argued from the appearances of the fixed stars, on the hypothesis of the quiescence of the centre and axis of the earth in space is accurate, although this hypothesis be false.

Besides the stars called fixed, because they retain always their positions with respect to one another on the sphere of the heavens, there are other bodies visible on it, whose position does not appear to be fixed, either in reference to one another or to the fixed stars; these are the sun, moon, and planets-these, it will now be shown, lie greatly nearer to us than the fixed stars, and thus within that great sphere which has been hitherto designated the sphere of the heavens-they describe enormous ellipses in space, which are yet so small in comparison with the dimensions of that sphere, that they may be considered scarcely to deviate from its centre, and that thus, infinitely great in themselves, but infinitely small in comparison with the distance of the stars, they are all described round one common focus, very near to which lies the centre of the sun.

The process of reasoning by which the complicated apparent motions of the sun, moon, and planets, are made to resolve themselves into these few real and elementary motions, is one of the highest and most successful efforts that has ever been made by the intellect of man.

If the heavens be watched from night to night, continual alteration of the positions of the planets among the fixed stars will, from such observations, continued for a few nights, be very plainly perceived; the planet Jupiter, for instance, being seen one night in the neighbourhood of a particular fixed star, will on the next be found slightly to have receded from it, the space of a week will produce a very marked separation, a month will have taken it completely away from it, and a year will probably have carried it into some opposite quarter of the heavens-into the discussion of these apparent motions of the planets, which are very remarkable, we shall not at present enter-it is enough here to state the fact, that there are such motions, and that they do not take place irregularly and towards all parts of the heavens, but that they are, for the most part, confined to a certain zone or belt of it, about 18° in width. This zone, or belt of the heavens, is called the zodiac. A line drawn along its centre would be a great circle of the heavens, and would cut the equinoctial at an angle of 23° 28'.

The moon, too, takes her wandering solitary course eastward along this zone in the heavens. And her broad disc is continually seen covering and passing over the stars which lie along her path. Her motion, although somewhat irregular, is very rapid, being upwards of 13° in 24 sidereal hours, or nearly half a degree every hour, so that almost be seen to move among the stars.

she may

Now the question at once suggests itself, does the sun too move, or appear to move over the concave of the heavens in which he, as well as the moon occupies a place, or does he remain in a fixed position among the stars? This question cannot be determined in reference to the sun, as we determine it of the moon-we cannot see the sun's motion among the stars, for when the sun is up, the stars are to the naked eye invisible ;—how is it then determined? Thus :-If the sun were apparently fixed like the stars, the time intervening between the passage of the meridian of any

particular place over the sun, and its return to the sun again, would evidently be precisely equal to the time of its passage over a fixed star, and its return to that fixed star again. Now this is not the case. One of these periods is called a solar, and the other a sidereal day, and the solar day is not of the same length with the sidereal day, it is always longer than it; that is, the meridian of any place on the earth's surface, always revolves from a fixed star to that star again, sooner than it revolves from the sun to the sun again. The sun then does not remain, or appear to remain, fixed like the stars, on the sphere of the heavens, it moves in the same direction in which the meridian moves, the meridian arriving at the place in the heavens where the sun was on the preceding day, before it arrives at the sun. Now the meridian revolves with the earth eastward, the apparent motion of the sun on the sphere of the heavens is therefore eastward.

And, moreover, the amount of this daily motion of the sun eastward may readily be found; we have only to subtract a sidereal day (that is, the time which the meridian occupies in revolving from the sun on one day to the same place in the heavens on the next) from a solar day, or the time of the revolution of the meridian from the sun on one day to the place which the sun actually occupies in the heavens on the next day. The difference will be the time which the meridian has occupied in revolving from the sun's place on the preceding day to its place on this day, this difference will be found different for different days in the year, but its average is 3′ 56′′ of sidereal time. This, then, is the mean sidereal time which the meridian occupies in revolving from the sun's place on one day in the heavens to its place on the next day. Now the meridian revolves through the whole 360° of the heavens in 24 sidereal hours, or over 15° of it in one sidereal hour; it revolves therefore, as may readily be found by the rule of three, over an arc of 59′ 8′′ in this 3′ 56′′ of time; and therefore the sun's place on the second day is 59′ 8′′ more to the east than on the first day, or its daily motion is 59′ 8′′ eastward. But an arc of 59′ 8′′ being multiplied by 3654 will give us 360°. In 365 days, therefore, the sun will have revolved eastward on the sphere of the heavens through 360°, that is, completely round it-this period is one solar year.

