604 GENERAL THEORIES. 



The quantity of electricity which traverses the section of the 

 first conductor in unit time is equal to mv + m^ ; if a denotes the 

 number of electrostatic units in the electromagnetic unit, we 

 have 



mv + m l v l = 

 m'v' + m\v\ = aVds' . 



Assuming the existence of equal and opposite currents, these 

 equations become 



(6) 



\ / / , ft i , 



2m v = alas . 



When we evaluate the action of the masses m and m l on the 

 masses m' and m' v the terms which depend on the product of the 

 velocities are, on the first hypothesis, 



(mv + mM) (m'v' + m'^) (mv + m^) (m'v' 4- 0/X) cos e, 



that is to say, 



and with the hypothesis of Weber, 



(mv + m-p-d (m 'v' + m\v'^) |~ , dV l)r dr~\ 



j (X -^- 13 i 



r* [_ ^sts ^ ds'\ 



2ll'dsds' f 4 Vr ^r^r~\ 



- a*fi' '- - + a 2 a'- 

 r* [_ DsW ^^'J 



The term, which is independent of the relative motion, is equal in 



both cases to MI ' , ^. This term should be null if 

 r 2 



there are two equal currents in opposite directions in each wire ; 

 if not it will represent an electrostatic action between the conduc- 

 tors, a phenomenon which up to the present time experiment has 

 not ascertained to exist. 



