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.

By inspecting this Table, we see the weight of each body compared with an equal volume of water. Thus, platina is 21 times as heavy as water; gold, 19 times as heavy; iron, 71⁄2 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 standard 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 prism of ice having 6 rectangular faces, and of which the height is 20.45 yards, the breadth 15.75 yards, and the 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?

12. A cylindrical vase having a base whose interior diameter is 4 inches, stands upon a horizontal plane: 26.2 pounds of mercury is poured into the vase. Required the height to which the liquid will rise, the specific gravity of mercury being 13.596.

13. A piece of alabaster weighs in the air 7.55 grains, in the water 5.17 grains, and in another liquid 6.35 grains what is the specific gravity of the alabaster and of the liquid?

14. What effort will be required to prevent a cubic inch of platinum, immersed in mercury, from sinking, the specific gravity of the platinum being 21.5, and that of the mercury 13.6?

15. What weight of mercury will a conical vase contain of which the radius of the base is 9 inches and the altitude 34 inches, the specific gravity of the mercury being 13.596?

MARIOTTE'S LAW.

390. This law, which relates to air and all other gases, steam, and all other vapors, was discovered by the abbé Mariotte, 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 a 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 ist 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 one-third 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:

390. To what is the volume of a vapor or gas proportional? To what is its density proportional?

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 ?

5. How will the density of the steam in the last example, at the second pressure, compare with that at the first?

6. Eight quarts of hydrogen gas are contained in a vessel and submitted to a pressure of 22 pounds: how many quarts of gas will there be if the pressure is changed 9 pounds?

APPENDIX.

DIFFERENT KINDS OF UNITS.

391. THERE are eight kinds of units;

1st. Abstract Units;

2d. Units of Currency or Coin;

3d. Linear Units, or Units of Length;

4th. Units of Surface, or Superficial Units;

5th. Units of Volume, including Cubic Units and Gallons; 6th. Units of Weight;

7th. Units of Time; and

8th. Units of Circular or Angular Measure.

ABSTRACT UNITS.

392. 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 numbers are formed from collections of these units.

UNITS OF CURRENCY.

393. 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 183 cents. 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.

391. How many kinds of units are there in Arithmetic? Name them. 392. What is said of the abstract unit 1 ? What is a unit of the 2d order? What of the 3d

formed from 1 ?

4th 5th? &c.

How are these numbers