(γεωγραφία), from γῆ terra, and γράφειν scribo); the doctrine or knowledge of the earth, both as in itself, and as to its affections; or a description of the terrestrial globe, and particularly of the known and inhabitable parts thereof, with all its different divisions. See EARTH and ASTRONOMY.

Sect. I. History of the Science.

At what time the science of geography began first to be studied among mankind is entirely uncertain. It is generally agreed, that the knowledge of it was derived to the Greeks, who first of the European nations cultivated this science, from the Egyptians or Babylonians; but it is impossible to determine which of these two nations had the honour of the invention. Herodotus tells us, that the Greeks first learned the pole, the gnomon, and the 12 divisions of the day, from the Babylonians. By Pliny, and Diogenes Laertius, however, we are told, that Thales of Miletus first found out the passage of the sun from tropic to tropic; which he could not have done without the assistance of a gnomon. He is said to have been the author of two books, the one on the tropic, and the other on the equinox; both of which he probably determined by the gnomon; and by this he was led to the discovery of the four seasons of the year, which are determined by the solstices and equinoxes.

Thales divided the year into 365 days; which was undoubtedly a method discovered by the Egyptians, and communicated by them to him. It is said to have been invented by the second Mercury, surnamed Trifmegistus, who, according to Eusebius, lived about 50 years after the Exodus. Pliny tells us expressly, that this discovery was made by observing when the shadow returned to its marks; a clear proof that it was done by the gnomon. Thales also knew the method of determining the height of bodies by the length of their shadows, as appears by his proposing this method for measuring the height of the Egyptian pyramids. Hence many learned men have been of opinion, that as the use of the gnomon was known in Egypt long before the dawn of learning in Greece, the use of the pyramids and obelisks, which to common travel, the Egyptian appeared only to be buildings of magnificence, must and were in reality as many fun-dials on a very large scale, obelisks, and built with a design to ascertain the season of the year, by the variation of the length of their shadows; and, in confirmation of this opinion, it was found by M. Chazelles in 1694, that the two sides, both of the larger and smaller pyramids, stood exactly north and south; so that, even at this day, they form true meridian lines.

From the days of Thales, who flourished in the sixth century before Christ, very little seems to have been done towards the establishment of geography for 200 years. During this period, there is only one astronomical observation recorded; namely, that of Meton and Euctemon, who observed the summer solstice at Athens, during the archonship of Apseudes, on the 21st of the Egyptian month Phamenoth, in the morning, being the 27th of June 432 B.C. This observation was made by watching narrowly the shadow of the gnomon, and was done with a design to fix the beginning of their cycle of 19 years.

Timocharis and Artililus, who began to observe Longitudes and latitudes determined, about 295 B.C. seem to have been the first who attempted tempted to fix the longitudes and latitudes of the fixed stars, by considering their distances from the equator. One of their observations gave rise to the discovery of the precession of the equinoxes, which was first observed by Hipparchus about 150 years after; and he made use of Timocharis and Aratus's method, in order to delineate the parallel of latitude, and the meridians on the surface of the earth; thus laying the foundation of the science of geography as we have it at present.

But though the latitudes and longitudes were thus introduced by Hipparchus, they were not attended to by any of the intermediate astronomers till the days of Ptolemy, Strabo, Vitruvius, and Pliny, have all of them entered into a minute geographical description of the situation of places, according to the length of the shadows of the gnomon, without taking the least notice of the degrees and minutes of longitude and latitude.

The discovery of the longitudes and latitudes immediately laid a foundation for making maps, or delineations of the surface of the earth in plan, on a very different plan from what had been attempted before. Formerly the maps were little more than rude outlines and topographical sketches of different countries. The earliest were those of Sesostris, mentioned by Eustathius; who says, that "this Egyptian king, having traversed great part of the earth, recorded his march in maps, and gave copies of his maps not only to the Egyptians, but to the Scythians, to their great astonishment."—Some have imagined, that the Jews made a map of the Holy Land, when they gave the different portions to the nine tribes at Shiloh: for Josephus tells us, that they were sent to walk through the land, and that they described it in seven parts in a book; and Josephus tells us, that when Joshua sent out people from the different tribes to measure the land, he gave them, as companions, persons well skilled in geometry, who could not be mistaken in the truth.

The first Grecian map on record is that of Anaximander, mentioned by Strabo, lib. i. p. 7. It has been conjectured by some, that this was a general map of the then known world, and is imagined to be the one referred to by Hipparchus under the designation of the ancient map. Herodotus minutely describes a map made by Aristaegoras, tyrant of Miletus, which will serve to give us some idea of the maps of those ages. He tells us, that Aristaegoras showed it to Cleomenes king of Sparta, with a view of inducing him to attack the king of Persia, even in his palace at Susa, in order to restore the Ionians to their ancient liberty. It was traced upon brafs or copper, and contained the intermediate countries which were to be traversed in that march. Herodotus tells us, that it contained "the whole circumference of the earth, the whole sea or ocean, and all the rivers;" but these words must not be understood literally. From the state of geography at that time, it may be fairly concluded that by the sea was meant no more than the Mediterranean; and therefore, the earth or land signified the coasts of that sea, and more particularly the Lesser Asia, extending towards the middle of Persia. The rivers were the Halys, the Euphrates, and Tigris, which Herodotus mentions as necessary to be crossed in that expedition. It contained one straight line, called the Royal High-

way, which took in all the stations or places of encampment from Sardis to Susa. Of these there were 111 in the whole journey, containing 13,500 stadia, or 168½ Roman miles of 5000 feet each.

These itinerary maps of the places of encampment were indispensably necessary in all armies. Athenaeus quotes Bacon as author of a work intitled, The encampments of Alexander's march; and likewise Amyntas to the same purpose. Pliny tells us, that Diogenes and Bacon were the surveyors of Alexander's marches, and then quotes the exact number of miles according to their mensuration; which he afterwards confirms by the letters of Alexander himself. It likewise appears, that Alexander was very careful in examining the measures of his surveyors, and took care to employ the most skilful in every country for this purpose. The same author also acquaints us, that a copy of this great monarch's surveys was given by Xenocles his treasurer to Patrocles the geographer, who, as Pliny informs us, was admiral of the fleets of Seleucus and Antiochus. His book on geography is often quoted both by Strabo and Pliny; and it appears, that this author furnished Eratothenes with the principal materials for constructing his map of the oriental part of the world.

Eratothenes was the first who attempted to reduce Parallel of geography to a regular system, and introduced a regular parallel of latitude. This was traced over certain places where the longest day was of the same length. He began it from the straits of Gibraltar; and it thence passed through the Sicilian sea, and near the southern extremities of Peloponnesus. From thence it was continued through the island of Rhodes and the Bay of Iulis; and there entering Cilicia, and crossing the rivers Euphrates and Tigris, it was extended to the mountains of India. By means of this line, he endeavoured to rectify the errors of the ancient map, supposed to be that of Anaximander. In drawing this parallel, he was regulated by observing where the longest day was fourteen hours and an half, which Hipparchus afterwards determined to be the latitude of 36 degrees.

The first parallel through Rhodes was ever afterwards considered with a degree of preference, like the foundation stone of all ancient maps; and the longitude of the then known world was often attempted to be measured in stadia and miles, according to the extent of that line, by many succeeding geographers. Eratothenes soon after attempted not only to draw other parallels of latitude, but also to trace a meridian at right angles to these, passing through Rhodes and Alexandria, down to Syene and Meroë; and as the progress he thus made tended naturally to enlarge his ideas, he at last undertook a still more arduous task, namely, to determine the circumference of the globe, by an actual measurement of a segment of one of its great circles. To find the measure of the earth is indeed a problem which has probably engaged the attention of astronomers and geographers ever since the globular figure of it was known. Anaximander is said to have been the first among the Greeks who wrote upon this subject. Archytas of Tarentum, a Pythagorean, famous for his skill in mathematics and mechanics, is said also to have made some attempts in this way; and Dr Long conjectures, that there are the authors of the most ancient opinion that the circumference of the earth is 400,000 stadia. Aristarchus of Samos is thought to have considered the magnitude of the earth as well as of the sun and moon. Archimedes makes mention of the ancients who held the circumference of the earth to be 30,000 stadia; but it does not appear what methods were made use of by these very ancient geographers to solve the problem. Probably they attempted it by observations of stars in the zenith or in the horizon, and actual mensuration from some part of the circumference of the earth. A proof of this we have from what Aristotle writes in his treatise De Caelo; that we have different stars pass through our zenith, according as our situation is more or less northerly; and that in the southern parts of the earth we have stars come above our horizon, which if we go northward will no longer be visible to us. Hence it appears, that there are two ways of measuring the circumference of the earth; one by observing stars which pass through the zenith of one place, and do not pass through that of another; the other, by observing some stars which come above the horizon of one place, and are observed at the same time to be in the horizon of another. Eratosthenes at Alexandria in Egypt made use of the former method. He knew that at the summer solstice the sun was vertical to the inhabitants of Syene, a town on the confines of Ethiopia, under the tropic of Cancer, where they had a well built for that purpose, on the bottom of which the rays of the sun fell perpendicularly the day of the summer solstice: he observed by the shadow of a wire set perpendicularly in a hemispherical basin, how much the sun was on the same day at noon distant from the zenith of Alexandria; and found that distance to be one-fifth part of a great circle in the heavens. Supposing then Syene and Alexandria to be under the same meridian, he concluded the distance between them to be the fifth part of a great circle upon the earth; and this distance being by measure 5000 stadia, he concluded the circumference of the earth to be 250,000 stadia; but as this number divided by 360 would give 694½ stadia to a degree, either Eratosthenes himself or some of his followers assigned the round number 700 stadia to a degree; which multiplied by 360, makes the circumference of the earth 252,000 stadia; whence both these measures are given by different authors as that of Eratosthenes.

In the time of Pompey the Great, Posidonius made an attempt to measure the circumference of the earth by the method of horizontal observations. He knew that the star called Canopus was but just visible in the horizon of Rhodes, and that at Alexandria its meridian height was the 48th part of a great circle in the heavens, or 7½ deg.; which shows what part of a great circle upon the earth the distance between those places amounts to. Supposing them both to be under the same meridian, and the distance between them to be 5000 stadia, the circumference of the earth will be 240,000 stadia; which is the first measure of Posidonius. According to Strabo, Posidonius made the measure of the earth to be 180,000 stadia, at the rate of 500 stadia to a degree. The reason of this difference is thought to be, that Eratosthenes measured the distance between Rhodes and Alexandria, and found it to be but 3750 stadia; taking this for a 48th part of the earth's circumference, which is the calculation of Posidonius, the whole circumference will be 180,000 stadia. This measure was received by Marinus of Tyre, and is usually ascribed to Ptolemy. Posidonius's method, however, is found to be exceedingly erroneous, on account of the uncertainty of refraction in the stars which are near the horizon. Cassini remarks, that taking exactly the mean betwixt the last dimensions of Eratosthenes and Posidonius, a degree of a great circle upon the earth will be 600 stadia, and a minute of a degree 10 stadia, which is just a mile and a quarter of the ancient Roman measure and a mile of the modern measure.

Several geographers after the time of Eratosthenes and Posidonius have made use of the different heights of the pole in distant places under the same meridian to find the dimensions of the earth. About the year 1080, the caliph Almamun had the distance measured by Almam of two places two degrees asunder, and under the same meridian, in the plains of Sinjar near the Red Sea. The result of the matter was, that the mathematicians employed found the degree at one time to consist of 56 miles, at another of 56½, or, as some will have it, 56¾ miles.

The next attempt to find the circumference of the earth was in 1525 by Fernelius, a learned French physician. To attain his purpose, he took the height of the pole at Paris, going from thence directly northwards, until he came to the place where the height of the pole was one degree more than at that city. The length of the way was measured by the number of revolutions made by one of the wheels of his carriage; and after proper allowances for the declivities and turnings of the road, he concluded that 68 Italian miles were equal to a degree on the earth.

Snellius, an eminent Dutch mathematician, succeeded Fernelius in his attempts to measure the circumference of the earth. Having taken the heights of the pole at Almam and at Bergen-op-zoom, he found the difference to be 1° 11' 30". He next measured the distance betwixt the parallels of these two places, by taking several stations and forming triangles; by means of which he found the degree to consist of 341,676 Leyden feet. Having measured the distance betwixt the parallels of Almam and Leyden, which differ only half a degree in their latitude, the calculation came out 342,120 Leyden feet to a degree. Hence he assigned the round number 342,000 Leyden feet to a degree; which, according to Picard, amounts to 55,621 French toises.

In 1635, Mr Norwood, an Englishman, took the elevations of the pole at London and at York; and wood's calculation having measured the distance betwixt the two parallels, assigned 69½ miles and two poles to a degree; each pole being reckoned 16½ feet.

After the year 1654, Ricciolus made use of several calculation methods to determine the circumference of the earth; from all which he concluded, that one degree contained 64,363 Bologna paces, which are equivalent to 61,650 French toises. The most remarkable attempt, however, was that of the French mathematicians, who French academically employed telecopic sights for the purpose, which had never been done before. These are much the best; as by them the view may be directed to an object at a greater distance, and towards any point with more certainty; certainty; whence the triangles for measuring distances may be formed with greater accuracy than otherwise can be done. In consequence of this improvement, the fundamental base of their operations was much longer than that made use of by Snellius or Ricciolus. The distance measured was between the parallels of Sourdon and Malvoisine; between which the difference of the polar altitude is somewhat more than one degree; and the result of the whole was, that one degree contained 57,060 French toises. As this problem can be the more accurately determined in proportion to the length of the meridian line measured, the members of the Royal Academy prolonged theirs quite across the kingdom of France, measuring it trigonometrically all the way. This work was begun in the year 1683, but was not finished till 1718. They made use of Picard's fundamental base, as being measured with sufficient accuracy; and an account of the whole was published by Cassini in the year 1720. In this work some mistakes were detected in the calculations of Snellius; and it was likewise shown, that there were errors in those of Ricciolus, owing principally to the latter having taken too short a fundamental base, and not having paid sufficient attention to the effects of refraction. Though Snellius, however, had made some mistakes in his calculations, there is no reason to doubt the accuracy of his observations. Holland, by reason of its flatness, is the fittest country in Europe for measuring an arc of the meridian; and Snellius had an uncommon opportunity of observing the exactness of his fundamental base, viz., the distance between one tower at Leyden and another at Souterwode. A frost happened just after the country round Leyden had been overflowed; by which means he was enabled to take two stations upon the ice, the distance between which he carefully measured three times over; and then from these stations he observed the angles which the visual rays pointing at those towers made with the straight line upon the ice. From these considerations professor Muenchenbroek was induced to make new calculations and form triangles upon the fundamental base of Snellius, which he did in the year 1700; and from these he assigns 57°-33' toises to a degree, which is only 27 less than had been done by the academicians.

The investigation of this problem of the circumference of the earth was essentially necessary for determining the radical principles of all maps; that of Eratosthenes, though the best of which antiquity can boast, was nevertheless exceedingly imperfect and inaccurate. It contained little more than the states of Greece, and the dominions of the successors of Alexander, digested according to the surveys above mentioned. He had seen, indeed, and has quoted, the voyages of Pytheas into the great Atlantic ocean, which gave him some faint idea of the western parts of Europe; but so imperfect, that they could not be realized into the outlines of a chart. Strabo tells us, that he was extremely ignorant of Gaul, Spain, Germany, and Britain. He was equally ignorant of Italy, the coasts of the Adriatic, Pontus, and all the countries towards the north. We are also told by the same author, that Eratosthenes made the distance between Epidaumus or Dyrrhachium on the Adriatic, and the bay of Thermae on the Aegean sea, to be only 900 stadia, when in reality it was above 2000; and in another instance, he had enlarged the distance from Carthage to Alexandria to 15,000 stadia, when in reality it was no more than 9000.

Such was the state of geography and the nature of the maps prior to the time of Hipparchus; who made a closer connection between geography and astronomy, by determining the longitudes and latitudes from celestial observations. It must be owned, however, that the previous steps to this new projection of the sphere had been in a great measure made easy by Archimedes, upwards of 50 years before the time of Hipparchus, when he invented his noble theorems for measuring the surface of a sphere and its different segments.

