II
ON INDUCTION IN ROTATING SPHERES
(Inaugural Dissertation, Berlin, 15th March 1880.)
THE interactions between magnets and rotating masses of
metals discovered by Arago were first explained by Faraday
as phenomena of electromagnetic attraction, and attributed to
currents induced by the magnets in the masses of metal.
Faraday succeeded in demonstrating the existence of such
currents, and in placing the inductive nature of the phenomenon
beyond doubt.
In 1853 Felici made the first attempt to apply the theory
since developed to some phenomena of this class. He succeeded
under simplified conditions in obtaining approximate solutions
agreeing with experiment sufficiently for a first approximation.
Great progress was made in 1864 by Jochmann. Start-
ing from Weber's laws he deduced the complete differential
equations of the problem, and integrated them for the case
when the rotating body is an infinitely extended plane plate
or a sphere. His calculations agreed most beautifully with
the observations. But he had to make the assumption, for
purposes of simplification, that the velocity of rotation was
very small, for he was unable to determine the effect of self-
induction.
Finally, in 1872 Maxwell gave a very elegant exposition
of the theory of the induction in an infinitely extended very
thin plate, and showed how it could be applied to the case of
Arago's disc.
In the present paper the problem is completely solved for