The DESCRIPTION and USE of the Celestial and Terrestrial Globes.

Globe or Sphere.

A Globe or Sphere is a round solid body, having every part of its surface equally distant from a point within it, called its Center; and it may be conceived to be formed by the revolution of a semicircle round its diameter.

Great Circle.

Hemispheres.

Any circle passing through the center of the sphere, thereby dividing into two equal parts or segments, is called a Great Circle; and the segments of the sphere so divided, are called Hemispheres.

Every great circle has its Poles and Axis.

Poles.

The Poles of a great circle are two points on the surface of the sphere, diametrically opposite to one another, and every where equally distant from the said circle.

Axis.

The Axis of a circle is a right line passing through the center of the sphere, and through the Poles of the said circle, and is therefore perpendicular to the Plane: Therefore

Secundaries.

All circles passing through the Poles of any great circle, intersect it in two places diametrically opposite, and also at right angles; and with respect to the said great circle, they may be called its Secundaries.

Parallel or lesser Circles.

All circles dividing the sphere into two unequal parts, are called lesser or parallel Circles, and are usually denominated by that great circle to which they are parallel.

Terrestrial Globe.

The Earth being globular, its outward parts, as the several Countries, Seas, &c. are best, and most naturally represented upon the surfaces of a Globe; and when such a body has the outward parts of the Earth and Sea delineated upon its surface, and placed in their natural order and situation, it is called a Terrestrial Globe.

Celestial Globe.

The Celestial Bodies appear to us as if they were all placed in the same concave sphere, therefore astronomers place the Stars according to their respective situations and magnitudes, and also the images of the constellations, upon the external surface of a Globe; for it answers the same purposes as if they were placed within a concave sphere, if we suppose the Globe to be transparent, and the eye placed in the center. A Globe having the Stars placed upon its surface, as above described, is called a Celestial Globe. These Globes are both placed in frames, with other appurtenances, as shall be described in a proper place.

The principal use of the Globes.

The principal uses of the Globes (besides their serving as Maps, to distinguish the outward parts of the Earth, and the situations of the fixed Stars) is to explain and resolve the phænomena arising from the diurnal motion of the Earth round its Axis.

There will be the same prospect of the fixed Stars whether the spectator be placed on the Earth, or in the Sun.

It has been shewed in the Introduction, that the distance of the Earth from the Sun, is no more than a point, when compared with the immense distance of the fixed Stars; therefore let the Earth be in what point soever of her orbit, there will be the same prospect of the Heavens, as a spectator would observe did he reside in the Sun: And if several circles be imagined to pass thro’ the center of the Earth, and others, parallel to them, be conceived to pass thro’ the center of the Sun, these circles in the Heavens will seem to coincide, and to pass exactly thro’ the same Stars. Wherefore as to the appearances of the fixed Stars, it is indifferent whether the Earth or the Sun be made the center of the Universe. But because it is from the Earth that we always observe the celestial bodies, and their apparent motions seem to us to be really made in the Heavens, it is more natural in explaining the phænomena arising from these motions, to place the Earth in the center. And again, because the semidiameter of the Earth, when compared to her distance from the Sun, is of no sensible magnitude, any point, upon the Earth’s surface, let her be in what part soever of the orbit, may be considered as being the center of the Universe. Upon these principles, the different phænomena arising from the diurnal motion of the Earth, and the different situation of a spectator upon its surface, are very naturally illustrated and explained by the Globes.

As to the alterations of seasons, &c. arising from the annual motion of the Earth round the Sun, it is indifferent which we suppose to move, the Earth or the Sun, for in both cases the effect will be the same. Wherefore because it is the Sun that appears to us to move, we say the Sun is in such a part of the ecliptic, without attributing any motion to the Earth, any more than if she had actually been at rest. For the same reason we say the Sun rises, or the Sun sets; by which we mean that he begins to appear or disappear, without considering in the least how these effects are produced. These things are here mentioned, to obviate the objections that might be made by beginners, after they have been told that the Sun stands still.

SECT. I.

An Explanation of the Circles of the Sphere, and of some Astronomical Terms arising therefrom.

The Circles of the Sphere.

In order to determine the relative situations of places upon the Earth, as well as the positions of the fixed Stars, and other Celestial phænomena, the Globe of the Earth is supposed to be environed by several imaginary circles, and these are called the Circles of the Sphere. These imaginary circles are either fixed, and always obtain the same position in the Heavens, or moveable, according to the position of the observer.

Those circles that are fixed, owe their origin to the two-fold motion of the Earth, and are the Equator, and the Ecliptic, with their Secundaries and Parallels. These fixed circles are usually delineated upon the surface of the Globes.

The moveable circles are only the Horizon, its Secundaries and Parallels: These are represented by the wooden frame, and the brass ring, wherein the Globe is hung, and a thin plate of brass to be screwed in a proper place, upon the said ring, as occasion requires.

I. Of the Equinoctial.

The Equator, or Equinoctial.

1. The Equator, or the Equinoctial, is that great circle in the Heavens, in whose plane the Earth performs her diurnal motion round her axis; or it is that great circle, parallel to which the whole Heavens seem to turn round the Earth from East to West in 24 Hours.

Note, The Equator and the Equinoctial are generally synonymous terms; but sometimes the Equator particularly signifies that great circle upon the surface of the Earth, which coincides with the Equinoctial in the Heavens. This circle is also by Mariners commonly called the Line.

Northern and Southern Hemispheres.

The Axis of the World.

Poles of the World, or of the Equator.

The equinoctial divides the globe of the Earth, and also the whole Heavens into two equal parts, North and South, which are called the Northern and Southern Hemispheres. The axis of this circle, is called the Axis of the World, or the Earth’s Axis, because the Earth revolves about it (from West to East) in 24 hours. The extreme of this axis are called the Poles of the World, whereof that which lies in the Northern Hemisphere, is called the North Pole, and the other is called the South Pole. The equinoctial circle is always delineated upon the surface of each globe, with its name at length expressed; the axis of this circle, or the Earth’s axis, is only an imaginary line in the Heavens, but on the globes it is expressed by the wires about which they really turn. The Poles of the world, are the two points upon the surface of the globe through which these wires pass; the North Pole is that which hath the little brass circle, with a moveable index placed round it; and the other opposite to it is the South Pole. The Northern Hemisphere is that wherein the North Pole is placed, and the opposite one is the Southern Hemisphere.

The astronomers divide all circles into 360 equal parts, called Degrees, each degree into 60 equal parts, called Minutes, each minute into 60 Seconds, &c. But besides this division into degrees, the equinoctial is also divided into 24 equal parts, or Hours, each hour into 60 Minutes, each minute into 60 Seconds, &c. so that one hour is equal to 15 degrees, each minute of time is equal to 15 minutes of a degree, &c.

Hour Circles or Circles of Ascension, also called Meridians.

2. All circles conceived to pass through the Poles of the world, intersecting the equinoctial at right angles, are, with respect to any point in the Heavens, called Hour Circles; and the Circles of Ascension, because the ascension of the Heavenly bodies, from a certain point, are by them determined.

These circles are also, with regard to places upon Earth, called Meridians.

The Brass Meridian.

The Meridians are commonly drawn upon the Terrestrial Globe thro’ every 15 degrees of the equinoctial, thereby making an Hour difference betwixt the places through which they pass. On the Celestial Globe there are commonly drawn but two of these Meridians, crossing the equinoctial in four points equidistant from one another, thereby dividing it into four quadrants; but the intermediate ones are here supplied, and also upon the Terrestrial Globe, by the brass circle on which they are hung, which, is therefore called the Brass Meridian, and sometimes only the Meridian, it serving for this purpose to all the points upon either Globe.

The Hour Circle.

There is also a little brass circle fixed upon this meridian, divided into 24 Hours, having an index moveable round the axis of the globe, to be turned to any particular Hour. The use of this circle is to shew the difference of time betwixt any two meridians, and is therefore called the Hour Circle.

Parallels of Declination.

3. All circles parallel to the equinoctial are, with respect to any point in the Heavens, called Parallels of Declination. So that,

Declination North and South.

4. The Declination of any Point in the Heavens (as of the Sun, a fixed Star, or the like) is an arch of the meridian passing through that point, and intercepted betwixt it and the equator; and if the said point be to the (Northward/Southward) of the equator, it is called (North/South) Declination.

Tropics and Polar Circles.

Of the parallels of declination, four are eminently distinguished by particular names, viz. The two Tropics, and the two Polar Circles.

Tropic of Cancer; of Capricorn.

The tropics are on different sides of the equator each 23 degrees and 29 minutes distant from it; that which lies in the Northern Hemisphere, is called the Tropic of Cancer, and the Southern one, the Tropic of Capricorn.

These circles are the limits of the Sun’s greatest declination, and are called tropics, because whenever the Sun arrives to them, he seems to return back again towards the equator.

Arctic Circle. Arctic Pole. Antarctic Circle. Antarctic Pole.

