A technique already successfully applied to the problem of 'fuel consumption' in thermal explosions is here applied to the related problems arising in the isothermal chain theory of explosions and the more general unified (chain-thermal) theory of explosions. The new results all reduce satisfactorily to known cases. It is shown that typical isothermal problems can be dealt with analytically and an explicit expression found for the induction period. Some nonisothermal problems can also be dealt with analytically to zeroth approximations and even when this is not possible a clear qualitative picture of the physical phenomena occurring is given. Quantitative data can be obtained by computation without difficulty as the problem is clearly formulated mathematically when analytical treatment is not possible.