102 THE EXPLOSIVE WAVE. 



specific heats of the elements under a constant pressure ; this is 

 the theoretical temperature, T, of the reaction ; the seventh 

 gives the theoretical values, 0, of the mean rate of translation 

 per second of the gaseous molecules constituting the products of 

 the combustion, a rate calculated for the temperature T, accord- 

 ing to the formula of Clausius (see p. 90). 



P 



This is a velocity which we propose to compare with the ex- 

 perimental velocity of the explosive wave, U, which is shown in 

 the eighth column. 



3. The temperature, T, is here calculated from the specific 

 heats of the elements under a constant pressure. The results 

 thus obtained, agree in general with the observations (columns 

 7 and 8) ; they agree far better than if the calculation were 

 made from the specific heats at a constant volume, although 

 the latter method would, on first thought, seem the more 

 plausible. 



We may account for the intervention of the specific heats 

 under a constant pressure, if we consider that the combustion, 

 in passing from layer to layer, is preceded by the previous 

 compression of the layer of gas that it is about to transform. 

 From that time the combustion takes place under a constant 

 pressure throughout the tube. It might be thought that the 

 temperature, T, must be increased by the elevation of tempera- 

 ture produced by this previous compression. But we must 

 take into account the fact that the combustion of each layer 

 produces, at the same time as heat, the work necessary for 

 compressing the following layer ; i.e. it loses in this way exactly 

 the same quantity of heat as it has gained by its own com- 

 pression. In short, as regards elevation of temperature, the 

 effect is the same as if we were working under a constant 

 pressure. The agreement ' between the figures calculated and 

 the numbers observed confirms this view of the phenomena. 1 



The fact is, the physical conception of the temperature, T, 

 does not enter into this estimate of the velocity, and the calcu- 

 lation simply shows that the energy of translation of the mole- 

 cules of the gaseous system produced by the reaction, and 



1 It is assumed here that the specific heat of a compound gas under a 

 constant p'ressure is the sum of the specific heats of its elements, which 

 assumption is, in reality, only true when the volume is constant, or, for the 

 two specific heats, in the case of gases formed without condensation. But 

 this underestimate in the case of the specific heat under a constant pressure, 

 of gases formed with condensation, is to a certain extent compensated by the 

 fact that the specific heat of these gases rises with the temperature : this is 

 proved by the study of the specific heats of carbonic acid, nitrogen monoxide, 

 etc. (" Essai de Mdcanique Chimique," torn. i. p. 440). This hypothesis may, 

 therefore, be admitted for a first approximation. 



