356 Mr. J. Parker on Thermoelectric Phenomena. 

 Hence, by (2) and (3), 



n =4* w 



Also we have seen that 



therefore 



d/8\_.fe-f. 

 dt 



Equations (4) and (5) contain the whole theory of the 

 Peltier effect and the difference of potential. 



Let us now consider the case of two portions of the same 

 metal at different temperatures. 



Let the quantities M, c, E, V, refer to a portion at the ab- 

 solute temperature t, and let M l7 c 1? E x , V 1? refer to another 

 portion at temperature t ly where t 1 = t + t, t being indefinitely 

 small. Also suppose the system to undergo the following 

 cycle of operations. 



(1) Let a quantity of electricity, q, be made to pass from 

 M to M x without altering the potential of either. The work 

 done on the system will be 



WV-vp— tej.r. 



The heat absorbed at the junction may be represented by 

 or . q. The increase of the energy of the system will be 



Hence 



_i <zv_ L dv V 

 a 2 * dt ~ 2 dt + dt ; 



therefore 



•-?♦* « 



(2.) Separate M and M 1; and then raise the temperature of 

 each by 0. The increase of entropy will be 



+ &i + <l)£ + 'j%o 



dt 



(3) After reducing M and M x to a state of electric equili- 

 brium, which may be done without producing any thermal 



