L. Page — Relativity and the Ether. 173 



of a tube of strain at P at a time later than the time at 



c 



773. 



which the charge was at 0. Then if t — 



c 



r = ct 



r, = (c + dc)(t-dt) 



p = r — r, — Mdt 



= (c-V)dt - tdc (4) 



where p has the direction of the tube of strain at the point P. 

 On account of onr choice of units the total number of tubes of 

 strain diverging from the particle will be equal to the charge 

 e on the particle. If the electron is a point-charge e will be 

 finite, while if the electron occupies a Unite portion of space e 

 will be an infinitesimal of the same order as the volume dr of 

 the particle under consideration. 



If K is the system of the charged particle at the instant the 

 strain under consideration leaves the charge, V = V and it fol- 

 lows from (2) that 



sin a! da! = sin ada -—; 



(1 — (3 cos a) 



where a is the angle between the vectors V and c. Hence 



e (1-/T) p 



E = 



■iirr (1-/3 cos a) 2 p cos BAH 

 e (1-ff ) _p_ 



(5) 



!, c-V\ a 



gives the strain in the ether at the point P at a time later 



than the time when the charged particle occupied the position 

 0. E is given in terms of the distance r — OP. the velocity V 

 of the charge at the instant when it was at 0. and the vector 



° 



p. Equation (i) gives p in terms of — , which will be shown 



dt 



to be a function of the velocity V and the acceleration f of the 

 charge at the instant when it was at 0. Then it will be pos- 

 sible to express E in terms of the known quantities r, V and f 



We wish to evaluate - at the point P (tig. 2) for the par- 



ticular tube of strain which originated at O at a time earlier 



