Étienne, one of the most eminent naturalists of modern times, was a native of Étampes (Seine-et-Oise), where he was born, April 15, 1772. By his genius, energy, and skilful investigations, during a long career as professor of zoology to the faculty of sciences of the Académie de Paris, and at the Jardin du Roi, he contributed more than any other naturalist, except his great contemporary and friend Cuvier, to the progress of the science and philosophy of natural history. Destined by his parents for the clerical profession, he was entered at the college of Navarre, in Paris, in order to study philosophy and the other branches reckoned necessary as preparatory to a theological course. At this time Brisson was professor of experimental philosophy in that college, and gained immense influence over the mind of the young student, who felt instilled into him an enthusiastic love of nature in all its wonderful variety. This inclination greatly strengthened the sympathy between Geoffroy and his teacher. Having completed the term of his literary studies, he left the college of Navarre, and obtained his father's permission to enter the college of Cardinal Lemoine. Notwithstanding the high and honourable position in the church held out to him through powerful patronage, Geoffroy wished to pursue studies more in harmony with his peculiar tastes and sympathies; and while hesitating about which department of natural science he should devote his attention to, he was much assisted in coming to a decision by making the acquaintance of the celebrated Haüy, then one of the professors in the Cardinal's college. Haüy became his warm, steady, and attached friend, and by his example and counsels greatly assisted him in developing the tastes which the lectures of Brisson had aroused. The consequence was, that from this moment Geoffroy enthusiastically devoted himself solely to the study of the natural sciences. In pursuance of his determination, he first, in company with Haüy, took the mineralogical course at the Collège de France. Daubenton, who filled this chair, was not slow to perceive the decided bent and talent of his pupil. At the conclusion of his lectures, being in the habit of entering into conversation with his pupils, for the purpose of affording explanations to his auditors on points which might to them seem obscure, Daubenton was struck with the depth of the remarks and questions elicited from the young Geoffroy on such occasions; and even then he predicted the distinguished rank which his pupil would one day occupy in the scientific world.

The labours of Geoffroy and his friend Haüy, however, were interrupted by the revolution of 1789. During the massacre of September 1792, Geoffroy, at the risk of his own life, was the means of saving several priests; and among them Haüy, who had been imprisoned for recusancy. This act of devotion so endeared him to his teachers, especially to Daubenton, that through his instrumentality he was ap- Geoffroy pointed, in 1793, to an office in the Jardin des Plantes, where he founded the vast zoological collections which form one of the true glories of Paris. By the law of June 10, 1793, the Jardin du Roi was constituted a school for advanced instruction in all branches of natural history, conducted by twelve eminent professors, each distinguished in his own branch. Scarcely entered on his twenty-fourth year, and very recently having applied himself to the study of mineralogy, Geoffroy was judicially selected by Daubenton for the chair of zoology (section, vertebrate animals), an appointment which he more recently shared with Lacépéde.

Having thus become the colleague of Daubenton, Fourcroy, Jussieu, Lacépéde, Lamarck, Vanquelin, and Latreille, Geoffroy devoted himself with enthusiastic energy to the study of zoology exclusively. For the purpose of extending the sphere of this science, he earnestly and cordially encouraged the efforts of all those who attempted to assist in its progress; and to this zeal it is that Europe owes one of the men who have rendered her pre-eminently illustrious in the science of natural history—the celebrated Cuvier. During the years 1795 and 1796, Geoffroy and Cuvier resided together, sharing with each other everything that could strengthen the already strong natural sympathy of their natures. Soon after this Cuvier was appointed joint professor of comparative anatomy with his bosom friend—an honour which justified the presage that called him to Paris, "pour remplir le rôle d'un nouveau Linné."

In 1798, Geoffroy was selected as one of the great scientific expedition to Egypt; and in the execution of his functions he displayed great firmness in preserving to his beloved Paris immense treasures of precious materials collected and prepared with infinite pains during that memorable expedition in behalf of science and art. After the capitulation of Alexandria, these treasures were only saved by Geoffroy threatening to destroy them when the English general wished to retain them: "We ourselves shall burn our treasures," said he, "and history will not fail to record that you have burned another library in Alexandria." From Egypt Geoffroy transferred to Paris a curious and most interesting collection of ancient animals; and he inserted in the great work upon Egypt learned observations on the natural history, as well as on the civil history and theology of that interesting and inexhaustible country. On his return to France he continued his course of lectures on natural history. He was one of the first men of science and literature on whom Napoleon bestowed the cross of honour, and in 1807 he became a member of the institute, and soon afterwards associate of the Académie de Médecine, as well as of most of the scientific institutions of Europe; then professor of zoology to the faculty of sciences (1809), still holding at the museum the chair created in 1793.

In 1810 a mission into Portugal for the re-organization of public instruction held out to his courage, his love of science, and his benevolence, a new occasion of manifesting themselves in all their comprehensiveness. Once more, we are told, did the English wish to despoil him of his rich choice collections; but these were saved to him by the intervention of the conservators of Ajuda, who attested to the English commissaries that these collections had been granted to the French naturalist in exchange for minerals brought from Paris, and that the classification of the Cabinet of Ajuda was the fruit of this philosopher's labour. This declaration, with the sacrifice which Geoffroy made of several cases containing his own property abandoned to the exigencies of the people, allowed him to enrich the museum of Paris with a complete collection of the productions of Brazil.

The works of Geoffroy Saint-Hilaire do not constitute a regular system; they are composed of detached Mémoirs in which are contained some new and bold ideas of which no one disputes the originality and depth, though in their application they often lose much of their justness and value. The limits of a brief notice permit only a very brief analysis of the systems he developed in order to arrive at the solution of philosophical and physiological questions of the highest interest.

In psychology, Geoffrey Saint-Hilaire enunciated some negative ideas only. The soul, which he calls a psychological element, is not an entity any more than a metaphysical abstraction, according to his theory. This being, composed at once of a spiritual and a material principle (spiritus corporeus) cannot represent the intelligent, since no part of matter can belong to intellectual functions. In this manner he tells us what the soul is not; but what it is he nowhere informs us, nor does he even attempt a solution of the question so often earnestly asked—What is the soul?

In his physiological views, however, Geoffroy is explicit and positive. In formal and direct opposition to the philosophy of final causes, he has exerted all his efforts to demonstrate that it was not with any view to their results that the organs of animated beings have been created. This miserable and arid system, which would prohibit us from contemplating with gratitude the boundless intelligence of the Author of nature, has been too successfully refuted ever to be mooted again with the faintest hope of success.

It was imputed to Geoffroy that his doctrine necessarily led to atheism; because if all the existing species of organic beings could have descended from one antediluvian species, the intervention of creative power was useless; and that if both unorganized matter and organic matter are eternal, the intervention of a creator was impossible. This imputation Geoffroy indignantly scouted and disavowed as necessarily arising out of his doctrines. In his Notions de Philosophie Naturelle (1838), he complains that he has been misunderstood; that his doctrine does not suppose the existence of such an antediluvian species; and that by the term "Typal Unity," he means unity of organic composition, which means quite a different thing.

The most important of the published works of Geoffroy Saint-Hilaire are:—Philosophie Anatomique, 1823; Système dentaire des Mammifères et des oiseaux, 1824; Histoire Naturelle des Mammifères, in concert with Cuvier, 1819, second edition, 1828, et seq., 4 vols. 4to; Cours d'Histoire Naturelle des Mammifères, 1828; Des Considérations sur les Singes qui se rapprochent le plus de l'Espèce Humaine, 1836; Notions de Philosophie Naturelle, and some biographical fragments, 1838. Besides all these, there are numerous contributions by him in several literary journals; and he was one of the collaborators of the Dictionnaire des Sciences Naturelles and of the Dictionnaire Classique d'Histoire Naturelle, in which he was chiefly aided by his son, Isidore Geoffroy Saint-Hilaire, M.D., and Member of the Académie des Sciences.

Geoffroy Saint-Hilaire died June 19, 1844; and his Life, Works, and Theories, have since been published by his son. The title is: Vie, Travaux, et Doctrine Scientifique D'Étienne Geoffroy Saint-Hilaire; par son fils, M. Isidore Geoffroy Saint-Hilaire, Paris, 1847. The term Geography, derived from two Greek words, γῆ, the earth, and γράφειν, I write, signifies a description of the earth. The description to which this title is applied may be more or less general; either embracing such truths only as belong to the earth considered as one whole, or extending to particulars which belong to and distinguish the several countries spread over its surface. In whichever of these two aspects the subject be regarded, a vast field opens to the view of the observer. In order to give a full and accurate description of the earth, it would be requisite to consider it in reference to its motion, figure, and magnitude; in reference to its relation to the other bodies of the universe, and more especially to the planetary system of which it forms a part; in reference to its surface, as diversified by land and sea, mountains and valleys, lakes and rivers; in reference to the materials which compose its crust, and to its internal structure; in reference to the constitution of the atmosphere with which it is surrounded, and the effects arising from the variations in atmospheric pressure, temperature, and humidity. Nor would it be enough to consider the earth only as a mass of inert and unorganized matter; it would be necessary to regard it in its relations to vegetable and animal life; and to trace the phenomena which these, in their endless variety, present in its various divisions and provinces. It would still further be necessary to view it as the abode of man himself, and as modified by his existence; divided into states and kingdoms; adorned with cities, and all the noble monuments of civilized life.

Such is an outline of the picture which geography, in the most unlimited meaning of the term, should exhibit of the globe. To fill up this picture in all its parts, it would evidently be necessary to call in the aid of the whole circle of the sciences. But the description is usually of a less extended character, being confined chiefly to the more obvious and striking features of the various regions and countries of the earth.

In the wide range which the subject presents, several divisions and subdivisions are suggested by the different views in which the earth may be considered. The three following divisions are the most important:

1. Mathematical Geography, which illustrates, on astronomical principles, the figure, magnitude, and motion of the earth; teaches how to determine the positions of places on its surface; explains the construction of globes, with their application to the solution of problems; and shows how the whole or any portion of the earth's surface may, on the principles of projection, be delineated on a map or chart.

2. Physical Geography, which treats of the mutual relations of the diversified objects found on the surface of the earth, including the atmosphere by which it is surrounded; and explains the causes, whether of a chemical or mechanical description, that produce the modifications and changes which are continually taking place in them.

3. Political or Historical Geography, which describes the earth as divided into countries, occupied by various nations, and improved by human art and industry. It traces the circumstances and character of the different races and tribes of mankind, explaining their social institutions, and ascertaining the place which each occupies in the scale of civilization.

From this general arrangement of the subject, it is evident that geography depends for its rank as a science on its intimate connection with various branches of knowledge, which, taking their rise from investigations instituted in reference to the nature and mutual relations of the objects on the earth, or connected with it, furnish those accurate views which must be obtained before anything like a precise description can be given of the globe we inhabit, or of any portion of it. With regard to what belongs to Physical Geography, we must refer the reader to the articles Physical Geography, Mineralogy, Meteorology, &c. in this work. What belongs to Political or Historical Geography will be found under the names of the respective countries. The following article will be limited to a view of the progress of Geographical Discovery, and to a brief explanation of the principles of Mathematical Geography.

L—VIEW OF THE PROGRESS OF GEOGRAPHICAL DISCOVERY.

There are many circumstances in the condition of man which connect him so closely with the globe which he inhabits, as to render absolutely necessary to his existence a knowledge of at least the neighbourhood of the spot where his lot is cast. It is from the earth that he must derive the means of subsistence and accommodation, the materials on which his industry is to be exerted, and those objects in the exchange of which commerce consists. In every stage of his progress, therefore, from barbarism to civilization, he must employ some attention and observation, in order to discover in what respects the objects with which he is surrounded are qualified to contribute to the supply of his wants, and to his comfort and convenience. Even while he roams the forest in the savage state, he must make himself acquainted with many circumstances, a knowledge of which is necessary either to give him success in the chase, or to direct him in retracing his steps to the place where he has fixed his dwelling. But it is not until men have united in society, and that neighbouring communities have begun to hold mutual intercourse, that those feelings and passions are effectually aroused which stimulate to the arduous pursuits of geographical discovery. Commerce and war, with the spirit of adventure which usually accompany them, have without doubt been among the first causes of geographical research. In the train of these have followed the workings of avarice and the aims of ambition. As the human mind has advanced in its career of improvement, curiosity, with an enlargement of views and desires, have been called into action; and voyages have been undertaken for the express purpose of discovering new countries and exploring unknown seas.

In tracing the effects which these causes have produced in the gradual increase of geographical knowledge, it will contribute to distinctness to keep in view a threefold division, which the subject naturally assumes, namely, ancient geography, extending from the earliest period of history down to the time when, the Roman empire having been overrun by barbarous nations from several quarters, Europe was overwhelmed in the darkness which preceded the revival of learning; the geography of the middle ages, extending from the revival of letters to the fifteenth century, when the discoveries of the Portuguese began to lay a History. wider foundation for the science; and modern geography, which embraces the most recent discoveries, and is progressively improving by the accessions which it is receiving from the labours and science of modern travellers and navigators.

The Phoenicians are the earliest commercial people of whose discoveries we have any correct accounts. This people seem first to have explored the coasts of the Mediterranean. Their navigators at length extending their voyages through the Straits of Gades, now called the Straits of Gibraltar, entered the Atlantic Ocean, and visited the western coasts of Spain and Africa. In many places to which they resorted they planted colonies; and sought, by instructing the inhabitants, in some measure, in their arts and improvements, to open a wider sphere for their commerce. The learned Bochart, led by the analogy between the Phoenician tongue and the oriental languages, has endeavoured to follow the tracks of the Phoenicians, both along the shores of the Mediterranean and those of the Atlantic. These analogies are not always sure guides; but there seems no reason to doubt that Cadiz was originally a Phoenician colony, and it is not likely that this was the only one formed by that enterprising people.

The Arabian Gulf, or Red Sea, offered to the Phoenicians another field of naval and commercial exertion, to the improvement of which the distance of Tyre, the emporium of their trade, was the only obstacle. This induced them to make themselves masters of Rhinocorura or Rhinocolura, the port in the Mediterranean nearest to the Red Sea. Commodities purchased in Arabia, Ethiopia, and India were landed at Elah, the safest harbour in the Red Sea towards the north; thence they were conveyed over land to Rhinocolura; and being there reshipped, they were carried to Tyre, whence they were distributed over the world.

The wealth and power which accrued to the Phoenicians from their being in the sole possession of the lucrative trade of the East, incited the Jews, their neighbours, under the prosperous reigns of David and Solomon, to desire a participation in its advantages. Their conquest of Idumea, which stretches along the Red Sea, put it in the power of Solomon to fit out a fleet; while his alliance with Hiram, king of Tyre, enabled him to command the skill of the Phoenicians for the conducting of the voyage. Passing through the Straits of Babelmandel, they carried on commerce in the Indian Ocean; and so distant were the countries to which they traded, that the voyage occupied no less than three years. But though the Jews thus for a time engaged in the pursuits of trade, yet the tendency of their institutions, which were expressly designed to preserve them a separate people, was unfavourable to the development of the commercial spirit which their monarchs wished to foster among them. This joined with the division of the kingdom on the death of Solomon, proved fatal to their rising greatness as a commercial people, and excluded them from ranking among the nations who have contributed to the advancement of geographical knowledge.

It is perhaps impossible to fix with certainty the limits which bounded the geographical researches of the Phoenicians, on account of the difficulty there is of assigning the precise places marked out by the names then given to the countries to which they traded. The length of time occupied in the voyage, and the nature of the cargoes brought home, with a few other circumstances of the same vague kind, are the only particulars afforded to direct us in the determination. Thus the country of Ophir, to which the Phoenicians navigated the ships of Solomon, must be ascertained by the facts that the voyage thither and homeward occupied three years, and that the cargo consisted of "gold and silver, ivory, and apes, and peacocks." Among the various opinions which have been entertained respecting the position of this distant country, the most probable appears to be that it was situated on the eastern coast of Africa, as far south as Sofala. To this quarter every indication seems clearly to point; and whatever objections may appear to stand in the way, in consideration of the remoteness of the region, and the difficulties to be encountered, these admit of being answered by a reference to the length of time required for the voyage, and to the wealth, naval skill, and ample resources, at the command of the monarchs engaged in the traffic.

The Carthaginians, a Phoenician colony, retained in full vigour the commercial spirit of the parent state. They did not, however, attempt to divide with Tyre the wealth and power which she derived from the monopoly of the trade carried on in the Arabian Gulf. They directed their efforts to the opposite quarter, and sailing through the Straits of Gades, pushed their researches far beyond the bounds which had been reached by the mother country in this part of the globe. They visited not only all the coast of Spain, but likewise that of Gaul, and penetrated at length as far as the south-western coast of Britain, where they obtained tin from the mines of Cornwall or in traffic with the natives. Nor was it only towards the northward that they directed their efforts; they explored also the regions southward of the straits, and sailing along the western coast of Africa almost as far as the northern tropic, they planted colonies, as the Phoenicians of Tyre had formerly done, with a view to prepare the natives for carrying on commercial intercourse. The Atlantic Ocean was destined to conceal for ages from the inhabitants of the old world the immense regions which lie beyond it. But the Carthaginians extended the boundary of navigation westward by the discovery of the Fortunate Islands, now known by the name of the Canaries.

The enlargement of views gradually generated by this spirit of commercial enterprise led at length to voyages of which discovery was the special object. The circumnavigation of Africa was one of the earliest attempts of this

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1 The regions always spoken of in Scripture as the most remote with which the Hebrews and Phoenicians were acquainted are, Tarshish, Ophir, the Isles, Sheba, and Dedan, the River, Gog, Magog, and the North. Without entering into any discussion, we may give what appear to be the most probable conclusions with regard to the positions of the countries to which these names were applied. Tarshish is a country from which two voyages are spoken of in Scripture as being made; one by the Mediterranean, bringing iron, silver, lead, and tin, the produce of Spain and Britain; the other by the Red Sea, bringing gold, ivory, and other productions of tropical Africa. These two voyages, though at first sight they appear incongruous if supposed to be made to the same country, may be reconciled by supposing that Tarshish is fundamentally Carthage, which monopolized almost entirely the commerce of Spain and Britain, and was the medium through which the commodities of the west were distributed; and that the name of this great African metropolis was extended to the whole of the continent of Africa. The Isles are the whole southern coasts of Europe, consisting either of real islands or peninsular tracts. Sheba is the southern portion of that part of the coast of Arabia which borders on the Red Sea; while Dedan lies further to the southward, on the borders on the Persian Gulf. These countries rose to commercial importance in consequence of the valuable commodities which were imported into the former from the African coast, and into the latter from India. Thence arose the traffic carried on by "the companies of Sheba," or caravans, and by "the travelling companies of Dedanim." The River was the name always applied to the Euphrates. Gog, Magog, and the North, appear to be the high table-land in the interior and north of Asia Minor, Phrygia, Galatia, Cappadocia, and Paphlagonia, regions in which may be recognised the peculiarly rude and formidable aspect which belonged to the countries to which in ancient times the names in question were applied. (See Encyclopaedia of Geography, by H. Murray, Esq.) History, kind made by the ancients. The direction which the coast takes beyond the Mediterranean on the one hand, and the Red Sea on the other, suggested the idea of a peninsula which it might be possible to sail round. This voyage was first undertaken by the Egyptians; a people exceedingly averse to engage in naval affairs, but who at this time were ruled over by Necho, a monarch whose active spirit prompted him to engage some Phoenicians to descend the Arabian Gulf, and, coasting along Africa, to endeavour to return by the Straits of Gades. Herodotus narrates in a few words the result of this enterprise, which was undertaken about six hundred and four years before the Christian era. He says, "the Phoenicians, setting sail from the Red Sea, made their way into the southern sea; and when autumn approached they drew their vessels to land, sowed a crop, and waited till it was grown; when they reaped it, and again put to sea. Having spent two years in this manner, in the third year they reached the pillars of Hercules, and returned to Egypt, reporting what does not find belief with me, but may perhaps with some other person; for they said that in passing Africa they had the sun on their right hand. In this manner Lybia was first known."

This passage has given rise to much controversy among the learned. But the voyage here so briefly described does not seem to involve any impossibility, notwithstanding the then infant state of navigation; and the circumstance which the historian objects to as incredible is the very point which, from its coincidence with what we know should have happened, renders the story more worthy of belief.

Xerxes king of Persia, according to Herodotus, gave a similar commission, about four hundred and eighty years before the Christian era, to one of his satraps, named Sataspes, who, for a heinous offence, had been condemned to die. If successful in the accomplishment of this voyage, Sataspes was to escape a cruel death; but the difficulties were too great to be surmounted by a navigator brought up amidst the luxury and indulgence of the Persian court. Having procured from Egypt a vessel and crew, he passed through the Straits of Gades, entered the Atlantic Ocean, and, bending his course towards the south, coasted the continent of Africa, until, after several months, he probably reached the coast of Sahara. The frightful and desolate shores along which he sailed, and the tempestuous ocean which beat against them, combined to fill his mind with alarm, and to shake his resolution. He retraced his course to the straits; and hoping perhaps that the labours he had undergone in the partial accomplishment of the task imposed on him would be accepted by his royal master as a sufficient atonement for his offence, or that the offence itself might in a great measure be forgotten, he returned home and presented himself before Xerxes. The cause which he assigned for the failure of the ultimate object of his mission was, that he had encountered a sea so full of herbage that his passage was completely obstructed. This reason (the grounds of which have never been satisfactorily explained, though it has been alleged that obstacles of this description occur in that part of the sea which lies between the Cape Verde Islands, the Canaries, and the coast of Africa) appeared so ridiculous to Xerxes, that he ordered the sentence of death by crucifixion, which had been pronounced upon Sataspes, to be immediately executed.

But the most celebrated voyage of antiquity undertaken for the purpose of discovery was the expedition under Hanno, fitted out by the authority of the senate of Carthage, and at the public expense, and that with the view of attempting a complete survey of the western coast of Africa. Of all the voyages performed by the Phoenicians and Carthaginians, this is the only one of which we have an authentic narrative. Mercantile jealousy prevented these two great commercial states from communicating to other nations the knowledge which they acquired of the remote regions of the earth; and from this cause, when the maritime power of the former was annihilated by Alexander's conquest of Tyre, and the empire of the latter was overthrown by the Roman arms, all monuments of their great skill in naval affairs appear in a great measure to have perished. Even the account of the voyage of Hanno (Periplus Hannonis) has been considered by its learned editor Mr Dodwell as a spurious work. But the arguments of M. de Montesquieu and of M. de Bougainville appear fully to establish its authenticity, which the learned world now generally admits.

Hanno set sail with a fleet of sixty vessels, so constructed that, according to the mode of ancient navigation, he could keep close in with the coast. We are told that, in twelve days after leaving the Straits of Gades, he reached the island of Cerne; that proceeding thence, and following the direction of the coast, he arrived, in seventeen days, at a bay, which he called The West Horn. From this he advanced to another bay, which he named The South Horn. The objects which are described as having been seen by Hanno in his progress belong to tropical Africa. But in attempting to ascertain the places which he visited, or the utmost distance which he sailed southward, much difficulty and uncertainty are experienced. Bougainville supposes Hanno to have reached the Gulf of Benin, and contends that this limit, distant as it is, cannot be regarded as beyond what may be conceived to have been accomplished by the most skilful navigator of antiquity. Major Rennell shortens the distance considerably by conceiving the voyage to have been extended no further southward than Sherbro Sound, a little beyond Sierra Leone. He thus obtains the advantage of avoiding a difficulty involved in the hypothesis of M. de Bougainville; namely, the supposition of ancient ships having sailed upwards of seventy geographical miles in a day. At the same time, the arguments which support the one hypothesis are equally applicable to the other.

According to the views of M. Gosselin, however, the voyage must be confined to much narrower limits southward than even those assigned by Major Rennell. He supposes it to have terminated about the river Nun; an opinion which he supports by alleging that, in such a voyage, the progress must necessarily have been slow. The Carthaginian navigator had to encounter all the obstacles and dangers incident to a course held along a shore, and in a sea, which were equally unknown. He must have found himself impeded by the requisite examination of every part of the coast, as well as by the many precautions which the safety of the fleet under his command must have rendered constantly necessary. With regard to the circumstances given in the narrative which appear to point to tropical Africa, M. Gosselin supposes that the same aspect of life and nature may, at that distant period, have belonged to Morocco, then thinly peopled by the rude native tribes, which is now specially characteristic of more southern regions.

Amidst such diversity of opinion among the learned, it is not easy to decide in reference to a subject beset with so many difficulties. If we assume either of the more remote distances assigned for the termination of the voyage, Cerne must be identified with the isle of Arguin; and, on Major Rennell's hypothesis, the Gulfs of Bissago and Sherbro present those numerous islands described by Hanno, to which there are no islands corresponding on any other part of the coast. On the whole, however, the most limited distance seems preferable, if we admit that part of M. Gosselin's hypothesis which assigns to Morocco features of man and of nature that are usually held to be characteristic of tropical Africa.

The circumnavigation of Africa was an enterprise which in ancient times not only called forth the naval efforts of the most powerful maritime states, but which also awaken- History, ed the ambition of private adventurers. Eudoxus, a native of Cyzicus, being sent on a mission to Alexandria, at that time the seat of naval enterprise and geographical knowledge, his ardent mind, naturally biased to these pursuits, was aroused to action by the spirit which prevailed in that city. He began his career under the auspices of Ptolemy Euergetes, the reigning Egyptian monarch, who fitted out a fleet, and placed it under his command. According to the destination assigned him, Eudoxus descended the Arabian Gulf, and proceeded probably as far as the southern shore of Arabia. Thence he appears to have returned, after a prosperous voyage, with a valuable cargo of aromatics and precious stones. But of this wealth he appears to have been deprived by Euergetes. After the death of this monarch, which in a short time took place, his widow Cleopatra sent Eudoxus on another voyage, in the course of which he was driven by unfavourable winds on the coast of Ethiopia, where he was kindly received by the inhabitants, and carried on with them an advantageous traffic. After other vicissitudes of fortune, he was induced by circumstances which occurred in his adventurous life to leave the court of Egypt, and repair to the commercial city of Cadiz, in Spain, and there to fit out an expedition for the purpose of African discovery. At Massilia (Marseilles), and other maritime places through which he passed on his way to Cadiz, he took care to make known his views and hopes of success, and to invite all who were actuated by any spirit of enterprise to accompany him. He succeeded in fitting out a ship and two large boats; on board of which he carried not only goods and provisions, but artisans, medical men, and even players on musical instruments. This was no doubt proceeding on a magnificent scale. But his crew was ill calculated to second his bold undertaking. To avoid the danger of stranding, Eudoxus was anxious to keep the open sea. His companions, however, alarmed at the swell, forced him to adopt the usual mode then followed of sailing along the shore; a measure which led to the disaster which he had anticipated. With one vessel of a lighter construction, on board of which was put the more valuable part of the cargo, Eudoxus pursued his voyage until he reached a part of the coast inhabited by a race of people that appeared to him to speak the same language with those whom he had found on the opposite side of the continent. Judging from this circumstance that he had ascertained the main object of his voyage, he returned and endeavoured to obtain the assistance of Bocchus, king of Mauritania. Suspecting, however, treachery on the part of that monarch, he again had recourse to Spain. Here he was again successful in equipping another expedition, consisting of one large vessel fitted for the open sea, and another of smaller size for the examination of the coast. This was a judicious preparation for the accomplishment of the object in view; but with regard to the issue of the voyage no accounts of any authority have been preserved.

Such are the leading circumstances connected with the voyages of Eudoxus, which are narrated by Strabo; and, notwithstanding the scepticism and severe criticisms of that geographer, there is really nothing to which the candid reader can reasonably refuse his belief. Prejudices, founded, for the most part, on his own want of information, led Strabo to treat likewise as fabulous the relation of the only ancient voyage having Europe, and more particularly the British isles, for its object, of which we have any detailed account.

