Abstract: "The critical mass both of an untamped and water-tamped sphere with parabolic radial variation of the intrinsic buckling is calculated by a perturbation method. The result is applied to finding the minimum critical mass of plutonium in water suspension with infinite water temper; the calculations show that the minimum critical mass at constant concentration may be reduced by an amount of the order of 7.6% when the concentration of plutonium is permitted to vary throughout the suspension."