It appears that war has been generally the occasion of making the most accurate maps of different countries; and therefore geography made great advances from the progress of the Roman arms. In all the provinces occupied by that people, we find that camps were everywhere constructed at proper intervals, and roads were raised with substantial materials, for making an easier communication between them; and thus civilization and surveying were carried on according to system throughout the extent of that large empire. Every new war produced a new survey and itinerary of the countries where the scenes of action passed; so that the materials of geography were accumulated by every additional conquest. Polybius tells us, that at the beginning of the second Punic war, when Hannibal was preparing his expedition against Rome, the countries through which he was to pass were carefully measured by the Romans. Julius Caesar caused a general survey of the Roman empire to be made, by a decree of the senate. Three surveyors, Zenodorus, Theodotus, and Polyclitus, had this task assigned them, and are said to have completed it in 25 years. The Roman itineraries that are still extant, also show what care and pains they had been at in making surveys in all the different provinces of their empire; and Pliny has filled the third, fourth, and fifth books of his Natural History with the geographical distances that were thus measured. We have likewise another set of maps still preserved to us, known by the name of the Peutingerian Tables, published by Wilfer and Bertius, which give a sufficient specimen of what Vegetius calls the Itineraria Picta, for the clearer direction of their armies in their march.

The Roman empire had been enlarged to its greatest extent, and all its provinces well known and surveyed, when Ptolemy, in the reign of Antoninus Pius, about 150 years after Christ, composed his system of geography. The principal materials he made use of for composing this work, were the proportions of the gnomon to its shadow, taken by different astronomers at the times of the equinoxes and solstices; calculations founded upon the length of the longest days; the measures or computed distances of the principal roads contained in their surveys and itineraries; and the various reports of travellers and navigators, who often determined the distances of places by hearsay and conjecture. All these were compared together, and digested into one uniform body or system; and afterwards were translated by him into a new mathematical language, expressing the different degrees of longitude and latitude, according to the invention of Hip... Hipparchus, but which Ptolemy had the merit of carrying into full practice and execution, after it had been neglected for upwards of 250 years. With such imperfect and inaccurate materials, it is no wonder to find many errors in Ptolemy's system. Neither were these errors such as had been introduced in the more distant extremities of his maps, but even in the very centre of that part of the world which was the best known to the ancient Greeks and Romans, and where all the famed ancient astronomers had made their observations.—Yet this system, with all its imperfections, continued in vogue till the beginning of the present century. The improvements in geography which at that time, and since, have taken place, were owing to the great progress made in astronomy by several eminent men who lived during that period. More correct methods and instruments for observing the latitude were found out; and the discovery of Jupiter's satellites afforded a much easier method of finding the longitudes than was formerly known. The voyages made by different nations also, which were now become much more frequent than formerly, brought to the knowledge of the Europeans a vast number of countries utterly unknown to them before. The late voyages of Captain Cooke, made by order of his Britannic Majesty, have contributed more to the improvement of geography than any thing that has been done during the present century; so that now the geography of the utmost extremities of the earth is in a fair way of being much better known to the moderns than that of the most adjacent countries was to the ancients. This, however, must be understood only of the sea-coasts of these countries; for, as to their internal geography, it is less known now than before, except in a very few places.

On the whole, it may be observed, that geography is a science even yet far from perfection. The maps of America and the eastern parts of Asia are, perhaps, more unfinished than any of the rest. Even the maps of Great Britain and Ireland are very imperfect and unsatisfactory; and the numbers we have of them, varied, and republished, without any real improvement, justly confirm an observation made by Lord Bacon, namely, that an opinion of plenty is one of the causes of want. The late Dr Bradley was of opinion, that there were but two places in England whose longitude might be depended upon as accurately taken; and that these were the observatory at Greenwich, and Serburn-castle the seat of the earl of Macclesfield in Oxfordshire; and that their distance was one degree in space, or four minutes in time. Even this was found to be inaccurate, the distance in time being observed by the late transit of Venus to be only three minutes and 47 seconds. It were well, however, if there were no greater errors with regard to other places; but if we examine the longitude of the Lizard, we shall find scarce any two geographers that agree concerning it; some making it 4° 40' from London; others 5°, and 5° 14'; while some enlarge it to 6°. Our best maps are therefore still to be considered as unfinished works, where there will always be many things to be added and corrected, as different people have an opportunity.

Sect. II. Principles and Practice of Geography.

The fundamental principles of geography are, the spherical figure of the earth; its rotation on its axis; its revolution round the sun; and the position of the axis or line round which it revolves, with regard to the celestial luminaries. That the earth and sea taken together constitute one vast sphere, is demonstrable by the following arguments. 1. To people at sea, the figure of land disappears, though near enough to be visible were it not for the intervening convexity of the water. 2. The higher the eye is placed, the more extensive is the prospect; whence it is common for sailors to climb up to the tops of the masts to discover land or ships at a distance. But this would give them no advantage were it not for the convexity of the earth; for, upon an infinitely extended plane objects would be visible at the same distance whether the eye were high or low; nor would any of them vanish till the angle under which they appeared became too small to be perceptible. 3. To people on shore, the mast of a ship at sea appears before the hull; but were the earth an infinite plane, not the highest objects, but the biggest, would be longest visible; and the mast of a ship would disappear by reason of the smallness of its angle long before the hull did so. 4. The convexity of any piece of still water of a mile or two extent may be perceived by the eye. A little boat, for instance, may be perceived by a man who is any height above the water; but if he flops down and lays his eye near the surface, he will find that the fluid appears to rise and intercept the view of the boat entirely. 5. The earth has been often divided round; as by Magellan, Drake, Dampier, Anson, Cook, and many other navigators; which demonstrates that the surface of the ocean is spherical; and that the land is very little different, may easily be proved from the small elevation of any part of it above the surface of the water. The mouths of rivers which run 1000 miles are not more than one mile below their sources; and the highest mountains are not quite four miles of perpendicular height: so that, though some parts of the land are elevated into hills, and others depressed into valleys, the whole may still be accounted spherical. 6. An undeniable and indeed ocular demonstration of the spherical figure of the earth is taken from the round figure of its shadow which falls upon the moon in the time of eclipses. As various sides of the earth are turned towards the sun during the time of different phenomena of this kind, and the shadow in all cases appears circular, it is impossible to suppose the figure of the earth to be any other than spherical. The inequalities of its surface have no effect upon the earth's shadow on the moon; for as the diameter of the terraqueous globe is very little less than 8000 miles, and the height of the highest mountain on earth not quite four, we cannot account the latter any more than the 200th part of the former; so that the mountains bear no more proportion to the bulk of the earth, than grains of dust bear to that of a common globe.

A great many of the terrestrial phenomena depend upon the globular figure of the earth, and the position of its axis with regard to the sun; particularly the globular rising figure of the earth. rising and setting of the celestial luminaries, the length of the days and nights, &c. A general explanation of these is given under the article Astronomy; but still it belongs to geography to take notice of the difference betwixt the same phenomena in different parts of the earth. Thus, though the sun rises and sets all over the world, the circumstances of his doing so are very different in different countries. The most remarkable of these circumstances is the duration of the light not only of the sun himself, but of the twilight before he rises and after he sets. In the equatorial regions, for instance, darkness comes on very soon after sunset; because the convexity of the earth comes quickly into between the eye of the observer and the luminary, the motion of the earth being much more rapid there than anywhere else. In our climate the twilight always continues two hours or thereabouts, and during the summer-season it continues in a considerable degree during the whole night. In countries farther to the northward or southward, the twilight becomes brighter and brighter as we approach the poles, until at last the sun does not appear to touch the horizon, but goes in a circle at some distance above it for many days successively. In like manner, during the winter, the same luminary sinks lower and lower, until at last he does not appear at all; and there is only a dim twinkling of twilight for an hour or two in the middle of the day. By reason of the refraction of the atmosphere, however, the time of darkness, even in the most inhospitable climates, is always less than that of light; and so remarkable is the effect of this property, that in the year 1682, when some Dutch navigators wintered in Nova Zembla, the sun was visible to them 16 days before he could have been seen above the horizon had there been no atmosphere, or had it not been endowed with any such power. The reason of all this is, that in the northern and southern regions only a small part of the convexity of the globe is interposed betwixt us and the sun for many days, and in the high latitudes none at all. In the warmer climates the sun has often a beautiful appearance at rising and setting, by reason of the refraction of his light through the vapours which are copiously raised in those parts. In the colder regions, halos, parhelia, aurora borealis, and other meteors, are frequent; the two former owing to the great quantity of vapour continually rising from the warm regions of the equator to the colder ones of the poles. The aurora borealis is owing to the electrical matter imbibed by the earth from the sun in the warm climates, and going off through the upper regions of the atmosphere to the place from whence it came. In the high northern latitudes, thunder and lightning are unknown, or but seldom heard of; but the more terrible phenomena of earthquakes, volcanoes, &c., are by no means unfrequent. These, however, seem only to affect islands and the maritime parts of the continent. See the articles Earthquake and Volcano.

Notwithstanding the seeming inequality in the distribution of light and darkness, however, it is certain, that throughout the whole world there is nearly an equal proportion of light diffused on every part, abstracting from what is absorbed by clouds, vapours, and the atmosphere itself. The equatorial regions have indeed the most intense light during the day, but the nights are long and dark; while, on the other hand, in the northerly and southerly parts, though the sun shines less powerfully, yet the length of time that he appears above the horizon, with the greater duration of the twilight, makes up for the seeming deficiency.

Were the earth a perfect plane, the sun would appear to be vertical in every part of it: For in comparison with the immense magnitude of that luminary, the diameter of this globe itself is but very small; and as the sun, were he near to us, would do much more than cover the whole earth; so, though he were removed to any distance, the whole diameter of the latter would make no difference in the apparent angle of his altitude. By means of the globular figure of the earth also, along with the great disparity between the diameters of the two bodies, some advantage is given to the day over the night: for thus the sun, being immensely the larger of the two, shines upon more than one half of the earth; whence the unenlightened part has a shorter way to go before it again receives the benefit of his rays. This difference is greater in the inferior planets Venus and Mercury than the earth.

To the globular figure of the earth likewise is owing the long moon-light which the inhabitants of the polar regions enjoy, the general reason of which is given under the article Astronomy, No. 373. The same thing likewise occasions the appearance and disappearance of certain stars at some seasons of the year in some countries; for were the earth flat, they would all be visible in every part of the world at the same time. Hence most probably has arisen the opinion of the influence of certain stars upon the weather and other sublunar matters. In short, on the globular figure of the earth depends the whole present appearance of nature around us; and were the shape of the planet we inhabit to be altered to any other, besides the real differences which would of consequence take place, the apparent ones would be so great that we cannot form any idea of the face which nature would then present to us.

In geography the circles which the sun apparently describes in the heavens are supposed to be extended as far as the earth, and marked on its surface; and in drawn out like manner we may imagine as many circles as we please to be described on the earth, and their planes to be extended to the celestial sphere, till they mark concentric ones on the heaven. The most remarkable of those supposed by geographers to be described in this manner are the following:

1. The Horizon. This is properly a double circle, one of the horizons being called the sensible, and the other the rational. The former comprehends only that space which we can see around us upon any part of the earth; and which is very different according to the difference of our situation. The other, called the rational, is a circle parallel to the former, and passing through the centre of the earth supposed to be continued as far as the celestial sphere itself. To the eyes of spectators, there is always a vast difference between the sensible and rational horizons; but by reason of the immense disparity betwixt the size of the earth and celestial sphere, places of both circles may be considered as coincident. Hence, in geography, when the horizon, or plane of the horizon is spoken of, the rational... tional is always understood, when nothing is said to the contrary. By reason of the round figure of the earth, every part has a different horizon. The poles of the horizon, that is, the points directly above the head, and opposite to the feet of the observer, are called the zenith and nadir.

2. A great circle described upon the sphere of the heaven, and passing through the two vertical points, is called a vertical circle, or an azimuth; and of these we may suppose as many as we please all round the horizon. Sometimes they are also called secondaries of the horizon; and in general any great circle, drawn through the poles of another, is called its secondary. In geography every circle obtains the epithet of great whole plane passes through the centre of the earth; in other cases they are called lesser circles. The altitudes of the heavenly bodies are measured by an arch of the azimuth or vertical circle intercepted between the horizon and the body itself. The method of taking them is explained under the article Astronomy, no. 379; but a more accurate method with regard to the sun and moon, is for two persons to make their observations at the same time; one of them to observe the altitude of the upper limb, the other of the lower limb of the luminary; the mean between these two giving the true height of the centre. The same thing may also be done accurately by one observer, having the apparent diameter of the luminary given. For, having found the height of the upper edge of the limb by the quadrant, take from it half his diameter, the remainder is the height of his centre; or having found the altitude of his lower edge, add to it half the diameter, and the sum is the height of the centre as before. When the observations are made with a large instrument, it will be convenient to use a sextant, or fifth part of a circle, rather than a quadrant, as being less unwieldy.

3. Almucantars are circles supposed to be drawn upon the sphere parallel to the horizon, and grow less and less as they approach the vertical points, where they entirely vanish. The apparent distances between any two celestial bodies are measured by supposing arches of great circles drawn through them, and then finding how many degrees, minutes, &c. of these circles are intercepted between them. The apparent diameter of the sun's disk is found by a circle of distance drawn through the centre of it; and the number of minutes continued between the two opposite points of that part of the circle which passes through the centre is the measure of the apparent diameter. The apparent diameter of the sun may be found by two observers, one taking the altitude of the upper, and the other of the lower edge of the limb; the difference between the two being the diameter required; or,

4. Sometimes the visible horizon is considered only with regard to the objects which are upon the earth itself; in which case we may define it to be a lesser circle on the surface of the earth, comprehending all such objects as are at once visible to us; and the higher the eye, the more is the visible horizon extended. It is most accurately observed, however, on the sea, on account of the absence of those inequalities which at land render the circle irregular; and for this reason it is called sometimes the horizon of the sea; and may be observed by looking through the sights of a quadrant at the most distant part of the sea then visible.

In making this observation, the visual rays AD and AE, fig. 2, will, by reason of the spherical surface of the sea, always point a little below the true sensible horizon SS; and consequently below the rational horizon which is parallel to it, and supposed to be coincident with it. The quadrant shows the depression of the horizon of the sea below the true horizon; and it is obvious from the figure, that the higher the eye is, the greater must this depression be. The depression of the horizon of the sea, however, is not always the same, even though there be no variation in the height of the eye. The difference indeed is but small, amounting only to a few seconds, and is owing to a difference in the atmosphere, which sometimes refracts more than at others. Without refraction, the visual ray would be AE, and in that case F is the most distant point which could be seen; but by refraction, the ray FG, coming from the point G, may be seen at F, so as to go on from thence in the line FA; and then the view is extended as far as G, and the depression of the horizon of the sea is in the line AF, which points higher than AE, but extends the view farther. From an inspection of the figure it is evident, that if the refraction were greater, the view would be extended still farther, as to M; though the depression of the horizon of the sea would then be less, as is shown by the line ALM: whence also it appears, that by reason of the difference of refraction in the air, our horizon is sometimes more extensive than at others.

5. The equator is a great circle upon the earth, every part of which is equally distant from the poles or extremities of the imaginary line on which the earth revolves. In the sea-language it is usually called the line, and when people sail over it they are said to cross the line.

6. The meridian of any place is a great circle on the earth drawn through that place and both poles of the earth. It cuts the horizon at right angles, marking upon it the true north and south points; dividing the globe into two hemispheres called the eastern and western from their relative situation to that place and to one another. The poles divide the meridians into two semicircles; one of which is drawn through the place to which the meridian belongs, the other through that point of the earth which is opposite to the place. By the meridian of a place geographers and astronomers often mean that semicircle which passes through the place; and which may therefore be called the geographical meridian. All places lying under this semicircle are said to have the same meridian; the semicircle opposite to this is called the opposite meridian. The meridians are thus immovably fixed to the earth as much as the places themselves on its surface; and are carried along with it in its diurnal rotation. When the geographical meridian of any place is, by the rotation of the earth, brought to point at the sun, it is noon or mid-day at that place; in which case, were the plane of the circle extended, it would pass through the middle of the luminary's disk. Supposing the plane of the meridians to be extended to the sphere of the fixed stars, in that case, when by the rotation of the earth the meridian comes to any point in the heavens, then, from the apparent motion of the heavens, that point is said to come to the meridian. The rotation of the earth is from west to east; whence the celestial bodies appear to move the contrary. Sect. II.

