| fur. M. L. deg. or o a great circle, or circumfer ence of the earth. 31. How many barley-corns 32. In 4755801600 barleywill reach round the globe, it corns, how many degrees? being 360 degrees? Note. To multiply by 2, is Note. The barley-corns beto take the multiplicand 2 ing divided by 3, and that times; to multiply by 1, is to quotient by 12, we have take the multiplicand 1 time; 132105600 feet, which are to to multiply by, is to take the be reduced to rods. We canmultiplicand half a time, that not easily divide by 16 on is, the half of it. Therefore, account of the fraction; but to reduce 360 degrees to stat- 16 feet 33 half feet, in 1 ute miles, we multiply first by rod; and 132105609 feet = the whole number, 69, and to 264211200 half feet, which, the product add half the multi-divided by 33, gives 8006400 plicand. Thus : rods. 360 69 3240 2160 Hence, when the divisor is encumbered with a fraction, or, &c., we may reduce the divisor to halves, or fourths, 180 half of the multiplicand. &c., and reduce the dividend to the same; then the quo 25020 statute miles in 360 de- tient will be the true answer. grees. 33. How many inches from 34. In 30539520 inches, Boston to the city of Wash-how many miles? ington, it being 482 miles? 35. How many times will a 36. If a wheel, 16 feet 6 wheel, 16 feet and 6 inches inches in circumference, turn in circumference, turn round round 12800 times in going in the distance from Boston to from Boston to Providence, Providence, it being 40 miles ?what is the distance ? LAND OR SQUARE MEASURE. Square measure is used in measuring land, and any other thing, where length and breadth are considered. The denominations are miles, acres, roods, perches, yards, feet and inches. ¶ 35. 3 feet in length make a yard in long measure; but it requires 3 feet in length and 3 feet in breadth to make a yard in square measure; 3 feet in length and one foot wide make 3 square feet; 3 feet in length and 2 feet wide make 2 times 3, that is, 6 square feet; 3 feet in length and 3 feet wide make 3 times 3, that is, 9 square feet. This will clearly appear from the annexed figure. 3 feet 1 yard. 3 feet = 1 yard. It is plain, also, that a square foot, that is, a square 12 inches in length and 12 inches in breadth, must contain 12 X 12 = 144 square inches. 144 square inches TABLE. 12 X 12; that is, 12 inches in length and 12 inches make 1 square foot. in breadth 9 square feet 3X3; that is, 3 feet in length and 3 feet in breadth 301 square yards = 5 × X 5, or 2721 16 × 161, roods, or 160 square rods, acres, 1 square yard. 1 square rod, perch or pole. 1 rood. 1 acre. 1 square mile. Note. Gunter's chain, used in measuring land, is 4 rods in length. It consists of 100 links, each link being 7 inches in length; 25 links make 1 rod, long measure, and 625 square links make 1 square rod. 37. In 17 acres 3 roods 12] 38. In 776457 square feet, rods, how many square feet? how many acres? Note. In reducing rods to Note. Here we have 776457 feet, the multiplier will be square feet to be divided by 2721. To multiply by 4, is to 2724. Reduce the divisor to take a fourth part of the mul- fourths, that is, to the lowest tiplicand. The principle is denomination contained in it; the same as shown T 34, then reduce the dividend to ex. 31. 39. Reduce 64 square miles o square feet? fourths, that is, to the same denomination, as shown T32, ex. 34. 40. In 1,784,217,600 square feet, how many square miles? 42. Reduce 23040 acres to 41. There is a town 6 miles square; how many square square miles. miles in that town? how many acres? yd.3 feet thick. SOLID OR CUBIC MEASURE. Solid or cubic measure is used in measuring things that have length, breadth, and thickness; such as timber, wood, stone, bales of goods, &c. The denominations are cords, tons, yards, feet, and inches. T 36. It has been shown, that a square yard contains 3 X 39 square feet. A cubic yard is 3 feet long, 3 feet vide, and 3 feet thick. Were it 3 feet long, 3 feet wide, ind one foot thick, it would contain 9 cubic feet; if 2 feet hick, it would contain 2 X 918 cubic feet; and, as it is 3 feet thick, it does contain 3 X 9= 27 cubic feet. This will clearly appear from the annexed figure. It is plain, also, that a cubic foot, that is, a solid, 12 inches in length, 12 inches in breadth, and 12 inches in thickness, will contain 12 X 12 X 12= 1728 solid or cubic inches. Note. What is called a cord foot, in measuring wood, is 16 solid feet; that is, 4 feet in length, 4 feet in width, and 1 foot in height, and 8 such feet, that is, 8 cord feet make 1 cord. 43. Reduce 9 tons of round timber to cubic inches. 45. In 37 cord feet of wood, how many solid feet? 47. Reduce 64 cord feet of wood to cords. 44. In 622080 cubic inches, how many tons of round timber? 46. In 592 solid feet of wood, how many cord feet? 48. In 8 cords of wood, how many cord feet? 49. In 16 cords of wood, 50. 2048 solid feet of wood, how many cord feet? how how many cord feet? many solid feet? many cords? WINE MEASURE. how Wine measure is used in measuring all spirituous liquors, ale and beer excepted; also vinegar and oil. The denominations are tuns, pipes, hogsheads, barrels, gallons, quarts, pints, and gills. Note. A gallon, wine measure, contains 231 cubic inches. ALE OR BEER MEASURE. Ale or beer measure is used in measuring ale, beer, and milk. The denominations are hogsheads, barrels, gallons, quarts, and pints. Note. A gallon, beer measure, contains 282 cubic inches. 57. Reduce 47 bar. 18 gal. of ale to pints. 59. In 29 hhds. of beer, how many pints? 58. In 13680 pints of ale, how many barrels ? 60. Reduce 12528 pints to hogsheads. DRY MEASURE. Dry measure is used in measuring all dry goods, such as grain, fruit, roots, salt, coal, &c. The denominations are chaldrons, bushels, pecks, quarts, and pints. Note. A gallon, dry measure, contains 2684 cubic inches. A Winchester bushel is 18 inches in diameter, 8 inches deep, and contains 2150 cubic inches. |