11
INDUCTION IN ROTATING SPHERES
115
Hence
or since
Ω,
=
Ω
8
=
2πω
-a#"gu
2x=0,
ax-nje
san
2πωα σχιζ=
2πωα η
- 2001 17 (1-5 + c),
k
an
ข่า
=
k +
ωα η
kr(r+c)
2
Hence the form of the lines of flow is independent of the
distance of the pole from the axis.¹ For the induction of the
second order we get
2
2πω
-끼
​દૃ +n
s2 = (270) a 3 ((5+ c = 7)m),
Owl
2
*₂ - - 2x (~) a 2
( 7
)
= -
2π
ωα
r²+cn²
Ę
(2x) { (1723 - 0²)x(x + c )r + ar +
- c²)(r+c)r
which formulæ are meaningless at infinity.
When the angular velocity is small, if the inducing pole
is not very close to the axis, we may regard the point = 0,
зв
=
to be
O as the centre of the distribution.
Its ordinate is found
no
=
2πωας
k
Hence in the neighbourhood of the pole the distribution Rotation of
is turned through the angle
the induced
distribu-
tion.
2πως
h
in the direction of rotation of the disc.
1 As already found by Jochmann.