578 
DR. H. DEBUS ON THE CHEMICAL THEORY OF GUNPOWDER. 
But to show the connexion between the quantities of the constituents of a given 
powder and those of its products of combustion, we need only consider relative, 
and not absolute quantities. 
If a straight line be drawn through the origin within the trihedral angle the ratios 
of the coordinates of every point upon it will be the same. 
A plane at right angles to the x axis will cut the faces of the trihedral angle so 
as to form a triangle B D C (see fig. 1), and the coordinates of the points inside 
this triangle will represent all possible proportions of carbon and sulphur which can 
with a given weight of saltpetre transform themselves into the products of combustion 
indicated in equation (XII.). If then in (XII.) we attribute to x the constant value 
16, we obtain : 
16KNO« 
+yC 
+ 2 S 
and from it the equations : 
M 64+ 8y—16«1(K,C0 8 ) 
+*[ 320 — 16y+ 4 z](K 2 S0 4 ) 
> = i +t&[—160+ 8 y +12z](K 3 S 2 ) . 
| ++ 8 [— 64+2 0 ?/+l 62 ] (C0 2 ) 
L + 8N 8 
64+ 8y—162 =0. 
320 —16y+ 42=0. 
— 160+ 8y+122=0. 
(XIII.) 
(XIV.) 
(XV.) 
(XVI.) 
of the lines of intersection of the plane at right angles to the x axis with the faces 
of the trihedral angle, in other words, the sides of the triangle B D C (fig. 1). 
Fig. 1. 
