Abstract When an inflammable gas mixture, contained in a long horizontal glass tube closed at one end and open at the other, is ignited at the open end, a flame begins to move at a uniform rate towards the closed end. This initial spread of flame, which has been termed the "uniform movement:," persists for some distance along the tube, but soon gives place to an accelerating movement, sometimes, but not always, vibratory, the mean speed of the flame increasing rapidly until finally, with certain mixtures, the detonation-wave is set up, the speed of the flame being extremely high but again becoming constant during this last phase. The speed of the Uniform movement of flame and that of the detonation-wave both being constant, these phases of the propagation of flame lend themselves particularly much attention. The most striking difference between the two modes of propagation is in the order of speed attained. Thus, with a methane-oxygen mixture containing 50 per cent. of methane, the speed of the uniform movement of flame in a horizontal glass tube, 2∙5 cm. in diameter, is only 2 metres per second, whereas the speed of the detonation-wave when set up in the same mixture is 2530 metres per second. There is good reason to believe that the difference between the two modes of propagation is not merely one of degree, and that they are, both physically and chemically distinct. During the intermediate phases the influence of either or both types of propagation may be observed. We may regard as "normal" that propagation (including the uniform movement) which takes place by conduction of heat, assisted by those factors which may increase conduction by increasing the efficiency of contact between hot and cold gases, namely, convection and turbulence. In the detonation type of propagation the transfer of hear may still take place partly by conduction, but a new factor also enters, namely, the heating of unburnt gases by shock or pressure waves generated by the burning gases during their rapid inflammation. According to these definitions, during the true uniform movement of flame the transfer of heat should be effected by condition alone between burning and unburnt gases. In the true detonation-wave itself, unburnt gases should be heated adiabatically to or above their temperature of instantaneous ignition by the pressure-wave produced by the burning gases, without condition coming into play in the same sense. Though it is probable that neither of these conditions is attained, or is theoretically attainable, they may be taken as defining the ideal modes of propagation during what we may term the true uniform movement of flame and the true detonation-wave. The conditions under which the one type of propagation gives place to another so dissimilar are naturally of great theoretical interest.