90 THE EXPLOSIVE WAVE. 



magnitude of the quantities of heat ; for instance, 68,200 cal. 

 for CO + ; 59,000 cal. for H 2 + 0, supposing the water to be 

 in the gaseous form ; it also results, for the same quantity of 

 heat, from the inequality of the specific heats. The calculation 

 of these temperatures remains doubtful, on account of dissocia- 

 tion and uncertainties surrounding the value of specific heats at 

 high temperatures. 



An idea of the theoretical relation that regulates the velocity 

 of the explosive wave may be formed, however, if it be noted 

 that the total energy of the gas, at the moment of explosion, 

 depends on its initial temperature, and on the heat given off 

 during the combination itself. These two data determine the 

 absolute temperature of the system, which is in proportion to 

 the energy of translation (Jrav 2 ) of the gaseous molecules. 

 That is to say, the excess of energy communicated to the mole- 

 cules by the act of the chemical combination is simply the heat 

 given off in the reaction ; the pressure exercised by the molecules 

 on the sides of the vessels is the immediate translation of it, 

 according to the most recent theories. 



Thus a point is reached where mechanical notions and 

 thermal notions tend to intermingle. 



To formulate this, the rate of translation of the molecules at 

 the moment of combination is proportional, according to the 

 relation of the energy, to the square root of the ratio of the 

 absolute temperature T, to the density of the gas as compared 

 with air, or, as M. Clausius expresses it, 



= 29-354 metres \/- 

 P 



In reality, the physical notion of the temperature T does not 

 enter into this estimation of the velocity, and the formula 

 simply expresses the fact that the translating energy of the 

 molecules of the gaseous system produced by the reaction, and 

 containing all the heat developed by the latter, is proportional 

 to the energy of translation of the same gaseous system, con- 

 taining only the heat which it retains at zero. 



This formula has been verified, approximately at least, for 

 a score of gaseous compounds, differing greatly in their com- 

 position (as described hereafter). 



2. Thus it seems, that in the act of explosion, a certain 

 number of gaseous molecules amongst those forming the portion 

 that is first ignited, are hurled forward with the velocity corre- 

 sponding to the maximum temperature developed by the 

 chemical combination, the shock which they impart determines 

 the propagation of this combination into the next section, and 

 the movement is reproduced from section to section with a 

 velocity if not identical with, at least comparable to, that of the 

 molecules themselves. 



