﻿deduced from the Electrical Theory of Matter, 69 



also be made to depend on a vector potential A of the form 



= ]}[/>wj 



fS 



where the square brackets have the meaning assigned above, 

 and W is the velocity of the electricity. It* we like, we may 

 interpret the above by saying, that an element of charge 

 pd$ at rest at the point O produces at P a force derivable 



from a potential yjr = — "- — , but when the charge is moving, 



and is at the point 0, this part of the total force does not 



make its appearance until a time — after the element has left 



\j 



0, this time oFcourse representing the time taken for light to 



travel from to P. An analogous remark applies to the 



expression for A. The magnetic field a, /3, y is related to 



the potential A in the manner expressed by 



i a , /3A_. BA y BA X "dA s BA y ?)AA 

 The force (X l5 Y l5 ZJ is given by 



and the total force acting on an electron at rest in the aether, 

 and of unit strength, is 



(\, i , L) - y - ^ - ~^ f , - d - - -^ -, - B - - ~^j. w 



Thus the quantities ty and A are all that are needed to com- 

 pletely determine the held. The values of ijr and A for a 

 single point electron of strength e moving with velocity W 

 are * 



where /• is the distance measured, not from the electron to 

 the point P, but from some point 0, previously occupied by 

 the electron, and so situated that the time taken for the 

 electron to pass from to its present position is the same as 

 the time taken for light to pass from to P. AV r is the 

 velocity of the electron resolved along the line OP. 



* Lorentz, * Theory of Electrons,' p. 50, 



