The amount of free4ree emission by intergalactic hydrogen is calculated and compared with observation. The calculations are carried out for the steady-state model and for closed evolving models with qo = 21 and 1. It is shown that the temperature of the intergalactic medium must be less than 4 X 106 K (steady-state model) or 3 X 106 K (qg = 2' or 1), judging by recent X-ray results. A simple analytic expression is derived for the emission in a steady-state model, which is finite for all assumed values of the temperature. The emission in evolving models depends critically on the behavior of temperature with density at distant points; for effective ratios of specific heat between and 2, the results indicate unbounded intensities at the Earth. Calculations of the intensities emitted by material out to limited values of the redshift indicate that future observations, particularly just shortward of 20 A, may provide decisive information on the state of the universe at earlier times.