188 W. A. MORDY 
TaBLE 4—Case I, 100 cm/sec 
N r n’ a 
1.28 X 107 21.2 
6.4 X 107 22.2 2710 0.954 
3.2 X 105 22.4 1950 | 0.946 
1.6 X 10° 22.7 1195 | 0.933 
8X 105 | 23.2 730 0.912 
4X 10° 23.6 436 0.897 
2x10 | 24.2 285 | 0.875 
105 25.2 203 0.840 
5X 10! | 26.2 134 0.809 
2x10! | 27.3 70 0.790 
3X 10° | 29.9 | 18 0.708 
verte || Seer 3 | 0.628 
10 38.6 1.8 0.548 
TaBLe 5—Case III, 5 cm/sec 
N 2 n a 
107 24.6 | 
3 X 106 26.1 232 | «0.943 
10° | 27.0 133 0.910 
9 105 “9 28/0 7 4175. Fy 0.878 
7 xX 105 29.2 197 | 0.842 
5x 10° | 30.6 | 199 0.803 
3 X 105 33.1 
192 0.748 
determines 7. Because of the very skew nature of 
the droplet distribution the mean radius and the 
minimum radius were assumed to be the same, 
an assumption which could lead to an error of a 
few per cent in the estimate of n’ at most. The 
four cases chosen were representative of the range 
of differences in nucleus spectra which resulted 
from different nucleus distributions and vertical 
velocities. 
In all of these cases except one there is a mark- 
edly higher number of potential collisions among 
the smallest cloud droplets. The exception is the 
case where there is an extremely slow rate of rise, 
5 em/see, and a dense nucleus distribution (which 
was taken from Woodcock’s data as characteris- 
tic of the distributions of salt particles produced 
at cloud base by a Beaufort Force 7 wind at the 
sea surface). 
The fact that there are a higher number of 
potential collisions between small droplets, how- 
ever, is not enough to determine whether colli- 
sions between the smallest droplets are of compa- 
rable importance to those between the larger and 
smaller droplets. It must be determined whether 
in a reasonable time a comparable number of 
larger droplets are originating by combining smal- 
ler droplets as from condensation on large salt par- 
ticles. To test whether this is true the resulting 
radius and number of the droplets produced by 
the combination of the smallest droplets in a 
reasonably short time, must be compared with 
the total number of condensation produced drop- 
lets which have about the same radius as the com- 
bined droplets (r = 2!87 = 1.26r). If these fig- 
ures are close to the same value then one must 
assume that collisions between the smaller drop- 
lets are more important than between large nu- 
cleus drops and small drops. The larger droplets 
are then being increased in number at a suffi- 
ciently rapid rate so that the number of originally 
large particles is relatively insignificant. 
A useful index therefore as to the importance 
of these collisions is the time of replacement of 
large nucleus droplets (droplets formed on 
large nuclei) by smaller coalescing droplets. If 
this is computed for the cases in Table 6 one 
finds that the number of coalescences between 
the smallest two categories of droplets replace 
1-100 
E 7 \ | 
C3 | 
mS x 
10° —J- |\ + -= 
PX 
| 
10?- - we 
| N 
tN 
10 - { 
| | 
Om 20p 304 ; 4p 
Radius 
Fic. 2—The distribution of cloud droplet sizes 
used in the computations; these distributions are 
derived from Mordy [1959] and represent the ex- 
treme differences in droplet concentration and 
spectrum width obtained in the different assumed 
cases of nucleus spectra and vertical velocities; 
the spectra represent the sizes of droplets expected 
if the liquid water content is 1g/m’ and is assumed 
constant (see text); the figures at the top give the 
distribution type and the vertical velocity in 
em/sec 
