which they are placed, is called the zodiac. The names of the twelve signs or constellations of the zodiac and the characters used for representing them, are the following:

Hypothesis of the Ancients.] The motions of the sun, and the still more irregular movements of a few stars termed planets, greatly perplexed the ancient astronomers, almost all of whom maintained that the earth was the centre of the universe, and immovable. Some philosophers, even among the ancients, however, particularly Pythagoras and his followers, seem to have been acquainted with the true motions of the earth. Their opinions on the subject, after lying hid for ages, were revived in the 16th century by Copernicus, and form the basis of the modern astronomy. Upon this foundation, that science, by the genius of Kepler, Newton, and many others, has been brought to a very high degree of perfection. It has been established by these philosophers, that the true system of the universe is the following:

Real Motion of the Earth.] The earth moves round every day upon an axis, and revolves round the sun, from west to east, in the course of a year. The orbit in which it moves is an ellipse, and has the sun placed in one of the foci. The other planets and the comets also revolve around the sun in elliptical orbits. Some of the planets are attended in their course by satellites, or moons, performing revolutions around them. All the other heavenly bodies, termed fixed stars, are placed at inconceivably greater distances from the earth than any of the planets, and are supposed to be similar to our sun, being each the centre of a system.

The rotatory motion of the earth is the cause of the apparent diurnal motion of the heavenly bodies around it; the motion of the earth round the sun from west to east, produces the apparent annual revolution of the sun among the stars in the same direction; the motion of the sun towards the north and south alternately, is produced also by the earth's annual revolution, and the inclination of the earth's axis to the plane of its orbit, the axis continuing parallel to itself, or nearly so, during the whole revolution. As this last motion, however, is the cause of the seasons, and of the change in the length of the days and nights at different periods of the year, it will require a fuller elucidation. We must first give a few definitions.

The Poles, Equator, Ecliptic, and Meridians.] The extremities of the earth's axis are termed poles of the earth, and the centre of that axis, is the centre of the earth, and also of the celestial sphere. The axis produced to the sphere of the fixed stars, forms the axis of the celestial sphere, and the points where it meets that sphere, are the celestial poles. The great circle of the celestial sphere, which is perpendicular to the axis, is the celestial equator, and its intersection with the surface of the earth, the terrestrial equator. Great circles of the celestial sphere at right angles to the equator, and which must consequently pass through the celestial poles, are termed circles of declination, or celestial meridians. The intersections of these circles and the earth, are termed terrestrial meridians. The terrestrial meridians must evidently

pass through the poles of the earth. Sometimes a semicircle only is termed the meridian, and the opposite semicircle is then called the opposite meridian. The distance of a star from the equator, measured upon a circle of declination passing through it, is termed the declination of that star; the orbit in which the earth moves round the sun, is called the ecliptic; the inclination of the planes of the equator and ecliptic, is termed the obliquity of the ecliptic-the obliquity must evidently be equal to the complement of the inclination of the axis and ecliptic. Some of the above definitions are not required for our present purpose, but they will be necessary afterwards, and we give them here for the sake of connexion.

P

E

Fig. 1.

Effects of the different positions of the Earth.] The effect which the inclination of the axis must have upon the declination of the sun, may be illustrated by first supposing the axis to be parallel, and then conceiving it to be perpendicular, and observing what the result in these extreme cases would be. In the annexed figure, S represents the sun, the lines Pp which are parallel to each other, the axis, E Q the equator, and ABCDE the ecliptic. If Pp were perpendicular to, and EQ parallel with the ecliptic, it is evident that the sun would never have any declination; for, in whatever part of its orbit the

P

E

earth might be, a line joining the centres of the earth and sun would always be in the plane of the equator. If, on the contrary, Pp were parallel, and EQ consequently at right angles to the ecliptic, the sun would have all possible degrees of declination. At some point A, the declination would be nothing, and the sun appear to move in the equator. In going from A to B the declination would continually increase; and at B, Pp would evidently coincide with the line joining the sun and the centre of the earth, so that the declination would then be ninety degrees, and the sun appear to be placed in the pole p. From B to С the declination must diminish, and at C the sun would again appear to move in the equator. From C to D the declination must again increase, and at D, the sun would be in the opposite pole P. When the earth arrived at A, the sun would again appear to have returned to the equator. But the axis of the earth is neither perpendicular to, nor parallel with the plane of the orbit, but inclined to it in a certain degree. This must occasion the declination to vary in the same manner as a parallel axis would do, but to a less extent. At two opposite points, A and C, the sun will be in the equator. The declination will be greatest at B and D, and will there be equal to the obliquity of the ecliptic; for, at each of these points, a line joining the centres of the earth and sun, will form with the plane of the equator, an angle equal to the inclination of the equator and ecliptic. The declination at B and D, however, will be on opposite sides of the equator.

