GLOBE

, a round or spherical body, more usually called a sphere, bounded by one uniform convex surface, every point of which is equally distant from a point within called its centre. Euclid defines the Globe, or sphere, to be a solid figure described by the revolution of a semi-circle about its diameter, which remains unmoved. Also, its axis is the fixed line or diameter about which the semi-circle revolves; and its centre is the same with that of the revolving semicircle, a diameter of it being any right line that passes through the centre, and terminated both ways by the superficies of the sphere. Elem. 11. def. 14, 15, 16, 17.

Euclid, at the end of the 12th book, shews that spheres are to one another in the triplicate ratio of their diameters, that is, their solidities are to one another as the cubes of their diameters. And Archimedes determines the real magnitudes and measures of the surfaces and solidities of spheres and their segments, in his treatise de Sphæra et Cylindro: viz, 1, That the superficies of any Globe is equal to 4 times a great circle of it.—2, That any sphere is equal to 2/3 of its circumscribing cylinder, or of the cylinder of the same diameter and altitude.—3, That the curve surface of the segment of a globe, is equal to the circle whose radius is the line drawn from the vertex of the segment to the circumference of the base.—4, That the content of a solid sector of the Globe, is equal to a cone whose altitude is the radius of the Globe, and its base equal to the curve superficies or base of the sector. With many other properties. And from hence are easily deduced these practical rules for the surfaces and solidities of Globes and their segments; viz,

1. For the Surface of a Globe, multiply the square of the diameter by 3.1416; or multiply the diameter by the circumference.

2. For the Solidity of a Globe, multiply the cube of the diameter by .5236 (viz 1/<*> of 3.1416); or multiply the surface by 1/6 of the diameter.

3. For the Sursace of a Segment, multiply the diameter of the Globe by the altitude of the segment and the product again by 3.1416.

4. For the Sol<*>dity of a Segment, multiply the square of the diameter of the Globe by the difference between 3 times that diameter and 2 times the altitude of the segment, and the product again by .5236, or 1/6 of 3.1416.

Hence, if d denote the diameter of the Globe, c the circumference, a the altitude of any segment, and p = 3.1416; then

See the art. Sphere, and my Mensuration, p. 197 &c, 2d edit.|

The Globe, or Terraque<*>s Globe, is the body or mass of the earth and water together, which is nearly globular.

, or Artificial Globe, is more particularly used for a Globe of metal, plaister, paper, pasteboard, &c, on the surface of which is drawn a map, or representation of either the heavens or the earth, with the several circles conceived upon them. And hence

Globes are of two kinds, Terrestrial, and Celestial; which are of considerable use in geography and astronomy, by serving to give a lively representation of their principal objects, and for performing and illustrating many of their operations in a manner easy to be perceived by the senses, and so as to be conceived even without any knowledge of the mathematical grounds of those sciences.

The fundamental parts that are common to both Globes, are an axis, representing the axis of the world, passing through the two poles of a spherical shell, representing those of the world, which shell makes the body of the Globe, upon the external surface of which is drawn the representation of the whole surface of the earth, sea, rivers, islands, &c, for the Terrestrial Globe, and the stars and constellations of the heavens, for the Celestial one; besides the equinoctial and ecliptic lines, the zodiac, the two tropics and polar circles, and a number of meridian lines. There is next a brazen meridian, being a strong circle of brass, circumscribing the Globe, at a small distance from it quite round, in which the globe is hung by its two poles, upon which it turns round within this circle, which is divided into 4 times 90 degrees, beginning at the equator on both sides, and ending with 90 at the two poles. There are also two small hour circles, of brass, divided into twice 12 hours, and fitted on the meridian round the poles, which carry an index pointing to the hour. The whole is set in a wooden ring, placed parallel to, and representing the horizon, in which the Globe slides by the brass meridian, elevating or depressing the pole according to any proposed latitude. There is also a thin slip of brass, called a Quadrant of Altitude, made to fit on occasionally upon the brass meridian, at the highest or vertical point, to measure the altitude of any thing above the horizon. A magnetic compass is sometimes set underneath. See the figure of the Globes so mounted, at fig. 1, plate xii.

