DOC.
23
147
1/2
(rO
+
r2) =
T1,
or,
if
we
write
out
the
arguments
of the function
r
and apply
the principle
of
the
constancy of
the
velocity of
light
in the
system
at rest,
1
2
r(0,0,0,t)
+ r
x
0.0,0,
+
r±-?
+
r±-5x
x',0,0,t
+
x
u
From
this
we
get,
if
x'
is
chosen infinitesimally small,
1
2
1
V
-
v
+
V
+ v
1
dr
Si
ÖT
+
1
ÖT
-
v
Si
or
dr
,
v
dr
A 3F
+
V*
-
«2
-
o.
It should
be
noted
that,
instead of the coordinate
origin,
we
could
have
chosen
any
other point
as
the starting
point
of the light
ray,
and the
equation
just
derived therefore holds for all values of x'
,
y,
z.
Analogous
reasoning-applied
to
the
H
and
Z
axes-yields,
if
we
consider that light
always
propagates along
these
axes
with the
velocity
V2
-
v2
when
observed
from the
system at
rest,
dr/dy
=
0
dr/dy
=
0.
These equations
yield, since
r
is
a
linear function,
a
v
t
yi
_
v2
x
where
a
is
a
function
p(v)
as
yet
unknown,
and where
we assume
for
brevity that
at
the
origin
of
k
we
have
t
=
0
when
t
=
0.