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ART. 84. AVOIRDUPOIS WEIGHT

Is used in weighing heavy articles; as, groceries, coarse metals and medicines at wholesale.

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NOTES.-1. The standard Avoirdupois pound of the United States is determined from the Troy pound, and contains 7000 grains Troy.

2. Formerly, 28 pounds were allowed for a quarter, 112 pounds for hundred weight, 2240 pounds for a tun; these, called the long kundred and long tun, are chiefly used at the Custom House.

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4. 3 T. 3 qr. to pounds.
5. 4 cwt. 1 qr. 19 lb. to pounds.
6. 5 T. 3 qr. 15 lb. to pounds.
7. 2 cwt. 3 qr. 2 lb. 12 oz. to ounces.
8. 2 cwt. 17 lb. 3 dr. to drams...

Ans. 10090 lb.

Ans. 4444 oz.
Ans. 55555 dr.

9. 1T. 6cwt. 4lb. 2 oz. 10 dr. to dr. Ans. 666666 dr.

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12. 2048000 dr. to tuns.

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13. 64546 dr. to cwt. Ans. 2cwt. 2qr. 2lb. 2 oz. 2 dr. 14. 97203 oz. to tuns.

Ans. 3T. 3qr. 3oz. 15. 544272 dr. to T. Ans. 1T. 1cwt. 1qr. 1 lb. 1 oz. 16. In 52 parcels of sugar, each containing 18 lb., how many hundred weight? Ans. 9 cwt. 1 qr. 11 lb.

REVIEW.-84. For what is Avoirdupois Weight used? Repeat the Table. NOTE 1. From what is the standard Avoirdupois pound determined? 2. What is the long hundred and long tun? Where used?

ART. 85. LONG OR LINEAR MEASURE:

Used in measuring lengths, breadths, thickness, &c.

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ALSO, 60 geographic, or 69 statute miles, make 1 degree. 360 degrees make a great circle, or circumference of the earth. 3 miles make 1 league, used in measuring distances at sea. 4 inches make 1 hand, used in measuring the height of horses 6 feet make 1 fathom, used in measuring the depth of water. NOTE.-The standard unit of length is the yard.

1. Reduce 2 yd. 2 ft. 7 in. to inches. 12. 7 yd. 11 in. to inches.

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Ans.

103 in.

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Ans. 263 in.

Ans. 3840 rd.

Ans. 2480 rd.

Ans. 2911 rd.

Ans. 3 yd. 2 ft. 1 in.

Ans. 5 yd. 1 in.
Ans. 7 mi.

Ans. 6 mi. 7 fur.

For examples involving Fractions, see page 170.

ART. 86. LAND OR SQUARE MEASURE

Is used in measuring land, or any thing in which both length and breadth are considered.

ART. 87. A figure having four equal sides, and four right angles (corners), is a square. Hence, A square inch is a square, each side of which is a linear inch; that is, 1 inch in length.

1 inch.

one

square

inch.

REVIEW.-85. For what is Long Measure used? Repeat the Tabie, NOTE. What is the standard unit of length?

3 feet.

A square foot is a square, each side of which is a linear foot. A square yard is a square, each side of which is a linear yard (3 feet).

one

sq. ft.

3 feet.

any

The figure shows that 1-square yard, that is, 3 feet square, contains 9 feet. square The number of small squares in large square, is equal to the number of units in one side of the large square multiplied by itself. Thus,

In a square figure, each side of which is 8 inches, there are 64 square inches: in 1 foot square, or 12 inches on each side, there are 12X12=144 square in.

ART. 88. By 3 inches square, we mean a square figure, each side 3 inches: but, 3 square inches are 3 small squares, each an inch long, and an inch wide; and,

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inches.

The difference between 4 in. square, and 4 square in., is 12 square inches; between 6 miles square, and 6 square miles, is 30 sq. miles.

TABLE.

3 in. square.

