II
69
INDUCTION IN ROTATING SPHERES
From this we get, by differentiating,
2n
d
d
P
dp
(p-² (p²+1F)) = -
(p²+1F)) = − 4ƒpƒ(p).
dp
-
The values of U, V, W corresponding to u, v, w are
U = FOX®
n V = Foxn
მა.
dwy
W = FaXn
მ.
Hence follow these currents induced by the system
u' =
=
@Fox'n, w = - F
K
x dwx
K dw₁
x dw₂
The disturbing function belonging to this system is
Hence the function
↓ = = = pFx ».
-
y = p.ĥ Xn
induces the second function
=
n°
- pFxx
Now let belong to the current-system actually existing
in the sphere under the influence of the external potential Xni
let belong to the current-system directly induced by ex-
ternal magnets. Then clearly the condition for the stationary
state is
*=yo+y.
Xn
To develop this equation further we analyse X, and con-
sider each term by itself. Let the one considered be
n
Xni
=
A
P
cos ίω . Ρnt.
We have then (p. 48)
n
W
Yo
=
・Ap
P
i
sin iw. Pri
K
R n+1
n
P
i
If we write
↓ = - "Ap({})" — (fi(p) sin iw+ƒ½(p) cos iw} Pí,
Αρ
K Ꭱ +1
ni,