In a paper on “The Motion of Electrons in Gases,” by Prof. Townsend and Mr. Tizard* it was shown how, by measuring the lateral diffusion of a stream of electrons in an electric field, it is possible to find
k
the factor by which the energy of agitation of the electrons exceeds that of the surrounding molecules. The ions come at a uniform rate through a slit S of width 2
a
in a large metal plate A, and traverse a distance
c
in the direction of an electric force Z. The plane of the plate A may be taken as that of
xy
, the origin of co-ordinates being the centre of the slit which latter is taken parallel to the axis of
y
. The ions are received on three insulated electrodes,
c
1
c
2
,
C
3
, which were portions of a disc of diameter 7 cm.,
c
2
being a narrow strip 5 mm. wide, cut from the centre of the disc and insulated by narrow air gaps from the two electrodes,
c
1
c
3
, on each side of it. The electric field between A and the electrodes C was maintained constant by a series of rings of diameter 7 cm., kept at uniformly decreasing potentials. In this case the differential equation giving the distribution
n
of electrons in the electric field is ∇
2
n
= 41 Z/
k
. ∂
n
/∂
z
. If
q
is defined to be ∫
ndy
, this equation becomes ∂
2
q
/∂
x
2
+ ∂
2
q
/∂
z
2
= 41 Z/
k
. ∂
q
/∂
z
. If
n
1
n
2
,
n
3
are the charges received by the electrodes
c
1
,
c
2
,
c
3
, it is shown that the values of Z/
k
can be found by determining the ratio R =
n
2
/(
n
1
+
n
2
+
n
3
),
i
.
e
. the value of
k
corresponding to any Z can be found. Experiments had previously been performed in which a circular stream of ions was collected on concentric circular electrodes, and from the results it appeared that the term ∂
2
n
/∂
z
2
was small compared with the others. By neglecting this term, Prof. Townsend obtained a solution of the differential equation in a simple form and plotted a curve with co-ordinates R and Z/
k
.
The diffusion of electrons through a slit