ward till the centre of the star cuts the given altitude on the quadrant; count the hours which the index has passed over, and they will show the time from noon when the star has the given altitude: the quadrant will intersect the horizon in the required azimuth.

Examples. 1. At London, on the 28th of December, the star Deneb in the Liou's tail, marked ß, was observed to be 40 deg. above the horizon, and east of the meridian, what hour was it, and what was the star's azimuth?

Answer. By bringing the sun's place to the meridian, and turning the globe westward on its axis till the star cuts 40 deg. of the quadrant east of the meridian, the index will have passed over 14 hours; conse quently the star has 40 deg. of altitude east of the meridian, 14 hours from noon, or at two o'clock in the morning. Its azimuth will be 62 deg from the south towards the east.

2. At London on the 28 of December, the star ẞ in the Lion's tail, was observed to be westward of the meridian, and to have 40 deg. of altitude; what hour was it, and what was the star's azimuth?

Answer. By turning the globe westward on its axis till the star cuts 40 deg. of the quadrant, west of the meridian, the index will have passed over 20 hours; consequently, the star has 40 deg. of altitude west of the meridian 20 hours from noon, or eight o'clock in the morning. Its azimuth will be 623 deg. from the south towards the west.

3. At London, on the 1st of September, the altitude of Benetnach in Ursa Major, marked », was observed to be 36 deg. above the horizon, and west of the meridian, what hour was it, and what was the star's azimuth ?

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

5. On the 12th of August, Menkar in the Whale's jaw, marked a, was observed to be 37 deg. above the horizon of London, and eastward of the meridian; what hour was it, and what was the star's azimuth?

PROBLEM LXXXVI.

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

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and

screw the quadrant of altitude upon the brass meridian. over that latitude; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to 12; then, if the given time be before noon, turn the globe eastward on its axis till the index has passed over as many hours as the time wants of noon; if the time be past noon, turn the globe westward till the index has passed over as many hours as the time is past noon let the globe rest in this position, and move the quadrant of altitude till its graduated edge coincides with the centre of the given star; the degrees on the quadrant, from the horizon to the star, will be the altitude; and the distance from the north or south point of the horizon to the quadrant, counted on the horizon, will be the azimuth from the north or south.

Examples. 1. What are the altitude and azimuth of Capella, at Rome, when it is five o'clock in the morning, on the second of December?

Answer. The Altitude is 41 deg. 58 min. and the azimuth 60 deg. 50 min. from the north towards the west.

2. Required the altitude and azimuth of Altair in Aquila on the sixth of October, at nine o'clock in the evening, at London.

3. On what point of the compass does the star Aldebaran bear at the Cape of Good Hope, on the fifth of March, at a quarter past eight o'clock in the evening; and what is its altitude?

Answer. The Azimuth is 49 deg. 52 min. from the north, and its altitude is 22 deg. 30 min.

4. Required the altitude and azimuth of Acyone in the Pleiades, marked », on the 21st of December, at four o'clock in the morning at London?

PROBLEM LXXXVII.

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

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude; find the sun's place in the ecliptic,

bring it to the brass meridian, and set the index of the hour circle to 12; bring the lower end of the quadrant of altitude to coincide with the given azimuth on the horizon, and hold it in that position; turn the globe westward till the given star comes to the graduated edge of the quadrant, and the hours passed over by the index will be the time from noon, the degrees on the quadrant, reckoning from the horizon to the star, will be the altitude.

Examples. 1. At London, on the 28th of December, the azimuth of Deneb in the Lion's tail, marked ß, was 624 deg. from the south towards the west; what hour was it, and what was the star's altitude?

Answer. By turning the globe westward on its axis the index will pass over 20 hours before the star intersects the quadrant; therefore, the time will be 20 hours from noon, or eight o'clock in the morning; and the star's altitude will be 40 deg.

2. At London, on the 5th of May, the azimuth of Cor Leonis, or Regulus, marked a, was 74 deg. from the south towards the west; required the star's altitude, and the hour of the night.

