In the secular equations used by Eyring and his school the equations are of high order in general. When cognizance is taken of the symmetry of the configuration considered the secular equation may factor considerably. It is to be expected that the wave function for the lowest state will be invariant under the group which expresses the symmetry of the atomic configuration. This expectation is fulfilled in all cases considered. A general method is set forth upon which a derivation of such symmetric states may be carried out, and the reduced secular equation obtained. Several interesting applications of this method are carried through, including the case of eight identical orbits, centered at the corners of a cube, and eight orbits possessing tetrahedral symmetry, as in methane. The vector model is discussed and applied to the cases considered.
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