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.

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.

Stresses set up by an insulating strip in the bond are estimated and found to be small compared to those normally present without the defect.

Warping of a rod by a variation in heat transfer coefficient around the periphery is considered. Estimates for some simple cases are given, and a more precise numerical calculation is carried out in ne instance.

Measurements made in a uranium cylinder result in a mean value of 1.55 cm. for the diffusion length L for distances of 1 to 4 cm. from the base of the cylinder. Calculations give a value which agrees with the experimental result and show further that L increases from 1.40 to 1.63 cm. as the neutrons diffuse a distance of 5 cm. into the uranium.

It is usual to determine the density of neutrons by using foils of metals which become radioactive as a result of bombardment in the region under investigation. From the rate of disintegration of the newly formed radioactive element the number of neutrons absorbed can be calculated. By use of the capture cross section of the element of which the foil is composed the density of the neutrons can then be computed. By counting the alpha particles from a bismuth foil of known weight after exposure to neutrons the density of the neutrons which produced this activity can be calculated. The least accurately known value which enters into this evaluation is the capture cross-section of bismuth for pile neutrons. This value may be improved by future measurements. It is of importance only for absolute measurements of neutron density so that relative values can be measured with considerable accuracy on the basis of known data.

Technical report with short reports from the (1) Physics Section I; (2) Physics Section II ; and (3) Physics Section III.