This paper is addressed to students and researchers in applied group theory who wish to compare force constants between similar molecules. We assume the reader has some familarity with the group theoretical methods presented by Wilson et al. (Wilson, E. B. Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, 1980). We cannot apply Wilson's method for obtaining symmetry coordinates from internal coordinates directly, as we demonstrate. Instead we must start with the irreducible representations of the symmetries of the moiety with the higher symmetry and then reduce them to the representations of the symmetries of the moiety with the lower symmetry. The symmetry coordinates are calculated for each species in order to factor the secular equation. The matrix representations of the generators of these point groups are a function of the specific symmetry coordinates. Finally, the symmetry coordinates are applied to the force constant matrix and the algebraic results are compared.