COMPOUND NUMBERS. 3. A pile of wood 4 feet wide, and 4 feet high, and 8 feet long contains 1 cord; and a cord foot is 1 foot in length of such a pile, thus: 4. A perch of stone or masonry is 16 feet long, 14 feet wide, and 1 foot high, and contains 24 cubic feet. 5. A brick is usually 8 inches long, 4 inches wide, and 2 inches thick, hence 27 bricks make a cubic foot. 6. Joiners, painters and masons make no allowance for windows, doors, &c. Masons make no allowance for the corners of the walls of houses or of cellars. The size of a cellar is estimated by the measurement of the outside of the wall. 7. Round timber when squared is estimated to lose one-fifth; hence a ton of round timber is said to contain only 40 cubic feet. 269. How many cords of wood in 37846 cubic feet? QUESTIONS.-How may every cubic solid be separated? ANS.-Into tiers. How may each tier be separated? ANS.- Into rows of cubes. How may each row be sepa rated? ANS.-Into cubes. [The teacher should with small cubes show the pupils the different shaped piles into which they may be placed. He should also show that the length of the side of a square or edge of a cube simply shows the number of squares or cubes that can be placed in one row across the square or pile.] LESSON XXXVI. PRACTICAL PROBLEMS. How many loads of earth must be removed to dig a cellar 40 feet long 18 feet wide and 9 feet deep? Anal. Steps.—1. Find the cu. ft. in 18 rows or 1 tier of cu. ft. 2. Find the cu. ft. in 9 tiers of cu. ft. 3. Find the number of loads. 274. How many loads of earth must be removed in digging a cellar 37 by 60 ft., 8 feet deep? 275. What will it cost to dig a cellar 27 by 60 ft., 10 ft. deep, at 75 cts. per load? 276. How many cubic feet in a bin 8 ft. long, 3 ft. wide, and 4 ft. deep? 277. Making no allowance for thickness of boards, how many square feet of boards will it take to make a box and cover, 15 ft. long 8 ft. wide and 4 ft. high? 278. How many cubic feet of stone in a wall 37 ft. long, 3 ft. high, and 2 ft. thick? 4 279. How many cubic feet of stone are required in the walls of a cellar 37 ft. long, 16 ft. wide, 5 ft. high, and 2 ft. thick? 280. How many perches of stone are required in the walls of a cellar 37 ft. long, 18 ft. wide, 6 ft. high, and 3 ft. thick? 281. How many bricks in a wall, 37 ft. long, 8 ft. high, and 2 ft. thick? 282. What will the brick cost to build a wall 37 ft. long, 6 ft. high, 8 ft. thick, at $3.30 per hundred ? 283. I am to build a house the walls of which are as follows: REVIEW.-What dimensions has a line? (83.) What has space? (84.) What has a surface? (86.) What has a solid? (87.) What is the use of Long Measure? (88.) Recite the table. (88., a.) The front wall 50 ft. high and 30 wide; the rear 40 ft. high and 30 wide; the two side walls each 50 by 120 ft. What will the brick cost me, if the walls are each 1 ft. thick at $0.50 per hun. dred? LESSON XXXVII. 284. How many cubic blocks one foot on each side can be sawed from a cube 1 yard on each edge allowing no waste for sawing? 285. How many 1 inch cubic blocks will it take to fill a mortise 1 foot deep, 1 foot wide, and 1 foot long? 286. How many 1 quarter inch cubic blocks will it take to fill a mortise one inch deep, one inch wide, and one inch long? 287. How many 1 inch cubic blocks will it take to fill a mortise 2 feet long, 2 feet wide, and 2 feet deep? 288. Bought 16 loads of hewn timber, at 4 cts. per foot; what was the cost? cubic 289. How many cubic feet in a block of marble 8 feet long, 3 feet wide, and 2 feet thick ? 290. How many cubic feet of earth in a pile 46 feet long, 38 feet wide, 17 feet thick? 291. How many cubic yards of earth in a pile 39 feet long, 25 feet wide, and 19 feet thick? 292. How many cubic yards of earth were removed from a cellar 37 feet long, 21 feet wide, and 11 feet deep? QUESTIONS.—In the 284th problem, how many tier of feet in the block? How many cu. ft. blocks in 1 row of a tier? How many tiers of cu. inch blocks in the 285th problem? How many tiers of quarter inch cubic blocks in the 286th problem? LESSON XXXVIII. 