The description and use of the globes and the orrery Joseph Harris 353 downloads.pdf

The Project Gutenberg eBook of The description and use of the
globes and the orrery
This eBook is for the use of anyone anywhere in the United States and most
other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms of
the Project Gutenberg License included with this eBook or online at
www.gutenberg.org. If you are not located in the United States, you will
have to check the laws of the country where you are located before using
this eBook.

Title: The description and use of the globes and the orrery

Author: Joseph Harris

Release date: March 26, 2020 [eBook #61683]
Most recently updated: October 17, 2024

Language: English

Other information and formats: www.gutenberg.org/ebooks/61683

Credits: Produced by deaurider, Paul Marshall and the Online
Distributed Proofreading Team at https://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)

*** START OF THE PROJECT GUTENBERG EBOOK THE
DESCRIPTION AND USE OF THE GLOBES AND THE ORRERY ***

The Great Orrery Four Feet in Diameter
Made by Tho: Wright Mathematical
Instrument-maker to His Majesty For the
Royal Academy at Portsmouth Now B. Cole,
at the same shop.
Who makes Orrery’s of different sorts as may
be seen at his Shop in Fleet Street

Where is Sold a Large Print of the Orrery
with the Explanation on a Sheet of Imperial
Paper. Price 2s.

THE
Description and Use
OF
THE GLOBES,
AND
THE ORRERY.
To which is prefix’d,

By Way of Introduction,
A brief Account of the Solar System.

By JOSEPH HARRIS,
Teacher of the Mathematics.

The Eleventh Edition.

LONDON:
Printed for B. Cole, at the Orrery, near
the Globe Tavern, in Fleet street, late
the Shop of Mr. Thomas Wright,
Instrument-maker to his late

Majesty; and E. Cushee, near St.
Dunstan’s Church, Fleet Street.
MDCCLXXIII.

Advertisement.
he great encouragement Mr. Wright has

T had for many years past in making large
Orreries, with the motions of all the
Planets and Satellites, and the true motion of
Saturn’s Ring, has made him so ready and
perfect, that Gentlemen may depend on
having them made reasonable and sound, not
liable to be out of Order.
As may be seen by one he made for Mr.
Watt’s Academy in Tower-street.
Another for his Majesty at Kensington.
Another for the New Royal Academy at
Portsmouth.
Another for his Grace the Duke of Argyle
(late Lord Ila.)
And several other large ones for
Noblemen and Gentlemen.
The above, and all other Mathematical,
Philosophical, and Optical Instruments, are
now made in the most complete manner, by
B. Cole, Servant to Mr. Wright, at the time
of the above being made, and successor to
him in the same Trade and Business.

THE CONTENTS.
The Introduction: Containing a brief
Account of the Solar System, and of the
Fixed Stars.

f the Order and Periods of the Primary
Sect. I.
O Planets revolving about the Sun; and of
the Secondary Planets round their respective
Primaries.
——— Of the Primary Planets 1
——— Of the Secondary Planets 5
——— Of the Annual and Diurnal Motion of the Planets 7
——— That the Planets are Opaque and Globular 9
——— That the Earth is placed betwixt the Orbits of Mars and
ibid.
Venus
——— That the Planets turn round the Sun ibid.
——— That the Earth also turns round the Sun 15
——— How the Annual and Diurnal Motion of the Planets are
ibid.
computed
——— How the relative Distance of the Planets from the Sun are
18
determined
——— How their absolute Distances from the Sun are computed 23
——— How the Magnitudes of the Planets are determined 26
——— Why the Moon appears bigger than any of the Planets 27
——— A Table of the Distances, Magnitudes, Periodical, and
28
Diurnal Revolutions of the Planets
——— Of Comets 29
Sect.
Of the Fixed Stars 32
II.
——— That the fixed Stars are luminous Bodies, at immense
ibid.
Distances from us

——— Of Telescopical Stars 35
——— The Stars digested into Constellations 36
——— Of the Galaxy, or Milky Way 38

The Description and Use of the Celestial and Terrestrial
Globes.

he Geometrical Definition of a Globe, and of the principal Use of
T the Artificial Globes
42

That there will be the same prospect of the Fixed Stars, whether
45
the Spectator be placed in the Sun, or on the Earth
Sect. I.
An Explanation of the Circles of the
Sphere, and of some Astronomical 47
Terms arising therefrom
——— Of the Division of Time 69
——— Of the Atmosphere 81
Sect. II. Geographical Definitions 84
——— Of the Situation of Places upon the Earth ibid.
——— Of Zones and Climates 90
——— Of the Poetical Rising and Setting of the Stars 96
——— Of the surface of the Earth, considered as it is
ibid.
composed of Land and Water
——— Of the appurtenances of the Globes 101
Sect. III. The Use of the Globes 104
Problem I. To find the Latitude and Longitude of any given
place upon the Globe; and on the contrary, the
ibid.
Latitude and Longitude being given to find the
Place
Prob. II. To find the Difference of Latitude betwixt any two
106
given places

Prob. III. To find the Difference of Longitude betwixt any two
ibid.
given places
Prob. IV. Any Place being given; to find all those places that
107
are in the same Latitude with the said place
Prob. V. The Day of the Month being given; to find the Sun’s
108
place in the Ecliptic, and his Declination
Prob. VI. To rectify the Globe for the Latitude, Zenith, and
109
Sun’s place
Prob. VII. To find the Distance between any two given Places
upon the Globe, and to find all those places upon
110
the Globe that are at the same Distance from a
given place
Prob. VIII. To find the Angle of a Position of Places; or the
angle formed by the Meridian of one place, and a 111
great circle passing through both the places
Prob. IX. To find the Antœci, Periœci, and Antipodes, to any
113
given place
Prob. X. The Hour of the Day at one Place being given; to
find the correspondent Hour (or what o’Clock it is 114
at that time) at any other place
Prob. XI. The Day of the Month being given; to find those
places on the Globe where the Sun will be Vertical, 115
or in the Zenith, that Day
Prob. XII. A place being given in the Torrid Zone; to find
those two Days in which the Sun will be Vertical to 116
the same
Prob. XIII. To find where the Sun is Vertical at any given time
assigned; or, the Day of the Month and the Hour at
ibid.
any place (suppose London) being given, to find in
what place the Sun is Vertical at that very time
Prob. XIV. The Day, and the Hour of the Day at one place, 117
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
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
119
Vicissitudes of Day and Night are really made by
the motion of the Earth round her Axis, in 24
Hours, the Sun standing still
Prob. XVI. To Explain in general the Alteration of Seasons, or
Length of the Days and Nights, made in all places
121
of the World, by the Sun’s, or the Earth’s Annual
motion in the Ecliptic
Prob. XVII. To shew by the Globe, at one View, the Length of
the Days and Nights, at any particular place, at all 128
times of the Year
Prob. XVIII. The Latitude of any place, not exceeding 69½
Degrees, and the Day of the Month being given; to
136
the time of Sun-rising and Setting, and the length of
the Day and Night
Prob. XIX. To find the length of the longest and shortest Day
and Night in any given place, not exceeding 66½ 137
Degrees of Latitude
Prob. XX. To find in what Latitude the longest Day is, of any
139
given length less than 24 Hours
Prob. XXI. A Place being given in one of the Frigid Zones
(suppose the Northern) to find what number of
Days (of 24 Hours each) the Sun doth constantly 140
shine upon the same, how long he is absent, and
also the first and last day of his appearance
Prob. XXII. To find in what Latitude the longest Day is, of any
141
given length, less than 182 natural Days
Prob. XXIII. The Day of the Month being given; to find when the
Morning and Evening Twilight begins and ends, in 142
any place upon the Globe
Prob. XXIV. To find the time when total Darkness ceases, or 144
when the Twilight continues from Sun-setting to

Sun-rising, in any given place
Prob. XXV. The Day of the Month being given; to find those
places of the Frigid Zones, where the Sun begins to
146
shine constantly without setting; and also those
places where he begins to be totally absent
Prob. XXVI. The Latitude, the Sun’s Place, and his Altitude
being given; to find the Hour of the Day, and Sun’s 149
Azimuth from the Meridian
Prob. XXVII. The Latitude, Hour of the Day, and the Sun’s Place
150
being given; to find the Sun’s Altitude
Prob. XXVIII. The Latitude of the Place, and the Day of the
Month being given; to find the depression of the
151
Sun below the Horizon, and his Azimuth, at any
Hour of the Night
Prob. XXIX. The Latitude of the Sun’s Place, and his Azimuth
152
being given; to find his Altitude, and the Hour
Prob. XXX. The Latitude, the Sun’s Altitude, and his Azimuth
being given; to find his Place on the Ecliptic, and ibid.
the Hour
Prob. XXXI. The Declination, and Meridian Altitude of the Sun,
or of any Star being given; to find the Latitude of 153
the Place
Prob. XXXII. The Day and Hour of a Lunar Eclipse being
known; to find all those Places upon the Globe in 154
which the same will be visible
Prob. XXXIII. The Day of the Month, and Hour of the Day,
according to our way of reckoning in England,
155
being given; to find thereby the Babylonish, Italic,
and Jewish, or Judaical Hour
Prob. XXXIV. To find the Right Ascension and Declination of the
156
Sun, or any Fixed Star
Prob. XXXV. To find the Longitude and Latitude of a given Star 158
Prob. XXXVI. The Latitude of the Place, the Day of the Month, 159
and the Hour being given; to find what Stars are
then rising and setting, what Stars are culminating,
or on the Meridian, and the Altitude and Azimuth of

any Star above the Horizon; and also how to
distinguish the Stars in the Heavens one from the
other, and to know them by their proper Names
Prob. XXXVII. The Latitude of the Place being given; to find the
Amplitude, Oblique Ascension, and Descension,
Ascensional Difference, Semi-diurnal Arch, and the 162
time of Continuance above the Horizon, of any
given Point in the Heavens
Prob. XXXVIII. The Latitude and the Day of the Month being given;
to find the Hour when any known Star will be on
165
the Meridian, and also the time of its Rising and
Setting
Prob. XXXIX. To find at what time of the Year a given Star will be
166
upon the Meridian, at a given Hour of the Night
Prob. XL. The Day of the Month and the Azimuth, of any
known Star being given; to find the Hour of the 167
Night
Prob. XLI. Two known Stars, having the same Azimuth, or the
same Height, being given; to find the Hour of the 168
Night
Prob. XLII. The Latitude, Day of the Month, and the Altitude of
any known Star being given; to find the Hour of the 169
Night
Prob. XLIII. Having the Latitude of the Place, to find the Degree
of the Ecliptic, which rises or sets with a given
171
Star; and from thence to determine the time of its
Cosmical and Achronical Rising and Setting
Prob. XLIV. Having the Latitude of the Place; to find the time
172
when a Star rises and sets Heliacally
Prob. XLV. To find the Place of any Planet upon the Globe, so
by that Means to find its Place in the Heavens; also
173
to find at what Hour any Planet will rise or set, or
be on the Meridian, at any Day in the Year
Prob. XLVI. To find all that space upon the Earth where an
Eclipse of one of the Satellites of Jupiter will be 175
visible

The Description of the 177
ORRERY
Of the Motions of the Planets in general 183
Of the Stations and Retrogadations of the Planets 186
Of the Annual and Diurnal Motion of the Earth 194
Of the Phases of the Moon, and of her Motion in
201
her Orbit
Of the Eclipses of the Sun and Moon 208
Of the Eclipses of Jupiter’s Satellites 212

THE
INTRODUCTION,
CONTAINING
A Brief Account of the Solar System, and of the Fixed Stars.

SECT. I.

Of the Order and Periods of the Primary Planets revolving
about the Sun; and of the Secondary Planets round their
respective Primaries.
he Sun is placed in the midst of an immense space,
wherein six opaque spherical bodies revolve about Planets.
him as their center. These wandering globes are
called the Planets, who, at different distances, and in different
periods, perform their revolutions from West to East, in the following order:
1. ☿ Mercury is nearest to the Sun of all
the planets, and performs its course in about
three months. 2. ♀ Venus in about seven
months and a half. 3. ♁ The Earth in a year.
4. ♂ Mars in about two years. 5. ♃ Jupiter in
twelve. And lastly, ♄ Saturn, whose[1] Orbit
includes all the rest, spends almost 30 years
in one revolution round the Sun. The
distances of the Planets from the Sun are
nearly in the same proportion as they are
represented in Plate 1. viz. Supposing the
distance of the Earth from the Sun to be
divided into 10 equal parts; that of Mercury
will be about 4 of these parts; of Venus 7; of
Mars 15; of Jupiter 52; and that of Saturn 95.

The Characters placed before the names of the Planets,
are for brevity’s sake commonly made use of by
Astronomers, instead of the words at length, as ♀, for Venus,
&c.

Plate 1.

The orbits of the Planets are not all in the same plane, but
variously inclined to one another; so that supposing one of them Nodes.

