1864.] 



of the Electromagnetic Field. 



533 



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 perpendicular to its direction at A and at B. Then any 

 change of velocity of k. will produce a force at B, unless A and B are 

 m.utually 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 electromo- 

 tive 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 mecha- 

 nical 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 Helm- 

 holtz* and Professor ^y. Thomson f, by the principle of the Conservation 

 of Energy. Here the electromagnetic attractions, as well as the forces of 

 induction, are deduced from the fact that every current when established 

 in a circuit has a certain persistency 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 pro- 

 blems, 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 per- 

 pendicular 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 force ; and if the 

 lines in any one part of their course are so distributed that the number of 

 lines enclosed by any closed curve is proportional to the electric momen- 

 tum " of the field referred to that curve, then the electromagnetic pheno- 

 mena may be thus stated : — 



The electric momentum of any closed curve whatever is measured by the 

 number of lines of force which pass through it. 



Conservation of Force. BerUn, 1847 : translated in Taylor's Scientific Memoirs, 

 Feb. 1853, p. 114. 



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



