on Thermo-electric Circuits. 451 
flow against this force, thus increasing the temperature of the 
hottest part of the circuit. 
Again, the current usually flows against the force at the 
cold junction, and therefore warms it; but it may flow with 
this force, thus lowering the temperature of the coolest portion 
of the circutt. 
It would be curious to obtain a case where the current 
flowed with the force at the cold junction and against that at 
the hot, thus carrying heat from the coldest to the hottest 
parts of the system. But, so long as the lines of a thermo- 
electric diagram are straight, this is not possible ; as may be 
seen by proving the following criteria: — 
Calling the temperature of the hot junction ¢,, 
Be * 3 cold junction ta, 
. 44 as neutral point fo, 
and denoting by ¢ the average temperature 4(t,+t.), we can 
say:-— 
The current flows against the force at the hot junction only 
when the neutral point lies between the highest and the 
average temperatures ; 
1. é. when 
fr, at 
The current flows with the force at the cold junction only 
when the neutral point lies between the lowest and 
average temperatures ; 
1. €. when 
SS te 
These conditions, though either of them is easily possible, 
are mutually incompatible ; hence both cases cannot occur at 
once. In other words, if the current flow against the force at 
the hot junction, it must flow against the force at the cold 
one too. 
The same thing is also evident by considering a thermoelec- 
tric diagram, though perhaps not quite so easily. It will then, 
however, be further perceived that the impossibility under 
consideration is not a fundamental one depending on thermo- 
dynamic laws, but is a mere consequence of the experimental 
straightness of the thermoelectric lines; and that if for any 
metal the line is really curved*, as may well be the case, so 
that between it and another there are two neutral points, it 
is quite possible to arrange so that the current shall be assisted 
by the force at the cold junction, and opposed by the force 
* Prof. Tait says that the line is strongly curved for nickel; and that 
an iron-nickel junction may have three neutral points (Tait’s ‘ Heat,’ 
p. 178). 
