374 MACHTA balloons to augment weather information), shows a long-period machine trajectory carried for 17 days at 500 mb. In this case, observed winds and pressure gradients, not forecasts, guide the computation of the air trajectory. Analysis of the results cf machine forecast and reconstructed trajectories suggests approximate agreement between hand subjective and machine objective procedures. Finally, it should be noted that techniques to incorporate the bene- fits of isentropic analysis into machine computations are available. Atmospheric Dispersion The prediction of atmospheric dispersion at distances beyond about 100 miles assumes Fickian diffusion; that is, the flux of material is in the direction of and proportional to the gradient of concentration. For simplicity, although the procedure is not necessarily correct, the coordinate axes are chosenin the vertical and the horizontal directions, In its simplest form, the standard deviation of the spread of a pollutant may be written as o, =v 2Kt and o, =¥ 2Kt where o = standard deviation of the Gaussian distribution of a pollutant around its mean position K coefficient of eddy diffusion t = time h and v = horizontal and the vertical directions, respectively In the quasi-empirical application of this law, it becomes necessary to use different values of K (particularly K,) with different transit times. Figure 5 is a graphical presentation of K, vs. time as summarized by Heffter.° There are many reasons to expect atmospheric dispersion to de- part from a simple Gaussian distribution described by Fickian diffu- sion. The dominant reason is the vertical wind shear (the change of wind direction and/or speed with altitude) superimposed on vertical diffusion. Figure 6 shows schematically how an initial cylinder of marked air parcels grows by diffusion (the light shading) and by wind shear and vertical mixing (the cross hatching), The latter process results from the stretching of the cylinder by the wind shear and the ver- tical mixing, which brings material upwards or downwards ahead of or behind the moving cylinder and adds to the growth resulting solely from horizontal mixing.