II
65
1
INDUCTION IN ROTATING SPHERES
W
w'
=
a
K
X_
dy
ax'"
y
To verify this we first express the conditions for in Proof.
terms of
Χη
We have (§ 1, 4)
▼²U = m(m+2n+1)p
ax
m-2 y az dy
V²V = m(m+2n+1)p' m-2
V²W=m(m + 2n+1)pm-2(x-
-
Xnx
მე:
az
-y·
dy
Jx
Xx -
nzxn
az
Xn
дх
a
yV²U − xV²V = m(m + 2n+1)pm-2(
m(m+2n+1)p™-²(p²
zV²V - yV²W = m(m+2n+1)pm-2(
2V²W - 2V²U = m(m + 2n+1)pm-:
And again-
av
да
aw
dy
-
-
au
dy
az
au aw
az Əx
=
=
-
Hence we get
mpm
m-2
mp
m-
Xn
xn),
nx Xn
dxn – nyx») ›
dy
(p³ ³X - naxa) - p" (n+1) X^,
Əz
2
Xn
Jx
nzXn
Əz
nxxn ) − p™ (n + 1)
- X",
до
mp"-2(p²?
JXn-
ǝy
— nyx« ) − p™ (n + 1)
Xn
Dy
0 =
=
-
n(n + 1)pmXn •
wm(m+2n+3)(p2
Xn
nzXn
Əz
³xn)pm-3
The conditions for become
² =
-
M. P.
- 2w(n + 1)pm Xn
Əz
F
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