268 Count Rumford’s Experiments to determine 
The barrel being rendered unfit for further service, by the 
bursting of its vent tube, an end was put to this set of expe- 
riments. 
In order that a clear and satisfactory idea may be formed of 
the results of these experiments 1 have drawn the figure (Tab. 
VI.), in which the given densities of the generated elastic fluid, 
or (which amounts to the same thing) the quantities of powder 
used for the charge, being taken on the line A B, from A to- 
wards B, the corresponding elasticities, as found by the expe- 
riments, are represented by lines perpendicular to the line AB, 
at the points where the measures of the densities end. 
As the irregularities of the dotted line AC are owing, no 
doubt, merely to the errors committed in making the experi- 
ments, these irregularities being removed, by drawing the line 
A D in such a manner as to balance the errors of the experi- 
ments, this line A D, which must necessarily be regular, will, 
by bare inspection, give us a considerable degree of insight into 
the nature of the equation which must be formed to express 
the relation of the densities to the elasticities; one principal 
object of these experimental inquiries. 
Putting the density = x, and the elasticity = y, the line AD 
will be the locus of the equation expressing the relation of x 
to y ; and had Mr. Robins’s supposition, that the elasticity is 
as the density, been true, x would have been found to be to y 
in a constant (simple) ratio, AD would have been a straight line, 
and AE would have been the position of this line, had Mr. 
Robins’s determination of the force of fired gunpowder been 
accurate. 
But A D is a curve, and this shows that the ratio of x to y 
