PROB. XVI. The value of a quantity at three consecutive whole hours, T-1, T, and T+1, being given, to find its value at an inter- PROB. XXIII. To calculate a Transit of Mercury, PROB. XXIV. To correct the observed altitude of a heavenly body PROB. XXVII. To find the Latitude of a place from an observed PROB. XXVIII. To find the time of day from an observed altitude of CHAPTE.. GENERAL PHENOMENA OF THE HEAVENS-DEFIN PRELIMINARY OBSERVATIONS. 1. Astronomy, or Plane Astronomy, is the science which treats of the motions, distances, magnitudes, and appear- 2. General Observations. If, on a clear night, we fix our attention on the heavens, and continue to observe them out of view, or set. In the southern part, some will be observed to rise, ascend to small elevations, and then descend and set, to the west of their places of rising.* 3. Circumpolar Stars. If we direct our attention towards the north, different phenomena are presented. In that part of the heavens, there are many stars which do not set. Those that are descending continue to do so till they arrive at certain lowest points, and then begin to ascend. They appear to revolve or describe circles about a certain star which seems to remain stationary. This star is called the Pole Star. All the stars that do not set are called Circumpolar Stars. 4. North Pole. When the pole star is more accurately observed by the aid of suitable instruments, it ceases to appear stationary. It is found to have an apparent motion in a small circle, round a certain point as a centre, or geometric pole, distant about 10 from it. This point is called the North Pole of the heavens, or simply the North Pole. 5. Diurnal Motion. If our observations are repeated on successive evenings, we find the same stars moving in the same manner, and occupying, at any given time in the evening, very nearly the same positions with regard to the earth as at the same time the preceding evening. The stars, therefore, and indeed all the heavenly bodies, appear to revolve round the earth from east to west, in about twentyfour hours. This motion is called the Diurnal Motion. 6. The Moon. If the situations of the moon be observed on successive nights, it will be found that she changes her position among the stars, moving among them from west . to east; that is, in a direction contrary to that of the diurnal motion. By this motion she makes a complete circuit of the heavens in about twenty-seven days. *Here and in other parts of the work, unless the contrary is mentioned, the observer is supposed to be in the United States, or southern or middle parts of Europe. 7. The Sun. The sun also appears to have this motion from west to east, among the stars. This may be inferred from observing the position of different groups of stars after the sun has set. If our observations are repeated at intervals for some weeks or months, we shall find that the sun appears continually to approach the stars to the eastward of him. He thus, in the course of a year, appears to make an entire circuit of the heavens. Owing to this apparent annual motion of the sun, the groups of stars visible at a given hour in the evening, and their positions at that hour, are very different at different seasons of the year. 8. Planets. There are likewise ten of the stars which have motions among the other stars, moving generally like the sun and moon, from west to east; though sometimes for short periods they appear to move in the contrary direction. These are called Planets. Five of the planets, named Mercury, Venus, Mars, Jupiter, and Saturn, are visible to the naked eye, and were known to the ancients. The other five, named Uranus, Vesta, Juno, Ceres, and Pallas, are not visible without the aid of a telescope, and have not been long known. 9. Satellites. Observations with the telescope show that each of the planets, Jupiter, Saturn, and Uranus, is accompanied by several smaller bodies, which revolve round it, at different distances and in different times. These are called moons, satellites, or secondary planets. Jupiter has four satellites, Saturn has seven, and, accord ing to the observations of Sir William Herschell, Uranus has six. 10. Planetary Regions. The sun, moon, and planets, with their satellites, move through nearly the same region of the heavens, the courses of the moon and planets not differing greatly from that of the sun. 11. Comets. There is a class of bodies that appear occasionally in various parts of the heavens, moving in various directions among the fixed stars, and only continuing visible for a few weeks or months. These are called Comets. A comet is not unfrequently accompanied by a faint brush of light, projecting from it on the side opposite the sun, and extending in some cases to a great distance. This is called the tail of the comet. 12. The Earth. The earth is a body of a globular form. This may be inferred from the following well known facts. When persons on board a ship at sea, observe another ship receding from them, they first lose sight of the hull; then of the lower sails; afterwards of those that are higher; and lastly of the most lofty sails. To an observer at the mast head, the receding ship continues visible long after it has ceased to be seen by those on deck; the different parts eventually disappearing to him in the same order as to those below. This takes place in whatever direction the ship recedes, and in whatever part of the ocean the observations are made. Hence it follows that the surface of the ocean must be globular; and as the general level of the land does not greatly differ from that of the ocean, the whole earth may be regarded as a globular body. By methods that will be noticed in a subsequent chapter, it has been ascertained that the earth is nearly, though not exactly, a perfect sphere, and that its diameter is about 7912 miles. 13. Fixed Stars. Those stars which do not sensibly change their positions with regard to one another are called fixed stars. They are at an immense distance from the earth. This may be inferred from the fact that the angular distance of any two of them is found to be the same at whatever part of the earth the observation is made. It has indeed been ascertained by means which may hereafter be understood, that the distance is so im mensely great that the angle contained between two lines conceived to be drawn from one of them to opposite sides of the earth must be less than the ten thousandth part of a second. We may therefore regard the diameter of the earth as an insensible quantity in comparison with the distance of the stars. In consequence of their immense distance, the fixed stars appear merely as luminous points, even when viewed with telescopes of high power; whereas the planets, when thus viewed, present sensible and measurable discs. 14. Celestial Sphere. It is not supposed that the fixed stars are all at the same distance from the earth. But since their distances are all so exceedingly great that no change of position on the earth produces any appreciable change in their positions with regard to one another, we may regard them as placed in the concave surface of an immense hollow sphere, having its centre at the centre of the earth. This imaginary sphere is called the Celestial Sphere. 15. Diurnal motions of the fixed stars. Each star in its diurnal motion, moves uniformly, in a circle of which the north pole of the heavens is a geometric pole. The method by which the truth of this proposition is established, will be given in a subsequent chapter. 16. Stars during the day. The strong light of the sun overpowering the feebler light of the stars renders them invisible to the naked eye during the day time. But by the aid of a telescope the brighter stars, except those near the sun, may be distinctly seen, and observations may be made on them in the full light of day. 17. Copernican System. Copernicus, a celebrated Prussian astronomer, who flourished in the early part of the sixteenth century, formed a theory or system to account for the apparent motions of the heavenly bodies. Accord |