GRAVITIES OF BODIES.

THE gravity of a body, or its weight above the earth's surface, decreases as the square of its distance from the earth's centre in semi-diameters of the earth.

EXAMPLE. If a body weigh 900 lbs. at the surface of the earth, what will it weigh 2000 miles above the surface? The earth's semi-diameter is 3993 miles (say 4000). Then 2000+4000-6000 or 1 semi-diameters, and 900 1.52 400 lbs., Ans.

Inversely, if a body weigh 400 lbs. at 2000 miles from the earth's surface, what will weigh at the surface?

400 x 1.52 900 lbs., Ans.

EXAMPLE. A body at the earth's surface weighs 360 lbs.; how high must it be elevated to weigh 40 lbs. ?

√360÷40=3, or 3 semi-diameters from the earth's surface, Ans. EXAMPLE.-At what height must a body be raised to lose half its weight?

√40002×2=5656-4000=1656 miles, Ans.

If the diameters of two globes be equal and their densities different, the weight of a body on their surfaces will be as their densities.

If their densities be equal and their diameters different, the weight of them will be as their diameters.

If the diameters and densities are both different, the weight will be as their products.

EXAMPLE. If a body weigh 10 lbs. at the surface of the earth, what will it weigh at the surface of the sun? their densities being 392 and 100, and their diameters 8000 and 883000 miles.

883000 × 100 × 10-8000 × 392-281.5 lbs., Ans.

SPECIFIC GRAVITIES.

THE specific gravity of a body is the proportion it bears to the weight of another body of known density, and water is well adapted for the standard; and as a cubic foot of it weighs 1000 ounces avoirdupois, its weight is taken as the unit, viz., 1000.

To find the Specific Gravity of a Body heavier than Water. RULE. Weigh it both in and out of water, and take the difference; then, as the weight lost in water is to the whole weight, so is 1000 to the specific gravity of the body.

EXAMPLE. What is the specific gravity of a stone which weighs 15 lbs., but in water only 10 lbs. ?

15-10-5. 5 15 1000: 3000, Ans.

When the Body is lighter than Water.

RULE.-Annex to it a piece of metal or stone, weigh the piece added and the compound mass separately, both in and out of water

find how much each loses in water by subtracting its weight in water from its weight in air, and subtract the less of these differences from the greater; then,

As the last remainder is to the weight of the light body in air, so is 1000 to the specific gravity of the body.

EXAMPLE. What is the specific gravity of a piece of wood that weighs 20 lbs. in air; annexed to it is a piece of metal that weighs 24 lbs. in air and 21 lbs. in water, and the two pieces in water weigh 8 lbs. ?

RULE. Take a body of known specific gravity, weigh it in and out of the fluid; then, as the weight of the body is to the loss of weight, so is the specific gravity of the body to that of the fluid. EXAMPLE. What is the specific gravity of a fluid in which a piece of copper (s. g. 9000) weighs 70 lbs. in, and 80 lbs. out of it? 80,80-70 :: 9000: 1125, Ans.

To find the Proportions of two Ingredients in a Compound, or to discover Adulteration in Metals.

RULE. Take the differences of each specific gravity of the ingredients and the specific gravity of the compound, then multiply the gravity of the one by the difference of the other; and, as the sum of the products is to the respective products, so is the specific gravity of the body to the proportions of the ingredients.

EXAMPLE. A body compounded of gold (s. g. 18.888) and silver (s. g. 10.535) has a specific gravity of 14; what is the proportion of each quantity of metal?

18.888-14-4.888 x 10.535 51.495 14.-10.535-3.465 x 18.888-65.447 65.447+51.495: 65.447 :: 14 : 7.835 gold,

65.447+51.495: 51.495:14:6.165 silver, Ans.

Proof of Spirituous Liquors.

A cubic inch of proof spirits weighs 234 grains; then, if an inch cube of any heavy body weigh 234 grains less in spirits than air, it shows that the spirit in which it was weighed is proof.

If it lose less of its weight, the spirit is above proof; and if it lose more, it is below proof.

The magnitude of a body in cubic feet multiplied by its specific gravity, in the following table, gives its weight in avoirdupois

ounces.

*Weight of a cubic foot, 258.3 grains.

† equal.0752914 lbs. avoirdupois.

APPLICATION OF THE ABOVE.

When the Weight of a Body is required.

RULE. Find the contents of the body in cubic feet or inches, anu

inultiply it by the factor in the table.

EXAMPLE.-What is the weight of a cube of Italian marble, the sides being 3 feet?

33×2708=73116 oz. 164569.7 lbs., Ans.

Or, of a 2 inch sphere of cast iron, 23×.5236×.260 weight of a cubic inch 1.089 lbs., Ans.

Comparative Weight of Timber in a Green and Seasoned State.

NOTE.-The average weight of the timber materials in a vessel of war (English) is about 50 lbs. to the cubic foot, and for masts and yards about 40 lbs.-Edye's N. C.

Given the Diameter of a Balloon to find what Weight it will raise. RULE. AS I cubic foot is to the specific difference between atmospheric air, and the gas used to inflate the balloon, so is the capacity of the balloon to the weight it will raise.

EXAMPLE.-The diameter of a balloon is 26.6 feet, and the gas used to inflate it is hydrogen; what weight will it raise?

Sp. gr. of air. Grains. Sp. gr. of hydr. Grains.

:

1.000 527.04.070 36.89 wt. of 1 cubic foot of hydrogen. Then 1: 527.04-36.89 :: 26.63×.5236: 4830293. grains, ÷7000 (grains in a lb.), 690.04 lbs., Ans.

Given the Weight to be raised to find the Diameter of a Balloon. By inversion of the preceding rule. The weight to be raised is 690.04 lbs.; what is the diameter?

490.15 (527.04—36.89) : 1 :: 69004×7000 : 9854.725 cubic feet,.5236, the cube root of the quotient, is 26.6 feet, Ans.