PHYSICS 539 



of the dielectric constant e corresponding to a fluctuation Jp 

 of density. It is assumed that e and p are connected by the 

 Lorentz formula 



(e — i)/(e + 2)p = constant. 



and so (^e)' can be obtained in terms of (Ap)^, whose mean 

 value is given above. After some steps it is shown that the 

 intensity of the light scattered by unit volume at right-angles is 



ttViS . RTyS/N . (ya= - lYifJl,' + 2)VV 



where yu,' is written for e. 



In the case of gases this formula degenerates to Rayleigh's. 



This formula explains the reason for the remarkable opales- 

 cence which appears in a vapour near the critical point ; for in 

 such a case the value /3 is relatively very large. It has been 

 quantitatively tested by Keesom [Ann. der Physik, 35 (191 1)] 

 for ethylene in this opalescent condition, with very satisfactory 

 results. Some experiments by Raman have shown that in 

 the case of water the molecular scattering is about 158 times 

 that of dust-free air ; the Einstein-Smoluchowski formula 

 yields the result that it should be above 140. This discrepancy 

 may be due to the difficulty of obtaining a liquid entirely free 

 from motes, which magnify the scattering effect ; or to the 

 anisotropy of the molecules referred to above. If the calculated 

 result is affected by the factor (6 + 6p)l{6 — yp) used by Cabannes 

 and mentioned above, it increases it to 160 from 140, in very 

 good agreement with the observed value. Also some recent 

 experiments of W. H. Martin [Jour, of Phys. Chem., 24 (1920)] 

 on the relative scattering of ether, alcohol, benzene, and toluene 

 to water, agree moderately well with the Einstein-Smoluchowski 

 formula combined with the factor (6 + 6/o)/(6 — yp) involved 

 in the anisotropy of the molecules. Some work of the present 

 Lord Rayleigh's [P.R.S., 95 (191 9)] on scattering by quartz 

 is also in fair agreement with the formula if the fluctua- 

 tions are calculated on the view that they arise from the 

 thermal agitation of the atoms in the crystalline space-lattice. 

 (This thermal motion of the space-lattice is the starting-point 

 of Debye's well-known theoretical work on the variation of 

 intensity of X-ray reflection with temperature, which has been 

 applied with success to X-ray experimental work.) Considering 

 the striking success of the formula for such different states of 

 matter, it is surprising to find that it breaks down signally for 

 gases under high pressure. For example, carbon dioxide at 

 21° C. and 60 atmospheres has been found by Strutt to scatter 

 102 times as much as at atmospheric pressure. The formula 

 yields the result that it should be at least 800 times. 



The importance of pursuing these researches has led Prof. 



