Experiments ttpon Gunpowder, 87 



And hence we are enabled to determine the natures of 

 the curves mn and^/(Fig. 16); for since B (which ex- 

 presses the weight of the bullet) is as the length taken 

 from A towards B in the several experiments, and as the 

 velocities are as the lines drawn perpendicular to the line 

 A B from the places where those lengths terminate, as w, u^ 

 &c. ending at the curve m, n; if we put ^ = i P, >v= B, 

 and y r=z w u^ then will the relation of x and y be de- 

 fined by this equation , = jy. And if 2; be put to 

 denote the line w r, and b the recoil when the given charge 



X 



Is fired without any bullet, it will be , — , — ^ 4- ^^ = z 



in the curve g f-, x being the abscissa, and % the corre- 

 sponding ordinate to the curve. 



In the 92d experiment half the weight of the powder 

 {= a) was •^i\ grains; the weight of the bullet was 

 2352 grains (= x) ; the recoil (=: %) was 32.25 inches, 

 and with the given charge without any bullet the recoil 

 {= b) was 4.4 inches ; if now from these data, and the 

 known weight of the bullet in each of the other experi- 

 ments in this set, the recoil be computed by means of 



X 



the theorem , — -, — - -\- b =. z v^o. shall see how the re- 

 suit of those experiments agrees with this theory, thus : 



T?ernil. 

 Weia;ht of 



Experiment. the Bullet. Actual. Computed. Difference. 



92 2352 32.25 32.25 



91 1754 27.18 27.23 -|-o.04 



90 1 184 21.92 21.85 — °-°7 



89 603 15.13 15.33 -f-0.20 



88 600 15.22 15-29 -(-0-07 



87 354 11-03 11.87 -I-0.S4 



86 251 9.62 10.21 -I-0.59 



85 90 7.16 7.03 — 0.14 



84 and 93 o 4,40 4.40 



