circumstances indicative of its figure, they conceived it to be an extensive plain meeting the heavens on every side. Such was, for ages, the general opinion. But there were exceptions to the prevailing ignorance, which are honorable testimonies to the value of a more enlarged and extended observation of nature. The Egyptians and Chaldeans are especially entitled to this praise. The philosophers of these nations were, in all probability, led to form a correct opinion of the figure of the earth from their great practical familiarity with the appearances of the heavenly bodies. But whatever may have been the source from whence their knowledge was derived, it is manifest that they were not ignorant of its true shape, as it must have formed an element in the calculations by which they were enabled to predict eclipses of the moon. From the Egyptians and Chaldeans, who were the fathers as well of geographical as of astronomical science, the Greek philosophers, with all their most correct notions in natural philosophy, derived also their knowledge of the earth's true shape. But (as Sir Isaac Newton remarks) the Greeks were of themselves more addicted to the study of philology (or language) than of nature: when therefore their communications with Egypt became less frequent, the ancient philosophy gradually declined among them; and no longer retaining the just ideas they once possessed, they put forth their own visionary speculations concerning the figure of the earth. Aristotle, the most celebrated of the Greek philosophers, did not escape the error of those who allow the suggestions of fancy to occupy the place of a severe investigation into facts; and we find him alleging the earth to be of a cylindrical shape, like a common drum. The remarkable ingeniousness of the Greeks was ever impatient of the restraint which scientific inquiry in order to a successful issue imposes upon the mind; and it is to be lamented that by reason of the admiration in which their writings were held, their errors should for so long have retained possession of the human mind, and by keeping down the spirit of inquiry retarded the full establishment of what is properly called experimental philosophy. During the greater part of that portion of the history of Europe, called the middle or dark ages, the earth was conceived to be a flat surface extending on

every side till it met the heavens. The overthrow of this popular opinion was rendered the more difficult by the Roman church admitting it into the number of articles of faith: the tenet thus became guarded with the sanction of religious belief, and by the apprehension of incurring the serious charge of heretical opinions. It is however remarkable, that the appearance of objects at sea, which are wholly inconsistent with the notion of the earth being a plain, and which lead most directly to the conclusion of its spherical shape, should not have redeemed the Venetians and Genoese, who had long been in the habit of making adventurous sea voyages, from the general ignorance. But notwithstanding the peculiar advantages enjoyed by navigators, it is evident that the best of those of the age of Columbus were not better informed of the earth's real figure. It is related as a matter of history, that the Portuguese who had arrived at the Moluccas (situated in the Pacific and to the West of America), by sailing continually in an easterly direction, were astonished by the appearance of Magellan's party, who reached the same point by sailing continually west. We may not, however, involve Columbus in this general censure; to him is properly due the glory of establishing the fact that the earth is a sphere. He was indeed eminently qualified to give a new direction to the current of opinion. In advance of the age he lived in by the extent and correctness of his information, and being at once bold in enterprise, enthusiastic in pursuit, and fertile in expedients, he possessed all the characteristics of one who is destined to overthrow a great and prevailing practical error. His persuasion that the earth was a sphere, furnished him with the happy idea of arriving at the East Indies by a shorter course than round the Cape of Good Hope, by sailing due West. He failed in his undertaking, having been misled by the error of the ancient geographers. Ptolemy's map was then in use, and the East Indies are there laid down considerably to the west of their true position. The western coast of India is by Ptolemy placed in longitude 165° east from the isle of Ferro, (one of the Canaries through which the first meridian passed,) whereas the true longitude is about 96°, thus making a difference of no less than 67°. The reasoning of Columbus was therefore right; and al

to have moved, corresponds with a similar arc traced upon the surface of the earth. Another most convincing proof is furnished by the eclipses of the moon. These eclipses are known to be caused by the earth coming between the sun and moon, and intercepting or cutting off the supply of light from the sun which illuminates the moon's surface or disk; the dark part of the moon's disk is, there fore, nothing more than a representation of the earth's shadow at the distance of the moon. In whatever position the earth happens to be at the time of an eclipse, its shadow upon the moon's disk is always in the form of a circle or of part of a circle: the earth must therefore be a sphere, since no other than a spherical body, in every position in which it can placed with respect to another body giving light, can cast a circular shadow upon a third body. If, however, the earth were [shaped like a circular flat plain, its shadow upon the moon's disk would be circular only when either of its sides directly faced the moon: if turned edgeways towards the moon, the shadow would be in the form of a streak, and in all other positions it would be more or less elliptical, as the earth happened to be turned more or less obliquely towards the moon when she is eclipsed.

