146 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



this circuit independent of the intensity. During a certain in- 

 terval the action of such a circuit will be changed in no respect 

 save in its chemical conditions and quantity of heat ; the law of 

 the conservation of force would therefore require that the heat 

 to be gained by the chemical processes which have taken place 

 must be equal to the quantity actually gained. In a simple 

 portion of a metallic conductor, with the resistance r, the heat 

 developed in a certain time t is, according to Lenz*, 



d = IV/, 



where as unit for r the length of wire is taken in which the unit 

 of current developes the unit of heat in the unit of time. For 

 branching wires, where the resistance in the single branches is 

 denoted by Va, the total resistance r is given by the equation 



r IrJ 



the intensity I in the branch r„ by 



i.=Ir. 



hence the heat ^« in the same branch, 



n 



and the total heat developed in all the branches 



d = 2[3„] = lV2[^]< = Pr.?. 



Hence the total quantity of heat developed in any circuit what- 

 ever, where the conduction is effected through any number of 

 branches, if the law of Lenz be true for fluid conductors, as 

 found by Joule, 



We have two kinds of constant batteries, those constructed 

 according to the system of Daniell and those on Grove's 

 principle. In the first the chemical process consists in the dis- 

 solution of the positive metal in an acid, while the negative one 

 is precipitated from its saline solution. Let us assume as the 



♦ Pogg. Ann. vol. lix. p. 203 and 407. From the Bulletin of the Acad, of 

 Scien. St. Petersburg. 