to coincide with the above scheme, the others will have one half above, and
the other half below it; intersecting one another in a line passing through the
Sun. The plane of the Earth’s orbit is called the Ecliptic; and this the
astronomers make the standard to which the planes of the other orbits are
judged to incline. The right line passing thro’ the Sun, and the common
intersection of the plane of the orbit of any planet and the Ecliptic, is called
the Line of the Nodes of that planet; and the points themselves, wherein the
orbit cuts the Ecliptic are called the Nodes.
The inclinations of the orbits of the Planets to the plane of
the ecliptic, are as follows, viz. the orbit of Mercury makes an Excentric
ity.
angle with it of almost 7 degrees; that of Venus something above
3⅓ degrees; of Mars a little less than 2 degrees; of Jupiter, 1⅓ degree; and
of Saturn, about 2½ degrees. The orbits of the Planets are not circles, but
ellipses or ovals. What an ellipsis is, may be easily understood from the
following description. Imagine two small pegs fixed upright on any plane,
and suppose them tied with the ends of a thread somewhat longer than their
distance from one another: Now if a pin be placed in the double of the
thread and turned quite round (always stretching the thread with the same
force) the curved described by this motion is an Ellipsis. The two points
where the pegs stood, (about which the thread was turned) are called the
foci of that ellipsis; and if, without changing the length of the thread, we
alter the position of the pegs, we shall then have an ellipsis of a different
kind from the former; and the nearer the focus’s are together, the nearer will
the curve described be to a circle; until at last, the two focus’s coincide, and
then the pin in the doubling of the thread will describe a perfect circle. The
orbits of all the Planets have the Sun in one of their focus’s, and half the
distance between the two focus’s is called the Excentricity of the orbits. This
excentricity is different in all the planets, but in most of them so small, that
in little schemes or instruments, made to represent the planetary orbits, it
need not be considered.
The six Planets above-mentioned, are called Primaries, or
Primary Planets; but besides these, there are ten other lesser Primary
Planets.
Planets, which are called Secondaries, Moons, or Satellites.
These moons always accompany their respective primaries, and
Secondar
perform their Revolutions round them, whilst both together are y Planets.
also carried round the Sun. Of the six Primary Planets, there are

but three, as far as observation can assure us, that have these attendants, viz.
the Earth, Jupiter, and Saturn.
The Earth is attended by the Moon, who performs her revolution in
about 27⅓ Days, at the distance of about 30 Diameters of the Earth from it;
and once a Year is carried round the Sun along with the Earth.
Jupiter has four Moons, or Satellites; the first, or innermost,
performs its revolution in about one Day, and 18½ Hours, at the Jupiter’s
four
distance of 5⅔ Semidiameters of Jupiter, from his Center; the Moons.
second revolves about Jupiter in 3 Days, 13 Hours, at the
distance of 9 of his Semidiameters; the third in 7 Days, and 4 Hours, at the
distance of 14⅓ Semidiameters; the fourth, and outermost, performs its
course in the space of 16 Days, 17 Hours; and is distant from Jupiter’s
center, 25⅓ of his Semidiameters.
Saturn has no less than five Satellites; the first, or
innermost, revolves about him in 1 Day, and 21 Hours, at the Saturn
has five
distance of 4⅜ Semidiameters of ♄, from his center; the second Moons.
compleats his period in 2¾ Days, at the distance of 5³/₅ of his
Semidiameters; the third, in about 4½ Days, at the distance of 8
Semidiameters; the fourth performs its course in about 16 Days, at the
distance of 18 Semidiameters; the fifth, and outermost, takes 79⅓ Days, to
finish his course, and is 54 Semidiameters of Saturn distant from his center.
The Satellites, as well as their primaries, perform their revolutions from
West to East: The planes of the Orbits of the Satellites of the same Planet
are variously inclined to one another, and consequently are inclined to the
plane of the Orbit of their primary.
Besides these attendants, Saturn is encompassed with a thin
plain Ring, that does no where touch his body; The diameter of Saturn’s
Ring.
this Ring is to the diameter of Saturn, as 9 to 4; and the void
space between the Ring and the body of Saturn is equal to the breadth of the
Ring itself; so that in some situations the Heavens may be seen between the
Ring and his body. This surprizing phænomenon of Saturn’s Ring, is a
modern discovery; neither were the Satellites of Jupiter and Saturn known
to the ancients. The Jovial Planets were first discovered by the famous
Italian philosopher Galilæus, by a telescope which he first invented; and
the celebrated Cassini, the French king’s astronomer, was the first that saw

all the Satellites of Saturn; which by reason of their great distances from the
Sun, and the smallness of their own bodies, cannot be seen by us, but by the
help of very good glasses.
The motion of the primary Planets round the Sun (as also of
the Satellites round their respective primaries) is called their Annual
Motion.
Annual Motion; because they have one Year, or alteration of
Seasons compleat, in one of these revolutions. Besides this
annual motion, four of the Planets, viz. Venus, the Earth, Mars, Diurnal
Motion.
and Jupiter revolve about their own Axis, from West to East; and
this is called their Diurnal Motion. For by this rotation, each point of their
surfaces is carried successively towards or from the Sun, who always
illuminates the hemisphere which is next to him, the other remaining
obscure; and while any place is in the hemisphere, illuminated by the Sun, it
is Day, but when it is carried to the obscure hemisphere, it becomes Night;
and so continues, until by this rotation the said place is again enlightened by
the Sun.
The Earth performs its revolution round its axis in
23 Hours, 56 Minutes;[2] Venus, in 24 Days, 8 Hours; Diurnal Motion of
the ♁, ♀, ♂ and ♃.
Mars, in 24 Hours, and 40 Minutes; and Jupiter moves
round his own axis in 9 Hours, and 56 Minutes. The Sun
also is found to turn round his axis from West to East, in ☉ and ☽ likewise
turn round their
27 Days: And the Moon, which is nearest to us of all the Axis.
Planets, revolves about her axis in a Month, or in the
same space of time that she turns round the Earth; so that the Lunarians
have but 1 Day throughout the Year.
I. The Planets are all Opaque bodies, having no light
but what they borrow from the Sun; for that side of them The Planets are
Opaque and
which is next towards the Sun, has always been Globular.
observed to be illuminated, in what position soever they
be; but the opposite side, which the Solar rays do not reach, remains dark
and obscure; whence it is evident that they have no light but what proceeds
from the Sun; for if they had, all parts of them would be lucid, without any
darkness or shadow. The Planets are likewise proved to be Globular;
because let what part soever of them be turned towards the Sun, its
boundary, or the line separating that part from the opposite, always appears
to be circular; which could not happen, if they were not globular.

II. That the Earth is placed betwixt the Orbs of Mars
and Venus, and that ☿, ♀, ♂, ♃ and ♄, do all turn round The Planets turn
round the Sun.
the Sun, is proved from observations as follow:
1. Whenever Venus is in conjunction with the Sun,
that is, when she is in the same direction from the Earth, Plate 2. Fig. 1. 2.
or towards the same part of the Heavens the Sun is in;
she either appears with a bright and round face, like a Full Moon, or else
disappears: Or, if she is visible, she appears horned, like a new Moon;
which phænomena could never happen if ♀ did not turn round the Sun, and
was not betwixt him and the Earth: For since all the Planets borrow their
light from the Sun, it is necessary that ♀’s lucid face should be towards the
Sun; and when she appears fully illuminated, she shews the same face to the
Sun and Earth; and at that time she must be above or beyond the Sun; for in
no other position could her illuminated face be seen from the Earth. Farther,
when she disappears, or if visible, appears horned; that face of her’s which
is towards the Sun is either wholly turned from the Earth, or only a small
part of it can be seen by the Earth; and in this case she must of necessity be
betwixt us and the Sun. Let S be the Sun, T the Earth, and V Venus, having
the same face presented both towards the Sun and Earth; here it is plain that
the Sun is betwixt us and Venus and therefore we must either place Venus in
an Orbit round the Sun, and likewise betwixt him and us, as in Fig. 1. or
else we must make the Sun to move round the Earth in an Orbit within that
of Venus, as in Fig. 2. Again, after Venus disappears, or becomes horned, at
her[3] ☌ with the ☉, she then must be betwixt us and the Sun, and must
move either in an Orbit round the Sun and betwixt us and him, as in Fig. 1.
or else round the Earth, and betwixt us and the Sun, as in Fig. 2. But Venus
cannot move sometimes within the Sun’s Orbit, and sometimes without it,
as we must suppose if she moves round the Earth; therefore it is plain that
her motion is round the Sun.
Besides the forgoing, there is another argument to
prove that Venus turns round the Sun in an Orbit that is Why Venus is
always either our
within the Earth’s, because she is always observed to Morning or
keep near the Sun, and in the same quarter of the Evening Star.
Heavens that he is in, never receding from him more
than about ⅛ of a whole circle; and therefore she can never come in
opposition to him; which would necessarily happen, did she perform her

course round the Earth either in a longer or shorter time than a Year. And
this is the reason why Venus is never to be seen near midnight, but always
either in the Morning or Evening, and at most not above three or four Hours
before Sun-rising or after Sun-setting. From the time of ♀ ’s superior
conjunction (or when she is above the Sun) she is more Easterly than the
Sun, and therefore sets later, and is seen after Sun-setting; and then she is
commonly called the Evening Star. But from the time of her inferior
conjunction, ’till she comes again to the superior, she then appears more
Westerly than the Sun, and is only to be seen in the morning before Sun-
rising, and is then called the Morning Star.
After the same manner we prove that Mercury turns round the Sun, for
he always keeps in the Sun’s neighbourhood, and never recedes from him
so far as Venus does; and therefore the Orbit of ☿ must lie within that of ♀;
and on the account of his nearness to the Sun, he can seldom be seen
without a Telescope.
Mars is observed to come in opposition, and
likewise to have all other aspects with the Sun; he The Orbit of Mars
includes the Earth’s.
always preserves a round, full, and bright face, except
when he is near his quadrate aspect, when he appears somewhat
gibbous, like the Moon three or four Days before or after the Fig. 3.
full: Therefore the Orbit of ♂ must include the Earth within it, and also the
Sun; for if he was betwixt the Sun and us at the time of his inferior
conjunction, he would either quite disappear, or appear horned, as Venus
and the Moon do in that position. Let S be the Sun, T the Earth, and A P
Mars, both in his conjunction and opposition to the Sun, and in both
positions full; and B C Mars at his quadratures, when he appears somewhat
gibbous from the Earth at T. ’Tis plain hence, that the Orbit of Mars does
include the Earth, otherwise he could not come in opposition to the Sun;
and that it likewise includes the Sun, else he could appear full at his
conjunction.
Mars when he is in opposition to the Sun, looks almost seven times
larger in diameter than when he is in conjunction with him, and therefore
must needs be almost seven times nearer to us in one position than in the
other; for the apparent magnitudes of far distant objects increase or decrease
in proportion to their distances from us: But Mars keeps always nearly at

the same distance from the Sun; therefore it is plain that it is not the Earth,
but the Sun, that is the center of his motion.
It is proved in the same way, that Jupiter and Saturn have both the Sun
and the Earth within their Orbits, and that the Sun, and not the Earth, is the
center of their motions; altho’ the disproportion of the distances from the
Earth is not so great in Jupiter, as it is in Mars, nor so great in Saturn, as it
is in Jupiter, by reason that they are at a much greater distance from the
Sun.
We have now shewn that all the Planets turn round
the Sun, and that Mercury and Venus are included Inferior and
Superior Planets.
between him and the Earth, whence they are called the
Inferior Planets, and that the Earth is placed between the Orbits of Mars
and Venus, and therefore included within the Orbits of Mars, Jupiter, and
Saturn, whence they are called the Superior Planets: And since the Earth is
in the middle of these moveable bodies, and is of the same nature with
them, we may conclude that she has the same sort of motions; but that she
turns round the Sun is proved thus:
All the Planets seen from the Earth appear to move
very unequally, as sometimes to go faster, at other times The Earth does not
stand still, but turns
slower; sometimes to go backwards, and sometimes to round the Sun.
be stationary, or not to move at all; which could not
happen if the Earth stood still. Let S be the Sun, T the Earth, the Fig. 4.
great circle A B C D the Orbit of Mars, and the numbers 1, 2, 3,
&c. its equable motion round the Sun; the correspondent numbers 1, 2, 3,
&c. in the circle a, b, c, d, the motion of Mars, as it would be seen from the
Earth. It is plain from this Figure, that if the Earth stood still, the motion of
Mars, will be always progressive, (tho’ sometimes very unequal;) but since
observations prove the contrary, it necessarily follows, that the Earth turns
round the Sun.
The annual periods of the Planets round the Sun are
determined by carefully observing the length of time The Annual and
Diurnal Motions of
since their departure from a certain point in the Heavens, the Planets, how
(or from a fix’d Star) until they arrive to the same again. computed.
By these sort of observations the ancients determined the
periodical revolutions of the Planets round the Sun, and were so exact in

their computations, as to be capable of predicting Eclipses of the Sun and
Moon. But since the invention of telescopes, astronomical observations are
made with greater accuracy; and of consequence, our tables are far more
perfect than those of the ancients. And in order to be as exact as possible,
astronomers compare observations made at a great distance of time from
one another, including several periods; by which means, the error that might
be in the whole, is in each period subdivided into such little parts as to be
inconsiderable. Thus the mean length of a Solar Year is known, even to
Seconds.
The Diurnal rotation of the Planets round their axis, was discovered by
certain spots which appear on the surfaces. These spots appear first in the
margin of the Planet’s disk, (or the edge of their surfaces) and seem by
degrees to creep toward their middle, and so on, going still forward, ’till
they come to the opposite side or edge of the disk, where they set or
disappear; and after they have been hid for the same space of time, that they
were visible, they again appear to rise in or near the same place, as they did
at first, then to creep on progressively, taking the same course as they did
before. These spots have been observed on the surfaces of the Sun, Venus,
Mars, and Jupiter; by which means it has been found that these bodies turn
round their own axis, in the times before-mentioned. It is very probable that
Mercury and Saturn have likewise a motion round their axis, that all the
parts of their surface may alternately enjoy the light and heat of the Sun,
and receive such changes as are proper and convenient for their nature. But
by reason of the nearness of ☿ to the Sun, and ♄’s immense distance from
him, no observations have hitherto been made whereby their spots (if they
have any) could be discovered, and therefore their Diurnal motions could
not be determined. The Diurnal motion of the Earth is computed from the
apparent revolution of the Heavens, and of all the Stars round it, in the
space of a natural Day. The Solar spots do not always remain the same, but
sometimes old ones vanish, and afterwards others succeed in their room;
sometimes several small ones gather together and make one large spot, and
sometimes a large spot is seen to be divided into many small ones. But,
notwithstanding these changes, they all turn round with the Sun in the same
time.
The relative distances of the Planets from the Sun,
and likewise from each other, are determined by the How the relative
distances of the

following methods: First, the distance of the two inferior Planets from the
Sun are determined.
Planets ☿ and ♀ from the Sun, in respect of the Earth’s
distance from him, is had by observing their greatest Elongation from the
Sun as they are seen from the Earth.
The greatest Elongation of Venus is found by
observation to be about 48 degrees, which is the angle S Fig. 5. Elongation.
T ♀ ; whence, by the known rules of Trigonometry, the
proportion of S ♀, the mean distance of Venus from the Sun to ST, the mean
distance of the Earth from him may be easily found. After the same manner,
in the right-angled triangle S T ☿, may be found the distance S ☿ of
Mercury from the Sun. And if the mean distance of the Earth from the Sun
S T be made 1000, the mean distance of Venus S ♀ from the Sun will be
723; and of Mercury S ☿ 387: And if the Planets moved round the Sun in
circles, having him for their center, the distances here found would be
always their true distances: But as they move in Ellipses, their distances
from the Sun will be sometimes greater, and sometimes less. Their
Excentricities are computed to be as follows, viz.
Mercury 80 of the parts
Excent. of Venus 5 above-mentioned.
Earth 169
The distances of the superior Planets, viz. ♂, ♃, and Heliocentric and
♄, are found by comparing their true places, as they are Geocentric Place,
seen from the Sun, with their apparent places, as they are what.
seen from the Earth. Let S be the Sun, the circle ABC
the Earth’s orbit, AG a line touching the Earth’s orbit, in which we’ll
suppose the superior Planets are seen from the Earth in the points of their
orbits ♂ , ♃, ♄; and let DEFGH be a portion of a great circle in the
Heavens, at an infinite distance: Then the place of Mars seen from the Sun
is D, which is called his true, or Heliocentric Place; but from the Earth, he
will be seen in G, which is called his apparent, or Geocentric Place. So
likewise Jupiter and Saturn will be seen from the Sun in the points E and F,
their Heliocentric places; but a spectator from the Earth will see them in the
point of the Heavens G, which is their Geocentric place. The arches DG,
EG, FG, the differences between the true and apparent places of the
Superior Planets, are called the Parallaxes of the Earth’s annual Orb, as

