The following represents a summary of calculations on the multiplication constant of homogeneous mixtures of uranium and different moderators. These calculations were made possible by Fermi's determination of the age of neutrons and by the extrapolation to higher scattering cross-sections of the resonance absorption of uranium as measured by C. Creutz. According to Fermi, the former quantity is 120 sq. cm. The latter is given in the two attached graphs. The first (Fig.1) of these goes as high as a scattering cross-section of 70 x 10-24 cm.2 per uranium atom, and its highest point is taken from a measurement of Cruetz's in which a mixture of U3O8 and graphite was used.

The importance of fast neutron fission (i.e., fission caused by neutrons before being slowed down) was recognized by Szilard, and calculations similar to the present one have already been carried out by him, Feld, Ashkin, Wheeler, Wigner and others. The purpose of the present paper is to give a general formula for the contribution of fast fission to the multiplication constant, which will include all the cases already considered and will be applicable to more complicated geometries than those considered by the previous writers.