Within the framework of the Chew-Low-Wick development an analysis of the scattering of photons from a nucleon is carried out. It is shown that an exact relationship exists between the Compton effect amplitude and the experimental meson-nucleon scattering phase shifts for all multipoles except magnetic dipole and electric quadrupole provided that effects arising from currents inside the nucleon source (i.e., line currents) are slowly varying functions of photon energy. That part of the magnetic dipole scattering which can be described in terms of the isotopic vector part of the anomalous magnetic moments of the nucleon is also treated exactly. The cross section for the Compton process is evaluated on the basis of the electric and magnetic dipole contributions only, since a nonrecoil theory is clearly expected to be poor for photon energies greater than 300 Mev. Fairly good agreement with experiment is achieved.