The sun, then, although we cannot see him moving on the heavens, there being no fixed object visible upon them when the sun can be seen to which we can refer his motion, does yet present the same phenomena as though he moved continually like the moon eastward among the stars, except that instead of completing his revolution, as the moon does, in one lunar month, his gyration takes him a whole year.

But what path does he describe in the heavens; he revolves round them, but in what route? As we cannot see him among the fixed stars, how shall we find out his course? Thus:-We may find out as is now to be shown, what declination circle he is on for every day of the year at noon, and also we may find what is his declination, that is, we may find where he is on his declination-circle. Knowing these two elements, we shall know his exact position on the sphere of the heavens, and referring to a celestial globe or chart, we shall tell what stars are in his neighbourhood.

The declination-circle on which the sun is, may be found thus:— let the exact time of the meridian passing over the sun's centre on any day be noted-now that meridian we know will return to its place in the heavens, or revolve through 360°, in 24 sidereal hours, it will therefore revolve through 180° in 12 sidereal hours. Let us then observe what stars the meridian is passing over precisely 12 sidereal hours after our first observation; we shall know that these stars are 180° from the sun's place on the preceding noon: counting, therefore, off 180° westward, on the equinoctial of a globe from that declination-circle on which are these stars, we shall know that the sun was on the declination-circle which passes through the point which we thus find on the preceding

noon.

H

Again, to determine the declination of the sun, we have only to find, by observation, his meridional zenith distance, zs, and subtract it from the latitude, z, the remainder will be the declination H S.

SZ

K

E

F

Finding thus the declination of the sun, and the position of his declination-circle for the noon of every day in the year, we can mark on the celestial globe his position for every day, and joining these positions, we shall obtain his path on the sphere of the heavens. Now, all this has been carefully done and the apparent path of the sun among the fixed stars is traced on all our celestial globes. The sun is thus ascertained to have, in common with the moon and planets, its path, called the Ecliptic, along that zone or belt of the heavens which we have called the zodiac; it is a great circle of the sphere, constituting in point of fact the centre of that belt which stretches 9° on either side of it. The ecliptic is inclined to the equinoctial, at such an angle, that at the greatest separation of these circles there are 23° 18′ interval between them, measured on one of the declination-circles of the sphere. Along this path in the heavens the sun would appear to us to move, as the moon does, among the fixed stars, were it not that, by the superior brilliancy of the sun, the stars are invisible to the naked eye so long as he is above the horizon.

The sun and moon both, then, have an apparent motion round the earth, the one in a year, and the other in a month. It is now to be shown that this apparent motion of the sun round the earth is not a real motion of the sun, but that it results from a real motion of the earth round the sun; and further, that the apparent motion of the moon is a real motion, resulting from an actual monthly revolution about the earth.

In the first place, then, it is asserted that a real motion of the earth round the sun would produce precisely those appearances which we observe in the heavens, and which have been attributed to an annual motion of the sun along that line which has been called the ecliptic.

