16. During how many seconds must a body fall in a vacuum to acquire a velocity of 1970 feet, which is that of a cannonball?

17. What time is required for a body to fall in a vacuum, from an elevation of 3280 feet?

18. From what height must a body fall to acquire a veocity of 984 feet?

19. A rocket is projected vertically upward with a velocity of 386 feet after what time will it begin to fall, and to what height will it rise?

454. The SPECIFIC GRAVITY of a body is the weight of a unit of volume compared with the weight of a unit of the standard. Distilled rain-water is the standard for measuring the specific gravity of bodies. Thus, 1 cubic foot of distilled rainwater weighs 1000 ounces avoirdupois. If a piece of stone, of the same volume, weighs 2500 ounces, its specific gravity is 2.5; that is, the stone is 2.5 times as heavy as water.

If, then, we denote the standard by 1, the specific gravity of all other bodies will be expressed in terms of this standard; and if we multiply the number denoting the specific gravity of any body by 1000, the product will be the weight in ounces of 1 cubic foot of that body.

If any body be weighed in air and then in water, it will weigh less in water than in air. The difference of the weights will be equal to the sustaining force of the water, which is found to be equal to the weight of an equal volume of water: hence,

Rule. If we know or can find the weight of a body in air and in water, the difference of these weights will be equal to that of an equal volume of water; and the weight of the body in air divided by this difference will be the measure of the specific gravity of the body, compared with water as a standard.

times as heavy as water; gold, 19 times as heavy; iron, 71 times as heavy, &c.

Examples illustrating Specific Gravity.

1. A piece of copper weighs 93 grains in air, and 821 grains in water what is its specific gravity?

2. How many cubic feet are there in 2240 pounds of dry oak, of which the specific gravity is .925, a cubic foot of andard water weighing 1000 ounces?

3. A piece of pumice-stone weighs in air 50 ounces, and when it is connected with a piece of copper which weighs 390 ounces in air, and 345 ounces in water, the compound weighs 344 ounces in water: what is the specific gravity of the stone?

4. A right prism of ice, the length of whose base is 20.45 yards, breadth 15.75 yards, and height 10.5 yards, floats on the sea; the specific gravity of the ice is .930, and that of the sea-water 1.026: what is the height of the prism above the surface of the water?

5. A vessel in a dock was found to displace 6043 cubic feet of water: what was the weight of the vessel, each cubic foot of the water weighing 63 pounds?

6. A piece of glass was found to weigh in the air 33 ounces, and in the water 21 ounces: what was its specific gravity?

7. A piece of zinc weighed in the air 17 pounds, and lost when weighed in water 2.35 pounds: what was its specific gravity?

8. If a piece of glass weighed in water loses 318 ounces of its weight, and weighed in alcohol loses 250 ounces, what is the specific gravity of the alcohol?

9. A flask filled with distilled water weighed 14 ounces; filled with brandy, it weighed 13.25 ounces; the flask itself weighed 8 ounces: what was the specific gravity of the brandy?

10. What is the weight of a cubic foot of statuary marble, of which the specific gravity is 2.837, the cubic foot of water weighing 1000 ounces?

11. A jar containing air weighed 24 ounces 33 grains; the air was then excluded, and the jar weighed 24 ounces; the jar being then filled with oxygen gas, weighed 24 ounces 36.4 grains what was the specific gravity of the oxygen, the air being taken as the standard?

MARIOTTE'S LAW.

455. This law, which relates to air and all other gases, steam ad all other vapors, was discovered by the Abbé Mariotto, a French philosopher, who died in 1684. It will be easily understood from a particular example.

Suppose an upright cylindrical vessel in a vacuum contains gas which is confined in the vessel by a piston at the upper end. Suppose the gas or vapor fills the whole vessel, and the piston is loaded with a weight of 5 pounds. If now, the piston be loaded with a weight of 10 pounds, the gas will be compressed and occupy only half its former space. If the weight be increased to 15 pounds, the gas will have only onethird of its original volume, and so on. At the same time, the density of the gas or vapor will be doubled, made three times as great, and so on. The law, therefore, may be thus stated:

Rule. The temperature remaining the same, the volume of a gas or vapor is inversely proportional to the pressure which it sustains. Also, the density of a gas or vapor is directly proportional to the pressure.

Examples.

1. A vase contains 4.3 quarts of air, the pressure being 10 pounds what will be the volume of the air when the pressure is 12.3 pounds, the temperature remaining the same?

2. Under a pressure of 15 pounds to the square inch, a certain quantity of gas occupies a volume of 20 quarts: what pressure must be applied to reduce the volume to 8 quarts?

3. A quart of air weighs 2.6 grains under a pressure of 15 pounds what will be the weight of a quart, if the pressure be reduced to 14.2 pounds?

4. The pressure upon the steam contained in a cylinder is increased from 25 pounds upon the square inch to 47 pounds: what part of the original volume will be occupied ?

APPENDIX.

DIFFERENT KINDS OF UNITS.

I. ABSTRACT UNITS.

456. THE ABSTRACT UNIT 1 is the base of all numbers, and is called a unit of the first order. The unit 1 ten, is a unit of the second order; the unit 1 hundred, is a unit of the third order; and so for units of the higher orders. These are abstract numbers formed from the unit 1, according to the scale of tens. All abstract integral numbers are collections of the unit one.

II. UNITS OF CURRENCY.

457. In all civilized and commercial countries, great care is taken to fix a standard value for money, which standard is called the Unit of Currency.

In the United States, the unit of currency is 1 dollar; in Great Britain it is 1 pound sterling, equal to $4.84; in France it is 1 franc, equal to 18% cents nearly. All sums of money are expressed in the unit of currency, or in units derived from the unit of currency, and having fixed proportions to it.

III. UNITS OF LENGTH.

458. One of the most important units of measure is that for distances, or for the measurement of length. A practical want has ever been felt of some fixed and invariable standard, with which all distances may be compared: such fixed standard has been sought for in nature.

There are two natural standards, either of which affords this desired natural element. Upon one of them, the English have founded their system of measures, from which ours is taken ; and upon the other, the French have based their system.