The day of the month and the sun's azimuth being given, to find the Sun's Altitude and the Hour of the Day.

See Problem VII., page 278.

To all places in the torrid zone, when the sun's declination is greater than the latitude, and of the same name with it, the sun has the same azimuth twice in the forenoon and twice in the afternoon; and the examples in that case admit of two answers.

EXAMPLES.-1. At Gibraltar, on November 25th, the sun's azimuth was observed to be 50° from the south towards the east; what was the time? Ans. 8 a.m.

2. At Madras, the sun's azimuth was observed to be N. 70° E. in the morning of June 15th; required the time. Ans. 24 min. past 7, or 52 min. past 8.

Having the sun's azimuth at the following places and days, required the hour and the sun's altitude.

PROBLEM XIX.

The sun's alt., day of month, and lat. of the place being given, to find the Sun's Azimuth, and Hour of the Day.

See Problem VIII., page 279.

The sun having the same altitude twice in the day, it must be known whether the time be in the morning or in the evening.

EXAMPLES.-1. At Newcastle, May 15th, p.m., the sun's alt. was 25°; required the hour and the sun's azimuth. Ans. 5 p.m.; azimuth, N. 88o W.

2. At Botany Bay, on April 23rd, the sun's altitude in the morning was observed to be 25"; required the hour and the azimuth, Ans. before 9; azimuth, N. 55o E.

Having the sun's altitude on the undermentioned days, required the hour and the sun's azimuth at

The latitude, the sun's altitude and azimuth being given, to find the Day of the Month, and the Hour of the Day. 1. Elevate the globe for the latitude, fix the quadrant upon the zenith, and bring it to the given azimuth.

2. Turn the globe about, and that degree of the ecliptic which cuts the quadrant at the given altitude will be the sun's place,--from which find the day of the month.

3. Keeping the quadrant in the same position, turn the globe till the sun's place come to the meridian, and set

the index to 12: then bring the sun's place again to the quadrant, and the index will show the hour.

Unless it be known whether the sun be in the ascending or descending signs, the examples admit of a double answer.

EXAMPLES.

1. The sun was observed, in the summer season, to be 33o high, when its azimuth was S. 70° E. at St. Petersburg; required the day and hour. Ans. July 27, 8 h. 14 m. a.m.

2. The sun at Lima, being 45° high, when its azimuth was N. 50o W.; required the day and hour. Ans. May 2, or Aug. 10, at 2 h. 33 m. p.m.

3. At London, the altitude being 17° high, when the azimuth was S. 17° E.; name the day and the hour.

4. At the Pelew Islands, the sun being in the descending signs, its altitude was found to be 37o, when its azimuth was S. 54° W.; required the day and hour.

5. At Owhyhee, the sun's altitude was 27, when its azimuth was S. 74° W.; required the day and the hour. 6. At London, the sun's altitude was 46° 31', when its azimuth was S. 4410 E.; required the time.

QUESTIONS FOR EXAMINATION IN SECTION II.

What is the diameter of the sun? What is its bulk compared with the earth? What is the power of gravitation at its surface? What is it that retains the planets in their orbits? Is the sun absolutely at rest? What is its distance from the earth? What is Sir William Herschel's opinion with respect to the sun? Describe the general appearance of the spots on its surface? What is the penumbra supposed

to be?

What produces the apparent motion of the sun among the stars? How are the sun's right ascension and declination found for any day? How are the sun's oblique ascension, ascensional difference, eastern amplitude, and time of rising found, on any given day?

How are the sun's oblique descension, descensional difference, western amplitude, and time of setting found? How may the time of the sun's rising be found from the ascensional difference?

From having the latitude, hour of the day, and day of the month given, how are the sun's altitude and azimuth found?

How are the sun's altitude and the hour of the day found in a given latitude, from having the day of the month and the azimuth?

