1.

Drake, sailing from Europe, have pursued a course always BOOK towards the west (making only some deviations, in order to double the lands which stretch towards the south;) and without quitting this general direction, have returned to the same place whence they set out. Upon a circular plane we might indeed perform a circular voyage, but that by continually changing the direction. Heemskerk, when he wintered at Nova Zembla, confirmed what astronomers had concluded from the spherical figure of the earth ;--namely, that the days and nights near the poles extend to several months. Finally, Cook, in approaching as near as possible to the southern polar circle, found that the voyage round was always diminished proportionably to the diminution of his distance from the pole; so that we have thus obtained an ocular proof of the rotundity of the earth towards the south pole, as well as towards the north.

this doc

So many united proofs, as well as the accuracy of so Prejudices many astronomical observations, all of which have been against made and calculated upon the supposition of the sphericity trine. of our earth, leave no room for reasonable doubts upon the subject. Respect for the Sacred Writings, which, in speaking of the earth, employ expressions borrowed from ordinary language, ought not to induce us to reject a physical truth altogether foreign to the moral truths which religion teaches. In vain does ignorance demand of us how the earth can remain suspended in the air without any support. Let us look upon the heavens, and observe how many other globes roll in space. The force which supports them is unknown to us; but we see its effects, and we investigate the laws according to which these effects take place. Let us then lay aside all uneasiness concerning the antipodes, that is, the people of the earth whose feet are turned towards ours: there is upon the globe neither high nor low; the antipodes see, in like manner as we do, the earth under their feet, and the sky over their heads.

* Psalm xxiv. 2. xxxvi. 6. Comp. Lactant. 1. iii. ch. 24. Augustin, De Civ. Dei, XVI. 9.

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rities of the

What would we gain by supposing, as Homer does, that under the earth are placed a range of columns guarded by Atlas, or by imagining it to rest upon nine pillars, as the Scandinavians believed, or upon four elephants, according to the opinion of the worshippers of Bramah? Upon what would these elephants or these columns rest? Our thoughts, however far they proceed, must always at length stop short, and, affrighted, recoil from that infinity which surrounds us on every side, and which it is folly to attempt to compreIrregula- hend. But, some more reasonable observers will say, Do not the Andes and the Alps make it evident that the earth globe. is an irregular body, and not at all round? We answer: the highest mountain known, which is Chimborazo in Peru, rises to 21,424† feet above the surface of the sea. This height is nearly of the earth's greatest circumference, and of its axis. Upon an artificial globe of twentyone feet in circumference, or of 63 feet in diameter, Chimborazo could only be represented by a grain of sand less than one-twentieth of an inch in thickness. Irregularities so imperceptible do not deserve to be taken into consideration. We shall see, in the following Book, that the true differences which exist between our globe and a perfect sphere, are known, measured, and estimated. But before setting forth this result, deduced from observations the most scientific which have been made in modern times, it is necessary to point out more precisely some of the relations which connect this earth with the other heavenly bodies, and to show, according to Lalande and Biot, in what manner these astronomical principles are connected with mathematical geography.

From a simple view, we learn that the stars with which the nocturnal vault of the heavens is bespangled, appear

*Voluspâ, stroph. 2.

"Nio mân ek heima

"Nio ividi."

† Or about 6531 French metres.

It has since been discovered, that some mountains in Tibet rise about 5000 feet higher. The accuracy of the data of this admeasurement is, however, dubious.

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to move from east to west, each describing a portion of a circle. If we observe this motion more attentively, it appears to be performed about a point which alone remains immovable: this point has received the name of pole, Poles. which signifies a pivot. The star which is situated nearest to this point, is called the pole star. The celestial vault is conceived to present itself under the appearance of a sphere; there must therefore be, in the half which is invisible to us, another immovable point: this point is the south celestial pole, as that which we see is the north celestial pole. The imaginary line which passes through these two points, and through the centre of the world, is named the axis of the world, from a Greek word which signifies an axle. This line passing through our globe forms at the same time its axis, and marks upon the surface of the earth two points corresponding to the poles of the heavens, and which are denominated terrestrial poles. That which answers to the pole star, is called the north pole, or the arctic pole ;* the opposite pole is named the south pole, or antarctic pole.†

The point of the horizon which corresponds to the north Horizon. pole, is the north, and the opposite point is the south. The circle perpendicular to the horizon, which passes Meridian. through these points, and consequently also through the poles, is called by astronomers the meridian; it divides the visible celestial hemisphere into two equal parts; so that the stars, at the moment when they appear upon this circle, are at the middle of their apparent course; it is the passage of the sun over this same circle which determines the instant of noon.

