126
11
INDUCTION IN ROTATING SPHERES
=
which may be written.
do 2
F
dt
2
1)
+ d(MTp²)
+2eF
2
(
2
αφ
dt = 0,
dt
so that the rate at which the heat is generated is
2eF
аф
dt
2
and thus we have
A periodic
state.
€ =
4πM²/1
-
3 KF r R
If e be small, we thence obtain for the logarithmic decre-
ment of the needle
30
or
42 R-r
Ꭱ
M³
λο
=
3k
Rr TF
In order that the aperiodic state may occur, we must have
MT
€2>
F
R-r 3K TF
Rr 4π M³
from which equation, for given values of T, F, M, x, it is easy
to calculate the thickness of the damper necessary to ensure
that the aperiodic state may be attained.