II
105
INDUCTION IN ROTATING SPHERES
Let
nim¹ mgr 1
x, y, t
sec
be the components of the polarisation,
€ (number)¹
the dielectric constant.
For x, y, we have the equations
I
=
-
- E
ab
дх
+ €X,
Эф
ນ
-E
+ey,
·24+ €Z,
dx dy
for p = R
xx + xy + zz=
ar dy dz 1
++
=
Əz 4π
♡²;
Papi ape
афі
-
4 п др др
Hence we have for
Απε Vaxa
² =
and for
p = R
(1+4πε)
az
+ +
1+4πεθα dy Əz
афі эфе 4 пе
др др
e
=
(xX+yY+zZ).
P
In external space we must have V² = 0.
If X again be the nth term of the external potential we
have, as above (p. 43)
ax _ 2w
+
+
მე dy
Əz
28
az
nz
2x + y + z = w({p¹²x² - n²x»).
xX+y+zZ
Əz
The units are again such that 1/A, the velocity of light, does not occur.
The corresponding magnitudes in magnetic measure are A²r, A²y, A²¿, A².