mi. fur. rd. yd. ft. in. 36 12. Note. A fathom is a length of six feet, and is gener. ally used to measure the depth of water. A hand is 4 inches, and is used to measure the height of horses. 3= 1= EXAMPLES. 1. In 675ft. 10in. 2bar., how many barleycorns ? We first reduce the feet OPERATION. to inches and then add in 675 the 10 inches : we next re 12 duce the inches to barley 8110 corns and add in the 2 3 barleycorns. Ans. 24332 barleycorns. lbar. 2. In 59mi. 7fur. 38rd., how many rods? Ans. 19198rd. 3. In 194656bar., how many feet? OPERATION. We first divide by the num 3)194656 ber of barleycorns in an inch, 12)64885 and then by the number of inches in a foot. 5407 lin. Ans. 5407ft. lin. 1bar. 4. In 115188 rods, how many miles ? Ans. 359mi. 7fur. 28rd. 5. In 719m. 7fur. 16rd., how many feet ? Ans. 3801204. 6. In 118°, how many statute and how many geographical miles ? 8210 statute miles. Ans. 7080 geographical miles, LAND OR SQUARE MEASURE. 86. 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 be. 1 Foot. tween four equal lines, drawn perpendicular to each other. Each line is called a side of the square. If each side Square be one foot, the figure is called a square foot. foot. 1 Foot. 1 yard=3 feet. 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 1 yard=3 feet. 9 square 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, 3x3=9 The number of square inches contained in a square foot is equal to 12x12=144. square feet. TABLE. 144 square inches, sq. in. make 1 square foot, Sq.ft. 9 square feet 1 square yard, Sq.yd. 30 square yards 1 square pole, P. 40 square poles 1 rood, R. 4 roods A. 640 acres 1 square mile, M. 1 acre, 86. 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. A. R. P. Sq.yd. Sq.ft. Sq. in. 9= 1296 1= 144 1= 87. 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. 7-1962 inches TABLE. 1. 4 rods or 66 ft. 1 chain, c. 80 chains 1 mile, mi. 1 square chain 16 square poles, P. 10 square chains A. Land is generally estimated in square miles, acres, roods, and square poles or perches. 1 acre, EXAMPLES. 1. In 32M. 25A. 3R., how many square poles ? OPERATION. 32 We first bring the square 640 miles to acres by multiplying 20505 by 640, and then add in the 25 acres. We next reduce 4 to roods and add in the 3 roods: 82023 roods we then reduce to poles. 40 Ans. 3280920 P. 2. In 19 A. 2R. 37P., how many square poles ? Ans. 31571. 3. In 175 square chains, how many square poles ? Ans. 2800P. 87. What chain is used in surveying land ? How long is it? How is it divided ? Repeat the table. How is land generally estimated ? 4. In 37456 square inches, how many square feet? 12)37456 12x12=144 12)3121 4 260 1 1x 12+4=16. Ans. 260 Sq. ft. 16 Sq. in. 5. In 14972 square rods, huw many acres ? Ans. 93A. 2R. 12P. 6. In 3674139P., how many square miles ? Ans. 35M. 563 A. 1R. 19P. SOLID OR CUBIC MEASURE. 88. Solid or cubic measure is used in measuring stone, timber, earth, and such other things as have three dimensions, length, breadth, and thickness. Its de nominations are ns, cords, yards, feet, and inches. 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 cubic or solid yard. The 3 feet=l yard. 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 cules, or 18 cubic feet; and if it were 3 feet high, it would con. tain three tiers, or 27 cubic feet. Hence, the content of a solid is equal to the product of its length, breadth, and 3 feet=1 yard. 88. For what is solid or cubic measure used? What are its de. nominations ? What is a cube? What is a cubic or solid foot! What is a cubic yard? How many cubic feet in a cubic yard ! What is the content of a solid equal to ? Repeat the table. What is a cord of wood ? How many solid feet does it contain ? thickness. Therefore, 1 cubic fnot contains 12 x 12 x 12 =1728 cubic inches. 1 ton, TABLE. 1728 solid inches, S. in. make 1 solid foot, S.ft. 27 solid feet 1 solid yard, S. yd. 40 feet of round, or 50 Ton. 128 solid feet=8X4 X4, that is, a make 1 cord of pile 8 feet in length, 4 feet in wood C. width, and 4 feet in height, Note. A cord foot, is one foot in length of the pile which makes a cord. It contains sixteen solid seet. EXAMPLES. 1. Reduce 14 tons of round timber to solid inches. Ans. 967680 solid inches. 2. In 55 cords of wood, how many solid feet ? Ans. 7040. 3. In 25 cords of wood, how many cord feet ? Ans. cord A. 4. Reduce 3058560 cubic inches to tons of round timber. OPERATION. ..10 1728)3058560(1770 We first divide 1728 by 1728, the number of solid inches 13305 in a solid foot, and 12096 next by 40, the 12096 410)17710 number of solid 12096 44.. feet in a ton. 00000 Ans. 44 tons 10f1. 5. Reduce 28160 solid feet to cords. Ans. 220 cords. 6. Reduce 174964 cord feet to cords. Ans. 21870 cords, 4 cord feet. 7. In 7645900 solid inches, how many tons of hewa timber? Ans. 88 tons 24 s. ft. 1228 S. in. |