486 Dynamical Theory of Currents [CH. xvi 



a direct consequence of this hypothesis. In this system the accessible parts 

 of the mechanism are the currents flowing in the wires ; the inaccessible 

 parts consist of the ether which transmits the action from one circuit to 

 another. 



Electrokinetic Momentum. 

 557. The generalised momentum corresponding to the coordinate x^ is 



Thus the generalised momenta corresponding to the currents in the 

 different circuits are N l} N 2) ..., the numbers of tubes of induction which 

 cross the circuits. The quantity N! is accordingly sometimes called the 

 electrokinetic momentum of circuit 1, and so on. 



Discharge of a Condenser. 



558. As a further illustration of the dynamical theory, let us consider 

 the discharge of a condenser. Let Q be the charge on the positive plate 

 at any instant, and let this be taken as a Lagrarigian coordinate. The 



current i is given by i ^ = Q. In the notation already employed 

 ( 516) we have 



and Lagrange's equation is 



-r ( - j ^Q + ^77 = fit, 



W +R 'dt + c ==0> 



which is the equation already obtained in 516, and leads to the solution 

 already found. 



Oscillations in a network of conductors. 



559. The equations governing the currents flowing in any network of 

 conductors when induction is taken into account can be obtained from the 

 general dynamical theory. 



Let us suppose that the currents in the different conductors are 

 hi Hi "-in, and let the corresponding coordinates be # lf # 2 , ...x n , these 



ri r/ y* 



being given by i 1 = -~ ) etc. If any conductor, say 1, terminates on a 

 condenser plate, let x^ denote the actual charge on the plate, and let the 