6. The Polar Circles are each of them at the same distance from the Poles of the world, that the tropics are from the equator, viz. 23° 29′. That which lies near the North Pole, is called the Arctic Circle, from Arctos, a constellation situated in the Heavens near that Place; whence also this Pole is sometimes called the Arctic Pole. The other Polar circle, which is situated near the South Pole; is called the Antarctic Circle, because its position is contrary to the other; and the South Pole is sometimes called the Antarctic Pole.

The tropics and the Polar circles have each their names expressed upon the Globes.

II. Of the Ecliptic.

Ecliptic. Equinoctial. Solstitial Points. Colures. Equinoctial Colure. Solstitial Colure.

7. The Ecliptic is that great circle in whose plane the Earth performs its annual motion round the Sun; or, in which the Sun seems to move round the Earth, once in a year. This circle makes an angle with the equinoctial of 23 degrees 29 minutes, and intersects it in two opposite points, which are called the Equinoctial Points; and the two points in the ecliptic that are at the greatest distance from the equinoctial points, are called the Solstitial Points. The two meridians passing through those points, are, by way of eminence, called Colures; whereof that which passeth thro’ the equinoctial points, is called the Equinoctial Colure; and that which is at right angles to it, passing through the Solstitial Points, is called the Solstitial Colure.

The Ecliptic divided into signs.

The ecliptic is divided into 12 equal parts, called Signs, each sign being 30 degrees, beginning from one of the equinoctial points, and numbered from West to East; the names and characters of the twelve signs are as follows, viz.

Aries, Taurus, Gemini, Cancer, Leo, Virgo,

1. ♈ 2. ♉ 3. ♊ 4. ♋ 5. ♌ 6. ♍

Libra, Scorpio, Sagittarius, Capricornus, Aquaries, Pisces.

7. ♎ 8. ♏ 9. ♐ 10. ♑ 11. ♒ 12. ♓

Northern Signs.

The first six of these are called the Northern Signs, and possess that half of the ecliptic which is to the Northward of the equator; beginning with the first point of ♈, and ending with the last point of ♍.

Southern Signs.

The latter six are called the Southern Signs, because they possess the Southern half of the ecliptic; beginning at the first point of ♎, and ending with the last point of ♓.

The division of the ecliptic into signs, and the names of the colures, are particularly expressed upon the globes.

The signs of the ecliptic took their names from 12 constellations mentioned in the Introduction to be situated in the Heavens near those places. It is to be observed, that the signs are not to be confounded with the constellations of the same name: For the Sign of Aries, is not the same with the Constellation Aries; the latter is a system of Stars digested into the figure of a Ram, but the sign of Aries is only 30 degrees of the ecliptic, counted from the equinoctial point ♈, (which is reckoned the first point in the ecliptic) to the beginning of Taurus: Or, it is sometimes taken for all that space upon the Celestial Globe contained between the two circles passing through the first points of ♈ and ♉. What has been here said of Aries, is to be noted of all the rest of the signs.

The constellations above-mentioned were formerly situated within the signs which now bear their names; but by a slow motion of the equinoctial points, being one degree in 72 years, the constellation Aries has now got into the sign ♉, and so of the rest. So that Pisces is now got into the Sign of ♈; this slow motion in the Heavens is called the Precession of the Equinoctial Points.

Poles of the Ecliptic.

The Poles of the Ecliptic are both situated in the Solstitial Colure, at 23 degrees, 29 minutes distance from the Pole of the world; and they take their denomination from the Hemisphere wherein they are placed, viz. that which lies in the (Northern/Southern) Hemisphere, is called the (North/South) Pole of the ecliptic. The arctic and antarctic circles, are described by the Poles of the ecliptic in the diurnal motion of the Earth round its axis, whence it seems these two circles are called Polar.

Circles of Longitude.

8. All great circles passing through the Poles of the ecliptic, and consequently intersecting it at right angles, are called Circles of Longitude: So that,

Longitude of any Point in the Heavens.

Place of a Star.

9. The Longitude of any Point in the Heavens (as a Star or Planet, &c.) is an arch of the ecliptic contained between the circle of longitude passing thro’ that point, and the equinoctial point ♈. And that degree of any sign which lies under the circle of longitude, passing thro’ any Star or Planet, is called the Place of that Star or Planet.

Note, The Sun never goes out of the ecliptic, and it is not usual to say the Sun’s longitude, but we commonly express it the Sun’s Place, which is that sign, degree, minute, &c., of the ecliptic, which he at any time passes.

10. All circles conceived to be drawn parallel to the ecliptic, are called Parallels of Latitude: So that,

Latitude of a Star, &c.

11. The Latitude of any point in the Heavens, (as a fixed Star, &c.) is an arch of the circle of longitude, in passing thro’ that point, and intercepted betwixt it, and the ecliptic; or, the latitude is the distance from the ecliptic; and if the said point be to the Northward of the ecliptic, it is called North Latitude; but if it be to the Southward, is called South Latitude.

Upon the Terrestrial Globe, none of the circles of longitude are described; and upon the Celestial, they are commonly drawn thro’ the beginning of every Sign; but they are all supplied upon both Globes, by fastening a thin plate of brass over one of the Poles of the ecliptic, and so as to be moved to any degree thereof at pleasure. The parallels of latitude are also supplied by the graduations upon the said plate, as shall be shewn in a proper place.

We have now done with all those circles that are fixed, and such as are drawn upon the Globes themselves; we next proceed to the moveable circles.

III. Of the Horizon.

Horizon.

12. The Horizon is that great circle which divides the upper, or visible Hemisphere of the world, from the lower, or invisible: This circle is distinguished into two sorts, the Sensible, and the Rational.

Sensible Horizon.

The Sensible, or Apparent Horizon, is that circle which limits or determinates our prospect, whether we are at land or sea, reaching as far as we can see, or it is that circle where the Sky and the Earth, or Water, seem to meet. When we are on Terra Firma, this circle commonly seems rugged and irregular, occasioned by the unevenness of the ground terminating our prospect; but at sea there are no such irregularities; the semidiameter of this circle varieth according to the height of the eye of the observer; if a man of six feet high stood upon a large plain, or the surface of the sea, he could not see above three miles round.

This circle determines the rising and setting of the Heavenly bodies, and distinguishes Day and Night.

Rational Horizon.

The Rational, or true Horizon, is a great circle passing thro’ the center of the Earth, parallel to the sensible Horizon, being distant from it by the Earth’s semidiameter, which is about 3980 miles: This distance is nothing in comparison of the immense distance of the Sun and the fixed Stars, therefore astronomers make no distinction between these two circles, but consider the apparent Horizon, or that wherein the Sun appears to rise and set, as passing thro’ the center of the Earth.

Cardinal Points of the Horizon.

This circle is divided by astronomers into four quadrants, and each of the quadrants into 90 degrees, &c. The four points quartering this circle are called the Cardinal Points, and are termed the East, West, North, and South. The East is that point of the Horizon where the Sun rises when he is in the equinoctial, or on that day when he ascends above the Horizon exactly at six o’clock; and the West is that point of the Horizon which is directly opposite to the East, or where the Sun Sets when he is in the Equinoctial. The South is 90 degrees distant from the East and West, and is toward that part of the Heavens wherein the Sun always appears to us in Great-Britain at Noon; and the North is that part of the Heavens which is directly opposite to the South: Or, the North and South points of the Heavens may be found by turning yourself either directly towards the East or the West: If you look towards the (East/West) the (South/North) will be to the right Hand, and the (North/South) to the left.

Points of the Compass.

Besides the aforementioned divisions of the Horizon into degrees. Mariners divide it into 32 equal parts, which they call the Points of the Compass; to each of which points they give a particular name, compounded of the four Cardinals, according to what quarter of the Compass is intended.

Zenith.

Nadir.

The center of the Horizon is the place of observation, and the Poles of it are one exactly over our heads, called the Zenith; and the other exactly under our feet, called the Nadir.

Vertical Circles.

Meridian.

Azimuth.

13. All circles conceived to pass thro’ the Zenith and Nadir, are called Vertical Circles, or Azimuths. Of these circles, that which passeth thro’ the North and South points of the Horizon, is called the Meridian; so that when any object is upon the Meridian, it then bears either due South, or due North from us; and the Azimuth of any object is an arch of the Horizon intercepted between the vertical circle passing through it, and either the North or South part of the Meridian; which part is commonly specified.

The meridian passes thro’ the Poles of the world, as well as through the Zenith and Nadir, and therefore is a secundary both of the equinoctial and the horizon: This circle divides the globe into the Eastern and Western Hemispheres, and the Poles of it are the East and West points of the Horizon. All the heavenly objects are, during one half of their continuance above the horizon, in the Eastern Hemisphere, and for the other half in the Western; so that whenever the Sun arrives upon the upper part of the meridian, it is then Noon, or Mid-day, which is the reason why this circle is called the meridian; and when he comes to the lower part, it is then Midnight.

Prime Vertical.

The vertical circle passing thro’ the East and West points of the horizon, is called the Prime Vertical, or Circle of East and West, so that when any object is upon this circle in the Eastern hemisphere, it appears due East; and if it be in the Western hemisphere, it appears due West.

Amplitude.

That degree in the horizon wherein any object rises or sets from the East or West points, is called the Amplitude; which for rising is called Amplitude Ortive, and Occasive for setting; which must be also denominated whether it be Northerly or Southerly.

