GEOGRAPHY is the science which describes the earth, the term being derived from two Greek words 1/C7, the earth, and yralchco, to write. By means of geography the surface of the earth is delineated and described, boundaries are defined, areas are exactly measured, and the relative positions of places are determined. Geography thus em- braces a wide range of subjects, and it has been found necessary to divide its study into several distinct sections.

I. Comparative Geography traces the history of discovery, and records the changes which have taken place in land and sea in historic times.

If. Mathematical Geography explains the figure, magnitude, and motion of the earth, teaches how to determine the positions of places on its surface, and shows how the whole or any portion of the earth may, on the principles of projection, be delineated on a map or chart.

Physical Geography is the description of the actual state of the earth's surface in its three great divisions - land, sea, and air.

Political Geography describes the earth as divided into countries, occupied by various nations, and improved by human art and industry.

The following article is limited to a view of the progress of geographical discovery, an explanation of the principles of mathematical geography, and a synopsis of physical geography. For details relating to political geography the reader must consult the descriptive articles under their particular headings.

I. VIEW OF THE PROGRESS OF GEOGRAPHICAL DISCOVERY.

Four main causes have led to geographical discovery and exploration, namely, commercial intercourse between different countries, the operations of war, pilgrimages and missionary zeal, and in later times the pursuit of knowledge for its own sake, which is the highest of all motives.

The Phoenicians are the earliest commercial people of whose discoveries we have any correct accounts. They first explored the shores of the Mediterranean, and eventually extended their voyages through the Straits of Gibraltar, and visited the western shores of Spain and Africa, planting colonies and opening wider fields for their commerce by instructing the natives in their arts and improvements. They also monopolized the trade with India; and their chief emporium, the rich city of Tyre, was the centre whence the products of the East and West were distributed. The trade of the West was brought from the port called Tarshish in Scripture, which is probably identical with Carthage, where the ships arrived from Spain, Africa, and distant Britain. Concerning the far eastern land reached by the Phoenicians, called Ophir in Scripture, there has been much dispute. The voyage to Ophir, we are told, occupied three years thither and homeward, and the cargo consisted of gold, ivory, apes, peacocks, and " algum" wood (1 Kings ix. 26, and x. 11). The following reasons lead to the conclusion that Ophir was the Malabar coast of India. In the Hebrew the word for apes is kople (without any etymology in Semitic tongues), in Sanskrit kaji. Ivory in Hebrew is shen-habbim ; in Sanskrit ibha is an elephant. Peacocks is in Hebrew toHi-ine from togei, the name still used on the Malabar coast, derived from the Sanskrit. Algum wood, or ahnug, is corrupted from valgu (ka), sandal wood from Malabar. Thus the Phoenicians were the first great carriers of the ancient world, extending their commercial operations from their central mart of Tyre on the Syrian coast to the tin-yielding isles of the Cassiterides in the far west, and to the ports of India in the east.

The great Phoenician colony of Carthage retained in full vigour the commercial spirit of the parent state. The Carthaginians traded on the coasts of Spain and Gaul, and extended their discoveries southwards along the coast of Africa, and to the Fortunate Islands, now known as the Canaries. Herodotus relates how the Phoenicians, setting sail from the Red Sea, made their way to the south, 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. But the most celebrated voyage of antiquity, undertaken for the purpose of discovery, was the expedition under Hamm, fitted out by the senate of Carthage with the view of attempting the complete survey of the western coast of Africa. Hanno is said, in the Periplus Hannonis, to have set sail with a fleet of 60 vessels, and the extent of his voyage has been variously estimated as reaching to the river Nun, to a little beyond Sierra Leone, and even as far as the Gulf of Benin, Another famous navigator, who sailed from the Carthaginian colony of Massilia (Marseilles) in about 320 B. C., was Pytheas. He steered northwards along the coasts of Spain and Gaul, sailed round the island of Albion, and stretching still further to the north, he discovered an island known to the ancients as Ultima Thule, which may possibly have been the Shetland Isles.

The conquests of Alexander the Great, by making known the vast empire of Persia, materially enlarged the bounds of geographical knowledge. Although the course of his expedition was mainly by land, the mind of the conqueror was also intent on commerce and maritime discovery. In 327 B.C. Alexander led an army of Greeks down the valley of the Cabul river into the Punjab, and his expedition resulted in a voyage of discovery from the month of the Indus to that of the Tigris, and in opening direct intercourse between Grecian and Hindu civilization. The Greeks who accompaniel Alexander were accurate observers, and described the towns and villages, the products and the aspect of the country, with care. The conqueror resolved to return through Gedrosia (the modern Baluchistan), but lie also intended to open the trade by sea between Europe and India, and his general Nearchus, a native of Crete, volunteered to lead this famous voyage of discovery. His fleet consisted of 30 galleys containing 2000 men. On October 2, 320 n.e., the fleet of Nearchus left the Indus, and the anchorages each night are carefully recorded. On the 17th of December Cape Jask was doubled and the fleet entered the Persian Gulf, and on the 9th of February it was at the mouth of the Karim. Nearchus rejoined Alexander at Susa ; and the conqueror himself embarked in the fleet and ascended the Tigris to Opis, above Baghdad. He then ordered his successful admiral to prepare another expedition for fhe circumnavigation of Arabia ; but unfortunately the great conqueror died at Babylon in 324 B.C., and the fleet was dispersed.

The dynasties founded by Alexander's generals, Seleucus, Antiochus, and Ptolemy, encouraged the same spirit of enterprise which their master had so carefully fostered, and extended geographical knowledge in several directions. Seleucus Nicator established the Greco-Bactrian empire, and continued the intercourse with India. The most authentic information respecting the Gangetic valley was supplied by Megasthenes, an ambassador sent by Selcucus, who reached the remote city of Patali-putra, the modern Patna-, on the Ganges.

. The Ptolemies of Egypt showed equal anxiety to extend the bounds of geographical knowledge. Ptolemy Euerget es sent an expedition which discovered Abyssinia, and fitted out a fleet under Eudoxus to explore the Arabian Sea. After two successful voyages, Eudoxus left the Egyptian service, and proceeded to Cadiz with the object of fitting • out an expedition for the purpose of African discovery ; and we learn from Strabo that the veteran explorer made at least two voyages southward along the coast of Africa. Tile Ptolemies sent fleets annually from their Red Sea ports of Berenice and Myos Hormus to Arabia, as well as to ports on the coasts of Africa and India.

The Romans did not encourage navigation and commerce with the same ardour as their predecessors ; still the luxury of Rome, which gave rise to demands for the varied products of -all the countries of the known world, led to an active trade both by ships and caravans. But it was the military genius of Rome, and the ambition for universal empire, which led not only to the discovery but also to the survey of nearly all Europe, and of large tracts in Asia and , Africa. Every new war produced a new survey and I itinerary of the countries which were conquered. In the height of their power the Romans had surveyed and explored all the coasts of the Mediterranean, Italy, Greece, the Balkan peninsula, Spain, Gaul, western Germany, and Britain ; but the eastern parts of Germany, Denmark, Sweden, and Russia were still unknown regions. In Africa their empire included Egypt, Carthage, Numidia, and Mauritania. In Asia they held Asia Minor and Syria, had sent expeditions into Arabia, and were acquainted with the more distant countries formerly overrun by Alexander, namely, Persia, Scythia, Bactria; and India. Roman intercourse with India especially led to the extension of geographical knowledge.

The first Roman who undertook a journey to India was solely influenced by the desire to acquire a knowledge of the people and their doctrines. This was Apollonius, a resident at Antioch, who set out towards the close of the first half century of our era. He and his attendants, Damis and Philostratus, reached the Indus, and journeying across the Punjab, came to a bronze pillar with the inscription "Here Alexander halted "; but it is doubtful whether the party advanced as far the Ganges. It was, however, in the reigns of Severns and his immediate successors that Roman intercourse with India was at its height.

In all time, while warriors and explorers extended the area of geographical knowledge, there have been students who have striven to systematize and put into due form the accumulated information. Front the first it was perceived that a knowledge of localities could not be attained without some notion of their relative positions, and their distances front each other. Consequently the attempts to establish fixed principles on which the surface of the earth, or any portion of it, could be delineated, were almost coeval with the earliest voyages of discovery.

The first attempt made to determine the position of places appears to have depended on the division of the earth into "climates,"distinguished by the species of aninialsaud plants produced in each. This method, however, was soon abandoned for another, which consisted in observing at places the length of the longest and shortest days by means of a "gnomon." An upright pillar of a known height being erected on a level pavement, by observing the lengths of the meridian shadows the progress of the sun from tropic to tropic was traced. The most ancient observation with the gnomon is that of Pytheas, in the days of Alexander the Great, who observed at the summer solstice at Massilia that the length of the meridian shadow was to the height of the gnomon as 213-I: to 600, an observation which makes the meridian altitude of the sun at Marseilles on that clay 70' 27'. The merit of the invention of the gnomon in Greece is ascribed to the astronomical school of Miletus ; but there is reason to believe that this method of observation was invented in Egypt, and that Tholes carried the knowledge of it into Greece. This was the first step towards connecting geography with astronomy; and little further advance was made until the establishment of the famous astronomical school of Alexandria, Eratosthenes (276-196 n.c.) 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 all the materials collected by Alexander and his generals. The doctrine of the sphericity of the earth had by this time been adopted, and the aim of Isis labours was to delineate, in conformity with this principle, the known parts of the earth's surface. 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 clay was known to be exactly of the same length. Such a line would evidently be a parallel to the equator. This first parallel passed through Rhodes, and was ever afterwards adopted as the basis of ancient maps. Eratosthenes continued his work by tracing other parallels at certain intervals from the first, one through Alexandria, another through Syene, a third through Meroe. He also traced, at right, angles to these, a meridian passim,b through Rhodes and Alexandria, southwards 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 next to determine the circumference of the globe by the actual measurement of a segment of one of its great circles. Posidonius made another measurement of an arc of the meridian between Rhodes and Alexandria about 170 years afterwards; but the amount of error in the calculations of Eratosthenes and Posidonius is uncertain, for want of a knowledge of the true length of the stadium in which their results are expressed. The ancients made their first meridian at the sacred promontory of Iberia, and their longitudinal error increased rapidly as they advanced eastwards. This is no doubt due to their longitudes being based entirely on distances calculated in the itineraries of travellers. Such data of course produced very great distortions in the representations given of the countries on the surface of the globe.

The improvements introduced by Eratosthenes were perfected in principle by Hipparehus, who flourished from 160 to 135 B.C. H.. was the first astronomer who undertook the arduous task of making 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 revolutions suggest two fixed points by which the position of the great circle of the celestial sphere, called the celestial 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 are of the meridian circle intercepted between tlr 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 Hipparchus arranged the stars according to their places in the heavens ; and 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 rule which he had introduced in the arrangement of the constellations. Thus he furnished the means of ascertaining the relative positions of places with far greater accuracy than could be obtained from itinerary measurements. He made a considerable number of observations for latitude, and pointed out how longitudes might be determined by observing the eclipses of the sun and moon.

. The most ancient maps that have reached modern times are those which illustrate Ptolemy's geography, but an earlier map made for Aristagoras, king of Miletus (500 me.), is minutely described by Herodotus. Ptolemy composed his system of geography in the reign of Antoninus Pius, about 150 A.D. His materials consisted of all the itineraries prepared by the Romans, 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, and various reports of travellers and navigators. Ptolemy undertook the task of comparing and reducing this mass of crude material into one system, following the principles laid down by Hipparchus, but which had been neglected during the two centuries and a half since his time, even by such men as Strabo and Pliny. In Ptolemy's work we find for the first time the mathematical principle of the construction of maps, as well as of several projections of the sphere.

The errors of Ptolemy arose from defective information, and the want in many instances, and especially as regards the remote parts of the then known world, of astronomical observations. He adopted the measure of a degree at 500 stadia ; and the latitudes along the chief parallel of Rhodes, as first laid down by Eratosthenes, are tolerably correct. But the elements for determining the longitudes were still derived from itineraries, and errors in latitude accumulated to the north and south of the central parallel.

Although Ptolemy was the first scientific geographer whose work has come down to us in a complete form, the earlier labours of Strabo, who lived in the reigns of Augustus and Tiberius, are of equal value, and we fortunately possess the whole of his 17 books. Pliny also devoted two books of his extensive work to geography ; and the scattered geographical notices of other ancient writers were collected into one work of four volumes by Hudson, and published between 1698 and 1712, with notes by Dodwell. From the days of Ptolemy to the revival of letters in Europe, little was done towards the scientific improvement of geographical science, though military and commercial enterprise led to a great extension of knowlege of the earth's surface.

After the dissolution of the Roman empire, Constantinople became the last refuge of arts, taste, and elegance ; while Alexandria continued to be the emporium whence were imported the commodities of the East. The em peror Justinian sent two Nestorian monks to China, who returned with eggs of the silkworm concealed in a hollow cane, and thus silk manufactures were established in the Peloponnesus and the Greek Islands. It was also in the reign of Justinian that Cosmas Indicopleustes, an Egyptian merchant, made several voyages, and afterwards composed his Topographia Christiana, containing a particular description of India. The great outburst of Mahometan conquest was followed by an Arabian civilization, having its centres at Cordova and Baghdad, in connexion with which geography again received a share of attention.

From the 9th to the 13th century intelligent _Mahometan travellers wrote accounts of what they had seen and heard in distant lands, which have been handed down to us ; ' while the caliphs of Baghdad encouraged the study of geographical science.

The caliph Al-Mamfin, the worthy son and successor of Harlin er-Rashid, caused an Arabic version of Ptolemy's great astronomical work (.,,,Ivra.;ts p.Ey1,0-7) to be made, which is known as the Almagest, the word being nothing more than the Greek p.Ey10-7,7 with the Arabic article al prefixed. The geography of Ptolemy is also constantly referred to by Arab writers. The learned men under Al-Mamfm began to apply themselves to astronomy in 813 A.D., following the system of Ptolemy ; and the first observations that are properly their own were made by El-Bathany in Mesopotamia, of the vernal and autumnal equinoxes, in 882 A.D. The Arab astronomers also measured a degree on the plains of Mesopotamia, and Ibn Yfinus observed three eclipses at Cairo. The caliph's librarian, Abu Jafar Muhammad Ben Musa, wrote a geographical work, now unfortunately lost, entitled Rasm el Arsi (" A Description of the World "), which is often referred to by subsequent writers as having been composed on the model of that of Ptolemy.

The earliest Arabian traveller whose observations have come down to us is the merchant Sulaiman, who embarked in the Persian Gulf and made several voyages to India and China, in the middle of the 9th century. Sulaiman's information was supplemented by that collected by another writer named Abu Zaid ; and, so far as India is concerned, this work is the most important that we possess before the grand epoch of the discoveries of Marco Polo. Next to Sulaiman followed the voyages of Sindbad the Sailor, whose narrative, though inserted in the Arabian Nights, also forms a distinct and separate work, which was translated into French by M. Langles in 1811. Baron Walckenaer ascribes to the voyages of Sindbad a date about coincident with those of Sulaiman. Ibn Khurdadra, a fire-worshipper converted to Islam, who died in 912 A.D., also wrote an account of India. Al Masudi, a great traveller who knew all the countries between Spain and China, described the plains, mountains, and seas, the dynasties and peoples, in his Muni ju-1 Zahab (" Meadows of Gold "). He died in 956. His contemporaries were Al Istakhri, who travelled through all the Mahometan countries, and wrote his Book of Climates in 950, and Ibn Haukal, whose Book of Roads and Kingdoms was written in 976. AI Idrisi was born at Ceuta, and after travelling far and wide, settled in Sicily, where he was induced by Roger II., the Norman king, to write his book on geography, the full title of which is The Delight of those who seek to 'wander through the Region-s of the-Wo•ld. Finally Al Kazwini, who was a compiler from the works of Istakhri and Ibis Hanka] in about 1263, brings us down to the times when the Italian explorers began to make known the vast realms of Asia to the people of Europe.

The Mongol and Turkish dynasties, which succeeded each other after the fall of the Arabian caliphs, also produced rulers who encouraged geographical science. Philosophers assembled at the court of Hulaku Khan (1253-1264) at Maraghah in the north of Persia; and his friend NilsiruidDin was the most famous astronomer of the age. He constructed the tables known as the Tables of the Ilkhany, which corrected some important errors in the former mode of adjusting the commencement of the new year. Nearly two centuries later, in 1446, Ulugh Begl, of the house of Titular, succeeded to the throne of Samarkand, and under his auspices the famous tables called " Zij Ulugh Begh " were composed. They continued to be authorities for long afterwards, and even Kinneir, in determining the latitudes of places in Persia, often quotes the tables of Ulugh Begh.

The Northmen of Denmark and Norway, who were the terror of all the coasts of Europe, and who established themselves in England and Ireland, in France and Sicily, were also great promoters of geographical discovery during the darkest period of the Middle Ages. The Northmen were far from being always vikings, bent only on rapine and plunder. They were very often peaceful merchants. King Alfred sent Ulfsten and the Norwegian Ottar on voyages of discovery towards the White Sea ; and the Scandinavian merchants brought the products of India to England and Ireland. From the 8th to the 11th century a commercial route from India passed through Kharism and Novgorod to the Baltic, and immense quantities of Arabian coins have been found in Sweden, and particularly in the island of Gothland, which are preserved at Stockholm. Five-sixths of them were from the mints of the Samanian dynasty, which reigned in Khorasan and Transoxiana from about 900 to 1000 A.D. It was the trade with the East that originally gave importance to the city of Visby in Gothlau d.

In the end of the 9th century Iceland was colonized from Norway ; and in 985 the intrepid viking Erik, surnamed the Red, discovered Greenland, and induced some of his Icelandic countrymen to settle on its inhospitable shores. In 986 young Bjorni, son of one of Erik's comrades, sailed from Iceland to join his father in Greenland, but shaped his course too far to the south, and was the discoverer of America. He sailed along the coasts of Connecticut, Massachusetts, and Nova Scotia, before he eventually found the fjord on the Greenland coast where his father dwelt. Then Leif, the son of. Erik, bought the ship from young Bjorni and made another voyage of discovery, and once more the coast of America was visited. Other-expeditions were undertaken by his two brothers, intercourse was kept up between Greenland and Norway, and the saga of Thorfinn tells us of other voyages to America. The last that was heard of the Norwegian colonies in Greenland was in a brief of Pope Nicolas V. in 1448, where it is stated that, 30 years before, the settlements had been destroyedlay the attacks of savages. Two noble Venetians, Nicolo and Antonio Zeno, who were in the service of the prince of the Faroe Islands in the end of the 13th century, recorded their observations respecting the Norse colonies. Antonio actually went to Greenland, and heard of the visits of fishermen to two parts of North America called Estotiland and Drogeo.

At length the long period of barbarism which accompanied and followed the fall of the Roman empire drew to a close in Europe. The crusades had a very favourable influence ' on the intellectual state of the Western nations. Interest ing regions, known only by the scant reports of pilgrims, were made the objects of attention and research ; while religous zeal, and 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. Among these was Benjamin of Tudela, who set out from Spain in 1160, travelled by land to Constantinople, and having visited India and some of the eastern islands, returned to Europe by way of Egypt after an absence of 13 years.

Christian missionary zeal was another motive for exploration. John of Plano Carpini in Perugia, a Franciscan monk, was the head of one of the missions despatched by Pope Innocent to call the chief and people of the Tatars to a better mind. He reached the headquarters of Bahl, on the Volga, in February 1246 ; and, after some stay, went on to the camp of the great khan near Karakorum, and returned safely in the autumn of 1247. A few years afterwards, a Fleming named Rubruquis was sent by St Louis on a mission to the Tatar chiefs, and wrote a very interesting narrative. He entered the Black Sea in May 1253, visited Batu and the court of the great khan Mangu near Karakorum, and got back to Antioch about the end of June 1255. Rubruquis had the merit of being the first modern traveller who gave a correct account of the Caspian Sea. He ascertained that it had no outlet. At nearly the same time Hayton, king of Armenia, made a journey to Karakorum in 1254, by a route far to the north of that followed by Carpini and Rubruquis. He was treated with honour and hospitality, and returned by way of Otrar, Samarkand, and Tabriz, to his own territory. The curious narrative of King Hayton was translated by Klaproth.

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. Among these were Nicole. and Maffeo Polo, two brothers who traded with the East and visited Tatary. The recital of their travels fired the youthful imagination of young Marco Polo, the son of Nicole, and he set out for the court of Kublai Khan, with his father and uncle, in 1265. After a journey of three years and a half they reached Yen-king, near.the spot where Peking now stands, and young Marcc was enrolled among the attendants of honour of the Grand Khan. During the seventeen years that he remained in this service, Marco Polo was employed on important missions ; and besides what he learnt from his own observation, he collected from others much information concerning countries which he did not visit. He returned to Europe possessed of a vast store of knowledge respecting the eastern parts of the world, and, being afterwards made a prisoner by the Genoese, he dictated the narrative of his travels during his captivity. The work of Marco Polo is the most valuable narrative of travels that appeared during the Middle Ages, and its latest and ablest editor truly says, "All other travellers of that time are but stars of a low magnitude beside the full orb of Marco Polo."

