INTRODUCTION.

GEOGRAPHY is that part of knowledge which describes the surface of the earth; its divisions, extent, and boundaries; the relative position of the several countries and places on the globe, and the manners, customs, and political relations of their inhabitants. The word is Greek, γεωγραφία from γῆ or γῆ, terra, "the earth," and γράφω, scribo, "I write." As everything that immediately contributes to the ascertaining of the situation and limits of countries and places on the surface of the earth, is within the province of geography, this science includes the description and use of globes, maps, and charts, with the methods of constructing them.

This science has been divided into Geography properly so called, or a description of the lands of the globe, and Hydrography, or a description of the waters; but this division is of little consequence, and is now seldom employed. Geography has also been divided into general and particular, terms which are variously understood by different writers on the subject. By Varenius, one of the oldest and best modern writers on general geography, general or universal geography is used to denote that part of the subject which considers the earth in general, and explains its affections as a terrestrial globe, without attending to its arbitrary division into different regions; and by particular or special geography, this writer understands the description of the particular regions of the earth: and he divides this latter into two parts; chorography, describing some considerable Geography may be conveniently divided into descriptive geography, or that part of the science which describes the form, limits, extent, and variety of surface of different countries, with the manners and customs of their inhabitants; and physical geography, or that part which teaches how to determine the situations of different places in the globe, and to lay down and delineate their positions for the information of others. Descriptive geography is the more popular and entertaining part of the subject. It is usually divided into ancient or classical geography, geography of the middle ages, and modern geography. The first branch of the subject considers the state of the earth so far as it was known or discovered at different periods, previous to the sixth century of the Christian era. The geography of the middle ages extends from the sixth to the fifteenth century, and modern geography from the fifteenth century to the present time. One of the most useful subdivisions of descriptive geography is that employed by Mr Pinkerton, who considers the geography of the several countries which he describes under four different heads. 1. Historical or progressive geography; in which he treats of the names, extent, original population, progressive geographical improvements, historical epochs and antiquities of the countries. 2. Political geography; under which he describes the religious and ecclesiastic institutions, government, laws, population, colonies, military force, revenue, and political relations. 3. Civil geography, comprehending manners and customs, language, literature, and the arts, education, cities and towns, principal edifices, roads, manufactures and commerce. And, 4. Natural geography, comprehending an account of the climate and seasons, face of the country, its soil, and state of agriculture, its rivers, lakes, mountains, and forests, and an enumeration of the natural productions and natural curiosities, which are usually found within each district*. Descriptive geography is sometimes styled political geography, while Geography, physical or general geography is called natural geography.

Among the other departments of this study we may mention sacred geography, or that which illustrates the sacred writings; and ecclesiastic geography, which describes the division of a country according to its church government, as into archbishoprics, bishoprics, &c.

Many writers of treatises or systems of geography give a detailed account of the historical events and commercial concerns of the several countries which they describe; but we consider this as unnecessary in a pure geographical work, as these departments belong rather to History and Political Economy.

Some systematic writers on geography considering the term in a very comprehensive view, as including a description of the internal structure of the earth, as well as of its surface, have thought it necessary to enter into discussions respecting the original formation of the earth, and the minerals of which it is composed. How far they are right in this we shall not pretend to determine. In this work, these subjects will be treated of under the articles Geology and Mineralogy.

Another subject relative to the affections of the earth, respects the physical and chemical changes that take place in its atmosphere. These properly belong to the science of Meteorology, and will be found under that article.

We propose in this article to offer only an introductory outline of descriptive geography, as the several quarters of the globe, and their subdivisions into empires, kingdoms, and states, are described as particularly as is compatible with the limits of this work, under the several articles to which they belong in the general alphabet.

Our attention will be chiefly directed to physical geography, especially that part of it which describes the construction and use of globes, maps, and charts.

Physical geography is properly a branch of mixed mathematics, and its principles depend on geometry, trigonometry, perspective, and its kindred sciences, trigonometry and perspective. It is intimately connected with astronomy; and as these two sciences mutually illustrate each other, they are commonly taught at the same time. The physical changes that take place on the earth, as far as it is considered in its general character of an individual of the solar system, have been already explained under Astronomy; and we shall have little here to add respecting them, except as they are modified by the situation of the observer on different parts of the earth's surface.

The principles and practice of physical geography, though strictly dependent on pure mathematics, may be, for the most part, explained in a popular way, so as to be understood by the generality of readers. This popular view of the subject we shall attempt in the present article, throwing every thing that is purely mathematical into the form of notes. It must be evident, however, that a reader who is conversant with mathematics will study physical geography to more advantage; and for this purpose, it will be sufficient to possess a moderate acquaintance with arithmetic, the elements of geometry, plane trigonometry, spherics, and perspective.

It is scarcely necessary to enlarge on the importance or utility of geography. It is one of those sciences, the knowledge of which is almost constantly required. Without an acquaintance with the geography of the countries that are the scenes of the actions which he relates, the historian must either be extremely concise, or his narration must be obscure and unintelligible. Geography affords the best illustration of history, and is equally necessary to the historian and his reader. To the traveller, under which denomination we may class the soldier, the sailor, the merchant, as well as those who travel for pleasure or curiosity, a previous knowledge of the countries, through which he is to pass, is always useful, and often indispensable. To the politician a comprehensive knowledge of geography is of the highest importance. If he is ignorant of the extent, form, boundaries, appearances, climates, &c. of the country with which he is at war, he will plan his hostile expeditions without effect, and will send his invading armies only to perish among the desiles of the enemy, or to meet a more inglorious and deplorable fate from the diseases of the climate.

Even, if we consider geography as a study of mere amusement and curiosity, it forms one of the most rational and interesting studies in which we can engage. Nothing can be more gratifying to the observer of mankind than to survey the manners and customs of various AN historical account of geography would be extremely interesting, as it would include, not only the progressive improvements of the science, considered as a branch of mixed mathematics, but an account of the successive discoveries of different parts of the earth that have been made by the more civilized communities. Such an account in detail, however, cannot be expected here; and we shall confine ourselves principally to a cursory view of the geographical discoveries of ancient and modern nations, reserving the progressive improvements of physical geography for those parts of the article to which they properly belong; as they would neither be so interesting nor so intelligible to a general reader, before he has been made acquainted with the principles of the science.

As soon as mankind had formed themselves into societies, and begun to establish connexions with their neighbours, they would find it necessary to inform themselves of the position of the countries which bordered on their own; and very soon their curiosity would lead them to desire to form an acquaintance with the extent of the country in which they lived, and with many particulars respecting those which were remote from them. Thus, we see that scarcely had the sciences arisen among the Greeks, before their philosophers began to occupy themselves in geographical pursuits. We are told that Anaximander exhibited to his countrymen a plan of Greece and the neighbouring countries, and in this he was imitated by his countryman Hecateus of Miletus. Of the nature of these ancient plans or maps, and their progressive improvements, we shall speak more at large hereafter.

Commerce, and the taste for adventures, which usually accompanies it, were doubtless among the first causes of geographical researches; but the Phoenicians are the earliest commercial people of whose discoveries we have any correct accounts. This people seem first to have investigated the coasts on the Mediterranean; and their navigators, extending their voyages beyond this sea, through the narrow channel which is now called the Straits of Gibraltar, entered the Atlantic ocean, and planted colonies in Iberia, a part of Spain, in the country of Tharsish, which is probably the modern Andalusia, and upon the western shores of Africa.

The learned Bochart, led by the analogy between the Phoenician tongue, and the oriental languages, has followed the tracks of the Phoenicians, both along the shores of the Mediterranean, and those of the Atlantic. These analogies are not always sure guides; but we can scarcely doubt that the city of Cadiz was a Phoenician colony, and it is not likely that this was the only one formed by that enterprising people.

In the time of Solomon, Phoenician ships, employed by him, set sail from a port in the Red sea, called Ophir, Azion-Gaber, and passing from that sea through the straits of Babelmandel, carried on their commerce in the Indian ocean. The country of Ophir, to which they sailed, must have been at a considerable distance from the Red sea, as we are told that a voyage thither required three years. "The king (says the author of the first book of Kings) had a navy of Tharsish, with the navy of Hiram. Once in three years came the navy of Tharsish, bringing gold and silver, ivory, and apes and peacocks." Some have placed Ophir upon the coast of Africa, where the modern Sofala is situated: Others suppose it was a port in the island of Ceylon, or in the island of Sumatra, in which latter island there is still a place called Ophir. The gold dust and ivory brought from thence, seem to show that it was an African port. (See OPHIR). M. Montucla supposes that the Phoeni-Montucians must even at this period have sailed round the continent of Africa, and that Ophir was some place on the Gold Coast (A).

The Carthaginians, a Phoenician colony, imitated their predecessors. We know that they sailed into the Atlantic ocean, as far as the coast of Cornwall in England, whence they procured large quantities of tin. The same people made several attempts towards a complete survey of the western coast of Africa. Of these we have an account only of one expedition, that of Hanno, of which we have already given an account under the article AFRICA.

The Carthaginian navigators, if we may believe the recital of Diodorus Siculus, (lib. xv.) discovered a country situated in the Atlantic ocean, which furnished all the necessaries and conveniences of life. Some pretend that this country was America, but it is much more probable that it was some one of the Cape de Verd islands.

(A) The most celebrated writers who have supported the opinion, that Ophir was a port in Africa, are Montesquieu, Bruce, and d'Anville. Dr Prideaux and M. Gosselin again contend, that Ophir was a port in Arabia Felix, and the same with Sabéa or Sheba; and their opinions have lately been ably supported by Dr Vincent. See Vincent's Periplus of the Erythrean Sea, Part II. The Carthaginian senate, fearful that the relation of the sailors who had discovered such a country might be the means of producing frequent emigrations, are said to have used every endeavour to stifle the memory of this expedition.

History speaks of several voyages undertaken by order of the kings of Egypt and of Persia, for the purpose of ascertaining the extent of Africa; and Herodotus relates that Pharaoh Necho, king of Egypt, employed some Phoenician navigators to sail along the coast of Africa, for the purpose of taking a more exact survey of it. See Africa.

M. Gosselin, who has considered the geography of the ancients in a very learned dissertation, maintains, that the different passages of ancient writers, who have always declared that the Phoenicians and the Greeks circumnavigated Africa, are not sufficient to prove the certainty of such a voyage. The passage in Herodotus has been discussed by him at considerable length, and he seems to have proved his relation to be nothing more than a romance, founded on the historical knowledge of the Egyptians. M. Gosselin, however, admits, that many ancient voyages took place from those countries in which geography had arrived at some perfection; and there are numerous arguments, proving that all the shores of the old continent had been sailed round. See Bailly's History of Astronomy, p. 307, edit. 1755.

Xerxes king of Persia, according to Herodotus, gave a similar commission about the year before Christ 480, to one of his satraps named Sataspes, who had been condemned to die. Sataspes entered the Atlantic ocean through the straits of Gibraltar, and bending his course towards the south, he coasted the continent of Africa, till he doubled a cape which was called Sylaco, and which Riccioli considers as the same with the Cape of Good Hope. He is said to have continued his course to the south for some time, and then to have returned home, assigning as a reason for not proceeding farther, that he had encountered a sea so full of herbage, that his passage had been completely obstructed. This reason appeared so ridiculous to Xerxes, that he ordered Sataspes to be crucified; but in this sentence he appears to have been rather too precipitate, as it is certain that in some latitudes there grows such a quantity of seaweed, that a vessel can scarcely make way through it; as in that part of the sea which lies between the Cape de Verd islands, the Canaries, and the coast of Africa, and is called by the Portuguese the sea of Saragossa. This shews that the relation of Sataspes may have been correct, as he might think it dangerous to attempt proceeding where he found himself so much entangled.

Herodotus has commemorated another marine expedition, undertaken by Scylax, by order of Darius the son of Hystaspes, and which probably took place about the year 422 B.C. Scylax embarked upon the river Indus, the course of which he followed to its mouth, from whence he sailed in the course of 30 months, either into the Arabian gulf, or the Red sea. This Scylax must not be confounded with a navigator of the same name, who, at a later period, made a voyage of investigation round the Red sea.

The conquests of Alexander the Great, if they added little to the happiness of mankind, had at least the advantage of throwing considerable light on the state of geography at that time, as they afforded to the Greeks a more perfect knowledge of the river Indus, and of many parts of that vast country which derives its name from that river. Alexander does not seem to have penetrated to the Ganges, though his expedition led the way to the knowledge of that river; for soon after he went as far as Palibothra, a town situated on the river Indus, at its confluence with another river coming from the west. The followers of Alexander went down the Indus, as far as its opening into the Indian ocean, where they witnessed for the first time the phenomenon of the flux and reflux of the sea,—a phenomenon which excited in them great astonishment and terror. It was after this that Alexander detached, about the year 327 before Christ, two of his captains, Nearchus and Onesicritus, to investigate the coast of the Indian sea. Nearchus was ordered to return by the Red sea, and this he effected. Some fragments of his voyage have come down to us, and upon these has been formed an excellent work by Dr Vincent, entitled the "Periples of the Erythrean Sea." This learned and valuable work is just completed by the publication of the Second Part, and affords much additional illustration of the geographical information and commercial enterprises of the ancients.

Onesicritus sailed to the east, and if we may believe the account that is left of his voyage, he gave us the first exact information respecting the island of Ceylon. The measure given by Onesicritus, of the extent of the island which he investigated, viz. 7000 stadia, does not correspond to Ceylon, whether we consider the length or circumference of the island, (see Ceylon); and if we take it as the measure of the length, it more nearly corresponds to that of Sumatra. The relations of Nearchus and Onesicritus were extant in the time of Strabo, by whom the latter is said to exceed, in point of exaggeration, all the other historians of Alexander's expedition. At the same time, it must be acknowledged that there are many things related by Onesicritus, as quoted by Strabo, which sufficiently agree with what we know of India, and the productions of that country: for he speaks of the sugar cane, the cotton plant, the bamboo, &c.

The kings of Egypt who succeeded Alexander, took considerable interest in the progress of geography. The second of these kings, Ptolemy Philadelphus, about the year 280 before Christ, sent into India two ambassadors, Megasthenes and Daimachus, accompanied by the mathematician Dionysius. Megasthenes was sent to the king of Palibothra on the banks of the Ganges, and Daimachus to another Indian potentate. No account remains of the proceedings of Dionysius and Daimachus, but Megasthenes left an account of his journey, which is frequently quoted by Strabo, by whom it is considered as a mixture of real adventures and improbable exaggerations. These quotations of Strabo are certainly all that remain of the relation of Megasthenes; for the work published under the name of Megasthenes is a literary imposture, similar to the works of Berossus, Manetho, and Ctesias.

In the reign of Ptolemy Lathyrus, about 115 years before Christ, other expeditions were undertaken, for the purpose of sailing round the continent of Africa. Eudoxus and Cysicus having incurred the displeasure of Ptolemy, were sent on this voyage of discovery. They They passed through the straits of Gibraltar, and circumnavigating Africa, returned by the Red sea. Lastly, in the reign of Ptolemy, surnamed Alexander, about 90 years before Christ, Agatharchides, who had been the king's governor, was sent to take a complete survey of the Red sea, and wrote an account of his voyage, of which, however, there remain only a few extracts that are preserved by Photius, in his Bibliotheca, a work of the ninth century.

The extension of commerce seems always to have been one of the principal objects of these voyages of discovery. It is not surprising, therefore, that the inhabitants of Marseilles, which was early celebrated as a commercial city, appear among the ancient navigators who laboured to extend geographical knowledge. Two voyagers, Pythias and Euthymenes, undertook an expedition about 320 years before the Christian era. Euthymenes entered the Atlantic through the straits of Gibraltar, and turned towards the south, for the purpose of taking a survey of the coast of Africa. This is all that we know of his route; but Pythias steered northward, and after reconnoitring the coasts of Spain and Gaul, sailed round the island of Albion, and stretching still farther to the north, discovered an island which is believed to be the modern Iceland, or the Thule of the ancients, terrarum ultima Thule. Perhaps, however, this was only one of the Ferro islands. Strabo, who appears to have been prejudiced against Pythias, treats his relation as fabulous, founding his opinion principally on the number of incredible circumstances that occur in his narration. Taking these circumstances, however, not according to their literal meaning, but in a figurative sense, they represent pretty well the state of the sea and sky in these countries which are so little favoured by nature. Pythias certainly seems to have been one of the first Greek navigators who entered the Baltic.

We have thus traced the progress of geographical discoveries to very nearly the period which we assigned as the limit of ancient geography; and shall now notice very briefly some of the principal scientific geographers of antiquity, whose names or writings have descended to posterity, and shall afterwards give a summary sketch of the knowledge which the ancients seem to have possessed of the habitable globe.

As geography is a branch of knowledge intimately connected with geometry and astronomy, it became an object of consideration with many of the ancient geometers and astronomers. We have already mentioned the names of Anaximander of Miletus, and his countryman Hecateus. Strabo also notices Democritus, Eudoxus of Cnidos, and Parmenides, to the last of whom he attributes the division of the earth into zones. These were followed by Eratosthenes, who lived about 240 years before the Christian era, and Hipparchus, who flourished about 80 years afterwards; Polybius, Geminus, and Posidonius. Eratosthenes wrote three books on geography, of which Strabo criticises some passages, though he frequently defends him against Hipparchus, who often affects an opposite opinion. Polybius wrote on geography as well as history, and, as well as Geminus and Posidonius, is frequently quoted by Strabo. Polybius and Geminus argue with considerable acuteness for the possibility of the torrid zone being inhabited, a circumstance which was generally disbelieved by the ancients; and they even adduce arguments which are very plausible, to prove that the climate of the countries under the equator is more temperate than that of those which are situated near the tropics.

We must not here omit a geographer and mathematician who lived about the time of Alexander the Great. This was Dicearchus of Messina, the disciple of Theophrastus, who wrote a description of Greece in iambic verses, of which some fragments yet remain. What renders this work most remarkable is, that it contains the height of several mountains measured geometrically by Dicearchus. Thus, for instance, the height of Mount Cyrene is stated at 15 stadia, and that of Satalyce at about 14. Taking the stadium at 94½ toises, we have for the latter of these heights, at most 1400 toises, whereas many of the ancients assigned 300, 400, or even 500 stadia, as the height of some of their mountains.

With Dicearchus we may mention another geometer noticed by Plutarch in his life of Paulus Emilius; viz. Xenagoras, a disciple of Aristotle, who also employed himself in measuring mountains, and has assigned only 15 stadia, which is equal to about 1417 toises, as the height of Mount Olympus. In some of the later periods previous to the Christian era, we find the names of several geographers, as Artemidorus of Ephesus, who wrote a geographical work in eleven books, of which nothing remains; Scymnus of Chio, author of a description of the earth in iambic verses, which remains in a very mutilated state; Isidorus of Charax, who left a description of the Parthian empire, and Scylax of Caryanda, author of a voyage round the Mediterranean sea, which is still extant.

The works of all these geographers, however, are trifling when compared with the geography of Strabo, a work in 16 books, which has come down to us entire. This is one of the most valuable works of antiquity, both from the spirit of discussion which runs through it, and the number of curious observations which the author has collected of different geographers and navigators who preceded him; and of whose works nothing remains except these extracts. Strabo lived in the reigns of Augustus and Tiberius, and was nearly contemporary with Pomponius Mela. This latter geographer wrote a work de situ orbis, which is little more than a bare summary, though it is valuable, as it gives us a sketch of what was known in his time respecting the state of the habitable globe. Pomponius Mela was followed by Julius Solenus, who has also treated of geography in his Polyhistor, a compilation which is sufficiently valuable from the number of curious observations which are there collected.

Of all the ancient geographers, posterity is most indebted to Ptolemy, who produced a work much more scientific than had ever before been written on this science; a geography in eight books, which must ever be considered as one of the principal monuments of the labours of its author. In this work there appear, for the first time, an application of geometrical principles to the construction of maps; the different projections of the sphere, and a distribution of the several places on the earth, according to their latitudes and longitudes. This work must have been the result of a great many relations both historical and geographical, that had been collected by Ptolemy. It has passed through numerous editions. Some time after Ptolemy, lived Dionysius the African, commonly called the Periegetic, from the title of a work that he composed in verse, containing a description of the world, which may be considered as one of the most correct systems of ancient geography, and was by Pliny proposed to himself as a pattern. This work was afterwards translated into Latin verses by Priscian, and by Avienus, the latter of whom also wrote a description of the maritime coasts in iambic verses, of which there remain about 700. Among the latest geographers of this period are reckoned Marcianus and Agathemares, of whom little is known, except that the latter was author of two books on geography.

The scattered works of most of these authors being difficult to procure, were collected by Hudson into one work, and published by him in four volumes octavo, in the years 1698, 1702, and 1712, under the title of Geographia veteris scriptores Graeciae minores, together with a Latin translation, and notes and dissertations on each by Dodwell. In this work we find the remains of Hanno, Scylax, Nearchus, Agatharchides, Arrian, Marcianus, Dioclearchus, Isidore of Charax, Scymnus, Agathemares, Dionysius the Periegetic, Artemidorus, Dionysius of Bisanse, Avienus, Priscian, and some fragments of Strabo, of Pintarch, of Ptolemy, of Albulfeda, and of Ulug Beg. This is the most valuable collection, and as it had become extremely scarce, was a few years ago reprinted at Leipzig.

The above is a hasty sketch of the names and characters of most of the geographical writers within the period which we have assigned to the ancient history of the science. We shall have occasion to make some further observations on the more eminent of these geographers in a future part of this article.

With respect to the knowledge of the globe that was possessed by the ancients, there have been various opinions; some have considered them as very extensively acquainted with almost every part of it, not excepting some portion of America; while others have confined their geographical knowledge within very narrow limits. The following observations are chiefly drawn from M. Montucla, an eminent judge in everything that relates to the history of the mathematical sciences.

As to the knowledge which the ancients possessed of the habitable globe, it is certain that they were well acquainted with Europe, or at least all that part of it which had been made subject to the Roman empire, as far as the banks of the Rhine and the Danube. They were tolerably well acquainted with Germany and Sarmatia. They had some knowledge of the Baltic sea, as a fleet had been sent by Augustus, which sailed as far as the peninsula then called the Cimbrian Chersonesus, the modern Jutland. The Baltic was at that time celebrated for the production of ambergrise. They had acquired a knowledge of the island of Britain, from the expeditions of Julius Caesar and Claudius; but the northern parts of this island, and the whole of Ireland, were to them nations of rude, uncivilized savages. The boundary of their knowledge of Europe to the north, was the Thule of Pythias, or Iceland; at least if it is certain, as is the general opinion, that this island is the ultima Thule.

With respect to Asia, they seem to have surveyed the country as far towards the east as the river Ganges; and the immense extent of country comprehended between the Indus and the Ganges, was called by them India on this side the Ganges. Further on towards the north of China, in the neighbourhood of the mountains where these rivers derive their source, they placed several nations of people, of whom they related the most ridiculous fables. Beyond these, still more towards the east, they placed the Seres, and upon the coast of the gulf, which is now the bay of Cochin China, called by Ptolemy the Great Bay, were situated the Sinæ, so called by Ptolemy, though they are not mentioned by Strabo, Pomponius Mela, or Solinus. The Seres were probably the inhabitants of the northern parts of China, and the Sinæ, those of the southern parts of China, who very early occupied Cochin China, Tonquin, &c., countries which in the sequel they have entirely subjugated. They maintained a commerce by land with the Seres, and their route is pointed out in one of Ptolemy's maps. Beyond the Seres, according to Strabo and Pomponius Mela, lay between the Oriental sea, though Ptolemy, for want of certain intelligence respecting that part of Asia, considers the point as undecided, and places there several unknown countries. The ancients carried this extremity of Asia much farther to the east than it is found to extend by modern geographers; for, according to them, the Seres and the Sinæ were situated about the longitude of 180°, while the meridian of Pekin, or about the middle of the Chinese empire, reaches no farther than to 134°, reckoning the longitude from the most distant of the Canary islands, as was done by Ptolemy. To the north of the Indus the ancient geographers placed the Scythians, and Hyperboreans (the Tartars and Samoiedes of more modern date) and some other nations to an indefinite extent, who were supposed to form on that side an insurmountable barrier, having behind them an ocean of ice, which was believed to communicate with the Caspian sea, though this was at least at the distance of 450 leagues.

The boundary of Asia, assigned by the ancients to the south, was the Indian ocean, and they were acquainted with its communication with the Red sea, by means of a strait, the figure of which is very ill expressed in their maps. This is also the case with the Persian gulf, with which they were acquainted, but which in the ancient maps has nearly the form of a rhombus, one side of which, towards the mouths of the Indus, was pretty well known to them, but the side next the mouths of the Ganges is very inaccurately delineated, being continued nearly in a straight line. It is even probable that the island which Ptolemy calls Taprobana, was only the peninsula of India very much disfigured in the delineation.

The situation of this island of Taprobana, so celebrated among the ancients, is a problem in geography that is yet unsolved. It is commonly supposed to be the modern island of Ceylon; but the dimensions of it, as laid down by ancient geographers, render this supposition doubtful, and there are some who rather believe it to be the modern Sumatra. The ancients had also some obscure knowledge of the peninsula of Malacca, which they called the Golden Chersonesus; and they seem to have examined the gulf formed by that land, which is now the gulf of Cochin China, or commonly called the gulf of Tonkin. It is somewhat extraordinary that they do not seem to have been acquainted quainted with Java, Borneo, and that numerous group of islands which form, in that quarter, the greatest Archipelago in world. It is equally singular that the Maldives had escaped the observation of these navigators. This seems to prove that they never ventured out into the open sea, but kept close along the shore. Ptolemy indeed says, that his island of Taprobana was surrounded with many hundreds of smaller islands, to some of which he gives names; but all this is involved in impenetrable obscurity.

Of Africa, the ancients knew only those parts which lay along the coast, and to a very small distance inland, if we except Egypt, with which they were well acquainted, at least as far as the cataracts of the Nile, and a little beyond them, as far as the island of Meröe, towards the 20th degree of north latitude. Their knowledge of the coasts of Africa on the side of the Red sea, extended no farther than the shores of that sea, except that part which was dependent on Egypt; the interior of the country being inhabited by ferocious and untractable people. They were still less acquainted with the countries which lay beyond the strait, and Ptolemy appears to have given no credit to the navigators who were said to have sailed round that part of the world, for he has left the continent of Africa imperfect towards the south. Strabo and Pomponius Mela were, however, decidedly of opinion that Africa was a peninsula, and that it was joined to the rest of the continent only by that narrow neck of land which is now called the isthmus of Suez. The ancients seem to have had no knowledge of that large and beautiful island of Madagascar, unless we suppose that Ptolemy had some imperfect acquaintance with it, under the name of the island Monuthius. The coast of Africa upon the Mediterranean sea, was once covered with towns, dependent on the Roman empire, flourishing and polished, while it presents at present nothing but a nest of pirates, whom the jealousy of the great commercial nations supports, to the disgrace and prejudice of civilized states. Proceeding from the straits of Gadez or Gibraltar, they had become acquainted with the coast as far as a cape which they called Hesperion-Keras, probably the modern Capo de Verd, or the cape that lies a little to the west of it, though in the maps of Ptolemy it is thrown a little back inland. The Fortunate islands, or the Hesperides, at present the Canaries, better known by name than in reality, seem to have been the boundaries of ancient geography to the west, as the Seres and Sinus were to the east. It appears, however, that the Cape de Verd islands were not entirely unknown to the ancients, and they are probably the same with what were then called the Gorgades or Gorgones, which were supposed to be two days sail to the west of Hesperion-Keras.

"There is little doubt (says Mr Patteson) concerning the names by which most of the principal countries of Europe were known to the ancients; nor is there any difficulty in disposing the chief nations, which ancient writers have enumerated in the south-west part of Asia or on the African coast of the Mediterranean; but with the north and north-east parts of Europe, about two-thirds of Asia towards the same quarters, and nearly the same proportion of Africa towards the south, they appear to have been wholly unacquainted. Of America they did not even suspect the existence; and if it ever happened, as some writers have imagined, that Phoenician merchants ships were driven by storms across the Atlantic to the American shores, it does not appear that any of them returned from thence to report the discovery.

"The names of provinces, subdivisions, and petty tribes, mentioned by ancient authors, in those countries which were the chief scenes of Roman, Grecian, or Israelitish transactions, are almost as numerous as in a modern map of the same countries; and the situations of many of them can be very nearly assigned: but the limits of each, or indeed of the states or nations to which they belonged, can, in very few instances, be precisely fixed. Thus the southern boundaries of the Sarmatia in Europe, cannot be ascertained within a degree at the nearest; and in France, neither the limits of the people called the Belge, Celte, and Aquitani; nor those of the Roman divisions, viz. Belgica, Lugdunensis, Aquitania, Narbonensis, and the Province, can be laid down, in many places, but by a hardy conjecture. The same observation may be justly applied to the Tarraconensis, Lusitania, and Betica of Spain; to the Canti, Catti, Suevi, &c. of Germany; and, above all, to the Britannia prima et secunda, and other divisions of the Roman government in Britain: of which not only the limits, but the situations are still in dispute."

