60 THE ROYAL SOCIETY OF CANADA 



on the grounds of the classical electromagnetic theory, allowing for 

 a damping term arising from the mechanical reaction due to radiation 

 and taking into special consideration the summation of the aggregate 

 radiation from the random distribution of doublets which are supposed 

 to constitute the molecules of the gas; the final result is a vindication 

 of the above expression for the coefficient of attenuation to a very 

 high order of accuracy. 1 It may be noticed in passing that the same 

 electromagnetic system forms the basis of Planck's 2 theory of "black 

 body" radiation, the interpretation of experiment in this case, however, 

 necessitating the hypothesis of discontinuous energy-flow, or the 

 emission of energy by "quanta." 



For an adequate experimental verification of Rayleigh's Law, 

 recourse must be had to observations on the extinction of solar radia- 

 tion of different wave-lengths by the earth's atmosphere. The im- 

 portance of the observations of the Smithsonian Astrophysical Ob- 

 servatory on atmospheric transmission recently carried out by Abbot 

 and Fowle 3 in connection with their determinations of the solar con- 

 stant at Mount Wilson, in furnishing material for a study of mole- 

 cular scattering was first pointed out by Schuster 4 ; the question was 

 examined in further detail by Natanson 5 and independently by the 

 writer. 6 



If S refer to the intensity of wave-length X outside the earth's 

 atmosphere and E (x) to the intensity normal to the sun's rays reach- 

 ing a level x above the sea from a zenith distance f , we have E(x) = 



S e * sec * , w h ere Q x [ s ti ie coefficient of attenuation at the 



station in question. If allowance be made for the conversion of 

 radiant energy into heat, it is shown by the writer that C* may be 

 expressed in the form C x = y + fa " 4 ; /3 is proportional to the 

 pressure of the atmosphere so that if /3 refer to standard condi- 

 tions of pressure and temperature we have (3 = (3p/p , where p is 

 the barometric pressure at the station at the time of observation. 

 Finally, in terms of the refractive index of air under standard condi- 

 tions, it is shown that (3 = t' 3 ^ — l) 2 H /« , where H is the height 

 of the "homogeneous atmosphere" calculated at 0°C. and n the 

 number of molecules of air per cm. 3 under standard conditions. It 



1 Natanson, Bull. Inter, de V Académie des Sciences de Cracovie, Jan. 5, 1914. 



2 Planck, "Theory of Heat Radiation," (Trans, by Masius, Blakiston's, Phila- 

 delphia, 1914), Part IV., Chapt. Ill, p. 165. 



3 Annals of the Smithsonian Astrophysical Observatory, Washington, Vol. II, 

 (1908); Vol. Ill (1913). 



'Schuster, "Nature," July 22, 1909: "Optics," 2nd éd., 1909, p. 329. 



5 Natanson, Bull. Inter, de l'Académie des Sciences de Cracovie, Dec. 13, 1909. 



6 King, Phil. Trans. Roy. Soc. 212A, p. 392, 1912. 



