DOC.
35
205
(4)
m
v
d2xv
i
dt2
d
Jt
dxv
m
v
~Jt
=
X
v
hence
we
also obtain
(5)
d
Jt
i
dx
ir\
v
v
~Jt
lXvKX
From equation (5)
and
equation (3)
one
obtains
(6)
J
157
+
1%
dx
v
Jt
=
const.
If
we
reintroduce the
hypothesis
that the quantities
mv
depend
on
energy,
and
thus also
on
time,
then
we
face the difficulty that the mechanical
equations
for that
case are no
longer
known;
the first
equal
sign
of
equation
(4)
thus
does not
hold
anymore. However,
one
should take into consideration
that the difference
A
dx"
Ö
m
V
7t
v
IT
d2xit
dmtl
dx"
1
r
"
dx"
'
mv
=
TT~TT
=

\
fcTr{uX+v¥+ wZ)dr
dt2
V2
is of
second
order in the velocities.
Hence,
if all velocities
are
so
small
that
terms
of
second
order
may
be
neglected,
then
even
if the
mass
mv
is
variable,
the
equation
d
Jt m
dxv
v
~Jt
=
X
v
certainly
holds with the
required
accuracy.
Then equations
(5)
and
(6)
hold
as
well,
and
one
obtains
from
equations
(6)
and
(2a):
(2b)
d
Jt
i
»"v
+
xpedr =
const
If
£
denotes the Xcoordinate of
the
center
of
gravity
of the
ponder
able
masses
and
of the
energy
mass
of the
electromagnetic
field,
then
we
have