Still these minor orbs continued to do useful geographical work, while striving to spread the truths of the Gospel. Among them were John of Monte Corvino, a Franciscan monk, Andrew of Perugia, John Marignioli, and Friar Jordanus, who visited the west coast of India, and above all Friar Odoric of Pordenone. Odoric set out on his travels in about 1318, and was in western India and northern China between 1321 and 1328, dying in 1331. He went by Constantinople to Trebizond, thence through Persia to Ormuz, where he embarked for Tana in Salsette. He then went to Malabar, Sumatra, and Java, and by the ports of China to Cambaluc or Peking, where he remained for three years. Turning westward he journeyed by Shensi into Tibet, and was the first European to visit Lassa. His homeward journey led him by Cabul and Khorasan to Tabriz, and thence to Venice. His companion was an Irishman named Friar James.1 Ibn Batuta, the great Arab traveller, is separated by a wide space of time from his countrymen already mentioned, and he finds his proper place in a chronological notice after the days of Marco Polo - for he was not born at Tangier until 1304. He began his wanderings in 1325, his career thus coinciding in time with that of Sir John Mandeville (1322-1356), but the Moor was more trustworthy than the Englishman. Ibn Batuta went by land from Tangier to Cairo, then visiting Syria, and performing the pilgrimages to Medina and Mecca. After exploring Persia, and again residing for some time at Mecca, he made a voyage down the Red Sea to Yemen, and travelled through that country to Aden, which remarkable place he correctly describes. Thence he visited the African coast, touching at Momboas and Quiloa, and then sailed across to Ormuz and the Persian Gulf. He crossed Arabia from Bahreyu to Jiddah, traversed the Red Sea and the desert to Syene, and descended the Nile to Cairo. After this lie revisited Syria and Asia Minor, crossed the Black Sea to Caffa, and proceeded to the camp of the khan of Kipchak at the foot of the Caucasus. Ibn Batuta crossed the desert from Astrakhan to Bokhara, and went over the Hindu Kush to Cabul, reaching the Indus somewhere below Larkhana, in 1333. Ile gives an interesting account of Muhammad Tughluk, then ruler of Delhi, in whose service the great traveller remained for about eight years. He was sent on an embassy to China in 1312, travelling by laud from Delhi to the seaport ; whence the ambassadors sailed down the west coast of India to Calicut, and then visited the Maldive Islands and Ceylon. He made a voyage through the Islands to China, and on his return he proceeded from Malabar to Baghdad and Damascus, where he got his first news from home and heard of his father's death. Finally he reached Fez, the capital of his native country, in November 1349, after an absence of twenty-four years, and came to the conclusion that there was no place like home. After a journey into Spain, he set out for Central Africa in 1352, and reached Timbuctoo and the Niger, returning to Fez in 1353. He had travelled over a length of at least 75,000 English miles. His narrative was committed to writing from his dictation, by order of the sultan of Fez, and the work was completed in December 1355. Ibn Batuta, died at the age of seventy-three, in the year 1377. His whole work was carefully edited in the original, with a translation into French under the auspices of the Asiatic Society of Paris, and published in 1858. Colonel Yule has given us an English version of the portion relating to China.

Ibn Batuta was certainly the greatest of Arab travellers, and soon after his death in the kingdom of Fez, the opposite realm of Spain began to send forth explorers to distant lands. The peaceful reign of Henry III. of Castile is fatuous for the attempts of that prince to extend the diplomatic relations of Spain to the remotest parts of the earth. Mariana tells us that he sent embassies to the princes of Christendom and to the Moors. In 1403 the Spanish king sent a knight of Madrid, named Ruy Gonzalez de Clavijo, to the court of the mighty Timur, at Samarkand. He re turned in 1406, and died soon after, but not before he had written a most valuable and interesting narrative of his travels from Constantinople through Persia and Khorasan to the Oxus, and thence by the Iron Gates to Samarkand.

Several Italians continued to make important journeys in the East during the 15th century. Among them was Nicolo Conti, who passed through Persia, sailed along the coast of Malabar, visited Sumatra, Java, and the south of China, returned by the Red Sea, and got home to Venice in 1441, after an absence of twenty-five years. He related his adventures to Poggio Bracciolini, secretary to Pope Eugenics IV. ; and the narrative contains much interesting information, Towards the end of the same century, the Venetians sent several embassies to Uzun Hassan, the ruler of Persia, and to Shah Ismail, his successor; and the narratives of the envoys furnish some new geographical information. The first of these was Caterino Zeno, who induced Uzun Hassan to make war on the Turks in 1472 ; and he was followed by Josafat Barbaro and Ambrogio Contarini. Another Venetian travellerof this period, whose narrative has been preserved, was Giovan Maria Angiolello. He was in the service of the Turks, and was present in their campaign against the Persians. One of the most remarkable of the Italian travellers was Ludovico di Varthema, whose insatiable desire to see foreign countries induced him to leave his native land in the year 1502. He went to Egypt and Syria, and for the sake of visiting the holy cities became a Mahometan. After many extraordinary adventures he got on board a ship at Aden. Varthema is the first European who gave an account of the interior of Yemen. He afterwards visited and described many places in Persia, India, and the Eastern Archipelago, returning to Europe in a Portuguese ship after an absence of five years.

In mentioning Varthema we have anticipated events ; but in the 15th century the time was approaching when the discovery of the Cape of Good Hope was almost indefinitely to widen the scope of geographical enterprise. The great event was preceded by the discovery of the polarity of the magnetic needle, and the consequent construction of the mariner's compass. This most important discovery appears to have been made in China, and it is uncertain when the compass was first used by Western nations. Its introduction has been attributed to Flavio Gioia, a citizen of Amalfi, in the kingdom of Naples, about the year 1307. 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 method of sailing along the shore, and boldly committed his bark to the open sea. Navigation was then destined to make rapid progress. The growing spirit of enterprise, combined with the increasing light of science, 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, and foremost in the front rank of the worthies of this little hero-nation stands the figure of Prince Henry the Navigator.

The work of Prince Henry is well defined by his biographer, Mr Major. Until his day the pathways of the human race had been the mountain, the river, and the plain, the strait, the lake, and the inland sea. It was he who first conceived the thought of opening a road through the unexplored ocean, - a road replete with danger but abundant n. promise. Born on March 4, 1394, Prince Henry war, a younger son of King Joao of Portugal and of Philippa of Lancaster, the grandchild of Edward III.; so that be was half an Englishman. Prince Henry relinquished the pleasures of the court, and took up his abode on the inhospitable promontory of Sagres, at the extreme south-western angle of Europe. To find the sea-path to the " thesauris Arabum et divitis " was the object to which he devoted his life. He collected the information supplied by ancient geographers, unweariedly devoted himself to the study of navigati in and cartography, and invited, with princely liberality of reward, the co-operation of the boldest and most skilful navigators of every country. The prince's motto was " Talent de Bien faire," - the word " talent," in those days, conveying not the idea of power or faculty, but of desire. Having acquired military renown by the capture of Ceuta in 1415, he set his mind upon the conquest of Guinea, and sent every- year two or three vessels to examine, the coasts beyond Cape Nun, which was then the limit of exploration. Yet none of his ships for many years had the hardihood to round Cape Bojador.

The first fruit of Prince Henry's explorations was the rediscovery of Madeira and Porto Santo, in 1418 and 1120. The truth of the romantic story of the first discovery of Madeira by two English lovers named Robert Machim and Anna d'Arfet, in the time of Edward III., has been demonstrated by Mr Major. Madeira and Porto Santo were granted to Prince Henry by his brother, King Duarte, in 1433. In the same year one of the prince's ships, commanded by Gil Eannes, at length doubled Cape Bojador. In 1435 Affonso Gonsalves Baldaya, the prince's cup-bearer, passed 50 leagues beyond the cape ; and eight years afterwards Nuiio Tristam got to a point 25 miles beyond Cape Blanco. But it was not until 1445 that the mouth of the Senegal was reached by Diniz Dias ; and in those days the Portuguese gave the name of Guinea to the country commencing at Cape Nun. In 1481 the king of Portugal assumed the title of lord of Guinea. Up to 1446 there had been 51 caravels to the Guinea coast, and almost every year some new advance was made. Meanwhile the Canaries and Azores were brought within the realms of Spain and Portugal. In 1402 a Norman named Jean de Bethencourt, accompanied by Gadifer de la Salle, had lauded on the island of Lancarote, and with reinforcements from Spain lie subjugated Forteventura and Ferro, and received the sovereignty of the Canaries from the king of Castile. But he returned to his lands in Normandy in 1406, and died there in 1425. Gomera, Palma, Teneriffe, and the Great Canary were still unconquered. Prince Henry made several attempts to establish Portuguese rule on these islands ; the right was long disputed with Spain ; and it was not until 1479 that the treaty of Alcacora provided for the concession of the sovereignty of the Canaries to Spain. Prince Henry, however, successfully colonized the Azores, and in 1444 St Michael's was discovered, the settlement of the other islands following soon afterwards.

In 1455 an important expedition was despatched by Prince Henry, under the command of a young Venetian adventurer named Advise Cadamosto. Touching at Madeira and the Canaries, Cadamosto made his way to Cape Blanco on the African coast, and thence to Senegal and the Gambia. He returned with a full report of all he had seen, and in the following year he again sailed from Lagos direct for Cape Blanco, with three ships, and discovered the mouth of a river which he named the Rio Grande (Jeba I). In 1457 Diogo Gomez sailed with orders to proceed as far as he could, and made his way to the Gambia. The Cape Vcrd Islands were discovered and colonized about 1462.

Prince Henry the Navigator died on the 13th of November 1460, and was buried near his father and mother in the monastery of Batalha. In 1839 a monument to his memory was erected at Sagres. During the long period in which the prince was continuing his maritime explorations, he did not cease to cultivate the science of cartography. The geographer Jayme of Majorca superintended his school of navigation at Sagres, and at the prince's instance the finest specimen of medireval map-making that has been preserved was prepared at Venice under the superintendence of Era Mauro of the Camaldolese convent of San de Marano. The geographical knowledge of the 15th century is also shown by the famous Borgia map (see PlateIl.), a bronze planisphere which came into the possession of Cardinal Borgia about 1794, and was published in 1797 by the cardinal's nephew. The Borgia map, however, is of the very beginning of the 15th century.

The progress of discovery for a time received a check from the death of Prince Henry, but only for a time. In 1462 Pedro de Cintra extended Portuguese exploration 600 miles beyond the furthest point reached by Cadamosto, and discovered Sierra Leone, Fenian Gomez followed in 1469, 'and opened the trade with the Gold Coast ; and in 1181 Diogo Cam discovered the mouth of the Congo. The king of Portugal next despatched two vessels of 50 tons in August 1486, under the command of Bartholomeu Dias, to continue discoveries southwards ; while, in the following year, he sent Pedro de Covilham and Alfonso de Payva to discover the country of Prester John. Dias succeeded in rounding the southern point of Africa, which he named Cabo Tormentoso ; but king Joao II., foreseeing the realization of the long-sought passage to India, gave it the endur- ing name of the Cape of Good Hope. t:Dias returned to Lisbon in December 1487 ; meanwhile Payva had died at Cairo ; but Covilham, having heard that a Christian ruler reicoled in the mountains of Ethiopia, penetrated into Abyssinia in 1490. He delivered the letter which Jolio II. had addressed to Prester John to the negfis Alexander of Abyssinia, but he was detained by that prince and never allowed to leave the country.

The results westward and eastward of the exertions of Prince Henry were the discovery of America by Columbus and of the Cape route to India by Vasco da Game.

Christopher Columbus was born at Genoa about 1435. His name in Italian was Colombo, and in Spain he is known as Cristoval Colon. The fame of the Portuguese discoveries attracted strangers from all parts of the world, and in 1470 Columbus arrived at Lisbon. He was in Portugal from 1470 to 1484, during which time lie made several voyages to the coast of Guinea in the Portuguese service. He married a daughter of Bartholomeu Perestrello, to whom Prince Henry had granted the commandership of Porto Santo, and lived for some time on that island. He learned, from many pilots experienced in the western voyages to the Azores, facts and signs which convinced him that there was an unknown land towards the west. Columbus also studied the Imago Hundi of Cardinal Pierre d'Ailly, whence he culled all he knew of Aristotle and Strabo ; and lie read the narrative of Marco Polo. By 1474 his grand project of discovery was established in his mind, and nothing afterwards could divert him from the pursuit of it. On the refusal of the king of Portugal to entertain his proposal, Columbus left Lisbon with his son in 1484, and he spent the interval until 1492 in appeals to the Spanish court. At length, having overcome all obstacles, lie set sail with a fleet of three ships from Palos, on the 3d of August 1492, on his unprecedented and perilous voyage. On the 12th of October, having crossed the Atlantic, Columbus sighted laud, which was named San Salvador. Mr Major has recently proved that this island is one of the Bahamas, now known as Watling Island. After discovering Cuba, Hispaniola, and many small islands, Columbus set sail on his return voyage on January 16, 1493, and arrived at Palos on the 15th of March. His reception in Spain was enthusiastic, and commensurate with the grandeur of his achievement ; and on the 25th of September 1493 he sailed from Cadiz on his second voyage, with a fleet of three large ships and fourteen caravels. On the 3d of November he discovered the • island of Dominica, and during the voyage his discoveries included the Windward Islands and Jamaica. He returned to Cadiz on June 11, 1496 ; and it was not until May 30, 1498, that he set sail on his third voyage. The first land lie came to formed a new discovery, which he named the island of Trinidad, and it was in this voyage that he reached the mainland of South America, and discovered the islands of Cubagua and Margarita. A colony had been formed on Hispaniola, and soon afterwards a judge named Francisco de Bobadilla arrived from Spain, having been sent, at the i instigation of the great discoverer's enemies, to inquire into his conduct. Bobadilla Kiized upon the government, and sent Columbus home in chains. Ferdinand and Isabella were overwhelmed with shame, and the people with astonishment, on his arrival. He was at once released, and false promises of restitution and reward were profusely made. I3ut Bobadilla was superseded, not by Columbus, but by Nicolas de Ovando. On the 9th of May 1502, however, Columbus was allowed to sail on a fourth and last voyage of discovery. He reached the island of Martinique on the 13th of June, and touched at Dominica and Hispaniola. Thence he sailed westward, discovering the coast of Veragua and the harbour of Porto Bello. After a stay in Jamaica, lie set sail for Spain on the 12th of September 1504, and arrived at San Lucar on the 7th of November. He lived for two years longer, experiencing the blackest ingratitude from the Spanish court. At length, in debt and poverty, and bowed down by disappointment, this great man died May 20, 1506, His body was buried at Valladolid, and removed in 1513 to Cartuja de las Cuevas near Seville. A monument was erected over his grave, with the inscription - A Castilla y Leon, Nuevo Mundo dig Colon.

In 1536 the bodies of Columbus and his son Diego were transported to St Domingo; and thence they were removed to Havana in 1795. The ashes of the immortal discoverer now repose in the cathedral of Havana.

While Columbus was discovering a new world, the Portuguese continued their persevering efforts to reach India by sea. Vasco da Gama sailed from Lisbon on the 8th of July 1497 with four vessels built expressly for the voyage, the largest not exceeding 120 tons, and called the " Sam Gabriel." His brother Paolo commanded the " Sam Raphael," and the " Berrio" was under Nicolas Coelho. On November 22, with a fair wind, Da Gam rounded the Cape of Good Hope, and anchored in the bay named San Bras by Bartholomeu Dias, on the 25th. On Christmas Day he sighted land, which, on that account, he named Natal. He reached Motriba,s on the 7th of April, and on the 20th of May 1498 lie anchored before Calicut. Da Gama returned to Lisbon in August 1499 ; and at his recommendation another fleet was fitted out, consisting of thirteen well-armed ships, under Pedro Alvarez Cabral, with 13artholomen Dias and Nicolas Coelho under his orders. The expedition sailed on the 9th of March 1500; and on the 22d of April Cabral discovered the coast of Brazil, and took formal possession for the king of Portugal. Resuming his voyage to the East, he reached Calicut in September, and obtained permission to build a factory, establishing friendly relations also at Cananor and Cochin. He returned to Lisbon in July 1501. Vasco da Game set sail, with a much larger fleet, on his second voyage in 1502. He visited several ports on the west coast of India, engaged in war as well as in commerce, and returned in September 1503. In 1503 Antonio da Saldanha and Affonso de Albuquerque sailed for India, and made terms of friendship with the chief of Quilon. Dom Francisco de Almeida, the first viceroy of the Indies, was sent out in 1505. He founded the ports of the Angediva and Cananor, and his son Laurette° discovered Ceylon. Tristam da Cunha, with Affonso de Albuquerque under his orders, was sent to occupy Socotra, and in 1506 Albuquerque came to India as second viceroy. He explored the coasts of Arabia and Persia, made the king of Ormus tributary to Portugal, and sent embassies to Abyssinia. In 1509 (7) a factory was established at Malacca ; and on November 25, 1510, the great Albuquerque conquered Goa, and established the seat of his government there. In 1512 the .Moluccas were discovered ; and in 1517 Fernam Peres de Andrade reached China, and entered into commercial relations with the governor of Canton. In 1524 Vasco da Gama arrived in India for a third time, as viceroy, and landed at Goa on the 11th of September. He died at Cochin on the 24th of December 1524, and in 1538 his body was transported to Portugal, and buried in his tomb at Vidigueira, of which town he was count.

The voyages of Vasco da Gama revolutionized the cornmerce of the East. Until then the Venetians held the carrying trade of India, which was brought by the Persian Gulf and Red Sea into Syria and-Egypt, the Venetians receiving the rich products of the East at Alexandria and Beyrout, and distributing them over Europe. This commerce was a great source of wealth to Venice ; but after the discovery of the new passage round the Cape, and the conquests of the Portuguese, the trade of the East passed into other hands.

The achievements of Columbus and Da Gama are immeasurably enhanced when we consider the inadequate means at their disposal, their small and ill-formed ships, and their defective knowledge of navigation. The mariner's compass had been in use for nearly two centuries, and it was Columbus himself who first observed the phenomena of variation. But the compass and rough sea-card were the only appliances, until the learned Nuremberger, Martin Behaim, invented the application of the astrolabe to purposes of navigation, winch enabled mariners to ascertain their latitude. This was in the year 1480. The astrolabe was used by Vasco da Gama on his first voyage round the Cape of Good Hope ; but the movement of a ship rendered accuracy impossible, and the liability to error was increased by the necessity for three observers. One held the astrolabe by a ring passed over the thumb, the second measured the altitude, and the third read off. The astrolabe was a metal circle graduated round the edge, with a limb called the alkidada fixed to a pin in the centre, and working round the graduated circle. The instrument had two sights fitted upon it, one at each end, and was suspended by a ring so as to hang vertically ou one hand, while the alhidada was worked up and down until the sun could be seen through both the sights. It then gave the zenith distance. The Ordemanzas of the Spanish council of the Indies record the course of instruction prescribed for pilots, which included the De Spluera Mundi of Sacrobosco, the spherical triangles of Regiomontanus, the ,Ilnut gest of Ptolemy, the use of the astrolabe and its mechanism, the adjustments of instruments, cartography, and the methods of observing the movements of heavenly bodies. The only observations employed by the ancients for finding the longitude were those of the eclipses of the moon, and it was not until 1610 that Galileo discovered another method by observation of Jupiter's satellites.

The discoveries of Columbus awakened a spirit of enter- S prise in Spain which continued in full force for a century ; e. adventurers flocked eagerly across the Atlantic, and dis- P covert' followed discovery in rapid succession. Many of the companions of Columbus continued his work. Pinzon in 1499 reached the mouth of the Amazon ; and in the same year Alonzo de Ojeda, accompanied by a Florentine named Amerigo Vespucci, touched the coast of South America A somewhere near Surinam, following the shore as far as the V Gulf of Maracaibo. Vespucci afterwards made three voyages to the Brazilian coast; and in 150 I he wrote an account of his four voyages, which was widely circulated, and became the means of procuring for its author the high honour of giving his name to the whole continent. Mr Major has discussed the hitherto obscure question of the way in which the name " America" originated, in a paper distinguished for great learning and very able criticism. He has shown that the word " America " first appeared on the Mappe Monde drawn by Leonardo da Vinci, and he explains the chain of circumstances which led to its adoption. The first map known to exist with America delineated upon it is that drawn by Juan de la Cosa, the pilot of Columbus in his second voyage, which is dated 1500. Juan de In Cosa was with Ojeda and Vespucci, and afterwards with Ojeda in his last ill-fated expedition. In May 1507, just a year after the death of Columbus, one Martin Waldseemiiller (Hylacornulus) wrote a work called Cosmogrophiw DntrQdsrctio, to which was appended a Latin edition of the four voyages of Vespucci. In this book, which was printed at St Die in Lorraine, he proposed that the name of America should be given to the New World. In 1508 the first engraved map containing the Ne w World appeared, in an edition of Ptolemy printed at Rome, but it does not bear the name of America. But in 1509 the name " America," proposed by HylacomuIns in 1507, appears, as if it was already accepted a-s a well-known denomination, in an anonymous work entitled Maus ilfundi, published at Strasburg. This was three years before the death of Vespucci. The Hoppe _.-ifonde of Leonardo da Vinci, to which Major assigns the date of 1514, has the name of America across the South American continent.

In 1508 Ojeda obtained the government of the coast of South America from Cabo de la Vela to the Gulf of Darien; and at the same time Diego Nicuesa was appointed governor of Veragua from the Gulf of Darien to Cape Gracias a Dios. The two adventurers arrived at Hispaniola together ; but Ojeda set out first for his government, landed at Carthagena in 1510, and sustained a bloody defeat from the natives, in which his lieutenant, Juan de la Cosa, was killed. Ojeda then embarked, and eventually selected a site on the east side of the Gulf of Darien for his seat of government. Here he was again defeated by the natives, and, returning to Hispaniola for aid, he died there in extreme poverty. Nicuesa was still more unfortunate, and died at sea. The Spaniards in the Gulf of Darien were left by Ojeda under the command of Francisco Pizarro, the future conqueror of Peru. After suffering from famine and disease, Pizarro embarked the survivors in small vessels, but outside the harbour they met a ship which proved to be that of the bachiller Martin Fernandez Enciso, Ojeda's partner, coming with provisions and reinforcements. They all returned to their settlement called San Sebastian, but found that the Indians had destroyed the fort, and Enciso determined to abandon it. One of the crew of Enciso's ship, Vasco Nunez de Balboa, the future discoverer of the Pacific Ocean, induced his commander to form a settlement on the other side of the Gulf of Darien. The soldiers became discontented and deposed Enciso, when Vasco Nunez, a clever and courageous adventurer, took command of the Darien settlement in March 1511. Enciso was a man of learning, and an accomplished cosmographer. His work Soma de Geoyrafia, which was printed in 1519, is the first Spanish book which gives an account of America. Vasco Nunez, the new commander, entered upon a career of conquest in the neighbourhood of Darien, which ended in the discovery of the Pacific Ocean on the 25th of September 1513. In 1514 Pedrarias de Avila, an old man of rank and some reputation, but with no ability, and of a malicious disposition, was appointed to supersede Vasco Nunez as governor of Darien, and the bachiller Enciso came out in his fleet. Pedrarias, on a false pretext, beheaded Vasco Nunez in 1517, which was one of the greatest calamities that could have happened to South America at that time ; for the discoverer of the South Sea was on the point of sailing with a little fleet into his unknown ocean, and a humane and judicious man would have been the conqueror of Peru, instead of the cruel and ignorant Pizarro. In the year 1510 Panama was founded by Pedrarias ; and the conquest of Peru by Pizarro followed a few years afterwards. Tiernan Cortes overran and conquered Mexico from 1518 to 1521, and the discovery and conquest of Guatemala by Alvarado, of Florida by -Hernando de Soto, and of Nueva Granada by Quesada, followed in rapid succession. The first detailed account of the west coast of South America was written by that keenly observant old soldier, Pedro de Cieza de Leon, who was travelling in South America from 1533 to 1550, and published his story at Seville in 1553.

