s 
PHYSICS: L. B. LOEB 
Proc. N. A. S. 
where W is the velocity of thermal agitation of the electron, K f is the 
mobility of the electron, L is its mean free path, V is the voltage, d is 
the distance between the plates, and n is the chance of ion formation per 
impact. 
Let us assume that when the voltage V is equal to V 0 all the Q Q carriers 
starting from P at atmospheric pressures can reach E. This simplifying 
assumption is contrary to fact for at V Q the carriers actually only begin 
to reach E. We may with this assumption impose the conditions im- 
plied in equation (1) on the equation (2). This will lead to the 
conclusion that out of a maximum possible current I Q , the real current / 
which reaches E as a function of the frequency N = 1/T, the pressure p, 
the plate distance d, and the voltage V, is given by the equation 
W / dHp/760)* _ K(p/760) \ 
I = I Q e » K 'L\ v n ) (3) 
where p is in mm. of mercury, and K is the mobility of the normal ion. 
Now it is possible to evaluate W from the mean kinetic energy of the mole- 
cules, for it is assumed in the theory that the electrons move in the elec- 
tric field with a velocity small compared to W. Let us further assume 
K' to be constant and equal to 200 cm. /sec, 7 ' 3 while we take L as 4V2 
times the mean free path of the molecules, and K as about 2.5. We 
thus have the equation 
9.9 X IP 3 / rf 2 (/>/760) 2 (2.5ft/760) \ 
I = I Q e « \ v N ) (4) 
This equation is open to experimental verification for it contains but 
one unknown quantity n, as I/I 0 can be determined experimentally under 
known conditions of N, p, V and d. 
I have recently made a series of determinations of the mobilities of the 
carriers produced in air at different pressures under essentially the simple 
conditions in the foregoing discussion. These determinations yielded 
mobility curves of which the set of curves shown in figure II are typical. 
As is seen at once the form of the curves resembles the curves to be expected 
from the qualitative discussion above. The values of I/I Q may be de- 
termined in such curves from the ratio of the current to E caused by a 
given alternating potential between P and E and that caused by an equal 
fixed negative potential on P. By substituting this value of I/I 0 in the 
equation with the corresponding values of N, P, V and d one may solve 
for n. As the result of a large number of determinations the value of n 
obtained under conditions best conforming to the theoretical assumptions 
was 250,000. With n determined the theory may be further tested by com- 
puting the curves for I/I Q as a function of V for different values of d, 
N and p. A large number of curves were thus computed. A typical 
comparison of the theoretical curves so obtained and the curves actually 
observed under the same conditions may be seen in figures III, IV and V. 
