An explicit form for the function representing the probability that a neutron with velocity v′shall be scattered into an element of volume in velocity spaced3vabout v, by elastic collisions with atoms of arbitrary mass numberAin a Maxwell-Boltzmann distribution characterized by a temperatureT, is derived. Analytical representations of this probability are presented for scattering cross sections which are either independent of relative speed or exhibit a Gaussian dependence. The scattering probability resulting from the former assumption is examined in some detail, and then employed in a calculation of the mean energy change per collision.