PROFESS OE CLERK MAXWELL OX THE ELECTROMAGNETIC FIELD, 
471 
Mechanical Action between Conductors. 
(34) The remaining terms, 
ld L 
2 dt 
t‘ 2 +^/ + ^ N 
T t y 
: =W 
(H) 
represent the work done in unit of time arising from the variations of L, M, and N, or, 
what is the same thing, alterations in the form and position of the conducting circuits 
A and B. 
Now if work is done when a body is moved, it must arise from ordinary mechanical 
force acting on the body while it is moved. Hence this part of the expression shows 
that there is a mechanical force urging every part of the conductors themselves in that 
direction in which L, M, and N will be most increased. 
The existence of the electromagnetic force between conductors carrying currents is 
therefore a direct consequence of the joint and independent action of each current on 
the electromagnetic field. If A and B are allowed to approach a distance ds, so as to 
increase M from M to M' while the currents are x and y, then the work done will be 
and the force in the direction of ds will be 
dM 
-df^ 
( 12 ) 
and this will be an attraction if x and y are of the same sign, and if M is increased as 
A and B approach. 
It appears, therefore, that if we admit that the unresisted part of electromotive force 
goes on as long as it acts, generating a self-persistent state of the current, which 
we may call (from mechanical analogy) its electromagnetic momentum, and that this 
momentum depends on circumstances external to the conductor, then both induction of 
currents and electromagnetic attractions may be proved by mechanical reasoning. 
What I have called electromagnetic momentum is the same quantity which is called 
by Faraday* the electrotonic state of the circuit, every change of which involves the 
action of an electromotive force, just as change of momentum involves the action of 
mechanical force. 
If, therefore, the phenomena described by Faraday in the Ninth Series of his Expe- 
rimental Researches were the only known facts about electric currents, the laws of 
Ampere relating to the attraction of conductors carrying currents, as well as those 
of Faraday about the mutual induction of currents, might be deduced by mechanical 
reasoning. 
In order to bring these results within the range of experimental verification, I shall 
next investigate the case of a single current, of two currents, and of the six currents 
in the electric balance, so as to enable the experimenter to determine the values of 
L, M, N. 
* Experimental Researches, Series I. 60, &c. 
