An explicit formula is derived for the zero point energy of a system of coupled harmonic oscillators. It is shown that for the. case of isotopic homologues this leads to an approximate linear relation in the number of equivalent isotopic substituents. It is shown that the zero point energy differences of successive members of an isotopic homologous series increases with further substitution of the heavy isotope. Through a study of the parabolic deviations from the linear rule, it is shown that

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... ntermediate members of an isotopic homologous series form a better basis for interpolation and extrapolation than the end members. The appropriate intermediate members are given by the second order sum rule.