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 4s. a dozen, being 4d. apiece, 78. 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 denths 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 88. 5d. 3qrs. how many farthings? £ s. d. qrs.- 20 888. 12 181 88 1061d. 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 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 88. 5d.=1061d. Again, as Id. 4qr. we multiply the pence by 4, joining the 3gr. to the product, and thus find £4 88. 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 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 12) 1061-3qr.is 1061 d. and 3qr. over. Then, as it takes 12 pence to make 1s. there will be as times 12 in 1061-88s. 5d. make £1, there will be as times 20 in 88s.£4 8s. 2:0)88-5d. £4 88. many shillings as there are Again, as it takes 208. to many pounds as there are Thus we find 4247or.= £4 Ss. 5d. 3qr. This process is called Reduction Ascending, becanse 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. 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. 140.-REDUCTION ASCENDING. 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. Troy Weight. 1. In 13lb. 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. 8qr. how many drams? 3. In 196lb. how many ounces? 1. In 143360oz, how many pounds? 2. In 222 208 drams, how many cwt.? 3. In 3136oz. how many pounds? Long Measure. 1. In 26 rods how many 1. In 143 yards how many rods? Circular Measure. 1. In 6 signs how many minutes? 2. In 47° 28′ 15′′ how many seconds? 1. How many signs in 10800 minutes? 2. In 170595" how many degrees? REDUCTION OF DECIMALS. 141. 1. Reduce 4 ounces to the decimal of a pound. 4oz. lb. As 1 lb. is 16)4.0(.25 16 oz. 4 oz. are of a pound, 32 142. 1. How many ounces are 0.25 of a pound? .25 16 150 25 Pounds are reduced to ounces by multiplication, (139) and .25 lb. multiplied by 16, the ounces in a pound, the product (122) is 4 ounces. and reduced 80 80 (130) is .25 of a 2. Reduce 3 inches to the decimal of a yard. 24 oz. 4.00 2. How many inches are 0.0833+of a yd 3 of 0.0833 12)3.0(.25 3 inches 60 3)0.2500 0.0833+ Ans. 3. Reduce 8 hours 24 min. to the decimal of a day. 60)24. 24m.=24h.=0.4h. then 8h. 24m.-8.4h. 12 Yards are reduced to feet by multiplying. them by 3, and feet to inches by multiplying by 12, (139.) Here it will be seen, by comparing this with the example at the left hand, that there is a loss of 12 ten thousandths of an inch, on account of the decimal being incomplete. 2.9988 3. In 0.35 of a day, how many hours and minutes? 0.35 140 70 24)8.40 and 8.4h. h. 8,40 0.35d. 0.35 of a day. 60 m. 24.00 To reduce days to hours, we multiply by 24, and the product is 8.4h. and .4 multiplied by 60 gives 24 minutes; then 0.35 d. 8 h. 24 min. The above methods of changing decimals to integers of a different denomination, and the reverse, are called the Reduction of Decimals |