Pythias, a Massilian navigator, undertook an expedition about three hundred and twenty years before the Christian era. He steered northward; and after examining the coasts of Spain and Gaul, he sailed round the island of Albion; and, stretching still farther to the north, he discovered an island, the Ultima Thule of the ancients. What island this was the learned are not agreed. It has been supposed to be the modern Iceland; but this implies too great History, an extent of open sea for an ancient navigator to traverse; besides, six days, the period during which he is said to have navigated to the northward of Albion before he made his discovery, are too short a time to admit of his reaching Iceland. Others, amongst whom is Malte-Brun, have considered Jutland as Ultima Thule. But it should be kept in view that Pythias uniformly regarded Thule as British, a character which he could scarcely conceive to belong to Jutland, seeing he could have reached that peninsula only by a long course along the coasts of Germany, which must have impressed on his mind the idea that he had left far behind him every thing belonging to Britain. On the whole, Shetland seems best entitled to be considered as the ancient Thule, and suits well with the appellation which Pythias gives it, when he expressly calls it the "furthest of the Britains."

Strabo endeavours to throw discredit on the statements of Pythias, by starting objections long known to be of the most groundless description; and it is an advantage which the traveller and navigator possess who describe faithfully the grand features of nature, that, however prejudice may dim their reputation for a time, yet will their accuracy as well as veracity at length, in the progress of knowledge, appear, and secure for them the respect and applause of mankind. At the same time, it must be admitted that, in describing what he saw beyond his Ultima Thule, the statement given by Pythias, as reported by Strabo, assumes a somewhat fabulous character. He asserted, it seems, that beyond Thule there commenced what was neither earth, sea, nor air, but a confused blending of all the three. But even here some allowance is to be made for the workings of imagination under very peculiar circumstances, and a readiness, not unnatural, to believe reports which represented him to have reached the extremity of the habitable globe. If his language is not too literally interpreted, it will be found to convey a strongly figurative, but not altogether imperfect, description of the state of the sea and sky in these climes, which have been so little favoured by nature.

The conquests of Alexander the Great, by making known the East, enlarged the bounds of geographical knowledge. Though the course of his expedition was for the most part by land, his mind was equally intent on commerce and maritime discovery. Checked as he had so long been in the career of his victories by the opposition and efforts of the republic of Tyre, he had an opportunity afforded him of observing the vast resources of a maritime power, and at the same time of forming a judgment respecting the immense wealth to be derived from commerce, especially from that carried on with India, which he found to be wholly in the hands of the Tyrians. With a view to secure this commerce, as soon as he had completed the conquest of Egypt, he founded the city of Alexandria, and thus established for it a station preferable in many respects to Tyre. After his final victory over the Persians, his march in pursuit of Bessus, who had carried off Darius into Bactria, often led him near to India, and among people accustomed to much intercourse with it, from whom he learned many things concerning the state of the country, that served so to confirm and inflame a desire which he had long cherished of extending his dominion over those regions, that he was induced to conduct his army from Bactria, for the purpose of invasion, across that ridge of mountains which form the northern barrier of India. After passing the Indus, Alexander directed his march to the Ganges, which, from the accounts he heard of it, and of the countries through which it flows, he was eager to reach. The route which he found it necessary to follow, in consequence of being successively engaged in hostilities with various native princes, led him through one of the richest and best peopled countries in India, now called Punjab. In his ultimate object, however, he failed. His march being performed during the rainy season, his troops had already suffered so much, that notwithstanding the high degree in which he possessed all those qualities that secure an ascendancy over the minds of soldiers, he was unable to persuade them to advance beyond the banks of the Hyphasis, the modern Bejah, which was accordingly the utmost limit of Alexander's progress in India.

By this expedition, Alexander first opened the knowledge of India to the people of Europe; and as he was accompanied, wherever he went, by skilful surveyors, Diogenes and Baeton, who measured the length and determined the direction of every route taken by the army, he furnished a survey of an extensive district of it, more accurate than could have been expected from the short time he remained in that country. The memoirs drawn up by his officers likewise afforded to Europeans their first authentic information respecting the climate, the soil, the productions, and the inhabitants of India.

Though Alexander did not penetrate to the Ganges, his expedition prepared the way to the knowledge of that magnificent stream. For soon after, Seleucus, one of his successors, sent Megasthenes as his ambassador to Paliobothra, the capital of a powerful nation on the banks of the Ganges. The site of Paliobothra was probably the same as that of the modern city of Allahabad, at the junction of the river Jumna with the Ganges. This embassy brought new and opulent provinces of India into view, an acquaintance with which served to raise still higher the idea generally entertained of the value and importance of the country.

The island Taprobane, so celebrated among the ancients, which appears, notwithstanding some great mistakes with respect both to extent and position, to be the modern Ceylon, seems not to have been known in Europe even by name before the age of Alexander. In consequence, however, of the enlightened and active curiosity with which he explored every country which he subdued or visited, some knowledge of it was at length obtained; and, after his time, it is mentioned by almost every ancient geographer.

Whilst Alexander was attempting to penetrate into India, a numerous fleet was assembled by officers whom he had left on the banks of the Hydaspes, the modern Behat or Chelum, with orders to build and collect as many ships as they could. The destination of this fleet was to sail down the Indus to the ocean, and from its mouth to proceed to the Persian Gulf; with a view of opening a communication between India and the centre of his dominions.

When Alexander reached the banks of the Hydaspes on his return, he committed the conduct of this expedition to Nearchus. The voyage down the Indus derived splendour from the greatness and magnificence of the armament, which consisted of an army of a hundred and twenty thousand men, and two hundred elephants, and of a fleet of nearly two thousand vessels. Alexander himself accompanied Nearchus in his navigation down the river, with one third of the troops on board; whilst the remainder, in two divisions, one on the right and the other on the left of the river, accompanied them in their progress. Having reached the ocean after the lapse of nine months, Alexander left Nearchus and his crew to pursue their voyage, and conducted his army back by land to Persia. A coasting voyage of seven months brought Nearchus, with the fleet, in safety, up the Persian Gulf into the Euphrates. It was at the mouth of the Indus that the Greeks witnessed for the first time, and that with astonishment and terror, the ebb and flow of the sea; a phenomenon scarcely perceptible in the Mediterranean, to which their navigation had formerly been confined. In the progress of the voyage they were also struck with surprise on observing phenomena belonging to the midsummer of the tropics. At noon objects were observed to project no shadows, or to project small shadows declining to the south. Their attention was still further attracted by the new appearance of the sky. Stars which they had been accustomed to see high in the heavens were now seen near the horizon. Some stars to the north disappeared, while other stars formerly invisible were seen in the south.

The opening of a communication between the Red Sea and the Persian Gulf was with Alexander another great object of ambition. But though with this view he seems to have sent expeditions down both seas, he failed in his attempts to accomplish this project.

Among the Romans, navigation and commerce, the handmaids of geographical science, were never made objects of pursuit, except in so far as they were found to be necessary to forward their schemes of universal dominion. Their conquests opened indeed the west, as those of Alexander had made known the east; and it might be truly said of that great people, that as they were the conquerors, so they were the surveyors of the world. Every new war produced a new survey and itinerary of the countries which were the scenes of action; so that the materials of geography were accumulated by every additional conquest. Some fragments of the itineraries thus composed still remain. The most memorable is that which bears the name of Antoninus, and which may be described as a mere skeleton road-book, exhibiting nothing more than the names of places, and their distances from each other. The Jerusalem Itinerary, which details minutely the route from Bordeaux to that holy city, is of the same description.

A more remarkable monument, however, is the Peutingerian Table, which forms a map of the world, constructed on the most singular principles. The map is twenty feet long and only one foot broad, so that we can easily conceive how incorrectly the proportion of the different parts is exhibited. Along the high road which traverses the Roman empire in the general direction of east and west, objects are minutely and accurately represented; but of those objects which lie to the north and south of it, only some general notion is conveyed. The Peutingerian Table serves as a specimen of what were called Itineraria Picta, the "painted roads" of the ancients, intended for the clearer direction of the march of their armies.

While the Romans by their surveys contributed much to increase the mass of materials out of which the structure of geographical science was to be reared, they never attempted themselves to combine these materials into one harmonious system. They imbibed in no degree the commercial spirit of the great maritime states of the ancient world, Carthage, Greece, and Egypt, which their valour and discipline obliged to submit to their dominion. But whilst the trade of the conquered countries continued to be carried on through nearly the former channels after they were reduced to the form of Roman provinces, the wealth accumulated in the capital of the world gave rise to a demand for luxuries of every description. This, combined with the comparative peace and security which for a long time prevailed after the complete establishment of the Roman dominion, gave new vigour to commercial enterprise. Alexandria continued the great centre of naval affairs. Obstacles which in the time of Alexander were deemed insurmountable, were completely overcome. Trade with India through Egypt acquired new energy, and was carried on to a greater extent. Continued intercourse with the shores of India at length made known to navigators the periodical winds which prevail in the Indian Ocean; and taking advantage of these, pilots were emboldened to abandon the slow and dangerous course along the coasts, and to make the open sea their high- Their course was from Ocelis, at the mouth of the Arabian Gulf, to Nelkunda (Nelisaram), on the western shores of the Indian continent (the coast of Malabar), which seems to have been the utmost limit of the ancient navigation in that quarter of the globe. The extensive regions which stretch beyond this to the east were very imperfectly known by the reports obtained from a few adventurers who visited them by land.

If we now bring into one view the amount of information possessed by the ancients respecting the habitable globe, we shall find that it was extremely limited. It was at those places on the earth where the human mind displayed greatest activity and enterprise that this knowledge was naturally accumulated. Proceeding from these stations, the boundary which separated the known from the unknown part of the world was gradually enlarged; but the regions comprehended within it constituted still but a small portion of the whole. In Europe the extensive provinces in the eastern part of Germany were but little known, while the whole of that vast territory which now forms the countries of Denmark, Sweden, Prussia, Poland, and Russia, was buried in the deepest obscurity. The inhospitable and dreary climes within the arctic circle were yet unexplored. In Africa little was known beyond the countries stretching along the Mediterranean Sea, and those bordering on the western shore of the Arabian Gulf. In Asia the rich and fertile countries beyond the Ganges, whence the commerce of modern times has drawn the most valuable commodities for the comfort and embellishment of civilized society, were known, if known at all, only by the most vague and uncertain reports. The immense regions on the north occupied by the wandering tribes called in ancient times by the general names of Sarmatians or Scythians, and which are now inhabited by various tribes of Tartars, and by the Asiatic subjects of Russia, seem never to have been penetrated. Add to this, that the fertile and populous regions within the torrid zone were imagined to be uninhabitable; and we have ample proof that the geography of the ancients was very imperfect.

Having thus far given a succinct view of the progressive steps by which the earth's surface, considered merely as tracts of territory inhabited by men, gradually became known, it will be proper next to trace briefly the advances made towards arranging into a systematic form the materials accumulated. Science required that the relative positions of places, with their distances from each other, should be ascertained in such a manner as to furnish fixed principles on which the whole, or any portion, of the surface of the earth might be represented or delineated with due regard to its figure and dimensions.

The first rude attempt made by the early geographers to determine the position of places appears to have depended on the division of the earth into climates, distinguished by the species of animals and plants produced in each. Thus the appearance of the negro, the rhinoceros, and the elephant, suggested to them the line of division where the torrid zone began towards the north, and ended towards the south. But instead of this very vague method, another was soon adopted, which consisted in observing at places the length of the longest and shortest day. This was determined with some accuracy by means of a gnomon, a method of observation much used by the ancients. An upright pillar of a known height being erected on a level pavement, by observing the lengths of the meridian shadows, they were enabled to trace the progress of the sun from tropic to tropic. The most ancient observation with the gnomon which we meet with is that of Pytheas, in the days of Alexander the Great. Pytheas observed at the summer solstice at Marseilles, that the length of the meridian shadow was to the height of the gnomon as $213\frac{1}{2}$ to 600; an observation which makes the meridian altitude of the sun at Marseilles on that day $70^\circ 27'$. The merit of the invention of the gnomon in Greece is ascribed to the astronomical school of Miletus, and particularly to Anaximander and Anaximenes. There is reason, however, to believe that this method of observation was originally invented by the Egyptians; and that Thales, who travelled into Egypt, carried thence the knowledge of it into Greece. It has even been conjectured that the Egyptian pyramids and obelisks were intended for the same purpose with the gnomon; and, though it would be extravagant to imagine that this was their sole use, this opinion appears to be countenanced by the fact of their being placed in the direction of the four cardinal points.

The determination of the length of the meridian shadow at the solstices for different parts of the earth, by observations made with the gnomon, is important as being the first step towards connecting geography with astronomy; and, when combined with just conceptions of the globular figure of the earth, leads, by a simple train of thought, to the notion of latitude by which the position of a place is fixed relatively to north and south. The position with regard to east and west is the only other element necessary for fixing the absolute situation of the place on the surface of the earth. It might have been supposed not to be more than a reflecting mind could easily accomplish, to reach the conception of both these elements, and to apply them to use. Yet so slow was the progress towards the apprehension of the principles on which an accurate system of geography might be founded, that from the days of Thales and his immediate successors, who flourished in the sixth century before the Christian era, there appears to have been little done for the improvement of geography, as a science, until the establishment of the famous astronomical school of Alexandria. Pythagoras had indeed maintained the true system of the world, by placing the sun in the centre, and giving the earth both a diurnal and annual revolution; but this doctrine was so much in advance of the age in which he promulgated it, that it was soon lost sight of.

Eratosthenes was the first who reduced geography to a regular system, and laid its foundations on clear and solid principles. Under the patronage of the Ptolemies, he had access to the materials collected by Alexander, his generals and successors, as well as to the immense mass of documents accumulated in the Alexandrian library. At an early period of the history of astronomical science, the vulgar opinion that the earth is a flat surface, with the heavens resting upon it as a canopy, was rejected; but it was not at once that distinct conceptions of its globular figure were acquired. It was only as astronomical observations increased that the doctrine of its sphericity was fully established. This point had been gained when Eratosthenes began his labours; and what he endeavoured to accomplish was to delineate, in strict conformity with this principle, the known parts of the earth's surface.

With this view, founding his system on the use of the gnomon, he supposed a line to be traced through certain places, in all of which the longest day was known to be exactly of the same length. This line would evidently be a parallel to the equator. But though his method was correct in principle, the want of accurate observations rendered it uncertain in practice. The line was supposed to comprise all the leading positions which lay near it, though they did not actually come within its range. Its western extremity was the Sacred Promontory of Iberia (Cape St Vincent); thence it passed through the Straits of Gades. Proceeding eastward, it passed through the Sicilian Sea, and near the southern extremity of the Peloponnesus, and was continued through the island of... History. Rhodes, and the Bay of Issus; whence entering Cilicia, and crossing the Euphrates and the Tigris, it was extended to the mountains of India, and terminated at the remote city of Thine, situated on the Eastern Ocean. The parallel thus drawn was understood to pass through all those places where the longest day was fourteen hours and a half. It stretched the whole length of what was supposed to be the habitable world, and measured about 70,000 stadia; a distance corresponding, according to the estimate of Eratosthenes, to about 140 degrees, which is rather more than one third of the circuit of the globe.

This first parallel drawn through Rhodes was afterwards preferred as the basis of ancient maps; inasmuch as it was traced through the middle of the Mediterranean, along the coasts of which were situated the principal nations of antiquity. Following out the same happy thought which he had thus successfully made the groundwork of his system, Eratosthenes was induced not only to trace other parallels at certain intervals from the first, as one through Alexandria, another through Syene, and a third through Meroe; but also to trace, at right angles to these, a meridian, passing through Rhodes and Alexandria southward to Syene and Meroe. As the progress which he thus made towards the completion of what he had so skilfully conceived, naturally tended to enlarge his ideas concerning geographical science, he attempted what seemed a still more difficult undertaking, namely, to determine the circumference of the globe by the actual measurement of a segment of one of its great circles. The method he pursued has already been pointed out in the article Astronomy, page 790. There is a difference among ancient authors respecting the result obtained by Eratosthenes. The great majority, however, state it to be 252,000 stadia, which give exactly 700 stadia for a degree of the equator, and 555 stadia for the degree of longitude upon the parallel drawn through Rhodes.

The knowledge of the circumference of the earth is a necessary element in the construction of maps; and hence the most eminent of the ancient astronomical geographers made repeated endeavours to determine it with accuracy. Posidonius, by an astronomical observation, determined the arc of the meridian between Rhodes and Alexandria to be a forty-eighth part of the whole circumference. With regard to the distance between these two places, 5000 stadia were the reputed distance; but Eratosthenes had made it only 3750 stadia upwards of 170 years before, and betwixt these two Posidonius had to make choice. The former number gives 240,000 stadia for the whole circumference, the latter 180,000 stadia. Of this last result, which gives 500 stadia for a degree of the equator, Posidonius is reported by Strabo to have approved. For want of the knowledge of the true length of the stadium, it is now impossible to judge of the actual quantity assigned either by Eratosthenes or Posidonius as the measure of the earth's circumference; but the great uncertainty about the distance between the points of observation in the case of the determination of the latter astronomer renders his conclusion of no value.

Notwithstanding the soundness of the principles which had now been laid down for the delineation of the globe, much remained to be done, in the way of observation, before an accurate representation of the whole, or a portion of the earth's surface, could be given. Both the latitudes and longitudes of the ancients are erroneous; more especially the latter. This is what might be expected at that early period. But in setting out from the Sacred Promontory of Iberia, the meridian of which the ancients made their first meridian, the errors in longitude accumulate, as we advance eastward, with a regularity, as well as rapidity, which is very surprising. The regularity of their increase induced M. Gosselin to conclude that they were to be attributed, not to the imperfection of independent observations, but to some general cause, which he endeavoured to assign by imagining that Eratosthenes had access to some early map, found probably by Alexander or his generals in some country in the East, where astronomy had been successfully cultivated; and that misapprehensions respecting the principle of delineation employed, which M. Gosselin supposes to have been that on which the plane chart is constructed, had led him into a regular system of errors. In the plane map the length of a degree of longitude is supposed to be the same at all distances from the equator. By taking for granted that Eratosthenes took his distances from a map of this kind, on which the parts of the globe had been accurately laid down, but that he divided the stadia expressing these distances, not by 700, the number of stadia in a degree at the equator, as he ought to have done, but by 555, the number corresponding to the parallel of Rhodes, M. Gosselin obtains results which have a wonderful coincidence with the positions actually given by Eratosthenes. These results, however, are deduced from a hypothesis which is unsupported by any evidence, except what may be supposed to arise from this coincidence. A more probable solution seems to be that Eratosthenes determined his longitudes from the itinerary measures, which he reduced to degrees at the rate of 700 stadia to a degree at the equator, and of 555 to a degree at the parallel of Rhodes; and that the errors are the consequences of the exaggerated accounts which merchants and travellers of that age gave of the distances over which they passed;—their exaggerations, of course, bearing some proportion to the length and hardships of the journeys undertaken.

The knowledge as yet possessed by geographers with regard to the outline of the habitable globe was far from being such as to enable them to delineate it with any degree of precision. This circumstance, combined with the unavoidable errors in latitude and longitude, produced very great distortions in the representations given of the countries on the surface of the globe. Under the guidance of sound principles of science, however, it was now certain that these imperfections would gradually disappear.

The improvements introduced into geography by Eratosthenes were perfected in principle by Hipparchus. This celebrated astronomer, who flourished between a hundred and sixty and a hundred and thirty-five years before the Christian era, was the first who undertook the arduous task of forming a catalogue of the stars, and fixing their relative positions. His object was to transmit to posterity a knowledge of the state of the heavens at the period of his observations. The extremities of the imaginary axis round which the heavens perform their diurnal revolution suggest two fixed points by which the position of the great circle of the celestial sphere called the equator is determined. If a great circle be supposed to pass through these points and any star, the position of the star will be ascertained if we measure in degrees and parts of a degree the arc of the meridian circle intercepted between the star and the equator, and also the arc of the equator intercepted between a given point in it, and the meridian circle passing through the star. Upon this principle did Hipparchus arrange the stars according to their places in the heavens, a work in which he appears, however, to have been in some measure anticipated by Timocharis and Aristillus, who began to observe about two hundred and ninety-five years before the Christian era. The great improvement which he introduced into geography consisted in this, that he applied to the determining of the position of any point on the surface of the earth the same artifice which he had already so happily introduced in the arrangement of the constel- History. lations; and thus furnished the means of ascertaining the relative situations of places with a precision which no itinerary measurements could possibly attain. If we suppose the earth to be a globe concentric with the celestial sphere, and intersected by the planes of the celestial equator and meridian, the principle on which the application of this artifice to the terrestrial sphere depends becomes at once obvious. Hipparchus made a considerable number of observations of latitude, and pointed out how longitudes might be determined by observing the eclipses of the sun and moon. Great as this improvement was, its importance seems not to have been duly estimated until the days of Ptolemy; for none of the intermediate authors, such as Strabo, Vettius, and Pliny, have given the least hint of the latitude and longitude of any one place in degrees and minutes, though all of them have given minutely the geographical position of places according to the length and shadows of the gnomon. Strabo, indeed, even justifies his neglect of the astronomical principles introduced by Hipparchus. "A geographer," says he, "is to pay no attention to what is out of the earth; nor will men engaged in conducting the affairs of that part of the earth which is inhabited, deem the distinction and divisions of Hipparchus worthy of notice."

The true principles of geography being pointed out by the application of latitude and longitude to places on the earth, the way was opened for the improvement of maps, which, with the single exception of the map drawn by Eratosthenes, had hitherto been little more than rude outlines and topographical sketches of the different countries.

No maps more ancient than those formed to illustrate Ptolemy's geography have reached modern times; but the earliest of which there is any account are those of Sesotris, of whom it is said, that having traversed great part of the earth, he caused his marches to be recorded in maps; and that he gave copies of these maps not only to the Egyptians, but to the Scythians, whose astonishment he thus greatly excited.

Some have imagined that the Jews made a map of the Holy Land when they gave the different portions to the nine tribes at Shiloh. For on that occasion, as we are informed by the sacred historian, men were sent "to walk through the land, and to describe it;" and when they had accomplished the object of their mission, by describing "it by cities into seven parts, in a book," they returned unto Joshua. What is here said, however, does not fully determine whether their mensuration of the land was only recorded in numbers, or regularly projected and digested into the form of a map.

The first Grecian map on record is that of Anaximander, mentioned by Strabo, which some have conjectured to have been a general map of the then known world. It has further been imagined to be the same with that referred to by Hipparchus under the designation of The Ancient Map, and which in some few particulars he preferred to that of Eratosthenes.

But some idea of the nature of the maps of those early days will be best obtained from the map of Aristagoras, king of Miletus, which is minutely described by Herodotus. The historian tells us that this map, which was traced on brass or copper, Aristagoras showed to Cleomenes, king of Sparta, in order to induce him to attack the king of Persia, even in his palace at Susa, for the purpose of restoring the Ionians to their ancient freedom. It contained the intermediate countries to be traversed in that march. We must not interpret, however, the words of Herodotus too literally, when he describes it as containing "the whole circumference of the earth, the whole sea or ocean, and all the rivers." Keeping in view the state of geography at that period, it may justly be concluded, that notwithstanding this pompous form of expression, the sea meant only the Mediterranean, and therefore the earth or land the coasts of that sea, and more particularly Asia Minor, extended towards the middle of Persia; by the rivers must be meant the Halys, the Euphrates, and the Tigris, which Herodotus mentions as necessary to be crossed in the expedition in question. The map contained one straight line, called the royal highway, embracing all the stations or places of encampment between Sardis and Susa, so that it was properly an itinerary.

The principle on which Eratosthenes constructed his map we have already considered. With regard to its extent, it seems to have contained little more than the states of Greece, and the dominions of the successors of Alexander, digested from the surveys of the marches of that great general. He had some faint idea respecting the western parts of Europe, which he had acquired from the voyage of Pytheas; but not such a conception as to enable him to delineate their outline on a chart. According to the report of Strabo, he was quite unacquainted with Spain, Gaul, Germany, and Britain; he was equally ignorant of Italy, the coasts of the Adriatic, Pontus, and of all the countries toward the north. His errors with regard to the distances of places were in some instances enormous. The distance of Carthage from Alexandria he represents at 15,000 stadia, instead of 9000.

It was not until Ptolemy commenced his labours that the improvements pointed out by Hipparchus were effectually applied to perfect the system which Eratosthenes had so happily begun. Ptolemy composed his system of geography, which escaped amidst the general wreck that consumed so many other ancient books of science, in the reign of Antoninus Pius, about 150 years after the fall of the Christian era. At this period the Roman empire had reached its utmost extent, and all the provinces had been surveyed, and were well known. The materials then in existence, and in the possession of Ptolemy for completing his great work, were the proportions of the height of the gnomon and its shadow, at the time of the equinoxes and solstices, taken by different astronomers; calculations founded on the length of the longest days; the measures or computed distances of the principal roads contained in the surveys and itineraries; and the various reports of travellers and navigators, whose determinations of the distances of places often rested, however, on no better foundation than hearsay and conjecture. Among these various particulars, there evidently existed considerable differences in point of authority. But Ptolemy undertook the difficult and laborious task of comparing, and reducing into one system, which should possess the order and beauty of science, this apparently incongruous mass. He converted and translated the whole into a new mathematical language, expressing in degrees and minutes the latitude and longitude of each place, according to the principles laid down by Hipparchus, but which had been allowed by geographers to lie useless for upwards of two hundred and fifty years. It is in Ptolemy's work, which consists of eight books, that we find for the first time the mathematical principles of the construction of maps, both general and particular, as well as of several projections of the sphere.

Notwithstanding that the light of accurate science thus directed the steps of the first geographer of antiquity, he was far from reaching the precision at which he aimed. This arose from the imperfection of the original materials upon which his work is based in reference to its details. With regard to the remoter boundaries of the then known world, in all its quarters, a wonderful advancement in knowledge had been made since the days of Eratosthenes and of Strabo. But still that additional information was not fitted to make up for the want of astronomical observations, by which alone accuracy could be secured. Besides, in relation to places situated beyond the limits of the Roman The great obstacle with which the ancients had to contend was the finding of the longitude with accuracy, a problem for the solution of which it was long before there was discovered any method sufficiently exact. This accounts for the erroneous longitudes of Ptolemy, and more especially for the length of time, even many centuries, during which the remarkable error with regard to the length of the Mediterranean remained undiscovered and uncorrected.

We have now traced the history of geography from the earliest period of which we have any information, to the time when it assumes a scientific character. We shall conclude our account of ancient geography by shortly noticing the principal geographers of antiquity, some of whom have not yet been mentioned, while others have only been quoted in tracing the rise and progress of the science.

The intimate connection between geography and the sciences of geometry and astronomy, rendered the former an object of attention to many who ancienly cultivated the latter. We have already mentioned Anaximander and Anaximenes, of the school of Miletus. Democritus, Eu- doxus of Cnidus, and Parmenides, are also reported to have improved geography; and to the last is attributed the division of the earth into zones. These were followed by Eratosthenes, who lived about two hundred and forty years before the Christian era; by Hipparchus about eighty years afterwards; by Polybius, Geminus, and Posidonius. Eratosthenes wrote three books on geography, some passages of which Strabo criticises, though he frequently defends him against Hipparchus, who appears to oppose his opinions with some degree of affectation. Polybius also wrote on geography; as did likewise Geminus and Posidonius, who are frequently quoted by Strabo. Polybius, according to Geminus, argued with considerable acuteness for the possibility of the torrid zone being inhabited; and he even adduced plausible arguments to prove that the countries under the equator enjoy a more temperate climate than the countries do that are situated near the tropics.

We must not here omit a geographer and geometer who lived about the time of Alexander the Great. This was Dicearchus of Messina, a disciple of Theophrastus, who wrote a description of Greece in iambic verses, of which some fragments yet remain. But what chiefly renders him remarkable is, that he measured geometrically several mountains, to which an excessive height had been before assigned.

