Mr,. Thompson's Experiments 
The agreement between the adtual and computed velocities 
is here very remarkable, and particularly in the five firft expe- 
riments, which are certainly thofe upon which the greateft 
dependence may be placed. 
And hence we are enabled to determine the natures of the 
and gf (fig. 1 6 ) ; for fince B ; (which expreffes the weight 
of the bullet) is as the length taken from A towards B in the 
figure in the feveral experiments ; and as the velocities are as 
the lines drawn perpendicular to the line AB from the places* 
where thofe lengths terminate, as w, u, See. ending at the 
curve m, n\ if we put a= f P, x = B, and y — wu ; then 
will the relation of x and y be defined' by this equation 
-~J==r =ry. And if z be put to denote the line w r , and 
fyT a -+• at 3 
the recoil when the given, charge is fired, without any bullet, it' 
will be —=== -p b ssr» in the curve gf r x being the abfcifla,. and 
v/ a + x 3 J 
z the correfponding ordinate to the curve. 
In the 93d experiment half the weight: of the powder ( = aj 
was yzi grains the weight of the bullet was 2352 grains 
(— at) ; the recoil ( = z) was 32,25 inches, and with the given 
charge without any bullet the recoil (~£) was 4,4 inches; if 
now from thefe data y and the known weight of the bullet in 
each of the other experiments in this let, the recoil be computed 
by means of the theorem —~~? 4 rb — z, we jfliall fee how the 
refult of thofe experiments agrees with , this theory thus, , 
J 
