DOC.
23
149
T =
ip(v)ß
t
-
yi
V
X
£
=
(p{v)ß(x
-
vi),
rj
=
v(v)y,
C
=
v(v)z,
ß
=
1
TT
1
-
7
where
and
p
is
a
function of
v
that is
as
yet unknown.
If
no
assumptions
are
made
regarding
the initial
position
of the
moving
system
and
the
zero
point of
T,
then
an
additive
constant
must be
attached
to
the
right-hand
sides
of
these
equations.
Now we
have to
prove
that
every
light
ray
measured in
the
moving
system
propagates
with the
velocity
V,
if it
does
so,
as we
have assumed,
in the
system
at rest;
for
we
have not yet provided
the
proof
that the principle
of
the
constancy
of the
velocity
of light is
compatible
with the
relativity
principle.
Suppose
that
at
time t
=
T
=
0
a
spherical
wave
is emitted
from
the
coordinate
origin, which
is
at
that time
common
to
the
two systems,
and
that
this
wave
propagates
in
the
system
K
with the
velocity
V.
Hence,
if
(x,y,z)
is
a
point
just
reached
by
this
wave, we
will
have
x2
+
y2
+
z2
=
V2t2.
We
transform these
equations using
our
transformation equations,
and,
after
a
simple
calculation, obtain
£2
+ + (2
=
V2T2.
Thus,
the
wave
under consideration is
a
spherical
wave
of
propagation
velocity
V
also
when
it is observed in the
moving
system.
This
proves
that
our
two
fundamental
principles
are
compatible.
[15]