196 
The ambient vapor pressure e at the time when 
the drops have grown from 7; to 7; is thus 
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This value of e is used in the growth equation 
(10). 
For the numerical integration of (10) on the 
electronic digital computer the method of Runge- 
Kutta was chosen. It was found that the equa- 
tion was subject to great computational insta- 
bility, so that very small time steps had to be 
used at first. A method was devised for testing 
when it was feasible to increase the time steps. 
Even with this procedure the machine time re- 
quired was very large. It had initially been hoped 
that it would be possible to carry out computa- 
tions for a number of cases in which the various 
parameters (size distribution and composition of 
nuclei, manner of cooling, etc.) were varied, but 
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Nucleus Radius 
Fic. 1—Assumed distributions of sizes of nuclei 
(solid curves, cumulative distributions, dashed 
curves, differential distributions) 
NEIBURGER AND CHIEN 
the machine time required was so large that only 
four cases were computed, representing three 
rates of cooling and two distributions of sizes of 
nuclei. 
The nuclei distributions used—The measure- 
ment of particulate matter in the atmosphere has 
been carried out by various means, each capable 
of counting particles in a portion of the range of 
sizes which occur. For a long time most counts 
were of the range called Aitken nuclei (<0.1 
micron) on which condensation occurs only at 
high supersaturation. Recently it has become 
recognized that the ‘large’ (0.1-1 micron) and 
‘giant’(>1 micron) nuclei are the only ones which 
participate in cloud formation. 
Size distributions in the various ranges have 
been summarized by Junge [1952, 1953], Gilbert 
[1954], Woodcock [1952, 1953}, and Lodge {1955}. 
Their data were combined into two idealized size 
distributions, shown in Figure 1. The difference 
between the two hes in the larger concentration 
of large and giant nuclei in Type B distribution. 
In the figure are shown both the concentrations 
of each size per unit size interval and the cumula- 
tive concentration of all nuclei greater than a 
given size. In Type A distribution there are 1030 
particles per cm# larger than 0.01 micron, 115 per 
cm? larger than 0.1 micron, about 1.5 per liter 
larger than one micron, and much less than one 
particle per cubic meter larger than ten microns. 
In Type B distribution the same numbers are re- 
spectively 1120, 135, 50, and 14. 
The models of cooling—The models of cooling 
were selected to simulate in a general way the 
conditions of formation of Stratus cloud or fog, 
Cumulonimbus, and trade-wind Cumulus. 
For the two Stratus cases it was assumed the 
cooling proceeded at constant pressure at a rate 
of 6°C per hour. The initial temperature was 
taken to be 288°K, and the initial relative hu- 
midity was about 75%. For the first Stratus case 
the Type A distribution of nucleus sizes was as- 
sumed, and for the second, Type B. Correspond- 
ingly, these cases will be called Stratus Case A 
and Stratus Case B. The pressure was assumed 
to be 1000 mb. 
For the Cumulonimbus model we assumed a 
distribution of vertical velocities based on the 
measurements of the Thunderstorm Project 
[Byers and Braham, 1949}. The initial temperature 
was taken to be 299.2°K, and the relative humid- 
ity about 75% at about 1000 mb pressure, and 
adiabatic cooling was assumed. Figure 2 shows 
the assumed variation of vertical velocity and 