With Dicearchus we may notice another geometer, Xenagoras, a disciple of Aristotle, mentioned by Plutarch in his life of Paulus Æmilius, who occupied himself in the measurement of mountains. He found the height of Mount Olympus to be fifteen stadia.

In some of the latter periods which preceded the Christian era there were several writers on geography, as Artemidorus of Ephesus, who wrote a geographical work of eleven books, of which nothing remains; Scymnus of Chio, author of a description of the earth in iambic verses, which remain in a very mutilated state; Isidorus of Charax, who gave a description of the Parthian empire; and Scylax of Caryades, author of a voyage round the Mediterranean, which is still extant.

The works of all these geographers are, however, but small in comparison with the Geography of Strabo; a work in seventeen books, which has come down to us entire. This is one of the most valuable works of antiquity, both from the spirit of discussion which runs through it, and the number of curious particulars which the author has collected from different geographers and navigators who preceded him, and of whose works nothing remains except these extracts. Strabo lived in the reigns of Augustus and Tiberius, and was nearly contemporary with Pomponius Mela. This latter geographer wrote a work De Situ Orbis, which, though little more than a bare summary, is valuable as it gives us a sketch of what was known in his time respecting the state of the habitable globe. Besides Mela, Rome produced in the most flourishing era of its literature another eminent geographer, Pliny. He devoted two books of his extensive work on natural history to a system of geography. His intimate connection with the imperial family, and with many of the most eminent commanders of the time, appears to have given him access to all the military measurements, as well as to the general survey of the Roman empire. Thus furnished with a greater store of authentic materials than any former writer, he has introduced a great number of itinerary details, which are for the most part accurate and valuable. Julius Solenus has also treated of geography in his Polyhistor, a compilation sufficiently valuable from the number of curious particulars which are there collected. Marinus of Tyre was another geographer who appears to have been distinguished, though his works have perished. Even under the Roman empire Tyre continued to be the seat of an extensive commerce; indeed the commercial relations of her citizens appear to have extended over a wider portion of the earth's surface than ever. The enlarged materials furnished by the lengthened journeys of his countrymen, which brought them even to the confines of China, Marinus collected, and sought to apply to them the astronomical principles of Hipparchus, so that he might give to geography a new and more accurate form. Ptolemy, whom Marinus preceded by a short time, employs a great part of his first book in discussing the means employed by the Tyrian geographer for fixing the relative position of places; and from the references and extracts it appears that the system of Marinus partook largely of the imperfections of a first effort.

The enlarged and scientific views of Ptolemy we have already considered. Some time after Ptolemy lived Dionysius, commonly called the Periegetes, from the title of a work in verse composed by him, namely, his Periegesis, or Survey of the World. This work was translated into Latin verse by Priscianus, and afterwards by Avienus. There is, besides, a description by Avienus, of the maritime coasts, in iambic verses, of which there remain about seven hundred.

The difficulty of procuring the small and scattered pieces of most of these authors, with those of a few others not here enumerated, induced the learned Hudson to collect them into one work, consisting of four volumes octavo, which were published in the years 1698, 1702, 1712, under the title of Geographia veteris Scriptores Graeci minores. The originals are accompanied with Latin translations, and notes and dissertations on each by Dodwell. This is a very valuable collection.

We now proceed to consider the progress of geography during the middle ages. From the days of Ptolemy until the revival of letters in Europe, little was done for its solid improvement. The calamities that ere long overwhelmed the Roman empire, were followed by a general intellectual darkness which settled down on the world and extinguished even the imperfect knowledge possessed by the ancient geographers. While barbarous nations poured in from several quarters, art and science ceased to be cultivated. The union by which the Roman power had bound together mankind being now dissolved, Europe was divided into small and independent, and, for the most part, hostile communities, which had but vague conceptions respecting the situation of each other, while no intercourse subsisted between their members. With regard to remote regions all knowledge was lost; their situations, their commodities, and almost their names, were unknown.

Amidst this ignorance there were but few channels open through which knowledge could be obtained. One circumstance, however, prevented commercial intercourse with foreign nations from being altogether suspended. The opulence and luxury of imperial Rome had long given life and energy to commercial enterprise; that stimulus was now withdrawn; but Constantinople still remained, the last refuge of ancient arts, and taste, and elegance, when the rest of Europe was overspread with barbarism. Fortunately that city had escaped the destructive rage of the fierce invaders; and there, under the cherishing influence of a demand for foreign productions and luxuries, commerce continued to flourish. Alexandria continued to be the emporium whence were imported the commodities of the East Indies, until Egypt, falling under the power of the Arabians, ceased to be a province of the Roman empire. After this event the industry of the Greeks succeeded in discovering a new channel by which Constantinople might still be supplied with the productions of India. These were first conveyed up the Indus as far as that river is navigable, thence by land-carriage they were brought to the Oxus, and were carried down that river to the Caspian Sea. Entering there the Volga, they were conveyed up it, and thence were again transported by land until they reached the Tanais, down which they were conveyed to the Euxine Sea, where vessels from Constantinople awaited their arrival. By this circuitous route was a channel of intercourse kept open with the most distant countries of the East; and an extensive knowledge of remote regions was still preserved in the capital of the Greek empire, while the rest of Europe was sunk in the grossest ignorance.

The missions sent for the conversion of the northern pagans to Christianity served somewhat to illustrate the geography of Europe; though there is sufficient proof that the monks employed were, in many instances, themselves grossly ignorant, some not even knowing the capital of their own country, or the cities nearest to their own. Something was also done by the great sovereigns of Europe towards dispelling the prevailing ignorance of the age on matters connected with geography. Nor did the piratical exploits of the Danes and Norwegians under their great sea-kings fail to make them acquainted with the seas and maritime coasts where they carried on their devastations. But it was in the East that a gleam of light and knowledge began now to appear, which was the harbinger of the noon-day splendour of science that was destined to succeed the darkness of ignorance which had so long oppressed the human mind. Under the influence of a fanaticism which prompted them to own no law but the Koran and the sword, the followers of Mohammed had rushed from the heart of Arabia, and had carried their conquests over half the world. At length, however, under a race of humane and polished princes, having contracted a relish for the sciences of the people whose empire they had contributed to overturn, they stood for some time distinguished as the most learned of nations. They translated into their own language the books of several of the Greek philosophers. The valuable work of Ptolemy was one of the first; and hence the study of geography became an early object of their attention. But the advancement which the science made in their hands towards precision was slow; for they copied and retailed all Ptolemy's principal errors. Still, in all the countries that were under Mohammedan dominion numerous observations were made, which, though not always strictly correct, were entitled to be considered as a step beyond the calculations made merely from the itineraries by the Alexandrian geographers. In the beginning of the ninth century, under their caliph Almanon, who may rank among the most distinguished patrons of science that ever filled a throne, they measured a degree of latitude on the plains of Sinjar, or Shinar, near Babylon, with a view to determine the cir- The progress and success of the Moslem arms removed the obscurity in which many countries had until then been concealed, as well as the barbarism in which they had been sunk. And even beyond the limits of the Mahommedan world they pushed their researches, by sending missions both to the east and to the west, which they explored to their remotest limits. At that time Europe remained ignorant of the improvements made by the Arabs, though she was destined in subsequent ages to perfect their discoveries.

At length the long period of barbarism which accompanied and followed the fall of the Roman empire, during which the traces of whatever had embellished society, or contributed to the comfort and convenience of life, were almost entirely effaced, drew to a close. Industry began again to shed its blessings on mankind, and Italy was the country where its benign influences were first perceptible. Having from the operation of various causes again obtained liberty and independence, the Italians soon began to feel the impulse of those passions which serve most powerfully to arouse men to activity and enterprise. The reviving demand for the comforts and luxuries of life led to the revival of foreign commerce. The valuable commodities of the East were at first obtained at Constantinople. But the exorbitant price demanded at that mart, in consequence of the circuitous route by which they were conveyed thither, induced the Italians to resort to other ports, as Aleppo and Tripoli, on the Syrian coast, and at length to Egypt itself. After the Soldans had revived the commerce with India in its ancient channel by the Arabian Gulf, Venice, Genoa, Pisa, rose from inconsiderable towns to wealthy and populous cities. Their trade extended to all the ports in the Mediterranean, and even beyond the straits to the towns on the coasts of Spain, France, the Low Countries, and England; and from these points they diffused through Europe a taste for the luxuries and enjoyments of civilized life, which they at the same time furnished the means of gratifying.

It was not long ere an event occurred, the most extraordinary perhaps in the history of human society, which gave a new impulse to the European mind, and forcibly directed its view eastward to the regions of Asia. Under the influence of a high-wrought enthusiasm, the martial spirit of the Europeans was aroused, and vast armies, composed of all the nations of Christendom, marched towards Asia on the wild enterprise of delivering the Holy Land from the dominion of Infidels. The crusades, however blind the zeal from which they took their rise, had a very favourable influence on the intellectual state of Europe, and prepared it for receiving the light of science which was soon to dawn upon it. Interesting regions, known hitherto only by the scanty reports of ignorant and credulous pilgrims, were now made the object of attention and research. Not only was the way opened for the European nations acquiring a correct knowledge of the Holy Land, with the kingdoms of Jerusalem and Edessa, founded by the victorious crusaders; but the extensive regions over which the Saracens and the Turks had extended their empire began to be explored. Search was now made in the writings of the ancient geographers; nor is it improbable that some light was derived even from the Arabian writers. Religious zeal, the hope of gain, combined with motives of mere curiosity, induced several persons to travel by land into remote regions of the East, far beyond the countries to which the operations of the crusaders extended. Prompted by superstitious veneration for the law of Moses, and by a desire of visiting his countrymen in the East, whom he hoped to find possessed of wealth and power, Benjamin, a Jew of Tudela, in the kingdom of Navarre, set out from Spain in the year 1160, and travelling by land to Constantinople, proceeded through the countries to the north of the Euxine and Caspian Seas. He then journeyed towards the south, and traversed various provinces of the further India, until having reached the Indian Ocean, he embarked and visited several of its islands; and at length, after thirteen years, returned by the way of Egypt to Europe. In his progress he had acquired much information respecting a large portion of the globe, until then altogether unknown to Europeans.

Various missions were sent by the pope and by Christian princes, for purposes which led them to traverse the remote provinces of Asia. Father John de Plano Carpini, at the head of a mission of Franciscan monks, and Father Ascolino, at the head of another mission of Dominicans, were in the year 1246 sent by Innocent IV. to enjoin Kayuk Khan, the grandson of Zengis, who was then at the head of the Tartar empire, to embrace Christianity, and to cease from desolating the world by his arms. In fulfilling the commands laid upon them by the head of the Christian church, the mendicants had an opportunity of visiting a great part of Asia. Carpini, having taken his route through Poland and Russia, travelled through the northern provinces as far as the extremities of Thibet; whilst Ascolino, who appears to have landed somewhere in Syria, advanced through the southern provinces into the interior parts of Persia.

Father William de Rubruquis, a Franciscan monk, having been sent in the year 1253 on a mission by St Louis of France, in search of an imaginary personage, a powerful khan of the Tartars, who was reported to have embraced the Christian faith, made a circuit through the interior parts of Asia more extensive than that of any European who had hitherto explored them. He had the merit of being the first modern traveller that gave a true account of the Caspian, which had been correctly described by the early Greeks as an inland separate sea; but a notion afterwards prevailed that it was connected with the Northern Ocean. Rubruquis ascertained that it had no connection with the ocean or any other sea. The account of his journey was so little read, however, that the old error was repeated in books of geography long after his time.

While the republics of Italy, and, above all, the state of Venice, were engaged in distributing the jewels, the spices, and the fine cloths of India over the western world, it was impossible that motives of curiosity, as well as a desire of commercial advantage, should not be awakened to such a degree as to impel some to brave all the obstacles and dangers to be encountered in visiting those remote countries where these precious and profitable commodities were produced. A considerable number of persons accordingly are recorded as having penetrated a greater or less depth into the interior of Asia. But the fame of all the other old travellers is eclipsed by that of Marco Polo, who has always ranked among the greatest discoverers of any age. This extraordinary man was a noble Venetian, whose family, according to the custom of his country, engaged in extensive commerce. Nicolo Polo, and Maffeo Polo, the father and uncle of Marco, were merchants, who, in partnership, traded chiefly with the East; and in pursuit of their mercantile speculations had already visited Tartary. The recital of their travels on their return fired the youthful imagination of Marco, then between seventeen and eighteen years old. Having, when in the East, gained the confidence of Kubali Khan, the great conqueror of China, at whose court they had resided for a long time, they were sent back by him to Italy, accompanied by an officer of his court, that they might repair to Rome as his ambassadors to the pope, of whom, and History, the potentates of the western world, they had given him an ample account. After many delays they were now, about the year 1265, to set out on their return to the court of Kublai, bearing the papal letters and benediction; and it was resolved that young Marco should accompany them. After a journey that occupied no less than three and a half years, and in the progress of which they passed through the chief cities in the more cultivated parts of Asia, they reached Yen-king, near the spot where Pekin now stands, where they were honourably and graciously received by the grand khan. Struck with the appearance of young Marco, the khan condescended to take him under his protection, and caused him immediately to be enrolled among his attendants of honour. By prudence and fidelity Marco gained so high a place in the esteem and confidence of his protector, that for seventeen years, during which he remained in his service, he was employed in confidential missions to every part of the empire and its dependencies. He made more than one voyage on the Indian Ocean, and traded with many of the islands. Besides what he learned from his own observation, he collected from others many things concerning countries which he did not visit. Considering the very favourable circumstances in which he was placed for geographical research, as well as his passion for travelling, which seems to have increased with his opportunities of gratifying it, it is not surprising that, after the long period of his wanderings in Asia, he should have returned to Europe possessed of the knowledge of many particulars, until his time unknown, respecting the eastern parts of the world. Marco, being afterwards made a prisoner by the Genoese, was induced, with a view to beguile the tediousness of his confinement, to dictate a narrative of his travels. His information was so far in advance of the age, that his veracity was exposed to the most injurious suspicions. But, if we make allowance for some tincture of credulity, characteristic of the times in which he lived, his narrative is supported in all its essential points by modern information.

While great accessions were thus made to the stock of knowledge possessed by the nations of Europe respecting the habitable globe, their ideas were at the same time gradually enlarged; and an adventurous spirit was generated, which prepared them for attempting further discoveries. Still their efforts were limited by certain bounds, in consequence of the imperfect state of navigation. Whatever conceptions a daring mind might venture to form respecting the existence of unknown regions, separated from the known continents by the mighty expanse of the Atlantic Ocean, mankind had not yet so obtained the dominion of the sea as to be able to bring such conceptions to the test of experiment. It was not until the fortunate discovery of the polarity of the magnetic needle, and the consequent construction of the mariner's compass, that man was enabled to visit every part of the globe which he inhabits. This important discovery was made by Flavio Gioia, a citizen of Amalfi, a town of considerable trade in the kingdom of Naples, about the year 1302. Encouraged by the possession of this sure guide, by which at all times and in all places he could with certainty steer his course, the navigator gradually abandoned the timid and slow method of sailing along the shore, and boldly committed his bark to the open sea. At the commencement of the fifteenth century, however, navigation appears to have advanced very little beyond the state which it had reached before the downfall of the Roman empire. But it was now destined to make rapid progress. The growing spirit of enterprise, combined with the increasing light of science, had prepared the states of Europe for entering upon that great career of discovery, of which the details constitute the materials for the history of modern geography.

Portugal took the lead in this new and brilliant path. Her first attempt was to discover the unknown countries situated along the western coast of Africa. Notwithstanding the vicinity of that great continent, and the strong inducement afforded, in the fertility of the countries already known in it, to its further exploration, Cape Non had hitherto limited the researches of the Portuguese, and had been regarded as an impassable barrier. In the year 1412, however, ships sent out for discovery doubled this formidable promontory, and reached Cape Bojador, a hundred and sixty miles to the southward, which became in its turn the boundary of Portuguese navigation; and it continued to be so for upwards of twenty years. Under the existing system, which still continued to be practised, it was not likely that the obstacles presented by its rocky cliffs, which stretch a considerable way into the Atlantic, would soon have been overcome. But a sudden squall of wind having driven out to sea the vessel next dispatched, this event fortunately led to the discovery of the small island Porto Santo; whence in a little time Madeira was discovered, being first mistaken for a small black cloud in the horizon; and at length, when the Portuguese by their voyages thither had gradually become accustomed to a boldier navigation, Cape Bojador was doubled. Thus, by repeated efforts, the Portuguese navigators gradually approached the northern boundary of the torrid zone. Here their progress was for some time arrested, not by any physical difficulties, but in consequence of the influence which the opinion of the ancient mathematicians and geographers, whom they had hitherto followed as their guides, had upon their minds, by leading them to believe that excessive heat rendered the middle regions of the earth uninhabitable. Experience, however, at length enabled them to triumph over ignorance and prejudice. A powerful fleet, fitted out in 1484, after discovering the kingdoms of Benin and Congo, advanced above 1500 miles beyond the equator. Their intercourse with the natives enabled them to obtain information concerning those parts of the country which they had not visited. Not only had they detected the error of the ancients in reference to the torrid zone, but they found also that the direction of the coast was very different from what the description given by Ptolemy had led them to expect. They saw reason to conclude that the continent gradually became narrower as they proceeded southward; so that there was room to believe that the ancient accounts respecting the circumnavigation of Africa were really founded in truth. New and more extensive prospects were thus opened to them; and the finding of a passage to India by sailing round the southern extremity of Africa became a favourite project. In the year 1488 the lofty promontory which terminates that continent was described by Bartholomew Diaz; but it was not until about ten years afterwards that it was doubled, and the coast of Malabar reached, by Vasco de Gama.

Meanwhile the Cape de Verd Islands, which are said to have been known to the ancients, but afterwards lost sight of, had been discovered in 1446; and soon after the Azores Isles. When we consider the distances at which these two groups of islands lie from the land, the former being upwards of 300 miles from the coast of Africa, and the latter distant 900 miles from any continent, it may be concluded that the Portuguese, when they entered so boldly into the open seas, had made no inconsiderable progress in the art of navigation.

But brilliant as is the lustre which these discoveries shed around the Portuguese name, their glory would have been still more dazzling had they seconded the profound views of Christopher Columbus, which led him to the discovery of the New World. That illustrious man and skilful navigator, by revolving in his mind the principles on which the Portuguese had founded their schemes of discovery and carried them into execution, was led to conceive that he could improve on their plan, and accomplish discoveries History, which they had hitherto attempted in vain. From the time that they had doubled Cape Verde, the great object at which the Portuguese aimed was to find a passage by sea to the East Indies. The direction in which their efforts were made implied necessarily a long and hazardous voyage, should they even be successful in accomplishing their design. But as the Atlantic Ocean stretched westward to an unknown distance, was it not possible that it might reach the shores of those very countries to which it was thought so desirable to find a naval route? This supposition was perfectly consistent with the known globular figure of the earth; and it was evident, on the same principle, that the farther India stretched to the east, the nearer it must approach to the western shores of Europe and Africa. Such was the idea suggested to the mind of Columbus, by the knowledge which he possessed of navigation and geography, both in theory and practice. While he found his views confirmed by a careful comparison of the observations of modern pilots with the hints and conjectures of ancient authors, he became thoroughly convinced that the navigator who should have the boldness to cross the Atlantic Ocean would have his toils rewarded by the most important discoveries.

These ideas had presented themselves to the mind of Columbus as early as the year 1474; but it was not until the year 1492, after several years of fruitless solicitation, and of discouragements and disappointments of the most vexatious kind, that he obtained the patronage of Ferdinand and Isabella, who then governed the united kingdoms of Castile and Arragon, and was by them put in possession of the means of carrying his schemes of discovery into execution. With no more suitable armament for his great enterprise than three small vessels, having ninety men, mostly sailors, on board, and victualled for twelve months, he sailed from the port of Palos in Andalusia on the 3rd day of August, and steered for the Canaries. Taking then his departure from Gomera, one of the most westerly of these islands, he stretched into unknown seas; and holding his course due west, reached Guanahani, one of the Bahama Islands, on the 12th day of October. After employing some time in making further discoveries, he returned to Spain to announce the success of his undertaking, the fame of which soon spread over Europe, and excited general attention. It was no easy matter to determine what relation the newly-discovered countries bore to the regions formerly known. Columbus's own views on the subject were in strict conformity with the idea which had taken so firm a hold of his mind, namely, that India might be reached by sailing towards the west. He imagined that the islands he had visited were some of those which were said to lie contiguous to the remote shores of Asia. In this opinion he was confirmed by the coincidence which he thought he could trace between certain names given to places by the natives and the appellations known to belong to countries situated in India. He thought he could recognise, in the answer given to his inquiries after the situation of the mines which yielded gold, the name Cipango, by which Marco Polo and other travellers in the East designated the island Japan. Ignorant of their language, and unaccustomed to their pronunciation, he even supposed that they spoke of the great khan; and hence concluded that the kingdom of Cathay or China, described by Marco Polo, was not far off. The same erroneous opinion was still further riveted in his mind, by what he supposed an identity between the animal and vegetable productions of the East Indies and those of the countries which he had discovered.

His second voyage led to the discovery of several more of the group of islands now called the West Indies, a name given them in conformity with the original notions of the discoverer. It was on his third voyage that he discovered the vast continent of America. Having unexpectedly found the island of Trinidad, with the neighbouring land, he encountered, before he was aware of danger, the adverse currents and tumultuous waves occasioned by the resistance which the waters of the Orinoco oppose to the tides in the ocean. His attention was thus forcibly called to the immense body of water which is here poured into the Atlantic. This he was convinced was vastly too great to be supplied by any island; and hence he concluded that he had now reached the continent which he had sought through so many dangers.

The tenacity with which an ingenious and enterprising mind adheres to a scheme which it has once proposed to itself as an object of pursuit, was strikingly evinced by Columbus, whose thoughts still dwelt with eagerness on his original and favourite plan of opening a new passage to India. It was not enough that he had astonished mankind by finding a new continent; he conceived the idea that beyond it there might lie a sea extending to the coasts of Asia, and that by diligent search some strait might be found which would conduct him into this sea, or some narrow neck of land, by crossing which it might be reached. To determine this important point, though hitherto his services had met with the most unworthy returns, though years crept upon him, though worn out by fatigue and broken with infirmities, he still undertook with alacrity another voyage. By a lucky conjecture he directed his efforts towards the east of the gulf of Darien; but he searched in vain for a strait; and though he frequently went on shore and advanced into the country, he never penetrated so far as to enable him to descry the great Southern Ocean.

After the first steps had been taken, the progress of discovery over the globe was astonishingly rapid. No expense or danger deterred even private adventurers from fitting out fleets, crossing oceans, and encountering the rage of savage nations in the most distant parts of the earth. Before Columbus had reached the continent at the mouth of the Orinoco, Newfoundland had been discovered by Cabot, a Venetian by descent, but sailing under the auspices of England. He had also coasted along the present territory of the United States, perhaps as far as Virginia. In the next two or three years, the Cortereals, a daring family of Portuguese navigators, began the long and unavailing search of a passage round the northern extremity of America. They sailed along the coast of Labrador, and entered the

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1. The American continent in its northern portions had been discovered in or before the eleventh century. Towards the close of the ninth century a Norwegian pirate, while attempting to reach the Faroe Islands, which had already been visited by the Irish, was driven by storms to the coast of Iceland. This led to the first settlement of the Norwegians in Iceland in 875. From that time the Faroe Islands and Iceland may be regarded as intermediate stations and starting points for attempts to reach the northern shores of America. Greenland was early seen; but it was not until 983 that it was peopled from Iceland. Colonization was carried through Greenland in a south-western direction to the new continent, and for some length of time an inconsiderable intercourse was maintained with the newly colonized countries. But a strong line of separation must be drawn between this early discovery of some parts of the high northern latitudes of America, and the discovery of its tropical regions by Columbus in the close of the fifteenth century. In consequence of the uncivilized condition of the people by whom the former discovery was made, as well as the nature of the countries to which it was limited, it produced no important or permanent results in relation either to commerce or science; the latter, on the other hand, has been attended with events of the utmost importance to mankind, as it has proved the opening of a new source of wealth, glory, and knowledge. The discovery of the new continent in the west, like the original discovery of its northern regions, may be said to be accidental, inasmuch as the object which Columbus had in view was to find a western passage to India. But the expedition under Columbus possessed this distinguishing feature, that it manifested the perfect character of being the following out of a plan sketched in accordance with the principles of science, and intelligently conducted to a successful issue. spacious inlet of Hudson's Bay. Two of them unfortunately perished in this enterprise. In the year 1501 Alvarez Cabral, a Portuguese navigator, destined for India, having stood out to sea in order to avoid the variable breezes and frequent calms which he was sure to meet with on the African coast, to his surprise, came upon the shores of an unknown country, the coast of Brazil, which he claimed for Portugal. Amerigo Vespucci, a Florentine gentleman, who had already sailed along a great part of Terra Firme and Guyana, now made two extensive voyages along the Brazilian coast. Soon after his return he drew up and transmitted to one of his countrymen an account of his adventures and discoveries, in which he insinuated that to him belonged the honour of having first discovered the continent in the New World. His performance, which was the first description published of the newly-discovered countries, circulated rapidly, was read with admiration, and became the means of procuring for its author the high honour of giving his name to the whole continent. Not many years elapsed before the conjecture of Columbus respecting the existence of an ocean beyond the continent which he had discovered was found to be true; and his favourite project of opening a passage to India by steering westward was actually accomplished. By crossing the narrow isthmus of Panama, Nunez Balbon reached the Pacific Ocean in the year 1513; and in 1521 Magellan discovered and sailed through the famous straits which bear his name. After twenty days occupied in navigating this dangerous channel, he beheld spread out before him the boundless expanse of the great Southern Ocean. Directing his course to the N.W., he continued his voyage for nearly four months without discovering land. From want of provisions and from sickness, he and his crew suffered dreadful distress. But when about to sink under their sufferings, they fell in with the Ladrones Islands, where they found refreshments in abundance. From these isles he proceeded on his voyage, and was not long of discovering the Philippines. Here, in an unfortunate quarrel with the natives, he was slain, with several of his principal officers. But his surviving companions, pursuing their voyage, and returning to Europe by the Cape of Good Hope, solved the great problem of the circumnavigation of the earth.

After the discovery of the Pacific Ocean by Balbon, the investigation of the western coasts of America went speedily forward. Expeditions were soon sent out both northward and southward; so that nearly a full view was obtained of the immense range of coast which the American continent presents to the Pacific Ocean, and at the same time of its great interior breadth.

On the other hand, discovery in the Eastern World was no less rapid. Within twenty years from the time that Gama reached India by the way of the Cape of Good Hope, all the coasts of Hindustan, those of Eastern Africa, of Arabia, and Persia, had been explored. Navigators had penetrated to Malacca and the Spice Islands. They had learned the existence of Siam and Pegu; and it was only the characteristic jealousy of the rulers of the Celestial Empire that prevented them from entering the ports of China.

