1889-90.] Sir William Thomson on Ohmic Resistance. 165 
for the static electrification is not negligible in a large variety of 
telegraphic and telephonic problems.* In the ocean cable problem 
it is of paramount importance ; and the electro-magnetic induction 
with which we are now occupied is negligible. In shorter cables 
and high-speed action both the electro-static and electro-magnetic 
induction must he taken into account, and both have been very 
practically taken into account by Heaviside in the mathematical 
theory of the telephone. 
In a vast variety of laboratory experimental arrangements the 
currents required for the static charges are quite negligible. In 
such a case* as that of Lord Armstrong’s experiment, the quantity of 
electricity required for producing or changing the electrification of 
every part of the circuits or of the conductors concerned is clearly 
quite insensible iu comparison with the quantity which must have 
flowed through the bar to produce the observed heating effect. 
But although we are not troubled with any difficulty in respect 
to electro-static charge, we have in Lord Armstrong’s case circum- 
stances of such extreme complexity that it is of no use to attempt 
to work out a complete mathematical theory. It seems probable, 
however, that the solution indicated above, and represented by my 
diffusion diagram, fairly illustrates the circumstances of the current 
which actually flowed through the steel bar, though scarcely with any 
approach to quantitative correctness. At all events we have a very 
striking illustration of what really took place, and ample explanation 
of the intensity and suddenness of the effect perceived by Lord Arm- 
strong, by working out the result numerically of what would take place 
if a difference of potentials of 100 volts were suddenly instituted, 
and forcedly maintained constant during one or two or three ten 
thousandths of a second between two points of the bar 15 J centi- 
metres asunder. This with any reasonable assumption as to the 
magnetic permeability of the iron or steel bar, and its diffusivity 
for electric currents, is easily done on the supposition A. = 0, and 
the solution conveniently represented by the diffusion diagram. 
We must not, however, suppose that the difference of potentials 
between the two points of the steel bar touched by the main elec- 
trodes of the dynamo was in reality constant at 103 volts, even for 
so long a time as two or three ten thousandths of a second. What was 
* Papers, Yol. II. Arts. 72-77 and 80-83. 
