  The classic meteorological law of diffusion in the atmosphere was given
experimentally, by Richardson in 1926, whose result that the mean squared
distance <R^2>=cT^3, the time cubed, is in accord with the scaling theory of
Komogorov [ Obukhov (1941)]. In some cases it might be important to have more
information than that provided by Richardson's law. An example would be the
distribution of pollutants in time by turbulent flow. Here small amounts of
material reaching relatively large distances are of importance. This motivates
our interest in the full distribution of the location of particles swept by the
fluid as a function of time. The distribution depends on the distance through
the dimensionless quantity X^2=R^2/<R^2(T)> . Using the Kolmogorov picture, we
find that for small X, the distribution is proportional to exp(-aX^2) and
exp(-bX^4/3) at its tail when X is large.
