92 Mr. D. L. Chapman on the 



the pressure at EF is always kept equal to the pressure 

 at XS. During this process the velocity of the wave will 

 gradually increase, until ultimately its velocity will be 

 uniform, its type constant, and the exploded gas within 

 the area EXSF homogeneous. It is this ultimate steady 



Fig. 1. 



state alone which I propose to consider. During the process 

 just described the velocity will of course constantly increase 

 until it attains a maximum. After the velocity has become 

 uniform, and the wave permanent in type, it is obvious that 

 another permanent state may be reached in the following- 

 way : — Suppose a piston is introduced immediately behind 

 the permanent wave, and that this piston is made to move 

 forward more rapidly than the previous one, the pressure and 

 density behind the wave will thus be increased, and after a 

 certain period of time another steady state will be reached. 

 All this is equivalent to the statement that the permanent 

 velocity of explosion is a function of the density of the 

 exploded gas. 



I shall now proceed to prove the latter statement. 



Since the discussion is limited to the wave of permanent 

 type, we may write down the condition of steady motion, 



V 



(1) 



where V and u are the velocities of the unexploded and 

 exploded gas respectively, referred to coordinates moving 

 with a velocity — V, and v and v are the volumes of a gram- 

 equivalent of the unexploded and exploded gas. 



Take as an example cyanogen and oxygen, the explosion 

 of which is represented by the equation 



C 2 N 2 + 2 2CO + N 2 . 



22-4 litres + 22'4 litres = 44*8 litres + 22*4 litres. 

 52 grms. + 32 grins. = 56 grms. + 28 grms. 



Here v = 44'8 litres, and v is the volume of carbon monoxide 



