266 Prof. E. Edlund on the Cause of the Phenomena 



great as that which it produced by its passage through the cir- 

 cuit. Hence it has only transferred the heat from the elec- 

 tromotor to the interpolar conductor without any loss or gain of 

 heat. That this conclusion is quite correct has been experimen- 

 tally proved by Favre*. This distinguished physicist has proved 

 that the amount of heat liberated by a voltaic element whose 

 poles are connected by a conducting-wire of greater or less re- 

 sistance agrees quite accurately with the amount of heat which 

 the operations which have taken place in the battery would have 

 furnished if no current had been formed. The heat obtained in 

 the interpolar conductor, together with that which appears in the 

 battery itself, form a total amount of heat which is equal to 

 that produced by the chemical action. The current has neither 

 increased nor diminished this quantity of heat. Hence, as was 

 remarked above, in a thermoelectric pile which is unaccompanied 

 by any chemical action, the total amount of heat produced must 

 be null. I will now apply these principles to the phenomena of 

 cooling and heating discovered by Peltier. 



2. Assuming we have an electromotor of any quality, the poles 

 of which are connected with each other by a conductor, if the elec- 

 tromotive force is e, and the entire resistance in the electromotor 

 together with that in the conductor is equal to /, the total quantity 



e e 



heat evolved by the current \§ — l=e -j, or, if s is the intensity, 



= es. But, from what has been said, as much heat must disappear 

 in the electromotor or be converted into electricity. Hence 

 there must be an absorption of heat which is proportional to the 

 electromotive force multiplied by the intensity of the current. 

 If there are two electromotors whose electromotive forces are 

 e + e', and these both act in the same direction, the entire quan- 



( e _{_ e l) 27 



tity of heat developed by the current is v ' l = (e + e')s v if ^ 



1 

 and ^ denote respectively the intensity and the resistance. Hence 



this quantity of heat must be absorbed in the two electromotors 

 together. It follows thence that in each electromotor there 

 must be an absorption of heat which is proportional to the com- 

 mon intensity multiplied by the electromotive force. The result 

 will, of course, be the same if there is a larger number of electro- 

 motors, provided only they act in the same direction. 



If the electromotive forces act in opposite directions and e is 

 greater than e v a current is obtained in the direction of the first 

 force ; the total quantity of heat developed by the current is 

 = {e — e l )s u when the intensity is s u ; and just this quantity of 

 heat must disappear in the two electromotors. But in the first the 



* Ann. de Chim. et de PInjs. S. 3. vol. xl. p. 293. 



