on its axis till the sun's place cuts the quadrant twelve degrees below the horizon, then all stars of the first magnitude, along the eastern part of the horizon, will rise heliacally; and, by continuing the motion of the globe eastward till the sun's place intersects the quadrant in 13, 14, 15, &c. degrees below the horizon, you will find all the stars of the 2d, 3d, 4th, &c. magnitude. By turning the globe eastward on its axis, in a similar manner, and bringing the quadrant to the western part of the horizon, you will find all the stars that set heliacally.

The principal use of this and the last three problems, (of which it is the reverse) is to illustrate several passages in the ancient writers, as Hesiod, Virgil, Ovid, Pliny, &c. The knowledge of these poetical risings and settings was held in great esteem among the ancients, and was very useful to them in adjusting the time set apart for their religious and civil duties, and for marking the seasons proper for their several parts of husbandry; for the knowledge which the ancients had of the motions of the heavenly bodies was not sufficient to adjust the true length of the year; and, as the returns of the seasons depend upon the approach of the sun to the tropical and equinoctial points, so they made use of these risings and settings to determine the commencement of the different seasons, the time of the overflowing of the Nile, &c. The knowledge which the moderns have acquired of the motions of the heavenly bodies, renders such observations as the ancients attended to in a great measure useless, and, instead of watching the rising and setting of particular stars for any remarkable season, they can consult an almanac for every purpose of husbandry.

EXAMPLES.

1. What stars rise and set achronically at Drontheim in Norway, latitude 63° 26' north, on the 18th of May?

Answer. Altair in the Eagle, the head of the Dolphin, &c. rise achronically; and Aldebaran, Betelgueze, &c. set achronically.

2. What stars rise and set achronically at Petersburg in Virginia, latitude 37° 15' north, on the 20th of November?

3. What stars rise and set achronically, cosmically, and heliacally, at New-York, on the 1st of January?

4. What stars rise and set achronically, cosmically, and heliacally, at Lexington in Kentucky, latitude 38° 6' north, on the 1st of March?

5. What stars of the 1st magnitude set heliacally at London, on the 5th of May?

PROBLEM XIV.

The latitude of a place and day of the month being given, to find the meridian altitude of any star or planet. RULE. Rectify the globe for the latitude of the given place; then,

For a Star. Bring the given star to the brazen meridian; the degrees on the meridian, contained between the star and the next point of the horizon, will be the altitude required.

When the meridian altitude of a star is required, it is not necessary to attend to the day of the month, since the meridian altitude of the stars on the globe are invariably in the same latitude.

For the Moon or a Planet. Find the longitude and latitude, or the right ascension and declination of the planet, for the given day, and mark its place on the globe, (by Prob. II. ;) bring the planet's place to the brazen meridian, and the number of degrees, on the meridian, between that place and the horizon, will be the altitude required.

The longitude and latitude, or the right ascension and declination of the moon or a planet, must be found by means of the Nautical Almanac.

EXAMPLES.

1. What is the meridian altitude of Aldebaran at

Philadelphia ?

2. What is the meridian altitude of Arcturus at Richmond?

3. What is the meridian altitude of the following stars, at Washington City: Vega, Sirius, Arcturus, Pollux, Castor, Regulus, Procyon, Denebola, Cor Caroli, and Cor Scorpio?

4. On the 25th of February, 1825, the right ascension of Venus was 20° 15', and declination 100 9' north; what was her meridian altitude at Greenwich, at that time?

PROBLEM XV.

The meridian altitude of a known star being given, to find the latitude of the place of observation.

RULE. Bring the given star to the brazen meridian; count the number of degrees in the given altitude, on the meridian, from the star, towards the south point of the horizon, if the place of observation be in north latitude, or towards the north if in south latitude, and mark where the reckoning ends; then, elevate or depress the pole till this mark coincides with that part of the horizon towards which the altitude was reckoned; and the elevation of the pole above the horizon will show the latitude.

EXAMPLES.

1. In what degree of north latitude is the meridian altitude of Spica Virginis 20 degrees? Answer. 60 degrees north.

2. In what degree of south latitude is the meri dian altitude of Vega in Lyra 50 degrees?

3. In what degree of north latitude is the meri

dian altitude of Regulus, 28 degrees ?

PROBLEM XVI.

Given the latitude of a place, day of the month, and the altitude of a star, to find the hour of the night, and the star's azimuth.

RULE. Rectify the celestial globe, (by Prob. VII.) screw the quadrant of altitude upon the brazen meridian over the given latitude; bring the lower end of the quadrant to that side of the meridian on which the star was situated when observed, and turn the globe westward till the centre of the star cuts the given altitude on the quadrant; then the hours which the index has passed over, will show the time from noon when the star has the given latitude; and the quadrant will intersect the horizon in the required azimuth.

EXAMPLES.

1. At New-York, on the 20th of August, the star Alpherast, in the head of Andromeda, was observed to be 19 degrees above the horizon, and east of the meridian; required the hour of the night and the star's azimuth.

Answer. The celestial globe being rectified, and turned westward till the star cuts 190 of the quadrant of the meridian, the index will have passed over 8 hours; consequently, the star has 190 of altitude east of the meridian, at S o'clock in the evening. Its azimuth will be 680 from the north towards the east.

2. On the 21st of December, the altitude of Sirius, when west of the meridian at London, was observed to be 8o above the horizon; what hour was it, and what was the star's azimuth?

PROBLEM XVII.

Given the latitude of a place, the day of the month, and azimuth of a star, to find the hour of the night and the star's altitude.

RULE. Rectify the celestial globe, (by Prob. VII.) screw the quadrant of altitude upon the brazen meridian, over the given latitude; bring the lower end of the quadrant to coincide with the given azimuth on the horizon, and hold it in that position; then, turn the globe westward, till the given star comes to the graduated edge of the quadrant; the hours passed over by the index will be the time from noon, and the degrees on the quadrant, reckoning from the horizon to the star, will be the altitude.

EXAMPLES.

1. On the 20th of August, the azimuth of Alpherast in the head of Andromeda, was observed to be 68 degrees from the north towards the east; required the hour of the night, and the star's altitude.

Answer. By turning the globe westward on its axis, till the given star coincides with the quadrant, the index will have passed over 8 hours; therefore, the time will be s o'clock in the evening, the altitude is found to be 19 degrees.

2. At London, on the 18th of December, the azimuth of Denebola was observed to be 62 degrees from the south towards the west; required the hour of the night and the star's altitude.

3. On the 20th of November, the azimuth of Aldebaran, was 78 degrees from the south towards the east; required its altitude at Philadelphia and the hour of the night.