108
II
INDUCTION IN ROTATING SPHERES
The determination of these currents presents no further
difficulty apart from self-induction. I shall not enter in detail
into the calculations. Fig. 10 represents the simplest case.
A homogeneous magnetic sphere rotates about its magnetic
axis. The figure drawn represents the lines of flow in a
FIG. 10.
meridional section. The form of the lines of flow does not
depend upon the resistances of the magnet and the liquid.
But the intensity vanishes when either resistance becomes
infinitely great.
§ 8. SOLUTION FOR THE FORMULÆ OF THE POTENTIAL LAW.
So far we have assumed for the induced electromotive
forces the expressions which Jochmann has deduced for them
from Weber's fundamental law. We shall now inquire what
changes the results undergo when we use the formula which
follow from the potential law and are given in vol. lxxviii. of
Borchardt's Journal.¹
If X, Y, Z denote the electromotive forces hitherto assumed,
X', ', ' those which follow from the potential law, we have
¹ Helmholtz, Wiss. Abhandl. vol. i. p. 702.