Family of nuclear mass relations

A family of simple nuclear mass relations, which includes as members the Garvey-Kelson transverse and longitudinal relations, is presented. Each member of this family gives a prediction of roughly equal statistical accuracy for the unknown mass of a given nuclide. The average of this family is statistically more reliable than is any single prediction. The essential physical observation that leads to these relations is that the empirical neutron-proton effective interaction is generally weak and that the strength of this interaction is strongly correlated separately for neighboring even-$A$ and for neighboring odd-$A$ nuclei.