Vol. 7, 1921 
PHYSICS: L. B. LOEB 
7 
the distance A covered as an electron would produce no measurable effect 
on V 0 and the values of K would be normal. Now let the pressure be 
reduced to 152 mm. The mobility of the electrons will be increased five- 
fold. Furthermore as the density of the gas is reduced to one-fifth the 
electrons will take five times as long to make the 250,000 impacts required 
to attach. The distance A will, therefore, become 1.5 mm. which is an 
appreciable fraction of the 15.0 mm. between the plates. The intercept 
V 0 as determined from the portion of the curve corresponding to the 
majority of the carriers will, therefore, be but 0.9 of the V Q required for 
ions, and the value of K will be about 10% higher than for normal ions. 
In other words assuming the Thomson mode of attachment the mobility 
constant of the ions will appear to increase with decreasing pressures 
below about 152 mm. 2 Since the number of impacts required to form an 
attachment is a chance phenomenon there will be an appreciable number 
of ions reaching E that have traversed distances greater than A before 
attaching. These will reach E at values of V Q below those for the majority 
of carriers. As a result the otherwise sharp intercepts of mobility curves 
with the voltage axis observed for ions will be masked by asymptotic 
feet of exponential form rising at values of V well below the V Q required 
for the majority of the ions. These will become rapidly more pronounced 
0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 
as the pressures decrease. Such curves are seen in the experimental 
curves II, III, IV, V and VI, figure II, obtained in air under conditions 
indicated in the legend. To estimate the hybrid mobilities of such carriers 
the asymptotic feet must naturally be ignored, as has been done by 
previous observers. 2 § 
With the method of analysis outlined above it would be possible to 
pursue the evolution of the mobility curves as a function of p and T in 
a qualitative manner indefinitely. Fortunately a much simpler and more 
accurate study of the theory is made possible by the application of the 
mathematical analysis of Thomson. On the basis of his theory Thomson 
has shown that out of Q Q electrons starting from P the number that can 
travel x cm. through the air without combining to form ions is given by 
O/Oo = ,-<**>A»*'«V« (2) 
