Rate of Explosion in Gases. 91 



idea *. Although Prof. Dixon's sound-wave formula has 

 yielded such excellent results, he has pointed out the necessity 

 of further a priori work in the subject. 



The Rate of Explosion for an Infinite Plane Wave. 



In the following attempt to establish a formula for the 

 velocity of explosion, I have made certain assumptions 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 Prof. 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 investi- 

 gation. 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 u 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 assumed to have 

 uniform densities and velocities. The statement that the 

 exploded gas possesses uniform density and velocity for some 

 distance behind the wave requires 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 investi- 

 gation. 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 started. 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 follow it in such a manner that 



* In the earlier researches Berthelot's theory was accepted as a working 

 hypothesis. It was only after the difficulties attending- the measurement 

 of the rates of explosion in mixtures containing inert gases had been over- 

 come that the inadequacy of Berthelot's theory became evident and the 

 superiority of the sound-wave theory could be demonstrated. 



