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7.

8.

of a cord to a decimal of a cu. yd.

of a cu. ft. to a decimal of a pch. 9. .73 of a cu. ft. to a decimal of a cd. 10. of 8 cd. to a decimal of 12 cd. 11. Find the sum of 12. How many North without any mortar?

pch., § cd., and 11 cd. ft. 38 cu. ft. River bricks make 1 cubic foot laid

13. A pile of wood containing 84 cd. 7 cd. ft. 12 cu. ft. was made into 5 equal piles; what was the size of each?

14. How many cords in a pile of wood 196 ft. long, 7 ft. 6 in. high, and 8 ft. wide?

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A Cord is a pile of wood, stone, etc., 8 ft. long, 4 ft. wide, and 4 ft. high.

A Cord Foot is 1 ft. long, 4 ft. wide, and 4 ft. high, or of cord, as shown in the cut.

15. What is the cost of a pile of stone 28 ft. long, 9 ft. wide, and 7 ft. high, at $3.85 per cord?

16. A load of wood containing 1 cord is 3 ft. 9 in. high and 4 ft. wide; what is its length?

17. How many perches of masonry will 18 cd. 5 cd. ft. of stone make, allowing 22 cu. ft. of stone for 1 perch of wall?

18. How many cords of stone will be required to enclose with a wall built without mortar a lot 28 rods long and 17 rods wide, the wall being 5 ft. high and 2 ft. 9 in. thick?

19. How many Philadelphia bricks in a cubic foot of wall 131⁄2 in. wide, laid in courses of mortar of an inch thick?

SOLUTION.-Since the mortar is of an inch thick, each brick in the wall is increased of an inch in length and in thickness. Hence the length occupied by a Philadelphia brick in the wall is 8 in. + in. 8 in., and the thickness is 28 in. + 4 in. = 2ğ in.

=

Again, since the wall is 13 in. wide, 3 bricks are placed side by side, and 131⁄2 in. ÷ 3 = 41⁄2 in. the width occupied by a brick in the wall.

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Hence, the volume occupied in the wall by a Philadelphia brick, with the given width of wall and thickness of mortar, is 8 in. × 2 × 41: 100.40625 cu. in. And since 1728 cu. in. equals 1 cu. ft., 1728÷100.40625 = 17.21 + the number of Philadelphia bricks in 1 cu. ft. of wall.

From this solution we obtain the following rule for finding the number of bricks of a given size in a given wall:

417. RULE.—Find the number of bricks of the given size in a cubic foot of the given wall. Multiply this number by the number of cubic feet in the wall.

20. How many Maine bricks will be required to build a house 54 feet long, 32 feet wide, and 25 feet high, the brick being laid in mortar of an inch thick, the wall being 11 in. wide, and 258 cu. ft. being allowed for doors and windows?

21. How many perches of stone laid dry will build a wall 9 ft. 6 in. high, 384 ft. long, and 2 ft. 9 in. thick?

22. What will it cost to remove an embankment 325 ft. long, 25 ft. wide, and 12.8 ft. high, at 58 cts. per cubic yard?

23. What is the cost of building a wall 89 ft. long, 28 ft. high, 19 in. wide, with brick 8 in. long, 41 in. wide, 23 in. thick, laid in mortar in. thick, at $12.85 a 1000 bricks laid in the wall?

24. What will be the cost of a pile of wood 114 yd. 2 ft. long, 4 ft. wide, and 6 ft. 8 in. high, at $4.50 per cord?

25. What will be the cost of removing the earth from the cellar of a house 48 ft. 9 in. by 32 ft., the cellar to be 9 ft. deep, at $.57 per load?

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2 feet vide.

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4 x 28 sq. ft. or 8 B. ft.

(2.)

4 feet long.

1. Diagram 1 represents a board where both dimensions are feet. Hence the product of the two dimensions gives the square feet in surface (405), or the number of board feet when the lumber is not more than 1 inch thick.

2. Diagram (2) represents a board where one dimension is feet and the other inches. It is evident (418) that a board 1 foot long, 1 inch thick, and any number of inches wide, contains as many board inches as there are inches in the width. Hence the number of square feet or board feet in a board 1 inch thick is equal to the length in feet multiplied by the width in inches divided by 12, the number of board inches in a board foot.

