COMPARISON OF THEORIES OF W. SCHMIDT AND SUTTON According to Schmidt's theory, = 2At/p, so, because t — x/u, we have log a = I log x -f 1 log (2A/pu). If this relation holds true in field tests, plotting experimental data for log a against log x should give a line of slope that is 26°34'. However, according to Sutton's theory therefore If this holds true, plotting the observed values of log a against log x should give a line of slope For values of Sutton's in between 1-75 z 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40° 36' and 45° Field tests with Lycopodium spores liberated over short grass by Gregory, Longhurst & Sreeramulu (unpublished) allow a direct comparison to be made of the theories of Schmidt and Sutton.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 to metres simultaneously at 24 points. Results plotted in Fig. 7a 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 a 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. 7b). On Sutton's theory at a given distance log Q varies only over a comparatively narrow range of values depending on the parameter in. The results of these experiments are compatible with Sutton's theory which requires a slope of 4o°36' for in = 1•75, and 45°o' for m — a•o.
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 Q 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.