## ABSTRACT

(a) The existence of a critical mass below which a self-sustaining chain reaction is not possible is an example of the 'square-cube law'. The fraction of fission neutrons which escape across the surface of a lump of fissionable material can be reduced by increasing the size of the lump since the rate of production is proportional to the volume (R^{3}) whilst the rate of escape is proportional to the area (R^{2}). At the critical mass on average each fission gives rise to an extra fission which is the condition for a self-sustaining chain reaction. A spherical lump minimises the critical mass as a sphere minimises the surface area to volume ratio.