The techniques and results of a previous paper are applied to the calculation of the second Born approximation of the one-photon radiative corrections to the scattering of electrons by nuclei. Nonrelativistic and high-energy approximations are calculated explicitly for pure Coulomb scattering. Modifications due to the finite extension of the nucleus are discussed. No definite conclusion is reached concerning the change of the correction due to this extension, but it is shown that at extremely high energies the relative radiative correction to the second Born approximation is independent of the nature of the charge distribution. It is also shown that the fictitious zeros of the first Born approximation disappear first in the third Born approximation. The shape factor occurring there is briefly discussed.