ON GASEOUS COMBUSTION. 477 



lite mean velocity of the molecules in the gas. Dixon's formula for the 

 rate of explosion of a given mixture is, therefore, as follows : — 



«=0-7x 29-354 



JdMM 



7-1 



where Q = the heat developed by the reaction, v. 2 and Vj=the chemical 

 volumes of the products and unburnt gases respectively, p — the mean 

 density of the products and the unburnt gases, and Gv = the specific 

 heat of the products at constant volume, which Dixon wrongly assumed 

 to be independent of the temperature, T = the temperature in C°, and 

 y —■ the ratio of the specific heats. 



But, whereas the values of v, calculated by this formula, do in many 

 instances correspond with those actually found (e.g., for mixtures of 

 cyanogen and oxygen, and in nearly all cases where the detonating mix- 

 ture is largely diluted with an inert gas), there are a large number of 

 cases of undiluted detonating mixtures in which the agreement is not 

 good (e.g., for 2H 2 + 2 the calculated value is 3,416, whereas that 

 actually found is only 2,821 metres per second). Dixon ascribed such 

 discrepancies to the partial dissociation of the products in the wave, but 

 there is now little doubt that the formula does not hold good, as Dixon 

 himself readily enough admits. 1 Nevertheless for many years it was a 

 valuable working hypothesis and inspired much fruitful investigation. 



In 1599 D. L. Chapman, following up a suggestion made by Schuster 

 at the time when Dixon's memoir was published, 2 deduced a formula 

 for rates of explosion from Eiemann's equation for the propagation of 

 an abrupt variation in the density and pressure of a gas, on the assump- 

 tion that such a variation can be propagated without change of type. 3 

 According to this view the explosion wave is to be regarded as a wave 

 of compression not in a homogeneous medium, but in a medium which 

 is discontinuous in the vicinity of the wave- front. It is assumed (1) that 

 the ' front ' of the wave (i.e., from the unexploded gas to the point of 

 maximum pressure) does not alter in character, or, in other words, chat 

 every portion of the wave travels with the same velocity ; (2) that the 

 velocity is the minimum velocity consistent with (1) ; and (3) that at the 

 point of maximum pressure the chemical change concerned in the propa- 

 gation of the wave is complete. The unburnt gases immediately in front 

 of the waves are, of course, fired by compression, and the abrupt varia- 

 tion in the density and pressure of the medium is due to the chemical 

 change. Chapman's formula for the velocity of the explosion wave in 

 centimetres per second is 



where E = the gas constant (1'985), J = the dynamical equivalent of 

 heat (42 x 10 6 ergs), //. = t-he gram equivalents of the mixture exploded 

 (e.g., 58 in the case of C:.H 2 + 2 ), n and ra = the number of gaseous 



1 Wee his recent presidential address to the Chemical Society, Trent". Chem. 

 Soc, 1910, 97, 665. 



3 Lor. cit., p. 152. ;1 Phil. Mag., 1899, p. 90. 



1910. I i 



