Now in fig. 4 let the ellipsoid PQ be determined by
, and the ellipsoid RS by
.
Let the angular coordinate of P and S be
, and let that of Q and R be
. Then the area PQRS
.
Now if the area PQRS revolve about the axis O
the volume of the ring traced out is
.
Thus for the magnetic part of the energy we have
Since
goes from 0 to
,
goes from
to
. The limits of
are 0 and
.
Now
.
Hence