The results of a series of neutron diffusion calculations relating to an untamped Orally sphere are presented in detail in this report. The three-velocity neutron transport theory was taken as the basis for the analytical work preceding the computations. This particular theory, also known as the transport approximation, is defined in LA-1271 and known to be quite accurate for assemblies primarily involving materials of large atomic weight. For a sphere of uniform density and atomic composition the transport theory has another advantage. It can readily be formulated in terms of simultaneous integral equations (in our case three), relatively simple in form, involving the collision densities [formula] and a set of parameter values describing the materials. Nb(r) is , as indicated, a function of the radial distance [formula] and the velocity index g, g - 1, 2, 3. The parameters, fifteen in number for the three-velocity theory, are comprised of the velocities, the inverse mean free paths, and the transfer coefficients.