seen from these Planets. If thro’ the Sun we draw SH parallel to AG, the
angles A ♂ S, A ♃ S, A ♄ S, will be respectively equal to the angles D S H,
E S H, and F S H; and the angle A G S is equal to the angle GSH, whose
measure is the arch GH; which therefore will be the measure of the angle
AGS, the angle under which the semidiameter A S of the Earth’s orbit, is
seen from the Starry Heavens. But this semidiameter is nothing in respect of
the immense distance of the Heavens or Fixed Stars; for from thence it
would appear under no sensible angle, but look like a point. And therefore
in the Heavens, the angle G S H, or the arch G H vanishes; and the Points G
and H coincide; and the arches D H, E H, F H, may be considered as being
of the same bigness with the arches D G, E G, and F G, which are the
measures of the angles A ♂ S, A ♃ S, A ♄ S; which angles are nearly the
greatest elongation of the Earth from the Sun, if the Earth be observed from
the respective Planets, when the line G ♄ ♃ ♂ A, touches the Earth’s orbit
in A. The nearer any of the superior Planets is to the Sun, the greater is the
Parallax of the annual Orb, or the angle under which the semidiameter of
the Earth’s orbit is seen from that Planet. In Mars the angle ♂ S, (which is
the visible elongation of the Earth seen from Mars, or the Parallax of the
annual Orb seen from that Planet) is about 42 degrees, and therefore the
Earth is always to the inhabitants of Mars either their Morning or Evening
Star, and is never seen by them so far distant from the Sun as we see Venus.
The greatest elongation of the Earth seen from Jupiter, being nearly equal
to the angle A ♃ S, is about 11 degrees. In Saturn the angle A ♄ S is but 6
degrees, which is not much above ¼ part of the greatest elongation we
observe in Mercury. And since Mercury is so rarely seen by us, probably the
astronomers of Saturn (except they have better Optics than we have) have
not yet discovered that there is such a body as our Earth in the Universe.
The Parallax of the annual Orb, or the greatest elongation of the Earth’s
orbit seen from any of the superior Planets, being given; the distance of that
Planet from the Sun, in respect of the Earth’s distance from him, may be
found by the same methods as the distances of the inferior Planets were.
Thus, to find the distance of Mars from the Sun, it will be as the Sine of the
angle S ♂ A is to the Radius, so is the distance AS (the distance of the Earth
from the Sun) to S ♂ , the distance from the Sun to Mars. After the same
manner the distances of Jupiter and Saturn are also found. The mean
distance of the Earth from the Sun being made 1000, the mean distances of

the superior Planets from the Sun are, viz. the mean distance from the Sun
of

♂ 1524 141
♃ 5201 and the Excentricity 250
♄ 9538 547
To which, if you add or subtract their mean distances, we shall have the
greatest or least distances of those Planets from the Sun.
There are other methods by which the relative distances of the Planets
might be found; but that which hath been here illustrated, is sufficient to
evince the certainty of that Problem.
Hitherto we have only considered the distances of
the Planets in relation to one another, without How the absolute
distances of the
determining them by any known measure; but in order to Planets from the
find their absolute distances in some determinate Sun are computed.
measure, there must be something given, whose measure
is known. Now the circumference of the Earth is divided Parallax of the
into 360 degrees, and each of these degrees into 60 Earth’s
Geographical miles, so that the whole circumference Semidiameter.
contains 21600; and by the known proportion for finding the
diameter of a circle from its circumference, the Earth’s diameter Fig. 7.
will be found to be 6872 miles, and its semidiameter 3436
miles. The Parallax of the Earth’s semidiameter, or the angle under which it
is seen from a certain Planet, may be found by comparing the true place of
the Planet, as it would be seen from the center of the Earth (which is known
by computation) with its apparent place, as it is seen from some point on the
Earth’s surface. Let CZA be the Earth, ZC its semidiameter, ♁ some Planet,
and BHT arch of a great circle in the Heavens, at an infinite distance. Now
the Planet ♁ will appear from the Earth’s center C, in the point of the
Heavens H; but a spectator from the point Z upon the Earth’s surface, will
see the same object ♁ in the point of the Heavens B; and the arch BH the
difference, is equal to the angle B ♁ H = Z ♁ C, the Parallax; which being
known, the side C ♁ the distance of the Planet from the center of the Earth,
at that time, may be easily found. Now if this distance of the Planet from
the Earth be determined, when the centers of the Sun, the said Planet, and of

the Earth, are in the same right line, we have the absolute distance of the
Planet’s orbit from the Earth’s in known measure; then it will be, as the
relative distance betwixt the Earth’s orbit and that of the Planet is to the
relative distance of the said Planet from the Sun; so is the distance of the
Planet’s orbit from the Earth’s in known measure to the distance of the said
Planet from the Sun in the same measure: Which being known, the distance
of all the other Planets from the Sun may be found. For it will be, as the
relative distance of any Planet from the Sun, is to its distance from him in a
known measure; so is the relative distance of any other Planet from him to
its distance in the same measure. This may be done by finding the distance
of the Planet Mars, when he is in opposition to the Sun, after the same
manner as we find the distance of a tree, or the like, by two stations.
Let ♂ be Mars, D the point on the Earth’s superficies, where Mars is
vertical when he is in opposition to the Sun, which may be found exactly
enough by calculation, at which time let an observer, at the point Z (whose
situation from D must be known) take the altitude of Mars, whose
complement will be the angle ♂ ZR; then in the triangle ♂ ZC will be given
the angle Z ♂ C, the angle C (whose measure is the arch DZ) and
consequently the angle Z ♂ C the Parallax, and also the side Z C the
semidiameter of the Earth; by which we may find C ♂ the distance of Mars
from the Earth. The extreme nicety required in this observation, makes it
very difficult to determine the exact distances of the Planets from the Sun;
but the celebrated Dr. Halley has, in the Philosophical Transactions, shewed
us a more certain method for finding the distances of the Planets; which is
by observing the Transit of Venus over the Sun.
The eye judgeth of the magnitudes of far distant
objects, according to the quantities of the angles under How the
Magnitudes of the
which they are seen (which are called their apparent Planets are
magnitudes;) and these angles appear greater or less in a determined.
certain proportion to their distances. Wherefore the
distances of the Planets from the Earth, and their apparent Fig. 8.
diameters being given, their true diameters (and from thence
their magnitudes) may be found. How the distances of the Planets may be
found has been already shewn; their apparent diameters are found by a
telescope, having a machine fix’d to it for measuring of angles, called a
Micrometer. Let BD, or the angle BAD be the apparent diameter of any

Planet, and AB, or AD, (which by reason of the great distance of the Planets
in respect of their magnitudes) may be considered as being the distance of
the said Planet from the observer. Now in the triangle ABD, having the
sides AB, AD, given, and the angle, A, we have also the other angles B and
D, (because the Side AB, AD, are equal) whence the side BD the diameter
of the Planet may be easily found by Trigonometry.
From hence it appears, that the same body at
different distances, will seem to have very different Why the Moon
appears bigger than
magnitudes. Thus the diameter BD will appear from the any of the Planets.
point E, to be twice as large as from the point A. It also
follows, that a small body, when at no great distance from us, may appear to
be equal, or even to exceed another at a great distance, tho’ immensely
bigger. Thus b d appears under the same angle, and consequently of the
same bigness from the point A, that the line B D doth, tho’ one vastly
exceeds the other. And this is the reason, why the Moon, which is much less
than any of the Planets, appears to us vastly bigger than either of them, and
even to equal the Sun himself, which is many thousand times greater in
magnitude.
The distances of the Planets, and periods round the Sun, their diameters
and velocities round their own axis, according to modern computations, are
as follows:
Revolves about
the Sun in the Distance
space of in Miles
Y. D. H.
Saturn 29:167:22 777.000.000
Jupiter 11:314:12 424.000.000
Mars 1:321:23 123.000.000
Earth 0:365: 6 81.000.000
Venus 0:224:16 59.060.000
Mercury 0: 87:23 32.000.000

Round the
Earth.
D. H. M.

Revolves about
the Sun in the Distance
space of in Miles
Y. D. H.
Moon 27: 7:43 240.000

Periods round
Diameters
their own axis
in Miles.
D. H. M.
Sun 25 : 6: 0 763.000
Saturn : : 61.000
Jupiter 0: 9 : 56 81.000
Mars 1: 0 : 40 4.440
Earth 0 : 23 : 56 7.970
Venus 24 : 8: 0 7.900
Mercury : : 4.240
Moon 27 : 7 : 43 2.170

The cause of Eclipses and Phases of the Moon, and some other
phænomena not here explained, shall be shewed when we come to give a
Description of the Orrery.
Plate 2.

Besides the Planets already mentioned, there are other great bodies that
sometimes visit our system, which are a sort of temporary Planets; for they
come and abide with us for a while, and afterwards withdraw from us, for a
certain space of time, after which they again return. These wandering
bodies are called Comets.
The motion of Comets in the Heavens, according to the best
observations hitherto made, seem to be regulated by the same Of

immutable law that rules the Planets; for their orbits are Comets.
elliptical, like those of the Planets, but vastly narrower, or more
excentric. Yet they have not all the same direction with the Planets, who
move from West to East, for some of the Comets move from East to West;
and their orbits have different inclinations to the Earth’s orbit; some
inclining Northwardly, others Southwardly, much more than any of the
Planetary orbits do.
Altho’ both the Comets and the Planets move in elliptic orbits, yet their
motions seem to be vastly different: For the excentricities of the Planet’s
orbits are so small, that they differ but little from circles; but the
excentricities of the Comets are so very great, that the motions of some of
them seem to be almost in right lines, tending directly towards the Sun.
Now, since the orbits of the Comets are so extremely excentric, their
motions, when they are in their Perihelia, or nearest distance from the sun,
must be much swifter than when they are in their Aphelia, or farthest
distance from him; which is the reason why the Comets make so short a
stay in our system; and when they disappear, are so long in returning.
The figures of the Comets are observed to be very different; some of
them send forth small beams, like hair, every way round them; others are
seen with a long fiery tail, which is always opposite to the Sun. Their
magnitudes are also very different, but in what proportion they exceed each
other, it is as yet uncertain. Nor is it probable, that their numbers are yet
known, for they have not been observed with due care, nor their theories
discovered, but of late years. The ancients were divided in their opinions
concerning them; some imagined that they were only a kind of Meteors
kindled in our atmosphere, and were there again dissipated; others took
them to be some ominous prodigies: But modern discoveries prove, that
they are Worlds subject to the same laws of motion as the Planets are; and
they must be very hard and durable bodies, else they could not bear the vast
heat that some of them, when they are in their Perihelia, receive from the
Sun, without being utterly consumed. The great Comet which appeared in
the year 1680, was within ¹/₆ part of the Sun’s diameter from his surface;
and therefore its heat must be prodigiously intense beyond imagination.
And when it is at its greatest distance from the Sun, the cold must be as
rigid.

SECT. II.

Of the Fixed Stars.
he fixed Stars are those bright and shining bodies,

T which in a clear night appear to us every where The fixed Stars are
dispersed through the boundless regions of space. at immense distance
from us.
They are term’d fix’d, because they are found to keep
the same immutable distance one from another in all ages, without having
any of the motions observed in the Planets. The fixed Stars are all placed at
such immense distances from us, that the best of telescopes represent them
no bigger than points, without having any apparent diameters.
It is evident from hence, that all the Stars are
luminous bodies, and shine with their own proper and The fixed Stars are
luminous bodies
native light, else they could not be seen at such a great like the Sun.
distance. For the Satellites of Jupiter and Saturn, tho’
they appear under considerable angles through good telescopes, yet are
altogether invisible to the naked eye.
Although the distance betwixt us and the Sun is
vastly large, when compared to the diameter of the The distance from
Earth, yet it is nothing when compared with the us to the Sun is
nothing in
prodigious distance of the fixed Stars; for the whole comparison of the
diameter of the Earth’s annual orbit, appears from the vast distance of the
fixed Stars.
nearest fixed Star no bigger than a point, and the fixed
Stars are at least 100,000 times farther from us than we are from the Sun; as
may be demonstrated from the observation of those who have endeavoured
to find the Parallax of the Earth’s annual Orb, or the angle under which the
Earth’s orbit appears from the fixed Stars.

Hence it follows, that tho’ we approach nearer to
some fixed Stars at one time of the year than we do at As to appearance,
the opposite, and that by the whole length of the the Earth may be
consider’d as being
diameter of the Earth’s orbit; yet this distance being so the center of the
small in comparison with the distance of the fixed Stars, Heavens.
their magnitudes or positions cannot thereby be sensibly
altered; therefore we may always, without error, suppose ourselves to be in
the same center of the Heavens, since we always have the same visible
prospect of the Stars without any alteration.
If a spectator was placed as near to any fixed Star, as
we are to the Sun, he would there observe a body as big, The fixed Stars are
Suns.
and every way like, as the Sun appears to us: and our
Sun would appear to him no bigger than a fixed Star: and undoubtedly he
would reckon the Sun as one of them in numbering the Stars. Wherefore
since the Sun differeth nothing from a fixed Star, the fixed Stars may be
reckoned so many Suns.
It is not reasonable to suppose that all the fixed Stars
are placed at the same distance from us; but it is more The fixed Stars are
at vast distance
probable that they are every where interspersed thro’ the from each other.
vast indefinite space of the universe; and that there may
be as great a distance betwixt any two of them, as there is betwixt our Sun
and the nearest fixed Star. Hence it follows, why they appear to us of
different magnitudes, not because they really are so, but because they are at
different distances from us; those that are nearest excelling in brightness
and lustre those that are most remote, who give a fainter light, and appear
smaller to the eye.

