people that have the same seasons, and at the same time, as London, and the same lengths of the days and nights, but have an opposite hour, it being midnight with the one when noon with the other. Lastly, While the place of the periæci is at the meridian, count by the meridian the same degree of latitude south, and that will give the place of the antipodes of London. They have all their hours and seasons opposite to those of London, being noon with the one when midnight with the other, and winter with the one when summer with the other.

IX. To find the sun's place in the ecliptic and also on the Globe at any given time.—Find in the calendar, on the wooden horizon, the given month, and day of the month, and immediately opposite will be found the sign and degree which the sun is in on that day. Then, in the ecliptic drawn upon the globe, find the same sign and degree, and that will be the place of the sun required.

X. The time being given at any place, as London, to find the place on the earth to which the sun is then vertical.-Find the sun's place on the globe by the last problem; and turn the globe about till that place come to the meridian; mark the degree of the meridian over it, which will show the latitude of the required place. Then turn the globe till the given place, London, come to the meridian, and set the index of the hour circle to the given moment of time. Lastly, Turn the globe till the index points to twelve at noon, and the place of the earth corresponding to that upon the globe which stands under the meridian at the point marked as before, is that which has the sun at the given time in the zenith.

XI. To find all those places on the earth to which the sun is vertical on a given day.—Find the sun's place in the ecliptic on the globe, as in the last problem, and bring that place to the meridian. Turn the globe round, and note all the places which pass under the same point. These will be the places sought.

This problem enables us to determine what people are ascii on any given day. It is evident, that in a similar manner we may also find to what places on the earth the moon or any other planet is vertical at a given time: the place of the planet on the globe at that time being found by its declination and right ascension.

XII. A place being given in the torrid zone, to find on what two days of the year the sun is vertical at that place.-Bring the given place to the meridian, and note the degree it passes under. Turn the globe round, and note the two points of the ecliptic which pass under the same degree of the meridian. Then, find by the wooden horizon on what days the sun is in these two points of the ecliptic, and on these days he will be vertical to the given place.

XIII. To find how long the sun shines without setting in any given place in the frigid zone. Subtract the degrees of latitude of the given place from ninety, which gives the complement of the latitude, and count this complement upon the meridian from the equator towards the pole, marking that point of the meridian; then turn the globe round, and observe what two degrees of the ecliptic pass exactly under the point marked on the meridian. It is evident that the sun will shine upon the given place without setting while it is in these, and all the points of the ecliptic that are nearer to the given place. Find, therefore, upon the wooden horizon the months, and days of the months in which the sun is

f

in the two points in question, and the intermediate time will be that during which the sun constantly shines at the given place.

XIV. To find how long the sun never shines upon any given place in the frigid zones.— -Count the complement of latitude towards the south, or farthest pole, and then proceed exactly as in the last problem.1

XV. To rectify the globe to the latitude of any place. Move the brass meridian in its grove, till the elevation of the pole above the horizon be equal to the latitude.

XVI. To rectify the globe to the horizon of any place.—Rectify the globe to the latitude of the place by the last problem; and then turn the globe on its axis till the given place come to the meridian. The place will then be exactly on the vertex of the globe, 90 degrees distant every way from the wooden horizon; and that horizon, therefore, will represent the horizon of the given place.

XVII. To find the bearing of one place from another, and their angle of position. Rectify the globe to the horizon of one of the places. Screw the quadrant of altitude to the zenith point of the meridian, and make it revolve till the graduated edge passes through the other place. Then look on the wooden horizon for the point of the compass, or number of degrees from the south, where the quadrant of altitude meets the horizon, and that will be the bearing of the latter place from the former, or the angle of position sought.

XVIII. To find all those places on the earth to which the sun at a given time is rising or setting; also what places are then illuminated by the sun, or in darkness; and where it is noon, or midnight.-Find the place to which the sun is vertical at the given time, and rectify the globe to its horizon, in which state the place will be in the zenith point of the globe. Then is all the hemisphere above the wooden horizon enlightened, or in daylight, while the hemisphere below the horizon is in darkness, or night; lastly, to all these places by the eastern side of the horizon, the sun is just setting, and to those by the western side, he is just rising.

