II
INDUCTION IN ROTATING SPHERES
93
We must accordingly replace—
av
au
by V2N+
ax
მე:
ty
212
au
Əz
-
aw
by V2M+
ax
(1),
Tx
Əy
aw ǝv
by V²L+
ax
dy
Iz
მეს
since
ƏL ƏM ƏN
+
Эх ду
+
=
-Χ
(2).
dz
But now
V2L
and
λ
210
= -
V2M =
V2N =
=
av
-
-
-
· 4πλ
Απμ
Απν
aw
Iz dy
-
ax
(3),
μ
₤10
Ө
ע
814
=
=
მე
aw
a
ax
(4).
дх dz dy
au av ax
ду да Əz
If by these equations we eliminate L, M, N from the
expressions (1), and add the forces directly exerted by the
currents, that is
av au
дх
-
dy'
etc., we get for the expressions,
which are now to be substituted for
ing:-
av
дх
au
ду
etc., the follow-
"
(1+4π0(
(:
av au ax
+
дх dy Əz
Vau aw
ax
(1+4π0)
+
(5).
Əz да
aw
dy
av ax
(1+40)
+
dy Əz
მე:
The differ-
ential equa.
tions.