DOC.
2
RELATIVITY AND
ITS CONSEQUENCES
131
y'-axis
will
remain
parallel
to
the
y-axis,
and
that,
in
addition,
the same-named
axes
have
the
same
orientation for the observer connected
with S.
We
will count
the
time from
the instant when the
origins
of the
two
systems
coincide.
Under these
conditions,
the
relations
sought are
homogeneous,
and the
following
equations
x'
=
0 and
y'
=
0
and
z'
=
0
and
x
-
vt
=
0
y
=
0
2
=
0
are
equivalent,
or,
in
other
words,
the coordinates
x, y, z,
x',
y',
z'
are
linked
by
relations of the form
(3)
x'
=
E(x
-
vt)
y'
=Fy
V
_
=
Ü2
To determine the
constants
A,
B, C,
D, E, F,
G
entering equations
(2)
and
(3),
we
assert
that,
according
to
the
principle
of
the
constancy
of
the
velocity
of
light,
the
velocity
of
propagation
has
the
same
value
c
with
respect
to
the
two
systems,
or,
in
other
words,
that the
two
equations
(4)
x2
+
y2
+
z2
=
c2t2
x'2
+
y'2
+
z'2
=
c2t2
are equivalent.
Replacing
in
the second
of these
equations
t',
x', y',
z'
by
their
values
[16]
obtained
from
(2)
and
(3),
and
equating
it
with
the first
equation,
one can easily
find that
the transformation
equations
sought are
of the
form
(5)
t'
=
p(v).ß.
t
-
-
X
c2
x'
= p(v).
ß.
(x
-
vt),,
y'
=
p(v).y
z'
=
p(v).2
where