over these places, you will see nearly the moon's path,* and, consequently, what stars lie in her way.

Examples. 1. What stars were in, or near, the moon's path, on the 10th, 11th, 13th, and 16th of De-. cember 1805 ?

10th, 's longitude

20° 12′ latitude 3° 34′ S.

11th,

13th,

16th,

m 10 11

4

26 S.

Answer The stars will be found to be Cor Leonis or Regulus, Spica Virginis, & in Libra, &c. See page 47, White's Ephemeris. 2. On the 16th, 17th, 18th, and 19th of May 1810, what stars will lie near the moon's way?

16th, C's right ascension, 206° 47', declination 9° 42′ S.

17th,

18th,

19th,

220 43

235 22

250 38

!

PROBLEM LXXX.

Given the latitude of the place and the day of the month, to find what planets will be above the horizon after sun setting.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place; find the sun's place in the ecliptic, and bring it to the western part of the horizon, or to ten or twelve degrees below; then look in the Ephemeris for that day and month, and you will find what planets are above the horizon; such planets will be fit for observation on that night.

Examples. 1. Were any of the planets visible after the sun had descended ten degrees † below the horizon

The situation of the moon's orbit for any particular day may be found thus: find the place of the moon's ascending node, in the Ephemeris, mark that place and its antipodes (being the descending node) on the globe; half the way between these points make marks 5° 20' on the north and south side of the ecliptic, viz. let the northern mark between the ascending and descending node, and the southern between the descending and ascending node; a thread tied round these four points will shew the position of the moon's orbit.

†The planets are not visible till the sun is a certain number of degrees below the horizon, and these degrees are variable accord

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of London, on the 1st of December 1805? their longi

tudes being as follow:

Answer. Venus and the moon were visible.

midnight o 9

2. What planets were above the horizon of London when the sun has descended ten degrees below, on the 25th of January 1810? their longitudes being as follow ?

Given the latitude of the place, day of the month, and hour of the night or morning, to find what planets will be visible at that hour.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place; 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 till the index has passed over as many hours as the time wants of noon; but, if the given time be past noon, turn the globe westward on its axis till the index has passed over as many hours as the time is past noon; let the globe rest in this position, and look in the Ephemeris for the longitudes of the planets, and, if any of them be in the figns 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

ing to the brightness of the planets. Mercury becomes visible wher the sun is about 10 degrees below the horizon; Venus when the sun's depression is 5 degrees; Mars 11° 30'; Jupiter 10°; Saturn 11°; and the Georgian 17° 30′

* It is not necessary to give the latitudes of the planets in this problem; for, if the signs and degrees of the ecliptic in which their longitudes are situated be above the horizon, the planets will like. wise be above the horizon.

follow: were any of them visible at London at five

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 1810, the longitudes of the planets in the fourth page of the Nautical Almanac were as follow: was any of them be visible at London at ten o'clock in the evening?

୪

7a 1°26'

2, 1°13'

C's longitude at midnight 7° 17°51′.

PROBLEM LXXXII.

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, bring it to the brass meridian, and set the index of the hour circle to twelve; 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. Turn the globe westward till the sun comes to the western edge of the horizon; the hours passed over by the index will be the time from noon when the sun sets: continue the motion of the globe westward till Venus comes to the western edge of the horizon, and the hours passed over by the index will be the time from noon when Venus sets the difference between these times will shew how long Venus sets after the sun.

When Venus is a morning star. Turn the globe eastward on its axis till the sun comes to the eastern edge

of the horizon; the hours passed over by the index will be the time which the sun rises before noon: continue the motion of the globe eastward till Venus comes to the eastern edge of the horizon, and the hours passed over by the index will be the time which the sun rises before noon the difference between these times will shew 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 lon gitude 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; the sun rose 5 hours before noon, or at half past 6; and Venus rose about 6 hours before noon, or at three quarters past five; consequently, Venus rose three quarters of an hour before the sun.

2. On the 25th of October 1805, the longitude of Jupiter was 8 signs 7 deg. 26 min., or 7 deg. 26 min. in Sagittarius, latitude 0 deg. 29 min. north; whether was 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 on evening star; the sun set at 5 o'clock, and Jupiter set about 20 minutes after six; consequently, he set 1 hour and 20 minutes after the sun.

3. On the first of November 1810, the longitude of Venus was 8 signs 24 deg. 30 min., latitude 4 deg. 7 min. south; was she a morning or an evening star? If she was 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 1810, the longitude of Jupiter was O signs 15 deg. 48 min., latitude 1 deg. 15 min. south, was he a morning or an evening star? If he was a morning star, how long did he rise before the sun; if an evening star, how long did he shine after the sun set?

A

PROBLEM LXXXIII.

The latitude of the 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 equator 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 planets'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 Problem LXVIII or LXVII ;) bring the planet's 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 Bootes, at London?

3. On the first of September 1810, the longitude of Mars was 4 signs 14 deg. 41 min., and latitude 1 deg. 9 min. north; what was his meridian altitude at London?

4. On the first of April 1810, the longitude of Saturn was 8 signs 15 deg. 17 min., and latitude 1 deg, 45 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 right ascension was 208 deg. 7 min.,† and declination

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

† By the Nautical Almanac, the moon passed over the meridian