196 
ME. J. ZELENY ON THE VELOCITY OF THE IONS 
The distance X travelled by the ion in the direction of the x axis while it is 
traversing the whole distance between the cylinders, i.e., from r — b to r = a, is 
v lcg e b\a f b 7 
X — —— u r dr 
■A.V J a 
( 6 ). 
Now the average velocity of the gas stream as measured by the quotient of the 
total volume of gas emitted in a second by the area of the cross section is 
U 
2 C b 
= W=*l' ,ra 
lr 
( 7 ). 
From (6) and (7) 
v \J(V - f d) b , nN n U b 
X =-xx-log*- . . . (8), and v = — 2 AX l ° Se a * * * ' 9 b 
2Av 
This gives the value of the ionic velocity in a unit field in terms of quantities which 
can be experimentally determined. 
The time required for the ions to pass from one cylinder to the other is 
T = 
b dr 
a V 
(V - c 2 ) 
2Ay 
X 
u 
■ ( 10 )- 
The equations above apply to ions starting from the inner surface of the outer 
cylinder and moving inward to the inner cylinder. In practice it is not possible to 
limit the production of the ions by the Rontgen rays to the inner surface of the outer 
cylinder, so a narrow beam of rays is passed at right angles through the cylinders, as 
is represented by dd of fig. 1. Of the ions of this layer which move inward under 
the influence of the electric force, those that start from the circumference at d are 
carried the farthest by the gas stream before they reach the inner cylinder. Under 
these conditions the equations obtained can be applied by determining the point along 
the inner cylinder farthest from the beam of rays that is still reached by ions. For 
obtaining this point, the inner cylinder DB is divided at k into two parts, insulated 
from each other, the part B to the right being connected to earth, while the part D, 
to the left of the division at k, is connected to a pair of the quadrants* of an 
electrometer. 
If a definite stream of gas is maintained between the two cylinders, then while the 
potential of the outer tube CCf is above a certain value, all of the ions from the 
volume dd which move inward will reach DB to the right of the juncture k, and so 
the electrometer reading will not change. By gradually diminishing the potential of 
CC' a value is finally reached such that the ions starting from the outer edge d reach 
DB just to the left of k, as will be indicated by a changing electrometer reading. The 
value of the voltage A in equation (9) is thus determined, and the value of X, which 
corresponds to it, is the distance from the beam of ra} r s to the juncture k. In getting 
X the corrections which must be made for the width of the beam of the rays and for 
