In November 1941, the third of three reports on atomic fission commissioned by Vannevar Bush through the National Academy of Sciences examined the prospects for explosive fission in U-235. This report, prepared by Arthur Compton, developed a model for estimating the critical mass and efficiency of an atomic bomb. I examine Compton’s physics, attempt to discern the provenance of the numbers he adopted for various parameters, and compare his results with those yielded by a full diffusion-theory approach with contemporary values for the fission parameters. I conclude that Compton’s physics is sound. A combination of somewhat optimistic parameter values and a conservative model for critical mass lead him to a numerical value for the bare critical radius of U-235 that is in fairly good accord with that yielded by diffusion theory. His estimated efficiency proved to be quite accurate for the Little Boy bomb.