H, Y. AO^OE^/l^ 

 [ 169 ] 



VIII. 



THE DYITAMICS OF A EIGID ELECTEON. 



By A. W. CONWAY, M.A., F.E.U.I., 



■Professor of Mathematical Physics, University College, Dublin. 



Read November 30. Ordered for Publication DiiCEMBEB 11, 1907. 

 Published Febhuaey 17, 1908. 



CONTENTS. 



Page. 



1. Introduction and Summary, . . 169 



2. Description of Method Employed, . 170 



3. Eesults of First Approximation, . 173 



4. Miscellaneous Properties of the 



Vector Functions Introduced, . 176 



Page. 



5. Hydrodynamical Analogy, . . 177 



6. Second Approximation, . .178 



7. Third Approximation, . . .179 



1. Introduction and Summary. 



In many investigations on the movements of electrons the electron is taken 

 to be of invariable shape, usually a sphere, and the electricity is supposed 

 to be fixed either as a uniform volume or surface distribution. It is a 

 generalization of this electron that is used in the present paper. 



A series of point charges is supposed to be connected together by a 

 rigid framework, the reactions of which are supposed to equilibrate amongst 

 themselves. Such a system will be referred to as an electron, and its velocity 

 throughout will be supposed less than the velocity of light. For very slow 

 motions if v is the velocity it is known that the motion is opposed by a 

 force ^ve-Ja where e is the charge, and a is the radius of the electron, or, 

 what is equivalent, the mass of the electron receives an increase ^e'^/a of 

 electrical origin. This is referred to as the electromagnetic mass. It is 

 also known that the motion is aided by a force ^ed'JK? where u is the 

 velocity of light, or, what is the same thing, the energy " wasted " or 

 radiated is ^e^v^jii^. The two first expressions are due to Lorentz, and the 

 last to Larmor. More extended investigations have been made by Abraham,* 

 and after him by several others. The electromagnetic mass of a sphere is 



* Annalen der Pliynik, January, 1903. 

 R. I. A. PEOC, VOL. XXVn,, «ECT. A. [241 