Principles

East and west, however, are terms merely relative; since a place may be west from one part of the earth, and east from another; but the true east and west points from any place are those where its horizon cuts the equator.

7. All places lying under the same meridian are said to have the same longitude, and those which lie under different meridians to have different longitudes; the difference of longitude being reckoned eastward or westward on the equator. Thus if the meridian of any place cuts the equator in a point 15 degrees distant from another, we say there is a difference of 15° longitude between these two places. Geographers usually pitch upon the meridian of some remarkable place for the first meridian; and reckon the longitude of all others by the distance of their meridians from that which they have pitched upon as the first; measuring sometimes eastward on the equator all round the globe, or sometimes only one half east and the other west; according to which last measurement, no place can have more than 180° longitude either east or west.

By the ancient Greek geographers the first meridian was placed in Hera or Junonia, one of the Fortunate Islands as they were then called; which is supposed to be the present island of Teneriffe, one of the Canaries. These islands being the most westerly part of the earth then known, were on that account made the seat of the first meridian, the longitude of all other places being counted eastward from them. The Arabians, ambitious of having the first meridian taken from them, fixed it at the most westerly part of the continent of Africa. Some later geographers placed the first meridian in the island of Corvo, one of the Azores (A); because at that time the magnetic needle on the island just mentioned pointed due north without any variation; and it was not then known that the needle itself was subject to variation, as has since been discovered. Bleau replaced the first meridian in the isle of Teneriffe; and to ascertain the place more exactly, caused it to pass through the famous mountain of that island, called the peak from el-pico, "a bird's beak."

Among modern geographers, however, it is now become customary for each to make the first meridian pass through the capital of his own country; a practice, however, which is certainly improper, as it is thus impossible for the geographers of one nation to understand the maps of another without a troublesome calculation, which answers no purpose. By the British geographers the royal observatory at Greenwich is accounted the place of the first meridian.

8. If we suppose 12 great circles, one of which is the meridian to a given place, to intersect each other at the poles of the earth, and divide the equator into 24 equal parts, these are the hour-circles of that place. These are by the poles divided into 24 semicircles, corresponding to the 24 hours of the day and night. The distance between each two of these semicircles is 15°, being the 24th part of 360°; and by the rotation of the earth, each succeeding semicircle points at the sun one hour after the preceding; so that in 24 hours all the semicircles point successively at the sun. Hence it appears that such as have their meridian 15° east from any other, have likewise noon one hour sooner, and the contrary; and in like manner every other hour of the natural day is an hour sooner at the one place than at the other. Hence, from any instantaneous appearance in the heavens observed at two distant places, the difference of longitude may be found, if the hour of the day be known at each place. Thus the beginning of an eclipse of the moon, when the luminary first touches the shadow of the earth, is an instantaneous appearance, as also the end of an eclipse of this kind when the moon leaves the shadow of the earth, visible to all the inhabitants on that side of the globe. If therefore we find, that at any place an eclipse of the moon begins an hour sooner than at another, we conclude that there is a difference of 15° of longitude between the two places. Hence also were a man to travel or sail round the earth from west to east, he will reckon one day more to have passed than they do who stay at the place from whence he set out; so that their Monday will be his Tuesday, &c. On the other hand, if he sails westward, he will reckon a day less, or be one day in the week later, than those he leaves behind.

9. The equator divides the earth into two hemispheres called the northern and southern: all places lying under the equator are said to have no latitude; and all others to have north or south latitude according to their situation with respect to the equator. The latitude itself is the distance from the equator measured upon the meridian, in degrees, minutes, and seconds. The complement of latitude is the difference between the latitude itself and 90°, or as much as the place itself is distant from the pole; and this complement is always equal to the elevation of the equator above the horizon of the place. The elevation of the pole of any place is equal to the latitude itself.

An inhabitant of the earth who lives at either of the poles, has always one of the celestial poles in his zenith and the other in his nadir, the equator coinciding with the horizon; hence all the celestial parallels are also parallel to the horizon; whence the person is said to live in a parallel sphere, or to have a parallel horizon.

Those who live under the equator have both poles right in the horizon, all the celestial parallels cutting the horizon at right angles; whence they are said to live in a right sphere, or to have a right horizon.

Lastly, those who live between either of the poles and the equator are said to live in an oblique sphere, or to have an oblique horizon; because the celestial equator cuts his horizon obliquely, and all the parallels in the celestial sphere have their planes oblique to that of the horizon. In this sphere some of the parallels intersect the horizon at oblique angles, some are entirely above it, and some entirely below it; all of them, however, so situated, that they would obliquely intersect the plane of the horizon extended.

The largest parallel which appears entire above the horizon of any place in north latitude is called by the ancient astronomers the arctic circle of that place; circle.

(a) These islands had their name from the number of goshawks found there; the word azor in Spanish signifying a "goshawk." within this circle, i.e., between it and the arctic pole, are comprehended all the stars which never set in that place, but are carried perpetually round the horizon in circles parallel to the equator. The largest parallel which is hid entire below the horizon of any place in north latitude was called the antarctic circle of that place by the ancients. This circle comprehends all the stars which never rise in that place, but are carried perpetually round below the horizon in circles parallel to the equator. In a parallel sphere, however, the equator may be considered as both arctic and antarctic circle; for being coincident with the horizon, all the parallels on one side are entirely above it, and those on the other entirely below it. In an oblique sphere, the nearer any place is to either of the poles, the larger are the arctic and antarctic circles, as being nearer to the celestial equator, which is a great circle. In a right sphere, the arctic and antarctic circles have no place; because no parallel appears either entirely above or below it. By the arctic and antarctic circles, however, modern geographers in general understand two fixed circles at the distance of $23\frac{1}{2}$ degrees from the pole. These are supposed to be described by the poles of the ecliptic, and mark out the space all round the globe where the sun appears to touch the horizon at midnight in the summer time, and to be entirely sunk below it in the winter. These are also called the polar circles. By the ancients the arctic circle was called maximus semper apparitum, and circulus perpetuae apparitionis; the antarctic circle, on the other hand, being named maximus semper occultorum, and circulus perpetuae occultationis.

According to the different positions of the globe with regard to the sun, the celestial bodies will exhibit different phenomena to the inhabitants. Thus, in a parallel, right, parallel sphere, they will appear to move in circles and oblique round the horizon; in a right sphere, they would appear to rise and set as at present, but always in circles cutting the horizon at right angles; but in an oblique sphere, the angle varies according to the degree of obliquity, and the position of the axis of the sphere with regard to the sun. The phenomena thence arising will be sufficiently understood from what is said under the article Astronomy, No. 345, &c. From thence we will easily perceive the reason of the sun's continual change of place in the heavens; but though it is certain that this change takes place every moment, the vast distance of the luminaries renders it imperceptible for some time, unless to very nice astronomical observers. Hence we may generally suppose the place of the sun to be the same for a day or two together, tho' in a considerable number of days it becomes exceedingly obvious to every body. When he appears in the celestial equator, his motion appears for some time to be in the plane of that circle, though it is certain that his place there is only for a single moment; and in like manner, when he comes to any other point of the heavens, his apparent diurnal motion is in a parallel drawn throughout. Twice a-year he is in the equator, and then the days and nights are nearly equal all over the earth. This happens in the months of March and September; after which the sun proceeding either northward or south, according to the season of the year and the position of the observer, the days become longer or shorter than the nights, and

N° 136.

summer or winter come on, as is fully explained under the article Astronomy. The recession of the sun from the equator either northward or southward is called his declination, and is either north or south according to the season of the year; and when this declination is at its greatest height, he is then said to nation, be in the tropic, because he begins to turn back (the word tropic being derived from the Greek τροπον κερα). The space between the two tropics, called the torrid zone, extends for no less than 47 degrees of latitude all pics, &c., round the globe; and throughout the whole of that space the sun is vertical to some of the inhabitants twice a-year, but to those who live directly under the tropics only once. Throughout the whole torrid zone also there is little difference between the length of the days and nights. The ancient geographers found themselves considerably embarrassed in their attempts to fix the northern tropic; for though they took a very proper method, namely, to observe the most northerly place where objects had no shadow on a certain day, yet they found that on the same day no shadow was cast for a space of no less than 300 stadia. The reason of this was, the apparent diameter of the sun; which being about half a degree, seemed to extend himself over as much of the surface of the earth, and to be vertical everywhere within that space.

When the sun is in or near the equator, he seems to change his place in the heavens most rapidly; so that about the equinoxes one may very easily perceive the difference in a day or two; but as he approaches the tropics this apparent change becomes gradually slower; so that for a number of days he scarce seems to move at all. The reason of this may easily be understood from any map on which the ecliptic is delineated; for by drawing lines through every degree of it parallel to the equator, we shall perceive them gradually approach nearer and nearer each other, until at last, when we approach the point of contact betwixt the ecliptic and tropic, they can for several degrees scarce be distinguished at all.

From an observation of the diversity in the length division of the days and nights, the rising and setting of the earth's sun, with the other phenomena already mentioned, the ancient geographers divided the surface of the earth into certain districts, which they called climates; and instead of the method of describing the situation of places by their latitude and longitude as we do now, they contented themselves with mentioning the climate in which they were situated. When more accuracy was required, they mentioned also the beginning, middle, and ending of the climates. This division, however, was certainly very vague and inaccurate; for the only method they had of determining the difference was by the length of the day; and a climate, according to them, was such a space as had the day in its most northerly part half an hour longer than in the most southerly. For the beginning of their first climate they took that parallel under which the day is twelve hours and three quarters long, those parts of the world which lie nearer the equator not being supposed to be in any climate; either because in a loose sense they may be considered as in a right sphere, or because they were unknown, or thought to be uninhabitable by reason of the heat. The northern climates were generally supposed to be seven; which must have Principles have an equal number of southern climates corresponding with them. The names of the northern climates, according to the ancients, were as follow: 1. Meroe. 2. Syene in Egypt. 3. Alexandria in Egypt. 4. Rhodes. 5. Rome; or, according to others, a parallel drawn through the Hellespont. 6. The parallel passing through the mouth of the river Borithenes. 7. The Riphean mountains.—Each of these places was supposed to be in the middle of the climate; and as the southern parts of the globe were then very little known, the climates to the southward of the equator were supposed to be as far distant from that circle as the northern ones; in consequence of which they took their names from the latter.

A parallel was said to pass through the middle of a climate when the day under that parallel is a quarter of an hour longer than that which passes through the most southerly part. Hence it does not divide the space into two equal parts, but that part next the equator will always be the larger of the two; because the farther we recede from that circle, the less increase of latitude will be sufficient to lengthen the day a quarter of an hour. Thus, in every climate there are three parallels; one marking the beginning, the second the middle, and the third the ending of the climate; the ending of one being always the beginning of another. Some of the ancients divided the earth by these parallels; others by a parallel did not mean a mere line, but a space of some breadth: and hence the parallel may be understood as the same with half a climate.

This method of dividing the surface of the earth into climates, though now very much diffused, has been adopted by several modern geographers. Some of these begin their climates at the equator, reckoning them by the increase of half an hour in the length of the day northward. Thus they go on till they come to the polar circles, where the longest day is 24 hours: betwixt these and the poles they count the climates by the increase of a natural day in the length of time that the sun continues above the horizon, until they come to one where the longest day is 15 of ours, or half a month; and from this to the pole they count by the increase of half months or whole months, the climates ending at the poles where the days are six months long. The climates betwixt the equator and the polar circles are called hour-climates, and those between the polar circles and the poles are called month-climates.—In common language, however, we take the word climate in a very different sense; so that, when two countries are said to be, in different climates, we understand only that the temperature of the air, seasons, &c., are different.

From the difference in the length and positions of the shadows of terrestrial substances, ancient geographers have given different terms to the inhabitants of certain places of the earth; the reason of which will be easily understood from the following considerations.

1. Since the sun in his apparent annual revolution never removes farther from the equator than $23\frac{1}{2}$ degrees, it follows, that none of those who live without that space, or beyond the tropics, can have the luminary vertical to them at any season of the year.

2. All who live between the tropics have the sun vertical twice a-year, though not all at the same time.

Thus, to those who live directly under the equator, he is directly vertical in March and September at the time of the equinox. If a place is in $10^\circ$ north latitude, the sun is vertical when he has $10^\circ$ north declination; and so of every other place.

3. All who live between the tropics have the fun at noon sometimes north and sometimes south of them. Thus, they who live in a place situated in $20^\circ$ north latitude, have the fun at noon to the northward when he has more than $20^\circ$ degrees north declination, and to the southward when he has less.

4. Such of the inhabitants of the earth as live without the tropics, if in the northern hemisphere, have the fun at noon to the southward of them, but to the northward if in the southern hemisphere.

5. When the fun is in the zenith of any place, the shadow of a man or any upright object falls directly upon the place where they stand, and consequently is invisible; whence the inhabitants of such places were called Ajici, or without shadows; those who live between the tropics, and have the fun sometimes to the north and sometimes to the south of them, have of consequence their shadows projecting north at some seasons of the year and south at others; whence they were called Araphysii, or having two kinds of shadows. They who live without the tropics have their noon shadows always the same way; and are therefore called Heterofici, that is, having only one kind of shadow. If they are in north latitude, the shadows are always turned towards the north; and if in the southern hemisphere, towards the south. When a place is so far distant from the equator that the days are 24 hours long or longer, the inhabitants were called Perifici, because their shadows turn round them.

Names have likewise been imposed upon the inhabitants of different parts of the earth from the parallels of latitude under which they live, and their situation with regard to one another. Thus, when two places distance are so near each other that the inhabitants have only of places, one horizon, or at least that there is no perceptible difference between them, the inhabitants were called Synaci, that is, near neighbours; the seasons, days, nights, &c., in both places being perfectly alike. Those who lived at distant places, but under the same parallel, were called Periaci, that is, living in the same circle. Those who are on the same side of the equator have the seasons of the year at the same time; but if on different sides, the summer season of the one is the winter of the other, as is fully explained under the article ASTRONOMY. Some writers, however, by the name of Periaci, distinguish those who live under opposite points of the same parallel, where the noon of one is the midnight of the other. When two places lie under parallels equally distant from the equator, but in opposite hemispheres, the inhabitants were called Antaci. These have a similar increase of days and nights, and similar seasons, but in opposite months of the year. According to some, the Antaci were such as lived under the same geographical meridian, and had day and night at the same time. If two places are in parallels equally distant from the equator, and in opposite meridians, the inhabitants were called Antichthones with respect to one another, that is, living on opposite sides of the earth; or Antipodes, that is, having their feet opposite to one another. When two persons are Antipodes, the zenith of the one is the nadir of the other. nadir of the other. They have a like elevation of the pole, but it is of different poles: they have also days and nights alike, and similar seasons of the year; but they have opposite hours of the day and night, as well as seasons of the year. Thus, when it is midnight with us, it is midnight with our Antipodes; when it is summer with us, it is winter with them, &c.

44. Division of the earth into zones.

From the various appearances of the sun, and the effects of his light and heat upon different parts of the earth, the division of it into zones has arisen. There are five in number. 1. The torrid zone, lying between the two tropics for a space of 47° of latitude. This is divided into two equal parts by the equator; and the inhabitants have the sun vertical to them twice a-year, excepting only those who dwell under the tropics, to whom he is vertical only once, as has already been explained. 2. The two temperate zones lie between the polar circles and the tropics, containing a space of 43° of latitude. And, 3. The two frigid zones lie between the polar circles and the poles. In these last the longest day is never below 24 hours, in the temperate zones it is never quite so much, and in the torrid zone it has never above 14. The zones are named from the degree of heat they were supposed to be subjected to. The torrid zone was supposed by the ancients to be uninhabitable by reason of its heat; but this is now found to be a mistake, and many parts of the temperate zones are more intolerable in this respect than the torrid zone itself. Towards the polar circles, also, these zones are intolerably cold during the winter season. Only a small part of the northern frigid zone, and none of the southern, is inhabited. Some geographers reckoned six zones, dividing the torrid zone into two by the equator.

When any parts of the heaven or earth are said to be on the right or left, we are to understand the expression differently according to the profession of the person who makes use of it; because according to that his face is supposed to be turned towards a certain quarter. A geographer is supposed to stand with his face to the north, because the northern part of the world is best known. An astronomer looks towards the south, to observe the celestial bodies as they come to the meridian. The ancient augurs, in observing the flight of birds, looked towards the east; while the poets look towards the Fortunate Isles. In books of geography, therefore, by the right hand we must understand the east; in those of astronomy, the west; in such as relate to augury, the south; and in the writings of poets, the north.