The astronomers distribute the Stars into several
orders or classes; those that are nearest to us, and appear The distribution of
brightest to the eye, are called Stars of the first the Stars into 6
classes.
magnitude; those that are nearest to them in brightness
and lustre, are called Stars of the second magnitude; Of Telescopical
those of the third class, are stiled Stars of the third Stars.
magnitude; and so on, until we come to the Stars of the
sixth magnitude, which are the smallest that can be discerned by the naked
eye. There are infinite numbers of smaller Stars, that can be seen through
telescopes; but these are not reduced to any of the six orders, and are only
called Telescopical Stars. It may be here observed, that tho’ the astronomers
have reduced all the Stars that are visible to the naked eye, into some one or
other of these classes, yet we are not to conclude from thence that all the
Stars answer exactly to some or other of these orders; but there may be in

reality as many orders of the Stars, as they are in number, few of them
appearing exactly of the same bigness and lustre.
The ancient astronomers, that they might distinguish
the Stars, in regard to their situation and position to each The Stars digested
into constellations
other, divided the whole starry firmament into Several
Asterisms, or systems of Stars, consisting of those that are near to one
another. These Asterisms are called Constellations, and are digested into the
forms of some animals; as Men, Lyons, Bears, Serpents, &c. or to the
images of some known things; as, of a Crown, a Harp, a Triangle, &c.
The starry firmament was divided by the ancients into 48
images, or constellations; twelve of which they placed in that Zodiac.
part of the Heavens wherein are the planes of the Planetary
orbits; which part is called the Zodiac, because most of the constellations
placed therein resemble some living creature. The two regions of the
Heavens that are on each side of the Zodiac, are called the North and South
parts of the Heavens.
The constellations within the Zodiac are, 1. Aries,
the Ram; 2. Taurus, the Bull; 3. Gemini, the Twins; 4. Constellations
within the Zodiac.
Cancer, the Crab; 5. Leo, the Lion; 6. Virgo, the Virgin;
7. Libra, the Balance; 8. Scorpio, the Scorpion; 9. Sagittarius, the Archer;
10. Capricornus, the Goat; 11. Aquarius, the Water-Bearer; and, 12. Pisces,
the Fishes.
The constellations on the North side of the Zodiac are
Twenty-one, viz. the Little Bear; the Great Bear; the Dragon; Northern
constellat
Cepheus, a king of Ethiopia; Bootes, the keeper of the Bear; the ions.
Northern Crown; Hercules with his Club, watching the Dragon;
the Harp; the Swan; Cassiopeia; Persius; Andromeda; the Triangle; Auriga;
Pegasus, or the Flying Horse; Equuleus; the Dolphin; the Arrow; the Eagle;
Serpentarius; and the Serpent.
The constellations noted by the ancients on the South side of
the Zodiac, were fifteen, viz. the Whale; the river Eridanus; the Southern
constellat
Hare; Orion; the Great Dog; Little Dog; the Ship Argo; Hydra; ions.
the Centaur; the Cup; the Crow; the Wolf; the Altar; the
Southern Crown; and the Southern Fish. To these have been lately added
the following, viz. The Phœnix; the Crane; the Peacock; the Indian; the Bird

of Paradise; the Southern Triangle; the Fly; Cameleon; the Flying Fish;
Toucan, or the American Goose; the Water Serpent, and the Sword Fish.
The ancients placed those particular constellations or figures in the
Heavens, either to commemorate the deeds of some great man, or some
notable exploit or action; or else took them from the fables of their religion,
&c. And the modern astronomers do still retain them, to avoid the confusion
that would arise by making new ones, when they compare the modern
observations with the old ones.
Some of the principal Stars have particular names given
them, as Syrius, Arcturus, &c. There are also several Stars that Unformed
Stars.
are not reduced into constellations, and these are called
Unformed Stars.
Besides the Stars visible to the naked eye, there is a very
remarkable space in the Heavens, called the Galaxy, or Milky The
Galaxy,
Way. This is a broad circle of a whitish hue, like milk, going or Milky
quite round the whole Heavens, and consisting of an infinite Way.
number of small Stars, visible thro’ a telescope, tho’ not
discernable by the naked eye, by reason of their exceeding faintness; yet
with their light they combine to illustrate that part of the Heavens where
they are, and to cause that shining whiteness.
The places of the fixed Stars, or their relative situations one from
another, have been carefully observed by astronomers, and digested into
catalogues. The first among the Greeks, who reduced the Stars into a
catalogue, was Hypparchus, who, from his own observations, and of those
who lived before him, inserted 1022 Stars into his catalogue, about 120
years before the Christian Æra: This catalogue has been since enlarged and
improved by several learned men, to the number of 3000, of which there are
a great many telescopical, and not to be discerned by the naked eye; and
these are all ranked in the catalogue as the Stars of the seventh magnitude.
It may seem strange to some, that there are no more than this number of
Stars visible to the naked eye; for sometimes in a clear night they seem to
be innumerable: but this is only a deception of our sight, arising from their
vehement sparkling, while we look upon them confusedly, without reducing
them into any order; for there can seldom be seen above 1000 Stars in the
whole Heavens with the naked eye at the same time; and if we should

distinctly view them, we shall not find many but what are inserted upon a
good Celestial Globe.
Altho’ the number of Stars that can be discerned by the naked eye are so
few, yet it is probable there are many more which are beyond the reach of
our optics, for through telescopes they appear in vast multitudes, every
where dispersed throughout the whole Heaven; and the better our glasses
are, the more of them we still discover. The ingenious Dr. Hook has
observed 78 Stars in the Pleiades, of which the naked eye is never able to
discern above 7; and in Orion, which has but 80 Stars in the British
catalogue (and some of them telescopical) there has been numbered 2000
Stars.
Those who think that all these glorious bodies were created
for no other purpose than to give us a little dim light, must An idea
of the
entertain a very slender idea of the Divine Wisdom; for we Universe.
receive more light from the Moon itself, than from all the Stars
put together. And since the Planets are subject to the same laws of motion
with our Earth, and some of them not only equal, but vastly exceed it in
magnitude, it is not unreasonable to suppose, that they are all habitable
Worlds. And since the Fixed Stars are no ways behind our Sun, either in
bigness or lustre, is it not probable, that each of them have a system of
Planetary Worlds turning round them, as we do round our Sun? And if we
ascend as far as the smallest Star we can see, shall we not then discover
innumerable more of these glorious bodies, which now are altogether
invisible to us? And so ad infinitum, thro’ the boundless space of the
universe. What a magnificient idea must this raise in us of the Divine Being!
Who is every where, and at all times present, displaying his Divine Power,
Wisdom and Goodness, amongst all his Creatures!

The DESCRIPTION and USE of the
Celestial and Terrestrial Globes.
Globe or Sphere is a round solid body, having every
part of its surface equally distant from a point within Globe or
it, called its Center; and it may be conceived to be Sphere.
formed by the revolution of a semicircle round its diameter.
Any circle passing through the center of the sphere, thereby
dividing into two equal parts or segments, is called a Great Great
Circle.
Circle; and the segments of the sphere so divided, are called
Hemispheres.
Hemisphe
Every great circle has its Poles and Axis. res.

The Poles of a great circle are two points on the surface of
the sphere, diametrically opposite to one another, and every Poles.
where equally distant from the said circle.
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 Axis.
therefore perpendicular to the Plane: Therefore
All circles passing through the Poles of any great circle,
intersect it in two places diametrically opposite, and also at right Secundari
es.
angles; and with respect to the said great circle, they may be
called its Secundaries.
All circles dividing the sphere into two unequal parts, are
called lesser or parallel Circles, and are usually denominated by Parallel
or lesser
that great circle to which they are parallel. Circles.
The Earth being globular, its outward parts, as the several
Countries, Seas, &c. are best, and most naturally represented Terrestria
upon the surfaces of a Globe; and when such a body has the l Globe.
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.

The Celestial Bodies appear to us as if they were all placed
in the same concave sphere, therefore astronomers place the Celestial
Stars according to their respective situations and magnitudes, Globe.
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 uses of the Globes (besides their
serving as Maps, to distinguish the outward parts of the The principal use of
the Globes.
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.
It has been shewed in the Introduction, that the
distance of the Earth from the Sun, is no more than a There will be the
same prospect of
point, when compared with the immense distance of the the fixed Stars
fixed Stars; therefore let the Earth be in what point whether the
soever of her orbit, there will be the same prospect of the spectator be placed
on the Earth, or in
Heavens, as a spectator would observe did he reside in the Sun.
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.
n order to determine the relative situations of places
I upon the Earth, as well as the positions of the fixed The Circles of the
Stars, and other Celestial phænomena, the Globe of
Sphere.

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.

1. The Equator, or the Equinoctial, is that great
circle in the Heavens, in whose plane the Earth performs The Equator, or
her diurnal motion round her axis; or it is that great Equinoctial.
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.
The equinoctial divides the globe of the Earth, and
also the whole Heavens into two equal parts, North and Northern and
Southern
South, which are called the Northern and Southern Hemispheres.
Hemispheres. The axis of this circle, is called the Axis of
the World, or the Earth’s Axis, because the Earth The Axis of the
revolves about it (from West to East) in 24 hours. The World.
extreme of this axis are called the Poles of the World,
whereof that which lies in the Northern Hemisphere, is Poles of the World,
called the North Pole, and the other is called the South or of the Equator.
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.
2. All circles conceived to pass through the Poles of
the world, intersecting the equinoctial at right angles, Hour Circles or
Circles of
are, with respect to any point in the Heavens, called Ascension, also
Hour Circles; and the Circles of Ascension, because the called Meridians.
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 Meridians are commonly drawn upon the Terrestrial
Globe thro’ every 15 degrees of the equinoctial, thereby making The
Brass
an Hour difference betwixt the places through which they pass. Meridian.
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.
There is also a little brass circle fixed upon this meridian,
divided into 24 Hours, having an index moveable round the axis The Hour
Circle.
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.
3. All circles parallel to the equinoctial are, with respect to
any point in the Heavens, called Parallels of Declination. So Parallels
of
that, Declinati
on.
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 Declination North
and South.
betwixt it and the equator; and if the said point be to the

(Northward/Southward) of the equator, it is called (North/South)
Declination.
Of the parallels of declination, four are eminently
distinguished by particular names, viz. The two Tropics, and the Tropics
and Polar
two Polar Circles. Circles.
The tropics are on different sides of the equator each
23 degrees and 29 minutes distant from it; that which Tropic of Cancer;
lies in the Northern Hemisphere, is called the Tropic of of Capricorn.

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

7. The Ecliptic is that great circle in whose plane the Earth
performs its annual motion round the Sun; or, in which the Sun Ecliptic.
Equinocti
seems to move round the Earth, once in a year. This circle al.
makes an angle with the equinoctial of 23 degrees 29 minutes, Solstitial
and intersects it in two opposite points, which are called the Points.
Colures.
Equinoctial Points; and the two points in the ecliptic that are at Equinocti
the greatest distance from the equinoctial points, are called the al Colure.
Solstitial Points. The two meridians passing through those Solstitial
Colure.
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 is divided into 12 equal parts, called
Signs, each sign being 30 degrees, beginning from one The Ecliptic
divided into signs.
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. ♓
The first six of these are called the Northern Signs, and Northern
possess that half of the ecliptic which is to the Northward of the Signs.
equator; beginning with the first point of ♈, and ending with the
last point of ♍.
The latter six are called the Southern Signs, because they
possess the Southern half of the ecliptic; beginning at the first Southern
Signs.
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.
The Poles of the Ecliptic are both situated in the
Solstitial Colure, at 23 degrees, 29 minutes distance Poles of the
Ecliptic.
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.
8. All great circles passing through the Poles of the
ecliptic, and consequently intersecting it at right angles, Circles of
Longitude.
are called Circles of Longitude: So that,
9. The Longitude of any Point in the Heavens (as a
Star or Planet, &c.) is an arch of the ecliptic contained Longitude of any
Point in the
between the circle of longitude passing thro’ that point, Heavens.
and the equinoctial point ♈. And that degree of any sign
which lies under the circle of longitude, passing thro’ any Star Place of a
or Planet, is called the Place of that Star or Planet. Star.

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,
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’ Latitude
of a Star,
that point, and intercepted betwixt it, and the ecliptic; or, the &c.
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.

12. The Horizon is that great circle which divides the upper,
or visible Hemisphere of the world, from the lower, or invisible: Horizon.
This circle is distinguished into two sorts, the Sensible, and the
Rational.
The Sensible, or Apparent Horizon, is that circle which
limits or determinates our prospect, whether we are at land or Sensible
Horizon.
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.
The Rational, or true Horizon, is a great circle passing thro’
the center of the Earth, parallel to the sensible Horizon, being Rational
Horizon.
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.
This circle is divided by astronomers into four
quadrants, and each of the quadrants into 90 degrees, Cardinal Points of
the Horizon.
&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.
Besides the aforementioned divisions of the Horizon into
degrees. Mariners divide it into 32 equal parts, which they call Points of
the
the Points of the Compass; to each of which points they give a Compass.
particular name, compounded of the four Cardinals, according
to what quarter of the Compass is intended.
The center of the Horizon is the place of observation, and
the Poles of it are one exactly over our heads, called the Zenith; Zenith.
and the other exactly under our feet, called the Nadir.
Nadir.
13. All circles conceived to pass thro’ the Zenith and Nadir,
are called Vertical Circles, or Azimuths. Of these circles, that
Vertical
which passeth thro’ the North and South points of the Horizon, Circles.
is called the Meridian; so that when any object is upon the
Meridian, it then bears either due South, or due North from us;
Meridian.
and the Azimuth of any object is an arch of the Horizon
intercepted between the vertical circle passing through it, and
Azimuth.

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.
The vertical circle passing thro’ the East and West points of
the horizon, is called the Prime Vertical, or Circle of East and Prime
Vertical.
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.
That degree in the horizon wherein any object rises or sets
from the East or West points, is called the Amplitude; which for Amplitud
e.
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.
14. All circles drawn parallel to the horizon, in the upper
hemisphere, are called Almacanthers, or Parallels of Altitude: Almacant
hers.
So that the Altitude of any point in the Heavens is an arch of the Altitudes.
vertical circle passing thro’ that point, and intercepted betwixt it Meridian

and the horizon; and if the object be upon the meridian, it is Altitude.
Zenith
commonly called the Meridian Altitude. The complement of the Distance.
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.
The fiducial edge thereof representing the Vertical Circles,
and the Degrees upon it, describing the Parallels of Altitude. Quadrant
of
This thin plate is called the Quadrant of Altitude. 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.
15. A Parallel Sphere is that position where the equator
coincides with the horizon, and consequently the poles of the Parallel
Sphere.
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.

16. A Right or Direct Sphere is that position where the
equator is perpendicular to the horizon, the inhabitants whereof Right
Sphere.
are those who live under the equinoctial.
17. An Oblique Sphere is when the equinoctial and
the horizon make oblique angles with each other, which Oblique Sphere.
every where happens but under the equator and the
poles.
The arch of any parallel or declination, which stands
above the horizon is called the Diurnal Arch; and the Diurnal and
Nocturnal Arch.
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,
18. The Right Ascension of the Sun, Moon, or any Star, &c.
is an arch of the equator contained betwixt the beginning of ♈, Right
Ascension
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.
19. Oblique Ascension, or Descension, is an arch of the
equinoctial intercepted between the beginning of ♈ , and that Oblique
Ascension
Point of the Equator which rises or sets with any point in the .
Heavens in an oblique sphere.
20. Ascensional Difference, is the difference betwixt the
right and oblique ascension or descension, and shews how long Ascension
al
the Sun rises or sets before or after the hour of six. Differenc
e.

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.
A Natural Day is the space of time elapsed while the
Sun goes from any meridian or horary circle, ’till he Natural and
Artificial Day.
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.
The Natural Day is divided into 24 Hours, each hour into 60
Minutes, each minute into 60 Seconds, &c. The Artificial Days Hours,
&c.
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 Equinoxes.
the 21st of March, and the 23d of September; at those
times the Sun rises at six and sets at six to all the Vernal and
inhabitants of the Earth. These days are called the Autumnal Equinox.
Equinoxes, or Equinoctial Days; the first of which, or
when the Sun is in the first point of Aries, is called the Vernal Solstices.
Equinox, and the latter is called the Autumnal Equinox.
In all places where the Sun descends below the horizon, Summer and Winter
excepting under the equator, the days continually Solstices.
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.
All nations do not begin their day, and reckon their hours
alike. In Great-Britain. France, and Spain, and in most places in The
different
Europe, the days is reckoned to begin at midnight, from whence beginning
is counted twelve hours ’till noon, then twelve hours more ’till of the
next midnight, which makes a compleat day; yet the day.
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.

