Previously we have shown how to obtain the electric properties of a polymer or other periodic system at the coupled Hartree-Fock level by direct, analytical calculation rather than by extrapolation of oligomer results. Here we add computationally simpler noniterative formulas and test the methodology for the longitudinal dipole moment (mu), polarizability (alpha), first hyperpolarizability (beta), and second hyperpolarizability (gamma) of five quasilinear polymers: (LiH)(n), (FH)(n), (H2O)(n), trans-polymethineimine (-CNH-)(n), and trans-polyacetylene (-CH=CH-)(n). The polymer values are in good agreement with large-oligomer calculations. In this connection the role of phase factors, particularly in determining the dipole moment, is elucidated. We are now in a good position to include electron correlation using methods analogous to those employed for molecular systems.