A DYNAMICAL THEORY OF THE ELECTBOMAGNETIC FIELD. 555 



Electromotive Force (P, Q, R). 



(56) Let P, Q, R represent the components of the electromotive force at 

 any point. Then P represents the difference of potential per unit of length in 

 a conductor placed in the direction of x at the given point. We may suppose 

 an indefinitely short wire placed parallel to x at a given point and touched, 

 during the action of the force P, by two small conductors, which are then 

 insulated and removed from the influence of the electromotive force. The value 

 of P might then be ascertained by measuring the charge of the conductors. 



Thus if I be the length of the wire, the difference of potential at its ends 

 will be PI, and if (7 be the capacity of each of the small x conductors the charge 

 on each will be \CPl. Since the capacities of moderately large conductors, 

 measured on the electromagnetic system, are exceedingly small, ordinary electro- 

 motive forces arising from electromagnetic actions could hardly be measured in 

 this way. In practice such measurements are always made with long conductors, 

 forming closed or nearly closed circuits. 



Electromagnetic Momentum (F, G, H). 



(57) Let F, G, H represent the components of electromagnetic momentum 

 at any point of the field, due to any system of magnets or currents. 



Then F is the total impulse of the electromotive force in the direction of 

 x that would be generated by the removal of these magnets or currents from 

 the field, that is, if P be the electromotive force at any instant during the 

 removal of the system 



F-jPdt. 



Hence the part of the electromotive force which depends on the motion of 

 magnets or currents in the field, or their alteration of intensity, is 



dF dG dH 



Electromagnetic Momentum of a Circuit. 

 (58) Let * be the length of the circuit, then if we integrate 



s (30) 



702 



