20. Boston is 71° 3', and the city of Washington is 77° 43' W. longitude; what is the difference of longitude between the two places? Ans. 6° 40'.. 21. The island of Cuba lies between 74° and 85° W. longitude; how many degrees in longitude does it extend? 40. 1. When it is 12 o'clock at the most easterly extremity of the island of Cuba, what will be the hour at the most westerly extremity, the difference in longitude being 11° ? Note. The circumference of the earth being 360°, and the earth performing one entire revolution in 24 hours, it follows, that the motion of the earth, on its surface, from west to east, is 15° of motion in 1 hour of time; consequently, 1° of motion in 4 minutes of time, and 1' of motion in 4 seconds of time. From these premises it follows, that, when there is a difference in longitude between two places, there will be a corresponding difference in the hour, or time of the day. The difference in longitude being 15°, the difference in time will be 1 hour, the place easterly having the time of the day 1 hour earlier than the place westerly, which must be particularly regarded. If the difference in longitude be 1°, the difference in time will be 4 minutes, &c. Hence,-If the difference in longitude, in degrees and minutes, between two places, be multiplied by 4, the product will be the difference in time, in minutes and seconds, which may be reduced to hours. We are now prepared to answer the above question. 11° 44 minutes. Hence, when it is 12 o'clock at the most easterly extremity of the island, it will be 16 minutes past 11 o'clock at the most western extremity. 2. Boston being 6° 40′ E. longitude from the city of Washington, when it is 3 o'clock at the city of Washington, what is the hour at Boston? Ans. 26 minutes 40 seconds past 3 o'clock. 3. Massachusetts being about 72°, and the Sandwich Islands about 155° W. longitude, when it is 28 minutes past 6 o'clock, A. M. at the Sandwich Islands, what will be the hour in Massachusetts ? Ans. 12 o'clock at noon. MULTIPLICATION & DIVISION OF COMPOUND NUMBERS. 41. 1. A man bought 2 yards of cloth, at 1 s. 6 d. per yard; what was the cost? 2. If 2 yards of cloth cost 3 shillings, what is that per yard? 3. A man has three pieces of cloth, each measuring 10 yds. 3 qrs.; how many yards in the whole ? 4. If 3 equal pieces of cloth contain 32 yds. 1 qr., how much does each piece contain ? 5. A man has five bottles, each containing 2 gal. 1 qt. 1 pt.; how much wine do they all contain? 6. A man has 11 gal. 3 qts. 1 pt. of wine, which he would divide equally into five bottles; how much must he put into each bottle? 7. How many shillings are 3 times 8 d. ? 3 x 10 d. ? 4 X 7 d.? 7 x 6 d.? 5 X 2 qrs.? 3 X 9 d.? 10 X Here, as the numbers are large, it will be most convenient to write them down before multiplying and dividing. OPERATION. 1 5 8 3 price of 1 yard. 6)7 14 4 2 cost of 6 yards. 6 number of yards. Ans. 7 14 4 2 cost of 6 yards. 1 583 price of 1 yard. Proceeding after the man 6 times 3 qrs. are 18 qrs.ner of short division, 6 is con4 d. and 2 qrs. over; we set tained in 7£. 1 time, and 1£. down the 2 qrs.; then, 6 times over; we write down the 8 d. are 48 d., and 4 to carry quotient, and reduce the remakes 52 d. 4 s. and 4 d. mainder (1£.) to shillings, over, which we write down; (20 s.,) which, with the given again, 6 times 5 s. are 30 s. shillings, (14 s.,) make 34 s.; and 4 to carry makes 34 s. 16 in 34 s. goes 5 times, and 4 s. 1. and 14 s. over; 6 times over; 4 s. reduced to pence 1£. are 6£., and 1 to carry = 48 d., which, with the makes 7£., which we write given pence, (4 d.,) make 52 down; and it is plain, that the d.; 6 in 52 d. goes 8 times, and united products arising from 4 d. over; 4 d. 16 qrs., the several denominations is which, with the given qrs. the real product arising from (2) 18 qrs. ; 6 in 18 qrs. goes the whole compound number. 3 times; and it is plain, that 11. Multiply 3£. 4 s. 6 d. by 7. 13. What will be the cost of 5 pairs of shoes at 10 s. 6 d. a pair? 15. In 5 barrels of wheat, each containing 2 bu. 3 pks. 6 qts., how many bushels? = the united quotients arising from the several denominations, is the real quotient arising from the whole compound number. 12. Divide 22£. 11 s. 6 d. by 7. 14. At 2. 