16 deg. 48 min south; required her meridian altitudeat Greenwich ?*

Answer. 21° 42'.

PROBLEM LXXXIV.

To find all those places on the earth to which the moon will be nearly vertical on any given day.

Rule. Look in an ephemeris for the moon's latitude and longitude for the given day, and mark her place on the globe (as in Prob. LXVIII;) bring this place to that part of the brass meridian which is numbered from the equator towards the poles, and observe the degree above it; for all places on the earth having that lati. tude will have the moon vertical (or nearly so) when she comes to their respective meridians.

Or, fake the moon's declination from page VI. of the Nautical Almanac, and mark whether it be north or south; then, by the terrestrial globe, or by a map, find all places having the same number of degrees of latitude as are contained in the moon's declination, and those will be the places to which the moon will be

at 40 minutes past ten o'clock in the evening, on the 11th of April 1805. 2080 48′ C's right ascension at midnight.—Declination 17o 3′ S. 202 47 do. at

noon.

6 1 increase in 12 hours from noon.

ditto

14 56 S.

27

12 h. 6° 1' :: 10 h 40': 5° 2′;||12h :: 2° 7' : : 10 h 40' ; 1° 52′ ;

:

hence, 202° 47' + 5° 20′=208° 7' the moon's right ascension at 40 minutes past 10.

hence, 14° 56′ + 1° 52′=16° 48′ the moon's declination at 40 minutes past 10.

The places of the planets may be taken out of the Ephemeris for noon without sensible error, because their declinations vary less than that of the moon.

*The moon will have the greatest and least meridian altitude to all the inhabitants porth of the equator, when her ascending node is in Aries; for her orbit making an angle of five and a third degrees with the ecliptic, her greatest altitude will be five and a third degrees more than the greatest meridional altitude of the sun, and her least meridional altitude five and a third degrees less than that of the sun. The greatest altitude of the sun at London is 62°; the moon's greatest altitude is therefore 87° 20'. The least meridional altitude of the sun at London is 15o; the least meridional altitude of the moon is therefore 9° 40′.

successively vertical on the given day. If the moon's declination be north, the places will be in north lati tude; if the moon's declination be south, they will be in south latitude.

Examples. 1. On the 15th of October 1805, the moon's longitude at midnight was 3 signs 29 deg. 14 min., and her latitude 1 deg. 35 min. south; øver what places did she pass nearly vertical ?

Answer. From the moon's latitude and longitude being given, her declination may be found by the globe to be about 190 north The moon was vertical at Porto Rico, St. Domingo, the north of Jamaica, O'why'hee, &c.

2. On the 20th of December 1810, the moon's longitude at midnight was 6 signs 20 deg., and her latitude 1 deg. 5 min. north, over what places on the earth did she pass nearly vertical ?

3. What is the greatest north declination which the moon can possibly have, and to what places will she be then vertical?

4. What is the greatest south declination which the moon can possibly have, and to what places will she be then vertical?

PROBLEM LXXXV.

Given the latitude of a place, the day of the month, and the altitude of a star, to find the hour of the night, and the star's 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; bring the lower end of the quadrant of altitude to that side of the meridian* on which

* It is necessary to know on which side of the meridian the star is at the time of observation, because it will have the same altitude on both sides of it. Any star may be taken at pleasure, but it is best to take one not too near the meridian, because for some time before the star comes to to the meridian, and after it has passed it, the altitude varies very little.

the star was situated when observed; turn the globe westward 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 trom 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 Lion's tail, marked 6, 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; consequently, 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 28th 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 624 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 ∞, 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 part of the brass meridian 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 6th of October, at 9 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?

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PROBLEM LXXXVII.

Given the latitude of a place, day of the month, and azi. muth 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 6, was 621 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; there fore 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 ẞ, 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.