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
shadowforming 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
shadowforming
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