To describe the apparent path of any planet, or of a comet, amongst the fixed stars, &c.

Draw a straight line O, O, to represent the ecliptic, and divide it into any convenient number of equal parts.

Set off eight of those equal parts northward and southward of the ecliptic, at each end thereof; and draw lines as in the figure, Plate V, these will represent the zodiac. Find the planets geocentric latitude and longitude in an ephemeris, or in the nautical almanac, and mark its place for every month, or for several days in each month, beginning at the right hand of the ecliptic line, and proceeding towards the left.*

Find the latitudes and longitudes † of the principal stars in the several constellations near which the planet passes, and set them off in a similar manner from the right hand towards the left; you will thus have a complete picture of any part of the heavens, with the positions of the several stars, &c. as they appear to a spectator on the earth.

Example. 1. Delineate the path of the planet Jupiter for the year 1811; the latitudes and longitudes being as follow:

Jupiter's path, when delineated, will appear south of the ecliptic in the order A, B, C, D, E, F, G, H. The planet will be at G on the 25th of August, and will ap

* The young student will recollect, that the stars appear in a contrary order in the heavens to what they do on the surface of a globe. In the heavens we see the concave part, on the globe the convex. This manner of delineating the stars will be found extremely useful, and will enable the student to know their names and places sooner than by the globe.

The places of the stars may likewise be laid down by their right ascensions and declinations, by drawing a portion of the equi. noctial instead of the ecliptic.

pear a little to the right hand of the star marked » in Gemini; when it arrives at H, which will happen on the 25th of October, it will apparently return again to G, a small matter above its former path, where it will be situated on the 25th of December.

In the same manner the places and situations of the stars may be delineated, thus, Aldebaran, the principal star in the Hyades, will be found by the Globe, (or a proper table, to be situated in 70 of Д, and in 5 of south latitude; Betelgeux in Orion's right shoulder, in about 26° of П, and in 16 of south latitude, and its place may be laid down on a map by extending the line of its longitude, as from L, till it meets a straight line passing through 16, 16, on the sides of the map. In the same manner, any other star's situation, may be described; thus, the Hyades will appear at Q, the Pleiades at P, &c. and Bellatrix &c, as in the figure.

PART IV.

CONTAINING,

1. A promiscuous Collection of Examples exercising the Problems on the globes.-2. A collection of Questions, with References to the Pages where the Answers will be found; designed as an Assistant to the Tutor in the Examination of the Scholar.-3. 'A Table of the Latitudes and Longitudes of the Principal Places in the World.

CHAPTER I.

A promiscuous Collection of Examples exercising the Problems on the Globes.

1. WHAT day of the year is of the same length as the 14th of August?

2. How many miles make a degree of longitude in the latitude of Lisbon ?

3. At what hour is the sun due east at London on the 5th of May ?

4. There is a place in the parallel of 31 deg. of north latitude, which is 31 degrees distant from London ; what place is it?

5. If the sun's meridian altitude at London be 30 deg. what day of the month, and what month is it?

6. On what month and day is the sun's meridian altitude at Paris equal to the latitude of Paris ?

7. When y Draconis is vertical to the inhabitants of London at ten o'clock at night, what day of the month, and what month is it?

8. What is the equation of time dependant on the obliquity of the ecliptic on the 14th of July?

9. I observed the pointers of the Great Bear, on the meridian of London, at eleven o'clock at night; in what month and on what night did this happen?

10. On what day of the month, and in what month, will the shadow of a cane placed perpendicular to the horizon of London, at ten o'clock in the morning, be exactly equal in length to the cane?

11. The earth goes round the sun in 365 days 6 hours nearly; how many degrees does it move in one day, at a medium? Or, what is the daily apparent mean motion of the sun?

12. The moon goes once round her orbit, from the first point of the sign Aries to the same again, in 27 days 7 hours 43 minutes 5 seconds; what is her mean motion in one day?

13. The moon turns round her axis, from the sun to the sun again, in 29 days 12 hours 44 minutes 3 seconds, which is exactly the time that she takes to go round her orbit from new moon to new moon; at what rate per hour are the inhabitants (if any) of her equatorial parts carried per hour by this rotation? The moon's diameter being 2144 miles.

14. How many degrees does the motion of the moon exceed the apparent motion of the sun in 24 hours? 15. The day of the month being given, it is required to find the moon's longitude when she is eight days old?

16. Travelling in an unknown latitude, I found, by chance, an old horizontal dial; the hour-lines of which were so defaced by time that I could only discover those of IV and V, and found their distance to be exactly 21 degrees; pray what latitude was the dial made for?

17. Required the duration of twilight at the south pole?

18. How far must an inhabitant of London travel southward to lose sight of Aldebaran ?

19. What is the elevation of the north polar star above the horizon of Calcutta?

20. Lord Nelson beat the French fleet near latitude 31 deg. 11 min. north, longitude 30 deg. 22 min. east; point out the place on the globe.