DOC.
49
317
d
Tr
! #
d
JeT
and
w t
i
+
i£
u
t
On
p. 462
the subscripts
in the
quantities
u
^
and
u^
have to be
added.
Also, in about the
middle
of this
page a
mistake
in
sign
should
be
corrected: the
equation
should read
Va
i
-4
A
letter
by
Mr.
Planck
induced
me
to add
the
following supplementary
remark
so as
to prevent
a
misunderstanding
that could arise
easily:
In
the
section
"Principle of
relativity
and
gravitation",
a
reference
system
at
rest
situated
in
a
temporally constant,
homogeneous
gravitational
field is treated
as
physically
equivalent to
a
uniformly
accelerated,
gravitation-free reference
system. The concept "uniformly
accelerated"
needs
further clarification.
If-as in
our
case-one
considers
a
rectilinear
motion (of
the
system
E),
the acceleration is
given
by
the
expression
dv/dt,
where
v
denotes
the
velocity.
According
to
the kinematics in
use up
to
now,
dv/dt
is
independent
of
the
state
of motion of the
(nonaccelerated)
reference
system,
so
that
one
might
speak
directly
of
(instantaneous) acceleration
when
the
motion
in
a
certain time
element
is
given.
According
to
the kinematics
used
by
us,
dv/dt
does
depend
on
the
state of motion
of the
(nonaccelerated)
reference
system.
But
among
all the values of acceleration that
can
be
so
obtained for
a
certain
motion
epoch,
that
one
is
distinguished which
corresponds
to
a
reference
system
with
respect to which
the
body
considered
has
the
velocity
v
=
0. It
is
this value of acceleration
which has
to
remain constant in
our
"uniformly
accelerated"
system.
The
relation
v
=
jt
used
on
p.
457
thus holds
only
in
first
approximation; however,
this is
sufficient,
because
only
terms
linear
in t and
r,
respectively, have
to
be taken into
account
in
these
considerations.
(Received
on
3
March
1908)
[3]