The foregoing plan may be indefinitely modified; hence this general direction: Multiply by two or more numbers whose product is nearly the multiplier, and add to, or subtract from, the product such numbers as the case may require. 31. Multiply 15yd. 2qr. 1na. by 47. 32. Multiply 27gal. 1qt. 1pt. 2gi. by 43. 33. What is the cost of 753 acres of land, at 4£ 10s. 8d. 2qr. per acre? Multiply by 100, i. e. by 10 and 10; then multiply the cost of 100 acres by 7, the cost of 10 acres by 5, and the cost of 1 acre by 3, which will give the cost of 700, 50, and 3 acres, severally; finally, add the cost of 700, 50, and 3 acres together, and thus find the cost of 753 acres, the answer. 34. If 1 acre of land yield 54 bush. 3pk. 6qt. 1pt. of corn, what will 643 acres yield? 35. If a man travel 33m. 6fur. 35rd. 5yd. 2ft. 11in. each day, how far will he travel in 313 days? 36. If a ship sail 2° 40′ 30′′ each day, how far will she sail in 127 days? 37. How much wine in 157 casks if each cask contains 53gal. 3qt. 1pt. 2gi.? 207. Mode of multiplying when the multiplier is large and not composite? 208. To find the difference of the time of day in two places, at the same absolute moment of time, when the longitude of each place is known. Since the sun appears to go from east to west round the earth, 360° (Art. 109), in 24 hours, it appears to go 4 of 360°, viz. 15° in 1 hour, and, consequently, 1° in of 1 hour, viz. 4 minutes, and l' of distance in of 4 minutes, viz. 4 seconds. These facts give us the following 38. When it is 12 o'clock, noon, at Washington, what time is it at London, Washington being 77° 2′ 48" west of London? о OPERATION. 77 2 48 4 5h. 8m. 1 11sec. Ans. Since 1" of longitude makes a difference of of a second of time, 48′′ of longitude give 123sec. of time, and for a like reason 2′ of longitude give 8sec. of time, which added to the 31sec. previously obtained, give 111sec., and, finally, 77° of longitude give 4 times 77: 308m. 5h. 8m. of time; .. the difference in time between London and Washington is 5h. 8m. 11 sec., and as London is farther east than Washington, the hour of the day is later in London than in Washington, i. e. it is 8m. 111sec. past 5 o'clock in the afternoon at London when it is noon at Washington. Hence, RULE. Multiply the difference of longitude, expressed in degrees, minutes, and seconds, by 4, and the product will be the difference in time, expressed in minutes, seconds, and 60ths of a second. 208. How far does the sun appear to move in one hour? Which way? Give the table of longitude and time. Rule for finding difference in time of two places when the longitude of each is known? NOTE. 1. The place most easterly, has its hour of the day, at a given moment, latest; i. e. the day begins first, noon comes first, and the day closes first at the place most easterly. 39. The longitude of Boston is 71° 4′ 9′′ west, and that of Washington is 77° 2′ 48′′ west; what is the difference in the time of the two places, and what time is it in Washington, at 3 o'clock, P. M., in Boston? By subtraction, the difference of longitude is found to be 5° 58′ 39′′, .. the difference in time is 23m. 543sec., and at 3 in Boston it is 36m. and 53sec. past 2 in Washington, Ans. 40. The longitude of Paris is 2° 20′ 15′′ east, and that of New York, 74° 0′ 3′′ west from Greenwich; what is the difference in time in the two places? Ans. 5h. 5m. 21sec. Ans. NOTE 2. Since Paris is in east longitude, and New York in west, their difference in longitude is found by adding 2° 20′ 15′′ to 74° 0′ 3′′. 