170 
but it may be used to determine the effects of con- 
tinued condensation on the size and size distribution 
of the cloud drops. The latent heat of condensation is 
released at the drop surface and transferred to the air 
by conduction. As a result the equilibrium temper- 
ature of the drop is greater than the air temperature 
and pow is therefore greater than the saturation water 
vapor density at the temperature of the air. Since 
(Pw—pow) is always positive, supersaturation must 
exist throughout the condensation process. Compu- 
tations show that the supersaturation can hardly ex- 
ceed a few tenths of one per cent for any reasonable 
rate of lift. As a result of the parabolic relation between 
the drop diameter and the time in equation (1) the 
drop diameters will become more uniform as the con- 
densation proceeds. This conclusion has been verified 
by Howell [24]. 
Howell [24] attempted to find the conditions most 
favorable to a broad distribution of cloud drop sizes 
but was unable to delineate them in a clear-cut fashion. 
Slow cooling was expected to allow the initial effects 
of the solute and radius of curvature to exercise a 
maximum effect in broadening the size of the distri- 
bution. The small number of nuclei activated largely 
compensated for any such broadening. Rapid cooling 
had the opposite effect and it appears that some inter- 
mediate rate of cooling will yield the broadest drop- 
size distribution. The computed drop-size distributions 
are of the same general form as those observed in 
natural clouds, but are quite narrow, corresponding 
to the more homogeneous half of the clouds measured 
at Mount Washington, New Hampshire. It does not 
seem possible to explain the broader size distributions 
often observed by a uniform lift process of the type 
treated by Howell. This conclusion appears to be 
definite, in spite of incomplete knowledge of the con- 
densation nucleus size spectrum, because of the con- 
trolling effect of the initial rate of condensation. 
Some other mechanism must be sought to explain 
broader size distributions than those which result from 
uniform lift. Arenberg [3] suggested that turbulence 
would bring condensation products of different histories 
into the same region, thus resulting in a broad size 
distribution. Arenberg also suggested that the alternate 
up and down excursions of the drops in a turbulent 
atmosphere might lead to a broadening of the size 
distribution. However, excluding the evaporation dur- 
ing the descending branches of the motion, turbulence 
tends to narrow the size distribution and its net effect 
is apt to be small. 
In nature the uniform lift process adopted by Howell 
[24] for his computations is subject to important modi- 
fications. The rate of lift of different samples of the 
air at the condensation level will not be the same. 
Because of the controlling influence of the rate of lift on 
the concentration and size of the cloud drops it is to be 
expected that the mean drop sizes of the samples will 
show a rather wide range. Subsequent mixing of these 
samples by turbulence will result in a size distribution 
broader than that produced by a uniform lift. It is to 
be noted that fine-grain turbulence is required for the 
CLOUD PHYSICS 
final intimate mixing essential to the broadening of the 
local drop-size distribution. It seems probable that 
any observed drop-size distribution can be explained 
on the basis of a suitable variation in the rates of con- 
densation of separate air parcels and their subsequent 
mixing. No data are available on the distribution of 
vertical velocities at the condensation level, so that a 
quantitative verification of this theory is not possible. 
Advective marine fogs also have broader drop-size 
distributions than might be expected from uniform 
cooling at the initiation of condensation. Such fog is 
formed at a much slower rate of cooling than any type 
of cloud. One anticipated result is that the drop con- 
centration in advective marine fogs is much smaller 
than in clouds. The cooling is produced at the under- 
lying surface and even in the usual stable stratification 
the mechanical turbulence is apparently sufficient to 
produce a range of cooling rates at the initiation of 
condensation. Such data as are available suggest that 
the drop-size distribution of radiation fog is quite 
narrow, presumably as a consequence of the more 
stagnant conditions of formation. 
The breadth of the drop-size distribution in clouds 
has an important bearing on the stability of the clouds 
and on the release of precipitation in clouds which do 
not reach the freezing level. It is important that further 
studies of the factors which determine the breadth of 
the distribution be undertaken. It appears that knowl- 
edge of the growth of the drops from condensation 
nuclei to large cloud drops is now well understood from 
the physical point of view. The missing information is 
concerned with those details of the air motion which 
determine the initial rate of cooling and the mixing of 
condensation products with diverse histories. 
Equation (1) shows that the time required for a drop 
to grow by condensation increases with the square of 
the drop diameter if the supersaturation is constant. 
This suggests that the maximum size of a condensation 
drop can be estimated by selecting a maximum time and 
a suitable supersaturation. An analysis of the drop 
growth process shows that the supersaturation reaches 
its maximum at the activation of the nucleus and 
thereafter rapidly declines, adjusting itself so that water 
will be condensed at the rate called for by the rate of 
lift. It is thus impossible to select an appropriate 
supersaturation for the computation of the maximum 
drop size. The factors that truly determime the maxi- 
mum drop size are the drop concentration and the 
amount of water vapor available for condensation. 
The former is dependent on the initial rate of conden- 
sation, the latter on the water-vapor content of the air 
and the total lift. It is now known that a considerable 
amount of unsaturated air from the environment is 
entrained by the rising column in cumulus convection. 
This desiccates the rising air and thus reduces the 
maximum drop size. Large drops are favored by slow 
initial lift, large water-vapor content, and large total 
lift. These factors are not all mutually compatible, so 
that the actual maximum drop size is considerably 
smaller than that computed for optimum values of 
each of the separate factors. It is generally believed 
Le 
