Now let us place the hypotheses together; on the one hand we have to suppose that these millions of stars, situated at immeasurable distances from our earth, and immeasurably greater than it, nevertheless whirl round it with inconceivable rapidity every twenty-four hours, and that besides this motion, certain of them wander perpetually through space in tortuous eccentric paths, subjected to some unknown and most complicated law of deviation.

On the other hand, take the hypothesis, that the earth revolves upon its axis perpetually and uniformly, and at the same time moves forward in space, an hypothesis rendered in the highest degree probable by the fact, otherwise ascertained, of its entire isolation in space.

The improbability of the first hypothesis, infinite as it is in itself, is infinitely increased by the probability of the second.

But however conclusive may be this balance of probabilities, the question admits of a still more rigid determination.

In the first chapter were stated the circumstances which absolutely prove the stars to be material bodies like our earth, subject to the same laws of attraction and motion as what we see around us; and the same is ascertained with equal certainty in respect to the sun and planets of our system. Now this being the case, it is impossible, from the nature of these laws of attraction and motion, that this sun, these planets, and these immense and distant stars, should turn continually round our little earth.

If two bodies, subject to the known laws of attraction and motion, revolve freely in space, we know that their revolution must take place, not about the actual centre of gravity of either body, but about their common centre of gravity. Now the common centre of gravity of two bodies is nearer to the greater of the two; so that the point about which the two revolve is always nearer to the greater body; and if the one body be infinitely greater than the other, it is infinitely nearer to it. And thus the effect is precisely the same as though the less body revolved about a point coincident with the centre of gravity of the greater.

But the sun is infinitely greater than the earth. The sun could not, therefore, if the earth and sun only were in existence, revolve round the earth, but the earth must revolve round a point infinitely near to the centre of the sun. And this result will scarcely be affected by the introduction of the other bodies of our system into the discussion;-the whole revolve about their common centre of gravity, which by reason of the great magnitude of the sun, when compared with any of them, is a point which may be considered as fixed, and which may be considered as exceedingly near its centre.

It is impossible, then, that the sun should revolve round the earth every twenty-four hours. And we must take the other hypothesis.

The earth turns upon one of its diameters called its axis every twenty-four hours, thereby causing that vast, hollow sphere, whose centre it may be imagined to occupy, to appear continually to revolve round it in that period.

Let us imagine the axis of the earth to be produced both ways, so as to meet the surface of this great sphere of the heavens in the points

P and Q. It will thus mark out the two poles of the heavens, about which the stars appear to have their diurnal paths, of which one is represented by the circle, RT, in the figure.

Let the plane of the equator of the earth, E C, be produced, to intersect the sphere of the heavens. The great circle, Q, in which it will thus intersect it, will be the equinoctial. Any plane drawn through the axis, PQ, of the heavens will intersect the celestial sphere in a circle called a declination-circle, of which circles PS M, shown in the figure, is one. Declination-circles are thus great circles which pass round the heavens from one pole to the other. Every position of the heavens is supposed to have one of these declination-circles passing through it. The use of them is to fix the position of any star on the vault of the heavens, in the same manner as the position of a place is fixed on the surface of the earth by its longitude and latitude.

If we know the particular declination-circle which passes through any star, and also the situation of the star on that circle, we have an accurate conception of the position of the star on the vault of the heavens. We can convey that conception to others, and by reference to a celestial globe, or to a chart of the heavens, we can tell what this particular star is, and what is its position in reference to other stars.

Each declination-circle passes through the poles of the heavens, and, of course, intersects the equinoctial, which lies midway between these poles at right angles. There is a particular point on the equinoctial, called the point Aries, marked in the engraving by the symbol, the position of which in the heavens will be explained hereafter The distance of the point where the declination-circle of any star cuts the equinoctial, from this point, Aries, being measured eastward along the equinoctial, is called the right ascension of that star; and the dis

tance of the star from the equinoctial, measured on its declination-circle, is called the declination of the star. Thus, knowing the right ascension and declination of a star, we know its exact position on the great sphere of the heavens, and can refer to it on a celestial sphere or chart; for from the right ascension we know the position of its declination-circle, and from the declination, its situation on that particular declinationcircle. Thus, in the figure, the declination-circle, PS M, which passes through the star, s, intersects the equinoctial in the point м, the distance of this point from, measured eastwards on the equinoctial; ÆQ is therefore the right ascension of s, whilst the distance, s м, measured on the declination-circle, between s and the equinoctial, is the declination of s.

If the plane of the meridian of longitude of any place on the earth's surface be continued to the celestial sphere, it traces out there what is called the celestial meridian of that particular place. Thus, if o be any place on the earth's surface, and if the plane of the meridian of longitude passing through o be produced to intersect the sphere of the heavens, the circle in which it will intersect it is the celestial meridian of o; it is represented in the figure by the circle NPZKF Q.

Since the earth is continually revolving in the position which it apparently occupies in the centre of the celestial sphere, the celestial meridian of each particular place is continually revolving over the face of the heavens, about its axis, coinciding in succession with all the declination-circles in the course of twenty-four hours. This is the real state of the case. The apparent state of the case is, however, precisely the opposite of this. The place of the observer appears to be fixed, and therefore, his celestial meridian to be fixed; whilst the stars, and with them their declination-circles, appear to revolve every twenty-four hours, each declination-circle coinciding in its turn with his meridian.

When the declination-circle of any star thus coincides with the celestial meridian of any place, the star is said to be on the meridian of that place, and its altitude at that moment above the horizon, is called its meridian altitude.

