Note. To multiply by 2, is to Note. The barley-corns being take the multiplicand 2 times; to divided by 3, and that quotient multiply by 1, is to take the mul- by 12, we have 132105600 feet, tiplicand i time; to multiply by which are to be reduced to rods. is to take the multiplicand We cannot easily divide by 16 half a time, that is, the half of it. on account of the fraction ; but Therefore, to reduce 360 degrees 16 feet 33 half feet, in 1 rod; to statute miles, we multiply first and 132105600 feet 264211200 by the whole number, 69, and to half feet, which, divided by 33, the product add half the multipli- gives 8006400 rods. Thus : cand. 360 69 3240 2160 180 half of the multiplicand. 25020 statute miles in 360 degrees. 33. How many inches from Boston to the city of Washington, t being 482 miles? Hence, when the divisor is encumbered with a fraction, or 4, &c., we may reduce the divisor to halves, or fourths, &c., and reduce the dividend to the same; then the quotient will be the true answer. 34. In 30539520 inches, how many miles? 35. How many times will a 36. If a wheel, 16 feet 6 inches wheel, 16 feet and 6 inches in in circumference, turn round circumference, turn round in the 12800 times in going from Boston distance from Boston to Provi- to Providence, what is the disdence, it being 40 miles? tance? 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 1S, 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. TABLE, 144 square inches 12 X 12; that is, in breadth,. 9 square feet 3X3; that is, 3 feet in length and 3 feet in breadth, 30 square yards: 5 X 5, or 2724 square feet 16 X 16, 40 square rods 4 640. roods, or 160 square rods, 1 square foot. 1 square yard. S1 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 792 inches in length; 25 links make 1 rod, long measure, and 625 square links make i square rod. 37. In 17 acres 3 roods 12 rods, how many square feet? Note. In reducing rods to feet, the multiplier will be 2724. To multiply by 4, is to take a fourth part of the multiplicand. The principle is the same as shown ¶ 34, ex. 31. 39. Reduce 64 square miles to square feet. 41. There is a town 6 miles square; how many square miles in that town? how many acres? 38. In 776457 square feet, how many acres? Note. Here we have 776457 square feet to be divided by 2724. Reduce the divisor to fourths, that is, to the lowest denomination contained in it; then reduce the dividend to fourths, that is, to the same denomination, as shown ¶ 34, ex. 32. 40. In 1,784,217,600 square feet, how many square miles? 42. Reduce 23040 acres to square miles. 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. 36. It has been shown, that a square yard contains 3 X 3 9 square feet. A cubic yard is 3 feet long, 3 feet wide, and 3 feet thick. Were it 3 feet long, 3 feet wide, and one foot thick, it would contain 9 cubic feet; if 2 feet thick, it would contain 2X9=18 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 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 I foot in heignt, and 8 such feet, that is, 8 cord feet, make 1 cord. 43. Reduce 9 tons of round f timber to cubic inches. 45. In 37 cord feet of wood, how many solid feet? 47. Reduce 64 cord feet of wood to cords. 49. In 16 cords of wood, how many cord feet? how many solid feet? 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? 50. 2048 solid feet of wood, how many cord feet? how many cords? WINE MEASURE. 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. 51. Reduce 12 pipes of wine to pints. 53. In 9 P. 1 hhd. 22 gals. 3 qts. how many ills? 55. In a tun of cider, how many gallons? qt. gal. bar. hhd. P. T. 52. In 12096 pints of wine, how many pipes? 54. Reduce 39032 gills tr pipes. 56. Reduce 252 gallons to tuns. ALE OR BEER MEASURE. Ale or heer 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? gal. bar. .hhd. 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. ch. A Winchester hushel is 18 inches in diameter, 8 inches deep, and contains 2150 cubic inches. The denominations of time are years, months, weeks, days, hours, minutes, and seconds. 37. The year is also divided into 12 calendar months, which, in the order of their succession, are numbered as follows, viz. January, 1st month, has 31 days. February, 2d, 5th, 6th, May, . . 28 Note. When any year can be divided by 4 without a remainder, it is called leap year, in which February has 29 days. The number of days in each month may be easily fixed in the mind by committing to memory the following lines: Thirty days hath September, The first seven letters of the alphabet, A, B, C, D, E, F, G, are used to mark the several days of the week, and they are disposed in such a manner, for every year, that the letter A shall stand for the 1st day of January, B for the 2d, &c. In pursuance of this order, the letter which shall stand for Sunday, in any year, is called the Dominical letter for that year. The Dominical letter being known, the day of the week on which each month comes in may be readily calculated from the following couplet : At Dover Dwells George Brown, Esquire, |