The paper presents a method for calculation the instantaneous pressure, velocity, acceleration, and radius associated with the collapse of a spherical gas-filled cavity in an infinite compressible liquid. The method is an independent approach which makes use of Hammings technique to numerically integrate Gilmores differential equations which describe the collapse. Included is a computer program which will perform the necessary calculation on a IBM 70901401 digital computer. It may be inferred that the peak shock wave pressure is significantly reduced by a decrease in ambient pressure, and increase in internal pressure, andor a variation of the specific heat ratio by proper selection of the gas. Control of the last two parameters can be investigated as a possible means of protecting glass spheres against sympathetic implosion in multiple sphere buoyancy systems.