Hydrostatics

3°7

by the greater Resistance of the Fluid, andconsequently the greater Loss of Weight in

the

W ^ w W

cause A — — and B — therefore A -f- B =-(-

a b a

W bfi-waa b

— Bulk of Water, which multiplied by

its specific Gravity ( c ) gives the Weight of Water

-— W-f-w rathe Weight of both the Bodies.

a b

Whence we have W b c iu a c — W s L -s- w a b ;and so W b'c — W a b — w a b — w a c •, consequently

Wbc—Wab .. , , Wb—Wab

-:- —w, orifc — I, then we have ---

a b—a c a b—a

— _ X W~uj —Weight of the Body B required.

9. bor Example; suppose the specific Gravity of aMan’s Body, Water, and Cork be as ic, 9, 2|; thena— 10, c=9, and b— 2|; let W = 150 Ib. ~ Weight

of the Man’s Body ; then will -—— - ^ ^ c ~ vj

a b — ac

— 5 ; therefore if such a Man were to take 5 Ib. of Corkwith him into the Water, he would be of the fame spe-cific Gravity of the Water, and ever so little more wouldmake it impossible for him to sink; whence the Art oflearning to swim might by this Problem be greatly fa-cilitated.

10. To find the Weight of a Globe of Water one Inchin Diameter. We shall here chuse Troy Weight, whereone Cubic Foot weighs 76 Ib. ; and therefore one cubic

. ,, , 76X12X20X24

of a Pound, or

Inch weighs -

I2XI2XI2

Grains, that is,

76x40 760

12X12X12Grains. But in Geo-

12 3

metry we prove the Cube is to its inscribed Sphere as 1

to 0,524; therefore as 1 : 0,524 : : 6^ : 132 Grains =

the Weight of a Globe of Water one Inch Diameter.

X 2