of cubic units equals the number on the base multiplied by the numbes of layers of these cubes, or 9x3=27; hence the whole number of cubes, or the contents, equals the product of the length, breadth, and height.

Rule II.-To find either dimension, divide the contents by the product of the other two dimensions.

WRITTEN EXERCISES.

1. What are the contents of a room 18 ft. long, 14 ft. wide nd 10 ft. high?

SOLUTION. To find the contents, we multiply the length, breadth, and height together, and we have 18x14x10-2520 cu. ft.; reducing this to cubic yards, we have 93 cu. yd. 9 cu. ft.

2. What are the solid contents of a cube whose edge measures 1 yd. 1 ft.? Ans. 2 cu. yd. 10 cu. ft. 3. A cistern 9 ft. square contains 405 cubic feet; what is its depth? Ans. 5 ft. 4. How many cubic inches in a rectangular block of marble 6 ft. long, 4 ft. wide, and 2 ft. thick? Ans. 103680.

5. How many cubic yards of air in a room 25 ft. long, 12ft 6 in. wide, and 9 ft. high? Ans. 10910 cu. yd.

6. A pile of bricks contains 125 cubic yards, and is 13 ft. 6 in. wide, and 8 ft. 4 in. high; what is its length? Ans. 30 ft. 7. How much earth will be dug out of a cellar 72 ft. long, 48 ft. wide, and 7 ft. 3 in. deep? Ans. 928 cu. yd.

THE CYLINDER.

353. A Cylinder is a round body of uniform size, with equal and parallel circles for its ends. The two circular ends are called bases.

354. The Altitude of a cylinder is the distance from the centre of one base to the centre f the other.

355. The Convex Surface of a cylinder is the surface of the curved part.

Rule I.-To find the convex surface of a cylinder, mul tiply the circumference of the base by the altitude.

Rule II.-To find the contents of a cylinder, multiply the area of the base by the altitude.

WRITTEN EXERCISES.

1. What is the convex surface of a cylinder, the diameter of whose base is 8 inches and whose altitude is 12 inches?

SOLUTION. The circumference of the base equals 8x3.1416, which is 25.1328 inches; multiplying by the altitude, 12, we have 301.5936 square inches, the convex surface.

2. I have a log 18 ft. long and 20 inches in diameter; how many square feet of bark on the log? Ans. 94.248 sq. ft. 3. A well is 10 feet deep, and 3 feet in diameter; how many cubic feet does it contain? Ans. 70.686 cu. ft.

4. What is the cost of digging a well 15 ft. deep and 9 ft. in circumference, at $.62 a cubic yard? Ans. $2.24-.

5. How much zinc will it take to line the sides of a cistern

8 ft. in diameter and 84 feet deep? Ans. 23.0384 sq. yd.

6. Dr. Hiestand put in his house a cistern, 10 ft. in diameter and 4 ft. 6 in. high; how many cubic feet of water did it hold? Ans. 353.43 cu. ft.

WOOD MEASURE.

356. The Measure of Wood is the cord, which is divided into cord feet, etc.

357. A Cord of wood is a pile 8 feet long, 4 feet wide, and 4 feet high. It contains 8 cord feet, or 128 cubic feet. 358. A Cord Foot

is a part of this pile 1 foot long. It is thus

1 foot long, 4 feet wide, and 4 feet high, and contains 16 cubic feet.

Rule. To find the number of cords in a pile of wood, find the number of cubic feet and reduce to cord feet and cords.

WRITTEN EXERCISES.

1. How many cords in a pile of wood 28 ft. long, 10 ft. high, and 10 ft. wide?

SOLUTION.-The number of cubic feet equals 28x10x10, which equals 2800; dividing by 16, to reduce this to cord feet, we have 175 cord feet; dividing by 8 to reduce this to cords, we have 21 cd. 7 cd. ft.

2. How many cords in a pile of wood 96 ft. long, 12 ft wide, and 8 ft. high? Ans. 72 cords. 3. A load of wood containing exactly 1 cord, is 5 ft. 4 in. wide, and 3 ft. 9 in. high; what is its length? Ans. 6 ft. 4. What is the height of a pile of wood containing 27 cords, if it is 75 ft. long and 10 ft. wide? Ans. 4.736 ft.

5. What will be the cost of the wood that can be piled in a shed 20 ft. long, 10 ft. wide, and 8 ft. high, at $4.75 a cord? Ans. $59.37.

BOARDS AND TIMBER.

359. Boards and Timber are usually estimated in what are called board feet, instead of in cubic feet.

360. A Board Foot is 1 foot long, 1 foot wide, and 1 inch thick. A cubic foot, therefore, contains 12 board feet. Hence, board feet may be reduced to cubic feet by dividing by 12, and cubic feet to board feet by multiplying by 12.

A standard board, in commerce, is 1 inch thick, and its contents in board feet are the product of its length and breadth in feet. Board feet are usually known as square feet. Boards are quoted by the hundred or the thousand, meaning a hundred square feet, or a thousand square feet. Round timber, as masts, etc., is estimated in cubic feet; hewn timber, as beams, etc., either in board or cubic feet; lumber and sawed timber, as planks, scantling, joists, etc., in board feet.

