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Using recently calculated models for massive stellar evolution and supernovaecoupled to a model for Galactic chemical evolution, neutron star and black holebirth functions (number of neutron stars and black holes as a function of theirmass) are determined for the Milky Way Galaxy. For those stars that explode asType II supernovae, the models give birth functions that are bimodal with peaksat 1.27 and 1.76 M\sun \ and average masses within those peaks of 1.28 and 1.73M\sun. For those stars that explode as Type Ib there is a narrower spread ofremnant masses, the average being 1.32 M\sun, and less evidence for bimodality.These values will be increased, especially in the more massive Type IIsupernovae, if significant accretion continues during the initial launching ofthe shock, and the number of heavier neutron stars could be depleted by blackhole formation. The principal reason for the dichotomy in remnant masses forType II is the difference in the presupernova structure of stars above andbelow 19 M\sun, the mass separating stars that burn carbon convectively fromthose that produce less carbon and burn radiatively. The Type Ib's and thelower mass group of the Type II's compare favorably with measured neutron starmasses, and in particular to the Thorsett et al. (1993) determination of theaverage neutron star mass in 17 systems; 1.35 $\pm$ 0.27 M\sun. Variations inthe exponent of a Salpeter initial mass function are shown not to affect thelocations of the two peaks in the distribution function, but do affect theirrelative amplitudes. Sources of uncertainty, in particular placement of themass cut and sensitivity to the explosion energy, are discussed, and estimatesof the total number of neutron stars and black holes in the Galaxy are given.Accretion induced collapse should give a unique gravitational mass of 1.27Comment: 32 pages including 7 figures. uuencoded compressed postscrip

The Neutron Star and Black Hole Initial Mass Function