132 PROFESSOR H. R. DIXOR OX THE RATE OF EXPLOSION IN OASES. 
collision to molecules of hydrogen and chlorine; these heated molecules, moving 
forwards, will meet unheated molecules moving backwards, when combination will 
occur between those of opposite kind. Heated hydrogen will thus combine with 
cool chlorine, and heated chlorine with cool hydrogen. The heat of combustion is 
thus communicated to a molecule of hydrogen or chlorine which shares it wdth 
a molecule of the opposite kind ; each hydrogen chloride molecule formed in 
turn will therefore have, on the average, a temperature corresponding to the 
heat of chemical combination plus half the heat of a molecule previously formed. 
According to this view the temperature reached by each successive layer would 
increase until it wms douhle that due to the chemical change alone. Tlie temperature 
of the explosion would then remain constant, and the wave wmuld advance at a 
uniform rate as long as it met the same mixture of gases. 
My conception may perhaps be illustrated by an analogy, although an imperfect 
one, Tmao'ine a kiloarram of water at 0° falling in vacuo through 425 metres into a 
vessel filled with an ecpial mass of water at 0° : its motion is stopped, but an equal 
mass of water is displaced. Imagine that the heat developed (wdiich wmuld raise the 
fallen waiter to 1°) be divided equally between the yvater which fell and that wdiicli 
wms displaced. The displaced kilogram of water, now at '5°, falls into a similar vessel 
425 metres below, where it divides its heat with, and displaces, a third kilogram of 
wmter, and so on. By successive divisions of heat, the temperature of the falling 
wmter wall approach 1°, beyond which it cannot rise. But if the heat developed w’ere 
not divided, and remained in the fallen water, the falling wvater would be always at 
0°, and the fallen water at 1°. The latter case is the analogue of the condition 
imagined by M. Berthelot, yvhere the heat of the burnt layer is not imparted to the 
unburnt layer next it ; the former case is the analogue of the condition wdiich I 
imagine holds in the propagation of the explosion-wave. 
Again, M. Berthelot considers the velocity of the w^ave to be solely goymrned by 
the mean rate of translation of the products of combustion. If, howey^er, we accept 
the hypothesis that the explosion is propagated by molecular collisions, we have just 
seen that the movement of the products of combustion is communicated to the 
unburnt molecules in front. It wdll, therefore, follow^ that the rate of the advancing 
explosion will depend not only on the rate of translation of the products of combustion, 
but also on the rate of translation of the \\Qdded hut yet unconibined niolecides. If 
the burnt molecules communicate their rise of temperature wdthout loss to the mole¬ 
cules in front, no difterence in the mean rate of motion wdll be caused bv this 
transference so long as the burnt and the unburnt gases are of the same average 
density. But if a change in density is produced lyy the combustion, the average 
velocity of the molecules in the burnt layer will difler from the average velocity of 
* [r make the assumption that a very thin layer of gas (comparahle in thickness vTth the mean free 
path of the molecules) may he raised by collisions to nearly the same temperature as the highly heated 
la.yer next it.—Jan., 1893.] 
