The theory of linear partitioning in binary solutions is here extended to solid-solid equilibria in P-X space at constant T, with general rules for formulating the linear relationship. When the interphase partition coefficient, formulated for the Fe endmember, is linear with the composition of the numerator phase, the exchange coefficient KD is constant, and vice versa. For olivine--wadsleyite in P-X, the four best experimental brackets in the literature give KD=0.56¿0.02 (1-s.d.) at 1600 ¿C. The S-S transition at XFe=0.1 is 2.8 kb or about 8 km wide for pure olivine. Half the olivine is converted to wadsleyite at 0.6 the P interval. However, a transition zone lid ≤4 km thick is consistent with a multiphase mantle in which the presence of a non-transforming phase (e.g., pyroxene) cuts the effective transformation window in half as recently shown by L. Stixrude. ¿ 1998 American Geophysical Union