But the great anxiety of the Spanish Government at that time was to find a westward route to the Moluccas. For this purpose Juan Diaz de Solis was despatched in October 1515, and in January 1516 he discovered the mouth of the Rio de la Plata. He was, however, killed by the natives, and his ships returned, In the following year Magellan laid before Charles V., at Valladolid, a scheme for reaching the Spice Islands by sailing westward. He had already served with his own countrymen, the Portuguese, on the coast of India and at the taking of Malacca, and he was an accomplished and resolute seaman. With a fleet of five ships, and the rank of captain-general, Magellan sailed from San Lucar on the 21st of September 1510. After touching on the coast of Brazil, at the Rio de la Plata, and at the ports on the east coast of Patagonia, Magellan entered the straits which bear his name in October 1520. In consequence of many fires being seen on the southern shores of the strait, he named that country Tierra del Fuego. The fleet, now consisting of the "Trinidad," " Vittoria," and "Concepcion," emerged from the strait and entered the Pacific Ocean on the 27th of November 1520. They then steered north-west, crossed the line on the 13th of February 1521, and on the 6th of March reached the Ladrone Islands. Thence Magellan proceeded to the Philippines. He was killed in an attack on the island of Matan, which he made in order to bring it under subjection to his ally the king of Zebu, on the 26th of April 1521. Thus fell this great navigator, who was second only to Columbus in the history of nautical exploration. His brother-in-law, Duarte Barbosa, was selected to succeed Magellan in command of the fleet, with Joao Serrao as his colleague. They were both killed in battles with the natives, and eventually a Biscayan named Sebastian del Cano, sailing home by way of the-Cape of Good Hope, reached San Lucar in command of the "-Vittoria" on the 6th of September 1522, with eighteen survivors. Del Cano was received with great distinction by the emperor, who granted him a globe for his crest, and the motto " Primus circumdedisti me."

While the Spaniards were circumnavigating the world and completing their knowledge of the coasts of Central and South America, the Portuguese were actively engaged on similar work as regards Africa and the East Indies.

In Abyssinia the mission of Covilham led to further: intercourse. In April 1520 the Portuguese viceroy of the • Indies took a fleet into the Red Sea, and landed an embassy consisting of Dorn Rodriguez de Lima and Father Francisco Alvarez, a priest whose detailed narrative is the earliest and not the least interesting account we possess of Abyssinia. It was not until 1526 that the embassy was dismissed ; and not many years afterwards the negfls entreated the help of the Portuguese against Mahometan invaders, and the viceroy sent an expeditionary force, commanded by his brother Cristoforo da Gama, with 450 musketeers. Da Gama was taken prisoner and killed, but his Portuguese enabled the Christians of Abyssinia to regain their power, and a Jesuit mission remained in the country. While Abyssinia was thus opened to the enterprise of the Portuguese on the east side of Africa, they also established a close connexion with the kingdom of Congo on the west side, and obtained much information respecting the interior of the continent. Duarte Lopes, a Portuguese settled in the country, was sent on a mission to Rome by the king of Congo, and Pope Sixtus V. caused him to recount to his chamberlain, Felipe Pigafetta, all he had learned during the nine years he had been in Africa, from 1578 to 1587. This narrative, under the title of Description of the Kingdom of Congo, was published at Rome by Pigafetta in 1591. A map was attached on which the two equatorial lakes, Victoria and Albert Nyanza, and Lake Tanganyika are shown, and the empire of Monomoezi or Uniamuezi is laid down. The most valuable work on Africa during the 16th century is, however, that written by Leo Africanus. This famous traveller was born at Granada, and retired into Africa when his native town was captured by the Spaniards. He travelled extensively in the north and west of Africa, and was eventually taken by pirates and sold to a master who presented him to Pope Leo X. At the pope's desire he translated his work on Africa into Italian, and died in about the year 1526.

In the East Indies the Portuguese acquired predominating influence at sea, establishing factories on the Malabar coast, in the Persian Gulf, at Malacca, and in the Spice Islands, and extending their commercial enterprises from the Red Sea to China. Their missionaries were received at the court of Akbar, and Benedict Goes, a native of the Azores, was despatched on a journey overland from Agra to China. He started in 1603, and, after traversing the least known parts of Central Asia, he reached the confines of China. He appears to have ascended from Cabul to the plateau of the Pamir, and thence onwards by Yarkand, Khotan, and Aksu. He died at a place called Socieu in March 1607; and thus, as one of the brethren pronounced his epitaph, "seeking Cathay he found heaven."

The activity and love of adventure, which became a passion for two or three generations in Spain and Portugal, spread to other countries. It was the spirit of the age ; and England, Holland, and France soon began to enter upon the same glorious career. English enterprise was first aroused by John and Sebastian Cabot, father and son, who came from Venice and settled at Bristol in the time of Henry VII. The Cabots received a patent, dated March 5, 1496, empowering them to seek unknown lands ; and John Cabot discovered Newfoundland and part of the coast of America. Sebastian afterwards made a voyage to Rio de la Plata in the service of Spain, but he returned to England in 1548, and received a pension from Edward VI. "in consideration of the good and acceptable services done and to be done." He was placed at the head of the Society of Merchant Adventurers, and, by his knowledge and experience, he was the means of keeping alive the spirit of enterprise in England, and of extending her foreign commerce. At his suggestion a voyage was undertaken for the discovery of a north-east passage to Cathay, with Sir Hugh - Willoughby as captain-general of the fleet, and Richard Chancellor as pilot-major. They sailed in May 1553, hut Willoughby and all his crew perished in a harbour on the Lapland coast. Chancellor, however, was more fortunate. He reached the White Sea, performed the journey overland to Moscow, where he was well received, and may be said to have been the founder of the trade between Russia and England. He returned to Archangel and brought his ship back in safety to England. On a second voyage, in 1556, Chancellor was drowned; and three subsequent voyages, led by Stephen Burrough, Pet, and Jackman, effected an examination of the straits which lead into the Sea of K ara.

The French followed closely on the track of Join Cabot, and the hardy Norman and Breton seamen frequented the banks of Newfoundland at the commencement of the 16th century. In 1524 Francis I. sent Giovanni da Verazzano of Florence on an expedition of discovery to the coast of North America ; and the details of his voyage were embodied in a letter addressed by him to the king of France from Dieppe, in July 1524. On April 20, 1534, Jacques Cartier sailed from St Malo with two vessels of 60 tons each, for the purpose of continuing the discoveries of Verazzano, and he visited Newfoundland and the Gulf of St Lawrence. In the following year he made another voyage, discovered the island of Anticosti, and ascended the St Lawrence to a place called Hochelaga, now Montreal. He returned, after passing two winters in Canada; and on another occasion he also failed to establish a colony. Admiral de Coligny made several unsuccessful endeavours to form a colony in Florida under Jean Ribault of Dieppe, Rene de Landonniere, and others, but the settlers were furiously assailed by the Spaniards and the attempt was abandoned.

The reign of Elizabeth is famous for the gallant enterprises that were undertaken by sea and land to discover and bring to light the unknown parts of the earth. The great promoter and father of English geographical discovery was Richard Hakluyt, who was born near London in 1553. He was at Westminster School, and when quite a boy he imbibed a love for cosmography and maritime discovery. At Oxford he read all the narratives of voyages and travels that came within his reach, and delivered lectures on cartography. In 1585 be was at Paris, as chaplain to the English embassy, and in 1605 he became a prebendary of Westminster. He was the chief promoter in the formation of the two companies for colonizing Virginia in 1606; and he devoted his life to the encouragement of similar undertakings, and to their record. Hakluyt died in 1616, and was buried in Westminster Abbey. He was incessantly employed in the collection, examination, and translation of accounts of voyages and travels, and of charters, letters, and other documents bearing on the subject, and in correspondence with men eager either to impart or receive information. Sir Philip Sidney, Sir Francis Walsingham, Lord Thomas Howard, and Sir Francis Drake were among those who supported and encouraged him, and Ortclius and Mercator were his correspondents. His first work was the Divers Voyages touching the Discoverie of America ; and the second was brought out while he was in Paris in 1586, entitled A Notable Historic containing FOUre Voyages made by French Captaynes unto Florida, In 1587 he published at Paris a revised edition of the De Orbe Eovo of Peter Martyr Anghiera. His Principal Xavigations was published in folio in 1589, and dedicated to Sir Francis Walsingham ; and the new edition, in three volumes, appeared in 159S. Hakluyt also got translations made of Leo Africanus, of Mendoza's History of China, and of Galvano's Discoveries of the World, which were"published. His last publication was a translation of Hernando de Soto's discoveries in Florida. He left many valuable papers at his death, most of which, together with a vast number of other narratives, were published in 1622 in the great work of the Rev. Samuel Purchas, entitled " Hakluytus Posthumus, or Purchas his P ilgr im es."

It is from the rich treasure-house of Hakluyt and Purchas that our knowledge of the gallant deeds of the English and other explorers of the Elizabethan age is mainly derived. The great collections of voyages and travels of De Bry and Hulsius served a similar useful purpose on the continent of Europe. One important object of English maritime adventurers of those days was to discover a route to Cathay by the north-west, a second was to settle Virginia, and a third was to beat up the Spanish settlements in the Indies. Nor was the trade to Muscovy and Turkey neglected ; while latterly a resolute and successful attempt was made to establish commercial relations with East India.

Martin Frobisher led the way in the direction of the north-west, sailing from the Thames in 1576, and sighting the southern part of Greenland on the 11th of July. In as this voyage he discovered a part of the coast of Labrador, and the strait (now known to be a deep bay) which bears his name. He brought home some stones which were believed to be gold, and the consequence was that there arose an eager desire to obtain more. Many speculators subscribed, and Frobisher was sent out on a second voyage, "more for the searching of this gold ore than for the searching any further discovery of the passage." He left Gravesend on May 27, 1577, wasted his time in picking up stones on the shores of Frobisher's Strait, and returned on the 22d of August.. The excitement about the gold ore still continued. The queen gave the name of ifeta Incognita to the newly discovered country ; and on May 21, 1578, Frobisher set out on a third voyage with a fleet of fifteen ships. After touching at Greenland, they made for the opposite shore through an ice-encumbered sea, and the fleet was separated during a heavy gale. They reached various ports in England during October, and by that time the bubble about the gold ore had burst, and the enterprise was considered a failure. The first of the three voyages alone was a voyage of discovery.

In 1585 John Davis, an admirable seaman and most resolute explorer, was employed by some merchants, chief among whom was Mr William Sanderson of London, to take up the glorious work where Frobisher had left off. He sailed from Dartmouth on the 7th of June 1585, and, reaching the south-west coast of Greenland, he called it the " Land of Desolation." He then stood over to the opposite coast, which he examined in the neighbourhood of Cape Walsingham, returning to Dartmouth on September 30. In 1588 he sailed on the 7th of June and coasted along Greenland, having friendly intercourse with the Eskimo. He also examined part of the Labrador coast. In his third voyage he sailed from Dartmouth on the 17th of May, and sighted Greenland on the 14th of June. On this occasion he went as far north as 72' 12', naming the great island bluff - which is now so well known to voyagers up Baffin's Bay - " Sanderson his Hope of a North-West Passage." Crossing over Davis Strait, the bold explorer discovered the strait which now bears the name of Hudson. Davis was followed in his northern voyages by Waymouth, and Knight ; and in 1607 Henry Hudson was despatched on a voyage of discovery in a small vessel of 80 tons. He sighted the east coast of Greenland in 73° N., examined the north-west end of Spitzbergen, as far as a point which he named Hakluyt Headland, and reached 80° 23' N. In 1608 he made a second voyage, during which he examined the edge of the ice between Spitzbergen and Greenland. In his third voyage, in 1609, he was employed by the Dutch, and discovered the Hudson River. In 1610 he was again employed by English merchants, and entered Hudson's Bay, but was infamously abandoned in an open boat by his crew. In 1612 Sir Thomas Button continued the exploration of Hudson's Bay, which was completed by Thomas James and Luke Fox in 1631.

In 1616 the little bark "Discovery," of 35 tons, was fitted out by those persevering adventurers Sir Thomas Smith, Sir Dudley Digges, John Wolstenholme, and Alderman Jones, for another attempt in the icy seas. This was the most successful Arctic voyage of the 17th century. Robert Bylot was appointed master of the " Discovery," and William Baffin was pilot. They sailed from Gravesend, with 17 souls on board, on the 26th of March, and were ull Hope Sanderson, the extreme point of Davis, on the 30th of May. The " Discovery " reached what is now called " the north water" of Baffin's Bay on the 1st of July, and, after discovering the head of the great bay which bears his name, the pilot Baffin returned by sailing down the west side of it.. On August 30 the " Discovery " was again safely anchored in Dover roads. It was exactly 200 years before any other vessel followed in her track, and reached "the north water." Both Davis and Baffin afterwards served and were killed in the East Indies.

The Dutch emulated the English in the Arctic seas during this period. Their merchants opened a trade avith Kola and Archangel as early as 1578, but the difficulty of penetrating into the Sea of Kara led them to try the possibility of finding a passage round the northern end of Novaya Zemlya. The credit of the conception of this voyage is due to the great cosmographer Peter Plancius, and the merchants of Amsterdam adopted the idea, and despatched a vessel of 100 tons called the " Mercurius," under the command of William Barents. He sailed from the Texel on June 4, 1594, and sighted Novaya Zemlya on the 4th of July. Sailing northwards along the coast he rounded Cape Nassau and reached the edge of the ice. For many days he perseveringly sought for a passage through it. In his second voyage he merely went to the entrance of the Sea of Kara. But his third voyage was the most important. Heemskerk was the commander, Barents was pilot, and the mate, Gerrit de Veer, was the historian of the voyage. They sailed from Amsterdam on May 13, 1596. On June 19, Spitzbergen was discovered, and the whole western coast and part of the northern examined. The record of the subsequent proceedings of Barents and his crew, of their famous voyage round the north-western end of Novaya Zemlya, and of their terrible sufferings in the first Arctic winter ever faced by Europeans, is deeply interesting as it is told in the simple narrative of Gerrit de Veer. Barents had long been ill, and when they set sail from their dismal winter harbour on June 14, 1597, in open boats, he was too weak to stand, and was carried from the house. He died on the 19th, and found a grave in the midst of his discoveries.

The maritime enterprise of England, in the days of Elizabeth, was mainly directed towards the discovery of a north-west passage ; but many voyages were also made to Guinea and the West Indies, and twice English vessels followed in the track of Magellan, and circumnavigated the globe.

In 1577 Francis Drake, who had previously served with Hawkins in the West Indies, undertook his celebrated voyage round the world. His fleet consisted of three ships and two pinnaces, which were broken up during the voyage. The ships were the " Pelican " of 100 tons, on board of which Drake himself embarked, the "Elizabeth "of 80, and the " Marigold" of 30 tons. After some stay at Port San Julian on the coast of Patagonia, the fleet entered the Straits of Magellan on the 20th of August 1578, when Drake changed the name of his ship to the " Golden Hind." They reached the western entrance on the 6th of September, and soon afterwards the "Marigold " parted company in a gale of wind, and was never heard of again, while the "Elizabeth" basely deserted her consort and returned to England. Drake, in the " Golden Hind," continued the voyage alone. At first he was driven to the southernmost point of Tierra del Fuego, and thus discovered that there was a passage, though he did not round Cape Thorn. He then proceeded northward along the west coast of America, touching at the island of Mocha off the Milan coast, at Valparaiso, Coquimbo, Tarapaca, Arica, Callao, and Payta. Off Cape San Francisco, nearly on the equator, lie captured a very rich Spanish treasure-ship called the " Cacafuego"; and it is right to observe that England was then at peace with Spain. Drake resolved to attempt the discovery of a passage from the Pacific to the Atlantic, and with this object he continued to shape a course northwards along the American continent. On the 5th of June 1579 the "Golden Hind" reached her most northern point in 48°, when the attempt was abandoned, and Drake put into a harbour to refit, named Port Drake, which appears to have been the modern harbour of San Francisco, on the coast of California. The coast from the southern extremity of the Californian peninsula to Cape Mendocino was discovered by Juan Rodriguez Cabrillo and Francisco de Ulloa in 1539. Drake's discoveries extend rum Cape Mendocino to 48° N.

Leaving California, Drake sailed across the Pacific and reached the Philippine Islands in October. He touched at Ternate and Java, and rounded the Cape of Good Hope on June 15, 1580. The "Golden Hind " anchored safely at Plymouth on the 26th of the following September. Drake was graciously received and knighted by the queen, and the " Golden Hind," the first English ship that circumnavigated the globe, was preserved for many years at Deptford. When at last she was broken up, a chair was made from one of her planks and presented to the university of Oxford.

Mr Th nnas Cavendish, a gentleman of Suffolk, emulous of Drake's example, fitted out three vessels for an expedition to the South Sea, and sailed from Plymouth on July 21, 1586. Cavendish passed through Magellan's Straits in January 1587, and, taking the same route as Drake along the west coast of America, he reached Mazatlan in September. A rich Spanish treasure-ship was captured off Cape San Lucas, the southern extremity of California, on the 4th of November, and Cavendish then steered across the Pacific, seeing no land until he reached the Ladrone Islands. He arrived safely at Plymouth on the 9th of September 1588. The third English voyage into the Pacific was not so fortunate. Sir Richard Hawkins sailed from Plymouth on the 12th of June 1593 in the good ship " Dainty," passed through Magellan's Straits, and all went well until they reached the bay of Atacames, 57 miles north of the equator, in June 1594. Here the English were attacked by a Spanish fleet, and, after a desperate naval engagement, Hawkins was forced to surrender. Hawkins declared his object to be discovery and the survey of unknown lands, and his voyage, though terminating in disaster, bore good fruit. The Observations of Sir Richard Hankins in. Ms Voyage into the South Sea, published in 1622, are very valuable, and form the most charming work of the kind which was written during that period. It was long before another English ship entered the Pacific Ocean. Sir John Narborough took two ships through the Straits of Magellan in 1670 and touched on the coast of Chili; but it was not until 1685 that Cook and Dampier sailed over the part of the Pacific where, nearly a century before, the " Dainty " had to strike her flag to the Spaniard.

The exploring enterprise of the Spanish nation did not wane after the conquest of Peru and Mexico, and the acquisition of the vast empire of the Indies. It was rather spurred into renewed activity by the audacity of Sir John Hawkins in the ,Vest Indies, and by the appearance of Drake, Cavendish, and Richard Hawkins in the Pacific.

In the interior of South America the Spanish conquerors had explored the region of the Andes from the isthmus of Panama to Chili ; and in 1541 Francisco de Orellana discovered the whole course of the Amazon from its source in the Quitenian Andes to the Atlantic. A second voyage down the great river was made in 1561 by the mad pirate Lope de Aguirre ; but it was not until 1639 that a full account was written of the mighty stream by Father Cristoval de Aculia, who ascended it from its mouth to the city of Quito. The voyage of Drake across the Pacific was preceded by that of Alvaro de Mendafia, who was despatched from Peru in 1567 to discover the Australian land which was believed to exist in the South Sea. After a voyage of eighty days across the Pacific,Mendafia discovered the Salomon Islands ; and the expedition returned in safety to Callao. The appearance of Drake on the Peruvian coast led to an expedition being fitted out at Callao, to go in chase of him, under the command of Pedro Sarmiento. He sailed from Callao in October 1579, and made a careful survey of the Straits of Magellan, with the object of fortifying that entrance to the South Sea. The colony which he afterwards took out from Spain was a complete failure, and is only remembered now from the name of "Port Famine" which Cavendish gave to the site at which he found the starving remnant of Sarmiento's settlers. In June 1595 Mendafia sailed from the coast of Peru in command of a second expedition to colonize the Salomon Islands. After discovering the Marquesas, he reached the island of Santa Cruz of evil memory, where he and many of the settlers died. His young widow took command of the survivors and brought them safely to Manila, The viceroys of Peru still persevered in their attempts to plant a colony in Australia. Pedro Fernandez de Quiros, who was pilot under Mendafia and Luis Vaez de Torres were sent in command of two ships to continue the tsork of exploration. They sailed from Callao on December 21, 1605, and discovered several islands of the New Hebrides group. They anchored in a bay of a large island which Quiros named " Australia del Espiritu Santo." From this place Quiros returned to America, but Torres continued the voyage, passed through the strait between Australia and New Guinea which bears his name, and explored and mapped the southern and (as has recently been proved) also the eastern coast of New Guinea.

The Portuguese, in the early part of the 17th century (1578-1640), were under the dominion of Spain, and their enterprise was to some extent damped ; but their missionaries extended geographical knowledge in Africa. Father Francisco Paez acquired great influence in Abyssinia, and explored its highlands from 1600 to 1622. Fathers Mendez and Lobo traversed the deserts between the coast of the Red Sea and the mountains, became acquainted with the shores of Lake Tsana, and discovered the sources of the Abai or Blue Nile in 1624-1633.

