DOC.
23
155
It is
noteworthy
that
v
and
w
enter
the
expression
for the resultant
velocity
in
a
symmetric
fashion. If
w
too has
the direction
of
the X-axis (E-axis),
we
obtain
JJ
-
v +
w
1
4-
VW
1
+ JJ
It follows from
this
equation
that the
composition
of
two
velocities that
are
smaller than
V
always
results
in
a
velocity that is smaller than
V.
For
if
we
put
v
=
V
-
k,
and
w
=
V
-
X,
where
K
and
X
are
positive and
smaller
than
V,
we
get
u
= V
2V
-
K A
.
V.
2V
-
k
-
\
+
t
It
follows further that the
velocity of light
V
cannot
be
changed
by
compounding
it with
a
"subluminal velocity."
For
this
case we
get
ij
=
Ljuh
=
v.
i
+
»
V
For the
case
that
v
and
w
have
the
same
direction,
the formula for
U
could also
have been
obtained
by
compounding two
transformations
according
to
§3.
If in addition
to
the
systems
K
and k, which figure
in
§3,
we
also
introduce
a
third
coordinate
system
k',
which
moves
parallel
to
k
and
whose
origin
moves
with velocity
w
along
the axis
E,
we
obtain relations
between
the quantities
x, y,
z, t
and
the
corresponding
quantities
of
k1
that
differ
from those
found
in
§3
only
insofar
as
"v"
is
being replaced
by
the
quantity
v +
w
1
4-
VW
1
+
JJ
(?;2 + w2 +
2vw
cos
a)
-
p
vw
sin
a
U
=
1
+
VW
COS ft