I 



HELMHOLTZ ON THE CONSERVATION OF FORCE. 145 



class may evidently be deduced from the assumption that dif- 

 ferent chemical substances possess diflferent attractive forces for 

 both electricities, and that these attractions are only exerted at 

 insensible distances ; while the mutual attractions of the electri- 

 cities themselves are exerted at measurable distances. The force 

 of contact would, according to this, be the difference of the 

 attractive forces which the metallic particles at the place of con- 

 tact exert upon the electricities at this place ; and electric equi- 

 librium would occur when an electric particle which passes from 

 the one to the other neither gains nor loses vis viva further. 

 Let Cf and c^y be the free tensions of the two metals, a^e and a^^e 

 the vires vivos gained by the electric particle e by its passage to 

 the one or the other uncharged metal, then the force gained by 

 its passage from one to the other charged metal is 



In the case of equilibrium this must be =0, and hence 



that is, the difference of tension in different portions of the same 

 metal must be constant, and in different metals must follow the 

 law of the tension series. 



In galvanic currents, with respect to the conservation of force, 

 we have specially to consider the following actions : the genera- 

 tion of heat, chemical processes, and polarization. The electro- 

 dynamic actions shall be considered under the head of mag- 

 netism. The development of heat is common to all currents ; 

 in regard to the two other actions, we can divide the currents 

 into those which excite chemical decomposition only, those 

 which excite polarization only, and those which excite both. 



We will, in the first place, investigate the conditions of the 

 conservation of force in those circuits in which the polarization 

 is completely annulled, inasmuch as these are the only ones for 

 which we have arrived at determinate quantitative laws. The 

 intensity of a current I in a battery of n elements is given by 

 the law of Ohm as 



where the constant A is the electromotive force of a single ele- 

 ment, and II is the resistance of the circuit ; A and R are in 



