61. Correspondence of time to longitude. Since 24 hours. correspond to 360° of longitude, we have the following:

62. Illustrative problem. The difference in time between two ships is 3 hr. 7 min. 3 sec. What is the difference in longitude?

1. Since 1 hr. corresponds to 15o, 3 hr. correspond to 3 times 15° 45°. =

2. Since 1 min. corresponds to 15', 7 min. correspond to 7 times 15' 105' = 1° 45'.

3. Since 1 sec. corresponds to 15′′, 3 sec. correspond to 3 times 51" 45". =

4. Therefore the difference in longitude is 46° 45′ 45′′. Evidently the mere figures of the answer could

be obtained by calling 3 hr. 7 min. 3 sec. 3° 7′ 3′′ and multiplying by 15, although the reason would not be so clear.

15

3° 7′ 3′′

46° 45′ 45′′

WRITTEN EXERCISE

1. The difference of time between two ships is 2 hr. 3 min. 10 sec. What is the difference in longitude?

2. When it is noon at Denver, it is 7 P.M. at Greenwich. What longitude does Denver use for its time purposes?

3. The difference in time between the Harvard and Columbia observatories is 8 min. 22.7 sec. What is the difference in longitude?

4. At 10:4 A.M. a steamer in longitude 26° 30' W. sends a wireless message to another steamer. It is received at 10:19 A.M. What is the longitude of the second steamer?

5. When it is noon in Greenwich it is 9 P.M. in Japan. What longitude does Japan use for its time purposes?

6. When it is noon in Melbourne it is 2 A.M. in Greenwich. What longitude does Melbourne use for its time purposes?

7. A traveler sails from New York with his watch set by the time of 75° W. If the watch indicates 2:30 P.M. when it is 5 P.M. by the ship's time, in what longitude is he?

8. A traveler sails from England with his watch set by Greenwich time. When he reaches 52° 30' 45" W., is his watch faster or slower than the time of that place, and how much?

9. Suppose a telegram sent from an observatory 121° 32' 48" W. at 8:40 A.M. to another observatory 73° 8' 16" W., and to require 16 min. for transmission. At what time will it be received?

10. Suppose a telegram sent at 4 P.M. from a place in Germany 15° E. to a place in California 120° W. At what time will it reach its destination, allowing 30 min. for repeating at various terminal offices?

11. A ship's captain observing the sun finds that when the ship is on the meridian (that is, at noon) the time is 3 hr. 7 min. 35 sec. P.M. by a chronometer set by Greenwich time. What is the ship's longitude?

12. Two observatories A and B are connected by a telegraph line. A telegram sent from A at 2 hr. 4 min. 6 sec. P.M. reaches B at 4 hr. 8 min. P.M. The longitude of B is 79° 12' 42.2" W. What is the longitude of A?

13. The officers of a steamer in the Mediterranean Sea find that when the sun is on the meridian the time is 10 o'clock 50 min. 15 sec. A.M. by a chronometer set by Greenwich time. What is the ship's longitude?

63. Standard time. It is so much trouble to think of differences of time like 1 hr. 2 min. 17.5 sec., that most civilized countries have adopted a system of standard time. They have considered all places in one section as having the same longitude, some multiple of 15°, so that the differences in time from Greenwich (the prime meridian) shall be exact hours, and therefore all differences in time shall also be exact hours.

For this reason New York (73° 58' 25.5" W.) is considered to have the longitude 75° W., and Chicago (87° 36' 42" W.) the longitude 90° W. Then when it is noon in England (which is all considered of longitude 0°) it is 5 hours earlier in New York, or 7 A.M., and it is 6 A.M. in Chicago.

64. Standard time map. This map shows the standard time sections in the United States, the irregularities of

PACIFIC TIME +120 MOUNTAIN TIME +105° CENTRAL TIME +90° EASTERN TIME

+75°

the divisions being due to the position of railway termini nearly 71° from the time meridians.

When it is noon in New York it is 11 A.M. in the Central Time section, 10 A.M. in the Mountain Time section, and 9 A.M. in the Pacific Time section.

65. Standard time problems. Since for practical purposes standard time is generally used, the exercises refer to that time unless the contrary is stated. The cities selected are near the time meridians. Cities on the line dividing two time sections usually adopt one or the other.

Questions concerning the date line and the change of day do not involve arithmetic, but belong rather to geography.

ORAL EXERCISE

1. When it is 10 A.M. in Iowa, what time is it in New York? in Wisconsin? in Louisiana? in Ohio?

2. What time is it now in your school? in Boston? in Florida? in Arkansas? in Colorado? in California?

3. When it is 10 A.M. in San Francisco, what time is it in Denver? in St. Louis? in Cleveland? in Albany?

4. When it is 9 A.M. in Denver, what time is it in Los Angeles? in New Orleans? in Cincinnati? in Boston?

5. When it is noon in California, what time is it in Illinois? in Massachusetts? (Consult the map, page 80.)

6. When it is 3 P.M. in Milwaukee, what time is it in Oregon? in Louisville? in New York? in Philadelphia?

7. When it is 1 P.M. in New York, what time is it in Richmond? in Philadelphia? in Chicago? in California?

8. When it is 9:30 A.M. in New Orleans, what time is it in Alabama? in Maine? in Wyoming? in San Francisco?

9. Suppose a telegram sent from New York at 1 P.M. to San Francisco. If it goes without loss of time, what time will it be when it crosses the Mississippi River? when it crosses Colorado? when it reaches San Francisco?

WRITTEN EXERCISE

1. France uses the time of Paris (2° 20′ 15′′ E.). When it is noon, standard time, in Iowa, what is the time in France?

2. Japan uses the time of 135° E. When it is noon at Greenwich, what is the time in Tokyo? in St. Louis? in Portland, Oregon ?

3. All of Great Britain uses Greenwich time. If it is 5:30 P.M. at Liverpool, what is the local time of a ship in 17° 16' 30" W. longitude?

4. The longitude of Chicago is 87° 36′ 42′′ W. What is the difference between the local (that is, the real meridian) and standard time?

5. Italy uses the Central European time (15° E.). When it is 7:30 A.M. in Springfield, Illinois, what time is it in Rome (7 hr. later)? in London?

6. When it is 1 P.M. in London, what is the time in Paris? (See Exs. 1, 3.)

7. The longitude of San Francisco is 122° 25' 40.8" W. Which is the later, local or standard time, and how much?

8. Berlin uses the standard time of 15° E. The tongitude of Berlin is 13° 23' 43.5". What is the difference between the local and standard time?

9. What is the difference in standard and in local time between Berlin and San Francisco? (See Exs. 7, 8.)

10. At midnight, December 31, 75° time, the United States Naval Observatory sends an electric time signal to various parts of the world, indicating that a new year is beginning at Washington. When does the signal reach California? Colorado? Alabama? England? Germany?