During the middle ages geography, as well as most other arts and sciences, seems rather to have gone backwards than advanced. The weakness of the Roman emperors, the relaxation of military discipline, the boundless passion for luxury and pleasure, and the continual incursions of the barbarous nations, while they contributed to hasten the fall of the western empire, also accelerated the ruin of the arts. It seems as if these destructive hordes of barbarians, the Goths, the Huns, and the Vandals, had enveloped the whole world in one profound and universal ignorance. This darkness, which overspread the whole of Europe, did not permit geography to make any advances for a very considerable time. There were indeed some navigators who investigated countries that were still little known, but they were so ignorant, that they afford us very little new light. There was one named Cosmas, who made a voyage to India, which procured him the name of Indo-Pleustes, and who gave an account of his voyage under the title of Sacred Geography. This man was so egregiously ignorant, as to believe that he had discovered that the earth was a plane, and that the diversity of the seasons, and the inequality of the days and nights, were owing to a very high mountain situated to the north, behind which the sun set to a greater or less depth.

The voyages of the Arabians to the East Indies (see the history of Commerce), contributed to throw of the farther light on that extensive part of the globe. Conquerors of the countries on the Red sea, and enthusiastic propagators of their religion, they carried their arms as far as the extremity of India. We see them in the 9th century extending to China; and Renaudot has published two of their narrations, in which we can trace, with tolerable accuracy, the places visited by their authors. The island of Serendib, so celebrated in their tales, is certainly the modern Ceylon; for dib or dir, in the Malay language, signifies island, so that Serendib signifies the island of Seren or Selan. Farther, these relations... relations do not give us as favourable an idea of the Chinese as we derive from their own history; on the contrary, if we may believe these Arabian travellers, this people were, even at that time, in a state not very civilized.

We are now arrived at the modern period of our history, during which the most important discoveries have been made, and our knowledge of the habitable globe more than doubled. The discoveries and improvements during this period are so numerous, that it will be impossible to give here any thing more than a chronological view of the most remarkable, referring for a detailed account of them to the geographical and historical articles in this work.

The taste for voyages of discovery began in Europe soon after the revival of literature in the 15th century, just before the commencement of which, namely, in the reign of Henry III. king of Spain, about the year 1395, the Canary islands were more fully surveyed than at any former period.

1415. Prince Henry III. son of John king of Portugal, sailed round the coast of Africa.

1417. The Canary islands were subdued by Bethancourt, nephew of the admiral of France.

1420. The island of Madeira was examined by John Gonsalvo and Tristan Vaz, two Portuguese.

1446. Cape de Verd was discovered by Dennis Fernandez.

1487. The Cape of Good Hope was discovered by Bartholomew Diaz. The discovery of this cape led the way to that of the new world. This great event, which gave a new flight to the genius of mankind, is one of the most important in the history of geography. A particular account of this discovery will be found under the article AMERICA. The following are the dates of the principal geographical discoveries which have taken place between that of Columbus, and the voyages of our celebrated navigator Cook.

1496. Florida, by Sebastian Cabot, an Englishman.

1498. The Indies, by Vasco de Gama.

1499. The river of Amazons, by Yanez Pinçon.

1500. Brazil, by Alvarez Cabral, a Portuguese.

1504. Newfoundland, by some Normans.

1518. Mexico, by Ferdinand Cortes.

1519. The straits of Magellan, South sea, and Philippine islands, by Ferdinand Magellan.

1525. Canada, by Jean Verrazan, a Florentine, sent by Francis I. of France.—Peru, by F. Pizarro of Spain.

1527. New Guinea, by Alvaro de Salvedra.

1534. Chili, by Diego Almagro.

1535. California, by Ferdinand Cortes.

1567. The islands of Solomon, by Alvaro de Mendoza.

1618. New Holland, by Zechaen.

1642. Van Diemen's land, by Abel Jansen Tasman.

1643. Brower's land.

1654. New Zealand.

1678. Louisiana, by Robert Cavelier de Lasalle, governor of Frontinian.

1700. New Britain, by Dampier, an Englishman.

1739. Cape Circumcision, contested between the French and English. Said by Montucla to be discovered by two French vessels.

1767. The island of Tahiti, by Wallis, an Englishman.

1773. The Sandwich islands, by Cook.

Within this period there are reckoned 25 voyages round the world, viz. those of Magellan, Drake, Cavendish, Noort, Spilburg, Lemaire, L'Hermitte, Cleopagton, Carreri, Shelvack, Dampier, Cowley, Woodroof Rogers, Le Gentil, Anson, Wallis, Roggewein, Bougainville, Sarville, Dixon, three voyages of Cook, La Peyrouse, Marchand, Vancouver, and Pages.

Within these few years, very considerable light has been thrown on the state of our geographical knowledge, by several valuable voyages and travels that have lately appeared. The discoveries that have been successively made in the great South sea, and in other parts of the world, especially the extensive island of New Holland, are now so fully established, as to add considerably to the certainty of our geographical knowledge; and the voyages of Cook, La Peyrouse, and Vancouver, have afforded us more exact surveys of the coasts of these countries, than we could, some years ago, have dared to hope for. The accounts of the late embassies to China, Tibet and Ava, afford many authentic materials for a modern system of geography, the place of which must have been supplied by more remote and doubtful information. From the latter of these accounts we are become familiarly acquainted with an empire (that of the Birmans), which a short time ago was scarcely known (see ASIA, 81—152). Our knowledge of Hindostan and the neighbouring countries has been greatly extended by the researches of the Asiatic Society, and some other late works; while our acquaintance with the interior of Africa has been rendered less imperfect by the exertions of the African Society, and by the travels of Park, Brown, and Barrow; and the northern boundaries of America, even as far as the sea which appears to surround the northern extremity of that vast continent, have been more fully disclosed by the journeys of Hearne and Mackenzie.

The late voyage of Turnbull, however insignificant it may be in other respects, has at least the merit of enlarging our knowledge of the manners and political transactions of the South sea islanders, and of introducing to our acquaintance, in the person of Tamabama, the chief of Owwhyhee, a sovereign, who, in ambition and desire of improvement, bids fair to vie with Peter the Great, and to transform a nation of savages, to a civilized people.

With all the advantages which geography has lately received, the science is still far from being perfect; and the exclamation which D'Anville is said to have made in his old age, "Ah! mes amis, il y a bien d'erreurs dans la géographie"—Ah! my friends, there are a great many errors in geography, may still be applied with considerable justice. Many points in the science have been but very lately ascertained. Thus, the extent of the Mediterranean sea was almost unknown at the beginning of the 17th century, although it is now almost as exactly ascertained as that of any country in Europe. In a book published by Gemma Frisius, de orbis divisione, in 1520, we find the difference of longitude between Cairo in Egypt and Toledo in Spain stated at $53^\circ$ instead of $35^\circ$, and other measures of extent are proportionally erroneous. Not many years ago there was an uncertainty with respect to the extremity of the Black sea and the Caspian, to the amount of $3^\circ$ or $4^\circ$. and so lately as the year 1769, the longitude of Gibraltar and of Cadiz was not known within half a degree.

Many parts of the geography of Europe are still very defective; Spain and Portugal have been but imperfectly explored, and European Turkey is still less known. It may appear extraordinary that we have yet no correct chart of the British channel, though we are assured by Major Rennel that this is the case; and it has been proved by the trigonometrical surveys of Britain that have yet been published, that there are many gross errors in our best county maps. We have had occasion to remark that geography has sometimes been retrogressive, and there cannot be a greater proof of the truth of the observation, than that in a map of the Shetland islands, published not long ago, by Preston, they are represented as too large by one third, both in length and breadth, and their relative positions are very inaccurate, though in the maps of the same islands published before the year 1750, they are laid down with much greater accuracy, as appears from surveys made by order of the late king of France, and from the maps published by Captain Donnelly, and at Copenhagen, in the year 1787.

In Asia we are imperfectly acquainted with Thibet, and some other central regions; and even Persia, Arabia, and Asiatic Turkey, are but little known. Of Australasia, or New Holland, and New Guinea, almost nothing is known except the coasts, and a great part of them towards the south has been but imperfectly explored. Of Polynesia, or the numerous islands in the South Pacific ocean, we are also very ignorant; and in the Pacific ocean, particularly towards the south pole, many discoveries probably remain to be made.

Our ignorance of the central parts of Africa is notorious, and the improvement of our geographical knowledge in that quarter has, for some years, been a favourite object. It may admit of doubt, however, whether this object will be speedily attained, as the obstacles to investigation in those inhospitable tracts, seem nearly insurmountable by human prudence and courage. Even the shores of Africa have not been completely surveyed, especially those towards the south and east.

America has of late been much more fully explored than at any former period; but still the western parts of North America, and the central and southern regions of South America are very little known; and the Spanish settlements towards the north are scarcely known, except to their own inhabitants.

The science of geography will probably be never perfectly understood, as, beside the numerous obstacles which oppose the progress of the traveller, it is scarcely possible that exact trigonometrical surveys of every place and country, the only certain method of ascertaining their exact situations and relative positions, can be made.

Political geography must ever remain the most uncertain part of the science. New changes are perpetually taking place in the relations of neighbouring states, according as ambition, tyranny, or commercial convenience dictates. Territory is transferred, by cession or by conquest, from one nation to another. Whoever will compare the relations of the European states, as they appear in the present maps, and in those published half a century ago, will scarcely recognise the countries to be the same. The great divisions indeed remain as before, but the boundaries of most of them are entirely changed. A number of independent states, and in one instance, a large kingdom, have been swallowed up by the unjustifiable ambition of their more powerful neighbours, and their names may be blotted from the map of Europe. The republics of Holland, of Switzerland, of Venice, are no more: the kingdoms of Poland and Sardinia have ceased to exist; the successor of St Peter, who once gave laws to princes, and governed Europe with unbounded sway, is now a wretched exile, and his dominions are doomed to increase the already overgrown power of despotic upstarts. Whether the present generation of emperors and kings, erected by the mighty Napoleon, will remain as long as did the states on whose ruins they have been raised, or are rather ephemeral productions, doomed to perish at the setting of that sun which now gives them life and vigour, is a question which future experience alone can determine.

The limits prescribed to this article do not permit us to enter on a critical examination, or even a characteristic sketch of the geographical works that have appeared in the modern period of the history of the science; and a bare enumeration of names would be equally tiresome and uninteresting. Some of the best modern works will be mentioned in the sequel; at present we shall conclude this Part in the words of an able judge of the present state of the science.

"The Spaniards and Italians (says Mr Pinkerton) have been dormant in this science; the French works of La Croix and others are too brief; while the German compilations of Buseck, Fabri, Ebeling, &c., are of a most tremendous prolixity, arranged in the most tasteless manner, and exceeding in dry names, and trifling details, even the minuteness of our gazetteers. A description of Europe in 14 quarto volumes, may well be contrasted with Strabo's description of the world in one volume: and geography seems to be that branch of science, in which the ancients have established a more classical reputation than the moderns. Every great literary monument may be said to be erected by compilation, from the time of Herodotus to that of Gibbon, and from the age of Homer to that of Shakespeare; but in the use of the materials there is a wide difference between Strabo, Arrian, Ptolemy, Pausanias, Mela, Pliny, and other celebrated ancient names, and modern general geographers; all of whom, except d'Anville, seem under-graduates in literature, without the distinguished talents or reputation, which have accompanied almost every other literary exertion. Yet it may safely be affirmed, that a production of real value in universal geography requires a wider extent of various knowledge than any other literary department, as embracing topics of the most multifarious description. There is, however, one name, that of d'Anville, peculiarly and justly eminent in this science; but his reputation is chiefly derived from his maps, and from his illustrations of various parts of ancient geography. In special departments Gosselin, and other foreigners, have also been recently distinguished; nor is it necessary to remind the reader of the great merit Geo. of Rennel and Vincent in our own country."

PART PART II. PRINCIPLES AND PRACTICE OF GEOGRAPHY.

CHAP. I. Of the Surface and General Divisions of the Earth.

IT has been supposed, by the less enlightened part of mankind in all ages, that the surface of the earth is nearly a plane, bounded on all sides by the sky. It was shewn, however, in the article Astronomy, (No 269—272,) that the earth is of a spherical figure, and an account was there given of the manner in which the true form of it was determined. Independently of the considerations there detailed, the spherical figure of the earth may be inferred, in a popular view, from the following facts.

1. When we stand on the sea-shore while the sea is perfectly calm, we easily perceive that the surface of the sea is not quite plain, but convex or rounded; and if we are on one side of a broad river or arm of the sea, as the frith of Forth, and, with our eyes near the water, look towards the opposite coast, we shall plainly see the water elevated between our eyes and the opposite shore, so as to prevent our seeing the land near the edge of the water.

2. When we observe a ship leaving the shore, and going out to sea, we first lose sight of the hull, then of the sails and lower rigging, and lastly of the upper part of the masts. Again, when a ship is approaching the shore, the first part of her that is seen from the land is the topmast, then the sails and rigging appear, and lastly the hull comes gradually into view. These appearances can arise only from the ship's sailing on a convex surface; as, if the surface of the sea was plain, a ship on its first appearance would be visible, though very small, in all its parts at the same time, or rather the hull would first appear, as being most distinguishable; and, in going out of sight, it would in the same manner disappear at once, or the hull would be the last part of which we should lose sight.

3. Many navigators sent on voyages of discovery, have, by keeping the same course, at length arrived at the port from which they set out, having literally sailed round the globe. This could not happen if the sea were a plain.

4. When we travel to a considerable distance, in a direction due north or due south, a number of new stars successively appear in the heavens, in the quarter to which we are travelling; while many of those in the opposite quarter gradually and successively disappear, and are seen no more till we return in a contrary direction.

5. In an eclipse of the moon, which has been shown (Astronomy, No 199,) to be owing to the obscuration of the moon's surface by the shadow of the earth, the boundary of the obscured part of the moon is always circular. Now, it is evident that no body, which is not spherical, can, in all situations, cast a circular shadow.

The diameter of the earth is generally computed at 7958 miles, though Mr Vince makes it 7939, nearer the medium derived from a comparison of the polar with the equatorial axis. Taking this last, therefore, as the mean diameter, the circumference will be = 24,912 miles, and consequently the extent of the surfaces will be = 197,553,160 miles, of which it is computed that at least two-thirds are covered with water.

In the above computation no account is taken of the mountains and other eminences on the surface of the globe; for, although these are of considerable consequence in a geographical point of view, as they constitute the most natural and remarkable boundaries of countries, and by their influence on the soil and climate of the different regions, contribute in a great degree to form those shades of distinction which diversify the inhabitants of the several quarters of the earth, they are, however, too trifling when compared with the diameter of so great a body, to make any sensible error in the calculation.

The surface of the earth is exceedingly diversified, almost everywhere rising into hills and mountains, or sinking into valleys; and plains of any great extent are extremely rare. Among the most extensive plains, are the sandy deserts of Arabia and Africa, the internal part of European Russia, and a tract of considerable extent in the late kingdom of Poland, now called Prussian Poland. But the most remarkable extent of level ground, is the vast platform of Tibet in Asia, which forms an immense table, supported by mountains running in every direction, and is the most elevated tract of level country on the globe. The chief elevations or mountains that occur, with their elevation, &c. will be mentioned under Geology. The greatest concavities of the globe are those which are occupied by the waters of the sea, and of these by far the largest forms the bed of the Pacific ocean, which stretching from the eastern shores of New Holland to the western coast of America, covers nearly half the globe. The concavity next in size and importance, is that which forms the bed of the Atlantic ocean, extending between the new and the old worlds; and a third concavity is filled by the Indian ocean. Smaller collections of water, though still large enough to receive the name of oceans, fill up the remaining concavities, and take the names of Arctic and Antarctic oceans.

Smaller collections of water that communicate freely with the oceans, are called seas, (vid. A; fig. 1,) and of these the principal are the Mediterranean, the Baltic, the Black sea, and the White sea. These seas sometimes take their names from the country near which they flow; as the Irish sea and the German ocean. Some large bodies of water which appear to have no immediate connexion with the great body of waters, being everywhere surrounded by land, are yet called seas; as the Caspian sea.

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

When two large bodies of water communicate by a narrow pass between two adjacent lands, this pass is called called a strait, or straits (C, fig. 1.) as the straits of Gibraltar, the straits of Dover, of Babelmandel, &c. The water usually flows through a strait with considerable force and velocity, forming what is called a current, and frequently this current always flows in the same direction. Thus, in the straits of Gibraltar there is a constant current from the Atlantic into the Mediterranean, though the surface of the latter never seems to be elevated beyond its usual level. There is always a current round Cape Finisterre and Cape Ortegal, setting into the bay of Biscay, and it has been discovered by Major Rennell, that this current is continued in a direction N. W. by W. from the coast of France to the westward of Ireland and the Scilly islands. Hence he draws this useful practical instruction for navigators who are entering the English channel from the Atlantic, viz. that they should keep no higher latitude than 45° 45', lest they should be carried by the current upon the rocks of Scilly. For want of this necessary precaution, it is said that many ships have been lost on these rocks.

A body of fresh water, entirely surrounded by land, is called a lake, loch, or lough (as D, fig. 1.), with the exception of the sea above mentioned; as the lake of Geneva, Lake Ontario, Lake Champlain, Loch Lomond &c.

This term, or its synonymes, loch or lough, is sometimes applied to what is properly a gulf or inlet of the sea, as Loch Fyse in Scotland, and Lough Swilly in Ireland.

A considerable stream of water rising inland, and running towards the sea, is called a river; a smaller stream of the same kind is called a rivulet or brook. Vid. E, fig. 1.

The great extent of land which forms the rest of the globe, is divided into innumerable bodies, some of which are very large, but the majority extremely small. There are three very extensive tracts of country, which may all be denominated continents, though only two of them have hitherto been distinguished by that appellation. The most considerable of these continents is what has been called the old world, comprising Europe, Asia, and Africa. The second comprehends North and South America, or what has been denominated the new world, and is little inferior in extent to the former. The third great division forms the country called New Holland.

A body of land entirely surrounded by water is called an island, (vid. a, fig. 1.) as Britain, Ireland, Jamaica, Madagascar, &c. According to the strict meaning of this definition, the large divisions just mentioned are islands; for it is almost certainly ascertained, that the continent of North America is everywhere bounded by the sea, and it has long ceased to be doubtful that New Holland is in the same circumstances, and it is generally called the largest island in the world. But perhaps it would be better to confine the term to those numberless smaller islands that appear above the surface of the waters. When a number of smaller islands are situated near each other, the whole assemblage is commonly called a group of islands, as b, b. The large assemblages of islands that have been discovered in the South Pacific ocean, have lately been comprehended under the name of Polynesia, constituting a sixth division of the whole earth; the other five being Europe, Asia, Africa, America, and the islands of New Holland and New Guinea, under the name of Australasia.

A body of land that is almost entirely surrounded by water is called a peninsula, as c, fig. 1.; as the peninsula of Malacca, the Morea, or Grecian Peloponnesus, &c. Indeed the continent of Africa may be considered as a vast peninsula, being united to Asia only by the small isthmus of Suez.

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

A narrow tract of land stretching far out into the Promontory sea, being united to the main land by an isthmus, is called a promontory, and its extremity next the sea, is called a cape, as e, fig. 1. The most remarkable capes are the Cape of Good Hope, at the southern extremity of Africa; Cape Horn at the southern extremity of South America; the North Cape at the northern extremity of Europe; and Cape Talmara, at the northern extremity of Asia.

It may assist the memory of the young geographer, to compare together the above divisions of land and water. We may remark that the large bodies of land, called continents, correspond to the extensive tracts of water called oceans; that islands are analogous to lakes; peninsulas to seas or gulfs; isthmuses to straits; promontories to creeks, &c.

The inhabited parts of the earth are calculated to occupy a space of 38,992,569 square miles, of which the four quarters into which the globe is usually divided are supposed to have the following proportions:

| Continent | Square Miles | |-----------------|--------------| | Europe | 4,456,065 | | Asia | 10,768,823 | | Africa | 9,654,807 | | America | 14,110,874 |

The whole population of the earth has been computed at 700,500,000 souls; and of these

| Continent | Population | |-----------------|--------------| | Asia | 500,000,000 | | Europe | 150,000,000 | | Africa | 30,000,000 | | America | 20,000,000 | | Australasia and Polynesia, &c. | 300,000 |

Hence the proportional number of inhabitants to every square mile in each quarter is as follows:

| Quarter | Proportional Number | |---------|---------------------| | Asia | 46 | | Europe | 34 | | Africa | 3 | | America | 3 to every two square miles |

**CHAP. II. Of the Construction and Use of the Globes.**

**SECT. I. Description and Use of the Terrestrial Globes.**

For the purpose of representing more accurately the globe which we inhabit, geographers have long had recourse to spherical balls, on the face of which are drawn the various divisions of the earth, and which are fitted up with such an apparatus, as enables us to illustrate and explain the phenomena produced by the motions... Principles of the earth, and the different situations of its various inhabitants. The ball thus prepared, is called an artificial globe, and what we have described is properly the terrestrial globe, so called to distinguish it from another of a similar form, and furnished in a similar manner, but the surface of which represents the various assemblages of stars or constellations that appear in the heavens, and therefore this is called the celestial globe.

In order to ascertain the relative positions of places and countries on the earth, certain circles are supposed to be drawn on its surface, analogous to those which were mentioned in ASTRONOMY, as supposed to be drawn in the heavens. As these circles are really represented on the artificial globes, it will be proper here to consider a little more particularly their nature and uses.

As the earth turns about on an imaginary axis, once in 24 hours, the artificial globe is furnished with a real axis, formed by a wire passing through the centre, and on which the globe revolves. The two extremities of this axis are its poles, the one being called the north, and the other the south pole.

A great circle drawn on the globe, at an equal distance from both poles, is the equator or equinoctial line, and represents on the globe a similar circle, supposed to be drawn round the earth, and distinguished by the same name. By sailors this is commonly called the line, and when they pass over that part of the water, where it is imagined to be drawn, they often make use of various superstitious ceremonies. The two parts of the globe into which it is divided by the equator, are called the northern and southern hemispheres.

The equinoctial line on the earth passes through the middle of Africa, in the almost unknown territories of Macoco, and Monemugi, traverses the Indian ocean, passes through the islands of Sumatra and Borneo, and the immense expanse of the Pacific ocean; then extends over the province of Quito in South America, to the mouth of the river Amazons.

As every circle is supposed to be divided into 360°, so the equator is thus divided on the artificial globe.

Through every 15° of the equator there is drawn on the globe a great circle passing through the poles. These circles are called meridians, because when the sun in his apparent course from east to west reaches the corresponding circle in the heavens, it is noon on that part of the earth over which the meridian is supposed to pass. Properly speaking, every place on the earth has its own meridian, though to prevent confusion, these circles are drawn on the artificial globe, only through every 15° of the equator. To supply the place of the other meridians, the globe is hung in a strong brazen circle, which is called the brazen meridian, or sometimes only the meridian. The brazen meridian, like the equator, is divided into 360°, but these are marked by ninetyes on each quadrant, being on one half of the meridian numbered from the equator to the poles, and on the other half from the poles to the equator. On the opposite side of the brazen meridian there are two concentric spaces, which are divided into degrees corresponding to the months and days of each month, the degrees being marked on concentric spaces from the north pole to about 23½° both ways. The use of these divisions will appear hereafter (b).

Through every tenth degree of the meridians, there are drawn on the globe circles parallel to the equator, which, for a reason that will appear presently, are called parallels of latitude.

Before we proceed in describing the other circles, &c. of the artificial globe, we shall here make a few remarks on the uses of the equator, the meridians and parallels (c).

The equator serves to measure the distance of one place from another, either to the eastward or westward, and this distance is called the longitude of the place. The meridians serve in like manner to measure the distance of one place from another in a direct line north or south of the equator, and the distance of the place thus measured is called its latitude.

The longitude and latitude of places may be illustrated in the following manner. Let PEP'Q (fig. 3) represent the earth or the globe, (supposed to be transverse) whose axis is PCP', the north pole being P, and the south pole P'; and let EAQR represent a circle passing through the centre C, in a direction perpendicular to the axis PP'. This circle corresponds to the equator, and it divides the earth of the globe into two hemispheres, EPQ being the northern, and EP'Q the southern hemisphere. Let G, I, K, represent the situations of three places on the surface of the globe, through which let the great circles PKP', PIP', and PGP', be drawn, intersecting the equator EQ, in n, m, a, respectively. The circles are the meridians of the places K, I, G. As every circle is supposed to be divided into 360°, there must be 90° from each pole to the equator. Hence the latitude of the place K is measured by the degrees of the arc intercepted between K and n, and the latitudes of G and I are measured by the degrees of the arcs intercepted between G and n, and I and m respectively. These latitudes will be called north

(b) The meridians are properly only semicircles, reaching from pole to pole, and of these there are twenty-four.

(c) In Geography, as in other sciences, there are two methods of conveying instruction. One is, to lay down the principles of the science first, and afterwards apply these to the practice of it; the other method is, to combine the principles and practice in one view. The former is usually considered as the more scientific, but we are inclined to think that the latter is often to be preferred, as being less dry and tedious, especially to a general reader. We have here, therefore, chosen to explain the nature of latitude and longitude, and the problems respecting them, before completing the description of the globe. We shall proceed in the same manner, uniting, as far as possible, the principles and practice in one view. Making, therefore, the terrestrial globe our text book, we shall thence explain the principles of geography, rather than detail these in a separate section, and afterwards illustrate them by the globe. principles north latitudes, because the places lie in the northern hemisphere. Let there be two other places, WV, in the southern hemisphere; the latitude of W will be measured by the degrees of the arc intercepted between W and a; and the latitude of V by the arc intercepted between V and m; these will be called south latitudes. Further, let the circle c, e, d, v, G, be drawn parallel to the equator; this circle is called a parallel of latitude, and as it does not pass through the centre, it is evidently less than the equator, or it is a small circle. Now, all the arcs, such as R, e, a, G, &c. intercepted between the parallel and the equator, must be equal, since the circle is parallel to the equator; and hence every point in this parallel, or every place on the earth through which it is supposed to pass, has the same latitude.

Latitude is the same all over the earth, being constantly measured from the equator to the poles.

The longitude of a place is measured by the degrees of an arc of the equator, intercepted between some particular meridian, and the meridian passing through the place. Thus, suppose G to represent the particular meridian, and m to represent the place whose longitude is required; the longitude of m is measured by the arc ma of the equator, intercepted between a, the point where the meridian of G meets the equator, and m the point of the equator where it is cut by the meridian of the place m. The particular meridian from which we begin to reckon the degrees of longitude is called the prime or first meridian, and it is different in different countries.

The method of estimating the distances of places by longitudes and latitudes, is of considerable antiquity, and was employed by Eratosthenes, who first introduced a regular parallel of latitude, which began at the straits of Gibraltar, passed eastwards through the island of Rhodes to the mountains of India; all the intermediate places through which it passed being carefully noted. Soon after drawing this parallel through Rhodes, which was long considered with a degree of preference, Eratosthenes undertook to trace a meridian, passing through Rhodes and Alexandria, as far as Syene and Meroë. Pythias of Marseilles, according to Strabo, considering the island of Thule as the most western point of the then known world, began to count the longitude from thence, while Mariannus of Tyre placed their first meridian at the Fortunate islands, or the Canaries; but they did not determine which was the westernmost of these islands, and consequently which ought to serve as a first meridian. Among the Arabs, Alfragan, Albategnus, Nassir Eddin, and Ulug Beg, also reckoned from the Fortunate islands; but Albulfeda began to reckon his longitude from a meridian 10° to the eastward of that of Ptolemy, probably because it passed through the western extremity of Africa, where, according to him, were situated the pillars of Hercules; or because it passed through Cadiz, which was at that time rendered famous by the conquests of the Moors in Spain.

When the Azores were discovered by the Portuguese in 1448, some geographers made use of the island of Tercera as the first meridian. Other geographers, at Bleau, father and son, placed the first meridian at the Peak of Teneriffe, a mountain so far elevated above the sea, that it may be easily known by navigators; while others have made the island of St Philip, one of the Cape de Verds, the first meridian, because they conceived this to be the place where the magnetic needle had no variation. For a long time it was customary to reckon the longitude in most countries from the isle of Ferro, one of the Canary isles; but it is now customary for each nation to reckon the longitude, either from the metropolis of the country, or from the national observatory situated near it. Thus in France, Paris is the first meridian, and in Great Britain, the Royal Observatory of Greenwich. As in several good maps, the isle of Ferro is still used as a first meridian, it may be proper to remark, that the observatory at Greenwich lies 17° 45' to the east of Ferro. Hence it is very Method of easy to reduce the longitude of Ferro to that of Greenwich; for if the longitude required be east, we have only to subtract 17° 45' from the longitude of Ferro, and the remainder is the longitude east from London; on the other hand, if the place be west from Ferro, we obtain the longitude west from London by adding to that of Ferro 17° 45'. If the place lies between Ferro and London, its longitude from London will be obtained by subtracting its longitude east from Ferro from 17° 45'. It is evident that by the reverse of this method, we may reduce the longitude from London to that of Ferro.

In the diagram referred to above, if G represent the observatory of Greenwich, a will be the point from which we begin to reckon the degrees of longitude, and all places situated to the east of a, such as R, m, will have east longitude, while those situated to the west, as n, will have west longitude. In reckoning the longitude, we sometimes number the degrees only as far as 180°; but at other times they are numbered all round the equator from the point a; for instance 180°, till we come to a again; hence reckoning in the direction a, R, m, we should say that every place was in so many degrees east longitude, while if we reckon in the direction n, E, we should say that all the places had so many degrees west longitude all round the equator. To accommodate the globes to both these modes of reckoning the longitude, the equator is usually divided both ways, in a continued series from 0° at the first meridian to 360°.

