On the Law of Force between Electric Currents, 451 



A detailed account of the results obtained by this method, 

 including determinations of the electric distribution on me- 

 tallic conductors, will be found in a paper recently communi- 

 cated by me to the Royal Society. 



Dulwich College, April 1881. 



LX. On the Law of Force between Electric Currents. 

 By H. W. Watson and S. H. Bukbury*. 



1. npHE laws of mutual action between electric currents, or 

 -L between separate elements of electric currents, have 

 been investigated by Ampere, and, following him, by F. E. 

 Neumann, Weber, Helmholtz, Clausius, and others. Their 

 object has been to discover a law of force between the ele- 

 ments which should give results in accordance with facts 

 established, or supposed to have been established, by experi- 

 ment. Ampere's experimental data are given by Professor 

 Tait in his work on Quaternions, second edition, p. 250, as 

 follows, using his own words : — 



"I. Equal and opposite currents in the same conductor 

 produce equal and opposite effects on other conductors ; 

 whence it follows that an element of one current has no effect 

 on an element of another which lies in the plane bisecting the 

 former at right angles. 



"II. The effect of a conductor bent or twisted in any 

 manner is equivalent to that of a straight one, provided that 

 the two are traversed by equal currents, and the former nearly 

 coincides with the latter. 



" III. No closed circuit can set in motion an element of a 

 circular conductor about an axis through the centre of the 

 circle and perpendicular to its plane. 



" IV. In similar systems traversed by equal currents the 

 forces are equal." 



To these canons, deduced from experiments of Ampere, 

 may now be added : — 



V. Oersted's experiments, showing that the action of a closed 

 circuit is equivalent to that of a magnetic shell of proper 

 strength whose boundary coincides with that of the circuit. 



Also VI., an experiment of which the details are given hi 

 Maxwell's ' Electricity,' vol. ii. p. 149, which is supposed to 

 prove directly that the force exerted by any closed electric 

 circuit on any element of another circuit is always normal to 

 the element The law of force, whatever it be, must satisfy 

 these conditions. 



* Communicated by the Authors, 