The scientific geographer had now abundance of materials to arrange and digest into one systematic whole. He was now called upon to give such a delineation of the earth's surface as should connect together the ranges of eastern and western discovery, and should exhibit the true outline and relative positions of countries, as these had been demonstrated by the astronomer and navigator. The ancient system of geography, to which the Arabs seem closely to have adhered, was founded on the idea of the whole earth being surrounded by an ocean as by a great zone. This the Arabians characterized as the "Sea of Darkness," an appellation most usually given to the Atlantic; while the northern sea of Europe and Asia, as inspiring still more gloomy and mysterious ideas, was styled the "Sea of Pitchy Darkness." Such notions could not now keep possession of the human mind, though it was only by degrees that mankind could be expected to be enlightened by doctrines which were not only new, but seemed likewise to be contradicted by the evidence of sense. The fundamental principles of a systematic arrangement had, as we have already seen, been known from the time of Hipparchus, and had been reduced to practice by Ptolemy. But the want of astronomical observations, or even of accurate surveys, which navigators seldom furnished, and for which science had not indeed yet provided suitable instruments, placed it still beyond the resources of modern geography to give anything like a just representation of the two hemispheres. The Venetian geographers were the first who attempted a systematic arrangement of the immense regions recently discovered, adjusting them to each other, and to the mass of information previously possessed. But a series of Venetian maps, preserved in the king's library, show how much their skill was counteracted by the difficulties with which they had to contend. Instead of exhibiting the vast ocean which separates the east coast of Asia from the west coast of America, the two continents are represented either as meeting, or as separated only by a narrow strait. The voyage of Magellan across the Southern Ocean had not shown with sufficient distinctness the presentation of the opposite coasts, to enable the geographers of the time to avoid this error. When maps of different dates are compared, we find, as we descend towards modern times, a gradual progress towards accuracy in the representations given of the earth's surface. This is what might be expected; for all maps should be considered as unfinished works, in which there will always be something to be corrected, or something new to be inserted.

At the period of the revival of letters in Europe, the latitudes and longitudes as given by Ptolemy were universally received with implicit confidence. When checked, however, by actual observation, they were found to differ materially from the truth. The latitudes in many instances were found very erroneous; that of Byzantium, for example, exceeded the truth by two degrees. As nearly the same excess was found to exist in some other cases, many geographers, unwilling to renounce the authority of Ptolemy, concluded that this difference had arisen from a change having taken place in the position of the earth's axis, in consequence of which the latitudes of all the places in Europe were increased. The progress of observation showed that this opinion was untenable, and that before geography could rest on a sure basis, a general revision of ancient graduation was indispensably necessary. The only observations employed by the ancients for determining longitudes were those of the eclipses of the moon; but it was found that the results derived from this source could not be depended on. In the year 1610, Galileo, having discovered three of Jupiter's satellites, pointed out the use which might be made of their eclipses for finding longitudes. But this method, which gives the greatest degree of accuracy, was turned to little account, until 1658, when Cassini published his tables of the revolutions and eclipses of these satellites. Three years afterwards, by means of simultaneous observations made by him and Picard at Paris, and by Tycho Brahe at Copenhagen, the difference of longitude of these two important points, which had been long a matter of dispute, was finally determined. Since that time, other accurate methods of finding the longitude have been discovered; and the instruments employed in observation have been brought to a high degree of perfection. The refinements and improvements of modern science have been brought to bear upon the great problem of determining the figure of the earth, which, though nearly, is not exactly spherical. (See Figure of the Earth.) The labours of scientific men to obtain accurate results on this subject, have contributed much to the improvement of geography. The expeditions sent out under Maupertuis to the arctic circle, and under Condamine to the equator, afforded an opportunity of making various observations of latitude and longitude in regions of which no delineation resting upon proper data had hitherto been given. Within the last fifty years, trigonometrical surveys of France and England have been executed, which have nearly completed the delineation of these countries.

Much advantage has accrued to geographical science, in point of accuracy and precision, from the application in modern times of a sound and judicious criticism to the immense mass of materials which had been accumulating for ages. The labours of M. d'Anville, in the eighteenth century, were employed with great success in this department. He undertook the revision of the whole system on which the delineation of the world, and of the countries into which it is divided, had hitherto been made; and by unhesitatingly rejecting every particular that did not rest on positive authority, he removed many false or uncertain features, and clearly distinguished the known from the unknown parts of the globe. Major Rennell has skilfully arranged and illustrated the important materials collected respecting India. Various authors have in modern times cultivated another interesting field of inquiry, the comparison between ancient and modern geography, and the tracing of the rise and progress of early discovery. These researches were diligently pursued by Vossius, Bochart, and other learned men of the seventeenth century, and with still more success by Rennell, Vincent, and Manbert, who appear to have pushed them as far as they admit; though much darkness still rests on some parts of the inquiry. Gosselin, notwithstanding that he has applied to the subject a great extent of investigation, as well as much skill and force of criticism, has failed, on account of the peculiar views in which he indulged, to make any solid addition to the science.

The discoveries made by the Spaniards and Portuguese had greatly increased the stock of geographical information. Still much remained to be done. The desire of finding a short and convenient route to India continued to supply a stimulus to exertion in the way of discovery. The English and Dutch made extraordinary efforts, and encountered fearful dangers and disasters, with the expectation of effecting a passage by the north-east, along the northern shores of Asia. A coast beset with the ices of the Polar Seas presented, however, obstacles too formidable to be overcome; though recent researches show that no barrier of land intervenes. But there was still another quarter where an attempt might be made; and to this point the commercial nations of Europe failed not to direct their efforts. The jealousy of Spain long prevented the other European states from visiting the north-western coast of America, so that they remained ignorant of the vast breadth to which the continent spreads out as it advances towards the north. They adopted, indeed, the opinion that, like the southern extremity, the northern terminated in a point or cape. This left room to hope for a north-western passage into the Pacific Ocean, by sailing round the imaginary cape. The English took the most decided lead in the exploratory voyages to which these views gave rise. In the reign of Queen Elizabeth, Frobisher and Davis were sent out on three successive voyages, which led to the discovery of the entrance into Hudson's Bay by the former navigator, and of the entrance into Baffin's Bay by the latter. These two capacious basins were afterwards discovered by the intrepid navigators whose names they bear. In sailing round the great sea which he had discovered, Baffin mistook the great opening into Lancaster Sound for a mere gulf; a misapprehension which checked for a time any further attempts in that quarter, as navigators were led to expect success only through the channel of Hudson's Bay. In 1631, Fox explored a part of that great opening on the north of Hudson's Bay, called Sir Thomas Roe's Welcome, which seemed now to hold out almost the only hope of accomplishing the object sought. The assertion of Middleton, an officer in the service of the Hudson's Bay Company, that he had discovered the head of the Welcome to be completely closed, and the circumstance of two other navigators, who were sent out the following year, failing to effect anything, produced an impression on the public mind that the passage so long sought had no existence.

The discoveries of Cook in the North Pacific Ocean, where he found the American coast stretching away in a north-western direction, joined to the circumstance that, when he penetrated through the strait discovered early in the last century by Behring and Tchirikof, which separates America from Asia, the coast appeared there to extend indefinitely to the north, seemed not only to confirm the conclusion that no passage into the North Pacific Ocean was here to be expected, but also that the American continent extended northward in one unbroken mass, perhaps even to the pole. The groundlessness of these views became apparent when, in the year 1771, Mr. Hearne, who had been despatched by the Hudson's Bay Company to explore the limits of the coast in this direction, sailed down the Copper-Mine River, and discovered its entrance into the sea; and again, when, in 1780, Sir Alexander Mackenzie traced also to the sea another river about twenty degrees farther to the west. Thus were there furnished strong grounds to believe that the pole was surrounded by an ocean which separated the northern coasts of Asia and America, making these two continents altogether distinct from each other; and that through this ocean lay the long-sought course which would certainly conduct the navigator who should succeed in forcing his way through the ice and storms of the polar regions, from the Atlantic into the North Pacific Ocean.

The determination of this great geographical question, so long agitated, has recently called forth the utmost efforts of the British government. In 1818 an expedition was sent out to Baffin's Bay under the command of Captain Ross, without leading to any important result, as he was led to conclude that no opening existed. Lancaster Sound had, however, forcibly attracted the attention of the late Sir Edward Parry, at that time lieutenant and second in command; and on returning with a new expedition under his immediate command, he succeeded in penetrating through Lancaster Sound, which he found gradually to widen till it opened into the Polar Sea. He found a chain of large islands to lie parallel to the American coast; and among these he continued his navigation until the accumulation of ice in the straits and channels through which he had to pass stopped his further progress. This circumstance induced him to make his next attempt through Hudson's Bay, by the channel of the Welcome, which had as yet been but imperfectly explored. Here he succeeded in reaching a point considerably beyond that at which Middleton had represented the bay as terminating. He found at length a narrow strait communicating with the Polar Sea, but so encumbered with ice as to preclude the hope of its ever affording an open passage. He was therefore again sent out to renew his efforts in the first direction, where he had already obtained partial success. But the obstacles which he had formerly been unable to overcome still continued, and prevented him from making any material addition to his former discoveries. Whilst these skilfully-conducted voyages were in progress, Sir John, then Captain Franklin, was sent out at the head of two successive expeditions by land, and, by actual survey, ascertained three-fourths of the boundary coast; his operations terminating at a point beyond the 149th degree of west longitude. On the other hand, an expedition under Captain Beechy, sent to meet Captain Franklin on his second toilsome journey, passed the Icy Cape of Cook, and pene- History. treated nearly as far as the 156th degree of west longitude, leaving only seven degrees, or 160 miles, between the farthest point thus reached and the utmost limit reached by Captain Franklin. The results of this investigation appeared to prove that the whole of the northern coast of America extends in a line not varying much from the parallel of the 70th degree of north latitude. The problem of a passage between the Atlantic and Pacific Oceans, to the north of the American continent, has now been finally solved; but this discovery, so well fitted in itself to afford satisfaction to the British nation, which has always taken the lead in such enterprises, has been made under circumstances of a very saddening kind. In 1845 Sir John Franklin and Captain Crozier were sent out on a voyage of discovery to the Arctic Seas. No tidings having been received of this expedition, it became, after two or three years, a subject of painful anxiety and suspense. Hence various expeditions were fitted out and sent in search of the missing voyagers, to succour them if still within reach of human aid, or, if otherwise, to ascertain their fate. In the course of these praiseworthy endeavours, Captain M'Clure was appointed to command the Investigator, under Captain Collinson of the Enterprise, and proceeded with that officer to Bering Straits in the early part of 1850. When on the eve of sailing, Captain M'Clure emphatically declared that he would find Sir John Franklin and Captain Crozier, or make the north-west passage. The latter part of this pledge he has, geographically speaking, redeemed; but the impenetrable mystery which from the first enveloped the fate of these gallant commanders remains the same.

Captain Collinson failed in his attempts to penetrate the pack ice that season, and so was separated from Captain M'Clure, who, notwithstanding a signal of recall from Captain Kellett of the Herald, the chief officer on that station, dashed onward with a bold determination to force a passage to the north-east—taking on himself all the responsibility of disobeying orders. Fortunately his daring has been crowned with success. He rounded Point Barrow on the 6th August 1850: continuing his course eastward along the coast, he reached Cape Parry on the 6th September, whence he steered through a channel called Prince of Wales Strait; which, running north-east, appeared a most promising course for reaching the sea south of Melville Island. Near the northern extremity of this strait, the Investigator was frozen in from the 8th of October, and remained stationary during the winter. Parties being sent out to explore, it was soon ascertained that the channel opened into Barrow's Strait; and thus was the existence of a north-west passage established. On the 14th July 1851 the Investigator was again fairly afloat, the ice having opened without any pressure. The great object now to be gained was to pass through the strait; but notwithstanding their utmost exertions, the expedition was completely arrested by strong north-east winds, driving great masses of ice to the southward. Thus baffled, Captain M'Clure resolved on running to the southward of the island, forming the western boundary of Prince of Wales Strait, which he had named Baring Island, and then to sail northward along its western side. This navigation, in which he was subjected to many delays and encountered many formidable obstacles, he accomplished, and succeeded in reaching the north side of the island on the 24th of September. Had open water existed to the east the rest of the passage might have been easily performed in this way, for Barrow's Strait lay before them, the navigation of which from their position to Lancaster Sound was known to be practicable. The hopes of this intrepid navigator were destined again to be disappointed. On the night of the above mentioned day the Investigator was frozen up, and at this point, in latitude 74° 6' N. and longitude 117° 54' W., they had their winter quarters in 1851, 1852, 1853. In April 1852 a party crossed the ice to Melville Island, and de-

posed there a document giving an account of their proceedings, and of the position of the Investigator. This document was happily discovered by the officers of Captain Kellett, who had been the last person with whom Captain M'Clure held communication when he entered the ice on the west, and was now, singularly enough, the person to rescue him at the expiration of three years on the side of Melville Island on the east. Steps were immediately taken to communicate with the party in their ice-prison, Lieutenant Pim being appointed by Captain Kellett to the service. Eventually it was found necessary that Captain M'Clure and his gallant companions should abandon their ship, however unwillingly; so that the navigation of the north-west passage has not yet been accomplished.

The discovery of a new continent greatly enlarged, as we have seen, the views of mankind respecting the constitution of the globe. But imagination, no longer limited in its range by the notion of a circumambient ocean that could not be passed, soon gave rise to the belief of a southern continent, which was supposed necessary to balance the land in the northern regions of the earth. The immense body of water that was found to occupy so large a portion of the known regions of the southern hemisphere gave ample room for supposing this unknown continent to be of vast dimensions. It was imagined that it might equal in extent as well as in wealth the American continent. Nor was it considered necessary to exclude it from the map of the world till its existence should be proved. It appears in all the early maps as an immense mass of land surrounding the south pole, and presenting to the ocean one unbroken coast. The discovery of certain great insular tracts in the South Seas, which, from ignorance of their true nature, navigators might mistake for continental promontories or portions of coast, no doubt at first gave some countenance to the belief of the existence of antarctic land. But the delusion was gradually dispelled before the light afforded by further discovery. The Portuguese, in less than twenty years after their passage of the Cape of Good Hope, pushed their researches to the most remote islands in the Indian Ocean, including Java and the Moluccas. They appear also to have observed some part of the coast of New Guinea. The Spaniards during their early and adventurous career put forth strenuous exertions to explore the Southern Ocean, and several of the groups of islands scattered over its surface were discovered by their navigators. In 1607, the Dutch having wrested from the Portuguese Java and the Spice Islands, established in them the centre of their Indian dominion. A great maritime power being thus placed so near to the northern shores of the largest portion of land on the globe that is regarded as an island, it became almost impossible that New Holland could long remain unknown. It was discovered early in the seventeenth century, and was long supposed to form a part of the great southern continent. Van Diemen, the Dutch governor of India, sent out several vessels successively to explore its coasts. Hertog, Carpenter, Nuytz, and Ulaming made very extensive observations on the northern and western shores, but found them so dreary and uniniting that no settlement was attempted. In the year 1642 Abel Jansen Tasman was commissioned to proceed on a voyage to ascertain its extent. On the 14th August he sailed from Batavia, directing his course first towards the Isle of France. He again set sail on the 3rd October, and proceeding southward and eastward, beyond the limits reached by his predecessors, he discovered and doubled the southern extremity of Van Diemen's Land, to which he gave its name; but he failed to discover that it is a separate island. Pursuing afterwards his course eastward, having reached about 42° 10' S. Lat. and 170° E. Long., he found himself in view of a high and mountainous country, which he named Staaten Land, but which is now known as New Zealand. He sailed along the coast towards the north-east, and after being detained by the variability of the weather, he resumed his voyage and returned home by the Friendly Islands, discovering many islands in his progress. He arrived at Batavia on 15th June 1648. Tasman's voyage proved that New Holland was no part of the southern continent, even if such a continent should be found to exist. Cook, who had been appointed in 1767 to conduct a voyage into the South Pacific Ocean for astronomical and geographical purposes, sailed southward in 1769 in quest of the unknown continent. Lofty mountains were seen on the 6th October, and it was supposed that the object of their search was found. But the land proved to be New Zealand. This land he circumnavigated, and found that it consisted of two large islands separated by a narrow channel. After six months employed in this manner, he directed his course westward, and reached the eastern side of New Holland early in 1770. By his extensive operations in that quarter—having run down the coast from latitude 38° to its northern extremity at Torres Strait—he left little more to be done there in the way of discovery. Passing between New Holland and New Guinea, he continued his voyage by Timor and the south coast of Java to Batavia; whence, after repairing the ship, he sailed for England, and reached the Downs on the 12th June 1771, with his crew weakened and reduced in number by the fatigue and hardships of their long voyage. By this voyage it was proved there was no such continent as that supposed to exist to the northward of 40° south latitude. But as many ingenious and well-informed men still adhered to the opinion that there did exist a southern continent, government determined to send out a second expedition under Cook, to make such an exploration of the Pacific Ocean in the higher southern latitudes as should finally and satisfactorily settle this much-agitated question. Cook was instructed to circumnavigate the globe in high latitudes, prosecuting his researches as near to the South Pole as possible, and to traverse every part of the Southern Ocean where the supposed continent could possibly lie. The expedition sailed from Plymouth 13th July 1772, and quitted the Cape of Good Hope 22nd November. Pursuing his course eastward, Cook, during three years, employed the summer months in those regions (corresponding to our winter months) in navigating high latitudes towards the South Pole, and the winter months in adding to his discoveries in the South Pacific Ocean. Notwithstanding, however, that he varied his course, and traversed in every direction which he thought afforded the slightest likelihood of finding land, and actually got so far south as 71°10' of latitude, he was unsuccessful. Having thus scrupulously and completely accomplished the object for which he was sent out, he directed his course homeward. He had encompassed the globe in high latitudes, and was led to conclude that the Southern Pole is surrounded only by isles and firm fields of ice, so that the hypothesis of an austral continent had no foundation. He reached the Cape of Good Hope 22nd March 1775, and anchored at Spithead on the 30th July, having, in the space of three years and eighteen days, sailed 20,000 leagues, mostly in inhospitable climates and unknown seas. In the course of this and his former voyage the same great navigator secured glory to his country and to himself by likewise completing the survey of the Great Pacific Ocean. Some of the interesting groups of islands scattered over its vast surface had already been made known by the previous voyages of Byron, Wallis, and Carteret. Cook fully traced the great chain of the Society Islands and the Friendly Islands. He determined also the form and relations, not only of New Zealand, but of New Caledonia and other lands and islands in that region of the globe.

The extensive island of New Holland has recently become doubly interesting from the important relations which now subsist between it and Europe. In the year 1788 the establishment of a British colony on the east coast paved the way for a more complete survey. By the different expeditions undertaken from 1795 to 1799, chiefly under the direction of Bass and Flinders, the east coast, together with Van Diemen's Land and Bass's Strait, which separates that island from New Holland, were accurately explored. In 1801 an expedition was sent out by the British government under the command of Captain Flinders, for the purpose of surveying a large portion of the coast. These surveys were prosecuted with unremitting ardour and perseverance. At the same time that Captain Flinders was carrying on his survey, the French captain Baudin was employed on the same service, and in some parts the discoveries of these navigators intermingle. Some additional observations have more recently been made; and by these various expeditions the whole coast of New Holland and Van Diemen's Land has been accurately surveyed, the position of every point has been ascertained, and every inlet and bay has been traced to its termination.

The strong presumption which the researches of Captain Cook in the Southern Ocean furnished of the non-existence of an austral continent, seemed to leave no room to expect that any further doubt would be entertained on the subject. Lieutenant C. Wilkes, commander of the expedition fitted out in 1838 by the government of the United States, for the exploration of the antarctic regions, has, however, claimed for his country and for himself the honour of at length discovering a continent within the antarctic circle. While this claim is pertinaciously adhered to, no distinct and unequivocal proof is produced that the continent alleged to have been seen by the American Expedition has a substantial existence. No continent or island was landed on; and, on the other hand, there is no doubt that the British Expedition under the command of Sir James C. Ross sailed over the very spot in south latitude 66°, and east longitude 163°–166°, where Lieutenant Wilkes supposed he saw mountainous land. This latter expedition was fitted out by the British government for scientific purposes in 1839, and arrived in Van Diemen's Land in August 1840. The French government had likewise sent an expedition into the southern seas, under the command of Captain Dumont d'Urville, about the same time. To avoid interference with the French and American discoveries, Sir James Ross determined on a more easterly meridian—that of 170° E.,—in which to endeavour to penetrate to the southward. The expedition sailed from Hobart Town on 13th November 1840, and on 27th December encountered a chain of icebergs. On the 5th January 1841 they entered the pack-ice, through which having forced their way, the ice having at the same time somewhat slackened, they found themselves on the 7th January again in a clear sea. Soon after 2 o'clock A.M. of the 11th January they discovered land, which, as they advanced southward, was found to extend continuously from the 70th to the 79th degree, with several adjacent islands. This land they called Victoria Land. It presented to their view ranges of mountains whose lofty peaks, covered with eternal snow, rose to elevations from seven to ten or even twelve thousand feet above the level of the ocean. The intervening valleys were filled with glaciers, which, descending from near the mountains' summits, projected in many places several miles into the sea, and terminated in perpendicular cliffs. The rocks breaking through in a few places their covering, afforded the only indication that land formed the nucleus of this, to appearance, enormous iceberg. On the 28th January, when they had nearly reached their highest latitude, about 78° S., they found that what appeared when first seen at a distance to be a high island, was a mountain 12,367 feet in height, emitting flames and smoke in great profusion. This volcano lies in latitude about 77° S., and in longitude about 167° E. From the most eastern point of land at a cape not far from the foot of this mountain, an icy barrier was found to extend eastward as far as the eye could discern. This barrier was a perpendicular wall of ice from 150 to 200 feet in height, and stretched 250 miles in one unbroken line, as was found on a second visit to the same interesting locality in February 1842; nor were they able to turn its extremity, so as to reach a higher latitude. At a point where the height of the barrier diminished to about 80 feet, they perceived from the mast-heads that it gradually rose to the southward, presenting the appearance of very lofty mountains perfectly covered with snow, but with a varied and undulating surface. And hence Sir James Ross, with nearly all his companions, felt assured that the presence of land there amounts almost to a certainty. Still, Sir James is of opinion that the recent discoveries in the antarctic regions made by the French and American navigators, and by himself, do not prove the existence of a great southern continent, but rather of a chain of islands.

In tracing the history of geographical discovery, it cannot fail to be observed that while discovery by sea admits of being pursued with great advantage, on account of the rapidity of its progress and the extent of its range, it does not supersede the slower and more confined operations of the discoverer by land, which are no less necessary to make known the interior features and circumstances of the different countries.

The British dominion in India has led to much additional information respecting the interior of Asia; information which is, however, in many respects, only the revival of ancient knowledge. The great mountainous chain which forms the northern boundary of India has been traced and found in many places to tower to such heights as to exceed the Andes, long supposed to be the highest mountains in the world. The source of the Ganges, and that of the Indus, with the early courses of these great rivers, have been found to be situated quite differently from what had been supposed to be their position by modern geographers. The mountainous territories of Cabul and Cashmere, the high interior tableland of Thibet, and the vast sandy plains of Meckran, have all been more or less explored. Information of an authentic character has also been recently obtained respecting the formerly celebrated capitals, Bochara and Samarkand. But a wide field still remains for future research.

The continent of Africa, however, is the quarter of the globe which, more than any other, has baffled the efforts of those who would explore its interior. The vast sandy deserts, high mountains, and impenetrable forests which occur on its surface, joined with the unremitting wars carried on between the petty tribes, as well as the deeply-rooted antipathy of the African Mohammedans towards the Franks, have presented obstacles of the most formidable kind. The ancients, whose knowledge of the African coasts was very imperfect, except where they border on the Mediterranean and the Red Sea, were accustomed to penetrate into the inland provinces, and are said to have been acquainted with many parts of it which are now altogether unknown. At an early period of modern history, reports that Prester John, the Christian prince, who had been sought for in vain in the East, was to be found in the interior of Africa, induced the Portuguese to explore Abyssinia; but the accounts which they gave of the extent of that country were greatly exaggerated. From the western coast they despatched embassies into the interior in quest of the object of their search; and on one occasion they appear to have reached the city of Timbuctoo, and to have obtained at Benin some information concerning the great interior kingdom of Ghana. The maritime nations of south-western Europe early formed settlements on the west coast of Africa, and, for commercial purposes, were naturally prompted to seek a knowledge of the neighbouring nations. But it was not until the formation of the African association in 1788 that any well-sustained efforts were made in the prosecution of discovery in the interior. There were two objects connected with the interior of Africa which had for a long time fixed the attention and awakened the curiosity of the nations of Europe. These were the city of Timbuctoo and the great central river, the Niger. Timbuctoo has been for many centuries the grand emporium of the central trade of Africa, and hence there has prevailed throughout Europe, ever since the rise of discovery and commercial enterprise, a strong desire to visit it, and to establish with it a friendly intercourse. The discovery of the course and mouth of the Niger has now opened up to commercial speculation what it is hoped will give a ready access to Timbuctoo as well as other places of traffic. The interest with which, in a geographical point of view, however, the Niger has been regarded, has arisen from the remarkable nature of the regions through which it flows, and still more from our ignorance, combined with the various and contradictory rumours which were so long abroad, respecting its course and termination. Herodotus is the earliest author who affords any ideas applicable to this subject. He mentions an expedition into the interior of Africa, undertaken by some Nasamonian youths, who, being made prisoners, were carried to a great city inhabited by negroes, and situated on the banks of a river which flowed from west to east. This stream he conjectures to be the remote source of the Nile, but the particulars given appear to leave little doubt that it was the Niger. A similar hypothesis was adopted by Strabo, Mela, and Pliny, identifying the waters of these two great rivers. But Ptolemy, whose residence in Alexandria afforded him ample means of information, rejects altogether the idea of any communication between them. He describes the Niger as terminated on the west by Mount Mandrus (Mandingo), and as giving rise to several extensive lakes as it proceeds in its course. His statements do not, however, involve anything positive as to the direction in which it flows. The Saracens or Arabians are the next great source of information; for, in the course of the dissensions which took place among their dynasties in Northern Africa, large bodies crossed the desert and founded kingdoms on the eastern part of the shore of the Niger, of which the kingdom of Ghana was the most splendid. According to their testimony, the Niger flows from east to west, and discharges itself into the sea, by which they understood the Atlantic, or great circumambient ocean. With regard to its source, they generally regarded it as the same with that of the Egyptian Nile, identifying the two rivers in the early part of their course. Some were of opinion that the waters of the Niger did not reach the sea; so that they must have supposed them to be discharged into a lake. The system adopted by modern Europeans was derived from Leo Africanus, who retained the delineations of the Niger as flowing from east to west, and falling into the ocean; but, instead of deriving it from the Nile, supposed it to rise from a lake lying deep in the interior of Africa. Following this hypothesis, all the early European navigators, when they saw the two broad estuaries of the Senegal and Gambia, concluded that one or both gave egress to the waters of the Niger. In the beginning of the seventeenth century, the French and English, having each formed a settlement, the one on the Senegal and the other on the Gambia, were induced by the hope of gain to seek a route up these rivers to the city of Timbuctoo; and in this enterprise they proved the falsity of the opinion which had been so long held. The streams were traced so near to their source as to become little more than rivulets; whilst the explorers were still far from the great central emporium of Africa, and from the great plain through which the Niger was understood to flow. This result led the two great French geographers, Delisle and D'Anville, to construct maps in which the Niger, after the lapse of so many ages, was again represented as flowing to the eastward. Instead of a single stream pursuing a course across the whole breadth of Africa and falling into the Atlantic, D'Anville distinguished three rivers—the Senegal, flowing westward; the Niger, flowing eastward into a lake in Wangara; and another river still farther east, and flowing in the opposite direction. The data on which this scheme rests were never fully made public.