The plane of the meridian passing through the axis of the earth passes through its centre, and is perpendicular to its surface. A line perpendicular to the earth's surface at any point, is, therefore, in the plane of the meridian at that point, and such a line being produced to the heavens, will intersect it in a point of the meridian of the place.

Thus the vertical, o z, at any place, o, on the earth's surface, being produced to the heavens, intersects them in the celestial meridian of the place. The point, z, where the vertical intersects the sphere of the heavens, when produced upwards, is called the Zenith; when produced downwards, the Nadir. The Zenith is that point of the heavens which an observer sees immediately above his head; the Nadir, that point which he would see if nothing intervened immediately beneath his feet.

The celestial meridian of any place has been shown to pass through its zenith. Also, by the definition of it, it appears that it passes through the poles of the heavens. The celestial meridian of any place is thus a great circle drawn through its zenith and the poles of the heavens. The points where this circle meets the horizon are called its

north and south points, and the points of the horizon half-way between these, its east and west points. Thus, if NBSA be the horizon of an observer at o, the points N and s, where the celestial meridian of that place intersect it, are its north and south points, and ▲ and в, half way between these, its east and west points. If a great circle, zs K, be imagined to be drawn from the zenith, z, to the horizon, through any star, s, it is called the azimuth circle of that star, K s is its altitude, zs its zenith distance, and N K its azimuth.

R

K

P

S

F

Let p represent the pole of the heavens; z, the zenith of an observer on the earth's surface at E; PZ QSH, a great circle of the heavens passing through these points: this circle is, therefore, the meridian of the observer at E. Let HK be the horizon of the observer at E, at right angles to Z E; also let RS be the equinoctial at right angles to the axis, PQ, of the heavens. The earth, E, may be considered as a mere point, in comparison with the sphere whose centre it occupies. Now the celestial meridian, PZ KS, being in the same plane, and concentric with the terrestrial meridian of the observer, the arc, Z R, between the equinoctial and the zenith, contains as many degrees as does the arc, EF, of the terrestrial meridian between the equator and the place of observation. fact, these arcs measure the same angle at the earth's centre. But the arc, EF, of the meridian intercepted between the equator and the observer's place, is his latitude; the arc, Z R, between the equinoctial and the zenith, is, therefore, equal to the latitude. And if we could but see exactly where the equinoctial was in the sky, if it were marked, for instance, upon it as it is upon our globes, by a band stretching across the heavens, we could at once determine the latitude of any place by measuring the distance upon the meridian between this band and the zenith of the place.

In

But although we cannot, without much difficulty, fix the position of the equinoctial in the heavens, the pole is much more readily found; and this will answer the same purpose, for the arc, Z R, is equal to P H; therefore the arc, PH, which is the distance of the pole from the horizon, or the elevation of the pole, as it is termed, is equal to the latitude of the place of observation. Here, then, is a very simple method of determining the latitude. We have only to observe the altitude of the pole of the heavens above the horizon.

But there is still another difficulty; for the pole of the heavens cannot at once and accurately be found. The polar star is usually said to be in the pole of the heavens, whereas it is, in reality, distant from it by about one degree and a-half.

How, then, shall we find the exact height of the pole, not being able to distinguish its place in the heavens. Thus, let us fix upon one of those stars which are not so remote from the pole as to be made by their revolution round it, to sink beneath the horizon, and are, therefore, called circumpolar stars.

Let R Q represent the diurnal path of one of these about the pole,

R

H

P; also, let ZRH be the celestial meridian of the observer.

Let the altitude of the star be observed when it is on the meridian at R, at what is called it superior passage over it, and also when at Q, at the time of its inferior passage; the altitudes HR and HQ

being thus known, exactly half their sum will be H P, the exact height of the pole P.

Take, then, half the sum of the two meridian altitudes of a circumpolar star, and you will obtain the altitude of the pole that is the latitude of your place of observation. It is clear that the star is at its highest point when at R, and at its lowest at Q. The rule, then, may be expressed thus: take half the difference of the greatest and least altitudes of a circumpolar star, and the result will be the latitude. Thus it becomes unnecessary to know exactly what is the position of the celestial meridian. This is probably the most accurate method of finding the latitude.

The practical objections to this method of determining the latitude, are these, it requires an interval of the half of a sidereal day between the two observations required; and it requires that the observer should remain in the same place during that interval. Now the latitude is sometimes required to be known at once, and, as in the case of a ship at sea, the same place cannot be retained during the interval in question. Again, these are observations which can only be made at night.

K

The following method will obviate all these difficulties.

Let s represent the position of any of the heavenly bodies, a star for instance, or a planet, or the sun, or moon, when on the celestial meridian of the observer.

S

B

B

This celestial meridian, then, coincides with the declination-circle of the star, and the distance, AS, of the equinoctial from the star measured on the meridian, is the declination of the star. Now suppose the declination to be known, and the declinations of all the principal stars are known, and have been inserted in tables; also the declination of the sun, which alters daily, but nevertheless admits of being calculated for every day of the year; and is so calculated and registered in the Nautical Almanack. Hence, therefore, the distance, a s, of the sun, or star, from the equinoctial, is known for every day in the year. Now, let the meridional distance of the sun from the ZENITH be observed, if the latitude be required to be found in the day-time, or the meridian distance of a known star from the zenith if the latitude be required at night. Thus, the distance s z will be known, and as, the declination, is known by the tables. The sum of these, A z, is the latitude. If it be more convenient to measure the distance of s from

S,