Total cross sections for neutron scattering from nuclei, with energies ranging from 10 to 600 MeV and from many nuclei spanning the mass range 6Li to 238U, have been analyzed using a simple, three-parameter, functional form. The calculated cross sections are compared with results obtained by using microscopic (g-folding) optical potentials as well as with experimental data. The functional form reproduces those total cross sections very well. When allowance is made for Ramsauer-like effects in the scattering, the parameters of the functional form required vary smoothly with energy and target mass. They too can be represented by functions of energy and mass.