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3 ft. = 1 yd.

27

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 I 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.

Since each side of a yard, as represented in the diagram (Art. 93), contains 9 sq. ft. of surface, it is plain, that 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 9 solid feet X 3 3 ft. = 1 yd.

solid feet; or 3 solid feet X 3 X 3

27 solid feet. Hence, To find the contents of a cubic body, multiply together the numbers denoting the length, breadth, and thickness.

MENTAL EXERCISES. 1. In 2,cubic feet how many cubic inches ? In 4 cu. ft. ? 2. In 3 cubic yards how many cubic feet? In 10 cu. yd. ? 3. How many cords of wood in 64 cord feet? In 96 c. ft. ? 4. How many tons in 80 cu. ft. of timber? In 160 cu. ft. ?

EXERCISES FOR THE SLATE. 1. In 48 cu. yd. and 15 cu. 2. In 2265108 cubic inches ft. how many cubic inches ? how many cubic yards ?

OPERATION.

48 yd. 15ft. 1728) 2 2 6 5 4 0 8 cu. in. 27

27)1311 cu. ft. 341

Ans. 48 yd. 15ft. 97 1 311 feet. 17 2 8 10 488

2 6 2 2 9177

1 311 Ans. 2 2 6 5 408 inches.

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OPERATION.

94. What is a cube? How do you find the contents of a cube? The reason for the operation. Describe a cubic foot. How do you reduce a ton to cubic inches? The reason for the operation. How do you reduce cubic inches to cubic yards? 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 64ft. high? How many cords? Ans. 30. 6 cu. ft.

6. How many cubic inches in a block of marble 4ft. long 3{ft. 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

Ans. $ 2610.50.

per ton ?

WINE OR LIQUID MEASURE.

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

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Note 1.- In some States 314 gallons, and others from 28 to 32 gal. lons, 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 277-2074 cubic inches ; so that 6 Winchester gallons make about 5 Imperial gallons.

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

many tuns ?

OPERATION.

63

MENTAL EXERCISES. 1. In 3 pints how many gills ? In 5 pints? In 9 pints ? 2. In 4 quarts how many pints? In 6 quarts? In 8 quarts ? 3. In 5 gallons how many quarts? In 7 gallons ? 4. How many gallons in 12 quarts? In 18 quarts ?

EXERCISES FOR THE SLATE: 1. In 47 tuns of wine how 2. In 379008 gills how many gills ?

OPBRATION.
47 tuns.

4) 3 7 9 0 0 8 gi.
4

2) 947 52 pt. 18 8 hogsheads.

4) 4 7 3 7 6 qto

63)118 44 gal.
5 64
11 28

4) 188 hhd.

Ans. 47 tuns. 118 4 4 gallons.

4
47 3 7 6 quarts.

2
9 4 7 5 2 pints.

4
Ans. 3 7 9008 gills.
3. Reduce 197 tuns 3hhd. 60gal. 3qu. 1pt. to gills.
4. In 1596604 gills how many tuns ?
5. What will 7 hogsheads of wine cost, at 5 cents a pint?

6. What cost 18 tuns 1hhd. 47gal. of oil, at $ 1.25 per gallon?

Ans. $ 5807.50. BEER MEASURE. 96. Beer Measure is used in measuring beer, ale, porter, and milk.

TABLE. 2 Pints (pt.)

make 1 Quart, 4 Quarts

1 Gallon, 54 Gallons

1 Hogshead,

hhd. qt.

pt. 1

2 1 4

8 54 216

432

66

qt. gal.

66

gal.

bhd.

1

96. Repeat the table of beer measuro.

Note 1. -- The gallon of beer measure contains 282 cubic inches; and as has been usually reckoned, 36 gallons equal i barrel; hogsheads, or 108 gallons, 1 butt; 2 butts, or 216 gallons, 1 tun. 1 gallon beer measure

Igall. 1pt. 3-4 gi. wine measure. NOTE 2. — Beer Measure is becoming obsolete. Milk and malt liquors, at the present time, are bought and sold, generally, by wine or liquid measure.

OPERATION.

EXERCISES FOR THE SLATE. 1. How many quarts in 76 2. In 16416 quarts how hogsheads ?

many hogsheads ?
OPERATION.
7 6 hhd.

4) 16 41 6 qt.
54

5 4 ) 41 0 4 gal. 304

Ans. 7 6 hhd. 380

410 4 gallons.

4
Ans. 1 6 41 6 quarts.

3. In 4 tuns 1hhd. 17gal. 1pt. how many pints ?
4. How many tuns in 7481 pints ?
5. What cost 7hhd. 18gal. of beer at 4 cents a quart?

Ans. $ 63.36. 6. At 15 cents per gallon, what will 18hhds. of ale cost?

Ans. $ 145.80. DRY MEASURE.

97. Dry Measure is used in measuring grain, fruit, salt, coal, &c.

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96. How many cubic inches does the beer gallon contain? How do you reduce hogsheads to quarts? Quarts to hogsheads ? -97. For what is dry measure used ? Repeat the table.

192 cubic

Note 1.- The Standard Unit of Dry Measure adopted by the United States government is the Winchester bushel, which is in form a cylinder, 18} inches in diameter, and 8 inches deep, containing, 2150140 cubic inches. The Standurd Imperial Bushel of Great Britain contains 221811 inches, so that 32 Imperial bushels equal about 33 Winchester bushels. The gallon in Dry Measure contains 2685 cubic inches.

Note. 2. — Igal. Dry Measure 268cu. in. Igal. 1pt. 13%gi. Wine Measure 3qt. 1233pt. Beer Measure ; Igal. W. M. = 231cu. in. 3qt. jpt. D. M. 3qt. pt. B. M.; Igal. B. M. 282cu. in. Igal. Ipt. 3-gi. W. M. Igal. Apt. D. M.; Iqt. D. M. = 67{cu. in. Iqt. išgi. W. M. ; Iqt. W. M. 57fcu. in. 13 pt. D. M.; Ipt. D M. 33fcu. in. 1pt. 1gi. W. M.; Ipt. W. M.

28]cu. in. fpt. D. M. MENTAL EXERCISES. 1. In 2 quarts how many pints? In 5 quarts? In 7 quarts ? 2. In 3 pecks how many quarts? In 6 pecks? In 9 pecks? 3. In 5 bushels how many pecks ? In 10 bushels ? 4. How many pecks in 16 quarts? In 25 quarts ?

EXERCISES FOR THE SLATE. 1. How many quarts in

2. In 56731 quarts how 49ch. 8bu. 3pk. and 3qt. ?

many chaldrons ?

OPERATION.

OPERATION.

49 ch. 8bu. 3pk. 3qt. 8) 5 6 7 3 1 qt.
36

4) 70 9 1 pk. 3qt.
3 0 2

3 6 ) 1 7 7 2 bu. 3pk.
147

49 ch. 8bu.
177 2 bushels.
4

Ans. 49ch. 8bu. 3pk. 3qt.
70 91 pecks.

8 Ans. 5 6 7 3 1 quarts.

3. Reduce 97ch. 30bu. 2pk. to quarts. 4. In 112720 quarts how many chaldrons ? 5. How many pints in 35bu. 1 pt. ? 6. Reduce 2241 pints to bushels. 7. Reduce 18qr. 3pk. 5qt. to quarts. 8. How many quarters in 4637 quarts ? 9. In 19bu. 3pk. 7qt. 1pt. how many pints? 10. In 1279 pints how many bushels ?

97. What is the standard unit of Dry Measure ?

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