of Force between Electric Currents. 457 



component of the force which a moving particle of electricity 

 e exerts on another, ef, is expressed by the formula 



J -rf ,Jd®<M jL*5L§!!LjL.**teS\-. ii_(l c h\\ 

 Ce \dx\ + \dt dt + dt dt + dtdtJ) dArdtJy 



where #, y, z relate to the first and a/, y r , z' to the second par- 

 ticle (see Phil. Mag. October 1880). 



10. It seems that the Continental physicists consider the 

 force between two elementary currents as a force of transla- 

 tion only, excluding from their consideration "couple-action," 

 whereby one element tends to turn the other round an axis 

 without altering its position in space. But such couple-action 

 results immediately, as will be shown later, from F. E. Neu- 

 mann's law of potential. 



11. Maxwell has treated the subject in a different way. 

 While giving Ampere's reasoning and his results, as well as 

 those of Weber, he founds his own theory on the hypothesis 

 that in nature all circuits are closed circuits, and proceeds to 

 obtain the known results of experiment, by the application of 

 ordinary dynamical methods to the theory of closed circuits — 

 that is, that if the circuits be not closed by conductors, there 

 arise changes of displacement of electricity in dielectrics which 

 have the effect of closing the currents. 



12. Now, if it be true, as Maxwell teaches, that in nature, or 

 within the range of our experiments, all currents are closed, 

 there can be no necessity for devising elaborate laws of force. 

 We have only to assume for each pair of elements the potential 



V = jdi' — - — ds ds'j 



and we cannot fail to obtain results in accordance with expe- 

 riment, and, in fact, exactly the same results as are obtained 

 from any of the more complicated laws above stated ; so that, 

 on this view, no experiment could furnish any reason for 

 accepting one law rather than the other. It appears to us, then, 

 that if Maxwell's theory, that all currents are closed, be ac- 

 cepted, the law that, for each pair of elementary currents, 



-r 7 . ., cos 6 , 



V =ixi%' dsds' 



r 



ought to find provisional acceptance also. 



13. But as Maxwell's theory is not accepted universally, 

 we proceed to examine some of the experimental evidence on 

 which the doctrine is based, that a closed circuit exerts a 