3 square in.

144 square inches make 1 square foot, marked sq. ft.

9

square feet
301 square yards

40 perches
4 roods

640 acres

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ALSO, 79 inches

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4 rods or 66 feet

80 chains

1

square yard,

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1 sq. rod or perch, .

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sq. yd. P.

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A.

sq. mi.

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mi.

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NOTE.-Land is measured with a surveyor's or Gunter's chain; it is 4 rods or 66 feet in length, and is divided into 100 links.

REVIEW.-86. For what is Land or Square Measure used? 87. What is a square? What is a square inch? A square foot? A square yard? To what is the number of small squares in a large square equal?

1. Reduce 8 sq. yd. to square inches. Ans. 10368 sq. in.

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Ans. 640 P. Ans. 102400 P. Ans. 3024 sq. in.

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ART. 89. A Rectangle is a figure having four sides nd four right angles. See the figure below.

The Area or Superficial content of a figure, is the nur zer of times it contains its unit of measure.

The unit of measure for surfaces, is a square whose ide is a linear unit, as a square inch, a square foot, &c.

1. How many square inches in a board 4 inches long and 3 inches wide?

SOL.-Dividing each of the longer sides into 4 equal parts, the shorter sides into 3 equal parts, and joining the opposite divisions by straight lines, the surface is divided into squares.

In each of the longer rows there are 4 squares, that is, as many as there are inches in the longer side; and there are as many such rows as there are inches in the shorter side. Hence,

The whole number of squares in the board is equal to the product obtained by multiplying together the numbers representing the length and breadth; that is, 4 X 3=12. Hence the

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RULE FOR FINDING THE AREA OF A RECTANGLE.-Multiply the length by the breadth: the product will be the superficial contents.

REVIEW. 88. What is meant by 3 inches square? By 3 sq. inches? What is the difference between 4 inches square, and 4 square inches? 89. What is a Rectangle? What is the Area of a figure? What is the unit of measure for surfaces?

NOTE-Both the length and breadth, if not in units of the same denomination, inust be made so, before multiplying.

2. In a floor 16 feet long and 12 feet wide, how many Ans. 192 sq. ft. square feet? 3. How many square yards of carpeting will cover a room 5 yds. long and 4 yds. wide? Ans. 20 sq. yd. 4. How many square yards of carpeting will cover two rooms, one 18 feet long and 12 feet wide, the other 21 feet long and 15 feet wide? Ans. 59 sq. yd.

5. How many square yards in a ceiling 18 feet long Ans. 28 sq. yd.

and 14 feet wide? 6. In a field 35 rods long and 32 rods wide, how many Ans. 7 A.

acres?

ART. 90. The Area of a Rectangle being equal to the product of the length by the breadth, and as the product of two numbers, divided by either of them, gives the other (Art. 37); therefore,

Rule.-If the area of a rectangle be divided by either side, the quotient will be the other side.

ILLUSTRATION-In Example 1, Art. 89, if the area, 12, be divided by 4, the quotient, 3, is the width; or, divide 12 by 3, the quotient, 4, is the length.

NOTE.-Dividing the area of a rectangle by one of its sides, is really dividing the number of squares in the rectangle by the number of squares

on one of its sides. Thus,

In dividing 12 by 4, the latter is not 4 linear inches, but the number of inches in a rectangle 4 in. long and 1 in. wide. See figure, Art. 89.

1. A floor containing 132 square feet, is 11 feet wide: what is its length?

Ans. 12 ft.

Ans. 15 ft.

2. A floor is 18 feet long, and contains 30 square yards: what is its width? 3. A field containing 9 acres, is 45 rods in length: what is its width? 4. A field 35 rods wide, contains 21 acres: what is its length?

Ans. 32 rd.

Ans. 96 rd.

REVIEW. 89. What is the Rule for finding the Area of a Rectangle? 90. The area and one side being given, how may the other side be found?

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