DR. H. DEBUS OR THH CHEMICAL THEORY OE GUNPOWDER. 
577 
according to equation (X.) 2’6 per cent, larger than it would have been if the carbonic 
oxide bad been taken into consideration. These errors nearly compensate each other 
in the product E in the equation (XI.), so that the values of E are but little affected 
by putting a, the carbonic oxide, =0 in equation (VIII.). 
Equation (XI.) can be used for the calculation of the relative energies of weights of 
pow r der containing 16 mols. of saltpetre, y atoms of carbon, and 2 atoms of sulphur. 
The question now arises for what values of y and 2 will E in equation (XI.) assume 
a maximum value, provided that y and z render the coefficients of equation (VIII.) 
positive,—the condition which must be fulfilled in a chemical equation. 
If we put a= 0 in equation (VIII.), we obtain : 
+yC 
+*s 
A£ 4x + 8y— 162 ](KoC0 3 ) 
ffi-srsC 20x—l 6y+ 4z] (K 2 S0 4 ) 
< +A[-10^+ 8y+12z](K 3 S 3 ) , 
| +*[- 4x+20y+l6z](CO 2 ) 
L +i^X 3 
(XII.) 
in which, as in (VIII.), x, y, and z denote positive numbers. Let a rectangular 
coordinate system be given with its origin in point A, and the coordinates of a 
point P be represented by x, y, and z. The coefficients of potassic carbonate, 
sulphate, and disulphide in (XII.) will for certain values of x, y, and z be equal to 0. 
The equations: 
kx-\- &y— 162=0 
20 a? — 16y+ 42=0 
— 10a?+ 8y+122=0 
satisfied by these values represent three planes which form a trihedral angle with its 
vertex in the origin and one edge in the x Ay plane. The points within the trihedral 
angle have coordinates which will render all the coefficients of (XII.) positive, those 
situated outside give values for x, y, and 2 , which will make at least one of the three 
coefficients of the potassium salts negative. Hence, coordinates of the points within 
the trihedral angle denote quantities of saltpetre, carbon, and sulphur, which can 
transform themselves completely into potassic carbonate, sulphate, disulphide, carbonic 
acid, and nitrogen, whereas the points outside represent, by their coordinates, quantities 
of the powder constituents which cannot do so entirely, because one or the other of these 
constituents is in excess or defect. 
The points on the faces of the trihedral angle correspond to mixtures which will 
burn with the production of two, those on the edges with only one of the three 
potassium salts. 
4 e 2 