XIX. The time of a solar or lunar eclipse being given, to find all those places at which the eclipse will be visible.—Find the place to which the sun is vertical at the given time, and rectify the globe to the horizon of that place. Then, by the last problem, it is evident, that if the eclipse be solar, a part of it at the beginning only will be seen in places which are not far above the eastern side of the horizon; while, in the rest of the upper hemisphere, the whole of the eclipse will be visible. A part of it at the end will be seen in places which are near to the lower side of the western part of the horizon. If the eclipse. be lunar, the moon will be in the opposite point of the ecliptic to the sun, and vertical to that point of the earth which is opposite to the place to which the sun is vertical. The eclipse, therefore, will be visible in the lower hemisphere.2

XX. To find the beginning and end of twilight, on any day of the year, for any latitude. It is twilight in the evening from sunset till the sun is eighteen degrees below the horizon; and in the morning from the time

In the above solutions of the last two problems no allowance is made for refraction, which raises the sun when near the horizon, more than half-a-degree. The problems, therefore, will be resolved more correctly, if we set the mark on the meridian half a degree higher up towards the north pole than the complement of latitude indicates.

In the last two problems no notice has been taken of refraction.

the sun is within eighteen degrees of the horizon till the moment of his rising. Therefore, rectify the globe to the given latitude, set the index of the hour-circle to twelve at noon, and screw on the quadrant of altitude. Find the point of the ecliptic which is opposite to the sun's place, and turn the globe on its axis westward along with the quadrant of altitude, till that point cut the quadrant in the eighteenth degree below the western side of the horizon. The index will then show the time of dawning in the morning. Next turn the globe and quadrant of altitude towards the east, till the same opposite point of the ecliptic meet the quadrant in the eighteenth degree below the eastern side of the horizon. The index will then show the time when twilight ends in the evening.

XXI. To rectify the globe to the present situation of the earth.-Rectify the globe to the horizon of the place. Its situation will then correspond to that of the earth; and, if it stand in the sun, it will be illuminated as the earth is.3

The invention of globes is of great antiquity. Anaximander, of Miletus, a disciple of Thales, who flourished, B. C. 580, is said to have invented the terrestrial globe. Some allusions to the globe may be found as early as Hipparchus' time, in the writings of Pliny and Ptolemy. The latter possessed an artificial globe with a universal meridian. Strabo makes mention of the terrestrial globe; and a cotemporary of his, Propertius, refers directly to depicted worlds; and Claudius, who describes Archimedes' glass sphere, evinces great knowledge of the constructions of orreries, spheres, &c. which must have then existed among mathematicians.

Among the improvers and makers of globes may be subsequently ranked the following as chief: Martin Behaim, Tycho Brahe, Regiomontanus, Schonerus, Gemma Frisius, Gr. Mercator, J. Hondius, Johnsonius, Wm. Saunderson, Wm. Bleau, &c. some of whom wrote learnedly on their uses: but, in this respect, the preference is certainly due to Mr. Robert Flues, whose Latin treatise was afterwards published by Hendrius, and then by Pontanus, with figures and notes. This work was translated into English by J. Chilmead, in the year 1637. The Venetian Caronelli, with the help of Claudius Molines, and other Parisian artists, executed a globe of 14 Parisian feet in diameter, for Louis XIV., and a celestial globe of the same size.

No globes had any pretensions to accuracy, taste, or elegance, till the time of John Senex, F. R. S.; who, about the year 1739, delineated and engraved sets of plates for globes of 9, 12, 17, and 28 inches in diameter, which he used with the globes then manufactured by himself, making these instruments more accurate and useful than any former maker. The terms and names of places on the globes of 17 and 28 inches in diameter, were Latin. About the year 1759, and just after the decease of Mr. Senex, Mr. Benjamin Martin, a learned optician, became possessed of Mr. Senex's plates, and continued for many years to manufacture the globes with various improvements. In the year 1765, the late Mr. George Adams caused new plates for 18 and 12 inch globes to be engraved. The terms and names of these, like the larger ones of Senex, were printed in Latin. Instead of horary circles fixed on the meridian, with moveable indices for computation of time, Mr. Adams contrived circular wires, to envelope the globe about the equinoctial circles, with sliding brass points; so that as the globes were revolved on their axis, the time by these was pointed out on the graduations of the great circle, which, consequently, gave a more extensive and conspicuous scale of time than could be had by means of the smaller horary circles. He also applied to each globe a semicircular slip of brass, connected at the poles, having on the terrestrial, a sliding compass, and on the celestial, a sliding sun. The brass slips were graduated each way from the equinoctial, so that the positions for rhomb-lines, right ascensions, and declinations, could be better and more readily obtained.