But the attention of the Portuguese was mainly devoted to vain attempts to maintain their monopoly of the trade of India against the powerful rivalry of the English and Dutch. The English enterprises were persevering, continuous, and successful. James Lancaster made a voyage to the Indian Ocean from 1591 to 1594 ; and in 1599 the merchants and adventurers of London resolved to form a company, with the object of establishing a trade with the East Indies. On the 31st of December 1599 Queen Elizabeth granted the charter of incorporation to the East India Company, and Sir James Lancaster, one of the directors, was appointed general of their first fleet. He was accompanied by John Davis, the great Arctic navigator, as pilot-major. This voyage was eminently successful. The ships touched at Achin in Sumatra and at Java, returning with full ladings of pepper in 1603. The second voyage was commanded by Sir Henry Middleton ; but it was in the third voyage, under Keelinge and Hawkins, that the mainland of India was first reached in 1607. Captain Hawkins landed at Surat and travelled overland to Agra, passing some time at the court of the Great Mogul. In the voyage of Sir Edward Michelborne, John Davis of Arctic fame lost his life in a fight with a Japanese junk on December 27, 1605. The eighth voyage, led by Captain Saris, extended the operations of the company to Japan ; and in 1613 the Japanese Government granted privileges to the Company ; but the English retired in 1623, giving up their factory. The chief result of this early intercourse between England and Japan was the interesting series of letters written by William Adams from 1611 to 1617. Ada ins, however, though an Englishman, went to Japan in a Dutch ship. From the tenth voyage of the East India Company, commanded by Captain Best, who left England in 1612, dates the establishment of permanent English factories on the coast of India. It was Captain Best who secured a regular firman for trade from the Great Mogul. From that time a fleet was despatched every year, and the Company's operations greatly increased geographical knowledge of India and the Eastern Archipelago.

The visits of Englishmen to Eastern countries, at this time, were not confined to the voyages of the Company. Journeys were also made by land, and, among others, Thomas Coryat, of Odcombe in Somersetshire, walked from France to India, and died in the Company's factory at Surat. n In 1561 Mr Anthony Jenkinson arrived in Persia with a letter from Queen Elizabeth to the shah. He travelled through Russia to Bokbara, and returned by the Caspian and Volga. In 1579 Christopher Burroughs built a ship at Nijni Novgorod and traded across the Caspian to Baku ; and in 1598 Sir Anthony and Robert Shirley arrived in Persia, and Robert was afterwards sent by the shah to Europe as his ambassador. He was followed by a Spanish mission under Garcia de Silva, who wrote an interesting account of his travels ; and to Sir Dormer Cotton's mission, in 1628, we are indebted for Sir Thomas Herbert's charming narrative•. In like manner, Sir Thomas Roe's mission to India resulted not only in a large collection of valuable reports and letters of his own, but also in the detailed account of his chaplain Mr Terry. But the most learned and intelligent traveller in the East, during the 17th century, was the German Kcempfer, who accompanied an embassy to Persia in 1684, and was afterwards a surgeon in the service of the Dutch East India Company. He was in the Persian Gulf, India, and Java, and resided for more than two years in Japan, from 1690 to 1692. His History of Japan, was published in England in 1727, Kcempfer himself having died in 1716. From these various sources a considerable increase was made in the knowledge of India, Persia, and the further East.

The Dutch nation, as soon as it was emancipated from Spanish tyranny, displayed an amount of enterprise which, for a long time, was fully equal to that of England. The memorable Arctic voyages of Barents were quickly followed by the establishment of a Dutch East India Company ; and Holland, ousting the Portuguese, not only established factories on the mainland of India and in Japan, but acquired a preponderating influence throughout the Eastern Archipelago. In 1583 Jan Hugen van Linschoten made a voyage to India with a Portuguese fleet, and his full and graphic descriptions of India, Africa, China, and the Eastern Archipelago must have been of no small use to his countrymen in the commencement of their distant voyages. The first of their Indian voyages was performed by ships which sailed from Holland in April 1595, and rounded the Cape of Good Hope. A second large Dutch fleet sailed in 1598 ; and, so eager was the young republic to extend her commerce over the world that another fleet, consisting of five ships of Rotterdam, was sent in the same year by way of Magellan's Straits, under Jacob Mahn as admiral, with William Adams as pilot. Mahn died on the passage out, and was succeeded by Simon de Cordes, who was killed on the coast of Chili. In September 1599 the fleet had entered the Pacific. The ships were then steered direct for Japan, and anchored of Bungo in April 1600. In the very same year, 1598, a third expedition was despatched under Oliver van Noort, a native of Utrecht. The fleet left Holland in September 1598, and entered the South Sea, through the Straits of Magellan, in February 1600, after a tedious, and in truth unskilful, navigation of nearly a year and a half from the time of leaving Holland. After keeping along the west coast of America nearly as far as the line, Van Noort shaped a course for the Ladrone Islands, and arrived off Manila. In August 1601 he anchored in front of Rotterdam, after an absence of three years, lint the voyage contributed nothing to geography. The Dutch Company in 1614 again resolved to send a fleet to the Moluccas by the westward route, and Joris Spilbergen was appointed to the command as admiral, with a commission from the States-General. He was furnished with 4 ships of Amsterdam, 2 of Rotterdam, and 1 from Zeeland. On May 6, 1615, Spilbergen entered the Pacific Ocean, and touched at several places on the coast of Chili and Peru, defeating the Spanish fleet in a naval engagement off Chilca, After plundering Payta and making requisitions at Acapnlco, the Dutch-fleet crossed the Pacific and reached the Moluccas in March 1616. At that time the Dutch Company had 37 sail of European shipping and 3000 troops in the East Indies.

The Dutch now resolved to discover a passage into the Pacific to the south of Tierra del Fuego, the existence of which was ascertained by Sir Francis Drake. The vessels fitted out for this purpose were the " Eerdracht," of 360 tons, commanded by Jacob le Maire, and the "Horn," of 110 tons, under Jan Schouten. They sailed from the Texel on June 14, 1615, and by the 20th of January 1616 they were south of the entrance of Magellan's Straits. Passing through the strait of Le Maire they came to the southern extremity of Tierra del Fuego, which was named Cape Horn, in honour of the town of Horn in West Friesland, of which Schouten was a native. They passed the cape on the 31st of January, encountering the usual westerly winds. The great merit of this discovery of a second passage into the South Sea lies in the fact that it was not'accidental or unforeseen, but was due to the sagacity of those who designed the voyage. On March 1 the Dutch fleet sighted the island of Juan Fernandez; and, having crossed the Pacific, the explorers sailed along the north coast of New Guinea, and arrived at the Moluccas on September 17, 1616. In 1623 the Dutch sent expeditions against Brazil and Peru, which, however, did little to advance geographical knowledge, except that the Brazilian invasion resulted in the valuable work of Nieuhof.

There were several early indications of the existence of the great Australian continent, which have been very ably discussed by Mr Major ; and the Hollanders endeavoured to obtain further knowledge concerning the country and its extent ; but only its northern and western coasts had been visited before the time of Governor Van Diemen. Dirk Hartog had been on the west coast in latitude 26' 30' S. in 1616. Pelsert struck ou a reef called " Houtman's Abrolhos " on June 4, 1629. In 1697 the Dutch captain Vlamingh landed on the west coast of Australia in 31° 43' S., and named the Swan River, where he saw some black swans. In 1642 the governor and council of Batavia fitted out two ships to prosecute the discovery of the south land, and entrusted the command to Captain Abel Jansen Tasman. This voyage proved to be the most important to geography that hind been undertaken since the first circumnavigation of the globe. Tasman sailed from Batavia in the yacht " Heemskirk " on the 14th of August 1642, and from Mauritius on the 8th of October, On November 24 high land was sighted in 42° 30' S., which was named Van Diemen's Land, and, after landing there, sail was again made, and New Zealand (at first called Staten Land) was discovered on the 14th of December. Tasman communicated with the natives and anchored in what he called Murderer's Bay. From New Zealand it was resolved to steer eastward to longitude 220°, and then north. On this course the ships arrived at Tongatabu, one of the Friendly Islands of Cook ; in April 1643 they were off the north coast of New Guinea ; and on June 15 Tasman returned to Batavia. In 1644 Tasman made a second voyage to effect a more full discovery of New Guinea.

The French directed their enterprise more in the direction of North America than of the Indies. One of their most distinguished naval worthies was Samuel Champlain, a native of Brouage in Saintonge, whose friend and patron was Aymar de Chastes, governor of Dieppe, a devoted follower of Henry IV. Champlain after the close of the war with the League in Brittany, in which he served, made a remarkable journey through Mexico and the West India Islands from 1599 to 1602, and on his return he found that M. de Chastes was, undeterred by previous failures, resolved to undertake the establishment of a colony in Canada. Champlain was sent on a voyage of reconnaissance, and on his return he found that the Sieur de Chastes was dead. In 1603 the Sieur de Monts was named vice-admiral of the coasts of Acadia, and Champlain sailed with him from Dieppe. He was for some years engaged in surveying all the coasts of Acadia and Cape Breton, and in 1607 he returned to France with De Monts, In the following year another attempt was made. Champlain, with a colleague named Du Pont Grave, sailed to the St Lawrence, and on July 3, 1608, they first arrived at Quebec. In 1609 Champlain ascended the Iroquois to the lake which still bears his name. By 1611 a regular colony was established at Quebec ; and in 1620 Champlain was installed as governor. He died towards the end of the year 1635. Champlain was an able navigator and a resolute explorer, and he made a very large addition to the knowledge of Canada and Acadia (Novia Scotia).

The last expedition of the 17th century was purely scientific. In 1699 Edmund Halley, the astronomer-royal, in command of the " Paramour Pink," undertook a voyage to improve the knowledge of longitude, and of the variation of the compass. The results of his voyage were the construction of a variation chart, and proposals for finding the longitude by occultations of fixed stars.

During the 17th century very considerable progress was made in the art of navigation, and in systematizing and delineating the vast mass of material that was accumulated by the ceaseless activity of explorers. The Dutch took the lead as map-makers. Mercator invented the useful projection which bears his name ; and Ortelius, Hondius, and Hulsius compiled a series of valuable maps. In finding the latitude at sea, the astrolabe very generally gave place to the cross-staff, because the graduation of the latter was larger and more easily read off. The cross-staff was a very simple instrument, consisting of a graduated pole with cross pieces, called transversaries (of which there were four used according to the altitude), also graduated, which were fitted to work on it. The bearings of the sun were taken by coin-pass, to ascertain when it was near the meridian ; then the end of the long staff was placed close to the observer's eye, and the transversary moved until one end exactly touched the horizon, and the other the sun's centre. This was continued until the sun dipped, when the meridian altitude was obtained. The back-staff was an improvement on the cross-staff, invented by the great Arctic navigator John Davis. It was fitted with a reflector, and it was this the first rough idea of the principle of the quadrant and sextant. The cross-staff was used for low altitudes, because both ends of the transversary could easily be seen at the same time, and the astrolabe for high altitudes. With the invention of these instruments came instructions for their use, and for working out observations. In England the first of these was The Old Rutter of the Sea, printed in 1490. Then followed the Seaman's Secrets of John Davis, and A Regiment of the Sea, containing very necessary Matters, with a perfect Sea Card, by Thomas Hood, published in 1596. Hood also sold compasses constructed on Mr Norman's principle, near the Minories. These manuals contained definitions, treatises on the use of the sea card and compass, tables of declination and rules for applying it, rules for dead reckonings and longitude, and instructions in the use of instruments. Latitude was obtained by observation, but longitude had usually to be reckoned on the chart from the meridian of Grand Canary, which in those clays was used by all civilized countries. The differences of time between the eclipses of the moon at the place of the observer and the place for which it was calculated in the ephemerides for that day was another method in use of finding the difference of longitude. Mariners were also provided with tables giving the number of miles in a degree of longitude for every degree of latitude. Much attention was bestowed upon the phenomena of the variation. and dip of the magnetic needle. Robert Norman, the hydrographer, discovered the dip or inclination of the needle in 1576, and in 1581 he observed the variation of the compass at London, and found it to be 11° 15' E. In the same year his Discowrse of the Hagnet or Loadstone was published by Ballard. In 1580 Mr Borough, comptroller of the navy, found the variation of the compass at Limehouse'to be 11° 19' E. It may be observed here that in 1657 there was no variation at London, and that it moved westerly until 1815, when it was 24° 27' W. It is now returning eastwards.

By means of these rough instruments and calculations our Elizabethan navigators and their contemporaries succeeded in delineating the vast regions that were discovered. Thus the sum of human knowledge was augmented, while men's minds were enlarged, and the wealth and prosperity of nations were increased, through the provision of safe guides by which lands and seas could be traversed, and distant countries visited.

In the 18th century, to a far greater extent than had ever been the case before, geography began to be cultivated for its own sake, and expeditions were fitted out with the objects of discovery and of acquiring knowledge. The same objects also generally formed part of those enterprises which were avowedly undertaken for conquest, in the search of wealth, or from motives of religious zeal.

The improvement of scientific apparatus naturally went hand in hand with the progress of discovery. The great desideratum was the means of finding the longitude ; and it was the creation of a commission for the discovery of longitude in 1713 which, so far as England is concerned, gave the greatest stimulus to inventions connected with geographical research. To the Board of Longitude is due the conception of the Nautical Almanac, and the establishment of a surveying branch of the naval service. The Nautical Almanac first appeared in 1767, under the auspices of Dr Maskelyne, the astronomer-royal, who, by furnishing tables of lunar distances, supplied another means of finding the longitude. The invention by Hadley, in 1731, of the quadrant for use at sea, which entirely superseded the astrolabe and cross-staff, was a still greater improvement ; and it was soon followed by better instruments on the same principle - the sextants of Dollond and Troughton. The work of travellers on land also became more accurate in proportion as instruments and maps were improved. Early explorers by laud were content with itineraries and maps which only indicated distances. The introduction of observations by compass bearings was an important improvemerit ; and after the invention of Hadley's quadrant, these rough route surveys began to be checked and verified by astronomical observations.

The most remarkable example of the early application of 1. these improvements is to be found in the survey of China by the Jesuit missionaries. They first prepared a map of the country round Peking, which was submitted to the emperor Kang-hi, and, being satisfied with the accuracy of the European method of surveying, he resolved to have a survey made of the whole empire on the same principles. This great work was commenced in July 1708, and the completed maps were presented to the emperor in 1718. The records preserved in each city were examined, topographical information was diligently collected, and the Jesuit fathers checked their triangulation by meridian altitudes of the sun and pole star, and by a system of remeasurements. The result was a more accurate map of China than existed, at that time, of any country in Europe. Kang-hi next ordered a similar map to be made of Tibet, the survey being executed by two lamas who were carefully trained as surveyors by the Jesuits at Peking. From these surveys were constructed the well-known maps which were forwarded to Duhalde, and from which D'Anville constructed his atlas. Ls Several European missionaries had previously found their t. way from India to Tibet. Antonio Andrada, in 1621, was the first European to enter Tibet since the visit of Friar Odoric in 1325. The next journey was that of Fathers Grueber and Dorville about 1660, who succeeded in passing from China, through Tibet, into India. In 1715 Fathers Desideri and Freyre made their way from Agra, across the Himalayas, to Lassa, the capital of Tibet ; and the Capuchin Friar Orazio delta Penna resided at Lassa from 1735 until 1747. But the most remarkable journey in this direction was performed by a Dutch traveller named Samuel Van de Putte. He is the only European who has ever completed the journey from India, through Lassa, to China, and returned to India by the same route. He left Holland in 1718, went by land through Persia to India, and eventually made his way to Lassa, where he resided for a long time. He went thence to China, returned to Lassa, and was in India in time to be an eye-witness of the sack of Delhi by Nadir Shah in 1737. In 1743 he left India, and died at Batavia on the 27th of September 1745. The premature death cf this illustrious traveller is the more to be lamented because his vast knowledge died with him. Two English missions sent by Warren Hastings to Tibet, one led by Mr George Bogle in 1774, and the other by Captain Turner in 1783, completes the list of Tibetan explorers in the 18th century. From Persia much new information was supplied by Chardin, Tavernier, Hamilton, Thevenot, and Krusiuski, and by English traders on the Caspian. In 1738 John Elton traded between Astrakhan and the Persian port of Enzeli on the Caspian, and undertook to build a fleet for Nadir Shah. Another English merchant, named Jonas Hanway, arrived at Astrabad from Russia, and travelled to the camp of Nadir at Kazvin. One lasting and valuable result of Hanway's wanderings was a most charming book of travels. The extension of the dominions of the Company largely increased the knowledge of India. In 1700 Guillaume Delisle, the principal creator of the modern system of geography, published his map of the continents of the Old World ; and Ids successor D'Anvil]e produced Ids map of India in 1752. D'Anville's map contained all that was then known, but ten years afterwards Major Rennell commenced his surveying labours, which extended over a period from 1763 to 1782. His survey covered au area 900 miles long by 300 wide, from the eastern confines of Bengal to Agra, and from the Himalayas to Calpi. Rennell was indefatigable in collecting geographical information ; his Bengal atlas appeared in 1781, his famous map of India in 1788, and the memoir iu 1792. Surveys were also made along the Indian coasts, and the charts of Huddert, Ritchie, and APCluer were the forerunners of the more accurate and elaborate productions of the succeeding century.

Arabia received very careful attention, in the 18th century, from the Danish scientific mission, which included Carsten Niebuhr among its members. Niebuhr lauded at Loheia, on the coast of Yemen, in December 1762, and went by land to Sana. All the other members of the mission died, and he proceeded from Mocha to Bombay. He then made a journey through Persia and Syria to Constantinople, returning to Copenhagen in 1767. His invaluable work, the Description of Arabia, was published in 1772, and was followed in 1774-78 by two volumes of travels in Asia. The great traveller survived until 1815, when he died at the age of eighty-two. James Bruce of Kinnaird, the contemporary of Niebuhr, was equally devoted to Eastern travel. After studying Arabic and Geez for some years, lie went out as consul to Algiers, and resided there from 1762 to 1765, exploring and sketching the Roman ruins in Algiers and Tunis. In i 765 he travelled by land from Tunis to Tripoli, and then took a passage for Candia, but was shipwreck-eel near Bengazi, and had to swim on shore. He eventually reached Candia, and, sailing thence to Sidon, travelled through Syria. In June 1768 he landed at Alexandria in the dress of an Arab, and soon afterwards we hear of him at Jiddab, the port of Mecca, in the dress of a Turkish sailor. He had resolved to attempt the discovery of the source of the Nile; and in 1769 he landed at Massowah, on time Abyssinian coast. He then penetrated to Axum and Gondar, and in November 1770 he reached the source of the Abai, then supposed to be the main stream of the Nile. He thus attained the great object of his ambition. Returning by time desert into Egypt, Bruce reached England in 1774, and settled once more at his old home at Kinnaird after an absence of ten years. Urged by his old friend, Mr Dailies Barrington, the great traveller at length published his Travels to Discover the Source of the Wile in the Years 1768-73 (5 vols. 4to) in 1790. Bruce, like many other conscientious and deserving explorers, was assailed by calumny and detraction. But every succeeding year has added to the high estimation in which his labours are held, and to the reverence with which his memory is cherished. He died at Kinnaird House, Stirlingshire, in 1794.

Before the death of Bruce an African Association was formed, in 1788, for collecting information respecting the interior of that continent, with Major Rennell and Sir Joseph Banks as leading members, and Bryan Edwards as secretary. The association first employed a Mr Ledyard to cross Africa from east to west on the parallel of the Niger, and Mr Lucas to cross the Sahara to Fezzan. Ledyard, who had previously made a most extraordinary journey into Siberia, died at Cairo in 1788. Lucas went from Tripoli to Mesurata, obtained some information respecting Fezzan, and returned in 1789. One of the chief problems the Association wished to solve was that of the existence and course of the river Niger, which Maxwell believed to be identical with the Congo. Mungo Park, then an assistant surgeon of an Indianian, volunteered his services, which were accepted by the Association, and in 1795 he arrived at the English factory of Pisania, 200 miles up the Gambia. Leaving this station in December he reached Ludamar, where a Moorish chief imprisoned him until the following July. He then crossed a mountainous tract to a Mandingo town called Kamalia. Quite destitute, and suffering from fever, he remained there for several months, but finally found his way back to Pisania, and returned to England. The interesting narrative of Ids adventures, with a goographical memoir by Rennell, was published in 1799. Five years afterwards he accepted an offer from the Government to command an expedition into the interior of Africa, the plan being to cross from the Gambia to the Niger, and descend. the latter river to the sea. Park left the factory of Pisania, on the Gambia, on the 4th of May 1805, accompanied by Lieutenant Martyn and 35 soldiers, besides guides. All died but four during the rainy season, and the rest, including Mango Park, perished in a rapid on the Niger, having been attacked from the shore by order of a chief who thought he had not received suitable presents. Park was only thirty-five at the time of his death. The details respecting the fate of the ill-fated explorer and his party were obtained from the guide.

While the English were at work in the direction of the Niger, the Portuguese were not unmindful of their old exploring fame. In 179S Dr Lacerda, an accomplished astronomer, was appointed to command a scientific expedition of discovery to the north of the Zambesi. He started in July, crossed the Muchenja Mountains, and reached the capital of the Cazernbe where he died of fever. Dr Lacerda left a valuable record of his adventurous journey ; but with Mango Park and Lacerda the history of African exploration in the 18th century closes.

In South America scientific exploration was busily at work during this period. The great event of the century, as regards that continent., was the measurement of an arc of the meridian. The undertaking was proposed by the French Academy, and a commission left Paris in 1735, consisting of La Condamine, Bonguer, and Godin. Spain appointed two accomplished naval officers, the brothers Ulloa, as coadjutors. The operations were carried on during eight years on a plain to the south of Quito ; and, in addition to his memoir on this memorable and most important measurement, La Condamine collected much valuable geographical information during a voyage down the Amazon. The arc measured was 3' 7' 3" in length; and the work consisted of two measured bases connected by a series of triangles, one north and the other south of the equator, on the meridian of Quito. Contemporaneously, in 1738, M. Maupertuis of St Malo measured an arc of the meridian in Lapland. Another result of this expedition was the publication of a valuable work by the brothers Ulloa.