It is evident, that as the parallels of latitude become smaller as they approach the poles, the arcs of these parallels intercepted between the same two meridians will be also smaller as we proceed from the equator to the poles, though in fact they consist of the same absolute number of degrees. Hence it will be easy to see that a degree of longitude must be smaller towards the poles than at the equator, and must become gradually smaller and smaller till we arrive at the poles, where it will be equal to nothing. Thus the arc G v. contains the same number of degrees as the arc a, m, though the former arc is much smaller than the latter. As a degree of longitude is therefore different at every degree of latitude, it becomes necessary to ascertain the relative proportion between the two; and for this purpose the following table has been constructed, which shows the absolute measure of a degree of longitude in geographical miles and parts of a mile for every degree of latitude, taking the degree of longitude at the equator, equal to 60 geographical miles. ### Table I. Shewing the length of a degree of longitude for every degree of latitude, in geographical miles.

| Lat. | Geo.miles | Lat. | Geo.miles | Lat. | Geo.miles | Lat. | Geo.miles | Lat. | Geo.miles | |------|-----------|------|-----------|------|-----------|------|-----------|------|-----------| | 1 | 59.96 | 16 | 57.60 | 31 | 51.43 | 46 | 41.68 | 61 | 29.04 | | 2 | 59.94 | 17 | 57.30 | 32 | 50.88 | 47 | 41.00 | 62 | 28.17 | | 3 | 59.92 | 18 | 57.04 | 33 | 50.32 | 48 | 40.15 | 63 | 27.24 | | 4 | 59.86 | 19 | 56.73 | 34 | 49.74 | 49 | 39.36 | 64 | 26.30 | | 5 | 59.77 | 20 | 56.38 | 35 | 49.15 | 50 | 38.57 | 65 | 25.36 | | 6 | 59.67 | 21 | 56.00 | 36 | 48.54 | 51 | 37.73 | 66 | 24.41 | | 7 | 59.56 | 22 | 55.63 | 37 | 47.92 | 52 | 37.00 | 67 | 23.45 | | 8 | 59.49 | 23 | 55.23 | 38 | 47.28 | 53 | 36.18 | 68 | 22.48 | | 9 | 59.20 | 24 | 54.81 | 39 | 46.62 | 54 | 35.26 | 69 | 21.51 | | 10 | 59.08 | 25 | 54.38 | 40 | 46.00 | 55 | 34.41 | 70 | 20.52 | | 11 | 58.89 | 26 | 54.00 | 41 | 45.28 | 56 | 33.55 | 71 | 19.54 | | 12 | 58.68 | 27 | 53.44 | 42 | 44.95 | 57 | 32.67 | 72 | 18.55 | | 13 | 58.46 | 28 | 53.00 | 43 | 43.88 | 58 | 31.79 | 73 | 17.54 | | 14 | 58.22 | 29 | 52.48 | 44 | 43.16 | 59 | 30.90 | 74 | 16.53 | | 15 | 58.00 | 30 | 51.96 | 45 | 42.43 | 60 | 30.00 | 75 | 15.52 |

As it is often more convenient to estimate degrees of longitude in English statute miles, we have added the following

### Table II. Shewing the length of a degree of longitude for every degree of latitude, in English statute miles.

| Lat. | Eng.miles | Lat. | Eng.miles | Lat. | Eng.miles | Lat. | Eng.miles | Lat. | Eng.miles | |------|-----------|------|-----------|------|-----------|------|-----------|------|-----------| | 0 | 60.2000 | 16 | 66.5192 | 32 | 58.6851 | 48 | 46.3038 | 64 | 30.3352 | | 1 | 60.1896 | 17 | 66.1760 | 33 | 58.0360 | 49 | 45.3994 | 65 | 29.2453 | | 2 | 60.1578 | 18 | 65.8134 | 34 | 57.3966 | 50 | 44.4811 | 66 | 28.1464 | | 3 | 60.1052 | 19 | 65.4300 | 35 | 56.6852 | 51 | 43.5489 | 67 | 27.0385 | | 4 | 60.0312 | 20 | 65.0265 | 36 | 55.9842 | 52 | 42.6237 | 68 | 26.9230 | | 5 | 60.0363 | 21 | 64.6937 | 37 | 55.2659 | 53 | 41.6453 | 69 | 25.7992 | | 6 | 60.0208 | 22 | 64.1629 | 38 | 54.5303 | 54 | 40.6751 | 70 | 23.6678 | | 7 | 60.0845 | 23 | 63.6986 | 39 | 53.7788 | 55 | 39.6917 | 71 | 22.5294 | | 8 | 60.0567 | 24 | 63.2177 | 40 | 53.0100 | 56 | 38.6959 | 72 | 21.3842 | | 9 | 60.0381 | 25 | 62.7167 | 41 | 52.2259 | 57 | 37.6891 | 73 | 20.2320 | | 10 | 60.0148 | 26 | 62.1903 | 42 | 51.4233 | 58 | 36.6705 | 74 | 19.0743 | | 11 | 60.0288 | 27 | 61.6579 | 43 | 50.6094 | 59 | 35.6408 | 75 | 17.9103 | | 12 | 60.0680 | 28 | 61.1001 | 44 | 49.7783 | 60 | 34.6000 | 76 | 16.7409 | | 13 | 60.0426 | 29 | 60.5237 | 45 | 48.9313 | 61 | 33.5489 | 77 | 15.5665 | | 14 | 60.0148 | 30 | 59.9293 | 46 | 48.0705 | 62 | 32.4873 | 78 | 14.3874 | | 15 | 60.0424 | 31 | 59.3162 | 47 | 47.1944 | 63 | 31.4161 | 79 | 13.2041 |

Hence it appears that the degrees of latitude are all equal, and that a degree of longitude at the equator is equal to a degree of latitude, as each is \( \frac{1}{360} \)th of a great circle. In the second of the above tables, a degree of longitude at the equator is estimated at 69.2 English miles, or about 69\(\frac{1}{2}\). The length of a degree in miles is usually estimated at 69\(\frac{1}{2}\), but this is too much. Hence, to reduce degrees of latitude, and those of longitude near the equator, to English miles, it is necessary to multiply them by 69.2, or, if great accuracy is not required, by 70.

**Problem I. To find the latitude and longitude of a given place.**

Bring the place below the graduated edge of the **brass meridian**, and the degree of the meridian that lies immediately over the place is its **latitude**. Observe where the meridian cuts the equator, and that degree will be the **longitude** of the place.

**Example.** To find the latitude and longitude of Edinburgh.—Bringing Edinburgh below the meridian, we find over it nearly the 56th degree of north latitude (55° 58'), and the point where the meridian cuts the equator is nearly 3\(\frac{1}{2}\) (3° 12' W. Long.) degrees west from London.

N. B. The longitude and latitude of places cannot be ascertained exactly by the globes, as these are not calculated to show the fractional parts of a degree; but they may be found with sufficient correctness for ordinary purposes.

**Corollary I.** The difference of latitude and longitude The construction of the hour circles was rendered somewhat more simple by Mr G. Wright of London. In his globes, there are engraved two hour circles, one at each pole, on the map of the globe, each circle being divided into a double set of 12 hours, as in the usual hour circles; but here the hours are numbered both to the right and left. (See fig. 4.) The hour hand, or index, is placed below the brazen meridian, in such a way that it may be moved at pleasure to any required part of the circle, and remain there sufficiently steady during the revolution of the globe on its axis, being entirely independent of the pole. In this manner the motion of the globe round its axis, carrying the hour circle, the time is pointed out by the stationary index.

In the globes constructed by the late Mr George Adams, the equator is made to answer the purpose of an hour circle, by means of a semicircular wire placed in its plane, (see Q F, fig. 5.) and carrying two indices F, one on the eastern, the other on the western, side of the brazen meridian. The method of using these indices will be shewn presently. In these globes the equator is also marked with twice 12 hours, which increase from east to west, the hours to the west of the first 12 being afternoon hours.

**Problem III.** The hour at any place being given, to find what hour it is at any other place.

*a.* By the ordinary globes.

Bring the place at which the hour is given to the meridian, and set the index of the hour circle to the given hour. Then turn the globe till the other place comes under the meridian, and the index will now point to the hour required.

N. B. Where there is no index, the edge of the meridian will in both cases point out the hour.

*b.* By Adams's globes.

The steps are here the reverse of the former. Bring the place at which the time is required to the brazen meridian, and set the index to the given hour. Then turn the globe till the other place comes below the meridian, and the index will shew the time required.

N. B. In the ordinary globes, where the hour circle is usually marked with two sets of figures, it is proper, in performing this problem, to make use of that set which increases towards the right hand, observing that whichever XII. is fixed on for noon, the hours to the right or east of this are hours P. M., and those to the left or west are hours A. M. On Adams's globes the contrary of this takes place, from the hours being marked on the equator. They increase from east to west, and, of course, those to the east of XII. are morning hours, and those to the west of it afternoon hours.

*Example 1.* When it is noon at London, what hour is it in the Society isles? Ans. Two A. M.

*Ex. 2.* When it is 3 P. M. at Edinburgh, what hour is it at Delhi in Hindoostan? Ans. Thirty minutes past eight P. M. Problem IV. Having the hour at any place given, to find all those places where it is noon.

a, By the ordinary globes.

Bring the given place to the meridian, and set the index to the given hour. Then turn the globe till the index point to 12 at noon, and the places then under the meridian are those required.

b, By Adams's globes.

Bring the given place to the meridian, and set the index to 12 at noon. Then turn the globe till the index shall point to the given hour; and all the places then under the meridian have noon at that time.

Ex. 1. It is now 30 min. past 10 A.M. at Edinburgh; In what places is it noon? Ans. Near Stockholm; at Dantzig, Breslaw, Presburg, Vienna, Posegu, Ragusa, Tarento, and the Cape of Good Hope.

Ex. 2. It is now midnight at London; Where is it noon? Ans. In the north-east parts of Asia, in the middle of Fox isles; at the Friendly isles (nearly), and at the east cape of New Zealand.

From the different situation of places with respect to latitude and longitude, the inhabitants of these places received from the ancients denominations that are still retained.

Thus, those places which have the same longitude, or are situated under the same meridian, but are in opposite latitudes, the one lying as many degrees to the north of the equator as the other lies to the south of it, are said to be antocii to each other. From this definition it is evident, that those places situated under the equator have no antocii.

The appearances arising from the changes of the heavenly bodies are different in the opposite places. Thus, 1. The days of the one are equal to the nights of the other, and vice versa; but they have noon, midnight, and all the other hours at the same time. 2. They have contrary seasons at the same time: when it is summer at one place it is winter at the other, and so of spring and autumn. 3. The stars that never set at one place, never rise at the other, and vice versa.

Again, those places that have the same latitude, or are under the same parallel, but are in opposite longitudes, i.e. lie under opposite arcs of the same meridional circle, or 180° from each other, are said to be periocii to each other. Those places which may be situated at the poles, have evidently no periocii.

The celestial appearances to the periocii are as follow. 1. The length of the day or night is the same to both places; but the hours, though distinguished by the same numbers, are contrary; noon at the one being midnight at the other; and any hour in the forenoon at the one being the same of the afternoon to the other. 2. Both places have the same seasons of the year at the same time. 3. The same stars that never rise or set to one place, also never rise or set to the other. 4. The heavenly bodies rise in the same point of the horizon at both places, and continue for the same interval above or below it.

Lastly, Those places which are situated directly opposite to each other, by a distance equal to the diameter of the earth, are said to be antipodes to each other. If we conceive a line through the centre of the earth, and terminated in two points of its surface, these points extreme points are antipodes to each other. Thus, the city of Lima in Peru is nearly the antipodes to Siam in the East Indies; and Pekin in China has for its antipodes Buenos Ayres in South America. These places are always in opposite longitudes, and (except under the equator) in opposite latitudes.

The celestial appearances to the antipodes are these. 1. The hours are contrary, as to the periocii. 2. The days of the one are of the same length with the nights of the other; hence the longest day to one is the shortest to the other, and vice versa. 3. They have contrary seasons at the same time. 4. Those stars which, at one place are always above the horizon, are, to the other, always below it. 5. When the heavenly bodies are rising at one place, they are setting at its antipodes, and vice versa. For various opinions respecting the antipodes, see the article Antipodes.

The antipodes of any places are the periocii to the antocii of that place; and the antocii to their periocii. This will account for the method presently described of finding the antipodes on the globe.

Problem V. To find the antocii to any given place.

Bring the given place to the meridian, and thus ascertain its latitude. Then count from the equator towards the opposite pole as many degrees as are equal to the latitude of the place; and the point where this reckoning ends is the place required.

Ex. 1. Where are the antocii to the Cape of Good Hope? Ans. At Malta nearly.

Ex. 2. What people are the antocii to the inhabitants of Quebec in North America? Ans. The inhabitants of Patagonia in South America.

Problem VI. To find the periocii of any given place.

Bring the given place to the brazen meridian, and set the horary index to the upper XII. Then turn the globe till the index point to the lower XII. The place which is then below the meridian in the same latitude with that of the given place, is the situation required.

Ex. 1. Where are situated the periocii of Newcastle upon Tyne? Ans. In the Aleouski or Fox islands.

Ex. 2. Required the periocii to California in North America. Ans. Near the mouth of the river Indus.

Problem VII. To find the antipodes to any given place.

Find the antocii of the given place (by Problem V.) and then find the periocii of the latter (by Problem VI.). This last is the place required.

Ex. 1. It is required to find the antipodes of London. Ans. The latitude of London is 51° 31' N., the antocii to this, or 51° 31' S. on the prime meridian, is in the south Atlantic ocean; the periocii to this is 180° W. Long. and 51° 31' S. Lat. a little to the south of the islands of New Zealand. The inhabitants of the southern island of New Zealand are therefore the nearest antipodes to London.

Several other circles besides those which we have mentioned are described on the artificial globe, and are supposed to be drawn on the earth. These we shall now proceed to describe, and explain their geographical uses. The Ecliptic (Astronomy, No. 43.) is a great circle drawn on the globe, crossing the equator obliquely in two points, called the equinoctial points. (Astronomy, No. 44.) This circle extends on each side of the equator to the latitude of 23° 28', and is divided into 12 great parts corresponding to the 12 signs of the zodiac (see Astronomy, No. 52.), and marked with their characters, and each sign is subdivided into 30 degrees. The ecliptic has also its poles, which are two points that are distant 90° every way from the circle on each side. As the ecliptic declines from the equator 23° 28', its poles are consequently distant from those of the equator, or of the globe, by the same measure. This circle properly belongs to the celestial globe, but as it is extremely useful in performing many geographical problems, it is always drawn on both globes, and requires to be noticed here, since it determines the position of several of the circles which we are about to mention.

Through those two points of the ecliptic, where it is at the greatest distance from the equator, there are drawn on the globes two circles parallel to the equator, called tropics. That in the northern hemisphere is called the Tropic of Cancer, as it passes through the sign Cancer; and, for a similar reason, that which is in the southern hemisphere is called the Tropic of Capricorn. The two points through which they are drawn are called solstitial points. The imaginary line which corresponds to the tropic of Cancer on the earth passes from near Mount Atlas on the western coast of Africa, past Syene in Ethiopia: thence, over the Red sea, it passes to Mount Sinai, by Mecca the city of Mahomet, across Arabia Felix to the extremity of Persia, the East Indies, China, over the Pacific ocean to Mexico, and the island of Cuba. The tropic of Capricorn takes a much less interesting course, passing through the country of the Hottentots, across Brazil, to Paraguay and Peru.

If the poles of the ecliptic be supposed to revolve about the poles of the earth, they will describe two circles parallel to the equator, and 23° 28' distant from it. Two such circles are drawn on the globes, and are called Polar Circles, that in the north being called the Arctic Polar Circle, or merely the Arctic Circle, while that in the south is called the Antarctic Polar Circle, or Antarctic Circle.

Both the tropics and the polar circles are marked on the globes by dotted lines, to distinguish them from the other parallels.

The meridional circles that pass through the equinoctial and solstitial points are called Colures; the former being called the Equinoctial and the latter the Solstitial Colure.

For an account of the variety of day and night in different parts of the globe, see Astronomy, Part II. ch. i. sect. 2.

By means of the tropics and polar circles, the earth is supposed to be divided into five spaces, to which the ancients gave the name of Zones, or Belts. Thus the space included between the two tropics was called the Torrid Zone, because it was supposed to be so much heated or roasted by the vertical sun, which there prevails, as to be uninhabitable. The ancient terms are still occasionally used, but the countries between the tropics are now more commonly called the Intratropical Regions. The two spaces included between each tropic and its corresponding polar circle were called Temperate Zones, and were distinguished according to their position into Northern and Southern Temperate Zones. Lastly, the spaces between the polar circles and the poles were called the northern and southern Frigid Zones, and were supposed uninhabitable from excessive cold. These last are usually denominated the Polar Regions.

The countries lying between the tropics are the greater part of Africa, the southern parts of Arabia, between the eastern and western peninsulas of India; all those clusters of islands lying between the southern continent of Asia and New Holland, called the Sunda, Molucca, Philippine, Pelew, Ladrone, and Carolina islands; the northern half of New Holland, New Guinea, New Britain; most of the groups of islands in the Pacific ocean, as the New Hebrides, New Caledonia, the Friendly and Society isles, the Sandwich and Navigators isles; the West India islands; the greater part of South America; the Cape de Verd islands, and those of St Helena, Ascension, St Matthew, and St Thomas. See the map of the world in Plate CCXXXVI. or the plain chart in Plate CCXXXVII.

All places situated between the tropics have the sun vertical twice in the year, at noon; but the time of the year when this happens is different in the different latitudes; at the equator, the sun is vertical when he is in the equinoctial points, or when he has no declination. The inhabitants of the other intratropical regions have the sun vertical when his declination is equal to their latitude, and on the same side of the equator. Thus, the inhabitants of New Caledonia, about 22° S. Lat., have the sun vertical when his declination is 20° S. To illustrate this, it will be sufficient to observe that, as the ecliptic is that circle in the heavens in which the sun is supposed to move, the sun's rays are perpendicular successively to every point of the earth which lies below that point of the ecliptic in which the sun happens to be, and he will therefore be vertical to all the places through which the ecliptic (continued to the earth) passes successively.

The inhabitants of the torrid zone have their shadows at noon day sometimes to the south, i.e. when the sun's declination is north, and sometimes to the north, i.e. when the sun's declination is south. They were therefore called by the ancients Amphiscii, from ἀπό, about, and σκιά, shadow. See AMPHISCII and ASCII.

In the north temperate zone are situated the whole of Europe except Lapland; Barbary, and part of Egypt, in the temple in Africa; nearly the whole continent of Asia; a great part of North America; the Azores, and the Canary and Madeira islands.

In the south temperate zone lie the southern part of Africa, the southern half of New Holland, New Zealand, and the southern part of South America.

In the temperate zones the sun is never vertical, and the length of the days and nights differs much more than in the torrid zone.

The inhabitants of these regions have their shadows Heteroscii, at noon always in the same direction; those in the north temperate zone having them directed to the north, The countries that are situated in the northern frigid zone, are Lapland, Spitzbergen, Nova Zembla, the northern parts of Asia and America, and part of Greenland.

No land has yet been discovered within the south polar circle, though it was long supposed that a large continent was situated there, which was called Terra Australis Incognita. Our celebrated navigator Cook made many attempts to penetrate the icy fields which abound in these seas, in search of this imaginary continent, but without success, he having penetrated no farther than 72°. See Cook's Discoveries, No. 49. and 71.

Within the polar circles the sun does not always rise or set every 24 hours as in the other zones; but for a certain number of days in summer he never sets, and for a certain number of days in winter he never rises; the number of days during which the sun is present or absent increasing from the polar circles to the poles, so that at the poles he never sets for six months, nor rises during a like period.

When the sun continues above the horizon more than 24 hours, the inhabitants of the polar regions have their shadows cast all around them; and hence they have been called Periscii. See Periscii.

The ancients did not employ regular parallels of latitude, but they divided the spaces between the equator and the poles into small zones corresponding to the length of the longest day in each division. To these subdivisions they gave the name of climates, the situation and extent of which they determined in the following manner. As the day at the equator is exactly 12 hours throughout the year, but the longest day increases as we approach the poles, the ancients made the first climate to end at that latitude where the longest day was 12½ hours, which by observation they found to be in the latitude of 8° 25′. The second climate extended to latitude 16° 25′, where the longest day is 13 hours, and thus a new climate extended, so as to divide the whole tract between the equator and the poles into 24 climates, in each of which the longest day was longer by half an hour than in that nearer the equator.

The space between the polar circles and the poles they divided into six climates, in each of which the length of the longest day increased by a month, till at the poles it was six months long. Hence, the 24 climates between the equator and the polar circles are called Hour Climates; and the six between the polar circles and the poles are called Month Climates. For further particulars respecting this ancient division of the globe, and a table of the climates by Ricciolus, see Climate.

As the table given under that article is calculated only for the middle of each climate, and neither mentions the breadth of each, nor is extended to all the climates, we shall here subjoin one in which are given the latitude at which each climate terminates, its breadth in degrees, and the length of the longest day at the parallel terminating each.

### Hour Climates

| Climates | Latitude | Breadth | Longest Days | |----------|----------|---------|--------------| | I | 8° 25′ | 8° 25′ | 12h 30m | | II | 16° 25′ | 8 | 13 | | III | 23° 50′ | 7 25 | 13 30 | | IV | 30° 25′ | 6 30 | 14 | | V | 36° 28′ | 6 | 14 30 | | VI | 41° 22′ | 4 54 | 15 | | VII | 45° 29′ | 4 7 | 15 30 | | VIII | 49° 1 | 3 32 | 16 | | IX | 52° | 2 57 | 16 30 | | X | 54° 27′ | 2 29 | 17 | | XI | 56° 37′ | 2 10 | 17 30 | | XII | 58° 29′ | 1 58 | 18 | | XIII | 59° 38′ | 1 29 | 18 30 | | XIV | 61° 18′ | 1 20 | 19 | | XV | 62° 25′ | 1 7 | 19 30 | | XVI | 63° 22′ | 0 52 | 20 | | XVII | 64° | 0 44 | 20 30 | | XVIII | 64° 49′ | 0 43 | 21 | | XIX | 65° 21′ | 0 32 | 21 30 | | XX | 65° 45′ | 0 26 | 22 | | XXI | 66° | 0 19 | 22 30 | | XXII | 66° 20′ | 0 14 | 23 | | XXIII | 66° 28′ | 0 8 | 23 30 | | XXIV | 66° 31′ | 0 3 | 24 |

### Month Climates

| Climates | Latitude | Breadth | Longest Day | |----------|----------|---------|-------------| | I | 67° 21′ | 50′ | 1 month | | II | 69° 48′ | 2° 27′ | 2 | | III | 73° 37′ | 3 49 | 3 | | IV | 78° 30′ | 5 8 | 4 | | V | 84° 5 | 5 35 | 5 | | VI | 90° | 5 55 | 6 |

As the division of the globe into climates, though now almost disused, is of service in shewing the length of the longest day in different countries, we shall here enumerate the principal places in each northern climate, these being best known and most interesting.

I. The Gold and Silver Coasts in Africa; Malacca in the East Indies; and Cayenne and Surinam in South America.

II. Abyssinia in Africa; Siam, Madras, and Pondicherry, in the East Indies; the isthmus of Darien; Tobago, the Grenades, St Vincent, and Barbadoes, in the West Indies.

III. Mecca in Arabia; Bombay, part of Bengal, in the East Indies; Canton in China; Mexico and the bay of Campeachy, in North America; and Jamaica, Hispaniola, St Christopher's, Antigua, Martinique, and Guadaloupe, in the West Indies. IV. Egypt and the Canaries in Africa; Delhi, the capital of the Mogul empire, in Asia; most of the gulf of Mexico, and East Florida, in North America; and the Havannah in the West Indies.

V. Gibraltar; part of the Mediterranean sea; the Barbary coast in Africa; Jerusalem, Ispahan, capital of Persia, and Nankin, in China, in Asia; and California, New Mexico, West Florida, Georgia, and the Carolinas in North America.

VI. In Europe, Lisbon, Madrid, the islands of Minorca and Sardinia, and part of Greece or the Morea; in Asia, Asia Minor, part of the Caspian sea, Samarand, Pekin, Corea, and Japan; and in North America, Maryland, Philadelphia, and Williamsburgh in Virginia.

VII. In Europe, the northern provinces of Spain, the southern provinces of France, Turin, Genoa, Rome, and Constantinople; in Asia, the rest of the Caspian, and part of Tartary; and in North America, Boston and New York.

VIII. Paris and Vienna, in Europe; and New Scotland, Newfoundland, and Canada, in North America.

IX. London, Flanders, Prague, Dresden, Cracow, in Europe; the southern provinces of Russia, and the middle of Tartary in Asia; and the northern part of Newfoundland, in America.

X. Dublin, York, Holland, Hanover, Warsaw; the west of Tartary, Labrador, and New South Wales, in North America.

XI. Newcastle, Edinburgh, Copenhagen, and Moscow.

XII. Southern part of Sweden; and Tobolsk in Siberia.

XIII. Stockholm; and the Orkney isles.

XIV. Bergen in Norway, and St Petersburg.

XV. Hudson's Straits in North America.

XVI. Most of Siberia; and the southern parts of Greenland.

XVII. Drontheim in Norway.

XVIII. Part of Finland in the Russian empire.

XIX. Archangel on the White sea.

XX. Iceland.

XXI. Northern parts of Russia in Europe, and Siberia in Asia.

XXII. New North Wales, in North America.

XXIII. Davis's Straits, in North America.

XXIV. Samoieda in Asia.

XXV. Northern parts of Lapland.

XXVI. West Greenland.

XXVII. Southern part of Nova Zembla.

XXVIII. Northern part of Nova Zembla.

XXIX. Spitzbergen.

XXX. Unknown.

The only parts of the terrestrial globe that we have yet to describe and illustrate are the Quadrant of Altitude, and the Wooden Horizon; and these it is necessary to explain, before we proceed to consider the remaining problems performed with this globe.

The Quadrant of Altitude is a thin flexible slip of brass, graduated into 90°, and made to fix on any part of the brazen meridian by means of a nut and screw. Round this nut it moves on a pivot, and by its flexibility may be applied close to the surface of the globe. The quadrant of altitude is used to measure the distances of places from each other on the terrestrial globe, and to ascertain the altitudes of the sun, stars, &c., on the celestial globe.

To measure the distance between two places on the globe, nothing more is required than to stretch the graduated edge of the quadrant between them, and mark the number of degrees intercepted. These reduced to geographical, or to English miles (by No. 63.) give the absolute distance between the places. It is most convenient to bring one of the places to the zenith, which may be done by rectifying the globe for the latitude of that place as immediately to be explained, and then to stretch the quadrant to the other place; the distance marked, subtracted from 90°, gives the true distance in degrees. If the distance required be greater than 90°, it is proper to rectify the globe for the antipodes of the given places, and add the distance observed to 90°; the sum is the distance required.

It has been very generally stated that the bearing of one of the places from the other may be found by observing, on the wooden horizon, in what point of the compass the quadrant of altitude, thus fixed in the zenith, cuts the horizon. This is considered by Mr Patteson as a mistake: "For (says he) supposing one of the places to lie due east of the other, they are in the same parallel of latitude, and consequently it is impossible that the prime vertical of either of them (that is, a circle cutting the east and west points of the horizon), should pass through the other, unless they both lay under the equator. A line shewing the bearings of places is called a rhumb line. The lines of north and south on the globe, being meridians, and those of east and west being parallels of latitude, are consequently circles; but all the remaining rhumbs are a kind of spiral lines."

The globes are supported by a wooden frame ending above in a broad flat margin, on which is pasted a paper marked with several graduated circles. This broad margin is called the wooden horizon, and represents the rational horizon of the earth, or the limit between the visible and the invisible hemispheres. On the paper with which the wooden horizon is covered, are drawn four concentric circles. The innermost of these is divided into 360 degrees, divided into four quadrants. The second circle is marked with the points of the compass, i.e. the four cardinal points, east, west, north, and south (D), each being subdivided into eight parts or rhumbs, (see Compass). The circle next to that just mentioned contains the twelve signs of the zodiac, distinguished by their proper names and characters; and

(d) The cardinal points of the compass are thus determined. The two points in which the meridian of any place when produced so as to pass through the nearest pole, cuts the horizon, (using this in an astronomical sense, see Astronomy,) are the north and south points; the former being that point where the meridian first cuts the horizon in the northern hemisphere, and the south, that where it first meets the horizon in the southern hemisphere. Again, the two points where a great circle, passing through the zenith at right angles with the meridian, (and and each sign is divided into 30 degrees. The last circle shews the months and days corresponding to each sign.

This wooden ring can represent the rational horizon of any place marked on the terrestrial globe only, when that place is situated in the zenith; and the method of bringing the place into this situation is called rectifying the globe.

To rectify the globe.

**Problem VIII. To rectify the globe according to the latitude of any place.**

Find the latitude of the place, (by Problem I.) and see whether it be north or south. Then elevate the pole of the globe which is in the same hemisphere with the latitude, as far above the wooden horizon as is equal to the latitude; bring the given place to the brazen meridian, and it will be in the zenith.

*Example.* To rectify the globe for the latitude of Edinburgh. The latitude of Edinburgh is $55^\circ 58'$ N., therefore raise the north pole $55^\circ 58'$ above the horizon, and bring Edinburgh below the brass meridian.

It is for the purpose of more easily rectifying the globe, that one half of the brazen meridian is graduated from the poles to the equator; as, where this is not done, it is necessary to take the complement of the latitude, or the difference between it and $90^\circ$, which in some cases requires a calculation.

