THE MICROBIOLOGY OF THE ATMOSPHERE 



the ratio of spores deposited to percentage leaves (or leaflets) diseased. 

 Waggoner used the findings of E. E. Wilson & Baker (1946) and of Scrase 

 (1930), to put the variance of concentration of vertical distribution (ct^^) 

 as equal to 4/9 of the variances in the x and y planes. This led to the 

 formula (in our symbols) : 



X = -^^^exp.[-x-(r2 + 9z2/4)], 



where r^ = x^ + y^- 



From observed gradients of late-blight [Phytophthora infestans) 

 around artificially inoculated potato plants in the field, Waggoner took k 

 as the ratio of spores deposited per square centimetre to the proportion 

 of leaflets diseased, and estimated the parameters p (deposition rate) and 

 Qp/k from the equation 



^ o-i35p(Qp/k) / ^ o u 



where D = proportion of leaflets diseased. (In Waggoner's tests, 

 D was comparatively small and did not need the multiple-infection 

 transformation.) 



In his experimental potato plots in Iowa in 1949 and 1950, respectively, 

 Waggoner found p = o- 12 and 0-15, and Qp/k = 18 X 10'' and 7-8 X 10^. 

 Subsequently for Perojiospora tabacma Qo was estimated at approximately 

 10^ spores per sq. cm. of lesion per day (Waggoner & Taylor, 1958). 



For assessing concentrations of radioactive clouds, Chamberlain 

 (1956, pp. 20-27) at Harwell developed expressions combining the eddy- 

 diffusion equations (of Sutton, 1947) and the allowance for loss by deposi- 

 tion (of Gregory, 1945). Chamberlain also modified the equations to allow 

 for elevation of the source above ground-level, illustrating the fact that 

 elevating the source greatly reduces the loss by deposition. 



Re-calculation of the Deposition Gradient 



With new information and further development of the statistical 

 theory, deposition gradients can now be calculated for a wider range of 

 conditions than was possible earlier. The values worked out here are 

 offered as giving a useful indication of trends, but much further work still 

 remains to be done. 



Chamberlain's modifications have been adopted, in preference to 

 Waggoner's, because the latter uses the parameter k, which can vary over a 

 wide range down to zero — depending as it does on leaflet size in a particular 

 crop, and on how favourable conditions were for infection. 



Two sets of graphs are provided. Fig. 24 gives Q_x for m ~ i"]Si 

 C — 0-6 (metres)^, and a variety of heights and distances from the source.* 



* The parameter 'C is now given in units of (metres)*, in place of (cm.)* used in 

 Gregory, 1945. 



170 



