A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 543 



as well as those of Faraday about the mutual induction of currents, might be 

 deduced by mechanical reasoning. 



In order to bring these results within the range of experimental verifica- 

 tion, I shall next investigate the case of a single current, of two currents, and 

 of the six currents in the electric balance, so as to enable the experimenter 

 to determine the values of L, M, N. 



Case of a single Circuit. 



(35) The equation of the current a; in a circuit whose resistance is R, 

 and whose coefficient of self-induction is L, acted on by an external electro- 

 motive force , is / 



.............................. (13). 



When $ is constant, the solution is of the form 



where a is the value of the current at the commencement, and b is its final 

 value. 



The total quantity of electricity which passes in time t, where t is great, is 



,L 



(14)- 



The value of the integral of of with respect to the time is 



(15). 



The actual current changes gradually from the initial value a to the final value 

 b, but the values of the integrals of x and a? are the same as if a steady 



current of intensity \ (a + b) were to flow for a time 2 -^ , and were then suc- 

 ceeded by the steady current b. The time 2 -p is generally so minute a fraction 



xc 



of a second, that the effects on the galvanometer and dynamometer may be 

 calculated as if the impulse were instantaneous. 



If the circuit consists of a battery and a coil, then, when the circuit is 

 first completed, the effects are the same as if the current had only half its 



