A similarity solution recently given by Stuart for spherically symmetric flow following an explosion in a rarefied atmosphere is extended by requiring it to satisfy the hydrodynamic energy conservation equation. This additional constraint allows one to determine the functional form of the pressure and density and avoids the necessity of making the virial theorem approximation. The differential equation for the radius of the disturbance is different from the earlier theory, especially at late times when it shows that the kinetic energy eventually is completely transformed into internal energy, but the disturbance velocities are identical in the limit as R → 0 .