DEPOSITION GRADIENTS AND ISOLATION 



seed crops by insect cross-pollination at distance (D) was fitted by the 

 expressions : 



F = ye-'^^s or 



D ' 



where y = contamination at zero distance, and k expresses the rate of 

 decrease of contamination with distance. 



Gregory & Read (1949) concluded that data for insect-borne viruses 

 could be fitted well by the empirical expression : 



log I = a + bx, 



where I = number of infective punctures at a distance x from the source 

 after a given time, and a and b are constants for any one given set of 

 field conditions. 



With the empirical method an equation canusuallybeobtained, contain- 

 ing at most three parameters, which gives a good fit to any particular set of 

 data. However, it is not easy to compare the results obtained by different 

 workers. The empirical method is difficult to use because point, strip, 

 and area sources are not distinguished, the multiple-infection transforma- 

 tion has not been applied even w^hen appropriate, and the parameters as 

 calculated from the data correspond to no obvious natural phenomena; 

 they may even conceal different units of measurement varying from centi- 

 metres to nautical miles! Progress with the empirical method requires 

 attention to these matters and, especially, the adoption of a standard 

 metric unit of distance. 



Diffusion and Deposition Theories 



The more difficult, but potentially more useful, theoretical approach 

 is derived from the diffusion phenomena described in Chapter V. 



w. Schmidt's theory 



Schmidt (19 18, 19 19) used his diffusion theory to calculate Q_x/Q^o> 

 the fraction of the eddy-diffusing spore-cloud which remained in the air 

 at distance x. To do this he assumed that any part of the cloud whose 

 diffusion path would have brought it down to ground-level, would have 

 been removed from the cloud by deposition. He represented the terminal 

 velocity of the particle as equivalent in effect to tilting the ground, and he 

 gives a table from which the 'dispersal limit' under average conditions of 

 wind-speed and turbulence could be read for particles with different 

 terminal velocities. Dispersal hmit (V) was defined as the distance 

 exceeded by only i per cent of the particles liberated. 



Schmidt's theory was developed further by Rombakis (1947), who 

 brought the fall velocity of the particles into the differential equation and 



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