168 Col. Beaufoy on the Force of [Serr 
experiments made with the eight ounce weight with each other, 
three values of the exponent m will be obtained, viz. m = 
log. of 12-900 — log. of 6600 5.9943 py = 108+ of 19+599 — log, of 12/900 
log. of 80235 — log. of 5°6736 *"" ™~ Jog, of 9827 — log. of 8°0238 
log. of 19°599 — log. of 6-600 " f 
— 2-0626 m= jog. of 9-827 — log. of 56136 IT 9817 3 the mean of 
these three exponents is 19929; which is so near the square of 
the velocity, that the momentum may be considered as the square 
of the velocity. 
From the experiments with the sphere of one pound moving 
with an uniform velocity of 5,6736 feet in a second, was given 
an impetus of 15,145 pounds; and they proved the momentum 
to increase as the square of the elasticity. Hence may be cal- 
culated the dead weight sufficient to stop an 18 pound shot, 
moving with a velocity of 1000 feet in a second, 5°6736° : 
15:143 Ibs. :: 10002 Ibs. : 470439: This number multiplied by 
18 gives the product 8467902, the impetus of the cannon ball ; 
which is nearly 3780 tons; a force so enormously great as hardly 
to be credible. 
The following experiments are suggested on a larger scale, 
and in a different manner. 
Suppose several iron pipes screwed together in the shape of an 
inverted syphon, the two legs parallel to each other, and united 
by one bent into a semicircular form; then into the shorter leg 
of the syphon insert a piston, with a projecting iron spindle cut 
into notches for a pawl to slide so as to prevent its return back 
after being forced down. The syphon is then to have as much 
water poured into the longer leg as will raise it sufficiently high 
to reach the bottom of the piston inserted in the other leg. 
Let a pile engine be afterwards brought over the piston, and 
the ram permitted to fall; this striking the iron spindle will, by 
pressing down the piston, force up the water in the other leg ; 
the pawl retaining the piston. The altitude of the elevated 
column of water may be determined by thie piston’s depression, 
and this quantity being known, with the diameter of the syphon 
previously measured, the weight of the water, and consequently 
the momentum of the falling body can be found by calculation. 
It is recorded that the weight of a large battering ram, includ- 
ing the head, beam, iron hoops, chains, &c. weighed 41112 Ibs. ; 
and if it be presumed that the engine when employed in demo- 
lishing walls was impelled with a velocity of 12 feet per second, 
the momentum is equal to 277,93 tons ; an impetus that equals 
an 18 pound cannon shot, moving at the rate of 271,15 feet in a 
second ; consequently the force communicated to balls by gun- 
powder is far more efficacious in destroying buildings than the 
most penderous weapons used before the invention of fire arms. 
I remain, dear Sir, truly yours, Mark Beavroy. 
