UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 
associates for the violent disruption of a water drop, the 
latter being about 2 stat coulombs for each cubic centi- 
meter of water that is involved. Perhaps the results re- 
ported by Findeisen and by Dinger and Gunn are in 
part attributable to the orderly freezing of wate. 
Other investigations of Workman and Reynolds indi- 
cate that cloud droplets may contain solutes of the 
right type and in suitable concentration for this process 
to occur in the atmosphere. Favorable results were also 
obtained in an experiment designed to imitate the 
growth of hail. 
The advantage which derives from the relatively 
large amount of electric charge separated in the orderly 
freezing of suitable solutions may be illustrated by the 
followmg simple calculation. If the amount of charge 
separated in the formation of one gram of hail or sleet 
is 10! stat coulombs (about 2 per cent of the largest 
value reported), then in order that the rate of charge 
regeneration of a charge-cloud be 4 amp, or 1.2 X 10!° 
stat amp (Item 6, of the foregoing list), it is necessary 
that at least 1.2 x 10° g (about one short ton) of hail be 
formed each second in the region of primary electrical 
activity. In contrast to this, the mass of water drops 
that would have to be violently disrupted each second, 
if the breaking-drop process were the basic factor, 
would be at least 6 X 10° g or more than 6500 short 
tons. This apparently shows that the breaking-drop 
process is not adequately active, but that generation of 
charge by orderly freezing may be sufficiently active 
provided that, among other conditions already indi- 
cated, hail is always a large constituent of the hydro- 
meteors in a typical thunderstorm. 
None of the other primary processes so far proposed 
has yet been shown to have the generating capacity re- 
quired. Acceptance or rejection of either Gunn’s or 
Frenkel’s theory depends on whether or not the re- 
laxation time of the process is adequate, that is whether 
1/(4mX) im the region of primary activity, is, on the 
average, about 5 sec (Item 6). This is equivalent to 
saying that these theories are not acceptable unless the 
air conductivity in the region of primary activity is at 
least ten times that for normal air at an altitude of 5 
km. At present it seems unlikely to the author that this 
condition is satisfied, but since this opinion is based 
chiefly on indirect evidence, more direct exploration in 
the future may bring forth evidence which contradicts 
this view. 
The ion-capture process which is elemental in C. T. 
R. Wilson’s theory also postulates that a relatively high 
concentration of ions prevails in the region of primary 
activity, where the initial separation of charge occurs. 
Since these ions are assumed to have a very small mo- 
bility, it seems likely that the air conductivity would be 
abnormally small in some parts of the cloud. This postu- 
late cannot be definitely refuted by evidence now avail- 
able. 
The large-scale separation of charge which follows 
the initial step in charge generation must also proceed 
at the rate of 4 amp for each typical center of electrical 
activity. In all theories mentioned in this article it is 
postulated (1) that after the initial step the larger drops, 
117 
or particles of precipitation, tend to have an electric 
charge of sign opposite to that of very small particles or 
of air ions, and (2) that, principally under the action of 
eravity, large particles fall away from the small ones at 
a velocity v which is equal to the difference in the ter- 
minal velocities. 
Although there are no obvious alternatives to these 
postulates, there seems to be some ground for doubting 
whether the second is acceptable. This is illustrated in 
the following paragraph. 
Let p denote the total net charge on the large par- 
ticles in a cubic centimeter of air; v, the average velocity 
of these particles relative to the smaller ones; and A, 
the cross-sectional area, normal to the direction of v, of 
the region of charge separation. The total current J’ 
from large-scale separation then is J’ = pvA. Now in 
order that the value of 7’ may be 4 amp, pvA must 
equal 1.2 X 10! stat amp. The space charge p is 
limited by several circumstances. One which is amenable 
to simple treatment is that for no considerable propor- 
tion of the drops or particles shall the charge g of each 
drop of radius r be greater than 1007. Larger values 
lead to electrical discharge. If there are n drops in each 
cubic centimeter, all of the same size and same charge, 
the maximum admissible space charge is p,, S 100nr?. 
The mass of drops m in 1 em# of air is also limited, 
and in terms of this m, the foregomg expression for the 
upper limit of p may be written p, S 300m/(4m7r). 
Now v is an increasing function of 7, but in such a way 
that p,,v decreases with an increase of r if m is constant. 
For a very large value of m, namely, 5 X 107° g cm, 
pnd is 0.25 for hailstones having a diameter of 3 cm, 
and is 1.1 for droplets of 0.4-mm diameter. If the inter- 
mediate value 0.5 for p,v is used, one finds that A 2 
2.4 km2. Such a value for A is of satisfactory magnitude, 
but in view of the assumptions made here this estimate 
is doubtless much smaller than is actually required. It 
seems unlikely that in nature a large proportion of the 
precipitation particles are highly charged at a given 
time, and it is also doubtful whether such a large con- 
centration of water, in either the liquid or the solid 
phase, occurs in a typical thunderstorm. The effect of 
the electric field, which tends to reduce v, especially if 
the particles are small, is also not considered here. Be- 
cause of these and other considerations it seems evident 
that the value required for A is much larger than 2 or 
3 km2. But if this conclusion is correct, that would en- 
tail the difficulty of accounting for the size, structure, 
and orientation of the charge-clouds—features which 
are, at least roughly, indicated by measurements of the 
electric field above thunderclouds, within them, and 
below them at the earth’s surface. 
The object of the foregoing statement is to indicate 
how unsatisfactory is the present status of theories re- 
garding the large-scale separation of charge in thunder- 
storms. No theory is yet secure if settling under the 
action of gravity is assumed to be essential in the large- 
scale separation of charge. If observations eventually 
show that the concentration of water in the typical 
thunderstorm is considerably greater than 5 g m™“, at 
least in the region of primary electrical activity, this 
