TJie Rate of Explosions in Gases. 131 



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 50 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. 



§2. In Berthelot's brilliant generalisation the actual 

 velocities of explosion are compared with the mean velocity 

 of translation of the gaseous products of combustion, sup- 

 posing 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 tempera- 

 ture 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 con- 

 stant pressure. Making these assumptions, he calculates 

 out the theoretical mean velocity of the products of com- 

 bustion of various mixtures, and finds a close accordance 

 between these numbers and the explosion rates of the same 

 mixtures. He concludes that the explosive wave is propa- 

 gated 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 