It may be observed, that the Amplitude and Azimuth are much the same; the amplitude shewing the bearing of any object when he rises or sets, from the East or West points of the horizon; and the azimuth, the bearing of any object when it is above the horizon, either from the North or South point thereof. As for example, if an object rises or sets within 10 degrees of the East or West, suppose towards the South, we accordingly say, its Amplitude is 10 degrees Southerly; but if an object, that is of any height above the horizon, should be in the vertical circle, passing thro’ the before-mentioned point, we then say, its Azimuth is 80 degrees from the South, or 100 degrees from the North, both which expressions signify the same.

Almacanthers. Altitudes. Meridian Altitude. Zenith Distance.

14. All circles drawn parallel to the horizon, in the upper hemisphere, are called Almacanthers, or Parallels of Altitude: So that the Altitude of any point in the Heavens is an arch of the vertical circle passing thro’ that point, and intercepted betwixt it and the horizon; and if the object be upon the meridian, it is commonly called the Meridian Altitude. The complement of the altitude, or what it wants of 90 degrees, is called the Zenith Distance.

The horizon (by which we mean the rational) is represented by the upper surface of the Wooden frame, wherein the globes are placed; upon this horizon are described several concentric circles, the innermost of which is divided into degrees, which ought to be numbered both ways from the East and the West, until they end at 90 degrees in the North and South points. The use of these divisions is to shew the amplitudes of the Sun and Stars, at their rising and setting: Also in some convenient place upon this horizon, there is commonly noted the points of the Compass. Without the before-mentioned circle there is drawn the ecliptic with its divisions, into signs, and degrees, and a circle of months and days: The use of these two circles is to serve as a kalendar to shew the Sun’s place at any time of the year, and by that means to find his place in the Ecliptic, drawn upon the globe itself.

The Vertical Circles, and the Parallels of Altitude, are supplied by a thin plate of brass, having a nut and screw at one end to fasten it to the brass meridian in the Zenith point; which being done, the lower end of it may be put between the globe it self, and the inner edge of the horizon, and so turned round about to any point required.

Quadrant of Altitude.

The fiducial edge thereof representing the Vertical Circles, and the Degrees upon it, describing the Parallels of Altitude. This thin plate is called the Quadrant of Altitude.

The center of the horizon being the place of observation, it is evident that this circle, and all the others belonging to it, are continually changed, which way soever we move; wherefore we may suppose the horizon, with its secundaries and parallels, to invest the globe like a rete or net; and to be moveable every way round it. This is very naturally illustrated by the globes; if we move directly North, or directly South, the change made in the horizon, is represented by moving the brass meridian (keeping the globe from turning about its axis) in the notches made in the wooden horizon, just so much as we travelled. If our course should be due East, or due West, the alterations made thereby are represented by turning the globe accordingly about its axis, the brass meridian being kept fixed; and if we steer betwixt the meridian and the East or West points, then we are to turn the brass meridian, and also the globe about its axis accordingly; the sum of which is, let the spectator be at what point soever of the Earth’s surface, he’ll there gravitate, or tend exactly towards its center, and imagine himself to be on the highest part thereof, (the unevenness of the ground not being here considered) wherefore if we turn the globe in such a manner as to bring the several progressive steps of a traveller successively to the Zenith, we shall then have the successive alterations made in the horizon, in every part of his journey. This explication being well considered, will be of help to young beginners, to conceive how the Earth is every where habitable; and how passengers can travel quite round it; for since every thing tends toward the center of the Earth, we are to conceive that point as being the lowest, and not to carry our idea of downwards any farther. Those that are diametrically opposite to us being as much upon the upper part of the Earth as we are, there being no such thing in nature as one place being higher than another, but as it is at a greater distance from the center of the Earth, let it be in what country soever.

We have now done with all the circles of the sphere, and it may be observed, that the Equinoctial, the Ecliptic, and the Horizon, with their Secundaries and parallels, are all alike; and altering their position, may be made to serve for one another. Thus, if the Poles of the World be brought into the Zenith and Nadir, the Equinoctial will coincide with the Horizon, the Meridians will be the same with the Vertical Circles, and the parallels of Declination will be the parallels of Altitude. After the same manner, if shifting the position, we bring the Ecliptic to coincide with the Horizon, the circles of Longitude will be the Vertical Circles, and the parallels of Latitude and Altitude will coincide.

The horizon and the equator may be either parallel, perpendicular, or oblique to each other.

Parallel Sphere.

15. A Parallel Sphere is that position where the equator coincides with the horizon, and consequently the poles of the world are in the Zenith and Nadir: The inhabitants of this sphere (if there be any) are those who live under the poles of the world.

Right Sphere.

16. A Right or Direct Sphere is that position where the equator is perpendicular to the horizon, the inhabitants whereof are those who live under the equinoctial.

Oblique Sphere.

17. An Oblique Sphere is when the equinoctial and the horizon make oblique angles with each other, which every where happens but under the equator and the poles.

Diurnal and Nocturnal Arch.

The arch of any parallel or declination, which stands above the horizon is called the Diurnal Arch; and the remaining part of it, which is below the horizon, is called the Nocturnal Arch.

That point of the equinoctial which comes to the (Eastern/Western) part of the horizon with any point of the Heavens, is called the (Ascension/Descension) of that point, counted from the beginning of ♈; and if it be in a right sphere, the ascension or descension is called right; but if it be an oblique sphere it is called an oblique ascension or descension. So that,

Right Ascension.

18. The Right Ascension of the Sun, Moon, or any Star, &c. is an arch of the equator contained betwixt the beginning of ♈, and that point of the equinoctial which rises with them in a Right Sphere, or which comes to the meridian with them in an oblique sphere.

Oblique Ascension.

19. Oblique Ascension, or Descension, is an arch of the equinoctial intercepted between the beginning of ♈, and that Point of the Equator which rises or sets with any point in the Heavens in an oblique sphere.

Ascensional Difference.

20. Ascensional Difference, is the difference betwixt the right and oblique ascension or descension, and shews how long the Sun rises or sets before or after the hour of six.

IV. Of the Division of Time.

The parts that time is distinguished into, are Days, Hours, Weeks, Months, and Years.

A Day is either natural or artificial.

Natural and Artificial Day.

A Natural Day is the space of time elapsed while the Sun goes from any meridian or horary circle, ’till he arrives to the same again; or, it is the time contained from noon, or any particular hour, to the next noon, or the same hour again: An Artificial Day is the time betwixt the Sun’s rising and setting; to which is opposed the Night, that is, the time the Sun is hid under the horizon.

Hours, &c.

Equinoxes.

Vernal and Autumnal Equinox.

Solstices.

Summer and Winter Solstices.

The Natural Day is divided into 24 Hours, each hour into 60 Minutes, each minute into 60 Seconds, &c. The Artificial Days are always unequal to all the inhabitants that are not under the equator, except when the Sun is in the equinoctial points ♈ and ♋, which happens (according to our way of reckoning) about the 21st of March, and the 23d of September; at those times the Sun rises at six and sets at six to all the inhabitants of the Earth. These days are called the Equinoxes, or Equinoctial Days; the first of which, or when the Sun is in the first point of Aries, is called the Vernal Equinox, and the latter is called the Autumnal Equinox. In all places where the Sun descends below the horizon, excepting under the equator, the days continually lengthen or shorten, and that faster or slower, according as the Sun is nearer to, or further from the equinoctial, until he arrives to either of the Solstitial Points ♋ or ♑. At those times the Sun seems to stand still for a few days, and then begins to return with a slow motion towards the equinoctial, still hastening his pace as he comes nearer to it: The Sun enters the tropics of ♋ and ♑, about the 21st of June, and the 22d of December, which days are sometimes called the Solstices; the first of which we call the Summer Solstice, and the latter the Winter Solstice.

The different beginning of the day.

All nations do not begin their day, and reckon their hours alike. In Great-Britain. France, and Spain, and in most places in Europe, the days is reckoned to begin at midnight, from whence is counted twelve hours ’till noon, then twelve hours more ’till next midnight, which makes a compleat day; yet the Astronomers (in these countries) commonly begin their day at noon, and so reckon 24 hours ’till next noon, and not twice twelve, according to the vulgar computation.

Babylonish Hours.

Italian Hours.

The Babylonians began their day at Sun-rising, and reckoned 24 hours ’till he rose again! This way of computation we call the Babylonish Hours. In several parts of Germany they count their hours from Sun-setting, calling the first hour after the Sun has set, the first hour, &c. ’till he sets the next day, which they call the 24th hour: These are commonly called the Italian Hours. According to both these ways of computation, their hours are commonly either a little greater or less than the ¹/₂₄ part of a natural day, in proportion as the Sun rises or sets sooner or later in the succeeding days. They have also this inconvenience, that their mid-day and midnight happen on different hours, according to the seasons of the year.

Jewish Hours.

Planetary Hours.