The place being brought below the meridian, when the pole is elevated to the proper degree, it is evidently in the zenith, or $90^\circ$ distant every way from the horizon. Thus, in the above example, if we count the degrees from that part of the meridian below which Edinburgh is situated, we shall find that they amount to $90^\circ$ each way; for counting from Edinburgh along the meridian to the north pole, we have $34^\circ 2'$; which added to $55^\circ 58'$, the elevation of the poles, gives $90^\circ$ on that side. Again, counting from the same point of the meridian towards the southern part of the horizon, we have $55^\circ 58'$, as far as the equator, and $34^\circ 2'$ from thence to the horizon, making, as before, $90^\circ$, and as the graduated edge of the meridian is $90^\circ$ both from the eastern and western side of the horizon, Edinburgh, in this situation of the globe, is in the zenith.

When either of the poles of the globe is thus elevated above the horizon, so as not to be in the zenith, the globe is said to be in the position of an oblique sphere, in which the equator and all its parallels are unequally divided by the horizon. This is the most common situation of the earth, or it is the situation which it has with respect to all its inhabitants, except those at the equator and the poles. To the inhabitants of an oblique sphere the pole of their hemisphere is elevated above the horizon as many degrees as are equal to their latitude, and the opposite pole is depressed as much below the horizon, so that the stars only at the former are seen; the sun and all the heavenly bodies rise and set obliquely, the seasons are variable, and the days and nights unequal. This position of the sphere is represented at fig. 6, where the equator EQ, and the parallels cut the horizon HO obliquely, and the axis PS is inclined to it. Hence this position is called oblique.

If the globe is placed in such a position that any point of the equator is in the zenith, it is said to be in the position of a right or direct sphere, because the equator and its parallels are vertical, or over the horizon at right angles. This position is seen at fig. 7, where the axis PS is in the plane of the horizon, and the equator EQ is in a plane perpendicular to it. The inhabitants of such a sphere, which are the inhabitants of the earth below the line, have no elevation of the poles, and consequently no latitude: they can see the stars at both poles, all the stars rise, culminate, and set to them; and the sun always moves in a curve at right angles to their horizon, and is an equal number of hours above and below it, making the days and nights always equal.

If the globe be so placed that one of the poles is in the zenith, and consequently the other in the nadir, it is in the position of a parallel sphere; so called because the equator EQ (fig. 8.) coincides with the horizon, and the parallels are of course parallel to it; while all the meridians cut the horizon at right angles. The inhabitants of a sphere, in this position, have the greatest possible latitude; the stars, which are situated in the hemisphere to which the inhabitants belong, never set, but describe circles all around; while those of the contrary hemisphere never rise: the sun is above the horizon for six months, during which it is day, and is below the horizon for an equal interval, when it is night.

The wooden horizon is a necessary part of the apparatus of both globes; but it has been shewn, that in the terrestrial globe, it can represent the rational horizon of a place, only when the globe is rectified for the latitude of that place. In the celestial globe, it represents the rational horizon in all positions.

In Adams's globes there is a thin brass semicircle NHS (fig. 5.) that is moveable about the poles, and has a small thin circle N sliding on it. This semicircle is graduated into two quadrants, the degrees of which are marked both ways from the equator to the poles in the terrestrial globe: this semicircle represents a moveable meridian; and the small sliding circle, which is marked with a few of the points of the compass, is called a visible horizon, the use of which will appear presently.

Before we proceed to the remaining problems on the terrestrial globe, it will be proper to take notice of some geographical principles that are connected with the horizon.

It is evident, that the extent of the sensible horizon of an observer depends on the height of his eye above the level surface of the earth. An eye placed on the surface of the earth sees scarcely any thing around it; but if it is elevated above that surface, it sees farther in proportion to its elevation, provided always that its view is not obstructed by intervening objects. Thus, in an extensive plain, the eye can see farther, if elevated to

called the prime vertical) cuts the horizon, are the east and west points; the former being on the left hand of a person facing the sun at noonday, while the latter is on his right hand. to a proper height, than it can from the same height in a town or among hills; and, at sea, where the surface is perfectly equal, the view is in proportion to the height of the eye. It becomes an interesting problem to ascertain the extent of the visible horizon, or the distance to which a person can see at any given height of the eye; as, when this is known, we can calculate pretty accurately the distance of an object seen from such a height, as land seen from the topmast of a ship at sea.

For solving this problem, it must be remarked, that the distance of an observer from the boundary of the horizon, or from a distant object, is different when measured along the surface of the earth, and when measured in a direct line. To illustrate this, let HDN (fig. 9.) represent a section of the earth, of which C is the centre, and let D be the situation of an observer, whose eye is elevated to B. The lines BA, BE, tangents to the curve at H and E, represent the limit of the visible horizon, or the radii of the circle circumscribing vision. If the eye were elevated still higher, as to G, it is evident, that the extent of the visible horizon will be increased, being now represented by the tangent GF. The length of the tangent BA, or GF, is easily found by plane trigonometry (E).

It was remarked above, that the visible horizon is most distinct at sea, from the absence of those objects which obstruct vision on land. Hence the sensible horizon is sometimes called the horizon of the sea, and this may be observed by looking through the sights of a quadrant at the most distant part of the sea. In making this observation, the visual rays BA, or GF, by reason of the spherical surface of the sea, always extend a little below the true sensible horizon SS, and consequently below the rational horizon HN, which is parallel to it. Hence the quadrant shews the depression of the horizon of the sea lower than it really is; and it is obvious from the figure, that the higher the eye is situated, the greater must be this depression. Thus, the depression, when the eye is at G, marked by GF, is evidently much greater than that marked by BE, when the eye is at B. The depression of the horizon of the sea is not always the same, though there be no variation in the height of the eye; but the difference in this case is very small, amounting only to a few seconds, and is owing to a difference of the degree of refraction in the atmosphere. Were there no refraction, the visual ray would be BE (when the eye is at B), and F would be the most distant point; but, by reason of the refraction, a point on the surface of the earth beyond E, as F, may be seen by an eye situated no higher than B; and if the refraction were still greater, a still more distant point might be observed.

It will be necessary here to anticipate a few remarks respecting the difference between the apparent and true levels; a subject that will be more fully discussed under Levelling. Two or more places are on a true level, when they are equally distant from the centre of the earth, and one place is higher than another, or above the true level, when it is farther from the centre of the earth. A line that is equally distant in all its points from the centre, is called the line of true level, and it is evident that this line must be curved: and either make part of the earth's surface, or be concentrical with it. Thus the line DAO, which has all its points, D, A, O, equally distant from the centre C, is the line of true level. But the line of sight DMP, as given by the operation of a level, is a straight line, which is a tangent to the earth's surface at D, always rising higher above the true line of level, according as it extends to a greater distance. This straight line is called the line of apparent level. Thus MA is the height of the apparent level above the true at the distance DA, and OP is the excess of the apparent above the true level, at the distance DO.

The following table was constructed by Cassini, for the purpose of shewing the excess of the apparent above the true level at various distances from the point of observation. It consists of three columns, in the first of which the distance of the observed object from the place of observation is given, from one second to 60 minutes, or a degree. In the second is given the length of the arc measured on a great circle of the earth, that corresponds to the observed distance, in feet and inches; and in the third is given the height of the apparent above the true level in feet and inches, corresponding to each observed and real distance of the object.

(E) In the right-angled triangle ACB (fig. 9.), the length of CB is given, supposing the height of the eye BD to be 6 feet; for adding 6 feet to 19,943,400 feet, the length of the semidiameter of the earth, we have 19,943,406 feet for the length of BC. Then, making the hypotenuse CB radius, we shall have, As radius to the sine of the angle BCA, so is CB to BA; and this will be nearly the same as the arc DA. Again, without finding the quantity of the angle at C, BA may be found, by considering that BA² is equal to the difference of the squares of CB and CA, i.e. \(BA^2 = CB^2 - CA^2 = (CB + CA) \times (CB - CA) = CB + CA\) into BD; and hence \(BA = \sqrt{(CB + CA) \times BD}\).

To illustrate the last in numbers, we have CB = 19,943,406 feet, and CA = 19,943,400 feet. Then, to find BA, we have \(19,943,406 + 19,943,400 = 39,886,806 \times 19,943,406 - 19,943,400 = 6 = 239,320,836\); whence \(BA = \sqrt{239,320,836} = 15470\) feet nearly, or about three miles.

The distance, to which a person can see, is found to vary as the square root of the altitude of the eye. To find a general expression for this quantity,

let \(a\) be the altitude of the eye in feet, \(d\) the distance at that altitude in miles;

then we have \(\sqrt{6} : \sqrt{a} = 3 : d = \frac{3}{\sqrt{6}} \times \sqrt{a} = 1.2247 \times \sqrt{a}\). Hence, we deduce this general rule: Multiply the square root of the height of the eye in feet by 1.2247, and the product will be the distance to which we can see. | Seconds | Feet | Inch | Inch | |---------|------|------|------| | 1 | 101 | 6.8 | | | 2 | 203 | 1.6 | | | 3 | 304 | 8.4 | | | 4 | 406 | 3.2 | | | 5 | 507 | 10.0 | 0.074| | 6 | 609 | 4.8 | | | 7 | 710 | 11.6 | | | 8 | 812 | 6.4 | | | 9 | 914 | 1.2 | | | 10 | 1015 | 8.0 | 0.296| | 11 | 1117 | 2.8 | | | 12 | 1218 | 9.6 | | | 13 | 1320 | 4.4 | | | 14 | 1421 | 11.2 | | | 15 | 1523 | 6.0 | | | 16 | 1625 | 0.8 | | | 17 | 1726 | 7.6 | | | 18 | 1828 | 2.4 | | | 19 | 1929 | 9.2 | | | 20 | 2031 | 4.0 | 1.186| | 21 | 2132 | 10.8 | | | 22 | 2234 | 5.6 | | | 23 | 2336 | 0.4 | | | 24 | 2437 | 7.2 | | | 25 | 2539 | 2.0 | | | 26 | 2640 | 8.8 | | | 27 | 2742 | 3.6 | | | 28 | 2843 | 10.4 | | | 29 | 2945 | 5.2 | | | 30 | 3047 | 0.0 | 2.670| | 31 | 3148 | 6.8 | | | 32 | 3250 | 1.6 | | | 33 | 3351 | 8.4 | | | 34 | 3453 | 3.2 | | | 35 | 3554 | 10.0 | | | 36 | 3656 | 4.8 | | | 37 | 3757 | 11.6 | | | 38 | 3859 | 6.4 | | | 39 | 3961 | 1.2 | | | 40 | 4062 | 8.0 | 4.746| | 41 | 4164 | 2.8 | | | 42 | 4265 | 9.6 | | | 43 | 4367 | 4.4 | | | 44 | 4468 | 11.2 | | | 45 | 4570 | 6.0 | | | 46 | 4672 | 0.8 | | | 47 | 4773 | 7.6 | | | 48 | 4875 | 2.4 | | | 49 | 4976 | 9.2 | | | 50 | 5078 | 4.0 | 7.409| | 51 | 5179 | 10.8 | | | 52 | 5281 | 5.6 | | | 53 | 5383 | 0.4 | | | 54 | 5484 | 7.2 | | | 55 | 5586 | 2.0 | | | 56 | 5687 | 8.8 | | | 57 | 5789 | 3.6 | | | 58 | 5890 | 10.4 | | | 59 | 5992 | 5.2 | | | 60 | 6094 | 0.0 | 10.680|

| Minutes | Feet | Feet | Inch | |---------|------|------|------| | 1 | 6094 | 0 | 10.680| | 2 | 12188| 3 | 6.580 | | 3 | 18282| 7 | 11.853| | 4 | 24376| 14 | 1.812 | | 5 | 30470| 22 | 1.932 | | 6 | 36564| 31 | 11.412| | 7 | 42658| 42 | 5.436 | | 8 | 48752| 56 | 9.384 | | 9 | 54846| 71 | 9.876 | | 10 | 60940| 88 | 7.728 | | 11 | 67034| 107 | 2.940 | | 12 | 73128| 127 | 7.512 | | 13 | 79222| 149 | 9.444 | | 14 | 85316| 173 | 8.736 | | 15 | 91410| 199 | 4.320 | | 16 | 97504| 226 | 9.264 | | 17 | 103598| 255 | 11.568| | 18 | 109692| 286 | 11.232| | 19 | 115786| 319 | 7.188 | | 20 | 121880| 354 | 0.504 | | 21 | 127974| 390 | 4.248 | | 22 | 134068| 428 | 5.352 | | 23 | 140162| 468 | 10.224| | 24 | 146256| 510 | 6.084 | | 25 | 152350| 553 | 11.232| | 26 | 158444| 599 | 1.776 | | 27 | 164538| 646 | 1.680 | | 28 | 170632| 694 | 10.944| | 29 | 176726| 745 | 5.568 | | 30 | 182820| 797 | 8.484 | | 31 | 188914| 851 | 9.828 | | 32 | 195008| 907 | 8.532 | | 33 | 201102| 955 | 3.528 | | 34 | 207196| 1024| 7.884 | | 35 | 213290| 1085| 9.600 | | 36 | 219384| 1148| 8.676 | | 37 | 225478| 1213| 5.112 | | 38 | 231572| 1277| 10.908| | 39 | 237666| 1348| 2.064 | | 40 | 243760| 1417| 1.764 | | 41 | 249854| 1496| 11.388| | 42 | 255948| 1569| 10.452| | 43 | 262042| 1638| 9.084 | | 44 | 268136| 1716| 0.108 | | 45 | 274230| 1794| 11.424| | 46 | 280324| 1875| 7.032 | | 47 | 286418| 1958| 0.000 | | 48 | 292512| 2042| 2.328 | | 49 | 298606| 2128| 2.016 | | 50 | 304700| 2215| 6.792 | | 51 | 310794| 2305| 5.472 | | 52 | 316888| 2396| 9.240 | | 53 | 322982| 2489| 10.368| | 54 | 329076| 2584| 8.856 | | 55 | 335170| 2681| 4.704 | | 56 | 341264| 2779| 9.912 | | 57 | 347358| 2880| 0.480 | | 58 | 353452| 2982| 0.408 | | 59 | 359546| 3085| 8.628 | | 60 | 365640| 3191| 2.208 |

From that height in miles. Example. Let the height of the eye be 49 feet. Multiply the square root of 49 or 7 by 1,2247, and we have 8.5729 or about 8½ miles for the distance to which the eye can see at the height of 49 feet. The above table will answer several useful purposes. In the first place, the height of the apparent level above the true may be found by it at any distance, from one second to one degree, or 69½ miles. Thus, at the distance of 30°—about 35 miles, we have 1828 feet for the length of the arch of a great circle on the earth, and corresponding to this we have 797 feet 8 inches 484 parts for the excess of the apparent level above the true. 2. The extent of the visible horizon corresponding to any height of the eye, may be found from the table by observation. The semidiameter of the horizon does not sensibly differ from an arc of a great circle on the earth, containing as many minutes and seconds as are equal to the angle of depression observed, and the number of feet contained in such an arc may be found in the table. Thus, if the depression, as observed by observation, be 40°, its semidiameter is also about 40°, and the length of the arc corresponding to it is 243,760 feet.

The following table, also taken from Cassini, shews the different depressions of the horizon of the sea at different heights of the eye, both by observation and calculation; with the difference betwixt the two occasioned by refraction.

| Height of the eye above the surface of the sea | Depression of the horizon of the sea | |-----------------------------------------------|-----------------------------------| | Feet. Inches. | Feet. Inches. | | 1157 | 6.9 | | | {32 30 by observation | | | {36 18 by calculation | | Difference by refraction | 3 48 |

| 775 | 2.3 | | | {27 0 by observation | | | {29 36 by calculation | | Difference by refraction | 2 36 |

| 571 | 11.0 | | | {24 0 by observation | | | {25 25 by calculation | | Difference by refraction | 1 25 |

| 387 | 3.4 | | | {19 45 by observation | | | {20 54 by calculation | | Difference by refraction | 1 9 |

| 288 | 4.3 | | | {15 0 by observation | | | {17 1 by calculation | | Difference by refraction | 2 1 |

In the above table, the depression, as estimated by calculation, is greater than that by observation in every case except the last, in which the latter is greater by two seconds than the former; but this difference was too small to be discovered by the instrument that Cassini employed.

Refraction lessens the angle of depression, by raising the objects observed; but as this refraction is itself variable, the depression and extent of the horizon also vary. We are informed by Cassini, that even in the finest weather he observed the refraction to differ at the same hour of different days, and at different hours of the same day. The truth of this observation may be easily ascertained by looking through a telescope furnished with cross hairs, and fixed in such a position that some highly elevated object, as the weathercock of a steeple, may be seen through it; for, on observing the weathercock at different times of the day, it will be seen sometimes on the centre of the object-glass; sometimes above, and sometimes below it. A similar experiment may also be made with plane sights fixed on a cross-staff. It has long been observed, that the top of a distant hill may sometimes, when the refraction is very great, be distinctly seen from a situation from which, at other times, when the refraction is much less, it is not discernible, even though the sky be very clear.

Many of the following problems may seem to belong to the celestial rather than the terrestrial globe; but as they may be solved equally well by means of both, and as persons not uncommonly possess a terrestrial globe without its usual companion, we shall throw as many problems as possible under this head.

**Problem IX. To find the sun's place in the ecliptic for any given time.**

Find the day of the month in the calendar on the wooden horizon; and opposite to it, in the adjoining circle, will be found the sign and degree in which the sun

From the above, it is easy to deduce the method of computing the distance of any object seen in the horizon from a certain height. Thus, suppose a man at the mast-head, 130 feet above the water, sees land or a ship just coming in sight. We know, that, at this height, an eye can see 14 miles, consequently the object seen will be about 14 miles or about five leagues distant. If the object is within the horizon, or nearer the place of observation, its distance may be calculated pretty exactly, by descending from the mast-head till the object just comes to the horizon; measuring the height at which this takes place, and thence computing the distance. sun is on the given day. Then look for the same sign and degree in the circle of the ecliptic drawn on the globe, and that is the sun's place at noon for the given time.

Ex. 1. What is the sun's place on the 4th of June? Ans. In $13^\circ 57'$ of the sign Gemini.

Ex. 2. Required the sun's place for the first day of every calendar month?

| Month | Sun's Place | |----------|-------------| | January | $11^\circ 23'$ | | February | $12^\circ 35'$ | | March | $11^\circ 9$ | | April | $11^\circ 56'$ | | May | $8^\circ 14$ | | June | $11^\circ 3$ | | July | $9^\circ 42'$ | | August | $9^\circ 18$ | | September| $9^\circ 9$ | | October | $8^\circ 27$ | | November | $9^\circ 16$ | | December | $9^\circ 33$ |

**Problem X. To find the sun's declination for any given time.**

Find the sun's place for the given day by Prob. X. and bring it to the brazen meridian. The degree marked on the meridian immediately over the place is the declination required.

Ex. Required the sun's declination for 18th March? The sun's place for the given day is $25^\circ 7'$ of $\lambda$, and this being brought to the meridian, will be immediately below $3^\circ 54'$ S. which is therefore the declination required.

From the above example, it is evident that the method of finding the declination of the sun corresponds to that of finding the latitude of a place on the globe, given in Problem I. the sun's declination being measured in the same way by an arc of the meridian interposed between the equator and the sun's place in the ecliptic (f).

**Problem XI. To rectify the globe for the sun's place and the day of the month.**

Find the sun's declination for the given day, by Problem XI.; then elevate the pole that is in the same hemisphere with the degree of declination, as many degrees as are equal to the declination.

Ex. Rectify the globe for the sun's place on the 6th October? Ans. The sun's declination on that day is $5^\circ$ S. therefore the south pole must be elevated $5^\circ$ above the horizon.

Rectifying the globe for the sun's declination corresponds to the rectifying of it for the latitude of a given place. See No 88.

**Problem XII. To find the time of the sun's rising and setting at a given place, for any given day.**

Rectify the globe for the declination on the given day, and bring the given place to the meridian, and set the index of the hour circle at XII. Turn the globe, till the given place come to the eastern edge of the horizon, and the time of sunrise will be shewn by the position of the index. Then turn the globe till the given place come to the western part of the horizon, and the position of the index will point out the time of sunset.

To perform the same problem by Adams's globes. Rectify the globe for the declination, bring the given place to the meridian, and set the horary index at 12 as before; then turn the globe towards the west, till the given place reach the western edge of the horizon, and the index will point to the time of sunrise. The time of sunset will be known, in like manner, by bringing the place to the eastern side of the horizon.

If the hour circle in the ordinary globes has a double row of figures, the sun's rising and setting may be found at the same time; for if the place be brought to the eastern part of the horizon, the time of sunrise will be shewn by the index, in that circle where the hours increase towards the east; and the time cut by the index in the circle where the hours increase towards the west, will shew the time of sunset.

Ex. 1. Required the time of the sun's rising and setting at London, on the 29th August? Ans. The sun rises at nine minutes after five, and sets nine minutes before seven.

Ex. 2. Required the time of sunrise and sunset at Edinburgh on the 1st of June? Ans. For sunrise, 27 minutes after three; for sunset, 33 minutes after eight.

**Corollary.** From this problem we may easily find the length of the day and night for any given time; for, having found by the globe the time of sunrise and sunset, the double of the latter is the length of the day, and the double of the former the length of the night.

**Problem XIII. To find the sun's meridian altitude on any given day, at a given place.**

Rectify the globe for the latitude of the given place, by Problem VIII.; find the sun's place on the given day by Problem IX. and bring it to the brazen meridian. Then fix the quadrant of altitude in the zenith, or over the given place, and bring it over the sun's place; and the degree of the quadrant lying over the sun's place will shew the meridian altitude.

If the globe has no quadrant of altitude, the sun's meridian altitude may be found by counting the number of degrees on the meridian, between the horizon and the sun's place.

Ex. Required the sun's meridian altitude at Edinburgh on the 21st of June? Ans. $57^\circ 30'$, or the greatest possible, this being the summer solstice.

**Corollary.** It may be known whether the sun's meridian altitude be north or south, by the following observations. When the sun's declination and the latitude of the place are of different names, i.e. the one north and the other south, the meridian altitude is of the same name with the declination. If the declination and latitude be both north or both south, the altitude is of the same name with the declination, if the latter be the greater; but, otherwise, the altitude is of an opposite name.

**Problem XIV. Having the latitude of the place and the day of the month given, to find the sun's altitude for any given hour.**

Rectify the globe for the latitude; find the sun's place, and bring it to the meridian, and set the horary index

(f) For a table of the sun's declination corresponding to his true place, see Vol. III. p. 170. index to noon; turn the globe till the index point to the given hour, then fix the quadrant of altitude in the zenith, and bring its graduated edge over the sun's place, and the degree cut by the sun's place will be the altitude required.

Ex. What will be the sun's altitude at 10 o'clock A.M. on the 30th of November at Edinburgh? Ans. 8° 50'.

PROBLEM XV. Having the sun's meridian altitude given at any place, to find the latitude of the place.

Bring the sun's place for the given day to the meri- dian, and move the globe in the horizon till the dis- tance between the sun's place and the northern or south- ern edge of the horizon, (according as the case may re- quire), be equal to the given altitude. The degree of elevation of the pole will show the latitude required.

Ex. The sun's meridian altitude observed at a cer- tain place on 5th August is 74° 24' N. What is the latitude of the place? Ans. 1° 36' N.

PROBLEM XVI. The latitude of the place and the day of the month being given, to find when the sun is due east or due west.

Rectify the globe for the latitude of the place, bring the sun's place to the meridian, and set the index to XII. Fix the quadrant of altitude in the zenith, and if the sun's declination be of the same name with the latitude, bring the graduated edge of the quadrant to the eastern side of the horizon; but if the declination is of a different name from the latitude, bring the qua- drant to the western part of the horizon. Turn the globe till the sun's place in the ecliptic come below the edge of the quadrant, and the index will point to the hour when the sun is due east. Subtract this from XII. and the remainder shows the time when the sun is due west.

Ex. At what hours is the sun due east and west at the summer and winter solstice at Greenwich? Ans. At the summer solstice he is due east at 20 minutes past seven, and due west at 20 minutes before five. At the winter solstice he is due east at 20 minutes before five, and due west at 20 minutes past seven.

COROLLARY. When the declination and latitude are of the same name, the sun is due east after rising; but when the declination and latitude are of different names, he is due east before rising. As it is not con- venient to observe on the globe when the sun is due east before rising, or while he is under the horizon, it is better to bring the opposite point of the ecliptic due west, and then the index shows the time when he is due east.

PROBLEM XVII. Having a place in the torrid zone given, to find on what two days of the year the sun is vertical at that place.

Find the latitude of the given place, and keeping that in view, turn the globe round, noting the two points at the ecliptic that pass below the degree of la- titude. Find in the calendar circle of the horizon the days corresponding to those points of the ecliptic; and these are the days on which the sun is vertical at the given place.

Ex. 1. On what days is the sun vertical at St He-

lens, in latitude 15° 53' S.? Ans. On the 6th February and 6th November.

Ex. 2. Required the days on which the sun is verti- cal at Tobago, in latitude 11° 29' N.? Ans. On April 19. and August 23.

PROBLEM XVIII. To find those places in the torrid zone where the sun is vertical on a given day.

Find the sun's place for the given day, and bring it to the brazen meridian; then turn the globe, and note all the places which pass under that point of the meri- dian: these will be the places to which the sun is ver- tical on the given day.

Ex. 1. In what places is the sun vertical at the sum- mer solstice? Ans. At Canton in China, at Calcutta in Bengal, at Mecca in Arabia, and at the Havana.

Ex. 2. To what places is the sun vertical on the 16th of May and 29th of July? Ans. At Bombay, Pegu, in the northern part of Manilla, in the middle of the Ladrones islands, at Owhyhee, Mexico, in Hispaniola, and at Tombuctoo in the central parts of Africa.

PROBLEM XIX. Having the day and hour at any given place, to find where the sun is then vertical.

Find the sun's declination by Problem XI. and the places where it is noon at the given time, by Problem III.; then any of those places where it is noon, whose latitude is the same as the sun's declination, will have the sun vertical at the given time.

Ex. On the 1st of August at Edinburgh, it being 35 minutes past four, P.M. it is required to find where the sun is vertical? Ans. The sun's declination on that day is 18° 14' N., and the place where it is noon at the given time, that lies nearest in latitude to the declina- tion, is Kingston in Jamaica: this, therefore, is the place required.

PROBLEM XX. A place in the northern frigid zone being given, to find when the sun begins to appear above the horizon, and when to disappear; as also the length of the longest day and night.

Rectify the globe for the latitude, and bring the as- cending signs of the zodiac (see ASTRONOMY, No. 52.) to the southern part of the horizon; observe what de- gree of the ecliptic is intersected by that point of the horizon, and in the calendar circle find the day of the month answering to that degree. That will show the time of the sun's first appearance above the horizon at the given place, and this is the end of the longest night in that latitude. Then bring the descending signs to the same part of the horizon, and observe the day which answers to the degree of the ecliptic intersected; this will show the time of the sun's disappearance, or the beginning of the longest night. Now bring the as- cending signs to the northern part of the horizon, and observe the degree of the ecliptic, and the correspond- ing day as before, which will give the time when the sun begins to shine continually, or the beginning of the longest day. Again, bring the descending signs to the same point, and thus will be given the time when the sun ceases to shine continually, or the end of the longest day.

Ex. At what time does the sun begin to appear Principles above the horizon at North Cape in Lapland, the latitude of which is 72° N.? When does he disappear, and how long is he entirely absent during the longest night? Ans. He begins to appear on the 26th of January, and entirely disappears on the 16th of November; he is therefore absent for 71 days.

Cor. From the sun's first appearance at the end of the longest night to the beginning of the longest day, and from the end of the longest day to the sun's total disappearance at the beginning of the longest night, he rises and sets every day.

Problem XXI. To find in what part of the northern frigid zone the sun begins to shine continually on a given day.

Find the sun's declination for the given day, and subtract this from 90°, the remainder will show the latitude required.

Note.—The given day must be between the 21st of March and the 21st of June, as at no other time does the sun begin to shine continually in the northern frigid zone.

Ex. Required the latitude in which the sun begins to shine without setting on the 1st of June? Ans. The sun's declination for that day is 22° N. and this subtracted from 90° leaves 68° N. the latitude required.

Problem XXII. The length of the longest day in any place being given, to find the latitude of that place.

Bring the 1st degree of Cancer to the meridian, and set the hour index at noon. Then turn the globe towards the west, till the index point to the hour of sunset, or half of the length of the given day; raise or depress the pole, till the sun's place in the ecliptic is exactly in the western edge of the horizon. The elevation thus obtained will be equal to the required latitude.

In Adams's globes, after bringing the first degree of Cancer to the meridian, and setting the index to noon, the globe must be turned towards the west, till the index shew the time of sunset, and the sun's place must be brought to the eastern side of the horizon.

Ex. In what latitude is the longest day 18 hours long? Ans. In latitude 58° 30' N.

By this problem the limits of the hour climates may be pretty nearly ascertained.

Problem XXIII. To find the latitudes of those places in the frigid zone where the sun is continually above the horizon for a given number of days.

Count from the first degree of Cancer towards the nearest equinoctial point, as many degrees as is equal to half the given number of days; bring the point thus obtained below the meridian, and note the degree of the meridian which it intersects. This subtracted from 90° will leave a remainder that is nearly equal to the latitude of the place.

