divided into quarter-sections. Hence, 640 acres make a section, and 160 acres a quarter-section. The quarter-sections are still further subdivided into half-quarter-sections, quarter-quarter-sections, and lots. Lots are often of irregular form on account of natural boundaries, but contain, as near as may be, a quarter-quarter-section.

NOTE. The pupil will remember that rods multiplied by rods give square rods, chains by chains give square chains; also, that 1 acre = 10 square chains or 160 square rods.

WRITTEN EXERCISES.

1. How many square rods in a grass plat 65 ft. long and 15 ft. wide?

SOLUTION.-The area equals 65×15, or 975 sq. ft.; reducing to square rods, we have 321 sq. rd.

2. How many acres in a rectangular meadow 725 rods long and 400 rods wide? Ans. 1812 A. 80 P.

3. What is the value of a farm 208.7 rods long and 120 rods wide, at $813 an acre? Ans. $12795.917. 4. Mr. A bought 64 A. 116 P. of land for $3.50 per square rod, and sold it for $3.75 per square rod; what did he gain? Ans. $2589.

5. A rectangular pond is 200 rd. 17 yd. long, and 150 rd. 15 yd. wide; required its area.

Ans. 193 A.

137 P. 15 sq. yd. 9.75 ch. wide; how Ans. 16 A. 14 P.

6. I have a field 16.5 ch. long and much land does it contain?

7. Mr. Wilson's farm contains 163 A. 3 ch., and its length is 71 ch.; how many rods of fence would be required to surround it? Ans. 752 rd.

8. If a township is equally divided among 480 families, how many acres does each receive, and what part of a section? Ans. 48 acres; of a section. 9. How many rails are required to fence a quarter-quarter-section, the fence being 5 rails high, and each rail 8 ft. long; and what will be the cost at $35 per thousand rails? Ans. 3300 rails; $115.50.

10. A field 80 rods long contains 15 acres, while another field of the same width contains 9 acres; what is the length of the latter field? Ans. 48 rods.

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 18 in. 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 303×72, or 2272 sq. ft., which equals 252 sq. yd.; hence the cost is $2.25×2522, or $568.123.

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?

5. A frame house is 50 ft. long, 28 ft.

Ans. $322.28. wide, and 35 ft.

high; what will be the expense of outside painting at $12.25

per square?

Ans. $668.85.

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 be the expense of papering a room 40 ft. long, 32 ft. 4 in. wide, and 15 ft. high, allowing 815 square feet for doors, windows, and washboards, at 25 per square foot; 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, PAPERING, ETC.

348. In Carpeting, Papering, etc., it is frequently necessary to find the quantity of material of a given width required to cover or line a given surface. We do this by the following

Rule. Divide the surface we wish to cover by the area contained in a yard of the material.

WRITTEN EXERCISES.

1. How many yards of carpeting, 1 yard wide, are required to cover a floor 18 ft. 8 in. by 15 ft. 9 in.?

SOLUTION.-18 ft. 8 in. equals 183 ft.; 15 ft. 9 in. equals 15& ft.; 183× 15 equals 294 sq. ft., which equals 323 sq. yd.; the area of 1 yard of the carpet is 1 sq. yd., and dividing 323 by 1 we have 323, the number of yards of carpet required.

2. How many sods, each 16 inches square, will be required to sod a grass plat 25 ft. long by 10 ft. 8 in. wide?

3. How many planks, 6 ft. long by 1 ft. require to floor a room 27 ft. long by 17 ft.

Ans. 150 sods.

6 in. wide, will it wide? Ans. 51 planks. yard wide; how

4. A lady bought 15 yd. of velvet of a much silk of a yard wide must she buy to line it?

Ans. 8 yd.

5. A housekeeper wishes to cover a floor 28 ft. long by 20 ft. 3 in. wide, with matting 4 ft. wide, at $1.28 a yard; what will be the cost?

Ans. $60.48.

6. Miss Hartman wishes to carpet a room 18 ft long by 15 ft. 6 in. wide, with Brussels carpet of a yard wide, at $1.25 a yard; what will it cost her? Ans. $62.

7. How many rolls of paper, 8 yards long and 20 inches wide, will be required to 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 windows and doors? Ans. 4118 rolls.

8. 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.

9. 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.

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 number 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 and 10 ft. high?

SOLUTION.-To find the content, we multiply the length, breadth, and height together, and we have 18×14×10=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 Lyd. 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 21⁄2 ft. thick? Ans. 103680.

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 of 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.