190 W. A. MORDY 
terms in (3) have been expressed as 
Ing= In. 3 = InwN,Ne2kAr + 3 In (2F + Ar) (13) 
where 7, = 7 
Tr, = i + Ar 
Ar = const 
Since for any pair of droplet sizes NN» is con- 
sidered constant in the model, then the variation 
of In n’ depends only on no’ and 7. Hence if one 
plots the number of collisions between two cate- 
gories of droplets as given in Tables 2 to 5 it is 
possible to extrapolate how the relative number 
of collisions change with time or with different 
liquid water contents. As Ar/r becomes small the 
points representing the number of collisions tend to 
line up more vertically as the points move along 
the diagonal lines (curve 4B becomes curve A’B’) 
showing that as time elapses the relative impor- 
tance of the small droplet collisions increases. 
The diagram also shows how important the ini- 
tial droplet spectra radii are in determining the 
relative importance of large and small droplets, 
for these show up as the separation of points in 
the curves in the diagram. When satisfactory in- 
formation about F# is available as a plot of In F vs. 
In (27 + Ar) and Ar, this will allow a more com- 
plete diagrammatic treatment. 
The calculations and reasoning in this paper 
have been made with the assumption that the 
collection efficiency of the droplet was 100%. 
Research and theory on the collection efficiency 
of droplets unfortunately does not yet converge 
on values which can be substituted into these 
equations to provide more conclusive arguments. 
However, if one follows the reasoning of Hocking 
[1959], it seems that few if any collisions occur 
before the droplets reach radii of 18 or more. 
At this point the collection efficiency rises rapidly 
to values exceeding unity. If these values were 
to be inserted in the present study an almost ex- 
plosive effect on the numbers of droplets coalesc- 
ing should occur at the point where the mean drop 
size exceeds this value, independently of whether 
one has a wide spectrum of cloud condensation 
produced droplets or not. Here the most impor- 
tant consideration would be the concentration of 
droplets per unit volume. This is largely fixed by 
the supersaturation conditions and nucleus con- 
centrations at cloud base. With different droplet 
concentration, considerable differences in liquid 
water content or cloud depth are required to pro- 
duce the large mean droplet size which Hocking 
states is necessary for coalescence. 
Acknowledgments—The writer wishes to ac- 
knowledge with thanks the helpful discussions of 
the work described in this paper with B. Bolin, 
P. Welander, and most especially with Mr. Claes 
Rooth of the International Meteorological Insti- 
tute in Stockholm. The work has been supported 
by the U. 8. Office of Naval Research and the 
Woods Hole Oceanographic Institution. 
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Discussion 
(Note: The discussion of this paper is combined 
with that following the next paper.) 
