246 F. A. P. Barnard on the Explosive Force of Gunpowder. 
Whence, finally, 
2Fa 
9) 
v 
ad 2Far _—s«2Fa (; ay-l\_ 2Fa (7) 
yl. Gaiert y—1\ eA] yl om 7 
In order to find the value of F, as compared with gravity, 
put p for the initial pressure of the gases in atmospheres, esti- 
mated at 14°72 lbs. per square inch, W, for the weight of the 
shot, S, for its specific gravity, and 0 for its diameter in a frac- 
tion of a foot, w, for the weight of the powder and §, for its 
specific gravity, 62°5 lbs. for the weight of a cubic foot of water, 
g for the force of gravity, represented by a velocity of 382} feet 
a second, c for the calibre of the gun in a fraction of a foot, 
its length of bore in calibres, 7 the length of the cartridge, 
and n for the ratio of the weight of the powder to the weight 
of the shot, or naw, Then the pressure per square inch of 
the section through the centre of the shot which gravity would 
produce is equivalent to 1440? 
And we have the proportion 
<i iatip: F= 
sc . 14-72 144b29p X40 
1446? Xdn 9 W; : 
For W,, substitute its equivalent, viz: 
W.==62°553S, X Aa, 
and we obtain the following: 
yp 14°72 144b279pX 40 gp 
625638, da ee ee 
Tnasmuch as the whole mass of the powder (or of the pro- 
ducts of its combustion) is moved as well as the ball, it is com- 
mon to make some allowance for this circumstance by consider- 
ing the weight of the ball to be effectively increased by a certain 
fraction of the weight of the charge. The fraction fixed on by 
Hutton as giving the most consistent results was one-third; and 
in this he has been generally followed. If we adopt the same 
value, we must substitute for W, in the foregoing, W:+4¢Ws= 
W.+40W,=W,(1 +4n)=w.(=2*). Whence | 
oe IP 
F=152°616 (G4n)8, i 
The value of a is a certain fraction (to be presently deter- 
mined) of the length (1) of the charge. To find J, we have 
Wy=c? X44 X 62'5IS,. 
Divide this by the value of W, before given, and we have 
Pe, an ant? XF7XO25ISy _ 8783p 
