let H O, Fig. 15, represent the horizon, E Q the equa E tor, and P P' the axis of ther north, the elevation of the diurnal circle above the horizon grows less and less, and consequently, the motions of the heavenly bodies more and more oblique to the horizon, until finally, at the pole, where the latitude is ninety degrees, the angle of elevation of the equator vanishes, and the horizon and the equator coincide with each other, as before stated. The circle of perpetual apparition is the boundary of that space around the elevated pole, where the stars never set. Its distance from the pole is equal to the latitude of the place. For, since the altitude of the pole is equal to the latitude, a star, whose polar distance is just equal to the latitude, will, when at its lowest point, only just reach the horizon; and all the stars nearer the pole than this will evidently not descend so far as the horizon. Thus m m, Fig. 15, is the circle of perpetual apparition, between which and the north pole, the stars never set, and its distance from the pole, O P, is evidently equal to the elevation of the pole, and of course to the latitude. In the opposite hemisphere, a similar part of the sphere adjacent to the depressed pole never rises. Hence, the circle of perpetual occultation is the boun dary of that space around the depressed pole, within which the stars never rise. Thus m' m', Fig. 15, is the circle of perpetual occultation, between which and the south pole, the stars never rise. In an oblique sphere, the horizon cuts the circles of daily motion unequally. Towards the elevated pole, more than half the circle is above the horizon, and a greater and greater portion, as the distance from the equator is increased, until finally, within the circle of perpetual apparition, the whole circle is above the horizon. Just the opposite takes place in the hemisphere next the depressed pole. Accordingly, when the sun is in the equator, as the equator and horizon, like all other great circles of the sphere, bisect each other, the days and nights are equal all over the globe. But when the sun is north of the equator, the days become longer than the nights, but shorter, when the sun is south of the equator. Moreover, the higher the latitude, the greater is the inequality in the lengths of the days and nights. By examining Fig. 15, you will easily see how each of these cases must hold good. Most of the appearances of the diurnal revolution can be explained, either on the supposition that the celestial sphere actually turns around the earth once in twenty-four hours, or that this motion of the heavens is merely apparent, arising from the revolution of the earth on its axis, in the opposite direction,-a motion of which we are insensible, as we sometimes lose the consciousness of our own motion in a ship or steamboat, and observe all external objects to be receding from us, with a common motion. Proofs, entirely conclusive and satisfactory, establish the fact, that it is the earth, and not the celestial sphere, that turns; but these proofs are drawn from various sources, and one is not prepared to appreciate their value, or even to understand some of them, until he has made considerable proficiency in the study of astronomy, and become familiar with a great variety of astronomical phenomena. To such a period we will therefore postpone the discussion of the earth's rotation on its axis. While we retain the same place on the earth, the diurnal revolution occasions no change in our horizon, but our horizon goes round, as well as ourselves. Let us first take our station on the equator, at sunrise; our horizon now passes through both the poles and through the sun, which we are to conceive of as at a great distance from the earth, and therefore as cut, not by the terrestrial, but by the celestial, horizon. As the earth. turns, the horizon dips more and more below the sun, at the rate of fifteen degrees for every hour; and, as in the case of the polar star, the sun appears to rise at the same rate. In six hours, therefore, it is depressed ninety degrees below the sun, bringing us directly under the sun, which, for our present purpose, we may consider as having all the while maintained the same fixed position in space. The earth continues to turn, and in six hours more, it completely reverses the position of our horizon, so that the western part of the horizon, which at sunrise was diametrically opposite to the sun, now cuts the sun, and soon afterwards it rises above the level of the sun, and the sun sets. During the next twelve hours, the sun continues on the invisible side of the sphere, until the horizon returns to the position from which it set out, and a new day begins. Let us next contemplate the similar phenomena at the poles. Here the horizon, coinciding, as it does, with the equator, would cut the sun through its centre and the sun would appear to revolve along the surface of the sea, one half above and the other half below the horizon. This supposes the sun in its annual revolution to be at one of the equinoxes. When the sun is north of the equator, it revolves continually round in a circle, which, during a single revolution, appears parallel to the equator, and it is constantly day; and when the sun is south of the equator, it is, for the same reason, continual night. When we have gained a clear idea of the appear ances of the diurnal revolutions, as exhibited to a spectator at the equator and at the pole, that is, in a right and in a parallel sphere, there will be little difficulty in imagining how they must be in the intermediate latitudes, which have an oblique sphere. The appearances of the sun and stars, presented to the inhabitants of different countries, are such as correspond to the sphere in which they live. Thus, in the fervid climates of India, Africa, and South America, the sun mounts up to the highest regions of the heavens, and descends directly downwards, suddenly plunging beneath the horizon. His rays, darting almost vertically upon the heads of the inhabitants, strike with a force unknown to the people of the colder climates; while in places remote from the equator, as in the north of Europe the sun, in Summer, rises very far in the north, takes a long circuit towards the south, and sets as far northward in the west as the point where it rose on the other side of the meridian. As we go still further north, to the northern parts of Norway and Sweden, for example, to the confines of the frigid zone, the Summer's sun just grazes the northern horizon, and at noon appears only twenty-three and one half degrees above the southern. On the other hand, in midwinter, in the north of Europe, as at St. Petersburgh, the day dwindles almost to nothing,-lasting only while the sun describes a very short arc in the extreme south. In some parts of Siberia and Iceland, the only day consists of a little glimmering of the sun on the verge of the southern horizon, at noon. LETTER IX. PARALLAX AND REFRACTION. "Go, wondrous creature! mount where science guides, Correct old Time, and regulate the sun."-Pope. I THINK you must have felt some astonishment, that astronomers are able to calculate the exact distances and magnitudes of the sun, moon, and planets. We should, at the first thought, imagine that such knowledge as this must be beyond the reach of the human faculties, and we might be inclined to suspect that astronomers practise some deception in this matter, for the purpose of exciting the admiration of the unlearned. I will therefore, in the present Letter, endeavor to give you some clear and correct views respecting the manner in which astronomers acquire this knowledge. In our childhood, we all probably adopt the notion that the sky is a real dome of definite surface, in which the heavenly bodies are fixed. When any objects are beyond a certain distance from the eye, we lose all power of distinguishing, by our sight alone, between different distances, and cannot tell whether a given object is one million or a thousand millions of miles off. Although the bodies seen in the sky are in fact at distances extremely various,-some, as the clouds, only a few miles off; others, as the moon, but a few thousand miles; and others, as the fixed stars, innumerable millions of miles from us,—yet, as our eye cannot distinguish these different distances, we acquire the habit of referring all objects beyond a moderate height to one and the same surface, namely, an imaginary spherical surface, denominated the celestial vault. Thus, the various objects represented in the diagram on next page, though differing very much in shape and diameter, |