Let A, B, C be positions of the earth, in an orbit which it is supposed to describe about the sun, at intervals each of a sidereal day. Also let AP, BP, CP, be lines drawn from a certain fixed star to a particular

place on the earth's surface. Since the star, P, is infinitely distant, the lines a P, B P, C P, may be considered parallel. Suppose the meridian, M, of this place to be in the position a of the earth, in the act of passing over this star; then, since there is an interval of a sidereal day between the positions A and B, the meridian of the same place will be passing over the star in the position B, and similarly in the position c. Now, let s be the sun, supposed to lie about the centre of the earth's orbit, and at a finite distance from it as compared with the distance of the fixed stars. Let

A

the small sphere described round A, as a nucleus, represent the sphere of the visible heavens in that position of the earth, or let it represent that sphere to which a spectator refers the positions of all the heavenly bodies, and on which he imagines them to be distributed. And let the spheres round b and c be similarly interpreted. At a the observer, at the place which we have supposed, will see the star P on his meridian at м*, and the sun at the same time on the meridian; at в he will see the star at N, and the sun at K; and at c the sun will be at L, and the star at R; thus it is manifest that every time the star comes upon the meridian, the sun will appear to have receded further from it than at the preceding transit, describing arcs N K, L R, of a circle, formed by the intersection of the plane of the earth's motion with the surface of the visible heavens.

It will be observed that although the spheres to which an observer refers the positions of the heavenly bodies, and which constitute his visible heavens, are in different positions of the earth different; nevertheless, they appear to him the same, because the stars which cover them, by reason of their immense distance, do not alter their relative positions upon them. Thus, then, the sun will appear to describe a circle among the stars, which circle is, in point of fact, the intersection of the plane of the earth's orbit with that sphere of the visible heavens, which, in every one of its positions, appears to surround the

He is supposed to have a telescope powerful enough to show him the stars in the day-time.

observer. This circle being then supposed to be the ecliptic,—that is, the intersection of the plane of the earth's orbit with the sphere of the heavens being supposed to be the ecliptic,—all the phenomena of the apparent annual motion of the sun through this ecliptic are explained by an annual revolution of the earth about the sun in that orbit.

Here, then, as in the case of the solar day, are two hypotheses, both of which explain the phenomena of the solar year: according to one, the sun revolves about the earth every year, in the middle of that band of the heavens called the zodiac;—according to the other, the earth revolves about the sun every year, having for the plane* of its revolution a plane which cuts the sphere of the heavens in the ecliptic.

Between these two hypotheses we have to choose. To that of the annual revolution of the sun about the earth, there are objections precisely similar to those which were adduced in the case of its apparent diurnal revolution. It is ninety-five millions of miles from us, and its bulk is more than one million times greater than that of the earth. Now, if it revolve round the earth in a year, this huge mass must sweep through space at the rate of about 1200 miles in every minute of time. This rapid revolution of an immensely large body about one which is in comparison with it infinitely small, at once strikes us as an improbability; it is more than this, it is a mechanical impossibility, as will plainly be perceived when we come to treat of the laws of physical astronomy.

Again, such are the motions of those other bodies which we have called wandering stars or planets, and which we shall discuss hereafter, as incontrovertibly to prove that these revolve each in an orbit about the sun; also their magnitudes may be ascertained by direct trigonometrical admeasurement, and many of them are thus found to be greatly larger than the earth. On the hypothesis we are discussing, not only, then, must the huge sun revolve continually with prodigious velocity about our earth, but the whole host of planets which accompany and revolve continually round him, and which are, many of them, as it respects magnitude, far more important elements of the material universe than our earth is, must nevertheless, together with the sun, and in combination with their motion round it, sweep with it in a perpetual circle round the earth.

It is a curious psychological fact, strongly illustrative of that waywardness and perversity of judgment of which we are all more or less the victims, that a philosopher, a laborious observer, and a man of considerable mathematical learning, was once found to take up this strange complicated hypothesis. The phenomena of the heavens were thus explained by Tycho Brahe, a Danish philosopher, the contemporary of Kepler, and the author of a very valuable catalogue of the fixed stars.

Again (to accumulate all the evidence on this point) it has been shown that the earth has a daily motion upon its axis. Now this fact of its daily motion renders also its annual motion highly probable. A probability founded on this other; that if there be two modes of explaining any phenomenon of nature, then cæteris paribus, that is the most probable which is the most simple. For by what we observe

*

By the plane of the revolution of the earth, is here meant a plane in which are found oes drawn in different posi

tions of the earth from its centre to the centre of the sun.