226 The Mathematical Electricians of the 



electric currents. Fechner supposed every current to consist in 

 a streaming of electric charges, the vitreous charges travelling 

 in one direction, and the resinous charges, equal to them in 

 magnitude and number, travelling in the opposite direction with 

 equal velocity. He further supposed that like charges attract 

 each other when they are moving parallel to the same direction, 

 while unlike charges attract when they are moving in opposite 

 directions. On these assumptions he succeeded in bringing 

 Faraday's induction effects into connexion with Ampere's laws 

 of electrodynamics. 



In 1846 Weber,* adopting the same assumptions as Fechner, 

 analysed the phenomena in the following way : 



The formula of Ampere for the ponderomotive force between 

 two elements ds, ds' of currents i t i ', may be written 



r ds ds r 2 ds ds' 



Suppose now that X units of vitreous electricity are contained 

 in unit length of the wire s, and are moving with velocity u ; 

 and that an equal quantity of resinous electricity is moving 

 with velocity u in the opposite direction ; so that 



Let X', u', denote the corresponding quantities for the other 

 current; and let the suffix ! be taken to refer to the action 

 between the positive charges in the two wires, the suffix 2 to 

 the action between the positive charge in s and the negative 

 charge in s, the suffix 3 to the action between the negative 

 charge in s and the positive charge in s', and the suffix 4 to the 

 action between the negative charges in the two wires. Then 

 we have 



'dr\ dr , dr 



= u + u ,, 

 dtji ds ds 



* Elektrodynamische Maassbestimmungen, Leipzig Abhandl., 1846 : Ann. d. 

 Phys. hcxiii (1848), p. 193: English translation in Taylor's Scientific Memoirs, 

 v (1852), p. 489. 



