134
DOC.
2 RELATIVITY
AND
ITS CONSEQUENCES
How
many
periods
will clock
H'
indicate
during
unit
time if observed
from the
system
S?
Clock
H'
will indicate
the end of
a
period
at
the
times
V
-
1
p0
z
=
'
-
2
=
3
'
3
-
/0 0
0
Since
we
seek the time
with
respect
to
S,
the
first
of the transformation
equations
(I)
will
have to
be written
t
=
ß
t'
-
-x'
and
since clock
H'
is
at rest
at
the
origin
of
S',
we
must
always
have
-
0,
which
yields
-
k
-
Po
Observed
from
S,
clock
H' thus
indicates
Po
p =p
o ß
N
1
-
periods
in
a
unit
time.
In other
words,
a
clock
moving uniformly
with
velocity v
with
respect
to
a
reference
system
runs,
as
observed
from this
system,
1
:
N
1-
v
times
slower
than
an
identical
clock
that
is at rest with
respect
to this
system.
And here
is
an
interesting application
of
the
preceding
formula.
In
1907,
Mr. J.
Stark13
remarked that
canal
ray
ions
emit
spectral
lines
that
give
rise
to
a
sort
of
Doppler phenomenon,
namely,
a displacement
of
spectral
lines
proceeding
from the
motion of
the
source.
Since
the
oscillatory
phenomena
that
produce a spectral
line must
be
viewed
as
intra-atomic
phenomena
whose
frequencies are uniquely
determined
by
the
nature
of the
ions,
we can use
these
ions
as
clocks.
The
frequency
p0
of the
oscillatory
motion of the
ions
provides us
with
a means
to
measure
time. This
frequency
is
found
by
observing
the
spectrum produced
by
ions
of
the
same
kind
but
at rest with
respect
to
13J.
Stark,
Ann.
der
Phys.
21
(1906):
401-456.
[18]