3. On the 8th of October, the azimuth of the star marked, in the shoulder of Auriga, was 50 deg. from the north towards the east; required its altitude at London, and the hour of the night.

4. On the 10th of September, the azimuth of the star marked in the Dolphin, was 20 deg. from the south towards the east; required its altitude at London, and the hour of the night.

PROBLEM LXXXVIII.

Two stars being given, the one on the meridian, and the other on the east or west point of the horizon, to find the latitude of the place.

Rule. Bring the star which was observed to be on the meridian, to the brass meridian; keep the globe from turning on its axis, and elevate or depress the pole till the other star comes to the eastern or western part of the horizon; then the degrees from the elevated pole to the horizon will be the latitude.

Examples. 1. When the two pointers* of the Great Bear, marked and ß, or Dubhe and s, were on the meridian, I observed Vega in Lyra to be rising; required the latitude.

Answer. 27 deg. north.

2. When Arcturus in Boötes was on the meridian, Altair in the Eagle was rising; required the latitude.

3. When the star marked in Gemini was on the meridian, in the shoulder of Andromeda was setting; required the latitude.

4. In what latitude are and ß, or Sirius and ß, in Canis Major rising, when Algenib, or a, in Perseus, is on the meridian?

PROBLEM LXXXIX.

The latitude of the place, the day of the month, and two stars that have the same asimuth,† being given, to find the hour of the night.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude: find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to 12; turn the globe on its axis from east to west till the two given stars coincide with the graduated edge of the quadrant of altitude; the hours passed over by the index will show the time from noon; and the common azimuth of the two stars will be found on the horizon.

* These two stars are called the pointers, because a line drawn through them, points to the polar star in Ursa Minor.

+ To find what stars have the same azimuth -Let a smooth rectangular board of about a foot in breadth, and three feet high (or of any height you please,) be fixed perpendicularly upon a stand; draw a straight line through the middle of the board, parallel to the sides; fix a pin in the upper part of this line, and make a hole in the board at the lower part of the line; hang a thread with a plummet fixed to it, upon the pin, and let the ball of the plummet move freely in the hole made in the lower part of the board: set this board upon a table in a window, or in the open air, and wait till the plummet ceases to vibrate; then look along the face of the board, and those stars which are partly hid from your view by the thread, will have the same azimuth.

Examples. 1. At what hour, at London, on the first of May, will Altair in the Eagle, and Vega in the Harp, have the same azimuth, and what will that azimuth be?

Answer. By bringing the sun's place to the meridian, &c. and turning the globe westward, the index will pass over 15 hours before the stars coincide with the quadrant: hence, they will have the same azimuth at 15 hours from noon, or at three o'clock in the morning; and the azimuth will be 424 degrees from the south towards the east.

2. On the 10th of September, what is the hour at London when Deneb in Cygnus, and Markab in Pegasus, have the same azimuth, and what is the azimuth?

3. At what hour on the 15th of April will Arcturus and Spica Virginis have the same azimuth at London, and what will that azimuth be?

4. On the 20th of February, what is the hour at Edinburgh when Capella and the Pleiades have the same azimuth, and what is the azimuth?

5. On the 21st of December, what is the hour at Dublin when «, or Algenib in Perseus, and in the Bull's Horn, have the same azimuth, and what is the azimuth?

PROBLEM XC.

The latitude of a place, the day of the month, and two stars, that have the same altitude, being given, to find the hour of the night.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to 12; turn the globe on its axis from east to west till the two given stars coincide with the given altitude on the graduated edge of the quadrant; the hours passed over by the index will be the time from noon when the two stars have that altitude.

Examples. 1. At what hour at London, on the second of September, will Markab in Pegasus, and in the head of Andromeda, have each 30 deg. of altitude? Answer. At a quarter past eight in the evening.

2. At what hour at London, on the fifth of January,