But we must turn from these attempts to discover a northwest or north-east passage to India, which, from the accounts given of them, it will be evident, contributed very little to the progress of geographical knowledge, though they necessarily increased the skill, confidence, and experience of navigators.

While these unprofitable voyages were undertaken in the north, discoveries of consequence were making in the southern ocean. These may be divided into two classes; viz., such as relate to what is now called Australasia; and those which relate to the islands which are scattered in the southern ocean.

We have already stated that there is reason to believe some part of New Holland was first discovered by the Portuguese: two ancient maps in the British Museum are supposed to confirm this opinion; but the date of one is uncertain; the other is dated 1542, and certainly contains a country, which, in form and position, resembles New Holland, as it was laid down prior to the voyage of Tasman. But allowing this to be New Holland, it only proves, that at the date of this map it was known, not that it had been discovered by the Portuguese.

The Dutch, however, certainly made several voyages to it between 1616 and 1644: the western extremity was explored in 1616. The same year Van Dieman's Land was discovered. In the course of the ten following years, the western and northern coasts were visited. The southern coast was first discovered in 1627, but we have no particulars respecting the voyage in which it was discovered. In 1642, Tasman, a celebrated Dutch navigator, sailed from Batavia, and discovered the southern part of Van Dieman's Land and New Zealand. From this time to the beginning of the eighteenth century, little progress was made in exploring the coast of New Holland. Dampier, however, a man of wonderful talents, considering his education and mode of life, collected, during his voyage, some important details respecting the west coast. And among the numerous voyages undertaken by the Dutch East India Company towards the close of the seventeenth and beginning of the eighteenth century, to examine this vast country, which the Dutch regarded as belonging to them, there was one by Van Vlaming deserving of notice: this navigator examined with great care and attention many bays and harbours on the west side; and he is the first who mentions the black swans of this country.

Papua, or New Guinea, another part of Australasia, was discovered by the Portuguese in 1528. The passage that divides this country from New Britain was discovered by Dampier, who was also the first that explored and named the latter country in 1683. The discovery of Solomon Islands by the Spaniards took place in 1575: Mendana, a Spanish captain, sailed from Lima, to the westward, and in steering across the Pacific, he fell in with these islands. On a second voyage he extended his discoveries, and he sailed a third time to conquer and convert the natives. His death, which took place in one of these islands, put an end to these projects. They are supposed to be the easternmost of the Papua Archipelago, afterwards visited by Carteret, Bougainville, and other navigators. Mendana, during his last voyage, discovered a group of islands to which he gave the name of Marquesas de Mendoza.

This group properly belongs to Polynesia: of the other islands in this quarter of the globe, which were discovered prior to the eighteenth century, Otaheite is supposed to have been discovered by Quiros in 1606. His object was to discover the imagined austral continent; but his discoveries were confined to Otaheite, which he named Sagittaria, and an island which he named Terra del Esperitu Sancto, which is supposed to be the principal of the New Hebrides. The Ladrones were discovered by Magellan in 1521. The New Philippines, or Carolinas, were first made known by the accidental arrival of a family of their natives at the Philippines in 1686. Easter island, a detached and remote country, which, however, is inhabited by the Polynesian race, was discovered by Roggewein in 1686.

Having thus exhibited a brief and general sketch of the progress of discovery, from the period when the Portuguese first passed the Cape of Good Hope to the beginning of the eighteenth century, we shall next, before we give an account of the state and progress of commerce during the same period, direct our attention to the state of geographical science in the sixteenth and seventeenth centuries.

We have already stated that the astrolobe, which had been previously applied only to astronomical purposes, was accommodated to the use of mariners by Martin Behaim, towards the end of the fifteenth century. He was a scholar of Muller, of Koningsberg, better known under the name of Regiomontanus, who published the Almagest of Ptolemy. The Germans were at this time the best mathematicians of Europe. Walther, who was of that nation, and the friend and disciple of Regiomontanus, was the first who made use of clocks in his astronomical observations. He was succeeded by Werner, of Nuremberg, who published a translation of Ptolemy's Geography, with a commentary, in which he explains the method of finding the longitude at sea by the distance of a fixed star from the moon. The astronomical instruments hitherto used were, with the exception of the astrolobe, those which had been employed by Ptolemy and the Arabians. The quadrant of Ptolemy resembled the mural quadrant of later times; which, however, was improved by the Arabians, who, at the end of the tenth century, employed a quadrant twenty-one feet and eight inches radius, and a sextant fifty-seven feet nine inches radius, and divided into seconds. The use of the sextant seems to have been forgotten after this time; for Tycho Brahe is said to have re-invented it, and to have employed it for measuring the distances of the planets from the stars. The quadrant was about the same time improved by a method of subdividing its limbs by the diagonal scale, and by the Vernier. The telescope was invented in the year 1609, and telescopic sights were added to the quadrant in the year 1668. Picard, who was one of the first astronomers who applied telescopes to quadrants, determined the earth's diameter in 1669, by measuring a degree of the meridian in France. The observation made at Cayenne, that a pendulum which beat seconds there, must be shorter than one which beat seconds at Paris, was explained by Huygens, to arise from the diminution of gravity at the equator, and from this fact he inferred the spheroidal form of the earth. The application of the pendulum to clocks, one of the most beautiful and useful acquisitions which astronomy, and consequently navigation and geography have made, was owing to the ingenuity of Huygens. These are the principal discoveries and inventions, relating to astronomy, which were made prior to the eighteenth century, so far as they are connected with the advancement of the art of navigation and the science of geography.

The discoveries of Columbus and Gama necessarily overturned the systems of Ptolemy, Strabo, and the other geographers of antiquity. The opinion that the earth was a globe, which had been conjectured or inferred prior to the voyage of Magellan, was placed beyond a doubt by that voyage. The heavenly bodies were subjected to the calculations of man by the labours of Copernicus, Tycho Brahe, and Galileo. Under these circumstances it was necessary, and it was easy, to make great improvements in the construction of maps, in laying down the real form of the earth, and the relative situations of the countries of which it is formed, together with their latitudes and longitudes. The first maps which displayed the new world were those of the brothers Appian, and of Ribeiro: soon afterwards a more complete and accurate one was published by Gemma Frisius. Among the geographers of the sixteenth century, who are most distinguished for their science, may be reckoned Sebastian Munster; for though, as we have already mentioned, he joins Greenland to the north of Lapland in his map, yet his research, labour, and accuracy were such, that he is compared by his contemporaries to Strabo. Ortelius directed his studies and his learning to the elucidation of ancient geography; and according to Malte Bran, no incompetent judge, he may yet be consulted on this subject with advantage.

But modern geography may most probably be dated from the time of Mercator: he published an edition of Ptolemy, in which he pointed out the imperfection of the system of the ancients. The great object at this time, was to contrive such a chart in plano, with short lines, that all places might be truly laid down according to their respective longitudes and latitudes. A method of this kind had been obscurely pointed at by Ptolemy; but the first map on this plan was made by Mercator, about the year 1550. The principles, however, on which it was constructed, were not demonstrated till the year 1559, when Wright, an Englishman, pointed them out, as well as a ready and easy way of making such a map. This was a great help to navigators; since by enlarging, the meridian line, as Wright suggested and explained, so that all the degrees of longitude might be proportional to those of latitude, a chart on Mercator's projection shews the course and distance from place to place, in all cases of sailing; and is therefore in several respects more convenient to navigators than the globe itself. Mercator, in his maps and charts, chose Corvo, one of the Azores, for his first meridian, because at that time it was the line of no variation of the compass.