and Dispersion of Light. <S33 



Thus, the scattered energy is 



p 4 4Y 2 r*t 



_ Jkdxe A rf 



67rc 4 m 2 (n 2 — n 2 — flN^/m)" 2 ' 



Then, defining the coefficient of scattering /c by the equation 



dl= —Kldxy 

 we have N*«tt* 



*~ 67rc 4 m 2 (v~^-aN* 2 /m) 2 * 



Again, if we denote by //, the refractive index of the 

 medium, we have * 



2 N. 2 1 



m » - 



; — aNe 2 /?n ' 



Hence ^6^S^" 1): 



rutting n ~~TT ' 



16,r» , . 



If we put further 

 we have finally 



_ 8tt 3 (^ 2 -1) 2 

 3 NA 4 * 



^-1=2(^-1), 



327r3(^~2) 2 

 3N A 4 ' 



which is Rayleigh's formula for the scattering coefficient for 

 a gaseous medium f. 



The correctness of this formula is acknowledged generally* 

 and its experimental verifications, too, are not wanting, the 

 latest and most extended treatment of the subject being 

 given by Cabannes in Annates de Physique, vol. xv. Jan.— 

 Feb. 1921. (There will also be found in it a complete list 

 of authors and works in this direction.) 



As for the theoretical deduction of the formula, the sug- 

 gestion is given in Lorentz's ' Theory of Electrons ' (p. 309, 

 Note 56*), and NatansonJ also derives the form after a long 

 and more or less complicated discussion. But so far as I am 

 aware, the way above indicated seems the simplest one to 

 arrive at the result. 



* H. A. Loreutz, he. cit. p. 144. 



t Phil. Mag. [51 xlvii. p. 379 (1899). 



% Phil. Mag. xxxviii. p. 269 (1919). 



Phil. Mag. S. 6. Vol. 43. No. 257. May 1922. 3 H 



