Multiple linear regression analysis has been used to determine the relationship between the unit cell parameters and the average radii, rM1 and rM2, of the octahedral cations in Fe-Mn, Ni-Fe, Mg-Mn, and Mg-, Fe-, and Mn-Ca binary olivines, using data from the literature. The resulting regression equations are given below. The coefficients of correlation exceed 0.997 in all cases. Fe-Mn binary olivines a= 3.527 + 1.341rM1 + 0.317rM2 b = 8.586 - 1.856rM1 + 4.281rM2 Mg-Mn binary olivines a= 3.798 + 1.014rM1 + 0.314rM2 b = 7.552 + 0.745rM1 + 2.922rM2 Ni-Fe binary olivines a= 4.007 + 1.052rM1 - 0.012rM2 b = 7.331 + 1.375rM1 + 2.636rM2 Mg-Ca binary olivines a= 3.919 + 0.814rM1 + 0.245rM2 b = 7.546 + 0.418rM1 + 3.261rM2 Fe-Ca binary olivines a = 4.153 + 0. 781 rM1 + 0.144rM2 b = 7.551 + 0.142rM1 + 2.532rM2 Mn-Ca binary olivines a= 4.048 + 0.905rM1 + 0. 124rM2 b = 7.494 + 0.352rM1 + 3.378rM2 The Mg-Fe binary yielded inconsistent regression results, most likely due to ambiguous site assignments. Because for both systems the a cell edge is mainly dependent on rM1 and b on rM2, these equations may be used to construct a vs. b diagrams which may be contoured for bulk composition, M2 site occupancy, and the distribution coefficient, K_D . Similar determinative diagrams may be drawn using calculated cl-spacings of the 130 peak, which is sensitive to cation order in the M1 and M2 site, and the 112 peak, which is composition dependent. Tests of these diagrams, using Shinno's (1980) d₁₃₀-spacings and cation site occupancy data for numerous synthetic Fe-Mn olivines, indicate that this model is reliable; agreement of predicted and observed Mn content of the M2 site is within 0.03 atoms on the average. Eleven natural olivines (Fa_45-85 Te_50-8 Fo_2-11), for which cell dimensions and, in several cases, site refinements were available, were critically evaluated using the equations and diagrams for the Fe-Mn binary, with mixed results. A preliminary investigation was undertaken to assess the use of Rietveld analysis to determine unit cell parameters, atomic positional and thermal parameters, and site distribution of divalent cations in the Mg-Mn binary olivine system. Results indicate that the method can be used successfully; however, systematic errors inherent in the diffractometer prevented refinement of useful (error-free) data. / M.S.