The English and French Governments despatched several expeditions of discovery into the Pacific and round the world during the 18th century. They were preceded by those wonderful and romantic voyages of the buccaneers, of such men as Woodes Rogers, Davis, Shelvocke, Clapperton, and Dampier, which can never fail to interest, while they are not without geographical value. The works of Dampier are especially valuable, and the narratives of William Funnell and Lionel Wafer furnished the best accounts then extant of the isthmus of Darien. Dampier's literary ability eventually secured for him a commission in the king's service ; and he was sent on a voyage of dis- covery, during which he explored part of the coasts of Australia and New Guinea, and discovered the strait which bears his name between New Guinea and New Britain, returning in 1701. Ia 1721 Jacob Roggewein was despatched on a voyage of some importance across the Pacific by the Dutch West India Company, during which he discovered Easter Island on April 6, 1722.

The voyage of Lord Anson to the Pacific in 1740-41 was of a predatory character, and he lost more than half his men from scurvy ; while it is not pleasant to reflect that at the very time when the French and Spaniards were measuring an arc of the meridian at Quito, the English under Anson were pillaging along the coast of the Pacific, and burning the town of Payta. But a romantic interest attaches to the wreck of the "Wager," one of Anson's fleet, on a desert island near Chiloe, for it bore fruit in the charming narrative of Byron, which will endure for all time. In 1764 Captain Byron himself was sent on a voyage of discovery round the world, which led immediately after his return, to the despatch of another to complete his work, under the command of Captain Wallis.

The expedition, consisting of the " Dolphin " commanded by Captain Wallis, and the " Swallow " under Captain Carteret, sailed in September 1766, but the ships were separated on entering the Pacific from the Straits of Magellan. Wallis discovered Tahiti on June 19, 1767, of which island he gave a detailed account, and Sir Charles Saunders's Island; he returned to England on May17, 1768. Carteret discovered the Charlotte and Gloucester Islands, and Pitcairn Island on July 2, 1767 ; revisited the Santa Cruz group, which was discovered by Mendatia and Quiros ; and discovered the strait separating New Britain from New Ireland. He reached Spithead again on February 20, 1769. Wallis and Carteret were followed very closely by the French expedition of Bougainville, which sailed from Nantes in November 1766. Bougainville had first to perform to him the unpleasant task of delivering up the Falkland Islands (Malonines), where lie had encouraged the formation of a French settlement, to the Spaniards. lie then entered the Pacific, and reached Tahiti on April 2, 1768. Passing through the New Hebrides group he touched at Batavia, and arrived at St Malo after an absence of two years and four months.

The three voyages of Cook form an era in the history of geographical discovery. All his work was thoroughly and completely done. He systematically surveyed every land lie discovered, collecting information touching every branch of inquiry, so that his labours form a very large addition to geographical knowledge. James Cook was born near Whitby, Yorkshire, in 1728, and had been marine surveyor of Newfoundland and Labrador from 1763 to 1767. In the latter year he commissioned the " Endeavour " and sailed for Tahiti, with the object of observing the transit of Venus, accompanied by Sir Joseph Banks and Dr Solander, a pupil of Linnwus. The transit was observed at Tahiti on June 3, 1769. After exploring Tahiti and the Society group, Cook was six months surveying the two islands of New Zealand, and the coast of New South Wales from latitude 38° S. to the northern extremity. Passing through Torres Strait, lie touched at Batavia, and arrived in England on June 12, 1771.

Cook's second voyage was mainly intended to explore the region round the Antarctic Circle ; and it may be mentioned that meanwhile a French ship, commanded by M. Kerguelen, had sailed southwards in 1771, and discovered the island which bears his name. Captain Cook was provided with two vessels built at Whitby, the " Resolution," which lie himself commanded, and the " Adventure " under Captain Furneaux, who had been with Wallis. After rounding the Cape the two vessels reached a south latitude of 57° 15'. On March 26, 1773, Captain Cook arrived at New Zealand and proceeded to the Society Islands, whence he made another voyage southwards between the meridians of 170° E. and 106° 54' W. On this occasion lie was stopped by ice in 71° 10' S. During the second voyage Cook visited Easter Island, discovered several islands of the New Hebrides and New Caledonia ; and on his way home by Cape Horn, in March 1774, he discovered the Sandwich Island group. Arrived at Spithead on July 30, 1774. The account of the second voyage was written by the young naturalist George Forster, whose subsequent work was so justly eulogized by Humboldt. The third voyage was intended to attempt the passage from the Pacific to the Atlantic by the north-east. The " Resolution " and " Discovery " sailed in 1776, and Cook again took the route by the Cape o: Good Hope. In 1777 he was at the Friendly group, anC on January 18, 1778, he discovered the Sandwich Islands He then proceeded to the North American coast, and, after a stay- of a month in Nuotka Sound, lie proceeded north wards, fixed the position of the western extremity of America, and surveyed Behring Strait. On August 17, 1778, In was stopped by the ice in 70' 41' N., and named tin farthest visible point on the American shore icy Cape. Id( then visited the Asiatic shore and discovered Cape North, bearing up on August 29 when he was in the 180th dogrel of longitude. Returning to the Sandwich Islands, Captain: Cook was murdered by the natives of Hawaii. On February- 14, 1779, his second, Captain Clerke, took the command, and proceeding to Petropaulowski in the following summer, he again examined the edge of the ice, but only got to 70' 33' N. The ships returned to England in October 1780.

In 1785 the French Government fitted out a very carefully-prepared expedition of discovery at Brest, which was placed under the command of La Perouse, an accomplished and experienced officer. After touching at Concepcion in Chili, and at Easter Island, La Perouse proceeded to the Sandwich Islands, and thence to the coast of California, of which he has given a very interesting account. He then went across the Pacific to Macao, and in July 1787 he proceeded to explore the Gall of Tartary and the shores of Saghalien, remaining some time at Castries Bay, so named after the French minister of marine. Thence he went to the Kurile Islands and Kamchatka, and sailed from the far north down a meridian to the Navigator and Friendly Islands. He was in Botany Bay in January 1788; and sailing thence, the explorer, his ship, and crew were never seen again. Their fate was long uncertain. In September 1791 Captain D'Entrecasteaux sailed from Brest with two vessels, to seek for tidings. He visited the New Hebrides, Santa Cruz, New Caledonia, and Salomon Islands, and made careful though rough surveys of the Louisiade Archipelago, islands north of New Britain, and part of New Guinea. D'Entrecasteaux died on board his ship ox July 20, 1793, without ascertaining the fate of La Perouse. It was Captain Peter Dillon who at length ascertained, in 1828, that the ships of La Perouse were wrecked on the island of Vanikoro during a hurricane.

The work of Captain Cook bore fruit in many ways. His master, Captain Bligh, was sent in the " Bounty " to convey breadfruit plants from Tahiti to the West Indies. He reached Tahiti in October 1788, and in April 1789 a mutiny broke out, and he, with several officers and men, was thrust into an open boat in mid-ocean. During the remarkable voyage he then made to Timor, Captain Bligh passed amongst the northern islands of the New Hebrides, which he named the Banks Group, and made several running surveys. He reached England in March 1790. The " Pandora," under Captain Edwards, was sent out in search of the " Bounty," and discovered the islands of Cherry and Mitre, east of the Santa Cruz group, but she was eventually lost on a reef in Torres Strait. In 1796-97 Captain Wilson, in the missionary ship " Duff," discovered the Gambier and other islands, and rediscovered the islands known to and seen by Quiros, but since called the Duff Group. Another result of Captain Cook's work was the colonization of Australia. On January 18, 1788, Admiral Phillip and Captain Hunter arrived in Botany Bay in the " Supply " and " Sirius," followed by six transports, and established a colony at Port Jackson. Surveys were then undertaken in several directions. In 1795 and 1796 M. Flinders and G. Bass were engaged on exploring work in a small boat called the " Tom Thumb." in 1797 Bass, who had been a surgeon, made an expedition southwards, continued the work of Cook from Ram Head, and explore( the strait which bears Ids name, and in 1798 he ani Hinders were surveying the east coast of Van Diemen'; Land. The planting of a colony at Port Jackson led ti the despatch of an expedition to complete the exploration of the Australian coasts. The command was given t( Captain Matthew Hinders. He was furnished with r vessel called the " investigator," and sailed from Englanc on July 18, 1801. Commencing from King George's Sound Captain Flinders discovered and made a preliminary surve2 of all the south coast of Australia to Bass Strait, and tin cast coast from the barrier reef to Torres Strait, as well a the east coast of the Gulf of Carpentaria. Hinders me the French expedition under Baudin and Freycieet with tin two ships " Geographe " and " Naturaliste," which was en gaged upon the same work. He was taken prisoner by tin French in 1804 and detained until 1810, so that his word did not appear before 1814.

Yet another out-come of Captain Cook's work was tit( voyage of George Vancouver, who had served as a midship. man in Cook's second and third voyages. The Spaniard( under Quadra had commenced a survey of north-western America and occupied Nootka Sound, which their Govern. meat eventually agreed to surrender. Captain Vancouver was sent out to receive the cession, and to survey the coast from Cape Mendocino northwards. He commanded the old "Discovery," and was at work during the seasons of 1792, 1793, and 1794, wintering at the Sandwich Islands. Returning home in 1795, he completed his narrative and very valuable series of charts, and died in 1798.

The 18th century saw the Arctic coast of North America reached at two points, as well as the first scientific attempt to reach the North Pole. The Hudson's Bay Company had been incorporated in 1670, and its servants soon extended their operations over a wide area to the north and west of Canada. In 1741 Captain Christopher Middleton was ordered to solve the question of a passage from Hudson's Bay to the westward. Leaving Fort Churchill in July 1742 he stood northwards and discovered the Wager Rivet and Repulse Bay, bearing up again on August 9. He was followed by Captain W. Moor in 1746, and Captain Coats in 1751, who examined the Wager Inlet up to the end. On November 6, 1769, Samuel Hearne was sent by the Hudson's Bay Company to discover the sea on the north side of America, but was obliged to return. On February 23, 1770, he set out again from Fort Prince of Wales ; but, after great hardships, he was again forced to return to the fort. lie started once more on December 7,1771, and at length reached the Coppermine River, which he surveyed to its month, but his observations are very unreliable. With the same object of reaching the sea, Alexander Mackenzie, with a party of Canadians, set out from Fort Chepewyan on June 3, 1789, and descended a river which bears the explorer's name. His account of the journey- is even more unsatisfactory than that of Hearne.

In February 1773 the Royal Society submitted a proposal to the king for an expedition to try how far navigation was possible towards the Pole. The " Racehorse " and " Carcass " bombs were selected as best adapted for the service, and Captains Phipps and Lutwidge were appointed to command them. The expedition sailed on June 2, 1773, and sighted the coast of Spitzbergen on the 28th. Captain Phipps stood into every opening he could find in the ice, but was invariably stopped by a solid barrier. He examined a line extending over twenty degrees of longitude, and found no opening in the heavy polar pack in any direction. After a very careful and persevering examination of the ice, the expedition returned to England in September. The highest latitude reached was 80° 48' N. But the most important Arctic work in the 18th century was performed by the Russians, for they succeeded in delineating the whole of the northern coast of Siberia. Some of this work, indeed, was done at a still earlier date. The Cossack Deselineff made an extraordinary voyage, in the summer of 1618, from the river Kolyma, through Behring Strait to Anadyr, a performance which has never since been equalled. Between 1738 and 1750 the mates Manila and Sterlegoff made their way in small sloops from the mouth of the Yenisei as far north as 75° 15' N. The land from Taimyr to Cape Cl telyuskin, the most northern extremity of Siberia, was mapped by the mate Chelyuskin, who discovered the extreme point in May 1742. To the east of Cape Chelyuskin the Russians encountered greater difficulties. They built small vessels at Yakutsk on the Lena, 900 miles from its mouth, whence the first expedition was despatched under Lieutenant Prontschieheff in 1735. He sailed from the mouth of the Lena to the mouth of the Olonek, where he wintered, and on September 1, 1736, he gat as far as 770 29' N., within five miles of Cape Chelyuskin, which is in 77' 34' N. Both he and his young wife died of scurvy, and the vessel returned. A second expedition, under Lieutenant Laptieff, started from the Lena in 1739, but encountered masses of drift ice in Chatanga bay, and with this ended the voyages to the westward of the Lena. Several attempts were also made to navigate the sea from the Lena to the Kolyma. In 1736 Lieutenant Laptieff sailed, but was stopped by time drift ice in August, and in 1739, during another trial, he reached the mouth of the Indigirka, where lie wintered. In the season of 1740 he continued his voyage to beyond the Kolyma, wintering at Nijni Kolymsk. In 1725 Vitus Behring, a Dane in the Russian service, received his instructions from Peter the Great a few days before the czar's death. Two vessels were built for Behring at Okhotsk, and sailing in July 1728, he ascertained the existence of the strait between Asia and America which bears Ins name. In September 1710 Behring again sailed from Okhotsk, with Steller on board as naturalist. In June 1741 Commodore Behring named the magnificent peak on the coast of North America Mount St Elias, and explored the Aleutian Islands. In November the ship was wrecked on Behring Island ; and the gallant Dane, worn out with scurvy, died there on the 8th of December 1741. In March 1770 a merchant named Lialthoff saw a large herd of reindeer coining from the north to the Siberian coast, which induced him to start in a sledge in the direction whence they came. Thus the New Siberian Islands were discovered, and for years afterwards the seekers for fossil ivory resorted to them. The Russian Captain Vassili Tchitschakoff in 1765 and 1766 made two persevering attempts to penetrate the ice north of Spitzbergen, and reached to 80' 30' N., and Russian parties twice wintered at Bell Sound. But the result was the same as all others have obtained before and since ; the Spitzbergen route is evidently not the way to the Pole.

The 18th century saw great progress in the collection and arrangement of geographical material, and in the work of surveying and map-making. Collections of voyages and travels were brought together in the four quarto volumes of Astley (1745) and the two folios of Harris (1764) ; while Dr Hawkesworth edited the Government voyages to the Pacific in 1773. Sir Joseph Banks was the great patron of geography in England, aided by the indefatigable labours of such critical geographers as Retinal, Dalrymple, and Barrington ; while in France the great cartographer D'Anvillc introduced a habit of critical accuracy, and caused a complete revolution in the art of map-making.

Towards the close of the century it was recognized that geography served more extensive and important uses than had ever before been supposed. The route survey was sufficient for the traveller or soldier, while accurate charts guided the mariner across the ocean. But surveys are also the basis of statistics and of administration, and rigorous accuracy became necessary. Surveys on a trigonometrical basis, which have been proceeding in all the countries in Europe (except Turkey) and in India during the present, were commenced in the last century. In Great Britain the Ordnance Survey was begun in April 1784, when General Roy measured a base line on Hounslow Heath. The triangulation of the British Isles was commenced in 1784 and completed in 1852. Maps based on trigonometrical surveys may eventually explain and illustrate the physical aspect of the whole globe, but at present they are necessarily confined to those nations which are in the front rank of civilization. Countries which are not so advanced are still obliged to be content with such maps as sufficed for all the world in the last century, before the results of trigonometrical surveys were available. These secondary maps are adapted for the requirements of the countries which use them, being based on positions fixed by astronomical observations, on cross bearings, and often on chained distances. The third class of maps includes the work of explorers of unknown or little known regions, and of geographers who delineate the features of such regions by compilation and by intelligent collation of the work of travellers. There are thus three grand divisions in the character and uses of maps. There are first those which aim at minute accuracy, and which are intended as documents for administrative purposes, and in pursuing exact statistical investigations. Secondly, there are maps which are based on less accurate surveys of countries less populous or less advanced in civilization ; these are useful for political, geographical, and military purposes, but are not to be relied on to the same extent or in the same way as is the case with those based on trigonometrical surveys. Thirdly, there are the roughly compiled maps of little known regions, which are constantly in course of improvement, and which do the work of pioneers.

In treating here of the progress of geographical discovery in the present century, it is to those who prepare the last class of maps, to the pioneers - the discoverers - that we must mainly, though not exclusively, confine our attention. We propose to review the work of discoverers and explorers of the 19th century in two sections as regards time, - first during the first thirty, and secondly during the last forty-eight years. The Royal Geographical Society was founded in 1830, and forms a landmark. In each period we shall take first the work done in Asia, then Africa, then America, then Australia, then Polynesia, and finally the Arctic and Antarctic regions.

At the beginning of the century British rule in India was ' extended over the plains of the Ganges almost to the Sutlej, and the attention of explorers was drawn to the mighty mass of the Himalayas. Captain Herbert, in 1818, attemped to give a general view of the physical character of this great range, and Moorcroft reached the Mansarowa lake, and the upper courses of the Indus and Sutlej ; while Mr Manning, in 1811, was the only Englishman who ever visited Lassa, the capital of Tibet. The mission of Sir John Malcolm to Persia in 1808 led to much geographical work being achieved. On his staff was Macdonald Kinneir, who wrote a valuable memoir on the geography of Persia ; while at the same time Lieutenant J. Macartney, under Mountstuart Elphinstone, was collecting materials for a map of Afghanistan. In 1810 Pottinger and Christie made an important journey through Baluchistan by different routes, Christie afterwards visiting Herat and Yezd ; and in 1827 Mr Stirling of the Bengal Civil Service crossed the Havarah mountains.

The close of the war in 1815 led to numerous efforts for the furtherance of geographical discovery, especially in Africa and the far north. In 1818 to 1820 Captain Lyon, R.N., and Mr Ritchie landed at Tripoli, and penetrated as far as Mourzotik ; and this led to the more important expedition of Major Denham and Captain Clapperton, R.N., which was despatched by the Government. They landed at Tripoli in 1823, and advanced into the interior as far as the east coast of Lake Tchatl, of which they gave a most interesting account, obtaining latitudes by meridian altitudes and longitudes by lunar observations. Clapperton's furthest point was at Saccatoo, westward. of the lake, and here he was forced to turn back. But in 1825 he was again employed to explore the interior of Africa, and this time he started from the Atlantic side with his faithful servant Richard Lauder. Landing in the Bight of Benin, he succeeded in reaching Saccatoo from the west side, thus completing a route from Tripoli on the Mediterranean to the coast of Guinea. But at Saccatoo the gallant sailor succumbed at last, dying on the 13th of April 1827. His faithful servant Lander returned to the coast ; and in 1S30 he and his brother were employed to explore the course of the Niger or Quorra. They embarked on the river near Boossa, passed through the Yorriba country, and came out at the mouth of the Nun.

The Admiralty also considered that a river of such magnitude as the Zaire or Congo ought to be explored. Captain Tuckey, R.N., was selected to conduct the Congo expedition, and received command of a steamer called the " Congo," with a crew of 49 officers and men. The expedition reached the mouth of the great river on July 5, 1816, and proceeded up to the foot of the falls of Yellala, the farthest point hitherto reached. Captain Tuckey, with 15 of his party, landed on the north shore on the 14th of August; and, after travelling for about 40 miles over a hilly country, Ile reached the head of the falls and the banks of the upper river. He had explored the river for a distance of 280 miles from the sea. But death overtook the commander of the expedition and several officers, and the " Congo" returned in command of the master, Mr Fitzmaurice, after executing the survey from the foot of the falls to Embomma.

South America had produced two eminent physical geo• graphers, namely, Caldas of Bogota and Unanue of Lima, before the scenery of the Orinoco and the Andes became familiar to Europe through the charming narratives of Humboldt. It was in 1799 that the great Prussian naturalist embarked at Coruna, and landed at Cumana on the coast of Venezuela. His observant eye and bright imagination, combined with habits of scientific thought, produced pictures of the physical aspects of the regions he explored which are quite unequalled. What he said of George Forster is even more true of himself : "He depicted in pleasing colours the changing stages of vegetation, the relations of climate and articles of food in their influence on the civilization of mankind. All that can give truth, individuality, and distinctiveness to the delineation of exotic nature is united in his work." The Orinoco and Cassiquiari, the falls of Tequendama, the mountains of Quindiu, Chimborazo, and Quito, Cajamarca, and the upper Amazon, and the varied scenery of Mexico, are imprinted on the imagination with life-like form and colouring by this great master of description. His service to geography was far greater than that of any mere discoverer. Humboldt left the New World in 1804.

The greatest and most important enterprise, after the . peace of 1815, was the renewal of Arctic exploration under the auspices of Sir John Barrow. To the great work of Scoresby, and to the careful observations of himself and his father, we are indebted for the most exhaustive account of the Spitzbergen seas, and of the ice which encumbers them.

When the Government expeditions were undertaken, the volumes of Scoresby formed a storehouse of useful and well-digested information. The true object of modern Arctic enterprise has been the advancement of science, a noble and sufficient reason for incurring expenditure and faxing dangers and hardships. In consequence of Sir John Barrow's representations, orders were given in 1818 for the preparation of four vessels for Arctic service, - two to attempt the passage from the Atlantic to the Pacific, and two to attempt an approach to the North Pole. But, as Sir John Barrow himself explained, the main objects were not the accomplishment of voyages by these routes, but the acquisition of useful knowledge. Sir John Ross, who commanded one of the two expeditions, circumnavigated Baffin's Bay on the track of that great navigator, and re-established his fame. Captain Buchan, who led the other, battled with the impenetrable pack to the north of Spitzbergen, like Phipps before him, and then returned. There can be no great success without continuity of effort and perseverance, and the early voyages of this century achieved lasting results, because those who sent them out were endowed with tenacity of purpose. No sooner had Ross returned than Parry was appointed to command two strongly built vessels, the "Heela" and " Griper," and to proceed on the same service. On the 11th of May 1819 Parry sailed, and on the 1st of August he entered the portals of Lancaster Sound, and commenced the discovery of a new region. He succeeded in sailing for 300 miles along the southern shores of the islands which now bear his name, among ice floes of moderate thickness, until he reached the edge of the impenetrable polar pack at the western extreme of Melville Island. He went as far as it will ever be possible for any vessel to go in this direction, and then wintered in a harbour of Melville Island. In 1820 he returned with a rich harvest of scientific observations, and of valuable in formation in all branches of inquiry. This first expedition was most successful. Parry's second voyage was into Hudson's Bay in search of a passage westward in that diree. tion. He discovered a strait (that of " Fury and Ilccla "), and passed two winters 1821-23 on the coast of Melville Peninsula. The third voyage (1824-25) was again up Baffin's Bay; but it was unsuccessful, and one of his vessels, the "Fury," was lost. Still every voyage, whether successful or not in its main object, brought back valuable results. Meanwhile the " Griper," commanded by Captain Clavering, had, in 1823, penetrated through the ice to the east coast of Greenland in 76° N., to enable Captain Sabine to take pendulum observations in that position. The Russian Captain Lutke had also surveyed the west coast of Novaya Zemlya from 1821 to 1824. Parry, after his return from the third voyage, proposed an attempt to reach the Pole by travelling over the ice during the summer, on the Spitzbergen meridians. He sailed on this service in the "Hecla" on the 3d of April 1827, and, after placing her in a secure harbour in Spitzbergen, he began his bold and interesting attempt with two boats, fitted with runners for being dragged over the ice. But the whole mass of ice was drifting south faster than Parry's men, with all their efforts, could advance north. However, on July 23, 1827, lie attained the latitude of 82° 45' N., which continued to be the highest parallel ever reached by man until Captain Markham went beyond it in 1875. Parry returned to England in October. Another expedition of a private character left England in June 1829 under the command of Sir John Ross, who was accompanied by his distinguished nephew James C. Ross. In August they reached Lancaster Sound, and then proceeded southwards down Regent's Inlet, wintering on the most northern peninsula of America, to which Ross gave the name of Boothia. Here they passed three winters, while, during the intervening summers, some exploring work was accomplish:A, and James Ross planted the Union Jack on the North Magnetic Pole on the 1st of June 1831. At last they were forced to abandon their little vessel the " Victory," and make their way to the whalers in Baffin's Bay in open boats. They were picked up and arrived in England after an absence of four years.