Under the article Astronomy, no 376, et seq., the method of drawing a meridian line is fully explained; the knowledge of which is absolutely necessary both for geographers and astronomers. To what is mentioned there we shall only add further, that the time for drawing a line of this kind is when the sun is nearly at the summer solstice; because the difference of declination is then scarce perceptible for several days, and in the few hours requisite for the operation may be totally disregarded. The winter solstice would do equally well, were it not that the sun is then so low in the heavens that a difference in the refraction might cause a considerable error in the result. The motion of the luminary above the horizon is likewise so oblique, that he changes his vertical faster than his altitude, which is inconvenient in an operation where we are to determine the vertical by the altitude. A clear day must be chosen for the purpose; and the ground on which the shadow falls ought to be white, that the shadow may be better defined. The tile ought not to be too high, because then the top of the shadow will be indistinct; neither ought it to terminate in a point, for the same reason. Dr Long recommends the top of it to be about an eighth of an inch thick. Having drawn a meridian line upon one plane, we may draw one upon another by the following method: Hang a thread with a plummet exactly over the fourth end of the meridian line given, and another on the plane on which the meridian line is to be drawn. Let one person observe at noon the moment when the shadow of the first thread falls exactly upon the meridian given, and let another observer at the same time mark two distant points in the shadow of the second thread: a line drawn through these points is the meridian line required. Thus also a meridian line may be drawn upon a fourth wall by marking two points in the shadow of a thread hung at a little distance from it. If the meridians are near, he that observes the shadow of the first thread may let the other know the moment it falls upon the meridian line by saying, Now; if far distant, it should be done by the motion of the hand, because sound takes up some time in passing from one place to another. A quadrant or other astronomical instrument may now be fixed in the meridian line in such a manner as to be capable of different elevations, in order to observe the altitudes of the different celestial bodies; the plane of that side of the instrument on which the degrees are marked being all the while kept in the meridian. The mural arc in the Royal Observatory at Greenwich is a wall of black marble; one side of which, standing exactly in the plane of the meridian, has a large and accurately divided brass quadrant fixed to it, moveable round its centre, and with telescope sights. See Astronomy, no 497. At sea, where they cannot have a meridian line, the greatest height of a star or the sun is taken for the meridian height.

Having got a meridian line by either of the methods mentioned under the article Astronomy, it may be prolonged to what length we please, and the distance of it measured. The meridian of the royal observatory at Paris being found, and an instrument through with telescopic sights placed vertically therein, the north and south points of the visible horizon were observed through the sights, and a pillar erected upon the north point; then, by another instrument placed horizontally, several distant objects, as steeples, &c. were viewed, and the angles which the visual lines made with the meridian line were observed. From the places of these new objects, then, others were observed; and where natural objects were deficient, they set up large poles. Thus several triangles were formed along the meridian: and in order to measure those triangles, a paved way from Villejuif to Juvisy was made choice of for the fundamental base, as lying in a straight line from north to south. For the actual mensuration of this way, two poles were made use of, each of them four toises in length, and made of two pike-staves joined together at the great ends by a screw. One of the measuring poles was first laid upon the ground; Sect. II.

Principles and Practice.

ground; the other was joined to it end to end along by a rope stretched from north to south: the first pole was then taken up and laid down at the end of the second, and so on successively; and for the greater ease in keeping the account, the measurer who laid down the second pole had ten little stakes given him, one of which he stuck into the ground at the end of his pole every time he laid it down; so that every stake marked eight toises; the whole, when stuck into the ground, marking 80 toises. Thus the length of the road above mentioned was twice measured, and found to be 5663 toises and 4 feet in going, and 5663 toises and 1 foot in returning; so that as a greater exactness could not be hoped for, 5663 toises were pitched upon as the true length of this fundamental base. This is represented fig. 5, by the line OP; and the calculations of the triangles upon it were made in the following manner. The angle COP was observed from O, one end of the base; from the other end the angle OPC; and from the station C the angle OCP: and thus all the angles of the triangle CPO, and the length of one side OP, being known, the lengths of the remaining sides OC and PC were found by calculation. The next step was to observe all the angles of the triangle OBC, and from thence, and the known length of the side OC, to calculate the other side OB and BC. Then all the angles being observed, and the side BC being known of the triangle ABC, which may be called the first or principal triangle of the meridian of the observatory, the other sides AB and AC were found. Then, from one of the sides now known, and the angles observed, all the sides of the next adjoining triangle CBE were found. Thus they proceeded from one triangle to another to the place where the meridian ended in the south part of France; and there the last triangle was terminated by a base of the length of 7246 toises, which was actually measured in order to verify the preceding operations. The meridian line of Paris being prolonged in the manner just now described, the situation of several other places in France was determined by trigonometry, and an accurate map of the country drawn, especially of those parts which lie near the meridian of Paris.

Having found a meridian line, the transits or passages of the heavenly bodies across it may be observed by hanging two threads with plumbets exactly &c. of the over it, at a little distance from one another, which consequently will be directly in the plane of the meridian: if you place your eye close to one of the threads in such a manner that you make it cover the other, and both appear as one thread, when a star is behind the threads, it is in the meridian. By the same method the sun may be viewed through a smoked glass: when the threads pass through his centre he is in the meridian. But the best way of observing either the sun, moon, stars, or planets, is through a telescope placed in the meridian, with two cross hairs, one of which is in a vertical, the other in a horizontal position. The sun is in the meridian when the vertical hair passes through his centre.

To find the elevation of the pole in any place, take the greatest and least height of some star which never sets, the middle height between these extremes is the elevation of the pole. Or the elevation of the pole may be found by one observation of the height of a star in the meridian, if the declination of that star be known; for as the distance from the pole is the complement of its distance from the equator, this being subtracted from the greatest height of the star, leaves the elevation of the pole desired. The same thing may be done by observing the least height of a star, and adding to that the distance from the pole; but for observations of this kind we ought to choose the time when the stars are in the zenith, and not pitch upon any who happen to be near the horizon; because the refraction occasions such errors as are too considerable not to affect the observations materially.

The height of the equator is found by taking the height of the sun or a star when we know by an almanack they have no declination; or it may be otherwise known by taking the meridian height of the sun, and adding or subtracting the known declination. Having found the height of the equator, we know the elevation of the pole; or, having found the elevation of the pole, we know that of the equator, the one being the complement of the other.

A method much used by the ancients was that of taking the altitudes of the celestial bodies by means of a gnomon, or upright pillar erected for this purpose. Thus the height of the pole and the seasons of the year might be known by observing the length of the meridian shadow, which would be greater or less according to the altitude of the sun at that time. The most ancient observations of this kind were those made by Pytheas in the time of Alexander the Great, at Marseille in France, by which he found the meridian of the shadow at the summer solstice to be to the height of the gnomon as 213½ to 600; the same which Gaffendus afterwards found it in the year 1636.

The elevation of the pole may be found by means of the gnomon, by finding the meridian height of the sun; for this being given, we have the elevation of the equator, and consequently that of the pole. The meridian height of the sun may be found in the following manner. Let AC, fig. 1, be the gnomon, Plate AB the shadow, and CB part of a ray drawn from the centre of the sun passing by the top of the gnomon and terminating the shadow at B. These three lines form a right-angled triangle BAC, whereof the two legs AB and AC are given, the number of feet and inches in them being found by actual mensuration. Hence the acute angles may be found in the following manner. Let one leg be radius, and the other will be tangent of the opposite angle. Thus, if we make AB radius, AC will be tangent of the opposite angle ABC. This tangent is found by the golden rule, as the number of feet, inches, &c. in AB, is to the number of feet, inches, &c. in AC; so is the radius to a fourth number, which is the tangent required. This fourth number looked for in the table of tangents gives the measure of the angle ABC, which is the meridian height of the sun required.

This method of observation, however, is by no means accurate; and Ricciolus takes notice of the following deficiencies in the ancient observations made in this manner: 1. They did not take into account the sun's parallax, which makes his apparent altitude ten seconds less than it would be if the gnomon were placed at the centre of the earth. 2. They neglected refraction. tion, by which the apparent height of the sun is somewhat increased. They made their calculations as if the shadow were terminated by a ray coming from the sun's centre; whereas it is bounded by one coming from the upper edge of his limb. In many cases, however, these errors are of no moment; but at any rate they may be corrected in the following manner: To the altitude of the sun found by the gnomon, add his parallax of 10°, and take from the sun the semidiameter of the sun at that time, which is about 16°; together with the refraction, which is different at different heights of the sun, and must be had from a table of refractions. Thus the altitude of the sun will be had free of any errors, excepting those unavoidable ones arising from the difficulty in finding the true length of the shadow by reason of the penumbra, which always accompanies it.

Some gnomons show the altitude of the sun not by the shadow, but by an hole in the top made in a plate of metal inserted there, through which the rays fall upon a level pavement. In gnomons of this kind the centre of the instrument is always exactly under the hole in the metal-plate; and the method of finding the height of the sun is the same as that already described. A gnomon of this kind was made in the year 1576 by Egnatio Dante in the church of St Petronia at Bologna. Near the top of the south wall of the church he placed a brass plate about three-eighths of an inch thick, in which was cut a circular hole almost exactly an inch in diameter. The plate was set in the wall at an angle of about 45° deg., the height of the equator in that place. The height of the hole in the plate from the ground is near 66 feet, and the length of the line drawn upon the pavement is 169 feet. This line, however, is not exactly in the meridian, but as near it as the pillars of the church would admit; and on it the rays of the sun, passing through the hole, formed an ellipse at different distances from the wall, according to the season of the year. Another gnomon of this kind was made in the same church by Dominico Cafini in 1645. He placed the brass-plate through which the rays of the sun were to pass in the roof of the church, and drew a meridian line 120 feet long upon the pavement; which performance was so much approved, that a medal was struck upon the occasion. In like manner Bianchini and Moraldi drew a meridian line upon the pavement of the great hall of the baths of Diocletian, now the church of the Carthusians at Rome.

To construct gnomons of this kind, place the brass-plate with the hole in it in the fourth end of the roof of the building; by a thread with a plummet at the end of it let down through the centre of the hole, find the point in the pavement which is exactly under it; this point is the centre of the gnomon; from this centre draw several concentric circles: an hour or two before and after noon mark the points where the northern as also where the southern edge of the sun's picture touches these circles, and there will be several arches, through the middle of which a line drawn from the centre of the gnomon is a meridian line, as will be understood from what has been already said concerning the method of drawing these lines. The meridians just mentioned are usually marked upon long plates of brass, with which the marble pavement is laid; there are also drawn upon it lines crossing the meridians at right angles, to show how far the centre of the sun's image reaches at different times of the year: when this at noon is farthest from the centre of the gnomon, the sun is then lowest, and it is the winter solstice; when the same picture is nearest to the centre of the gnomon, the sun is highest, and consequently he is then in his greatest north declination, and it is then the summer solstice.

The time of the solstice is observed, by marking exactly the distance of the sun's picture from the centre of the gnomon the day before and the day after the solstitial day; if these distances be exactly equal, the meridian heights of the sun are for these two days exactly equal; and then the time of the sun's being in the solsticial point is exactly at noon: if the distance of the sun's picture from the centre of the gnomon be greater the day before the solstice than it is the day after, it shows that the time of the solstice is before noon; and if less, that it is after noon. It is, however, extremely difficult to determine the exact moment of the solstice by this method, or even to approach within some hours of it; for at those times the sun's declination, and consequently his meridian height, alters not above 15° in a natural day; and therefore an error of more than 15° in the observation of the sun's meridian height will occasion an error of a whole day in fixing the time of the solstice, an error of one half of 15° will occasion an error of half a day; and so in proportion.

The time of the equinox is found by a gnomon in the following manner: On the day of the equinox find the meridian height of the sun and the height of the equator. If these be equal, the equinox is exactly at noon; if the height of the sun be different from that of the equator, then as many minutes as the sun is higher than the equator, so many hours is the moment of the equinox before noon; as many minutes as the sun is lower than the equator, so many hours is the equinox after noon. The reason of this computation is, that at the equinox the declination of the sun alters at the rate of 24 minutes in a natural day, which is at the rate of a minute in an hour; whence it appears that the equinoxes are much more easily observed than the solstices. It is probable that many of the obelisks in Egypt were erected for the purpose of observing the altitude of the sun by the length of the shadow. It is likewise worth observing, that the Spaniards at the conquest of Peru found pillars of curious and costly workmanship, by the meridian shadows of which their astronomers or philosophers had by long experience and observation learned to determine the time of the equinoxes; these seasons of the year were celebrated by them with great festivity and rejoicing in honour of the sun, whom they imagined to sit at those times in all his glory upon the throne they had erected for him; and therefore on those days they presented him with rich offerings of gold, silver, jewels, and other valuable gifts; adorning his throne, as they did also the pillars, with fragrant herbs and flowers.

The principal uses which geographers have for observing the altitudes of the celestial bodies with such accuracy, are to determine the length of the year, the observations seasons, but especially the distance of places on the earth, their situation with regard to one another, and, finally, the declinations. Sect. II.

Principles the dimensions of the whole. An account of the most and remarkable attempts for discovering the circumference Practice. of the globe has been given in the preceding section.

The foundation of the whole is to obtain an exact measure of one degree of the meridian; which being once got, we have only to multiply the number of miles, feet, or any other measure employed, by 360, the number of degrees in the circumference, and the product is that of the whole globe. This being obtained, we may easily determine its superficial and solid contents by the geometrical methods employed in other cases. According to the best calculations which have yet appeared, the dimensions of this globe are as follow.

One minute of a degree contains \( \frac{1}{5} \) English miles.

A degree \( = 69\frac{1}{2} \)

The circumference \( = 24,930 \)

The diameter \( = 7935\frac{3}{4} \)

The semidiameter \( = 3967\frac{1}{2} \)

The superficial measure \( = 200,000,000 \)

The solid contents two hundred and sixty-five thousand millions of cubic miles.

A second of a degree is no more than 101\(\frac{1}{2}\) English feet.

In making measurements of this kind, the principal difficulty arises from the want of an absolutely level surface, the length of which may be determined by actual mensuration as the foundation of our calculations. Snellius, as has already been mentioned, had a singular opportunity of this kind by means of a great extent of ice; and similar conveniences might be had on the frozen lakes in the north of Europe, though difficulties would there arise from the great refraction of the atmosphere. It must likewise be considered, that there is always some difference between the apparent level and the true, which in great distances is apt to affect our calculations materially. A truly level surface is the segment of any spherical surface concentric to the surface of the earth; thus the surface of the sea or any large piece of water when at rest forms itself into a true level. A true line of level then is an arc of a great circle, which we suppose to be described upon a truly level surface. The apparent level is a straight line drawn tangent to the true level; whence every point of the apparent level, excepting only that of contact, is somewhat higher than the true level. This difference is easily known after the semidiameter of the earth is known. Thus in fig. 6, let the observer standing at A look through a telescope placed horizontally at the object B; here BAC is a right-angled triangle, in which if AC be made radius, AB will be tangent, and CB secant of the angle ACB.

Now, to find this tangent, say, as the number of feet in AC is to the number of feet in AB, the distance of the object; so is AC as radius to AB as tangent.

