Abstract : The successive stages of the fireball due to a nuclear explosion in air are defined. This paper is chiefly concerned with Stage C, from the minimum in the apparent fireball temperature to the point where the fireball becomes transparent. In the first part of this stage, the shock (which previously was opaque) becomes transparent due to decreasing pressure. The radiation comes from a region in which the temperature distribution is given essentially by the Taylor solution; the radiating layer is given by the condition that the mean free path is about 1/50 of the radius. The radiating temperature during this stage increases about as p(exp -0.25) , where p is the pressure. To supply the energy for the radiation, a cooling wave proceeds from the outside into the hot interior. When this wave reaches the isothermal sphere, the temperature is close to its second maximum. Thereafter, the character of the solution changes; it is now dominated by the cooling wave (Stage C). The temperature would decrease slowly (as p(exp 1/6)) if the problem were one-dimensional, but in fact it is probably nearly constant for the three-dimensional case. The radiating surface shrinks slowly. The cooling wave eats into the isothermal sphere until this is completely used up. The inner part of the isothermal sphere, i.e., the part which has not yet been reached by the cooling wave, continues to expand adiabatically; it therefore cools very slowly and remains Opaque. After the entire isothermal sphere is used up, the fireball becomes transparent and the radiation drops rapidly. The ball will therefore be left at a rather high temperature, about 5000 deg C. The cooling wave reaches the isothermal sphere at a definite pressure. The radiating temperature at this time is about 10,000 deg C. The slight dependence of physical properties on yield is exhibited in approximate formulae.