Royal Society of Edinburgh. 531 



circuit ; an agency which is not reversed when the direction of the 

 current is changed. As it cannot be shown that the thermal effect 

 of this agency is infinitely small, compared with that of the electric 

 current, unless y be so large that the term By 2 , expressing the 

 thermal effect of another irreversible agency, cannot be neglected, 

 the conditions required for the application of Carnot and Clausius's 

 principle, according to the demonstrations of it which have been 

 already given, are not completely fulfilled : the author therefore con- 

 siders that at present this part of the theory requires experimental 

 verification. 



1. A first application of the theory is to the case of antimony and 

 bismuth ; and it is shown that the fact discovered by Seebeck is, ac- 

 cording to equation (c), a consequence of the more recent discovery 

 of Peltier referred to above, — a partial verification of the only doubtful 

 part of the theory being thus afforded. 



2. If 6y denote the quantity of heat evolved [or — Gy the 

 quantity absorbed] at the surface of separation of two metals in a 

 compound circuit, by the passage of a current of electricity of strength 

 y across it, when the temperature t is kept constant ; and if <p denote 

 the electromotive force produced in the same circuit by keeping the 

 two junctions at temperatures t and t', which differ from one another 

 by an infinitely small amount, the magnitude of this force is given 

 by the equation 



<p=Qn(t'—t) (d) 



and its direction is such, that a current produced by it would cause 

 the absorption of heat at the hotter junction, and the evolution of 

 heat at the colder. A complete experimental verification of this con- 

 clusion would fully establish the theory. 



3. If a current of electricity, passing from hot to cold, or from cold 

 to hot, in the same metal produced the same thermal effects ; that 

 is, if no term of "La t depended upon variation of temperature from 

 point to point of the same metal ; we should have, by equation (a), 



0=J-_ (t'— t) ; and therefore, by (d), — — =~Qu. 

 dt dt J 



From this we deduce 



e=e e J ' /o ; and <{,=((> -t) f iQ e ]Jo ' 



A table of the values of — -f — - for every tenth degree from to 



0o(£ — 

 230 is given, according to the values of /x*. used in the author's 

 previous papers ; showing, that if the hypothesis just mentioned were 

 true, the thermal electromotive force corresponding to a given very 

 small difference of temperatures, would, for the same two metals, in- 

 crease very slowly, as the mean absolute temperature is raised. Or, 



* The unit of force adopted in magnetic and electro-magnetic researches, 

 being that force which, acting on a unit of matter, generates a unit of ve- 

 locity in the unit of time, the values /x and J Med in 1 oil paper an obtained 

 by multiplying the values used in the author's former papers, bv 82'2i 

 2M2 