The Babylonians began their day at Sun-rising, and
reckoned 24 hours ’till he rose again! This way of computation Babylonis
we call the Babylonish Hours. In several parts of Germany they h Hours.
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, Italian
Hours.
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.
The Jews and the Romans formerly divided the artificial
days and nights each into 12 equal parts; these are termed the Jewish
Hours.
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 Planetary Hours.
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 is a system of seven days, in which each day is
distinguished by a different name. In most countries these days A Week.
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 is properly a certain space of time measured by the
Moon in his course round the Earth. A Lunar Month is either A Month.
Periodical or Synodical. A Periodical Month is that
space of time the Moon takes to perform her course from Periodical and
one point in the ecliptic ’till she arrives to the same Synodical Month.
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.
The compleatest period of time is a Year, in which
all the variety of seasons return, and afterwards begin A Year Sydereal and
Tropical.
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.
The Civil Year is the same with the Political established
with the laws of a country; and is either moveable or Egyptian
Year.
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:

Thirty Days hath September,
April, June, and November;
February hath Twenty-eight alone,
And all the rest have Thirty-one.

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.
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 Bissextile
, or Leap-
than four solar years by a whole day; and therefore in 365 times Year.
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.
This method of reckoning the year, viz. making the common
year to consist of 365 days, and every fourth year to have 366 Julian
Account
days, is now used in Great-Britain and Ireland, and some of the or the Old
Northern parts of Europe, and is called the Julian Account, or Style.
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.
At the time of the Council of Nice, when the terms were
settled for observing of Easter, the Vernal Equinox fell upon the Gregoria
n
21st of March; but by its falling backwards 11 minutes every Account,
year, it was found that in Anno 1582, when the kalendar was or New
corrected, the Sun entered the equinoctial circle on the 11th of Style.
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.
The Atmosphere is that thin body of air which surrounds the
Earth, in which the clouds hover, and by which in their descent Atmosphe
re.
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.
This small illumination of the atmosphere, and the
state of the Heavens between day and night, is called the Twilight, or
Crepusculum.
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.
he situations of places upon the Earth, are determined by their Latitude
T and Longitude.
1. The Latitude of any place (upon the Earth) is its nearest
distance, either North or South from the Equator; and if the Latitude.
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.
2. Difference of latitude is the nearest distance betwixt any Differenc
two parallels of latitude, shewing how far the one is to the e of
Northward or Southward of the other, which can never exceed Latitude.
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.
3. The Longitude of any place (upon the Earth) is an arch of
the equator, contained betwixt the meridian of the given place, Longitude
.
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.

4. Zones are large tracts of the surface of the Earth,
distinguished by the tropics and polar circles, being five Zones, Torrid,
Temperate, and
in number; viz. one Torrid, two Temperate and two Frigid.
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.
The inhabitants of the Earth are also distinguished by the
diversity of their Shadows. Those who live in the torrid zone, Amphisci
ans.
are called Amphiscians, because their noon-shadow is cast Ascians.
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.
The inhabitants of the temperate zones, are called
Heteroscians, because their noon-shadow is always cast Heteroscians.
Ascians
the same way: But those who live under the tropics are Heteroscians.
called Ascians Heteroscians; those who live in the frigid

zones are called Periscians, because sometimes their shadow is
cast round about them. Periscian
s.
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.
5. The Periœci are those who live under opposite points of
the same parallel of latitude. They have their seasons of the year Periœci.
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.
6. The Antœci live under the same meridian, and in the same
latitude, but on different sides of the equator; their Seasons of Antœci.
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.
7. The Antipodes are those who live diametrically opposite
to one another, standing, as it were, exactly feet to feet: Their Antipodes
.
days and nights, summer and winter, are at direct contrary times.
The surface of the Earth is by some distinguished into 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 Climates.
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.

Longest Latitude. Breadth
Climates
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

Longest Latitude. Breadth
Climates
Day. D. M. D. M.
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.

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

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.
9. A Continent is a large quantity of land, in which many
great countries are joined together, without being separated from Continent
.
each other by the sea: such are Europe, Asia, Africa, and the Main
vast continent of America; which four are the principal divisions Land.
of the Earth. A continent is sometimes called the Main Land.
10. An Island is a country, or portion of land, environed
round with water: such are Great-Britain and Ireland; Sardinia, Island.
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.
11. A Peninsula is a part of land almost environed with
water, save one narrow neck adjoining it to the continent; or Peninsula
.
which is almost an island: such is Denmark joining to Germany;
also Africa is properly a large peninsula joining to Asia.
12. An Isthmus is a narrow neck of land joining a peninsula
to the continent; as the Isthmus of Sues, which joins Africa to Isthmus.
Asia, that of Panama, joining North and South America, &c.
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 Promonto
ry.
Cape of Good Hope in the South of Africa; Cape Finistre on the Mountain
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.
14. A Coast or Shore is that part of land which
borders upon the sea, whether it be in islands or a A Coast or Shore.
Inland.
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.
15. The Ocean, or Main Sea, is a vast spreading
collection of water, not divided or separated by lands The Ocean, or Main
Sea.
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.
16. A Lake is a collection of deep standing water, inclosed
all round with land, and not having any visible and open A Lake.
communication with the sea: But when this lake is very large, it
is commonly called a sea; as the Caspian Sea in Asia, &c.
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 A Gulf.
Creek or
Gulf of Venice, &c. But if it be very large, ’tis rather called an Haven.
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.
18. A Strait is a narrow passage lying between two shores,
whereby two seas are joined together; as, the Straits of Dover, A Strait.
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.
1. That side of the Brazen Meridian, which is divided into
degrees, represents the true Meridian; this side is commonly Brass
Meridian.
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.
2. The upper side of the wooden frame called the Wooden
Horizon; represents the true horizon; the circles drawn upon this Wooden
Horizon.
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.
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 Quadrant
of
meridian of either globe, as occasion requires. The edge of this Altitude.
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.

4. The Horary or Hour Circle, is divided into twice twelve
hours, the two XII’s coinciding with the meridian; the Hour
Circle.
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.

urn the globe round its axis, ’till the given place lies exactly under the

T (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. 2½E.
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 52P. M.
Constantinople 2 07P. M.
At
Vera-Cruz 5 30A. M.
Pekin in China 7 50P. 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.
In the preceding problem, the globe being rectified according to the
Sun’s declination, the upper parts of the parallels of latitude, represented the
Diurnal Arches, or the length of the days all over the world, at that
particular time: Here we are to rectify the globe according to the latitude of
the place, and then the upper parts of the parallels of declination are the
diurnal arches; and the length of the days at all times of the year, may be
here determined by finding the number of hours contained between the two
extreme meridians, which cut any parallel of declination in the Eastern and
Western points of the horizon; after the same manner, as before we found
the length of the day in the several latitudes at a particular time of the year.
1. Let the place proposed be under the equinoctial, and let the globe be
accordingly rectified for 00 degrees of latitude, which is called a direct
position of the sphere. Here all the parallels of latitude, which in this case
we will call the parallels of declination, are cut by the horizon into two
equal parts; and consequently those who live under the equinoctial, have the
days and nights of the same length at all times of the year; and also in this

part of the Earth, all the Stars rise and set, and their continuance above the
horizon, is equal to their stay below it, viz. 12 hours.
If from this position we gradually move the globe according to the
several alterations of latitudes, which we will suppose to be Northerly; the
lengths of the Diurnal Arches will continually increase, until we come to a
parallel of declination, as far distant from the equinoctial, as the place itself
is from the Pole. This parallel will just touch the horizon, and all the
heavenly bodies that are betwixt it and the Pole never descend below the
horizon. In the mean time, while we are moving the globe, the lengths of
the diurnal arches of the Southern parallels of declination, continually
diminish in the same proportion that the Northern ones increased; until we
come to that parallel of declination which is so far distant from the
equinoctial Southerly, as the place itself is from the North Pole. The upper
part of this Parallel just touches the horizon, and all the Stars that are
betwixt it and the South Pole never appear above the horizon. And all the
nocturnal arches of the Southern parallels of declination, are exactly of the
same length with the diurnal arches of the correspondent parallels of North
declination.
2. Let us take a view of the globe when it is rectified for the latitude of
London, or 51½ degrees North. When the Sun is in the tropic of ♋, the day
is about 16½ hours; as he recedes from this tropic, the days proportionably
shorten, until, he arrives into ♑, and then the days are at the shortest, being
now of the same length with the night, when the Sun was in ♋ , viz. 7½
hours. The lower part of that parallel of declination, which is 38½ degrees
from the equinoctial Northerly, just touches the horizon; and the Stars that
are betwixt this parallel and the North Pole, never set to us at London. In
like manner the upper part of the Southern parallel of 38½ degrees just
touches the horizon, and the Stars that lie betwixt this parallel and the
Southern Pole, are never visible in this latitude.
Again, let us rectify the globe for the latitude of the Arctic Circle, we
shall then find, that when the Sun is in ♋, he touches the horizon on that
day without setting, being 24 hours compleat above the horizon; and when
he is in Capricorn, he once appears in the horizon, but does not rise in the
space of 24 hours: When he is in any other point of the ecliptic, the days are
longer or shorter, according to his distance from the tropics. All the Stars
that lie between the tropic of Cancer, and the North Pole, never set in this

latitude; and those that are between the tropic of Capricorn, and the South
Pole, are always hid below the horizon.
If we elevate the globe still higher, the circle of perpetual Apparition
will be nearer the equator, as will that of perpetual Occultation on the other
side. For example, Let us rectify the globe for the latitude of 80 degrees
North: when the Sun’s declination is 10 degrees North; he begins to turn
above the horizon without setting; and all the while he is making his
progress from this point to the tropic of ♋, and back again, he never sets.
After the same manner, when his declination is 10 degrees South, he is just
seen at noon in the horizon; and all the while he is going Southward, and
back again, he disappears, being hid just so long as before, at the opposite
time of the year he appeared visible.
Let us now bring the North Pole into the Zenith, then will the
equinoctial coincide with the horizon; and consequently all the Northern
parallels are above the horizon, and all the Southern ones below it. Here is
but one day and one night throughout the year, it being day all the while the
Sun is to the Northward of the equinoctial, and night for the other half year.
All the Stars that have North declination, always appear above the horizon,
and at the same height; and all those that are on the other side, are never
seen.
What has been here said of rectifying the globe to North latitude, holds
for the same latitude South; only that before the longest days were, when
the Sun was in ♋, the same happening now when the Sun is in ♑; and so of
the rest of the parallels, the seasons being directly opposite to those who
live in different hemispheres.
I shall again explain some things delivered above in general terms, by
particular problems.
But from what has been already said, we may first make the following
observations:
1. All places of the Earth do equally enjoy the benefit of
the Sun, in respect of time, and are equally deprived of it, the
Days at one time of the Year, being exactly equal to the
Nights at the opposite season.

2. In all places of the Earth, save exactly under the
Poles, the Days and Nights are of equal length (viz. 12
hours each) when the Sun is in the equinoctial.
3. Those who live under the equinoctial, have the days
and nights of equal lengths at all times of the year.
4. In all places between the equinoctial and the Poles,
the days and nights are never equal, but when the Sun is in
the equinoctial points ♈ and ♎.
5. The nearer any place is to the equator, the less is the
difference between the length of the artificial days and
nights in the said place; and the more remote the greater.
6. To all the inhabitants lying under the same parallel of
latitudes the days and nights are of equal lengths, and that
at all times of the year.
7. The Sun is vertical twice a year to all places between
the tropics; to those under the tropics, once a year; but
never any where else.
8. In all places between the Polar Circles, and the Poles,
the Sun appears some number of days without setting; and
at the opposite time of the year he is for the same length of
time without rising; and the nearer unto, or further remote
from the Pole, those places are, the longer or shorter is the
Sun’s continued presence or absence from the Pole.
9. In all places lying exactly under the Polar Circles, the
Sun, when he is in the nearest tropic, appears 24 hours
without setting; and when he is in the contrary tropic, he is
for the same length of time, without rising; but at all other
times of the year, he rises and sets there, as in other places.
10. In all places lying in the (Northern/Southern)
hemisphere, the longest day and shortest night, is when the
Sun is in the (Northern/Southern) tropic, and on the
contrary.

Prob. XVIII. The Latitude of any place, not
exceeding 66½ degrees, and the day of the Month
being given; to find the time of Sun-rising and
setting, and the length of the Day and Night.

Having rectified the globe according to the latitude, bring the Sun’s
place to the meridian, and put the hour index to 12 at noon; then bring the
Sun’s place the Eastern part of the horizon, and the index will shew the time
when the Sun rises. Again, turn the globe until the Sun’s place be brought to
the Western side of the horizon, and the index will shew the time of Sun-
setting.
The hour of Sun-setting doubled, gives the length of the day; and the
hour of Sun-rising doubled, gives the length of the night.
Let it be required to find when the Sun rises and sets at London on the
20th of April. Rectify the globe for the latitude of London, and having
found the Sun’s place corresponding to May the 1st, viz. ♉ 10¾ degrees,
bring ♉ to 10¾ degrees to the meridian, and set the index to 12 at noon;
then turn the globe about ’till ♉ 10¾ degrees be brought to the Eastern part
of the horizon, and you’ll find the index point 4¾ hours, this being doubled,
gives the length of the night 9½ hours. Again, bring the Sun’s place to the
Western part of the horizon, and the index will point 7¼ hours, which is the
time of Sun-setting; this being doubled, gives the length of the day 14½
hours.

Prob. XIX. To find the length of the longest and
shortest Day and Night in any given place, not
exceeding 66½ degrees of Latitude.

Note, The longest day at all places on the (North/South)
side of the equator, is when the Sun is in the first point of
(Cancer/Capricorn) Wherefore having rectified the globe
for the latitude, find the time of Sun-rising and setting, and
thence the length of the day and night, as in the last problem,
according to the place of the Sun: Or, having rectified the
globe for the latitude, bring the solstitial point of that
hemisphere, to the East part of the horizon, and set the index

to 12 at noon; then turning the globe about ’till the said
solstitial point touches the Western side of the horizon, the
number of hours from noon to the place where the index
points (being counted according to the motion of the index)
is the length of the longest day; the complement whereof to
24 hours, is the length of the shortest night, and the reverse
gives the shortest day and the longest night.
Longest Day. Shor. N.
Deg. Hours. Hours.
45 15½ 8½
Thus in Lat. 51½ 16½ 7½
60 18½ 5½
If from the length of the longest day, you subtract 12 hours, the number
of half hours remaining, will be the Climate: Thus that place where the
longest day is 16½ hours, lies in the 9th Climate. And by the reverse,
having the Climate, you have thereby the length of the longest day.

Prob. XX. To find in what Latitude the longest Day
is, of any given length, less than 24 hours.