Still new doubt was thrown around this subject by the reports collected by Mr Lucas, who travelled under the auspices of the African Association, and who was assured at Tripoli, by a native merchant, that the river flowed with rapidity in a westerly direction. The time, however, at last arrived, when these conflicting opinions were to be silenced, and when new light was to be thrown on the subject, by the labours of our illustrious modern traveller, Mr Mungo Park. In his first expedition, in 1795–96, he proceeded from the west coast in the direction of the river Gambia, until at Medina he left it, and turned to the north. Having passed through the kingdoms of Bondou, Kasson, and Kaarta, he reached Sego, the capital of Bambarra, where he beheld "the long-sought majestic Niger glittering in the morning sun, as broad as the Thames at Windsor, and flowing slowly to the eastward," directing its course into the depths of the interior of Africa. This stream, he found, was called by the natives the Joliba, or Great Water. Park advanced beyond this point to another town called Silla on the same river, and acquired also some valuable information respecting the further course of the stream which was the object of his research, as well as respecting the position of Timbuctoo, which he was told was not more than 200 miles from Silla. Following upwards the course of the Joliba until he reached Bammakoo, which was stated to be about ten days' journey from its source, he returned to the Gambia by a more southerly tract. In 1805 this adventurous traveller was sent out at the public expense on his second expedition. After reaching Silla, he embarked at a place in its neighbourhood on the Joliba or Niger, with the determination of sailing down the stream until he should reach its mouth, whithersoever its course might conduct him. He is ascertained to have passed successively the cities of Jenné, Timbuctoo, Yaour or Yaouri, and to have reached Boussa, a short distance farther down, where he was killed. No part of his journal, however, after he embarked on the river, has been recovered. In the meantime, a strong and general interest being now excited in reference to African geography, information flowed in from various sources respecting the regions in the interior, as well as some parts nearer the coast. Many particulars became known concerning the countries to the east of Timbuctoo, especially the kingdom of Bornou, then the most powerful state of Central Africa. The knowledge possessed of the people of the interior was also considerably increased. These circumstances prepared the way for a more successful attempt than any hitherto made to explore the interior of Africa, when Major Denham and Lieutenant Clapperton were sent out in 1822. Setting out from Tripoli with a caravan of Arab merchants, these travellers crossed the desert, and reached the great inland sea or lake called Tchad, which is the receptacle of immense volumes of water collected from the most distant recesses of inner Africa. Major Denham examined the coasts of this lake to the east and south; while Lieutenant Clapperton directed his researches westward, through the kingdom of Bornou and the country of the Fellatahs, until he arrived at Sackatoo, situated on a stream which probably flows into the Joliba. In the course of this journey Clapperton obtained a great mass of information concerning those hitherto unvisited regions which lie eastward of Timbuctoo; but with regard to the course of the unexplored part of the river Niger (or Quorra, as it was called at Sackatoo), he heard little that could be depended upon. Having returned to England, he was again sent out by the government in command of a new expedition, with instructions that he should endeavour to penetrate to the scene of his former adventures from the coast of Guinea. In the execution of this plan of research he reached the Niger at Boussa, where Park perished; and, after traversing some of the adjoining regions on the farther side of the river, as far as the great commercial city of Kano, the capital of Houssa, where he had been in his former journey, he turned again to the west, and having reached Sackatoo, there died. His servant, Richard Lander, with a praiseworthy zeal, embarked on one of the branches of the Niger for the purpose of finally determining, if possible, its termination by sailing down the stream; but he was stopped by the natives, and compelled to turn back. The city of Timbuctoo was in the meanwhile reached by Major Laing, who succeeded, in August 1826, in making his way thither across the desert from Tripoli. In this famous city he spent some weeks, but was murdered in the desert on his return; nor did the results of his inquiries and observations ever reach Europe. Such are the formidable difficulties and dangers which have hitherto encompassed the path of discovery in the interior of Africa. Still, by renewed efforts, the object of research has been gained. The grand question of the termination of the Joliba, Quorra, or Niger, has at length been fully resolved—a discovery which is the result of the fortunate and well-conducted enterprise on which Richard Lander and his brother were sent out in 1830. Having followed nearly the same route which had been taken by Clapperton in his second journey, these two travellers reached Boussa on the 17th June. They first ascended the river as far as Yaouri, and then returned to Boussa. After remaining there for some time, they embarked on the river to follow the stream in its course downward, hoping that it would conduct them to the sea. In this expectation they were not disappointed; for they reached the Bight of Benin by the larger branch, which is there called the river Nun. There is another great branch a little farther to the south; and by these two outlets, with several smaller channels, the river known in Europe by the name of Niger discharges its waters into the Atlantic.

The zeal for discovery in Africa, which has been so active during the last sixty years, has sent forth a succession of travellers (missionaries and others) to explore the southern regions of that vast continent. We can mention briefly only the most remarkable results of their researches.

It is now (1855) about six years since intelligence was received in Europe of the discovery of snowy mountains in Eastern Africa. The discovery was in itself so remarkable, that the report was not at first universally credited. It was, however, subsequently confirmed. The mountains in question are Kilimanjaro, in about latitude 3° S. and longitude 37° E.; and Kenia, in about latitude 1° S., and longitude 38½° E. They were discovered by the missionaries Rebbmann and Krapf, stationed near Mombasa. Kilimanjaro is an isolated and very conspicuous peak, probably connected on its western side with the tableland of inner Africa. The missionaries have become acquainted with its eastern, southern, and northern aspects; but Mount Kenia has been seen only from the south, at a distance of six days' journey, or about 80 geographical miles.

Another important discovery made in the interior of Africa within the same time is that of Lake NGami, by the missionary the Rev. Dr Livingston, accompanied by Mr Oswell and Mr Murray. It seems to be situated about 19° south latitude—about 560 miles N.N.W. of Kolobeng, the scene of Dr Livingston's missionary labours, and the headquarters of the Baquain tribe. These and other explorers have made us in some measure acquainted with an extensive system of rivers, between 10° and 22° south lati- An important expedition to Central Africa, headed by Mr James Richardson, left Tripoli in March 1850. It was sent out under the orders and at the expense of the British government. The object of this mission was to survey Lake Tchad, and to explore the neighbouring countries. The scientific interests of the expedition were entrusted to two German gentlemen, Dr Barth and Dr Overweg. Instead of travelling from Tripoli across the desert with the great caravan, the mission formed a small caravan of its own, amounting to about one hundred persons and as many camels. The journey from Tripoli to Murzuk and thence to Ghat is less interesting than that from the latter place, where they entered on entirely new ground. But even in the former part of the march many important discoveries were made, as the travellers selected new routes not before explored, and thus rendered every part of the journey subservient to the purposes of the mission. At Ghat their personal danger was increased to such a degree that they found it necessary to trust for protection to the friendship of the sultan of the Kelois, in whose country they were detained about three months, during which time Dr Barth made an interesting journey to Agadez, while much valuable information was also collected by Mr Richardson and by Dr Overweg who had remained. At the close of 1850 the party reached Zinder, where the three travellers separated, each proceeding with his followers by another route. Mr Richardson took the direct way to Kuka, not far from the shores of Lake Tchad, and the capital of the empire of Bornou. At Kuka all the three hoped again to meet very soon afterwards, but this hope was disappointed. Mr Richardson was of a weak constitution, yet his health appeared to suffer little from the fatigue of crossing the desert; but he sunk before he reached Lake Tchad, which was the termination of his mission, and from which he was to return by direct road to Tripoli. He died in the country of Bornou at Ungurutua, a place six days' journey from Kuka, during the night intervening between the 3d and the 4th of March 1851. Thus was added another name to the large number of those who have fallen a sacrifice to the cause of African discovery.

The two surviving travellers, undaunted by the prospect of danger, proposed as the plan of their operations to approach the Upper Nile, as soon as they had explored the vicinity of Lake Tchad,—provided they were supported by the British and Prussian governments; and to be ready even to pursue their researches from Kuka to the Indian Ocean. The route in a straight line to Mombas lies nearly south-east; but from all they could learn, the route more to the south, in the direction of Lake Nyasa, seemed more practicable. The gigantic journey which they thus contemplated lay through many powerful kingdoms, densely peopled, intersected by numerous rivers, very fertile, and abounding in forests, but where the most formidable obstacles were to be expected from the warlike dispositions of the surrounding nations.

In the meantime they prosecuted with zeal the immediate objects of the mission, embracing every opportunity of collecting information. On the 29th May 1851, Dr Barth started from Kuka to visit the kingdom of Adamana, which, from the accounts he had received, he judged to be the most beautiful country of Central Africa. He reached Yola, the capital, on the 22d June, where he was permitted to remain only three days. He was kindly received, however, both by the sultan and by the inhabitants, and at his departure was treated with consideration and honour. Four days' journey before reaching Yola, he had to cross at the point of their junction the two principal rivers of Adamana, the Benueh and the Faro, the latter being a tributary of the former. The Benueh he describes as the largest and most imposing stream which he had seen since leaving Europe. He found it half a mile broad and about ten feet deep. The distance of the source from the point at which he crossed it was said to be nine days' journey. This magnificent river is in fact the upper course of the Tchadda, which itself falls into the Quorra or Niger, not far from its mouth. The discovery thus made of the identity of the two streams, the Benueh and the Tchadda, has opened up a way of access to the very heart of inner Africa which seems destined eventually to become the line from the west along which the blessings of commerce and civilization are to flow to the surrounding nations. The consideration of the immense importance of following up this discovery, and of the advantages which might be expected to accrue from it, suggested the idea of sending out a steamboat expedition from England to ascend the Tchadda. Former attempts to reach Central Africa by ascending the Quorra had been attended with very disastrous consequences. But the expedition which left the British shores in May 1854 to ascend the Tchadda was eminently successful, while not a single life was lost. It reached the mouth of the Quorra in the beginning of July, and, entering the Tchadda, ascended the stream to within about 50 miles of the confluence of the Benueh and the Faro. Thus it has been fully proved that this important river is navigable to Yola, the capital of Adamana.

While Dr Barth was prosecuting this journey his fellow-traveller was employed in surveying Lake Tchad. This lake is described as an immense marsh, the only portion fit for navigation being a deep channel formed by the river Shary, which pours into the lake a vast volume of water. What Major Denham has described as small islands were found to be extensive meadow-lands of much greater surface than the lake itself. The explorations of Dr Overweg led to results considerably at variance with what had been reported by Denham; but the discrepancies are perhaps more apparent than real, and may find their explanation in the fact that the lake is augmented during the rainy season to an immense body of water; but during the season of drought is so much reduced by evaporation as to appear at times to be almost dried up.

In the course of the summer of 1852, Dr Barth, setting out from Kuka, made a journey in a south-easterly direction towards the Nile; and so near did he approach to the eastern boundary of the basin of that great river that he was able to collect information likely to throw light on some intricate questions connected with it. He succeeded also in exploring a portion of Bagirmi, a powerful kingdom between Lake Tchad and the Upper Nile, which had never before been visited by any European. In uniting, by means of his itineraries, Bagirmi with Dar Fór, he has completed a line of direct route across Central Africa from the Quorra to the Nile; and thus from the Gulf of Guinea to the Red Sea and the Indian Ocean.

Dr Overweg left Kuka at the same time with Dr Barth, but took a south-westerly direction towards the Quorra. Between the end of March, the time of his setting out, and the end of May when he returned, he successfully performed an important journey, which brought him within 150 English miles of Yacoba, the great town of the Fellatahs. Dr Barth's journey occupied a considerably longer time; and it appears that Dr Overweg's anxiety to await the return of his companion, which was not until the 20th August, induced him to remain at Kuka, notwithstanding the danger to be apprehended from too long exposure to the influence of the unhealthy season. The consequence was, that though he set out, immediately after Dr Barth's arrival, on an excurs- sion to healthier regions, yet the advantage derived proved only temporary. He died on the 27th September 1852 at Madiai, about ten miles east of Kuka, and near Lake Tchad.

As it was known that the travellers had expected to be ready to start from Kuka towards the Indian Ocean in August or September 1853, it was intended by their friends in England, that before they left Kuka they should be joined by an additional fellow-labourer to take a part in their arduous undertaking. Dr Vogel, an astronomer and botanist, was accordingly sent out, accompanied by two chosen volunteers from the corps of the Sappers and Miners. By a singular coincidence, on the very morning on which Dr Vogel and his companions went on board the vessel which was to take them to Malta on their way to Tripoli, letters from Dr Barth were received in London announcing the death of Dr Overweg.

Though now left alone, as being the only surviving member of the mission, Dr Barth continued to prosecute with zeal the work in which he was engaged. Up to the 23rd November 1852 he was still at Kuka; but he had fixed on the 25th of the same month to leave that place, and to enter on his journey to Timbuctoo. All his journals and papers, arranged and completed up to that date, he intended to forward to Tripoli, there to be deposited with the English consul. By the beginning of March 1853 he had performed more than one-third part of his journey, and had reached the capital of the territories of the Fellatahs, whose friendship and assistance he had secured. After being subjected to the disappointments and delays incident to the traveller in that part of the world, he reached at length the termination of his perilous journey. During his stay at Timbuctoo his life was exposed to great danger, from the influence of unfavourable climate, and much more so from the hostile disposition towards Christians of the most fanatical Mohammedan population of Northern Africa. He thus describes his distressing situation during his sojourn in that magnificent city,—the "Queen of the Desert," as it is justly called by the natives:—"Like a helpless vessel on the ocean waves am I thrown about on a sea of uncertainty between the power and passion of contending parties. Every day brings something new,—now of a satisfactory kind, then again of the reverse. Death, captivity, safe return home, are my visions by turns, and it is yet impossible to say which shall be my fate." To have left Timbuctoo without sufficient protection, would have been to expose himself to certain death. Hence his stay in this place of danger was unavoidably protracted to nearly a year, when he was at last succoured by Anah, the chief of a Tuareg tribe inhabiting the regions east of Timbuctoo, along the Quorra, who came with an escort of a hundred horsemen, and conducted him in safety through his dominions on his way back to Sackatoo.

The news of Dr Vogel having been despatched from Europe to join him had reached Timbuctoo before Dr Barth left that place. On the 1st December 1854 he had the inexpressible pleasure of meeting him at Bundi, a small town situated at about 200 geographical miles due west of Kuka. Once more he looked on the face of a European—his countryman—and grasped the hand of a friend in whom he could place implicit confidence. Exactly six years had elapsed since he left Europe, in company with Mr Richardson and Dr Overweg. Since the decease of the latter he had been isolated from civilized society, and had been left to contend single-handed with manifold hardships and dangers. To revisit Europe he now considered as indispensable for the preservation of life and health; and accordingly he moved on to Kuka, whence he intended to proceed homeward without further delay. We are happy to say that he arrived at Marseilles early in September 1855.

The limits of the great unexplored region of Africa may be roughly indicated as extending between the parallels of 10° north and south of the equator, and from Adamana in the west to the Somali country in the east. This extensive region has just been touched by the routes of recent travellers. But in all parts of the habitable globe the spirit of research, which has already done so much, is still active; nor is it directed only to the determining of the outlines of continents and countries, or to the marking of the leading features of mountains, rivers and cities, with their relative positions and distances. These are regarded by the geographical inquirer merely as affording a proper basis on which to rest the description of the earth considered as the habitation of man, and as affording him ample the means of improvement and happiness. The picture can be completed only by the continued labours of the scientific observer, who makes the earth, with its various productions, whether natural or artificial, the treasures hid in its bosom, the animals found upon its surface, and, above all, the human beings who people its different regions (and these in all their mutual bearings and relations), the objects of attentive examination and study.

II.—MATHEMATICAL GEOGRAPHY.

CHAP. I.—PRINCIPLES AND DEFINITIONS: OF THE TERRESTRIAL SPHERE.

We have already stated that mathematical geography treats of the figure, magnitude, and motion of the earth; its relations to the other bodies of the system to which it belongs; the relative positions of places on its surface, and the methods of delineating the whole or any part of its surface. Several of these topics belong as much to astronomy as to geography; for the former science regards the earth, on the one hand, as the grand observatory whence the phenomena of the heavens are contemplated by man; and, on the other hand, as itself constituting a portion of the planetary system, the laws of which it is the object of the astronomer to investigate and explain. It is only, indeed, by celestial observation that the position of a point on the surface of the earth can be accurately determined; so that the first principles of geographical science must necessarily be drawn from astronomy.

We take for granted, then, the doctrine of the celestial sphere; the globular form, the magnitude and motion of the earth, with the phenomena arising out of and depending upon its motion. These points are fully discussed in the article ASTRONOMY, part ii. It will be necessary, however, for the sake of distinctness, to state briefly such of the results derived from the reasoning there employed as belong specially to the subject of this article.

The doctrine of the earth's rotundity is that with which the student of geography must first make his mind familiar. To the eye the earth appears a circular plane, at the centre of which the spectator imagines himself placed; whilst the heavens, spread over his head like a magnificent canopy, seem to meet the earth all round in a circle which bounds the view. The space comprehended within this circle is found to present often a very irregular surface, rising into mountains, or sinking into cavities, so as apparently to exclude the idea of its bearing any resemblance to a portion of a globe or sphere. This is, however, nearly its true figure. Were we placed at such a distance from the earth that the eye would be able to take in at one glance the vast mass in its full dimensions, it would present the appearance of a circular disc, of greater or less diameter according to our distance. If viewed on all sides, its circular form would remain unchanged; a property characteristic of no other body but a globe or sphere. The highest mountains would be found to bear so little proportion to the whole bulk, as to cause no perceptible deviation from the globular form; and the same thing may be said of the difference which exists between the polar and equatorial diameters, though that quantity amounts to about twenty-eight miles.

The portion of the earth, then, seen from any point above its surface, is to be regarded as the segment of a sphere, which, increases in extent according as the eye is more elevated. When the semidiameter of the earth, and the height of the eye above the surface are known, it is easy to find the diameter of the circle which bounds our view on the earth; supposing, as is the case at sea, that no object intervenes to obstruct our vision. Thus, let \( AB \) be the height of a mountain on the earth's surface. From \( A \) draw the line \( AD \), a tangent to the surface in any direction; \( D \) will be the most distant point seen by a spectator whose eye is placed at \( A \), the summit of the mountain. If the line \( AD \) be supposed to be carried round the point \( A \), while it at the same time continues to be a tangent to the surface, until having passed through every possible position, it returns to that from which it set out, the point \( D \) will trace the circumference of the circle which bounds the terrestrial view, and of which the radius will not differ much from \( AD \). Now \( AD \) being a tangent to the arc \( BD \), we have \( AD^2 = (2BC + AB) \times AB = 2BC \times AB \) nearly, since \( AB \) must always be very small compared with \( 2BC \), the diameter of the earth. Assuming the diameter equal to 7912 English miles, we have \( AD^2 = 7912 \times AB \); or, if \( AB \) is expressed in feet, \( AD^2 = \frac{7912}{5280} \times AB \), in miles. Hence we obtain

\[ AD = 1:224126 \sqrt{AB}. \]

The result obtained from this formula will deviate from the truth in consequence of the effect of refraction; which, at a medium, may be considered as increasing the distance by about \( \frac{1}{100} \), or '0714 of the whole. Applying this correction to the above formula, it becomes

\[ AD = 1:3115 \sqrt{AB}. \]

For example, if the Peak of Teneriffe is 12,358 English feet in height, then \( AD = 1:3115 \sqrt{12358} = 145:8 \) miles is the radius of the circle which bounds the view from that elevation.

The circle bounding terrestrial vision, which we have now been considering, does not, except when the eye is close to the surface of the earth, coincide with the sensible horizon as determined by a plane passing through the eye along the line \( HO \) and perpendicular to the vertical line \( CZ \). The angle contained between the visual ray \( AD \) and the horizontal plane is called the dip of the horizon. For ordinary purposes, however, it is sufficiently accurate to say that the sensible horizon is the circle which bounds the view, where the heavens and the earth appear to meet. To this circle the rational horizon is parallel, being determined by a plane passing through the centre of the earth perpendicular to the vertical line \( CZ \), and continued in every direction to the sphere of the heavens.

Let \( NESQ \) be the terrestrial sphere, of which \( C \) is the centre; and let \( HO \) be the rational horizon of the point \( M \). The rotatory motion of the earth determines the position of the line \( NS \) on which it revolves, and which is called its axis. The two points \( N, S \), in which the axis meets the surface, are called the poles of the earth. The circle \( EQ \) upon the earth, the plane of which passes through \( C \) the centre, and is perpendicular to \( NS \) the axis, is called the equator or equinoctial line. This circle is equidistant from the poles of rotation, and its plane coincides with the plane of the celestial equator. The rational horizon and equator being two great circles of the terrestrial sphere, that is, the plane of each passing through the centre, they are mutually bisected. This is a property which belongs to all great circles. Any great circle \( NPS \) passing through the two poles is called a meridian. Any given point \( P \) may have a meridian passing through it; and the plane of that circle will coincide with the plane of the celestial meridian which passes through the zenith of that point. Every meridian cuts the equator at right angles.

The horizon \( HO \) corresponding to any point \( M \) upon the globe, is divided into four equal parts by the equator and the meridian passing through that point. The points of division are called the four cardinal points. Those through which the meridian passes are called the north and south points of the horizon. Those points, again, through which the equator passes are called the east and west points.

The earth is divided by the horizon into two hemispheres, called the upper and lower or under hemispheres; by the equator it is divided into the northern and southern hemispheres; and by the meridian, into the eastern and western hemispheres.

The position of any point \( P \) on the surface of the earth is determined by referring it to the co-ordinate circles, the equator and meridian. The distance \( PA \) of the place \( P \) from the equator, measured in degrees and parts of a degree on the meridian passing through the place, is called its latitude, which is said to be north or south, according as the place is situated in the northern or southern hemisphere. The arc \( EA \) of the equator, intercepted between the meridian passing through the place \( P \) and some particular meridian \( NMS \), called the first meridian, as being that fixed on from which the reckoning is to commence, is called the longitude of the place in question; and is east or west, according as the place is situated in the eastern or western hemisphere in reference to the first meridian. The difference of longitude between two places is the arc of the equator intercepted between their meridians; and is found by subtracting or adding the longitudes, according as the places are on the same or on opposite sides of the first meridian. The ancients assumed for their first meridian that of the Fortunate Islands, which they conceived to be the western limit of the habitable world. In later times, the meridian passing through Ferro, one of the Canary Islands, was used as the first meridian by the geographers of many countries. It nearly coincided with that of the ancients. But in modern systems of geography the first meridian is usually that which passes through the capital of the country to which the geographer belongs; or if there is an observatory in or near the capital, the meridian of the observatory is assumed as the first. By British geographers the meridian of the observatory at Greenwich is reckoned the first meridian. It is usual to call the semicircle \( NPS \), passing through the two poles and a given place, the meridian of that place; and the other semicircle \( NRS \) passing through the opposite point on the globe, the opposite meridian. All places lying under the same meridian have the same longitude, and at all of them noon or any other hour occurs at the same instant of absolute time. As the sun in his apparent diurnal revolution moves over fifteen degrees in an hour, it is evident that difference of longitude, which causes difference in the rela- If a great circle $Bd$ be supposed to be drawn on the terrestrial sphere, cutting the equator obliquely at an angle of about 23° degrees, this circle will mark out the course of the sun through the year, and is called the ecliptic. It corresponds with the celestial ecliptic, and is divided in the same manner into signs and degrees. The parallel of latitude which passes through the point of the ecliptic in which the sun is placed on any particular day, shows to what points of the earth's surface the sun is vertical on that day. The two parallels BLD, bld, which touch the ecliptic at the points where it recedes farthest from the equator to the north and south, are called the tropics; the one, BLD, the northern tropic, or the tropic of Cancer; and the other, bld, the southern tropic, or the tropic of Capricorn; because they touch the ecliptic in the first points of these signs. These circles lie in the planes of the corresponding circles in the celestial sphere.

Of the two poles, that which lies in the northern hemisphere is called the north or arctic pole; and the opposite, lying in the southern hemisphere, is called the south or antarctic pole. The two parallels of latitude FG, fg, which encircle these poles respectively at an angular distance equal to the obliquity of the ecliptic, are called the polar circles, the one the north or arctic, and the other the south or antarctic.

Suppose a great circle to be drawn on the terrestrial sphere everywhere equally distant from that point on the surface to which the sun is vertical at any given time; this circle is called the circle of illumination, because it separates the enlightened from the dark hemisphere of the earth. It is upon the position of the circle of illumination that the equal or unequal lengths of the days and nights throughout the year depend over the face of the earth. At every season of the year this circle bisects the equator, so that under the equator the days and nights are always equal. When the sun is over either of the equinoctial points E, Q, the circle of illumination bisects not only the equator, but likewise all the parallels to the equator, in consequence of cutting them at right angles; and hence, as the parallel of latitude passing through any point on the earth's surface may be regarded as the path along which that point is carried by the diurnal motion of the earth, at that season of the year the days and nights are equal over all the earth. When the sun is over any other point of the ecliptic, the parallels of latitude are cut obliquely by the circle of illumination, so that they are divided by it into two unequal parts, and hence the days and nights are unequal all over the earth, except at the equator. If the sun is in north declination, at all places to the north of the equator the days are longer than the nights; but at all places to the south of the equator, the nights are longer than the days; because with regard to places to the north, the larger portion of the parallel of latitude lies within the enlightened hemisphere, while with regard to places to the south the larger portion lies within the dark hemisphere. The reverse has place when the sun is in south declination. When the sun is over the northern tropic BD, or over the southern tropic bd, the day is then the longest or shortest of the year; and the adjacent polar circle is wholly in the light, and the opposite one wholly in darkness.

Table showing the Length of a Degree of Longitude for every Degree of Latitude, in Geographical and in English Miles.

| Lat. | Geo. Miles | Eng. Miles | Lat. | Geo. Miles | Eng. Miles | Lat. | Geo. Miles | Eng. Miles | |------|------------|------------|------|------------|------------|------|------------|------------| | 1 | 59° 09' | 69° 05' | 31 | 51° 43' | 59° 20' | 61 | 61° 29' | 33° 48' | | 2 | 59° 50' | 69° 02' | 32 | 50° 58' | 58° 57' | 62 | 62° 17' | 32° 42' | | 3 | 59° 52' | 68° 56' | 33 | 50° 33' | 58° 32' | 63 | 62° 04' | 31° 35' | | 4 | 59° 55' | 68° 59' | 34 | 49° 47' | 57° 55' | 64 | 61° 24' | 30° 27' | | 5 | 59° 57' | 68° 50' | 35 | 49° 15' | 56° 57' | 65 | 60° 44' | 29° 19' | | 6 | 59° 57' | 68° 58' | 36 | 48° 54' | 55° 57' | 66 | 60° 24' | 28° 00' | | 7 | 59° 55' | 68° 55' | 37 | 47° 42' | 55° 15' | 67 | 59° 24' | 26° 58' | | 8 | 59° 42' | 68° 39' | 38 | 47° 28' | 54° 42' | 68 | 58° 24' | 25° 57' | | 9 | 59° 26' | 68° 21' | 39 | 46° 63' | 53° 67' | 69 | 57° 24' | 24° 57' | | 10 | 59° 09' | 68° 01' | 40 | 45° 96' | 52° 90' | 70 | 56° 24' | 23° 62' | | 11 | 58° 50' | 67° 79' | 41 | 45° 28' | 52° 12' | 71 | 55° 53' | 22° 48' | | 12 | 58° 49' | 67° 55' | 42 | 44° 59' | 51° 32' | 72 | 55° 24' | 21° 34' | | 13 | 58° 46' | 67° 29' | 43 | 43° 88' | 50° 51' | 73 | 54° 54' | 20° 19' | | 14 | 58° 22' | 67° 01' | 44 | 43° 16' | 49° 68' | 74 | 54° 24' | 19° 04' | | 15 | 57° 96' | 66° 71' | 45 | 42° 43' | 48° 83' | 75 | 53° 53' | 17° 57' | | 16 | 57° 68' | 66° 38' | 46 | 41° 68' | 47° 97' | 76 | 53° 24' | 16° 71' | | 17 | 57° 38' | 66° 04' | 47 | 40° 92' | 47° 10' | 77 | 52° 54' | 15° 54' | | 18 | 57° 06' | 65° 68' | 48 | 40° 15' | 46° 21' | 78 | 52° 24' | 14° 35' | | 19 | 56° 73' | 65° 39' | 49 | 39° 36' | 45° 31' | 79 | 51° 54' | 13° 18' | | 20 | 56° 38' | 64° 90' | 50 | 38° 57' | 44° 43' | 80 | 51° 24' | 11° 59' | | 21 | 56° 01' | 64° 47' | 51 | 37° 75' | 43° 41' | 81 | 50° 54' | 10° 50' | | 22 | 55° 61' | 64° 03' | 52 | 36° 94' | 42° 52' | 82 | 50° 24' | 9° 61' | | 23 | 55° 23' | 63° 50' | 53 | 36° 11' | 41° 55' | 83 | 49° 54' | 8° 42' | | 24 | 54° 51' | 63° 14' | 54 | 35° 31' | 40° 56' | 84 | 49° 24' | 7° 22' | | 25 | 54° 28' | 62° 59' | 55 | 34° 41' | 39° 61' | 85 | 48° 54' | 6° 02' | | 26 | 53° 53' | 62° 07' | 56 | 33° 55' | 38° 62' | 86 | 48° 24' | 4° 43' | | 27 | 53° 46' | 61° 53' | 57 | 32° 68' | 37° 61' | 87 | 47° 54' | 3° 31' | | 28 | 52° 93' | 60° 58' | 58 | 31° 79' | 36° 60' | 88 | 47° 24' | 2° 41' | | 29 | 52° 48' | 60° 40' | 59 | 30° 90' | 35° 57' | 89 | 46° 54' | 1° 21' | | 30 | 51° 93' | 59° 81' | 60 | 30° 00' | 34° 53' | 90 | 46° 24' | 0° 00' |

VOL. X. Thus within the arctic and antarctic circles the inhabitants have their light and darkness extended to a great length; the sun sometimes skirting round a little above the horizon for many days together, and at another season never rising above the horizon at all, but making continual night for a considerable length of time.

