SOLUTION. Since there are 5 yards in 1 rod, there are in 2 rods 2 times 5 yards; 2 times 5 yards are 10 yards, and 2 times a yard are 1 yard; 10 yards and 1 yard are 11 yards. Therefore, etc.

7. In 30 feet how many yards? In 45 feet? 8. How many square yards in 2 square rods? rods?

9. In 54 cubic feet how many cubic yards?

In 48 feet?

In 3 square

10. In 10 gallons, how many quarts? In 15 gallons? 11. How many rods in 11 yards? In 22 yards?

SOLUTION. Since there is in 5 yards, or in 11 half yards, 1 rod, there are as many rods in 11 yards, or 22 half yards, as 11 half yards are contained times in 22 half yards, which are 2. Therefore, etc.

12. How many minutes in 3 degrees? In 5 degrees? 13. How many quarts in 7 pecks? In 10 pecks? In 12 pecks?

14. How many square rods in of an acre? In of an acre? In of an acre?

of an

SOLUTION. Since in 1 acre there are 160 square rods, in acre there must be of 160 square rods, or 40 square rods; and if 1 fourth is 40 square rods, 3 fourths must be 3 times 40 square rods, or 120 square rods. Therefore, etc.

15. How many minutes in In of an hour? In of

of an hour? In of an hour? an hour?

16. How many pounds in of a bushel of wheat? In of a bushel of corn? In 3 of a barrel of beef?

17. What part of a furlong are 5 rods? Of a pound Troy are 8 ounces? Of a cubic yard are 18 cubic feet?

SOLUTION. Since 1 furlong is 40 rods, 5 rods are of a furlong. Therefore, etc.

18. What part of a hogshead are 15 gallons? Of a bushel are 24 quarts? Of a day are 18 hours?

19. What part of an acre are 120 rods? Of a bushel of wheat are 48 pounds? Of a barrel of beef are 60 pounds?

REVIEW QUESTIONS. What is Arithmetical Analysis? (75) What is a Rule? (11) What is a Formula? (69) What is a Solution? (10) An OpAn Answer? (9)

eration? (8)

METRIC WEIGHTS AND MEASURES.*

231. The Metric System of weights and measures, authorized by Congress in 1866 to be used in the United States, is formed according to the decimal scale.

The LOWER DENOMINATIONS are expressed by prefixing to the unit name of a measure Milli, .001; Centi, .01; Deci, .1. The HIGHER DENOMINATIONS by prefixing Deka, 10; Hecto, 100; Kilo, 1000; Myria, 10000.

MEASURES OF LENGTH.

232. The Meter, the principal unit for the measure of length, is very nearly one ten-millionth of the distance on the earth's surface from the equator to the poles.

1

12

14

16

17

18

Centimeters.

4

Inches.

The meter is used as the unit of measure for all common lengths and distances. It is equal to 39.37 inches, or about 3 feet 3 inches. The kilometer is taken as the unit in measuring long distances, as the length of roads, distances between cities, etc. It is equal to 3280 feet 10 inches, or about 200 rods, or § of a mile.

The myriameter is equal to 6.2137 miles.

25 millimeters nearly replace the inch; 3 decimeters, the foot; 5 meters, the rod; and 1600 meters, the mile.

How is the Metric System formed? How are the Lower Denominations of each weight or measure expressed? The Higher Denominations? To what is the Meter equal? Repeat the Table. About how much is a Meter? * This and the next 6 pages are optional.

MEASURES OF SURFACE.

233. The Square Meter, the principal unit for the measur of surface, is the square whose side is one meter.

Since the side of a square meter is 1 meter, or 10 decimeters, a square meter is equal to 10 X 10 = 100 square decimeters; since the side of a square decimeter is 1 decimeter, or 10 centimeters, a square decimeter is equal to 10 × 10 = 100 square centimeters, etc. Hence, The scale is 100, and two orders of figures must be allowed to each denomination.