The Jews and the Romans formerly divided the artificial days and nights each into 12 equal parts; these are termed the Jewish Hours, and are of different lengths, according to the seasons of the year; a Jewish Hour in summer being longer than one in winter, and a night-hour shorter. This method of computation is now in use among the Turks, and the hours are stiled the first hour, second hour, &c. of the day or night; so that Mid-day always falls on the sixth hour of the day. These hours are also called Planetary Hours, because in every hour one of the seven Planets were suppose to preside over the World, and so take it by turns. The first hour after Sun-rising on Sunday was allotted to the Sun; the next to Venus, the third to Mercury; and the rest in order to the Moon, Saturn, Jupiter, and Mars. By this means on the first hour of the next day, the Moon presided, and so gave the name to that day; and so seven days by this method had names given them from the Planets that were supposed to govern on the first hour.

A Week.

A Week is a system of seven days, in which each day is distinguished by a different name. In most countries these days are called after the names of the seven Planets, as above noted. All nations that have any notion of religion, lay apart one day in seven for public worship; the day solemnized by Christians is Sunday, or the first day of the week, being that on which our saviour rose from the grave, on which the apostles afterwards used more particularly to assemble together to perform divine worship. The Jews observed Saturday, or the seventh day of the week, for their sabbath, or day of rest, being that appointed in the fourth commandment under the Law. The Turks perform their religious ceremonies on Friday.

A Month.

Periodical and Synodical Month.

A Month is properly a certain space of time measured by the Moon in his course round the Earth. A Lunar Month is either Periodical or Synodical. A Periodical Month is that space of time the Moon takes to perform her course from one point in the ecliptic ’till she arrives to the same again, which is 27 days, and some odd hours; and a Synodical Month is the time betwixt one new Moon, and the next new Moon, which is commonly about 29½ days. But a Civil Month, is different from these, and consists of a certain number of days, fewer or more, according to the laws and customs of the country where they are observed.

A Year Sydereal and Tropical.

The compleatest period of time is a Year, in which all the variety of seasons return, and afterwards begin anew. A Year is either Astronomical or Civil. An Astronomical Year is either a Sydereal wherein the Sun departing from a fixed Star, returns to it again; or Tropical, which is the space of time the Sun takes to perform his course from any point of the ecliptic, ’till he returns to it again.

A Tropical Year consists of 365 days, 5 hours, and 49 minutes; this is the time in which all the seasons compleatly returns, which is a small matter less than a Sydereal Year.

Egyptian Year.

The Civil Year is the same with the Political established with the laws of a country; and is either moveable or immoveable. The moveable year consists of 365 days, being less than the tropical year by almost six hours, and is called the Egyptian Year, because observed in that Country.

The Romans divided the year into 12 kalendar months, to which they gave particular names, and are still retained by most of the European nations, viz. January, February, March, April, May, June, July, August, September, October, November, and December. The number of days in each month may be known by the following verses:

The year is also divided into four quarters or seasons, viz. Spring, Summer, Autumn, and Winter. These quarters are properly made when the Sun enters into the equinoctial and solstitial points of the ecliptic; but in civil uses they are differently reckoned, according to the customs of several countries. In England, we commonly reckon the first day of January to be the first in the year, which is therefore vulgarly called New-Year’s-Day; but in political and ecclesiastical affairs, the year is reckoned to commence on Lady-day which is the 25th of March; and from thence to Midsummer-day, which is the 24th of June, is reckoned the first quarter; from Midsummer-day to Michaelmas-day, which is the 29th of September, is the second quarter; the third quarter is reckoned from Michaelmas-day to Christmas-day, which is the 25th of December; and from Christmas-day to Lady-day, is reckoned the last quarter in the year. In common affairs, a quarter is reckoned from a certain day to the same in the fourth month following. Sometimes a month is reckoned four weeks, or 28 days, and so a quarter 12 weeks. To all the inhabitants in the (Northern/Southern) Hemisphere, their Midsummer is properly when the Sun is in the tropic of (Cancer,/Capricorn,) and their Midwinter at the opposite time of the year; but those who live under the equinoctial have two winters, &c. when the Sun is in either tropic; tho’ indeed properly, there is no season that may be called winter in those parts of the world.

Bissextile, or Leap-Year.

The Egyptian year of 365 days being less than the true solar year, by almost six hours, it follows, that four such years are less than four solar years by a whole day; and therefore in 365 times four years, that is, in 1460 years, the beginning of the years move through all the seasons. To remedy this inconveniency, Julius Cæsar (considering that the six hours, which remain at the end of every year, will in four years make a natural day) ordered that every fourth year should have an intercalary day, which therefore consists of 366 days; the day added was put in the month of February, by postponing St. Matthias’s day, which in common years fall on the 24th, to the 25th of the said month, all the fixed feasts in the year from thenceforwards falling a week-day later than otherwise they would. According to the Roman way of reckoning, the 24th of February was the sixth of the kalends of March, and it was ordered that for this year there should be two sixths, or that the sixth of the kalends of March should be twice repeated; upon which account the year was called Bissextile, which we now call the Leap-Year.

To find whether the year of our Lord be leap-year, or the first, second, or third after; divide it by four, and the remainder, if there be any, shews how many years it is after leap-year; but if there be no remainder, then that year is leap-year: Or, you may omit the hundreds and scores, and divide the residue by 4, Examp. 1757, omitting the hundreds and the twenties, I divide the residue 17, by 4, and the remainder 1, shews it to be the first after leap-year.

Julian Account or the Old Style.

This method of reckoning the year, viz. making the common year to consist of 365 days, and every fourth year to have 366 days, is now used in Great-Britain and Ireland, and some of the Northern parts of Europe, and is called the Julian Account, or the Old Style. But the time appointed by Julius Cæsar for the length of a solar year is too much; for the Sun finishes his course in the ecliptic, in 365 days, 5 hours, and 49 minutes, which is 11 minutes less than the civil year; and therefore he again begins his circuit 11 minutes before the civil year is ended; and so much being gained every year, amounts in 131 years, to a whole day. So that if the Sun in any year entered the equinox upon the 20th of March at noon, after the space of 131 years, he’ll enter the same point on the same hour, on the 19th of March. And therefore the exquinoxes will not always fall on the same day of the month, but by degrees will move towards the beginning of the year.

Gregorian Account, or New Style.

At the time of the Council of Nice, when the terms were settled for observing of Easter, the Vernal Equinox fell upon the 21st of March; but by its falling backwards 11 minutes every year, it was found that in Anno 1582, when the kalendar was corrected, the Sun entered the equinoctial circle on the 11th of March, having departed ten whole days from its former place in the year: and therefore Pope Gregory the XIIIth, designing to place the equinoxes in their situation with respect to the year, took these ten days out of the kalendar, and ordered that the 11th of March should be reckoned as the twenty-first: And to prevent the seasons of the year from going backwards for the future, he ordered every hundredth year, which in Julian form was to be a Bissextile, should be a common year, and consist only of 365 days; but that being too much, every fourth hundred was to remain Bissextile. This form of reckoning being established by the authority of Pope Gregory XIII. is called the Gregorian Account, or the New Style; and is observed in all the countries where the authority of the Pope is acknowledged, and likewise by several nations of the reformed religion. There being now above an hundred years past, since the reformation was made in the kalendar, the Gregorian account has accordingly got before the Julian one day more than it was in the time of its institution, the difference between these two accounts being now eleven days; so that the first day of any month, according to that way of reckoning, is the 12th of the same month, according to the New Style.

I shall conclude this section with a brief account of the Atmosphere.

Atmosphere.

The Atmosphere is that thin body of air which surrounds the Earth, in which the clouds hover, and by which in their descent they are broke into drops of rain; which sometimes, according to the warmth or coldness of air, are froze into Snow, or Hailstones. Thunder and Lightning are also made in the Atmosphere, and wind is nothing else but a percussion of the air, occasioned by its different density in different places. The benefits we receive from the atmosphere are innumerable; without air no earthly creature could live, as is plainly proved by experiments made by the Air-Pump; and the wholsomeness of a climate chiefly depends upon that of its air: If there was no atmosphere to reflect the rays of the Sun, no part of the heavens would be lucid and bright, but that wherein the Sun was placed; and if a spectator should turn his back towards the Sun, he would immediately perceive it to be quite dark, and the least Stars would be seen shining as they do in the clearest night; and the Sun immediately before his setting would shine as brisk as at noon, but in a moment, as soon as he got below the horizon, the whole hemisphere of the Earth would be involved in as great a darkness as if it were midnight.

But by means of the atmosphere it happens, that while the Sun is above the horizon, the whole face of the heavens is strongly illuminated by its rays, so as to obscure the faint light of the Stars, and render them invisible; and after Sun-setting, though we receive no direct light from him, yet we enjoy its reflected light for some time: For the atmosphere being higher than we are, is a longer time before it is withdrawn from the Sun (as if a man was to run to the top of a steeple, he might see the Sun after it had been set to those at the bottom.) The rays which the atmosphere receives from the Sun, after he is withdrawn from our sight, are by refraction faintly transmitted to us; until the Sun having got about 18 degrees below the horizon, he no longer enlightens our atmosphere, and then all that part thereof which is over us becomes dark. After the same manner in the morning, when the Sun comes within 18 degrees of our horizon, he again begins to enlighten the atmosphere, and so more and more by degrees, until he rises and makes full day.