The supposition that the earth is a sphere, accounts for all the appearances we have described; while, on the other hand, the various suppositions which have from time to time been advanced, and which differ from this, are totally inconsistent with one or other of them. Sir Isaac Newton, in his "Principles of Natural Philosophy," has laid it down as a rule (and it is a rule as indisputably just as it is important), that in experimental philosophy we are to look upon propositions collected by general induction from phenomena, as accurately or very nearly true, notwithstanding any contrary hypothesis may be imagined, till such time as other phenomena occur by which they may either be made more accurate or liable to exceptions;" he adds, "this rule we must follow, that the argument of induction may not be evaded by hypotheses." Applying this rule to the present subject, we may observe that the objections urged against the conclusion that the earth is spherical, however plausible, are entitled to no weight whatever, unless they are grounded upon some certain facts and natural

appearances arising from the figure of the earth, either inconsistent with the present-received theory, or which that theory is insufficient to account for.

It is hardly necessary to remark, that the expressions occasionally to be met with in the Bible with regard to the figure of the earth, and which may appear to contradict the foregoing conclusion, have been improperly and very ignorantly applied to this subject. The object of the inspired writers who used them, was not to advance a true system of natural philosophy, or to correct the popular errors of the day in matters of mere science, but to illustrate or enforce some precept or doctrine, or to record the occurrence of some remarkable event, which could not be done intelligibly, but by adopting expressions in agreement with the opinions of the age.

The re-establishment of the old and long neglected opinion of the earth's spherical shape, may justly be regarded as furnishing an epoch in the history of modern Europe. When admitted into the number of those truths which are assumed and acted upon without proof, it had an immediate and practical effect upon the common concerns of life. To traverse boundless seas was no longer matter for apprehension: the seaman was now provided with a method of discovering his relative position upon the globe, the course he had already described, and the distance and bearing of his destined port. Navigation thence assumed a bolder and more systematic character; an extensive commerce added to the wealth, and stimulated the efforts of European nations; and the more general and frequent intercourse inseparable from commerce softened the prejudices of men, and opened to them in distant climates and countries the richest and most varied stores of knowledge. We should not perhaps be justified in placing this discovery in the same rank with the other great events which happened about this æra: the invention and general introduction of the art of printing-the reformationand the establishment of experimental philosophy, must stand alone; but it forms together with them a class of great and brilliant events, which exhibit the human mind as once more in a state of activity, and putting forth all its energies in the attainment of whatever might most conduce to the social and moral improvement of mankind.

CHAPTER II.

The Circles of the Sphere-Extent of the Visible Horizon - Method of Drawing a Meridian Line-Circles of Position-Equator-LatitudeFirst Meridian-Longitude.

THE modes of precisely fixing the situation of places upon the earth are founded upon the circumstance just now proved of its spherical form, and upon the supposition which, for the purposes to which it is applied, is not a false one, that it is enclosed in a concave or hollow sphere of the heavens, of which it occupies the middle spot or centre.

and p the south pole; now suppose a plane to cut this sphere into two equal Fig. 1.

Upon the surface of the earth considered as a globe, various lines are supposed to be drawn for the purposes of geographers, and in order to determine or explain the truths of their science; and as the heavens present to us a concave sphere, having the same centre as the earth, there are also imaginary lines supposed to be traced upon the inner surface of the heavens, which exactly correspond with those traced upon the earth. By this device geography has become allied with astronomy, and has thence derived its most important improvements. We now proceed to the description of the abovementioned lines which are supposed to divide the earth, and which are seen drawn upon the common geographical globe.

parts in a direction perpendicular to the axis, this plane will pass through the centre O, and the circle Qab Qcd, which is the boundary of the cutting plane upon the surface of the globe, will represent the equator, and is every where at an equal distance from both poles. This circle and all other circles, the planes of which pass through the centre of the sphere, are called great circles. All circles such as PapcP PbpdP, which pass through both poles P,p, of the earth, and which have the axis of the earth Pop for a common diameter, are called meridians, because when the centre of the sun is over or upon that one of these circles which passes through any place, it is mid-day or noon at that place. The plane of every meridian cuts the plane of the equator at right angles, so that the equator divides every meridian (as for instance Papc P) into four equal parts; thus Pa and ap, and pc and cP are equal to one another, and are called quadrants or quarters of a circle. Meridians are also called circles of latitude, because upon them the latitudes of places are measured. The Ecliptic found traced upon common globes (although it is properly an imaginary circle in the concave sphere of the heavens representing the apparent path of the sun in the course of a year) is a great circle upon the globe of the earth, the plane of which is inclined at a certain angle to the plane of the equator, and is represented in the figure by the circle Ê×L^. All circles upon the sphere which do not pass through its centre are called small circles; those which are parallel to the equator, as mrns, are called