Then having found the tangent AB in the table, we have the secant CB; from which if the radius CG be taken, the remainder GB is the excess of the secant above the radius, or the height of the apparent level above the true. The following table was constructed by Cassini.

| Seconds | Feet | Inch | |---------|------|------| | 1 | 101 | 6.8 | | 2 | 203 | 1.6 | | 3 | 304 | 8.4 | | 4 | 406 | 3.2 | | 5 | 507 | 10.0 | | 6 | 609 | 4.8 | | 7 | 710 | 11.6 | | 8 | 812 | 6.4 | | 9 | 914 | 1.2 | | 10 | 1015 | 8.0 | | 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 | | 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 | | 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 | | 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 | | 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 |

Plate CCXI. ### The Continuation of the Foregoing Table

| Min. | 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| 558 | 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| 965 | 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 |

The uses of this table are, 1. An arc of a great circle on the earth being given in seconds or minutes, to find the length of it in miles or feet. Thus an arc of 8 seconds is 812 feet fix inches and four-tenths of an inch; and thus again an arc of 20' is 121880 English feet. 2. An arc of a great circle upon the earth being given in seconds or minutes, or in feet or inches, to find the height of the apparent level above the true. In very small arcs this is so little, that it may be disregarded, and is therefore marked only at 5", and afterwards at every 10" in the table of seconds, and at every single minute in the other. 3. The distance of any object which is viewed through sights placed horizontally being given, the height of it may be found; or conversely, the height of any object being given, the distance of it may be found. Thus, if the distance of an object whose top is in the horizon be 15' or 91410 feet, the height of that object is 199 feet 4 inches; and thus conversely, if the height of an object whose top is in the horizon be 199 feet 4 inches, the distance will be 91,410 feet. 4. If the distance of an object given be a number of feet which is not in the table, take that which is next to it, and say, as the square of the number thus taken is to the square of the number given; so is the height of the apparent level above the true, corresponding to the number taken, to the height of the apparent level which corresponds to the number given. Thus, if it be inquired what is the height of the apparent level above the true when the distance of the object is 200,000 feet, the nearest number to this in the table is 201,102; the height of the level corresponding thereto is 965 feet; say then, as the square of 201,102 is to the square of 200,000; so is 965 to a fourth number by which the apparent level exceeds the height of the true one, at the distance of 200,000 feet.

Hitherto we have supposed the line of level to be a tangent to an arc of a great circle drawn upon the surface of the earth; whereas in levelling, the eye is usually at some distance above the surface, suppose 4 feet; but this makes no difference in levelling; for as the height of the eye must be added to the secant CB, fig. 6. because ML is supposed in levelling to be parallel to HD, there is indeed a difference between the length of AI and BL, but it is quite insensible. Another use of the table is for levelling, in order to convey water from one place to another. See Levelling. We shall now proceed to give a solution of some geographical problems relating to the horizon.

1. To find the extent of the visible horizon, the semidiameter of the earth and height of the eye being the extent given. Let ADE, fig. 3. be any arc of a great circle of the horizon, C the centre of the earth, B the eye of the observer, BD the height of the eye, BA and BE lines drawn from the eye touching the surface of the earth at A and E, and terminating the visible horizon; the length of BA is required. In order to find it, add DB the height of the eye, which suppose to be 5 feet, to DC the semidiameter of the earth, which is 20,949,660 feet, and you have the length of CB 20,949,660 feet; draw CA, and you have a triangle BAC whole angle at A is a right one; make the hypotenuse CB radius, and CA will be the sine of the opposite angle ABC. Say then, as CB is to CA, so is the whole sine or radius to the sine of the angle ABC. ABC. This angle being found, its complement ACB is known, and consequently also the arc AD, which may be found in feet or miles by the table: Thus, in the foregoing example, as 20,949,660 is to 20,949,655; so is the radius 1000, &c. to a fourth number, viz. 9,999,993, which number is the sine of an angle of 89° 56′; the angle ABC then is 89° 56′; and therefore its complement ACD is 4°, and the arc DA is 4°; that is, by the table, 24376 feet.

2. To find the depression of the visible horizon of the sea at a given height of the eye. In fig. 3, if the eye be at B, the sensible horizon is FG, the depression of the horizon of the sea is the angle FBA; which, being the complement of ABC, is equal to ACD, that is, 4°.

3. To find the extent of the visible horizon at any height of the eye by observation. The semidiameter of the horizon does not sensibly differ from an arch of a great circle upon the earth of the same number of minutes and seconds as the angle of depression is observed to be; and the number of feet contained in that arc may be found in the table: Thus, if the depression of the horizon be 30°, its semidiameter is also 30°; that is, by the table 182,820 feet. Various accounts of the extent of the visible horizon are given by different authors; either because they differ in their accounts of the earth’s semidiameter from whence that of the horizon is computed, or in the measures they make use of.

The following table, taken from Cassini, shows 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.

| Feet | Inches | The height of the eye above the surface of the sea. | The depression of the horizon of the sea. | |------|--------|--------------------------------------------------|------------------------------------------| | | | Feet | Inches | " | " | by observation | by calculation | | 1157 | 6, 9 | 32 | 30 | 36 | 18 | 3 | 48 | | Difference by refraction | 3 | 48 | | 775 | 2, 3 | 27 | 0 | 29 | 36 | | | | Difference by refraction | 2 | 36 | | 571 | 11, 0 | 24 | 0 | 25 | 25 | | | | Difference by refraction | 1 | 25 | | 387 | 3, 4 | 19 | 45 | 20 | 54 | | | | Difference by refraction | 1 | 9 | | 288 | 4, 3 | 15 | 0 | 17 | 1 | | | | Difference by refraction | 2 | 1 | | 187 | 0, 9 | 13 | 0 | 14 | 41 | | | | Difference by refraction | 1 | 41 | | 9 | 7, 3 | 3 | 20 | 3 | 18 | | |

Here the calculated depression is greater than that by observation in all the cases except the last, which is less by two seconds; but the instrument used by our author would not discover such a small difference. Refraction by raising the objects of vision makes the angle of depression less; but refraction itself is variable, and of consequence the depression and extent of the horizon also. Cassini informs us, that, even in the finest weather, refraction was different at the same hours of different days, and at different hours of the same day. The truth of this position is easily seen by fixing a telescope with cross hairs, so that the weather-cock of a distant steeple may be viewed through it; for at different times of the day the weather-cock will sometimes appear in the centre of the object-glass, sometimes above and sometimes below it; the same experiment may also be tried with plain sights. It has long been observed, that the top of a distant hill may at some times, when the refraction is greatest, be seen from a station from which at other times, when refraction is less, it cannot be seen, even when the weather is sufficiently clear.

Hitherto we have supposed the circumference of the Earth not to be exactly circular, or the globe itself to be an exact perfect sphere; but, from some observations, this sphere appears not to be the case. Some time ago, the French made an observation, showing that a pendulum vibrates slower in proportion as it is brought nearer to the equator; that is, the gravity or celerity of descent of the pendulum, and of all other bodies, is less in countries approaching to the equator than in places near either pole. This excited the curiosity of the celebrated philosophers Huygens and Newton, who thence conjectured that the earth must have some other figure than what was commonly supposed. Sir Isaac Newton afterwards demonstrated that this diminution of weight naturally arises from the earth’s rotation round its axis; which, according to the laws of circular motion, repels all heavy bodies from the axis of motion; so that this motion, being swifter at the equator than in parts more remote, the weight of bodies must also be much less there than nearer the poles.—To determine this matter, several mathematicians were by the French king employed to measure a degree on the earth’s surface in different parts of the world; and, according to their mensurations, the diameter of the earth from north to south is shorter than that from east to west by 36 miles.

With regard to the method of finding the longitudes of particular places, rules have been already laid down under Astronomy, no 408, and 482, latitudes 483. The same thing, however, may be done by other methods. Thus the latitude may be found by observing exactly the meridian altitude of the sun, and knowing his declination for that day, the declination subtracted from the meridian altitude gives the complement of the latitude, and this last subtracted from 90° leaves the latitude required. As to the longitude, Mr Harrison, by his invention of time-pieces which go much more exactly than either clocks or watches could be made to do formerly, hath in a great measure facilitated that. For supposing any person possessed of one of these time-pieces, to set out on a journey, e.g., from London. If he adjusts his time-piece properly before he goes away, he will know the hour... hour at London exactly, let him go where he pleases; and when he hath proceeded so far either eastward or westward, that a difference is perceived betwixt the hours shown by his time-piece, and those on the clocks or watches at the place to which he goes, the distance of that place from London in degrees and minutes of longitude will be known; and if the length of a degree of longitude is known, the real distance between the two places may also be easily found. It is not to be expected, however, that any instrument, with whatever care it may be constructed, can always be depended upon as an exact measure of time; and therefore frequent corrections of longitudes taken in this manner will be necessary. The method of finding the longitude from the eclipses of Jupiter's satellites appears to be the best of any. Eclipses of the sun, and occultations of the stars by the moon, are also very proper, though they happen but seldom. Eclipses of the moon have also been made use of for this purpose; but it is found impossible to observe either the beginning or end of a lunar eclipse with the accuracy necessary for determining the longitude of any place.—All these different methods agree in this, that they determine the longitude by the difference of time between the observation of the phenomenon in two different places; and of this time, four minutes are to be allowed for every degree of longitude either east or west.

After the geographer is thus become acquainted with the longitudes and latitudes of a great number of different places, he may delineate them upon paper, or make a map, either of the whole world, or of any particular country with which he is best acquainted. General maps of the world, or of very large tracts, answer the purpose of showing in what manner the different countries of the world lie with respect to each other. They cannot be made of such a size as to admit the delineation of many particular towns or cities, neither indeed is it at all required. Where the whole world is delineated at once, the mind can hardly take in more than the idea of the situations of different kingdoms from one another; the situations of the different cities of each particular kingdom being almost wholly overlooked, and not attended to; and this happens likewise where a very large portion of the globe, as one of the four quarters, is represented on a single map. Besides these, therefore, it is necessary to have particular maps of all the different countries done upon a larger scale, that thus the mind may not be fatigued by endeavouring to comprehend too much at once. The qualifications which maps ought to have, in order to render them complete, are, 1. That they represent the countries exactly of the same shape, and in the same proportions to the eye, that they really have on the earth itself. 2. That the divisions of one country from another be distinctly marked, and readily perceptible, without a disagreeable and tedious search. 3. That the longitudes and latitudes of different places be found exactly on the map, and with little or no trouble.

The foundation of all maps is what is called the projection of the sphere, i.e. the delineation of those circles apparently traced out by the sun in the heavens, upon some substance, either plane or spherical, designed to represent the surface of the earth; upon which also are delineated the parallels of latitude, and the meridians,

§ 1. Of Projections of the Spheres and Maps.

Of projections there are two kinds, the orthographic and stereographic; both of which represent the surface of the earth projected upon the plane of one of its great circles.

I. The orthographic supposes the eye to be placed at Orthographic projection, while the stereographic supposes it to be only in the pole of that circle. The circles on which the projections are usually made, are, the equator, some of the meridians, or the rational horizon of some particular place. For maps of the world a meridian is generally chosen; and most commonly that one which passes through Ferro, one of the Canary islands, because thus the continents of Europe, Asia, and Africa, are conveniently delineated in one circle, and America in the other.

To project the sphere orthographically on the plane of any meridian, we have only to consider, that the rays which come from the disk of the earth are parallel; and consequently all lines drawn from the eye to the disk must be perpendicular to the latter. Let therefore, A B C D, (fig. 1.) represent the plane of one of the meridians. The equator, which cuts all the meridians in the middle, must be represented by an infinite number of points let fall upon the plane of projection, and dividing it exactly in the middle; that is, by the right line B D. The parallels of latitude, being also perpendicular to the plane of the meridian, will be marked out by an infinite number of right lines let fall from their peripheries upon that plane, thus forming the right lines a b, c d, &c. The meridians will likewise be represented on the disk by an infinite number of right lines let fall perpendicularly from their peripheries upon the plane of projection, and thus will form the elliptic curves A r o C A z o C, &c. From an inspection of the figure, therefore, it appears, that in this projection both longitudes and latitudes are measured by a line of fines, and both of them decrease prodigiously as we approach the edges of the disk; and hence the countries which lie at a distance from the equator are exceedingly distorted, and it is even impossible to draw them with any degree of accuracy. The orthographic projection on the plane of a meridian, therefore, is never used but for a map of the world. 2. On the plane of the equator, the orthographic projection represents the meridians as straight lines diverging from a centre, and the parallels of latitude as concentric circles. The latter, however, are by no means to be placed at equal distances from each other; for the meridians are to be divided by the line of lines, as in the last; and thus the equatorial parts of the globe are as much distorted and confused as the polar ones were in the foregoing. This projection, therefore, is seldom used for a map of the whole world, though it answers very well for a representation of the polar regions.

3. On the horizon of any particular place, except either of the poles, or any point lying directly under the equator, the orthographic projection represents both parallels and meridians by segments of ellipses. The figure shows a map done on the horizon of Ur of the Chaldees: it is obvious, however, that a considerable degree of distortion takes place here also; though less than in the former cases. Projections of this kind, therefore, are used only for the construction of solar eclipses. See Astronomy, sect. x.

II. The stereographic projection of the sphere supposes the eye to be in the pole of the circle of projection. The laws of this projection are,

1. A right circle is projected into a line of half tangents.

2. The representation of a right circle, perpendicularly opposed to the eye, will be a circle in the plane of the projection.

3. The representation of a circle placed oblique to the eye, will be a circle in the plane of the projection.

4. If a great circle is to be projected upon the plane of another great circle, its centre will lie in the line of measures, distant from the centre of the primitive by the tangent of its elevation above the plane of the primitive.

5. If a lesser circle, whose poles lie in the plane of the projection, were to be projected, the centre of its representation would be in the line of measures, distant from the centre of the primitive, by the secant of the lesser circles distance from its pole, and its semidiameter or radius be equal to the tangent of that distance.

6. If a lesser circle were to be projected, whose poles lie not in the plane of the projection, its diameter in the projection, if it falls on each side of the pole of the primitive, will be equal to the sum of the half tangents of its greatest and nearest distance from the pole of the primitive, set each way from the centre of the primitive in the line of measures.

7. If the lesser circle to be projected fall entirely on one side of the pole of the projection, and do not encompass it: then will its diameter be equal to the difference of the half tangents of its greatest and nearest distance from the pole of the primitive, set off from the centre of the primitive one; and the same way in the line of measures.

8. In the stereographic projection, the angles made by the circles of the surface of the sphere, are equal to the angles made by their representatives in the plane of their projection.

For a demonstration of these laws, see the articles Perspective and Projection. The method of deli-

Vol. VII. Part II. titude, with the equator, tropics, and polar circles. For the meridians, first describe a circle through the three points A, P, C. This will represent the meridian 90 degrees from London. Let its centre be M in BD (continued to the point N, which represents the south pole), PN being the diameter: through M draw a parallel to AC, viz. FH, continued each way to K and L. Divide the circle PHNF into 360 degrees, and from the point P draw right lines to the several degrees cutting KFHL: through the several points of intersection, and the poles P, N, as through three given points, describe circles representing all the meridians. The centres for describing the arches will be in the same KL, as being the same that are found by the former intersection; but are to be taken with this caution, that for the meridian next BDN towards A, the most remote centre towards L be taken for the first, the second from this, &c.—The circles of longitude and latitude thus drawn, insert the places from a table.

Maps of this kind may be useful for particular purposes; but the irregular length of the degrees, both of longitude and latitude, render them very unfit for representing the countries in their proper shape; and the difficulties in finding the particular degrees of longitude and latitude are even greater in this than any other projection, as is evident from the inspection of fig. 4.

III. Besides these, there may be a variety of other projections, though few of them are applicable to any particular purpose. The three following are those most generally useful, as having each some peculiar property which cannot be found in any other but themselves.

1. If, instead of its globular figure, we suppose the earth to have a conical one, it is plain, that the meridians would be represented by straight lines diverging from the apex of the cone, while the parallels are shown by concentric circles placed at equal distances. This kind of projection is shown in Plate CCXIII. fig. 1, 2. It hath this great advantage, that the longitudes and latitudes may be found with the greatest ease by means of a moveable index placed on the centre. The whole earth may also be thus represented on a single circle: but thus the countries towards the south pole are prodigiously augmented in breadth in proportion to their length; for the degrees of longitude constantly increase the farther we are removed from the pole, while those of latitude still remain the same. This apparent error, however, doth not in the least affect the real proportion of the map, or render it more difficult to find the longitudes or latitudes upon it.

2. Mercator's projection supposes the earth, instead of a globular, to have a cylindrical figure; in consequence of which, the degrees of longitude become of an equal length throughout the whole surface, and are marked out on the map by parallel lines. The circles of latitude also are represented by lines crossing the projection, former at right angles, but at unequal distances. The farther we remove from the equator, the longer the degrees of latitude become in proportion to those of longitude, and that in no less a degree than as the secant of an arch to the radius of the circle: that is, if we make one degree of longitude at the equator the radius of a circle; at one degree distant from the equator, a degree of latitude will be expressed by the secant of one degree; at ten degrees distance, by the secant of ten degrees; and so on*. A map of the world, therefore, cannot be delineated upon this projection, without distorting the shape of the countries in an extraordinary manner. The projection itself is, however, very useful in navigation, as it shows the different bearings with perfect accuracy, which cannot be done upon any other map. See CCXIII. fig. 3.

