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. EXAMPLES FOR PRACTICE. 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 32 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 $81 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. 16 A. 14 P. 9.75 ch. wide; how 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 surround it? SUPPLEMENTARY EXAMPLES. To be omitted unless otherwise directed. be required to Ans. 752 rd. 8. If a township is equally divided among 480 families, how many acres does each family receive, and what part of a section does each re ceive? Ans. 48 acres; of a section. 9. How many rails are required to fence a quarter-quarter-section, the fence being 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 ihan 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. EXAMPLES FOR PRACTICE. 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 303×71, or 2272 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? 5. A frame house is 50 ft. long, 28 ft. Ans. $322.28. wide, and 35 ft. hign; what will be the expense of outside painting at $12.25 Der square? Ans. $668.85. SUPPLEMENTARY EXAMPLES. 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 be the expense of papering a rcom 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, the ceiling not included? Ans. $356.831. 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 124 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. EXAMPLES FOR PRACTICE. 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 183 ft.\5=93} ft., or 31 yds. 2. A lady wishes to cover her sitting-room, 31 ft. long and 15 ft. wide, with matting 23 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 off each strip except the first? Ans. 613 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 yd. waste in matching? Ans. $62.50. SUPPLEMENTARY EXAMPLES. To be omitted unless otherwise directed. 5. How many rolls of paper, 8 yd. long and 20 in. wide, will cover the walls and ceiling of a room 30 ft. long, 22 ft. wide and 10 ft. high, deducting 142 sq. ft. for doors and windows? Ans. 4118. 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 number of layers of these cubes, or 9×327; 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. EXAMPLES FOR PRACTICE. 1. What are the contents of a room 18 ft. long, 14 ft. wide and 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. 109103 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, multiply 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. |