( 4f^.'5 ) 



the Wear in which these forces act, and of th(^ i)i'(»|»ei-ties of the elec- 

 tron, than we have as yet ohiaiiied. If e. ,u'. we introduce the so 

 called quasi-elastic force iuto the e([uations of inolion of the electron, 

 then this does not brins us any nearer to our aim. In order to show this 

 we may write tiie et|ua(ions for translation of an electron in the 

 form of a dilferential equation as Lorkntz has done in equation 73 

 p. 190 of his article "Elektronentheorie" in the Encycl. der Math. 

 Wiss. V 14. If we introduce the quasi-elastic force — fj' we may 

 write the equation as follows: 



cPx d\v d\r 



' ^ ' de ^ ■ d.e ^ ' dt' ^ 



As it is only my aim to determine the order of magnitude I have not 



determined the coefKicients {A^ and .4., have been determined by Lorkntz). 



The only thing- we have to know is that the order of magnitude of 



^l„_|_i a 

 the ratios of two successive coefiicients is — -— = ~ . The solution 



An C 



of this equation is .r= -^'ci?^' where s is a root of the equation: 



f^A,s' + A,s' -^ A,s' ....:= 



This equation has two kinds of roots, namely 1^^ two I'oots for 



wdiich the other terms are small compared with ƒ'-[- .Ij .s-' ; these 



will represent the light vilirations; 2"^' an infinite number of roots 



for which s is so large that /' may be neglected conqiared with the 



c 

 other terms. For these .s- must be of the order — , and the period of 



a 



a 

 the order — . The appearance of the term / has little inlluence on 



c 



the value of these I'oots, the periods of these vibrations are there- 

 fore nearly independent of the quasi-elastic force, and an isolated 

 electron might have executed vibrations with nearly tiie same ])eriods. 

 We might have expected a ])i'iori that we should tind periods of the 



2a . , , 



oi'der — : it represents the time re(|un'ed for the |»ropagation of an 

 c 



electric force over the diameter of the electron. The periods of these 

 vil)rations are of the same order as those of the rotatory vibi'ations 

 the periods of which have been accurately calculated in the interesting- 

 treatises of Herglotz ^) and Sommerfeld. 



The lines of the spectral series are not accounted for in this way. 

 Yet the periods of the rotation and translation vibrations of the 

 isolated electron must have a physical interj)retation. Perhaps we 

 should see them appear if we succeeded in forming the s[KH'truui of 

 RöNTGEN radiation. 



1) Herglotz, Gött. Nachr., 1903. 



