The paper gives the results of the authors' statistical analysis of tests made by the Safety in Mines Research Board (S.M.R.B.) to establish conditions of flameproofness of flange gaps for electrical gear for use in hazardous atmospheres. The chance of occurrence of an ignition of an external explosive atmosphere when an explosion occurs inside the flanged vessel, is found to increase approximately linearly with the size of the gap at the flanges. From a study of this variation of chance of ignition with flange gap, it has been possible to determine a gap which is safe within a certain approximately known risk, both for the case of a linear increase of chance with gap, and for the more accurate empirical law of variation of chance with gap deduced from the experimental data. Thus values of the statistical maximum safe gap are given for a number of hazardous atmospheres; these are such that, so far as can be determined, there is only a chance of the order of 1 in 1012that the true maximum safe gap is actually less than the value given.These data afforded a basis for the determination of the maximum permissible gaps given in B.S. 229: 1946.