DOC.
2 RELATIVITY
AND
ITS CONSEQUENCES
141
S
there
exists
only
a
magnetic
field
(Mx,
My,
Mz),
but
not
any
electric
field.
In
contrast,
with
respect
to
S' there exists-as
can
be
seen
from
the
expression
for
E'y
and
E'z-an electric
field
that
acts
on
the electric
charge
at rest relative to
S'.
Thus,
the
manner
of
considering
the
phenomena
varies with
the
state
of motion of
the reference
system:
all
depends
on
the
point
of
view,
but in
this
case
these
changes
in
the
point
of
view
play no
essential
role
and
do
not
correspond
to
anything
that
one
could
objectify,
which
was
not
the
case
when
these
changes
were being
attributed
to
changes
of
state
of
a
medium
filling
all
of
space.
As
we
have
already
noted,
we can
find at
once
the
laws
applying
to
a
body
in
rapid
motion
if
we
know
the
laws
applying
to
a
body
at rest.
In
this
way we can obtain,
for
example,
the
equations
of motion
for
a
material
point
of
mass
m
carrying
a
charge
e
(an
electron,
for
example)
and
subjected
to
the
action
of
an
electromagnetic
field.
We
know,
in
fact,
the
equations
of
motion
of
a
material
point
at
the instant when
its
velocity
is
zero.
According
to
Newton's
equations
and the definition of
the
electric
field
strength,
we
have
(2)
dhc
m-
=
eEc
dt2
and two
other,
similar
equations
with
respect
to
the coordinates
y
and
z. Applying
the
transformation
equations (I)
and
the
equations
(1) given above, we
find
then
for
a
point
in
any
motion whatever
(3)
d
dt
m
dx
dt
N
•
-
F.,
1
u
where
and F
=
X
(cfr)2
+
(dy)2
t
(dz'~2
~dt)
tdt)
~dt)
1(dy dz
M-
cit
and
two,
other, similar
equations
for the other
two
axes.
These
equations
make it
possible
to follow
the
path
of
cathode
rays
and
ß-rays
in
an electromagnetic
field. Their
accuracy
is
almost
beyond
doubt,
more so
than the
experiments
of Bucherer
and
Hupka.
If
one
wants to
retain the relation between the
force,
mechanical
work,
and
the
theorem of
the
conservation of
momentum,
then the
vectors
Fx,
Fy,
Fz
entering
these
equations
have to be viewed
as
the
vector
components
of the
ponderomotive
force
acting
on
the material
point
in
motion. Under these
conditions, equations (3)
have to be
[22]