DOC.
36
209
The
dimensions
should
be chosen such
that
slow
cathode
rays
move
approximately
in
a
circle,
at
a
short distance
from
R2.
The rays
then
enter
the
somewhat
conical metal tube
t',
which
is connected
by
metal with
R2
and
inside
which
there is
a
phosphorescent
screen
S
on
which
there shall fall the
shadow
of
a
vertical wire
D
set
up
at
the interior
end
of t'.
When
slow
cathode
rays are
applied,
the
shadow
of
D
on
S
takes
up
a
quite
definite position
(zero
position).
If the
rays' generating potential
is
increased, the
shadow
of the wire will shift.
By
inserting
a
battery
B
into
the
ground
connection of
R1
the
shadow
shall
be
returned
to
the
zero
position.
If
II
denotes
the
potential at which
the
shadow-forming rays
get
deflected,
then
II
is also the potential difference that
imparts
the kinetic
energy
to
the deflected
rays.
Further,
if
p
denotes the radius of
curvature
of the
shadow-forming
rays,
then
we
have
/'
-
£
1
[4]
Here
ut
denotes the
"transverse
mass" of
the
electron,
ul
that
longitudi-
nal
mass
which
is defined
by
the
equation
kinetic
energy
=
ulv2/2,
and
X
the
deflecting
electric force.
If
P
denotes the potential of
R2
(potential of
the
positive
pole
of
the
current
source
M),
and
p
the
potential
of
R1
at which
the
shadow
is
in
the
zero
position,
then
II
=
P
-
a(P
-
p)
,
where
a
denotes
a
constant
that
depends
on
the dimensions
of
the
apparatus
and
is small
compared
with
1.
Further, the
quantity
X
is
proportional
to
[5]
the potential
difference
P
-
p.
Thus,
one
obtains
from
the
above equation