HORIZONTAL DIFFUSION 



of slope tan-1 1, that is 26°34'. However, according to Sutton's theory 

 (T^ = |Cx™, therefore 



log cr = — log X + ^ log (iO) 

 2 



If this holds true, plotting the observed values of log a against log x 



111 

 should give a line of slope tan-^ — . For values of Sutton's m between 1-75 



and 2-0, the line should slope at an angle between 40° 36' and 45°. 



Field tests with Lycopodium spores liberated over short grass by 

 Gregory, Longhurst & Sreeramulu {impublished) allow a direct comparison 

 to be made of the theories of Schmidt and Sutton. Spore-cloud concen- 

 trations were measured near ground-level at distances up to 10 metres 

 simultaneously at 24 points. Results plotted in Fig. 7^ show the lines 

 sloping at angles varying between 40° and 46°. This is incompatible with 

 Schmidt's theory which requires a slope of 26°34'. Furthermore, if log 

 CT is plotted against log t (calculated from the distance and mean wind 

 speed) according to Schmidt's theory a should be the same after a given 

 time whatever the wind speed, but this is not so (Fig. ']b). On Sutton's 

 theory at a given distance log a varies only over a comparatively narrow 

 range of values depending on the parameter m. The results of these 

 experiments are compatible with Sutton's theory which requires a slope 

 of 40°36' for m = 1-75, and 45°o' for m = 2-0. 



In biological applications we are usually interested in the relation 

 between diffusion and distance rather than between diffusion and time. 

 As we often lack measurements of the variable wind velocities in which 

 dispersion has occurred, Schmidt's theory would be inconvenient to 

 handle. On Schmidt's theory a varies with time, on Sutton's o- varies 

 with distance travelled. Sutton's theory not only fits experimental results 

 well, but is also convenient because it does not require a knowledge of 

 wind speed. 



57 



