136 PROFESSOR W. THOMSON ON THE 
with the two junctions kept at temperatures differing by an infinitely small 
amount 7. In this case we have 
a Oak 
n(T)-m(T")=F-7, 
T 
Wp (0,—,) dt=(6,—@,) 7; 
7m 
and equation (13) becomes 
Pad {204 0,-0,}+ PEAS 28) SN Oe 
If we make use of (16) in this, we have 
VJ 7 Sas yee tidied iene ao ee 
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 toa small difference 
of temperature, 7, in any thermo-electric pair, and to determine, in known ther- 
mal units, the amount of the Petrier 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 Jouxe 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 Petrer 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 
