308
THE
RELATIVITY
PRINCIPLE
quantities
p,
u, X,
L, £,
etc.,
if
we
limit ourselves
to
an
infinitesimally
short
period1
that is
infinitesimally
close
to
the time of relative
rest
of
S' and E.
Further,
we
have to replace
t'
by
the local time
a.
However,
we
must not
simply
put
d d
~5i
because
a
point which
is
at rest
relative
to
S,
and to which equations
transformed
to
S
should
refer,
changes
its
velocity
relative
to S'
during
the time element
dt'
=
da,
to which
change,
according
to
equations
(7a)
and
(7b),
there
corresponds
a
temporal
change
of the S-related field
component.
Hence
we
have to put
AT
dX
dV
31
=
Ta
IV
=
T
dY'
W
dY
Ta
+
2
N
dM dM
y
To
cZ7
dV
W
dN'
W
dN
To
+
1
Y
Hence
the
E-referred
electromagnetic
equations
are
1
c
+
If
dN
dM
Tj
1
c
dY
puV
+
To
+
c
%
N
dl
dN
^
M
1
c
dZ
[pu(
+
To
XCM
dM
dl
Tj
1
dl
c
T
dY
dZ
Tj
1
c
dM
y
7
To
c
Z
dZ
dX
1
c
dN
X
To
+
c
Yy
dX dY
Tj
M
1This
restriction
does
not
affect the
range
of
validity
of
our
results because
inherently
the
laws to be
derived
cannot
depend
on
the time.