100 JAMES CLERK MAXWELL 



an electro-magnetic system energy is stored accord- 

 ing to these laws. It follows, then, that the electro- 

 magnetic field resembles a dynamical system in 

 which energy is stored. Can we discover more of 

 the mechanism by which the actions in the field 

 are maintained? Now the motion of any point of a 

 connected system depends on that of other points of 

 the system ; there are generally, in any machine, a 

 certain number of points called driving-points, the 

 motion of which controls the motion of all other 

 parts of the machine; if the motion of the driving- 

 points be known, that of any other point can bo deter- 

 mined. Thus in a steam engine the motion of a 

 point on the fly- wheel can be found it' the motion of 

 the piston and the connections between tho piston 

 and the wheel be known. 



In order to determine tho force which is acting on 

 any part of the machine we must find its momentum, 

 and then calculate the rate at which this momentum 

 is being changed. This rate of change will give us 

 the force. Tho method of calculation which it is 

 necessary to employ was first given by Lagrange, and 

 afterwards developed, with some modifieations, by 

 Hamilton. It is usually referred to as Hamilton's 

 principle; when the equations in the original form 

 are used they are known as Lagrango's equations. 



Now Maxwell showed how these methods of calcu- 

 lation could be applied to the electro-magnetic field 

 The energy of a dynamical system is partly kinetic, 

 partly potential Maxwell supposes that the magnetic 

 energy of tho field is kinetic energy, the electric 

 energy potential. When the kinetic energy of a 



