May 19, 1923] 

NATURE 
667 










that in the crystal of beryllium acetate an 
_ oxygen atom has four equal valencies suggests also a 
_reconsideration of the doctrine of ‘‘ residual valencies,”’ 
as used by Langmuir in his theory. 
fae W. M. Baytiss. 
_ April 30. 
_ The Complex Anisotropic Molecule in Relation to 
, the Theory of Dispersion and Scattering of 
Light in Gases and Liquids. 
__ OBSERVATIONS by Cabannes,! the present Lord 
_ Rayleigh,* Gans,* and others have shown that the 
light scattered by various gases in a direction at 
_ right angles to the incident beam is not completely 
_ polarised. This is accounted for by Cabannes in 
terms of a simple anisotropic molecule of the type 
_ first used by Langevin ‘ in 1910 to account for electric 
and magnetic double refraction. Such a molecule 
contains a single dispersion electron acted on by 
oom en quasi-elastic restoring forces along the prin- 
cipal directions and capable of vibrating with three 
different frequencies. 
The present writer has extended the theory to 
gaseous and liquid media composed of complex aniso- 
tyopic molecules, in which there are any number of 
dispersion charges the principal directions of which 
_ are not parallel. For an isotropic medium in which 
all molecular orientations are equally probable, a 
sapiae dispersion formula of the Lorentz type is 
erived. 
In gaseous media, owing to rapidly varying changes 
of position, each molecule contributes independently 
to the intensity of the scattered radiation. For un- 
_ polarised incident light of intensity I, the depolarisa- 
tion is measured experimentally as the ratio of 
minimum to maximum intensity when the light 
scattered at right angles to the incident beam is 
_ examined by a Nicol prism, and as observed in gases 
is a quantity characteristic of the molecule. The 
intensity I,@ scattered in a direction @ with the 
incident beam of wave-length \, to a distance y from 
a volume V is given by the formula 
1,0 _ 4? (u2—1)? | 6(1 +) I-p 
ease as eee 
where « is the refractive index corresponding to 
_ molecular density n. 
The corresponding formula for the coefficient of 
extinction by scattering is 
__ 87? (u?— 1)? | 6+ 39 
Baie eee (2) 
Bn 
A remarkable feature of these formule is their 
invariance with respect to such details of molecular 
structure as number and magnitude of dispersion 
charges and mutual orientation of principal directions. 
In liquids, from the observations of Martin,’ Lord 
_ Rayleigh, Kenrick,* Raman,’ and others, it is now 
definitely established that dust-free liquids are able 
to scatter light. According to Smoluchowski*® and 
Einstein,® the explanation of this phenomenon, first 
2 Cabannes, J., Comptes rendus, 160, 1915, pp. 62-63; Ann. de Physique, 
15 (1922). 
2 Strutt, R. J. (Lord Rayleigh), Proc. Roy. Soc. 944 (1918), p. 4533 
954 (roto), PP- 155-176 ; ose (1919), PP. 476-479. 
* Gans, R., Ann. der Physik, 65 (1921), pp. 97-123. 
* Langevin, P., Le Radium, 7 (1910), pp. 249-260. 
® Martin, W. H., . Roy. Soc. Canada, 7 (1913), p. 219; J. Phys. 
Chem. 24 (1920), p. 478; 26 (1922), p. 75; J. Phys. Chem. 26 (1922), p. 
471; Bibliography, Trans. Roy. Soc. Canada, 16 (1922), p. 276. 
* Kenrick, F. B., J. Phys. Chem. 26 (1922), Pp. 72. 
7 Raman, C. V., “ Molecular Diffraction of Light" (Univ. of Calcutta 
Press, 1922). Letters to NatuRE, 1922-23. 
* Smoluchowski, M., Ann. der Physik, 25, 1908, pp. 205-226. 
* Einstein, A., Ann. der Physik, 33, 1910, pp. 1275-1298. 
NO. 2794, VOL. 111] 

observed near the critical point of a liquid, lies in 
fluctuations of molecular density due to thermal 
agitation. Since a volume of linear dimensions small 
compared with a light-wave contains several million 
comparatively stationary molecules, it is necessary 
in dealing with liquid media to sum the components 
of the electric vector in the scattered light-wave from 
each molecule. In these circumstances, it may be 
shown that equally probable orientations of complex 
anisotropic molecules within this small volume would 
result in the scattered light being completely polarised, 
contrary to observation. It is concluded, therefore, 
that liquids have an extremely fine-grained crystalline 
structure, the crystalline aggregates being supposed to 
be incapable of withstanding stress owing to molecular 
vibrations, and to be continually breaking up and 
re-forming under the influence of these elastic waves, 
which according to Debye’s” theory constitute the 
energy of thermal agitation. If we suppose the 
energy of one degree of freedom to be associated 
with the random pulsations of these crystalline 
aggregates, we derive instead of (1) the following 
formula for scattering, 
71,0 ti 6(1 +p) RT« I- ‘ 
EAB Gage WT (rey) ) 
where, in addition to the symbols already defined, 
R is the gas-constant per gram molecule =83'2 
x1o® C.G.S., N is Avogadro’s constant =6°06 x 10%, 
T is the absolute temperature, and a is the adiabatic 
compressibility. 
As in the case of the preceding formule, (3) en- 
joys the property of invariance with respect to details 
of molecular structure, and it is derived on the 
hypothesis that the molecules in each crystalline 
aggregate are not greatly disturbed from perfect 
alignment by angular oscillations which result in a 
diminution of the depolarisation p as the critical 
point is approached, as has, in fact, been recently 
observed by Ramanathan ™ in the case of liquid ether. 
For light scattered at right angles to the incident 
beam, Martin has shown that the inverse fourth 
power law holds good for benzene and water. For 
\=4358 A. and 20° C., we find for r*I,(47)/(VI) the 
following comparisons, 
Benzene 21°5 x to-® (cale.) 26°0 x 10~® (obs.). 
Water 1°85 x1o-* (calc.) 1°77 x 10-® (obs.). 
Formula (3) also accounts theoretically for the 
relative scattering of some twenty organic liquids 
studied by Martin. 
This satisfactory agreement between theory and 
observation goes far to justify the hypothesis of the 
crystalline structure of liquids as just described. To 
this view strong support is lent by the observations 
of Debye," Keesom,'* and more recently of Hewlett," 
on the scattering of a beam of X-rays by various 
liquids. 
Although the results thus far have been based on 
a general type of “static ’’ molecule, the theory is 
by no means opposed to the modern conceptions of 
the ‘‘dynamic’”’ atom. For wave-lengths long com- 
pared with molecular dimensions, we may suppose 
those perturbations which contribute principally to 
dispersion to consist of forced oscillations of each 
atomic system of electrons with respect to the cor- 
responding positive system. 
- te Louis V. Kina. 
McGill University, Montreal. 
1© Debye, P., Ann. der Physik, 39 (1912), pp. 789-839. 
1 Ramanathan, K. R., Proc. Roy. Soc. 102A (1922), p. 151. 
2 Debye, P., and Scherer, P., Nach. Ges. Wiss., Gdttingen, 1916, p. 1; 
Phys. Zettschrift, 17 (r916), P. 277 ; 18 (1917), p. 291 
nd S 
13 13 Keesom, W. H., a medt, J. de, K. ‘Akad. Amsterdam, Proc. 25, 
3 and 4, pp. 118-12 
24. 
Hewlett, C. W., Physical Review, xx. 6, December 1922, pp. 688-708, 