Twilight, or Crepusculum.

This small illumination of the atmosphere, and the state of the Heavens between day and night, is called the Twilight, or the Crepusculum.

The duration of twilight is different in different climates, and in the same place at different times of the year. The beginning or ending of twilight being accurately given, we may from thence easily find the height of the atmosphere, which is not always the same. The mean height of the atmosphere is computed to be about 40 miles; but it is probable, the air may extend itself a great deal further, there being properly no other limits to it, as we can conceive, but as it continually decreases in density the farther remote it is from the Earth, in a certain ratio; which at last, as to our conception, must in a manner terminate.

SECT. II.

Geographical Definitions.

Of the Situations of Places upon the Earth; of the different Situations of its Inhabitants; of Zones and Climates.

The situations of places upon the Earth, are determined by their Latitude and Longitude.

Latitude.

1. The Latitude of any place (upon the Earth) is its nearest distance, either North or South from the Equator; and if the place be in the (Northern/Southern) hemisphere, it is accordingly called (North/South) Latitude; and is measured by an arch of the meridian intercepted betwixt the zenith of the said place, and the equator. And all places that lie on the same side, and at the same distance from the equator, are said to be in the same parallel of latitude: the parallels in Geography, being the same with the parallels of declination in Astronomy.

From this definition arise the following Corollaries.

(1.) That no place can have above 90 degrees of latitude, either North or South.

(2.) Those places that lie under the equinoctial (or thro’ which the equator passes) have no latitude, it being from thence that the calculation of latitudes is counted; and those places that lie under the Poles have the greatest latitude, those points being at the greatest distance from the equator.

(3.) The latitude of any place is always equal to the elevation of the Pole in the same place above the horizon; and is therefore often expressed by the Pole’s height, or elevation of the Pole; the reason of which is, because from the equator to the Pole there is always the distance of 90 degrees, and from the zenith to the horizon the same number of degrees, each of these including the distance from the zenith to the Pole: That distance therefore being taken away from both, will leave the distance from the zenith to the equator, (which is the latitude) equal to the distance of the Pole to the horizon.

(4.) The elevation of the equator in any place is always equal to the complement of the latitude of the same place.

(5.) A ship sailed directly (towards/from) the equator (lessens/augments) her latitude, (or (depresses/raises) the Pole) just so much as is her distance sailed.

Difference of Latitude.

2. Difference of latitude is the nearest distance betwixt any two parallels of latitude, shewing how far the one is to the Northward or Southward of the other, which can never exceed 180 degrees. And when the two places are in the same hemisphere (or on the same side of the equator) the lesser latitude subtracted from the greater, and when they are on different sides of the equator, the two latitudes added, gives the difference of latitude.

Longitude.

3. The Longitude of any place (upon the Earth) is an arch of the equator, contained betwixt the meridian of the given place, and some fixed or known meridian; or, it is equal to the angle formed by the two meridians, which properly can never exceed 180 degrees, tho’ sometimes the Longitude is counted Easterly quite round the globe.

Since the meridians are all moveable, and not one that can be fixed in the heavens, (as the equinoctial circle is fixed, from whence the latitudes of all places are determined to be so much either North or South) the longitudes of places cannot so well be fixed from any other meridian, but every Geographer is at his liberty to make which he pleases his first meridian, from whence to calculate the longitudes of other places. Hence it is that geographers of different nations reckon their longitudes from different meridians, commonly choosing the meridian passing through the metropolis of their own country for their first: Thus, the English geographers generally make the meridian of London to be their first, the French that of Paris, and the Dutch that of Amsterdam, &c. and mariners generally reckon the longitude from the last known land they saw. This arbitrary way of reckoning the longitude from different places, makes it necessary, whenever we express the longitude of any place, that the place from whence it is counted be also expressed.

From the preceding definitions arise the following corollaries:

1. If a body should steer directly North, or directly South, quite round the globe, he’ll continually change his latitude; and pass through the two Poles of the world, without deviating the least from the meridian of the place he departed from; and consequently on his return will not differ in his account of time from the people residing in the said place.

2. If a body should steer round the globe either due East, or due West, he’ll continually change his longitude, but will go quite round without altering his latitude; and if his course should be due East, he’ll gain a day compleatly in his reckoning, or reckon one day more than the inhabitants of the place from whence he departed; or if his course had been West, he would have lost one day, or reckon one less.

The reason of which is evident; for admitting our traveller steers due East; so many miles in one day as to make his difference of longitude equivalent to a quarter of an hour of time, it is evident that the next day the Sun will rise to him a quarter of an hour sooner than to the inhabitants of the place from whence he departed; and so daily, in proportion to the rate he travels, which in going quite round, will make up one natural day. In like manner, if he steers due West after the same rate, he’ll lengthen each day a quarter of an hour, and consequently the Sun will rise to him so much later every day; by which means, in going quite round, he’ll lose one day compleat in his reckoning. From whence it follows,

3. If two bodies should set out from the same place, one steering East, and the other West, and so continue their courses quite round, until they arrive at the place from whence they set out, they’ll differ two days in their reckoning at the time of their return.

4. If a body should steer upon an oblique course (or any where betwixt the meridian and the East or West points) he’ll continually change both latitude and longitude, and that more or less, according to the course he steers; and if he should go quite round the globe, he’ll differ in his account of time, as by the second Corol.

5. The people residing in the Easternmost of any two places, will reckon their time so much the sooner than those who live in the other place, according to the difference of longitude betwixt the two places, allowing one hour for every 15 degrees, &c. and the contrary.

II. Of Zones and Climates, &c.

Zones, Torrid, Temperate, and Frigid.

4. Zones are large tracts of the surface of the Earth, distinguished by the tropics and polar circles, being five in number; viz. one Torrid, two Temperate and two Frigid.

The Torrid, or Burning Zone, is all the space comprehended between the two tropics; the ancients imagined this tract of the Earth to be uninhabitable, because of the excessive heat, it being so near the Sun. All the inhabitants of the torrid zone have the Sun in their zenith, or exactly over their heads twice in every year; excepting those who live exactly under the two tropics, where the Sun comes to their zenith only once in a year.

The two Temperate Zones lie on either side of the globe, between the tropics and the polar circles.

The two Frigid Zones are those spaces upon the globe that are included between the two polar circles.

Amphiscians. Ascians.

The inhabitants of the Earth are also distinguished by the diversity of their Shadows. Those who live in the torrid zone, are called Amphiscians, because their noon-shadow is cast different ways, according as the Sun is to the northward or southward of their zenith; but when the Sun is in their zenith, they are called Ascians.

Heteroscians. Ascians Heteroscians.

Periscians.

The inhabitants of the temperate zones, are called Heteroscians, because their noon-shadow is always cast the same way: But those who live under the tropics are called Ascians Heteroscians; those who live in the frigid zones are called Periscians, because sometimes their shadow is cast round about them.

These hard names are only Greek words, importing how the Sun casts the shadow of the several inhabitants of the Earth; which would be a too trifling distinction to be made here, was it not for the sake of complying with custom.

The inhabitants of the Earth are also distinguished into three sorts, in respect to their relative situation to one another, and these are called the Periœci, Antœci, and Antipodes.

Periœci.

5. The Periœci are those who live under opposite points of the same parallel of latitude. They have their seasons of the year at the same time, and their days and nights always of the same length with one another, but the one’s Noon is the other’s Midnight; and when the Sun is in the equinoctial, he rises with the one, when he sets with the other. Those who live under the Poles have no Periœci.

Antœci.

6. The Antœci live under the same meridian, and in the same latitude, but on different sides of the equator; their Seasons of the year are contrary, and the days of the one are equal to the nights of the other, but the hour of the day and night is the same with both; and when the Sun is in the equinoctial, he rises and sets to both exactly at the same time. Those who live under the equator have no Antœci.

Antipodes.

7. The Antipodes are those who live diametrically opposite to one another, standing, as it were, exactly feet to feet: Their days and nights, summer and winter, are at direct contrary times.

The surface of the Earth is by some distinguished into Climates.

Climates.

8. A Climate is a tract of the surface of the Earth, included between two such parallels of latitude, that the length of the longest day in the one exceeds that in the other by half an hour.

The whole surface of the Earth is considered, as being divided into 60 climates, viz. from the equator to each of the polar circles 24, arising from the difference of ½ hour in the length of their longest days; and from the polar circles to the Poles themselves, are six, arising from the difference of an entire month, the Sun being seen in the first of these a whole month without setting; in the second two; and in the third, three months, &c. These climates continually decrease in breadth, the farther they are from the equator. How they are framed, viz. the parallel of latitude in which they end (that being likewise the beginning of the next) with the respective breadth of each of them, is shewed in the following table:

A TABLE of the Climates.

Climates

between the Equator and the Polar Circles.

Climates Longest Latitude. Breadth

Day. D. M. D. M.