293. How many cubic feet of masonry in a wall 67 feet long, 12 feet high, and 4 feet thick? REVIEW.—What is the use of cloth measure? (89.) Recite the table. (89., a.) What instrument is used by surveyors in measuring land? (90.) What is its length? Recite the table. (90., a.) What is the length of the chain used by civil engineers? (90., a, 2.) 294. How many perches of masonry in a wall 49 feet long, 11 feet high, and 5 feet thick? 295. How many perches of stone in the wall of a cellar 14 feet long, 13 feet wide, and 9 feet deep, making allowance for the corners, the wall being 1 foot thick ? 296. How many perches of stone in the wall of a cellar 37 feet long, 26 feet wide, and 11 feet deep, making allowance for the corners, the wall being 2 feet thick? 297. How many perches of stone will it take to enclose a lot 38 rods long, 14 feet wide, the wall being 7 feet high and 4 feet thick, making allowance for the corners ? 298. How many cubic feet of masonry in a rectangular fort 138 feet long, 97 feet wide, the wall being 28 feet high and 13 feet thick, allowance being made for the corners? How many perches ? 299. If 128 cubic feet of wood cost $5.00, what will 1 foot cost? 300. If 128 cubic feet or 1 cord cost $5.888, what will 39 feet cost? 46 feet? 84 feet? 37 feet? 301. Bought a pile of wood 19 feet long, 4 feet wide, and 4 feet high; how many cubic feet? 302. Bought a pile of wood 27 feet long, 4 feet wide, 7 feet high; what was the cost, at $4.992 per cord? QUESTIONS.-How are cubic feet changed to perches? ANS.-1. Change cu. ft. to quarter cu. ft. 2. Change quarter cu. ft. to perches. In the 295tlı problem what is meant by making allowance for the corners? ANS.-Since the wall is 1 foot thick, the end walls prevent the side walls from extending the entire length of the cellar; but the latter lack 1 foot on each end, thus the side walls are each two feet shorter than the cellar. How much shorter are the side walls in the 296th problem than the end walls? How much shorter are the side walls in the 297th problem than the end walls? REVIEW.-What is a square? (91.) Recite the table. (91., a.) What is a square yard? (92.) Recite the rule for finding the area of surfaces. (92., a.) What is the use of square measure? (92., b.) How do artificers estimate their work? (92., c.) What is the use of surveyor's square measure? (93.) Recite the table. (93., a.) What is a cube? (94.) What is the use of apothecaries' weight? (82.) What is the use of apothecaries' fluid measure? (83.) What has space? (84.) What has a line? (85.) What has a surface? (86.) What has a solid? (87.) What is the use of long measure? (88.) What is the use of cloth measure? (89.) What is the use of surveyor's measure? (90.) LESSON XXXIX. MEASURES OF CAPACITY. 96. Measures of capacity are cubic measures, and are the liquid or dry measures. LIQUID OR WINE MEASURE. 97. Liquid measure is, of course, used in measuring liquids. (b.) The following denominations are sometimes used: (c.) NOTES.-1. The barrel, hogshead, tierce, pipe, butt and tun are the names of casks, which are usually gauged, having the number of gallons they hold marked on them. 2. Ale or beer measure formerly used in measuring beer, ale, and milk, is now seldom used. 3. 1 gallon of pure water weighs nearly 8 lb. avoirdupois; hence a pint weighs about a pound. REVIEW.—Recite the table. (94., a.) What is a cubic yard? (95.) Give the analysis of the cubic yard. (95., a.) Recite the rule. (95., b.) What is the use of cubic measure? (95., c.) How many cubic feet in a load of earth? (95., d.) How do R. R. companies estimate heavy freight? (95, d., 2.) How light freight? How large is a cord of wood? (95., d., 3.) What are the dimensions of a perch of masonry? What is the usual size of a brick? (95., d., 5.) How many bricks make a cubic foot? How do carpenters, joiners, and masons estimate their work? (95., d., 6.) |