black lead pencil, fixed in the other leg of the compasses; these arcs will intersect each other in the zenith; the zenith or point of intersection, being then brought to the brazen meridian, will show the latitude required.

EXAMPLES.

1. The altitude of Markab in Pegasus was 30°, and that of Altair in the Eagle 65°; required the latitudes, supposing it north.

Answer. 29 degrees north.

2. At sea in north latitude, the altitude of Capella was observed to be 30°, and that of Aldebaran 350; what was the latitude of the place of observation?

PROBLEM XXV.

The latitude of a place and day of the month being 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 given latitude; find the longitude and latitude of Venus in the Nautical Almanac, or any good ephemeris, and mark her place on the globe; and bring the sun's place in the ecliptic to the 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 part 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's place to the eastern part 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 part of the horizon; and the hours passed over by the index, will show how long Venus rises before the sun.

It may not be improper to observe, that the same rule will answer to show when any of the planets rises before the sun, or sets after him, and how long.

EXAMPLES.

1. On the 1st of March, 1825, the longitude of Venus was O sign, 26° 44', or 26° 44' in the sign Aries, latitude 1° 50′ north; was she a morning or an evening star at that time? If a morning star, how long did she rise before the sun at New-York; if an evening star, how long did she shine after the

sun set?

Answer. Venus was an evening star, and set 2 hours 45 minutes after the sun.

2. On the 19th of November, 1825, Jupiter's longitude will be 5 signs 11° 56', or 11° 56′ in the sign Virgo; will Jupiter be a morning or an evening star? If a morning star, how long will he rise before the sun at Madrid; if an evening star, how long will he shine after sun-set ?

3. On the 25th of April, the longitude of Venus was 2 signs, 6 degrees, 26 minutes, latitude 5o 30 north; was she a morning or an evening star? If a morning star, how long did she rise before the sun; if an evening star, how long will she shine after sun-set?

1

QUESTIONS.

For the examination of the student in the preceding

problems.

The questions referring to the rules are in italics, in order that the student may distinguish them from those questions which refer to the examples.

1. How do you find the right ascension and declination of a fixed star?

2. What is the right ascension and declination of Dubhe in the back of the Great Bear?'

3. The right ascension and declination of a star, or planet, being given, how do you find its place on the globe?

4. What star has 95° 1' of right ascension, and 52° 36′ 11′′ south declination?

5. How do you find the longitude and latitude of a star or planet?

6. Required the longitude and latitude of Acubene in Cancer.

7. The longitude and latitude of a star being given, how do you find its place on the celestial globe?

8. What star has 8s. 7° 19′ of longitude, and 40 32′ 43" of south latitude ?

9. The hour of the day and the latitude of a place being given, how do you find what stars are rising, culminating, setting, &c.?

10. At 9 o'clock in the evening at St. Helena, on the 20th of June, required those stars that are rising, culminating, setting, &c.

11. How do you find the distance between any two known stars in degrees?

12. Required the distance in degrees between Alphacca and Dubhe.

13. How do you rectify the globe for the latitude of a given place, and for the sun's place in the ecliptic on a given day?

14. Rectify the celestial globe for the latitude of Lima, and for the sun's place on the 21st of June.

15. The latitude of a place and day of the month being given, how do you find the time of the year when a known star will rise, culminate, and set ?

16. At what time will Canopus rise, culminate, and set at Buenos Ayres?

17. How do you find the amplitude, oblique ascension, &c. of a known star, for any given place?

18. Required the rising and setting amplitude of Antares, its oblique ascension and descension, its diurnal arc, at the Cape of Good Hope.

19. The latitude of a place being given, how do you find the time of the year at which any known star rises or sets achronically?

20. At what time of the year does Bellatrix rise achronically at Quito in Peru, and when does it set achronically?

21. The latitude of a place being given, how do you find the time of the year at which any known star rises or sets cosmically?

22. At what time of the year does Alphard in the heart of the Scorpion, rise cosmically at Cape Horn; and at what time of the year does it set cosmically?

23. How do you find the time of the year at which any known star rises and sets heliacally, at any given place?

24. At what time of the year does Procyon rise at Canton, and at what time of the year does it set heliacally ?

25. The day of the month being given, how do you find those stars that rise and set achronically, cosmically, and heliacally?

26. What stars rise and set achronically, cosmically, and heliacally, at Alexandria in Egypt, on the 21st of March?

27. How do you find the meridian altitude of any star or planet, the latitude of a place and day of the month being given?

28. What is the meridian altitude of Regulus at Moscow in Russia?

29. The meridian altitude of a known star being given, how do you find the latitude of the place of observation?

30. In what degree of north latitude is the meridian altitude of Regulus 66 degrees ?

31. The latitude of a place, day of the month, and altitude of a know star, being given; how do you find the hour of the night, and star's azimuth?

32. At London on the 28th of December, the star Denebola, in the Lion's tail, was observed to be 40 degrees of altitude; what hour was it, and what was the star's azimuth?

33. The latitude of a star, day of the month, and azimuth of a star, being given, how do you find the hour of the night and the star's altitude?

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

35. The day of the month and hour when any known star rises and sets, being given, how do you find the latitude of the place ?

36. In what latitude does Regulus rise at 10 o'clock at night, on the 21st of January?

37. Two stars being given, the one on the meridian, and the other at the east or west part of the horizon, how do you find the latitude of the place ?