years. All the rest have thirty-one, Excepting February alone, Which hath twenty-eight, nay more, Hath twenty-nine one year in four. The true solar year consists of 365 days, 5 h. 48 m, 57 s. or nearly to 8654 days. A common year is 365 days, and one year is added in Leap years to make up the loss of 4 of a day in each of the three preceding This method of reckoning was ordered by Julius Caesar, 40 year before the birth of Christ, and is called the Julian account, or Old Style But as the true year fell 11 m. 3 s. short of 3654 days, the addition of a day every fourth year was too much by 44 m. 12 s. This amounted to one day in about 130 years. To correct this error, Pope Gregory, in 1582, ordered that ten days should be struck out of the calendar, by calling the 5th of October the 15th; and to prevent its recurrence, he ordered that each succeeding century, divisible by 4, as 16 hundred, 20 hundred, ard 24 hundred, should be Leap vears, but that the centuries not divisible by 4, as 17 hundred, 18 hundred, and 19 hundred, should be common years. This reckoning is called the Gregorian or New Style. The New Style differs now twelve days from the old style. *The original standard of all our weights was a corn of wheat, taken from the middle of the ear, and well dried. These were called grains, and 32 of them made one pennyweight. But it was afterwards thought sufficient to divide this same pennyweight into 24 equal parts, still calling the parts grains, and these are the basis of the table of Troy weight, by which are weighed gold, silver and jewelry. Apothecaries' weight is the same as Troy weight, only having different divisions between grains and ounces. Apothecaries make use of this weight in compounding their medicines, but they buy and sell their drugs by Avoirdupois weight. In buying and selling coarse and drossy articles, it became customary to allow a greater weight than that used for small and precious articles, and this custom at length established the Avoirdupois, or common weight, by which all articles are now weighed, with the foregoing exceptions. Avoirdupons weight is about one sixth part more than Troy weight, a pound of the former being 7000 grains, and of the latter 5760 grains. In buying and selling by the hundred weight, 28 pounds have been called a quarter, and 112 pounds a cut. but this practice of grossing, as it is called, is now pretty generally laid aside, and 25 pounds are considered a quarter and 4 quarters, or 100 pounds, a hundred weight. 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 solid yard. This will be obvious from an inspeo 144 inches make 1 square foot, ft. in. 1441 9 feet 66 1 sq. yard, yd. 30 yards, 1 sq. rod, rd. 272 feet, 1 sq. rod, rd. 40 rods 1 rood, ro. 1296 39204 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. 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, meant so much round timber, as will make forty feet after it is squared, is * 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 custoin 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, &e. 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 4s. a dozen, being 4d. apjece, 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. 138, 139, 140. REDUCTION. 1. REDUCTION. 138. Reduction is the method of changing numbers from one denomination to another, without altering their value. (40) In £4 8s. 5d. 3qrs. how many farthings? 1. £ s. d. qrs. 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 88. Then because 18.-12d. there are 12 times as many pence as there are shillings; we therefore multiply the 88s. by 12, joining the 5d. to the product, and thus find £4 Ss. 5d.-1061d. Again, as 1d.=4qr. we multiply the pence by 4, joining the 3qr. 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. As it takes 4qr. to make 1 penny, there are evidently as many pence in 4247gr. as there are times 4 in that number. is 1061 d. and 3qr. over. Then, as it takes 12 pence We therefore divide by 4, and the quotient to make 1s. there will be as many shillings as there are times 12 in 1061-88s. 5d. Again, as it takes 20s. to nake £1, there will be as many pounds as there are £4 83. times 20 in 88s. £4 8s. Thus we find 4447or.= £4 8s. 5d. 3qr. This process is called Reduction Ascending, becanse by it a lower denomination is brought into a higher. it will be seen that Reduction Ascending and Descending mutually prove By these examples each other. 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. | 140.-REDUCTION ASCENDING. 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 quired. 10 |