41. What is the difference in time between Philadelphia, 75° 9′ west longitude, and Chicago, 87° 35' west longitude? 42. What is the difference in time between New Orleans 90° 7′ west, and St. Petersburg, 29° 48′ east longitude? 43. What is the difference in time for 90° in longitude? DIVISION. 209. Here, as in the three preceding sections, the principle is the same as in the corresponding operation in simple numbers. Hence, To divide a compound by a simple number, RULE. Divide the highest denomination of the dividend, and set down the quotient; if there is a remainder, reduce it to the next lower denomination; to the result add the given quantity of that denomination, and divide as before, setting down the quotient and reducing the remainder, etc. 208. Which has the hour of the day latest, the most easterly or most westerly place? How is the difference in longitude found when one place is in east and the other in west longitude? 209. Rule for dividing a Compound by a Simple Number? Principle? Ex. 1. Divide 30£ 7s. 1d. 1qr. by 7. OPERATION. £ S. d. qr. 7)30 7 1 1 4 6 8 3, Ans. 30 7 1 1, Proof. 30£ 7 give a quotient of 4£ and a remainder of 2£; 2£ reduced to shillings and added to 7s. give 47s., which, divided by 7, give a quotient of 6s. and a remainder of 5s., etc. 2. Divide 1fur. 9rd. 2yd. Oft. 9in. 1b.c. by 5. Ans. 9rd. 4yd. 2ft. 6in. 2b,c. 3. Divide 20gal. 2qt. Opt. 2gi. by 7. Ans. 2gal. 3qt. 1pt. 2gi, 4. Divide 18 lb. 1oz. 15dwt. 8gr. by 4. 8. Divide 3wk. 6d. 14h. 17m. 57sec. by 3. 10. Divide 107gal. 1qt. by 12. 11. Divide 98bush. 3pk. 2qt. 1pt. by 11. 12. Divide 51c. 7c.ft. 15 cu.ft. 1716cu.in. by 4. 13. Divide 16a. lyd. 4ft. 70in. by 2. 14. Divide 37t. 12cwt. 3qr. 5lb. 10oz. 4dr. by 9. 15. Divide 71a. 3r. 14rd. 8yd. 1ft. 72in. by 6. 16. If 9 silver spoons weigh 1lb. 4oz. 17dwt. 12gr., what is the weight of each spoon? Ans. 1oz. 17dwt. 12gr. 17. If a family use 29gal. 3qt. 2gi. of molasses in 6 months, what is the average per month? 18. If 10t. 18cwt. 1qr. of hay is harvested from 5 acres, what is the crop on one acre? 19. If 8 boxes of sugar weigh 2t. 7cwt. 2qr. 10lb., what is the weight per box? 20. If 9 grain-bins contain 143bush. 2pk. 2qt. 1pt. of grain, what does one bin contain? 21. If a man travel 212m. 1fur. 26rd. 2yd. in 7 days, what distance does he travel per day? 22. Divide 96£ 5s, 7d. 2q. by 10, 210. To divide by a composite number, we may divide by its factors, as in division of simple numbers (Art. 79). 23. Divide 341 lb. Ooz. 12dwt. by 72. 8)37 10 14 16 4 8 16 20, Ans. 24. Divide 396£ 2s. 3d. by 54. First divide by 9 and then the quotient by 8, and thus by 72. 25. Divide 725bush. Opk. 6qt. 1pt. by 81. 26. Divide 397 fb 113 73 19 4gr. by 63. 27. Divide 958m. 5fur. 5ch. 12 li. 51gin. by 48. 211. When the divisor is large and not composite, set down the work of dividing and reducing. There is no device for rendering the operation easier. 28. Divide 135bush. 3pk. 3qt. 1pt. by 47. bush. pk. qt. pt. 47) 135 3 3 1 (2bush. 3pk. 4qt. 1pt., Ans. 94 4 1 bush. 167 pk. 26 pk. 211 qt. 23 qt. Having found that 47 is contained twice in 135, multiply 47 by 2, and subtract the product, 94, from 135, which leaves a remainder of 41 bushels; reduce the 41 bushels to pecks, and add the 3 pecks, making 167 pecks; then divide the 167 pecks by 47, and so continue the process till the work is done, 47 pt. 47 0 210. Rule for dividing by a composite number? 211. Method of dividing when the divisor is large and not composite? Is there no easier mode? |