DEPOSITION GRADIENTS AND ISOLATION 



(i) Point source. D, the /c/^z/ number of spores deposited on an anniilus 

 I cm. wide at a distance x from a point source, is given by : 



Vin) Cx-"' 



(ii) And d, the mean number of spores deposited per square centimetre 

 on an annulus i cm. wide at a distance x from a point source, is given by: 



277tCx*(- + ^* 



(iii) And d„., the number of spores deposited per square centimetre 

 at a distance x do\Miwind from a point source, is given by: 



_ p2Q^x 

 " ttCV"' 



(iv) Line source, d,,,., the number of spores deposited per square 

 centimetre at a distance x downw ind from a line source, is given by : 



. _ P2Q.X 



d... = ,. !^:t^^ — .x'-'"'" 



*aw 



W 



V(^)Cx^'" 

 di.v is thus numerically equal to D. 



(v) Strip source, d^.^, the number of spores deposited per square 

 centimetre at a distance x do\Miwind from a strip source of width w, is 

 given by integration as : 



P4ax 



\/{tt)C (2 — w) 



Gregory (1945, p. 69) gave a set of calculated values for D, d, d,,. and 

 di„., assuming Q^o = io^°, p = 0-05, C ~ o-6 (cm.)% ;;/ = 1-75 and 1-24. 

 With further knowledge of these parameters, revised calculations are now 

 given (pp. 1 7 1-6). 



Meanwhile, in a series of papers on pollen contamination of seed 

 crops, Bateman (1947, 1947':?, 1947'^) gave many examples of dispersal 

 gradients, adopting and simplifying the Gregory formulae and using a 

 regression method for testing the adequacy of the diffusion theories of 

 W. Schmidt and of Bosanquet & Pearson (1936). Bateman's method also 

 makes it possible to estimate p/C and Q_„, provided all measurements are 

 expressed in the same units. Regression tests showed that pollen dispersal 

 was best fitted by the 1945 formulae of Gregory, but the data were inade- 

 quate for choosing between the values 1-76 and 1-24 for the parameter 

 m of Sutton's equations. 



Combining field inoculation studies with eddy-diffusion models, 

 Waggoner (1952) made an important contribution by adapting the for- 

 mulae: (i) to allow for non-isotropic turbulence; and (2) to incorporate 



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