PRODUCED IN GASES BY RONTGEN RAYS. 
195 
different potentials and the gas between them is at rest, an ion starting from the 
point d at the inner surface of the outer cylinder will move directly across to l 
under the electric force. But when a stream of gas is passing between the cylinders 
from right to left, the ion will also be carried along by the stream, and so follow a 
path somewhat like that represented by the curve die, finally reaching the inner 
cylinder at some point, Jc, which can be determined. The paths of the ions are not 
straight lines, because the electric intensity and the velocity of the gas stream vary 
from point to point between the cylinders and according to a different law for each. 
The distance X that the ions have been carried along the tube by the gas stream 
while they are crossing between the two cylinders under the electric force is a 
measure of the relative velocities of the gas and of the ions, and so may be used in 
determining the velocity with which the ions move in a given electric field. 
Let the outer cylinder be kept at a potential of A volts and the inner one at zero 
potential. 
Let b be the inner radius of the outer cylinder and a the outer radius of the inner 
cylinder. 
Then the potential at any point between the cylinders at a distance r from the 
common axis of the two cylinders is 
p _ A r/a / -i \ 
* log eb/a .^ 
and the electric intensity at this point is 
cm _ a 
dr r log*, bjcc 
(2). 
If we letv represent the velocity with which an ion moves when in an electric field 
whose intensity is 1 volt per centim., and assume that its velocity is proportional 
to the strength of the field, then at a point whose electric intensity is represented by 
equation (2), the radial velocity of the ion will be 
V = 
Av 
r log, bjcc 
( 3 ). 
The ion being carried by the moving gas also has a motion along the tubes. The 
velocity of the gas stream at any point depends upon its distance from the axis of 
the cylinders, which will be called the x axis. 
Suppose that at the distance r from this axis the gas velocity is u. 
The motion of the ion is represented by 
dx u 
dr ~ V 
( 4 ), 
and substituting the value of V from (3), 
