292 THE
RELATIVITY
PRINCIPLE
t
f ft
t
(Wx)dV =
ar
X
f
vx
~7l
t
t
dt!
=
v
f
vx
c
I
After similar evaluation
of
the third integral
one
obtains
n
Wx)dt
-
d
h
Now
the
energy
and
momentum
can
be
calculated
from equations
(16)
and
(18)
without difficulty.
One
obtains
E
=
1
1
~
s
4cl
1
-
SCL
(16b)
[73]
Q
=
£
1
4
c2
P
+
-
S(^05)~
7
(18b)
where
Kos
denotes
the
component
in
the direction
of motion of
a
force
evaluated
in
a co-moving
reference
system
and
s0
denotes the distance,
measured
in the
same
system,
between
the
point
of application of
that force
and
a
plane
perpendicular to
the direction
of motion.
If,
as we
shall
assume
henceforth, the external force consists
of
a
pressure
p0
which
is
independent
of
the direction
and
always
acts
perpendicularly to
the surface
of
the
system,
we
will
have in
particular
W0Ä)
=
-PoVo
(19)
where
V0
is the
volume
of
a system
evaluated
in the
co-moving
reference
[74] system. Equations (16b)
and
(18b)
then take the
form