' THE FORCE OF

56

123. In the theorem

(121), if the known ,value*

f—rm

of c, n, f, m be substituted, and r=—; that is to fay, ifthe density of the non-elastie substances be equal to the den-sity of the fixed nitre, " - ”- — = 04.2; the density of the elas-s—-rm

tic fluid is then 942 times greater when inclosed in the salt-petre, than when in equilibrio with the pressure of theatmosphere. 1

124. The quantity and density of the elastic fluid con-tained in saltpetre being known, it will be easy to find thedensity of that generated from a quantity of powder fired ina close vessel. Suppose the vessel be expressed by a mass ofsaltpetre, the weight of which—G; the elastic fluid will

the non-elastic substances =

and their mass —

3s O (122). Thus O——will be the volume

ol o 0I oI

of the fluid —.

3

If the quantity of powder fired in the vessel G be expres-sed by h+p, where h denotes the quantity of fluid containedin the powder, and p the sulphur, charcoal and fixed nitre;and after the explosion, the mass of non-elaflic substances= qp , then the volume of the fluid, after the powder is fired,

Q

will be G— qp. Now, if the value of this fluid was=—,

3

its density in the volume G — pq would be to its density in

itG nc nc 43 O

the volume -gp at x 8lÆr ^ :: t

43 O coo G t. ... .

042 x - /— ps—-• But if the volume of the fluid81 xG — qp ij—qp

be only h, then the proportion will be —: h :: |f° — :1S ooi . J 3 G-pq

q_ pg the density required. For example, suppose the ves-

sel