( 686 ) 
those places from which electrons are carried away by the two cur- 
rents, the loss is supplied by a new production of free electrons. 
This hypothesis would imply a state of the circuit that is not, strietly 
speaking, stationary and which I shall call “quasi-stationary”. Moreover, 
we should be obliged to suppose that the production of free electrons 
or the accumulation of these particles in the metallic atoms could 
go on for a considerable length of time without making itself any- 
ways felt. 
In the second place we may conceive each element of volume to 
contain not only free positive and negative electrons, but, in addition 
to these, a certain number of particles, consisting of a positive and 
a negative electron combined. Then, the number of free electrons 
might be kept constant by a decomposition or a building up of such 
particles and we could arrive at a really stationary state by imagining 
a diffusion of this “compound electricity” between different parts of 
the circuit. 
§ 18. The mathematical treatment of our problems is much sim- 
plified by the introduction of two auxiliary quantities. 
In general, in a non-homogeneous part of the circuit, the accele- 
ration Y will be composed of the part Y,,, represented by (30), and 
e : - . > Sy 
the part — /, corresponding to the electric force /. The formula (21) 
m 
for the flow of a swarm of electrons may therefore be replaced by 
2 1 2hAdV  2heA _ dA A dh 
yp—=— al| — | — - + # ——|+2——]}. . (oi) 
3 h? m de m de) hè dz 
7 
Hy 
This will be 0, if the electric force # has a certain particular 
value, which I shall denote by E and which is given by 
E 1 dV m dlog A i md (1 (52 
nn — ZE oe EE 
e da cle Zhe de edx\h ) 
For any other value of the electric force the flow of electrons 
will be 
4 eA 
NS 
En) 
hm 
and if, in order to obtain the corresponding electric current, we mul- 
tiply this expression by e, we shall find the product of 4 — E by 
the coeflicient of conductivity, in so far as it depends on the kind 
of electrons considered. 
Substituting in (52) the value (14) and applying the result to the 
positive and the negative electrons separately, we find 
