HELMIIOLTZ ON THE CONSERVATION OF FORCE. 159 



if the iron be soft the same induced current will proceed in the 

 opposite direction when the circuit is broken, and the heat will 

 be gained again. If it be a piece of steel which retains its mag- 

 netism, the heat is permanently lost, and in place of it we gain 

 mechanical magnetic force equal, as shown in No 4, to half the 

 potential of the said magnet when the binding is complete. From 

 analogy with the foregoing cases it does not appear to be impro- 

 bable that, as Neumann has concluded, the electromotive force 

 corresponds to its entire potential, and that a portion of the mo- 

 tion of the magnetic fluids on account of their velocity is lost as 

 heat, which is gained in the magnet. 



8. If two closed conductors of currents be moved towards each 

 other, the intensity of the current may be changed in each. Let 

 V be their potential towards each other for the unit of current, 

 we must then, for the same reason as in the former case, have 



A,I,+A„I„=I,%+I/R„+il,I„§. 



If the intensity of the current in the conductor R^^ be much 

 less than that in R^ so that the electromotive force of induction 

 which is excited by Ry^ in R^ vanishes in comparison to the 



force Ap and we can set I = r^', we obtain from the equation 



A_ll^ 

 _ " a'dt 



"~ R 



The electromotive force of induction is therefore the same that 

 a magnet would generate which possesses the same electro- 

 dynamic force as the inducing current. This law has been 

 proved experimentally by W. Weber*. 



If, on the contrary, the intensity in R^ be a vanishing quan- 

 tity compared to that in Ry^, we find 



' a"dt 

 R, • 



The electromotive forces of the conductors upon each other are 

 therefore equal, when the intensities of the currents are equal, 

 whatever may be the form of the conductor. 



Here again the total force of induction, which, during a certain 



* Electro-dynamische Massbestirnmungen, p. 71-75. See also Scientific 

 Memoirs, Part XX. p. 189. 



