we might deduce from it expressions for the fall of potential in each 
point and for the difference of potential between the ends of the bar. 
It is more interesting, however, to make a calculation of this kind 
for a more general case. Before doing so, we may observe that the 
equations (21) and (22) may be applied to a thin curved wire or 
bar and that we may as well suppose the normal section slowly to 
change from one point to another. The line passing through the 
centres of gravity of the normal sections may be called the axis of 
the conductor and we shall understand by « the distance from a 
fixed point, measured along this axis. We shall also assume that in 
all points of one and the same normal section the properties of the 
bar and the temperature are the same, but that, generally speaking, 
both depend on z, changing from one section to the next. By making 
different assumptions in this respect, we come to consider circuits 
of different kinds, composed of one or more metals and with any 
distribution of temperature we like. 
For the sake of generality we shall introduce the notion of 
“molecular” forces of one kind or another exerted by the atoms of 
the metal on the electrons and producing for each electron a resulting 
force along the circuit in all points where the metal is not homo- 
geneous. Actions of this nature have been imagined long ago by 
HermnorLtz for the purpose of explaining the phenomena of contact- 
electricity. We may judge of their effect in the simplest way by 
introducing the corresponding potential energy WV of an electron 
relatively to the metallic atoms. This quantity, variable with » 
wherever the metal is not homogeneous, will be a constant in any 
homogeneous part of the circuit; we shall suppose this even to be 
so in case such a part is not uniformly heated. If, as before, we 
write p for the electric potential, the force X divides into two parts 
X = Xn + Xe, 
1 dV en 
We shall now consider an open circuit, calling the ends Pand Q, 
and reckoning wv from the former end towards the latter. Putting in 
(21) vr =O and attending to (30), we obtain for the stationary state 
dp 1dV md ( -) m dlog A 
ite eda eo dc Nh 2eh dx 
be Bue et) 
whence by integration 
31* 