3. The globular projection is an invention of M. de la Hire, and is more useful than any of the former for exhibiting the true shape of the countries. It may be made in the following manner: Having drawn a circle representing one-half of the earth's dié, draw two diameters as before, which represent the equator and vertical meridian. Divide each of these into 180 equal parts for the measures of the degrees of longitude and latitude. Then through the two poles, and every tenth division on the equator, draw arches of circles for the meridians; and in like manner through every tenth degree on each semicircle draw an arch, which shall likewise pass through every tenth division on the meridian for the parallels of latitude.

IV. The construction of maps of particular parts of the earth requires a different operation. Large portions of its surface may indeed be drawn on the plane of the meridian, as before directed; but when a small part, as the island of Britain, for instance, is to be represented on a large scale, it would be found difficult to draw the arches of such large circles as are necessary, and therefore the following method may be adopted. In this case, the degrees of longitude and latitude may be both represented by straight lines. It is to be remembered, however, that though the degrees of latitude always continue of an equal length, it is not so with those of longitude. They must necessarily decrease as we approach the pole. The proportion in which they decrease may be found by the line of longitudes on the plane scale; or by the following

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TABLE, ### TABLE, showing the Number of Miles contained in a Degree of Longitude, in each Parallel of Latitude from the Equator.

| Degrees of Latitude | Miles | Tooth parts of a mile | |---------------------|-------|-----------------------| | 1 | 59 | 96 | | 2 | 59 | 94 | | 3 | 59 | 92 | | 4 | 59 | 86 | | 5 | 59 | 77 | | 6 | 59 | 67 | | 7 | 59 | 56 | | 8 | 59 | 40 | | 9 | 59 | 20 | | 10 | 59 | 08 | | 11 | 58 | 89 | | 12 | 58 | 68 | | 13 | 58 | 46 | | 14 | 58 | 22 | | 15 | 58 | 00 | | 16 | 57 | 60 | | 17 | 57 | 30 | | 18 | 57 | 04 | | 19 | 56 | 73 | | 20 | 56 | 38 | | 21 | 56 | 00 | | 22 | 55 | 63 | | 23 | 55 | 23 | | 24 | 54 | 81 | | 25 | 54 | 38 | | 26 | 54 | 00 | | 27 | 53 | 44 | | 28 | 53 | 00 | | 29 | 52 | 48 | | 30 | 51 | 96 |

Suppose, then, it is required to draw the meridians and parallels for a map of Britain. This island is known to lie between 50 and 60 degrees of latitude, and two and seven of longitude. Having therefore chosen the length of your degrees of latitude, you must next proportion your degrees of longitude to it. By the table you find, that in the latitude of 50° the length of a degree of longitude is to one of latitude as 38.57 is to 60; that is, a degree of longitude in latitude 50° is somewhat more than half the length of a degree of latitude. The exact proportion may easily be taken by a diagonal scale; after which, you are to mark out seven or eight of those degrees upon a right line for the length of your intended map. On the extremities of this line raise two perpendiculars, upon which mark out ten degrees of latitude for the height of it. Then, having completed the parallelogram, consult the table for the length of a degree of longitude in lat. 60°, which is found to be very nearly one half a degree of latitude. It will always be proper, however, to draw a vertical meridian exactly in the middle of the parallelogram, to which the meridian on each side may converge; and from this you are to set off the degrees of longitude on each side. Then, having divided the lines bounding your map into as many parts as can conveniently be done, to serve for a scale, you may by their means set off the longitudes and latitudes with much less trouble than where curve lines are used. This method may always be followed where a particular kingdom is to be delineated, and will represent the true figure and situation of the places with tolerable exactness. The particular points of the compass on which the towns lie with respect to one another, or their bearings, cannot be exactly known, except by a globe or Mercator's projection. Their distances, however, may by this means be accurately expressed, and this is the only kind of maps to which a scale of miles can be truly adapted.

§ 2. Description and Use of the Globes and Armillary Sphere.

When we have thus discovered, by means of maps, or any other way, the true situation of the different places of the earth with regard to one another, we may easily know every other particular relative to them; as, how far distant they are from us, what hour of the day it is, what season of the year, &c. at any particular place. As each of these problems, however, would require a particular and sometimes troublesome calculation, machines have been invented, by which all the calculations may be saved, and every problem in geography may be solved mechanically, and in the most easy and expeditious manner. These machines are the celestial and terrestrial globes, and the armillary sphere; of which, and the method of using them, we proceed to give a description.

If a map of the world be accurately delineated on a terrestrial spherical ball, the surface thereof will represent the surface of the earth: for the highest hills are so insignificant with respect to the bulk of the earth, that they take off no more from its roundness than grains of sand do from the roundness of a common globe; for the diameter of the earth is 8000 miles in round numbers, and no known hill upon it is much above three miles in perpendicular height.

With regard to what we call up and down, see the article Gravity.

To an observer placed anywhere in the indefinite space, where there is nothing to limit his view, all remote objects appear equally distant from him; and seem to be placed in a vast concave sphere, of which his eye is the centre. The moon is much nearer to us than the sun; some of the planets are sometimes nearer and sometimes farther from us than the sun; others of them never come so near to us as the sun always is; the remotest planet in our system is beyond comparison nearer to us than any of the fixed stars are; and yet all these celestial objects appear equally distant from us. Therefore, if we imagine a large hollow sphere of glass to have as many bright fluids fixed to its inside as there are stars visible in the heavens, and these fluids to be of different magnitudes, and placed at the same angular distances from each other as the stars are; the sphere will be a true representation of the starry heaven, to an eye supposed to be in its centre, and viewing it all around. And if a small globe, with a map of the earth upon it, be placed on an axis in the centre of this starry sphere, and the sphere be made to turn round on this axis, axis, it will represent the apparent motion of the heavens round the earth.

If a great circle be so drawn upon this sphere as to divide it into two equal parts or hemispheres, and the plane of the circle be perpendicular to the axis of the sphere, this circle will represent the equinoctial, which divides the heaven into two equal parts, called the northern and the southern hemispheres; and every point of that circle will be equally distant from the poles, or ends of the axis in the sphere. That pole which is in the middle of the northern hemisphere, will be called the north pole of the sphere; and that which is in the middle of the southern hemisphere, the south pole.

If another grand circle be drawn upon the sphere in such a manner as to cut the equinoctial at an angle of $23\frac{1}{2}$ degrees in two opposite points, it will represent the ecliptic, or circle of the sun's apparent annual motion; one half of which is on the north side of the equinoctial, and the other half on the south.

If a large stud be made to move eastward in this ecliptic in such a manner as to go quite round it in the time that the sphere is turned round westward 366 times upon its axis, this stud will represent the sun changing his place every day a 365th part of the ecliptic, and going round westward the same way as the stars do; but with a motion so much slower than the motion of the stars, that they will make 366 revolutions about the axis of the sphere in the time that the sun makes only 365. During one half of these revolutions, the sun will be on the north side of the equinoctial; during the other half, on the south; and at the end of each half, in the equinoctial.

If we suppose the terrestrial globe in this machine to be about one inch in diameter, and the diameter of the starry sphere to be about five or six feet, a small insect on the globe would see only a very little portion of its surface; but it would see one half of the starry sphere, the convexity of the globe hiding the other half from its view. If the sphere be turned westward round the globe, and the insect could judge of the appearances which arise from that motion, it would see some stars rising to its view in the eastern side of the sphere, whilst others were setting on the western: but as all the stars are fixed to the sphere, the same stars would always rise in the same points of view on the east side, and set in the same points of view on the west side. With the sun it would be otherwise; because the sun is not fixed to any point of the sphere, but moves slowly along an oblique circle in it. And if the insect should look towards the south, and call that point of the globe, where the equinoctial in the sphere seems to cut it on the left side, the east point; and where it cuts the globe on the right side, the west point; the little animal would see the sun rise north of the east, and set north of the west, for 182½ revolutions; after which, for as many more, the sun would rise south of the east, and set south of the west. And in the whole 365 revolutions, the sun would rise only twice in the east point, and set twice in the west. All these appearances would be the same, if the starry sphere stood still (the sun only moving in the ecliptic), and the earthly globe were turned round the axis of the sphere eastward. For, as the insect would be carried round with the globe, he would be quite insensible of its motion, and the sun and stars would appear to move westward.

1. Description of the Terrestrial Globe.

The equator, ecliptic, and tropics, polar circles, and meridians, are laid down upon the globe in the manner already described. The ecliptic is divided into 12 signs, and each sign into 30 degrees. Each trial globe tropic is $23\frac{1}{2}$ degrees from the equator, and each polar circle $23\frac{1}{2}$ degrees from its respective pole. Circles fig. 1, are drawn parallel to the equator, at every 10 degrees distance from it on each side to the poles: these circles are called parallels of latitude. On large globes there are circles drawn perpendicularly through every tenth degree of the equator, intersecting each other at the poles: but on globes of or under a foot diameter, they are only drawn through every fifteenth degree of the equator; these circles are generally called meridians, sometimes circles of longitude, and at other times hour-circles.

The globe is hung in a brass ring (A), called the brass meridian, and turns upon a wire in each pole sunk half its thickness into one side of the meridian ring; by which means that side of the ring divides the globe into two equal parts, called the eastern and western hemispheres; as the equator divides it into two equal parts, called the northern and southern hemispheres. The ring is divided into 360 equal parts or degrees, on the side wherein the axis of the globe turns. One half of these degrees are numbered, and reckoned, from the equator to the poles, where they end at 90: their use is to show the latitudes of places. The degrees on the other half of the meridian are numbered from the poles to the equator, where they end at 90: their use is to show how to elevate either the north or south pole above the horizon, according to the latitude of any given place, as it is north or south of the equator.

The brass meridian is let into two notches made in a broad flat ring called the wooden horizon, B, C; the upper surface of which divides the globe into two equal parts, called the upper and lower hemispheres. One notch is in the north point of the horizon, and the other in the south. On this horizon are several concentric circles, which contain the months and days of the year, the figures and degrees answering to the sun's place for each month and day, and the 32 points of the compass and the circles of amplitude and azimuth.—The graduated side of the brass meridian lies towards the east side of the horizon, and should be generally kept towards the person who works problems by the globes.

There is a small horary circle D, so fixed to the north part of the brass meridian, that the wire in the north pole of the globe is in the centre of that circle; and on the wire is an index, which goes over all the 24 hours of the circle, as the globe is turned round its axis. Sometimes there are two horary circles, one between each pole of the globe and the brass meridian.

There is a thin slip of brass, called the quadrant of altitude, which is divided into 90 equal parts or degrees, answering exactly to so many degrees of the equator. It is occasionally fixed to the uppermost point of the brass meridian by a nut and screw. The divisions end at the nut E, and the quadrant is turned round upon it.

There is also applied occasionally to the globe a magnetic needle, freely moving over a circle divided into... Principles into four times 90 degrees; reckoning from the north and south points towards the east and west, and also into the 32 points of the compass. As this needle makes nearly a certain constant angle with the meridian in every place, called the variation; therefore this compass being added to the frame, will rectify the position of the meridian of the globe when the variation of the needle is known. Thus at London, the variation of the needle is at this time about 23 degrees northward; therefore, by moving the frame of the globe about till the needle settles itself over the 23rd degree, reckoning westward from the north point or fleur de lis, we shall have the brass meridian coinciding with the true meridian. The compass is sometimes fixed between the legs underneath the globe.

2. Description and Use of the Armillary Sphere.

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 showing the sun's right ascension in degrees; and also into 24 hours, for showing 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 degree or point 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 north and south 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 showing 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 showing 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 d, on which is another quadrantal wire, with a small moon Z upon it, which may be moved round by the 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 an 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 the 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 showing the amplitude of the sun and moon both in degrees and points. The celestial meridian LL, passes thro' 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 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 in 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 (as in Dr Long's sphere), 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, and 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 came when the earth kept at rest and they were carried round it; showing 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 show either the real motion of the earth or the apparent motion of the heaven.

To rectify the sphere for use, first slacken the forewheels in the upright item 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 item 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 Principles 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 fun comes to the meridian LL, or until the meridian comes to the fun (according as you want the sphere or 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 fun or moon rise and set in the horizon, and the hour-index will show the times thereof for the given day.

As those who understand the use of the globes will be at no loss to work many other problems by this sphere, it is needless to enlarge any farther upon it.

3. Directions for using Globes.

In using globes, keep the east side of the horizon towards you (unless the problem requires the turning of it), which side you may know by the word East upon the horizon; for then you have the graduated side of the meridian towards you, the quadrant of altitude before you, and the globe divided exactly into two equal parts, by the graduated side of the meridian.

In working some problems, it will be necessary to turn the whole globe and horizon about, that you may look on the west side thereof; which turning will be apt to jog the ball so, as to shift away that degree of the globe which was before set to the horizon or meridian: to avoid which inconvenience, you may thrust in the feather-end of a quill between the ball of the globe and the brazen meridian; which, without hurting the ball, will keep it from turning in the meridian, whilst you turn the west side of the horizon towards you.

PROB. I. To find the latitude and longitude of any given place upon the globe.—Turn the globe on its axis, until the given place comes exactly under that graduated side of the brazen meridian on which the degrees are numbered from the equator; and observe what degree of the meridian the place then lies under; which is its latitude, north or south, as the place is north or south of the equator.

The globe remaining in this position, the degree of the equator, which is under the brazen meridian, is the longitude of the place, which is east or west, as the place lies on the east or west side of the first meridian of the globe.—All the Atlantic ocean, and America, is on the west side of the meridian of London; and the greatest part of Europe, and of Africa, together with all Asia, is on the east side of the meridian of London, which is reckoned the first meridian of the globe by the British geographers and astronomers.

PROB. II. The longitude and latitude of a place being given, to find that place on the globe.—Look for the given longitude in the equator (counting it eastward or westward from the first meridian, as it is mentioned) to be east or west); and bringing the point of longitude in the equator to the brazen meridian, on that side which is above the fourth point of the horizon: then count from the equator, on the brazen meridian, to the degree of the given latitude, towards the north or south pole, according as the latitude is north or south; and under that degree of latitude on the meridian you will have the place required.

PROB. III. To find the difference of longitude, or difference of latitude, between any two given places.—Bring each of these places to the brazen meridian, and see what its latitude is: the lesser latitude subtracted from the greater, if both places are on the same side of the equator, or both latitudes added together if they are on different sides of it, is the difference of latitude required. And the number of degrees contained between these places, reckoned on the equator, when they are brought separately under the brazen meridian, is their difference of longitude, if it be less than 180°; but if more, let it be subtracted from 360°, and the remainder is the difference of longitude required. Or,

Having brought one of the places to the brazen meridian, and set the hour-index to XII, turn the globe until the other place comes to the brazen meridian; and the number of hours and parts of an hour, passed over by the index, will give the longitude in time; which may be easily reduced to degrees, by allowing 15 degrees for every hour, and one degree for every four minutes.

N. B. When we speak of bringing any place to the brazen meridian, it is the graduated side of the meridian that is meant.

PROB. IV. Any place being given, to find all those places that have the same longitude or latitude with it.—Bring the given place to the brazen meridian; then all those places which lie under that side of the meridian, from pole to pole, have the same longitude with the given place. Turn the globe round its axis; and all those places which pass under the same degree of the meridian that the given place does, have the same latitude with that place.

Since all latitudes are reckoned from the equator, and all longitudes are reckoned from the first meridian, it is evident, that the point of the equator which is cut by the first meridian, has neither latitude nor longitude.—The greatest latitude is 90° degrees, because no place is more than 90° degrees from the equator; And the greatest longitude is 180° degrees, because no place is more than 180° degrees from the first meridian.

PROB. V. To find the antæci, periæci, and antipodes, of any given place.—Bring the given place to the brazen meridian; and having found its latitude, keep the globe in that situation, and count the same number of degrees of latitude from the equator towards the contrary pole; and where the reckoning ends, you have the antæci of the given place upon the globe. Those who live at the equator have no antæci.

The globe remaining in the same position, set the hour-index to the upper XII on the horary circle, and turn the globe until the index comes to the lower XII; then the place which lies under the meridian, in the same latitude with the given place, is the periæci required. Those who live at the poles have no periæci.

