500 POWDERS WITH A NITRATE BASE. 



empiricism, incapable of serving as guide for the perfecting of 

 the practical applications. We shall now apply these ideas in 

 detail. Take, for instance, the mean value given above, accord- 

 ing to Debus (p. 498) ; it corresponds to an equation which is 

 too complicated to be admitted as the general representation of 

 the phenomenon, but it is easy to see that it results from a 

 certain system of transformations in which a fourth of the salt- 

 petre has been destroyed according to equation (1) the sulphide, 

 moreover, having been changed into polysulphide at the expense 

 of the excess of sulphur ; an eighth of the saltpetre has been 

 destroyed according to equation (5) ; three-eighths according to 

 equation (3) ; and a fourth according to equation (2). 



On the other hand, the analyses which have given the 

 maximum of carbonate also correspond to the maximum of 

 carbonic oxide, and to a very small proportion of sulphate, all 

 these being correlative circumstances which may be expressed 

 by the system according to simultaneous equations, viz. equa- 

 tion (1) for a third of the saltpetre ; equation (3) for the half ; 

 equation (2) for about a sixth. 



The opposite extreme is that in which the potassium sulphate 

 gives the maximum proportion, or a fifth of the potassium ; 

 while the carbonate retains the half of it, and the carbonic oxide 

 tends to disappear. These relations still show regular reactions, 

 always expressed by a certain system of simultaneous equations : 

 or equation (1) for a third of the saltpetre, and equation (2) for 

 nearly the half, which corresponds to the carbonate ; while the 

 formation of potassium sulphate would correspond for an eighth 

 of the substance to equation (4), and for a twelfth to equa- 

 tion (5). 



3. The five simultaneous equations, therefore, represent the 

 extreme cases ; but it is easy to prove that their combinations 

 also represent in an approximate manner the intermediate cases. 



Consequently, the system of equations expresses the chemical 

 transformation of powder, at least as regards the fundamental 

 products. Further, it represents the variations, which could not 

 be done by a single equation. 



The transformation reduces itself definitively to five simple 

 reactions, which cause the formation of the potassium sul- 

 phate, sulphide, and carbonate, of carbonic acid, and carbonic 

 oxide. 



4. It is also easy to prove that the combustion of any 

 powder may be represented by a certain combination of the 

 above five equations; the first members being taken in such 

 relative proportions that they represent the initial composition 

 of the powder under consideration, provided the more or less 

 abundant formation of the polysulphide, and of the deficit of 

 about a fourth compared with real carbon, which results from 

 the use of charcoal, be taken into account. 