While these bold and perilous voyages were being conducted in the Arctic seas, a series of land journeys completed the delineation of the northern coast of America, which had just been touched at two points in the last century, by Hearne and Mackenzie. From 1819 to 1823 the gallant Sir John Franklin, with Dr Richardson and George Back, were struggling to explore the Arctic coast eastward from the mouth of the Coppermin a River. After great sufferings they embarked on the river on June 30, 1820, reaching the mouth on July 18, and exploring 550 miles of coast line to the eastward, as far as Point Turnagain. On the return journey across the barren lands, the party escaped death from starvation almost by a miracle. Undaunted by this terrible experience, Franklin, Richardson, and Back started on another expedition in 1825, this time by descending the Mackenzie River. Reaching its mouth on July 7, Franklin and Back discovered 374 miles of coast to the westward, as far as Return Reef ; while Richardson explored the space between the mouths of the Mackenzie and Coppermine. In 1833 Back undertook a third journey with the object of succouring the Bosses, who had long been missing. He discovered and explored the Back or Great Fish River for 530 miles, and in July 1831 reached its mouth in the Arctic Ocean. The gaps on the north coast, which were left by Franklin and Back, were subsequently filled in by servants of the Hudson's Bay Company. In 1837 Messrs Simpson and Dease, in a boat, connected Return Reef with Cape Barrow. In 1839 the same explorers went from Cape Turnagain to the month of Back's River, and still further eastward to Castor and Pollux River. Ou August 26, 1839, Simpson built a cairn at Cape Herschel, on King William Island, separated by a strait ten miles wide from the mainland. Dr Rae was sent in 1816 to winter in Repulse Bay, and in 1847 he travelled round the Gulf of Akkoolee and connected the work of Ross in Boothia with that of Parry during his second voyage. In 1854 he united the work of Ross with that of Simpson, and ascertained that Boothia was connected with the mainland of America by an isthmus. Thus the whole northern coast of America was explored and delineated without a break.

The Russians were engaged on daring Arctic exploration at the same time. In 1S09 to 1812 a Russian officer named Hedenstrom surveyed the New Siberia Islands ; and in 1821 Lieutenant Anjou made further investigations respecting the state of the ice to the northward. Baron Wrangell prosecuted similar researches from his headquarters at Nijni Kolymsk, near the mouth of the Kolyma. He made four sledge journeys over the Polar Sea from 1820 to 1823, exploring the coast from the Kolyma to Cape Chelagskoi, and making several attempts to advance northwards, but always encountering weak ice. Wrangell's interesting narrative is an important addition to Arctic literature.

The Russians, as well as the French, sent several voyages info the Pacific during the first half of the 19th century. In 1801 Admiral Krusenstern made a voyage round the world, and his pupil, Otto von Kotzebue, son of the dramatist, commanded the "Rurick" from 1815 to 1818 on a voyage of discovery. He discovered the great bay known as Kotzebue Sound, sounded in Behring Strait, and madQ careful observations of the currents. Wintering in California he returned to the Aleutian Islands in the following springy; and during the voyage homewards he discovered several new islands in the Pacific, especially Romanzoff and Krusenstern in the Dangerous Archipelago. During another Russian voyage, commanded by Billinghausen, Lazareff and other coral islands in the Dangerous Archipelago were discovered, and in 1828 Captain Lutke, in the " Seniavine," surveyed the Caroline group. Captain Freycinet, the officer who served with Baudin and edited his work, also examined the Caroline Islands in the "Uranie" in 1819, but his voyage was mainly in the interests of natural history. Duperry in 1822-23 did some surveying work on the coast of New Ireland. But the most important French voyage was that of Dumont D'Urville, who was sent out to seek for traces of La Perouse in 1828. He visited Tecopia and other islands in the " Astrolabe," and was nearly a month at Vanikoro collecting relics of the iIlfated expedition. The voyage of D'Urville contributed largely to the advancement of science, and resulted in the publication of a magnificent work in 1830.

The only English scientific voyage to the Pacific in this period was sent out mainly to co-operate with Parry in his third voyage, and Franklin in his second journey. It was commanded by Captain Beechey, who had been first lieutenant with Parry during his first Arctic voyage, and on May 19, 1825, lie sailed from Spithead in H.M.S. "Blossom." After visiting Easter, Gambier, Pitcairn, and other islands, the "Blossom " arrived at Honolulu on May 20, 1826, and in July she was in Behring Strait, entering Kotzebue Sound on the 22d. Proceeding along the north coast of America, the ship's barge got as far as 156' 21' W. to a low cape called Point Barrow, at the very time when Franklin and Back were at Return Reef. The accurate examination of the coast was made under circumstances which demanded great fortitude and perseverance, and reflects credit on the officers and crew. The "Blossom" returned to Honolulu in January 1827, and arrived at Macao on the 12th of April. Captain Beechey next proceeded to survey the Loo Choo and Bonin Islands, and, after another visit to the far north, and the coasts of California and Mexico, lie returned home by Cape Horn and arrived at Woolwich on October 12, 1828. His valuable and interesting narrative, in two volumes, was published in 1831. Mr James 'Weddell, a master in the navy, made a voyage to the Antarctic Ocean in 1822-24, and went as far south as 710.

The Royal Geographical Society was founded in 1830, and forms a landmark in the history of discovery. The men who initiated the idea and gave it shape were Sir John Barrow, Sir John Cam Hobhouse, Sir Roderick Murelison, Mr Robert Brown (Princeps Botanicorum), and Mr Bartle Frere. They formed the Foundation Committee. The first president was Lord Goderich, and the vice-presidents Sir John Barrow, Colonel Leake, Sir John Franklin, and Mr Greenough. Through this organization explorers and students were encouraged and assisted, information was systematically collected and arranged, and the work of discovery was advanced. A similar society in Paris preceded that of London in point of time, and now every civilized country has established a Geographical Society.

Our rapid review of the progress of discovery since the . foundation of the Geographical Society will commence with the continent of Asia, where there were and still are vast and most interesting unexplored regions. In British India the Trigonometrical Survey has been proceeded with, and is now approaching completion. During its progress the Himalayan peaks were measured, and in 1848 Sir Andrew ] Waugh fixed the height of the loftiest, which he named 1 Mount Everest, at 29,002 feet above the sea. In 1831 1 Humboldt published his Asie Centrale, which, with the Erdkunde von Asien of Carl Ritter, gave new and clearer ideas of the orography of Central Asia. Many travellers explored the remoter parts of the Himalayan chain ; in 1848, Dr Hooker in Sikkim, and Dr Thomson in Ladak, - reached the summits of the passes leading to Tibet and Yarkaucl. Our relations with Afghanistan led to further exploration. In 1840 Lieutenants Abbott, Conolly, and Shakespear visited Khiva, and in 1811 Colonels Stoddart and Conolly were murdered at Bokhara, while Eldred Pottinger gallantly defended Herat. Sir Alexander Burnes had previously made his remarkable journey from Cabul to Bokhara and back through Persia, and in 1838 Lieutenant Wood of the Indian Navy discovered the source of the Oxus. Butakoff and other Russian officers, in 1848 and subsequent years, surveyed the sea of Aral, and Middendorf made extensive explorations and discoveries in Siberia. After the Afghan war it was long before any progress was made in the exploration of Central Asia, but through the opening of the treaty ports in China and the navigation of the Yangtsze considerable increase was made in our knowledge of the Celestial Empire. In 1869 Mr E. B. Shaw and Mr Haywood reached the cities of Yarkand and Kashgar, and Mr Shaw published a most graphic account of the physical aspects of Eastern Turkestan. In the previous year Mr Ney Elias surveyed the Yellow River of China, and afterwards made a journey through a previously unknown portion of western Mongolia ; and during 1866-68 the distinguished French geographer Lieutenant Garnier surveyed the course of the great Cambodian river. The Russians, meanwhile, in their advance into Central Asia, had enabled scientific travellers like Fedchenko and others to explore Khokand and the northern part of the Pamir, and the more adventurous Prjewalski made important journeys through Mongolia and to the frontiers of Tibet. Colonels Walker and Montgomerie, of the great Trigonometrical Survey of India, organized a system of training native explorers, who made journeys across the Pamir and to the upper waters of the Oxus, as well as through the previously unknown parts of Tibet. In the last mission of Sir Douglas Forsyth to Kashgar, Captain Trotter of the Trigonometrical Survey of India formed one of the staff. He did much valuable exploring work on the Pamir table-land, and verified the work of Lieutenant Wood at the source of the Oxus. In 1845 MM. Huc and Gabet travelled through Tibet ; and in western China the French missionaries have since done useful geographical work. English diplomatic officers have found their way from the south-western provinces of China into Burmah, and Baron Richthofen has made very extensive exploring journeys through the Chinese empire. The most important journey across Arabia in the present century was made by Mr W. Gifford Palgrave in 1863.

Geographical discoverers of the 19th century have had a great work to do in Africa. D'Anville and his successors cleared off all that was uncertain on the map, all that had come from the information given by Duarte Lopez to Pigafetta, and from Leo Africanus, and left a great blank. James Bruce and Mungo Park, Clapperton and Tuckey, merely touched the edges or penetrated in single lines across the vast unknown area. But they have been followed by many others, and now great progress has been made. In 1831 Monteiro and Gamitta were sent by the Portuguese Government, in the footsteps of La Cerda, to the capital of Cazembe ; while, in 1849 and 1813-17, Ladislaus Magyar and Grata explored some of the southern affluents of the Congo. Riippell (1838), Harris (1843), and Dr Beke (1840), Lefebvre and Dillon (1839-43), Ferret and Galinier (1847) improved the existing knowledge of Abyssinia, to which a further important contribution was made by the expeditionary field force sent in 186768 to enforce the release of English captives; and progress was made, under the auspices of the Egyptian Government, in exploring the White Nile above Khartoum. In 1849 the discoveries of Denham and Clapperton were followed up by Richardson, Overweg, and Barth, who, like their pre decessors, went from Tripoli to Mourzonk, the capital of Fezzan. The two first died in Africa, but Dr Barth returned home with a rich harvest of results. He reached. Kouka the capital of Bornou, on Lake Tchad, and in 1851 he visited the south side of that lake, and advanced some distance to the eastward. In 1852 he was at Saccatoo, where Clapperton died, whence he crossed the Niger and eventually reached Timbuctoo. After a stay of some months Dr Barth left Timbuctoo in March 1854, and got back to Tripoli in the end of 1855, being the sole survivor of his party. Dr Vogel, in 1853-57, followed up the discoveries in the direction of Lake Tchad, and fell a victim to science ; and the researches of Dr Baikie in 1854 supplemented the work of the Landers in the lower part of the course of the Niger. Dr Baikie also explored 250 miles of the river Chadda or Benue.

On the eastern coast of Africa, the missionaries Rebmann and Krapf ascertained the existence of the snowy peaks of Kenia and Kilimanjaro near the equator, and collected reports touching the equatorial lakes in the interior. This led to the expedition of Captain Burton in 1857, who, accompanied by Captain Spoke, landed opposite to Zanzibar, and, advancing westward, discovered Lake Tanganyika. Captain Burton's admirable description of the region between the coast and the great lake he had discovered is one of the most valuable contributions to African descriptive geography. His companion, Captain Speke, made an excursion northwards to the southern coast of a lake which he judged to be a main source of the Nile. In this belief he again set out in 1860 to attempt the achievement of a journey from Bagamoyo, opposite Zanzibar, to the Nile. This great enterprise was crowned with success. Speke traced out the western shore, and visited the northern outlet, of the Victoria Nyanza, the main reservoir of the White Nile. He then marched northwards to Gondokoro and descended the Nile. He had heard of a second great Nile reservoir, which Sir Samuel Baker discovered in 1864, and named the Albert .Nyanza. The Bahr el Ghazal and other western feeders of the Nile were visited by Consul Petherick, and explored in 1868-71 by Dr Schweinfurth, whose work ranks with that of Burton as a record of African discovery.

The travels of Dr Livingstone in Southern Africa also I added considerably to our knowledge of the geography of that continent. In 1848 he started from Cape Colony, visited Lake Ngami in 1849, and eventually reached the Portuguese town of St Paul Loauda in 1855. Thence he marched across the continent, discovering the great falls and a considerable part of the course of time Zambesi. In his second expedition lie proceeded up the Zambesi and its tributary the Shire, and discovered the Lake Nyassa. On his third and last expedition he landed on the east coast at the mouth of the Rovuma, and made his way thence to Lake Nyassa. The great traveller then followed in the footsteps of Dr Laeerda and Monteiro to the Cazembe's capital, and thence to Lake Tanganyika. From Ujiji, on that lake, he made his way westward to the river Lualaba (the upper course of the Congo), and returning in a destitute condition to Ujiji, he was there succoured by Mr Stanley. Finally he once more started, and died in the midst of his discoveries among the remoter sources of time Congo. Lieutenant Cameron's expedition in 1873 had for its main object the succour of Livingstone, but the news of the great traveller's death was received at Unyanyembe. Cameron then continued his march by a new route to Ujiji, and completed the survey of the southern half of Lake Tanganyika, discovering the Lukuga outlet. Thence he advanced westward across the Manyuema country to Living-stone's furthest point at Nyangwe, crossed the Lualaba, and traversed the whole width of the African continent, reaching St Paul Loanda on the west coast. Mr Stanley followed in 1874. He circumnavigated and fixed the outline of the Victoria Nyanza, followed Cameron across Lake Tanganyika to Nyangwe, and then descended the great River Congo, discovering its course, and connecting the work of Livingstone with that of Tuckey. Mr Young has since completed the survey of Lake Nyassa ; Nachtigal has supplemented the work of Barth and Vogel in the Tchad region ; while Duveyrier and other French explorers have examined the region of the Sahara. In the far south the Limpopo basin, and the country intervening between the Limpopo and Zambesi, have been made known to us by St Vincent Erskine and Elton, Carl Mauch and Baines. Thus the extent of the unknown parts of Africa has been rapidly curtailed, while our knowledge has been widened during the last half century.

On the American continent scientific progress has been made in the United States and the dominion of Canada, where, within the last half century, boundary commissions and surveys have fixed positions and described previously unknown regions of great extent. In South America there are vast unexplored regions to the eastward of the Andes, and in the basins of the great rivers. Sir Robert Schomburgk did much valuable work in Guiana, and explored the delta of the Orinoco in 1841 ; while Spix and Martins, Pueppig and CasteNan, Maw and Smyth, Herndon and Gibbon, Spruce and Bates, Wallace and Chandless, and others, explored the basin of the Amazon. The labours of Pissis in Chili, of Raimondi and Werthermann in Peru, of Codazzi in Colombia and Venezuela, and of Morales and others in the Argentine Republic, have been most valuable to'geographical science. In Patagonia, Fitz Roy:and King explored the Santa Cruz river, Cox and Morales have since added to our knowledge, and Commander Musters, R.N., was the first traveller who traversed the whole of Patagonia from south to north, 960 miles of latitude, of which 780 were previously unknown to Europeans.

The difficulty of exploring the interior of the Australian continent was caused by. the scarcity of water, and the immense distances it was necessary to cross without supplies of any kind. Hence the work of exploration has required and called forth high and noble qualities in a degree quite equal to any that have been recorded in any other part of the world, The names of Sturt and Leichhardt, of Eyre and Grey, of Macdouall Stewart and Burke, of Gregory, of Forrest and Warburton, will be handed down as those of intrepid and courageous explorers who laid open the secrets of the interior of Australia.

The Pacific Ocean was explored by numerous expeditions during the 18th and early part of the 19th centuries. Still much remained to be done in the way of verification and more complete survey. From 1826 to 1836 Captain Fitzroy, with the naturalist Darwin, surveyed Magellan's Strait and the west coast of South America ; and further important surveys in the Pacific were afterwards executed by Captain Wilkes of the United States Navy, and by Belcher, Kellett, and Denham.

But the great geographical work of the present century must be the extension of discovery in the Arctic and Antarctic regions. Progress has been made in both directions, and in both much remains to be clone. It is this polar work which calls forth the highest qualities of an explorer ; it is here that the greatest difficulties must be overcome; and it is here that the most valuable scientific results are to be obtained.

Between the years 1830 and 1843 much was done in the Antarctic regions. In 1830-32 Mr John Biscoe, R.N., made a voyage in a brig belonging to Messrs Enderby, and discovered "Enderby Land" and "Graham Land" in 67° S. ; and from 1837 to 1840 Dumont d'Urville discovered "La Terre Adele " and "Cote Cleric," going as far south as 66° 30'. Auckland Island was discovered by Bristow in 1806. In 1839 Balleny, in another vessel belonging to Messrs Enderby, discovered the Balleny Islands in 66° 44' S., and Sabrina Island in 65° 10' S. The Antarctic expedition of Sir James Ross sailed from England in 1839. In 1840 Sir James explored Kerguelen Island, and wintered at Hobart Town. He then visited the Auckland Islands, and, crossing the Antarctic Circle, reached the great icy barrier, and discovered Victoria Land, with its lofty volcanoes, in January 1841. He gained the latitude of 78° 4' S. in 187° E., and established the continuity of the southern continent from 70° to 79° S. In 1841 Ross again wintered at Van Diemen's Land, and in January 1842 crossed the Antarctic circle in 156° 28' W. He was once more stopped by the great icy barrier in 78° 10' S., after having penetrated through ice floes of more than 1000 miles in width. Extraordinary dangers were encountered in the ice, many valuable observations were taken, and in 1842 the expedition wintered at the Falkland Islands. In the following season another exploring voyage was made beyond the Antarctic Circle, and in September 1843 this most important expedition returned to England.

On the return of Sir James Ross attention was once more turned to the Arctic regions; and in the spring of 1845 Sir John Franklin's Arctic expedition, consisting of the " Erebus " and " Terror," sailed from Woolwich. His instructions were to make the North-West Passage, but the main object of the expedition was the advancement c,f science, and to secure it the most accomplished officers in the navy were appointed, as well as the eminent naturalist Dr Goodsir. It is now known that, in the first and second seasons, the expedition was very successful. In 1845 Sir John Franklin made a remarkable run up Wellington Channel to 77' N. ; in 1846, proceeding south, he had almost achieved the North-West Passage when his ships were permanently beset to the north of King William Island in 70° 5' N. and 98' 23' W. Here the veteran explorer died on June 11, 1847 ; and all his companions perished in the attempt to reach one of the Hudson's Bay Company's settlements in the summer of 1848. Those among them who reached Cape Herschel, and it is certain that some did reach that point, undoubtedly discovered the North-West Passage.

The expeditions which were sent out in search of Sir John Franklin's ships did much important geographical work ; but their principal use was the establishment, through their means, of the truemethod of extensive Arctic exploration. The grand_object of the officers and men employed on this service was the relief of their missing countrymen, and their utmost efforts were devoted to the examination of the largest possible extent of coast-line. Hence the discovery of the modern system of Arctic sledge travelling, the only efficient means of exploring the icy regions around the North Pole. In 1848-49 Sir James Ross discovered the western side of North Somerset, and Sir Leopold M'Clintock served his first apprenticeship in the ice under that veteran explorer. Austin's expedition sailed in 1850, and wintered nearly in the centre of the region discovered by Parry during his first voyage. It was then that M'Clintock developed and put in practice the system of Arctic sledge-travelling which has since achieved such grand results; and Captain Ommanney, M'Clintock, and his colleagues Sherard Osborn, Frederick Meehan], Robert Aldrich, and Vesey Hamilton made what were then unparalleled journeys in various directions. In December 1849, also, Captains Collinson and M'Clure went out to conduct further search by way of Behring Strait. The former made the most remarkable voyage on record along the north coast of America, while M'Clure took his ship between the west coast of Banks Island and the tremendous polar pack, until he was wi tido sight of the position attained by Parry in his first voyage from Baffin's Bay. Here McClure's ship was finally iced up in the Bay of God's Mercy. On the return of Austin's expedition, the same ships were again sent out under Captains Belcher and Kellett by Baffin's Bay ; and McClintock, Osborn, Meehan), and Hamilton, who were once more in the front rank of searchers, surpassed even their former efforts. Mecham discovered a record left by McClure on Melville Island which revealed his position, and thus he and his officers and crew, by marching from their abandoned ship to the " Resolute " and returning to England with the expedition of Belcher and Kellett, were enabled to make the North-West Passage partly by ship and partly sledging over the ice. They all returned in 1851. But the concluding search was made by Sir Leopold McClintock in the "Fox" from 1857 to 1859, when he found the record on King William Island, and thus discovered the fate of Franklin. These search expeditions added immensely to our knowledge of the Arctic regions, and established the true method of exploration. Sea voyages in the summer season are useful for reconnaissances, but efficient polar work can only be achieved by wintering at a point beyond any previously reached, and sending out extended sledge parties in the spring.

