362 DOC.
71
PRINCETON LECTURES
THE GENERAL
THEORY
[;~4]
-
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-~-~;-+~-.0Y4MO'Y~i
[:~]
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`~3~Y4M
a-y4a\
-
[~I=o
in which
a,
ß
and
u
denote
space
indices.
We therefore
obtain
from
(116),
in
the usual
vector
notation,
The
equations
of
motion,
(118),
show
now,
in
fact,
that
[132]
1.
The inert
mass
is proportional to
1
+
a,
and therefore
increases
when
ponderable
masses
approach
the
test
body.
[133]
2.
There
is
an
inductive
action
of accelerated
masses,
of
the
same
sign,
upon
the
test
body.
This
is
the
term
dA/dl.
3.
A
material
particle, moving perpendicularly to
the
axis
of
rotation inside
a
rotating
hollow
body,
is
deflected
in
the
sense
of
the
rotation
(Coriolis field).
The
centrifugal
action,
mentioned
above,
inside
a
rotating
hollow
body,
also follows from
the
theory,
[134]
as
has
been
shown
by
Thirring.*
*That
the
centrifugal
action
must
be
inseparably
connected
with the
existence of
the
Coriolis
field
may
be
recognized,
even
without
calculation,
in the
special case
of
a
co-ordinate
system
rotating
uniformly relatively to
an
inertial
system; our general
co-variant
equations
naturally must
apply
to
such
a case.
(118)
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[102]