C

The Equinox, Solstices, and Tropics.] The seasons in which the sun moves in the equator, are termed equinoxes, and that circle is called the equinoctial; because, when he moves in it, the day and night-for a reason that will be afterwards seen-are equal over the whole earth. The seasons at which the sun's declination is greatest, are termed solstices; because his declination appears then to remain stationary for a while. The circles in which he then moves are denominated tropics, or circles of return. The tropics pass through the constellations of the crab and goat, and are therefore called the tropics of cancer and capricorn. The tropic of cancer is situated on the north of the equator, and that of capricorn to the south.

Before showing how the greatest declination of the sun may be found, it is necessary to give some explanations regarding the altitude of heavenly

bodies and the horizon.

The Visible and Rational Horizon.] We have already said that the circle in which the heavens appear to meet the earth, is termed the visible horizon. The plane of that circle must evidently be a tangent to the earth at the point where the observer is situated, if he be not placed in an elevated position. A great circle of the celestial sphere parallel to the visible horizon, is termed the rational horizon. From the distance of the fixed stars, by which the magnitude of the celestial sphere is determined, being almost infinite in comparison of the distance of any point on the surface of the earth from the centre, the visible and rational horizons must coincide.

M

G

D

Fig. 2.

F

Thus, in the annexed figure, suppose AB and EL to be two concentric spheres representing the earth and the heavens, and DF and GH to be the visible and rational horizon. If the radius C E be but a point in comparison of CA, DF and G H must coincide. The visible and rational horizons, however, will coincide only when the plane of the former is a tangent to the earth. If the observer be placed in an elevated position, as upon the top of a tower, or a mountain, his view of the heavens will be extended, and its -boundary the visible horizon, will be depressed below the rational; thus, in the above figure, let P be the elevated position of the observer, and PM PN tangents drawn from that point to the earth, and produced to the heavens. The intersections of these tangents with the celestial sphere, mark out MN to be the position of the visible horizon. When we speak of the horizon simply, the rational horizon is always meant.

B

H

The Zenith and Nadir.] The point in which a line drawn through any plane perpendicular to the horizon meets the celestial sphere above us, is termed the zenith of that place, and the point in which the same line meets the heavens in the opposite direction, the nadir of the place. The direction of gravity being always perpendicular to the horizon, the zenith must be directly over our heads, while the nadir will be under our feet. Since the earth is not exactly spherical, the line joining the zenith and nadir of any place will not pass through the centre of the earth. Great circles perpendicular to the horizon are termed

verticals. The altitude of a star above the horizon, is equal to the arc of a vertical passing through the star, intercepted by it and the horizon. True and Apparent Place of a Star.] Unless the distance of a body be very great, its altitude will appear to be different to two observers placed one on the surface, and the other at the centre of the earth; thus, in Fig. 3, suppose AC the earth, BD the rational horizon of an observer at A, and BED the sphere of the heavens. The star S will appear at A to be situated at M, while, to an observer at C, it will seem to be at L. The difference in these elevations will be the arc M L. The greater the distance less will the difference in

of the star is, the

B

Fig. 3.

E

L

N

P

M

C

D

these altitudes be. Thus, if the star be at P, the difference in the elevation will be only the arc NL, which is less than ML. The distance of the fixed stars being so indefinitely great, compared with the semidiameter of the earth, that the visible and rational horizons coincide, their elevation must appear the same whether seen from the surface of the earth or the centre. It is otherwise, however, with the sun and planets. Their distance bearing a sensible proportion to the radius of the earth, will appear a little more elevated as seen from the centre, than at the surface. The difference between the altitude of a body as seen from the centre and surface of the earth, is termed its parallax. The parallax will evidently be greatest when the body is in the horizon, and least when in the meridian. The horizontal parallax of the sun has been found to be about 8′′ 6, while that of the moon varies from about 54′ to 62′, her distance from the earth not being always the same. To render all observations capable of comparison, astronomers always make allowance for the parallax, and consider the altitude of a body as it would be seen from the centre. The point of the celestial sphere to which the body is referred when so seen, is termed its true place, while the point to which it is referred when seen from the surface, is called its apparent place.

