383 
5. Calculation of the Pressure- Effect. 
a. It is seen that only circumstances are dealt with in which 2 
is “sufficiently” great with respect to D. In the thus restricted category 
two cases should, however, be distinguished: 
I. The gas pressure is higher than 0,1 mm., and the discharge 
takes place at comparatively low potential differences. 
Il. The gas’ pressure is lower than 0,1 mm., and the discharge 
takes place at high potential differences. This category has been 
treated by Stark, WeEuNerLT and Frank, and will be left out of conside- 
ration here. The pressure effects belonging to this are very slight, 
and of opposite sign to those found under I. 
When the gas pressure is higher than 0,1 mm., and the potential 
of discharge is slight, both the positively and the negatively charged 
particles may be considered to be at least partially loaded with matter. 
Let us suppose for a moment that all the charged particles are in 
this case. 
Let us consider the conduction of electricity through a gas, that 
contains only univalent ions, in a cube the sides of which are 1 cm. 
long, the direction of the current being parallel to one of the sides. 
When in this cube the direction of the electromotive force be taken 
as x-axis of a system of coordinates, then with a potential difference 
v between the end-planes, a positively charged particle undergoes 
an acceleration expressed by the known equation of motion: 
dz 
B 
(In this e is the charge, m, the mass of the positive ion). The 
electrie force acts undisturbed on the charged particle during a time 
which elapses between two collisions. Be À, the mean free length 
of path, and c, the mean velocity of the positive ion, this time is 
a 
By integration of the equation of motion, taking the value of t 
into account, summation of the components of velocity for all posi- 
tively charged particles n, per volume unit, the formula 
n,eVdpy 
on an average — tT — 
2m, Cy 
is found’) for the number of positive ions that passes per second 
through the cross-section of the conductor. 
Likewise follows from the theory of the conduction of electricity 
through gases for the number of negative ions: 
') Cf. eq. G. Jäcer. Theor. Phys. IV. Samml. G. 8 57, 61. 