Rule I. To find the contents of a board, multiply the length in feet by the width in inches, and divide the product by 12.

Rule II. To find the contents of a plank, joist, etc., multiply the length in feet by the width and thickness in inches, and divide the product by 12.

NOTES.-1. If one of the dimensions is inches and the other two are feet, the product will be board feet.

2. When a board tapers regularly, the length must be multiplied by the mean width, which is half the sum of the two ends.

WRITTEN EXERCISES.

1. What are the contents of a board 14 feet long and 9 inches wide?

SOLUTION. Multiplying the length in feet by the width in inches, we have 14×9-126; and dividing by 12, we have 10 board feet, or square feet.

2. What are the contents of a board 16 feet long and 1 ft. wide? Ans. 24 sq. ft.

3. Required the contents of a board 20 ft. long, the ends being 18 and 14 inches respectively.

4. How many square feet in 14 inches wide, and 4 inches thick?

Ans. 26 sq. ft. planks 16 ft. long, 18 Ans. 1344 sq. ft.

5. How many square feet in a stick of timber 40 feet long,

14 inches wide, and 9 inches thick?

6. What must be the width of a board

it may contain 9 square feet?

Ans. 420 sq. ft.

6 ft. 4 in. long that

Ans. 18 inches.

7. How many square feet of inch boards will it require to make an enclosed box 3 ft. by 2 ft. 6 in. and 18 in. high on the outside, allowing for the overlapping of the boards? Ans. 293 sq. ft.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

8. What is the cost of 40 boards 12 ft. long, 15 in. wide, at $2.75 per hundred square feet?

Ans. $16.50.

9. What is the cost of 9 pieces of scantling 4 in. by 5 in. and 10 ft. long at $8.75 per thousand square feet? Ans. $1.314.

10. What is the cost of flooring a three-story house, the floors being 56 ft. by 32 ft. and the plank 14 inches thick, at $33 per thousand ? Ans. $266.112.

11. I wish to fence a field 36 rd. long and 18 rd. wide, the posts to be set 9 ft. apart, the boards to be 18 ft. long, and 11 inches wide, the fence being 3 boards high; the posts cost $30 per C, and the boards $15.50 per M, and it required 2 men 3 days, at $3.50 each a day, to build the fence; required the number of posts, the amount of lum. ber, and the whole cost. Ans. 198 posts; 4900 sq. ft.; $156.357.

MASONRY, BRICKWORK, ETC.

361. Masonry is usually estimated by the perch and the cubic foot; sometimes by the square foot or the square yard.

362. A Perch of stone or of masonry is 16 ft. long, 12ft. wide, and 1 ft. high; it contains 24 cubic feet, but when stone is built into a wall, 22 cubic feet 23 cu. ft. being allowed for mortar and filling.

make a perch,

363. Excavations and Embankments are estimated by the cubic yard. A cubic yard of earth is called a load.

364. Brickwork is generally estimated by the thousand bricks, but sometimes in cubic feet.

In estimating labor, bricklayers and masons measure the length of the wall on the outside. The corners are thus measured twice, but this is considered an allowance for the greater difficulty of building them. No allowance is made for windows and doors, except by special contract, in which case it is customary to allow one-half the space actually required. In estimating material, allowance is made for doors, windows and corners.

The average size of bricks is 8 in. x4x2, but Phila. and Baltimore bricks are 8 in. x 4×23; Maine bricks, 7 in. x33x23; North River bricks, 8 in. ×3×2; and Milwaukee bricks, 8 in. x 4×23.

To build one square foot of wall 1 brick or 4 inches thick, requires 7 common bricks; 2 bricks, or 9 in. thick, 14 bricks; 3 bricks, or 13 in. thick, 21 bricks. In practice, the thickness of the wall is regarded as the same for each kind of brick.

Rule I. To find the number of perches in a piece of masonry, divide the number of cubic feet by 243.

Rule II. To find the number of common bricks required for a wall or building, multiply the number of square feet in the wall by 7, if the wall is 1 brick thick; by 14, if 2 bricks thick; by 21, if 3 bricks thick.

The following is a general rule for all kinds of brick:-To find the number of any kind of bricks required for a wall, or building, add

of an inch to the length and the thickness of the brick, divide 144 by the product of these two sums to find the number of bricks in a square foot of wall 1 brick thick, and multiply by the number of bricks in the thickness, and this product by the number of square feet in the wall.

NOTE.-An old rule was-Deduct of the solid contents for the mortar, and divide the remainder by the contents of one brick. We may also find the contents of a brick with the mortar surrounding it, and divide a cubic Foot by this quantity, to find the number of bricks in a cubic foot.

WRITTEN EXERCISES.

1. How many perches of masonry in a wall 60 ft. long, 4 ft. 6 in. high, and 15 inches thick?

SOLUTION.-Multiplying the length, breadth, and height together, we have 60×4×14, or 337 cu. ft., which, divided by 24, the number of cubic feet in a perch, equals 13 perches.