470 REPORTS ON THE STATE OF SCIENCE. 



couchc, dans la masse lout entiere, -par suite de la transmission des 

 chocs successes des molecules gazeuses amenees a un etui vibratoire plus 

 intense en raison de la chaleur deyagce dans leur combinaison, el trans- 

 fofmies sur place, ou, plus exactement, avec un faible deplacement 

 relatif . . .' Such conditions are comparable with those of a sound 

 wave passing through the gaseous mixture, with, however, the im- 

 portant difference that, whereas a sound wave is propagated from layer 

 to layer with a small compression and a velocity determined solely by 

 the physical condition of the vibrating medium, it is an abrupt change 

 in chemical condition which is propagated in the explosion wave, and 

 which generates an enormous force as it passes through each successive 

 layer of the medium. Berthelot considered that the mean velocity of 

 translation of the molecules of the products of combustion, retaining the 

 total kinetic energy corresponding to the heat developed in the reaction, 

 may be regarded as the limiting maximum rate of propagation of the 

 explosion wave (6), which would be given in metres per second by the 

 equation. 



29354 / T 



where T is tlic absolute temperature and p the density of the products 

 referred to air. In calculating T, Berthelot made two erroneous 

 assumptions — namely, (1) that the specific heats of the products are 

 independent of temperature and equal to the sum of the specific heats of 

 the reacting gases, and (2) that the gases burn under conditions of 

 constant pressure. He was also of opinion that, owing to the high pres- 

 sures generated, dissociation plays no appreciable part in the phenomena 

 of the wave. 



In their experimental work Berthelot and Vieille proved that the 

 velocity of the explosion wave is independent of the length of the column 

 of gas traversed, and of the material or diameter of the tube employed 

 (at least above a certain small limiting diameter). It was also im- 

 material whether the tube was laid out straight, coiled round a drum, or 

 even zigzagged. They also concluded that the velocity is independent 

 of the initial pressure, but this is not strictly correct, as H. B. Dixon 

 has since shown. The rate increases slightly with the initial pressure, 

 attaining a nearly constant value at a pressure of about two atmospheres. 



H. B. Dixon, the bearing of whose researches upon the ques- 

 tion of the mechanism of combustion will be discussed later, 

 modified Berthelot's theory in the following particulars : 1 namely, 

 by assuming (1) that the explosion wave is carried forward by move- 

 ments of molecules of density intermediate between that of the 

 products of combustion and that of the unburnt gas ; (2) that the gases 

 are heated at constant volume; (3) that the temperature of the gas 

 propagating the wave is double that due to chemical reaction alone ; 

 (4) that the temperature is increased when the chemical volume of the 

 products is larger, and diminished when it is smaller, than that of the 

 unburnt gases ; and (5) that the velocity of a sound wave is only 0'7 of 



1 The reader is referred to the original memoir in the Phil. Trans., 1893, 184, 97, 

 for the details of the argument. 



