( 443 ) 
component along the line of the centres and another perpendicular 
to it; the latter of these components will remain unchanged and the 
former will have its direction reversed. 
In applying this to the encounters of the particular kind specified 
at the beginning of this §, we may take for all of them the line of 
centres to coincide with the axis of the cone dw. Our conclusion 
may therefore be expressed as follows: Let V be a plane through 
the origin in the diagram of velocities, perpendicular to the axis of 
the cone. Then, the veloeity-point of the electron after impact will 
be the geometrical image of the original point with respect to this 
plane. It is thus seen that all electrons whose velocity-points before 
the encounters are found in the element J2 will afterwards have 
their representative points in d2,, the image of dà with respect to 
the plane V. 
By this it becomes also clear, in what way the number 5 ean 
be calculated; indeed, in encounters taking place under the circum- 
stances considered, velocity-points may as well jump from di, to 
dk as from dà to dj,. The number of cases in which the first takes 
place is found from (8), if in this expression we replace §, 4, § by 
the coordinates §', 7,6 of the image of the point (&, 7, $) with respect 
to the plane V. It is to be remarked that the factor 7 cos 9 d 2 may 
be left unchanged, because the lines drawn from the origin of the 
diagram to the points (6, 7,5) and (§', 7), 6’) have equal lengths and 
are equally inclined to the axis of the cone. Also d’,=d4. The 
increase per unit volume of the number of electrons in the group 
(6), insofar as it is due to encounters in which the line of centres 
lies within the cone da, is thus found to be 
n I? fF (S', nj, 8) r cos Hdd 
and, in order to find 6, it remains only to divide this by da and to 
integrate with respect to all cones that have to be taken into account. 
Using the formula (8) we may as well calculate directly the 
difference /—a. By this the equation (7) becomes 
n R? „fire. n,8) — 7 (En, $)} cos Bd w = 
Oe Oene wf òf 
SE ya : eae Ee PRT ; 
We must now express §',7/,6' in §, 7,6. Let Jig, be the angles 
between the axes of coordinates and the axis of the cone dw, this 
last line being taken in such a direction that it makes the acute 
angle 9 with the velocity (§, 7, 5). Then 
' 
(10) 
=§ — 2r cos dos f, n= — 2rcos Heosg, § =§ — Arcos Heos h, (11) 
