The definition of the adiabatic modulus, KS, is used as the basis of an isentropic P(V) equation of state (EoS) to find the density isentrope at lower mantle conditions. The adiabatic constraint makes temperature depend on pressure in the EoS. Thus one can calculate the density isentrope corresponding to the lower mantle values of P at every depth, and this is done for perovskite. A silicate perovskite with iron concentration fp=0.12 and without the addition of magnesiow¿stite produces a density distribution exactly matching that of PREM (the chondritic case), the same result as presented by Stixrude et al. However, this apparent agreement results from ignoring higher-order terms of the EoS; when such terms are included, the agreement between the calculated density of perovskite and the density of the lower mantle is not good. A smaller amount of iron in perovskite lowers the isentropic density and suggests the addition of magnesiow¿stite in order to match the PREM density distribution (the pyrolitic case). Recent results of Stacey and of Kesson and Fitzgerald strongly suggest that fp=0.05--0.06, requiring that the remaining iron be in magnesiow¿stite (pyrolite).¿ 1997 American Geophysical Union