DOC.
1
MANUSCRIPT ON SPECIAL
RELATIVITY
7
[curl ifM + [curl
C,C]
=
|^
{-
[*M}
+
4P
OA:
c
Integrating
this
by parts, one
obtains
easily
the identities
[curl
\)M\r
=
a
(2
ÜA)
a
(*x
V
a
0ty
MZ)
dx 2
dy
az
r) £
Ie^
a
[curl
£,£]x
- Cx
div e
+
-
(
VXVX'
ee)
(Cy
Cz).
dx
2
dz
Thus,
if
one
sets[13]
1
P_=
XX
±(e2+
2
f2)
vxvx
e
e
I
/^rv
xy
Pvr
yx
vxvy
t
C
xvy
/XZ
= P7x - vxvz
c
e
zx
etc.
and takes into
account
the second of
equations
(I), one
obtains three
relations,
the first
of
which is
p
{e
+
}«-
"
dPxx
fyxy
_
^P_
xz
1
ds
. . .
(6)
dx dx dx
2
dt
If
we
denote the left-hand side
of
this
equation,
which is the
x
component
of
a
vector,
by
fx
and
integrate
both sides
over a
finite
volume,
we
obtain
ffxdr
=
-
A.
{f-LSxdr}
+
f
(pxxcos
(nx)
+
p^cos
{ny)
+
pxzcos
(/zz))
da
or
in short
/Mt
"
"
I
/3s-',r
*
...(6a).
H. A. Lorentz
designates
the
vector
f
as
the
ponderomotive
force[14]
per
unit volume
exerted
by
the field
on
the
electricity.[15]
By
means
of this
conception
he does
justice
to the Biot-Savart
empirical law,
on
the
one
hand, and,
on
the other
hand,
he
succeeds in
having
his
electrodynamics satisfy
the
energy
law and the momentum
law. For
if,
in
setting up
(5a)
and
(6a), one
chooses the
integration space
in
such
a
manner
that the field
strengths
vanish
permanently
at
the boundaries of the
space,
then when the relation
nf
=
np{e
+
•»
}
- p!*
is
taken into
account,
these relations
turn
into
f
4?dx
=
d
{ J
wdr}
dt
...(5b)
[p. 5]