We have already spoken of the meridian line, or of the line which joins the north point of the horizon with the south. A line perpendicular to the meridian line, and con- Cardinal ceived to be extended both ways till it meets the hori- points. zon, marks upon this circle two opposite points, each 90

From the Greek word agaros the bear, a constellation in the neighbourhood of the north pole.

+ From the Greek words arri, opposite to, and agxros, the bear.

BOOK degrees distant from the north and south; and to which are appropriated the names of east and west.

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Illustration.

We may illustrate these definitions upon an artificial globe, or by means of figure 1.

Let the circle NEMO represent the horizon, and the point A the centre, at which the observer is placed; the letters a, b, c, and d, e, f, will indicate portions of circles which the stars appear to describe about the pole. Those stars whose polar distance is not greater than the arc PN, which measures the elevation of the north pole above the horizon, appear to describe complete circles, such as S h, i, k; the point N marks the north point of the horizon, M. the south; and consequently MN represents the meridian line. The celestial meridian is represented by the semicircle MZN, of which the plane is supposed perpendicular to that of the horizon NEMO, and which passes through the points M and N. This circle cuts at the points c and e, the arcs a b c and d e f into two equal parts. The east point of the horizon is represented by the point E, and the west by the point 0: it is from E towards O that the stars appear to move, passing in the middle of their course through some point of the celestial meridian.

The true cause of these appearances, is the motion by which the earth turns round its own axis from west to east in the space of twenty-four hours. We proceed now to explain this motion by means of figure 2, which represents the globe of the earth. We shall suppose the point A to be the place of the observer, EMON his horizon, and the straight line P p to represent the axis round which the earth performs its motion of rotation.

It is easy to perceive, that the horizon of the observer, since it turns along with him during the rotation of the earth, must advance towards the stars successively, so as to give them the appearance of gradually approaching the horizon; in the same manner as a vessel leaving or approaching the land causes the objects on shore to appear to the eyes of an observer on board to be in motion.

As the plane MZN of the meridian turns at the same

time with the horizontal plane NEMO, to which it is perpendicular, it must point successively to the same stars, which will then appear in the middle of that part of their course which they describe above the horizon. As soon as the star touches the western verge of the horizon, that star appears to set, and ceases to be visible until the motion of the earth has brought back upon it the eastern boundary of the same circle.

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measures.

This explanation gives directly a reason for the diurnal appearing and disappearing of the stars, and of the sun. But in order to conceive the use which is made of these celestial appearances in astronomy and geography, it must be observed that these motions are measured only by angles, without any regard to absolute length and real distances. For example, if the star, fig. 2, appear first in Angular the horizon in the direction of the visual ray AF, and be scen afterwards in the direction of the ray AG, the eye of Degrees, the spectator measures only the angular space FAG; it determines only the arc of the circle comprehended in this angle, and not the length of the radius. This arc is estimated in degrees and parts of a degree. The circumference of every circle, whether a great circle or a small, is supposed to be divided into 360 degrees; each degree is divided into 60 minutes, and each minute is subdivided into 60 seconds.

It is easy to see that we may, with regard to the heavenly bodies, substitute, for the plane NEMO, which touches the earth, a parallel plane, passing through the centre. The reason is, that, when a star situated at I appears in the horizontal plane which touches the earth at the point A, an observer, placed at the centre of the earth, would see the same star upon the line CI, so that it would appear elevated only by the angle IC n, which will be so much the smaller, according as the star is more distant. The figure renders this evident with regard to the star situated at the point H. The distance of the stars being almost infinite, compared with the semidiameter of the earth, which separates the place of the observer from the centre of the globe,

&c.