DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
519 
of the gas, with a term included expressing a resistance proportional to the velocity, 
are not true at any particular instant, hut only when the average is taken over a time 
which is large compared with the time a molecule takes to traverse its own free path. 
The irreversible effects which have the closest connection with the phenomena we 
have been considering in this paper are those of electrical resistance, and we shall now 
go on to consider the application of dynamical principles to phenomena of this type. 
In accordance with what we have already stated, we regard the ordinary electrical 
equations containing the terms which express the effects of the resistance as equations 
which only apply to the average state of the system, the average being taken over a 
time which is too small to allow us to perceive the changes taking place inside it; 
about these changes the ordinary equations give us no information. It is evident 
from this point of view that we cannot hope to deduce directly the ordinary electrical 
equations from these dynamical equations, which are always true, and which, if we 
could solve them, would describe the whole history of the electrical configuration. 
We should expect the electrical equations to be obtained from the dynamical ones 
by some process of averaging. 
If this view is right, the passage of a “ steady ” current is not, strictly speaking, a 
steady phenomenon ; but only one in which the average effect, taken over some very 
small time, is steady. We must therefore take a view of the electric current some¬ 
what different from that usually taken. In order to explain this view, let us begin by 
considering a case which is plainly discontinuous, but which, when the changes succeed 
each other sufficiently rapidly, will produce the same effect as a steady current. The 
case is that of the passage of electricity through a tube containing gas at a low 
pressure. In this case the electric force inside the tube increases until it gets too 
great for the electric strength of the gas, the field then'breaks down, and for a 
moment the electric force either vanishes or is very much diminished, or, what is the 
same thing, a quantity of electricity passes from the one terminal to the other; after 
this the force increases until it gets great enough to again overcome the electric strength 
of the gas, when discharge again takes place. The constant succession of such dis¬ 
charges produces the same effect as a current flowing through a metallic conductor. 
In the case of metallic conductors we may suppose that very much the same kind of 
thing goes on, only that now the electric field is dissipated by the breaking up of 
molecular aggregations which split up independently of the electric field. Let us 
imagine a conductor placed in the electric field, and suppose that at first induction 
occurs in it as well as in the surrounding dielectric : then in each unit of volume of 
the conductor there is a certain amount of energy. If the molecules or the atoms in 
the molecules can move so that this energy diminishes, they will do so ; in general, 
however, we should expect the forces existing between the atoms in the molecule to 
be so large that no very extensive re-arrangement of the atoms or molecules in the 
way suggested by the electric forces would take place unless the electric field were 
excessively strong. If, however, the molecules or the aggregations of molecules were to 
