Principle oj Molecular Scattering of Radiation. 161 



claim to have proved that all energy is kinetic. I only 

 suggest that Fermat's law is capable of an interpretation 

 which will yield this conclusion. I trust the proof will be 

 forthcoming in due course. At present, however, I have no 

 illusion on that point. 



Yours truly, 



D. JN". Mallik. 



XV. The Principle of Molecular Scattering of Radiation. 

 By Sir Joseph Larmor, F.R.S.* 



A FUNDAMENTAL element in the theory of radiation is 

 the principle first elucidated by Lord Rayleigh |, that 

 when light is scattered by the particles of a fog or haze, or 

 even by the molecules of the air, they act independently, 

 without sensible mutual interference as regards the distri- 

 bution of the energy. 



The condition necessary for this independence is that the 

 disturbances (such as strain, velocity) must arrive from the 

 scattering particles in phases which are entirely uncor- 

 rected : so that on an average taken over a short interval 

 of time, the square of the sum of the disturbances is equal 

 to the sum of their squares, and thus the total energy would 

 come from addition of energies of independent scattered 

 disturbances. 



This condition will be secured if the scattering particles 

 are distributed at random, provided the intervals between 

 adjacent ones are substantial fractions of the wave-length 

 of the radiation that is being scattered : for then the phases 

 of the scattered disturbances coming from adjacent particles 

 will be uncorrelated. It holds good usually for particles of 

 dust in the atmosphere. But in the case of a gas there are 

 10 6 molecules in a cubic wave-length, and in the case of a 

 liquid or solid 10 9 , giving differences of adjacent phases of 

 the order of only 10 ~ 2 of the period in the former case and 

 ID" 3 in the latter. 



Even for a gaseous medium the question thus arises, 

 whether it is wrong to consider the distribution of the 

 scattering molecules as based upon uniform spacing, but 

 subject to uncorrelated deviations from this regularity which 



* Communicated by the Author. 



t Proc. London Math. Soc. 1870; Phil. Mag. x. 1880: and later 

 papers, including the one under special reference in Phil. Mag., Dec. 1918. 



Phil. Mag. S. 6. Vol. 37. No. 217. Jan. 1919. M 



