11. How much less will it cost to fence a field 72 rods square than a rectangular field 3 times as long and † as wide, if fencing cost $2.50 a rod ?

Ans. $480.

12. A mechanic having a lot of ground 50 rods square, planted 3 acres with corn, 200 square rods with vegetables, 15 rods square with flowers, and the remainder he kept to pasture his cow; how much of the lot was pasture?

Ans. 9 A. 155 P.

COST OF ARTIFICERS' WORK.

345. By Artificers' Work we mean plastering, painting, papering, paving, stone-cutting, etc.

346. Plastering, painting, papering, paving, and ceiling are estimated by the square foot or square yard. Roofing, flooring, partitioning, slating, etc., generally by the square, which consists of 100 square feet, but sometimes by the square foot or yard.

347. Shingles, which commonly measure 18in. by 4in. are estimated by the thousand or bundle. 1000 are gener

ally allowed to a square of 100 sq. ft.

WRITTEN EXERCISES.

1. What will be the expense of paving a sidewalk 303 ft. long and 7 ft. wide, at $2.25 per square yard?

SOLUTION.-The area equals 303×73, or 22724 sq. ft., which equals 252 sq. yd.; hence the cost is $2.25 × 2524, or $568.12}.

2. What will it cost to plaster a school-room 40 ft. long, 20 ft. wide, and 10 ft. high, at $0.36 a square yard?

Ans. $80.

3. What is the cost of wainscoting a room 28 ft. long by 15 ft. 4 in. wide, to a height of 4 ft. 3 in. at $0.45 per square yard? Ans. $18.41.

4. What is the cost of slating a roof 52 ft. 10 in. long, each side being 20 ft. wide, at $15.25 per square?

Ans. $322.284. 5. A frame house is 50 ft. long, 28 ft. wide, and 35 ft. high; what will be the expense of outside painting at $12.25

per square?

Ans. $668.85

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed

6. What will it cost to shingle a roof 64 ft. long and 32 feet from eaves to ridge, the first course along the eaves being double, at $14.87 a thousand ? Ans. $614.992.

7. What will it cost to paper a room 40 ft. long, 32 ft. 4 in. wide, and 15 ft. high, allowing 815 sq. ft. for doors, windows and washboards, at 25 per sq. ft.; ceiling not included? Ans. $356.83.

8. A cistern 7 ft. 5 in. long, 4 ft. 6 in. wide, and 6 ft. 3 in. deep, is to be lined with zinc costing 12 a pound, allowing 5 lb. to the square foot; what will be the expense? Ans. $109.40.

CARPETING AND PAPERING.

348. In Carpeting we take into consideration the width of the carpet, the allowance for matching the figures, and whether the strips run lengthwise or crosswise.

To match the figures we must often turn under or cut off one of the ends. When an exact number of strips is a little too wide for the room, one breadth is turned under.

Rule.-Find the number of strips required, and multiply the number of yards in each strip by the number of strips.

WRITTEN EXERCISES

1. How many yards of carpet, 1 yd. wide, will be required to carpet a floor 18 ft. 8 in. by 14 ft. 9 in., running lengthwise.

SOLUTION.-The room is nearly 5 yd. wide, hence it will require 5 strips, or breadths, each 183 ft. long; and it will take 18 ft. X5= 93 ft., or 31 yds.

2. A lady wishes to cover her sitting-room, 31 ft. long and 15 ft. wide, with matting 2 ft. wide, no allowance required for matching; how many yards will it take, running lengthwise? How many running crosswise? Ans. 62 yds.; 65 yds.

3. How many yards of Brussels carpet, yd. wide, will it take to carpet a parlor 26 ft. long by 15 ft. wide, the strips running lengthwise, the matching of figures requiring 6 in. to be cut of each strip except the first ?

Ans. 61 yds.

4. Miss Hartman wishes to carpet (lengthwise) a room 18 ft. long by 14 ft. 6 in. wide, with Brussels carpet of a yard wide, at $1.25 a yard; what will it cost, 2 yards waste for matching? Ans. $62.50.

SUPPLEMENTARY PROBLEMS,

To be omitted unless otherwise directed.

5. How many rolls of paper 8 yds. long and 20 in. wide, will cover the walls and ceiling of a room 30 ft. long, 22 ft. wide and 10 ft. 8 in. high, deducting 142 sq. ft. for openings? Ans. 418 rolls.

6. What will be the cost of papering the above room at $2.40 a roll, putting also a gilt moulding around the top of the walls, at 12 cents a foot? Ans. $111.78.

7. A room contained 3 windows, which were curtained with brocatelle of a yard wide; 10 yards were required for each window @ $1.50, and the curtains were lined with silk of a yard wide @ $.87; how many yards of silk were required, and what was the whole cost of the curtains? Ans. 24 yd.; $66.

MEASURES OF VOLUME.

349. A Volume is that which has length, breadth, and thickness or height. These three elements are called dimensions. A volume is also called a solid.

350. A Rectangular Volume or Solid is a volume bounded by six rectangles. The bounding rectangles are called faces. Cellars, boxes, rooms, etc., are examples of rectangular volumes.

3 feet high.

3 feet wide.

351. A Cube is a volume bounded by six equal squares. Or, a cube is a rectangular volume whose faces are all equal. 352. By the Contents or Solidity of a volume we mean the amount of space it contains. The contents are expressed by the number of times it contains a cube as a unit of meas

ure.

Rule I. To find the contents of a cube or rectangular volume, take the product of its length, breadth, and height.

For, in the volume above, the number of cubic units on the base equals the length multiplied by the breadth, or 3x3-9. and the whole number

of cubic units equals the number on the base multiplied by the numbe 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 H.-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 content, we multiply the length, breadth, and height together, and we have 18x14x 10-2520 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? 4. How many cubic inches in a rectangular block of marble 6 ft. long, 4 ft. wide, and 2 ft. thick? Ans. 103680.

Ans. 5 ft.

5. How many cubic yards of air in a room 25 ft. long, 12ft 6in. wide, and 9 ft. high? Ans. 10918 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 uave 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 diame ter 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 ane 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.