PHYSICS: L. B. LOEB 
349 
the arc), one finds that the mobilities are absolutely normal. Even at 
pressures as low as 300 mm., where the potential fall per mean free path 
is larger still, there is no abnormal mobihty. 
These results as regards the mobihty of the positive ion for high 
values of the product, field strength times mean free path, seem to be in 
direct contradiction to the results of Todd,^ who, working at very low 
pressures and small field strengths, got an apparent abnormal increase 
in the mobihty of the positive ion. The value of this product may be 
expressed as the ratio X/p, to which it is proportional, where X is field 
strength in volts per centimeter and p is the pressure in millimeters 
of mercury. The value of X/p for which Todd^ observed the abnor- 
mality of the positive ions is 2.6. The values of X/^ at which I worked 
are as high as 18.0. The latter 's results agree, however, with those of 
WelHsch^ recently obtained at pressures as low as 0.05 mm. of mercury. 
Wellisch^ found no abnormal mobilities of the positive ions for values 
of X/p as high as 34.5. This value of X/p is close to that for ionisation 
by collision at this pressure. 
The results obtained by me with negative ions for high pressure for 
values oi X/p near where ionisation by collision must begin, seem to 
be contrary to the results of most of the observers who worked at low 
pressures with much smaller values of X/p. Townsend,^ basing his 
assertions on the work of Lattey,^ states that for low pressures the 
abnormal mobility, i.e., the breaking up of the cluster, should begin at 
X/p = 0.1. This appears to be in direct contradiction to the results 
of the writer obtained with air at pressures as low as 300 mm., and 
with X/p = 16.0, where strictly normal negative mobilities are found. 
In view of this contradiction, I worked over the results of Kovarick,^ 
who obtained abnormally high negative mobilities at low pressures, 
to see whether the appearance of the abnormally high mobihties in 
his work was a function of X/p. The initiation of these abnormal 
mobihties was found to be a function of p rather than of X/p, which 
indicated, since my pressures were much higher than Kovarick's,^ that 
the two sets of results were not necessarily in conflict. 
All of the above facts are in accord with the recent results of WelHsch^ 
on the mobilities of negative ions at low pressures. He found that, 
even at the lowest pressures at which he worked, the negative carriers 
were in part at least perfectly normal negative ions. This was the case 
for values of X/p close to the value of X/p for ionisation by colhsion at 
those pressures. He also found increasingly great numbers of free elec- 
trons in air as the pressure was reduced below 8 cm., but no intermediate 
negative ions. These free electrons could not, according to WelHsch, 
