452 On Thermo-electric Circutts. 
at the hot. In other words, it is possible for the hot junction 
to be heated and the cold junction cooled, or for the initial 
inequality of temperature to be increased by the current ex- 
cited by reason of that very inequality; unless the electric 
convection of heat along the metals reduces the inequality of 
temperature to a greater extent. But for this act of repa- 
ration there is no necessity ; for instance, in the special 
cases considered, the current opposes the flow of heat by 
conduction both in iron and in copper; carrying cold with it, 
so to speak, in both cases. Thus the electric convection of 
heat, on the whole, tends to accentuate the difference of 
temperature in these cases. Conduction may reduce it, but 
in Thomson’s theory conduction is carefully regarded as a non- 
essential concomitant. 
Now howis it possible for the hottest part of a system to be 
automatically warmed, and for the coldest portion to be auto- 
matically cooled? Or, again, how can an automatically 
generated current be assisted by heat derived from the coldest 
part of a system, and be opposed by having to generate heat 
at the hottest part ? 
According to some statements of the second law of thermo- 
dynamics, such a result would be paradoxical or impossible. 
And yet the result is deduced by help of the second law itself: 
0 
or 7 is a complete differential of a temperature-function ; 
the form of the law being, ($° =(Q when taken round a circuit, 
dependent therefore on end-temperatures only, not on nature 
of metal or distribution of intermediate temperatures. 
If H is the heat converted into electrical energy at any 
part of the circuit, and E the resultant total H.M.F., then no 
doubt, as in any reversible heat-engine, the work done per cycle 
Ky=J i taken round the circuit ; 
and the disappearance of heat exactly accounts for the elec- 
trical energy without having to fall back upon degradation 
by irreversible processes such as conduction. But the note- 
worthy thing is that, whereas usually heat is destroyed at the 
hotter parts and generated at the colder parts of a system, in 
this case heat may be generated at the hottest and destroyed 
at the coldest parts ; the great bulk of the conversion of heat 
into electrical energy being carried on at intermediate tempe- 
ratures. H is not a bit proportional to absolute temperature, 
as it is in a simple heat-engine; it may even be zero or nega- 
tive, and may attain its maximum at any temperature, except 
indeed at the very lowest in the system. 
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