The evolution in the static longitudinal polarizability and second hyperpolarizability of the C4H2 through C54H2 oligomers of polyyne is studied at the Hartree-Fock level of theory. We find that the calculated values are highly sensitive to the adopted geometry. Using improved geometries, new extrapolation procedures and careful finite field determinations we extend earlier work by others so as to provide reliable estimates for the above properties in the infinite polymer limit.