154 PROFESSOR H. B. DIXON ON THE RATE OF EXPLOSION IN GASES. 
The excess of pressure in the waves, therefore, will be, as far as the equations hold. 
If the factor 
be retained, the calculated pressure P would be rather smaller than that given ; thus if the maximum 
density of the wave is only double that of the undisturbed state, the calculated value of P would have 
to be reduced in the ratio of 1’4 to 1. 
In order to test the equation 
V = 
P 
I have applied it to compare the rates of explosions in the mixtures H- + O, Ho + 0 + N 5 , Ho + Og. 
In these three cases the explosive mixture H, + 0 is diluted with the same volume of inert gases, and 
according to the equation the rates should be inversely as the square roots of the densities of unburnt 
gases, for the pressure P may be expected to be the same in all three cases. The rates found by 
Professor Dixon are 3532; 1822; 1707. Assuming 3532 to be right, I calculate for the other two 
combinations 1806 and 1711, which so far confirms the equation. But I am doubtful w'hether this 
means much, as the same result could be deduced from arguments relating merely to the dimensions of 
the quantities involved. 
I have not discussed the question wdiether a steady wave is really possible, but assuming it to be 
steady I believe that the equation 
V = / p -Po . 
^ l‘ — Po Po 
holds. In the strict sense of the word I do not think the exjilosion-Avave can be steady, because if the 
motion is, as assumed, linear, compression must precede the explosion, and Lord Rayleigh’s objection 
would hold for the front part of the wave in Avhich no combination takes place. 
But it seems possible to me that the motion may not strictly be a linear one, and that yet taking the 
average velocities over a cross-section of the tube the ordinary equations wmuld apply. It seems 
probable that jets of hot gases are projected bodily forward from that part of the wave in which the 
combination takes place, and that these jets, which would correspond to the spray of a breaking wave, 
really fire the mixture. 
Cap. XI.— Some Difficulties in the “Wave” Theory. 
§ 1. Ill calculating a theoretical velocity for the rate of the explosion-wave in gases, 
I am aware that I have passed over many difficulties which demand consideration. 
For some of the problems raised here we have, I believe, no data which might enable 
us to solve them. Riemann’s theory of the propagation of an intense disturbance in 
a gas recpiires, in order to calculate the velocity of propagation, a knowledge of the 
highest pressure reached in the wave. But concerning the pressures produced for 
extremely short periods in the ex plosion-wave, we have less exact knowledge than of 
the velocities, and possibly the rates of explosion may be used to calculate the 
pressures produced. 
The question, indeed, may be raised whether the propagation of the ignition is due 
