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spherical segments, with which the ball destined for a terrestrial globe is covered. Copies of such map may be multiplied at little additional expense. It belongs to the theorist of maps, to explain the principles on which the surface of the earth is delineated upon these spherical segments. We shall now suppose that the artificial globe exactly represents the surface of the earth, and proceed to explain the lines which are commonly drawn upon the globe, besides the equator and first meridian, and to describe the apparatus usually attached to it. In order that we might be able to find out from the globe itself, the latitude and longitude of any place, a parallel to the equator and a meridian line would require to be drawn through that place. It is impossible that such lines could be drawn through every point on the globe, and it is unnecessary, for the brass circle placed around it, enables us to find out the latitude and longitude. In this circle, which is placed at right angles to the equator, and is therefore a meridian, the globe is suspended by the axis. One of the sides of the meridian is graduated, or divided into degrees, minutes, and seconds. The globe can be turned round its axis, while the general meridian remains stationary, so that every point of the surface of the globe must pass under some point of the meridian. To find out the latitude and longitude of any place, therefore, we have only to turn the globe round till the given place be brought to the meridian. The number of degrees, minutes, &c. under which the place lies will be its latitude, and the number intercepted upon the equator its longitude. In addition to the general meridian, meridians and parallels of latitude are usually drawn upon the globe, through every 5th or 10th degree of latitude and longitude, according to the size of the globe. These lines point out accurately the latitude or longitude of those places which are situated upon them, and give us a general idea of the situation of other places. Besides meridians and parallels of latitude, the ecliptic is usually drawn upon globes, and also the tropics and polar circles. All these last are commonly drawn with double lines to distinguish them from other meridians and parallels of latitude.

The globe suspended in the general meridian, is placed upon a wooden frame. The upper surface of this frame divides the globe into two hemispheres, one superior, and the other inferior, and represents, therefore, the rational horizon of any place which is brought to the zenith point of the meridian. There are two notches for the meridian to slide in, by which different elevations of the pole may be exhibited. The horizon has commonly drawn upon it the points of the compass, the twelve signs of the zodiac, the months of the year, &c.

There is attached to the general meridian a quadrant, composed of a thin pliable plate of brass, answering exactly to a quadrant of the meridian. It is graduated, and has a notch, nut, and screw, by which it may be fixed to the brazen meridian in the zenith of any place. When so fixed, it turns round a pivot, and supplies the place of vertical circles. It is hence dénominated a quadrant of altitude.

A small circle of brass is placed on the north pole. It is divided into 24 equal parts, and is termed an hour-circle. On the pole of the globe is fixed an index, which turns round the axis, and points out the hours upon the hour-circle.

There is also often attached to the globe a compass, which is placed upon the pediment of the frame, parallel to the horizon.

Problems solved by the Globe.] Having thus described the globe

and its apparatus, we shall now explain some of the problems that may be resolved by it.

I. To find the latitude and longitude of any place. We have already seen that this is done by bringing the place to the graduated side of the general meridian; the degree of the meridian cut by the place being equal to the latitude, and the degree of the equator then under the meridian being the longitude.

II. To find a place upon the Globe, its latitude and longitude being given. Find the degree of longitude on the equator, and bring it to the brass meridian; then find the degree of latitude on the meridian, either north or south, and the point of the globe under that degree of latitude is the place required.

III. To find all the places on the Globe that have the same latitude as a given place, suppose London.-Turn the globe round, and all the places that pass under the same point of the meridian as the given place, London, does, have the same latitude with it.

IV. To find all the places that have the same longitude or hour with a given place, as London.-Bring the given place, London, to the meridian, and all places then under the meridian have the same longitude as London.

V. To find the difference in the time of the day at any two given places, and their difference of longitude.-Bring one of the places to the meridian, and set the hour-index to twelve at noon, then turn the globe till the other place come to the meridian, and the index will point out the difference of time. By allowing 15 degrees to every hour, or one degree to four minutes of time, the difference of longitude will be known. The difference of longitude may also be found without the time, in the following manner :-Bring each of the places to the meridian, and mark the respective longitudes. Subtract the one number from the other, and we obtain the difference of longitude sought.

VI. The time being known at any given place, as London, to find what hour it is in any other part of the world.-Bring the given place, London, to the meridian, and set the index to the given hour; then turn the globe till the other place come to the meridian, and the hour at which the index points will be the time sought.

VII. To find the distance of two places on the Globe.-If the two places be either both on the equator or both on the same meridian, the number of degrees in the distance between them, reduced into miles, at the rate of 69 to the degree, will give the distance nearly. If the places be in any other situation, lay the quadrant of altitude over them, and the degrees intercepted upon it by the two places, and turned into miles, as above, will give their distance.

VIII. To find the antæci, periæci, and antipodes of any given place, suppose London.-Bring London to the meridian, and find by the meridian the point upon the globe, of which the latitude is as much south as that of London is north. The place thus arrived at will be the situation of the antæci, where the hour of the day or night is always the same as at London, and where the seasons and lengths of the days and nights are also the same, but at opposite times of the year. London being still under the meridian, set the hour-index to 12 at noon, or pointing towards London, then turn the globe half round, till the index points to the opposite hour, or 12 at night. The place that comes under the same point of the meridian where London was, is where the periæci dwell, or

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

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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 carth.-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 Archi medes' 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. e. 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.

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