Data from the High Altitude Dust Diffusion Project have been analyzed, and the rates of growth of 18 smoke puffs produced in the upper troposphere and stratosphere are presented. There was an increase in the rate of growth of the cloud size with increasing height, and a decrease in the rate of growth of the cloud mass with increasing stability of the atmosphere. From an initial diameter of 15 to 20 meters, the diameter of the smoke puffs increased fivefold in about 3 minutes, on the average. A theoretical analysis of the growth of a smoke puff resulted in an equation describing the visual diameter as a function of time and a variety of turbulence parameters. Comparison between theory and experiment, based on Taylor's theory of “diffusion by continuous movement,” suggests that the root-mean-square eddy velocity in the stratosphere is of the order of 4 to 10 centimeters per second and increases with height.