94 



<p = J — — (t' — t); and therefore, by (d), — !_=_ 0^. 

 Cu t oL t o 



From this we deduce 



0=0^ e ^•'^ ; and ^ = (^^-0/. 0,6'^*^" 

 A table of the values of ^^ ^ for every tenth degree from to 



230 is given, according to the values of ^,* used in the author's 

 previous papers ; shewing, 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, 



if Mayer's hypothesis, which leads to the expression — — — for /a, 



were true, the electromotive force of the same pair of metals would 

 be the same, for the same difference of temperatures, whatever be 

 the absolute temperatures. Whether the values of ^ previously 

 found were correct or not, it would follow, from the preceding expres- 

 sion for <p, that the electro-motive force of a thermo-electric pair is 

 subject to the same law of variation, with the temperatures of the two 

 junctions, whatever be the metals of which it is composed. This 

 result being at variance with known facts, the hypothesis on which 

 it is founded must be false ; and the author arrives at the remark- 

 able conclusion, that an electric current produces different thermal 

 effects, according as it passes from h.ot to cold, or from cold to hot, 

 in the same metal. 



4. If ^ (f — *) be taken to denote the value of the part of 2 a^ which 

 depends on this circumstance, and which corresponds to all parts of 

 the circuit of which the temperatures lie within an infinitely small 

 range t to t' ; the equations to be substituted for the preceding are, 



^ = ,j'i^(^t'-t)+J^(t'-t) .... (e) 



and therefore, by {d) 



+ ^=0^ (/) 



dt J 



5. The following expressions for F, the electromotive force in a 



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

 ing that force which, acting on a unit of matter, generates a unit of velocity in 

 the unit of time, the values of fx, and J used in this paper are obtained by mul- 

 tiplying the values used in the author's former papers, by 32-2. 