Such is the plain and simple construction of the artificial Globe, whether celestial or terrestrial, as adapted to the time only for which it is made. But as the angle formed by the equator and ecliptic, as well as their point of intersection, is always changing; to remedy these inconveniences, several contrivances have been made, so as to adapt the same Globes to any other time, either past or to come; as well as other contrivances to answer particular purposes.

Thus, Mr. Senex, a celebrated maker of Globes, had a contrivance which, by means of a nut and serew, caused the pole of the equator to revolve about the pole of the ecliptic, by any quantity answering to the precession of the equinoxes, since the time for which the Globe was made. Philos. Trans. number 447, or Abr. vol. 8, p. 217, also Philos. Trans. vol. 46, p. 290.

Mr. Joseph Harris, late assay-master of the Mint, made some contrivances to shew the effects of the <*>arth's motions. He fixed two horary circles under the brass meridian, to the axis, one at each pole, so as to turn round with the Globe, and that meridian served as an index to cut the horary divisions. The Globe in this state serves equally for resolving problems in both north and south latitudes, as 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 shewing 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 divides 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. Mr. Harris also gives an account of a cheap machine for shewing how the annual motion of the earth in its orbit causes the change of the sun's declination, without the great expence of an orrery. Philos. Trans. number 456, or Abr. vol. 8, p. 352.

The late Mr. George Adams made also some useful improvements in the construction of the Globes. Besides what is usual, his Globes have a thin brass semicircle moveable about the poles, with a small thin sliding circle upon it. On the terrestrial Globe, the former of these is a moveable meridian, and the latter is the visible horizon of any particular place to which it is set. But on the celestial Globe, the semi-circle is a moveable circle of declination, and its small annexed circle an artisicial sun or planet. Each Globe has a brass wire circle, placed at the limits of the twilight. The terrestrial Globe has many additional circles, as well as the rhumb-lines, for resolving all the necessary geographical and nautical problems: and on the celestial Globe are drawn, on each side of the ecliptic, 8 parallel circles, at the distance of one degree from each other, including the zodiac; which are crossed at rightangles by segments of great circles at every 5th degree of the ecliptic, for the more readily noting the place of the moon or of any planet upon the Globe. On the strong brass circle of the terrestrial Globe, and about 23 1/2 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 semi-circular wire placed in the plane of the equator, carrying two indices, one of which is occasionally to be used to point out the time. For a farther account of these Globes, with the method of using them, see Mr. Adams's treatise on their construction and use.

There are also what are called Patent Globes, made by Mr. Neale; by means of which he resolves several astronomical problems, which do not admit of solution by the common Globes.|

Mr. Ferguson likewise made several improvements of the Globes, particularly one for constructing dials, and another called a planetary Globe. See Philos. Trans. vol. 44, p. 535, and Ferguson's Astron. p. 291, and 292.

Lastly, in the Philos. Trans. for 1789, vol. 79, p. 1, Mr. Smeaton has proposed some improvements of the celestial Globe, especially with respect to the quadrant of altitude, for the resolution of problems relating to the azimuth and altitude. The difficulty, he observes, that has occurred in fixing a semicircle, so as to have a centre in the zenith and nadir points of the Globe, at the same time that the meridian is left at liberty to raise the pole to its desired elevation, I suppose, has induced the Globe-makers to be contented with the strip of thin flexible brass, called the quadrant of altitude; and it is well known how imperfectly it performs its office. The improvement I have attempted, is in the application of a quadrant of altitude of a more solid construction; which being affixed to a brass socket of some length, and this ground, and made to turn upon an upright steel spindle, fixed in the zenith, steadily directs the quadrant, or rather arc, of altitude to its true azimuth, without being at liberty to deviate from a vertical circle to the right hand or left: by which means the azimuth and altitude are given with the same exactness as the measure of any other of the great circles. For a more particular description of this improvement, illustrated with figures, see the place above quoted.

Prob. I. To find the latitude and longitude of any place. —Bring the place to the graduated side of the first meridian: then the degree of the meridian it cuts is the latitude sought; and the degree of the equator then under the meridian is the longitude.

II. To find a place, having a given latitude and longitude.—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 of the equator, as the given latitude is north or south; then the point of the Globe just under that degree of latitude is the place required.