As the globe now stands (with the index at the lower XII), the antipodes of the given place will be under the same point of the brazen meridian where its antæci stood before. Every place upon the globe has its antipodes.

PROB. VI. To find the distance between any two places Principles places on the globe.—Lay the graduated edge of the quadrant of altitude over both the places, and count the number of degrees intercepted between them on the quadrant; then multiply these degrees by 60, and the product will give the distance in geographical miles: but to find the distance in miles, multiply the degrees by 69½, and the product will be the number of miles required. Or, take the distance betwixt any two places with a pair of compasses, and apply that extent to the equator; the number of degrees, intercepted between the points of the compasses, is the distance in degrees of a great circle; which may be reduced either to geographical miles, or to English miles, as above.

Prob. VII. A place on the globe being given, and its distance from any other place; to find all the other places upon the globe which are at the same distance from the given place.—Bring the given place to the brazen meridian, and screw the quadrant of altitude to the meridian directly over that place; then keeping the globe in that position, turn the quadrant quite round upon it, and the degree of the quadrant that touches the second place will pass over all the other places which are equally distant with it from the given place.

This is the same as if one foot of a pair of compasses was set in the given place, and the other foot extended to the second place, whose distance is known; for if the compasses be then turned round the first place as a centre, the moving foot will go over all those places which are at the same distance with the second from it.

Prob. VIII. The hour of the day at any place being given, to find all those places where it is noon at that time.—Bring the given place to the brazen meridian, and set the index to the given hour; this done, turn the globe until the index points to the upper XII, and then all the places that lie under the brazen meridian have noon at that time.

N.B. The upper XII always stands for noon; and when the bringing of any place to the brazen meridian is mentioned, the side of that meridian on which the degrees are reckoned from the equator is meant, unless the contrary side be mentioned.

Prob. IX. The hour of the day at any place being given, to find what o'clock it then is at any other place.—Bring the given place to the brazen meridian, and set the index to the given hour; then turn the globe, until the place where the hour is required comes to the meridian, and the index will point out the hour at that place.

Prob. X. To find the sun's place in the ecliptic, and his declination, for any given day of the year.—Look on the horizon for the given day, and right against it you have the degree of the sign in which the sun is (or his place) on that day at noon. Find the same degree of that sign in the ecliptic line upon the globe, and having brought it to the brazen meridian, observe what degree of the meridian stands over it; for that is the sun's declination, reckoned from the equator.

Prob. XI. The day of the month being given, to find all those places of the earth over which the sun will pass vertically on that day.—Find the sun's place in the ecliptic for the given day, and having brought it to the brazen meridian, observe what point of the meridian is over it; then, turning the globe round its axis, all those places which pass under that point of the meridian are the places required; for as their latitude is equal, in degrees and parts of a degree, to the sun's declination, the sun must be directly over-head to each of them at its respective noon.

Prob. XII. A place being given in the torrid zone, to find those two days of the year on which the sun shall be vertical to that place.—Bring the given place to the brazen meridian, and mark the degree of latitude that is exactly over it on the meridian; then turn the globe round its axis, and observe the two degrees of the ecliptic which pass exactly under that degree of latitude: lastly, find on the wooden horizon the two days of the year in which the sun is in those degrees of the ecliptic, and they are the days required: for on them, and none else, the sun's declination is equal to the latitude of the given place; and, consequently, he will then be vertical to it at noon.

Prob. XIII. To find all those places of the north frigid zone, where the sun begins to shine constantly without setting, on any given day, from the 21st of March to the 23d of September.—On these two days, the sun is in the equinoctial, and enlightens the globe exactly from pole to pole: therefore, as the earth turns round its axis, which terminates in the poles, every place upon it will go equally through the light and the dark, and so make the day and night equal to all places of the earth. But as the sun declines from the equator, towards either pole, he will shine just as many degrees round that pole as are equal to his declination from the equator: so that no place within that distance of the pole will then go through any part of the dark, and consequently the sun will not set to it. Now, as the sun's declination is northward from the 21st of March to the 23d of September, he must constantly shine round the north pole all that time; and on the day that he is in the northern tropic, he shines upon the whole north frigid zone; so that no place within the north polar circle goes through any part of the dark on that day. Therefore,

Having brought the sun's place for the given day to the brazen meridian, and found his declination (by Prob. IX) count as many degrees on the meridian, from the north pole, as are equal to the sun's declination from the equator, and mark that degree from the pole where the reckoning ends; then turning the globe round its axis, observe what places in the north frigid zone pass directly under that mark; for they are the places required.

The like may be done for the south frigid zone, from the 23d of September to the 21st of March, during which time the sun shines constantly on the south pole.

Prob. XIV. To find the place over which the sun is vertical at any hour of a given day.—Having found the sun's declination for the given day (by Prob. X.) mark it with a chalk on the brazen meridian: then bring the place where you are (suppose Edinburgh) to the brazen meridian, and set the index to the given hour; which done, turn the globe on its axis, until the index points to XII at noon; and the place on the globe, which is then directly under the point of Principles the sun's declination marked upon the meridian, has and the sun that moment in the zenith, or directly over head.

Prob. XV. The day and hour of a lunar eclipse being given; to find all those places of the earth to which it will be visible.—The moon is never eclipsed but when she is full, and so directly opposite to the sun, that the earth's shadow falls upon her. Therefore, whatever place of the earth the sun is vertical to at that time, the moon must be vertical to the antipodes of that place: so that the sun will be then visible to one half of the earth, and the moon to the other.

Find the place to which the sun is vertical at the given hour (by Prob. XIV.) elevate the pole to the latitude of that place, and bring the place to the upper part of the brazen meridian, as in the former problem: then, as the sun will be visible to all those parts of the globe which are above the horizon, the moon will be visible to all those parts which are below it, at the time of her greatest obscuration.

Prob. XVI. To rectify the globe for the latitude, the zenith, and the sun's place.—Find the latitude of the place (by Prob. I.) and if the place be in the northern hemisphere, raise the north pole above the north point of the horizon, as many degrees (counted from the pole upon the brazen meridian) as are equal to the latitude of the place. If the place be in the southern hemisphere, raise the south pole above the south point of the horizon as many degrees as are equal to the latitude. Then, turn the globe till the place comes under its latitude on the brazen meridian, and fasten the quadrant of altitude so, that the chambered edge of its nut (which is even with the graduated edge) may be joined to the zenith, or point of latitude. This done, bring the sun's place in the ecliptic for the given day (found by Prob. X.) to the graduated side of the brazen meridian, and set the hour-index to XII at noon, which is the uppermost XII on the hour-circle; and the globe will be rectified.

Prob. XVII. The latitude of any place, not exceeding 66½ degrees, and the day of the month, being given; to find the time of the sun's rising and setting, and consequently the length of the day and night.—Having rectified the globe for the latitude, and for the sun's place on the given day (as directed in the preceding problem), bring the sun's place in the ecliptic to the eastern side of the horizon, and the hour-index will show the time of sunrise; then turn the globe on its axis, until the sun's place comes to the western side of the horizon, and the index will show the time of sun-setting.

The hour of sun-setting doubled, gives the length of the day; and the hour of sun-rising doubled, gives the length of the night.

Prob. XVIII. The latitude of any place, and the day of the month, being given; to find when the morning twilight begins, and the evening twilight ends, at that place.—This problem is often limited: for, when the sun does not go 18 degrees below the horizon, the twilight continues the whole night; and for several nights together in summer, between 49 and 66½ degrees of latitude; and the nearer to 66½, the greater is the number of these nights. But when it does begin and end the following method will show the time for any given day.

Rectify the globe, and bring the sun's place in the

N 137. Principles place to the eastern side of the horizon; then observe what point of the compass on the horizon stands right against the sun's place, for that is his amplitude at rising. This done, turn the globe westward, until the sun's place comes to the western side of the horizon, and it will cut the point of his amplitude at setting. Or, you may count the rising amplitude in degrees, from the east point of the horizon, to that point where the sun's place cuts it; and the setting amplitude from the west point of the horizon, to the sun's place at setting.

**Prob. XXII. The latitude, the sun's place, and his altitude, being given; to find the hour of the day, and the sun's azimuth, or number of degrees that he is distant from the meridian.**—Rectify the globe, and bring the sun's place to the given height upon the quadrant of altitude; on the eastern side of the horizon, if the time be in the forenoon; or the western side, if it be in the afternoon; then the index will show the hour; and the number of degrees in the horizon, intercepted between the quadrant of altitude and the fourth point, will be the sun's true azimuth at that time.

**Prob. XXIII. The latitude, hour of the day, and the sun's place, being given; to find the sun's altitude and azimuth.**—Rectify the globe, and turn it until the index points to the given hour; then lay the quadrant of altitude over the sun's place in the ecliptic, and the degree of the quadrant cut by the sun's place is his altitude at that time above the horizon; and the degree of the horizon cut by the quadrant is the sun's azimuth, reckoned from the fourth.

**Prob. XXIV. The latitude, the sun's altitude, and his azimuth, being given; to find his place in the ecliptic, the day of the month, and hour of the day, though they had all been lost.**—Rectify the globe for the latitude and zenith, and set the quadrant of altitude to the given azimuth in the horizon; keeping it there, turn the globe on its axis until the ecliptic cuts the quadrant in the given altitude: that point of the ecliptic which cuts the quadrant there, will be the sun's place; and the day of the month answering thereto, will be found over the like place of the sun on the wooden horizon. Keep the quadrant of altitude in that position; and, having brought the sun's place to the brazen meridian, and the hour-index to XII at noon, turn back the globe, until the sun's place cuts the quadrant of altitude again, and the index will show the hour.

Any two points of the ecliptic, which are equidistant from the beginning of Cancer or Capricorn, will have the same altitude and azimuth at the same hour, though the months be different; and therefore it requires some care in this problem, not to mistake both the month and the day of the month; to avoid which, observe, that from the 20th of March to the 21st of June, that part of the ecliptic which is between the beginning of Aries and beginning of Cancer is to be used; from the 21st of June to the 23rd of September, between the beginning of Cancer and beginning of Libra; from the 23rd of September to the 21st of December, between the beginning of Libra and the beginning of Capricorn; and from the 21st of December to the 20th of March, between the beginning of Capricorn and beginning of Aries. And as one can never be at a loss to know in what quarter of the year he takes the sun's altitude and

**Prob. XXV. To find the length of the longest day at any given place.**—If the place be on the north side of the equator, find its latitude (by Prob. I.) and elevate the north pole to that latitude; then, bring the beginning of Cancer to the brazen meridian, and set the hour-index to XII at noon. But if the given place be on the south side of the equator, elevate the south pole to its latitude, and bring the beginning of Capricorn to the brazen meridian, and the hour-index to XII. This done, turn the globe westward, until the beginning of Cancer or Capricorn (as the latitude is north or south) comes to the horizon; and the index will then point out the time of sun-setting, for it will have gone over all the afternoon hours, between midday and sun-set; which length of time being doubled, will give the whole length of the day from sun rising to sun-setting. For, in all latitudes, the sun rises as long before mid-day, as he sets after it.

**Prob. XXVI. To find in what latitude the longest day is, of any given length, less than 24 hours.**—If the latitude be north, bring the beginning of Cancer to the brazen meridian, and elevate the north pole to about 66° degrees; but if the latitude be south, bring the beginning of Capricorn to the meridian, and elevate the south pole to about 66° degrees; because the longest day in north latitude is, when the sun is in the first point of Cancer; and in south latitude, when he is in the first point of Capricorn. Then set the hour-index to XII at noon, and turn the globe westward, until the index points at half the number of hours given; which done, keep the globe from turning on its axis, and slide the meridian down in the notches, until the aforesaid point of the ecliptic (viz. Cancer or Capricorn) comes to the horizon; then, the elevation of the pole will be equal to the latitude required.

**Prob. XXVII. The latitude of any place, not exceeding 66° degrees, being given; to find in what climate the place is.**—Find the length of the longest day at the given place, by Prob. XXV, and whatever be the number of hours whereby it exceedeth twelve, double that number, and the sun will give the climate in which the place is.

**Prob. XXVIII. The latitude, and the day of the month, being given; to find the hour of the day when the sun shines.**—Set the wooden horizon truly level, and the brazen meridian due north and south by a mariner's compass; then, having rectified the globe, stick a small sewing-needle into the sun's place in the ecliptic, perpendicular to that part of the surface of the globe; this done, turn the globe on its axis, until the needle comes to the brazen meridian, and set the hour-index to XII at noon; then, turn the globe on its axis, until the needle points exactly towards the sun (which it will do when it casts no shadow on the globe), and the index will show the hour of the day.

4. **The Use of the Celestial Globe.**

Having done for the present with the terrestrial globe, we shall proceed to the use of the celestial; how to use first premising, that as the equator, ecliptic, tropics, the celestial polar globe. polar circles, horizon, and brazen meridian, are exactly alike on both globes, all the former problems concerning the sun are solved the same way by both globes. The method also of rectifying the celestial globe is the same as rectifying the terrestrial. N.B. The sun's place for any day of the year stands directly over that day on the horizon of the celestial globe, as it does on that day of the terrestrial.

The latitude and longitude of the stars, or of all other celestial phenomena, are reckoned in a very different manner from the latitude and longitude of places on the earth: for all terrestrial latitudes are reckoned from the equator; and longitudes from the meridian of some remarkable place, as of London by the British, and of Paris by the French. But the astronomers of all nations agree in reckoning the latitudes of the moon, stars, planets, and comets, from the ecliptic; and their longitudes from the equinoctial colure, in that semicircle of it which cuts the ecliptic at the beginning of Aries; and thence eastward, quite round, to the same semicircle again. Consequently those stars which lie between the equinoctial and the northern half of the ecliptic, have north declination and south latitude; those which lie between the equinoctial and the southern half of the ecliptic, have south declination and north latitude; and all those which lie between the tropics and poles, have their declinations and latitudes of the same denomination.

There are six great circles on the celestial globe, which cut the ecliptic perpendicularly, and meet in two opposite points in the polar circles; which points are each ninety degrees from the ecliptic, and are called its poles. These polar points divide those circles into 12 semicircles; which cut the ecliptic at the beginnings of the twelve signs. They resemble so many meridians on the terrestrial globe; and as all places which lie under any particular meridian-semicircle on that globe have the same longitude; so all those points of the heaven, through which any of the above semicircles are drawn, have the same longitude.—And as the greatest latitudes on the earth are at the north and south poles of the earth, so the greatest latitudes in the heaven are at the north and south poles of the ecliptic.

For the division of the stars into constellations, &c. see Astronomy, p. 403, 406.

Prob. I. To find the right ascension and declination of the sun, or any fixed star—Bring the sun's place in the ecliptic to the brazen meridian; then that degree in the equinoctial which is cut by the meridian, is the sun's right ascension; and that degree of the meridian which is over the sun's place, is his declination. Bring any fixed star to the meridian, and its right ascension will be cut by the meridian in the equinoctial; and the degree of the meridian that stands over it is its declination.

So that right ascension and declination, on the celestial globe, are found in the same manner as longitude and latitude on the terrestrial.

Prob. II. To find the latitude and longitude of any star.—If the given star be on the north side of the ecliptic, place the 90th degree of the quadrant of altitude on the north pole of the ecliptic, where the 12 semicircles meet, which divide the ecliptic into the 12 signs; but if the star be on the south side of the ecliptic, place the 90th degree of the quadrant on the south pole of the ecliptic; keeping the 90th degree of the quadrant on the proper pole, turn the quadrant about, until its graduated edge cuts the star: then the number of degrees in the quadrant, between the ecliptic and the star, is its latitude; and the degree of the ecliptic, cut by the quadrant, is the star's longitude, reckoned according to the sign in which the quadrant then is.

Prob. III. To represent the face of the starry firmament, as seen from any given place of the earth, at any hour of the night.—Rectify the celestial globe for the given latitude, the zenith, and sun's place in every respect, as taught by the XVIth problem for the terrestrial; and turn it about, until the index points to the given hour: then the upper hemisphere of the globe will represent the visible half of the heaven for that time; all the stars upon the globe being then in such situations, as exactly correspond to those in the heaven. And if the globe be placed duly north and south, by means of a small sea-compas, every star in the globe will point toward the like star in the heaven; by which means, the constellations and remarkable stars may be easily known. All those stars which are in the eastern side of the horizon, are then rising in the eastern side of the heaven; all in the western, are setting in the western side; and all those under the upper part of the brazen meridian, between the south point of the horizon and the north pole, are at their greatest altitude, if the latitude of the place be north; but if the latitude be south, those stars which lie under the upper part of the meridian, between the north point of the horizon and the south pole, are at their greatest altitude.