Such are the circles supposed to be drawn on the terrestrial sphere. Though these circles are altogether imaginary, and have really nothing corresponding to them on the earth's surface, yet as the positions of the corresponding circles in the heavens can be accurately determined by observation on the celestial bodies, they become actually as effective for fixing the relative positions of places on the globe of the earth, and for other purposes of geography, as if that globe were reduced to such a magnitude as to admit of its being grasped by the hand of man, and surveyed by a single glance of his eye.

The height NO of the pole adjacent to any place M above HO the horizon of that place, is equal to the latitude of the place; for the arcs MO and EN are equal, each being a quadrant; and taking away from each the common arc MN, the remaining arc NO, the elevation of the pole N, is equal to the remaining arc ME, the latitude of the place M.

Hence there are, with regard to the horizon, three positions of the terrestrial sphere, as there are of the celestial, depending on the latitude of the place. If an observer were placed on the pole, the latitude being 90°, his horizon would coincide with the equator, and all the parallels of latitude would be parallel to the horizon. This is the parallel position of the sphere, which is represented in fig. 7. Again, if an observer were placed on any point of the equator, the latitude being 0, the poles of the earth must be in the horizon; and from the properties of the sphere, the equator, and all the small circles parallel to the equator, must be at right angles to the horizon. This is the right position of the sphere, which is represented in fig. 8. With regard to an observer placed at any point between the equator and either pole, the axis of the earth lies obliquely to the plane of his horizon, which is therefore cut obliquely by the equator and all the small circles parallel to the equator: this is the oblique position of the sphere, and is that represented in figure 2.

The method of determining the latitude of a place, and the difference of longitude between two points on the earth's surface, is given in the article ASTRONOMY, part iv. chap. i. prob. ix. and x. The latitudes and longitudes of two points on the surface of the earth being given, the angular distance may be found; and hence the length of a degree on the earth's surface being known, the distance between the points may be expressed in miles. Thus, let A and B be two points on the earth's surface, let P be the adjacent pole, Mathematical Geography, and PA, PB the meridians passing through A and B; then PA and PB will be the complements of the latitudes, and therefore given; and the spherical angle APB will be the difference of the longitudes, and therefore also given. In the spherical triangle PAB, the base AB of which is the distance required, we have therefore two sides and the included angle, so that the base AB can be found. Put D and D' for the complements of the given latitudes, and P for the difference of the given longitudes; then, by spherical trigonometry, we have

\[ \cos AB = \cos D \cos D' + \sin D \sin D' \cos P. \]

By assuming tan. \( \phi = \tan D \cos P \), this formula may be reduced to the more convenient form

\[ \cos AB = \frac{\cos D \cos (D' - \phi)}{\cos \phi}. \]

From the above expression the number of degrees and parts of a degree contained in the arc intercepted between the points A and B are to be found; and allowing for each degree 69°06 English miles, the distance will be obtained, expressed in English miles, which will necessarily differ a little from the truth, in consequence of the earth not being truly spherical. To determine the distance between two points on the earth's surface with precision, requires the application of some of the most refined improvements in modern mathematics. See FIGURE OF THE EARTH.

As an example of the above formula, let it be required to find the distance between Edinburgh and Constantinople. Colat. of Edinburgh...34° 3' = D: its long. 3° 12' W. Colat. of Constantinople 48° 59' = D': its long. 28° 55' E.

| Difference of longitude | 32° 7' | |-------------------------|--------| | Tan. D = tan. 34° 3' = 9-829805 | | Cos. P = cos. 32° 7' = 9-927867 | | Tan. \( \phi = 29° 47' \) = 9-757672 | | \( D' = 48° 59' \) | | \( D' - \phi = 19° 12' \)........... Its cosine = 9-975145 | | Cos. D = 9-918318 | | Arith. compl. cosine \( \phi = 0-061525 \) | | Cos. AB, 25° 38'...= 9-954988 |

Hence the arc of a great circle of the sphere intercepted between Edinburgh and Constantinople is 25° 38', or 1770 English miles nearly.

Each of the four quadrants into which the horizon is divided by the equator and the meridian is supposed to be divided into eight equal parts; so that the whole circumference is divided into thirty-two equal parts, which are called points of the compass; and to each point of division a name is given indicating its position with regard to the four cardinal points.

The position of one place with regard to another, as estimated by the points of the compass, is called the bearing of the former from the latter. Thus, when a place is said to bear N.E. (north-east), N.N.E. (north-north-east), &c., the meaning is, that it lies in the direction of those points in the horizon from the present position of the observer. If a series of points be assumed on the earth's surface, so situated that all of them, when taken in regular succession, lie towards any the same point of the compass, except either of the four cardinal points, the assumed points lie, not in the circumference of a circle of the sphere, but in a sort of spiral line, the characteristic property of which is, that it cuts all the meridians at the same angle. This line is called a rhumb line; and, whilst it continually approaches the pole, it can never arrive at it, except after an infinite number of revolutions. In passing, therefore, from one point of the surface of the globe to another, by pursuing the direction in which the latter lies from the former, we do not take the shortest way, which is an arc of a great circle, but move over a portion of a rhumb line, passing through the two points. This is the line described by a ship whilst her course is continually directed towards one and the same point of the compass.

CHAP. II.—OF THE SURFACE OF THE EARTH, AND ITS GENERAL DIVISIONS: DEFINITIONS.

The surface of the earth contains about 196,663,400 square miles. By much the larger portion of this space is water, which is, indeed, more than twice the extent of the land. The surface of the land is exceedingly diversified, almost everywhere rising into hills and mountains, or sinking into valleys, and sometimes stretching out into plains of great extent. Amongst the most extensive plains are the sandy deserts of Arabia and Africa, the internal part of European Russia, and a tract of considerable extent in Prussian Poland. But the most remarkable extent of level ground is the vast table-plain of Thibet in Asia, which is the most elevated tract of level ground on the globe. The principal mountain ridges are the Alps and Pyrenees in Europe, the Altai and Himalaya Mountains in Asia, the mountains of Atlas in Africa, and the Andes or Cordilleras in South America. The greatest concavities of the globe are those which are occupied by the waters of the ocean; and of these by far the largest forms the bed of the Pacific Ocean, which, stretching from the eastern shores of Asia and of New Holland to the western coast of America, covers nearly half the globe. The concavity next in extent is that which forms the bed of the Atlantic Ocean, extending between the new and the old worlds; and a third concavity is occupied by the Indian Ocean. The Arctic and Antarctic Oceans fill up the remaining concavities.

Smaller collections of water which communicate freely with the oceans are called seas; and of these, the principal are the Mediterranean, the Baltic, the Euxine or Black Sea, and the White Sea. Seas sometimes take their names from the countries near which they flow; as the Irish Sea, the German Ocean. Some large collections of water, though they have no immediate connection with the great body of waters, being on all sides surrounded by land, are yet called seas; as the Caspian Sea.

A part of the sea running up into the land, so as to form a large hollow, is called a bay or gulf; as the Bay of Biscay, the Gulf of Mexico; but if the hollow be small, it is called a creek, a road, a haven.

When two large bodies of water communicate by a narrow pass between two adjacent lands, the pass is called a strait or straits, as the Straits of Gibraltar, the Straits of Dover, the Straits of Babelmandel. A channel is a wider kind of strait. The water usually flows through a strait with considerable force and velocity, forming what is called a current; and frequently this current, as in the case of the Straits of Gibraltar, flows continually in the same direction.

A body of fresh water entirely surrounded by land is called a lake, as the Lake of Geneva, Lake Champlain.

A considerable stream of water rising inland, and draining a portion of country more or less extensive, discharging its waters into the sea, is called a river. A smaller stream of the same kind is called a rivulet, or brook.

Of the land, which forms the rest of the surface of the globe, two portions of vast extent are called continents; the one the eastern continent, or the old world, comprehending Europe, Asia, and Africa; the other the western continent, or new world, comprehending North and South America. New Holland is a third portion of land, however, which has by some been also reckoned a continent on account of its great extent.

A portion of land, of comparatively small dimensions entirely surrounded by water is called an island, as Britain, Ireland, Jamaica, Madagascar. New Holland is the largest portion of land which is called an island. When a number of smaller islands lie near each other they are said to form a group of islands.

A portion of land which is almost entirely surrounded by water is called a peninsula, as the peninsula of Malacca, the Morea or Grecian Peloponnesus, &c. The term peninsula is often applied to a large extent of country. Thus we speak of Spain as a peninsula.

The narrow neck of land which joins a peninsula to the mainland, or which connects two tracts of country together, is called an isthmus. The most remarkable isthmuses in the world are the Isthmus of Suez which joins Africa and Asia, and the Isthmus of Darien which connects the continents of North and South America.

A narrow tract of land stretching out into the sea, and appearing to terminate in a point, is called a cape. The most remarkable capes are, the Cape of Good Hope, at the southern extremity of Africa; Cape Horn, at the southern extremity of South America; and the North Cape, at the northern extremity of Europe. A large portion of land jutting out into the sea is called a promontory.

Until of late, in systems of geography, the earth used to be considered as divided into four quarters; Europe, Asia, Africa, and America. A classification in which the whole world is arranged under seven divisions has now, however, been very generally adopted: These divisions are, Europe, Asia, Africa, North America, South America, Australasia, and Polynesia. With regard to the last two, the one, Australasia, or South Asia, comprehends certain of the great islands, particularly New Holland, which are usually considered as belonging to Asia; and the other, Polynesia, signifying many islands, comprehends all the smaller islands which are scattered over the great expanse of the Pacific Ocean.

This classification of the parts of the earth's surface is founded on the most obvious points of distinction. We shall now explain two divisions employed by the ancients, which are founded upon different principles; that into zones, and that into climates.

The division into zones is suggested by the different degrees of temperature which prevail in different regions of the earth. The temperature of a country depends on a variety of circumstances (see Physical Geography); but of these, one of the most obvious is the position of the sun with regard to the zenith. The more nearly his rays are received vertically, the higher will be the temperature; and, on the contrary, the more obliquely they fall, the less effect will they produce in raising the temperature. Now to every point of the earth's surface between the tropics the sun is vertical twice in the year. It is in this region, then, that the highest temperature will prevail. Again, within the polar circles the sun's rays at all times fall very obliquely; and for a length of time they do not reach these two regions of the globe at all. Here, then, the temperature must be lower than anywhere else, as all other places enjoy more of the sun's genial influence. In the two regions between the tropics and the polar circles, a medium temperature is found, increasing as we approach the former, and diminishing as we approach the latter. Thus is the earth's surface divided, by the two tropics and two polar circles, into five zones, distinguished from one another by the prevailing temperature in each. That between the tropics is called the torrid zone, because there the heat is understood to be extreme. This region, which has the equator passing through the middle of it, the ancients, indeed, considered as uninhabitable. The two regions comprehended within the arctic and antarctic polar circles are called the northern and southern frigid zones, on ac- count of the severity of the cold which there prevails. The two regions situated between the tropics and the polar circles, the one in the northern hemisphere, bounded by the tropic of cancer and the arctic circle, the other in the southern hemisphere, bounded by the tropic of capricorn and the antarctic circle, are called the northern and southern temperate zones, because there neither the heat nor cold is excessive; but the heat reaches the highest temperature of summer, and the cold sinks to the lowest temperature of winter, without either becoming extreme.

As each tropic lies about 23° from the equator, the breadth of the torrid zone is about 47°, or nearly 3240 English miles. The breadth of each of the frigid zones, that is, from the circumference of the polar circle to the pole, is 23°, or nearly 1620 miles; so that there remains for the breadth of each of the temperate zones about 43°, or nearly 2970 miles. The superficial content of each zone is easily calculated by the ordinary rules of mensuration. Let \( s \) be the surface of a segment of the sphere, \( d \) the diameter of the sphere, and \( h \) the height of the segment; then

\[ s = 3 \cdot 1416 \cdot dh. \]

To apply this formula; let NESQ be the sphere divided into five zones. It is evident that, for the torrid zone, \( h \) must be equal to \( Ld \), or to twice the sine of BE to the radius EC; that for each of the temperate zones \( h \) must be equal to LR or \( r \), the difference of the sines of FE and BE to the same radius CE; and that for the space comprehended within each polar circle, \( h \) must be equal to NR, the excess of the radius NC above CR, the sine of FE corresponding to that radius. Hence, if we put \( m \) for twice the natural sine of the arc BE; for the difference of the natural sines of the arcs BE and FE; and for the excess of radius above the natural sine of FE, successively; —since in the case of the terrestrial sphere CE or CN is equal to 3956 miles, we have \( h = 3956 \). Putting, therefore, instead of \( d \), its value, 7912, and giving the above formula a logarithmic form, we obtain

\[ \log_s = \log_m + 7 \cdot 9926935. \]

Now, for the torrid zone, \( m = 2 \cdot \text{nat. sin. } 23^\circ 30' = 7975 \). Hence,

\[ \log_m = 1 \cdot 9017307 - 7 \cdot 9926935 \]

\[ s = 78419520 \ldots \log_s = 7 \cdot 8944242. \]

The torrid zone contains, therefore, about 78,419,500 square miles.

Again, for each of the temperate zones, we have \( m = \text{nat. sin. } 66^\circ 30' - \text{nat. sin. } 23^\circ 30' = 51831 \). Hence,

\[ \log_m = 1 \cdot 7145896 - 7 \cdot 9926935 \]

\[ s = 50966300 \ldots \log_s = 7 \cdot 7072831. \]

So that each of the temperate zones contains about 50,966,300 English square miles.

Lastly, for the space contained within each of the polar circles we have \( m = \text{rad. } - \text{sin. } 66^\circ 30' = 1 - 0 \cdot 91706 = 0 \cdot 08294 \); hence,

\[ \log_m = 2 \cdot 9187640 - 7 \cdot 9926935 \]

\[ s = 8155630 \ldots \log_s = 6 \cdot 9114575. \]

The portion of the surface of the globe comprehended within each polar circle is therefore nearly equal to 8,155,600 square miles.

It is evident that the superficial content of any other zone of the terrestrial sphere may be found by the above formula, by putting \( m \) equal to the difference of the natural sines corresponding to the latitudes of the parallels by which the zone is bounded.

If it is required to find the area of a segment of a zone bounded at both extremities by meridians, it is only necessary to find first the area of the whole zone, and then to multiply the result by the number of degrees and parts of a degree in the length of the segment, and to divide by 360. Thus, the number of square miles contained in the portion of the torrid zone terminated by two meridians which are separated from each other by 8° 45' is equal to 78419520 × 8° 45' ÷ 360, which gives 272,290 square miles. By dividing any particular country or district into segments of zones by means of parallels of latitude, its area can easily be calculated.

The division of the earth's surface into climates was employed by the ancients for ascertaining the situation of places. They supposed the northern and southern hemispheres to be each divided into small zones, to which they gave the name of climates, the breadth of each zone being such as to make half an hour of difference in the length of the longest day at the two parallels of latitude by which the climate was bounded. Proceeding from the equator, where the length of the day is always twelve hours, they thus divided the space between it and each polar circle into twenty-four climates. Having reached the polar circles northward and southward, where the longest day is twenty-four hours, they divided the space within each polar circle in such a manner as to make the difference in the length of the longest day at the beginning and termination of each climate one month. Hence, as the poles are alternately illuminated for six months, there were just six climates within each polar circle.

### Table of Climates

| Climates | Latitude of the Higher Parallel | Breadth of the Climate | Longest Day under the Higher Parallel | |----------|---------------------------------|------------------------|-------------------------------------| | I | 8° 34' | 8° 34' | 12° 30' | | II | 16° 43' | 8° 9' | 13° 0' | | III | 24° 10' | 7° 27' | 13° 30' | | IV | 32° 43' | 6° 36' | 14° 0' | | V | 40° 28' | 5° 42' | 14° 30' | | VI | 48° 21' | 5° 33' | 15° 0' | | VII | 56° 29' | 4° 8' | 15° 30' | | VIII | 64° 59' | 3° 30' | 15° 0' | | IX | 72° 57' | 2° 58' | 16° 30' | | X | 80° 28' | 2° 31' | 17° 0' | | XI | 88° 36' | 2° 8' | 17° 30' | | XII | 96° 25' | 1° 49' | 18° 0' | | XIII | 104° 57' | 1° 32' | 18° 30' | | XIV | 113° 16' | 1° 19' | 19° 0' | | XV | 121° 24' | 1° 8' | 19° 30' | | XVI | 129° 20' | 0° 56' | 20° 0' | | XVII | 137° 48' | 0° 48' | 20° 30' | | XVIII | 146° 48' | 0° 40' | 21° 0' | | XIX | 155° 20' | 0° 32' | 21° 30' | | XX | 163° 46' | 0° 26' | 22° 0' | | XXI | 172° 6' | 0° 20' | 22° 30' | | XXII | 180° 20' | 0° 14' | 23° 0' | | XXIII | 188° 48' | 0° 8' | 23° 30' | | XXIV | 196° 32' | 0° 4' | 24° 0' |

Besides dividing the surface of the globe into zones and climates, the ancients likewise distinguished the in- habitants of the different regions of the earth by the particular direction in which the shadows of bodies are projected in each region, and by some other circumstances depending on the position of the sun relatively to the zenith or to the meridian. The inhabitants of the torrid zone have their shadows at noon projected, sometimes towards the south and sometimes towards the north, according to the position of the sun in the ecliptic. They were therefore called by the ancients *Amphictici*, a term derived from ἀμφί, about, and ὅρα, a shadow. In the temperate zones, the sun is at noon always on the same side of the zenith. Hence the shadows of objects at noon always fall in the same direction; in the northern temperate zone towards the north; and in the southern temperate zone towards the south. The inhabitants of these regions were accordingly called *Heteroceci*, from ἕτερος, different, and ὁρά, a shadow. Within the polar circles the sun does not always rise and set every twenty-four hours, as in the other zones; but for a certain number of days in our summer he never sets to places within the arctic polar circle, nor rises to places within the antarctic; and the contrary takes place for a certain number of days during our winter. The number of days during which the sun is present or absent increases as we advance from the polar circle towards the pole. When the sun continues above the horizon for twenty-four hours or upwards, the shadows will make a complete circuit round the objects from which they are projected; hence the inhabitants of the frigid zones were called *Periseii*, from περί, about, and ὁρά, a shadow.

Again, the inhabitants of two places which lie under the same meridian, and have the same latitude, but are situated on opposite sides of the equator, were called, relatively to each other, *Antececi*, from ἀντί, opposite to, and ὁρά, a habitation. At such places the hours of the day will always correspond, but the seasons of the year will be opposite. The inhabitants of two places which have the same latitude, and are situated on the same side of the equator, but under opposite meridians, were called *Periseii*, from περί, about, and ὁρά. They have always the same season of the year at the same time; but any hour of the day at the one place corresponds to the same hour of the night at the other. The inhabitants of two places which have the same latitude, but are situated on opposite sides of the equator, and under opposite meridians, are called *Antipodes* to each other, from ἀντί, opposite to, and πόδις, a foot. They have always opposite seasons and opposite hours.

**CHAP. III.—DESCRIPTION AND USE OF THE GLOBES.**

When geographers became familiar with the doctrine of the sphericity and motion of the earth, it was an obvious step to have recourse to an artificial sphere for illustrating that doctrine. From a very early period, accordingly, the instruments called the *terrestrial* and *celestial globes* have been employed for this purpose. A sphere made of metal, ivory, plaster, paper, pasteboard, or some other convenient substance, is suspended in a brass ring, of somewhat greater diameter, on two pins, upon which it can be made to revolve. The sphere, thus suspended, is placed in a frame, which may be in many respects variously constructed, according to the taste of the workman; but its upper part always consists of a broad ring made of metal or wood, and supported in a horizontal position. The inner circumference of this ring is equal to that of the brass circle in which the globe is suspended; and two notches in its inner edge, diametrically opposite to each other, receive the brass ring, which also rests in a groove below, in such a position that the plane of the horizontal ring bisects the sphere. By this arrangement the globe can be made to revolve on its axis, and the brass circle can be made to slide round in its own plane. On the surface of the globe are delineated the equator or equinoctial line, situated exactly in the middle between the two points on which the globe is suspended, and divided into 360 degrees; the ecliptic, divided into twelve signs, and each of these subdivided into thirty degrees; the two tropics; the two polar circles, with as many more parallels to the equator as are found convenient; and generally twenty-four meridians passing through the points of suspension, which represent the poles. The first meridian is usually made to pass through the intersections of the equator and ecliptic, the points of the vernal and autumnal equinoxes; and from the former of these points the reckoning of the degrees on the equator and ecliptic begins. The brass circle in which the globe hangs may be made to represent the meridian of any given point on the surface of the globe, by simply bringing the given point under it by turning the globe round on its axis. Hence the brass circle is called the *universal meridian*. It is divided, by the equator and two poles, into four quadrants, each of which is graduated; and on the one semicircle the degrees are reckoned from the equator towards either pole, while on the opposite semicircle they are reckoned from either pole towards the equator. On the broad horizontal circle of the frame in which the globe stands are drawn several concentric circles, the outer of which is divided into 365 equal parts, answering to the number of days in the year; whilst the other circles are graduated, the innermost (or rather another circle concentric with it, but larger) being, besides, divided into thirty-two equal parts corresponding to the points of the compass. The circle next the outer edge forms the calendar, and it has the names of the months arranged in order around it, whilst the divisions are distributed so as to mark the number of days in each. The adjacent circle contains the signs and degrees of the ecliptic, so arranged that against each day of the year is found the point of the ecliptic in which the sun is situated on that day. The innermost circle represents the horizon; and the two notches in which the brazen meridian rests pass through the north and south points. It is divided into four quadrants by the cardinal points; and the degrees of the two quadrants, which form the northern semicircle, are reckoned from the east and west points towards the north; while the degrees of the other two quadrants are reckoned from the east and west towards the south.

Such is a general view of the parts which belong alike to both globes, the terrestrial and the celestial. A more minute description seems unnecessary, as a careful inspection of the globes themselves, with their appendages, will convey a much more distinct conception of them than can be given either by description or by drawings. It will be necessary, however, to describe shortly the horary or hour circle, the quadrant of altitude, and the compass.

The hour-circle is a small circle of brass, divided into twenty-four equal parts corresponding to the hours of the day, the divisions being reckoned in two twelves to suit the hours before and after noon. The circle is fixed on the axis of the globe, having its centre coinciding with the north pole. It can be adjusted with the hand to any meridian, but is at the same time tight enough to be moved along with the globe. Some globes have the hour-circle fixed on the meridian, with an index that admits of being adjusted with the hand, but is carried round with the globe.

The quadrant of altitude is a thin flexible slip of brass, equal in length to one-fourth part of the circumference of a great circle on the globe. It is graduated on one side, and is furnished with a nut and screw at one end, for the purpose of making it fast to the brazen meridian. Its use is to measure degrees on the surface of the globe in any direction.

The compass is simply a magnetic needle suspended over the centre of a circle, on the circumference of which are marked the thirty-two points of the compass. It is fixed to the under part of the frame in which the globe is suspended, and is used for the purpose of placing the meridian due north and south.

On the terrestrial globe the land and water which compose the surface of the earth are delineated, with the various divisions belonging to each. If we suppose the globe to be six or seven feet in diameter, the true height of the mountains on the earth's surface must be reduced, in order to be represented on the globe in due proportion to its bulk, in the ratio of 7912 miles to six or seven feet; that is, the height of the protuberance on such a globe which shall represent any particular mountain must be somewhat about the six-millionth part of the actual elevation of the mountain above the general surface of the earth. Apply this to the highest mountain in the world, which does not exceed five and a half miles in height; the elevation of the protuberance representing it on a globe of the supposed dimensions would be about one-seventeenth part of an inch above the general surface. It is seldom, however, that globes are made of this size. One-third of the supposed diameter is more near to the ordinary dimensions. Hence we see with what propriety the earth is represented by a globe having a smooth surface.

But in order to render the representation more complete, it may be supposed necessary that the terrestrial globe should be inclosed in a hollow sphere which would represent the heavens surrounding the earth on all sides. In conformity with this idea the armillary sphere was contrived, in which the several circles of the system of the world, put together in their natural order, are represented, with a small globe in the centre of the sphere to represent the earth. The ordinary way, however, of representing the heavens, proceeds on the supposition that the eye of the observer is placed, not in the centre of the celestial sphere, but beyond its bounds, so as to look down on a convex surface. Thus are the stars and constellations represented in their relative positions on the celestial globe, with which the concave surface of the visible heavens is easily compared.

Besides answering the general purposes of illustration, the globes furnish also the means of resolving with facility, and with a degree of accuracy sufficient for ordinary purposes, many problems in geography and practical astronomy. It is only requisite to consider the circumstances on which the solution of a problem depends, and to arrange on the globe these circumstances, according to their natural order and dependence, and the result is at once obtained. We proceed to give a few of the more useful problems, with their solutions by the globes.

I. Solution of Problems by the Terrestrial Globe.

Prob. 1. To find the latitude and longitude of a given place.

Bring the place under the graduated edge of the brazen meridian, then the degree of the meridian immediately over it is its latitude north or south, and the degree of the equator cut by the meridian is its longitude east or west.

Prob. 2. The latitude and longitude of a place being given, to find the place itself on the globe.

Bring the point of the equator corresponding to the given longitude to the brazen meridian; under the degree of latitude on the meridian the place is found.

Prob. 3. To find the distance between any two places on the globe.

Lay the quadrant of altitude over the two places, and mark the number of degrees between them. The degrees may then be converted into English miles, if required, by multiplying by 69°06'.

Prob. 4. The hour at any one place being given, to find what hour it is at any other place; or to find the difference of longitude between the places in time.

Bring the place at which the hour is given to the brazen meridian, and set the index, or the hour-circle, to that hour; then turn the globe till the other place comes under the meridian, and the index, or the hour-circle, will show the hour required. The difference between the time found and the time given is the difference of the longitudes of the places in time.

Prob. 5. To rectify the globe for a given place.

Elevate the pole that is adjacent to the place as many degrees above the wooden horizon as are equal to the latitude.

Prob. 6. To find at what hour the sun rises and sets at a given place, for any given day.

Rectify the globe for the latitude of the place; find from the wooden horizon the sun's place in the ecliptic for the given day, and bring it to the meridian. Set the index to XII., and turn the globe till the sun's place comes to the eastern edge of the horizon, the index will show the hour of rising; then turn the globe till the sun's place comes to the western edge of the horizon, and the index will show the time of setting.

