Section III., 1914. [59] Trans. R.S.C. 



On a Determination of Avogadro's Number and the Electronic Charge 



by the Application of Rayleigh's Law to the Smithsonian Observations 



of the Absorption of Solar Radiation by the Earth's Atmosphere. 



By Louis V. King, B.A., Assistant Professor of Physics, 

 McGill University. 



Presented by Professor H. T. Barnes, F.R.S. 



(Read May 27, 1914). 



The bearing of Rayleigh's Law of gaseous extinction on some of 

 the fundamental aspects of radiation theory does not seem to have 

 been sufficiently emphasized in recent reports and publications on 

 modern molecular physics. The coefficient of attenuation K of radia- 

 tion of wave-length X travelling through a gas containing n mole- 

 cules per unit volume was given by Rayleigh 1 as long ago as 1871 

 in the form k = U 3 (»l - D 2 \ - 4 M>, Mo bein § the refractive 

 index of the gas. It is of importance to notice that the law in ques- 

 tion is one of the most fundamental results of molecular dynamics, 

 its final expression being an invariant with respect to the theories 

 of the œther or of the molecule employed, 2 while in its derivation 

 there is no need to draw on resources outside classical dynamics and 

 continuous energy-flow. From the point of view of elementary 

 electromagnetic theory, the above expression for K is very easily 

 derived along lines suggested in a problem set in Part II. of the Mathe- 

 matical Tripos 3 : use is made of the conventional electrical doublet 

 set into forced vibrations by a train of electromagnetic waves; by 

 making use of the radiation formula for accelerated charges and Poyn- 

 ting's Theorem, the flow of energy from the doublet is easily calculated 

 in terms of the amplitude of vibration; the oscillations of the doublet 

 contribute a term to Maxwell's displacement current, enabling the 

 amplitude to be expressed in terms of the refractive index of the gas; 

 by considering the depletion of energy from the original beam as a 

 result of this scattering, and eliminating the amplitude, the above 

 expression for K is easily obtained. In a recent paper Natanson 

 has subjected the derivation of Rayleigh's La w to minute criticism 

 i Rayleigh, Phil. Mag. 41, pp. 107, 274, 447 (1871); "Collected Works" I, pp. 

 87, 104, 518. 



2 Schuster, "Theory of Optics," 2nd ed. (1909), p. 325. 



3 Mathematical Tripos, Part II., June 2, 1906. 