234. The Are, the principal unit in measuring land, is a square whose side is ten meters.

Table,

100 centiares are (ca.)

100 ares,

1 ARE (a.), equal to 119.6 sq. yd.
1 hectare (H&.),
2.471 acres.

A centiare, or square meter, is about 1 square yards, and a hectare about 2 acres.

40 ares nearly replace an acre of common surface measure.

MEASURES OF VOLUME.

235. The Cubic Meter, the principal unit for the measure of volume, is the cube, whose edge is one meter.

Table.

1000 cu. millimeters (cu. mm.), are 1 cu. centimeter(cu.cm.),—.061 cu. in.

Since the edge of a cubic meter is 1 meter, or 10 decimeters, a cubic meter is equal to 10 X 10 X 10 = 1000 cubic decimeters; since the edge of a cubic decimeter is one decimeter, or 10 centimeters, a cubic decimeter is equal to 10 X 10 X 10 = 1000 cubic centimeters, etc. Hence,

The scale is 1000, and three orders of figures must be allowed to each denomination.

236.

The Liter, the principal unit for liquid or dry measure,

is a cubic decimeter.

Table.

10 milliliters

10 centiliters,

10 deciliters,

10 liters,

10 dekaliters,

10 hectoliters,

are 1 centiliter (L), equal to .338 fluid oz.

The liter is used in measuring liquids, and is about 1

.845 gill.

1.0567 quarts.

2.6417 gallons,

26.417 gallons,

264.17 gallons.

liquid quart.

The hectoliter is used in measuring grains and like articles, and is 2.837 bushels, or about 2ğ bushels, or of a barrel; a liter is very nearly .908 of a dry quart.

4 liters a little more than replace the liquid gallon, and 35 liters very nearly the common bushel.

A milliliter is equal to 1 cubic centimeter; a centiliter is equal to 10 cubic centimeters.

237.

The Stere, the principal unit for measuring wood, is 2 cubic meter, or 1000 liters.

Table.

1 dekastere,

10 decisteres are 1 STERE (st.), equal to 1.308 cubic yards. 10 steres, 13.08 cubic yards. 36 decisteres, or 3.6 steres, very nearly replace the common cord.

The com

What is the Liter? Repeat the Table. For what is the liter used? About how much is a liter? For what is a hectoliter used? About how much is a hectoliter? What nearly replaces the liquid gallon? mon bushel? What is the Stere? Repeat the Table. replaces the common cord?

What very nearly

WEIGHTS.

238. The Gram, the principal unit of weights, is the weight, in a vacuum, of a cubic centimeter of distilled water, at its greatest density.

The kilogram, or, for brevity, kilo, is the ordinary weight of commerce. It is about 21⁄2 pounds.

The tonneau (pronounced tonno), or metric ton, is used in weighing heavy articles, and is about 2200 pounds.

The gram is used in mixing medicines, weighing letters, gold, jewels, etc. 28 grams nearly replace an avoirdupois ounce; and ↓ kilo, a little more than a pound.

239. In expressing Metric Weights and Measures, by figures, the decimal point, as in United States Money, is placed between the unit, and its subdivisions written as decimal orders.

One, two, or three orders of figures must be allowed to each denomination lower than the unit, according as the scale is 10, 100, or 1000.

Thus,

3 kiloliters, 7 hectoliters, 2 dekaliters, 5 liters, 6 centiliters, is writ ten, as liters, 3725.06 lt.

4 cubic meters, 630 cubic centimeters, as cubic meters, 4.00063 m2. 240. The integer of a metrical expression may be read as a number of its primary unit; and the decimal part, if any, as a number of the lowest denomination denoted. Thus,

What is the Gram? Repeat the Table. What is the kilogram called for brevity? About how much is a kilo? A tonneau ? What very nearly replaces the avoirdupois ounce? The pound? How is the decimal point placed?