130 PROFESSOR H. B. DTXON ON THE RATE OP EXPLOSION IN GASES. 
(2.) 
Mixture. 
H, + N3O 
With addition of 
2 vols. nitrogen. 
H3 + N2O -h N2 
With addition of 
3 vols. nitrogen. 
Ho -h NoO -h N3 
Theory, 6 . . 
2319 
1912 
1782 
Found, V 
2305 
1991 
1880 
Now M. Berthelot especially insists that the formula gives a maximum velocity 
which may be reached, but not surpassed, by the actual explosion-wave. If, then, 
the rates of explosion of the diluted mixtures had fallen below the calculated rates, 
such divergence might be explained on the supposition that the diluent gases 
interfere with the normal propagation of the wave, an explanation which is indeed 
advanced by Berthelot to account for the falling off in the rate of certain diluted 
mixtures observed by him. But since the theory assumes that the explosion-wave 
travels at the rate of the gaseous molecules themselves while they still retain all the 
heat developed by the reaction, the presence of inert molecules could not possibly 
increase this rate of motion.'* 
Since the amount and regularity of the divergence between the found and 
calculated rates precluded the idea of experimental error being its sole cause, I was 
driven to conclude either that the hypothesis was incorrect, or that the formulas 
used failed to express the hypothesis with exactness. 
M. Berthelot’s theory is that the explosion does not travel with the velocity of 
sound in the heated gases, but with a velocity equal to the mean rate of translation of 
the molecules produced in the explosion. 
Let us examine the mode in which Berthelot calculates the theoretical velocity, 
i.e., the mean rate of translation of the products of combustion at the temperature of 
the explosion. In Clausius’ formula 
V — 29-354 
M, Berthelot calculates the absolute temperature of the explosion by dividing the 
quantity of heat developed in the complete reaction by the specific heat of the 
products of combustion taken at constant joressnre. He argues that each layer of gas, 
in transmitting the explosion, is heated under constant pressure, I cannot follow his 
reasoning. 
“ The combustion,” he says, “ in propagating itself from layer to layer, is 
preceded by the compression of the gaseous layer which it is about to transform. 
* It will be shown in the seqnel that Berthelot’s formula fails to express the rates of explosion of 
some undiluted explosive mixtures, viz., hydrogen aiid chlorine, ammonia and nitrous oxide. 
