30. Find by this table the total time required to make 100 medium-grade coats by hand; by machinery. 31. Find the difference in time for hand and machine work for each operation; for all. 32. A merchant vessel passed through the Suez Canal four times one year, the time for each passage being, respectively, 15 hr. 32 min., 19 hr. 58 min., 17 hr. 15 min., and 18 hr. 12 min. Find the average time of passage. 33. A shipment of candles to Calcutta consisted of 124 cases, each containing 21 lb. 14 oz. of candles. How much did the shipment of candles weigh? 34. Each case held 25 packets of 6 candles each. Find the weight of a packet; of a candle. 35. A man owned 84 A. 82.5 sq. rd. of land and bought 16 A. 1475 sq. rd. Afterward he sold of his land. How much land did he then own? 36. The number and length of the spans of the bridge across the Firth of Tay, Scotland, the longest bridge in the world, are as follows: 28 spans, each 3 rd. 10 ft.; 2 spans, each 4 rd. 14 ft.; 21 spans, each 7 rd. 43 ft.; 12 spans, each 8 rd. 4 ft.; 13 spans, each 13 rd. 15 span, 9 rd. 11⁄2 ft.; 1 span, 9 rd. 6 ft.; 6 spans, each 10 in miles, rods, and feet. ft.; 1 Find the length of the bridge LONGITUDE AND TIME 254. An imaginary line passing north and south from one pole of the earth to the other is called a meridian. from some selected meridian, called the prime meridian. The prime meridian commonly used is that passing through the Royal Observatory at Greenwich, England. 257. Distance east or west of the prime meridian, measured in degrees along the equator, is called longitude. East longitude is the distance east of the prime meridian; west longitude is the distance west of it. 258. 1. Since the earth rotates on its axis once in 24 hours, any meridian passes through 360° in that time. Then how many degrees of longitude pass under the sun's rays during 24 hours? during 1 hour? 2. Since 15° of longitude pass under the sun's rays in 1 hour, what part of a degree passes in 1 minute? How many minutes (') of longitude pass in 1 minute of time? 3. Since 15' of longitude pass under the sun's rays in 1 min., how many seconds (") of longitude pass in 1 sec. of time? 259. The relation between longitude and time may be expressed as follows: 360° of longitude correspond to 24 hours of time. 260. When the sun's rays are vertical at any point on a meridian, it is noon at all places on that meridian that are then lighted by the sun. Since the earth turns from west to east, the sun appears to move from east to west. Therefore when it is noon at any place it is before noon, or earlier, at all places west, because the sun has not yet reached the meridians of those places. It is after noon, or later, at all places east, because the sun has already crossed the meridians of those places. EXERCISES 261. 1. What is the difference in longitude between a place 15° west of Greenwich and a place 30° west? Which place has the earlier time and how much earlier? 2. How far westward must one go to pass from meridian 15° E. to Greenwich? from Greenwich to 15° W.? How many degrees west of 15° E. is 15° W.? Compare their times. Compare the times of places on the following meridians : 8. 30° E. and 30° W. 3. 15° W. and 45° W. 9. 10° E. and 5° W. 10. 20° E. and 10° W. 11. 40° E. and 20° W. 12. 30° E. and 45° W. In the following exercises refer to this table for longitudes and find answers to the nearest second. WRITTEN EXERCISES 262. 1. When it is noon at San Francisco, what is the time at Washington? 122° 24' 32" 77° 3' 6" 15)45° 21' 26" 3° 1' 26" 3 hr. 1 min. 26 sec. is the difference in time. The difference in longitude is found to be 45° 21' 26". Since 15° corresponds to 1 hr., 15′ to 1 min., and 15" to 1 sec., the difference in time between San Francisco and Washington is as many hours, minutes, and seconds, respectively, as there are degrees, minutes, and seconds in of the difference in longitude. Therefore the difference in time is 3 hr. 1 min. 26 sec., and since Washington is east of San Francisco, the time is later in Washington; that is, when it is noon at San Francisco it is 1 min. 26 sec. past 3 P.M. at Washington. Find the true time in each of the following cities when the sun is on the meridian of Washington: 11. What is the longitude of St. Petersburg, if its time is 6 hr. 57 min. 19 sec. later than that of New York? Since 1 hr. corresponds to 15°, 1 min. to 15', and 1 sec. to 15", the difference in longitude between New York and St. Petersburg is as many degrees, minutes, and seconds, respectively, as there are hours, minutes, and seconds in 15 times the difference in time between the two places. Therefore the difference in longitude is 104° 19′ 45′′, and since the time of St. Petersburg is later than that of New York, St. Petersburg is east of New York; but New York is only 74° 00′ 24′′ west of the prime meridian, and since the difference in longitude is greater than this, St. Petersburg must be east of the prime meridian. Subtracting, we find the longitude of St. Petersburg to be 30° 19′ 21′′ E. Find the longitude of places having the following times when the sun is on the meridian of Washington: 21. The longitude of Norwich, Eng., is 1° 18′ W.; of Norwich, Conn., 72° 4' W. How much later does the sun cross the meridian of the American city than that of the English city? 22. An astronomer in Boston observed the moon entering the shadow of an eclipse at 1:13 A.M. At what times did astronomers in Chicago, Denver, and San Francisco observe the same? 23. When the people of Boston were celebrating the passing of the 19th century at midnight Dec. 31, 1900, how long had Parisians been living in the 20th century? How much of the 19th century was left for the people of Galveston, 94° 47' 26" W.? |