AND MODERN PHYSICH. 191 



system is known, the momentum of any part of the 

 system can bo calculated by recognised processes. 

 Thus if we consider a circuit in an electro-magnetic 

 field wo can calculate the energy of the field, and 

 hence obtain tho momentum corresponding to this 

 circuit. If wo deal with a simple case in which the 

 conducting circuits are fixed in position, and only the 

 current in each circuit is allowed to vary, the rate of 

 change of momentum corresponding to any circuit 

 will givo tho force in that circuit. The momentum 

 in question is electric momentum, and the force is 

 electric force. Now we have already seen that the 

 electric force at any point of a conducting circuit is 

 given by tho rate of change of the vector potential 

 in the direction considered. Hence we are led to 

 identify tho vector potential with the electric mo- 

 mentum of our dynamical system ; and, referring to 

 tho original definition of vector potential, we see that 

 tho electric momentum of a circuit is measured by the 

 number of lines of magnetic induction which are 

 interlinked with it 



Again, tho kinetic energy of a dynamical system 

 con be expressed in terms of the squares and products 

 of the velocities of its several parts. It can also be 

 expressed by multiplying the velocity of each driving- 

 point by the momentum corresponding to that driving- 

 point, and taking half tho sum of the products. 

 Supposo, nqw, wo are dealing with a system consisting 

 of a number of wire circuits in which currents are 

 running, and let us suppose that wo may represent 

 tho current in each wire as the velocity of a driving- 

 point in our dynamical system. We con also express 



