2. What is the latitude of the place at which the sun's m. alt., August 5th, is 74° 24′ N.? Answ. 1° 36' N. Required the latitudes coinciding with the annexed meridian altitude of the sun, on the days given.

3. Sun's meridian altitude 38° S.

January 13th.

12. Observing the sun's meridian altitude, on June 5th, to be 7010 S.; and at the same instant observing a timepiece regulated for Greenwich, found it to be 10 min. past 11 a.m.; required the place of observation.

13. On March 21st the sun's meridian altitude was found by observation to be 52° 30′ S., and the difference of time between the place of observation and London was 1 hr. 32 min. sooner,-required the place.

14. The sun's meridian altitude, May 15th, was observed to be 36° 45′ N., and it was 13 min. past 1 when it was noon at London,-required the place.

p.m.

15. Required the latitude and longitude of that place where the sun's meridian altitude, on May 21st, was 78° S., and where it was 3 p.m. when it was noon at London.

16. A ship, sailing from Jamaica, took the sun's meridian altitude on January 21st, and found it to be 50o S. ; and at the same instant observed a time-keeper, regulated for London, to point to 42 min. past 2 p.m.; how far was the ship distant from Jamaica?

17. At a certain place, where the clocks are 2 hrs. faster than at London, the sun's meridian altitude was observed to be 30° to the south of the observer, on the 21st of March; required the place.

18. At a place where the clocks are 3 hrs. 32 min. faster than at London, the sun's meridian altitude was observed to be 8010 S. on June 9th; required the place.

19. Where the clocks are 5 hrs. slower than at London, the sun's mer. alt. was observed to be 60° to the south of the observer, on April 16th; required the place. 20. In what latitude is the sun's greatest meridian altitude 79° S.?

21. Where has the sun no zenith distance on Sept. 23d?

PROBLEM XXI.

To find when the Sun is due East or West, the latitude of the place and the day of the month being given.

1. Elevate the globe for the latitude of the place, bring the sun's place to the meridian, and set the index to 12.

2. Fix the quadrant of altitude in the zenith, and bring it, if the sun's declination be of the same name with the latitude, to the eastern point of the horizon; then turn the globe till the sun's place come to the edge of the quadrant, and the index will show the time when the sun is due east.

3. If the declination and latitude are of different names, bring the quadrant to the western point of the horizon, and turn the globe till the point in the ecliptic, opposite to the sun's place, come to the edge of the quadrant, and the index will show the time when the sun is due east.

4. Subtract the hour, when the sun is due east, from 12, for the time when it is due west.

When the declination and latitude are of the same name, the sun is due east after rising, but when of different names, the sun is due east before rising.

As it is not so convenient to observe when the sun is due east below the horizon, the opposite point of the ecliptic is brought due west, and the index then shows the time of the sun's being due east.

EXAMPLES.

1. When is the sun due east and west at Newcastle, Nov. 3d? Answ. E. past 5, and W.

before 7. 2. At Leghorn, June 21st? Ans. E. 73, and W. 44. 3. At London, on the summer and winter solstices? 4. Liverpool, April 23d and Dec. 15th ?

5. At the following places, on March 21st, and Sept. 23d; viz. Panama, on the Isthmus of Darien; Truxillo in Peru; and Paramariboo, in Surinam?

6. At Buenos Ayres, Feb. 2d?

7. At Carlscrona, April 4th ?
8. At Bursa, on December 2d ?

9. At Demerara, on November 27th?

QUESTIONS FOR EXAMINATION IN SECTION IV.

What is the ecliptic? Why is it so called? What angle does it make with the equator? What is this angle called? Into how many parts or signs is it divided, and how many degrees does each contain? What are the names of the six northern signs? Write their characters. What are the names of the six southern signs? Write their charac

ters.

Name the spring, summer, autumnal, and winter signs.

Which are the ascending, and which are the descending signs? What are the tropics, and at what distance are they from the equator? What are their names, and why are they so called? What is it that determines the distance at which they are drawn from the equator? What are the polar circles? At what distance are they from the poles, and at what distance from the equator? What are the equinoctial points? What are the solstitial points? What is meant by the sun's altitude? How often in the year are the days and nights equal to all places upon the earth? What are these days called? In what places of the earth are the days and nights always equal? Which is the longest day to all places in the northern hemisphere? What is this day called? Which is the shortest day to all places in the northern hemisphere? What is this day called? Which is the longest and which is the shortest day to all places in the southern hemisphere? During what time are the days constantly increasing to all places in the northern hemisphere? During what time are the days continually increasing in the southerr hemisphere? What time of the year is the sun's declination north How is the sun's place in the ecliptic found? How is the sun's de

clination found?

