PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
481 
placed in the direction of x at the given point. We may suppose an indefinitely short 
wire placed parallel to x at a given point and touched, during the action of the force P, 
by two small conductors, which are then insulated and removed from the influence of 
the electromotive force. The value of P might then be ascertained by measuring the 
charge of the conductors. 
Thus if l be the length of the wire, the difference of potential at its ends will be PZ, 
and if C be the capacity of each of the small conductors the charge on each will be 
^CPZ. Since the capacities of moderately large conductors, measured on the electro- 
magnetic system, are exceedingly small, ordinary electromotive forces arising from 
electromagnetic actions could hardly be measured in this way. In practice such measure- 
ments are always made with long conductors, forming closed or nearly closed circuits. 
Electromagnetic Momentum (F, G, II). 
(57) Let F, G, II represent the components of electromagnetic momentum at any 
point of the field, due to any system of magnets or currents. 
Then F is the total impulse of the electromotive force in the direction of x that would 
be generated by the removal of these magnets or currents from the field, that is, if P 
be the electromotive force at any instant during the removal of the system 
F=fP dt. 
Hence the part of the electromotive force which depends on the motion of magnets or 
currents in the field, or their alteration of intensity, is 
P=-~^, Q= — — , R= — 1? (29) 
i it dt dt 
Electromagnetic Momentum of a Circuit. 
(58) Let s be the length of the circuit, then if we integrate 
j*(F£+G2+n£)* (30, 
round the circuit, we shall get the total electromagnetic momentum of the circuit, or the 
number of lines of magnetic force which pass through it, the variations of which measure 
the total electromotive force in the circuit. This electromagnetic momentum is the 
same thing to which Professor Faraday has applied the name of the Electrotonic State. 
If the circuit be the boundary of the elementary area dy dz , then its electromagnetic 
momentum is 
(f-S)** 
and this is the number of lines of magnetic force which pass through the area dy dz. 
Magnetic Force (a, /3, y). 
(59) Let a, ft, y represent the force acting on a unit magnetic pole placed at the 
given point resolved in the directions of x, y, and z. 
