Forces in Voltaic and Thermoelectric Piles. 265 



arguments on either side without definitely committing him- 

 self to either view ; but I must protest against their assumption 

 that his equations support theirs. " But/' say they, " his 

 equations are the same as ours/'' So far as the mere shape of 

 the formulas is concerned, they are ; but their tacit under- 

 standing, implied in the very symbols they use, as to the phy- 

 sical meaning of the expressions, is quite different, and involves 

 a gratuitous assumption with which [ entirely disagree. On 

 this outpost, therefore, it is necessary that I join issue before 

 proceeding to attack the position already specified. 



I will first, for convenience, rehearse the general theory of 

 thermoelectricity as laid down by Dr. Hopkinson, because 

 nothing more concise and comprehensive than this portion of 

 his paper has yet been written on the subject. With the 

 statements so made I expect complete agreement. I shall 

 then try to show that the particular interpretation Ayrton and 

 Perry put upon these equations is certainly unnecessary and 

 probably false. I cannot indeed prove it to be false ; I can only 

 show that it is unnecessary, and that to grant it requires an 

 improbable hypothesis concerning electricity. This has been 

 shown already, but perhaps too briefly and judicially, by Dr. 

 Hopkinson. 



The statement of the general theory may run thus : — 



1. By experiment the total E.M.F. in a closed circuit of 

 any one metal is zero, however temperature be distributed. 

 Hence E.M.F. in a metallic circuit depends on a thing like a 

 potential, or dE is a perfect differential of a function of the 

 temperature ; whence, in a simple thermoelectric circuit of 

 two metals A and B, with junctions at t° and t 2 ° } 



E=/fe)-/fe) (1) 



2. The measure of E.M.F. in any complete circuit is the 

 work done per unit electricity conveyed round it, 



W 



E =f < 2 ) 



Let Tl(t) stand for the reversible heat generated per unit 

 electricity at an AB junction whose temperature is t. Let 

 S A (t)dt represent the reversible heat generated per unit elec- 

 tricity transmitted in the metal A from the temperature t to 

 the temperature t + dt; and let ® B (t)dt represent the same 

 thing for the other metal. Then, by direct application of the 

 first and second laws of thermodynamics and by differentiation, 

 Hopkinson gets, in a few lines which can hardly be abbre- 

 viated or improved, 



