LONG MEASURE, § 62. Long measure is used when length only is considered. Its denominations are degrees, leagues, miles, furlongs, rods, yards, feet, inches, and barley-corns. NOTE. A fathom is six feet, and is generally used to measure the depth of water. A hand is 4 inches, and is used to measure the height of horses. Q. When is Long Measure used? Repeat the table. What is a fathom? What are its denominations? EXAMPLES. 1. In 675 ft. 10in. 2bar.; how many barley-corns? We first reduce the feet to inches and then add in the 10 inches: we next reduce the inches to barleycorns and add in the 2 barley-corns. OPERATION. 12 8110 3 Ans. 24332 barley-corns. 2. In 59mi. 7fur. 38rd.; how many rods? 3. In 194656 bar.; how many feet? We first divide by the number of barley-corns in an inch, and then by the number of inches in a foot. Ans. 19198rd. OPERATION. 3)194656 12)64885...lbar. 5407... lin. Ans. 5407ft. lin. 1bar. 4. In 115188 rods, how many miles? Ans. 359mi. 7fur. 28rd. CLOTH MEASURE. § 63. Cloth measure is used for measuring all kinds of cloth. Its denominations are Ells French, Ells English, Ells Flemish, yards, quarters, nails, and inches. Q. For what is Cloth Measure used? What are its denominations? Repeat the Table. EXAMPLES. 1. In 35yd. 3qr. 3na., how many nails? We first reduce the yards to quarters and add in the 3qr.; we next reduce the quarters to nails and add in the 3 nails. OPERATION. 35 4 143 4 Ans. 575 na 2. Reduce 49 Ells English to nails. Ans. 980na. Ans. 623na. 4. In 3278 nails, how many yards? We first divide by 4 which brings the number to quarters, and then again by 4, which brings it to yards. OPERATION. 4)3278 4)819.. 2na. 204.. 3qr. Ans. 204yd. 3qr. 2na. 5. Reduce 340 nails to Ells Flemish. Ans. 28 E. Fl. 1qr. 6. In 67 quarters, how many yards? Ans. 16yd. 3qr. LAND OR SQUARE MEASURE. § 64. Land or square measure is used in measuring land, or any thing in which length and breadth are both considered. A square is the space included between four equal lines, drawn perpendicular to each other. Each line is called a side of the square. If each side be one foot, the figure is called a square foot. If the sides of the square be each one yard, the square is called a square yard. In the large square there are nine small squares, the sides of which are each one foot. Therefore, the square yard contains 9 square feet. 1 Foot. 1 Foot. Square. 1 yard=3 feet. 1 yard=3 feet. The number of small squares that is contained in any large square is always equal to the product of two of the sides of the large square. As in the figure, 3×3=9 square feet. The number of square inches contained in a square foot is equal to 12×12=144. TABLE. 144 square inches, sq. in. make 1 square foot, Sq.ft. 9 square feet 301 square yards 40 square poles 4 roods 640 acres 1 square yard, Sq.yd. Sq. in. A. R. P. Sq. yd. Sq. ft. 1= 40=1210=10890-1568160 The Surveyor's or Gunter's chain is generally used in surveying land. It is 4 poles or 66 feet in length, and is divided into 100 links. 10 square chains 1 acre, Land is generally estimated in square miles, acres, roods, and square poles or perches. Q. For what is square measure used? What is a square? If each side be one foot, what is it called? If each side be a yard, what is it called? How many square feet does the square yard contain? How is the number of small squares contained in a large square found? Repeat the Table. What chain is used in surveying land? How long is it? How is it divided? Repeat the Table. How is land generally estimated? EXAMPLES. 1. In 32M. 25A. 3R., how many square poles? Ans. 3157 P. 2. In 19A. 2R. 37P., how many square poles? 3. In 175 square chains, how many square rods? Ans. 2800P. 4. In 37456 square inches, how many square feet? 260..1 1x12+4=16. Ans. 260 Sq. ft. 16 Sq. in. 5. In 14972 square rods, how many acres? Ans. 93A. 2R. 12P. 6. In 3674139P. how many square miles? Ans. 35M. 563A. 1R. 19P. SOLID OR CUBIC MEASURE. § 65. Solid or cubic measure is used in measuring stone, timber, earth, and such other things as have three dimensions of length, breadth, and thickness. Its denominations are tons, cords, yards, feet, and inches. 3 feet=1 yard. A cube is a body, or solid, having six equal faces, which are squares. If the sides of the cube be each one foot long, the solid is called a cubic or solid foot. But when the sides of the cube are one yard, as in the figure, the cube is called a 3 feet-1 yard. cubic or solid yard. The base of the cube, which is the face on which it stands, contains 3x3=9 square feet. Therefore 9 cubes, of one foot each, can be placed on the base. If the solid were one foot high it would contain 9 cubic feet; if it were 2 feet thick it would contain two tiers of cubes, or 18 cubic feet; and if it were 3 feet high, it would contain three tiers, or 27 cubic feet. Hence, the content of a solid is equal to the product of its length, breadth, and thickness. Therefore, I cubic foot contains 12x12x12=1728 cubic inches. |