EXAMPLES. 1. How many seconds in a year of 365da. 6hr.? 2. In 12 years of 365da. 23hr. 57m. 39sec. each, how many seconds? Ans. 379467108 sec. 3. In 49 weeks, how many minutes? Ans. 493920. 4. In 126230400 seconds, how many years of 365 days? 5. In 756952018 seconds, how many years of 365 days, each? Ans. 24yr. Ida. 26m. 58sec. 6. In 5927040 minutes, how many weeks? Ans, 588. CIRCULAR MEASURE OR MOTION. § 70. Circular measure is used in estimating latitude and longitude, and also in measuring the motions of the heavenly bodies. Every circle is supposed to be divided into 360 equal parts, called degrees. TABLE. 60 seconds" make 1 minute, marked'. Q. For what is circular measure used? How is every circle supposed to be divided? Repeat the Table. EXAMPLES. 1. Reduce 5s 29° 25' to minutes. 2. In 2 circles, how many seconds? Ans. 10765'. Ans. Q. How many things make a dozen? How many dozen a gross? How many gross a great gross? How many things make a score? How many pounds a quintal of fish? How many sheets a quire of paper? How many quires a ream? BOOKS. A sheet folded in two leaves is called a folio. 66 folded in four leaves a quarto, or 4to. 66 folded in eight leaves แ folded in twelve leaves 66 folded in eighteen leaves an octavo, or 8vo. a duodecimo or 12mo. an 18mo. Q. When a sheet is folded in two leaves, what is it called? When folded in four leaves? When folded in eight leaves? When folded in twelve? When folded in eighteen? APPLICATIONS IN REDUCTION. 1. In 6169 pence, how many pounds? Ans. £25 14s 1d. 2. In 5976. 13pwt. 5gr., how many grains? Ans. 340157. 3. In £85 8s, how many guineas? Ans. 81 guineas 7s. 4. How many strokes does a regular clock strike in a year of 365 days, striking once at one, twice at two, &c., for the 24 hours in the day? Ans. 5. In 757 boxes of sugar containing 2876. each, how many tons? Ans. tons, cwt. qr. 6. How many cords are there in a pile of wood that is 36 feet long, 6 feet high, and 4 feet wide? Ans. 6 cords, and 6 cord feet. 7. A man has a journey to perform of 288 miles; supposing him to travel 12 hours each day for 6 days in succession, at what rate must he travel per hour to accomplish it in that time? Ans. miles. 8. How many yards of carpeting which is one yard in width, will be required to carpet a room 18 feet wide and 20 feet long? Ans. 9. Reduce 346 Ells Flemish to Ells English. Ans. 207 Ells Eng. 10. Suppose the number of inhabitants in the United States to be 12 millions, how long would it take to count them, counting at the rate of 50 a minute? Ans. 166 days 16 hours. 11. A merchant wishes to bottle a cask of wine containing 63 gallons, into bottles containing one pint each: how many bottles are necessary ? Ans. 12. There is a cube, or square piece of wood, 2 feet or 24 inches each way; how many small cubes of one inch each way can be sawed from it, allowing no waste in sawing? Ans. 13824. 13. A merchant wishes to ship 285 bushels of flax seed, in casks containing 7 bushels 2 pecks each: what number of casks are required? Ans. 38. ADDITION OF DENOMINATE NUMBERS 1. John buys a knife for 1s 8d, and a bunch of quills for 1s 2d: what do they cost him? Ans. 2s 10d. 2. James gives 4s 9d for a pair of shoes, and 2s and 4d for a pair of stockings: how much do they cost him? Ans. 7s 1d. 3. How many hours in 8hr.+6hr.+7hr.+9hr.? Ans. 30hrs. 4. In 8yd.+7yd.+5yd.+6yd.: how many yards? Ans. 26yds. 5. How many pounds shillings and pence, in £4 8s 9d, £27 148 11d, and £156 17s 10d? We write the denominations under each other, and draw a line beneath them. We then add up the column of pence, and find the sum to be 30. But 30 pence are equal to 2 shillings and 6 pence: we therefore write down the 6 and carry 2 to the shil OPERATION. £ S d 4 8 9 27 14 11 156 17 10 £189 1s 6d. lings. We then find the sum of the shillings to be 41: that is, 2 pounds and 1 shilling over. Carrying the 2 to the column of pounds, we find the sum to be 189. § 71. Addition of denominate numbers, like that of simple numbers, teaches how to express the value of several numbers by a single one, which is called their sum. RULE. I. Set down the numbers to be added so that all the denominations of the same kind shall stand in the same column. II. Begin with the column of the lowest denomination, and add it up as in whole numbers. III. Then consider how many units of this denomination make one unit of the next higher, and divide the sum by this number. Write down the remainder under the units of its kind, and carry the quotient to the next column, as in addition of simple numbers. IV. Proceed in the same way for all the columns to the last, and set down the entire sum of the last column. The proof is the same as in the addition of simple numbers. Q. What is Addition of Denominate Numbers? How do you set down the numbers for Addition? Where do you begin to add? What do you do with the first sum? What do you write down? What do you carry to the next column? "How do you prove Addition? EXAMPLES. 1. What is the sum of £16 18s 9d, £14 13s 8d, and £15 17s 6d? For OPERATION. £ S d 16 18 9 14 13 8 15 17 6 Sum 47 9 11 30 11 2 NOTE. In simple numbers 10 units of any one of the columns, make one unit of the next left hand column § 8. We therefore carry one for every 10. But in denominate numbers the higher denominations are formed differently. example, 12 pence make 1 shilling, the unit of the next higher denomination; and 20 shillings make 1 pound. In passing from pence to shillings, we must therefore carry 1 for every 12, and 1 for every 20 in passing from shillings to pounds. And in general, we must carry 1 for so many units of the lower denomination as make one unit of the next higher. Proof 47 9 11 Q. In simple numbers how many units of one order make one unit of the next higher order? How do you carry in simple numbers? How do you carry in passing from pence to shillings? In passing from shillings to pounds? Generally, how do you carry? |