of Vo It a ic Co o ling and He a ting. 265 



strated. The proof rests upon the general principles which 

 have been introduced into science by the mechanical theory of 

 heat. 



An electromotive force, like any other natural force, cannot pro- 

 duce mechanical work out of nothing-. The well-known principle, 

 ex nihilo nihil fit, finds everywhere a confirmation. Electromotive 

 forces are only ""transforming forces," which change one kind of 

 motion into another, and always in such a manner that the kind of 

 motion which is changed has the same mechanical value as that 

 into which it is changed; they are mechanically equivalent to 

 each other. If a closed conducting-wire is brought near a voltaic 

 current or is removed from it, induction-currents are formed in 

 the conducting-wire; and a certain amount of work is required 

 to effect this approximation or removal. By the force of induc- 

 tion this work is changed into electricity, which in turn pro- 

 duces a quantity of heat, which, as I have elsewhere* shown, 

 constitutes the mechanical equivalent of the work used. If one 

 soldering of a closed ring consisting of two metals be heated, a 

 thermoelectric current is formed which produces heat in the 

 conductors which it traverses. But this heat cannot be pro- 

 duced from nothing. The mechanical theory of heat requires 

 that just as much heat shall disappear at the heated junction, 

 or, to speak more correctly, be changed into electricity. When 

 the temperature has become the same at both junctions and the 

 thermoelectric current has ceased to circulate, as much heat will 

 have been developed in the circuit as has been changed into 

 electricity at the point of contact. Hence work has neither 

 been produced nor destroyed by the thermoelectric current. 

 If we join by a metallic wire the poles of an electromotor, for 

 instance a voltaic battery, in which chemical combinations result 

 from the action of the current, an amount of heat is produced 

 which is proportional to the square of the intensity, and to the 

 entire resistance in the battery and in the interpolar. Now, from 

 the mechanical theory of heat, as much heat must disappear in 

 the electromotor or be changed into electricity. If the heat re- 

 sulting from the chemical combinations be designated by a, that 

 produced in the electromotor by the action of the current by b, 

 and that produced in like manner in the interpolar conductor by 

 c } the quantity of heat produced in the electromotor will be 

 equal to (a-\-b) — (b + c) =a — c. Hence the entire quantity of 

 heat obtained in the electromotor and the interpolar conductor 

 will be equal to that which would have been formed from the 

 same chemical action without any current having been formed. 

 The current, therefore, has neither produced nor consumed heat ; 

 the heat necessary for the production of the current was just as 

 * Pogg. Ann. vol. exxiii. p. 193. 



Phil. Mag. S. 4. Vol. 38. No. 255. Oct. 1869. T 



