132 REPORT—1885. 
if the medium be taken into account, that of the polarisation currents in 
the dielectric. This self-induction produces very much the same effect 
as if the electric current possessed momentum—(2) the electrostatic action 
of the free electricity which tends to bring things to a definite state, and 
corresponds very much to the spring in a material system. Then, lastly, 
there is the electrical resistance, which corresponds to friction in an ordinary 
system. We see from the analogy that if the resistance be small enough, 
the electrical system will vibrate ; if, however, the resistance is large, 
the electrical disturbance will be propagated in the same way as heat. 
Kirchhoff in his paper considers the propagation of electrical disturbance 
along a wire under various conditions: we shall only consider here one 
of these cases; that of an endless wire. In his solution Kirchhoff only 
considers the self-induction of the current flowing along the wire; he 
does not consider the effects in the surrounding dielectric. He shows 
that if e be the quantity of electricity per unit length of the wire, and 
e=X sin ns, 
where s is the length of a portion of the wire measured from some fixed 
point, then X satisfies the differential equation 
OR , Wer gx Ac? aX 
de Y67i dt 2 at? 
where ¢ is a quantity which occurs in Weber’s theory, and is the velocity 
with which two charged particles must move if the electrodynamic 
attraction between them balances the electrostatic repulsion ; 
r is the resistance of the wire in electrostatic measure ; y = log L/a, 
where / is the length of the wire and a the radius of its cross section. 
The form of the solution of this equation depends on the magnitude of 
32y 
oro 
If this quantity be large, the solution takes the form representing the 
propagation of a wave along the wire with the velocity c/./2. Weber’s 
researches show that this velocity is very nearly equal to the velocity of 
light. If, however, the above-mentioned quantity be small, then the 
solution of the equation takes the same form as the formula which 
expresses the conduction of heat along the wire. We must not, however, 
take this to mean that the electric disturbance is propagated with an 
infinite velocity, so that if we had an infinitely delicate electrometer at a, 
finite distance from the source of disturbance we could detect an electrifi- 
cation after an indefinitely short time, for it seems obvious that the 
electrical resistance cannot increase the velocity of propagation any more 
than the resistance of the air could increase the velocity of propagation of - 
a disturbance along a line of particles connected by an elastic string. 
The conditions at the end help to determine the form of the solution, and 
these cannot make themselves felt until the disturbance has reached it;. 
thus the heat form of solution probably only holds after a time from the 
commencement of the disturbance greater than the time taken by light. 
to travel along the wire. If we take the case of a copper wire one square 
centimetre in area, we shall find that the wave form of solution will hold 
if the wire is not more than 100 miles in length, while the heat form 
will correspond to wires which are much longer than this. Kirchhoff’s 
