136 PROFESSOR W. THOMSON ON THE 



with the two junctions kept at temperatures differing by an infinitely small 

 amount t. In this case we have 



J 



xJ m 



n(T)-n(T0=^r, 



T 



T' 



and equation (13) becomes 



If we make use of (16) in this, we have 



n 



F=J t t (19). 



The first of these expressions for the electro-motive force involves no hypothesis, 

 but only the general principle of equivalence of heat and work. Its agreement 

 with any experimental results is only to be looked on as a verification of the ac- 

 curacy of the experiments, and can add nothing to the certainty of the part of 

 the theory from which it is deduced. On the other hand, it would be extremely 

 important to test the second expression (18) by direct experiment, and so confirm 

 or correct the only doubtful part of the theory. The way to do so would be to de- 

 termine, in absolute measure, the electro-motive force, F, due to a small difference 

 of temperature, t, in any thermo-electric pair, and to determine, in known ther- 

 mal units, the amount of the Peltier effect at a junction of the two metals, with 

 a current of strength measured in electro-dynamic units, as we should then, by 

 these determinations, be able to evaluate from direct experiments the values of 

 the two members separately which appear equated in (18). As yet no observa- 

 tions have been made which lead, directly or indirectly, to the evaluation of the 

 second member of (18) in any case; but I hope before long to succeed in carry- 

 ing out a plan I have formed for this object. Neither have any observations been 

 made yet, which give in any case a determination of the first member ; but they 

 may easily be accomplished by any person who possesses a conductor of which 

 the resistance has been determined in absolute measure. Mr Joule having kindly 

 put me in possession of the silver wire on which his observations of the electrical 

 generation of heat, in 1845, were made with currents measured by a tangent gal- 

 vanometer used by him about the same time in experimenting on the electrolysis 

 of sulphate of copper and sulphate of zinc, I hope to be able to complete the test 

 of the theoretical result without difficulty, in any case in which I may succeed 

 in determining the amount of the Peltier thermal effect. 



117. In the mean time, it is interesting to form an estimate, however rough, 

 of the absolute values of the thermo-electric elements, in any case in which ob- 

 servations that have been made afford, directly or indirectly, the requisite data. 

 This I have done for copper and bismuth, and copper and iron, in the manner 



