the index will show the time of the sun's rising, and to the western edge for the time of setting.

EXAMPLES.

1. Required the time of sun-rise and sun-set at Edinburgh on June 1. Answ. Rises 3 h. 27 m., sets 8 h. 33 m.

2. At what time does the sun rise and set at London on July 17th, and what is the length of the day and night? Answ. The sun rises at 4, and sets at 8, the length of the day is 16 hours, and the night eight hours. Required the rising and setting of the sun at 3. Pekin, April 10. 4. Newcastle, Oct. 13. 5. Gibraltar, Jan. 22.

6. Petersburg, June 21.

7. Hamburgh, Dec. 21. 8. North Cape, Dec. 21. 9. Botany Bay, May 25. 10. London, Aug. 29.

27. At Archangel, London, Vienna, Jerusalem, Quito, and Cape of Good Hope, on March 21st and Sept. 23rd. What is the length of the longest and shortest day, and the difference between them, at the following places?

What is the length of the day, and of the night, on December 26th, at the following places?

49. What is the hour of the sun's rising at Pekin, Naples, and Philadelphia, on August 29th?

50. How much longer is the sun above the horizon, on June 21st, to Edinburgh than to London?

51. How much longer is June 21st at St. Peterburgh, than at Jerusalem ?

52. At what time does the sun rise and set at Spitzbergen, on April 5th ?

PROBLEM XVIII.

To find the Sun's Meridian Altitude for any Day. BY THE GLOBE.-1. Elevate the globe for the latitude of the given place; find the sun's place for the given day, and bring it to the brass meridian.

2. Fix the quadrant of altitude on the zenith, and bring it over the sun's place; then the degree upon the quadrant cut by the sun's place will be its meridian altitude.

Note.-The sun's meridian altitude may be found without the quadrant, by counting upon the meridian the number of degrees intercepted between the horizon and the sun's place.

BY THE ANALEMMA.-Elevate the globe for the latitude, and bring the analemma to the brass meridian. The number of degrees intercepted between the day of the month marked on the analemma, and the nearest point of the horizon, either north or south, will be the meridian altitude required.

BY CALCULATION.-1. Find, from the Table, the sun's declination for the given day.

2. If the declination be of the same name as the latitude, their difference will be the zenith distance.

3. If the declination and latitude be of different names, their sum will be the zenith distance.

4. The zenith distance, taken from 90°, will give the altitude.

To know whether the Sun's Meridian Altitude be North or South. RULE.-1. When the declination and latitude are of different names, i. e. the one north and the other south, the altitude is always of the same name as the declination.

2. When the latitude and declination are of the same name, if the declination be the greater, the altitude is also of the same name, otherwise it is of a name contrary to that of the declination.

3. What is the sun's meridian altitude at the Cape of Good Hope on May 15?

The lat. 34° 29' S. added to the dec. 18° 46′ N. gives 53° 15′ zenith dist., and this taken from 90 36° 45′ altitude N., being of the same

name with the declination.

=

4. What is the sun's meridian altitude at Corinth, on March 21st?

On March 21st the sun has no declination; hence the zenith distance is equal to the latitude, 37° 30′; which taken from 90° gives 52° 30' south altitude.

5. Required the sun's meridian altitude at Newcastle :

Dec. 21.

March 21.

June 21.

6. What is the sun's meridian altitude at Cairo, on

Dec. 21?

March 21, or Sept. 23? June 21?

7. What is the sun's meridian altitude at Port Royal, March 21, or Sept. 23? June 21?

Dec. 21? 8. Required the sun's meridian altitude for the following places, on December 21st and June 21st?

Bergen,

Quebec.

Athens.

Mocha (Arabia).
Batavia.

St. Helena Isle.

Botany Bay.
Cape Horn, in

S. America.

9. What is the sun's meridian altitude at the following

places, on the following days?

Gottingen,

Canary Isles,

Port Mahon,
Smyrna,

April 17th, and August 1st?

May 15th, and December 25th?
February 28th, and July 7th?
May 1st, and November 11th?

To all places situated north of the tropic of cancer the sun's meridian altitude is always south; to all places situated south of the tropic of capricorn its meridian altitude is always north; and to those places situated between the tropics its meridian altitude is sometimes north and sometimes south.

From the above examples it will be seen, that the difference between the sun's greatest and least meridian altitudes, at any place situated without the tropics, is equal to 46° 56', or twice 23° 28′, the distance of each tropic from the equator.

PROBLEM XIX.

To find the Sun's Altitude for any Hour, aving the latitude and the day of the month given.

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

2. Turn the globe till the index point to the given hour; and having screwed the quadrant of altitude on the zenith, bring it over the sun's place.

3. Then the degree on the quadrant cut by the sun's place will be the altitude required.

EXAMPLES.

1. Required the altitude of the sun at Jerusalem, on October 21st, at ten o'clock, a.m.

2. At Petersburg, June 21st, at 6 p.m.

Answ. 38°.

Answ. 20o.

Required the sun's altitude at the following places:

3. Jamaica, Dec. 1st, at 3 p.m.

4. London, May 1st, 10 a.m.

5. Spitzbergen, June 21st, midnight.

6. New Orleans, Dec. 21st, 4 p.m.

7. Cape of Good Hope, May 15th, 10 a.m.
8. Washington, Sept. 25th, 3 p.m.

9. Louisburg, March 27th, 11 a.m. 10. Edinburgh, Nov. 30th, 10 a.m. 11. Malta, June 9th, 8 a.m.

12. Glasgow, April 4th, 3 p.m.

For more examples, see Problem XVII., on the celestial globe.

PROBLEM XX.

Having the Sun's Meridian Altitude, to find the Latitude of the place.

Bring the sun's place to the meridian, and move the globe up or down, till the distance between the sun's place and the north or south point of the horizon (as the case requires) be equal to the given altitude; then will the elevation of the pole be the latitude required.

By Calculation.-1. Subtract the altitude from 90° for the zenith distance, which is N. if the zenith be north of the sun; or S., if it be the contrary.

2. If the zenith distance and declination be both north or both south, add them together; but if one be north and the other south, subtract the less from the greater, and the sum or difference will be the latitude of the same name with the greater.

EXAMPLES.

1. The sun's meridian altitude on the 18th of May, was 42o 13' S.; required the latitude.

In this case, the sun's altitude being S., the zenith will be N. of the sun,-being always of the contrary name to the altitude.