TRACT 34.

IN GUNNERY.

331

the first velocity is to the last velocity, as A ex to 1 . Andthe velocity lost by the resistance of the medium is nearly\A ex — l)v or-v.

33. Now to adapt this to the case of our bails, whichweighed on a medium 16| ounces, when the diameter wasl'S6 inches ; we shall have 1-96 3 X ‘5236 == the magnitudeof the ball; and as 1 cubic foot, or 1128 cubic inches, of

1728 x

water, weighs 1000 ounces, therefore , _

7‘344 = n is the specific gravity of the iron ball ; which isvery justly something less than the usual specific gravity ofsolid cast iron, on account of the small air bubble whiph iswithin side of all cast metal balls. Also the mean specificgravity of air is ‘0012, which is the value of n. Hence_ 3 n _ 3 x -0012 x 12 _ 1

~ 8 d n — 8 x 1-96 x'7'34i — 2666‘

Now the common distance of the face of the pendulumfrom the trunnions of all the guns, was 35| feet; and thedistance of the muzzles of the four guns, was nearly 34 a forthe 1st or shortest gun, 34 for the 2d, 33 for the 3d, andfor the 4th. But as the elastic fluid pursues and urgesthe ball for a few feet after it is out of the gun, it may besupposed to counter-balance the resistance of the air for a fewfeet, the number of which cannot be certainly known, andtherefore we shall suppose 32 feet to be the common dis-tance, for each of the guns, which the ball passes through,before it reach the pendulum. Hence then the distancex = 32; and consequently ex =

Then A ex — 1 = '01207 = ^ nearly. That is, the ball

loses nearly the 83d part of its last velocity, or the 84thpart of its first velocity, in passing from the gun to the pen-dulum, by the resistance of the air. Or the velocity at themouth of the gun, is to the velocity at the pendulum, as 84to 83 ; so that the greater diminished by its 84th part givesthe less, and the less increased by its 83d part gives thegreater. But if the resistance to such swift velocities as our?

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