Prob. IV. The latitude of the place, and day of the month, being given; to find the time when any known star will rise, or be upon the meridian, or set.—Having rectified the globe, turn it about until the given star comes to the eastern side of the horizon, and the index will show the time of the star's rising; then turn the globe westward, and when the star comes to the brazen meridian, the index will show the time of the star's coming to the meridian of your place; lastly, turn on, until the star comes to the western side of the horizon, and the index will show the time of the star's setting. N.B. In northern latitudes, those stars which are less distant from the north pole than the quantity of its elevation above the north point of the horizon, never set; and those which are less distant from the south pole than the number of degrees by which it is depressed below the horizon, never rise; and vice versa in southern latitudes.

Prob. V. To find at what time of the year a given star will be upon the meridian, at a given hour of the night.—Bring the given star to the upper semicircle of the brazen meridian, and set the index to the given hour; then turn the globe, until the index points to XII at noon, and the upper semicircle of the meridian will then cut the sun's place, answering to the day of the year sought; which day may be easily found against the like place of the sun among the signs on the wooden horizon.

Prob. VI. The latitude, day of the month, and azimuth of any known star being given; to find the hour of the night.—Having rectified the globe for the latitude, zenith, Sect. II.

Principles and Practice.

zenith, and sun's place, lay the quadrant of altitude and to the given degree of azimuth in the horizon; then turn the globe on its axis, until the star comes to the graduated edge of the quadrant; and when it does, the index will point out the hour of the night.

Prob. VII. The latitude of the place, the day of the month, and altitude of any known star, being given; to find the hour of the night.—Rectify the globe as in the former problem, guess at the hour of the night, and turn the globe until the index points at the supposed hour; then lay the graduated edge of the quadrant of altitude over the known star; and if the degree of the star's height in the quadrant upon the globe answers exactly to the degree of the star's observed altitude in the heaven, you have guessed exactly; but if the star on the globe is higher or lower than it was observed to be in the heaven, turn the globe backwards or forwards, keeping the edge of the quadrant upon the star, until its centre comes to the observed altitude in the quadrant; and then the index will show the true time of the night.

Prob. VIII. An easy method for finding the hour of the night by any two known stars, without knowing either their altitude or azimuth; and then of finding both their altitude and azimuth, and thereby the true meridian.—Tie one end of a thread to a common musket bullet; and having rectified the globe as above, hold the other end of the thread in your hand, and carry it slowly round betwixt your eye and the starry heaven, until you find it cuts any two known stars at once. Then guessing at the hour of the night, turn the globe until the index points to that time in the hour circle; which done, lay the graduated edge of the quadrant over any one of these two stars on the globe which the thread cut in the heaven. If the said edge of the quadrant cuts the other star also, you have guessed the time exactly; but if it does not, turn the globe slowly backwards or forwards, until the quadrant (kept upon either star) cuts them both through their centres; and then the index will point out the exact time of the night; the degree of the horizon, cut by the quadrant, will be the true azimuth of both these stars from the south; and the stars themselves will cut their true altitudes in the quadrant. At which moment, if a common azimuth-compass be so set upon a floor or level pavement, that these stars in the heaven may have the same bearing upon it (allowing for the variation of the needle) as the quadrant of altitude has in the wooden horizon of the globe, a thread extended over the north and south points of that compass will be directly in the plane of the meridian; and if a line be drawn upon the floor or pavement, along the course of the thread, and an upright wire be placed in the southernmost end of the line, the shadow of the wire will fall upon that line, when the sun is on the meridian, and shines upon the pavement.

Prob. IX. To find the place of the moon, or of any planet; and thereby to show the time of its rising, setting, and setting.—See in Parker's or Weaver's ephemeris the geocentric place of the moon or planet in the ecliptic, for the given day of the month; and according to its longitude and latitude, as shown by the ephemeris, mark the same with a chalk upon the globe. Then, having rectified the globe, turn it round its axis westward; and as the said mark comes to the eastern side of the horizon, to the brass meridian, and to the western side of the horizon, the index will show at what time the planet rises, comes to the meridian, and sets, in the same manner as it would do for a fixed star.

For an explanation of the harvest-moons by a globe, see Astronomy, p. 370.

For the equation of time, see Astronomy, no. 383.

4. Description of the Modern Improvements applied to Globes.

Globes mounted in the common manner, and with their hour circles fixed on the meridian, although instructive instruments for explaining the first principles of geography and the spherical doctrine of astronomy, yet contain several defects; as they prevent any elevation of the north and south poles near to their axes, or the brass meridian from being quite moveable round in the horizon. They do not show how all the phenomena illustrated by them arise from the motion of the earth; a matter of consequence to beginners; and they are only adapted to the present age; consequently do not serve accurately the purposes of chronology and history, which they might be made to do, if the poles whereon they turn were contrived to move in a circle round those of the ecliptic, according to its present obliquity.

The late 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 consisting of brass at the distance of 23½ deg. 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 time, past or future, one of the brass shoulders is brought under the meridian, and held fast to it with one hand, whilst 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 brass 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 23½ and 66½ degrees on the brass meridian, the tropics and polar circles will be 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 axis round the annual axis. Senex's celestial globes, especially the two greatest, of 17 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 ecliptic. Phil. Trans. No. 447. p. 201, 203. or Metya's Abr. Vol. VIII. p. 217. and No. 493. art. 18. in Phil. Trans. Vol. XLVI. p. 290.

To represent the above phenomena in the most natural and easy manner, the late Mr B. Martin applied Mr Martin's addition to Mr Senex's Mr Joseph Harris, late essay-master of the mint, contrived to remedy the former of the defects above mentioned, by placing two horary circles under the meridian, one at each pole; these circles are fixed tight between two brass rollers placed about the axis, so that when the globe is turned they are carried round with it, the meridian serving as an index to cut the horary divisions. The globe in this state serves universally and readily for solving problems in north and south latitudes, and also in places near the equator; whereas in the common construction, the axis and horary circle prevent the brass meridian from being moveable quite round in the horizon. This globe is also adapted for showing how the vicissitudes of day and night, and the alteration of their lengths, are really occasioned by the motion of the earth: for this purpose, he divided the brass meridian at one of the poles into months and days, according to the sun's declination, reckoning from the pole. Therefore, by bringing the day of the month to the horizon, and rectifying the globe according to the time of the day, the horizon will represent the circle separating light and darkness; and the upper half of the globe, the illuminated hemisphere, the sun being in the zenith.

Phil. Trans. No. 456. p. 321, or Martyn's Abr. Vol. VIII. p. 352.

The late Mr George Adam, mathematical instrument maker, has made some additional improvements in the construction of the globes. His globes, like others, are suspended at their poles in a strong brass circle NZÆS (see fig. 2 representing the celestial), and turn therein upon two iron pins, which form the axis. They have each a thin brass semicircle NHS moveable about these poles, with a small, thin, sliding, circle H thereon; which semicircle is divided into two quadrants of 90 degrees each, from the equator to both the poles. On the terrestrial globe this semicircle is a moveable meridian, and its small sliding circle, which is divided into a few points of the compass, is the visible horizon of any particular place to which it is set. On the celestial globe this semicircle is a moveable circle of declination, and its small annexed circle an artificial sun or planet. Each globe has a brass wire TWY placed at the limits of the crepusculum or twilight; which, together with the globe, is mounted in a wooden frame, supported by a neat pillar and claw-feet, with a magnetic needle in a compass-box marked M in the figure. On the strong brass circle of the terrestrial globe, and about 23½ degrees on each side of the north pole, the days of each month are laid down according to the sun's declination; and this brass circle is so contrived, that the globe may be placed with the north and south poles in the plane of the horizon, and with the south pole elevated above it. The equator on the surface of either globe serves the purpose of the horary circle, by means of a semicircular wire placed in the plane of the equator (ÆF), carrying two indices (F); one on the east, the other on the west side of the strong brass circle; one of which is occasionally to be used to point out the time upon the equator. In these globes, therefore, the indices being set to the particular time on the equator, the globes are turned round, and the indices point out the time by remaining fixed; whereas in the globes as generally mounted, the indices move over the horary circles while the globe is moving, and thus point out the change of time. For farther particulars of these globes, and the method of using them, Mr Adam's Treatise on their Construction and Use, &c. 1772, may be consulted.

The additions and alterations above mentioned, made by Mr Adam, may save trouble to a practitioner in the performance of a few complex problems, and render the globes more elegant and costly; but to a young beginner, the more simple the construction of the globes, the better will they be adapted to initiate him into the rationale and practice of the problems in general; and as such, the globes, as improved by the late Mr B. Martin and Mr Wright, described below, appear to have considerably the advantage in simplicity, and to obviate several material defects that attend the construction of the other globes. The chief of the defects in the old globes is, that the horary circle being screwed on the meridian at the north pole, prevents the elevation of the south pole; which is necessary for the performance of problems for all latitudes. In Mr Adam's, the semicircular wire ÆF preventing the equator being placed exactly in the horizon, or the poles in the zenith, the great distance of the strong brass circle NZÆS from the surface of the globe, on account of the brass semicircles, renders the solution of problems, which require the use of the strong circle, not very easy nor accurate.

An easy and expedient method of elevating the fourth pole of the terrestrial globe, and by which Mr Martin's improvements are made, is by Captain Cook and other eminent navigators in the South Seas, may be clearly seen and traced by the eye over all the Southern Ocean, was made use of by Mr B. Martin in the construction of the following improvement.

There is a groove turned out on the back part of the brass meridian A (fig. 1); and by unscrewing the nut of the hour circle D at the north pole, the circle is made to slide away to any other part of the meridian, as at G. The meridian is fixed or moveable at pleasure by a screw passing into the groove, through the piece or side of the notch in which it moves, on the bottom or nadir point: by properly loosening this screw, the meridian is free to move, and the globe with it, into any required position; but at the same time, it is confined within the notch of the brass-piece, and thereby the globe is prevented from falling out of the frame in any position thereof whatsoever. The hour-circle being removed, both the north and south poles of the globe may be placed in the horizon, and thereby form a right sphere, which the usual mounting of the globes does not admit of.

Also by this construction, the south pole may be elevated for all latitudes: for this purpose there is an hour-circle about the south pole between the meridian and the globe, which does not obstruct the sight of any land, none having been theretofore discovered. Consequently the globe is thus equally useful for the fo- Principles of all common geographical problems in the northern hemisphere, and more extensively so than heretofore.

In this new method of mounting the globe, it may readily be converted into a tellurian; for as the globe cannot fall out of the frame, the horizon of the globe may be placed in a perpendicular position; then the sun's place in the ecliptic being brought to the meridian, and its declination found, the pole of the globe must be elevated to that declination; which may be done by means of the degrees cut on the outer edge of the meridian for that purpose. If a lighted candle be placed at a considerable distance, exactly the height of the centre of the globe, and in a line with the meridian, the globe will exhibit all the phenomena of our earth for that day; for in this case the horizon of the globe becomes the solar horizon, and divides the whole into the enlightened and dark hemispheres: therefore upon turning the globe about its axis from west to east, it will clearly appear that all places emerging out of the dark hemisphere into the luminous one, under the western part of the horizon, will see the sun then as rising; when they arrive at the meridian, it will be their noon; and when they descend into the dark hemisphere at the eastern part of the horizon, they will see the sun as setting.

When any place is under the meridian, set the hour-index to XII, and revolve the globe; then you will see the natural motion and position of that place at hours of the day; at what time the sun rises or sets to it; the length of the diurnal and nocturnal arches, or of day and night; at what places the sun does not rise and set at that time; and from whence the visibilities of the seas throughout the year in all latitudes, &c. &c.

To give this experiment the best effect, the candle should be enclosed within a common dark lanthorn, and its light issue through a hole or lens made for that purpose.

On the outer part of the sliding hour-circle, at the north pole, are usually engraved the points of the compass; so that by bringing that circle centrally over any place on the globe, it will appear by inspection only upon what point of the compass any other place bears from it, and that all over the globe.

This method of the sliding hour-circle is equally applicable to the celestial globe. Mr G. Wright of London has yet further simplified the construction of the hour-circles, and it is thereby rather less expensive than Mr Martin's above mentioned. It consists of the following particulars: There are engraved on the globes two hour-circles, one at each of the poles; which are divided into a double set of 12 hours, as usual in the common bras ones, except that the hours are figured round both to the right and left (see fig. 3.). The hour-hand or index (A) is placed in such a manner under the bras meridian, as to be moveable at pleasure to any required part of the hour-circle, and yet remain there fixed during the revolution of the globe on its axis and is entirely independent of the poles of the globe. In this manner the motion of the globe round its axis, carrying the hour-circle, the fixed index serves to point out the time, the same as in the reverse way by Mr Martin's or other globes.

There is a small advantage by having the hour-circle figured both ways, as one hour serves as a complement to XII for the other, and the time of sunrise and setting, and vice versa, may be both seen at the same time on the hour circle. In the problems generally to be performed, the inner circle is the circle of reckoning, and the outer one only the complement. Fig. 4. is a representation of the globe, with Mr Wright's improved hour-circle at C.

Mr William Jones, mathematical instrument maker, Holborn, who mounts globes according to the improvements above mentioned of Messrs Martin and Wright, applies a compass of a portable size to the east part of the wooden horizon circle of both globes (see F, fig. 1.), by a dove-tail slider on the lid of the compass-box; which method is found more convenient and ready in the performance of problems, than when fixed underneath the frame at their feet; and as it occasionally slides away from the globes, the compass becomes useful in other situations.

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 ideas of the construction, they may be described as follows: Instead of a thin flexible slip of brass, which generally accompanies the globes, called the quadrant of altitude, Mr Smeaton substitutes an arch of 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 usual with the common quadrant put to globes. That end of this circular arch at which the divisions begin, 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 edge of the brass meridian, directly over the zenith of the globe. This socket is fitted to and ground with a steel spindle of the same length, so that it will turn freely on it without sticking; 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 to it, and to 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 shown 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 directs to place the index which is usually fixed on one end of the axis to point out the hour, in such a manner that its upper surface may move in the plane of the hour-circle rather than above it, as it usually does. He files off the end of this index to a circular arch, of the same radius with the inner edge of the hour-circle, to which it is to fit very exactly; and a fine line is drawn on its upper surface to determine the time by, instead of the tapering point which is generally Principles rally used. By these means half minutes may be distinguished, if the hour circle be four inches in diameter. Mr Smeaton also describes a contrivance for preventing the meridian from shifting after being rectified for the latitude of the place, and while the operator is engaged in adjusting other parts of the apparatus. But as the purpose which this is intended to answer appears to be much better performed by the turned groove on the meridian in Mr Martin's contrivance described above, we shall omit the particular description; and for farther explanations and figures of Mr Smeaton's improvements, refer the reader to the Phil. Trans. Vol. LXXIX, Part i.

For another improvement made to the celestial globe, by Mr Ferguson, see Astronomy, p. 493, and fig. 187 of plate LXXXI.

Most of the above problems may also be performed by means of accurate maps; but this requires a great deal of calculation, which is often very troublesome. The Analemma, or Orthographic Projection, delineated on Plate CCXII, will solve many of the most curious; and with the assistance of the 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 $23\frac{1}{2}$ 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 show the hours of sun-rising or sun-setting 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, show 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 Lizardpoint in England, Franckfort in Germany, or Abbeville in France, on the 30th of April. The latitude of these places by the maps will be found nearly $50^\circ$ north. 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 wrote. 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 compasses; and this shows, 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 E.N.E., and sets a little to the northward of W.N.W. To find the beginning and ending of 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 for the 30th of April, 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 an half; which shows, 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.—The small circles on the same plate, marked Island, Promontory, &c. are added in order to render the maps more intelligible, by showing how the different subjects are commonly delineated on them.

Having thus explained the use of the globes, and general principles of geography, we must refer to the Maps for the situation of each particular country, with regard to longitude, latitude, &c. and to the names of the countries as they occur in the order of the alphabet, for the most remarkable particulars concerning them.