LONG-DISTANCE DISPERSAL 



release point by the cloud at the greatest distance was only about half that 

 subtended by the cloud at i or 2 km. (Charnock, 1956). At distances 

 greater than those considered in Chapter XIII, the difference between 

 turbulence in a vertical and horizontal direction evidently becomes im- 

 portant. Further diffusion is limited by the tropopause, if not by the top 

 of the turbulent layers of the atmosphere. 



Samples taken after the accidental emission of about 20,000 curies of 

 iodine-131 from a stack 122 metres high at Windscale atomic pile on 10 

 October 1957, have provided detailed records of ground contamination 

 by the main plume over distances up to 290 km. (Booker, 1958). These 

 records provide some evidence over longer distances for which microbial 

 data are lacking. Plotted on a log.-log. scale, the radioactivity'- deposition 

 curves, whether measured on herbage or in milk, are relatively flat up to 

 15 km. — a fact that is consonant with the height of emission. From about 

 28 km. onwards the slope is similar to that of d„. for m = 1-75. There 

 seems no reason, therefore, why we should not use our formulae for 

 distances of several hundreds of kilometres — bearing in mind that, as in 

 the Windscale accident, the trajectory of the cloud is not likely to be in a 

 straight line over the Earth's surface. 



Another view of long-distance dispersal of 'crowd diseases' of crop 

 plants comes from Plank (1948, 1949, i949(^i', i960), who used gradients to 

 define the novel concept of a 'horizon of infection' around a field, from 

 beyond which the amount of infection received is negligible. Crowd 

 diseases are defined as : 'diseases which neither spread far in considerable 

 amount nor persist long in the soil'. They can be controlled by mixed 

 cropping and by isolation. Plank put forward the generalization that 'if 

 disease entering fields can easily be controlled by isolation, it can also 

 be controlled by making the fields larger and proportionally fewer' ; this 

 is thought to be true, \\hether infection enters from uncultivated plants 

 outside the field or moves from field to field. 



For airborne spores travelling over distances between fields, Plank 

 empirically estimates the probability' that a spore will settle at a distance 

 'x' from its source as p = k/x", where 'k' and 'n' are constants. From 

 published data n is 2 or more for distances over 30 metres, and approaches 

 4 as the distance from the source increases. With a number of uniform 

 fields scattered evenly over a large area. Plank sho^^■s that, if Q^is the 

 number of spores received by one field from immediately neighbouring 

 fields, the total number of spores received from all other fields, however 

 distant, would be : 



If n = 2 or less, the series is divergent and there is no horizon. If n 

 is more than 2, the series is convergent and, if n = 3 or more, a useful hor- 

 izon exists (Table XXVIII). The data suggest that, for potato late-blight 



183 