The horary, or hour-circle, of the globes being usually attached to the external edge of the meridians, prevented a free and uninterrupted motion of the meridians, with their poles, through the horizons of the globes, to admit of an universal position of the axis, with respect to the horizon, for all latitudes of places. Mr. James Harris, of the Mint, in the year 1740, contrived a method of fixing the brass horary circles at the poles, under the meridians, i. c. between the surface of the globes and the interior edge of the meridian, and to be occasionally moveable, independent either of the globe or meridian. In this manner, the globes were rendered completely useful for the solution of problems in all latitudes.

About the year 1785, Mr. G. Wright contrived a moveable index, applicable to the poles of a globe, to act in a similar manner as the circle of Mr. Harris, which pointed to circles of hours engraved round the poles of each globe. This he considered a method of obviating the great friction or adherence that sometimes inconveniently takes place between the surfaces of the circle and globe.

Maps.] The necessity of maps arises from large globes being very expensive and inconvenient; while, on small ones, sufficient details cannot be exhibited. As it is impossible to represent accurately upon a plane any part of a spherical surface, globular maps, that is, maps drawn upon a piece of pasteboard, or other substance, formed into the segment of a sphere have been proposed. Such maps would exhibit every place in the same relative position as upon the earth, but they are never made use of, owing to their inconvenient shape. Maps are constructed by making a projection of the globe, on the plane of some particular circle, supposing the eye placed at some particular point, according to the rules of perspective.

In maps three things are required: First to show the latitude and longitude of places, which is done by drawing a certain number of meridians and parallels of latitude. Secondly, the shape of the countries must be exhibited as accurately as possible; for real accuracy cannot be

From the lapse of years, the numerous astronomical and geographical discoveries, and the Latin terms adopted in the larger globes of Senex and Adams, these globes became inconvenient, embarrassing, and finally obsolete. A short time before the year 1800, sets of new and accurately engraved plates were suggested, and considered as a desideratum in astronomy, by the Astronomer Royal, Dr. Maskelyne, Sir Joseph Banks, Professor Vince, and others; and conformably to this object, in the year 1800, were completed and produced a set of entirely new plates, for globes of eighteen inches in diameter, under the denomination of New British Globes.' On these, the graduation and lines are laid down in the most correct manner, and with much greater accuracy than in any former globe plates. The drawing from which the terrestrial globe is engraved, was an entirely new one, from the hands of Mr. Arrowsmith, an eminent geographer. The latitudes and longitudes of places are rectified from the latest and best authorities; and there are likewise inserted all the authentic discoveries to the present time. The celestial globe contains a description of a complete catalogue of stars, clusters, planetary nebulæ, &c., to the amount of nearly 6000, from the observations and communications of Dr. Maskelyne, Dr. Herschell, Rev. Mr. Wollaston, &c., and inserted from calculations made by Mr. W. Jones, optician, of Holborn, London, in their exact positions, to the present period. To the principal stars are annexed Bayer's Greek letters of reference; and the whole are circumscribed by well-designed figures of the constellations, faintly engraved. The great circles are divided into twenty minutes of a degree, and the equinoctial in addition into two minutes of time, so that, by estimation, the solution of problems may be obtained to five minutes of a degree, or half-a-minute of time; a degree of accuracy sufficiently useful, not only for all the common problems, but most of the trigonometrical ones. As the reading of time is found to be a ready and convenient method, by hour-circles attached to the meridians, the horary circle has been contrived to admit of being slid away from its pole, upon the exterior edge of the meridian; this is done by making the extremity of the pole, which carries the index of the horary circle, moveable by unscrewing. The horary circle being attached to the meridian barely by springs, when the index is unscrewed, the circle may consequently be slid to any part of the meridian. This contrivance is necessary only for the circle of the north pole of Messrs. W. & S. Jones' terrestrial globe, who have adopted this circle; and at the south pole of the globes, have employed the interior brass index, or circles above mentioned. Plates for the British globes of 12 inches diameter, have been reduced and abridged from the 18 inches above mentioned. Plates for globes of 9, 12, and 21 inches diameter, have been engraved by Mr. Carey. The stars of his celestial globes, are not circumscribed with the figures of the constellations.

4 Anaximander, it is said, about 500 years before Christ, first invented geographical tables, or maps. The Peutingerian tables, published by Cornelius Peutinger of Augsburg, contain an itinerary of the whole Roman empire; all places, except seas, woods, and deserts, being laid down according to their measured distances, but without any mention of latitude, longitude, or bearing.