1 12½ 8 25 8 25

2 13 16 25 8 00

3 13½ 23 50 7 25

4 14 30 25 6 30

5 14½ 36 28 6 8

6 15 41 22 4 54

7 15½ 45 29 4 7

8 16 49 1 3 32

9 16½ 51 58 2 57

10 17 54 27 2 29

11 17½ 56 37 2 10

12 18 58 29 1 52

13 18½ 59 58 1 29

14 19 61 18 1 20

15 19½ 62 25 1 7

16 20 63 22 0 57

17 20½ 64 6 0 44

18 21 64 49 0 43

19 21½ 65 21 0 32

20 22 65 47 0 26

21 22½ 66 6 0 19

22 23 66 20 0 14

23 23½ 66 28 0 8

24 24 66 31 0 3

Climates

between the Polar Circles and the Poles.

Length of Days. Latitude.

Months. D. M.

1 67 21

2 69 48

3 73 37

4 78 30

5 84 5

6 00 00

III. Of the Poetical rising and setting of the Stars.

Cosmical, Acronical, and Heliacal rising and setting.

The ancient Poets make frequent mention of the Stars rising and setting, either Cosmically, Acronically, or Heliacally; whence these distinctions are called Poetical.

A Star is said to rise or set Cosmically, when it rises or sets at Sun-rising; and when it rises or sets at Sun-setting, it is said to rise or set Acronically. A Star rises Heliacally, when first it becomes visible, after it had been so near the Sun as to be hid by the splendor of his rays: And a Star is said to set Heliacally, when it is first immersed, or hid by the Sun’s rays.

The Fixed Stars, and the three superior Planets, Mars, Jupiter, and Saturn, rise Heliacally in the morning; but the Moon rises Heliacally in the evening, because the Sun is swifter than the superior Planets, and slower than the Moon.

IV. Of the surface of the Earth, considered as it is composed of Land and Water.

The Earth consists naturally of two parts, Land and Water, and therefore it is called the Terraqueous Globe. Each of these elements is subdivided into various forms and parts, which accordingly are distinguished by different names.

I. Of the Land.

The land is distinguished into Continents, Islands, Peninsula’s, Isthmus’s, Promontories, Mountains, or Coasts.

Continent. Main Land.

9. A Continent is a large quantity of land, in which many great countries are joined together, without being separated from each other by the sea: such are Europe, Asia, Africa, and the vast continent of America; which four are the principal divisions of the Earth. A continent is sometimes called the Main Land.

Island.

10. An Island is a country, or portion of land, environed round with water: such are Great-Britain and Ireland; Sardinia, Sicily, &c. in the Mediterranean Sea; the Isles of Wight, Anglesey, &c. near England. Also a small part of dry land, in the midst of a river, is called an island, when compared to a lesser, is called the continent; as if we compare the Isle of Wight to England, the latter may be properly called the continent.

Peninsula.

11. A Peninsula is a part of land almost environed with water, save one narrow neck adjoining it to the continent; or which is almost an island: such is Denmark joining to Germany; also Africa is properly a large peninsula joining to Asia.

Isthmus.

12. An Isthmus is a narrow neck of land joining a peninsula to the continent; as the Isthmus of Sues, which joins Africa to Asia, that of Panama, joining North and South America, &c.

Promontory. Mountain.

13. A Promontory is a high part of land stretching out into the sea, and is often called a Cape or Headland: such is the Cape of Good Hope in the South of Africa; Cape Finistre on the West of Spain; also the Lizard Point, and the Land’s End, are two Capes or Headlands on the West of England. A Mountain is a high part of land in the midst of a country, over topping the adjacent parts.

A Coast or Shore. Inland.

14. A Coast or Shore is that part of land which borders upon the sea, whether it be in islands or a continent: And that part of the land which is far distant from the sea, is called the Inland Country. These are the usual distinctions of the land.

The Water is distinguished into Oceans, Seas, Lakes, Gulfs, Straits, and Rivers.

The Ocean, or Main Sea.

15. The Ocean, or Main Sea, is a vast spreading collection of water, not divided or separated by lands running between; such is the Atlantic or Western Ocean; between Europe and America; the Pacific Ocean, or South Sea, &c.

Note, Those parts of the ocean which border upon the land, are called by various names, according to those of the adjacent countries; as, the British Sea, the Irish Sea, the French and Spanish Sea.

A Lake.

16. A Lake is a collection of deep standing water, inclosed all round with land, and not having any visible and open communication with the sea: But when this lake is very large, it is commonly called a sea; as the Caspian Sea in Asia, &c.

A Gulf. Creek or Haven.

17. A Gulf is a part of the sea almost encompassed with land, or that which runs up a great way into the land; as, the Gulf of Venice, &c. But if it be very large, ’tis rather called an Inland Sea; as the Baltic Sea, the Mediterranean Sea, the Red Sea, or the Arabian Gulf, &c. And a small part of sea thus environed with land is usually called a Bay. If it be but a very small Part, or, as it were, a small arm of the sea, that runs but a few miles between the land, it is called a Creek or Haven.

A Strait.

18. A Strait is a narrow passage lying between two shores, whereby two seas are joined together; as, the Straits of Dover, between the British Channel and the German Sea; the Straits of Gibralter, between the Atlantic and the Mediterranean Sea. The Mediterranean itself is also sometimes called the Straits.

These are all the necessary terms commonly used in Geography. The names of the several countries and seas, and all the principal divisions of the Earth, the reader will find expressed upon the Terrestrial Globes. To give a tolerable account of the produce of each country, the genius of the people, their political institutions, &c. is properly a particular subject of itself, and quite foreign to our design. We shall next proceed to the use of the Globes; but first it may not be amiss to take a short review of their appurtenances.

Those circles of the sphere that are fixed, are (as has been already said) drawn upon the Globes themselves; those that are moveable, are supplied by the Brass Meridian, the Wooden Horizon, and the Quadrant of Altitude.

Brass Meridian.

1. That side of the Brazen Meridian, which is divided into degrees, represents the true Meridian; this side is commonly turned towards the East, and ’tis usual to place the globe so before you, that the North be to the right hand, and the South to the left. The meridian is divided into 4 quadrants, each being 90 degrees, two of which are numbered from that part of the equinoctial, which is above the horizon, towards each of the Poles; the other two quadrants are numbered from the Poles towards the equator. The reason why two quadrants of the meridian are numbered from the equator, and the other two from the Poles, is because the former of these two serve to shew the distance of any point on the globe from the equator, and the other to elevate the globe to the latitude of the place.

Wooden Horizon.

2. The upper side of the wooden frame called the Wooden Horizon; represents the true horizon; the circles drawn upon this plane have been already described; we may observe, that the first point of ♈ is the East, and the opposite being the first point of ♎ is the West, the meridian passing through the North and South points.

Quadrant of Altitude.

3. The Quadrant of Altitude is a flexible plate of thin brass, having a nut and screw at one end, to be fastened to the meridian of either globe, as occasion requires. The edge of this quadrant which has the graduations upon it, called the fiducial edge, is that which is always meant whenever we make mention of the quadrant of altitude.

Hour Circle.

4. The Horary or Hour Circle, is divided into twice twelve hours, the two XII’s coinciding with the meridian; the uppermost XII is that at Noon, and the lowermost towards the horizon is XII at Night. The hours on the East side of the meridian are the Morning Hours, and those on the West side the Hours after Noon. The axis of the globe carries round the Hand or Index which points the hour, and passes through the center of the hour circle.

The things above described are common to both globes; but there are some others which are peculiar or proper to one sort of globe. The two Colures, and the Circles of Latitude from the ecliptic, belong only to the Celestial Globes; also the ecliptic itself does properly belong only to this globe, tho’ it is always drawn on the Terrestrial, for the sake of those that might not have the other globe by them. The equinoctial on the celestial globe is always numbered into 360 degrees, beginning at the equinoctial point ♈; but on the terrestrial, it is arbitrary, where these numbers commence, according to the meridian of what place you intend for your first; and the degrees may be counted either quite round to 360, or both ways, ’till they meet in the opposite part of the meridian, at 180.

SECT. III.

The USE of the Globes.

Problem I. To find the Latitude and Longitude of any given Place upon the Globe; and on the contrary, the Latitude and Longitude being given, to find the Place.

1.

Turn the globe round its axis, ’till the given place lies exactly under the (Eastern side of the brass) meridian, then that degree upon the meridian, which is directly over it, is the Latitude; which is accordingly North or South, as it lies in the Northern or Southern hemisphere, the globe remaining in the same position.

That degree upon the equator which is cut by the brazen meridian, is the Longitude required from the first meridian upon the globe. If the longitude is counted both ways from the first meridian upon the globe, then we are to consider, whether the given place lies Easterly or Westerly from the first meridian, and the longitude must be expressed accordingly.

The Latitudes of the following places: and upon a globe where the longitude is reckoned both ways from the meridian of London, their longitudes will be found as follow:

Latitude. Deg. Longitude. Deg.

Rome 41¾ North. 13 East.

Paris 48¾ N. 2½ E.

Mexico 20 N. 102 W.

Cape Horn 58 S. 80 W.

2. The Latitude and Longitude being given to find the Place.

Seek for the given longitude in the equator, and bring that point to the meridian; then count from the equator on the meridian the degree of latitude given, towards the arctic and antarctic Pole, according as the latitude is Northerly or Southerly, and under that degree of latitude lies the Place required.

