THEORY OF THE COMBUSTION OF POWDER. 499 



complementary change. Similarly the carbon will be shared 

 between the potassium carbonate, carbonic acid, and carbonic 

 oxide, which are complementary. The variations in the 

 sulphur have less influence on the other compounds, owing 

 to the formation of the polysulphide, which absorbs a variable 

 excess of this element. The nitrogen becoming free almost in 

 its entirety does not enter into account. 



The free carbonic acid changes but little. 



But the variations in the carbonic oxide and carbonic acid, 

 combined with the potassium, are complementary to the more 

 or less advanced transformation of the sulphate into sulphide. 



We are about to attempt to account, by a theory, for the 

 formation of the fundamental products, together with the fluctua- 

 tions observed in their relative proportions. 



3. Theory of the Combustion of Powder. Simultaneous Equations. 



1. In the case of powder, as well as in that of ammonium 

 nitrate (p. 5), and generally of the substances which do not 

 undergo total combustion, several simultaneous reactions are 

 produced, due to the diversity of the local conditions of combus- 

 tion in the unavoidable absence of homogeneousness in a purely 

 mechanical mixture of three pulverised bodies, and to the 

 rapidity of the cooling of the mass, which does not allow of the 

 reactions attaining their limits of definite equilibrium. If we 

 limit ourselves to the principal products these equations may be 

 reduced to the following : 



(1) 2KN0 3 + 8+30 = ^8 + 3C0 2 + 2N 



(2) 4KN0 3 + 50 = 2K 2 CO, + 3C0 2 + 4N 



(3) 2KN0 3 + 30 = K 2 C0 3 + C0 2 + CO + 2N 



(4) 2KN0 8 + S + 2C = KjS0 4 + 2CO + 2N 



(5) 2KN0 3 + S + C = K^ + C0 2 + 2N 



By combining them with each other, two by two, three by 

 three, etc., we obtain systems of simultaneous equations repre- 

 senting all the analyses, the extreme as well as the intermediate 

 cases. 



In this way equations less numerous, but more complicated, 

 are formed, which any one may combine so as to represent any 

 particular circumstance of the explosion to which he attaches a 

 special importance. But all these arrangements essentially 

 belong to an analogous conception. Kepresentations of this 

 kind are, moreover, indispensable, unless by an arbitrary fiction 

 we suppress the experimental variations, which it is precisely 

 the object of the simultaneous equations to express. 



2. On the contrary, by devoting exclusive attention to the 

 variations, one would run the risk of falling into a blind 



2 K 2 