Having the sun's altitude, day of the month, and latitude of the place given, how are the sun's azimuth and hour of the day found? From having the latitude, the sun's altitude, and azimuth given, how are the day of the month and hour of the day found?

QUESTIONS FOR EXERCISE IN SECTION II.

1. Required the sun's right ascension and declination for the last day in each of the calendar months.

2. What are the sun's oblique ascension, ascensional difference, eastern amplitude, and time of rising, at the following times and places:— York, February 5th; Berlin, January 29th; Juan Fernandez, March 1st; Quito, June 21st; Samarcand, December 21st; Pegu, May 15th; Alexandria, August 10th; Bender, July 11th; Cape Horn, December 25th; Pelew Islands, November 5th?

3. Give the sun's oblique ascension, descen. difference, western amplitude, and time of setting, for the same places and times.

4. What are the sun's altitude and azimuth at the following places and times:-Copenhagen, March 5th, 10 a.m.? Marquesas, July 7th, 3 p.m.? Pekin, August 12th, 7 a.m.? Batavia, January 1st, 11 a.m.? Cape of Good Hope, December 21st, 6 p.m. ? Guadaloupe, June 4th, 8} a.m.?

5. April 15th, in the afternoon, the sun's altitude at Madrid was 50°; required the hour and the azimuth.

6. At London, on May 1st, the sun's azimuth was S. 44° E.; required the hour and the sun's altitude.

7. At Canton, on March 10th, the sun's azimuth was S. 74° E.; what were the hour and altitude.

8. At Jerusalem, on February 22nd, the sun's azimuth was S. 55° E.; required the hour and altitude.

9. At Rome, on March 10th, the sun's azimuth was S. E. 6° 24′ E.; required the hour and altitude.

10. In lat. 5110, the sun's altitude was 4630, on June 21st; required the hour and the azimuth.

11. At Oonalashka, on June 21st, in the evening, the sun's altitude was 10°; required the hour and the azimuth.

12. At London, what are the sun's altitude, and the hour, when it is due east or west on the longest day?

13. At London, on June 21st, how far from the north does the sun rise and set?

14. At Paris, on November the 5th, in the evening, the sun's altitude was 20°; required the hour and azimuth.

15. In the morning of June 21st, the sun's altitude at London was 46° 20′; what was the hour?

16. The sun being in the ascending signs, its altitude at Newcastle was observed to be 22o, when its azimuth was N. 87° W.; required the day of the month and the hour of the day.

17. At Stockholm, in the summer season, the sun's altitude was 12o, when its azimuth was N. 63° E.; required the day of the month and the hour of the day.

18. At Edinburgh, June 21st, how far from N. does the sun rise? 19. How many degrees are there between that point of the horizon in which the sun rises at Newcastle on June 21st, and that point in which it rises on December 21st?

20. In what part of the horizon does the sun rise at Quito, on June 21st and December 21st.

SECTION III.

OF PLANETS AND COMETS.

The planets are heavenly bodies which do not, like the fixed stars, shine by their own light, but by the reflection of the light of the sun. Eleven are at present known.

In the order of their distance from the sun they areMercury, Venus, the Earth, Mars, Vesta, Juno, Ceres, Pallas, Jupiter, Saturn, and Uranus. — Mercury and Venus, which are nearer the sun than the earth is, are called inferior planets, and the others which are more distant are called superior planets.

The inferior planets, in consequence of their comparative contiguity to the sun, are never seen in opposition to it: that is, they are never seen in the east when the sun is in the west, nor in the west when the sun is in the east; nor are they ever seen on the meridian at midnight. But the superior planets, whose orbits are much farther removed from the sun than that of the earth, are often seen in opposition to the sun.

All the planets, with the exception of Juno, Ceres, and Pallas, confine their movements to that zone of the heavens called the zodiac.

The obvious conclusion from this is, that the planes of the orbits of the planets are inclined to each other at very small angles, and that they correspond very nearly with the plane of the ecliptic.