III. To find all the places on the Globe that have the same latitude, and the same longitude, or hour, with a given place, as suppose London.—Bring the given place London to the meridian, and observe what places are just under the edge of it, from north to south; and all those places have the same longitude and hour with it. Then turn the Globe quite round; and all those places which pass just under the given degree of latitude on the meridian, have the same latitude with the given place.

IV. To find the Antœci, Periœci and Antipodes, of any given place, suppose London.—Bring the given place London to the meridian, then count 51 1/2 the same degree of latitude southward, or towards the other pole, and the point thus arrived at will be the Antœci, or where the hour of the day or night is always the same at both places at the same time, and where the seasons and lengths of days and nights are also equal, but at half a year distance from each other, because their sea- sons are opposite or contrary. London being still under the meridian, set the hour index to 12 at noon, or pointing towards London; then turn the Globe just half round, or till the index point to the opposite hour, or 12 at night; and the place that comes under the same degree of the meridian where London was, shews where the Periœci dwell, or those people that have the same seasons and at the same time as London, as also the same length of days and nights &c at that time, but only their time or hour is just opposite, or 12 hours distant, being day with one when night with the other, &c. Lastly, as the Globe stands, count down by the meridian the same degree of latitude south, and that will give the place of the Antipodes of London, being diametrically under or opposite to it; and so having all its times, both hours and seasons opposite, being day with the one when night with the other, and summer with the one when winter with the other.

V. 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 70 English miles to the degree, (or more exact 69 1/3), will give the distance nearly. But in any other situations of the two places, lay the quadrant of altitude over them, and the degrees counted upon it, from the one place to the other, and turned into miles as above, will give the distance in this case.

VI. To find the Difference in the Time of the day at any two given places, and thence the Difference of Longitude.—Bring one of the places to the meridian, and set the hour index to 12 at noon; then turn the Globe till the other place comes to the meridian, and the index will point out the difference of time; then by allowing 15° to every hour, or 1° to 4 minutes of time, the difference of longitude will be known.—Or the difference of longitude may be found without the time, thus:

First bring the one place to the meridian, and note the degree of longitude on the equator cut by it; then do the same by the other place; which gives the longitudes of the two places; then subtracting the one number of degrees from the other, gives the difference of longitude sought.

VII. The time being known at any given place, as suppose 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 look at what hour the index points, which will be the time sought.

VIII. To find the Sun's place in the ecliptic, and also on the Globe, at any given time.—Look into the calendar on the wooden horizon for the month and day of the month proposed, and immediately opposite stands the sign and degree which the sun is in on that day. Then in the ecliptic drawn upon the Globe, look for the same sign and degree, and that will be the place of the sun required.

IX. To find at what place on the earth the sun is vertical, at a given moment of time at another place, as suppose London.—Find the sun's place on the Globe by the last problem, and turn the Globe about till| that place come to the meridian, and note the degree of the meridian just over it. Then turn the Globe till the given place, London, come to the meridian, and set the index to the given moment of time. Lastly, turn the Globe till the index points to 12 at noon; then the place of the earth, or Globe, which stands under the before noted degree, has the sun at that moment in the zenith.

X. To find how long the sun shines without setting, in any given place in the frigid zones.——Subtract the degrees of latitude of the given place from 90, which gives the complement of the latitude, and count the number of this complement upon the meridian from the equator towards the pole, marking that point of the meridian; then turn the Globe round, and carefully observe what two degrees of the ecliptic pass exactly under the point marked on the meridian. Then look for the same degrees of the ecliptic on the wooden horizon, and just opposite to them stand the months and days of the months corresponding, and between which two days the sun never sets in that latitude.

If the beginning and end of the longest night be required, or the period of time in which the sun never rises at that place; count the same complement of latitude towards the south or farthest pole, and then the rest of the work will be the same in all respects as above.

Note, that this solution is independent of the horizontal refraction of the sun, which raises him rather more than half a degree higher, by that means making the day so much longer, and the night the shorter; therefore in this case, set the mark on the meridian half a degree higher up towards the north pole, than what the complement of latitude gives; then proceed with it as before, and the more exact time and length of the longest day and night will be found.

XI. A place being given in the torrid zone, to find on what two days of the year the sun is vertical at that place.——Turn the Globe about till the given place come to the meridian, and note the degree of the meridian it comes under. Next turn the Globe round again, and note the two points of the ecliptic passing under that degree of the meridian. Lastly, by the wooden horizon, find on what days the sun is in those two points of the ecliptic; and on these days he will be vertical to the given place.

