The change in the simple [formula] distribution of neutrons in a spherical lump of uranium caused by the distribution in velocities of thermal neutrons is calculated. If the calculated curve is fitted as well as possible by a simple [formula] curve, it is shown that the value of [formula] obtained in this way is a function of [formula], the radius of the sphere. For small radii the [formula] obtained in this manner will be as much as 25% greater than the [formula] corresponding to average velocity neutrons. The change in the thermal utilization caused by the distribution in velocities is discussed. The flux of neutrons into a sphere is calculated taking into account the velocity distribution and this is compared with the usual theory.

Measurements made in a uranium cylinder result in a mean value of 1.55 cm. for the diffusion length L for distances of 1 to 4 cm. from the base of the cylinder. Calculations give a value which agrees with the experimental result and show further that L increases from 1.40 to 1.63 cm. as the neutrons diffuse a distance of 5 cm. into the uranium.

Warping of a rod by a variation in heat transfer coefficient around the periphery is considered. Estimates for some simple cases are given, and a more precise numerical calculation is carried out in ne instance.