NUCLEI OF ATMOSPHERIC CONDENSATION 
where B = mobility (sec g~), 
1 = free path length (em), 
r = radius of particle (em), 
A = numerical factor of 0.9, 
n = viscosity of air (g em sec“). 
The viscosity 7 is practically independent of the at- 
mospheric pressure, so that with decreasing pressure, 
B increases with 1. 
1. The fall velocity of the particles is 
V = BMg, 
lI 
I] 
where 17 = mass of the particles (g), 
. . Ip . 
g = gravitational acceleration (em sec”). 
Despite the small fall velocity, the sedimentation proc-_ 
ess that takes place continuously and everywhere in 
the immediate vicinity of the earth’s surface is probably 
important for the nuclei balance [24]. The same holds 
true for the charged particles settling in the electric 
field of the earth. 
2. The diffusion coefficient that is valid for the ad- 
hesion of particles to surfaces of all kinds is 
Da 8 
where R = gas constant (erg deg—! mol"), 
T = absolute temperature (deg), 
N = Loschmidt number. 
The diffusion coefficient D greatly increases with de- 
creasing radius of the particle and has been used for 
the determination of the average particle size [28]. In 
contrast to sedimentation, adhesion affects especially 
the small particles. In closed spaces or vessels, the 
influence o diffusion increases with increasing ratio of 
surface to volume [80]. 
Diffusion is effectual in forests and grassland with 
their very large surface areas (filter effect) and in the 
clouds, in which the decreased nuclei concentration [23] 
is probably caused not so much by consumption during 
condensation as by adhesion to the droplets. For this 
reason, analyses of traces of substances in hoarfrost 
and other condensation products in combination with 
measurements of droplet number and size do not permit 
any conclusions regarding the mass of the individual 
nuclei. 
3. As regards coagulation, reference is made to 
the exemplary investigations of Whytlaw-Gray and 
Patterson [42]. The decrease in the number of particles 
m per unit time and volume in homogeneous aerosols is 
ain _ 8tkT ope _ 4kT l 2 
phar yy Brn = P+ al)e, 
that is, the small particles coagulate more rapidly. The 
numerical results given in Table IV clearly show that 
coagulation is much more effective for the originally 
very small combustion nuclei that are highly concen- 
trated in city air, ete., than for the coarser and less 
concentrated dust and ocean spray aerosols. Mixed 
nuclei are, therefore, to be expected especially from 
industrial and similar nuclei sources. The laws of co- 
189 
agulation, experimentally confirmed by Whytlaw-Gray, 
become more complicated m natural aerosols because 
of the broad distribution of sizes and occasional electro- 
static charges. For example, if two particle sizes are 
present, the greater coagulation rate of the smaller 
Taste IV. THe DrcrREASE IN THE NUMBER OF PARTICLES 
PER Hour IN HomoGENEOUS AEROSOLS 
Nuclei number Rages (em) 
(cm=*) 
1076 10 1054 
108 6.86 X 10° 1.66 X 107 1.13 X 107 
104 6.86 & 10? 1.66 X 10! 1.13 X 101 
105 6.86 < 10 1.66 X 103 1.13 X 108 
nuclei is further increased by adhesion to the larger 
nuclei. Therefore, aged aerosols contain only a small 
percentage of small nuclei. 
Since the large particles grow more rapidly with 
increased humidity than do the small ones, a slight 
increase in coagulation rate with humidity is to be 
expected. This was confirmed by Landsberg [23] who 
found a decrease in the number of nuclei in rooms when 
the humidity was increased. Effenberger [10] also found 
by simultaneous nuclei and dust counts m the open air 
that, with increasing humidity, the nuclei concentration 
decreases while the dust content increases. However, in 
this case it must be noted that there is a possible 
selective effect of the synoptic situation. Moreover, the 
sedimentation rate in the dust counters is greater with 
higher humidity because of the growth of the dust 
particles. 
Concluding Remarks 
Because of lack of space it has been impossible to 
include a compilation of the results of the many works 
dealing with nuclei counts. However, such a compilation 
is not really necessary, since the reader can refer to 
exhaustive monographs [8, 23], and no new information 
has been obtained on the subject. In the various sections 
we have touched upon those relationships, determined 
by such investigations, of the nuclei count, etc., ta 
other meteorological elements that were of interest from 
the point of view of the physics of nuclei. In many cases 
these relationships have only a limited value in ex- 
plaining physical processes, since the correlations gen- 
erally overlap. For this reason, it has been suggested 
by various investigators that stress should be put on 
additional laboratory research work. A number of open 
questions touched upon in the sections above could 
thereby be clarified. 
In conclusion some of the areas of study that seem 
especially important to the author are summarized: 
1. The growth of nuclei, especially at humidities of 
less than 70 per cent, and the associated problem con- 
cerning the physical structure of nuclei (mixed nuclei, 
supersaturation of solution, and crystallization). 
2. The chemical composition of the aerosol. Parallel 
measurements of the traces of substances and of the 
number of nuclei, dust particles, and haze droplets 
