584 DR. H. DEBUS ON THE CHEMICAL THEORY OF GUNPOWDER. 
and move from B towards 0, the amounts of heat produced by the mixtures repre¬ 
sented by the coordinates of the several points will constantly decrease, and the 
volumes of gas increase, until the former reach in C their minimum, and the latter 
their maximum value. 
We calculate for B and C 
Volume of gas. Units of heat. 
B . . . 32 1,621,450 
C . . . 64 1,280,346 
and between these numbers, 32 and 64 for the volume of the gas, and 1,280,346 and 
1,621,450 for the units of heat, fluctuate the quantities of heat and gas which any 
possible mixture of 16 mols. of saltpetre with carbon and sulphur can produce, 
provided that these constituents, during combustion, transform themselves according to 
equation (XIII.). We will now show that the product, E, of the units of heat and 
the molecules of gas as given by equation (XI.), is greater for mixtures represented by 
points of line B C than for such as are represented by any other point within the 
triangle. 
If we take, on the line D W, perpendicular to B C, the point y= 1*7, z=6, then 
the mixture corresponding to this point and the one corresponding to point W will 
produce the same quantity of heat. The amount of gas generated by the mixture 
represented by point y— 17, z=6, must be less than the quantity produced by the 
mixture corresponding to point W. Because, if we draw a line through y=l7, z=6, 
parallel to D V, the point of intersection with B C will lie between W and V, but 
the further the point of intersection is away from W in the direction towards B the 
smaller the volumes of gas will be. Hence, the product of gas and heat for y— 17, 
z=6 must be smaller than the one for point W, and the further we proceed from W 
towards D the smaller this product must be. But what holds good for the line D W 
also applies to every other perpendicular which can be drawn to B C. 
Therefore the maximum value of the product of gas and heat must be produced by 
a mixture the composition of which is expressed by the coordinates of one o± the points 
of the line B C. 
If we represent the function on the right of the equation (XI.) by F(y, z), and the 
equation of the line B C (XIY.) by <£(y, z) = 0, then the differential equation 
dF clef) dF d<f) _ 
clz dy dy dz 
together with <f>(y, z)= 0 give the values of y and z, for which E in equation (XI.) 
becomes a maximum. We find y= 38'02 and z=23‘Q. Hence, a powder composed of 
16KN0 3 + 38C + 23S 