XII. To find those places in the torrid zone to which the sun is vertical on a given day.——Having found the sun's place in the ecliptic, as in the 8th problem, turn the Globe to bring the same point of the ecliptic on the Globe to the meridian; then again turn the Globe round, and note all the places which pass under that point of the meridian; which will be the places sought.

After the same manner may be found what people are Ascii for any given day. And also to what place of the earth, the moon, or any other planet, is vertical on a given day; finding the place of the planet on the globe by means of its right ascension and declination, like finding a place from its longitude and latitude given.

XIII. To rectify the Globe for the latitude of any place. ——By sliding the brass meridian in its groove, elevate the pole as far above the horizon as is equal to the latitude of the place; so for London, raise the north pole 51 1/2 degrees above the wooden horizon: then turn the Globe on its axis till the place, as London, come to the meridian, and there set the index to 12 at noon. Then is the place exactly on the vertex, or top point of the Globe, at 90° every way round from the wooden horizon, which represents the horizon of the place. And if the frame of the Globe be turned about till the compass needle point to 22 1/2 degrees, or two points west of the north point (because the variation of the magnetic needle is nearly 22 1/2 degrees west), so shall the Globe then stand in the exact position of the earth, with its axis pointing to the north pole.

XIV. To find the length of the day or night, or the sun's rising or setting, in any latitude; having the day of the month given.——Rectify the Globe for the latitude of the place; then bring the sun's place on the globe to the meridian, and set the index to 12 at noon, or the upper 12, and then the Globe is in the proper position for noon day. Next turn the Globe about towards the east till the sun's place come just to the wooden horizon, and the index will then point to the hour of sunrise; also turn the Globe as far to the west side, or till the sun's place come just to the horizon on the west side, and then the index will point to the hour of sunset. These being now known, double the hour of setting will be the length of the day, and double the rising will be the length of the night.—And thus also may the length of the longest day, or the shortest day, be found for any latitude.

XV. To find the beginning and end of Twilight on any day of the year, for any latitude.——It is twilight all the time from sunset till the sun is 18° below the horizon, and the same in the morning from the time the sun is 18° below the horizon till the moment of his rise<*> Therefore, rectify the Globe for the latitude of the place, and for noon by setting the index to 12, and screw on the quadrant of altitude. Then take the point of the ecliptic opposite the sun's place, and turn the Globe on its axis westward, as also the quadrant of altitude, till that point cut this quadrant in the 18th degree below the horizon, then the index will shew the time of dawning in the morning; next turn the Globe and quadrant of altitude towards the east, till the said point opposite the sun's place meet this quadrant in the same 18th degree, and then the index will shew the time when twilight ends in the evening.

XVI. At any given day, and hour of the day, to find all those places on the Globe where the sun then rises, on sets, as also where it is noon day, where it is day light, and where it is in darkness.——Find what place the sun is vertical to, at that time; and elevate the Globe according to the latitude of that place, and bring the place also to the meridian; in which state it will also be in the zenith of the Globe. Then is all the upper hemisphere, above the wooden horizon, enlightened, or in day light; while all the lower one, below the horizon, is in darkness, or night: those places by the edge of the meridian, in the upper hemisphere, have noon day, or 12 o'clock; and those by the meridian below, have it midnight: lastly, all those places by the eastern side of the horizon, have the sun just set-| ting, and those by the western horizon have him just rising.

Hence, as in the middle of a lunar eclipse the moon is in that degree of the ecliptic opposite to the sun's place; by the present problem it may be shewn what places of the earth then see the middle of the eclipse, and what the beginning or ending; by using the moon's place instead of the sun's place in the problem.

XVII. To find the bearing of one place from another, and their ang'e of position.——Bring the one place to the zenith, by rectifying the Globe for its latitude, and turning the Globe till that place come to the meridian; then screw the quadrant of altitude upon the meridian at the zenith, and make it revolve till it come to the other place on the Globe; then look on the wooden horizon for the point of the compass, or number of degrees from the fouth, where the quadrant of altitude cuts it, and that will be the bearing of the latter place from the former, or the angle of position sought.

