Chapter III: Part 3

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we enjoy its reflected light for some time: For the atmosphere being higher than we are, is a longer time before it is withdrawn from the Sun (as if a man was to run to the top of a steeple, he might see the Sun after it had been set to those at the bottom.) The rays which the atmosphere receives from the Sun, after he is withdrawn from our sight, are by refraction faintly transmitted to us; until the Sun having got about 18 degrees below the horizon, he no longer enlightens our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.

[Sidenote: _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.

[Sidenote: _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._

[Sidenote: _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.

[Sidenote: _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.

[Sidenote: _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.

[Sidenote: _Amphiscians._]

[Sidenote: _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_.

[Sidenote: _Heteroscians._]

[Sidenote: _Ascians Heteroscians._]

[Sidenote: _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_.

[Sidenote: _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_.

[Sidenote: _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_.

[Sidenote: _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_.

[Sidenote: _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._

[Sidenote: _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_.

[Sidenote: _Continent._]

[Sidenote: _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_.

[Sidenote: _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.

[Sidenote: _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_.

[Sidenote: _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.

[Sidenote: _Promontory._]

[Sidenote: _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.

[Sidenote: _A Coast_ or _Shore_.]

[Sidenote: _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_.

[Sidenote: _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_.

[Sidenote: _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.

[Sidenote: _A Gulf._]

[Sidenote: _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_.

[Sidenote: _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_.

[Sidenote: _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.

[Sidenote: _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.

[Sidenote: _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.

[Sidenote: _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._ _Longitude._
Deg. 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.
{ _Rome_ 0 52 P. M.
At { _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.

PROB. XVII. _To shew by the globe, at one
view, the longest of the Days and Nights in any
particular places, at all times of the Year._

Because the Sun, by his motion in the ecliptic, alters his declination a small matter every day; if we suppose all the torrid zone to be filled up with a spiral line, having so many turnings; or a screw having so many threads, as the Sun is days in going from one tropic to the other: And these threads at the same distance from one another in all places, as the Sun alters his declination in one day in all those places respectively: This spiral line or screw will represent the apparent paths described by the Sun round the Earth every day; and by following the thread from one tropic to the other, and back again, we shall have the path the Sun seems to describe round the Earth in a year. But because the inclinations of these threads to one another are but small, we may suppose each diurnal path to be one of the parallels of latitude, drawn, or supposed to be drawn upon the globe. Thus much being premised, we shall explain this _Problem_, by placing the globe according to some of the most remarkable positions of it, as before we did for the most remarkable seasons of the year.