Answer. It will rise at seven o'clock in the morning, come to the meridian at three in the afternoon, and set at eleven o'clock at night

2. On the first of August 1805, the longitude of Jupiter was 7 signs 26 deg. 34 min., and his latitude 45 min. N.; at what time did he rise, culminate, and set, at Greenwich, and whether was he a morning or an evening star?

Answer Jupiter rose at half past two in the afternoon, came to the meridian at about ten minutes to seven, and set at a quarter past eleven in the evening. Here Jupiter was an evening star, because he set after the sun.

3. At what time does Sirius rise, set, and come to the meridian of London, on the 31st of January?

4. On the 1st of January 1810, the longitude of Venus was 8 signs 22 deg. 54 min. and her latitude 0 deg. 26 min. N., at what time did she rise, culminate, and set at Greenwich, and whether was she a morning or an evening star?

5. At what time does Aldebaran rise, come to the meridian, and set at Dublin, on the 25th of November? 6. On the first of February 1810, the longitude of Mars was 1 signs 16 deg. 9 min.; and latitude 0 deg. 46 min. S. at what time did he rise, set, and come to the meridian of Greenwich?

PROBLEM LXXII.

To find the amplitude of any star, its oblique ascension and descension, and its diurnal arch, for any given day.

Rule. Elevate the pole to the latitude of the place, and bring the given star to the eastern part of the horizon; then the number of degrees between the star and the eastern point of the horizon will be its rising amplitude; and the degree of the equinoctial cut by the horizon will be the oblique ascension: set the index of the hour circle to 12, and turn the globe westward till the given star comes to the western edge of the horizon; the hours passed over by the index will be the star's diurnal arch, or continuance above the horizon. The setting amplitude will be the number of degrees between the star and the western point of the horizon, and the oblique descension will be represented by that

degree of the equinoctial which is intersected by the horizon, reckoning from the point Aries.

Examples. 1. Required the rising and setting amplitude of Sirius, its oblique ascension, oblique descension, and diurnal arch, at London ?

Answer. The rising amplitude is 27 deg. to the south of the east; setting amplitude 27 deg south of the west; oblique ascension 120 deg.; oblique descension 77 deg; and diurnal arch 9 hours 6 minutes.

2. Required the rising and setting amplitude of Aldebaran, its oblique ascension, oblique descension, and diurnal arch, at London ?

3. Required the rising and setting amplitude of Arcturus, its oblique ascension, oblique descension, and diurnal arch, at London?

4. Required the rising and setting amplitude of y Bellatrix, its oblique ascension, oblique descensión, and diurnal arch, at London?

PROBLEM LXXIII.

The latitude of a place given, to find the time of the year at which any known star rises or sets achronically, that is when it rises or sets at sun setting.

Rule. Elevate the pole to the latitnde of the place, bring the given star to the eastern edge of the horizon, and observe what degree of the ecliptic is intersected by the western edge of the horizon, the day of the month answering to that degree will show the time when the star rises at sun-set, and consequently when it begins to be visible in the evening. Turn the globe westward on its axis till the star comes to the western edge of the horizon, and observe what degree of the ecliptic is intersected by the the horizon, as before; the day of the month answering to that degree will show the time when the star sets with the sun, or when it ceases to appear in the evening.

Examples. 1. At what time does Arcturus rise achronically at Ascra* in Baotia, the birth place of Hesiod; the latitude of Ascra, according to Ptolemy, being 38 deg. 45 min. N.?

See page 15.

Answer. When Arcturus is at the eastern part of the horizon, the eleventh degree of Aries will be at the western part, answering to the first of April, the time when Artturus rises achronically: and it will set achronically on the 30th of November.

2. At what time of the year does Aldebaran rise achronically at Athens, in 38 deg. N. latitude? and at what time of the year does it set achronically?

3. On what day of the year does y in the extremity of the wing of Pegasus rise achronically at London? and on what day of the year does it set achronically?

4. On what day of the year does in the right foot of Lepus rise achronically at London? and on what day of the year does it set achronically?

PROBLEM LXXIV.

The latitude of a place given, to find the time of the year at which any known star rises or sets cosmically; that is, when it rises or sets at sun rising.

Rule. Elevate the pole to the latitude of the place, bring the given star to the eastern edge of the horizon, and observe what sign and degree of the ecliptic are intersected by the horizon; the month and day of the month, answering to that sign and degree, will show the time when the star rises with the sun. Turn the globe westward on its axis till the star comes to the western edge of the horizon, and observe what sign and degree of the ecliptic are intersected by the east

* Hence, Arcturus now rises achronically in latitude 37° 46′ N, about 100 days after the winter solstice. Hesiod, in his Opera and Dies, lib. ii. verse 185, says:

When from the solstice sixty wintry days

Their turns have finished, mark, with glitt❜ring rays,

From Ocean's sacred flood, Arcturus rise,

Then first to gild the dusky evening skies.