After the return of McClintock, England neglected the great work of Arctic exploration for fifteen years ; but a deep interest was taken in the discovery of the unknown polar regions by other nations, and numerous efforts to explore them were made in the interval. In 1853-55 Dr Kane, with the American brig " Advance," wintered just within the entrance of Smith Sound, and sent an exploring party for some distance up the east side of the channel ; and in 1860-61 Dr Hayes wintered near the same spot, and made a sledge journey up the west side. Ten years afterwards Captain Hall, accompanied by Dr Bessels, a German scientific explorer, sailed in the " Polaris" in August 1871, and succeeded in making his way up the channels leading north from Smith Sound for 250 miles, wintering in 81° 38' N. Captain Hall unfortunately died in the autumn of 1871, and his comrades returned after suffering great hardships. The " Polaris " was abandoned, but she had attained the highest latitude ever reached by any vessel up to that date. In the direction of Spitzbergen and Novaya Zemlya the Norwegian walrus hunters made many daring voyages. They circumnavigated both those masses of Arctic land, and yearly frequented the hitherto closed Sea of Kara. The Swedes, under the lead of the accomplished and indefatigable Nordenskiold, have made voyage after voyage to Spitzbergen, and afterwards to the north-east. The first Swedish expedition to Spitzbergen was in 1857, the second in 1861, the third in 1861, the fourth in 1868, consisting of the steamer " Sophia," which reached the highest latitude ever attained by a vessel trying the Spitzbergen route, namely, 81° 42' N. In 1872 a fifth expedition started, and Nordenskiold then passed his first winter in the Arctic regions, and gained experience of sledge-travelling in the spring, exploring a large area of North-East Land. Experience also proved that the Spitzbergen route was not one by which large results could be secured, although the scientific researches of the Swedes in Spitzbergen itself were most valuable. In 1875 therefore Professor Nordenskiold made his first attempt towards the north-east, reaching the mouth of the Yenisei ; and in 1876 lie made= equally successful voyage in the same direction. The Germans also entered the field of Arctic enterprise. In 1868 Captain Koldewey made a summer voyage to Spitzbergen, and in 1869-70 he went in the " Germania " to the east coast of Greenland, accompanied by Lieutenant Payer, wintered at the Pendulum Island, discovered by Clavering in 1823, whence they made a sledge journey to thc northward as far as 77', and explored a deep fjorl in about 73° 15' N. during the navigable season. English yachtsmen, notably Lamont and Leigh Smith, were also in the field ; and the latter made important corrections of the charts of North-East Land. But by far the most important and successful , voyage in this period was that of Lieutenants Weypreeht anil Payer in the Austrian steamer " Tegethotf." Sailing I in 1872, they were beset in the ice to the north of Novaya Zemlya during the winter of 1872-73, and were drifted northwards until, on August 31,1873, they- sighted a previously unknown country. It proved to be very extensive, and was named Franz Josef Land. In March 1871 Lieutenant Payer started on an extended sledge journey, in the equipment of which lie closely followed McClintock's system. He discovered a great extent of coast-line, and attained a latitude of 82° 5' N. at Cape Fligely. The Austrian explorers were eventually obliged to abandon the " Tegethoff," reaching Norway in September 1874; but their expedition was a great success, and they added an extensive region to the map of the known world.

In England the very important branch of geographical = research relating to the Arctic regions was neglected by the Government during this interval of fifteen years, while A mericans, Swedes, Norwegians, Germans, Austrians, and English yachtsmen were making praiseworthy efforts with more or less success. The resumption of English Arctic research on an adequate scale is due to the exertions and arguments of Admiral Sherard Osborn from 1865 until 1875. He set forth the valuable results to be obtained, and the means of success. Basing his arguments on long experience, lie showed that it was necessary for success that an expedition should follow a coast-line, that it should pass beyond any point previously reached and there winter, and that the work should be completed by extended sledge parties in the spring. . At length an expedition was fitted out on these principles, the Smith Sound route was selected, and in May 1875 the " Alert " and " Discovery " sailed from Portsmouth under the command of Captain Nares. As regards the ice navigation the success of the expedition was complete. Captain Nares, in the face of unparalleled difficulties, brought the ships to a point farther north than any vessel of any nation had ever reached before, wintered the " Alert " in 82' 27' N., and, in the face of still greater difficulties, brought both vessels safely home again. The extended ;ledge-travelling called forth an amount of heroic devotion to duty, and of resolute perseverance in spite of greater obstacles than had ever been encountered before, which add a proud page to the history of English naval enterprise. The exploring parties were led by Commander Markham and Lieutenants Aldrich and Beaumont, Advancing over the great frozen Polar Sea, Markham reached 83° 20' 26" N., the highest latitude ever attained by any human being. He thus won the blue ribbon of Arctic discovery. Aldrich discovered 200 miles of coast to the west-. ward, while Beaumont added to our knowledge of the north coast of Greenland. The results of the Arctic expedition of 1875-76 were the creation of a young generation of experienced Arctic officers, the discovery of 300 miles of new coast-line and of a large section of the Polar Ocean, the attainment of the highest latitude ever reached by man, a year's magnetic and meteorological observations at two stations both further north than any before taken, tidal observations, the examination of the geology of a vast region and the discovery of a fossil forest in 820 N., and large natural history collections representing the fauna and flora of a new region.

The return of this memorable expedition again incites( D our neighbours to further efforts. In the summer of 1878 A the Dutch entered the field, and the schooner " William ' Barents," under Lieutenants de Bruyne and Koolemans Beyncn, made a useful reconnaissance of the Barent's Sea ; while Professor Nordenskiiild left Sweden in July 1878, in the well-equipped steamer " Vega, " to achieve the North-East Passage. In August he rounded Cape Chelyuskin, the most northern point of the Old World, and reached the mouth of the Lena. But much work remains to be done in the polar regions, in order to complete the connexion between Aldrich's furthest in 1876 and M'Clintock's in 1851, to complete the discovery of the north side of Greenland, to explore the northern bounds of Franz Josef Laud, and to discover lands north of Siberia.

There is one great branch of physical geography which has only been effectively studied within the last thirty years, namely, the physical geography of the sea. Mathew Fontaine Maury, by his wind and current charts, by his trade wind, tortri, rain, and whale charts, and above all by his charming work The Physical Geography of the Sea, gave the first impulse to this study. It was Captain Maury who organized the first deep-sea soundings in the North Atlantic, which up to that time was deemed to be unfathomable ; and when his work was published, the illustrious Humboldt declared Maury to be the founder of a new and important science - the meteorology of the sea. He first took charge of the Washington Observatory in 1812 ; be resigned that post under a deep sense of duty in April 1861, after a career of great usefulness ; and he ended a noble and well-spent life in 1872. The investigations into the physical geography of the sea, which were combined into a system by Maury, have since been ably and zealously continued by others, among whom the names of Dr Carpenter, Sir Wyville Thomson, and Professor Mohn of Christiania are pre-eminent. The voyage of the "Challenger " from 1873-1876, under Captains Nares and Thomson, with Sir Wyville Thomson as chief of the scientific staff, was organized with the object of examining and mapping the bottom of the ocean, of describing the fauna of the great depths, of ascertaining the temperatures at various depths, and of solving questions relating to oceanic circulation. The area thus explored in the Atlantic, Antarctic, Pacific, and Indian Oceans is of vast extent, and the researches, ably and zealously conducted, have resulted in an important addition to geographical knowledge.

In this rapid sketch of the history of geographical discovery, the labours of numerous explorers during many generations have been enumerated ; but its perusal will show that, notwithstanding all this work, there is much remaining to be clone. Vast areas round both poles, and in the interior of Asia, Africa, South America, and New Guinea, are still unknown, even more extensive regions have only been partially explored, and millions of square miles remain to be surveyed, before the work of geographers is complete. (c. R. M.) All our knowledge of the planet on which we live, whether obtained from the explorations of travellers, the voyages of navigators, or the discoveries of astronomy in modern times, goes to confirm the doctrine held and taught by philosophers in a remote antiquity that the earth is spherical. What is spherical, however, is not the actual surface of the earth, but rather that of the sea produced in imagination to pass through the continents. That the surface of the sea is convex any one may - at a seaside station where there is a high cliff - convince himself, by noting with a telescope at the top of the cliff the exact appearance of a ship in, or slightly beyond, the horizon, and then, immediately after, repeating at the foot of the cliff the same observation on the same ship. By a more precise observation of the sea horizon from a known altitude one may even calculate the radius of the earth.

Let m (fig. 1) be a point on the top of a mountain ; lank a portion of the earth's surface ; 27/1/2/ a line drawn from m towards the centre of the earth ; mit a tangent from 7n to the spherical surface ; and ml a horizontal line through at, that is, ml is perpendicular to my. Then by the mere measure of the angle lmh, or the depression of the sea horizon, one can, knowing mn, calculate very simply the radius of the earth. Let the height mu = A, the angle lath = 8, and the radius of the earth =2'; then since the angle subtended at the earth's centre by An is 8, it is clear that (It + r) cos8 = r, which gives r in terms of h and 6, known quantities. In fact, since h and 6 are both small, r=ivha sin24,8. But here we have assumed that the ray of light proceeding from It to m takes a rectilinear course ; this is not true however, for the path is curved, its concavity being turned towards the earth--a consequence of terrestrial refraction. From the laws of terrestrial refraction, which have been very minutely studied, we know that the formula last written down should be r= .422h sin2P. Now to take an actual case - the depression of the sea horizon at the top of Ben Nevis is 64' 48" (this is the mean of several observations, taken with special precautions for the express purpose of this experimental calculation), and the height of the hill is 4406 feet, or •8345 of a mile. The formula gives at once r = 3965 miles, which is remarkably near the truth. But this method is not capable of precision on account of the variableness of terrestrial refraction. In connexion with the appearance of the sea horizon from a height the following formulm are useful : - hbeing the height in feet, 8 the depression or dip of the horizon in minutes, s the distance of the horizon in miles, then 8=0. - 1 )hilt ; 3N/h, Thus, for instance, to a spectator on the top of Snowdon, which is 3590 feet in height, the distance of the sea horizon is about 80 miles.

The first great fact in the description of the earth being that it is spherical (or at any rate so nearly so that, were a perfect model of it constructed, no one could, by unaided vision, discover that it is not spherical), the next points to be noted are, - secondly, that the earth rotates uniformly round an axis passing through its centre, and fixed, or very nearly fixed as to direction, in space; and thirdly, that its figure is not spherical but spheroidal, the surface being that found by the revolution of an ellipse round its minor axis, the axis of figure corresponding with the axis of diurnal rotation. The spheroidal figure is a necessary consequence of the rotation. The rotation of the earth once in 24 hours, although made evident by the rising and setting of the heavenly bodies, is rendered perhaps more distinctly visible by Foucault's pendulum experiment. Let a heavy ball be suspended by a fine thread, free from tension, from a fixed point. Let it be drawn aside from the position of equilibrium and then dropped so that it commences to oscillate in a vertical plane passing through the point of suspension. Then a careful observation of the pendulum will show that its plane of oscillation is not fixed, but has a uniform rotation in a direction opposite to that of the earth's rotation. Suppose, for instance, that the pendulum were suspended at the north pole and that it were set oscillating in a plane passing through any one fixed star, then it will continue to oscillate in that same plane notwithstanding the earth's rotation, Consequently, to the observer there the plane of the pendulum's oscillation will appear to rotate through 360r in 21 hours. At the equator, since there is no component of rotation there, the pendulum would continue to move in one and the same plane. At intermediate stations the rate of rotation is easily calculated ; and observations confirm the calculations, and have made the earth's rotation actually visible.

The poles of the earth are the points in which the axis of rotation, or of figure, meet the surface ; and the equator is the circle in which the surface is intersected by a plane through the earth's centre, perpendicular to the axis of rotation. Every point of the equator is therefore equidistant from the poles.

To determine the position of a point in space three co-ordinates or measurements are necessary ; they may be three lines, or two lines and one angle, or two angles and oue line. Thus, to define the precise position of a point on the earth's surface, we express it by latitude, longitude, and altitude ; the first two are angular measures, the third a linear magnitude, namely the height above the surface of the sea.

The line in which the surface of the earth is intersected by a plane through the axis of rotation is called a meridian, and all meridians are evidently similar curves. A line perpendicular to the surface at any point is called a vertical line ; it corresponds with the direction of gravity there ; being produced outwards, that is, away from the earth's centre it meets the heavens in the zenith; and produced downwards it intersects the axis of revolution ; it would of course pass through the earth's centre were it a sphere ; as it is, it passes near the earth's centre.

The angle between the meridian planes of two stations as A and B is called the difference of longitude of A and B, or the longitude of B with reference to A. In British maps the longitudes of all places are expressed with reference to the Royal Observatory of Greenwich.

The latitude of any point is the angle made by the vertical line there with the plane of the equator, or the co-latitude is the angle between the vertical line and the axis of rotation. The surface of the earth being one of revolution, any intersecting plane parallel to the equator cuts it in a circle. If we imagine the vertical lines drawn at any two points, as P and Q, in such a circle it is evident from the symmetry of thc surface that these verticals make the same angle with the equator ; in other words, the latitudes of all points on this circle are equal. Such circles are called parallels ; they intersect meridians at right angles.

If we suppose that at any point Q of the surface the meridian, or a small bit of it, is actually traced on the surface, and also a portion of the parallel through the same point, then these lines, crossing at right angles in Q, mark there the directions which we call north and south, east and west - the meridian lying north and south, the parallel east and west. Planes containing the vertical line at Q are vertical planes there. A vertical plane is defined by its azimuth, which is thc angle it makes with the meridian plane ; the azimuth at Q of any object (or point) celestial or terrestrial is the angle which the vertical plane passing through the object makes with the meridian. The south meridian is generally taken as the zero of azimuth. The plane touching the surface at Q is the visible horizon there - a plane parallel to this through the centre of the earth being called the rational horizon. The altitude at Q of a heavenly body, as a star, is the angle which the line drawn from Q to the star makes with the plane of the horizon, - the zenith distance of the same star being the angle between its direction and the vertical at Q.

By a degree of the meridian is meant this : if E, F are points on the same meridian such that the directions of their verticals make with each other an angle of one degree - a ninetieth part of a right angle - then the distance between E and F measured along the meridian is a degree of the meridian. As the radius of curvature of an ellipse is increasing ncreasing from the extremity of the major axis to the extremity of the minor axis, so on the earth's surface a degree of the meridian is found by geodetic measurement to increase from the equator to the poles.

The actual length of a degree of the meridian at the equator is 362746• feet ; at either pole it is 366479•8 feet. The length of one degree of the equatorial circle is 365231.1 feet.

With regard to the figure of the earth as a whole, the polar radius is 3949.79 miles, and the radius of the equator 39633C miles ; the difference of these, called the ellipticity, ise'u-of the mean radius. A spheroid with these semiaxes is equivalent in volume to a sphere having a radius of 395S'79 miles. Without referring further here to the spheroidal figure, we shall now, having given the precise dimensions, regard the earth as a sphere whose radius is 3959 miles. On such a sphere one degree is 6909 miles. From the definitions given above it appears that the radius of the parallel which corresponds t.o all points whose latitude is 0 is 3959 cos 0 ; and that one degree of this circle, i.e., one degree of longitude in the latitude 0 is 69.09 cos expressed in miles.

In the representation of the spherical earth (fig. 2) P is the pole, QQ the equator, E,F any two points on the surface, PEe, IT/ the meridians of those points intersectingthe equator in e and/ Join EF by a great circle; then in the spherical triangle PEF the angle at P is the difference of longitude of E and F, PE is the co-latitude of F, and PF the co-latitude of F, the latitudes being el: and fF respectively. The angle at E, being that contained between the meridian there and a vertical plane passing through F, is the azimuth of F (measured in this case from the north), while the angle at F is the azimuth of E. If, then, there be given the latitudes and longitudes of two places, to find their distance apart, and their relative bearings, it becomes necessary to calculate a spherical triangle (PEF) in which two sides and the included angle are given, - the calculation bringing out the third side, which is the required distance, with the adjacent azimuthal angles.

The latitudes and longitudes of places on the earth's surface are determined by observations of the stars, of the sun, and of the moon. As the earth rotates, the zenith of any place (not being on the equator) traces out among the stars a small circle having for centre that point in which the axis of rotation meets the heavens. If there were a star at this last point it would be apparently motionless, having always the same altitude and azimuth. The pole star, though very conveniently near the north pole of the heavens, and without. perceptible motion to the unaided eye, is in reality moving in a very small circle. The zenith of a point on the equator traces out in the heavens a great circle, namely, the celestial equator.

As the positions of points on the earth are defined with reference to the equator and a certain fixed meridian, so the positions of stars are defined by their angular distance from the celestial equator, called in this case declination, and by their right ascension, which corresponds to terrestrial longitude. Stars which are on the same meridian plane (extended to the heavens) have the same right ascension. Right ascension is expressed in time from Oh to 24% A sidereal clock, going truly, indicates 24h for every revolution of the earth : at every observatory, the sidereal clock there shows, at each moment, the right ascension of the stars which at that moment are on the meridian. Thus the right ascension of the zenith is the sidereal time.

in the left hand circle of the diagram (fig. 3) two

If we consider in the first circle the changes of distance between any one star and the zenith of Q as the latter traces out its path in the heavens, we see that the distance becomes alternately a maximum and a minimum everytwelve hours, namely, when the meridian of Q passes through the star. This is called the star's culmination or meridian transit. It will be clear from an inspection of the figure that, if for instance the star culminate to the south of the zenith, the star's declination plus its zenith distance at culmination is equal to the latitude of the zenith, that is, of Q. A corresponding rule is easily made for a northern transit. Thus the simplest manner of determining the latitude is to measure the zenith distance of a known star at its meridian transit.

The position of the zenith at any moment may be determined by simultaneous observation of the zenith distance of two known stars. For these distances clearly determine a point hi the heavens (two points rather, which however need not be confounded) whose declination and right ascension can be computed by spherical trigonometry. Thus, at the same time, are obtained both the time and the latitude. For the success of this method, which is suitable for travellers exploring an unknown country, it is desirable that the stars should differ in azimuth by about a right angle.

If the path of the zenith, that is, the latitude, be known, then clearly a single observation of the zenith distance of a known star, which should be towards the east or west, not towards the north or south, will fix the place or right ascension of the zenith, that is, the sidereal time, at the moment of observation. Here the pole, the zenith, and the star are the angular points of a spherical triangle, of which the three sides are known : the angle at the pole, being computed, is the difference of right ascension of the star and the zenith. Thus the sidereal time is found.

The determination of the difference of longitude of the two stations AB on the earth's surface requires that the true time be kept at each. All that is necessary is a comparison of these times at any instant. For instance, the time at B may, by the transport of chronometers, be brought to A, and thus the difference of the local times be ascertained, or the indications of the clock at A may be conducted by electro-telegraphy to B. The difference of the local times at A and B is the time a star takes to pass from the meridian of the one to that of the other ; and this is the difference of longitude which maybe converted into angle at the rate of 3G0° to 2411.

But the traveller in unknown lands, who seeks to fix astronomically his position, has no telegraph to count on and his expectations for longitude depend chiefly on observations of the moon. In the .N-autical Almanac are published the angular distances of the moon from certain stars in its path for every three hours of Greenwich time. Therefore, by actually observing the distance of the moon from one of these stars, one can infer the corresponding Greenwich time at the moment of observation. The comparison of this with the local time gives the longitude.

Observations on the sun have shown that it traces out amongst the stars in the course of a year a great circle, inclined to the equator at an angle of 233° ; at midsummer it attains a maximum northern declination of 24°, and at midwinter a maximum southern declination of the same amount. Hence it is inferred that the earth moves round the sun in a plane, completing one orbital revolution yearly, the axis of the earth's diurnal rotation being inclined to this plane at an angle of 663°. Upon this angle of inclination depend the seasons, and in great measure the climates of the different portions of the earth's surface.

It is usual to draw on globes and in maps a circle or parallel at the distance of 231° from the equator on either side ; of these circles the northern is called the Tropic of Cancer, the southern is the Tropic of Capricorn. A circle drawn with a radius of 233° from the North Pole as centre is the Arctic Circle ; a similar and equal circle round the South Pole is the Antarctic Circle.

When the sun is in the equator - which it crosses from north to south in September, and from south to north in March - it is in the horizon of either pole. When the sun has northern declination, the North Pole is in constant daylight and the South Pole in darkness. When the sun has southern declination the North Pole on the contrary is in constant darkness while the South Pole is illuminated by sunshine. At midsummer in the northern hemisphere the whole region within the Arctic Circle is in constant daylight, and that within the Antarctic Circle is in darkness; at midwinter this state of things is exactly reversed. The portion of the globe lying between the Tropic of Cancer and the Arctic Circle is called the North Temperate Zone; that between the Tropic of Capricorn and the Antarctic Circle is the South Temperate Zone. In the former the sun is always to the south of the zenith; in the latter it is always to the north.

In the Torrid Zone, which lies between the Tropics, the sun, at any given place, passes the meridian to the north of the zenith for part of the year, and to the south for the remainder.

When the sun is to the north of the equator the days are longer than the nights in the northern hemisphere, while in the southern hemisphere the nights are longer than the days; when the sun has southern declination this condition is reversed. As the sun increases his north declination from 0° to 23F, not only do the days increase in length in the northern hemisphere, but the rays of the sun - in the Temperate and Arctic regions - impinge more perpendicularly on the surface ; hence the warmth of summer. Even iu summer the rays of the sun in the Arctic regions strike the surface very obliquely ; this, combined with the protracted season of darkness, produces excessive cold. Summer in the northern hemisphere is thus contemporaneous with winter in the southern ; while winter in the northern hemisphere is simultaneous with summer in the southern.

