be in the signs which are above the horizon, such planets will be visible.

Examples. 1. On the first of December, 1805, the longitudes of the planets, by an ephemeris, were as follows: were any of them visible at London at five o'clock in the morning?

8' 15° 27' 's longitude at

Answer. Saturn and the Georgium Sidus were visible, and both nearly in the same point of the heavens, near the eastern horizon; Saturn was a little to the north of the Georgian.

2. On the first of October, 1813, the longitudes of the planets in the fourth page of the Nautical Almanac, were as follows: were any of them visible at London at ten o'clock in the evening?

The latitude of the place and day of the month given, to find how long Venus rises before the sun, when she is a morning star, and how long she sets after the sun, when she is an evening star.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place; find the latitude and longitude of Venus in an ephemeris, and mark her place on the globe; find the sun's place in the ecliptic, and bring it to the brass meridian; then, if the place of Venus be to the right hand of the meridian, she is an evening star; if to the left hand, she is a morning

star.

When Venus is an evening star. Bring the sun's place to the western edge of the horizon, and set the index of the hour circle to 12; turn the globe westward on its axis till Venus coincides with the western edge of the horizon; and the hours passed over by the index will show how long Venus sets after the sun.

When Venus is a morning star. Bring the sun place to the eastern edge of the horizon, and set the index of the hour circle to 12; turn the globe eastward on

its axis till Venus comes to the eastern edge of the horizon, and the hours passed over by the index will show how long Venus rises before the sun.

Note. The same rule will serve for Jupiter, by marking his place instead of that of Venus.

Examples. 1. On the first of March, 1805, the longitude of Venus was 10 signs 18 deg. 14 min. or 18 deg. 14 min. in Aquarius, latitude 0 deg. 52 min. south; was she a morning or an evening star? If a morning star, how long did she rise before the sun at London? If an evening star, how long did she shine after the sun set?

Answer. Venus was a morning star, and rose three quarters of an hour before the sun.

was

2. On the 25th of October, 1805, the longitude of Jupiter was 3 signs 7 deg. 27 min. or 7 deg. 27 min. in Sagittarius, latitude 0 deg. 29 min. north; he a morning or an evening star? If a morning star, how long did he rise before the sun at London ? If an evening star, how long did he shine after the sun set? Answer. Jupiter was an evening star, and set 1 hour and 20 minutes after the sun.

3. On the first of November, 1813, the longitude of Venus was 8 signs 18 deg. 50 min. latitude 2 degrees 3 min. south; was she a morning or an evening star? If she were a morning star, how long did she rise before the sun at London? If an evening star, how long did she shine after the sun set?

4. On the seventh of January, 1813, the longitude of Jupiter was 5 signs 6 deg. 36 min. latitude 0 deg. 56 min. north, was he a morning or an evening star? If he were a morning star, how long did he rise before the sun? If an evening star, how long did he shine after the Sun set?

PROBLEM LXXXIII.

The latitude of a place and day of the month* being given, to find the meridian altitude of any star or planet.

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

For a star. Bring the given star to that part of the brass meridian which is numbered from the equinoctial towards the poles; the degrees on the meridian, contained between the star and the horizon, will be the altitude required.

For the moon or a planet. Look in an ephemeris for the planet's latitude and longitude, or for its right ascension and declination, for the given month and day, and mark its place on the globe (as in Prob. LXVIII or LXVII ;) bring the planets place to the brass meridian; and the number of degrees between that place and the horizon will be the altitude.

Examples. 1. What is the meridian altitude of Aldebaran in Taurus at London ?

Answer. 54° 36'.

2. What is the meridian altitude of Arcturus in Boötes, at London ?

3. On the first of September, 1813, the longitude of Mars was 10 signs 2 deg. 20 min. and latitude 5 deg. 48 min. south; what was his meridian altitude at London?

4. On the first of April, 1813, the longitude of Saturn was 9 signs 18 deg. 47 min. and latitude 0 deg. 23 min. north; what was his meridian altitude at London?

5. On the eleventh of April, 1805, at the time of the moon's passage over the meridian of Greenwich, her

* The meridian altitude of the stars on the globe, in the same latitude, are invariable; therefore, when the meridian altitude of a star is snught, the day of the month need not be attended to.

right ascension was 208 deg. 7 min.* and declination 16 deg. 48 min. south; required her meridian altitude at Greenwich.t

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 equinoctial towards the poles, and observe the degree above it; for all places on the earth having that latitude will have the moon vertical (or nearly so) when she comes to their respective meridians.

Or take 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 successively

* By the Nautical Almanac, the moon passed over the meridian at 40 minutes past ten o'clock in the evening, on the 11th of April 1805. 208° 48' 's right ascension at midnight.----Declination 17° 3' S. 202 47 do. at 14 56 S.

· noon

6 1 increase in 12 hours from noon

do.

2 7

12 h. 6° 1' :: 10 h. 40: 5° 20′;12 h. : 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 min. 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 north of the equator, when her ascending node is in Aries; for her orbit making an angle of 510 with the ecliptic, her greatest altitude will be 51° more than the greatest meridional altitude of the sun, and her least meridional altitude 51° less than that of the sun. The greatest altitude of the sun at London is 62°; the moon's greatest altitude is therefore 67° 20. The least meridional altitude of the sun at London is 15°; the least meridional altitude of the moon is therefore 9° 40',

vertical on the given day. If the moon's declination be north, the places will be in north latitude; 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; over 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 19° north. The moon was vertical at Porto Rico, St. Domingo, the north of Jamaica, O'why'hee, &c.,

2. On the 20th of December, 1813, the moon's longitude at midnight was 8 signs 9 deg. and her latitude 4 deg. 7 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, 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 the star was situated when observed; turn the globe west

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 the meridian, and after it has passed it, the altitude varies very little.