248 FA. P. Barnard on the Explosive Force of Gunpowder. 
gravity of the charge and the projectile may be found by the 
proportion, Wien) utes) 
7 : ‘as --= 3 e aes 
Wet Wo: We: H(l-p8) ka AS 
& being the distance of the common centre of gravity from the 
centre of the charge. The entire distance of this common cen- 
tre from the bottom of the bore (which distance we will repre- 
sent by q) is therefore 
sen __ +4(6-+2l) 
ga2k+y= ei yak 
If, in any stage of the expansion, we represent the length of 
the charge by /’, and the entire distance from the bottom of the 
bore of the common centre, by g’, we shall in like manner obtain 
tom Bib pte UH OnT') 
q=k+VW= as 
And the movement of the common centre in the mean time, 
which is g'—gq, will be 
2-+-n 
* q- i 2+-2n (?’—2). 
But /'=x—a+1; whence 
; 2-+-n 
q—qI= ae ,-93 and d(q’—q)= zie dz. 
If, therefore, we represent by v’ the velocity which will be 
acquired by the common centre, we shall obtain the equation, 
_, 2Fa 2-+4+n 2ht—ahi 
afl Rete, el 
in which F must have the value, F=50:872 a = B YS; because the 
mass moved is now the entire weight of the powder added to 
that of the projectile. Substituting and reducing as before, there 
Tesults the equation, 
ta 9846-09 2. . 2 
v ee ig sq a ; 
Now the velocities of the common centre and of the projectile 
will be to each other as the spaces simultancously ses over 
by them; and the squares of the velocities will be as the squares 
of those spaces. ‘I'he space passed over by the common centre 
is q’—q; and that passed over in the same time by the projectile 
isz—a. Hence a 
y'2 
Qn ghtaart 
3 ied (=(45)'e-9) : (z—a)? ref: ph (49a, : q 
62 pn = 2-+-n = (2+4-2n)? gPt git) 
a Bie ORARIOS oo 6 cr ig a a el ee . 
oe . areieed ec? I--n 242n (2-+n)? aF ; 
