The optical model of the nucleus has been used with the phase shift method of calculate the scattering of 340 MeV neutrons and protons in carbon and lead, and of 4, 14, 36 and 100 MeV neutrons in nitrogen, for different forms of potential well and with different amounts of nuclear absorption. The results are used to establish the range of validity of the approximations of Born, of Montroll and Greenberg, and of Fernbach, Serber and Taylor. The latter gives remarkably accurate values over a wide energy range for the total elastic and absorption cross sections and forward elastic scattering. It is the only approximation which gives a satisfactory account of the effect of absorption. Unfortunately it does not give the angular distribution simply, and the most accurate approximation which does so, that of Montroll and Greenberg, has a very limited range of validity. Comparison with the experimental angular distributions of 340 MeV protons in carbon and lead leads to limited conclusions about the nuclear potential. An approximate calculation of the angular distribution of the scattering of 22 MeV α-particles in silver and lead indicates that the optical model can account for the observed results in terms of a rounded-off potential well.