On what two days of the year is the sun's declination greatest, north or south? On what days has the sun no declination? How is the globe rectified for the sun's place and day of the month? How are the rising and setting of the sun found by the globe? How is the length of the day and night found? How is the sun's meridian altitude found for any given day at any given place? How is the sun's altitude for any hour of the day found? Having the sun's meridian altitude, how is the latitude found? How is it found when the sun is due east or west at any given place?

QUESTIONS FOR EXERCISE IN SECTION IV.

1. At what hour does the sun rise at N. Cape, Dec. 21st?

2. Is June 21st longer at Jerusalem or Newcastle, and how much? 3. At which of these places is Dec. 21st the longest?

4. Which is the longest day to Quito ?

5. The difference between the longest and shortest day at Paris? 6. What is the sun's m. altitude at St. Petersburg, June 21st? 7. How high will the sun ascend on Christmas day at Bastia? 8. How high will the sun ascend at Samarcand on Sept. 29th ? 9. The sun's altitude June 21st at North Cape at midnight? 10. What is the sun's altitude at Moscow, at 8 a.m. May 1st? 11. When does the sun rise due east at Carlisle ?

12. What time does the sun rise and set at St. Petersburg, Naples, and Canton, on January 24th?

13. At what hour does the sun rise and set at Dublin, Gibraltar, Teneriffe, and Vienna, April 15th, July 4th, and Nov. 20th?

14. What is the length of the day and night on April 22nd, at London, Madrid, and Batavia?

15. What is the length of the day and night on June 10th, at St. Helena, Mexico, New York, and Canton?

16. What is the sun's declination, June 14th, and Aug. 31st? 17. What is the sun's m. altitude at London, on October 26th ? 18. Give the sun's alt. at London, May 21st, at 9 a.m. ? 19. What is the sun's alt. at Newcastle, May 21st, at 9 a.m. ? 20. The sun's altitude at Constantinople, June 4th, at 3 p.m. ? 21. How much longer is June 5th at Archangel than at Madras ? 22. What is the sun's greatest altitude in Magalhaen's Strait? 23. What is the sun's least meridian altitude at Stockholm-at Malta at Warsaw?

SECTION V.
DEFINITIONS.

1. The surface of the earth is divided into five zones.

M

2. The torrid zone is that space of the earth included between the tropics.

It is bounded by the tropic of cancer on the north, and the tropic of capricorn on the south its breadth is 46° 56', that being the distance

of the tropics from each other.

3. The two temperate zones are those parts lying between the tropics and polar circles.

The north temperate zone is bounded on the south by the tropic of cancer, and on the north by the arctic circle; its breadth is 43° 4′, that being the distance between the tropic of cancer and the arctic circle. The south temperate zone is bounded on the north by the tropic of capricorn, and on the south by the antarctic circle: its breadth is the same as that of the north temperate zone.

4. The two frigid zones are those spaces included within the polar circles.

These circles are at the same distance from the poles as the tropics from the equator, viz., 23° 28′.

5. If the latitude of any place be less than 231, it lies in the torrid zone; if it be more than 231" and less than 661, it is in one of the temperate zones; and if it be more than 66, it is in the frigid zone.

6. The inhabitants of these zones are distinguished by the different direction of their shadows.

Those who live in the torrid zone are called amphiscii; that is, having both kinds of meridian shadows. Twice in the year they have no shadow at noon, and are then called ascii.

Those who live in the temperate zones are called heteroscii; that is, having only one kind of meridian shadow. Those who live in the south temperate zone have their shadows at noon always towards the south; and those in the north temperate zone always towards the north.

Those who live in the frigid zones have, when their days are more than 24 hours long, the sun, and therefore their shadows, moving all around them; hence they are called periscii.

7. The sun is said to be vertical when it is in the zenith, or directly over head.

OF THE APPEARANCES OF THE SUN IN THE SEVERAL ZONES.

To all places in the torrid and temperate zones, the sun rises and sets daily.