Ex. In what latitude does the sun never set during 76 days? Ans. In latitude 71° 30', or very near the southern part of Nova Zembla.

Note.—This problem cannot be performed accurately by the globe; for as the sun requires 365 days six hours to move through the whole 360° of the ecliptic, he does not advance quite a degree in 24 hours.

By this problem the limits of the month climates may be pretty nearly ascertained.

Problem XXIV. The hour and day being given at any place, to find in what places the sun is rising, and in what he is setting; where it is noon, and where midnight.

Find by Problem XIX. the place to which the sun is vertical at the given time; rectify the globe for the latitude of that place, and bring the place below the meridian. In this position of the globe all those places that lie within the western edge of the horizon will have the sun rising, and all those which are in the eastern edge of the horizon will have it setting. Again, to those places which lie under the upper semicircle of the brazen meridian, it will be noon; and to those which lie below the lower semicircle, it will be midnight.

Ex. Suppose it be four o'clock P.M. on the 4th of June at London; where is the sun at that time rising, and where is he setting; to what places is it noon, and to what midnight? Ans. The north-eastern part of Siberia, Kamtschatka, the most western of the Sandwich isles, and the most eastern of the Society isles, are within the western edge of the horizon, and consequently to these the sun is rising. At Tobolsk, in the Caspian sea, in the desert of Arabia, in the middle of the Red sea, in Abyssinia, in the central parts of Africa, and in the country of the Hottentots, the sun will be setting, as these places lie within the eastern edge of the horizon. New Britain, the islands of Martinique and Trinidad, and the middle part of South America, which lie below the upper semicircle of the meridian, have noon; and Chinese Tartary, the eastern part of China, the Philippine isles, and the western part of New Holland, which are situated below the under edge of the semicircle, have midnight.

As the remaining problems on the terrestrial globe chiefly respect the continuance of twilight, it is proper before we proceed, to make a few remarks on this subject. For the explanation of the term, see Crepusculum and Twilight.

The Crepusculum, or Twilight, it is supposed, usually begins and ends when the sun is about 18° below the horizon; for then the stars of the 6th magnitude disappear in the morning, and appear in the evening. It is of longer duration in the solstices than in the equinoxes, and longer in an oblique sphere than in a right one; because in those cases the sun, by the obliquity of his path, is longer in ascending through 18° of latitude.

Twilight is occasioned by the sun's rays refracted in our atmosphere, and reflected from the particles of it to the eye. For let A (fig. 10.) be the place of an observer on the earth ADL, AB the sensible horizon, meeting in B the circle CBM bounding that part of the atmosphere which is capable of refracting and reflecting light to the eye. It is plain that when the sun is under the horizon, no direct rays can come to the eye at A; but the sun being in the refracted line CG, the particle C will be illuminated by the direct ray of the sun; and that particle may reflect those rays to A, where they enter the eye of the spectator. And thus the sun's light illuminating an innumerable multitude of particles, may be all reflected to the spectator at A. A. From B draw BD touching the circle ADL in D, and let the sun be at S in the line AD; then the ray SB will be reflected into the situation BA, and will enter the eye, because from a principle in optics the angle of incidence DRC is equal to the angle of reflection ABE. See Optics. This ray SB, or BA, will therefore be the first that reaches the eye at dawn in the morning, and the last that falls on the eye at night, when twilight ceases, because as the sun gets lower down, the particles of the air at B will no longer be illuminated.

The depth of the sun below the horizon at the beginning of the morning or end of the evening twilight, is determined by observing the moment when the air first begins to shine in the morning, or ceases to shine in the evening; then finding the sun's place for that time, and hence the time till his rising in the horizon, or after his disappearance below. This depth of the sun below the horizon has been variously stated by different astronomers, but it is now generally estimated at $18^\circ$. Accordingly in Mr Adams's globes there is a circular wire fixed $18^\circ$ below the horizon, to represent the limits of the crepusculum (see PWY, fig. 5.).

As the cause of twilight is not constant, its limits must continually vary; for if the exhalations in the atmosphere be more copious or more extensive than usual, the morning twilight will begin sooner, and that of the evening last longer than ordinary; as the more copious the exhalations, the more rays will be reflected from them, and consequently the more they will shine, and again, the higher they are, the sooner they will be illuminated by the sun. From this circumstance the evening twilight is commonly longer than the morning, at the same time, and in the same place. The refraction is also greater according as the air is more dense, and not only is the brightness of the atmosphere variable, but the same takes place in its height above the earth; therefore, the twilight is longest in hot weather, and in hot countries, all other things being equal. The chief differences, however, arise from the different situations of places on the earth, or from the difference of the sun's place in the heavens. Thus, the twilight is longest when the earth is in the position of a parallel sphere, and shortest in that of a right sphere (see No. 90): and in an oblique sphere, the twilight continues longer at any place, in proportion as that place is nearer to either of the poles; a circumstance which affords considerable relief to the inhabitants of the northern countries in their long winter nights. Twilight continues longest in all places of north latitude, when the sun is in the tropic of Cancer, and to those in south latitude when he is in the tropic of Capricorn. The time of the shortest twilight also varies in different latitudes; thus, in England, the shortest twilight is about the beginning of October and of March, when the sun is in $\alpha$ and $\beta$; hence, when the difference between the sun's declination and the depth of the equator is less than $18^\circ$, so that the sun does not descend more than $18^\circ$ below the horizon, the twilight will continue through the whole night, as happens in Britain from the 22d of May to the 22d of July.

In the latitude of $49^\circ$ N. twilight continues for the whole night, only on the 21st of June, or the time of the summer solstice: but at all places further to the north it continues for a certain number of days before and after the summer solstice.

Near the north pole there is continual twilight from the 22d of September, the time of the sun's permanent absence, to the 12th of November. It then ceases till about the 30th of January, when it again appears, and continues till the 21st of March, the time of the sun's permanent appearance. Hence the inhabitants of those places nearest the pole, though they never see the sun for nearly six months, have, however, the benefit of twilight for above the half of that time, and are entirely excluded from the sun's light little more than 12 weeks, during six of which the moon is constantly above the horizon.

Were it not for the gradual change from light to darkness, and vice versa, which is the consequence of twilight, much inconvenience would arise. A sudden change from the darkness of midnight to the full splendour of the sun, and the reverse, would injure the sight, and would, in many cases, be productive of much danger to travellers, who would be overtaken by utter darkness before they had time to prepare for its approach.

**Problem XXV. To find where it is twilight at any given time.**

Find where the sun is vertical at the given time, and rectify the globe for the latitude of that place. Observe what places are within the limits of twilight, or not quite $18^\circ$ below the horizon. To those which are situated within the western zone, between the horizon and the parallel of $18^\circ$, it will be twilight in the morning; and those which are in the eastern zone will have it twilight in the evening.

This problem may be more conveniently performed by rectifying the globe for the antipodes of the place which has the sun then vertical, and observing what places are situated in the zone formed above the horizon, between it and a parallel circle of $18^\circ$.

Ex. It is required to find where it is twilight on the 4th of June, when it is three o'clock P.M. at London.

Ans. Kamtschatka, the Sandwich isles, and the Marquesas, have twilight in the morning; and the inhabitants of Madagascar, of Tibet, and the eastern part of Persia, have twilight in the evening.

**Problem XXVI. To find the duration of twilight at a given place on any given day.**

Rectify the globe for the latitude of the place; find the sun's place for the given day by Problem X. and bring it below the meridian, and set the horary index to XII. Turn the globe till the sun's place be just within the circle that marks the limits of twilight, and the index will shew the beginning of twilight. Subtract the time of the beginning of twilight from the time of sunrise at the given place (found by Problem XII.) and the remainder will shew the duration of twilight at the given place.

Note.—The above rule will answer both for the ordinary globes, and for those of Adams, except that in the latter the sun's place must be brought below the western part of the horizon. A more convenient way in both globes will be, to bring that point of the ecliptic which is opposite to the sun's place, $18^\circ$ above the... the western horizon, and the index will then show the beginning of twilight.

Ex. How long will twilight continue at London on the following days: March 2d; September 25th; and December 26th? Ans. On the 2d of March it will continue one hour and fifty minutes; on the 25th of September two hours; and on the 26th of December, two hours ten minutes (G).

Problem XXVII. To show the cause of day and night by the globe.

It will have appeared, from the consideration of the cause of day and night given under the article Astronomy, that only that half of the earth which is opposite to the sun, is illuminated by his rays, while that which is turned from him is involved in darkness. As the earth revolves on its axis from west to east, in the space of 24 hours, every place on the earth in the course of that time alternately enjoys the light of the sun, and is deprived of it.

To illustrate this by the globe, rectify the globe for the sun's declination, so as to place the sun in the zenith, and the horizon will represent the boundary between light and darkness; that hemisphere which is above the horizon being illuminated by the sun's rays, and that which is below the horizon being deprived of light. If now a patch is put on the globe, so as to represent any place, and if the globe be made to revolve from west to east; when the place is brought to the western edge of the horizon, the sun will appear to the inhabitants of that place to be rising in the east, though, in fact, the appearance arises from the place itself coming beyond the limit of darkness. As the globe continues to turn, the place rises towards the meridian, and this produces the appearance as if the sun were advancing towards the meridian in a contrary direction. When the place comes below the meridian, it is noon to that place, and the sun appears to have attained its greatest height.

As the place proceeds towards the east, it gradually recedes from the meridian, and the sun appears descending in the west. When it reaches the eastern edge of the horizon, and is proceeding below the boundary of light and darkness, the sun appears to be setting; and during the whole time that the place is moving below the horizon, the sun will not appear till the place once more rises in the west.

Problem XXVIII. To find at what places an eclipse of the moon is visible at any given time.

Find the place to which the sun is vertical at the given time, and rectify the globe for the latitude of that place. As the moon is opposite to the sun, which illuminates the superior hemisphere of the globe, the eclipse of the moon will be visible to all the places that lie below the horizon.

As the places below the horizon are not easily examined, this problem may be more conveniently performed by rectifying the globe for the antipodes of the place to which the sun is vertical at the given time, rather than for the place itself; as in this latter position of the globe the moon being in opposition to the sun, will be vertical to the place below the zenith, and its eclipse will be visible at all the places now above the horizon.

Ex. 1. On the 4th of January 1806, at 55 minutes past 11 P.M. reckoning the time at Greenwich, there was an eclipse of the moon. It is required to find those places to which the eclipse was visible? Ans. Through the greatest part of Africa, in some part of Europe, in Asia, South America, and a great part of North America.

Ex. 2. On the 10th of May 1808, when it is eight o'clock A.M. at Greenwich, the moon will be totally eclipsed. In what places will the eclipse be visible? Ans. In most parts of America; in the islands of the Pacific ocean, and on the eastern coast of New Holland.

Sect. II. Of the Use of the Celestial Globe.

The celestial globe, with respect to the circles that are described on it, and the apparatus with which it is furnished, scarcely differs from the terrestrial globe, which has been so fully described in the preceding section. The surface of the celestial globe is made to represent all the stars that are commonly visible to the naked eye, arranged under their constellations, and bounded by the figures which have been given to these constellations by the early astronomers. (See fig. 5.) In Adams's celestial globe the moveable semicircle (No. 91.) turning round the poles represents a circle of declination, and the small circle on it, an artificial sun or planet.

Both the globes are often furnished with a mariner's compass, which is usually placed in the lower part of the frame.

It must here be remarked, that the representation of the heavens on the celestial globe, though probably much more accurate than that of the earth on the terrestrial, is not so natural as the latter; for, in viewing the stars on the external surface of a globe, the spectator sees them in an opposite position to that in which he observes them in the heavens, so that to form a just conception of their exact situation, he must suppose his eye to be seated in the centre of the globe. Hence, if a large hollow hemisphere were made of glass, and if the stars in the corresponding hemisphere of the firmament were painted in transparent colours on its surface; an eye situated in the centre of such a hemisphere

(g) If we have the latitude of a place, and the sun's declination given, we may find the beginning of the morning and the end of the evening twilight by calculation. Thus, in the oblique-angled spherical triangle ZPN (fig. 11.) we have given ZP the co-latitude; PN the co-declination, and ZN = 1° 50' being the sum of 90° the quadrant, and 18° the depression at the extremity of twilight. Then by spherical trigonometry we may calculate the triangle ZPN, the hour angle from noon, and this reduced to time, at the rate of 15° per hour, gives the time from noon to the beginning or end of twilight. For the mode of calculation, see SPHERICS. The great use of the celestial globe is to perform a variety of problems with respect to the stars, and the motions of the heavenly bodies through the space which they occupy.

**Problem I. To place the celestial globe in such a situation as that it shall exhibit an accurate representation of the face of the heavens at any given place, and at any given time.**

Rectify the globe for the latitude of the place, as in Problem VII. of the terrestrial globe, or by setting the pole of the celestial globe pointing to the pole of the earth, by means of the compass that is usually annexed to the globes; find the sun's place in the ecliptic; bring this to the meridian, and set the horary index at noon. Again, make the globe turn on its axis till the index point to the given time, and in this position the globe will exactly represent the face of the heavens, corresponding to the given time and place; every constellation and star in the heavens answering in position to those on the globe. Hence, by examining the globe, it will immediately be seen what stars are above or below the horizon, which are on the eastern and western parts of the heavens, which have just risen above the horizon, and which are about to sink below it.

As this problem will be found extremely useful to the student of astronomy, we shall here quote the example given in illustration of it by Messrs Bruce of Newcastle.

"Required the situation of the stars for the latitude of Newcastle, on October 6th, at eight o'clock in the evening?"

"In our present survey of the heavens, we shall commence at the north point of the horizon, and proceed round eastward; noticing the different constellations, and the relative situation of the principal stars in these constellations.

"The first star which strikes the eye of the observer, in the north-east part of the heavens, is Capella, in the constellation Auriga, or the Waggoner: It is of the first magnitude, of the altitude of 23°, or nearly the fourth part of the distance from the horizon to the zenith. There are two stars of the second magnitude, which form with Capella a triangle.—The star which forms the short side of the triangle is in the right shoulder of Auriga, and is marked β; it lies at the distance of about 8° from Capella, further to the north; its altitude is 18°.—The star forming the longer side of the triangle is in the Bull's northern horn; its distance from Capella is more than 26°; its altitude not more than 5°, and azimuth N. E. There are three stars of the fourth magnitude, a little to the south of Capella, that bear the name of the Kids.

"If a line be drawn through the two stars that form the upper side of the triangle, and continued to the horizon, it will point out Castor, α, in Gemini just rising, azimuth E. N. E.: it is between the first and second magnitude. The other stars in this constellation have not yet risen.

"A line drawn between Castor and Capella, and continued higher in the heavens, will point out Perseus, in which there are three stars, one of the second magnitude, α, named Algenib, and two of the third magnitude, one on each side of Algenib, at the distance of about 5°: they form a line a little curved on the side next Auriga. The altitude of Algenib is 37°; azimuth N. E. by E.

"A little to the south of Perseus is the Head of Medusa, which Perseus is holding in his hand. Besides two or three small stars it contains one of the second, and one of the third magnitude. The name of the brightest is Algol; altitude 33°, azimuth E. N. E. Algol is only 1° distant from Algenib.

"Directly below the Head of Medusa, about 14° above the horizon, are the Pleiades or seven stars: They are seated in the shoulder of Taurus, and are so easily known, that no description is necessary. Aldebaran, a star of the first magnitude, which forms the eye of Taurus, is just rising; azimuth E. N. E. A vertical circle drawn through Algol will point to it. There are two stars of the third magnitude, and several smaller very near Aldebaran, which form with it a triangle. The whole cluster is called the Hyades.

"A line drawn from Aldebaran through Algol, and continued to the zenith, will direct to Cassiopeia. This contains five stars of the third magnitude, besides several of the fourth: it is in form something like the letter Y, or, as some think, an inverted chair. It is situated above Perseus, within 30° of the zenith. The altitude of the brightest star, α, called Schedar, is 60°; azimuth, E. N. E.

"Below Cassiopeia and west of Perseus is Andromeda, which contains three stars of the second magnitude. A line from Algenib, parallel to the horizon towards the south, will pass very near these three stars; and, as they are all of the same magnitude, and placed nearly at the same distance of 1° from each other, they may easily be known. The name of the star nearest Perseus, and which is in the foot of Andromeda, marked γ, is Almak: its altitude is 49°; azimuth E. N. E. The name of δ, in the girdle, is Mirach: its altitude 44°; azimuth E. The altitude of ε, in the head of Andromeda, is 46°; azimuth E. S. E.

"About 15° below Mirach are two stars in Aries, not more than 5° distant from each other, forming with Mirach an isosceles triangle: the most eastern star, α, is of the second magnitude; the other, β, of the third, attended by a smaller star, marked γ, of the fourth magnitude. A line drawn from Mirach, perpendicular to the horizon, will pass between the two, and besides, will point to a star of the second magnitude, directly E., not above 3° from the horizon.

"This star is the first of Cetus, marked α, and is of the second magnitude: it is named Menkar. A line drawn from Capella through the Pleiades will also point to it. Cetus is a large constellation, and contains eight stars of the third magnitude; they all lie to the west of Menkar; β, a star in the tail, is more than 40° distant from it. The azimuth of β is S. E. by E.; altitude nearly the same as Menkar.

"The constellation Pisces is situated next to Aries; it contains one star of the third magnitude, marked α: its altitude is 10°, azimuth E. by S. It is distant from Menkar 15°. A line drawn from Almak, through α in Aries, will point to it.

"If we return again to α in the head of Andromeda, we shall find three other stars nearer the meridian, which, Principles with it, form a square. These stars are in Pegasus, and are placed at the distance of 15° from each other; they are all of the second magnitude. The two stars forming the western side of the square are called—the upper one Scheat, which is marked β, and which is in the thigh of Pegasus; the under one Markab, which is marked α, and which is in the wing; the lowest star in the eastern side of the square is in the tip of the wing, and is marked γ. The altitude of Scheat is 55°; azimuth S. E. 3° E. Altitude of Markab, 43°; azimuth S. E. by S. 3° E.

"A line drawn through γ and β (the diagonal in the square of Pegasus) and continued to the meridian, will point out Cygnus, a remarkable constellation in the form of a large cross, in which there is a star of the second magnitude, named Deneb or Arided; it is marked α, and is almost directly upon the meridian at the altitude of 82°. Cygnus contains six stars of the third magnitude. The constellation Cepheus, which contains no remarkable stars, is situated between Cygnus and the north pole.

"Below Pegasus, and nearer the meridian, is Aquarius, containing four stars of the third magnitude. A line drawn from α in Andromeda, through Markab, will point to α in Aquarius. Its altitude is 32°; azimuth S. S. E.

"A bright star of the first magnitude named Fomalhaut, in Pisces Australis, is then upon the horizon; azimuth S. S. E.

"Delphinus is a small constellation, situated about 30° below Cygnus upon the meridian; it contains five stars of the third magnitude, four of them being placed close together, and forming the figure of a rhombus or lozenge. A line drawn through the two under stars of the square will point to it. Its altitude is about 50°.

"A little to the west of Delphinus, but not quite so high, is Aquila, containing one very bright star of the first magnitude, named Atair: It may very easily be known from having a star on each side of it of the third magnitude, forming a straight line. The length of the line is only about 5°; altitude of Atair 40°; azimuth S. S. W.

"Considerably above Atair, and a little to the W. of Cygnus, is Lyra, containing a star of the first magnitude, one of the most brilliant in the firmament. It is called Lyra or Vega, and is 35° to the N. W. of Atair; altitude 60°; azimuth W. S. W. Lyra, Atair, and Arided, form a large triangle.

"We come now to notice three constellations, which occupy a large space in the western side of the heavens: these are Hercules immediately below Lyra; Serpentarius between Hercules and the horizon, extending a little more towards the south; and Boötes, reaching from the horizon W. N. W. to the altitude of 45°.

"Hercules contains eight stars of the third magnitude; the star in the head, α, named Ras Algethi, is within 5° of α in the head of Serpentarius. This last is a star of the second magnitude, and is named Ras Alhague: its altitude is 30°; azimuth, S. W. by W. 3° W. A line drawn from Lyra, perpendicular to the horizon, will pass between these two stars. The other stars in Hercules extend towards the zenith, and those in Serpentarius towards the horizon.

"The constellation Boötes may easily be known from the brilliancy of Arcturus, a star of the first magnitude, and supposed to be the nearest to our system of any in the northern hemisphere: it is within 10° of the horizon; azimuth W. N. W. Boötes also contains seven stars of the third magnitude, mostly situated higher in the heavens than Arcturus. The star immediately above Arcturus is called Mezen Mirach, and is marked α. The star in the left shoulder, δ, named Seginus, forms with Mirach and Arcturus a straight line.

"Between Serpentarius and Boötes is Serpens, containing one star of the second magnitude, and eight of the third: α in Serpens is nearly at the same distance from the horizon, as Arcturus; azimuth W.

"Above Serpens, and a little to the east of Boötes, is the Northern Crown, containing one star of the second magnitude, named Gemma, and several of the third, which have the appearance of a semicircle. A line drawn from Lyra to Arcturus will pass through this constellation.

"We come now to Ursa Major, a constellation containing one star of the first, three of the second, and seven of the third magnitude. It may easily be distinguished by those seven stars, which, from their resemblance to a wagon, are called Charles's Wain. The four stars in the form of a long square, are the four wheels of the wagon; the three stars in the tail of the Bear, are the three horses, which appear fixed to one of the wheels. The two hind wheels, α named Dubhe, and β, are called the pointers, from their always pointing nearly to the north pole. Hence the pole star may be known. The altitude of Dubhe is 30°; azimuth N. by W. 3° W. The distance between the two pointers is 5°; the distance between the pole star and Dubhe, the upper pointer, is 30°.

"Ursa Minor, besides the pole star of the second magnitude, situated in the tail, contains three of the third, and three of the fourth magnitude. These form some resemblance to the figure of Charles's Wain inverted, and may easily be traced.

"Draco, containing four stars of the second and seven of the third magnitude, spreads itself in the heavens near Ursa Minor: the four stars in the head are in the form of a rhombus or lozenge: the tail is between the pole star and Charles's Wain.

"Besides these constellations, there are a number of others, which, as they contain no remarkable stars, we have not described; an enumeration of these will suffice. The Lynx, between Ursa Major and Auriga; Camelopardalis, between Ursa Major and Cassiopeia; Musca, and the Greater and Less Triangles between Aries and Perseus, Aculeus, close to the head of Pegasus; Sagittarius setting in the south-west; Antinous and Sobieski's Shield below Aquila; the Fox and Goose between Aquila and Cygnus; the Greyhounds and Berenice's Hair between Boötes and Ursa Major, and Leo Minor below Ursa Major."

The astronomical terms that we must here employ in describing the method of performing the problems on the celestial globe, will be found explained in the article Astronomy, or under their proper heads in the general alphabet of this work. See Ascension, Azimuth, Declination, &c.

Problem **Problem II. To find the right ascension and declination of any given star.**

Bring the given star below the brazen meridian, and mark the degree of the meridian under which it lies. That degree shews the declination of the star, and the degree of the equator cut by the meridian gives the star's right ascension.

The right ascension of a star may also be found by placing the globe in the position of a right sphere, and then bringing the star to the eastern part of the horizon; for that point of the equator which comes to the horizon at the same time with the star, marks its right ascension. See Astronomy, No. 249, 250.

Ex. 1. What is the right ascension and declination of the star Sirius? Ans. Its right ascension is 9° 9', and its declination 16° 27' S.

Ex. 2. Required the right ascension and declination of Aldebaran, or the star in the Bull's Eye marked α? Ans. Its right ascension is 6° 6', and its declination 16° 5' N.

**Problem III. Having the right ascension and declination of a star given, to find the star on the globe.**

Bring the degree of the equator which marks the right ascension below the brazen meridian, and counting along the meridian towards the north or south, as far as the degree of declination, the required star will be there found.

Ex. 1. The right ascension of a certain star is 16° 2' 35", and its declination is 5° 27' N.; what is the name of the star? Ans. The lower pointer of Ursa Major, marked β.

Ex. 2. The right ascension of Arcturus is 21° 3' 30", and its declination is 20° 13' N.: it is required to find it on the globe.

This problem is extremely useful in discovering the names and relative situations of the different stars.

**Problem IV. To find the latitude and longitude of a given star.**

Bring the solstitial colure (see No. 75.) below the brazen meridian, and there fix the quadrant of altitude over the pole of the ecliptic which is in the same hemisphere with the given star. Then, keeping the globe steady, bring the graduated edge of the quadrant over the given star, and the degree of the quadrant cut by the star, counted from the ecliptic, marks its latitude, and the degree of the ecliptic that is cut by the quadrant is the longitude of the given star (ii). See Astronomy, No. 252, 253.

Ex. 1. What is the latitude and longitude of Arcturus? Ans. Lat. 31° N. Long. Libra 2°.

Ex. 2. What is the latitude and longitude of Capella? Ans. Lat. 23° N. Long. Gemini 18° 30'.

**Problem V. Having the day of the month given, to find at what hour any star comes below the meridian.**

Find the sun's place, and bring it to the meridian, and set the horary index to XII.; turn the globe till the given star come below the meridian, and the index will point out the hour.

To know whether the hour is in the forenoon or afternoon, it is necessary to observe, that if the star be to the east of the sun, it will reach the meridian later than the sun, but if it be to the west of that luminary, it will come to the meridian sooner: hence, in the former case, the hour will be P.M. and in the latter A.M.

Ex. 1. At what hour does Sirius come to the meridian on the 9th of February? Ans. At 7 minutes past 9 P.M.

Ex. 2. Required the hour when Castor passes the meridian on the same day. Ans. At 52 minutes past 9 P.M.

**Problem VI. Having any star given, and a given hour, to find on what day the star will come to the meridian at a given hour.**

Bring the given star below the meridian, and set the horary index to the given hour. Make the globe revolve till the index come to twelve at noon; and the day of the month which corresponds to the degree of the ecliptic then below the meridian, found in the calendar circle of the wooden horizon, will be the day required.

Ex. 1. On what day does Algenib, the first star of Perseus, come to the meridian at midnight? Ans. On the 13th of November.

Ex. 2. On what day does Arcturus come to the meridian at 9 o'clock P.M.? Ans. On the 10th of June.

**Problem VII. Having the latitude, the day of the month, and the hour of the night given, to find the altitude and azimuth of any given star.**

Rectify the globe for the given latitude; bring the sun's place below the meridian, and set the horary index to XII.; then turn the globe till the index point at the given hour. Fix the quadrant of altitude at 90° from the horizon, that is, in the zenith, and bring its graduated edge over the place of the star: the degree of the quadrant intercepted between the horizon and the star is the altitude required; and the distance between the foot of the quadrant and the nearest part of the horizon, will be the azimuth.

It is evident that this problem on the celestial globe is exactly similar to Problem XIII. on the terrestrial globe, for finding the altitude of the sun.

Ex. 1. What will be the altitude and azimuth of Cor Hydras on the 21st of December at London, at 4 o'clock A.M.? Ans. The altitude 30°, the azimuth S. 14° W.

Ex. 2. Suppose an observer at the Cape of Good Hope, on the 21st of June at midnight; required the altitude and azimuth of Arcturus to him? Ans. Altitude 12°, azimuth N. 55° W.

**Problem VIII. Having given the azimuth of any given star, and the day of the month in a given latitude; to find the hour of the night, and altitude of the star.**

Rectify the globe as in the last problem; fix the quadrant of altitude in the zenith, and bring it to the given azimuth. Turn the globe till the star comes below

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(ii) It must be remembered that the longitude of the heavenly bodies is not estimated in degrees and minutes like their right ascension, but in signs, degrees, and minutes, as the sun's place is reckoned. Principles low the graduated edge of the quadrant, when the and horary index will point out the hour, and the altitude of the star will be seen by the quadrant.

Ex. Suppose the azimuth of Dubhe to be N. 23° W. at London on the first of September; it is required to find the altitude of the star, and the hour of the night? Ans. The altitude of Dubhe at that time is 31°, and the hour is 9 o'clock P.M.

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

Rectify the globe as before, and having fixed the quadrant of altitude in the zenith, turn the globe and quadrant of altitude till the latter comes over the star at the given degree of altitude. In this position the in- dex will shew the time of night, and the position of the quadrant at the horizon will shew the azimuth of the star.

In the same way the hour of the night and the azimuth of the sun may be found, by fixing a patch on the globe in the sun's place, and bringing it to the quadrant as directed for the star.

As the sun and stars have the same altitude twice in the day, it is proper to know whether they are to be east or west of the meridian; or whether the hour re- quired be in the evening or the morning.

Ex. At Edinburgh, on the 25th of December, in the forenoon, when the sun's altitude is 7° 20', requir- ed the hour and the sun's azimuth? Ans. It is 10 o'clock A.M. and the sun's azimuth is S. 27° 30' E.

Problem X. Having the azimuth of the sun or a star, the latitude of the place, and the hour of the day given; to find the altitude and day of the month.

Rectify the globe for the latitude of the place, fix the quadrant in the zenith, and bring its edge under the given azimuth. Bring the sun's place or the star to the edge of the quadrant, and set the index at the given hour. The degree marked in the quadrant will shew the altitude; and if the globe be turned till the index points to twelve at noon, the day of the month, answering to that degree of the ecliptic which is in- tersected by the brazen meridian, is the day required.

Ex. The azimuth of the star α in the Northern Crown was observed at London at 9 o'clock P.M. to be S. 89° W.; required the altitude and day of the month? Ans. Altitude 30°; day of the month 1st of September.

