5. In 1905 the value of the lumber products in the Southern states was $250,000,000. In 1880 the lumber products of the rest of the United States were worth $194,000,000. By what per cent did the value of Southern lumber products in 1905 exceed that of the rest of the country in 1880? 6. A timber belt extending through Idaho, Washington, and Oregon is estimated to contain 8,000,000 acres of available timber, with an average of 10,000 ft. per If 9,000,000,000 feet of this is white pine, what per cent of the total is white pine? acre. 7. The output of a Maine paper mill is 180 tons of paper a day. If the average spruce tree supplies wood pulp for 500 lb. of paper, how many days will the timber from 225,360 spruce trees supply pulp for this mill? 8. In a recent year the output of the lumber mills of this country was 35,084,166,000 ft. At $16.25 per M, what was its value? If 33% of the value was profit to the lumber manufacturers, what was their profit? PRAC. ARITH.-21 2. How many degrees are there in any line (circle) passing around the earth on its surface? 444. In measuring circumferences, each degree is divided in 60 equal parts, called minutes, and each minute into 60 equal parts, called seconds. In this measure, degrees, minutes, and seconds are written with symbols. Thus, 3 degrees, 25 minutes, and 20 seconds is written 3° 25' 20". 445. A line on the earth's surface running north and south from pole to pole is called a Meridian. All places on the same meridian have wo their midday, or noon, at the same time; that is, when the sun is directly above that meridian. 10,0 N 120130 140 150 160 170 180 170 180 1 60°6040 30° 20° 10° 0 WEST LONGITUDE 30120 10° 20° 30° 40° 50 800 8 EAST LONGITUDE 100° 90°E 446. The distance in degrees east and west from a given meridian is called Longitude. The given meridian from which longitude is generally reckoned is called the Prime Meridian. It passes through the Royal Observatory at Greenwich, England. From this meridian longitude is reckoned east 180° and west 180°. 447. Places are located on a map, or on the earth's surface, by giving their distance in degrees from the equator north or south, and from the prime meridian east or west; that is, by giving their latitude and longitude. 1. In how many hours does the earth rotate (turn about on its axis) once? 2. If a city in the rotation passes through 360° in 24 hours, through how many degrees does it pass in one hour? (4 of 360° = 15°.) 448. A train standing on a sidetrack appears to move in the opposite direction when we pass it rapidly. In like manner the sun appears to move westward as the earth turns eastward. In reality, however, the earth makes a complete rotation in 24 hours, turning every place on its surface through 360 degrees in that time. Hence we may deduce the following: (a) 360° of longitude correspond to 24 hours of time. of 24 hr., or 1 hr., or 4 min. (b) 24 hours of time correspond to 360° of longitude. 1 hour of time corresponds to 24 of 360°, or 15°. 1 minute of time corresponds to 1 second of time corresponds to ¿ of 15°, or 15'. of 15', or 15". From the foregoing it will be seen that when it is noon at any given place it is 1 P.M. 15° east of that place, and 11 A.M. 15° west of that place. Hence clocks show later (faster) time at places east of a given place, and earlier (slower) time at places west of a given place. For example, clocks in New York show later time than clocks in Chicago. 449. The following short list of cities with their longitude is given for reference: 450. To find the difference in time, when the difference in longitude is given. WRITTEN EXERCISES 1. The difference in longitude between two cities is 78° 3' 30". What is the difference in time? (a) 78° corresponds to 78 xhr., or 5 hr., or 5 hr. 12 min. (Art. 448, (a).) 3' corresponds to 3 x min., or min., or 12 sec. 15 sec., or 2 sec. 30 corresponds to 30 × 5 hr. 12 min. + 12 sec. + 2 sec. in time. 15)78° 3′30′′ 5 12 14 Since the numbers expressing the difference in time between two places are of those expressing the difference in longitude between the same places, we may divide as at the left, and interpret the result as 5 hr. 12 min. 14 sec. 2. Find the difference in time between New York and Austin. Longitude of Austin Longitude of New York Subtracting, we have 97° 44' 0" 73° 58′ 251" 23° 45′ 34, difference in longitude. The difference in time is readily found as in problem 1. If two places are both east or both west of the prime meridian, the difference in longitude is found by subtracting as above; but if one is east and the other west of the prime meridian, the difference is found by adding. Find the difference in time between 3. New Orleans and Denver. 4. New York and St. Louis. 5. Chicago and New York. 6. Washington and Paris. 7. If a cablegram is filed in London (on prime meridian) at 7 A.M., what time does it reach New York, if no allowance is made for loss of time in transmission ? 8. An ocean liner leaving this country passes a signal ship in 75° W. longitude. Eight days are required to reach London. How must the clocks be changed each day if the rate of traveling is uniform? 9. A traveler sails from London with his watch set by Greenwich time. When he reaches Boston in longitude 71° 3' 30" W., is his watch faster or slower than the time of Boston, and how much? 10. If the polls open in a general election at sunrise at every place, how long may voting begin in New York before it begins in San Francisco? 451. To find the difference in longitude, when the difference in time is given. WRITTEN EXERCISES 1. The difference in time between two cities is 3 hr. What is their difference in longitude? 8 min. 45 sec. Since there are 15 times as many degrees, minutes, and seconds of longitude between two places as there are hours, minutes, and seconds of time, we may multiply as at the left, and interpret the result as 47° 11′ 15′′. (See Art. 448, (b).) |