# 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

The surface. | The solidity | |

In the Globe | pd^{2} = cd | 1/<*> pd^{3} |

In the Segt. | pad | 1/6 pa^{2} × ―(3d - 2a) |

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.

*Description of the Globes.*

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.

*The use of the Terrestrial Globe.*

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 Use of the Celcstial Globe.*

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.