Problem XI. Having observed two stars to have the same azimuth; to find the hour of the night.

Rectify the globe as before; turn the globe and move the quadrant till the edge of the latter comes over both stars, and the horary index in this position of the globe will give the hour required.

The following is a simple and easy method of finding when two stars have the same azimuth. Hold a small line with a plummet at its lower extremity between the eye and the two stars, and if both stars fall within the line, they have the same azimuth. The same may be done by observing when any two stars pass behind the perpendicular edge of a wall at the same time.

Ex. Vega and Atair were observed to have the same azimuth at London on the 11th of May; required the hour of the night? Ans. 15 minutes past 2 A.M.

This problem may be applied to the regulating of pri- vate clocks and watches, by reducing apparent to real time, as explained under ASTRONOMY.

Problem XII. To find the rising, setting, and cul- minating of any star or planet, its continuance above the horizon, its oblique ascension and descension, and its eastern and western amplitude; the place and day being given.

Rectify the globe as in the foregoing problems; bring the given star or the given planet (finding its place in an ephemeris for the given day, and marking it by a patch on the globe) to the eastern part of the horizon, and the index of the hour circle will point out the time of rising: the degree of the equator that comes to the horizon with the given star or planet, marks its oblique ascension, and the eastern amplitude is shown by the dis- tance of the star or planet from the eastern part of the horizon.

Bring the star or planet to the meridian, and the in- dex will point to the time of its culminating.

Move the globe till the star or planet come to the western part of the horizon, and the time of its setting, its oblique descension, and its western amplitude, may be found in the same manner as directed above; for its rising, oblique ascension, and eastern amplitude, the number of hours passed over by the index, while the star or planet is moving from east to west, will shew the time of its continuance above the horizon.

Ex. 1. Required the above circumstances with respect to Sirius on the 14th of March at London. Ans. It rises at 24 minutes past two P.M.; comes to the meri- dian, or culminates, at 57 minutes past six P.M.; and sets at half-past eleven P.M. Hence it remains above the horizon nine hours and six minutes. Its oblique ascension is 120° 47', its oblique descension 77° 17', and its amplitude 27° S.

Ex. 2. It is required to find the situation of the sev- eral planets on the 19th of January 1806. Ans. Mer- cury is about 22° to the west of the sun, and rises south- east by east, at 20 minutes before seven A.M. Venus is an evening star, and sets about half past eight. Mars is a very little to the east of the sun, and rises and sets so near the same time with the sun, that he cannot be seen. Jupiter is a morning star, and rises about six o'clock. Saturn is a little to the east of the star Spica Virginis, and rises about half an hour after midnight. Herschel is very near Saturn, and rises about the same time.

Problem XIII. To find those stars which never rise, and those which never set, in a given latitude.

Rectify the globe for the latitude of the place; then, holding a black lead pencil so as to touch the surface of the globe at the northern point of the horizon, turn the globe, so that the pencil may describe a circle: all the stars which are between this circle and the ele- vated pole, never set. Again, holding the pencil at the southern point of the horizon, turn the globe so as to describe another circle there, and all the stars that are between that circle and the pole, below the horizon, never rise.

If the place is in southern latitude, the stars that ne- ver set are found by describing a circle at the southern point of the horizon, and those that never rise by a similar circle at the northern point (1).

Throughout almost the whole year, the moon rises later every successive day, by above three quarters of an hour; but at a considerable distance from the equator, as in the latitude of Britain, France, and some other countries, a remarkable anomaly takes place in the moon's motion about the time of harvest. At this season, when the moon is about full, she rises for several nights successively at about 17 minutes later only than on the preceding day. This is attended with considerable advantage, for as the moon rises before twilight is well ended, the light is as it were prolonged, and thus an opportunity given to the industrious farmer to continue longer in the field, for the purpose of gathering in the fruits of the earth. From the advantage derived from the full moon at the season of harvest, it has been called the harvest moon. The following problem has been contrived for the purpose of illustrating the phenomenon by means of the globe.

**Problem XIV.**

Rectify the globe for any considerable northern latitude, suppose that of London. As the angle which the moon's orbit makes with the ecliptic is but small, we may suppose, without any considerable error, her orbit to be represented by the ecliptic. In September the sun is in the beginning of \( \omega \), so that the moon, when full, being in opposition to the sun, must be in or near the beginning of \( \gamma \). Put a patch, therefore, in the globe at the first point of \( \gamma \) in the ecliptic; and as the moon's mean motion is about \( 13^\circ \) in a day, put another patch on the ecliptic \( 13^\circ \) beyond the former, and it will point out the moon's place the night after it is full. A third and fourth patch, put at the distance of \( 13^\circ \) farther on, will shew the moon's place on the second and third nights after full, &c. Now, bring the first patch to the horizon, and observe the hour pointed out by the index; turn the globe till the second patch comes to the horizon, and it will appear by the index that there are only 17 minutes between the time of the first patch rising, and that of the second. This small difference in the motion of the moon evidently arises from the small angle which her orbit makes with the horizon. The remaining patches will come to the horizon with a little greater difference of time, and this difference will gradually increase as the moon advances in the ecliptic; but for the first week after the full moon at harvest the difference will not be more than two hours. If patches be continued on to the first point in \( \omega \), it will be found that the time of their 'rising,' or coming to the horizon, will increase considerably till the last will be above \( 1\frac{1}{2} \) hour later in coming to the horizon, because that point of the ecliptic makes the greatest angle with the horizon.

The point of the ecliptic, which makes the least angle with the horizon at rising, makes the greatest angle at setting; and, consequently, when the difference is least at the time of rising, it is greatest at the time of setting.

**Problem XV. To explain the equation of time by the globe.**

The difference between apparent time and mean or equal time, has been explained in Astronomy, from No. 50 to 60; and the method of computing the equation of time is also there described.

To explain the equation of time on the globe, make, with a black lead pencil, marks all round the equator and ecliptic, beginning with \( \gamma \), at equal distances from each other, suppose about \( 15^\circ \). Then, on turning the globe, it will be seen that all the marks on the first quadrant of the ecliptic, reckoning from \( \gamma \) to \( \omega \), come to the brazen meridian sooner than the corresponding marks on the first quadrant of the equator. Now, as the former marks represent time as measured by the sun, or a dial, and the latter represent it as measured by an accurate clock, it will be evident, that through the first quarter the dial is faster than the clock.

Still turning the globe, it will be seen that the marks on the second quarter of the ecliptic, reckoning from \( \omega \) to \( \gamma \), come to the meridian later than the corresponding marks of the equator; consequently in this quarter the sun or the dial is slower than the clock. By moving the globe round, and marking the approach of the dots in the third quadrant, it will be seen that, as in the first, the dial now precedes the clock, and in the fourth quadrant, that it is behind it, according to the explanation given in Astronomy.

**Sect. III. Of the Construction of Globes.**

The construction of globes is of considerable importance; as, in performing the problems in which they are employed, very much depends on the accuracy with which they have been constructed. We shall here, therefore, describe pretty minutely the methods in which the artists of Britain and France make their globes.

There are certain general circumstances which are attended to in the construction of every globe.

There is first provided a wooden axis, somewhat less than the intended diameter of the globe, and to the extremities of this axis, which is the basis of the whole succeeding structure, there are fixed two metallic wires, to serve as poles. Now, two hemispherical caps formed on a wooden mould or clock, are applied in the axis. These caps are composed of pasteboard, or folds of paper laid one over another on the mould, till they are of the thickness of a crown piece; and after the whole has stood to dry, and has become a solid body, an incision is made with a sharp knife along the middle, and the two caps are thus slipped off the mould. These caps are now to be applied on the poles of the axis, as they were before on those of the mould; and to fix them

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(1) This problem may be performed without the globe, by the following method. Find the latitude of the place in a table, and subtract it from \( 90^\circ \); the remainder will be the complement of the latitude. Then, if the declination of the given star be of the same name with the co-latitude, and exceed it in quantity, it will never set. If it be of a contrary name, and exceed it, it will never rise. Principles them firmly on the axis, the two edges are sewed together with packthread.

When the rudiments of the globe are thus laid, the artist proceeds to strengthen the work, and make the surface smooth and equal. For this purpose, the two poles are fixed in a metallic semicircle, of the proposed size; and a composition made of whitening, mixed with water and glue, heated, melted, and incorporated together, is daubed all over the paper surface. While the plaster is applied, the globe is turned round in the semicircle, the edge of which pares away all the matter that is superfluous and exceeds the proper dimensions, and spreads the rest over those parts that require it. After this operation the ball stands to dry, and when it is thoroughly dried, it is again put in the semicircle, and fresh plaster applied to it; and thus they continue to apply composition and dry the ball alternately, till the surface accurately touches the semicircle in every point, when it becomes perfectly firm, smooth, and equal.

When the ball of the globe is thus finished, the map, containing a delineation of the surface of the earth, is to be pasted on the globe. For this purpose, the map is engraved in several gores or gussets, so that when these are accurately joined together on the spherical surface, they may cover every part of the ball, without overlapping each other. The greatest nicety is required in forming these engraved gussets, as well in the accuracy of the engraving, as in the choice and shape of the paper employed. The method of describing the gores or gussets, usually employed by the British artists, is as follows.

1. From the given diameter of the globe there is found a right line AB (fig. 12.), equal to the circumference of a great circle corresponding to that diameter; and this line is divided into 12 equal parts.

2. Through the several points of division, 1, 2, 3, 4, &c., with a distance equal to ten of the divisions, arches are described crossing each other as in D and E.; and these figures are pasted on the globe, so as when joined together to cover its whole surface.

3. Each part of the line AB is divided into 30 equal parts, so that the whole line, which may represent the equator, is divided into 360°.

4. From the points D and E., which represent the poles, with a distance = 23°5', there are described arches a b, a b, (fig. 13.) which form twelfth parts of the polar circles.

5. In a similar manner about the same poles D and E., with a distance = 66°50', reckoned from the equator, there are described other arches, c d, c d, which are the twelfth parts of the tropics.

6. In forming the celestial globe, through the point of the equator marked e (fig. 13.) representing the right ascension of a given star, and through the two poles D and E., there is drawn an arch of a circle; and if the complement of the declination from the pole D be taken in the compasses, and an arch be described, intersecting the former in the point i, this point i will be the place of the given star.

7. In this way all the stars of each constellation are laid down, and the circumscribing outline of the constellation is drawn as figured in the tables of Bayer, Flamstead, &c.

8. In the same manner are determined the declinations and right ascensions of every degree of the ecliptic, &c.

The above is the method described by Mr Chambers, of laying down or delineating the gores of a celestial globe. Those of the terrestrial globe are delineated in much the same manner, only that every place is laid down on the gores, according to its longitude and latitude, determined by the intersection of circles; and then the outline of the coasts, boundaries of countries, &c., are added, like the figures of the constellations above mentioned.

9. When the surface of the globe has been thus projected on a plane, the gussets are to be engraved on copper, to save the trouble of making a new projection for every globe.

10. In the mean time, a ball of paper, plaster, or the like, of the intended diameter of the globe, is prepared in the manner above described, and by means of a semicircle and style, great circles are drawn on its surface, so as to divide it into a number of equal parts, corresponding to the number of gussets; and subdividing each of these according to the other lines and divisions of the globe. When the ball is thus prepared, the gussets are to be accurately cut from the printed engraving, and pasted on the ball.

When the papers have been thus pasted on, and suffered to dry, nothing remains but to colour and illuminate the globe, and to cover it with a thin layer of the finest varnish, that it may the better resist dust and moisture. The ball of the globe is now finished, and is to be hung in a strong brazen meridian furnished with hour circles and a quadrant of altitude, and fitted into a strong wooden horizon.

The method employed by the French artists in projecting the gussets of globes, is thus described by Mr La Lande.

"To form celestial and terrestrial globes, it is necessary to engrave gores, which are a sort of projection or development of the globe. The length PC (fig. 14.) of the axis of the curve, is equal to a fourth part of the circumference of the intended globe; the intervals of the parallels on the axis PC are all equal; the radii of the circles K D I., which represent the parallels, are equal to the co-tangents of the latitude, and the arches of each, such as K I., are nearly equal to the number of degrees that correspond to the breadth of the gore (usually 30°), multiplied by the sine of the latitude; thus, there will be found no difficulty in tracing them; but the principal difficulty proceeds from the change which those parts of the gores undergo, when they are glued upon the globe; as, in order to adjust them to the space which they ought to occupy, it is necessary to make the paper less on the sides than in the middle, because the sides are too long.

"The method employed by artists for engraving these gores, is thus described by Bion (Usages des Globes, tom. iii.), and by Robert de Vaugondy in the seventh volume of the Encyclopédie, and this method is sufficient for practical purposes.

"Draw on the paper a line AC, equal to the chord of 15°, to make the half breadth of the gore; and a perpendicular PC, equal to three times the chord of 30°, to make the half length: for these papers, the dimensions of which will be equal to the chords, become equal to the arcs themselves when they are pasted on the globe. Divide the height CP into nine parts, if the parallels are to be drawn in every 10°; divide also the quadrant BE into nine equal parts; through each di- vision point of the quadrant, as G, and through the corresponding point D of the right line CP, draw the perpendiculars HGF and DF, the meeting of which in G gives one of the points of the curve BFP, which will terminate the circumference of the gore. When a sufficient number of points are thus found, trace the outline PIB with a curved rule. By this construction are given the gore breadths, which are on the globe, in the ratio of the cosines of the latitudes, supposing those breadths taken perpendicular to CD, which is not very exact; but it is impossible to prescribe a rigid operation sufficient to make a plane which shall cover a curved surface, and that on a right line AB shall make lines PA, PC, PD, equal to each other, as they ought to be on the globe. To describe the circle KDI, which is at the distance of 36° from the equator, there must be taken above O, a point that shall be distant from D the value of the tangent of 60°, which may be taken either from tables, or may be measured on a circle equal to the circumference of the globe that is to be drawn; this point will serve as a centre for the parallel DI, which ought to pass through the point D; for it is supposed equal to that of a cone circumscribing the globe, and which would touch it at the point D.

The meridians are traced to every 10°, by dividing each parallel, as KI, into three equal parts at the points L and M, and drawing from the pole B, through all these points of division, curves which represent the intermediate meridians lying between PA and PB, such as BR and ST (fig. 15).

The ecliptic AQ (fig. 15.) is traced by means of the known declination, from different points of the equator, as found in the tables; for 10° it is equal to 3° 58′; for 20° = 7° 50′ = BQ 20°; for 30° = 11° 29′, &c.

In general, it is observed that the paper on which maps are printed, such as that called in France colomier, contracts itself 4/7, or a line in six inches, upon an average, when it is dried after printing; hence it is necessary to prevent this inconvenience in engraving the gores: if, however, notwithstanding this, the gores are still found too short, it must be remedied by taking from the surface of the ball a little of the white with which it is covered; thus making the dimensions of the ball correspond to those of the gores as they are printed. But, what is singular, in drawing the gore, moistened with the paste to apply it on the globe, the axis GH lengthens, and the side AN shortens in such a manner that neither the length of the side ACK, nor that of the axis GEH of the gore are exactly equal to the quarter of the circumference of the quarter of the globe, when compared to the figure on the copper, or to the numbers shewn on the side of fig. 15.

Mr Bonne having made several experiments on the dimensions which the gores take after being covered with paste in order to apply them to the globe, especially of the paper called Jesus, which had been employed in covering globes of a foot in diameter; found that it was necessary to give to the gore engraved on copper the dimensions laid down in fig. 15. Supposing that the radius of the globe contains 720 parts, the half of the breadth of the gore AG = 188.5; the distance AC for the parallel of 10° taken on the straight line LM is = 128.1, the small deviation from the parallel of 10° in the middle of the gore ED is 4, the line ABN is a straight line, the radius of the parallel of 10° or of the circle CET, is 4083, &c. The small circular cap which is placed under H, has its radius 253, instead of 247, which it would have if the sine of 20° had been the radius of it.*

Globes are made of various sizes, from a diameter of three inches, to that of as many feet; but their most usual diameter is that of 18 inches, which are sufficiently large for most of the purposes for which globes are employed. Some large globes were made about 100 years ago, in France, by P. Coronelli, a Franciscan monk, which were in considerable reputation. They were engraved, and the plates are still to be seen at Paris, at the house of M. Desnos, in the Rue St Jacques. There are some large globes at Cambridge, which were drawn by the hand; but the largest globes of which we have any account, are those which were made for the late unfortunate Louis XVI. and were kept in the palace of Marly. They were 12 feet in diameter, and we believe, are still existing at Paris, where they occupy four entire rooms, each of them being partly in an upper room, and partly in that below it, the floor of the upper room forming the horizon.

The account which we have given of the method of constructing globes, will be useful to those who purchase these instruments; but to assist them still further, we shall subjoin the following practical rules for the choice of globes.

1. The papers should be well and neatly pasted on the globes, which may be known by the lines and circles meeting exactly, and continuing all the way even and whole; the circles not breaking into several arches, nor the papers either coming short, or lapping over one another.

2. The colours should be transparent, and not laid too thick upon the globe, to hide the names of the places.

3. The globe should hang evenly between the brazen meridian and the wooden horizon, not inclining either to the one side or the other.

4. The globe should move as close to the horizon and the meridian as it conveniently may, otherwise there will be too much trouble to find against what part of the globe any degree of the meridian or horizon is.

5. The equinoctial line should be even with the horizon all round, when the north or south pole is elevated 90° above the horizon.

6. The equinoctial line should cut the horizon in the east and west points, in all the elevations of the pole from 0° to 90°.

7. The degree of the brazen meridian marked 0° should be exactly over the equinoctial line of the globe.

8. Exactly half of the brazen meridian should be above the horizon, which may be known by bringing any of the decimal divisions on the meridian to the north point of the horizon, and finding their complement to 90° on the south point.

9. When the quadrant of altitude is placed as far from the equator, or the brazen meridian, as the pole is elevated above the horizon, the beginning of the degrees of the quadrant should reach just to the plane surface of the horizon.

10. When the index of the hour circle passes from one... Principles one hour to another, 15 degrees of the equator must pass under the graduated edge of the brazen meridian.

The wooden horizon should be made substantial and strong; it being generally observed, that, in most globes, the horizon is the first part that fails, on account of its having been made too slight.

In using a globe, the eastern side of the horizon should be kept towards the observer, (unless in particular problems which require a different position); and that side may be known by the word east on the horizon. In this position the observer will have the graduated side of the meridian towards him, and the quadrant of altitude directly before him; and the globe will be exactly divided into two equal parts by the graduated side of the meridian.

In performing some problems, it will be necessary to turn about the whole globe and horizon, in order to look at the west side; but this turning will be apt to disturb the ball, so as to shift away that degree of the globe which was before set to the horizon or meridian. This inconvenience may be avoided by thrusting the feather end of a quill between the ball of the globe and the brazen meridian, and thus, without injuring the surface of the globe, it will be kept from turning in the meridian, while the whole is moved round, so as to examine the western side.

We have already mentioned some improvements which have been made on the globes, for the purpose of remedying the defect in the old construction, of placing the hour circles on the outside of the brazen meridian. Some other improvements and modifications have been contrived by various artists; but of these we shall only mention those of Mr Senex, Mr B. Martin, Mr Smeaton, and Mr Adams.

Mr John Senex, F.R.S. invented a contrivance for remedying these defects, by fixing the poles of the diurnal motion to two shoulders or arms of brass, at the distance of $23^\circ$ from the poles of the ecliptic. These shoulders are strongly fastened at the other end to an iron axis, which passes through the poles of the ecliptic, and is made to move round with a very stiff motion; so that when it is adjusted to any point of the ecliptic which the equator is made to intersect, the diurnal motion of the globe on its axis will not disturb it. When it is to be adjusted for any particular time, either past or future, one of the brazen shoulders is brought under the meridian, and held fast to it with one hand, while the globe is turned about with the other; so that the point of the ecliptic which the equator is to intersect may pass under the 0 degree of the brazen meridian; then holding a pencil to that point, and turning the globe about, it will describe the equator according to its position at the time required; and transferring the pencil to $23^\circ$ and $66^\circ$ degrees on the brazen meridian, the tropics and polar circles will be so described for the same time. By this contrivance, the celestial globe may be so adjusted, as to exhibit not only the rising and setting of the stars in all ages and in all latitudes, but likewise the other phenomena that depend upon the motion of the diurnal round the annual axis. Senex's celestial globes, especially the two greatest, of 27 and 28 inches in diameter, have been constructed upon this principle; so that by means of a nut and screw, the pole of the equator is made to revolve about the pole of the primary ecliptic.

To represent the above appearances in the most natural and easy manner, Mr B. Martin applied to the contrivance of Mr Senex a moveable equinoctial and solstitial colore, a moveable equinoctial circle, and a moveable ecliptic; all so connected together as to represent those imaginary circles in the heavens for any age of the world.

In order to the performance of the problems which relate to the altitudes and azimuths of celestial objects, Mr Smeaton, F.R.S. has made some improvements applicable to the celestial globe; and to give some idea of the construction, they may be described as follows:

Instead of a thin flexible slip of brass, which generally accompanies the quadrant of altitude, Mr Smeaton substitutes an arch or a circle of the same radius, breadth, and substance, as the brass meridian, divided into degrees, &c. similar to the divisions of that circle, and which, on account of its strength, is not liable to be bent out of the plane of a vertical circle, as is usual with the common quadrant put to globes. That end of this circular arch at which the division begins, rests on the horizon, being filed off square to fit and rest steadily on it throughout its whole breadth; and the upper end of the arch is firmly attached, by means of an arm, to a vertical socket, in such a manner that when the lower end of the arch rests on the horizon, the lower end of this socket shall rest on the upper end of the brass meridian, directly over the zenith of the globe. This socket is fitted to and ground with a steel spindle of the length, so that it will turn freely on it without shaking; and the steel spindle has an apparatus attached to its lower end, by which it can be fastened in a vertical position to the brass meridian, with its centre directly over the zenith point of the globe. The spindle being fixed firmly in this position, and the socket which is attached to the circular arch put on it, and so adjusted that the lower end of the arch just rests on and fits close to the horizon; it is evident that the altitude of any object above the horizon will be shewn by the degree which it intersects on this arch, and its azimuth by that end of the arch which rests on the horizon.

Besides this improvement, Mr Smeaton proposes that, instead of fixing the hour index, as is usually done, on one end of the axis, it be placed in such a manner that its upper surface may move in the plane of the hour circle rather than above it. To effect this, he directs the extremity of the index to be filed off so as to form a circular arc, of the same radius with the inner edge of the hour circle, to which it is made to fit exactly, and a fine line is drawn in the middle of its upper surface, to point out the hour, instead of the tapering point usually employed. By this contrivance, if the hour circle be made four inches in diameter, the time may be shewn to half a minute. For a more particular account of Mr Smeaton's improvements, we refer the reader to the 79th volume of the Philosophical Transactions.

Another improvement of the celestial globe, by which it is better adapted to astronomical purposes, is described in the article ASTRONOMY, Vol. III. p. 178.

Besides the modifications in the construction of globes, introduced by Mr Adams, and which have been al- ready described, there are some others which we must briefly mention, respecting principally the placing the globe in an inclined position, and fitting it with a moveable or floating meridian and horizon.

The globes constructed after this manner do not hang in a frame like the ordinary globes, but are fixed on a pedestal, and supported by an axis which is inclined 66° to the ecliptic, and is of course always parallel to the axis of the earth, supposing the orbit of this planet to be parallel to the ecliptic. On the pedestal below the globe is a graduated circle, marked with the signs and degrees of the ecliptic; and adjoining to this is a circle of months and days, answering to every degree of the ecliptic; and within this is a third circle shewing the sun's declination for every day of the month. There is a moveable arm on the pedestal, which being set to the day of the month, immediately points out the sun's place and declination.

Round the globe there is a circle representing the horizon of any place, and at right angles to this is fixed a semicircle, serving for a general meridian. The middle point of this semicircle serves to represent the situation of any inhabitant on the earth; for this purpose there is fixed a steel pin over the middle point of this semicircle.

Mr Adams alleges that only one supposition is necessary for performing every problem with this globe, namely, that a spherical luminous body will enlighten one half of a spherical opaque body, and consequently that a circle at right angles with the central solar ray, and dividing the globe in half, will be a terminator shewing the boundary of light and darkness for any given day. For this purpose, at the end of the moveable arm, opposite to the sun, there is a pillar, from the top of which projects a piece carrying a circle that surrounds the globe, dividing it into equal portions, and separating the illuminated from the dark parts; and 18° behind this there is another circle parallel to it, representing the limit of twilight.

There are two plates below the globe, which are turned by the diurnal revolution of the globe, each of them being divided into twice 12 hours, and on the outside being marked with the degrees of longitude corresponding to every hour; so that these circles give at sight the hour of the day at any two places on the globe, and the corresponding difference of longitude.

The celestial globe is mounted in a similar manner, except that it is fixed on the axis, and the ecliptic exactly coincides with the sun's apparent path from the earth.

Sect. IV. Of the Armillary Sphere.

If a machine be constructed that is composed only of the circles of the sphere, and made so as to revolve like a globe, a great many of the most useful problems relating to the heavenly bodies may be solved by it. An instrument of this kind is called an armillary sphere, and of these there are various forms. One of the most convenient is that contrived by the late Mr James Ferguson, and is thus described in his Lectures. It is represented at fig. 16.

The exterior parts of this machine are a compass of brass rings, which represent the principal circles of the heaven, viz. 1. The equinoctial AA, which is divided into 360 degrees, (beginning at its intersection with the ecliptic in Aries) for shewing the sun's right ascension in degrees; and also into 24 hours, for shewing his right ascension in time. 2. The ecliptic BB, which is divided into 12 signs, and each sign into 30 degrees, and also into the months and days of the year, in such a manner, that the degrees or points of the ecliptic in which the sun is on any given day, stands over that day in the circle of months. 3. The tropic of Cancer, CC, touching the ecliptic at the beginning of Cancer in e; and the tropic of Capricorn DD, touching the ecliptic at the beginning of Capricorn in f; each 23½ degrees from the equinoctial circle. 4. The Arctic circle E, and the Antarctic circle F, each 23½ degrees from its respective pole at N and S. 5. The equinoctial colure GG, passing through the south and north poles of the heaven at N and S, and through the equinoctial points Aries and Libra, in the ecliptic. 6. The solstitial colure HH, passing through the poles of the heaven, and through the solstitial points Cancer and Capricorn, in the ecliptic. Each quarter of the former of these colures is divided into 90 degrees, from the equinoctial to the poles of the world, for shewing the declination of the sun, moon, and stars; and each quarter of the latter, from the ecliptic at e and f, to its poles b and d, for shewing the latitude of the stars.

In the north pole of the ecliptic is a nut b, to which is fixed one end of a quadrantal wire, and to the other end a small sun Y, which is carried round the ecliptic BB, by turning the nut: and in the south pole of the ecliptic is a pin at d, on which is another quadrantal wire, with a small moon Z upon it, which may be moved round by hand; but there is a particular contrivance for causing the moon to move in an orbit which crosses the ecliptic at an angle of 5½ degrees, in two opposite points called the moon's nodes; and also for shifting these points backward in the ecliptic, as the moon's nodes shift in the heaven.

Within these circular rings is a small terrestrial globe I, fixed on the axis KK, which extends from the north and south poles of the globe at n and s, to those of the celestial sphere at N and S. On this axis is fixed the flat celestial meridian LL, which may be set directly over the meridian of any place on the globe, and then turned round with the globe, so as to keep over the same meridian upon it. This flat meridian is graduated the same way as the brass meridian of a common globe, and its use is much the same. To this globe is fitted the moveable horizon MM, so as to turn upon two strong wires proceeding from its east and west points to the globe, and entering the globe at opposite points of its equator, which is a moveable brass ring let into the globe in a groove all around its equator. The globe may be turned by hand within this ring, so as to place any given meridian upon it, directly under the celestial meridian LL. The horizon is divided into 360 degrees all around its outermost edge, within which are the points of the compass, for shewing the amplitude of the sun and moon, both in degrees and points. The celestial meridian LL, passes through two notches in the north and south points of the horizon, as in a common globe; but here, if the globe be turned round, the horizon and the meridian turn with it. At the south pole of the sphere is a circle of 24 hours, fixed to the rings, and on the axis is an index which goes round that circle, if the globe be turned round its axis.

The whole fabric is supported on a pedestal N, and may be elevated or depressed upon the joint O, to any number of degrees from 0 to 90, by means of the arc P, which is fixed into the strong brass arm Q, and slides in the upright piece R, in which is a screw at r, to fix it at any proper elevation.

In the box T are two wheels and two pinions, whose axes come out at V and U; either of which may be turned by the small winch W. When the winch is put upon the axis V, and turned backward, the terrestrial globe, with its horizon and celestial meridian, keep at rest; and the whole sphere of circles turns round from east, by south, to west, carrying the sun Y, and moon Z, round the same way, causing them to rise above and set below the horizon. But when the winch is put upon the axis U, and turned forward, the sphere with the sun and moon keep at rest; and the earth, with its horizon and meridian, turn round from west, by south, to east; and bring the same points of the horizon to the sun and moon, to which these bodies come when the earth kept at rest, and they were carried round it; shewing that they rise and set in the same points of the horizon, and at the same times in the hour circle, whether the motion be in the earth or in the heaven. If the earthly globe be turned, the hour index goes round its hour circle; but if the sphere be turned, the hour circle goes round below the index.