The Celestial Globe differs from the terrestrial only in this; instead of the several parts of the earth, the images of the stars and constellations are designed. The meridian circle drawn through the two poles and through the point Cancer, represents the solstitial colure; but that through the point Arics, represents the equinoctial colure.

Pros. XVIII. To exhibit the true representation of the face of the heavens at any given time and place.—— Rectify for the lat. of the place, by prob. 13, setting the Globe with its pole pointing to the pole of the world, by means of a compass. Find the sun's place in the ecliptic, and turn the Globe to bring it to the meridian, and there set the index to 12 at noon. Again revolve the Globe on its axis, till the index point to the given hour of the day or night: so shall the Globe in this position exactly represent the face of the heavens as it appears at that time, every constellation and star, in the heavens, answering in position to those on the Globe; so that, by examining the Globe, it will immediately appear which stars are above or below the horizon, which on the east or western parts of the heavens, which lately risen, and which going to set, &c. And thus the positions of the sevcral planets, or comets, may also be exhibited; having marked the places of the Globe where they are, by means of their declination and right ascension.

XIX. To find the Declination and Right-ascension of any star upon the Globe.——Turn the Globe till the star come to the meridian: then the number of degrees on the meridian, between the equator and the star, is its declination; and the degree of the equator cut by the meridian, is the right-ascension of the star.——In like manner are found the declination and right-ascension of the sun, or any other point.

XX. To find the Latitude and Longitude of any star drawn upon the Globe.——Bring the solstitial colure to the meridian, and there fix the quadrant of altitude over the pole of the ecliptic in the same hemisphere with the star, and bring its graduated edge to the star: then the degree on the quadrant cut by the star is its latitude, counted from the ecliptic; and the degree of the ecliptic cut by the quadrant its longitude.

XXI. To find the place of a star, planet, comet, &c. on the Globe; its declination and right-ascension being known.——Find the given point of right-ascension on the equinoctial, and bring it to the meridian; then count the degrees of declination upon the meridian from the equinoctial, and there make a mark on the Globe, which will be the place of the planet, &c, sought.

XXII. To find the place of a star, planet, comet, or other object on the Globe; its latitude and longitude being given.——Bring the pole of the ecliptic to the meridian, and there fix the quadrant of altitude, which turn round till its edge cut the given longitude on the ecliptic; then count the given latitude, from the ecliptic, upon the quadrant of altitude, and there make a mark on the Globe, which will be the place of the planet, &c, sought.——The place on the Globe, of any such planet, &c, being found by this or the foregoing problem, its rising, or setting, or any other circumstance concerning it, may then be found, the same as the sun, by the proper problems.

XXIII. To find the rising, setting, and culminating of a star, planet, sun, &c; with its continuance above the horizon, for any place and day; as also its oblique ascension and descension, with its eastern and western amplitude and azimuth.——Adjust the Globe to the state of the heavens at 12 o'clock that day. Bring the star, &c, to the eastern side of the horizon: which will give its eastern amplitude and azimuth, and the time of rising, as for the sun. Again, turn the Globe to bring the same star to the western side of the horizon: so will the western amplitude and azimuth, with the time of setting, be found. Then, the time of rising, subtracted from that of setting, leaves the continuance of the star above the horizon: this continuance above the horizon taken from 24 hours, leaves the time it is below the horizon. Lastly, bring the star to the meridian, and the hour to which the index then points is the time of its culmination, or southing.

XXIV. To find the altitude of the sun, or star, &c, for any given hour of the day or night.——Adjust the Globe to the position of the heavens, and turn it till the index point at the given hour. Then six on the quadrant of altitude, at 90 degrees from the horizon, and turn it to the place of the sun or star: so shall the degrees of the quadrant, intercepted between the horizon and the sun or star, be the altitude sought.

XXV. Given the altitude of the sun by day, or of a star by night, to find the hour of the day or night.——Rectify the Globe as in the foregoing problem; and turn the Globe and quadrant, till such time as the star or degree of the ecliptic the sun is in, cut the quadrant in the given degree of altitude; then will the index point at the hour required.

XXVI. Given the azimuth of the sun or a star, to find the time of the day or night.——Rectify the Globe, and bring the quadrant to the given azimuth in the horizon; then turn the Globe till the sun or star come to the quadrant, and the index will then shew the time of the day or night.