Prob. II. To find the Difference of Latitude betwixt any two given Places.

Bring each of the places proposed successively to the meridian, and observe where they intersect it, then the number of degrees upon the meridian, contained between the two intersections, will be the Difference of Latitude required. Or, if the places proposed are on the same side of the equator, having first found their latitudes, subtract the lesser from the greater; but if they are on contrary sides of the equator, add them both together, and the difference in the first case, and the sum in the latter, will be the difference of latitude required.

Thus the difference of latitude betwixt London and Rome will be found to be 9¾ degrees; betwixt Paris and Cape Bona Esperance 83 degrees.

Prob. III. To find the Difference of Longitude betwixt any two given Places.

Bring each of the given places successively to the meridian, and see where the meridian cuts the equator each time; the number of degrees contained betwixt those two points, if it be less than 180 degrees, otherwise the remainder to 360 degrees, will be the difference of longitude required. Or,

Having brought one of the given places to the meridian, bring the index of the hour circle to 12 o’clock; then having brought the other place to the meridian, the number of hours contained between the place the index was first set at, and the place where it now points, is the difference of longitude in time betwixt the two places.

Thus the difference of longitude betwixt Rome and Constantinople will be found to be 19 degrees, or 1 hour and a quarter; betwixt Mexico and Pekin in China, 240 degrees, or 9⅓ hours.

Prob. IV. Any Place being given to find all those Places that are in the same Latitude with the same Place.

The latitude of any given place being marked upon the meridian, turn the globe round its axis, and all those places that pass under the same mark are in the same latitude with the given place, and have their days and nights of equal lengths. And when any place is brought to the meridian, all the inhabitants that lie under the upper semicircle of it, have their Noon or mid-day at the same point of absolute time exactly.

Prob. V. The day of the Month being given; to find the Sun’s Place in the Ecliptic, and his Declination.

1. To find the Sun’s Place: Look for the day of the month given in the kalendar of months upon the horizon, and right against it you’ll find that sign and degree of the ecliptic which the Sun is in. The Sun’s place being thus found, look for the same in the ecliptic line which is drawn upon the globe, and bring that point to the meridian, then that degree of the meridian, which is directly over the Sun’s place, is the Declination required; which is accordingly either North or South, as the Sun is in the Northern or Southern signs. Thus,

Sun’s Place. Declination.

Deg. Min. Deg. Min.

April 23 ♉ 3 00 12 32 N.

July 31 ♌ 7 51 18 20 N.

October 26 ♏ 2 49 12 28 S.

January 20 ♒ 0 49 20 07 S.

Prob. VI. To rectify the Globe for the Latitude, Zenith, and the Sun’s Place.

1. For the Latitude: If the place be in the Northern hemisphere, raise the arctic Pole above the horizon; but for the South latitude you must raise the antarctic; then move the meridian up and down in the notches, until the degrees of the latitude counted upon the meridian below the Pole, cuts the horizon, and the globe is adjusted to the latitude.

2. To rectify the Globe for the Zenith: Having elevated the globe according to the latitude, count the degrees thereof upon the meridian from the equator, towards the elevated Pole, and that point will be the zenith or the vertex of the place; to this point of the meridian fasten the quadrant of altitude, so that the graduated edge thereof may be joined to the said point.

3. Bring the Sun’s place in the ecliptic to the meridian, and then set the hour index to XII at Noon, and the globe will be rectified to the Sun’s Place. If you have a little mariner’s compass, the meridian of the globe may be easily set to the meridian of the place.

Prob. VII. To find the Distance between any two given places upon the Globe, and to find all those places upon the globe that are at the same distance from a given place.

Lay the quadrant of altitude over both the places, and the number of degrees intercepted between them being reduced into miles, will be the distance required: Or, you may take the distance betwixt the two places with a pair of compasses, and applying that extent to the equator, you’ll have the degrees of distance as before.

Note, A geographical mile is the ¹/₆₀th part of a degree; whereof if you multiply the number of degrees by 60, the product will be the number of geographical miles of distance sought; but to reduce the same into English miles, you must multiply by 70, because about 70 English miles make a degree of a great circle upon the superficies of the Earth.

Thus, the distance betwixt London and Rome will be found to be about 13 degrees, which is 780 geographical miles.

If you rectify the globe for the latitude and zenith of any given place, and bring the said place to the meridian; then turning the quadrant of altitude about, all those places that are cut by the same point of it, are at the same distance from the given place.

Prob. VIII. To find the angle of position of Places, or the angle formed by the meridian of one Place, and a great circle passing through both the Places.

Having rectified the globe for the latitude and zenith of one of the given places, bring the said place to the meridian, then turn the quadrant of altitude about, until the fiducial edge thereof cuts the other place, and the number of degrees upon the horizon, contained between the said edge and the meridian, will be the angle of position sought.

Thus, the angle of position at the Lizard, between the meridian of the Lizard and the great circle, passing from thence to Barbadoes is 69 degrees South-Westerly; but the angle of position between the same places at Barbadoes, is but 38 degrees North-Easterly.

SCHOLIUM

The angle of position between two places is a different thing from what is meant by the bearings of places; the Bearings of two places is determined by a sort of spiral line, called a Rhumb Line, passing between them in such a manner, as to make the same or equal angles with all the meridians through which it passeth; but the angle or position is the very same thing with what we call the azimuth in astronomy, both being formed by the meridian and a great circle passing thro’ the zenith of a given place in the heavens, then called the azimuth, or upon the Earth, then called the angle of position.

From hence may be shewed the error of that geographical paradox, viz. If a place A bears from another B due West, B shall not bear from A due East. I find this paradox vindicated by an author, who at the same time gives a true definition of a rhumb line: But his arguments are ungeometrical; for if it be admitted that the East and West lines make the same angles with all the meridians through which they pass, it will follow that these lines are the parallels of latitude: For any parallel of latitude is the continuation of the surface of a Cone, whose sides are the radii of the sphere, and circumference of its base the said parallel; and it is evident, that all the meridians cut the said surface at right (and therefore at equal) angles; whence it follows, that the rhumbs of East and West are the parallels of latitude, though the case may seem different, when we draw inclining lines (like meridians) upon paper, without carrying our ideas any farther.

Prob. IX. To find the Antœci, Periœci, and Antipodes to any given place.

Bring the given place to the meridian; and having found its latitude, count the same number of degrees on the meridian from the equator towards the contrary Pole, and that will give the place of the Antœci. The globe being still in the same position, set the hour index to XII at noon, then turn the globe about ’till the index points to the lower XII; the place which then lies under the meridian, having the same latitude with the given place, is the Periœci required. As the globe now stands, the Antipodes of the given place are under the same point of the meridian, that its Antœci stood before: Or, if you reckon 180 degrees upon the meridian from the given place, that point will be the Antipodes. Let the given place be London, in the latitude of 51½ degrees North, that place which lies under the same meridian and the latitude 51½ degrees South, is the Antœci; that which lies in the same parallel with London, and 180 degrees of longitude from it, is the Periœci, and the Antipodes is the place whose longitude from London is 180 degrees, and latitude 51½ degrees South.

Prob. X. The Hour of the Day at one place being given; to find the correspondent Hour (or what o’Clock it is at that time) in any other place.

The difference of time betwixt two places is the same with their difference of longitude; wherefore having found their difference of longitude, reduced into time (by allowing one hour for every 15 degrees, &c.) and if the place where the hour is required lies (Easterly/Westerly) from the place where the hour is given, (add/subtract) the difference of longitude reduced into time (to/from) the hour given; and the sum or remainder will accordingly be the hour required. Or,

Having brought the place at which the hour is given to the meridian, set the hour index to the given hour; then turn the globe about until the place where the hour is required comes to the meridian, and the index will point out the hour at the said place.

Thus when it is Noon at London, it is

H. M.

At Rome 0 52 P. M.

Constantinople 2 07 P. M.

Vera-Cruz 5 30 A. M.

Pekin in China 7 50 P. M.

Prob. XI. The Day of the Month being given, to find those places on the globe where the Sun will be Vertical, or in the Zenith, that day.

Having found the Sun’s place in the ecliptic, bring the same to the meridian, and note the degree over it; then turning the globe round, all places that pass under that degree will have the Sun vertical that day.

Prob. XII. A place being given in the Torrid Zone, to find those two Days in which the Sun shall be Vertical to the same.

Bring the given place to the meridian, and mark what degree of latitude is exactly over it; then turning the globe about its axis, those two points of the ecliptic, which pass exactly under the said mark, are the Sun’s place; against which, upon the wooden horizon, you’ll have the days required.

Prob. XIII. To find where the Sun is Vertical at any given time assigned; or the Day of the Month and the Hour at any Place (suppose London) being given, to find in what place the Sun is Vertical at that very time.

Having found the Sun’s declination, and brought the first place (London) to the meridian, set the index to the given hour, then turn the globe about until the index points to XII at noon; which being done, that place upon the globe which stands under the point of the Sun’s declination upon the meridian, has the Sun that moment in the Zenith.