And so, by this construction, the machine is equally fitted to shew either the real motion of the earth, or the apparent motion of the heaven.

To rectify the sphere for use, first slacken the screw r in the upright stem R, and taking hold of the arm Q, move it up or down until the given degree of latitude for any place be at the side of the stem R; and then the axis of the sphere will be properly elevated, so as to stand parallel to the axis of the world, if the machine be set north and south by a small compass; this done, count the latitude from the north pole upon the celestial meridian LL, down towards the north notch of the horizon, and set the horizon to that latitude; then turn the nut b until the sun Y comes to the given day of the year in the ecliptic, and the sun will be at its proper place for that day; find the place of the moon's ascending node, and also the place of the moon, by an Ephemeris, and set them right accordingly; lastly, turn the winch W, until either the sun comes to the meridian LL, or until the meridian comes to the sun (according as you want the sphere or the earth to move), and set the hour index to the XII marked noon, and the whole machine will be rectified. Then turn the winch, and observe when the sun or moon rise and set in the horizon, and the hour index will shew the times thereof for the given day.

Those who have made themselves acquainted with the use of the globes, as described in the first and second sections of this chapter, will be at no loss to perform many problems respecting the motions of the heavenly bodies by means of this sphere.

Dr Long, some years ago, constructed an armillary sphere of glass, in Pembroke hall at Cambridge. It was 18 feet in diameter, and could contain below it more than 30 persons, sitting in such a manner within the sphere, as to view from its centre the representation of the heavens drawn in its concavity. The lower part of the sphere, or that part which is not visible in the latitude of Britain, is wanting; and the whole apparatus is so contrived, that it may be turned round with as little exertion as is requisite to wind up a common jack. Dr Long has given a description of this sphere, accompanied with a figure, in his Astronomy.

The invention of the armillary sphere is thought by La Lande to be as ancient as that of astronomy itself. It has been attributed to Atlas, to Hercules, to Anaximander, and Musaeus; while others have supposed that it originated in Egypt. The sphere of Archimedes, which became so celebrated, appears to have been something like that of Dr Long, as it was certainly composed of a globe of glass, which, besides containing the circles of the sphere, served as a planetarium, and represented the motions of the planets. Claudian has celebrated it in some beautiful lines. See ARCHIMEDES.

A combination of the armillary sphere with a planetarium was constructed by the late Mr George Adams, and is figured in Plate XIII, fig. 1, of his Astronomical and Geographical Essays.

CHAP. III. Of the Construction and Use of Maps and Charts.

SECT. I. Description of Maps and Charts.

It has been seen, that the surface of the earth may be delineated, in the most accurate manner, on the surface of a globe or sphere. This mode of delineation, however, can be employed only for the purpose of representing the general form and relative proportions of countries on a very confined scale; and is, besides, from its bulk and figure, not well suited to many of the purposes of the geographer. To obviate these inconveniences, recourse has been had to maps and charts, or delineations of the earth's surface on a plane; where the form and boundaries of the several countries, and the objects most remarkable in each, whether by sea or land, are represented according to the rules of perspective, so as to preserve the remembrance that they are parts of a spherical surface. In this way, the several countries or districts of the earth may be represented on a larger scale, and delineations of this kind admit of more easy reference.

In maps, the circles of the sphere, and the boundaries of the countries within them, are drawn as they would appear to an eye situated in some point of the sphere, or at a considerable distance above it. In maps of any considerable extent of country, the meridians and parallels of latitude are circular lines, but, if the map represents only a small district, as a province or county, those circles become so large, that they may, without any considerable error, be represented by straight lines. In charts, which are also called hydrographical maps, as they are representations rather of the water than land, the meridians and parallels are usually represented by straight lines, crossing each other at right angles, as in the smaller maps; and, in particular parts, there are drawn lines diverging from several points, in the direction of the points of the compass, in order to mark the bearings of particular places. In maps, the inland face of the country is chiefly regarded in the delineation; but in charts, which are designed for the purposes of navigation, the internal face of the land is left nearly blank, and only the sea coast, with the principal objects on it, such as churches, light-houses, beacons, &c., are accurately delineated; while particular care is taken to mark the rocks, shoals, and quicksands in the sea, that may endanger the safety of vessels; the depths or soundings of the principal bays and harbours, and the direction of the winds, where these are stationary or peculiarly prevalent. Another distinction of maps and charts is, that in the former, the sea-coast is shaded on the side next the land, while, in the latter, it is shaded towards the sea.

In maps the upper side represents the north, the lower side the south; that on the right hand the east, and that on the left hand the west. All the margins of the map are graduated; the upper and lower showing the degrees of longitude, and the right and left margins the degrees of latitude. (See fig. 1., to which the reader must refer in going over the following description). If the map is on a small scale, only every ten degrees of longitude or latitude are marked on the margin; but, if the map is drawn on a large scale, every degree is numbered, and sometimes every half degree is marked with the number 30 in smaller figures. The space included between every two degrees in small maps, or between every two degrees in those on a larger scale, is usually divided into ten spaces, which are alternately left blank, and marked with parallel lines, to denote the subdivisions of single degrees or minutes. Through every ten degrees of latitude a line is drawn, representing a parallel of latitude; and through every ten degrees of longitude, or at smaller intervals in each, where the size of the map will admit of it, there are drawn lines representing meridians. In some maps these lines are continued from side to side, or from top to bottom, across both sea and land; but in other maps, they are sometimes only drawn across the sea. The first meridian, however, and the principal circles of the sphere, as the equator, tropics, &c., should always be drawn directly across the map. In most maps, it is marked on the margins whether the longitude is east or west, and the latitude north or south; but, if this is not marked, it may easily be known, by observing towards what part of the map the degrees increase. If the degrees of latitude increase from the lower to the upper part of the map, the country delineated lies in north latitude; but if they increase from above downwards, it lies in south latitude. Again, if the degrees of longitude increase towards the right, the countries are in east longitude; but if towards the left, they are in west longitude.

The principal objects that diversify the face of the country delineated in the map, such as rivers, mountains, forests, lakes, roads, cities, towns, forts, &c., are marked in such a manner as that they may be most easily distinguished. A river is denoted by a black crooked line, drawn very fine towards the source or head of the river, and gradually becoming broader as it approaches towards the mouth; and the lesser rivers or rivulets, which unite their waters with those of their principal stream, are denoted by similar lines appearing to branch off from the first.

Mountains are represented by the figures of little hills; and if these figures are placed in a row, they denote a ridge of mountains running across the land. If a mountain is a volcano, it is denoted in the map by the appearance of smoke issuing from its summit. Woods or forests are represented by a number of little trees or shrubs, placed in a group. Lakes are denoted by a circumscribed spot shaded with dark lines, and bogs or fens by a more regular spot of the same kind, more lightly shaded, or, where the map is coloured, painted of a light green. Roads are represented in a map by two straight lines drawn parallel to each other, for the principal roads, or by a single straight line for the lesser or cross roads. Cities are denoted by a large house, or the figure of a church with the steeple in the middle; and if the city is the metropolis of the country, this is denoted by a white circular space in the middle of the house or church. Small towns are usually represented by circles; and where a small church with the steeple at one end occurs, it denotes a parish. Where the map is on a large scale, or represents only a small district, the towns are denoted by a group of small houses, or more commonly by a number of small shaded spots on each side of the road. A fort, castle, or fortified town, is denoted by a semicircular space surrounded by an angular edge representing bastions. The shoals upon the coast are represented by small dots; the depth of water in bays and harbours by figures, denoting the number of fathoms, among which is sometimes drawn the figure of an anchor, to show that in that place there is good anchorage for ships.

The boundaries or limits that divide countries from each other are distinguished in maps by dotted lines drawn round each country or district, in such a direction as to show its proper form. Where the map is coloured, the countries or districts are distinguished from each other by the side of the boundary next each being shaded by a different colour from that of the adjoining. Thus, in a map of Europe the boundary of France may be shaded green, that of Spain red, that of Italy yellow, that of Germany blue, &c. In one corner of the map there is usually drawn a scale divided into a number of equal parts, by which the number of miles or leagues, from one part of the map to another may be measured. Sometimes the parts into which the scale is divided are used to denote geographical miles, of 60 to a degree; but more commonly they correspond to the miles in use in the country where the map is made, as in Britain, to British statute miles of 69½ to a degree.

To mark more distinctly the bearings of different parts of the map, there is usually added in some blank space a circle with four radii, marking the four cardinal points of the compass; the north point being distinguished by the figure of a fleur de lis, and the east point by a cross.

Till of late, the only distinction between the land and water in maps and charts, was afforded by the shading of the sea-coasts, as mentioned above. In this way, however, the eye cannot easily and expeditiously distinguish the form and extent of the land; and, where the shading is carried much beyond the boundary of the coast, as is often done, especially in engraving small islands, the land is made to appear much larger than it really is.

The ingenious Mr. Wilson Lowry having lately contrived an instrument for engraving parallel straight lines, in a much more clear and commodious way Principles than could be done by the common graver, it occurred to Mr Pinkerton, while preparing his Modern Geography, that this invention might be applied with advantage to the improvement of maps. A set of maps was accordingly engraved by Mr Lowry for Pinkerton's Geography, in which the water was marked by dark parallel lines to discriminate it from the land. These lines are drawn horizontally; and Mr Pinkerton proposed that, in engraving charts, the land should be marked with similar lines drawn in a perpendicular direction, while the water should be left blank. This improvement has since been adopted by other constructors of maps and charts, and bids fair to be generally used. The effect is pleasing; and the progress of instruction will be greatly facilitated by the new method, as the extent and bearings of the several countries are seen, as it were, with a glance of the eye. In many of these maps which we have seen, however, the lines are drawn too strongly, which renders the sea so dark, that the names of islands and places on the sea coast can with difficulty be perused. As the line of coast in these maps is strongly marked, the parallel lines denoting the sea should be engraved in a light and soft style; and in this way Mr Lowry's first specimens are executed.

Sect. II. Of the Construction of Maps and Charts.

The construction of maps consists in making a projection of the surface of the globe on the plane of some one of its circles, supposing the eye to be placed in some particular point. The describing of these projections depends on the principles of perspective, and the projection of the sphere. The general principles will be explained under those articles, but the particular mode of drawing maps properly forms a part of the present treatise.

The methods of constructing maps vary according to the size or scale of the map, and to the projection employed in constructing it.

There are three projections employed in constructing maps, the orthographic, the stereographic, and the globular projections. In the orthographic projection the eye is supposed to view the part of the globe to be projected, from an infinite distance. In this projection the parts about the middle of the map are very well represented, but those towards the margin are too much contracted.

In the stereographic projection, the eye is supposed to be situated in the surface of the globe to be represented, presented, and looking towards the opposite surface. This is the method usually employed in constructing most maps, especially maps of the world, or planispheres.

In constructing a map of the world, as well as most partial maps, the part of the sphere to be represented is supposed to be in the position of a right sphere (see No. 95.). In this mode of projection, the hemisphere to be represented is supposed to be delineated on the plane of that meridian by which it is bounded, in the same manner as its concave surface, conceiving the sphere to be transparent, would appear to an eye placed in the opposite hemisphere, where the equator crosses a meridian; that is 90° distant from that which forms the plane of the projection. In a delineation of this kind, the meridians and parallels of latitude are represented by arches of circles, except the equator and the central meridian, which are straight lines; and each parallel or meridian forms an arc of a greater circle, in proportion as it approaches nearer to the centre of the map.

By either of these projections only half the globe can be represented in one projection; but in the map of the world, the two hemispheres are usually drawn on the plane of the same circle, adjacent to each other. By Mercator's projection, usually employed for charts, and to be described presently, the whole globe may be represented in one projection, but much distorted.

If the projection of a map of the world be formed on the plane of a meridian, the two projections will represent the eastern and western hemispheres of the globe.

When the projection is made on the plane of the equator, in the situation of a parallel sphere, the projections represent the northern and southern hemispheres, which appear as their concave surface would be seen by an eye placed at the opposite pole. In this way the meridians become straight lines diverging from the same centre, and the parallels are circles having the same common centre.

The following is the method of constructing a map of the world, on the plane of a meridian, according to the globular projection. (See fig. 17.)

About the centre C, with any radius as CB, describe a circle, representing the meridian that is to form the proper plane of the hemisphere. Draw the diameters NS, of a and AB, crossing each other at right angles, and the former of these will be the central meridian, and the latter the equator. Divide each semidiameter into nine equal parts, and divide each quadrant of the circle also into nine equal parts, each of which will be equal to 11°. If the scale of the map be sufficiently large, each of these may again be divided into ten equal parts or degrees. The next object is to describe the meridians passing through every 10° of the equator. Suppose we are to draw the meridian of 80° west of Greenwich. We have here three points given, the two poles and the point 80° on the equator, and it is easy to describe a circle that shall pass through these three points. This arch will be the meridian. The method of drawing a circle through any three points is, in this case as follows: About the centre S, with the radius SC, describe a circular arch, as XX; and about the centre N, with the same radius, describe the arch ZZ; then about the centre 80° with the same distance, describe arches 1, 2, 3, 4, crossing the former, and draw lines from 2 to 1 on each side of AB, crossing each other, and AB produced, in D. D is the centre of the circular arc, representing the meridian of 80° west from Greenwich; and with the same radius the meridian of 130° west longitude may be drawn. All the other meridians are to be drawn in a similar manner by describing a circular arch through three points N, S, and the required degree. (See GEOMETRY).

For describing the parallels, suppose that of 60° N. Lat.; about the centre O, with any radius, describe the circle FGH, and about the points 60°, 60°, in the primitive circle, with the same distance, describe the arcs cc, dd, cutting the circle FGH: through the points of intersection draw straight lines, and the point where these lines meet in NS produced, as in I, is the centre of the arch that will represent the parallel of 60°. The other parallels are drawn in a similar manner, observing that the first circle, such as FGH, must have for its centre that point in the central meridian through which the parallel is to be drawn. Fig. 18. represents this projection. If the map is very large, and the paper on which it is to be drawn does not admit of so many circles, the centres of the meridians and parallels are more easily found in the following manner. Having divided the semi-diameters and quadrants, each into 9 equal parts, find, from a scale of equal parts, the length of the half chord of each arc, and the versed sine of half the same arc; then add together the square of the half chord, and the square of the versed sine, and divide the sum by the versed sine; the quotient is equal to the diameter, and \( \frac{1}{2} \) of this to the radius of the circle required. In this manner the radii of all the meridians and parallels may be found.

As, in drawing maps on a large scale, compasses of an ordinary size will not answer for describing the circular arcs, it is convenient to have some other mechanical contrivance for this purpose; and it is found that a thin flexible ruler of tough wood, called a bow, may be so bended as to form a curve, very nearly circular, that will pass through the three points that are to determine the meridian or parallel. In this way the circles on maps on a large scale are usually drawn by engravers and students of geography, and where the circle is of very large radius, the method is sufficiently accurate; but it ought by no means to be employed where compasses of a proper size can be procured, or conveniently used.

The following is the method given by Dr Hutton, for describing a globular projection of the earth on the plane of the equator. For the north or south hemispheres draw AQBE, for the equinoctial (fig. 19.), dividing it into the four quadrants EA, AQ, QB, and BE; and each quadrant into 9 equal parts, representing each 10° of longitude; and then from the points of division, draw lines to the centre C, for the circles of longitude. Divide any circle of longitude, as the first meridian EC, into 9 equal parts, and through these points describe circles from the centre C, for the parallels of latitude, numbering them as in the figure. In this method equal spaces on the earth are represented by equal spaces on the map, as nearly as any projection will bear; for a spherical surface can in no way be represented exactly upon a plane. Then the several countries of the world, seas, islands, sea-coasts, towns, &c. are to be entered in the map, according to their latitudes and longitudes.

To draw a Map of any particular Country.

There are three methods of doing this.

1st. For this purpose its extent must be known as to latitude and longitude; as suppose Spain, lying between the north latitudes 36° and 44°, and extending from 10° to 23° of longitude, so that its extent from north to south is 8°, and from east to west 13°.

Draw the line AB for a meridian passing through the middle of the country (fig. 20.), on which set off 8° from B to A, taken from any convenient scale; A being the north and B the south point. Through A and B draw the perpendiculars CD, EF, for the extreme parallels of latitude. Divide AB into eight parts, or degrees, through which draw the other parallels of latitude parallel to the former.

For the meridians, divide any degree in AB into 60 equal parts, or geographical miles. Then, because the length in each parallel decreases towards the pole, take the number of miles answering to the latitude of B, which is 48° nearly, and set it from B, seven times to E, and six times to F; so is EF divided into degrees. Again, from the same table take the number of miles of a degree in the latitude A, viz. 43° nearly; which set off from A, seven times to C, and six times to D. Then from the points of division in the line CD, to the corresponding points in the line EF, draw so many right lines for the meridians. Number the degrees of latitude up both sides of the map, and the degrees of longitude on the top and bottom. Also in some vacant place make a scale of miles, or of degrees, if the map represent a large part of the earth; to serve for finding the distances of places upon the map.

Then make the proper divisions and subdivisions of the country; and having the latitudes and longitudes of the principal places, it will be easy to set them down in the map; for any town, &c. must be placed where the circles of its latitude and longitude intersect. For instance, Gibraltar, whose latitude is 36° 11', and longitude 12° 27', will be at G; and Madrid, whose latitude is 40° 10', and longitude 14° 44', will be at M. In the same manner the mouth of a river may be set down; but to describe the whole course of the river, the latitude and longitude of every turning, and of the towns and bridges by which it passes, must also be marked down. The same is necessary for woods, forests, mountains, lakes, castles, &c. The boundaries are described by setting down the remarkable places on the sea coast, and drawing a continued line through them all. This method is very proper for small countries.

2nd Method. Maps of particular places are but portions of the globe, and may therefore be drawn in the same manner as the whole globe, either by the orthographic or stereographic projection of the sphere. But in partial maps a more easy method is as follows. Having drawn the meridian AB in the last figure, and divided it into equal parts as before, draw lines through all the points of division; put them together to AB, to represent the parallels of latitude. Then to divide these, set off the degrees in each parallel; diminish after the manner directed for the two extreme parallels CD and EF, and through all the corresponding points draw the meridians, which will be curved lines; these were right lines in the last method, because only the extreme parallels were divided according to the table. This method is proper for a large tract, as Europe, &c. in which case the parallels and meridians need be drawn only through every 5° or 10°. This method is much used in drawing maps, as all the parts are nearly of their due magnitude, except being a little distorted towards the outside, from the oblique intersection of the meridians and parallels.

3rd Method. Draw PB of a convenient length, for a meridian; divide it into nine equal parts, and through the points of division, describe as many circles for the parallels of latitude, from the centre P, which represents the pole. Suppose AB (fig. 21.) the height of the map; then CD will be the parallel passing through the greatest latitude, and EF will represent the equator. Divide the equator EF into 9 equal parts of the same size as those in AB, both ways beginning AB; Principles divide also all the parallels into the same number of equal parts, but lesser, in proportion to the numbers for the several latitudes, as directed in the last method for the rectilineal parallels. Then through all the corresponding divisions draw curved lines which will represent the meridians, the extreme meridians being EC and FD. Lastly, number the degrees of latitude and longitude, and place a scale of equal parts, either in miles or degrees, for measuring distances.

When the place of which a map is to be made is but small, as when a county is to be delineated, the meridians will be so nearly parallel to one another, and the whole will differ so little from a plane, that the map may be laid down in a much more easy manner than what is given above. It will be here sufficient to measure the distances of places in miles, and note them down in a plane rectangular manner. The method of delineating such partial maps is the province of the surveyor. See Surveying.

Mercator's projection is chiefly confined to charts for the purposes of navigation. In this projection the meridians, parallels, and rhumbs, are all straight lines; but instead of the degrees of longitude being everywhere equal to those of latitude, as is the case in plain charts, the degrees of latitude are increased as we approach towards either pole, being made to those of longitude in the proportion of radius to the sine of the distance from the pole, or cosine of the latitude, or, what is the same thing, in the ratio of the secant of the latitude to radius. Hence all the parallel circles are represented by equal and parallel straight lines, and all the meridians are parallel lines also; but these increase indefinitely towards the poles.

From this proportional increase of the degrees of the meridian, it is evident that the length of an arc of the meridian beginning at the equator is proportional to the sum of all the secants of the latitude; or that the increased meridian bears the same proportion to its true arc as the sum of all the secants of the latitude to as many times the radius. The increased meridian is also analogous to a scale of the logarithmic tangents, though this is not at first very evident. It is not certain by whom this analogy was first discovered, but the discovery appears to have been made by accident. It was first published and introduced into the practice of navigation by Mr Henry Bond, by whom this property is mentioned in an edition of Norwood's Epitome of Navigation, printed about 1645. This analogy, though it had been found true by actual measurement, was not accurately demonstrated. Nicholas Mercator offered to disclose, for a sum of money, a method which he had discovered for demonstrating it; but this was not accepted, and the demonstration was, we believe, never disclosed. See Nicholas Mercator. About two years after, however, the demonstration was again discovered, and published by James Gregory.

The meridian line in Mercator's scale is a scale of logarithmic tangents of the half colatitudes. The differences of longitude on any rhumb, are the logarithms of the same tangents, but of a different species; those species being to each other as the tangents of the angles made with the meridian. Hence any scale of logarithmic tangents is a table of the differences of longitude, to several latitudes, upon some one determinate rhumb; and therefore as the tangent of the angle of such a rhumb is to the tangent of any other rhumb, so is the difference of the logarithms of any two tangents, to the difference of longitude on the proposed rhumb, intercepted between the two latitudes, of whose half complements the logarithmic tangents were taken.

It was the great study of our predecessors to contrive such a chart in plano, with straight lines, on which all or any parts of the world might be truly set down, according to their longitudes and latitudes, bearings, and distances. A method for this purpose was hinted at by Ptolemy, near 2000 years since, and a general map, in such an idea, was made by Mercator: but the principles were not demonstrated, and a ready way shown of describing the chart, till Wright explained how to enlarge the meridian line by the continual addition of secants, so that all degrees of longitude might be proportional to those of latitude, as on the globe; which renders this chart, in several respects, far more convenient for the navigator's use, than the globe itself, and which will truly shew the course and distance from place to place, in all cases of sailing.

For further particulars respecting the construction, and for the use of charts, see Navigation.

In choosing maps, it is proper to examine particularly whether the curved lines of those that ought to have the meridians and parallels arches of circles be truly circular. If the map is composed of more than one sheet, the sheets should be so joined together as that the corresponding meridional lines and parallels be each in one continued line. The colours in painted maps, as was observed with respect to globes, should be fine and transparent, and not laid on too thickly.

Maps folded for the pocket answer very well for travelling, in so far as they point out the relative situation of places; but owing to the intervals at which the parts are pasted on the canvas, the distances between places cannot be ascertained with any degree of accuracy.

Sect. III. Of the use of Maps.

Maps are of great utility in the study of geography and history; and if they are accurately drawn, many of the problems that are usually performed on the globes, may be solved mechanically by means of maps.

In consulting a map, it is not sufficient to find out in it the name of the place of which you desire to know the situation, although this is frequently all at which the consultor of a map aims: it is, besides, proper for the student to inform himself respecting the relative position of the place, with regard to its vicinity to other places; its bearings and distance from the principal places in the same or neighbouring districts; whether it is near the sea-shore, and is near a convenient harbour; whether it be seated on some principal river, and on what side of the river; whether it is in the neighbourhood of a considerable canal; whether it be near a lake, mountain, forest, &c. and many other little particulars that will readily suggest themselves to an attentive reader.

The problems that are usually performed by means of maps, are the following.

Problem I. To find the latitude and longitude of any given place.

In maps on a large scale, or where the meridians and parallels of latitude are straight lines, the latitude of the place place may be easily found by stretching a thread over the place, so that it may cross the same degree of lati- tude on each side of the map; and the degree crossed will be the latitude required. Or, with a pair of com- passes measure the shortest distance of the place from the nearest parallel, and apply this distance to either side of the map, so as to keep one point of the compas- ses on the same parallel; then the other point will shew the degree of latitude as measured on the graduated margin, counting from the parallel north or south, ac- cording as the place is in north or south latitude.

The longitude of the place may be found in a similar manner, by stretching the thread over the place, or laying a ruler across it, so as to cut the same degree of longitude on the top and bottom of the map, and that is the degree required.

The above methods answer very well in plain charts or in maps of counties; but when the meridians and paral- lels are curved lines, we must find how often the dis- tance of the place, measured by the compasses from the nearest parallel, will reach the next parallel in a straight direction, and from thence the latitude may be found with sufficient exactness. Thus, suppose we are requir- ed to find the latitude of Berlin, the capital of Prussia. The nearest parallel is that of 50° north latitude; the distance of Berlin from this parallel will reach the pa- rallel of 60° in four times, measuring on the map of Europe. The fourth part of ten, or two and a half, added to 50°, gives the latitude required, or 52°.

To find the longitude on such maps, measure how of- ten the distance of the place from the nearest meridian will reach the next meridian. Thus, in the same in- stance, the distance of Berlin from the meridian of 10°, which is the nearest towards the east, taken three times, will extend a little beyond the meridian of 20°. Add to 10° the third part of this distance, which is about three and a half, and we have 13° 30' for the longitude of Berlin east from London.

**Problem II.** The latitude and longitude of a place be- ing given; to find the place on the map.

Where the meridians and parallels are straight lines, this is done by stretching one thread from the given latitude on one side of the map to the same latitude on the other side; while another thread is stretched be- tween the corresponding degrees of longitude. The intersecting point of the two threads shews the place required. Thus, suppose we are required to find the place whose latitude is 34° 29' S. and longitude 18° 23' E. Stretching one thread between the given lati- tudes, and another between the given longitudes, we shall find that they cross over the Cape of Good Hope, which is therefore the place required.

When the meridians and parallels are curved lines, the most accurate way will be to describe a circle of la- titude through the given degree of latitude on each side, and a circle of longitude through the corresponding de- grees of longitude, and the intersection of these circles will shew the place. An easier method will be, know- ing between what two parallels of latitude and longitude the place lies, and consequently by what four lines it is bounded, to find the place by trial, by considering the proportional distance of it from each line.

**Problem III.** The latitude of a place being given; to find all those places on the same map that have the same latitude.

If a parallel of latitude happen to be drawn on the map through the given place, this problem is easily solved, by tracing along the parallel, and seeing what other places it passes through. If a parallel is not drawn through the given place, take with a pair of compasses the distance of the place from the nearest pa- rallel; then keeping one foot on the parallel, and the other in such a position as to describe a line parallel to the parallel of latitude, move the compasses, and all the places over which the point that is not on the parallel passes, have the same latitude with the given place.

This method will not succeed in maps on which a large tract of country is delineated on a small scale.

**Problem IV.** Given the longitude of a place; to find on the map all those places that have the same longi- tude.

Find the longitude of the given place, and if a meri- dian passes through it, observe all the places that lie under this meridian; or, if a meridian does not pass through the place, find by the compasses, as in the last problem, those places that are situated at the same pa- rallel distance with the given place from the nearest meridian. These places have nearly the same longi- tude with the given place.

**Problem V.** To find the antoci of a given place.

Find the latitude and longitude of the place by Pro- blem I. and find another place of the same longitude, whose latitude is equal to that of the former, but in a contrary direction. The inhabitants of this latter place are the antoci to the latter.

Ex. Suppose a ship to be in the Indian ocean, in lat. 13° S. and long. 85° E. it is required to find the antoci to her present situation? Ans. The place which has nearly the same longitude, and an equal latitude in a contrary direction, viz. 13° N. is Madras.

**Problem VI.** To find the perioci of a given place.

Find the longitude of the given place, and subtract it from 180°: the remainder will be the longitude in an opposite direction of the perioci. Then find a place having an equal longitude with this last, and having the same latitude with that of the given place: this latter is the situation required.

Ex. It is required to find the perioci to the inhabi- tants of the gulf of Siam. Ans. The longitude of Siam is 100° 50' E. which, subtracted from 180°, leaves 79° 10' W. Now, the place that has this longitude, and the same latitude with Siam, viz. about 14° N. is the isthmus of Darien.

**Problem VII.** To find the antipodes of a given place.

This problem is solved on maps in the same manner as on the globe.

**Problem VIII.** Having the hour at any place given; to find what hour it is in any part of the world.

Find the difference of longitude between the two places, and reduce this to its equal value in time, by Add this value to the given hour, if the place where the time is required be to the eastward of the given place, and the sum is the time required. If the place at which the time is required lie to the westward of the given place, subtract the difference of longitude in time from the given hour, and the difference is the time sought.

Note.—If, after adding, the sum is found greater than 12, 12 must be cancelled, and the hours must be changed from A.M. to P.M. and vice versa; and if, on subtracting, the difference in time between the two places happens to be greater than the given hour, 12 must be added to the given hour, and the hours changed as before mentioned.

Ex. Suppose it to be at present 9 A.M. at Lisbon, what time of the day is it at Pekin in China? Ans. The difference of longitude between Pekin and Lisbon is $125^\circ 33'$, which reduced to time gives 8 hours 22 minutes; and since Pekin lies to the east of Lisbon, this must be added to 9, the given hour, giving a sum of 17 hours, 22 minutes; but as this is greater than 12, we must take 12 away, and the difference, 5 hours 22 minutes, changed from morning to afternoon hours, is the time required. It is therefore 22 minutes past five P.M. at Pekin.

Problem IX. To find those places in the torrid zone to which the sun is vertical on any given day.

Find in an ephemeris, or nautical almanack, the sun's declination for the given day; then observe, in the map of the world, all those places which lie under that parallel of latitude, which is the same with the declination, and these will be the places required.

