644 Mr. C. H. Livens on the Initial Accelerated 



The electromagnetic mass of the sphere, defined as the ratio 

 T/sj is therefore 



2 e 2 s\ -fa <*SZ\ 2 e 2 e-L m cty /% 

 ™= o —2[ 1 "' e cos— — 5 — 2 sin-^-—. 



3 ac 2 \ 2a J 3 ac 2 ^3 B 2a 



The value of m is initially zero, but rapidly approaches the 



2 e 2 

 ordinarily assigned value 7, — 2 • The sphere therefore starts 



o ac 



off without offering any electromagnetic inertia to its motion 

 initially. The force and mass, however, both differ from 

 zero at any finite time, however small, after the initial 

 instant. This fact is explained quite easily from general 

 principles. The system to be moved is specified by a certain 

 state in the aether around the sphere. Now the aether at any 

 place is not affected by any motion of the sphere until after 

 the time that radiation, leaving the sphere at the initial 

 instant of its disturbance, takes to reach that place ; and it 

 cannot, therefore, offer any reaction to the motion of the 

 sphere until after that time. 



Other conclusions, similar to those deduced by Walker, 

 can be deduced ; the only distinction being that none of the 

 results here given involve the "material'" mass of the sphere. 

 The production of a small uniform acceleration causes a 

 readjustment of the charge distribution. The readjustment 

 of the charge, however, involves an oscillation which sends 

 out a damped periodic wave train into the aether. The oscil- 

 lations and wave-motion are, however, soon damped out of 

 the system, and a sort of steady state is reached in which 



a e 2se n 



4-770-= — — 5COSC7 



or acr 

 9 ^2 

 o ac 



II. The sphere accelerated from a uniform motion 

 with velocity v. 



The velocity is supposed to have been uniform for an 

 indefinite time before the initial instant considered. 



Now, according to Larmor*, if we refer the phenomena 

 to a set of axes moving with a velocity v, the fundamental 

 equations of the theory, the Maxwell equations referred to 

 moving axes, assume exactly the same form as they had 

 originally referred to fixed axes. 



* See '^Etlier and Matter,' pp. 173-175. 



