DOC.
47 277
K
=
e
X
+
V-
N
- -
M
x c
c
Kq
=
6'
Y
+
-
L
- -
N
y
Kz=-
Z
+
-
M
-
L
c c
(12)
These
equations do not
change
their
form with
the introduction
of
a new
coordinate
system
with differently directed
axes,
which
is relatively
at rest.
Hence they
are
valid in
general
and not
only
when
y
=
z
=
0.
The
vector
(Kx,Ky,Kz)
shall
be
called the force
acting
on
the
material
point.
If
q2
is
vanishingly
small
compared
with
c2,
then
according
to
equations
(11) Kx,Ky,Kz
reduce
to
the force
components according
to Newton's
definition.
In
the
next
section it will
be
shown
that in other
respects, too,
that
vector plays
the
same
role
in
relativity
mechanics
as
the force
does in
classical mechanics.
We
shall maintain
equations (11)
also in the
case
that the force
exerted
on
the
mass
point
is
not of
electromagnetic
nature. In
the
latter
case
equa-
tions
(11) do
not have
a
physical
content
but
are
rather
to
be
understood
as
defining
equations
of the force.
§9.
Motion
of
the
mass
point
and the principles
of
mechanics
If
equations
(5)
and
(6)
are
successively
multiplied
by
X/4r,
Y/4r
...
N/4r,
and integrated
over a
space
on
whose
boundaries the field
strengths vanish,
one
obtains
where
J
h{uxX
+
uyY
+
uzZ)dw
+
dE
=
0,
1
(P
+
P
+ Z)
+
^_(Z2
+
IP
+
N2)
du)
S?
(13)