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Ans. $1799.05.

2. A note for $4200, given May 27, 1862, was payable on demand, with interest at 6 % annually; what was due on the note May 27, 1867, the following payments having been made: (Aug. 9, 1865,

Payments,

$50.72.

Jan. 27, 1867, 3000.00. Ans. $2500.48. 3. A note given for $5000, on demand, at 6 % annual interest, was dated January 1, 1860, and endorsed as follows:

July 1, 1860, $50.

66 1, 1861, 500.

July 1, 1865, $500.
66 1, 1866, 2500.

What remained due after the last payment was made?

Ans. $3703.62.

540. To COMPUTE INTEREST AT 7% %.

Multiply the principal by twice the number of days, and point off four places if the principal contains only dollars, six places if it contains cents..

EXAMPLES.

1. What is the simple interest of $100 for 12 days, at 7% %? Ans. $.24.

2. What is the simple interest of $300 for 9 days, at 73% %?

Ans. $.54.

1

THE METRIC SYSTEM OF WEIGHTS AND

MEASURES.

NOTE.--The Metric System of weights and measures was first adopted in France in 1795. A length supposed to be one ten millionth of a quadrant, or one forty millionth of a circumference of the earth measured over the poles, was taken as a provisional measure for the base of the system; this length was called a METER.

In order to ascertain more accurately the length of a quadrant, new measurements of the earth were subsequently instituted under the direc tion of eminent mathematicians, who measured the arc of a meridian between the parallels of Dunkirk and Barcelona. From their measurements, the length of the meter now in use was determined. This length was adopted as the base of the system, in 1799. The use of the metric system was not, however, legally enforced, to the exclusion of any other system, until January 1, 1840.

In Spain, Portugal, and Belgium, this system is also used exclusively, while in many other countries it is adopted wholly or in part. Among these are Holland, Italy, Greece, Austria, Switzerland, and Poland, in Europe, and Mexico, Chili, Venezuela, Brazil, Ecuador, Guatemala, San Salvador, and the Argentine Republic, on this continent.

Movements are also being made to adopt it in England, Germany, Sweden, and Norway. Its use in the United States was legalized by an act of Congress, passed in July, 1866.

Notwithstanding so much has been done to make the meter exactly one ten millionth of a quadrant, it is now thought to be too short by a small fraction, which is, however, less than one eight thousandth of itself. The length of the meter is nearly 39.37079 English inches, or 39.3685 United States inches; but for ordinary purposes, may be considered 39.37 inches.

541. The Metric System is so called from the METER, which is the base of all the weights and measures which it employs. The Meter is the primary unit of length, and equals about 39.37 inches, or nearly 3 ft. 3 in.

Upon the Meter are based the following primary units: the Square Meter, the unit of measure for small surfaces; the Are, the unit of land measure; the Cubic Meter, or Stere, the unit of volume; the Liter, the unit of capacity; and the Gram, the unit of weight.

From these primary units the higher and lower orders of units are derived decimally.

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542. The names of the higher orders of units are formed by prefixing to the name of the primary unit the following, from the Greek numerals:

Deka (10), Hecto (100), Kilo (1000), Myria (10000).

The names of the lower orders of units are formed by prefixing to the name of the primary unit the following, from the Latin numerals:

Deci (10th), Centi (100th), Milli (1000th).

Consequently, the word dekameter signifies ten meters; dekaliter, ten liters; hectometer, one hundred meters; hectogram, one hundred grams; kilometer, one thousand meters; myriameter, ten thousand meters, etc.

So, also, the word decimeter signifies the tenth part of a meter; centigram, the hundredth part of a gram; milliliter, the thousandth part of a liter, etc.

MEASURES OF LENGTH.

NOTE. In this table, and in those which follow, the name of the primary unit is designated by capitals, and the names of other important units by italics.

543. TABLE.

10 millimeters (mm) = 1 centimeter, marked (cm).

10 cen'timeters

10 dec'imeters

1 decimeter,

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(decím).

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10 METERS

1 dekameter,

66

dekam).

10 dek'ameters

1 hectometer,

66

(hm).

10 hec'tometers

1 kilometer,

66

(km).

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(myriam).

EXERCISES.

1. How many meters equal 1 dekameter? 1 hectometer?

1 kilometer? 1 myriameter?

2. How many dekameters equal 1 hectometer? 1 kilometer?

3. 1 meter equals how many decimeters? how many centimeters? how many millimeters?

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544. The outer diagram in the margin represents a measure 4 inches in length; the inner diagram represents a measure 1 decimeter or 10 centimeters in length.

These diagrams will enable the pupil to compare the units of length of the metric system with those in common use.

NOTE 1.-The new five-cent piece (of 1866) is 2 centimeters in diameter.

NOTE 2.25 millimeters, or 2 centimeters,
nearly equal 1 inch.

NOTE 3.5 meters are nearly equal to 1 rod.
NOTE 4. 1 kilometer is a little less than §

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545. The manner of writing the different orders of units of length is illustrated by the following

TABLE.

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1.

In writing numbers by the metric system, the decimal point is usually placed at the right of the figure denoting the primary unit; thus, the number 5 meters, 9 decimeters, is written 5.9m.

If in writing a number any intermediate orders of units are wanting, their places should be supplied by zeros; thus, 1 dekameter, 2 millimeters, is written 10.002m.

EXERCISES.

Write the following in figures:

1. Three dekameters, four meters.

2. Seven hectometers, three meters.

3. Three hectometers, one dekameter, five meters.

Ans. 34m.

Ans. 703.

4. Three kilometers, two hectometers, seven meters. 5. Nine myriameters, five hectometers.

6. Two meters, four decimeters.

7. Two meters, two centimeters, four millimeters.

Ans. 2.4m.

8. Five dekameters, two decimeters, eight centimeters.

546. When numbers are expressed by figures, the part of the expression at the left of the decimal point is usually read in the denomination of the primary unit; the part at the right of the decimal point may be read either as a decimal part of the unit, or in the denomination indicated by the place of the last figure. Thus, in reading the expression 34.62m, we may say either 34 and 62 hundredths meters, or 34 meters and 62 centimeters.

EXERCISES.

Read the following, giving the name of each order of units :— 1. 23m. 2. 25.1m. 3. 321.05m 4. 7137.008m.

5. Read the above in the denomination of the units as indicated by the abbreviation m.

6. Read the same, giving each decimal part the denomination indicated by the place of the last figure.

Since the metric system is a decimal system, a number expressed in units of one order may be reduced to units of another order by multiplying or dividing by ten, or some power

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