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APPENDIX.

THE METRIC SYSTEM

OF WEIGHTS AND MEASURES.

NOTE TO TEACHER.-The Metric System may be omitted by classos w how time for arithmetic is limited, at the option of the teacher.

INTRODUCTION.

The old system of weights and measures in our country is irregular, difficult to learn, and inconvenient to apply. The same is true with the old systems of all nations. Originating by chance, rather than by science, they lacked the simplicity of law; and were, therefore, irregular and chaotic.

In 1795, France adopted a system of weights and measures called the Metric System, based upon the decimal method of notation, all the divisions and multiples being by 10. It was regarded as so great an improvement upon the old methods that it has since been introduced into Spain, Belgium, Portugal, Switzerland, Holland, Italy, Germany, Austria, Sweden, Denmark, Greece, Mexico, Brazil, and by most of the South American States, and in the most of these countries its use is compulsory. In 1864, the British Parliament passed an act permitting its use throughout the empire whenever parties should agree to use it.

The introduction of the Metric System into this country had been long recommended by scientific men, and by such statesman as Madison, Jefferson, John Quincy Adams, etc. In 1866, through the influence of Charles Sumner, Congress authorized its use in the United States, and provided for its introduction into the post-offices for the weighing of letters and papers. To facilitate its adoption, a convenient standard of comparison was furnished, by making the new five-cent piece five grams in weight and one fiftieth of a meter, or two centimeters, in diameter. This system will, without doubt, in a few years be in general use in this country.

The advantages of the Metric System are numerous and important. 1. It is easily learned; a school-boy can learn it in a single afternoon.

2. It is easily applied, all the operations being the same as in simple Qumbers.

3. It does away with addition, subtraction, multiplication, division, and reduction of compound numbers.

4. It will facilitate commerce, giving the nations a universal system of weights and measures.

785. The Metric System of weights and measures is based upon the decimal system of notation.

786. In this system we first establish the unit of each measure, and then derive the other denominations by taking decimal multiples and divisions of the unit.

787. Names. - We first name the unit of any measure and then derive the other denominations by adding prefixes to the unit name.

788. The higher denominations are expressed by prefixing to the name of the unit Deca,

Hecto, Kilo, Myria.
10
100

1000 10,000 The lower denominations are expressed by prefixing to the name of unit Deci, Centi,

Milli.
1
1

1
10
100

1000 789. Units.—The following are the different units, with their English pronunciation. Unit. Pronunciation.

Pronundation, LENGTH, Meter, (meter.) CAPACITY, Liter, (leeter.) SURFACE Are, (air.) WEIGHT, Gram, (gram.) VOLUME Stere, (stair.) VALUE, Dollar,

Measure.

Measure.

Unit.

MEASURE OF LENGTH. 790. The Meter is the unit of length. It is the ten millionth part of the distance from the equator to the poles, and equals 39.37 inches, or 3.28 feet.

TABLE.

10 millimeters (mm.) equal 1 centimeter, 10 centimeters

1 decimeter, 10 decimeters

1 meter, 10 meters

1 decameter, 10 decameters

1 hectometer, 10 hectometers

1 kilometer, 10 kilometers

1 myriameter,

cm. dm. M. DM. HM. км. M.

NOTES.–1. The meat is very nearly 3 feet 3 inches and 3 eighths of an Inch in length, which may be easily remembered as the rule of three threes.

2. Cloth, etc., are measured by the meter; very small distances, by the millimeter; great distances, by the kilometer.

3. The 5 cent piece of 1866 is very nearly all of a meter in diameter ; hence its diameter is about $ of a decimeter, or 2 centimeters. It was ordered to be of a meter in diameter, but owing to the composition of the alloy it was necessary to make its diameter a little greater; 48.6 nickel 5 cent pieces laid side by side measure one meter.

4. A decimeter is about 4 inches : a kilometer, about 200 rods, or $ of a mile; a millimeter, about # of an inch. The inch is about 24 centimeters; the foot, 3 decimeters ; the rod, 5 meters; the mile, 1600 meters, or 16 hectometers.

MENTAL EXERCISES. 1. How many centimeters in a meter? 2. How many millimeters in a meter? 3. How many decimeters in a decameter ? 4. How many meters in a hectometer? 5. How many meters in a kilometer?

MEASURES OF SURFACE. 791. The Are is the unit of surface used to measure land. The are is a square decameter. It equals 119.6 sq. yd., or 0.0247 acre.

