THEORY OF HELMHOLTZ AND THOMSON. 495 



It will be seen that the differential plays the part of an 



at 



electromotive force acting in the contrary direction to E, and 

 capable of producing a current i in the contrary direction to the 

 principle current, so that the resultant current I still satisfies Ohm's 

 law, under the form 



(6) E-g-IR. 



The quantity ~= is called the electromotive force of induction ; 



if is equal to the differential, in respect of time, of the flow of magnetic 

 force which traverses the circuit. 



If the value of ^Q is positive that is to say, if the flow of 

 force increases, the electromotive force of induction diminishes 

 the strength of the current, and the work of the electromagnetic 

 forces is positive. If, on the contrary, the value of */Q is negative, 

 the magnet is displaced in resisting the electromagnetic forces, and 

 this operation introduces a fresh energy into the system ; the strength 

 of the current is then greater than in a state of rest. 



515. The quantity dm or idt of electricity induced in the wire 

 is given by the equation 



(7) . i^dt=Kdm = dQ. 



The total quantity of electricity m corresponding to a finite dis- 

 placement, for which the flow of force passes from the value Q x to 

 the value Q 2 , is therefore 



516. The establishment of the current in a circuit requires itself 

 work which we have not taken into account, and this work (to which 

 we shall subsequently revert) is a function "SP of the strength of the 

 current During the variable period, the energy of the chemical 

 action should also furnish the work d"*P which corresponds to an 

 increase d\ of strength. Equations (3) and (5) then become 



(9) 



