340
PONDEROMOTIVE FORCES
§1.
Forces that
do
not
depend
on
the
velocities
of elementary
particles
In
this derivation
we
will
consistently
base ourselves
on
the
standpoint
[4]
of
the electron
theory1;
hence
we
put
(2)
®
=
5
+
p,
(3)
= S)
+
0,
where

denotes
the electric
and
0 the
magnetic
polarization
vector.
We
think
of
electric
and
magnetic
polarizations,
respectively,
as
consisting of
spatial
displacements
of
electric
and
magnetic mass
particles
of dipoles that
are
bound to equilibrium
positions.
In addition,
we
also
assume
the
presence
of mobile
electric
particles
not
bound
to dipoles (conduction
electrons).
Let
Maxwell's
equations
for
empty
space be
valid
in
the
space
between
the
above
particles,
and let,
as
in Lorentz,
the
interactions between matter and
elec-
tromagnetic
field
be
exclusively
brought
about
by
these particles.
Accord-
ingly,
we assume
that the forces exerted
by
the
electromagnetic
field
on
the
volume
element of the
matter equal
the resultant
of
the
ponderomotive
forces
exerted
by
this field
on
all
elementary
electric
and
magnetic
particles
in the
volume
element
considered.
By
a
volume
element of the
matter
we
always
understand
a
space
so
large
that it contains
a
very
large
number
of electric
and
magnetic
particles.
The
boundaries
of
a
volume
element
must
always
be
imagined
as
drawn
such that
the
boundary
surface
does
not cut through
any
electric
or
magnetic
dipoles.
[6]
First
we
calculate
that
force
acting
on a
dipole which is due
to
the
field
strength
£
not being exactly
the
same
at
the
locations
of
the
elemen-
tary
masses
of the
dipole. If
p
denotes the
vector
of
the
dipole
moment,
one
obtains the
following expression
for the
x-component
of the force
sought:
?(£

M
c
_
y.
X
_
X_
_
X
~
^x
dx
^y
dy
^z
dz
[5] 1However,
we
stick
to
the dual
treatment
of electric
and
magnetic phenomena
for the
sake of
a
simpler
presentation.
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