PROFESSOR H. B. DIXON ON THE RATE OF EXPLOSION IN GASES. 
133 
the molecules in the heated but yet iinburnt layer, and this difference must be taken 
into account. Lastly, there is a correction to be applied for changes of density in the 
explosion which in part counteracts the foregoing correction. In the oxidation of 
hydrogen and of carbonic oxide there is a contraction from three volumes to two; in 
the burning of cyanogen to carbonic oxide there is aii expansion of two volumes to 
three.^ If each layer of the reacting gases is heated at constant volume, a change 
in the number of molecules must affect the temperature reached. 
If the number of molecules is increased by the chemical change the temperature 
from which the velocity of the wave is calculated will be higher than that directly 
deduced from calorimetric observations ; and vice versa. In allowing for this change 
we may suppose that the new formed molecules have been suddenly compressed or 
expanded, without loss of heat, into the volume previously occupied by the initial 
molecules, in which case the temperature would be altered according to Rankine’s 
formula 
Ayp-i 
Ti \yj 
where and are the absolute temperatures, and V 3 the volumes before and 
after the reaction, and y the ratio of the specific heats at constant pressure and at 
constant volume. 
Cap. VIII.— Comparison of the Rate of Explosion to that of a Sound-wave. 
The criticisms wdiich I have ventured to make on Berthelot’s method of calcu¬ 
lating the mean rate of translation of the gaseous molecules concerned in the 
propagation of the explosion-wave, tend to show that the rate so calculated must be 
too small. But in attempting to apply corrections suggested by these criticisms, one 
is beset with difficulties. As an approximation I assume ( 1 ) that the explosion-wave 
is carried forward by the movements of molecules of density intermediate between 
that of the products of combustion and that of the imburnt gas ; ( 2 ) that the 
temperature of the gas propagating the wave is double that due to the chemical 
reaction alone ; (3) that the temperature is increased when the chemical volume of the 
products is larger, and is diminished when the chemical volume of the products is 
smaller than that of the initial gases ; (4) that the gases are heated at constant 
volume, and their specific heats remain constant at high temperatures. On calculating 
the mean rate of translation of the molecules on these assumptions one arrives at 
numbers greatly in excess of any of the observed rates of explosion ; but some of the 
observed rates agree with the velocity of sound in a gas of the temperature and density 
so calculated. For instance, when one volume of cyanogen is exploded with an equal 
* M. Berthelot rightly takes this change into account in interpreting Bunsen’s experiments on the 
temperature produced in explosions. ‘Ann. Chiiii. et Phys.,’ [V.], vol. 12, p. 302. 
