it is sufficient to show that Pasteur’s model of an 
irregular tetrahedron can be used to predict the existence and the approxi- 
mate magnitude of such a molecule in terms of the linear dimensions and 
the refractive indices of the radicals. 
Detailed calculations by Mr. H. F. Willis have shown that the simple 
rotatory dispersion of sec-butyl alcohol, 43;3/a%54,; = 1-661, can be 
deduced exactly from the factor RsR,R-Rp/? of Boys’ formula, or 
less exactly if the factor (u?+2) (u?++5) is included. On the other hand, 
the dispersion-ratio of act-amyl alcohol, o435g/%54g, = 1-700, is higher 
than the maximum value which can be deduced from the formula. 
Moreover, the anomalous rotatory dispersion of aldehydes and ketones 
in the region of absorption cannot be represented even qualitatively by 
means of a formula of this kind, since the refractivity of the carbonyl- 
radical never approaches the zero axis, and cannot therefore give rise to 
a reversal of sign in the region of absorption ; but a zero value for the 