Ex. It is required to find at what places the sun will be vertical on the 20th of March and 23rd of September? Ans. The sun's declination on the 20th of March, is $19^\circ S.$ and on the 23rd of September $6^\circ N.$ Now the principal places that lie near the parallel of $19^\circ S.$ and $6^\circ N.$ are the island of St Thomas, the middle part of the islands of Sumatra and Borneo; the Galapagos isles, and Quito in South America.

The Analemma, or Orthographic Projection delineated in Plate CCXXXV., will solve many of the most curious problems, and with the assistance of maps will be almost equivalent to a terrestrial globe. The parallel lines drawn on this figure represent the degrees of the sun's declination from the equator, whether north or south, amounting to $23^\circ$ nearly. On these lines are marked the months and days which correspond to such and such declinations. The size of the figure does not admit of having every day of the year inserted; but by making allowance for the intermediate days, in proportion to the rest, the declination may be guessed at with tolerable exactness. The elliptical lines are designed to shew the hour of sunrising or sunsetting before or after six o'clock. As 60 minutes make an hour of time, a fourth part of the space between each of the hour-lines will represent 15 minutes; which the eye can readily guess at, and which is as great exactness as can be expected from any mechanical invention, or as is necessary to answer any common purpose. The circles drawn round the centre at the distance of $11\frac{1}{2}$ each, shew the point of the compass on which the sun rises and sets, and on what point the twilight begins and ends.

In order to make use of this analemma, it is only necessary to consider, that, when the latitude of the place and the sun's declination are both north or both south, the sun rises before six o'clock, between the east and the elevated pole; that is, towards the north, if the latitude and declination are north; or towards the south, if the latitude and declination are south. Let us now suppose it is required to find the time of the sun's rising and setting, the length of the days and nights, the time when the twilight begins and ends, and what point of the horizon the sun rises and sets on, for the Lizard point in England, Frankfort in Germany, or Abbeville in France, on the 30th of April. The latitude of these places by the maps will be found nearly $50^\circ N.$ Place the moveable index so that its point may touch $50^\circ$ on the quadrant of north latitude in the figure; then observe where its edge cuts the parallel line on which April 30th is written. From this reckon the hour-lines towards the centre, and you will find that the parallel line is cut by the index nearly at the distance of one hour and 15 minutes. So the sun rises at one hour 15 minutes before six, or 45 minutes after four in the morning, and sets 15 minutes after seven in the evening. The length of the day is 14 hours 30 minutes. Observe how far the intersection of the edge of the index with the parallel of April 30th is distant from any of the concentric circles, which you will find to be a little beyond that marked two points of the compass, and this shews that on the 30th of April the sun rises two points and somewhat more from the east towards the north, or a little to the northward of east-north-east, and sets a little to the northward of west-north-west. To find the beginning and ending of the twilight, take from the graduated arch of the circle $17\frac{1}{2}$ degrees with a pair of compasses; move one foot of the compasses extended to this distance along the parallel of April 30th, till the other just touches the edge of the index, which must still point at $50^\circ$. The place where the other foot rests on the parallel of April 30th, then denotes the number of hours before six at which the twilight begins. This is somewhat more than three hours and a half, which shews that the twilight then begins soon after two in the morning, and likewise that it begins to appear near five points from the east towards the north. The uses of this analemma may be varied in a great number of ways; but the example just now given will be sufficient for the ingenious reader.

Sect. IV. Of the Origin and Progress of Maps.

The first map of which we have any certain record, or is that of Anaximander, about 560 years before the Christian era. This is mentioned by Strabo, book i., and is supposed to be that referred to by Hipparchus, under the name of the ancient map.

It has been alleged, that Sesostris, king of Egypt, on his return from his boasted expedition, after having traversed great part of the earth, recorded his march in maps, of which he gave copies, not only to the Egyptians, but to the Scythians, to the great admiration of both people. This is the relation of Eustathius; but M. Montucla considers it as a very improbable story, and thinks that the invention of maps cannot be dated prior to Anaximander*. Some have supposed that the Jews laid down the holy land in a map, when they dis- principles tributed the different portions to the nine tribes at Shiloh; a supposition which is derived from Joshua's account, that they were sent to walk through the land, and that they described it in seven parts in a book. Josephus also relates, that when Joshua sent people from the different tribes to measure the land of promise, he sent with them men well skilled in geometry. All this, however, is no proof that these persons drew a sketch of the country, according to our idea of a map; but probably only wrote down, for the satisfaction of their employers, the extent, boundaries, and general characteristics of the divisions of the land.

Herodotus has given a minute description of a map constructed by Aristagoras, tyrant of Miletus, an abridgement of which will serve to give some notion of the maps of those times. It was drawn upon brass or copper, and seems to have been merely an itinerary containing the route through the countries which were to be traversed in a march which Aristagoras proposed to Cleomenes, king of Sparta, for the purpose of attacking the king of Persia at Susa, that he might thus assist in restoring the Ionians to their liberty. The rivers Halis, Euphrates, and Tigris, which, according to Herodotus, must have been crossed in that expedition, were laid down in this map; and it contained one straight line, called the royal road or high way, which comprehended all the stations or places of encampment, from Sardis, the beginning of the route, to Susa, a distance of 13,500 stadia, or 1687½ Roman miles of 5000 feet each. The number of encampsments in this whole route was 111.

Ptolemy of Alexandria, the celebrated geographer mentioned in No. 21, constructed maps to illustrate his description of places, and these are the first that have regular meridians and parallels, the better to define and determine the situation of places. Ptolemy acknowledges that his maps, with the addition of some improvements of his own, the principal of which was certainly the introduction of meridians and parallels, were copied from previous maps made by Mariannus Tyrius, &c. They are, however, often very inaccurate.

According to Athenaeus, a work which seems to have contained maps, was written by Baetos, under the title of Alexander's march; and a work on the same subject is mentioned as the production of Amyntas. We are informed by Pliny, that this Baetos was one of the surveyors of Alexander's marches; and he quotes the exact number of miles of these marches, according to Baetos's mensuration, and confirms their authenticity by the letters of Alexander. Pliny also remarks, that a copy of this conqueror's surveys was given by Zenobius, his treasurer, to the geographer Patrocles, who was admiral of the fleets of Seleucus and Antiochus.

Among the most celebrated of the ancient maps, are the Peutingerian tables, so called, because published by Peutinger of Augsburg. These tables contain an itinerary of the whole Roman empire; all places except seas, wood, and deserts, being laid down according to their measured distances, though without any mention of latitude, longitude, or bearing. A particular description of this monument of antiquity is given in the 18th volume of the History of the Academy of Inscriptions, and in the History of the Academy of Sciences for 1761, from which M. Montucla has drawn up the following account. The map of Peutinger, as it is in the original in the imperial library, is exactly one French foot in height, and 20 feet eight inches in length, according to measures taken by Buache, from a copy of the splendid edition given by Scheele in 1753. It comprehends the whole extent of the Roman empire, from Constantinople to the ocean, and from the shores of Africa to the northern parts of Gaul; but the table which it affords of this vast extent of country is by no means calculated to give us an idea of its figure, since the 35° of longitude which it comprehends, occupy 20 feet 8 inches, while the 13° of latitude are comprised within the space of one foot; thus the countries represented are so disfigured, that the Mediterranean appears only like a broad river, and all the countries are so distorted, towards the north and south, that they cannot be recognised.

Most of those who have seen this ancient map, have considered it as the rude and bungling work of a man little conversant with geography, and still less so with mathematics; but Edmund Brutz considers the distortion of this map as similar to what we see in some pieces of perspective, and that it ought to be examined from some certain near point in order to perceive the objects in their natural proportion.

Buache supposed long ago, that this map was constructed with more scientific skill than it appears to be at the first glance; and that the apparent irregularities which we observe in it, might have been introduced designedly, for the purpose of deriving greater advantages as to what was intended for the principal object. In fact, as the Roman routes extended almost entirely from east to west, they paid more attention to the measures in this direction than those between north and south; and the map in this way might have had the greater convenience of being more easily rolled up, and consequently more portable.

Thus far Buache hazarded no more than conjecture; but a labour undertaken by him with a very different view, led him to the true design of the map of Peutinger. He had been tracing a scale of climates, and of the length of the days and nights, for the purpose of attaching it to small maps of the different countries of Europe. As the space occupied by the scale was pretty much extended in height, but had very little breadth, he formed the idea of drawing a kind of map upon two scales, one pretty much extended for the latitudes, and the other very much contracted for the longitudes, preserving the hollows of the coasts and boundaries of each state. As this disposition of his map strangely disfigured the countries which it was intended to represent, he was led to imagine that this map might be the reverse of that of Peutinger. This was sufficient to engage him to construct another map upon the same principle; but in which the scale of longitudes was much greater than that of the latitudes. He then saw that he had been right in his supposition, and that the map which he had last constructed had a considerable resemblance to that of Peutinger. This latter is in fact only a plain chart, constructed upon two scales, of which that of the longitudes is very great, and that of the latitudes much smaller.

One difficulty alone arose. By supposing that he observed in this map a custom at present established among geographers, of representing the meridians by lines drawn perpendicular to the base of the chart, and the Principles parallels to the equator by straight lines drawn parallel and to this same base, Buache found a considerable error.

Practice. The bottom of the gulf of Venice and Rome did not then appear, as they ought to do, under the same meridian. He soon, however, saw the solution of this difficulty. The method of drawing the meridians parallel to the sides of the chart, is a matter of pure agreement, and had probably not been observed in the map of which we are speaking. The ancient Roman geographers having considered that Italy was naturally divided by the Appenines, according to its length, into two parts that were nearly equal, had therefore delineated the length of Italy from Trent to the end of the peninsula, parallel to the lower margin of the map, and had afterwards arranged the other parts which the map was to contain, conformably to this disposition; and as the length of Italy is not in a direction parallel to the equator, it would happen necessarily that the meridians and parallels, if they had been drawn on this map, would have been parallel neither to the sides nor to the lower margins of the map, and that the vertical line passing through Rome must intersect the gulf of Venice at about the middle: but this line is not a meridian.

Thus, this map is not so rude a work as has been imagined, but has been entirely constructed according to rule; and it even appears that the author had employed pretty good materials in its compilation, as the positions are laid down in a manner that differs little from modern observation.*

From the time of Ptolemy till about the 14th century, no new maps were published; and the first maps of any esteem among the moderns were constructed by Mercator, to whom we are indebted for the projection according to which marine charts are constructed. Mercator was followed by Ortelius, who undertook to construct a new set of maps with the modern divisions of countries and names of places, for want of which the maps of Ptolemy were become almost useless. After Mercator and Ortelius, many others published maps, which were chiefly copied from those above mentioned, till about the middle of the 17th century, when Blaeu published his large atlas, or Cosmographie blaviane, in which is a pretty accurate description of the earth, the sea, and the heavens, comprised in 12 folio volumes. About the same time an atlas in two folio volumes was published in France by M. Sanson, the maps of which are in general very correct, containing many improvements of the travellers of those times. The maps of Blaeu and Sanson were copied with little variation both in England, France, and Holland, till from later observations De Lisle, Robert, Wall, &c. published still more accurate and copious sets of maps.

The works of recent travellers and navigators have considerably improved the construction and accuracy of our maps and charts; but there is still much to be done, especially with respect to trigonometrical surveys, before any high degree of correctness can be acquired. Among the latest maps and charts, those constructed by Mr Arrowsmith are in the greatest estimation.

As a collection of good and accurate maps is of the greatest importance in the study of geography and history, we shall here subjoin a list of some of the best modern maps that have been published.

Those maps which may be collected for the purpose of forming an atlas, have been arranged under three heads, according to their size, or the extent of their scale. 1st, Those which consist of more than six sheets, such as De Bouge's map of Europe in 50 half sheets, and Cassini's map of France in 183 sheets. 2dly, Those from six to four sheets, to which class belong several maps of kingdoms. And, 3dly, Those from one sheet to four, which is the smallest size that can answer the purpose of an atlas. We shall briefly notice the best maps of each size.

Planispheres, or Maps of the World.—We know of no very large map of the world that can at present be confidentially relied on: the best is that of Mr Arrowsmith in four sheets; and Faden has published very good maps in one sheet.

Maps of Europe.—1st Size. That of De Bouge, published at Vienna, or that by Sortzmann in 16 sheets, which is the better of the two. 2d Size. Arrowsmith's in four sheets. 3d Size. That by Faden in one sheet.

Maps of England.—I. The trigonometrical surveys of the counties, published by Lindley and Gardner, and by Faden. II. Cary's atlas of the counties, and his England and Wales in 8x sheets. III. Faden's map in one sheet.

Maps of Wales.—I. That of Evans in nine sheets. III. The maps in Pennant's Tours, and Evans's Cambrian Itinerary.

Maps of Scotland.—I. The surveys of the several counties. II. Ainslie's nine sheet map. III. An excellent map by General Roy, and Ainslie's reduced map, in one sheet.

Maps of Ireland.—I. Survey of counties. III. A valuable map by Dr Beaufort, in two sheets, or Faden's in one sheet.

Maps of France.—I. Cassini's mentioned above, and the atlas nationale, in 85 sheets. III. Faden's one sheet map, and a map, in departments, by Bellyeime, in four sheets.

Maps of the Netherlands.—I. Ferran's map in 25 sheets. II. Atlas de Department Belgique. III. Ferrari's map reduced by Faden.

Maps of Holland.—II. Kep's maps of the United Provinces. III. Faden's map of the Seven United Provinces in one sheet.

Maps of Germany.—II. Chauchard's map of Germany. III. A map of the Austrian dominions, in one sheet, by Baron Lichtenstern.

Maps of Prussia.—I. Sortzmann's atlas in 21 sheets. III. Sortzmann's reduced, in one sheet.

Maps of Spain.—Lopez's atlas, not, however, very accurate. II. A map of Spain in nine sheets by Montelle and Chanlairre. III. Faden's map in one sheet.

Maps of Portugal.—II. Geoffry's improved by Rainsford, in six sheets. III. De la Rochette's chorographical map in one sheet, published by Faden.

Maps of Italy.—I. The maps of the several states. III. D'Anville's map of Italy improved by De la Rochette, in four sheets, published by Faden.

Maps of Turkey in Europe.—III. Arrowsmith's map of Turkey in two sheets. De la Rochette's map of Greece in one sheet.

Maps of Switzerland.—I. Weiss's atlas, published at Strasbourg in 1800. III. Weiss's reduced map in one sheet.

Maps of Denmark.—I. Maps of the provinces, under the direction of Bygge. III. Faden's maps of Denmark, Sweden, and Norway, in one sheet. Maps of Sweden.—I. Atlas of the Swedish provinces, by Baron Hermelin. III. De la Rochette's, by Faden, in one sheet.

Maps of Asia.—The best general map of Asia is that by Arrowsmith in four sheets, published in 1801; and D'Anville's, in six sheets, may still be consulted with advantage.

There are few good maps of the individual countries; but the following are esteemed among the best.

Of China.—D'Anville's atlas, and a map by Arrowsmith.

Of Tartary.—A map by Witsen, in six sheets, and one by De Witt in one sheet.

Of Japan.—Robert's map in one sheet.

Of the Birman Empire.—The maps published in Mr Symes's embassy.

Of Hindostan.—Rennell's map in four sheets. His atlas of Bengal, and his map of the southern provinces.

Of Persia.—La Rochette published a beautiful map to illustrate the expedition of Alexander the Great; and a good modern map has been published by Mr McDonald Kinneir.

Of Arabia there are some good partial maps in Niebuhr's journey.

Of the Asiatic Islands there is an excellent chart by Arrowsmith, in four sheets.

Of Australasia, or New Holland, the best drawing is contained in Arrowsmith's chart of the Pacific ocean.

Maps of Africa.—The best general map of Africa is still that of D'Anville, though some little additions may be made to it, derived from the journeys of Park and Brown. Major Rennell's partial maps may be consulted with advantage.

Of Abyssinia there is a good map in Bruce's travels.

Of Egypt, the best maps are that of the Delta by Niebuhr, and that of Lower Egypt by la Rochette.

Of the Mahometan States, the best maps are those by Shaw, and a chart of the Mediterranean in four sheets, by Faden.

Of the Cape of Good Hope, the best is Barrow's survey.

Maps of America.—There is no modern general map of America that can be relied on. The best is that of D'Anville, in five sheets, published in 1746 and 1748.

Mr Arrowsmith has published an excellent map of North America, on a very large scale, but has omitted the Spanish dominions.

Of the United States, the best map is Arrowsmith's in four sheets, published in 1802; and a good map, including the recent states, was published by Mr Melish in 1816.

Of the British Possessions in America, besides Arrowsmith's map above mentioned, there is a good map of Upper Canada by Smith, in one sheet.

Of the West India Islands, the best map is that of Jefferys in 16 sheets, from which a smaller one in one sheet has been reduced.

Of South America, the best map is that published by Faden in 1799, in six sheets, from an engraving done at Madrid some years before.

APPENDIX.

BEFORE we conclude this article, we must make a few observations on the method to be followed for acquiring or imparting geographical knowledge.

As some knowledge of geography, as well as of chronology, is absolutely necessary, before history can be properly understood, the rudiments of these sciences should be learned, as soon as the capacity of the pupil will allow. It happens fortunately, that some of the most useful parts of geography, those which consider the relative situations, extent and boundaries of countries, with the manners and customs of their inhabitants, are highly interesting; and provided that a knowledge of them be conveyed to a child in a pleasing manner, they are well fitted to interest his curiosity, and awaken his attention. The more scientific parts of geography, and a detailed account of the minute circumstances respecting each country, though extremely useful, and indeed necessary to the more advanced student, may be withheld for a little without any great loss, till his age and judgment permit him to see their utility and application.

In teaching geography to very young children, their chief attention should be directed to those circumstances which are most interesting; and even with this limited view much may be learned at a very early period. For this purpose the dissected maps that are usually sold at toy shops, may be employed with considerable advantage; but it is to be regretted, that the maps used in preparing these are seldom taken from the most correct copies. Those works also which, under the disguise of fictitious voyages and travels, are intended to convey a geographical knowledge of various countries, afford a very pleasing and profitable method of instruction. A late work of this kind, by M. Jaufret, entitled the Travels of Roland, may be advantageously put into the hands of young people; and, as they are farther advanced, the travels of Anacharsis the younger by the abbe Barthélemy will give them considerable information respecting the manners, customs, and historical events of ancient Greece.

When the young student is sufficiently advanced to prosecute the study of geography on a more extensive and scientific plan, it would be desirable that he should begin by reading some elementary treatise on astronomy, such as that of Mr Bonnycastle, or the Spectacle de la Nature; or, if he has acquired a proper degree of mathematical knowledge, he may read Laplace's Système du Monde, the astronomical part of Robison's Mechanical Philosophy, or the astronomical article in this dictionary.

It may happen, that, from a defect of early education, or want of time, a preliminary course of astronomy cannot be commanded. Still, however, considerable progress may be made in geography, by the mechanical means of maps and globes. The student should, therefore, provide himself with a pair of the best globes, chosen according to the directions laid down in No 107; and with a few good maps of those countries which are... are most interesting, particularly maps of Europe, Asia, Africa, and North and South America, the British islands, France, Germany, Italy, Russia, and Denmark, which may be collected from the list given at No. 126.

Being provided with these materials, the student should first read over Chap. I. of Part II. of this treatise, or a similar part of some elementary work in geography. On the elementary principles of geography we would recommend the general principles prefixed to Mr Patteson's general and classical Atlas; and for teaching the use of the globes, Bruce's Introduction to Geography and Astronomy. For a complete account of modern geography we cannot refer to a better work than that of Mr Pinkerton; and for a combined account of ancient and modern geography, the pupil may have recourse to a work on that subject by Dr Adam of Edinburgh.

After reading over the preliminary part above mentioned, the pupil may go through the second Chapter of Part II., solving all the problems as he goes along on the terrestrial globe; and thus he may proceed progressively through the whole article, leaving that part of Part I. which treats of the history of geography for the last object of his enquiry.

In studying the particular circumstances of each country, the pupil should always have the map of the country before him; and, as he goes along, should trace there the situation of each particular place; of the principal mountains, lakes, the sources and directions of the rivers, the form and bounding of the shores, &c. In his progressive view of particular geography, it will be proper for the pupil to begin with the country in which he resides; and, after having made himself master of that, to proceed successively to those which border on it, or whose connection with it is the most interesting.

Thus an inhabitant of these islands, after having taken a view of Europe in general, should make himself acquainted with Britain and Ireland (by perusing the articles England, Scotland, and Ireland in this Dictionary or in other works); whence he may proceed to France and its dependencies in the Netherlands, Switzerland, Italy; thence to Germany and the Austrian territories, Prussia, Sweden, Denmark, and Russia; whence he may return to the south of Europe to Spain, Portugal, and Turkey, &c. After Europe, the United States of America will probably be found the most interesting; the pupil may therefore study the geography of North America before that of Asia. From Asia he may proceed to Australasia and Polynesia; thence to Africa, and so conclude with South America. Nothing will contribute more to the advancement of geographical studies than the construction of maps. If the pupil has time therefore he should early be instructed in this part of the subject by at first drawing a map of the world according to the directions laid down in No. 118; then one of Europe, and so of other quarters and countries. In constructing this map, it will be proper first to lay down those places which are near the coast, in order to form the outline of the maritime part of the country, and only the most remarkable places inland, especially those which are situated in the course of the principal rivers. In every map the most prominent features of the country, as the mountains, lakes, rivers, and principal cities and towns, should first be attended to, and from these the pupil may be introduced to the other places in the order of their magnitude or importance.

The most agreeable and interesting method of studying particular geography, after having become acquainted with the elementary principles of the science, would be to peruse the best books of voyages and travels; for from those, where the traveller can be depended upon, the most correct systems of geography are compiled. Many of these, however, are too prolix and particular to be put into the hands of most young people, and a judicious abridgement of the best of them will answer every purpose; and perhaps Dr Mavor's collection may be recommended, as the best of the kind in the English language. For those whose time and convenience will admit of their reading the best writers of voyages and travels, there is no want of such works; and Mr Pinkerton has given at the end of his excellent work, a list of the best in most languages. We shall here only notice a few of the best and latest.

Pennant's Tours in Britain. Young's Tours in the British isles. Saintfond's Travels in England and Scotland. Young's Travels in France. Holcroft's Tour in France. Spallanzani's Travels in the two Sicilies. Cox's Travels in Russia, &c. Pallas's Travels in the Russian empire. Carr's Northern Summer. Staunton's Account of China. Barrow's Travels in China. Percival's Account of Ceylon. Syme's Embassy to Ava. Collins's Account of New South Wales. Bruce's Travels in Abyssinia. Barrow's Travels in Africa. Park's Travels in the interior of Africa. Brown's Travels in Africa. Sonnini's Travels in Egypt. Percival's Cape of Good Hope. Mackenzie's Journey in North America. Davis's Travels in America. Mackinnon's Tour in the West Indies; with the voyages of Anson, Byron, Cook, Phipps, Bligh, Wilson, Wallis, La Peyrouse, &c. &c. # INDEX

**A.** - **AMS's improvement of the globes**, No 111 - **circumnavigation of**, 11 - **Alexander the Great improves geography**, 14 - **arc, quadrant of**, 86 - **axis**, 78 - **formula for solving geographical problems**, 123 - **Arminander, the inventor of maps**, 124 - **Arts, geographical knowledge of**, 25 - **in Europe**, 26 - **Asia**, 27 - **Africa**, 29 - **Arrows**, 70 - **Arrows, discoveries of**, 68 - **Auxiliary sphere, Ferguson's**, 112 - **Long's**, 113

**B.** - **As defined**, 44 - **Bohr's elucidation of the Peutingerian tables**, 125

**C.** - **Caesar, division of the earth into**, 102 - **Celestial globe described**, 83 - **Celestial division of the earth into**, 84 - **Northern places in the**, 85 - **problems relating to the**, 96 - **Circles explained**, 75 - **Comets defined**, 49 - **Comets defined**, 46

**D.** - **Day and night, cause of, illustrated by the globe**, 100 - **Darius the Perigetic**, 22

**E.** - **Earth, spherical form of, how proved**, 39 - **magnitude of**, 40 - **divisions of**, 41 - **population of**, 53 - **Eclipses, lunar, problem respecting**, 101 - **Eclipses explained**, 72 - **Equation of time illustrated by the globe**, 104

**F.** - **Ferguson's armillary sphere**, 112

**G.** - **Geographer, ancient, enumerated**, 18 - **Hudson's collection of**, 23 - **Geography, definition of**, 1 - **division of**, 2

**Geography, physical,** - **importance of**, No 4 - **history of**, p. 503 - **origin of**, No 7 - **improved by Alexander the Great**, 14 - **by Ptolemy Philadelphus**, 95 - **of the ancients**, 25 - **middle ages**, 31 - **modern discoveries in**, 33 - **present defects of**, 36 - **general observations on the mode of studying**, 127 - **Globes, nature of**, 54 - **circles on the**, 55 - **axis and poles of**, 56 - **equator of**, 57 - **meridians of**, 58 - **brass meridian of**, 59 - **parallels of latitude**, 60 - **horary circles of**, 66 - **ecliptic on the**, 72 - **tropical circles of**, 73 - **polar circles of**, 74 - **colours of**, 75 - **quadrant of altitude**, 86 - **wooden horizon of**, 87 - **celestial, described**, 102 - **general construction of**, 105 - **gores of, how formed**, 106 - **rules for choosing**, 107 - **using**, 108 - **improvement of, by Senex**, 109 - **by Smeaton**, 110 - **by Harris**, 66 - **by Wright**, 44

**Gulfs defined**, 66

**H.** - **Harris's improvement on the hour-circle of the globes**, 66 - **Harvest moon illustrated by the globes**, 103 - **Heterocci**, 80 - **Horary circles on the globe**, 66 - **Horizon, wooden, of globes**, 87 - **of the sea, explained**, 93 - **depression of, how estimated**, p. 523

**I.** - **Islands defined**, No 50 - **Isthmus defined**, 52

**Lakes defined**, 47

**Latitude and longitude explained and illustrated**, 61 - **parallels of**, 60 - **introduced by Eratosthenes**, 61 - **problems on**, 64

**Level, true and apparent,** - **table for estimating the difference of**, p. 522 - **Long's armillary sphere**, No 113 - **Longitude, how reduced to any single meridian**, 62 - **how reduced to miles**, 63 - **how computed in time**, 65

**M.** - **Maps, and charts, distinction of**, 114 - **description of**, 115 - **construction of**, 116 - **by the orthographic projection**, 117 - **by the stereographic projection**, 118 - **of the world, how projected by the globular projection**, 119 - **particular construction of**, 120 - **use of**, 122 - **origin of**, 124 - **Peutingerian**, 125 - **catalogue of the best**, 126 - **Mercator's projection**, 128 - **Meridians on the globe**, 58 - **brass**, 59 - **prime or first**, p. 513

**O.** - **Oblique sphere**, No 89 - **Oceans defined**, 42 - **Ophir, situation of, discussed**, 9

**P.** - **Parallel sphere**, 91 - **Peutingerian table described**, 125 - **Peninsula defined**, 51 - **Perieci**, 69 - **Periscii**, 82 - **Phoenicians, discoveries of**, 8 - **Polar circles explained**, 74 - **Pomponius Mela, an ancient geographer**, 20 - **Problems on latitude and longitude**, 68 - **I. To find the latitude and longitude of a given place**, p. 514 - **II. Latitude and longitude given, to find the place, respecting time**, No 67 - **III. Hour at any place being given, to find the hour at any other place**, p. 515 - **IV. Hour at any place being given, to find where it is noon, respecting the antecoi, &c.**, No 71 - **V. To find the antecoi of a given place**, p. 516 - **VI. To find the pericoci**, ib.

**Problems**

XXVIII. To find where an eclipse of the moon is visible, p. 528

Problems on the celestial globe,

I. To place the globe so as to represent the heavens for any evening in any latitude, ib.

II. To find the right ascension and declination of a star, 531

III. Having the right ascension and declination given, to find the star, ib.

IV. To find the latitude and longitude of a given star, ib.

V. To find on what day a given star comes to the meridian at a given hour, ib.

VI. To find the altitude and azimuth of a given star, ib.

VIII. The azimuth, &c., given, to find the altitude, ib.

IX. To find the azimuth and hour of the night, 532

X. Azimuth and latitude given, to find the altitude and day of the month, ib.

XI. Observing two stars to have the same azimuth, to find the hour of the night, ib.

XII. To find the rising, setting, &c. of a star or planet, 533

XIII. To find those stars which never rise, or never set, ib.

XIV. To illustrate the phenomena of the harvest moon, 534

XV. To illustrate the equation of time, ib.

Problems performed by maps, Promontory defined, Ptolemy's work on geography, Ptolemy Philadelphus improves geography, Pythias, voyage of, R.

Right sphere, Rivers defined, S.

Sataspes, voyage of, Scylax, expedition of, Seas defined, Senex's improvement of the globes, Smeaton's improvement on the globes, Sphere, oblique, right, parallel, armillary, by Ferguson, by Long, invention of, Strabo's work on geography, Straits defined, Sun, problems respecting, T.

Tagrobana, situation of, Time, problems relating to, Tropics explained, Twilight explained, uses of, problems respecting, W.

Wright's improvement of the hour circle of the globes, Z.

Zones, division of the earth into, Zone, torrid, countries in, temperate, places in, frigid, countries in,