The velocity of the cavity wall is all important in the calculation of the far-field signature for a water gun firing in the ocean. I use a method of successive approximation to solve Herring's energy equation for the collapse of a spherical cavity in a compressible liquid. The velocity of the collapse of the cavity wall depends upon the compressibility of the liquid, the amount of residual gas in the cavity, and the amount of acoustic radiation.The compressibility of the liquid has a significant effect on cavity velocity, but it has very little effect on the collapse period. The maximum value of the cavity velocity determines the peak magnitude of the far-field pressure signature; the pressure signature depends strongly on the amount and rate of residual gas compression. The results from solving Herring's equation agreed satisfactorily with a numerical solution of the fluid equations of motion. This solution to Herring's equation includes the compressibility of the liquid, the residual gas compression, and the acoustic radiation, all necessary factors in accurate calculation of the velocity of the cavity wall and thus the far-field signature.