DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY 15
Since
-&XE
is the work transferred from field to matter
corresponding
to
the
[p.
11]
displacement
Sx,
we
have to
set
bxE
=
/
tAA,
where
fx
denotes the force that the
field
exerts
upon
the
matter
in the direction
of
the
X-coordinate.
Accordingly,[27]
e
_
"
1
"2
de
fx
xP"
2
dx^.
Here, too,
fx
can
be
represented
in
a
form that makes it evident that the momentum
law is satisfied. For
1
2de
d
i
,
dex dev de7
2eS
=
S2ee)-eS'fc+e^
+
eS»'
or, according
to
the second and the
third of
equations (Ia')
and the first
of
equations
(8),
1
2
de
=
_d_(
_
bx)
)
_
_d
(
b
)
_
d_
2
dx
dxK 2
x
dyK
x
y)
dz
Therefore,
if
one
sets
eii
p'xx =
y
-
CA
P'xy
=
~CA
p'xz
=
-txK
etc.,
one
obtains
f
=
dp'XX
_
Wjy_
_
dx
dy
dz.
Analogous expressions
are
obtained for
fy
and
fz.
The
9
quantities
p'xx
etc.
are
the
"Maxwell
pressure
forces"
for the
special
case
of the electrostatic field.
Totally
analogous expressions
are
obtained for the
case
of the
magnetostatic problem
insofar
as
the second
of
equations
(8) correctly
describes the relation between
h
and
b. Thus,
one
obtains the
ponderomotive
forces for static
problems
in
general
if
one
sets
,
+
/ c
L.
L
P
XX
=
-2
-
~ - I)
A
P
xy
=
~
^y
~
Wy
P'r,
=
~ ~
kK
(10)
xz
^ z "x~z
etc.
As will be shown in what
follows,
from
H. A.
Lorentz's
standpoint
it
can
easily
be
recognized
that these
expressions
are
also valid for
electrodynamic processes
in
bodies
at rest.
In that
case,
we
have
to
bear in mind that the
pressure
forces
given
here consist of
components
of
physically
diverse kinds that
can
easily
be
separated.
That
is to
say,
we
have, first,
those
pressure
forces
by
means
of which
we represented
in
§2
the
ponderomotive
effects of the
electromagnetic
field
(h, e) on
the set of
all