L6

THE FORCE OF

shot, and substitute it in the place of S in the theorem

T

jjj: In the room of g and D insert their known

values, which will give the relative value of u : then by ana-logy, the relative velocity of the bullet is to its initial velocity,as the relative velocity of the cannon shot is to its innial velo-city. Suppose, for example, that the leaden bullet firedfrom the wall-piece be i inch in diameter —I) and that itspenetration 8 — 4. feet; as the specific gravity of lead is

£ = 9060 then u= = ,

g u 90 60

Suppose again, that

the cannon shot be 6 inches in diameter = D and its penetra-tion into the butt 14 feet—8, as the specific gravity of iron

is 6115 ; »— v'-

:V A

/TsT

Then if the known initial

g D v 6115'velocity of thf bullet fired from the wall-piece be 2023 feet,

x/jK -

:: 2023 :1880 feet, which will be the

9060 6115

value of the velocity sought.

This theorem will serve to resolve other problems; forinstance, by knowing the diameter, density, velocity andpenetration of one shot, the penetration of the other shot dif-fering in density, velocity and diameter into the same butt maybe found.

177. From a series of experiments made according to theforegoing principles, under a mean slate of the atmospherewith guns, (89) charged with a quantity of common cannonpowder, equal to about -J of the weight of the shot in 32 and16 prs ; and to \ its weight in 8 and 4 prs: it results that1349 feet will be the mean initial velocity of 32 prs; 1433of 16 prs; more than 1517 of 8 prs; and less than 1517 of

4 P rs -

Lieut, de Butet invented in 1764 a very simple ma-chine for measuring the initial velocity of projectiles. Heapplies a little plate of metal provided with a moveable indexto any wheel that turns with an equable motion, and suf-ficient velocity; the index is held at some distance from thecircumference of the wheel, by a thread that is stretchedacross the mouth of the gun. When the gun is fired, theshot breaks the thread, and sets at liberty a spring, which

instantly