An iterative method outlined by Green & Southwell (1944), but not applied in their paper for the reason that it makes no use of 'relaxation methods', is here applied to determine the supersonic regime for gas flowing irrotationally through a convergent-divergent nozzle, i.e. that (unique) regime in which the pressure and density of the gas decrease continuously in its passage from end to end. Osborne Reynolds's approximate treatment of the problem (1886) assumed the velocity to be distributed uniformly over each cross-section, and in consequence found a unique value for the limiting mass-flow, whether the velocity be subsonic or supersonic downstream of the 'throat' (upstream it is always subsonic). Here, a more exact treatment shows that the supersonic value is very slightly ($0\cdot 045$%) greater than the subsonic value, which Reynolds's theory overestimates by $0\cdot 083$%. The two regimes of course imply two different values of the pressure at exit, and for intermediate pressures (on the assumptions of this paper) there is no solution of the problem. Even in the subsonic regime (when the mass flow is critical) velocities exceeding the local speeds of sound are attained in regions adjoining the nozzle walls near the throat.