830 Mr. U. Doi on Scattering 



an electron. Lorentz* assumes on the contrary that there 

 is no damping, but that the electron can continue to vibrate 

 further and further, restrained only by radiation, until 

 the molecule collides with another. When this happens, he 

 assumes that all the energy of the vibration will be trans- 

 ferred to energy of translation, or thermal agitation as it is 

 called, of molecules. The effect of this he proves equivalent 



to a damping force -j , where m is the mass of an 



electron, and t is the mean time between collisions of mole- 

 cules. Thus, denning the absorption coefficient Jc by the 

 equation 



dx 

 he finds j 



±7rn 2 g'Ne 2 /c ( _%m\ 



2/ m '2 __ Iyi 2\ _j_ ™2„,2 ' V~ T / 



k = 



m\n ' 2 -n 2 ) -\-n 2 g- 



The meanings of the notations may need no explanation, as 



one is, if necessary, rather preferably referred to the 



original. 



It seemed, next, to Nagaoka J and Planck § that the 



f 2 ■ •• 

 reaction, ~-^ P. to the radiation of an electron, when it has 

 br * 



an acceleration, f, will act frictionally. Along this line of 

 idea Planck derives the coefficient of extinction, which 

 agrees with Payleigk's formula for the scattering coefficient. 

 The general process of deriving the coefficient is to insert 

 a term of this frictional force in the equation of motion of 

 the electron, and to calculate the energy dissipated in 

 overcoming this friction. The calculation, however, requires 

 too complicated a process to be summarized here clearly. 



Be that as it may, the scattering is another thing, in a 

 rigorous sense, than the extinction or absorption ; and the 

 calculation of what part of the energy of the incident radi- 

 ation is dissipated in overcoming any frictional force exerted 

 by molecules of the medium through which the light travels, 

 does not offer us any means of deducing the coefficient of 

 scattering, as the energy absorbed by the medium is not all 

 scattered by it, — a part, at least, of the absorbed energy is 

 converted, as we know, to the heating agent of the medium, 



* H. A. Lorentz, ' The Theory of Electrons,' p. 141 (1916). 



t Phys. Eev. iv. p. 189 (1914). 



% Proc. Tokvo Math.-Phys. Soc. ii. p. 280 (1904). 



§ Sitzungsber. d. Kgl-Pr. Akad. d. Wiss. p. 748 (1904V 



