6 
PHYSICS: L. B. LOEB 
Proc. N. A. S. 
parallel to P and d cm. above it. On applying an alternating potential 
difference of half period T between P and E the ions starting from P 
will alternately be driven from, and drawn back to P, for periods of T 
seconds. If u is the velocity of the ion in unit field, then for given values 
of T and d there will be no current to E until V reaches a value V Q such 
that uTVo/d = d. At V 0 then a current to E will become manifest 
which will increase with increasing V to a saturation value. On plotting 
the current i as ordinate against the voltage V as abscissa we will get a 
curve of the type of curve I, figure II. Such a curve will be termed a 
mobility curve for if the value of the intercept V Q of such an experimental 
curve be substituted in the equation 
the mobility u of the carrier is at once obtained if d and T are known. 
When the pressures are j*educed the curves remain the same but the value 
of the mobility u of the ion is found to increase inversely as the pressure. 
In other words up/760 = K, where K, the mobility constant of the ions, is 
independent of pressure. 
Now let us assume with J. J. Thomson 1 that an electron does not at- 
tach to form an ion on its first encounter with a gas molecule, but that the 
attachment is a chance phenomenon occurring on the average in one out 
of n impacts with molecules. Let us further assume that for air n is 
large, say, about 250,000. Under ordinary conditions the velocity of 
thermal agitation of the electron is great compared with its velocity 
acquired in the electric field. The electron, therefore, covers a zigzag 
path drifting slowly all the while in the direction of the electric field. 
Consequently while making the 250,000 impacts necessary for attachment 
the majority of the electrons will move a distance, A, in the field, which 
may be estimated. Since A is covered by the electron in 1/100 of the 
time that an ion would take, one may practically assume that the majority 
of the ions start at a point distant A cm from P instead of from P. For 
appreciable values of A the values of V required to drive the majority of 
the carriers to E may become notably lower than they are for ions starting 
at P. The values of u and hence of K obtained from experiments where 
A becomes significant will then be high. In air at atmospheric pressure 
the time taken for an electron to make 250,000 impacts is about 1.2 X 10 ~ 6 
sec. In a field of 40 volts with d = 15 mm. the electron would cover a 
distance of 6.3 X 10 ~ 2 mm. towards E in this time. This small value of 
u = d 2 /V Q T 
(1) 