TABLE.

1 are,

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10 milliares (ma.) equal 1 centiare, ca.
10 centiares

1 deciare, da.
10 deciares

A. 10 ares

1 decare, DA. 10 decares

1 hectare, HA. 10 hectares

1 kilare, KA. 10 kilares

1 myriare, MA. NOTES.-1. The are, centiure, and hectare, are the denominations princh dpally used, as these are exact squares. The centiare is a square whose de 18 1 meter; the hectare is a square whose side is 100 meters. The are a 100 square meters. The centiare = 1 square meter,

The hectare 10,000 square meters. 2. The deciare is not a square, it is merely the tenth of an are; the decar is not a square, It is merely ten ares.

3. A hectare equals nearly 21 acres ; a centiare equals Dearly 1} sq. yd. An acre is very nearly 40 ares.

MEASURES OF OTHER SURFACES. 792. All surfaces besides land are measured by the square meter, square decimeter, etc. The measures are shown by the following table :

TABLE

100 sq. millimeters (mm.2) 1 sq. centimeter, cm. 100 sq. centimeters = 1 sq. decimeter, dm. 2 100 sq. decimeters

= 1 sq. meter, NOTE.—The measures higber tban these are not generally used. The usual method of notation is to write sq. before the denomination ; but I suggest as an abhreviation that we indicate the square by an exponents

M.2

MENTAL EXERCISES, 1. How many centiares in an are? 2. How many ares in a hectare? 3. How many square meters in an are ? 4. How many square decimeters in an are ? 5. How many ares in 640 square meters?

MEASURES OF VOLUME. 793. The Stere is the unit of volume. It is a cubio meter, and equals 35.3166 cubic ft., or 1.308 cu. yd.

TABLE.

CS.

10 millisteres (ms.) equal 1 centistere,
10 centisteres

1 decistere, ds.
10 decisteres

1 stere,

8. 10 steres

1 decastere, DS. 10 decasteres

1 hectostere, HS. 10 hectosteres

1 kilostere, KS. 10 kilosteres

1 myriastere, MS. NOTz.—Wood 18 measured by this measure. The stere, decistere, and decastere are principally used. 3.6 steres, or 36 decisteres, very nearly equal the common cord.

MEASURES OF OTHER VOLUMES. 794. Other solid bodies are doually measured by the cubic meter and its divisions. The measures are shown by the following table:

TABLE.

1000 cubic millimeters (mm.8) =cubic centimeter, cm. 1000 cubic centimeters

=l cubic decimeter, dm. 1000 cubic decimeters

=l cubic meter,

M.:

NOTE.—The higher denominations are not generally used. I indicato the cubic measures with an exponent, instead of writing cu, before the denominations.

MENTAL EXERCISES. 1. How many centisteres in a stere? 2. How many decisteres in a decastere? 3. How many decasteres in a kilostere ? 4. How many cubic meters in a hectostere ?

MEASURES OF CAPACITY. 795. The Liter is the unit of capacity. It equals a cubic decimeter ; that is, a cubic vessel whose size is onetenth of a meter.

796. This measure is used for measuring liquids and dry substances. The liter is a cylinder, and holds 2.1135 pints wine measure, or 1.816 pints dry measure.

TABLE.
10 milliliters (ml.) equal 1 centiliter, cl.
10 centiliters

1 deciliter, dl.
10 deciliters

1 liter,

L. 10 liters

1 decaliter, DL. 10 decaliters

1 hectoliter, HL. 10 hectoliters

1 kiloliter, KL. 10 kiloliters

1 myrialiter, ML. Notes.-1. The liter is principally used in measuring liquids, and the hectoliter in measuring grains, etc.

2. The liter equals nearly 1f liquid quarts, or A of a dry quart, or nearly so of a bushel measure.

3. The hectoliter is about 20 bushels, or of a barrel. 4 liters are a little more than a gallon ; 35 liters, very nearly a bushel.

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MENTAL EXERCISES. 1. How many liters in a hectoliter ? 2. How many liters in a kiloliter ? 3. How many deciliters in a decaliter ? 4. How many liters in a cubic meter? 5. How many liters in a stere?

Ano. 1000.
Ano. 1000.

MEASURES OF WEIGHT. 797. The Gram is the unit of weight. It is the weight of a cabic centimeter of distilled water at the temperature of melting ice. The gram equals 15.432 Troy grains.

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