134 PROFESSOR H. B. BIXOR" ON THE RATE OF EXPLOSION IN GASES. 
volume of oxygen, two volumes of carbonic oxide are formed, and one volume of 
nitrogen :—■ 
C 2 N 3 + 0. = 2C0 + Ns. 
Taking the quantity of heat evolved as 126,100 calories, and the specific heat at 
constant volume of the products of combustion as 4’8 X 3 = 14’4, the temperature 
produced by the chemical change is 8694° C. If the gases were initially at 13°, or 
286° degrees above absolute zero, the chemical reaction will raise the temperature to 
8980°. But, since three molecules are formed where two previously existed, the 
temperature is further raised by the heat developed in compressing three volumes to 
two. This will raise the temperature to 10,595°. At double this temperature the 
mean rate of translation of a molecule of the mean density of the burnt and unburnt 
gases would be 3892 metres per second. If the formula for the velocity of sound 
under ordinary conditions held good in the explosion, the velocity of the sound wave 
would be 2670 metres per second—a rate which is about 2 per cent, less than 
the observed velocity of the explosion-wave. Now, the theoretical velocity of sound 
is calculated on the assumption that the disturbance is very sm.all; if the displace¬ 
ments are large the velocity of sound should be higher. Direct measurements of the 
velocity of sound-waves of great intensity have confirmed this anticipation. Under 
ordinary conditions the rate of the sound-wave is to the mean rate of the molecules as 
'688:1. If we take the ratio in an explosion as '7 : 1 the velocity of the sound-wavm 
agrees with the observed rate of explosion in this particular case. 
We may now compare the rate of the sound-wave so calculated with the velocity 
of explosion of cyanogen wdth oxygen (1) in presence of excess of oxygen, (2) in 
presence of excess of nitrogen ; (3) of cyanogen with nitrous oxide alone, and (4) in 
presence of excess of nitrogen ; and lastly (5) of cyanogen with nitric oxide. 
Taking the data furnished by Berthelot’s experiments, we have, for the quantities 
of heat evolved, the expansion on explosion, the specific heat of the products, and for 
the mean density of the burnt and unburnt gases :— 
