SECTIONAL TRANSACTIONS .—B. 469 
assuming a centre of symmetry in the structure. It can then be shown 
that the coefficients Ag, are proportional to the structure factors of the 
crystal, which can be determined from experimental measurements of 
intensity. ‘These measurements, however, do not tell us the phase constant, 
or sign, which must be attached to each term. These must at present be 
found by trial and error. In practice a double Fourier series is the most 
convenient to apply, representing a projection of the structure on a given 
plane. 
Examples of such projections from anthracene, naphthalene and durene 
were shown. ‘The benzene ring in all these compounds consists of a regular 
plane hexagon of carbon atoms, the distance between the centres being 
1°41 A. In durene the methyl groups are reasonably spherical, and are 
situated at 1°47 A. from the adjacent aromatic centres. These methyl 
groups are also displaced slightly away from each other, towards the unsub- 
stituted positions of the benzene ring, the displacement being about 3° from 
the symmetrical or unstrained position. 
Dr. J. D. BERNAL. 
Mr. E. J. BoweEn.—Forces between atoms in molecules. 
The characteristic vibration frequencies of simple molecules can be 
found from Raman spectra, near infra-red absorption spectra, and from 
electronic absorption spectra in the visible and ultra-violet region. 
A diatomic molecule has one characteristic frequency, from which the force 
constant of vibration can be calculated. More complex molecules have 
a number of characteristic frequencies which must be assigned to specific 
modes of vibration. For this purpose use is made of selection rules due to 
Placzek and to Dennison. In the case of certain simple types of organic 
molecules (e.g. the cyanogen halides) it is possible to assign frequencies 
with some degree of reliability by intercomparison of the observed fre- 
quencies with those of other molecules, but in general it is necessary to 
examine the infra-red absorption bands at high dispersion in order to apply 
Dennison’s assignment rules. Such infra-red work at high dispersion has 
been carried out in few cases at present. When the observed frequencies 
of a simple molecule such as SO, have been correctly assigned to specific 
modes of vibration, approximate values for the force constants of the links 
and the apex angle of the molecule can be obtained by treating the molecule 
as an assemblage of masses and springs. A more refined treatment must 
take into consideration ‘resonance degeneracy’ and the anharmonic 
character of the vibrations. This necessarily means the introduction of 
many new constants into the problem. A very complete treatment of the 
vibrations of the CO, molecule, allowing for these factors, has recently been 
given by Adel and Dennison. From the experimental values of the funda- 
mental frequencies (allowing for resonance interaction), of the overtones 
(which are not the sum of integral multiples of the fundamentals), and of 
the rotational structure of the vibration bands (which is modified by the 
vibration), they build up an equation of twelve constants which completely 
expresses the experimental results. The next development lies in the 
elimination of many of these constants by the discovery of a suitable potential 
energy function which will also reproduce the results. Adel and Dennison 
apply a Morse potential energy function to each of the C=O links in the 
molecule, and an empirical exponential function to allow for the repulsion 
of the oxygen atoms for each other. The resulting equation containing four 
constants is capable in a semi-quantitative way of reproducing the features 
