MATHEMATICAL GEOGRAPHY. CHAPTER I. Universal Geography-Mathematical Spherical figure of the Earth. UNIVERSAL GEOGRAPHY is the science that conveys to us a knowledge of the earth, both as a distinct and independent body in the universe, and as connected with a system of heavenly bodies. The figure, structure and dimensions of the earth, the properties and mutual relations of its parts-the features of its surface-its productions and inhabitants-and the laws which govern, or partially affect it as a heavenly bodyare all included within the comprehensive term of universal geography. This definition, or rather description of the objects of geography, serves as the basis of M. Malte-Brun's elaborate work ;* but it manifestly embraces a great variety of subjects, commonly classed and treated of under distinct heads of natural philosophy. To avoid, therefore, the confusion of ideas which the extensiveness of this definition may give rise to, it will be convenient to reduce its terms within the limits usually assigned to geography. And we are the rather induced to do this, because the interests of science have been promoted in no slight degree, by a judicious and welldefined arrangement of its parts, which at once excludes a great number of fanciful resemblances, and like a division of labour in mechanical employments, renders every branch more easy to be acquired, and more likely to be extended and improved. In its proper and more confined sense, geography comprises a knowledge of the figure and dimensions of the earth, and the situation of places upon it-of the natural and political features and divisions of its surface-and of its various productions and inhabitants. These particulars may be arranged under three heads, namely, mathematical, physical, and general geography. See Malte-Brun's Universal Geography. MATHEMATICAL GEOGRAPHY is that branch of the general science which is derived from the application of matheOf this we shall treat first, because the matical truths to the figure of the earth. other branches of geography owe to it much of their accuracy and perfection. the first subject for inquiry;-for the The figure of the earth is manifestly principles by which we may ascertain the various truths that lie within the altogether different, on the different scope of mathematical geography, are circular plain, a cylinder, or a sphere. suppositions of the earth being a flat A great variety of appearances, both heavens, (which will be described preon the surface of the earth and in the sently) prove conclusively, that the earth is a spherical or round body. The possession of this important truth enables the geographer, by the application of the known mathematical properties of the sphere, to solve many interesting problems, the most useful of which is to determine the relative situation of places upon the earth's surface. For this and is taken to be a perfect sphere; and some other practical purposes, the earth although this supposition be not strictly be adopted without sensible error in the true, it is sufficiently near the truth to investigations into which it is commonly introduced. The nature and quantity of its deviation from a perfectly spherical shape will be for future inquiry. At what particular period of the world the spherical figure of the earth was first discovered, cannot now be ascertained. It is natural to suppose, that the curiosity of mankind would early be directed to the shape of the earth they lived upon. But when first it engaged their attention, it fared with this as with all other parts of what is called natural philosophy. Men were led to entertain trusting too much to single appearances. the most erroneous notions of it, by Deceived by the plain-like appearance of the earth, and disregarding all other B 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 though he was disappointed of the immediate object of his voyage, he became the discoverer of a new world, and eventually established his own opinion of the earth's spherical shape. Magellan was the first navigator who practically demonstrated the roundness of the earth; following up the opinions which Columbus among the moderns had the merit of originating, he sailed upon the project of reaching the Moluccas by a westerly passage; but being killed in the Philippine Islands by the natives, he did not complete the entire voyage round the world. Our own countryman, Sir Francis Drake, was the first person who in one voyage circumnavigated the globe; he accomplished the voyage (undertaken however solely for purposes of plunder, and marked by rapine and bloodshed) in the space of three years; and returned to England in 1560. After these voyages, the spherical figure of the earth was generally admitted by the philosophers of Europe. A spirit of investigation soon after arose, and furnished an abundance of satisfactory proofs, which, though of daily or frequent occurrence, had hitherto been unobserved or unheeded. These proofs consist in certain remarkable appearances, either of objects upon the surface of the earth itself, or of the heavenly bodies. They are of the following description: If a person were situated upon an open and extensive plain, he would find, that as he departed from objects, the view of which was not hindered by any unevenness in the plain, they would gradually disappear from their base upwards; in like manner, the hull of a ship proceeding out to sea becomes invisible first, and afterwards the masts and rigging. The order in which the parts of these objects successively disappear, cannot be explained by the mere supposition that the distance between the object and the spectator gradually increasing, the object becomes first indistinct, and at last invisible; because with respect to bodies whose bulk is the same from the top to the bottom, this reason is applicable to all the parts alike, and would not account for the highest part of them being always the last visible; and with respect to bodies, the bottom part of which is the largest (as in the case of a ship), it would not only be insufficient to explain the fact, but would be directly contrary to experience, by which we are taught, that where distance alone is the cause of a body becoming first indistinct and then invisible, the larger and more bulky parts of it are seen the longest. The only supposition which can account for the order in which the parts of an object disappear is, that the surface of the earth is continually and gradually bending or curving downwards-in other words, that it is a convex surface; and the circumstance that these appearances are the same both in kind and degree all over the earth, and in whatever direction the spectator moves from the object, or the object from the spectator, proves that this convex surface is every where and in all directions precisely or very nearly the same, and, consequently, that the earth is a sphere. The voyages of Magellan and Drake, of Anson, Cook, and Vancouver, all tend to establish the same fact; for by holding a course due west or due east, these navigators have at last arrived at the point of their departure-thus they have sailed upon a line which in one revolution returns into itself, ending where it began; and, therefore, the surface on which it was described must be a sphere, or resembling a sphere: this was further confirmed by the voyages of Captain Cook towards the South pole, from which it appeared that the course round the earth gradually diminished as it approached the pole. The proofs derived from the appearances of heavenly bodies are even more conclusive than the foregoing. By tra velling on the earth's surface from the north towards the south, a certain star in the heavens, called the pole star (which is itself almost stationary,) is observed to change its place in the heavens relatively to the spectator's horizon, and gradually to descend; by a movement of the spectator in the opposite direction (from south to north), the height of the same star above the horizon is observed gradually to increase; and in both cases this apparent change of place in the star is in proportion to the distance travelled over. This change being also observed from whatever place the movement is made (supposing it to be in a direction perpendicular to the equator or on a meridian line), cannot be otherwise accounted for than by the supposition that the earth is a sphere; and that the arc or circular space in the heavens through which the star appears to have moved, corresponds with a similar The supposition that the earth is a 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. |