of Force betiveen Electric Currents, 455 



This law of force gives no potential of the action of one ele- 

 ment upon another ; but, as we have said, it gives the potential 



ii' \ \ ds ds f 



'f 



for the mutual action of two closed circuits. 



6. Weber has further shown that if an 'electric current be 

 supposed to consist of positive electricity moving with velo- 

 city v in one direction, and an equal quantity of negative 

 electricity moving with the same velocity in the opposite 

 direction, then a certain hypothesis regarding the force exerted 

 on one another by particles of electricity in motion not only 

 leads to Ampere's law of force, but also explains the ordinary 

 phenomena of induction by variation of the primary current, 

 or by variation of the position of the circuits. Weber's hypo- 

 thesis is that the mutual potential of two particles of electri- 

 city e and e r is 



r \ 2c 2 \dt) S' 



dr 

 where c is a constant. If the particles be at rest, -=- = 0, and 



this expression gives the ordinary electrostatical potential — -. 



If they be in motion, it will be found to lead to Ampere's 

 law, as shown by Briot*. The coincidence appears at first 

 sight remarkable, and has done much to facilitate the accept- 

 ance of Ampere's results as well as Weber's. It will be seen, 

 however, on further considering the subject, that Ampere and 

 Weber both start from the same fundamental assumption with 

 regard to the nature of the action between two elementary 

 currents — viz. that it depends not only on their directions 

 relative to each other, but also on their directions relative to 

 the line joining them. This may perhaps account for their 

 leading to the same result. 



7. Stefan has shown f that, assuming the only forces acting 

 to be, as Ampere assumes, 



-5 cos 6 cos 6'ii f ds ds', 

 r 2 ' 



and 



~2 sin sin 6' cos $ii' ds ds f , 



then, if there be a potential for two closed circuits, such poten- 



* Theorie mecanique de la Chaleur, chap, ix, 

 f Sitzungsb&ichte, Vienna, 1869, 