By doubling the hour of sunrise, we obtain the length of the night; and by doubling the hour of sunset, we obtain the length of the day. It is evident also that the same arrangement of the globe will give the point of the compass on which the sun rises and sets, by simply observing what point of the circle of rhumbs, on the wooden horizon, is cut by the sun's place in the ecliptic at the time of rising and setting. Further, by observing when the sun is about eighteen degrees below the eastern and western parts of the horizon, the time of the beginning of the morning twilight, and of the ending of the evening twilight, is found.

Prob. 7. To find the sun's declination for a given day of a given month, and to what places the sun will be vertical on that day.

Find, on the wooden horizon, the sun's place in the ecliptic for the given day; bring that point of the ecliptic to the meridian, the degree immediately over it on the meridian is the declination north or south. Turn round the globe till it has made a complete revolution; and to every place which passes under that degree of the meridian, the sun will be vertical on that day.

Prob. 8. The hour and day being given at a particular place, to find where the sun is then vertical.

Find the sun's declination by the preceding problem; bring the given place under the meridian, and set the index to the given hour; then turn the globe till the index points to XII. noon; and all the places under the meridians will have noon at the given time; and that place which is under the degree of the meridian that corresponds with the sun's declination will have the sun in the zenith.

Prob. 9. The hour and day being given at a particular place, to find where the sun is then rising or setting, and where it is noon or midnight.

Rectify the globe for the given place; and having previously found by last problem the place to which the sun is vertical at the given time, bring that place to the meridian. Then, to all the places under the western edge of the horizon the sun is rising, and to those under the eastern he is setting; to those under the upper half of the meridian it is noon, and to those under the lower half it is midnight.

Prob. 10. A place in the torrid zone being given, to find on what two days of the year the sun will be vertical to that place.

Find the latitude of the place; turn round the globe, and note the two points of the ecliptic which pass below the degree of latitude on the meridian. Find in the calendar circle of the wooden horizon the days corresponding to these two points of the ecliptic, and these are the days required. Prob. 11. To find the sun's meridian altitude at a given place on a given day.

Rectify the globe for the latitude of the place; bring the sun's place for the given day to the meridian; count the number of degrees between that place and the horizon for the altitude required.

Prob. 12. To find the altitude of the sun at any given place and hour.

Rectify the globe for the latitude; bring the sun's place to the meridian, and set the index to XII. noon; turn the globe till the index point at the given hour; fix the quadrant of altitude on the meridian at the degree of latitude, and lay it over the sun's place; count the number of degrees on the quadrant between that point and the horizon for the altitude required.

Prob. 13. To find all the places to which a lunar eclipse is visible at any instant.

Find the place to which the sun is vertical at the given time; rectify the globe for the latitude of that place, keeping the place under the meridian; set the index to XII. noon; then turn the globe till the index point to XII. midnight; the eclipse will be visible to all those places which are above the horizon.

Prob. 14. Any place in the north frigid zone being given, to find how long the sun shines there without setting, and how long he is totally absent.

Rectify the globe for the latitude of the place; bring the ascending signs of the ecliptic to the north point of the horizon, and note at what degree the ecliptic is intersected by that point; find on the wooden horizon the day and month corresponding to that degree; from that day the sun begins to shine continually. Next, bring the descending signs to the north point of the horizon, and by observing at what degree the ecliptic is now cut, and referring to the horizon, we find the time when the sun ceases to shine without setting, which is the termination of the longest day. By proceeding in the same manner with the southern point of the horizon, we will find the beginning and end of the longest night.

Prob. 15. Two places being given, to find the angle which a great circle passing through them makes with the meridian of each.

Rectify the globe for both places successively, bringing in each case the place for which the globe is rectified to the meridian; fix the quadrant of altitude in each operation on the meridian over the place for which the globe is rectified, and lay it over the other place; the two arcs intercepted successively on the horizon between the quadrant and the meridian measure the angles required. It is evident, that if both places lie on the same meridian the angle is 0°; and that if both lie on the equator the angles will be each 90°.

If a ship be supposed to sail from the one place to the other, on a great circle of the terrestrial sphere (which supposition implies that the ship's course is altered every instant), then the one angle found by this problem will be the course with which the ship left the one place, and the other angle the course with which she arrived at the other place. The arc of the great circle intercepted between the places would be the distance sailed.

Prob. 16. To construct a horizontal dial by the globe for a given latitude.

Rectify the globe for the latitude; bring the first meridian under the brazen meridian, and note the arcs of the horizon intercepted between the southern point and the several meridians in the eastern and western hemispheres. If the number of meridians drawn on the globe be twenty-four, which is usually the case, the arcs intercepted on the horizon will measure the angles which the hour-lines make with the meridian. To find the angles corresponding to half-hours and quarters, turn the globe gradually from its position in which the first meridian was under the brazen meridian, noting for each arc of 3° 15' of the equator that passes under the brazen meridian, the arc of the horizon intercepted between the southern point and the first meridian; the arcs thus found give the positions of the lines corresponding to the half-hours and quarters. The style of the dial represents the axis of the earth, and must therefore make with the plane of the horizon an angle equal to the latitude of the place.

A direct north or south dial for any latitude may be constructed in the same manner, by considering it as a horizontal dial for a latitude which is the complement of the given latitude.

II. Solution of Problems by the Celestial Globe.

Prob. 1. To find the latitude and longitude of any star.

Bring the pole of the ecliptic to the meridian. Then having fixed the quadrant of altitude over the pole, place it over the given star; the number of degrees between the ecliptic and the given star is the latitude; and the number of degrees on the ecliptic between the edge of the quadrant and the first point of Aries indicates the longitude.

Prob. 2. To find a star's place in the heavens, its latitude and longitude being given.

Place the extremity of the quadrant of altitude on the pole of the ecliptic, and make its graduated edge cut the ecliptic in the longitude of the star; then the star will be found under the degree of the quadrant that denotes its latitude.

Prob. 3. To find the right ascension and declination of the sun or of a star

Bring the sun's place, or the star, to the meridian; the degree of the equator cut by the meridian gives the right ascension, and the degree of the meridian over the sun's place, or the star, shows the declination north or south.

Prob. 4. The latitude of a place, the day and hour being given, to arrange the celestial globe so as to exhibit the appearance of the heavens at that place and time.

Rectify the globe for the latitude of the place; bring the sun's place for the given day to the meridian; set the index to XII.; then turn the globe till the index point to the given hour. In this position, the globe will represent the actual appearance of the heavens.

Prob. 5. To find the time when any of the heavenly bodies rises, sets, or comes to the meridian, on a particular day at a given place.

Rectify the globe for the latitude of the place; bring the sun's place to the meridian, and set the index to XII.; then turn the globe till the star comes to the eastern edge of the horizon; the index will show the time of rising. Next, turn the globe till the given star comes to the western edge of the horizon; the index will show the time of setting. Lastly, bring it to the meridian, and the index will show the time of its culmination or southing.

Prob. 6. To find on what day of the year any given star comes to the meridian at a given hour.

Bring the given star to the meridian, and set the index to the given hour; turn the globe till the index points to XII. noon, and note the degree of the ecliptic cut by the meridian; the day of the month which corresponds to that degree is the day required.

Prob. 7. The latitude of a place, the altitude of a star, and the day of the month, being given; to find the hour of the night.

Rectify the globe for the latitude; bring the sun's place to the meridian, and set the index to XII.; fix the quadrant in the zenith, then move the globe and the quadrant till the star comes under the degree of the quadrant which denotes the given altitude, and the index will show the hour required. The year and day being given, to find the place of a planet.

Find the sun's place for the given day, and bring it to the meridian; set the index to XII.; then find in the Nautical Almanac for the year the time when the planet passes the meridian on the given day, and turn the globe till the index points to the hour thus found; find in the almanac the declination of the planet for the same day, and under it on the globe is the place of the planet.

These are a few of the more important problems that can be resolved by the globes, and will be sufficient to illustrate the principle of solution. The solution of problems by the armillary sphere depends upon the very same principles.

CHAP. IV.—OF THE CONSTRUCTION AND USE OF MAPS.

In representing the geographical divisions of the earth's surface, two objects are to be kept in view; on the one hand, to exhibit accurately to the eye the relative position of the different countries; and on the other hand, to give a delineation sufficiently minute to furnish a distinct knowledge of the necessary details. As a globe has very nearly the exact figure of the earth, the representation which it affords of the surface fulfils the first of these objects in the most perfect manner; but to attain the second it would be requisite to enlarge the globe beyond all convenient size. A globe of the ordinary dimensions serves almost no other purpose in this respect, but to convey a clear conception of the earth's surface as a whole; exhibiting the figure, extent, position, and general features of the great continents and islands, with the intervening oceans and seas. To obtain a detailed representation of any part of the earth's surface, geographers have therefore found it necessary to have recourse to Maps, in which countries are delineated on a plane, while the mutual proportions of the distances of places are preserved as nearly as possible the same as on the globe.

For the construction of maps different mathematical hypotheses have been adopted.

By one method of construction, that of projection, the boundaries of countries, and their more remarkable features, are represented according to the rules of perspective, on the supposition of the eye being placed on some point of the sphere, or at some given distance from it, which may be increased indefinitely. Wherever the eye is supposed to be situated, the representation thus obtained answers very well, provided the surface to be represented is of small extent, and the point of view, or projecting point, is nearly over the centre; but when the surface is of great extent, for example, a whole hemisphere, those places which are situated near the border of the projection are in all of them much distorted.

Another method, that of development, is founded on the supposition that the spherical surface to be represented is a portion of a cone, of which the vertex is situated somewhere in the polar axis produced, and the conical surface is supposed either to touch the sphere in the middle parallel of the map, or to fall within the sphere at the middle parallel, and without it at the extreme parallels. The surface of the cone is then supposed to be spread out into a plane.

A third method, which depends on the development of a cylindrical surface, is that according to which maps are so delineated as to have the parallels of latitude and circles of longitude respectively represented by parallel straight lines. By this method marine charts are constructed. As the rhumb makes equal angles with every meridian, it necessarily, according to this method of delineation, becomes a straight line. Such a representation of the earth's surface is commonly called Mercator's Chart, although the invention is due to an English mathematician, Edward Wright.

These are the three principal methods employed to represent to the eye the several countries on the surface of the earth.

I. Construction of Maps by Projection.

The representation of any portion of the earth's surface obtained by projection, varies, of course, its character according to the several situations of the eye and of the plane of projection, in relation to the meridians, parallels, and various points or places so represented. It is usual to assume the plane of a great circle of the sphere as the plane of projection, and to suppose the eye situated at some point in a straight line perpendicular to this plane, and passing through the centre of the circle. If the distance of the eye from the plane of projection be supposed indefinitely great, the projection is called the orthographic; if it is supposed to be upon the surface of the sphere, the projection is called the stereographic; and if the eye is supposed to be in such a position that the projections of the meridians and parallels of latitude are nearly equidistant, as the meridians and parallels themselves are upon the globe, the projection is called the globular. In order to apply these projections to the construction of maps, we must attend to the properties of each.

1. Orthographic Projection of the Sphere.

The fundamental principle in this projection is, that the representation of any point on the sphere is where a perpendicular from that point meets the plane of projection. Hence it follows that the projection of a line of any kind is determined by supposing perpendiculars to fall from every point in that line upon the plane of projection, and a line to pass through the points of intersection of these perpendiculars with that plane.

If the proposed line be a straight line, its orthographic projection will also be a straight line, being the intersection of the plane of projection with the plane perpendicular to it passing through the proposed line.

If the proposed line be the circumference of a circle parallel to the plane of projection, its orthographic projection will also be a circle of the same diameter; since the circle and its projection are the equal and parallel extremities of the cylinder formed by the perpendiculars falling upon the plane of projection.

If the proposed line be the circumference of a circle, of which the plane is perpendicular to the plane of projection, its orthographic projection will be a straight line equal to its diameter.

If the proposed line be the circumference of a circle, of which the plane is neither parallel nor perpendicular to the plane of projection, its projection will be an ellipse, being the curve in which the plane of projection intersects the cylinder formed by the perpendiculars falling upon it from every point in the circumference of the circle.

An accurate idea of the orthographic projection of any line or figure may be obtained by holding it up in the light of the sun, and observing the shadow formed on a plane perpendicular to the direction of the sun's rays. The rays which pass close to the figure are the perpendiculars to the plane of projection, and the shadow is the orthographic projection of the figure.

From the nature of this projection, the orthographic representation of half the surface of the globe shows nearly the true figure and proportions of countries about the middle of the map, that is, directly opposite to the supposed position of the eye; but towards the extremities the true figure and position of the countries are imperfectly exhibited. For this reason this method of projection is seldom employed in geography, but in astronomy it is frequently used. We shall give, however, the orthographic projection of the sphere on the plane of the equator and on the plane of the meridian.

To project the Sphere orthographically on the Plane of the Equator. From any point C as a centre, with any radius CA, describe the circle ABD. Let this circle represent the equator, upon the plane of which it is required to project the sphere orthographically. It is evident that the centre C will be the projection of the poles of the equator, and that since the planes of the meridian circles are perpendicular to the plane of the equator, these circles will be projected into diameters, making with each other the same angles as do the planes of the meridians. Let A90, B180, be two perpendicular diameters; they will represent two meridian circles at right angles to each other: divide the semicircle B90D into twelve equal parts at the points 15, 30, 45, &c., and let diameters be drawn through the points of division; then the twenty-four radii CB, C15, C30, &c. will be the projections of the twenty-four meridians usually drawn upon the globe, any one of which, as BC, may be considered as the first meridian.

Next, it is evident that the parallels of latitude will be projected into circles, which have C for their common centre, and of each of which the radius will be equal to that of the corresponding parallel of latitude, or to the cosine of the latitude of the parallel. Let us suppose that a parallel is drawn on the globe for every tenth degree of latitude; then divide the quadrant AB into nine equal parts, at the points 80, 70, 60, &c.; from these points of division let fall perpendiculars upon BC, meeting it in the points 80, 70, 60, &c.; the lines C80, C70, C60, &c. are equal to the cosines of the arcs B80, B70, B60, &c. to the radius BC. From the centre C, therefore, describe circles with these lines as radii; and these circles will be the projections of the parallels corresponding to the 80th, 70th, 60th, &c. degrees of latitude.

Lastly, the projections of the polar circles and of the tropics may be found by setting off from the point A towards B, and from the point B towards A, twenty-three and a half degrees, drawing perpendiculars to BC through these points of division, and describing circles from C as a centre through the points in which these perpendiculars cut BC.

Thus will the projection of the sphere upon the plane of the equator be completed. The representation given of the polar regions in a map of this description is tolerably correct, but the countries towards the equator are very much distorted.

To project the Sphere orthographically on the Plane of the Meridian. From any point C as a centre, with any distance CA, describe a circle PASB, to represent the meridian circle, on the plane of which it is required to project the sphere orthographically. Draw the diameters PS and AB at right angles to each other: then may PS be assumed as the projection of the meridian which is at right angles to the plane of projection; and AB will be the projection of the equator, since that circle cuts all the meridians at right angles. The other meridians cutting the projecting plane obliquely are projected into ellipses, having PS for their common transverse axis, and the cosines of their inclinations to the projecting plane for their several semiconjugate axes. Let the quadrant AS be therefore divided into six equal parts in the points 15, 30, &c. from which let 15m, 30m, &c. be drawn perpendicular to AC, and meeting it in m, n, &c. Describe the ellipses PamS, PanS, &c. having a common transverse axis PS, and Cm, Cn, &c. for their semiconjugate axes: these ellipses are the projections of the meridians passing through every fifteenth degree of the equator.

Again, to project the parallels of latitude: Divide either of the quadrants AP or BP into nine equal parts, in the points 10, 20, 30, &c. and draw through the points of division straight lines parallel to AB, the projection of the equator: these lines are the projections of the parallels on the one side of the equator to every tenth degree of latitude. The parallels on the other side of the equator are to be drawn in the same manner; as are also the tropics and polar circles, the former at 23°15' on each side of the equator, and the latter at 23°15' from the poles.

In this projection there is great distortion in the appearance of the regions about the poles, and of all the countries near the meridian PASB. It is as we approach the centre of the map that this distortion begins so far to disappear as to allow a projected portion of the earth's surface to acquire any considerable resemblance to its delineation on the globe.

2. Stereographic Projection of the Sphere.

In the stereographic projection of the sphere the eye is supposed to be situated at one of the points where the surface of the sphere is intersected by a straight line passing through the centre, and perpendicular to the plane on which the projection is to be made. This plane, as we have already remarked, is that of a great circle of the sphere; so that the point on the sphere at which the eye is supposed situated will be everywhere 90° distant from the circumference of that circle whose plane is assumed as the plane of projection. In order that the lines and circles on the sphere may be visible to the eye in this position, it will be necessary to suppose the sphere to be transparent. Let, then, ABEC be a great circle drawn on a sphere of this description, and let it pass through the eye at E. Let FG be a plane passing through a, the centre of the sphere, in such a manner as to cut the plane of the circle ABEC at right angles in the diameter HK, and to make each of the arcs EH, EK, equal to 90°; then FG will be the plane of projection. Draw EA the diameter of the sphere passing through the eye; also draw EB, EC, to B and C, any two points in the circumference of the circle ABEC; and let the lines EA, EB, EC, intersect the plane FG in the points a, b, c. By the fundamental principle of the stereographic projection, namely, that the representation of any point is where the straight line drawn from it to the eye intersects the plane of projection, the points a, b, c are the projections of the points A, B, C. It is evident also that the line bc, in which the planes EBC and FG intersect each other, is the projection of the line BC, or of the arc BAC; and that the lines ab, ac, are the projections of the arcs AB, AC.

Since aEb is a right angle, ab is the tangent of the angle aEb to the radius Ea. But the angle aEb is measured by half the arc AB; hence ab is the tangent of half the arc AB, or the semitangent of AB. Thus it appears, that if a great circle pass through the projecting point E, any arc of it reckoned from the opposite point of the sphere is projected into a straight line passing through the centre, and equal to the semitangent of that arc. Let BDC be any circle drawn on the sphere, and having BC for a diameter. Take D any point in the circumference of that circle, and draw ED intersecting the plane FG in the point d. If the point D be carried round the circumference BDC, the line ED will trace the surface of a cone of which BDC is the base; and the line bdc (the intersection of the plane FG with the conical surface), which is traced by the point d, is the projection of the circle BDC.

Now, it can be demonstrated that the angles EBC, ECB, are equal to Ecb, Ebc, each to each; so that the cones EBC, Ebc are similar. Hence the projection bdc is a circle, whose diameter bc is found by taking ab and ac equal to the semitangents of the arcs AB, AC.

Thus it appears that every circle of the sphere is, according to the stereographic projection, represented by a circle; but a circle can be described when three points in the circumference are given, or when two points in the circumference and the radius are given. Hence this property renders the projection of the sphere by this method very easy.

Another very elegant and important geometrical property of this projection is, that any two straight lines touching the sphere at one and the same point are represented by two straight lines which make with each other on the plane of projection an angle equal to that contained by the touching lines themselves. Hence also the angle formed by any two circles of the sphere is equal to the angle formed by their projections.

When it is further considered that the stereographic projection gives a representation of a hemisphere, in which the parts about the extremity of the map are less distorted than in the representation obtained by the orthographic projection, it must be concluded that the former method is preferable to the latter.

To project the Sphere stereographically on the Plane of the Equator. Upon C as a centre describe a circle ABGE to represent the equator, on the plane of which it is required to project the sphere; or rather that hemisphere which lies remote from the point of sight. As the eye must be supposed to be situated at the pole, it is evident that the centre C will be the projection of the opposite pole, and that the meridians will be projected into straight lines passing through C, and dividing the circumference of the circle ABGE into as many equal parts as there are meridians supposed to be drawn on the globe. If there are twenty-four meridians, then draw AG any diameter, and divide the semicircle AEG into twelve equal parts. Through the points of division draw diameters, as BCE FCK, DCH, &c., and the radii thus found will be the projections of the meridians corresponding to every fifteenth degree of the equator, any one of which may be assumed for the first meridian.

Again, to project the parallels of latitude; let AG and BE be perpendicular diameters. Divide the quadrant AB into nine equal parts in the points 10, 20, 30, &c. From E to the several points of division draw straight lines intersecting AC in the points 10, 20, 30, &c. The lines C10, C20, C30, &c. are the semitangents of the distances of the several parallels of latitude from the pole. Hence the points 10, 20, 30, &c. are the points of intersection of the projected parallels with the projected meridian AG. Upon C, then, as a centre, at the distances C10, C20, C30, &c. describe concentric circles, and these will be the projections of the parallels corresponding to every tenth degree of latitude. The tropics and polar circles are found in the same manner.

To project the Sphere stereographically on the Plane of a Meridian. From the centre C, with any radius CA, describe the circle ASBP to represent the meridian on the plane of which it is required to project the sphere stereographically. As the eye, in this case, is supposed to be situated at a point in the equator, that circle will be projected into a straight line passing through the centre C; let it be represented by the diameter AB. Draw the diameter PS perpendicular to AB; then will PS represent the meridian passing through the eye, and P and S will be the poles. To project the other meridians, divide the quadrant AP into nine equal parts (supposing a meridian to pass through every tenth degree of the equator) at the points 10, 20, 30, &c., and from S draw straight lines to these points of division intersecting AC in the points 10, 20, 30, &c. The lines C10, C20, C30, &c., are the semitangents of the arcs of the equator which measure the distances of the points in which the several meridians cut the equator from the point of the sphere opposite to the eye. Hence the points 10, 20, 30, &c., are the points in which the projected meridians will intersect the projected equator AB. But the projected meridians also pass through the points P and S. In each, therefore, there are three points given. If we describe, then, the arcs P10S, P20S, P30S, &c., these arcs will be the projections of the meridians on one side of that passing through the point opposite to the projecting point, and those on the other side are to be found in like manner.

Again, by dividing each of the quadrants PA, PB into nine equal parts, we find two points in each of the parallels of latitude. A third point in each will be found by drawing straight lines from B to each of the points of division 80, 70, 60, &c. so as to intersect PC in the points 80, 70, 60, &c.; for the lines C80, C70, C60, &c. are the semitangents of the arcs intercepted upon that meridian of which PS is the projection between the several parallels and the point of the sphere opposite to the projecting point. Describe, then, the several arcs through the three points found in each; and in this manner the parallels on one side of the equator are found. Proceed in the same manner with regard to the parallels on the other side of the equator, and with regard to the tropics and polar circles, and the projection will be completed.

It is evident that the centres of all the projected meridians will lie in the line AB, or in that line produced; and from the construction it is easy to show that the distance of the centre of each projected meridian from the point C is equal to the tangent of the inclination of the meridian to the plane of projection; while the radius of the projected meridian is equal to the secant of the same angle.

Further, the centres of all the projected parallels of latitude lie in the line PS, produced; and the centre of each projected parallel is distant from C by the secant of the arc which measures the distance of the parallel from the pole; while the radius of the projected parallel is equal to the tangent of the same arc.

To project the Sphere stereographically on the Plane of the Horizon for a given Latitude. We must here suppose the eye to be situated at the point of the sphere opposite to the place of which the latitude is given. From the centre C, with any radius CN, describe a circle NWSE to represent the horizon upon which it is required to project the sphere. To avoid intricacy among the lines necessary to be drawn for the construction, let the subsidiary circle NWSE be described with the same radius. Through C, the centre of the former circle, and C', the centre of the latter, draw two diameters WE, NS, and WE', NS', intersecting each other at right angles. Let the diameters NS, WE be the projections of the meridian of the given place, and of a semicircle at right angles to that meridian, and passing also through the given place. It is evident that the points N, W, S, E are the four cardinal points of the horizon. On the circumference of the subsidiary circle NW'S'E' take NP equal to the given latitude; and draw the straight line WP' intersecting CN in P': then will CP' be the semitangent of the distance of the pole from the point on the sphere opposite to the projecting point. Make therefore CP equal to CP', and the point P is the projection of the pole. Draw the diameters PP', FA' at right angles to each other; then will EA' be equal to the latitude; and by drawing WA' to intersect CS in A', we obtain CA' the semitangent of the distance of the point in which the equator intersects the meridian from the point of the sphere opposite to the projecting point. Make CA equal to CA'; and through the three points W, A, E describe an arc of a circle; the arc WAE will be the projection of the equator. Next, we shall show the manner of drawing the parallels of latitude, by taking as an example the two parallels which are twenty and forty degrees distant from the pole. In the subsidiary circle take P'20 and P'40, equal to 20° and 40° on each side of P'. Draw from W' to the points thus found straight lines intersecting CN and CS in the points a', b', and c', d'. The lines ab' and cd' are the diameters of the projected parallels corresponding to 50° and 70° of latitude. Make Ca, Cb, Cc, Cd, equal Ca', Cb', Cc', Cd' respectively, and upon ab and cd as diameters describe circles; these circles are the projections of the parallels required. In the same manner are the other parallels of latitude, the tropics, and the polar circles to be drawn.

Again, to project the meridians—the straight lines NP, PS, are the projections of the opposite meridians which pass through the north and south points of the horizon. The meridian circle, which is at right angles to that represented by NS, passes through the east and west points of the horizon, so that three points in its projection are given, namely, the points W, P, E; its projection may therefore be drawn. But it may be more conveniently found by considering that the meridian in question makes with the plane of projection an angle equal to the given latitude; the centre of its projection, which is in CS produced, must therefore be distant from the point C by the tangent of the given latitude, and its radius will be equal to the secant of the same. From the point S draw SD', touching the circle in S', and meeting PP' produced in D; then DS and DC are the tangent and secant of the given latitude. In CS produced take CB equal to DS'; and on B as a centre describe an arc through the point P, which will also pass through W and E. The arcs PW, PE will represent the opposite meridians, which are at right angles to the meridian of the place for which the projection is made. With regard to the other meridians, it is not difficult to see that their centres will lie in a straight line GH drawn through B at right angles to CB; and that the distance of the centre of each projection from the point B will be equal to the tangent of the inclination of the corresponding meridian circle to that meridian circle which passes through the east and west points; while the radius of the projection will be equal to the secant of the same inclination. Let us suppose, then, that the meridians are to make with each other angles each equal to 15°; at the point P make the angles BP15, BP30, &c., equal to 15°, 30°, &c., respectively, and let P15, P30, &c. meet the line GH in the points 15, 30, &c. Upon these points, as centres, describe through the point P the arcs mPm, nPn, &c.; then will Pm, Pn, &c., Pm', Pn', &c. be the projected meridians required. In this manner the projection may be completed.

3. Globular Projection of the Sphere.

In the globular projection of the sphere a point is assumed for the position of the eye, at a finite distance from the centre greater than the radius, and so situated that the degrees in the representation shall be nearly equal to each other, and the deviations from equality in the representations of equal portions of the spherical surface thus in some measure corrected. To determine the position of the point of view so as to answer these conditions, let ADBF be a section of the sphere made by a plane passing through C the centre, and through the point E which is assumed as the projecting point required. Through C draw EB, meeting the circumference ADBF in A and B, and draw the diameter DF at right angles to EB. Bisect the quadrant DB in I, and draw EI meeting DC in G; the point G will be the projection of the point I. But by hypothesis the projections of equal arcs are nearly equal; let then DG be assumed equal to GC. Join DB, and draw CI meeting DB in H. Join GH, and draw IK parallel to DC, or at right angles to AB. Then it is evident that DH is equal to HB; and therefore DH : HB :: DG : GC. Hence the line GH is parallel to CB; and we have IH : HC :: (IG : GE) : KC : CE. But IH is equal to BK, and HC to KC; therefore BK : KC :: KC : CE, and we have BK · CE = KC² = IK² = BK · KA. Hence CE is equal to KA; and taking away the common part AC, there remains EA equal to KC or to IK; that is, EA, the distance of the point of view above the surface, is equal to the sine of 45°. If the radius CA be divided into 100 equal parts, EA is therefore nearly equal to 71 of these parts.

