With the help of the generalized function theory, the macroscopic treatment of neutrons slowing down in a homogeneous medium is investigated. As a result, it is found that the balance equation for neutron flux is exactly expressed by for a monoenergetic source as well as a fission source, where the moderating parameter is defined as the ratio of slowing down density to collision integral .Source dependence of this parameter, (u), is also examined analytically and numerically. In the transient region the difference of (u)’s for a monoenergetic source and a fission source is shown to be remarkable. For a monoenergetic source the asymptotic value is found to be a monotonically decreasing function of the absorbing ratio, a, while the of fission neutrons is also a decreasing function for the smaller absorbing ratio than a certain critical absorbing ratio and for large a it has the constant value .