9 in. wide.

1 ft. by 9 in.

× 9=36 B. in.; 36 B. in.+12=3 B. ft.

3. In case the lumber is more than 1 inch thick, the number of board feet is equal to the number of square feet in the surface multiplied by the thickness.

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Find the contents of boards measuring

10. 15 ft. by 1 ft. 3 in.

11. 27 ft. by 1 ft. 6 in.

12. 19 ft. by 2 ft. 4 in.
13. 23 ft. by 1 ft. 5 in.

14. Find the contents of a board 18 ft. long and 9 in. wide. 15. How many board feet in a stick of square timber 48 ft. long, 9 inches by 14 inches.

16. Find the length of a stick of timber 8 in. by 10 in., which will contain 20 cu. ft.

OPERATION.—(1728 × 20)÷(8 × 10) = 432; 432÷12 = 36 ft., the length. 17. A piece of timber is 10 in. by 12 in. What length of it will contain 26 cubic feet?

Find the cost of the following:

18. Of 234 boards 14 ft. long 8 in. wide, at $3.25 per hundred. 19. Of 5 sticks of timber 27 ft. long, 9 in. by 14 in., at $1.75 per hundred feet board measure.

20. Of 84 plank 20 ft. long, 11 in. wide, 3 in. thick, at $1.84 per hundred feet board measure.

UNITS OF CAPACITY.

421. The Standard Units of capacity are the Gallon for Liquid, and the Bushel for Dry Measure.

TABLE OF UNITS.

4 gi. = 1 pt. 2 pt. = 1 qt. 4 qt. = 1 gal. 31 gal. 1 bbl.

=

LIQUID MEASURE.

1. Denominations.-Gills (gi.), Pints (pt.), Quarts (qt.), Gallons (gal.), Barrels (bbl.)

=

2. Equivalents.-1 gal. = 4 qt. = 8 pt.
32 gi.

3. Use.-Used in measuring liquids.
4. The capacity of cisterns, vats, etc., is

usually estimated by considering a barrel 31 gal.; but barrels are made of various sizes, from 30 to 56 gallons. The hogshead, butt, tierce, pipe, and tun are names of casks, and have usually their capacity in gallons marked upon them.

APOTHECARIES' FLUID MEASURE.

TABLE OF UNITS.

m 60 = ƒ 31 f38f31 f316 0.1

0. 8 = Cong. 1

1. Denominations.-Minims or drops (m), Fluid Drachm (f 3), Fluid Ounce (f 3 ), Pint (0., for octarius, the Latin for oneeighth or pint), Gallon (Cong., for congius, the Latin for gallon).

2. Equivalents. — Cong. 1 = 0. 8 = f3 128 = f3 1024 = m 61440.

3. Use.-Used in prescribing and compounding liquid medicine. 4. The symbols precede the numbers, as in Apothecaries' Weight, as shown in the table of units.

TABLE OF UNITS.

2 pt.

= 1 qt.

8 qt.1 pk. = 1 bu.

4 pk.

DRY MEASURE.

1. Denominations.-Pints (pt.), Quarts (qt.), Pecks (pk.), Bushels (bu.)..

2. Equivalents.—1 bu. = 4 pk. = 32 qt. =

64 pt.

3. Use.-Used in measuring grain, roots, fruits, salt, etc.

4. Heaped measure, in which the bushel is heaped in the form of a cone, is used in measuring potatoes, corn in the ear, coarse vegetables, large fruits, etc. Stricken measure is used in measuring grains, seeds, and small fruits.

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422. Solve and explain orally the following:

1. How many gills in 4 qt.? In 2 gal.? In 7 qt.? In

3 qt. 1 pt.? In 3 gal. 3 qt.?

2. How many pints in 2 bu. ?

2 pk. 7 qt.?

In 3 pk. 5 qt.? In 1 bu.

3. What is the sum of O. 5 f3 12 f37 and f38f33 m15? 4. Multiply 3 pk. 5 qt. 1 pt. by 3; by 5; by 10; by 7; by 12. Reduce

5. m 8465 to gallons.
6. 23649 pt. to bushels.
7.93584 pt. to barrels.

8. f3 7649 to gallons.
9. 57364 gi. to barrels.
10. 93654 pt. to bushels.

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