' Manchester Memoirs, Vol. lit. {igoj). 5 



personally, M. Jouguet has recently published a series of 

 elaborate mathematical memoirs on the propagation of 

 the explosion-wave in gases. His data are taken from 

 the work of Berthelot, Le Chatelier and my own. He 

 tells us that we have made unjustifiable assumptions, and 

 that we have proceeded by a sort of intuition rather than 

 with the mathematic rigour necessary in such a research. 

 I, for one, plead guilty. I may recall the fact that I found 

 empirically that the rate of the explosion-wave in a 

 number of gaseous mixtures was equal to the velocity of 

 sound in the buvjiing gases assumed to be at a temperature 

 double that of ordinary combustion. I did not of course 

 mean to explain the explosion-wave as being itself a 

 sound-wave produced in the gaseous products of com- 

 bustion, i.e.^ a cause following its own effect ; and I 

 thought I had sufficiently guarded myself by calling my 

 formula ' an empirical expression ' which was found to be 

 so far parallel to the truth that it might be useful as a 

 " working hypothesis." I compared the explosion-wave 

 to an intense compression-wave, propagated like a sound- 

 wave by exchange of moinenta on molecular collisions, 

 and maintaining its intensity by reason of the chemical 

 reactions set up. For instance, in the explosion of 

 electrolytic gas, I imagined a steam molecule just formed 

 in the wave front communicating momentum by collision 

 to an unburnt hydrogen or oxygen molecule, and this in 

 turn combining when it met an unlike molecule. 

 According to this view the chemical reaction does not 

 take place between cold molecules but between molecules 

 half of which have been heated by collision with the 

 products of combustion. There is a most remarkable 

 agreement between the velocities given by my formula 

 and the measured rates of the explosion-wave in a number 

 of gases ; and the use of this formula in the investigation 



