A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 545 



To find the total quantity of electricity which passes, we have only to 

 integrate these equations with respect to t ; then if x , y a be the strengths of 

 the currents at time 0, and x u y l at time t, and if X, Y be the quantities 

 of electricity passed through each circuit during time t, 



(14*). 



When the circuit R is completed, then the total currents up to time t, 

 when t is great, are found by making / 



then X = Xl t-, Y=~x, ..................... (15*). 



The value of the total counter-current in R is therefore independent of the 

 secondary circuit, and the induction current in the secondary circuit depends only 

 on M, the coefficient of induction between the coils, S the resistance of the 

 secondary coil, and x l the final strength of the current in R. 



When the electromotive force ceases to act, there is an extra current 

 in the primary circuit, and a positive induced current in the secondary circuit, 

 whose values are equal and opposite to those produced on making contact. 



(38) All questions relating to the total quantity of transient currents, as 

 measured by the impulse given to the magnet of the galvanometer, may be 

 solved in this way without the necessity of a complete solution of the equa- 

 tions. The heating effect of the current, and the impulse it gives to the 

 suspended coil of Weber's dynamometer, depend on the square of the current 

 at every instant during the short time it lasts. Hence we must obtain the 

 solution of the equations, and from the solution we may find the effects both 

 on the galvanometer and dynamometer ; and we may then make use of the 

 method of Weber for estimating the intensity and duration of a current uniform 

 while it lasts which would produce the same effects. 



VOL. I. 69 