Here is a difference of 40 days in the achronical rising of this star (supposing Hesiod to be correct) between the time of Hesiod and the present time; and as a day answers to about 59′ of the ecliptic (see the note page 14), 40 days will answer to 39 deg; consequently, the winter solstice in the time of Hesiod was in the 9th deg. of Aquarius. Now, the recession of the equinoxes is about 501" in a year; hence, 501": 1 year:: 392: 2794 years since the time of Hesiod; so that he lived 990 years before Christ, by this mode of reckoning. Lempriere, in his Classical Dictionary, says, Hesiod ‹ li ved 907 years before Christ.

N n

ern edge, as before; these will point out, on the hori zon, the time when the star sets at sun-rising.

Examples. 1. At what time of the year do the Pleiades set cosmically at Miletus in Ionia, the birthplace of Thales; and at what time of the year do they rise cosmically; the latitude of Miletus, according to Ptolemy, being 37 deg. N.?

Answer The Pleiades rise with the sun on the 10th of May, and they set at the time of sun-rising on the 22d of November.*

2. At what time of the year does Sirius rise with the sun at London; and at what time of the year will Sirius set when the sun rises?

3. At what time of the year does Menkar, in the jaw of Cetus, rise with the sun, and at what time does it set at sun-rising, at London?

4. At what time of the year does Procyon, in the Little Dog's stomach, set when the sun rises at London, and at what time of the year does it rise with the sun?

PROBLEM LXXV.

To find the time of the year when any given star rises or sets heliacally.†

Rule. The heliacal rising and setting of the stars will vary according to their different degrees of magnitude

Pliny says (Nat. Hist. lib xviii. cap 25.) that Thales determined the cosmical setting of the Pleiades to be twenty-five days after the autumnal equinox. Supposing this observation to be made at Miletus, there will be a difference of thirty-five days in the cosmical setting of this star since the time of Thales; and, as a day answers te about 59' of the ecliptic, these days will make about 34° 25'; consequently, in the time of Thales, the autumnal equinoctial colure passed through 4o 35' of Scorpio; and as before, 501": 1 year: : 34° 25': 2465 years since the time of Thales, so that Thales lived (2465 — 1804) 661 years before the birth of Christ. According to Sir I. Newton's Chronology, Thales flourished 596 before Christ Thales was well skilled in geometry, astronomy, and philosophy; he measured the height and extent of the Pyramids of Egypt, was the first who calculated with accuracy, a solar eclipse: he discov ered the solstices and equinoxes, divided the heavens into five zones, and recommended the division of the year into 365 days. Miletus was situated in Asia Minor, south of Ephesus, and south east of the island of Samos.

See Definition 89, page 22.

and brilliancy; for it is evident that the brighter a star is when above the horizon, the less the sun will be depressed below the horizon when that star first becomes visible. According to Ptolemy, stars of the first magnitude are seen rising and setting when the sun is twelve degrees below the horizon; stars of the second magnitude require the sun's depression to be thirteen degrees; stars of the third magnitude fourteen degrees, and so on, reckoning one degree for each magnitude. This being premised,

To solve the problem. Elevate the pole so many de grees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian over that latitude; bring the given star to the eastern edge of the horizon, and move the quadrant of altitude till it intersects the ecliptic twelve de grees below the horizon, if the star be of the first magnitude; thirteen degrees, if the star be of the second magnitude; fourteen degrees if it be of the third magnitude, &c.: the point of the ecliptic, cut by the quadrant, will show the day of the month, on the horizon, when the star rises heliacally. Bring the given star to the western edge of the horizon, and move the quadrant of altitude till it intersects the ecliptic below the western edge of the horizon, in a similar manner as before; the point of the ecliptic, cut by the quadrant will show the day of the month, on the horizon, when, the star sets heliacally.

Examples. 1. At what time does bright star in the Bull's Horn, of the tude, rise and set heliacally at Rome?

Tauri, or the second magni

Answer. The quadrant will intersect the 3d of Cancer 13 deg. below the eastern horizon, answering to the 24th of June; and the 7th of Gemini 13 deg. below the western horizon, answering to the 28th of May.

2. At what time of the year does Sirius, or the Dog Star, rise heliacally at Alexandria in Egypt; and at what time does it set heliacally at the same place?

Answer. The latitude of Alexandria is 31 deg. 13 min. north; the quadrant will intersect the 12th of Leo, 12 deg. below the eastern horizon, answering to the 4th of August; and the 2d of Gemini, 12 deg. below the western horizon, answering to the 23d of May.

• The ancients reckoned the beginning of the dog days from the heliacal rising of Sirius, and their continuance to be about 40 days