36
II
INDUCTION IN ROTATING SPHERES
Coordin-
ates.
the case when the body considered is a solid or hollow sphere
rotating about a diameter. The inducing magnets may be
outside, or in the case of the hollow sphere in the inside space.
The solution is also extended to the case where the material
of the sphere is capable of magnetisation. Clearly this problem
involves those previously solved as special cases.
I have attempted to exhibit the results obtained by means
of several drawings.
§ 1. DEFINITION OF THE SYMBOLS.
In this paragraph the symbols to be employed will be
defined and some formula will be collected together which
will be constantly required in the sequel.
1. The system of coordinates selected is that shown in
Fig. 6. The positive directions of rotation are marked in the
figure. The axis of z will be taken to
coincide with the axis of rotation.
Polar coordinates p, w, 0 will be used:
w is to correspond to geographical
longitude, is to be 0 in the zx-plane
for positive x, and is to increase in
the direction of positive rotation;
is to correspond to the complement
of the geographical latitude, and is to
We shall occasionally use the
FIG. 6.
Ө
be 0 in the positive z-axis.
notation
a
giờ giờ gi
y
მე
-
a a a
=
=
Y ax
dx dw₂ dw'
X
2
ә
=
a
Əzawy
a
by
=
dwi
Further, as in Lagrange's notation, differentiation with respect
to w will be denoted by a dash, e.g.
=