176 L. Page — Relativity and the Ether. 



(sin0'cosy' + cos0'sini//sin y ')sin0' C J4/ i + (i-W^V 



d?i' = - ' c \dyj 



Substituting these values in the expressions for dc x , dc y and 

 dc z , and reducing, we obtain the following vector equation ; 



[dVx(c--V)] xc (6) 



Hence, from (4), since t— where r = OP, 



p • r = (c 2 - V • c) I dt 



Therefore 

 E 



* (i-ff) j , p _„, , r [f X (C-V)]XC 1 



47rr 2 c/ i c-V\ 3 1 l ° Vj+ c 3 (l-/T) " | 



1 



(-) 



= «q-/n j/ r ^ v u [fx(r "- )3xr i 



If E v is the value of E for a charged particle moving with con- 

 stant velocity V, (T) can be put in the form 



(fxE.)xr 

 E — E. + c*(i-/} 2 ) <8) 



This perfectly general expression gives the ether strain at P 

 due to a charged particle at O moving with any velocity V and 

 acceleration f. However E at P is not determined by this 

 expression for the time when the charge is at 0, but for a time 

 later equal to the time taken by light to travel from to P. 

 (7) and (8) are identical with the expressions that have been 

 derived from Lorentz's retarded potentials.* It is to be noted, 

 however, that the preceding derivation is based on nothing 

 more than the assumption of the existence of an ether which 

 is in accordance with the Principle of Relativity — i. e. one 

 that transmits all non-homogeneities in straight lines with the 

 velocity of light — , and the assumption that every charged 

 particle is a center of uniformly diverging tubes of strain. 



♦Compare G. A. Schott, Electromagnetic Radiation, p. 23. 



