4. In 54m. 66cha. how many chains?
5. In 75m. 49cha. how many poles?
6. How many miles in 24196 poles?
7. How many links in 7m. 4fur. 30rd.?
8. How many miles in 60750 links?

SQUARE MEASURE.

ART. 93. Square Measure is used in measuring surfaces of

S. M.

R.

A.

1=

1= 4

S. M.

in. 144

1296

=

40

301 = 1210=

2721 = 10890=

39204

1568160

160= 4840 = 43560 1=640 = 2560 = 102400 309760027878400 =

= 4014489600

NOTE.A square is a figure bounded by four equal lines, perpendicular to each other.

When the four lines are each 1 foot in length, the space enclosed is 1 square foot; when 1 yard in length, 1 square yard; when 1 rod in length, 1 square rod; and so for any other dimension.

3ft. lyd.

3ft.= lyd.

Square
foot.

In this diagram the large square represents a square yard, and each of the smaller squares within it represents one square foot. Now, since there are three rows of small squares, and three square feet in each row, there will be 3 times 3: 9 sq. ft. in the large square. But the large square is 3ft. in length, and 3ft. in breadth; hence,

=

To find the contents of a square, multiply its length by its breadth.

For what is square measure used? Repeat the What is a square foot? How may the contents of a square be found? Explain by the diagram the reason of the operation.

table. What is a square?

MENTAL EXERCISES.

1. In 2 square feet how many square inches?

2. In 3 square yards how many square feet? In 10 sq. yd.? 3. In 5 roods how many poles? In 20 roods? In 30 roods? 4. In 7 acres how many roods? In 24 acres? In 40 acres? EXERCISES FOR THE SLATE.

1. How many square inches in 12A. 3R. 24p. 144ft. 72in.?

NOTE.

many inches?

1089) 2248272 fourths of a foot.

40) 2064 poles. 576÷4=144ft.
4)51 R. 24p.

Ans. 12 A. 3R. 24p. 144ft. 72in.

To divide by the 2724, we first reduce the divisor and dividend to fourths, and then divide. The remainder obtained, being fourths, is reduced to whole numbers by dividing by 4.

Give the reason

What is the

QUESTIONS.-How do you reduce acres to square inches? for the operation. How do you reduce square inches to acres? reason for the operation? How do you multiply by ?

3. In 49A. 3R. 16p. how many square feet? 4. In 2171466 square feet how many acres?

5. What is the value of 365A. 3R. 17p. at $1.75 per square rod or pole? Ans. $102,439.75. 6. Sold a valuable piece of land, containing 3A. 1R. 30p., at $1.25 per square foot; what was received for the land?

Ans. $187,171.87,5.

7. In a tract of land 12 miles square, how many square miles? How many acres? Ans. 92160 acres.

8. In 18A. OR. 16p. how many square feet?

Ans. 788436 square feet. 9. Purchased 48A. 3R. 14p. of land for $2.25 per square rod, and sold the same for $3.15 per square rod; what did I gain by my bargain? Ans. $7032.60.

CUBIC OR SOLID MEASURE.

ART. 94. Cubic or Solid Measure is used in measuring such bodies or things as have length, breadth, and thickness; as timber, stone, &c.

NOTE 1.

T.

1

1728

1

27

=

46656

31

122/2

113
429

40

69120

128

221184

1

A pile of wood 8ft. in length, 4ft. in breadth, and 4ft. in height, contains a cord.

100

Also, one ton of timber, as usually surveyed, contains 5092 cubic or solid feet.

QUESTIONS. How do you divide by 272? Of what denomination is the remainder? How is the true remainder found?- Art. 94. For what is cubic measure used? Recite the table. What are the dimensions of a pile of wood containing 1 cord? How many solid feet does a ton of timber contain, as usually surveyed?

NOTE 2.-A cube is a solid bounded by six square and equal sides.

If the cube is 1 foot long, 1 foot wide, and 1 foot high, it is called a cubic or solid foot. If the cube is 3 feet long, 3 feet wide, and 3 feet thick, it is called a cubic or solid yard.

Now, since each side of a cubic yard, as represented in the diagram, contains 9 sq. ft. of surface (Art. 93), it is plain, if a block be cut off from one side, one foot thick, it can be divided into 9 solid blocks, with sides 1 foot in length, breadth, and thickness, and therefore will contain 9 solid feet; and since the whole block or cube is three feet thick, it must contain 3 times 927 feet; for 3ft. X 3ft. X

To find the contents of a cubic or solid body, multiply its length, breadth, and thickness together.

MENTAL EXERCISES.

1. In 2 cubic feet how many cubic inches?
2. In 3 cubic yards how many cubic feet?
3. How many cords of wood in 64 cord feet?
4. How many tons in 80 cu. ft. of timber?
EXERCISES FOR THE SLATE.

1. In 48 cu. yd. and 15 cu. ft. how many cubic inches?

OPERATION.

In 4 cu. ft.? In 10 cu. yd.? In 96 c. ft.? In 160 cu. ft.?

2. In 2265408 cubic inches how many cubic yards?

OPERATION.

1728) 2265 408 cu. in.

48 yd. 15ft.

27

341

97

1311 feet.

1728

10488

2622

9177

1311

27) 1311 cu. ft.

Ans. 48 yd. 15ft.

QUESTIONS. -What is a cube? How do you find the contents of a cube? Give the reason for the operation. Describe a cubic foot. How do you reduce a ton to cubic inches? Give the reason for the operation. How do you reduce cubic inches to cubic yards? Give the reason for the operation.

3. In 45 cords of wood how many cubic inches?

4. In 9953280 cubic inches how many cords of wood? 5. How many cubic feet in a pile of wood 15ft. long, 4ft. wide, and 6ft. high? How many cords? Ans. 3C. 6 cu. ft. 6. How many cubic inches in a block of marble 4ft. long 31ft. wide, and 2ft. thick? Ans. 44928. 7. In a room 14ft. long, 12ft. wide, and 8ft. high, how many cubic feet? Ans. 1344. 8. What will 9080 cubic feet of ship-timber cost, at $11.50 per ton? Ans. $2610.50

WINE OR LIQUID MEASURE.

ART. 95. Wine or Liquid Measure is used in measuring all kinds of liquids, except, in some places, beer, ale, porter, and milk.

In

1 = 2 = 4

NOTE 1. By laws of Massachusetts, 32 gallons make 1 barrel. some states 31 gallons, and in others from 28 to 32 gallons, make 1 barrel. 42 gallons make 1 tierce, and 2 tierces, 1 puncheon.

NOTE 2. The term hogshead is often applied to any large cask that may contain from 50 to 120 gallons, or more.

NOTE 3.-The Standard Unit of Liquid Measure adopted by the government of the United States is the Winchester Wine Gallon, which contains 231 cubic inches. It has the name Winchester, from its standard having been formerly kept at Winchester, England. The Imperial Gallon, now adopted in Great Britain, contains 277 27 cubic inches; so that 6 Winchester gallons make about 5 Imperial gallons.

QUESTIONS. Art. 95. For what is wine or liquid measure used? Repeat the table. How many gallons make a barrel? How many a tierce? How many a puncheon? How is the term hogshead often applied? What is the standard unit of liquid measure?