The maps published by Ptolemy of Alexandria, A. D. 144, have meridians and parallels, the better to define and determine the situation of places, and are great improvements in the construction of maps: though Ptolemy himself owns that his maps were copied from some that were made by Marinus, Titianus, &c., with the addition of improvements of his own. Agathodemon, in the 5th century after Christ, executed some maps for the geography of Ptolemy. In the 8th and following centuries, metal planiglobes and maps were found in the libraries of the rich. Charlemagne possessed a silver planiglobe; and Roger I. of Sicily, a silver globe of great weight. There is a map existing, dated 1265, of the then known earth, drawn on twelve skins of parchment. In 1513, the Brothers Appian drew a map containing what was then known

obtained by any projection, because the map is on a plane surface, whereas the earth is globular. Thirdly, the bearings of places, and their distances from each other must be shown: The projection of maps is made, as we have observed, according to the rules of perspective. If the eye be supposed to view the earth from an infinite distance, the appearance represented on a plane is called the orthographic or straight projection. In this case, the parts about the middle are very well represented, but the extreme parts are contracted. Geographers usually employ the stereographic projection, where the eye is supposed to be on the surface of the earth, and looking at the opposite hemisphere. There is likewise the globular projection, in which meridians, equidistant upon the surface of the earth, are represented by equidistant circles in the map. Mercator's projection, is that in which both the meridians and parallels of latitude are represented by straight lines.

In all maps, the upper part is the north, the lower the south, the right is eastern, and the left hand western.5 On the right and left, the

of the New World. In 1514, the mathematician Werner divided the earth into four parts. Mercator of Ruremonde, who died in 1594, was the first of note among the moderns, and next to him Ortelius, who undertook to make a new set of maps, with the modern divisions of countries and names of places; for want of which, those of Ptolemy were become almost useless. After Mercator, many others published maps, but for the most part they were mere copies of his. Gemma Frisius, who invented the present manner of engraving maps in 1595, gave a map of the world, with the discoveries in the East and West Indies. Towards the middle of the 17th century, Bleau, in Holland, and Sanson, in France, published new sets of maps, with many improvements from the travellers of those times, which were afterwards copied, with little variation, by the British, French, and Dutch; the best of these being those of Vischer and De Witt. And later observations have furnished us with still more accurate and copious sets of maps, amounting perhaps to 6000 original works. The best among the English, are Arrowsmith, Bogue, and Ackrell; among the French, De Lisle, D'Anville, and Barbier; among the Italians, Rizzi Zannoni; and among the Germans, Dussefeld, Sotzmann, and Reichard.

The Map which fronts the title page of this work, is a representation of the world upon two hemispheres, one containing the continent of America, and the other the continent formed by Europe, Asia, and Africa. The Equator, or Equinoctial Line, is represented by a graduated straight line passing through the centres of the circles which form the map, and the Meridians by arches of circles cutting the equator, at the distance of every 10 degrees, and terminating in the poles. Parallels of latitude, at the distance of every 10 degrees, are represented by arches of circles, lying from right to left, and terminating in the circumference of the circles which bound the hemispheres, so as to divide each of the quadrants between the poles and the equator into nine equal parts. The Tropics and Polar Circles are also drawn. The latitude of each of the parallels is marked at its extremities on the margins of the map, and the longitude of each meridian is marked on the equator, and reckoned eastward and westward from the meridian of London. To find the latitude and longitude of any point in this map, if the given point be at the intersection of a parallel of latitude and a meridian, the latitude will be found at the extremities of the parallel on the margin, and the longitude at the point where the meridian cuts the equator; thus the latitude of the most easterly point of Italy will be found to be 40 degrees north, and the longitude about 20 degrees east from London. If the given point be not at the intersection of a parallel and a meridian, its latitude and longitude may yet be found, by carrying one's finger from it, as near as can be guessed, along an imaginary parallel of latitude, and observe at what degree it meets the margin of the map, and that will be the latitude sought; in like manner the longitude may be found, by tracing an imaginary meridian through the place till it meet the equator.

Kingdoms or provinces are divided from each other by a row of single points, and they are often further distinguished by being painted with different colours. Mountains are imitated in the form of little rising hillocks; and forests are sometimes represented by a collection of little trees. The names of villages are written in a running hand, those of cities in a Roman character, and those of provinces in large capitals. The sea is generally left as empty space on the map, except where there are rocks, sands or shelves, currents of water, or wind. Sands or shelves are denoted by a great heap of little points placed in the shape of these sands, as they have been found to lie in the ocean, by sounding the depths. Currents of water are described by several long parallel crooked strokes, imitating a current. The course of winds is represented by