In an earlier paper (Carter et al. 1979), estimates and bounds were derived for the critical initial reactant concentration in a thermal explosion with reactant consumption. In this paper, a greatly improved estimate for the critical concentration is obtained and its accuracy investigated. Arising from this, an excellent approximation is obtained for the relation between the critical value of the parameter a (expressing heat loss rate), the dimensionless adiabatic temperature rise B and the dimensionless ambient temperature $\epsilon$. For $\epsilon$ = 0, this approximation is much closer to the known exact curve than any previously obtained estimates.