498 ON PHYSICAL LINES OF FORCE. 



Let the body whose electricity is e, be moved in any way, the electricity 

 moving along with the body, then since the distribution of tension , moves 

 with the body, the value of ,e, remains the same. 



also remains the same ; and Green has shewn (Essay on Electricity, 

 p. 10) that ,<;, = ^Ai 8 that the work done by moving the body against 

 electric forces 



W =817=82(^)87 ........................ (125). 



And if e l is confined to a small body, 



or Fdr = e t dr ............................ (126), 



where F is the resistance and dr the motion. 



If the body e, be small, then if r is the distance from e,, equation (123) 

 gives 



= J? - 

 * r ' 



whence F=-E >e ?' ............................... (127); 



or the force is a repulsion varying inversely as the square of the distance. 



Now let 17, and 17, be the same quantities of electricity measured stati- 

 cally, then we know by definition of electrical quantity 



and this will be satisfied provided 



t) 1 = Ee l and t) t = Ee, .......................... (129); 



so that the quantity E previously determined in Prop. XIII. is the number by 

 which the electrodynamic measure of any quantity of electricity must be 

 multiplied to obtain its electrostatic measure. 



That electric current which, circulating round a ring whose area is unity, 

 produces the same effect on a distant magnet as a magnet would produce 

 whose strength is unity and length unity placed perpendicularly to the plane 

 of the ring, is a unit current ; and E units of electricity, measured statically, 



