A study by Smiles et al. <1995> investigated the spread of tritium in relatively dry soil, using a spherically symmetrical diffusion equation with radioactive decay to model the evolution of tritium profiles from the initial release of tritium in a uniform concentration over a small spherical volume of soil. They found that numerical cancellation errors affected the accurate evaluation of the analytical solution of Carslaw and Jaeger <1959>, and they used a point source solution as an approximation to the solution for the correct initial conditions. We derive a new and more accurate approximation, based on the principle that the concentration distribution ''forgets'' the precise initial conditions and is determined mainly by the total quantity of tritium and the spatial variance of the distribution. The actual distribution is approximated by that from a point source which started spreading some time before the actual release time, and the value of the time shift which gives the correct variance is found. ¿ American Geophysical Union 1996