52
DOC.
43 JANUARY
1915
In
this coordinate
system
the Earth
rotates at constant
angular
velocity
w,
let
us
say,
around the
z-axis. If
we now
introduce
a
coordinate
system
of
axes
II
which
this rotation
accepts,
then
we
obtain the
equations
d2x'
dt2
+
2
UJ~~
+
wV
rA
dt
dy'
d2y'
dt2
dx'
dt
+
u2y'
dV__ £
dt2
^rz
(2)
The
simpler
form of
(1)
suffices
to
prefer
I
over II,
and hence to
say:
the
descrip-
tion
becomes
the
simplest
if
we use as a
basis
a
coordinate
system
in which
the
Earth
rotates. This would
thus
be
the
meaning
of
the
statement: “the
Earth
rotates.”
However, something
else
can
be added. Our
experience
has
taught
us
that
often when
the
motion of
a
body
takes
place according
to
the
equations
Ê1=X
-
-7
dt2 ’ dt2 ’ dt2
’
the
values for
X,
Y,
Z
clearly are
linked with
the
presence
of
other
bodies
and
with the
distance,
size,
etc.,
of these bodies. Thus
we can
establish in
a
rational
way
a
connection between the
terms
-ax/r3,
etc.,
and the existence of the Earth’s
body
and refer
to
a
gravitation emanating
from
the latter.
If
to
begin
with
we
had learned
to
describe
the
motion of
a
mass-point
using
equations
(2),
and had
the
idea not occurred to
us
to
change
it
into form
(1)
through
modification of
the coordinate
system,
then the
endeavor to establish
a
connection also between
the
terms
2wdy'/dt,
w2x',
etc.,
and
the
existence of
some
body
or
other
would have
suggested
itself.
Well,
this
has not
happened, though;
at
least
nothing
clear
or
precise
has
come
out of
it.[8]
I
am
thinking
here
of
Mach’s “masses
of the
universe”
and the
“average
rotational
motion
of
ponderable
distant
masses
in
the
vicinity”
which
you
are
talking
about.
We
can
imagine
that for
a
time
equations
(2)
were
the
only ones
available
and
a
“meaning”
was
agonizingly being sought
for the
terms
2wdy'/dt,
w2x',
etc.
If
someone
then
came
along
who
by
introducing
coordinate
system
I
derives
(1)
from
equations
(2),
then
each
one
of
us
would
welcome
it
as a
real deliverance
and
everyone
would
prefer system
I.