1891.] on the Bate of Explosions in Gases, 445 



tube, they found the velocity of the flame regularly increased, as 

 far as their instruments were able to record the rapidly increasing 

 pace. 



Mixtures of coal-gas with air, and of fire-damp with air, show 

 phenomena of the first and second kind. Ignited at the open end of 

 a tube these mixtures burn at a uniform rate for a certain distance, 

 and then the flame begins to vibrate. 



The vibrations acquire greater or less velocity according to the 

 nature of the mixture and the conditions of the experiment ; but the 

 third regime of uniform maximum velocity is not set up. In narrow 

 tubes the explosion soon dies out. 



The phenomena studied by Mallard and Le Chatelier have been 

 observed on a large scale in explosions in coal mines. It has been 

 noticed that little damage was caused at the source of an explosion, 

 and for a distance varying from 60 to 80 yards from the origin of 

 the flame, while beyond that distance falls of roof, broken tubs, and 

 blown-out stoppings have testified to the violence exerted by the 

 explosion. Great as the destruction is which an explosion of fire- 

 damp and air causes in a mine, it is fortunate that these mixtures do 

 not detonate. 



Passing on to Berthelot's researches on the regime of detonation, 

 I will briefly summarise the results he has arrived at. 



The actual velocities of explosion are compared by Berthelot with 

 the mean velocity of translation of the gaseous products of combus- 

 tion, supposing these products to contain all the heat that is 

 developed in the reaction. 



For instance, we know the total heat given out when hydrogen 

 and oxygen combine. If this heat is contained in the steam produced, 

 we can calculate what its temperature must be if we know its heat 

 capacity. And if we know the temperature of the steam, we can 

 calculate the mean velocity with which the molecules must be 

 moving. Now Berthelot supposes that the heat is all contained in 

 the steam produced. He assumes that the heat capacity of steam is 

 the same as the sum of those of its constituents ; and he supposes, 

 moreover, that the steam is heated at constant pressure. Making 

 these assumptions, he calculates out the theoretical mean velocity of 

 the products of combustion of varit>us mixtures, and finds a close 

 accordance between these numbers and the explosion rates of the 

 same mixtures. He concludes that the explosive wave is propagated 

 by the impact of the products of combustion of one layer upon the 

 unburnt gases in the next layer, and so on to the end of the tube at 

 the rate of movement of the products of combustion themselves. If 

 his theory is true, it accounts not only for the extreme rapidity of 

 explosion of gaseous mixtures, and gives us the means of calculating 

 the maximum velocity obtainable with any mixture of gases, but it 

 also affords us information on the specific heats of gases at very high 

 temperatures, and it explains the phenomena of detonation whether 

 of gases or of solid or liquid explosives. 



