Experiments upon Gunpowder. 87 



And hence we are enabled to determine the natures of 

 the curves mn and gf( 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, #, 

 &c. ending at the curve m, n; if we put a ==. \ P, x= B, 

 and y = w u, then will the relation of AT and y be de- 

 fined by this equation - = y. And if z be put to 



ya-\- if . r 



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



v 



is fired without any bullet, it will be - - 4- b = z 



\Ja -\- x-* 



in the curve g f, x being the abscissa, and -2 the corre- 

 sponding ordinate to the curve. 



In the 9id experiment half the weight of the powder 

 (= a) was 72^- grains ; the weight of the bullet was 

 2352 grains (= x) ; the recoil ( z) 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 - - -4- b = z we shall see how the re- 



y a -\- x 3 



suit of those experiments agrees with this theory, thus : 



Recoil. 



