THE MICROBIOLOGY OF THE ATMOSPHERE 



with dimensions (L)^; and 'w' is a number varying between 1-24 in 

 extremely stable, non-turbulent wind, and 2-0 under conditions of extreme 

 turbulence. The value for normal overcast conditions with a steady wind 

 is m = 1-75. 



Because wind-speed multiplied by time equals distance we can write 

 Sutton's formula : a^ = IC^x"'. This suggestion that a^ is a function of 

 the distance, x, is not unreasonable, because the surface roughnesses which 

 generate eddies are spread out along the distance travelled by the cloud. 

 It is moreover a tempting theory, because we need not know the wind- 

 speed under which dispersal takes place. 



Values of C decrease with height because conditions at great heights 

 are unfavourable for the formation of eddies. Values for m appear to 

 increase with longer sampling periods, and Sutton suggests that m itself 

 is a function of time. In making continuous observations over a long period 

 on the density of a cloud, he suggests that the random element may 

 become smoothed out, so that, over a sufficiently long period, m = 2. 

 These possibilities should be borne in mind when the density formulae 

 described below are applied to some biological data where the sampling 

 period is very long. 



In practice it is found that near ground-level, diffusion takes place 

 faster on the x- and y-axes than on the vertical z-axis. Turbulence is 

 then said to be 'non-isotropic', and C has to be represented by its com- 

 ponents : Cx, Cy, and Q. 



The number m is an indicator of the degree of turbulence of the air 

 and is, as a first approximation, independent of the mean wind-velocity. 

 It is primarily affected only by those factors which tend to damp out or 

 increase turbulence, such as the vertical temperature gradient and the 

 roughness of the ground. For conditions of spore dispersal tests it seems 

 appropriate to assume values of Cy = 0-5-1 -o (metre)^, Q = o- 1-0-2 

 (metre)", and m = 1-75-2-0. 



Expressions for the concentration of particles in a cloud emitted from 

 various types of source were deduced by Sutton (1932), and are analogous 

 to heat-conduction equations, as follows : 



(i) An instantaneous point source^ such as a puff of Q^grams of smoke, 

 or a number Q^of spores emitted at an instant of time. Here the concen- 

 tration in the cloud is given by 



Q_ r r2 



^ 7rtC3xt"'^''P\ CH' 



where 'r' = distance from the centre of the puff or cloud. 



(ii) A continuous point source^ such as a factory chimney emitting Q_ 

 particles per second. Here, to obtain an integral that can be handled 

 conveniently, the assumption is made that the spread of the cloud laterally 

 and vertically is small compared with its spread down-wind. When 



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