OF ARTS AND SCIENCES. 39 



Investigations on Liqht and Heat, published with an appropriation from thb 

 RciTFOED Fund. 



III. 



TPIERMO-ELECTRICITY. — PELTIER AND THOMSON 

 EFFECTS. 



By Charles Bingham Penrose. 



Presented by Professor Trowbridg'e, June 8, 1881. 



There are two theories regarding the cause of the thermo-electric 

 current. Tliat held by Le Roux, Clausius, and most French phy- 

 sicists is that the heat effects which cause the current take place only 

 at the junctions. The theory held by Sir William Thomson, Tait, and 

 Maxwell is that the heat effects which cause the current take place, not 

 only at the junctions, but along the metals themselves. 



Let TT and ir^ denote the heat — measured in dynamical equivalents — 

 absorbed and evolved at the hot and cold junctions respectively in unit 

 time by unit current. Let -E be the electromotive force of a battery, 

 maintaining a current / in such a direction as to cause absorption of 

 heat at the hot junction. Then if H be the whole resistance of the 

 circuit, we have by Joule's law and the first law of thermodynamics : — 



EI-\-iTl—7rJ=EI\ (1) 



Supposing the whole energy of the current wasted in heat. Also : — 



I=^±^ (2) 



It appears, then, that, owing to the excess of the absorption of heat 

 at the hot junction over the evolution at the cold junction, there arises 

 an electromotive force tt-tti helping to drive the current in the direc- 

 tion giving heat absorption at the hot junction. "We may suppose, 

 and shall henceforth suppose, that ^=0, and then the current will 

 be maintained entirely by the electromotive force tt-ttj. 



Now, apply the second law of thermodynamics. " The application 

 of the second law is of a more hypothetical character. Still it seems a 

 reasonable hypothesis to assume that the Peltier effects, and other heat 



