166 
Proceedings of Royal Society of Edinburgh. [sess. 
really constant may during a part of the time more really have 
been the strength of the current through the electrodes leading 
from the complex dynamo-circuit of armature and of shunt and 
series coils of the electro-magnet, to the external permanent electric 
lighting circuit and temporary circuit through the steel bar. The 
difference of potentials between the two points of the steel touched 
must have been at first 103 volts, and must have fallen very rapidly, 
while the current which it produced in the steel rose from 0 to 85 
amperes, against ohmic resistance sinking from infinity towards 
*000137 of an ohm (this being the actual resistance of Lord Arm- 
strong’s bar to a current running full-hore through it, as I have 
found by measurement). 
The immense quasi-inertia of each partial circuit within the dynamo 
forbids the supposition that there can have been any great augmenta- 
tion of the outgoing current during the few hundredths of a second 
of the short-circuiting by the steel bar ; and, possibly with no prac- 
tical error, we may suppose that current to have been constant during 
the whole time. Hence, at each instant the electric lighting circuit 
must have lost just as much current as that which was passing 
through the steel bar. Hence, considering the smallness of the 
quasi-inertia of the electric lighting circuit, the 85 amperes through 
it before the accident must, after two or three ten-thousandths of a 
second, have been very nearly annulled, and, therefore, very nearly 
a constant current of 85 amperes must have passed for the rest of 
the time through the outer skin of the steel bar.* We have thus 
* This suggests an interesting and, happily, an easy problem regarding 
electro-magnetic induction in rectilinear electric current through a conductor 
surrounded by an insulator. Let the electromotive action, whatever its kind, 
be so regulated that the integral amount of current crossing the normal section 
of the conductor is kept constant. The mathematical statement of this con- 
dition, according to the notation of the text above, is, 
where JJdh. denotes surface integration over the cross-section of the con- 
ductor. From this, by the first of the equations of the text, 
Now, as is well known, and very easily proved, we have in every case, 
