206 DOC.
10 RESEARCH NOTES
[eq. 10]
*'2
/2
z'2
,
-^
ö
-- -
1
B2
C2
[eq.
11]
[eq.
12]
(u1x
+
v1y
+
w1z)2
+
(u2x
+
v2y
+
w2z)2
+
[eq. 13]
2
2
2
Wj
+
U2
+
«3 =
OCjj Vj
Wl
+
V2W2
+
V3W3
V2
+
V2
+
V2
=
oc22
= 1
X'
Y'
Z'
X
CCi
«2
0C3
y Pi
ß2
p3
z
Yi
Y3
=
a
[13]
12
1
1
1
A
B
c
M3
V1
V2
v3
Wi
W2
w3
[eq.
14] u1u2
+
v1v2
+
w1w2 =
0
2
2
2 1
U\
+
V\
+
*l
= "2
[10]Einstein
symmetrizes
g12g24
to
the
sum
of the
terms
indicated,
the
only
three
terms
nonredundant under the
symmetries
gik = gki
and
gikgmn = gmngik.
[11]Associating
g12
with
s2Q/sX1sX2
etc.,
Einstein forms
[eq.
8], symmetric
in
the coordinate
derivatives, in
accord with the method
of
[p. 3].
[12]Einstein
transforms the
ellipsoid [eq. 9] to
[eq. 10] by
the
orthogonal
transformation
[eq.
11].
The
new
x',
y',
z'
coordinates
are
rescaled
by
multiplication
with
1/A, 1/B,
and
1/C,
respectively, to complete
the transformation of
[eq. 9]
to
the unit
sphere
[eq. 12].
[13]The
coefficients of the total transformation
are u1...w3
and
satisfy
[eq.
13]
identically
("a12"
should
be
"a23")
and
would
satisfy
[eq. 14]
if the
aik
adopt
the values
of
[eq.
10].