Bring the solstitial point to the meridian, and set the index to 12 at noon;
then turn the globe Westward, ’till the index points at half the number of
hours given; which being done, keep the globe from turning round its axis,
and slide the meridian up or down in the notches, ’till the solstitial point
comes to the horizon, then that elevation of the Pole will be the latitude.
If the hours given be 16, the latitude is 49 degrees; if 20 hours, the
latitude is 63¼ degrees.

Prob. XXI. A place being given in one of the Frigid
Zones (suppose the Northern) to find what
number of Days (of 24 hours each) the Sun doth
constantly shine upon the same, how long he is
absent, and also the first and last Day of his
appearance.

Having rectified the globe according to the latitude, turn it about until
some point in the first quadrant of the ecliptic (because the latitude is
North) intersects the meridian in the North point of the horizon; and right
against that point of the ecliptic on the horizon, stands the day of the month
when the longest day begins.
And if the globe be turned about ’till some point in the second quadrant
of the ecliptic cuts the meridian in the same point of the horizon, it will
shew the Sun’s place when the longest day ends, whence the day of the
month may be found, as before: Then the number of natural days contained
between the times the longest day begins and ends is the length of the
longest day required.
Again, turn the globe about, until some point in the third quadrant of the
ecliptic cuts the meridian in the South part of the horizon; that point of the
ecliptic will give the time when the longest night begins. Lastly, turn the
globe about, until some point in the fourth quadrant of the ecliptic cuts the
meridian in the South point of the horizon; and that point of the ecliptic will
be the place of the Sun when the longest night ends.
Or, the time when the longest day or night begins, being known, their
end may be found by counting the number of days from that time to the
succeeding solstice; then counting the same number of days from the
solstitial day, will give the time when it ends.

Prob. XXII. To find in what Latitude the longest Day
is, of any given length less than 182 Natural
Days.

Find a point in the ecliptic half so many degrees distant from the
solstitial point, as there are days given, and bring that point to the meridian;
then keep the globe from turning round its axis, and move the meridian up
or down until the aforesaid point of the ecliptic comes to the horizon; that
elevation of the Pole will be the latitude required.
If the days given were 78, the latitude is 71½ degrees.
This method is not accurate, because the degrees in the ecliptic do not
correspond to natural days; and also because the Sun does not always move

in the ecliptic at the same rate; however, such problems as these may serve
for amusements.

Prob. XXIII. The day of the Month being given, to
find when the Morning and Evening Twilight
begins and ends, in any place upon the Globe.

In the foregoing problem, by the length of the day, we mean the time
from Sun-rising to Sun-set; and the night we reckoned from Sun-set, ’till he
rose next morning. But it is found by experience, that Total Darkness does
not commence in the evening, ’till the Sun has got 18 degrees below the
horizon; and when he comes within the same distance of the horizon next
morning, we have the first Dawn of Day. This faint light which we have in
the morning and evening, before and after the Sun’s rising and setting, is
what we call the Twilight. [4] Having rectified the globe for the latitude, the
zenith, and the Sun’s place, turn the globe and the quadrant of altitude until
the Sun’s place cuts 18 degrees below the horizon (if the quadrant reaches
so far) then the index upon the hour circle will shew the beginning or
ending of twilight after the same manner as before we found the time of the
Sun-rising and setting, in Prob. 18. But by reason of the thickness of the
wooden horizon, we can’t conveniently see, or compute when the Sun’s
place is brought to the point aforesaid. Wherefore the globe being rectified
as above directed, turn the globe, and also the quadrant of altitude,
Westward, until that point in the ecliptic, which is opposite to the Sun’s
place, cuts the quadrant in the 18th degree above the horizon; then the hour
index will shew the time when day breaks in the morning. And if you turn
the globe and the quadrant of altitude, until the point opposite to the Sun’s
place cuts the quadrant in the Eastern hemisphere, the hour hand will shew
when twilight ends in the evening. Or, having found the time from midnight
when the morning twilight begins, if you reckon so many hours before
midnight, it will give the time when the evening twilight ends. Having
found the time when twilight begins in the morning, find the time of Sun-
rising, by Prob. 18, and the difference will be the duration of twilight.
Thus at London on the 12th of May twilight begins at three quarters past
one o’clock: The Sun rises at about half an hour past four: Whence the
duration of twilight now is 2¾ hours, both in the morning and evening. On

the 12th of November, the twilight begins at half an hour past six, being
somewhat above an hour before Sun-rising.

Prob. XXIV. To find the time when total Darkness
ceases, or when the Twilight continues from Sun-
setting to Sun-setting, in any given place.

Let the place be in the Northern hemisphere; then if the complement of
the latitude be greater than (the depression) 18 degrees, subtract 18 degrees
from it, and the remainder will be the Sun’s declination North, when total
darkness ceases. But if the complement of the latitude is less than 18
degrees, their difference will be the Sun’s declination South, when the
twilight begins to continue all night. If the latitude is South, the only
difference will be, that the Sun’s declination will be on the contrary side.
Thus at London, when the Sun’s declination North is greater than 20½
degrees, there is no total darkness, but constant twilight, which happens
from the 26th of May to the 18th of July, being near two months. Under the
North Pole the twilight ceases, when the Sun’s declination is greater than 18
degrees South, which is from the 13th of November, ’till the 29th of
January: So that notwithstanding the Sun is absent in this part of the world
for half a year together, yet total darkness does not continue above 11
weeks; and besides, the Moon is above the horizon for a whole fortnight of
every month throughout the year.

Prob. XXV. The day of the Month be given; to find
those places of the Frigid Zones, where the Sun
begins to shine continually without setting; and
also those places where he begins to be totally
absent.

Bring the Sun’s place to the meridian, and mark the number of degrees
contained betwixt that point and the equator; then count the same number of
degrees from the nearest Pole (viz. the North Pole, if the Sun’s declination is
Northerly, otherwise the South Pole) towards the equator, and note that
point upon the meridian; then turn the globe about, and all the places which
pass under the said point, are those where the Sun begins to shine

constantly, without setting on the given day. If you lay the same distance
from the opposite Pole towards the equator, and turn the globe about, all the
places which pass under that point, will be those where the longest night
begins.
The Latitude of the place being given, to find the hour of the
day when the Sun shines.
If it be in the summer, elevate the Pole according to the latitude, and set
the meridian due North and South; then the shadow of the axis will cut the
hour on the Dial plate: For the globe being rectified in this manner, the hour
circle is a true Equinoctial Dial; the axis of the globe being the Gnomon.
This holds true in Theory, but it might not be very accurate in practice,
because of the difficulty in placing the horizon of the globe truly horizontal,
and its meridian due North and South.
If it be in the winter half year, elevate the South Pole according to the
latitude North, and let the North part of the horizon be in the South part of
the meridian; then the shade of the axis will show the hour of the day as
before: But this cannot be so conveniently performed, tho’ the reason is the
same as in the former case.
To find the Sun’s altitude, when it shines, by the Globe.
Having set the frame of the globe truly horizontal or level, turn the
North Pole towards the Sun, and move the meridian up or down in the
notches, until the axis casts no shadow; then the arch of the meridian,
contained betwixt the Pole and the horizon, is the Sun’s altitude.
Note, The best way to find the Sun’s altitude, is by a
little quadrant graduated into degrees, and having sights and
a plummet to it: Thus, hold the quadrant in your hand, so as
the rays of the Sun may pass through both the sights, the
plummet then hanging freely by the side of the instrument,
will cut in the limb the altitude required. These quadrants are
to be had at the instrument-makers, with lines drawn upon
them, for finding the hour of the day, and the azimuth; with
several other pretty conclusions, very entertaining for
beginners.

The Latitude and the Day of the Month being given, to find
the hour of the day when the Sun shines.
Having placed the wooden frame upon a level, and the meridian due
North and South, rectify the globe for the latitude, and fix a needle
perpendicularly over the Sun’s place: The Sun’s place being brought to the
meridian, set the hour index at 12 at noon, then turn the globe about until
the needle points exactly to the Sun, and casts no shadow, and then the
index will shew the hour of the day.

Prob. XXVI. The Latitude, the Sun’s Place, and his
Altitude, being given; to find the hour of the Day,
and the Sun’s Azimuth from the Meridian.

Having rectified the globe for the latitude, the zenith, and the Sun’s
place, turn the globe and the quadrant of altitude, so that the Sun’s place
may cut the given degree of altitude: then the index will show the hour, and
the quadrant will cut the azimuth in the horizon. Thus, if at London, on the
21st of August, the Suns altitude, be 36 degrees in the forenoon, the hour of
the day will be IX, and the Sun’s azimuth about 58 degrees from the South
part of the meridian.
The Sun’s Azimuth being given, to place the Meridian of the
Globe due North and South, or to find a Meridian Line
when the Sun shines.
Let the Sun’s azimuth be 30 degrees South-Easterly, set the horizon of
the globe upon a level, and bring the North Pole into the zenith; then turn
the horizon about until the shade of the axis cuts as many hours as is
equivalent to the azimuth (allowing 15 degrees to an hour) in the North-
West part of the hour circle, viz. X at night, which being done, the meridian
of the globe stands in the true meridian of the place. The globe standing in
this position, if you hang two plummets at the North and South points of the
wooden horizon, and draw a line betwixt them, you will have a meridian
line; which if it be on a fixed plane (as a floor or window) it will be a guide
for placing the globe due North and South, at any other time.

Prob. XXVII. The Latitude, Hour of the Day, and the
Sun’s place being given, to find the Sun’s Altitude
and Azimuth.

Rectify the globe for the latitude, the zenith, and the Sun’s place, then
the number of degrees contained betwixt the Sun’s place and the vertex, is
the Sun’s meridional zenith distance; the complement of which to 90
degrees, is the Sun’s meridian altitude. If you turn the globe about until the
index points to any other given hour, then bringing the quadrant of altitude
to cut the Sun’s place, you will have the Sun’s altitude at that hour; and
where the quadrant cuts the horizon, is the Sun’s azimuth at the same time.
Thus May the 1st at London, the Sun’s meridian altitude will be 61½
degrees; and at 10 o’clock in the morning, the Sun’s altitude will be 52
degrees, and his azimuth about 50 degrees from the South part of the
meridian.

Prob. XXVIII. The Latitude of the place, and the day
of the Month being given; to find the depression
of the Sun below the Horizon, and the Azimuth at
any Hour of the Night.

Having rectified the globe for the latitude, the zenith, and the Sun’s
place, take a point in the ecliptic exactly opposite to the Sun’s place, and
find the Sun’s altitude and azimuth, as by the last problem, and these will be
the depression and the altitude required. Thus, if the time given be the 1st of
December, at 10 o’clock at night, the depression and azimuth will be the
same as was found in the last problem.

Prob. XXIX. The Latitude, the Sun’s Place, and his
Azimuth being given, to find his Altitude, and the
Hour.

Rectify the globe for the latitude, the zenith, and the Sun’s place, then
put the quadrant of altitude to the Sun’s azimuth in the horizon, and turn the
globe ’till the Sun’s place meet the edge of the quadrant, then the said edge
will shew the altitude, and the index point to the hour. Thus, May the 21st at

London when the Sun is due East, his altitude will be about 24 degrees, and
the hour about VII in the morning; and when his azimuth is 60 degrees
South-Westerly, the altitude will be about 44½ degrees, and the hour about
2¾ in the afternoon.
Thus, the latitude and the day being known, and having besides either
the altitude, the azimuth, or the hour; the other two may be easily found.

Prob. XXX. The Latitude, the Sun’s Altitude, and his
Azimuth being given; to find his Place in the
Ecliptic and the Hour.

Rectify the globe for the latitude and zenith, and set the edge of the
quadrant to the given azimuth; then turning the globe about, that point of
the ecliptic which cuts the altitude, will be the Sun’s place. Keep the
quadrant of the altitude in the same position, and having brought the Sun’s
place to the meridian, and the hour index to 12 at noon, turn the globe about
’till the Sun’s place cuts the quadrant of altitude, and then the index will
point the hour of the day.

Prob. XXXI. The Declination and Meridian Altitude
of the Sun, or of any Star being given; to find the
Latitude of the Place.

Mark the point of declination upon the meridian, according as it is either
North or South from the equator; then slide the meridian up or down in the
notches, ’till the point of declination be so far distant from the horizon, as is
the given meridian altitude; that elevation of the Pole will be the latitude.
Thus, if the Sun’s, or any Star’s meridian altitude be 50 degrees, and its
declination 11½ degrees North, the latitude will be 51½ degrees North.

Prob. XXXII. The Day and Hour of a Lunar Eclipse
being known; to find all those Places upon the
Globe where the same will be visible.

[5]
Find where the Sun is vertical at the given hour, and bring that point
to the zenith; then the Eclipse will be visible in all those places that are
under the horizon; Or, if you bring the Antipodes to the place where the Sun
is vertical, into the zenith, you will have the places where the Eclipse will
be visible above the horizon.
Note, Because Lunar eclipses continue sometimes for a
long while together, they may be seen in more places than
one hemisphere of the Earth; for by the Earth’s motion
round its axis, during the time of the eclipse, the Moon will
rise in several places after the eclipse began.
Note, When an eclipse of the Sun is central, if you bring
the place where the Sun is vertical at that time, into the
zenith, some part of the eclipse will be visible in most places
within the upper hemisphere; but by reason of the short
duration of Solar eclipses, and the latitude which the Moon
commonly has at that time (tho’ but small) there is no
certainty in determining the places where those eclipses will
be visible by the globe; but recourse must be had to
calculations.

Prob. XXXIII. The Day of the Month, and Hour of
the Day, according to our way of reckoning in
England, being given; to find thereby the
Babylonic, Italic, and the Jewish, or Judaical
Hour.

1. To find the Babylonic Hour (which is the number of hours from Sun-
rising.) Having found the time of Sun-rising in the given place, the
difference betwixt this and the hour given, is the Babylonic Hour.
2. To find the Italic Hour (which is the number of hours from Sun-
setting.) Subtract the hour of Sun-setting from the given hour, and the
remainder will be the Italic Hour required.
3. To find the Jewish Hour (which is ¹/₁₂ part of an Artificial Day.) Find
how many hours the day consists of; then say, as the number of hours the

day consists of is to 12 hours, so is the hour since Sun-rising to the Judaical
hour required.
Thus, if the Sun rises at 4 o’clock (consequently sets at 8) and the hour
given be 5 in the evening, the Babylonish hour will be the 13th, the Italic
the 21st and the Jewish hour will be nine and three quarters.
The converse being given, the hour of the day, according to our way of
reckoning in England, may be easily found.
The following Problems are peculiar to the Celestial Globe.

Prob. XXXIV. To find the Right Ascension and
Declination of the Sun, or any Fixed Star.

