162 Sir Joseph Larmor on the Principle of 



obey the law of statistics of gas-theory and amount at most 

 to a few hundredths of the wave-length. This representation 

 would seem to be permissible, at any rate for each group of 

 say about 10 6 molecules occupying the cubic wave-dength ; 

 and such groups will be practically independent. 



Now if the molecules were spaced with exact uniformity 

 at distances of smaller order than the wave-length, as they 

 are in a crystal, the disturbances scattered from an incident 

 beam, instead of being additive as regards their energy, 

 would interfere completely ; so that there ought to be no 

 radiation scattered in traversing a crystalline medium. This 

 has in fact been remarked by Lord Rayleigh in his recent 

 paper*, and I think previously by Prof. Lorentz. A beautiful 

 experiment by Prof. R. J. Strutt, which I had the advantage 

 of seeing some time ago, showed that the actual scattering 

 in a column of quartz crystal was small compared with what 

 occurs in optical glass or even in a liquid such as ether. 

 Quantitative comparison would be of interest on various 

 grounds. 



This principle that a crystal should scatter no radiation 

 seems to be unimpeachable, provided the molecules are fixed 

 and do not partake of thermal agitation. And it seems 

 difficult to see why it should not also apply to the molecules 

 of a gas, if they could be regarded as fixed while the 

 radiation is passing, subject to correction for the statistical 

 deviations aforesaid from their mean positions. 



If this were so the individual molecules of a gas, and 

 a fortiori of a liquid or a solid on account of their closer 

 packing, ought in conjunction to scatter radiation far less 

 than they would do separately, the reason being the vast 

 number contained in a cubic wave-length and the statistical 

 regularity of their distribution. And accordingly Lord 

 Rayleigh's announcement f that the blue sky could be due 

 to scattering by the molecules of the air itself came as a 

 surprise, which subsequent quantitative verifications did not 

 wholly resolve. 



The suggestion now to be advanced for consideration is 

 that the principle is to be maintained, even to some extent 

 for crystals, but its logical basis is to be shifted. 



The molecules of the atmosphere are in thermal motion, 

 with velocities in uncorrected directions which are at 

 ordinary temperatures of the order of 10" 6 of that of 

 radiation. The wave-length of the radiation scattered from 



* Phil. Mag., Dec. 1918, p. 445, footnote. 



+ Phil. Mag. 1899 ; Scientific Papers, iv. p. 397. 



