DOC.
47
263
The
formula
v=v0
1
- v2/c2
permits
a
very
interesting application.
Mr.
J. Stark
showed
last
year1
that the ions
constituting
canal
rays
emit
line
spectra
by
observing
a
shift in spectral lines
which
he interpreted
as a
Doppler
effect.
Since the oscillation
process
that
corresponds to
a
spectral
line is
to
be
considered
an
intra-atomic
process
whose frequency
is determined
by
the
ion
alone,
we may
consider
such
an
ion
as a
clock
of
a
certain
frequency
v0,
which
can
be
determined, for
example,
by
investigating
the light emitted
by
identically constituted ions
which
are
at rest
relative
to
the observer.
The
above
consideration
shows,
then,
that the effect of
motion
on
the light
frequency
that is
to be
ascertained
by
the observer is
not completely
given
by
the
Doppler
effect.
The
motion
also reduces the
(apparent)
proper
frequency
of the
emitting
ions in accordance with the relation
given
above.2
[24]
S5.
The
addition
theorem
of
velocities
Let
a
point
move
uniformly
relative
to
the
system
S'
according to
the
equations
x'
=
u'
t'
x
y'
=
u't'
y
y
z1
=
u't'
z
If x', y',
z',
t'
are
replaced
by
their
expressions
in
x, y, z,
t
with
the
help
of
transformation
equations
(1),
one
obtains
x,
y,
z as
functions of
t, and
thus also the point's
velocity
components
w, w,
w
x
y
z
with
respect to
S.
We
thus
get
1J.
Stark,
Ann. d.
Phys.
21
(1906): 401.
2Cf.
§6,
equation (4a).
[23]