HELMHOLTZ ON THE CONSERVATION OF FORCE. 153 



which occasion polarization and those which give rise to che- 

 mical decomposition, as required by the conservation of force, 

 is the only means whereby the difficulties of the theory of con- 

 tact and of the chemical theory will be alike avoided. 



TJiermo-electric currents, — In these currents we must seek 

 the origin of force in the actions discovered by Peltier at the 

 place of contact, by which a current opposed to the given one is 

 developed. Let us suppose the case of a constant hydro-electric 

 current into the conducting wire of which a piece of another 

 metal is soldered, the temperatures of the places of union being 

 t^ and t", the electric current will then, during the element of 

 time dt, generate in the entire conduction the heat V^Kdt ; besides 

 this, at one of the points where the metals are soldered together, 

 the quantity q^dt will be developed, and at the other the quantity 

 q^^dt absorbed. Let the electromotive force of the entire circuit 

 be A, hence Aldt the heat to be generated chemically, it then 

 follows from the law of the conservation of force, 



M^l^R + q-q, (1) 



Let the electromotive force of the thermo-circuit be B^, when 

 one of the soldered junctions possesses the temperature t, and 

 the other any constant temperature whatever, for example 0° ; 

 then, for the entire circuit, we have 



^^ A-B^-B,, ^^j 



When ^/=/yy, we have 



1=^. 

 R 



This set in equation (1) gives 



that is, when the temperatures of the places of soldering are 

 both the same and the intensity of the current constant, the 

 heat developed and that absorbed must be equal, independently 

 of the cross section. If we assumed that the process is the same 

 in every point of the cross section, it would follow that the heat 

 developed in equal spaces of different cross sections is propor- 

 tional to the density of the current, and from this again, that 

 the quantities generated by different currents in the whole of the 

 transverse sections are directly proportional to the intensity of 

 the current. 