Bring the Sun’s place in the ecliptic to the meridian; then that degree of
the equator, which is cut by the meridian, will be the Sun’s Right Ascension;
and that degree of the meridian, which is exactly over the Sun’s place, is the
Sun’s Declination.
After the same manner, bring the place of any Fixed Star to the
meridian, and you will find its Right Ascension in the equinoctial, and
Declination of the meridian.
Thus, the right ascension and declination is found, after the same
manner as the longitude and latitude of a place upon the Terrestrial Globe.
Note, The right ascension and declination of the Sun
vary every day; but the right ascension, &c. of the Fixed
Stars is the same throughout the year[6].
The Sun’s Right Ascension. Declin.
Deg. Deg.
January 31 314 17⅓ S.
April 5 14¼ 6 N.
Thus on
July 21 120¼ 20½ N.
November 26 242¼ 21 S.

R. Asc. Dcl.
Deg. Deg.

The Sun’s Right Ascension. Declin.
Deg. Deg.
Aldebaran 65 16 N.
Spica Virginis 197¾ 9¾ S.
Capella 74 45⅔
Syrius, or the Dog-Star 98¼ 16⅓
Note, The declination of the Sun may be found after the
same manner by the Terrestrial Globe, and also his right
ascension, when the equinoctial is numbered into 360
degrees, commencing at the equinoctial point ♈: But as the
equinoctial is not always numbered so, and this being
properly a Problem in Astronomy, we choose rather to place
it here.
By the converse of this problem, having the right ascension and
declination of any point given, that point itself may be easily found upon
the globe.

Prob. XXXV. To find the Longitude and Latitude of
a given Star.

Having brought the solstitial colure to the meridian, fix the quadrant of
altitude over the proper Pole of the ecliptic, whether it be North or South;
then turn the quadrant over the given Star, and the arch contained betwixt
the Star and the ecliptic, will be the latitude, and the degree cut on the
ecliptic will be the Star’s longitude.
Thus the latitude of Arcturus will be found to be 31 degrees North, and
the longitude 200 degrees from ♈, or 20 degrees from ♎: The latitude of
Fomalhaut in the Southern Fish, 21 degrees South, and longitude 299½
degrees, or ♑ 29½ degrees. By the converse of this method, having the
latitude and longitude of a Star given, it will be easy to find the Star upon
the globe.
The distance betwixt two Stars, or the number of degrees contained
betwixt them, may be found by laying the quadrant of altitude over each of
them, and counting the number of degrees intercepted; after the same

manner as we found the distance betwixt two places on the Terrestrial
Globe, in Prob. VII.

Prob. XXXVI. The Latitude of the Place, the Day of
the Month, and the Hour being given; to find
what Stars are then rising or setting, what Stars
are culminating, or on the meridian, and the
Altitude and Azimuth of any Star above the
Horizon; and also how to distinguish the Stars in
the Heavens one from the other, and to know
them by their proper Names.

Having rectified the globe for the latitude, the zenith, and the Sun’s
place, turn the globe about until the index points to the given hour, the
globe being kept in this position.
All those Stars that are in (Eastern/Western) side of the horizon, are then
(Rising/Setting).
All those Stars that are under the meridian, are then culminating. And if
the quadrant of altitude be laid over the center of any particular Star, it will
show that Star’s altitude at that time; and where it cuts the horizon, will be
the Star’s azimuth from the North or South part of the meridian.
The globe being kept in the same elevation, and from turning round its
axis, move the wooden frame about until the North and South points of the
horizon lie exactly in the meridian; then right lines imagined to pass from
the center thro’ each Star upon the surface of the globe, will point out the
real Star in the heavens, which those on the globe are made to represent.
And if you are by the side of some wall whose bearing you know, lay the
quadrant of altitude to that bearing in the horizon, and it will cut all those
Stars which at that very time are to be seen in the same direction, or close
by the side of the said wall. Thus knowing some of the remarkable Stars in
any part of the heavens, the neighbouring Stars may be distinguished by
observing their situations with respect to those that are already known, and
comparing them with the Stars drawn upon the globe.
Thus, if you turn your face towards the North, you will find the North
Pole of the globe points to the Pole Star; then you may observe two Stars

somewhat less bright than the Pole Star, almost in a right line with it, and
four more which form a sort of quadrangle; these seven Stars make the
constellation called the Little Bear; the Pole-Star being in the tip of the tail.
In this neighbourhood you will observe seven bright Stars, which are
commonly called Charles’s Wane; these are the bright Stars in the Great
Bear, and form much such another figure with those before-mentioned in
the little Bear: The two foremost of the square lie almost in a right line with
the Pole Star, and are called the Pointers, so that knowing the Pointers, you
may easily find the Pole Star. Thus the rest of the Stars in this constellation,
and all the Stars in the neighbouring constellations may be easily found, by
observing how the unknown Stars lie either in quadrangles, triangles, or
strait lines from those that are already known upon the globe.
After the same manner the globe being rectified, you may distinguish
those Stars that are to the Southward of you, and be soon acquainted with
all the Stars that are visible in our hemisphere.

SCHOLIUM.
The globe being rectified to the latitude of any place, if
you turn it round its axis, all those Stars that do not go below
the horizon during a whole revolution of the globe, never set
in that place; and those that do not come above the horizon
never rise.

Prob. XXXVII. The latitude of the place being
given; to find the Amplitude, Oblique Ascension
and Descension, Ascensional Difference, Semi-
diurnal Arch, and the time of continuance above
the horizon, of any given point in the heavens.

Having rectified the globe for the latitude, and brought the given point
to the meridian, set the index to the hour of 12; then turn the globe until the
given point be brought to the Eastern side of the horizon, and that degree of
the equinoctial which is cut by the horizon at that time, will be the Oblique
Ascension; and where the given point cuts the horizon, is the Amplitude
Ortive: If the globe be turned about until the given point be brought to the
Western side of the horizon, it will there show the Amplitude Occasive; and

where the horizon cuts the equinoctial at that time, is the Oblique
Descension.
The time between the index at either of these two positions, and the
hour of 6; or half the difference between the oblique ascension and
descension is the Ascensional Difference.
If the place be in North latitude and the declination of the given point be
(North/South) the ascensional difference reduced into time, and (added
to/subtracted from) 6 o’Clock, gives the Semi-diurnal Arch; the
complement whereof to a semicircle, is the Semi-nocturnal Arch. If the
place be in South latitude, then the contrary is to be observed with respect
to the declination.
The semi-(diurnal/nocturnal) arch being doubled, gives the time of
continuance (above/below) the horizon. Or the time of continuance above
the horizon, may be found by counting the number of hours contained in the
upper part of the horary circle, betwixt the place where the index pointed
when the given point was in the Eastern or Western parts of the horizon. If
the given point was the Sun’s place, the index pointed the time of his rising
and setting, when the said place was in the Eastern and Western parts of the
horizon, as in Prob. 18. Or the time of Sun-rising may be found by adding
or subtracting his ascensional difference, to or from the hour of six,
according as the latitude and declination are either contrary or the same
way.
Thus, at London, on the 31st of May, the Sun’s

Amplitude is 24 degrees Northerly.
Oblique Ascension, 20.
Oblique Descension, 58.
Ascensional Difference, 19.
Semi-diurnal Arch, 109.
His continuance above the horizon, 14½ hours.
Sun rises at three quarters past four.
Sun sets a quarter past seven.

These things for the Sun vary every day; but for a Fixed Star the day of
the month need not be given, for they are the same all the year round.

In the latitude of 51½ North,
Syrus’s Amplitude is about 28 degrees Southerly.
Oblique Ascension, 121.
Oblique Descension, 75.
Ascensional Difference, 23.
Semi-diurnal Arch, 67.
Continuance above the horizon, 9 hours.

Prob. XXXVIII. The Latitude and the Day of the
Month being given; to find the Hour when any
known Star will be upon the meridian, and also
the time of its rising and setting.

Having rectified the globe for the latitude of the Sun’s place, bring the
given Star to the meridian, and also to the East or West side of the horizon,
and the index will shew accordingly when the Star culminates, or the time
of the rising or setting.
Thus at London, on the 21st of January, Syrius will be upon the
meridian, at a quarter past ten in the evening; rises at 5¼ hours, and sets at
three quarters past two in the morning.
By the converse of this problem, knowing the time when any Star is
upon the meridian, you may easily find the Sun’s place. Thus, bring the
given Star to the meridian, and set the index to the given hour; then turn the
globe ’till the index points to 12 at noon, and the meridian will cut the Sun’s
place in the ecliptic. Thus when Syrius comes to the meridian at 10½ hours
after noon, the Sun’s place will be ≈ ¼ deg.

Prob. XXXIX. To find at what time of the Year a
given Star will be upon the Meridian, at a given
Hour of the Night.

Bring the Star to the meridian, and set the index to the given hour, then
turn he globe ’till the index points to 12 at noon, and the meridian will cut
the ecliptic in the Sun’s place; whence the day of the month may be easily
found in the kalendar upon the horizon.

Prob. XL. The Day of the Month, and the Azimuth of
any known Star being given; to find the Hour of
the Night.

Having rectified the globe for the latitude and the Sun’s place, if the
given Star be due North or South, bring it to the meridian, and the index
will show the hour of the night. If the Star be in any other direction, fix the
quadrant of altitude in the zenith, and set it to the Star’s azimuth in the
horizon; then turn the globe about until the quadrant cuts the center of the
Star, and the index will shew the hour of the night.
The bearing of any point in the heavens may be found by the following
methods.
Having a meridian line drawn in two windows, that are opposite to one
another, you may cross it at right angles with another line representing the
East and West; from the point of the intersection describe a circle, and
divide each quadrant into 90 degrees; then get a smooth board, of about 2
feet long, and ¾ foot broad (more or less, as you judge convenient) and on
the back part of it fix another small board crossways, so that it may serve as
a foot to support the biggest board upright, when it is set upon a level, or an
horizontal plane. The board being thus prepared, set the lower edge of the
smooth, or fore side of it, close to the center of the circle, then turn it about
to the meridian, or to any azimuth point required (keeping the edge of it
always close to the center) and casting your eye along the flat side of it, you
will easily perceive what Stars are upon the meridian, or any other bearing
that the board is set to.

Prob. XLI. Two known Stars having the same
Azimuth, or the same Height, being given; to find
the Hour of the Night.

Rectify the globe for the latitude, the zenith, and the Sun’s place.
1. When the two Stars are in the same azimuth, turn the
globe, and also the quadrant about, until both Stars coincide
with the edge thereof; then will the index shew the hour of

the night; and where the quadrant cuts the horizon, is the
common azimuth of both Stars.
2. If the two Stars are of the same altitude, move the
globe so that the same degree on the quadrant will cut both
Stars, then the index will shew the hour.
This problem is useful when the quantity of the azimuth of the two Stars
in the first case, or of their altitude in the latter case, is not known.
If two Stars were given, one on the meridian, and the other in the
East or West part of the horizon; to find the Latitude.
Bring that Star which was observed on the meridian, to the meridian of
the globe, and keep the globe from turning round its axis; then slide the
meridian up or down in the notches, ’till the other Star is brought to the East
or West part of the horizon, and that elevation of the Pole will be the
Latitude sought.

Prob. XLII. The Latitude, Day of the Month, and the
Altitude of any known Star being given; to find
the Hour of the Night.

Rectify the globe for the latitude, zenith, and Sun’s place: Turn the
globe, and the quadrant of altitude, backward or forward, ’till the center of
that Star meets the quadrant in the degree of altitude given; then the index
will point the true hour of the night; and also where the quadrant cuts the
horizon, will be the azimuth of the Star at that time.
If the Latitude, the Sun’s Altitude, and his Declination (instead of his
Place in the Ecliptic) are given; to find the Hour of the Day and
Azimuth.
Rectify the globe for the latitude and zenith, and having brought the
equinoctial colure to the meridian, set the index to 12 at noon; which being
done, turn the globe and the quadrant, until the given declination in the
equinoctial colure, cuts the altitude on the quadrant; then the index will
shew the Hour of the day, and the quadrant cut the Azimuth in the horizon.
If the Altitude of two Stars on the same Azimuth were given; to find
the Latitude of the Place.

Set the quadrant over both Stars at the observed degrees of altitude, and
keep it fast upon the globe with your fingers; then slide the meridian up or
down in the notches, ’till the quadrant cuts the given azimuth in the horizon;
that elevation of the Pole will be the latitude required.

Prob. XLIII. Having the Latitude of the place, to find
the degree of the Ecliptic, which rises or sets
with a given Star; and from thence to determine
the time of its Cosmical and Achronical rising
and setting.

Having rectified the globe for the latitude, bring the given Star to the
Eastern side of the horizon, and mark what degree of the ecliptic rises with
it: Look for that degree in the wooden horizon, and right against it, in the
kalendar, you will find the month and day when the Star rises Cosmically.
If you bring the Star to the Western side of the horizon, that degree of the
ecliptic which rises at that time, will give the day of the month when the
said Star sets Cosmically. So likewise against the degree which sets with the
Star, you will find the day of the month of the Achronical setting; and if you
bring it to the Eastern part of the horizon, that degree which sets at that time
will be the Sun’s place when the Star rises Achronically.
Thus, in the latitude of London, Syrius, or the Dog-Star, rises
Cosmically the 10th of August, and sets Cosmically the 10th of October.
Aldebaran, or the Bull’s Eye, rises Achronically on the 22d of May, and sets
Achronically on the 19th of December.

Prob. XLIV. Having the Latitude of the place, to find
the time when a Star rises and sets Heliacally.

Having rectified the globe for the latitude, bring the Star to the Eastern
side of the horizon, and turn the quadrant round to the Western side, ’till it
cuts the ecliptic in 12 degrees of altitude above the horizon, if the Star be of
the first magnitude; then that point of the ecliptic which is cut by the
quadrant, is 12 degrees high above the Western part of the horizon, when
the Star rises; but at the same time the opposite point in the ecliptic is 12
degrees below the Eastern part of the horizon, which is the depression of a

Star of the first magnitude, when she rises Heliacally; or has got so far from
the Sun’s beams, that she may be seen in the morning before Sun-rising.
Wherefore look for the said point of the ecliptic on the horizon, and right
against it will be the day of the month when the Star rises Heliacally. To
find the Heliacal setting, bring the Star to the West side of the horizon, and
turn the quadrant about to the Eastern side, ’till the 12th degree of it above
the horizon, cuts the ecliptic; then that degree of the ecliptic which is
opposite to this point, is the Sun’s place when the Star sets Heliacally.
Thus you will find that Arcturus rises Heliacally the 28th of September,
and sets Heliacally December the 2d.

Prob. XLV. To find the place of any Planet upon the
globe; and so by that means, to find its place in
the Heavens: Also to find at what Hour any
Planet will rise or set, or be on the meridian at
any one Day in the Year.

