226 DOC. 10
RESEARCH NOTES
[51]The
function
[eq. 63]
solves the harmonic differential
equation
[eq.
62].
[52]Einstein
extends the two-dimensional construction of
[p.
19] to nondiagonal
transfor-
mations for which
p12
#
0 and
p21
#
0. The metric
is
yuv
=
5uv.
[Eq.
64] is
the
condition that
det
(pua) =
1.
[Eq.
65]
and
[eq.
66]
are
both the
first
component
of
yaapxua,a =
0;
[eq.
67]
is
the second
component.
[Eq.
68]
and
[eq.
69]
are
solutions of the harmonic
equations
[eqs.
66-67],
modeled after
[eq.
63]. The
determinant condition
[eq.
64]
becomes
[eq.
70]
with the
help
of
[eq.
68]
and
[eq.
69];
[eq. 71]
follows from
[eq.
70]
[p.
21]
[eq.
72]
Drehung[53]
x
=
xcoswt + ysinwt
'
-x
sinwt
+ ycoswt
y
dt'
dt
dx'
=
coswt
dx
+
sinwt
dy
+
(-xsinwt
+
ycoswt) wdt
dy'
=
sinwt
dx
+
coswt
dy + (-xcoswt
-
ysinwt)
wdt
dt'
=
0
dx
+
0
dy
+
dt
Tabelle der
p [eq.
73]
1
wt
+
yw
-wt
1
xw
0 0
1
-yw
+xw [eq.
74]
stimmt.
Beschleunigung
dt'=
-
y(üdx + xiddy +
dt
3(p
dcp
3(p
[-]
dy dz
unmöglich
[eq.
75]
Tafel der
p
coswt
sinwt
-
xsinwt
+
ycoswt
-sinwt
coswt
-
(xcoswt-ysinwt)
0
0
l
c
=
C0)e
ax
/
CI
2ax'
[54]
[eq. 76]
x
=
x
+
-e
t,2
z
2
ax
[eq.
77]
t.
=
e
t,/
/
a
•2
X
=
X
-
~t
2
t'
=
t
(1
-
(2
)ax)
Tafel der
n
coswt sinwt
0
-sinwt
coswt
0
x
.
0
+ y.
y.0
+
x.
1
[x sinwt
coswtx]
3tc
I
=
0
dxv
immer erfüllt.
dx'
=
(1
+ (2)[--])
dx-atdt
[eq. 78]
dt'
- -
(2)atdx+
(1
-
(2)ax)
dt
stimmt
auch.
bei
geeigneter
Massstabverschiebung.