*The original standard of English long measure was a barley com taken from the middle of the ear, and well dried. Three of these in length were called an inch, and then the others as in the table. Long measure is employed for denoting the distance of places, and for measuring any thing where length only is concerned. When measure is applied to surfaces, where length and breadth are both concerned, it is called square measure. A square inch is a square measuring an inch on every side. The table of square measure is made from that of long measure by multiplying the several numbers of the latter into themselves. Thus, 12 inches are a foot in length, a square foot then is a square which measures 1 foot, or 12 inches, on every side, and contains 12X12-144 square inches. 3 feet in length make a yard; a square yard is a square measuring 3 feet on each side: but such a square contains (see figure) nine (3X3=9) squares measuring a foot on each side, or 9 square feet; and when we say that a surface contains so many square feet, or square yards, we mean that the surface is equal to such a number of squares measuring a foot or a yard, on each side. When measure is applied to solids which have length, breadth, and thickness, it is called solid or cubic measure. A solid inch is a body, or block, 3ft. having six sides, each of which is an inch square, and the number of inches in a solid foot is equal to the number of such blocks that would be required to make a pile a foot square and a foot high. Now it would require 144 blocks to cover a square foot one inch high. Hence to raise the pile twelve inches high would require twelve times 144-1728 blocks or inches. In like manner it would require 9 solid blocks, a foot each way, to cover a square yard to the height of one foot, and 3 times 9=27, to raise it three feet, or make one soliá yard. This will be obvious from an inspec 30 yards, 1 sq. rod, rd. 39204 2724 feet, 1 sq. rod, rd. 40 rods. 1 rood, 4 roods, 1 acre, 640 acres 1 sq. mile, ro. acr. mi. ft. 1 yds. Irds ro.\mi. 9 1 272 30 1 1568160 10890 1210 40 1 6272640 43560 4840 160 4 1 10 sq. chains make 1 acre, acr. 6400 chains make 1 sq. mile, mi. X. SOLID, or CUBIC MEASURE. 1728 inches, in. make 1 foot, ft. 40 ft. of round timber, or 50 ft. of hewn timber, make 1 ton, ton. tion of the diagram. The cord of wood is sometimes called eight feet. In this case four feet in length, four in breadth, and one in height=16 solid feet, is called one foot; or eight feet in length, four in breadth, and six inches in height, a foot, that is, 1-8th of a cord is called one foot, 2-8ths, two feet, &c. In measuring lands, roads, &c. the distances are usually taken in chains and links. In ordinary business, feet and inches are the most common measures. Many mechanics, however, now take dimensions in feet and tenths of a foot, instead of inches, and if all would do the same, they would find all their calculations much more simple and easy. By forty feet of round timber, in the table of solid measure, is meant so much round timber, as will make forty feet after it is squared. * Four pounds Troy weight of wheat gathered from the middle of the ear, and well dried, were called one gallon, and this was the original standard of all English measures, both liquid and dry, and this was the same as the present wine gallon. But in time it became customary to use a larger measure in selling cheap liquors, and this custom at length established the beer measure, which bears about the same proportion to wine measure that avoirdupois does to troy weight. The dry measure was also made larger than the wine measure, and was at length established at about a mean between wine and beer measure. By wine measure are measured wine, all kinds of spirits, cider, vinegar, oil, &c. By beer measure are measured ale and beer, and by dry measure are measured al kinds of dry goods, corn, grain, salt, roots, fruit, &c. A standard bushel is 18 inches diameter and 8 inches deep. The statute bushel for measuring coal, ashes and lime, in Vermont, contains 38 quarts, or 2553.6 cubic inches. * Every circle, without regard to its size, is supposed to be divided into 360 equal parts, called degrees, and these again to be subdivided into minutes and seconds; so that the absolute quantity expressed by any of these denominations must always depend upon the size of the circle. In this measure are reckoned latitude, longitude, the planetary motions, &c. The habit of reckoning by the dozen is well adapted to the English method of reckoning money; articles which were 48. a dozen, being 4d. apiece, 7s. a dozen, 7d. apiece, &c. Points, lines and inches are used in measuring the length of clock pendulums. Hands are used in measuring the height of horses, and fathoms in measuring depths at sea. 1. REDUCTION. 138. Reduction is the method of changing numbers from one denomination to another, without altering their value.(40) 1. In £4 8s. 5d. 3qrs. how many farthings? £ s. d. qrs. 20 888. 12 181 88 1051d. 4247qr. Ans. As £1-208. there are 20 times as many shillings as there are pounds; we therefore multiply the pounds by 20, and to the product, 80s. join the 8s. making 88s. Then because Is.=12d. there are 12 times as many pence as there are shillings; we therefore multiply the 888. by 12, joining the 5d. to the product, and thus find £4 88. 5d.=1061d. Again, as Id.=4qr. we multiply the pence by 4, joining the 3gr. to the product, and thus find £4 8s. 5d. 3qr.= 4247 farthings. This process is called Reduction Descending, because by it numbers of a higher denomination are brought into a lower denomination. 2. In 4247 farthings, how many pounds? 4) 4247 12) 1061-3qr. 210)88-5d. £4 89. As it takes 4qr. to make 1 penny, there are evidently as many pence in 4247qr. as there are times 4 in that number. We therefore divide by 4, and the quotient is 1061 d. and 3qr. over. Then, as it takes 12 pence to make 1s. there will be as many shillings as there are times 12 in 1061-88s. 5d. Again, as it takes 20s. to make £1, there will be as many pounds as there are times 20 in 88s.£4 8s. Thus we find 4247qr.= £4 88. 5d. 3qr. This process is called Reduction Ascending, because by it a lower denomination is brought into a higher. By these examples It will be seen that Reduction Ascending and Descending mutually prove each other. 140.-REDUCTION ASCENDING. As a process similar to the above may be employed in the reduction of time, weights and measures, as well as moneys, it may be stated in the following general terms: 139.-REDUCTION DESCENDING. RULE.-Multiply the highest denomination by that number which it takes of the next lower to make one in the higher, adding the number, if any, of the lower denomination; and so proceed to do, till it is brought as low as the question requires. RULE.-Divide the lowest denomination by the number which it takes of that to make one in the next higher denomination; and so continue to do, till you have brought it into the denomination required. 44 Troy Weight. 1. In 181b. how many grains? 2. In 22lb. 6oz. 10pwt. how many grains? 1. In 74880grs. how many pounds? 2. In 129840gr. how many pounds? Avoirdupois Weight. 1. In 4 tons how many ounces? 2. In 7cwt. 3qr. how many drams? 8. In 1961b. how many ounces? 1. In 143360oz. how many pounds? 2. In 222 208 drams, how many cwt.?. 3. In 31360z. how many pounds? Long Measure. 1. In 26 rods how many yards? 26 55.5 130 130 As 5 yds. make 1 rod, 143.0yd. proceed as in decimals. (122) 1. In 143 yards how many rods? Here we reduce to a decimal, as before, and divide as in decimals,(128). Whenever a frac tion occurs, it may be changed to a decimal, and used as such. |