148
ELECTRODYNAMICS OF MOVING
BODIES
Using
this result,
we can
easily
determine the
quantities
£, n,
(
by
expressing
in
equations
that
(as
demanded
by
the
principle of
the
constancy
of
the
velocity of
light
in
conjunction
with the
principle
of relativity)
light
propagates
with
velocity
V
also
when
measured
in the
moving
system.
For
a
light
ray
emitted
at
time
T =
0
in
the direction
of increasing
£,
we
will
have
or
{ =
Vt,
{ =
aV
t
-
ft
-
v
V1
x
But
as
measured
in the
system
at
rest,
the
light
ray
propagates
with
velocity
V
-
v
relative
to
the
origin of
k,
so
that
x
V
-
v
=
t.
Substituting this value of t
in
the equation
for f,
we
obtain
V2
i
~
a
yi
_
v2
x
-
Analogously,
by
considering
light
rays
moving
along
the
two
other
axes,
we
get
j)
-
Vt
=
aV
i
~
j/2
V
V1
x]
I
=
t;
x*
=
0;
\V*
-
v2
V
rj
=
y
-
v*
c
-
V
z.
\V*
-
V2
where
hence
and
If
we
substitute for x' its value,
we
obtain