VI. <i>On the rate of explosion in gases</i>

Abstract

idea *.Although Prof. Dixon's sound-wave formula has yielded such excellent results, he has pointed out the necessity bf further & priori work ill the subject.The Rate of Es'plosion fov an Infinite Plane Wave.]n the following attempt to establish a ibrmula for the velocity of explosion, 1 have made certain assmnptions which have not as yet received sufficient experimental confirmation ; hut they are, I think, justified by the results.For instance, it is assumed that~ once the maximum velocity is reached~ the front of the explosion wave is of such a character that we may suppose steady motion.This, as ProL Schuster has pointed out in a note to the Bakerian Lecture, is not an impossibility when chemical change is taking place, since the implied relation between pressure and density is possible under such circumstances.This point, however, requires further investigation.The wave is assumed to be an infinite plane wave.This assumption is justified by the fact that the diameter of the tube is without influence on the found velocity.I propose to limit the term" explosive wave "to the space within which chemical change is taking place.This space is bounded by two infinite planes.On either side of' the wave are the exploded and unexploded gases, which are assmned to have uniform densities and velocities.The statement that the exploded g.as possesses uniform, density" and velocity for some distance behind the wave reqmrcs further justification, which can only be imperfectly given after a discussion of the general problem.How the true explosive wave is actually generated in practice is a question without the scope of the present investigation, in order to avoid the discussion of this point, I shall substitute for it a physical conception, which, although unrealizable in practice, will render aid in illustrating the views here advanced.Let us suppose that the gas is enclosed in an infinite cylinder ABCD, provided with a piston E, and that the explosive wave XYZS has just star~ed.The initial velocity of this wave will be small; the initial pressure along the plane XS will also be small compared with that ultimately attained.As the wave proceeds in the direction AB, the piston E is supposed to ibllow it in such a manner that * In the earlier researches Berthelot's theory was accepted as a working h~pothesis.It was only after the difficulties attending the measurement otthe rates of explosion in mixtures containing inert gases had been overcome that the inadequacy of Berthelot's theory became evident and the superiority of the sound-wave theory could be demonstrated.