Prob. XIV. The Day, and the Hour of the Day at one place, being given; to find all those places upon the Earth, where the Sun is then Rising, Setting, Culminating (or on the meridian) also where it is Day-light, Twilight, Dark Night, Midnight; where the Twilight then begins, and where it ends; the height of the Sun in any part of the illuminated hemisphere; also his depression in the obscure hemisphere.

Having found the place where the Sun is vertical at the given hour, rectify the globe for that latitude, and bring the said place to the meridian.

Then all those places that are in the Western semicircle of the horizon, have the Sun rising at that time.

Those in the Eastern semicircle have it setting.

To those who live under the upper semicircle of the meridian, it is 12 o’clock at noon. And,

Those who live under the lower semicircle of the meridian, have it at midnight.

All those places that are above the horizon, have the Sun above them, just so much as the places themselves are distant from the horizon; which height may be known by fixing the quadrant of altitude in the zenith, and laying it over any particular place.

In all those places that are 18 degrees below the Western side of the horizon, the twilight is just beginning in the morning, or the day breaks. And in all those places that are 18 degrees below the Eastern side of the horizon, the twilight is ending, and the total darkness beginning.

The twilight is in all those places whose depression below the horizon does not exceed 18 degrees. And,

All those places that are lower than 18 degrees, have dark night.

The depression of any place below the horizon is equal to the altitude of its Antipodes, which may be easily found by the quadrant of altitude.

Prob. XV. The Day of the Month being given; to show, at one view, the length of Days and Nights in all places upon the Earth at that time; and to explain how the vicissitudes of Day and Night are really made by the motion of the Earth round her axis in 24 hours, the Sun standing still.

The Sun always illuminates one half of the globe, or that hemisphere which is next towards him, while the other remains in darkness: And if (as by the last problem) we elevate the globe according to the Sun’s place in the ecliptic, it is evident, that the Sun (he being at an immense distance from the Earth) illuminates all that hemisphere, which is above the horizon; the wooden horizon itself, will be the circle terminating light and darkness; and all those places that are below it, are wholly deprived of the solar light.

The globe standing in this position, those arches of the parallels of latitude which stand above the horizon, are the Diurnal Arches, or the length of the day in all those latitudes at that time of the year; and the remaining parts of those parallels, which are below the horizon, are the Nocturnal Arches, or the length of the night in those places. The length of the diurnal arches may be found by counting how many hours are contained between the two meridians, cutting any parallel of latitude, in the Eastern and Western parts of the horizon.

In all those places that are in the Western semicircle of the horizon, the Sun appears rising: For the Sun, standing still in the vertex (or above the brass meridian) appears Easterly, and 90 degrees distant from all those places that are in the Western semicircle of the horizon; and therefore in those places he is then rising. Now, if we pitch upon any particular place upon the globe, and bring it to the meridian, and then bring the hour index to the lower 12, which in this case, we’ll suppose to be 12 at noon; (because otherwise the numbers upon the hour circle will not answer our purpose) and afterwards turn the globe about, until the aforesaid place be brought to the Western side of the horizon; the index will then shew the time of the Sun rising in that place. Then turn the globe gradually about from West to East, and minding the hour index, we shall see the progress made in the day every hour, in all latitudes upon the globe, by the real motion of the Earth round its axis; until, by their continual approach to the brass meridian (over which the Sun stands still all the while) they at last have noon day, and the Sun appears at the highest; and then by degrees, as they move Easterly the Sun seems to decline Westward, until, as the places successively arrive in the Eastern part of the horizon, the Sun appears to set in the Western: For the places that are in the horizon, are 90 degrees distant from the Sun. We may observe, that all places upon the Earth, that differ in latitude, have their days of different length (except when the Sun is in the equinoctial) being longer or shorter, in proportion to what part of the parallels stands above the horizon. Those that are in the same latitude, have their days of the same length; but have them commence sooner or later, according as the places differ in longitude.

Prob. XVI. To explain in general the alteration of Seasons, or length of the Days and Nights made in all places of the World, by the Sun’s (or the Earth’s) annual motion in the Ecliptic.

It has been shewed in the last problem, how to place the globe in such a position as to exhibit the length of the diurnal and nocturnal arches in all places of the Earth, at a particular time: If the globe be continually rectified, according as the Sun alters his declination, (which may be known by bringing each degree of the ecliptic successively to the meridian) you’ll see the gradual increase or decrease made in the days, in all places of the World, according as a greater or lesser portion of the parallels of latitude, stands above the horizon. We shall illustrate this problem by examples taken at different times of the year.

1. Let the Sun be in the first point of ♋ (which happens on the 21st of June) that point being brought to the meridian, will shew the Sun’s declination to be 23½ degrees North; then the globe must be rectified to the latitude of 23½ degrees; and for the better illustration of the problem, let the first meridian upon the globe be brought under the brass meridian. The globe being in this position, you’ll see at one view the length of the days in all latitudes, by counting the number of hours contained between the two extreme meridians, cutting any particular parallel you pitch upon, in the Eastern and Western part of the horizon. And you may observe that the lower part of the arctic circle just touches the horizon, and consequently all the people who live in that latitude have the Sun above their horizon for the space of 24 hours, without setting; only when he is in the lower part of the meridian (which they would call 12 at night) he just touches the horizon.

To all those who live between the arctic circle and the Pole, the Sun does not set, and its height above the horizon, when he is in the lower part of the meridian, is equal to their distance from the arctic circle: For example, Those who live in the 83d parallel have the Sun when he is lowest at this time 13½ degrees high.

If we cast our eye Southward, towards the equator, we shall find, that the diurnal arches, or the length of days in the several latitudes, gradually lessen: The diurnal arch of the parallel of London at this time is 16½ hours; that of the Equator (is always) 12 hours; and so continually less, ’till we come to the Antarctic Circle, the upper part of which just touches the horizon; just those who live in this latitude have just one sight of the Sun, peeping as it were in the horizon: And all that space between the antarctic circle and the South Pole, lies in total darkness.

If from this position we gradually move the meridian of the globe according to the progressive alterations made in the Sun’s declination, by his motion in the ecliptic, we shall find the diurnal arches of all those parallels, that are on the Northern side of the equator, continually decrease; and those on the Southern side continually increase, in the same manner as the days in those places shorten and lengthen. Let us again observe the globe when the Sun has got within 10 degrees of the equinoctial; now the lower part of the 80th parallel of North latitude just touches the horizon, and all the space betwixt this and the pole, falls in the illuminated hemisphere: but all those parallels that lie betwixt this and the arctic circle, which before were wholly above the horizon, do now intersect it, and the Sun appears to them to rise and set. From hence to the equator, we shall find that the days have gradually shortened; and from the equator Southward, they have gradually lengthened, until we come to the 80th parallel of the South latitude; the upper part of which just touches the horizon; and all places betwixt this and the South Pole are in total darkness; but those parallels betwixt this and the antarctic circle, which before were wholly upon the horizon, are now partly above it; the length of their days being exactly equal to that of the nights in the same latitude in the contrary hemisphere. This also holds universally, that the length of one day in one latitude North, is exactly equal to the length of the night in the same latitude South; and vice versa.

Let us again follow the motion of the Sun, until he has got into the equinoctial, and take a view of the globe while it is in this position. Now all the parallels of latitude are cut into two equal parts by the horizon, and consequently the days and nights are of equal lengths, viz. 12 hours each, in all places of the world; the Sun rising and setting at six o’clock, excepting under the two Poles, which now lie exactly in the horizon: Here the Sun seems to stand still in the same point of the heavens for some time, until by degrees, by his motion in the ecliptic, he ascends higher to one and disappears to the other, there being properly no days and nights under the Poles; for there the motion of the Earth round its axis cannot be observed.

If we follow the motion of the Sun towards the Southern tropic, we shall see the diurnal arches of the Northern parallels continually decrease, and the Southern ones increase in the same proportion, according to their respective latitudes; the North Pole continually descending, and the South Pole ascending, above the horizon, until the Sun arrives into ♑, at which time all the space within the antarctic circle is above the horizon; while the space between the arctic circle, and its neighbouring Pole, is in total darkness. And we shall now find all other circumstances quite reverse to what they were when the Sun was in ♋; the nights now all over the world being of the same length that the days were of before.

We have now got to the extremity of the Sun’s declination; and if we follow him through the other half of the ecliptic, and rectify the globe accordingly, we shall find the seasons return in their order, until at length we bring the globe into its first position.

The two foregoing problems were not, as I know of, published in any book on this subject before; and I have dwelt the longer upon them, because they very well illustrate how the vicissitudes of days and nights are made all over the world, by the motion of the Earth round her axis; the horizon of the globe being made the circle, separating light and darkness, and so the Sun to stand still in the vertex. And if we really could move the meridian, according to the change of the Sun’s declination, we should see at one view, the continual change made in the length of days and nights, in all places on the Earth; but as globes are fitted up, this cannot be done; neither are they adapted for the common purposes, in places near the equator, or any where in the Southern hemisphere. But this inconvenience is now remedied (at a small additional expence) by the hour circle being made to shift to either Pole; and some globes are now made with an hour circle fixed to the globe at each Pole between the globe and meridian, so as to have none without side to interrupt the meridian from moving quite round the wooden horizon.