The earth has a daily motion from west to east, about one of its diameters (called the earth's axis), which causes all the heavenly bodies to appear to move daily round the earth in an opposite direction from east to west. The two extremities of this axis are called the poles of the earth, from a Greek word signifying a pivot; one is called the North pole, being that which is opposite or nearly opposite to the star in the heavens called the pole star; the other extremity of the axis is called the South pole; the north pole is also known by the name of the arctic pole, from a Greek word signifying a bear, the 'great bear' being the name of a constellation or collection of stars in the immediate neighbourhood of the pole star, and commonly known as Charles's wain: the South pole has the corresponding term of the antarctic pole, or the pole opposite to the arctic.

Let PEPQP (fig. 1) be a sphere representing the globe of the earth, O the centre, POp the axis, P the north

circles of longitude or parallels of latitude; and as all meridians cut the equator at right angles, they also cut all circles of longitude at right angles, which is evident from these latter circles being parallel to the equator. Every circle traced upon the earth is supposed to have a corresponding circle traced upon the concave or hollow spherical surface of the heavens. All circles, whether great or small, are divided into 360 equal parts called degrees; every degree is again divided into 60 equal parts called minutes, and every minute into 60 seconds these various parts are distinguished by certain signs, thus 15 degrees is written 15°, 32 minutes is written 32', and 5 seconds 5"; so that 15° 32′ 5", signifies 15 degrees together with 32 minutes and 5 seconds. The magnitude of degrees is of course different in great and small circles; the amount and variation of this difference in the circles of the globe, will be explained afterwards.

The zenith of any place on the earth is that point in the concave surface of the heavens which is immediately opposite to the extremity of a line drawn from that place to the centre of the earth, or in the direction of a plumb line; it is the point in the heavens directly over our heads. The nadir is the corresponding point in the opposite hemisphere of the heavens. Of all the meridian circles, that which passes through the zenith of a place in the heavens, or through the place itself upon the earth, is the meridian of that place. The horizon of a place is the boundary of view at that place: with respect to the earth it is called the visible, sensible, or apparent horizon; with respect to the heavens it is called the rational, true, or astronomical horizon. The visible horizon is most accurately observed upon the sea where it is distinct and unbroken, and is, therefore, sometimes called the horizon of the sea. The extent of the visible horizon may easily be found if the height of the spectator's eye above the surface of the earth be known, and also the length of the earth's radius or semi-diameter. For if (fig. 2.) BEDF be a great circle, C the centre of the earth, A E the height of the eye, E C the semi-diameter of the earth, and A B be drawn from A, just touching the earth's surface at B, E B will be the extent in one direction of the visible horizon. If B and C be joined, BC will be perpendicular to AB. The

Fig. 2.

E

F

length of A E and E C or AC and also of B C, which is the semi-diameter, being known, the angle A C B may be found by a very simple mathematical process; and this angle being measured by the arc EB, the required distance is found. AB, the direct distance of the horizon at B from the spectator's eye at A, may also be found in a somewhat similar manner :—if A E be equal to 5 feet, and E C, the semi-diameter of the earth, be taken at 29,949,655 feet, the angle at C, or the arc BE, will be found to be equal to 2' or 12,188 feet, which is nearly equal to 2 miles and 532 yards; D B is of course equal to twice BE, as the spectator sees as far one way as another, therefore D B is equal to 4 miles 1064 yards. This, however, is not quite true in practice, as by the refracting power of air and vapour, the apparent horizon is a little more extensive. The rational horizon is in every part of it 90°, or a quadrant distant from the zenith. When a heavenly body first appears above the horizon of a place, it is said to rise, and to set when it disappears or sinks below the horizon. When a heavenly body is upon the meridian of any place, it has obtained its greatest height or altitude above the plane of the horizon of that place.

The north point of the horizon is that which is nearest to the north pole of the heavens or the pole star, the point 180° distant from it is the south. The meridian line of a place passes through the north and south points. The east point is 90° distant from the north or south in that portion of the heavens where the sun, stars, &c. appear to rise; the west is 180° distant from the east point. Thus all the cardinal or principal points of the compass are determined.

By means of the observed altitudes of heavenly bodies, when at their highest or on the meridian of a place, many