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of ten. If the number is written in figures, it is only necessary to remove the decimal point to the right of the figure indicating the required order, and give the expression its proper abbreviation; thus, 59.36m may be reduced to 5.936dekam,.5936hm, .05936km, .005936myriam, 593.6decim, 5936.cm, 59360..

547. EXAMPLES.

1. Express 5.24 meters as centimeters. 2. Express 37.2 meters as kilometers.

3. Express 12 hectometers as meters.

4. Express 25 millimeters as meters.

Ans. 524cm.

Ans. .0372km

Ans. 1200m.

5. In 518 meters how many decimeters? how meters? how many millimeters?

Ans. .025m.

many centi

6. In 3687 metres how many dekameters? how many hectometers? how many kilometers?

7. Express in meters the following, and add them: 4075 centimeters, 27 dekameters, .075 kilometers. Ans. 385.75m. 8. Express in kilometers the following, and add them: 2400 meters, 500 dekameters, .79 myriameters. Ans. 15.3km.

9. If 7.08 kilometers are taken from 42 kilometers, how many meters will remain? Ans. 34,920. 10. The distance round a certain park is 2.58 kilometers; how many meters will a man go who rides around it six times? Ans. 15,480m.

11. A schoolboy walked one third around the above park in 12 minutes; how many meters did he walk in 1 minute?

Ans. 71.66m+.

many kilometers Ans. 4666.66m+.

12. The latitude of Chicago is 42° N.; how is it from Chicago to the equator?

MEASURES OF SURFACE.

548. In the measurement of small surfaces the Square Meter is the primary unit.

Each side of a square meter is 10 decimeters in length, and hence a square meter contains 10 X 10, =100, square deciEach side of a square decimeter is 10 centimeters in

meters.

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100,

length, and hence a square decimeter contains 10 × 10, = square centimeters, etc. Thus it may be seen that while measures of length increase and decrease by a scale of tens, measures of surface increase and decrease by a scale of hundreds.

Since the values of units of surface increase and decrease by a scale of hundreds, it is necessary, in writing numbers denoting surfaces, to allow two places for sq. decimeters, two for sq. centimeters, and two for sq. millimeters: thus,

4 sq. meters, 8 sq. decimeters, are written 4.08sqm.

In what places at the right of the decimal point are sq. decimeters written? sq. centimeters? sq. millimeters?

EXAMPLES.

1. Express the following numbers in sq. meters and add them: 5 sq. decimeters, 87 sq. meters, 26 sq. centimeters, 5.9 sq. Ans. 92.9526sqm.

meters.

2. How many sq. meters are there in a rectangular court 5 meters long and 22 meters wide?

Ans. 110sq m

3. What is the cost of polishing the surface of a rectangular piece of marble 2 meters 8 decimeters long, and 1 meter 2 decimeters wide, at $2.50 per sq. meter? Ans. $8.40.

549. We have seen that the meter and its subdivisions are used to measure small surfaces; but to measure surfaces of great extent, as a field, a township, etc., the Are is the primary unit. The Are is a square whose side is 10 meters and whose surface contains 100 square meters.

In land measure, centares, ares, and hectares only are used.

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NOTE. The are equals 119.6 square yards, nearly 4 square rods, or about of an acre. The hectare equals about 2 acres.

TABLE.

100 cen'tares (ca) = 1 ARE,

100 ĀRES

66 = 1 hectare

marked (ar).
(ha).

550. The following table shows the method of writing numbers in land measure, also the relation of the units to the square meter and its subdivisions.

TABLE.

01 010101

EXAMPLES.

1. Express the following in ares and add them: 1.3 hectares, 155.5 ares, 43 hectares, 26 centares. Ans. 4585.76ar.

2. Mr. Jenks owned 25 hectares, 32 ares, 16 centares of land, and afterwards bought 36 hectares, 5 ares, 8 centares; how many ares did he then have? Ans. 6137.24ar.

3. A had 6 hectares, 7 ares, 9 centares of land, and sold † of it at $54 an are; how many dollars did he receive for what he sold? Ans. $5960.52.

