646 Mr. G. H. Livens on the Initial Accelerated 



In fact, i£ the force per unit charge on any element executing 

 any motion in the system at rest be determined as (P x Q x R x ), 

 then the force per unit charge on the element executing the 

 corresponding motion relative to the moving axes is deter- 

 mined by (P, Q 7 R), where 



Again, the accelerations of any point determined as 

 (si,Si, a/'), when referred to the axes at rest in the aether, 

 become when they refer to the point executing a corresponding- 

 motion in the correlated system (s, s', s"), where 



(*i, V, s l ") = e* (es, eV, eh"), 



if the point is always near the origin of the coordinates. 



Thus if in the case of a system referred to fixed axes we 

 have determined the equations of linear motion, considered 

 merely in its electrodynamic aspects, in the form 



(P 1 Q 1 B 1 ) = (m l5l ,m 1 '.9/,m 1 V) J 



mi nil m" being determined as the electromagnetic masses 

 for the system in motion, as a whole, along the three axes of 

 coordinates ; then the equations of motion for the same 

 system executing a corresponding motion referred to axes in 

 uniform motion along the ^-axes will be 



(P, Q, R) = (m^^s, m-^ei $/, m{'e§ a/'). 



The electromagnetic masses for the new system, which has 

 the additional motion with velocity v along the x x axis, are 

 therefore 



(m, m' , m") = (m : e 3 ' /2 , 7ft/ e*, fti/'e*). 



From these preliminary remarks it will be at once seen that 

 the solution which we have already obtained for the initial 

 accelerated motion of a charged perfectly conducting sphere 

 can be transferred to the case for the sphere initially in 

 uniform motion with any velocity v, if the vectors are inter- 

 preted properly. One other condition has to be satisfied. 

 The equation of the sphere has to remain of the form 



x*+f + z 2 = a 2 , 



and to ensure this we must accept the Lorentz contraction 

 hypothesis, which I propose to do, and have already tacitly 

 done in the previous general discussion. Jn the solution 

 transferred to the case of initial uniform motion the general 

 electrodynamic vectors (/ 2 g 1 /ii)(«i A c x ) determined in terms 



