TRAVERSED BY CATHODE RAYS. 
75 
Table XI.—Conductivity under Rontgen Rays. 
Gas. 
Density. 
Measured by 
J. J. Thomson. 
Rutherford. 
Perrin. 
HC1 
1-25 
8-9 
11 
8 
so 2 
2-23 
6-4 
4 
6 
Cl> 
2-45 
17-4 
18 
— 
H,S 
1T9 
6-0 
6 
— 
Although the laws of ionization and absorption for cathode rays are clearly defined 
by these results, it is difficult to apply them in practice to the direct calculation of 
the relative ionizations in any particular experiment. 
Take, for example, the case of a pencil of parallel rays, 1 scp centim. in cross 
section, traversing air at a pressure p. 
Let q — the rate at which ions are produced in 1 cub. centim. of air at unit 
pressure by cathode rays of unit intensity 
and X 0 = the coefficient of absorption of air for unit pressure. 
Consider then the ionization between two planes distant x and x -f- dx, from the 
source of the rays. 
If I denotes the original intensity of the rays, I. e~ pX ° x will represent their 
intensity at a distance x, and p . q . I. t~ pKx dx will then represent the total number of 
ions produced between these two planes in one second. 
Imagine now a saturating electric field applied at right angles to the rays and 
confined between the limits r and r -f- d. 
The value of the total saturation current obtained with this field would then be 
r v+d 
represented by p . q . I. e~ pXoX dx, 
J r 
or 7 = ~. e~ Xr (1 — e~ xd ) . (1), 
where pX 0 is replaced by the quantity X, whose values for different pressures are 
given in Table IX. 
If the air traversed be now subjected to diminishing pressures, the saturation 
current will assume different values and will reach a maximum when 
i.e. 
cli 
dX 
0, 
(r + d) e xd — r = 0 , 
e 
\d _ 
r + cl 
L 
or 
r 
( 2 ). 
