VOL. LXA'III.] 



PHILOSOPHICAL TRANSACTIONS. 



289 



safely omitted in the theorem: and our only aire must be to guard against acci- 

 dental errors in the actual execution of the business. 



Of the Experiments. — The gun, with which the experiments were made, was 

 of brass ; the diameter of the bore or cylinder at the muzzle was 1-^*^, or 2.1 6 

 inches; but its diameter next the breech was a small matter less, being there only 

 2-g»3-, or 2.08 inches; so that the greatest cast-iron ball it would admit was just 

 \Q\ ounces avoirdupois, or \\ pound wanting half an ounce; but sometimes 

 leaden balls were used, which weighed above 1^ pound; and sometimes long or 

 cylindrical shot, which weighed near 3 lb. The length of the bore was 42-|-, or 

 42.6 inches, so that it was nearly 20i calibers long. 



The powder used was of the sort commonly made for government; the quan- 

 tity was 2, 4, or 8 ounces, to a charge, which was always put into a light 

 flannel bag, and rammed more or less, as expressed in each day's experiments, 

 but without using any wad before it. The distance of the gun from the pen- 

 dulum was 29 or 30 feet; which distance was found to be proper by firing the 

 piece, with 8 oz. of powder without a ball, at different distances, till the force of 

 the elastic fluid was found not to move the pendulum. The penetrations of the 

 balls into the wood were attempted to be taken, but were soon neglected on 

 account of their uncertainty, because of so many balls striking in or near the 

 same part of the wood. The depth of the penetration seemed to be near about 

 3 inches in solid wood when 2oz. of powder were used. 



The first course of experiments was on the 13th of May, 1775, being a clear, 

 dry day. The weights and measures then taken were thus, viz. 



p = 328 pounds, the weight of the pendulum. 



g = 72 inches, the distance of the centre of gravity. 



A = 88 inches = 7^ feet, the distance of the centre of oscillation. 



r = 1 024- inches, the distance to the bottom or tape. 



The value of h =: 88 was determined from the number of 40 vibrations being 

 made in a minute; for 40'^ : 6o^ :: 4 : 9 :: 39.2 : 88. The number of rounds or 

 shot was 8, and the circumstances and results as exhibited in the following table: 



— ■ I ° 



O =3 

 n 0) 





0-,ffi 





In. 



i.9>s 

 1.98 

 1.98 

 1.97 

 1.97 

 1.96 

 1.97 

 1.96 



Inches. Inches. 



.£P<u 



Oz. 



I7h 

 i7h 



'U 



I7i 



17 



171 



17 



5PJ 



Pounds 



VOL. XIV. 



1.094 

 1.094 

 1.094 

 1.078 

 1.078 

 1 .063 

 1.078 

 1.0ti3 



Pp 



Values 

 of p. 



Pound; 



328.0 

 329.1 

 330.2 

 331.3 

 332.3 

 333.4 

 334.4 

 335.5 



Values 

 of g. 



Inches. 



72.0 

 72.1 

 72.2 

 72.3 

 723 

 72.4 

 72.5 

 72.5 



Chord 

 of die 

 arc, c. 



Veloc. 

 per se- 

 cond. 



Inches. ' Feet. 



13.0 I 



17.8 I 



18.1 



17.6 



16.3 



16.2 



24.0 



25.0 



458 

 631 

 650 



646 

 604 



598 

 881 

 950 



