168 
of nuclei yield the actual geometric diameter or mass. 
With the sole exception of the application of mobility 
measurements to large ion-nuclei, none of these methods 
can be used in the size range which includes the 
majority of the natural condensation nuclei of the 
atmosphere. An indirect measure of the effective size 
of condensation nuclei may be obtained by causing 
condensation to occur on them under controlled con- 
ditions. To discuss this procedure it is necessary to 
review briefly the theory of condensation on nuclei 
as first presented by Thomson [50] for neutral nuclei 
and Ké6hler [29] for hygroscopic nuclei. Thomson showed 
that the vapor pressure in equilibrium with a curved 
surface is greater than the vapor pressure in equilibrium 
with a plane surface at the same temperature. The 
supersaturation required to initiate condensation on the 
surface of a small sphere, which is wetted by water, is 
nearly inversely proportional to the radius. This effect 
is illustrated by the upper curve in Fig. 1. The vapor 
150 
nS 
[e) 
PERCENT RELATIVE HUMIDITY 
RADIUS OF DROP IN CENTIMETERS 
Fie. 1—Growth curves of sodium chloride nuclei of masses 
as indicated at OC. The dashed line is for pure water drops. 
pressure over a solution of a hygroscopic salt is lower 
than that over pure water. In the case of a hygroscopic 
nucleus, both effects are in evidence and act in op- 
position. The net result is indicated by the lower curves 
of Fig. 1. The effect of the dissolved salt is dependent 
upon its concentration and thus is a function of the 
mass of the hygroscopic material and of the radius of 
the droplet. The Thomson effect is a function only of 
the radius of curvature. The three lower curves of 
Fig. 1 are for nuclei of sodium chloride of different 
masses as indicated on the curves. It is readily apparent 
that hygroscopic nuclei grow more slowly as the relative 
humidity increases toward saturation. In all cases, the 
growth curves reach a maximum in excess of 100 per 
cent relative humidity. This peak relative humidity 
must be exceeded if the nucleus is to become a cloud 
drop. The general behavior of these curves has been 
verified experimentally by Junge [25] who determined 
the size of hygroscopic nuclei at various relative hu- 
midities from the mobility of the nuclei as large ions. 
Wright [58] has obtained data on the variation of visi- 
CLOUD PHYSICS 
bility with humidity which seem to confirm the general 
shape of the curves of Fig. 1 below saturation. 
The supersaturation corresponding to the maximum 
of the curves of Fig. 1 is a measure of the effective size 
of the nucleus. The geometric size can be determined 
only if the nature of the hygroscopic salt is known. 
An adaptation of the Aitken nucleus counter can be 
used to determine the effective size of the nuclei, as was 
shown by Junge [25]. He produced expansions of known 
and increasing amounts in a chamber and determined 
the number of drops after each expansion. In this way 
he obtained a nucleus spectrum. Earlier, Aitken [2] 
performed a similar experiment with his apparatus. 
The principal difference in the two techniques was that 
Junge used a large chamber and applied his successive 
expansions rapidly so that none of the previously acti- 
vated nuclei would evaporate. Aitken first produced a 
small expansion and counted the number of drops which 
fell out in the usual manner. He then proceeded to an 
increased expansion, waiting each time until the acti- 
vated nuclei had fallen out of the air. Aitken’s pro- 
cedure is open to the objection that some of the drops 
might evaporate before fallmg out and thus leave 
nuclei to be counted again in subsequent expansions. 
Junge’s method involves the errors of counting the 
number of drops while they are suspended in the air. 
Most of Junge’s experiments were carried out with 
artificially produced nuclei, whereas Aitken used natural 
air. Qualitatively their results were very similar. The 
evidence is that a large number of nuclei are activated 
at the lowest expansion used, with smaller numbers 
requiring greater expansions or supersaturations. Aitken 
found that all of the ordinary nuclei in the samples of 
natural air were activated by a relative humidity of 
150 per cent. Further imcreases in the expansion 
ratio had no effect until the supersaturation required to 
produce condensation on small ions was reached. Junge 
found that 110 per cent relative humidity was sufficient 
to activate all of the nuclei in a sample of outdoor air. 
Number and Distribution of Nuclei. Literally thou- 
sands of measurements of the number of nuclei in the 
air have been made with the aid of the Aitken imstru- 
ment. As ordinarily used, this instrument produces a 
supersaturation of from 200 to 300 per cent and there- 
fore activates all natural nuclei but not small ions. 
As will be pointed out below, only a small fraction of the 
total number of nuclei are activated mm natural con- 
densation processes. For this reason the total number 
of nuclei as determined by the Aitken counter is of 
limited value since no information regarding the size 
or the size distribution of the nuclei is obtaimed. A 
very complete summary of the measurements which 
have been made has been given by Landsberg [83], 
and no attempt will be made here to give any of the 
detailed results. The maximum concentration was found 
in cities, with an average of 150,000 per cubic centi- 
meter and a maximum of some four million. In the 
country, the average is of the order of 50,000 and the 
maximum near 400,000. Much lower concentrations 
are found over the oceans with an average of about 
1000 and a maximum of about 40,000. At a given 
