278
THE
RELATIVITY PRINCIPLE
is the
electromagnetic energy
of
the
space
under
consideration.
According
to
the
energy
principle,
the first
term of equation
(13)
equals
the
energy
delivered
by
the
electromagnetic
field
to
the carrier
of
the electric
masses
per
unit time. If electric
masses are
rigidly
bound
to
a
material
point
(electron), then
their
part in
the
above term equals
the
expression
e(Xx
+
Yy
+ Zz),
where
(X,Y,Z)
denotes the external electric field
strength, i.e.,
the field
strength minus
that
part which
is
due to
the
charge
of
the electron itself.
Using
equations
(12),
this
expression becomes
Kxx
+
Kyy
+
Kzz
.
Thus
the
vector
(Kx,Ky,Kz)
denoted
as
"force" in the last
paragraph
has
the
same
relation
to
the
work
performed
as
in Newtonian mechanics.
[44] Thus,
if
one
successively
multiplies
equations (11)
by
x, y, z,
then
adds and integrates
over
time, this
must
yield
the kinetic
energy
of
the
material point (electron).
One
obtains
(Kx
x
+
K
y
+
K
z)dt
=
^
+
const.
y
z
i
-
4c2
(14)
By
this
we
have
demonstrated that the
equations
of motion
(11)
are
in accord
with the
energy
principle.
We
will
now
show
that
they
are
also in accord with
the
principle of conservation
of
momentum.
Successively multiplying
the
second and
third
of
equations
(5)
and
the
second and
third
of
equations
(6)
by
N/4r,
-M/4r, -Z/4r,
Y/4r,
adding
them and
integrating
over a
space
at
whose
boundaries the field
strengths vanish,
we
obtain
d
jLa
-
»!.]
•
f
/,['
u. u
It du)
=
0 (15)
or,
according to equations
(12),