The length of the day at any place at any season of the year is easily ascertained from the following considerations. Let us (fig. 4) be the axis of rotation, eq the equator orthographically projected on a meridian plane, ab the parallel of the given place 3 draw the diameter fg making concentric small circles are drawn such that the sum of their radii is a right angle or 90°. Let the inner circle be that traced among the stars by the zenith of any given place, say Q, then the outer circle encloses all those stars the angle nay equal to the sun's declination, which we suppose to be north, then the hemisphere ynaPf is in sunshine, while the hemisphere Ow-is in darkness. As the earth rotates, a point which is at a at midday is carried from a towards b, which it reaches at midnight ; h is reached at 6 o'clock r.m. and k at sunset. Now if th be the latitude of the place and 8 the sun's declination hk = sin sk. tan 6; this in the parallel whose radius is eos0 corresponds to an angle whose sine is tan(/' tan& Call this angle n; the time taken to rotate through it is 11,77 ; hence the length of the daylight is 1211+-1''b7, and the length of night 12" - Now '7 vanishes when either or 8 is zero ; that is, at the equator the nights and days are equal in length throughout the year ; and again when the sun is in the equator, that is, at the equinox, the nights and days are equal in all latitudes. When the sun's declination is equal to the co-latitude, y is a right angle, and the sun does not actually set ; this can only happen at places within the polar circle. The longest day at Gibraltar is 14h 27m, at Falmouth 16h 11m, and in Shetland 18" 14m; while in Iceland it is 20h on the south coast and 24h on the north. At Washington the longest day is 14h 441", and at Quebec 15h 40m.

All this, however, is on the supposition that day ends with sunset; but the length of apparent day is increased by atmospheric refraction and reflection. When the disk of the setting sun first seems to touch the horizon it is in reality wholly below it and is only seen by refraction. After the sun has wholly set at any given place his light still continues to illuminate the upper portion of the atmosphere there, so that, instead of ending abruptly, daylight gradually fades away until the sun is 18° below the horizon.

In a diagram (fig. 5) similar to the last draw mi parallel to cif, and at a distance from it equal to the sine of 18°; then gbf being the hemisphere unenlightened by the direct rays of the sun, gnuf will represent the twilight zone. A point in the latitude of a describing the parallel ab loses sight of the sun at k, and is in twilight until it reaches the small circle mi, when the sun's zenith distance is 108°. The duration of twi light corresponds then to the portion kl of ab, the angle rotated through being sin -1(h1 : ht) - sin-1 (hk : hh) ; this converted into time gives the duration of twilight. Here ltle=sin cbtan6 ; kl = sin18° sec& At any given latitude the twilight is shortest when the great circle passing through k and l passes also through the sun. Expressed algebraically, if T be the duration of the shortest twilight in angular measure and 8 the sun's declination at the time, then Suppose in the last diagram the sun to be at his greatest northern declination, then uff = 23r, gm = 18°, and mg = Hence a place whose latitude is 48.1,-° N. has, at midsummer, twilight lasting from sunset to midnight and continuing from midnight to sunrise, that is, for a few days there is no absolute darkness. A little further south this twiligl it is interrupted by a :;11-)rt period of darkness.

Since is = 231° - 18° = we see from the diagram that the South Pole is at this time in total darkness, which extends to all places within 5r of it. When the sun's declination is 9° south, the North Pole is in the centre of the twilight belt ; thus all places whose latitude is greater than 81° then move in continual twilight, alternating between clearness and dinmess, never attaining either daylight or total darkness. The actual period during which either pole is in total darkness is about two mid a half months.

At the equator, the shortest twilight occurs at the equinox, when it is lh 12"' ; the longest when the sun is in the tropics, being lh 181". At London, in latitude 51P, twilight continues all night from May 22 to July 21 ; it is shortest about three weeks after the autumnal and three weeks before the vernal equinox, when its duration is 1" 501n. At Washington the shortest twilight (being 1" 33m) occurs on the 6th of March and 7th October; at Quebec the shortest is lh 46m, falling on the 3d March and 10th October.

At page 205, fig. 19 is a perspective representation of the earth - of more than a hemisphere, in fact - namely, the segment mynafi in fig. 5. It exhibits all those regions of the earth which at Greenwich apparent noon at midsummer are in sunshine and twilight. It is very remarkable how Asia and America, but especially the former, just escape going into darkness.

Construction of Haps.

In the construction of maps, one has to consider how a portion of spherical surface, or a configuration traced on a sphere, can be represented on a plane. If the area to be represented bear a very small ratio to the whole surface of the sphere, the matter is easy : thus, for instance, there is no difficulty in making a map of a parish, for in such cases the curvature of the surface does not make itself evident. If the district is larger and reaches the size of a county, as Yorkshire for instance, then the curvature begins to be sensible, and one requires to consider how it is to be dealt with. The sphere not being a developable surface cannot be opened out into a plane like the cone or cylinder, consequently- in a plane representation of configurations on a sphere it is impossible to retain the desired proportions of lines or areas or equality of angles. But though one cannot fulfil all the requirements of the case, we may fulfil some by sacrificing others ; that is to say, we may, for instance, have in the representation exact similarity to all very small portions of the triginal, but at the expense of the areas, which will be quite misrepresented. Or we may retain equality of areas if we give up the idea of similarity. It is therefore usual, excepting in special cases, to steer a middle course, and, by making compromises, endeavour to obtain a representation which shall not offend the eye.

A globe gives a perfect representation of the surface of the earth ; but practically, the necessary limits to its size make it impossible to represent in this manner the details of countries. A globe of the ordinary dimensions serves scarcely any other purpose than to convey a clear conceptiov of the earth's surface as a whole, exhibiting the figure, extent, position, and general features of the continents and islands, with the intervening oceans and seas ; and for this purpose it is indeed absolutely essential and cannot be replaced by any kind of map.

The construction of a map virtually resolves itself into the drawing of two sets of lines, one set to represent meridians, the other to represent parallels. These being drawn, the filling in of the outlines of countries presents no difficulty. The first and most natural idea that occurs to one as to the manner of drawing the circles of latitude and longitude is to draw them according to the laws of Let Pm, Prs (fig. 7) be two contiguous meridians crossed by parallels rp, sq, and OpV, 0/13' the straight lines representing these meridians. If the angle at P is du, this also is the value of the angle at 0. Let the co-latitude Pp =u,Pq=u+da; Op' =p, p- F clp, the circular arcs p'r', q's' representing the parallels Fr, qs. If the radius of the sphere be unity, p' q' = d p ; pY pd ,u, pq = du ; - sinudg.

then p'q'– apq and y'r' =a/pr. That is to say, a, a' may be regarded as the relative scales, at co-latitude u, of the represen tation, a applying to meridional measurements, a' to measurements perpendicular to the meridian. A small square situated in colatitude u, having one side in the direction of the meridian - the length of its side being i - is represented by a rectangle whose sides are iv and fa' ; its area consequently is Vac'.

If it were possible to make a perfect representation, then we should have a- =1, oi= 1 throughout. This, however, is impossible. We may make CI= 1 throughout by taking p = u. This is known as the Equidistant Projection, a very simple and effective method of representation.

Or we may make =1 throughout. This gives p = sin u, a perspective projection, namely, the Orthographic. Or we may require that areas be strictly represented in the development. This will be effected by making fro/ = 1 , or • pdp = sin udu, the integral of which is p = 2 sinlv, which is the Equivalent Projection of Lambert, sometimes referred to as Lorgna's Projection. In this system there is misrepresentation of form, but no misrepresentation of areas. Or we may require a projection in which all small parts are to be represented in their true forms. For instance, a small square on the spherical surface is to be represented as a small square in the development. This condition will be attained by making 0-= of, or - p " u ; the integral of secnu at any point, applies to all directions round that point.

These two last projections are, as it were, at the extremes of the scale ; each, perfect in its own way, is in other respects very objectionable. We may avoid both extremes by the following considerations. Although we cannot make o = 1 and o-'=1, so as to have a perfect picture of the spherical surface, yet considering cr –1 and cr' –1 as the local errors of the representation, we may make (a – 1)2+ (o= - 1)2 a minimum over the whole surface to be represented. To effect this we must multiply this expression by the element of surface to which it applies, viz., sin se du d and then integrate from the centre to the (circular) limits of the snap. Let /3 be the spherical radius of the segment to be represented, then the total misrepresentation is to be taken as perspective. But, as Lagrange has remarked, one may regard geographical maps from a more general point of view as representations of the surface of the globe, for which purpose we have but to draw meridians and parallels according to any given law; then any place we have to fix must take that position with reference to these lines that it has on the sphere with reference to the circles of latitude and longitude. Let the law which connects latitude and longitude, ck and w, with the rectangular coordinates x and y in the representation be such that dx = mcicA + ode,, and dy = nedy5 + n'do). In fig. 6 let the lines intersecting in the parallelogram PQRS be the representations of the meridians rp, sq and parallels rs, pq intersecting in the indefinitely small rectangle pqrs on the surface of the sphere. The coordinates of P being x and y, while those of p are 4, and w the coordinates of the other points will stand thus q • • • 1, c + Ciro r . . . - thp ar s . . . ¢ +do co+do, Q . . . x +?tdu, y + It . . . x + mdc:. y+ m',1 S . . . x +nciro y+oeti0+it'aco.

Thus we easily see that PR= (m2 + ne2)1d95 ; and PQ = (a2+n'2)tdw ; also the area of the parallelogram PQRS is equal to (nen – nue)dy5d0). If 90° are the angles of the parallelogram, then ma + nen' tangy=Den - If the lines of latitude and of longitude intersect at right angles, then mn + ni ri = 0. Since the length of pr is = dtk, its representation PR is too great in the proportion of (m2+ m!2)t : 1; and pq being in length cosOdw, its representation PQ is too great in the ratio of (a2+re2)1 : cos 0. Hence the condition that the rectangle PQRS is similar to the rectangle pqrs is (m2 + m'2) cos24 = ri2 + 2o, together with ma + nen = 0; or, which is the same, the condition of similarity is expressed by - n' VI, cos 0; n=ot cos O.

Since the area of the rectangle pqrs is cosikdOdw, the exaggeration of area in the representation will be expressed by 111.'21 - 77/1/,' : cos.O Thus when the nature of the lines representing the circles of latitude and longitude is defined we can at once calculate the error or exaggeration of scale at any part of the map, whether measured in the direction of a meridian or of a parallel; and also the misrepresentation of angles.

The lines representing in a map the meridians and parallels on the sphere are constructed either on the principles of true perspective or by artificial systems of developments. The perspective drawings are indeed included as a particular case of development in which, with reference to a certain point selected as the centre of the portion of spherical surface to be represented, all the other points are represented in their true azimuths, - the rectilinear distances from the centre of the drawing being a certain function of the corresponding true distances on the spherical surface. For simplicity we shall first apply this method to the projection or development of parallels and meridians when the pole is the centre. According to what has been said above, the meridians are now straight lines diverging from the pole, dividing the 360° into equal angles ; and the parallels are represented by circles having the pole as centre, the radius of the parallel whose co-latitude is u being p, a certain function of u. The particular function selected determines the nature of the development.

which is to be made a minimum. Putting p= u+ y, and giving to y only a variation subject to the condition Sy= 0 when u= 0, the equations of solution - using the ordinary notation of the calculus of variations - are This method of development is due to Sir George Airy, whose original paper - the investigation is different in form from the above - will be found in the Philosophical Magazine for December 1861. The solution of the differential equation leads to this result - The limiting radius of the map is R= 20 tan i(3. In this system, called by the Astronomer-Royal the "Projection by balance of errors," the total misrepresentation is an absolute minimum.

Returning to the general case where p is any function of it, let us consider the local misrepresentation of direction. Take any indefinitely small line, length = i, making an angle a with the meridian in co-latitude a. Its projections on a meridian and parallel are i cos a, i sin a, which in the map are represented by iv cos a, is sin a. If then a' be the angle in the map corresponding to a, tan a'=. FL tan a.

a a. sin udp and the error a' - a of representation = c, then tan E =(1-1) tan a Put = cot' C, then c is a maximum when a = C, and the corresponding value of c is e - 2- - 2C .

For simplicity of explanation we have supposed this method of development so applied as to have the pole in the centre. There is, however, no necessity for this, and any point on the surface of the sphere may be taken as the centre. All that is necessary is to calculate by spherical trigonometry the azimuth and distance, with reference to the assumed centre, of all the points of intersection of meridians and parallels within the space which is to be represeated in a plane. Then the azimuth is represented unaltered, and any spherical distance a is represented by p. Thus we get all the points of intersection transferred to the representation, and it remains merely to draw continuous lines through these points, which lines will be the meridians and parallels in the representation.

The exaggeration in such systems, it is important to remember, whether of linear scale, area, or angle, is the same for a given distance from the centre, whatever be the azimuth ; that is, the exaggeration is a function of the distance from the centre only.

We shall now examine and exemplify some of the most important systems of projection and development, commencing with Perspective Projections.

In perspective drawings of the sphere, the plane on which the representation is actually made may generally be any plane perpendicular to the line joining the centre of the sphere and the point of vision. if V be the point of vision, P any point on the spherical surface, then p, the point in which the straight line VP intersects the plane of the representation, is the projection of P.

In the orthographic projection, the point of vision is at an infinite distance and the rays consequently parallel ; in this case the plane of the drawing may be supposed to pass through the centre of the sphere. Let the circle (fig. 8) represent the place of the equator on which we propose to make an orthographic representation of meridians and parallels. The centre of this circle is clearly the projection of the pole, and the parallels are projected into circles having the pole for a cmimon centre. The diameters aa', bb' being at right angles, let the semicircle bob' be divided into the required number of equal parts ; the diameters drawn through these points are the projections of meridians. The distances of c, of d, and of e from the diameter aa' are the radii of the successive circles representing the parallels. It is clear that, when the points of division are very close, the parallels will be very much crowded towards the outside of the map; so much so, that this projection is not much used.

For an orthographic projection of the globe on a meridian plane, let q11TS (fig. 9) be the meridian, 128 the axis of rotation, then qr is the'projection of the equator. The parallels will be represented by straight lines passing through the points of equal division; these lines are, like the equator, perpendicular to 128. The meridians will in this case be ellipses described on ns as a common major axis, the distances of c, of d, and of e from 228 being the minor semiaxes.

Let us next construct an orthographic projection of the sphere on the horizon of any place. Set off the angle aop (fig. 10) from the radius oa, equal to the latitude. Drop the perpendicular pP on oa, then P is the projection of the pole. On ao produced take ob= pP, then ob is the minor semi axis of the ellipse representing the equator, itsmajor axis being r at right angles to ao. The points in which the meridians meet this elliptic equator are determined by lines drawn parallel to aob through the points of equal subdivision cdefgh. Take two points, as d and g, which are 90° apart, and let ik be their projections on the equator ; then i is the pole of the meridian which passes through k. This meridian is of course an ellipse, and is described with reference to i exactly as the equator was described with reference to I'. Produce io to 1, and make to equal to half the shortest chord that can be drawn through i; then to is the semi-axis of the elliptic meridian, and the major axis is the diameter perpendicular to iol.

For the parallels : let it be required to describe the parallel whose co-latitude is ; take pm= pa = le, and let Wed be the projections of in and n on oPa; then m'n is the minor axis of the ellipse representing the parallel. Its centre is of course midway between m and a', and the greater axis is equal to mu. Thus the construction is obvious. When pna is less than pa, the whole of the ellipse is to be drawn. When per is greater than pa, the ellipse touches the circle in two points ; these points divide the ellipse into two parts, one of which, being on the other side of the meridian plane aqr, is invisible.

Stereographic Projection. - In this case the point of vision is on the surface, and the projection is made on the plane of the great circle whose pole is V. Let Pp1V (fig. 12) be a great circle through the point of vision, and ors the trace of the plane of projection. Let c be the centre of a small circle whose radius is cp = cl ; the straight line pl represents this small circle in orthographic projection.

We have first to show that the stereographic projection of the small circle pl is itself a circle ; that is to say, a straight line through V, moving along the circumference of p1, traces a circle on the plane of projection ors. This line generates an oblique cone standing on a circular base, its axis being cV (since the angle pVc= angle cV/); this cone is divided symmetrically by the plane of the great circle kp/, and also by the plane which passes through the axis Vc, perpendicular to the plane 1p1. Now Irv- Vp, being = Vo sec kVp •VA: cos Ail)) = Aro •k, is equal to Vs-V/; therefore the triangles Vrs, l'Ip are similar, and it follows that the section of the cone by the plane rs is similar to the section by the plane pl. But the latter is a circle, hence also the projection is a circle ; and since the representation of every infinitely small circle on the surface is itself a circle, it follows that in this projection the representation of small parts is (as we have before shown) strictly similar. Another inference is that the angle in which two lines on the sphere intersect is represented by the same angle in the projection. This may otherwise be proved by means of fig. 13, where VA is the diameter of the sphere passing through the point of vision, yi/h, the plane of projection, kt a great circle, passing of course through V, and one the line of intersection of these two planes. A tangent plane to the surface at I cuts the plane of projection in the line rvs perpendicular to or; to is a tangent to the circle kt at t, to and is are any two tangents to the surface at t. Now the angle vtu (a being the projection of t) is 90° - otV = 90' - oVt = ouV = tar, therefore to is equal to av ; and since tos and ens are right angles, it follows that the angles vts and yes are equal. Hence the angle its also is equal to its projection macs; that is, any angle formed by two intersecting lines on the surface is truly represented in the stereographic projection.

We have seen that the projection of any circle of the sphere is itself a circle. But in the case in which the circle to be projected passes through V, the projection becomes, for a great circle, a line through the centre of the sphere ; otherwise, a line anywhere. It follows that meridians and parallels are represented in a projection on the horizon of any place by two systems of orthogonally cutting circles, one system passing through two fixed points, namely, the poles and the projected meridians as they pass through the poles show the proper differences of longitude.

To construct a stereographic projection of the sphere on the horizon of a given place. Draw the circle v/kr (fig. 14) with the diameters kv, /r at right angles ; the latter is to represent the central meridian. Take koP equal to the co-latitude of the given place, say u; draw the diameter of the poles, through which all the circles representing meridians have to pass. All their centres then will be in a line smn, which crosses pp at right angles through its middle point m. Now to describe the meridian whose west longitude is w, draw pn making the angle opn, = 90° - 0), then a is the centre of the required circle, whose direction as it passes through p will make an angle opg = w with pp'. The lengths of the several lines are op =tan mu ; W. - cot ?,pc ; oin = cotu ; mu= cosec ac cot w.

Again, for the parallels, take Pb = Pc equal to the co-latitude, say c, of the parallel to be projected ; join vb, vc cutting lr in e, d. Then ed is the diameter of the circle which is the required projection ; its centre is of course the middle point of ed, and the lengths of the lines are ad= tan (u - c); oc = tan 1(u + c).

The line sa itself is the projection of a parallel, namely, that of which the co-latitude c = 180° - ac, a parallel which passes through the point of vision.

A very interesting connexion, noted by Professor Cayley, exists between the stereographic projection of the sphere on a meridian plane (i.e., when a point on the equator occupies the centre of the drawing) and the projection on the horizon of any place whatever. The very same circles that represent parallels and meridians in the one case represent them in the other case also. In fig. 15, abs being a projection in which an equatorial point is in the centre, draw any chord ab perpendicular to the centre meridian cos, and on ab as diameter describe a circle, when the property referred to will be observed. This smaller circle is now the stereographic projection of the sphere on the horizon of some place whose co-latitude we may call u. The radius of the first circle being unity, let ac= sinx, then by what has been proved above co =sinx cotu= cosx ; therefore a = x, and ac = sin a. Although the meridian circles dividing the 360° at the pole into equal angles must be actually the same in both systems, yet a parallel circle whose co-latitude is c in the direct projection abs belongs in the oblique system to some other co-latitude as c'. To determine the connexion between c and c, consider the point t (not marked), in which one of the parallel circles crosses the line soc. In the direct system, p being the pole, pt =1 - tan i(90° - c) - 1+ cot is and in the oblique, pt = ac (tan mac - tan ,1(2c - c')), which, replacing ac by its value sin it, becomes cos i(gt - c') mu cot me' therefore tanisx= tana is the required relation.

Notwithstanding the facility of construction, the stereo-graphic projection is not much used in map-making. But it may be made very useful as a means of graphical interpolation for drawing other projections in which points are represented in their true azimuths, but with an arbitrary law of distance, as p =.10). We may thus avoid the calculation of all the distances and azimuths (with reference to the selected centre point) of the intersections of meridians and parallels. Construct a stereographic projection of the globe on the horizon of the given place ; then on this pro. jection draw concentric circles (according to the stereo-graphic law) representing the loci of points whose distances from the centre are consecutively 5', 10', 15', 20', kc., up to the required limit, and a system of radial lines at intervals of 5'. Then to construct any other projection, - commence by drawing concentric circles, of which the radii are

We now conic to the general case in which the point of vision has any position outside the sphere. Let abed (fig. 17) be the great circle section of the sphere by a plane passing through c, the central point of the portion of surface to be represented, and V the point of vision. Let nj perpendicular to Vc be the plane of representation, join mV cutting pj in f, then f is the projection of any point rn in the circle abc, and of is the representation

This vanishes when h= 1, that is, if the projection be stereo- graphic; ; or for v =0, that is, at the centre of the map. At a distance of 90' from the centre, the greatest alteration is 90° - 2 cot-1s/Is.(Sec Philosoph. 1Iog., April 1862.) The constants h and 2 can be determined, so that the total misrepresentation, viz., shall be a minimum, /3 being the greatest value of u, or the spherical radius of the map. On substituting the expressions for a• and CI the integration is effected without difficulty. Put x - cos s ; v- (h-l)a , 11=, -(h+1) log, (x + 1), 11'=.- (2 --y-FAy').

Then the value of M is 1I=4 sin' ',$+ all + When this is a minimum, clh =0 ; < -Till (eh Therefore M= 4 sine -1 H=' f3- - and h must be determined so as to make He : Ir a maximum. In any particular case this maximum can only be ascertained by trial, that is to say, log He - log IF must be calculated for certain equidistant values of h, and then the particular value of It which corresponds to the required maximum can be obtained by interpolation. Thus we find that if it be required to make the best possible perspective representation of a hemisphere, the values of It and k are h= 1.47 and k = 2.0:34; so that in this case 2•034 sin 1+.

P