Diagram No. 1 shows the subdivisions of a Township into Sections, and how they are numbered, commencing at the N.E. corner. Diagram No. 2 shows the subdivisions of a Section, on an enlarged scale, and how they are named. A Lot is a subdivision of a section, usually of irregular form, on account of bordering upon a navigable river or lake-containing as nearly as possible the area of a Quarter-Quarter-Section, and described as lot No. 1, 2, 3, etc., of a particular section. City and village plots are usually subdivided into Blocks, and these into Lots. EXAMPLES. 1. If a township of land is equally divided among 288 families, how many acres does each receive? part of a section? What 2. What number of rails will inclose a quarter-section of land with a fence 6 rails high, and 3 lengths for every 2 rods; and what will be the cost of the rails, at $40 per thousand? Ans. $340. 3. A man bought the S. of a section of land at $24 an acre, and afterward sold the E. of what he bought at $4.37 an acre. What did he gain on what he sold? 4. If I buy the N. E. section of land, how many part of a whole section? How are the parts located in respect to each other? and the E. 1 of N. W. † of a acres do I purchase? What 5. A speculator bought of the Ill. Central R.R. Co., the S. of Section 4, township 10 north, range 6 east, at $2 an acre. He afterward sold the E. of S. E. at $2.75 an acre; the N. W. of S. E. 1 at $34 an acre; and the N. of S. W. at $3.84 an acre. How many What was his gain on the purchase Draw diagram. Ans. $27.20. acres has he left? price of the whole? 230c. The old French Linear, and Land Measure, is still used to some extent in Louisiana, and in other French settlements in the United States. The French Foot equals 12.8 inches, American, nearly. The Arpent is the old French name for Acre, and contains nearly of an English Acre. In Texas, New Mexico, and in other Spanish settlements of the United States, the following denominations are still used: The Spanish Foot 11.11+ in. (Am.); 1 Vara =33 in. (Am.); 108 Varas = 100 Yards, and 1900.8 Varas = 1 Mile. MASONRY AND PAVING. 230d. Masonry is estimated by the cubic foot, and by the perch; also by the square foot and the square yard. 1. Materials are usually estimated by cubic measure; the work by cubic or square measure. 2. A Perch of stone, or of masonry, is 161 ft. long, 14 ft. wide, and 1 ft. high, and is equal to 24.75 cu. ft. 3. When stone is built into a wall, 22 cu. ft. make a perch, 2 cu. ft. being allowed for mortar and filling. 4. Embankments and Excavations are estimated by the cubic yard. 5. A cubic yard of common earth is called a load. 6. Brickwork is generally estimated by the thousand bricks; sometimes in cubic feet. In walls, brickwork is estimated at the rate of a brick and a half thick. 7. North River bricks are 8 in. × 3 × 21; Maine bricks are 71 in. × 3 × 2; Philadelphia and Baltimore bricks are 8 in. × 4 × 2; and Milwaukee bricks, 8 in. × 43 × 28. 8. In estimating material, allowance is made for doors, windows, and cornices. 9. In estimating the work, masons measure each wall on the outside, and ordinarily no allowance is made for doors, windows, and corners; but sometimes an allowance of one half is made, this being, however, a matter of contract. EXAMPLES. 230e. To find the number of bricks in a cu. ft. of masonry. RULE. -I. Add to the face dimensions of the kind of bricks used, one half the thickness of the mortar or cement in which they are laid, and compute the area. II. Multiply this area by the quotient of the thickness of the wall divided by the number of bricks of which it is composed; the product will be the volume of a brick and its mortar in cubic inches. III. Divide 1728 by this volume, and the quotient will be the number of bricks in a cubic foot. 1. How many Milwaukee bricks are there in a cubic foot of wall 123 in. wide, laid in courses of mortar of an inch thick ? 8.5.25 8.75 in. = 8.75 x 2.625 = OPERATION. length of brick and joint. 2.375+.252.625 in. = thickness of brick and joint. 22.96875 sq. in. = area of its face. 12.75 ÷ 3 (number of bricks in width of wall) = 4.25 in. of brick and mortar. 22.96875 x 4.25 97.617+ = cubic inches in a brick. = width 172897.617+ = 17.7+ = number of bricks in a cubic foot. 2. How many bricks, 8 in. x 4 x 2, will be required to build a wall 42 ft. long, 24 ft. high, and 16 in. thick, laid in courses of mortar of an inch thick? 3. How many perches of stone, laid dry, will build a wall 60 ft. long, 161 ft. high, and 18 in. thick? RULE. -I. Multiply the number of cubic feet in the wall, or work to be done, by the number of bricks in a cu. ft.; the product will be the number of bricks required. II. Divide the number of cubic feet in the work to be done by 24.75; the quotient will be the number of perches. 4. How many perches of masonry are there in a wall 120 ft. long, 6 ft. 9 in. high, and 18 in. thick? 5. What will be the cost of building a wall 60 ft. long, 213 ft. high, and 17 in. thick, of Philadelphia bricks, laid in courses of mortar of an inch thick, at $121 per M.? Ans. $423.52. 6. A street 650 ft. long and 72 ft. wide, averages 4.5 ft. below grade. Find the cost of filling it in, at $.42 a cubic yard. 7. Find the cost of paving a sidewalk 4 ft. wide, and 63 ft. long, at $.21 per sq. ft. Ans. $52.92. 8. What will it cost to pave a sidewalk 250 ft. x 12 ft. with North River bricks, 42 to a square yard, laid flat, at $9 per M. Ans. $126. BOARDS AND TIMBER. 230f. A Board Foot is 1 ft. long, 1 ft. wide, and 1 in. thick. Hence 12 board ft. make 1 cu. ft. Board feet are changed to cubic feet by dividing by 12; and cubic feet are changed to board feet by multiplying by 12. 1. In Board Measure all boards are assumed to be 1 inch thick. 2. Lumber and sawed timber, as plank, scantling, etc., are usually estimated in board measure, hewn and round timber in cubic measure. RULE. I. When lumber is not more than 1 inch thick, multiply the length in feet by the width in inches, and divide the product by 12. II. When it is more than 1 inch thick, multiply the length in feet by the width and thickness in inches, and divide the product by 12. EXAMPLES. 1. Find the contents of a board 15 ft. long, 8 in. wide. OPERATION. 15 x 812 = 10 board feet. 2. What are the contents, in board measure, of a joist 16 ft. long, 10 in. wide, and 3 in. thick? OPERATION. 3 x 10 x 16÷ 12 = 40 board feet. 3. How many board feet are there in 4 boards 16 ft. long, 10 in. wide? 4. How many board feet are there in 2 joists 17 ft. long, 11 in. wide, and 3 in. thick? 5. Find the contents of a board 18 ft. long, 1 ft. 8 in. wide at one end, and 14 in. at the other. OPERATION. 20 in. +14 in. + 2 = 17 in.; 18 x 17+12=251 board ft. |