DOC. 42 SPECIAL AND GENERAL RELATIVITY 331
TWENTY-THREE
Behaviour
of
Clocks
and
Measuring-Rods on
a
Rotating
Body
of
Reference
Hithertothe
I
have
purposely
refrained
from
speaking
about
physical interpretation
of
space-
and time-
data
in
the
case
of the
general theory
of
relativity. As
a
consequence,
I
am
guilty
of
a
certain slovenliness of
treat-
ment, which,
as we
know
from
the
special theory
of
relativity,
is
far from
being unimportant
and
pardonable.
It
is
now
high
time that
we
remedy
this
defect;
but
I
would mention
at
the
outset,
that this
matter
lays no
small claims
on
the
patience
and
on
the
power
of abstraction of the reader.
We
start
off
again
from
quite special cases,
which
we
have
frequently
used before. Let
us
consider
a
space-time
domain
in
which
no
gravitational
field
exists relative
to
a
reference-
body K
whose
state
of
motion has
been
suitably
chosen.
K
is
then
a
Galileian
reference-body
as
regards
the domain
con-
sidered,
and the results of the
special theory
of
relativity
hold
relative
to
K.
Let
us
suppose
the
same
domain referred
to
a
second
body
of
reference
K',
which
is rotating uniformly
with
respect to K.
In order
to
fix
our
ideas,
we
shall
imagine
K'
to
be
in
the
form
of
a
plane
circular
disc,
which
rotates uniformly
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