110
II
INDUCTION IN ROTATING SPHERES
the direction of its motion.¹ Let the coordinates of the pole
be 0, 0, c; then its potential is
-
1
x= √§²+n²+(5+c)²
1
=-
Thus the induced potential of the first order becomes for
positive
01
-
k
2πα όχας
მუ
=
Σπα n
' +n†
8+0
1
Hence we get for the potential of the second order
Ωρ
=
-
2πα (ΘΩ.
k an
=
2πα)² ((+c − r)n`
_/ \_ ફ઼ + m
k θη §2+n²
n
Σπα
2
1 (
n²
=
k
§² + n² 1
2(5+
2
§² + n²
+ c − r) - 12² } .
r
›
In the same way the calculation may be continued.
We get for the current-functions of the first and second
orders
α η
× = 1 = 7, (1-1) =
=
+ n²
a
α η
kr(r+c)'
- 2x (2) - ++² + cm²
-
where now r² = §² + n² + c².
k) (r² − c²)(r+c)r'
In the n-axis we have (since = 0)
-
Displace-
thus
42
=
-
2
a
C
2π
=
(k) (r + c)r'
a 1
k (r+c)r
We may regard the point = 0,
η
-
=
2παι
k
0 as the centre of
ment of the the distribution: thus it appears displaced through a distance
induced
distribu-
tion.
1
a then becomes positive.
2 This result agrees exactly with that obtained by Jochmann.