154 Royal Society : — Prof. Maxwell on a 



when these are given the whole is determined. The mechanical 

 conditions therefore are those of a system of bodies connected with 

 two driving-points A and B, in which we may determine the rela- 

 tion between the motions of A and B, and the forces acting on them, 

 by purely dynamical principles. It is shown that in this case we may 

 find two quantities, namely, the "reduced momentum " of the system 

 referred to A and to B, each of which is a linear function of the 

 velocities of A and B. The effect of the force on A is to increase 

 the momentum of the system referred to A, and the effect of the force 

 on B is to increase the momentum referred to B. The simplest 

 mechanical example is that of a rod acted on by two forces perpen- 

 dicular to its direction at A and at B. Then any change of velo- 

 city of A will produce a force at B, unless A and B are mutually 

 centres of suspension and oscillation. 



Assuming that the motion of every part of the electromagnetic 

 field is determined by the values of the currents in A and B, it is 

 shown — 



• 1st. That any variation in the strength of A will produce an elec- 

 tromotive force in B. 



2nd. That any alteration in the relative position of A and B will 

 produce an electromotive force in B. 



3rd. That if currents are maintained in A and B, there will be a 

 mechanical force tending to alter their position relative to each other. 



4th. That these electromotive and mechanical forces depend on the 

 value of a single function M, which may be deduced from the form 

 and relative position of A and B, and is of one dimension in space ; 

 that is to say, it is a certain number of feet or metres. 



The existence of electromotive forces between the circuits A and 

 B was first deduced from the fact of electromagnetic attraction, by 

 Professor Helmholtz* and Professor W. Thomsonf, by the principle 

 of the Conservation of Energy. Here the electromagnetic attrac- 

 tions, as well as the forces of induction, are deduced from the fact 

 that every current when established in a circuit has a certain persis- 

 tency or momentum — that is, it requires the continued action of an 

 unresisted electromotive force in order to alter its value, and that 

 this •' momentum " depends, as in various mechanical problems, on 

 the value of other currents as well as itself. This momentum is what 

 Faraday has called the Electrotonic State of the circuit. 



It may be shown from these results, that at every point in the field 

 there is a certain direction possessing the following properties : — 



A conductor moved in that direction experiences no electromotive 

 force, 



A conductor carrying a current experiences a force in a direction 

 perpendicular to this line and to itself. 



A circuit of small area carrying a current tends to place itself 

 with its plane perpendicular to this direction. 



A system of lines drawn so as everywhere to coincide with the 

 direction having these properties is a system of lines of magnetic 



* Conservation of Force. Berlin, 1847: translated in Taylor's Scientific 

 Memoirs, Feb. 1853, p. 114. 



t Reports of British Association, 1848. Phil. Mag. Dec. 1851. 



