280 THE
RELATIVITY PRINCIPLE
[48]
where
the time
t
and
the initial
and
final
position remain
unvaried,
and
where
A
denotes the virtual
work
A
=
Kdx
+
Kdy
+
Kdz
. x
y
z
Finally,
we
establish
Hamilton's canonical
equations
of
motion.
This is
done
by
introducing
the
"momentum
coordinates"
(components
of the
momentum)
£,
rj,
(,
setting
as
above
i
=
dH=
__M_
^
etc.
dx
If
one
considers
the
kinetic
energy
L
as a
function
of
£,
rj,
(,
and
sets
£2
+
rj2
+ (2
=
p2, one
obtains
W
L
-
fie2
1
+
7§-r
+
const.
,
i
P
c
and
Hamilton's
equations
of motion
become
H
=
x
=
x
^
=
K
t
x
at
y
dt
z
dx
_
dL dy
_
dL
dz
dL
li
Ht
Hrj
Hi
~
§10.
On
the
possibility
of
an
experimental test of the
theory
[49]
of
motion
of
the
material point.
Kaufmann's
investigation
A
prospect
of
comparison
with
experience
of the results derived
in
the
last section exists
only
where
the
moving
electrically
charged
mass
points
possess
velocities
whose square
is
not negligible
compared
to
c2.
This
condition is satisfied in the
cases
of the faster cathode
rays
and
the elec-
tron
rays
(/?-rays)
emitted
by
radioactive substances.
There
are
three quantities for electron
rays whose
mutual
relationships
can
be
the
subject
of
a more
detailed
experimental
investigation,
i.e., the