This projection was first suggested by M. Delahire, and the approximation which it gives to equality in the projection of equal arcs of a circle perpendicular to the plane of projection is considerable. The circles of the sphere are, according to this method of projection, represented by ellipses. An approximation to this method is, however, generally all that is aimed at. The circles of the sphere are represented by circles; and, without any regard to the distance of a projecting point, the degrees of longitude on the equator and of latitude on the meridian are made all equal to one another; the plane of the meridian being assumed as the projecting plane. The following is the construction by which such a representation of a hemisphere of the earth's surface is obtained.

From the centre C (fig. 19), with any radius CA, describe a circle PASB to represent the meridian on which it is required to project the hemisphere. Draw the diameters AB, PS, at right angles to each other; and let PS represent the meridian of which the plane is at right angles to the Mathematical Geography.

To project the parallels on the north side of the equator, divide each of the quadrants PA, PB, into nine equal parts; also divide the radius CP into the same number of equal parts. Let 80, 70, 60, &c., d, e, f, &c., be the points of division; the parallel corresponding to 80° of latitude will pass through the three points 80, d, 80; that corresponding to 70° of latitude through the three points 70, e, 70, and so on. Describe circles, accordingly, through these points, and the parallels on the north side of the equator will be drawn. In the same manner are the parallels on the south side of the equator to be projected, as are also the tropics and polar circles.

Again, to project the meridians, divide the radius AC into six equal parts in the points a, b, c, &c., and through the points P and S, and these points of division, describe circles PaS, PbS, &c. Proceed in the same manner on the other side of PS, and the circles thus described will represent the meridians passing through every fifteenth degree of the equator, any one of which may, in laying down places by their latitudes and longitudes, be assumed for the first meridian. Plate CCLXVIII. is a planisphere, or map of the world, projected in this manner.

II. Construction of Maps by Development.

The practical application of the three methods of projection which we have now explained, to the construction of maps is usually confined to the representation of a hemisphere; whilst for the delineation of the geographical features of a single country, the method of development is commonly employed. The particular purpose for which a map is to be used may make it more or less important that it should exhibit, with all the precision that can be attained, some particular features of the country represented. The purposes of civil government require maps that give the true figure and dimensions of territory. For military affairs, maps that give correct distances are chiefly useful; whilst for the purposes of the navigator, the bearings of places, one from another, must be correctly, and, at the same time, simply exhibited. The first two objects are nearly gained in ordinary maps. But, for the attainment of the last, a map of a peculiar construction, called Mercator's Chart, has been invented; which, while it answers completely the purpose of the navigator, is not immediately applicable to any other.

It is an obvious property of a cone and of a cylinder, that the surface of each admits of being spread out on a plane. If a cone be laid with its slant side on a plane, the former will coincide with the latter along a line stretching from the point of contact in the base to the apex of the cone. Hence, if the cone is rolled round, whilst the apex continues at the same point, every point upon the surface of the cone will come in contact with a corresponding point in the plane surface; so that a sector of a circle will be described, with which the surface of the cone, if expanded, would exactly coincide. A cylinder admits of being rolled along a plane surface in a similar manner. But this is not the case with respect to a sphere. For since a sphere touches a plane only in a point, if the former be rolled along the latter in one direction, the successive points of contact will mark out a straight line. A narrow zone of the sphere may, however, be supposed, without great error, to coincide with the surface of a cone or cylinder; and this hypothesis gives rise to a twofold construction by development, that by the development of a conical surface, and that by the development of a cylindrical surface.

1. Development of the Curve Surface of a Cone.

Let NAMB be a section of the sphere by the plane of the meridian. Let NM represent the axis; then AB drawn through the centre C, at right angles to NM, will represent the diameter of the equator. Take EF, any arc of the meridian, and bisect it in the point G. Through G draw LD a tangent to the circle NAMB, and meeting the axis MN produced in the point L. Let the plane figure LGMB be now supposed to revolve about the axis LM; then will the semicircle NAM generate a sphere, and the line LD will generate a conical surface, which will touch the sphere. Further, the points E, G, F will describe circles, which will be parallels of latitude represented by the straight lines Eg, Gg, Ff, according to the principles of the orthographic projection. If EF be an arc of not many degrees, the zone comprised between the parallel circles Ee, Ff will nearly coincide with the corresponding portion of the conical surface intercepted between the planes of the same circles. Take any point H in the circumference of the circle described by G, the middle point of the arc EF, and join LH.

Let us now suppose the conical surface comprehended between the straight lines LG, LH, and the arc GH, to be spread out into a plane L'G'H'. Then it is evident that the arc GH on the middle parallel, of which the radius is the cosine of the middle latitude, is changed into an arc G'H' of which the radius is L'G' = LG the cotangent of the middle latitude. In the line L'G', and in L'G' produced, take G'F', G'E' equal to the arc EG or GF. Then, on the point L' as a centre, at the distances L'E', L'F' describe the arcs E'P, F's, and the plane surface E'F'sr may be considered as nearly equal to the spherical surface comprehended between the meridians passing through G and H, and the arcs of the parallels Ee, Ff intercepted by these meridians. Hence, if any tract of country situated on the corresponding portion of the earth's surface be delineated on the plane E'F'sr, the representation of it thus obtained will bear a near resemblance to its delineation on the globe, the resemblance increasing according as the zone comprehended between the extreme parallels is diminished in breadth.

Such is the principle of the conical development. Let us now consider how the line L'G' and the angle G'L'H' are to be determined, so as to suit the space E'F'sr to any given difference of longitude and given middle latitude; also in what manner the parallels of latitude and the meridians are to be drawn on that surface.

We have already seen, that L'G' is equal to the cotangent of the middle latitude to the radius of the sphere. If the radius of the sphere be considered equal to unity, the trigonometrical tables will give the length of L'G' in parts of the radius. But it will be more convenient to have it expressed in minutes of a degree. Now, since the semi-circumference is to radius as $3\cdot1416$ is to 1, if we put R for radius, we have $3\cdot1416 : 1 :: 180 \times 60 : R = 3437\cdot7$, which is the radius expressed in minutes of a degree. Hence L'G' expressed in the same manner will be equal to $3437\cdot7 \times \cotan$, middle latitude. Again, since the arc GH is equal in length to the arc G'H' by hypothesis, the angle at K measured by the former, must be to GL'H' measured by the latter, as the radius L'G' is to the radius GK; that is, if we put D for the difference of longitude, and ϕ for the angle GL'H', we will have \( \frac{D}{\phi} = \frac{(L'G')}{(GK)} : \cot. \text{mid. lat.} : \cos. \text{mid. lat.} \)

rad. : sine mid. lat. Hence we obtain

\[ \phi = D \times \text{sine mid. lat.} \]

The angle L' being thus determined, and the lines L'G', GE', GF' being known, and expressed in minutes of a degree, we can describe the figure EF'sr, so that it shall be accommodated to any given middle latitude and given difference of longitude. Then having divided EF' into as many equal parts as there are minutes in the difference of latitude, or as there are some given number of minutes in it, the points must be ascertained through which the parallels intended to be drawn pass, and from L' their common centre, these parallels are to be drawn accordingly. The parallels Er, Fs are in like manner to be divided each into as many equal parts as there are minutes, or some given number of minutes, in the difference of longitude; and points being ascertained in each of these parallels through which the meridians proposed to be drawn pass, the straight lines joining the corresponding points are the meridians required. It is by this method that common maps of particular countries are constructed.

As an example, let it be required to construct a map of Great Britain and Ireland, which must extend from 50° of latitude to about 61° north, and from 2° east to about 11° west longitude.

To find L'G', L'E', LT'.

| 61° | 61° | |-----|-----| | 50° | 50° |

\( 2)111 \quad 2)11 \quad \text{diff. of lat.} = 660' \)

\( 55°30' = \text{mid. lat.} \quad 5°30' = 330' = G'E' \text{or} G'F' \)

Log. cot. mid. lat., 55°30', 9-8371343

\( 343777 \ldots \ldots \ldots \log. 3-3562680 \)

\( L'G' = 2362'7 \ldots \ldots \log. 3-3734023 \)

\( G'E' \text{or} G'F' = 330'0 \)

\( L'E' = 2692'7 \)

\( L'F' = 2032'7 \)

To find the angle GL'H'.

Log. sine mid. lat., 55°30', 9-9159937

Diff. of long. = 13° = 780'. . . . log. 2-8920946

Angle GL'H' = 643° = 10°43'...log. 2-8080883

To find the chords of the arcs Er, Fs.

Chord of arc Er = \( \frac{2L'E'}{\sin \frac{1}{2} L'} \ldots \ldots \log. 3-7312180 \)

Chord of arc Fs = \( \frac{2L'F'}{\sin \frac{1}{2} L'} \ldots \ldots \log. 3-6098179 \)

Chord of arc Fs = \( \frac{2L'F'}{\sin \frac{1}{2} L'} \ldots \ldots \log. 3-6098179 \)

Chord of arc Fs = 379'1...log. 2-5787032

Having now determined the four sides of the trapezoid formed by the meridians EF' and rs, and the chords of the arcs Er, Fs, it is easy to describe that trapezoid, the length of the sides being measured on any convenient scale of equal parts, which is to be considered as a scale of minutes of a degree on the meridian. Let it be described accordingly, and let the sides EF', rs, be produced to meet in a point, which will be the point L'. Then, from that point as a centre describe the arcs Er, Fs, and divide these arcs each into thirteen equal parts, since the difference of longitude is 13°. Also, divide EF' and rs each into eleven equal parts corresponding to the given difference of latitude 11°. Having fixed upon the number of meridians and parallels of latitude that are to be drawn, describe from the point where the lines EF', rs, intersect when produced, as a centre, the parallels through the proper points of division in EF' or rs; and draw straight lines joining the proper corresponding points of division in Er, Fs for the meridians: we shall here suppose the meridians and parallels to be drawn for every second degree. Number the degrees of latitude and longitude as in the figure, and the map is prepared for having traced upon it the outline of the coasts of the British isles, and places laid down according to their latitudes and longitudes.

It is evident that if the point in which EF' and rs intersect each other becomes very distant, it may be exceedingly troublesome, or practically impossible, to describe from it as a centre the parallels of latitude. An obvious remedy for this inconvenience is, to join together two rulers, as AB, AC, at the point A, in such a manner as that they may contain an angle equal to the angle in the segment which has for its arc the parallel to be drawn. If the edges of the rulers be made, by means of two pins, to slide over the extremities D, E of the parallel, a pencil fixed at the angular point A will trace the parallel on the map. In the present instance the rulers must be placed so as to form an angle of

\[ \left( \frac{360° - 10°43'}{2} \right) = 174°38'30'' \]

The conical development has been variously modified, so as to remove as much as possible its defects. Thus, one modification was given by the Rev. Patrick Murdoch in the London Philosophical Transactions, 1758. He supposed the cone to pass through points of the meridian between the middle latitude and the extremities of the arc to be projected, its side being parallel to the tangent at the middle latitude, while the points where the cone intersects the meridian are so situated as that the conic surface is exactly equal to the spherical surface which it represents. Let M denote the arc of the meridian to be represented in the map; then, according to this method of development, L'G', the radius of the middle parallel on the map, is equal to

\[ \frac{\text{chord of arc } M}{\text{arc } M} \times \cot. \text{mid. lat.} \]

the cotangent being supposed to be expressed in parts of the radius of the sphere. In other respects the construction is the same as in the ordinary conical projection.

But the simplest and most successful method of remedying the defects of the conical development is that known by the name of Flamsteed's projection. The English astronomer by whom this method was invented, and whose name it bears, made use of it in constructing his celestial atlas. He developed all the parallels of latitude on the sphere into straight lines, and also one of the meridians, namely, that which passes through the middle of the chart. To this meridian the lines representing the parallels are perpendicular, and the length of each is the same with that of the parallel on the sphere which it represents. Dividing the parallels in the projection into equal parts, in like manner as the parallels on the sphere are divided, he supposed curved lines to be drawn through the corresponding points of division, and these curve lines represent the meridians. Flamsteed employed this projection in representing the position of the stars; but it is also made use of in geography, particularly for the delineation of countries which extend on both sides of the equator. To suit it more effectually to this purpose, it has undergone, however, a modification of very considerable importance, as it corrects in some measure the distortion in the figure of countries lying near the extremities of the map, which arises from the obliquity of the curve lines representing the meridians to the straight lines representing the parallels of latitude, the obliquity increasing as the former recede from the centre of the map. On the globe the meridians cut all the parallels of latitude at right angles; and by employing concentric circles instead of straight lines, as in Flamsteed's projection, to represent the parallels of latitude, the curves representing the meridians on the map may be made more nearly to fulfil this condition. For this purpose the common centre of the circles, which is situated in a straight line drawn through the middle of the map as an axis, is so assumed that the radius of the middle parallel of latitude is equal to the cotangent of the middle latitude; an assumption which diminishes as much as possible the obliquity of the angles made at the intersections of the curves which represent the meridians, with the circles which represent the parallels. In the position of the common centre of the circles representing the parallels of latitude, this modified projection of Flamsteed coincides with the ordinary conical projection.

We shall exemplify this construction by showing how to describe, according to it, the parallels and meridians for a map of Europe.

Let the map be supposed to extend from 35° to 70° north latitude. Hence the middle latitude will be 52° 30', and the radius of the middle parallel of the map (being equal to $3437\cdot7 \times \cot 52° 30'$) will be equal to 2637\cdot8'.

Draw, then, any line LE for the axis of the map; and assuming any point C for the point of intersection of the axis with the parallel of middle latitude, set off the length of the radius of that parallel from C to L, taken from any convenient scale of equal parts, which is to be considered as a scale of minutes of a degree. Thus the point L, the common centre of the circles representing the parallels, is determined.

Let us now suppose that a parallel is to be drawn through every tenth degree of latitude: that is, through 40°, 50°, 60°, 70°. As the middle latitude exceeds 50° by 150 minutes, take 150' from the scale of equal parts, and set it off from C to 50. Again, take 600, which are equal to 10°, from the scale of equal parts, and set off that distance from 50 to 40, from 50 to 60, and from 60 to 70. The point E, corresponding to 35°, is found by setting off 300' from the point 40. If we were to proceed according to Flamsteed's method, as originally employed by him, it would be necessary to draw straight lines through the points E, 40, 50, &c., perpendicular to DE, and therefore parallel to each other, and to make these lines equal respectively to the portions of the parallels on the sphere which they represent; then, dividing each line on both sides of the axis into as many equal parts as are indicated by the number of meridians intended to be drawn on each side of the axis, through the extremes and corresponding points of division to trace curve lines to represent the meridians. In this case the point L would not be required. But in the modification of the method which we are now exemplifying, from the point L as a centre an arc of a circle is to be described through each of the points E, 40, 50, &c., and each of these arcs of longitude is to be made equal to the arc of the parallel on the sphere which it represents. Let us then fix upon some meridian of a given number of degrees of longitude to the eastward and westward of that represented by the line DE, which is to be so drawn as to fulfil this condition. Let AB and ab be the meridians assumed, the former 30° to the westward, and the latter 30° to the eastward, of DE.

The arc BE or bE is equal in length to an arc of 30° on the parallel of latitude 35°. Now, the latter arc may be determined in geographical miles or minutes of the meridian by means of the table (page 481), showing the length of a degree of longitude for every degree of latitude in geographical miles. Thus, 30° on the parallel of 35° latitude is found equal to 1474\cdot5. But the arc BE is of the same length. Therefore we have BE or bE = 1474\cdot5.

We might next find the angle which the arc BE subtends at the centre L, and thus determine the points B and b. But it is more convenient to find the chord of the arc, which may be easily done as follows:

Put $a$ for any arc of a circle whose radius is $r$. Then

$$\sin a = a - \frac{a^3}{6r}$$ nearly, if the arc is not very great.

In this expression put $\frac{1}{2}a$ instead of $a$, and it becomes

$$\sin \frac{1}{2}a = \frac{1}{2}a - \frac{a^3}{48r}$$ nearly.

Doubling both sides of this equation, and observing that $2 \sin \frac{1}{2}a = \text{chord of } a$, we obtain

$$\text{chord of } a = a - \frac{a^3}{24r}$$ nearly.

For arcs not exceeding 30°, this formula will give the length of the chord with sufficient exactness. Let us apply it to find the chord of the arc BE.

Here $a = 1474\cdot5$, and $r = LE = 2637\cdot8$.

Log. $r = 3\cdot421242$

Log. $a = 3\cdot168645$

Log. $r^2 = 6\cdot842484$

Log. $a^2 = 9\cdot505935$

Log. $24 = 1\cdot380211$

Log. $24r^2 = 8\cdot222695$. Diff. of arc and chord, 19\cdot2, 1\cdot283240

Hence the chord of the arc BE is 1455\cdot3 of the meridian. Taking this number from the scale of equal parts, and setting it off from E towards B and b, the points B and b are determined.

Proceeding in the same manner, we may find the arcs of 30° of longitude, with their chords, on the other parallels of latitude; and thence determine the remaining points through which each of the projected meridians AB, ab passes. The curves drawn through these points will be the representations of the two meridians which have 30° of longitude to east and west of the meridian represented by DE.

The points in which the projections of the intermediate meridians intersect the projected parallels, may be found by dividing each parallel into thirty equal parts from the axis, both towards the right and left; then, by tracing curves through the proper corresponding points of division, as many meridians may be represented as are judged to be necessary. If the map is to extend farther than 30° on each side of its middle meridian, the division of the parallels may be extended to the necessary distance beyond the meridians AB and ab.

It is a consequence of the properties of this projection, that distances on the map may be readily and accurately measured by a scale of equal parts. This scale may be constructed as follows:

Draw a straight line AB (fig. 25) equal to any assumed number of degrees of latitude. If we assume 35 degrees, AB will be equal to DE. From B draw an indefinite line BC, making with AB any angle. Then, since AB is equal to 35°, or to 2417 English miles nearly, take 2417 from any convenient scale of equal parts and set that distance off from B towards C, making BD equal to 2417. From the same scale of equal parts take 100, or 200, &c. (in the present instance we shall take 300), according to the number of miles which each of the divisions of the scale is intended to represent; and with this distance in the compasses set off from B towards C the divisions Bm, mn, np, pq; the remaining part qD, being only 417, will not again contain it. Join AD; and through the points of division m, n, p, q, draw straight lines parallel to AD, and intersecting AB. Each of the divisions of AB thus found will represent 500 miles, with the exception of that adjacent to A, which will correspond to 417 miles. The distance of two places of the map applied to this scale will give the distance in English miles.

2. Development of the Curve Surface of a Cylinder.

The principle of this development is analogous to that of the conical, and may be illustrated in a similar manner. Let the arc AB be a fourth part of a meridian, and draw the lines AC, BC to the centre; these lines will be at right angles to each other, so that if we suppose BC to represent the semi-axis of the sphere, then AC will be the radius of the equator. Let EF be any arc of the meridian, and let it be bisected in G. Through G draw DH perpendicular to AC, or parallel to BC. If the plane figure BDGAC be supposed to revolve round BC as an axis, the arc AB will describe one-half of the surface of the sphere, the line DH will describe the surface of a right cylinder, the point A will describe the equator, and the points E, F, G will describe parallels of latitude. If EF be a small arc, the zone of the sphere which it describes will nearly coincide with the corresponding zone of the cylinder. Any tract of country delineated upon the former may, therefore, be nearly represented upon the latter; which being developed, the meridians and parallels of latitude become parallel straight lines, the former at right angles to the latter. Let EFe be a portion of the zone described by EF comprehended between two meridians of which the difference of longitude is equal to the difference of latitude of the parallels described by the points E and F. Since the difference of latitude and difference of longitude are supposed equal, the arc Gg is the same part of the middle parallel that EF is of the meridian. Hence rad.: cos. mid. lat.: EF : Gg; so that Gg, the breadth of the map representing the portion EFe of the spherical surface, may be found in minutes of the meridian. Upon these principles depends the construction of the plane chart, which is said to have been invented by Henry, son of John king of Portugal.

As an example, let it be required to construct a plane chart extending from 30° to 50° north latitude, and from 5° to 25° west longitude. Here the difference of latitude and difference of longitude are each equal to 20°, and the middle latitude is 40°. Hence we have EF, the length of the chart, equal to 1200', and the breadth of it equal to 919'25. Construct a rectangle EFeF, of which the sides EF, Fe are respectively equal to 1200 and 919'25 taken from any the same scale of equal parts, which is to be considered as a scale of minutes of the meridian. Divide EF and Fe each into four equal parts, and through the points of division draw straight lines parallel to Fe and EF, and these lines will represent the parallels of latitude and meridians for every fifth degree of latitude and longitude. If the chart is to extend to a greater number of degrees of longitude east or west, the parallels of latitude may be produced, and additional meridians drawn on the left of EF, or on the right of ef.

In the plane chart the degree of longitude evidently bears to the degree of latitude its proper proportion only at the middle parallel of latitude. Hence the rhumbs, as shown by this chart, are altogether erroneous, except when the places between which the rhumb is drawn are very near the equator.

To serve the purposes of navigation, for which the plane chart was utterly inadequate, the chart was published by Gerard Mercator in 1556 which usually bears his name; but the true principles of its construction were first demonstrated about 1590 by Edward Wright of Caius College, in Cambridge. This chart is constructed on the hypothesis that the globe is expanded so as to meet the interior surface of a cylinder constituted on the equator as its base, and having its axis coincident with that of the globe. The spherical surface is supposed to be stretched in such a manner that at every point the meridian and parallel are lengthened in the same proportion; so that at every point of the chart the ratio of the degree of longitude to the degree of latitude is preserved the same as it is at the corresponding point on the globe. Hence while the meridians become parallel straight lines, and consequently the rhumbs on the developed cylinder are also straight lines, the mutual bearings of places are still correctly shown. The problem of finding the lengthened meridians can be accurately resolved only by the assistance of the fluxional calculus (see Fluxions). But we may approximate to the solution by reasoning as follows:

Let AB be a quadrant of the meridian; draw AC, BC, to the centre; and let BC represent the semi-axis; then AC will be the radius of the equator; and if any point D be taken in the quadrant AB, the arc AD will be the latitude of the point D. Draw AG, CG, the tangent and secant of the arc AD, and DE, DF, its sine and cosine. The increase which the arc AD acquires in being transferred from the sphere to the cylinder is made at every individual point of the arc, so that the whole augmentation is the sum of these indefinitely small increments. Let us suppose, then, that AD is divided into a number of small portions, for example, into minutes. Then if we put L for any latitude, we have rad.: cos. L :: 1' of the meridian : 1' on the parallel whose latitude is L. But from the similar triangles GAC, CED, it is evident that CD : CE :: CG : CA; that is, for any latitude L, rad.: cos. L :: sec. L : rad.

Therefore we have, sec. L : rad.: 1' of the meridian : 1' on the parallel whose latitude is L; and this applies alike to every minute of which the arc AD is made up. Let us now suppose a minute on any one parallel to become equal to a minute on the equator, or to a minute of the meridian, by the parallel being brought into coincidence with the surface of the cylinder, in consequence of the expansion of the spherical surface. The minute on the meridian undergoes a corresponding increase. Let d denote it in its lengthened state; then, taking for granted that the increase on each minute of the meridian depends entirely on that of the higher of the two parallels which pass through its extremities, we obtain

\[ \text{sec. L : rad.} :: d : 1' \text{ of equator, or } 1' \text{ of meridian}; \]

hence \( d = \frac{\text{sec. L} \times 1' \text{ of meridian}}{\text{rad.}} \).

Let 1' of the meridian be now assumed as the radius; then \( d = \text{sec. L to the radius } 1' \text{ of the meridian}; \) or, since secants to different radii are proportional to one another, Thus the increased minute on the chart for each successive minute of which the arc AD on the sphere is made up, is proportional to the secant of the latitude of the higher of the two parallels which pass through the extremities of that minute. Let \( m \) denote the number of minutes in the arc AD, and take \( L = 1', 2', 3', \ldots, m' \) successively; and we obtain for the lengthened meridian corresponding to AD,

\[ \sec 1' + \sec 2' + \sec 3' + \ldots + \sec m'. \]

If we had divided AD into smaller portions than minutes, the approximation would have been so much the nearer to the truth. Upon this principle a table of the lengthened meridians corresponding to every degree and minute of latitude, called a table of meridional parts, is calculated; and by means of such a table Mercator's chart is easily constructed. The following table shows the length of the enlarged meridian for every fifth degree of latitude:

| Lat. | Merid. Parts. | Lat. | Merid. Parts. | |------|---------------|------|---------------| | 6° | 0-00 | 50° | 347-47 | | 5 | 300-28 | 55 | 3967-97 | | 10 | 603-07 | 60 | 4527-37 | | 15 | 910-46 | 65 | 5178-81 | | 20 | 1225-14 | 70 | 5965-92 | | 25 | 1549-99 | 75 | 6970-94 | | 30 | 1888-38 | 80 | 8375-20 | | 35 | 2244-29 | 85 | 10764-62 | | 40 | 2622-69 | 90 | Infinite | | 45 | 3029-94 | | |

The approximate numbers obtained in the manner now pointed out are sufficiently correct for all nautical purposes. From the more rigorous investigation afforded by the fluxional calculus, it is found that the enlarged meridian is proportionally equal to the logarithmic tangent of an arc found by adding to 45° half the arc of latitude reckoned from the equator. Thus, the meridional parts corresponding to 40° of latitude are equal to the logarithmic tangent of \((45° + 20°) = \log \tan 65° = 33133\); and the meridional parts corresponding to 50° are equal to \(\log \tan (45° + 25°) = \log \tan 70° = 43389\). These two numbers will be found to be nearly proportional to the numbers set down in the above table as denoting the meridional parts corresponding to 40° and 50° of latitude.

To construct Mercator's chart: Draw two straight lines WE, NS, cutting each other at right angles in the point C. Of these lines, WE is to represent the equator, and NS the meridian passing through the middle of the chart. From the point C set off equal parts on the equator both ways. These divisions are to represent degrees of longitude; and if the size of the chart will admit, each should be subdivided into minutes. Assuming the equator as a scale of minutes, set off from C towards the north and south on the middle meridian the number of minutes in the enlarged meridian, corresponding to each degree of latitude, as shown by a table of meridional parts. Draw straight lines through every fifth or every tenth degree of the equator and divided meridian, and at right angles to them. The lines at right angles to the equator will be the meridians; and those at right angles to the divided meridian, and therefore parallel to the equator, will be parallels of latitude. Any one of the meridians may be assumed as the first meridian.

To find the bearing of any one place from another, it is only necessary to draw a straight line from the one to the other, and to observe the angle which that line makes with the meridians: that angle is the bearing required, or the course on which a ship must be steered in sailing from the one place to the other. Thus, if L be the Lizard Point on the chart, and M the east end of the island of Madeira, join LM, and draw LK parallel to NS, and the angle KLM will be the course to be steered from the Lizard to reach Madeira. The distance of the places may be found by considering that it is the hypotenuse of a right-angled triangle of which the proper difference of latitude (not the meridional difference) is one side, and the course the adjacent angle.

Plate CCLXIX. is a chart of the world according to Mercator's projection. The great elongation of the degrees of latitude as we advance northward and southward, renders this projection very defective, in as far as the figure of countries and the relative distances of places are concerned. It answers, however, perfectly the purposes for which it was originally constructed, and has supplied what before its invention was a desideratum in geography.

To complete a map after the circles of latitude and longitude have been projected by any one of the foregoing methods the various objects within the range of the map are to be delineated on it in such a manner as to present to the eye a correct view of the country to be represented. The methods employed to give distinctness and extent to the information conveyed, will be best learned from the actual examination of good maps, both general and particular.

(J. W.—E.)