12 s. 6 d. for 5 pairs of shoes, what is that a pair? 16. If 14 bu. 2 pks. 6 qts. of wheat be equally divided into 5 barrels, howe bushels will each contain ? 17. How many yards of 18. If 9 coats contain 39 cloth will be required for 9 yds. 3 qrs. 3 na., what does 1 coats, allowing 4 yds. 1 qr. coat contain? 3 na. to each ? 19. In 7 bottles of wine, 20. If 5 gal. 1 gill of wine each containing 2 qts. 1 pt. 3 be divided equally into 7 botgills, how many gallons?" tles, how much will each con tain? 21. What will be the 22. If 8 silver cups weigh weight of 8 silver cups, each 3 lb. 9 oz. 1 pwt. 16 grs., what weighing 5 oz. 12 pwt. 17 is the weight of each? grs.? 24. If 119 cwt. 1 qr. of su 23. How much sugar in 12 hogsheads, each containing gar be divided into 12 hogsheads, how much will each hogshead contain ? 9cwt. 3 qrs. 21 lb. ? 25. In 15 loads of hay, each weighing 1 T. 3 cwt. 2 qrs., how many tons? 26. If 15 teams be loaded with 17 T. 12 cwt. 2 qrs. of hay, how much is that to each team? When the multiplier, or divisor, exceeds 12, the operations of multiplying and dividing are not so easy, unless they be composite numbers; in that case, we may make use of the component parts, or factors, as was done in simple numbers. Thus 15, in the example 15 being a composite numabove, is a composite number ber, and 3 and 5 its compoproduced by the multiplica- nent parts, or factors, we may tion of 3 and 5, (3 × 5 divide 17 T. 12 cwt. 2 qrs. by 15.) We may, therefore, one of these component parts, multiply 1 T. 3 cwt. 2 qrs. by or factors, and the quotient one of those component parts, thence arising by the other, or factors, and that product by which will give the true the other, which will give the answer, as already taught, true answer, as has been al- (T 20.) ready taught, (¶ 11.) OPERATION. T. cut. qr. 1 3 2 One factor, OPERATION. 3) 17 12 2 3 one of the factors. The other factor, 5) 5 17 2 2 5 the other factor. 17 12 2 the answer. 27. What will 24 barrels of flour cost, at 2£. 12 s. 4 d. a barrel? 29. What will 112, lb. of augar cost, at 74 d. per lb. ? Ans. 1 3 2 28. Bought 24 barrels of flour for 62 £. 16 s.; how much was that per barrel ? 30. If 1 cwt. of sugar cost 3 £. 7 s. 8 d., what is that per Note. 8, 7, and 2, are fac-lb. ? tors of 112. 31. How much brandy in 32. Bought 84 pipes of 84 pipes, each containing 112 brandy, containing 9468 gal. gal. 2 qts. 1 pt. 3 g.? 1 qt. 1 pt.; how much in a pipe? 33. What will 139 yards of doth cost, at 3 £. 6 s. 5 d. per yard? 34. Bought 139 yards of cloth for 461 £. 11 s. 11d.; what was that per yard? When the divisor is such a number as cannot be produced 139 is not a composite number. We may, however, decompose this number thus, by the multiplication of small 139: 100+30 + 9. numbers, the better way is to We may now multiply the divide after the manner of price of 1 yard by 10, which long division, setting down will give the price of 10 yards, the work of dividing and reand this product again by 10, ducing in manner as folwhich will give the price of lows: 100 yards. We may then multiply the price of 10 yards by 3, which will give the price of 30 yards, and the price of 1 yard by 9, which will give the price of 9 yards, and these three products, added together, will evidently give the price of 139 yards; thus: £. S. d. £. 3. d. 139) 461 11 11 ( 3£ .* 417 44 20 891 (68. 57 12 332 1 .99 12 29 17 10 695 ( 5 d. 695 The divisor, 139, is contained in 461 £. 3 times, 8 price of 100 yds. (3£.,) and a remainder of 6 price of 30 yds. 44., which must now be 9 price of 9 yds. reduced to shillings, multiplying it by 20, and bringing 461 11 11 price of 139 yds. in the given shillings, (11 s.,) Note. In multiplying the making 891 s., in which the price of 10 yards (33£. 4 s. divisor is contained 6 times, 2 d.) by 3, to get the price of (6 s.,) and a remainder of 30 yards, and in multiplying 57 s., which must be reduced the price of 1 yard (3£. 6 s. to pence, multiplying it by 12, 5 d.) by 9, to get the price of and bringing in the given 9 yards, the multipliers, 3 and pence, (11 d.,) together mak9, need not be written down, ing 695 d., in which the dibut may be carried in the visor is contained 5 times, mind. (5 d.,) and no remainder. The several quotients, 3, 6 s., 5 d., evidently make the answer. |