XIII
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EXPERIMENTS ON THE CATHODE DISCHARGE
of air; and hence the equipotential lines on the plane in
which the magnet moves will be very similar to the current-
lines. The most elegant way of investigating these equi-
potential lines would be to move the plate beneath the magnet
in such a way that the latter always remains undeflected.
The curve then described by the projection of the magnet on
the plate is an equipotential line, and therefore a current-line.
But as the deflection of the magnet had to be read off from a
distance with mirror and scale, this method could not be
carried out without elaborate mechanism. Hence the follow-
ing method was adopted. The case was moved under the
magnet in such a way that the projection of the latter upon
it described a parallel to one side of the square case, and so
that the magnet in its undeflected position was perpendicular
to this parallel. The current being maintained constant, the
deflections for a series of points along this straight line were
determined. These were proportional to the differential co-
efficients of the potential along this straight line. These
differential coefficients were plotted graphically and carefully
interpolated; the area of the curve, obtained by a mechanical
quadrature, gave the changes of potential along the
straight line examined. The same process was carried
out for a series of straight lines parallel to the first, and
for one straight line perpendicular to them. Thus the
potential for all points in the plane investigated could be
specified, and it was easy to connect the equipotential
points and draw the connecting lines at such distances that
the potential increased by a constant amount in passing from
each one to the next. In consequence of the method followed
there was bound to be some uncertainty as to the values
obtained, and it was necessary to get an estimate of this. For
this purpose the potential was measured along several straight
lines perpendicular to the parallel ones, instead of along one
only. Thus the value of the potential at every point could be
determined in a corresponding number of independent ways.
By adjusting these we obtain not only a trustworthy result,
but a measure of the uncertainty attaching to the method. It
turned out that this was not large enough to interfere much
with the results.
These results can best be represented by Fig. 32, a, b, and c.