Sun's Declination.] We return now to consider the method of finding the greatest declination of the sun. This is done by observing at the same place the altitudes of the sun when it passes the meridian, at the summer and winter solstices. Half the difference between the altitudes will evidently be equal to the greatest declination. This declination, which must be equal to the obliquity of the ecliptic, is found at present to be about 23° 28'. But ancient observations, as well as the calculations of the forces by which the motions of the planets are produced, show that the obliquity is not invariable. It diminishes at the rate of 50′′ in a century, till it reach a certain limit, after arriving at which it must begin again to increase.

Variation in the length of The change in the declination of the sun the Days and Nights. is the cause of the variation in the length of the days and nights. It will be necessary in illustrating this subject, and explaining the appearances which the sun must present in different latitudes, to consider how the celestial sphere will appear to observers differently situated in regard to the earth's axis. The horizon of a person on the terrestrial equator being parallel to the axis, the planes of the circles in which the stars appear to move will be perpendicular to the horizon, and will be divided by it into two equal parts, since the horizon is a great circle. All the heavenly bodies, therefore, whatever their declination

may be, will, at the equator, be visible during half their course. The poles will be in the horizon, and the celestial equator directly over the observer's head. The inhabitants of the earth at the equator, are said to live in a right sphere. The horizon of a person placed on either of the terrestrial poles being, on the contrary, perpendicular to the axis, the planes of the circles in which the stars move will be parallel to the horizon, and that circle will therefore constantly divide the heavens into the same two hemispheres. All the heavenly bodies which are in one of these hemispheres will be constantly to be seen, while those in the other will never be visible. One of the celestial poles will be in the zenith of the observer, and the equator will coincide with the horizon. The inhabitants at the poles, if there be any such, are said to live in a parallel sphere. At all intermediate parts of the earth, the horizon being placed more or less obliquely to the axis, the heavenly bodies will appear to move in circles, the planes of which are more or less inclined to the horizon; and the parts into which the circles are divided by it, must become more unequal as we recede from the equator. The time during which the heavenly bodies continue visible, therefore, will vary as their distance from the equator is augmented; and around one of the poles a number of stars will be seen during the whole period of their revolution, while an equal portion of the heavens at the other pole will be always invisible. The pole and the equator will be more or less elevated above the horizon. The inhabitants of the earth between the equator and the poles are said to live in an oblique sphere.

We are now prepared to explain the change which takes place in the length of the days and nights, and the different appearances which the sun must present to the inhabitants in different latitudes. To the inhabitants at the equator, the sun will be vertical at the equinoxes, and his least meridian altitude is at the solstices, when it will be 66° 32', which is more than his greatest altitude is with us. At all places within the tropics the sun must be vertical twice in the year, and when in the meridian, he will be seen sometimes to the north, and sometimes to the south. At the tropics the sun is vertical only once in the year, when in the solstice corresponding to that tropic; and at the opposite solstice his meridian altitude is only 43° 4. No place without the tropics can ever have a vertical sun, and in all such places he will be always seen in the same direction. At the equator the length of the day-apart from refraction, of which we shall not at present take any notice-must be always twelve hours; and when the sun moves in the equinoctial, the day and night must also be equal over the whole earth. As the declination of the sun increases, however, the day and night at all places which are not under the equator, must become more and more unequal. The day will be longer than the night in that hemisphere which is on the same side with the sun, and shorter in the other, and the difference must increase with the latitude. The day at any place will be longest when the sun is in the tropic next that place, and shortest when in the other. At the poles the sun will be visible during half a year at a time, and invisible during the other half. At either pole he will annually appear to describe a spiral of which each coil is nearly horizontal, half of the spiral being above the horizon and half below. The declination of the sun changing fastest at the equinoxes, and slowest at the solstices, the coils will be much more open in the middle than near the ends. Around the pole which is nearest to the sun, a portion of the earth, corresponding in