The initial disturbance due to the detonation of an uncased spherical charge of explosive, initiated at its centre, is analyzed in full. The equations of unsteady spherical motion are solved in the neighbourhood of the singularity at the origin of the air blast wave in the time-distance plane. Expansions are used in series of half-powers of the radial distance from this origin, with coefficients depending on the transverse co-ordinate. Two singular characteristics are found to start at this origin, and it is shown that the inner of these develops into a shock wave. This is identified as the secondary blast wave previously observed in experimental and numerical work. The wave is very weak at first with a strength which is zero initially and then begins to grow in proportion to the radial distance. In the present paper the explosive gas is assumed to be polytropic, with $\gamma $ = 3, but the method developed here can be extended to apply to any type of gas at the cost of additional labour.