242
XIII
EXPERIMENTS ON THE CATHODE DISCHARGE
It was only 2 mm. above the surface of the upper glass
plate, and therefore 12 mm. above the mean stria of gas
through which the current passed. When the current was
turned on, the magnet was deflected, the deflection depending
upon the strength of the current and the direction of its path
with reference to the needle. The total current used was from
Too to do Daniell/S.U. In favourable positions of the needle
this gave deflections up to eighty scale-divisions. As one-
tenth of a division could be read off, the measurements could
be made accurately. With the help of the squared paper the
position of the plate with reference to the magnet could be
altered and accurately read off. Such an arrangement enables
us to determine with considerable accuracy the distribution of
magnetic force which the current in the stria of air pro-
duces just above and parallel to itself. But what we have to
do is to deduce from this distribution the distribution of the
current in the air-stria itself.
This can be done with the aid of the following pro-
position: The current-function of the electric current in a
plane stria is equal to the potential function of the mag-
netic force excited by the current in the immediate neighbour-
hood of the stria, multiplied by a constant. The current-
lines therefore coincide with the magnetic equipotential lines,
and the current-strengths between every two equipotential
lines, between which the potential increases by the same
amount, are equal. A proof of this proposition may be found
in Maxwell's Treatise on Electricity and Magnetism. But it
can easily be seen to be true if we consider the case of a
magnetic pole brought infinitely near to a plate traversed by
a current; for only those parts of the current which are in its
immediate neighbourhood can exert upon the pole a force
parallel to the plate.
1
The current-stria which we have to investigate is not
infinitely thin, and the testing magnet does not lie in the
immediate neighbourhood of its mean plane, but 12 mm. above
it. Hence it only enables us to investigate the distribution
of the potential in a plane which is 12 mm. above the mean
plane of the stria of air. But the magnetic force in this
plane will be approximately the same as that inside the stria
1 Vol. ii. p. 264, 1873.