432= 36 = 3 = 1 yard. 2376 198 = 16 = 5 = 1 pole. 95040 7920 = 660 = 220 = 40 = 1 furlong. 760320= 63360 = 5280 =1760=320= 8=1 mile. 2280960=190080=15840=5280=960=24=3=1 league. 53. In 12m. 3fur. 4p. lyd. how many yards? OPERATION. 99 furlongs. 40 3964 poles. 5 19821 1982 Ans. 21803 yards. Explanation. The miles are here multiplied by 8, (because 8 furlongs make a mile,) and the 3 furlongs are added to the product, this gives furlongs; these are multiplied by 40, (because 40 poles make a furlong,) and the 4 taken in, this gives poles; these are multiplied by 5, (because 5 yards make a pole,) and the I is taken in to the product, this gives yards. To multiply 3964 by 5, I first multiply it by 5, then divide it by 2, and lastly I add the product and quotient together. 54. In 96800 yards, how many miles? OPERATION. yards. 8) 220)96800 (440 88 88 $8 Ans. 55 miles. Explanation. The division by 5 cannot be performed conveniently without fractions; I therefore divide by 220, (because 220 yards make a furlong,) this gives furlongs; these I divide by 8, (because 8 furlongs make a mile,) and the result is miles. If you wish to bring the yards into poles, multiply by 2, and divide the product by 11; then dividing successively by 40 and by 8, will produce the very same answer. 55. In 50 leagues, how many yards? Ans. 264000. Multiply by 3, 8, 40, and 51⁄2. 56. In 2661120 barley-corns, how many miles? Divide by 3, 12, 3, 220, and S. Ans. 14. 57. In 1m. 2fur. 3p. how many yards? Ans. 2216. 58. In 4755801600 barley-corns, how many leagues? Ans.8340. 59. In 7 miles, how many lines? Ans. 5322240. 61. In 1720 nails, how many English ells? Ans. 86. 64. In 1264 yards, how many Flemish ells? Ans. 1685 F. E. 1 qr. Multiply by 4, and divide by 3. 65. In 1792 Flemish ells, how many yards? Ans. 1344. Multiply by 3, and divide by 4. 66. In 480 English ells, how many Flemish ells? Ans. 800. Ans. 9840. 67. In 12300 yards, how many English ells? SQUARE OR SUPERFICIAL MEASURE. 54. Square Measure is used to measure surfaces in which both length and breadth are estimated, as land, flooring, roofing, walling, wainscotting, plastering, painting, &c. The smallest measure (called the measuring unit) here used is a square inch, or a little square, every side of which is an inch in length". 'As in Long Measure a line of an inch in length was taken for the measuring unit, so here a square surface of an inch in length, and consequently the same in breadth, is assumed as the measuring unit; and as many times as this little square is contained in any superficial space, so many square inches is that space said to consist of: thus a square foot contains 144 square inches; for if the sides of a square of a foot each way be divided each into 12 equal parts, each part will be an inch; and if the opposite divisions be joined, the square foot will be divided into 144 equal squares, each a square inch. Hence a square foot 39204 2724≈ 304 = 1 pole. 1568160=10890=1210= 40=1 rood. 6272640=43560=4840160=4=1 acre. 69. In 12 acres, how many square yards? 70. In 12345 square poles, how many acres? Ans. 4475, Ans. 28a. 3r. 37p. 71. In 27a. 3r. 35p. how many perches? 72. In 4637 perches, how many acres? 73. In 25 square yards, how many square inches? Ans. 32400. = 12 x 12 inches; a square yard=9 × 9 square feet; a square pole=54 × 54 square yards, &c. Land is usually measured by a chain invented by the Rev. Edmund Gunter, Professor of Astronomy at Gresham College, and therefore called Gunter's chain; this chain is 66 feet long, and consists of 100 equal links. Ten chains in length, and one in breadth, (or 100 X 100 X 10=100000 links) make one acre. CUBIC OR SOLID MEASURE. 55. Cubic Measure is used for measuring solid bodies, in which length, breadth, and thickness, are estimated. The smallest measure here used, and which is therefore called the measuring unit, is a cubic inch, or a solid in the shape of dice, of an inch long, an inch wide, and an inch in depth '. 74. In 120 cubic yards, how many cubic inches ? Every thing in nature to which measuring can be applied has three dimensions, namely, length, breadth, and thickness: but for the sake of convenience some things are considered of one dimension only, viz. length; such as distances of places, ropes, cloths, tapes, ribbon, &c. to these Long Measure is applied: others are considered as of two dimensions, viz. length and breadth; as land, painting, paving, &c. these are estimated by Square Measure: but there are many things which require to be estimated by all three of their dimensions, such as timber, stone, the capacity of vessels, &c. these are the subject of Cubic Measure. If each side of a cube (which is a solid contained by 6 equal squares) be 12 inches long, and divided into inches, and if the similar divisions of the opposite sides be joined by straight lines, (as has been shewn in the preceding note,) the given cube will be divided into 1728 equal cubes, each a cubic inch. Hence a cubic foot = 12 × 12 × 12 cubic inches; a cubic yard=3 × 3 × 3 cubic feet, &c. 75. In 2799360 cubic inches, how many cubic yards? Ans. 60. Divide by 1728, and 27. 76. How many cubic inches are there in a load of rough timber? Ans. 69120. 77. How many bales of cotton of a cubic yard each can be stowed in a ship of 100 tons burthen? Ans. 155, and 15 over. WINE MEASURE. 56. Wines, spirits, cider, perry, mead, vinegar, oil, and milk, are sold by this measure". ▾ The measure for different kinds of wine differs considerably, the pipe containing from 110 to 140 gallons: hence it is usual for dealers to charge for what the pipe contains, which is found by actual guaging. A statute made in the reign of Henry III. ordained, that the wine gallon should contain eight pounds troy of wheat taken from the middle of the ear, and well dried. During many ages Wine Measure was the only measure sanctioned by law for measuring any commodity whatever; at length other measures were introduced for less pure liquors, and for dry goods. A law was made in the reign of Queen Anne, whereby the wine gallon is required to measure 231 cubic inches; consequently a pint measures 287 cubic inches. A tun of distilled water weighs 18cwt. avoirdupois, and a tun of wine about 12cwt. 3qrs.; consequently a pint of wine will weigh about 16oz. 9 drams. |