MEASURES OF VOLUME.

551. In the measurement of solids, the Cubic Meter is the primary unit.

Each edge of a cubic meter is 10 decimeters in length, and hence a cubic meter contains 10 X 10 X 10,= 1000, cubic decimeters. Each edge of a cubic decimeter is 10 centimeters in length, and hence a cubic decimeter contains 10 X 10 X 10, 1000, cubic centimeters, etc.

Thus it may be seen that while measures of length increase and decrease by a scale of tens, measures of volume increase and decrease by a scale of thousands. Hence, in writing numbers denoting volume, three places must be allowed for cu. decimeters, three for cu. centimeters, and three for cu. millimeters. In what places at the right of the decimal point are cu. decimeters written? cu. centimeters? cu. millimeters?

EXAMPLES.

1. Express the following numbers in cu. meters and add them: 58.5 cubic meters, 1.7 decimeters. Ans. 58.5017cu m

2. How many cu. meters in a cube whose edge is 2.7 meters? Ans. 19.683cu

m

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3. How many cubic meters of air will a room contain whose length is 5.2 meters, whose breadth is 4 meters, and whose height is 35 decimeters? Ans. 72.8cu m

552. For measuring firewood, stone, etc., the Stere is the primary unit. Dekasteres and decisteres are also used. The stere is a cubic meter, or 1.308 cubic yards, and is a little more than of a cord.

TABLE.

10 dec'isteres (ds) = 1 STERE,

10 STERES

marked (").
(dekas).

66 = 1 dekastere

The method of writing numbers in wood measure is the same as that of writing numbers in measures of length. (Art. 545.) EXAMPLES.

1. How many steres will a pile of wood contain that is 1 meter long, 1 meter wide, and 1 meter high? 2 meters high? 2. What part of a stere will a pile of wood contain that is 1 meter long, 1 meter wide, and 1 decimeter high?

3. How many steres in a pile of stone that is 1 meter wide, 8.24 meters long, and 4 decimeters high? Ans. 3.296'.

4. What must be the height of a pile of wood 2.5 meters long and 1 meter wide, to contain a stere?

MEASURES OF CAPACITY.

Ans. 4decim

553. In measuring liquids, as milk, and dry articles, as beans, barley, and salt, the Liter is the primary unit.

The Liter is 1 cubic decimeter, and contains .908 of a quart dry measure, or 1.0567 quarts liquid measure.

TABLE.

10 milliliters (ml) = 1 centiliter, marked (d).

10 cen'tiliters

= 1 deciliter,

66

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(decil).
(1).

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(dekal).

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(hl).

= 1 kiloliter,

66

(*1).

NOTE 1.
NOTE 2.

-

-

A kiloliter has the same capacity as a stere, or cu. meter.
A hectoliter equals about 25 bushels.

Numbers denoting capacity are written in the same manner as numbers denoting length. (Art. 545.)

EXAMPLES.

1. Express the following numbers as liters and add them: 458 centiliters, 82 dekaliters, 765 milliliters. Ans. 825.3451.

2. From a vessel containing 1 hectoliter of oil were drawn 25 liters, 6 centiliters; how many liters remained? Ans. 74.94'. 3. How many liters of wheat can be put into a bin that is 2 meters long, 1.3 meters wide, and 1.5 meters high? 4. What must be the length of a bin that is 1 and 1 meter high, to contain 4000 liters of grain?

MEASURES OF WEIGHT.

Ans. 3900!. meters wide

554. The Gram is the primary unit of weight.

Ans. 2.5m.

The Gram is the weight, in a vacuum, of a cubic centimeter of distilled water at the temperature when it is most dense, which is at 394° Fahrenheit.

NOTE 1.-The gram equals 15.432 grains.

NOTE 2. The new five-cent piece (of 1866) weighs 5 grams.

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The kilogram, sometimes called the kilo, is considered the unit in weighing gross, heavy articles. The kilogram equals about 2 pounds avoirdupois, or, more nearly, 2.2046 pounds. The tonneau equals a little more than 2204 pounds.

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