In the latter case, we could intercompare 1/TR and 1/TRO and eliminate the common interaction parameter B from them. In this way, Eq. (24) could be tested. This would not only test the present theory, but also Eq. (18), i.e., the theory of the anharmonic relaxation time of local modes. In other cases, a cruder test is possible by taking Ac^B and intercomparing TRO and m>According to the theory of Montroll and Potts, 4 one would expect local vibrational modes to occur at paramagnetic ions which are substitutional impurities and are either of lighter mass than the normal atom at that site, or are bound to the neighboring atoms with forces stronger than the normal forces. If a lighter atom was also more weakly bound, such that the effect of the mass was compensated by weaker bonds, a local mode would not occur. In general, we know little about interatomic forces, but it may be presumed that if the paramagnetic ion is substantially lighter than the parent atom (say half), a local mode will occur, and the present considerations will apply. Unfortunately, none of the paramagnetic ions in various environments, whose spin lattice relaxation has been studied to date, fulfills this * This research has been made possible through the support and sponsorship of the U. S. Department of Army, through its European Research Office.

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A tensor notation for electric multipole interactions between molecular charge distributions is developed and applied to the evaluation of first-and second-order interaction energies. An equivalence theorem between cylindrically symmetric and linear assemblies of charge is established. The mathematical implications of using a multipole Taylor expansion in regions of configuration space where the series has no validity is discussed for the first and second orders of perturbation theory. 6 E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics (Cambridge University Press, New York, 1931), Chap. IV.