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The therm al stability of an exothermic chemically reacting slab with timeperiodic surface tem perature variation is examined. I t is shown, on the basis of a good approximation due to Boddington, Gray and Walker, th a t the behaviour depends on the solutions of an ordinary differential equation of first order. The equation contains a modified amplitude, for small values of which it can be reduced to a particular form of Hill's equation. Critical values of the Frank-Kamenetskii param eter, as adoi:10.1098/rspa.1982.0167 fatcat:efzfwitnxfc53fgjrdpjln5yky