You must first seek in an Ephemeris (White’s Ephemeris will do well
enough) for the place of the Planet proposed on that day; then mark that
point of the ecliptic, either with chalk, or by sticking on a little black patch;
and then for that night you may perform any problem, as before, by a Fixed
Star.
Let it be required to find the situation of Jupiter among the Fixed Stars
in the heavens, and also what time he rises and sets, and comes to the
meridian on the 19th of May, 1757, N. S. at London.
Looking for the 19th of May, 1757, in White’s Ephemeris, I find that
Jupiter’s place at that time is in about 12 degrees of ♏; latitude about 1¼
degree North. Then looking for that point upon the Celestial globe, I find
that ♃ is then nearly in conjunction with the bright Star in the Southern
Balance, and about 1 degree North of it.
To find when he rises and sets, and comes to the meridian: Having put a
little black patch on the place of Jupiter, elevate the globe according to the
latitude, and having brought the Sun’s place to the meridian, set the hour
index to 12 at noon; then turn the mark which was made for Jupiter, to the
Eastern part of the horizon, I find ♃ will rise somewhat more than half an

hour after three in the afternoon; and turning the globe about, I find it
comes to the meridian a little before eleven at night; and sets almost a
quarter past six next morning.
This example being understood, it will be easy to find when either of
the other two superior Planets, viz. Mars and Saturn, rise, set, and come to
the meridian.
I shall conclude this subject about the Globes with the following
problems.

Prob. XLVI. To find all that space upon the Earth,
where an Eclipse of one of the Satellites of
Jupiter will be visible.

Having found that place upon the Earth, in which the Sun is vertical at
the time of the eclipse, by Prob. 13, elevate the globe according to the
latitude of the said place; then bring the place to the meridian, and set the
hour index to 12 at noon. If Jupiter be in consequence of the Sun, draw a
line with black lead, or the like, along the Eastern side of the horizon, which
line, will pass over all those places where the Sun is setting at that time;
then count the difference betwixt the right ascension of the Sun, and that of
Jupiter, and turn the globe Westward, ’till the hour index points to this
difference; then keep the globe from turning round its axis, and elevate the
meridian, according to the declination of Jupiter. The globe being in this
position, draw a line along the Eastern side of the horizon; then the space
between this line, and the line before drawn, will comprehend all those
places of the Earth where Jupiter will be visible, from the setting of the
Sun, to the setting of Jupiter.
But if Jupiter be in antecedence of the Sun (i. e. rises before him)
having brought the place where the Sun is vertical, to the zenith, and put the
hour index to 12 at noon, draw a line on the Western side of the horizon;
then elevate the globe according to the declination of Jupiter, and turn it
about Eastward, until the index points to so many hours distant from noon,
as is the difference of right ascension of the Sun and Jupiter. The globe
being in this position, draw a line along the Western side of the horizon;
then the space contained between this line, and the other last drawn, will

comprehend all those places upon the Earth where the Eclipse is visible,
between the rising of the Sun, and that of Jupiter.

The DESCRIPTION of the Great Orrery, lately
made by Mr. Thomas Wright, Mathematical
Instrument-Maker to his late Majesty, and now
by Benjamin Cole, his Successor.
he Orrery is an Astronomical Machine, made to represent the
motions of the Planets. These machines are made of various
sizes, some having more Planets than others; but I shall here
confine myself to the description of that above-mentioned.
In the Introduction we gave a short account of the Order, Periods,
Distances, and Magnitudes of the Primary Planets; and of the Distances
and Periodical Resolutions of the Secondary Planets round their respective
Primaries. We shall here explain their Stations, Regradations, Eclipses,
Phases, &c. but first let us take a general view of the Orrery.
The frame which contains the wheel-work, &c. that
regulates the whole Machine, is made of fine ebony, and The Description of
the Orrery.
is near four feet in diameter; the outside thereof is
adorned with twelve pilasters, curiously wrought and
gilt: Between these pilasters the twelve Signs of the Vide Frontispiece.
Zodiac are neatly painted, with gilded frames. Above the frame is a broad
ring, supported with twelve pillars: This ring represents the Plane of the
Ecliptic, upon which there are two scales of degrees, and between those the
names and characters of the twelve Signs. Near the outside is a scale of
months and days, exactly corresponding to the Sun’s place at noon, each
day throughout the year.
Above the ecliptic stands some of the principal circles of the sphere,
according to their respective situations in the heavens, viz. N° 10, are the
two Colures, divided into degrees, and half degrees; N° 11, is one half of
the Equinoctial Circle, making an angle with the ecliptic of 23½ degrees.
The Tropic of Cancer, and the Arctic Circle, are each fixed parallel, and at
their proper distance from the equinoctial. On the Northern half of the
ecliptic is a brass semicircle, moveable upon two points fixed in ♈ and ♎:

This semicircle serves as a moveable horizon, to be put to any degree of
latitude upon the North part of the meridian. The whole machine is also so
contrived, as to be set to any latitude, without in the least affecting any of
the inside motions: For this purpose there are two strong hinges (N° 13,)
fixed to the bottom frame, upon which the instrument moves, and a strong
brass arch, having holes at every degree, thro’ which a strong pin is to be
put, according to the elevation. This arch and the two hinges, support the
whole machine, when it is lifted up according to any latitude; and the arch
at other times lies conveniently under the bottom frame.
When the machine is set to any latitude (which is easily done by two
men, each taking hold of two handles, conveniently fixed for that purpose)
set the moveable horizon to the same degree upon the meridian, and you
may form an idea of the respective altitude, or depressions of the Planets,
above or below the horizon, according to their respective positions, with
regard to the meridian.
Within the ecliptic, and nearly in the same place thereof, stands the Sun,
and all the Planets, both Primary and Secondary. The Sun (Nº 1.) stands in
the middle of the whole system, upon a wire, making an angle with the
plane of the ecliptic, of about 82 degrees; which is the inclination of the
Sun’s axis, to the axis of the ecliptic. Next to the Sun is a Small ball (Nº 2.)
representing Mercury: Next to Mercury is Venus (Nº 3.) represented by a
larger ball (and both these stand upon wires,) so that the balls themselves
may be more visibly perceived by the eye. The Earth is represented (Nº 4.)
by an ivory ball, having some of the principal meridians and parallels, and a
little sketch of a map described upon it. The wire which supports the Earth,
makes an angle with the plane of the ecliptic 66½ degrees, which is the
inclination of the Earth’s axis to that of the ecliptic. Near the bottom of the
Earth’s axis is a Dial Plate (Nº 9.) having an index pointing to the hours of
the day, as the Earth turns round its axis.
Round the Earth is a ring, supported by two small pillars, which ring
represents the Orbit of the Moon, and the division upon it answers to the
Moon’s latitude; the motion of this ring represents the motion of the Moon’s
Orbit, according to that of the Nodes. Within this ring is the Moon (Nº 5.)
having a black cap or case, which by its motion, represents the Phases of
the Moon according to her age. Without the Orbits of the Earth and Moon is
Mars (Nº 6.) The next in order to Mars is Jupiter, and his four Moons (Nº

7); each of these moons is supported by a crooked wire fixed in a socket,
which turns about the pillar that supports Jupiter. These satellites may be
turned by the hand to any position; and yet when the machine is put in
motion, they will all move in their proper times. The outermost of all is
Saturn, and his five Moons (Nº 8.) These moons are supported and
contrived after the same manner with those of Jupiter. The whole machine
is put into motion by turning a small winch (like the key of a clock, Nº 14.)
and all the inside work is so truly wrought, that it requires but very small
strength to put the whole motion.
Above the handle there is a cylindrical pin, which may be drawn a little
out, or pushed in, at pleasure: when it is pushed in, all the Planets, both
primary and Secondary, will move according to their respective periods, by
turning the handle: When it is drawn out, the motions of the Satellites of
Jupiter and Saturn will be stopped, while all the rest move without
interruption. This is a very good contrivance to preserve the instrument
from being clogged by the swift motions of the wheels belonging to the
Satellites of Jupiter and Saturn, when the motions of the rest of the Planets
are only considered.
There is also a brass lamp having two convex glasses, to be put in the
room of the Sun; and also a smaller Earth and Moon, made somewhat in
proportion to their distance from each other, which may be put on at
pleasure.
The lamp turns round in the same time with the Earth, and by means of
the glasses cast a strong light upon her; and when the smaller Earth and
Moon are placed on, it will be easy to shew when either of them may be
eclipsed.
Having thus given a brief description of the outward part of this
machine, I shall next give an account of the phænomena explained by it,
when it is put into motion.

Of the Motions of the Planets in general.

Having put on the handle, push in the pin which is just above it, and
place a small black patch (or bit of wafer) upon the middle of the Sun (for
instance) right against the first degree of ♈ ; you may also place patches

upon Venus, Mars, and Jupiter, right against some noted point in the
ecliptic. If you lay a thread from the Sun to the first degree of ♈, you may
set a mark where it intersects the orbit of each Planet, and that will be a help
to note the time of their revolutions.
One entire turn of the handle answers to the diurnal motion of the Earth
round her axis, as may be seen by the motion of the hour index, which is
placed at the foot of the wire on which the terella is fixed. When the index
has moved the space of ten hours, you may observe that Jupiter has made
one revolution compleat round its axis; the handle being turned until the
hour index has passed over 24 days, 8 hours, will bring the patch upon
Venus to its former situation with respect to the ecliptic, which shews that ♀
has made one entire revolution round her axis. Mars makes one compleat
revolution round its axis in 24 hours and about 40 minutes. When the
handle is turned 25½ times round, the spot upon the Sun will point to the
same degree of the ecliptic, as it did when the instrument was first put into
motion. By observing the motions of the spots upon the surface of the Sun,
and of the Planets in the heavens, their diurnal motion was discovered; after
the same manner as we do here observe the motions of their representatives,
by that of the marks placed upon them.
If while you turn the handle you observe the Planets, you will see them
perform their motions in the same relative times as they really do in the
heavens, each making its period in the times mentioned in the Tables, Page,
28, 27¼ turns of the handle will bring the Moon round the Earth, which is
called a Periodic Month; and all the while she keeps the same face towards
the Earth; for the Moon’s annual and diurnal motion are performed both in
the same time nearly, so that we always see the same face or side of the
Moon.
If before the instrument is put into motion, the satellites of Jupiter and
Saturn be brought into the same right line from their respective primaries,
you will see them, as you turn the handle, immediately dispersed from one
another, according to their different celerities. Thus one turn of the handle
will bring the first of Jupiter’s Moons about ⁴/₇ part round Jupiter, while the
second has described but ²/₇ part, the third but above ¹/₇, and the fourth not
quite ¹/₁₆ part, each of its respective orbits. If you turn the handle until the
hour index has moved 18½ hours more, the first satellite will then be
brought into its former position, and so has made one entire revolution; the

second at the same time will be almost diametrically opposite to the first,
and so has made a little more than half of one revolution; the others will be
in different aspects, according to the length of their periods, as will be
plainly exhibited by the instrument. The same observations may be made
with respect to the satellites of Saturn.
The machine is so contrived, that the handle may be turned either way;
and, if before you put it into motion, you observe the aspect (or situation
with respect to each other) of the Planets, and then turn the handle round
any number of times; the same number of revolutions being made
backwards, will bring all the Planets to their former situations. I shall next
proceed to particulars.

Of the Stations and Retrogradations of the Planets.

The primary Planets, as they all turn round the Sun,
at different distances, and in different times, appear to us Retrograde Motion
from the Earth to have different motions; as sometimes of the Planets.
they appear to move from West to East, according to the order of the signs,
which is called their Direct Motion; then by degrees they slacken their pace,
until at last they lose all their motion, and become Stationary, or not to
move at all; that is, they appear in the same place with respect to the fixed
Stars for some time together; after which they again begin to move, but
with a contrary direction, as from East to West, which is called their
Retrograde Motion; then again they become stationary, and afterwards
reassume their direct motion. The reason of all these appearances is very
evidently shewn by the Orrery.

Of the Stations, &c. of the Inferior Planets.

We shall instance in the Planet Mercury, because his motion round the
Sun differs more from the Earth’s than that of Venus does.
When Mercury is in his superior conjunction (or when he is in a direct
line from the Earth beyond the Sun) fasten a string about the axis of the
Earth, and extend it over Mercury to the ecliptic; then turning the handle,
keep the thread all the while extended over ☿, and you will find it move
with a direct motion in the ecliptic, but continually slower, until Mercury

has the greatest elongation from the Earth. Near this position, the thread for
some time will lay over Mercury without being moved in the ecliptic, tho’
the Earth and Mercury both continue their progressive motion in their
respective orbits. When Mercury has got a little past this place, you will
find the thread must be moved backward in the ecliptic, beginning first with
a slow motion, and then faster by degrees, until Mercury is in his inferior
conjunction, or directly between the Earth and the Sun. Next this position of
☿, his retrograde motion will be the swiftest; but he still moves the same
way, tho’ continually slower, ’till he has again come to his greatest
elongation, where he will appear the second time to be stationary; after
which he begins to move forward, and that faster by degrees, until he is
come to the same position with respect to the Earth, that he was in at first.
The same observations may be made relating to the motions of Venus. In
like manner the different motions observed in the superior Planets may be
also explained by the Orrery. If you extend the thread over Jupiter, and
proceed after the same manner as before we did in regard to Mercury, you
will find that from the time Jupiter is in conjunction with the Sun, his
motion is direct, but continually slower, until the Earth is nearly in a
quadrate aspect with Jupiter, near which position Jupiter seems to be
stationary: After which he begins to move, and continually mends his pace,
until he comes in opposition to the Sun, at which time his retrograde motion
is swiftest. He still seems to go backward, but with a slower pace, ’till the
Earth and he are again in a quadrate aspect, where Jupiter seems to have
lost all his motion; after which he again resumes his direct motion, and so
proceeds faster by degrees, ’till the Earth and he are again in opposition to
each another.
These different motions observed in the Planets, are easily
illustrated, as followeth: The lesser circle round the Sun is the Plate 3.
Fig. 1.
orbit of Mercury, in which he performs his revolution round the
Sun, in about three months, or while the Earth is going thro’ ¼ part of her
orbit, or from A to N. The numbers 1, 2, 3, &c. in the orbit of Mercury,
show the spaces he describes in a week nearly, and the distance AB, BC,
DC, &c. in the Earth’s orbit, do likewise show her motion in the same time.
The letters A, B, C, &c. in the great orb, are the motions of Mercury in the
Heavens, as they appear from the Earth. Now if the Earth be supposed in A,
and Mercury in 12, near his superior conjunction with the Sun; a spectator
on the Earth will see ☿, as if he were in the point of the Heavens A, and

while ☿ is moving from 12 to 1, and from 1 to 2, &c. the Earth in the same
time also moves from A to B, and from B to C, &c. All which time ☿
appears in the Heavens to move in a direct motion from A to B, and from B
to C, &c. but gradually slower, until he arrives near the point G; near this
place he appears stationary, or to stand still; and afterwards (tho’ he still
continues to move uniformly in his own orbit, with a progressive motion)
yet in the sphere of the fixed Stars he will appear to be retrograde, or to go
backwards, as from G to H, from H to I, &c. until he has arrived near the
point L, where again he will appear to be stationary; and afterwards to
move in a direct motion from L to M, and from M to N, &c.
What has been here shewed concerning the motions of Mercury, is also
to be understood of the motions of Venus; but the conjunctions of Venus
with the Sun do not happen so often as in Mercury; for Venus moving in a
larger orbit, and much slower than Mercury, does not so often overtake the
Earth. But the retrogradations are much greater in Venus than they are in
Mercury, for the same reasons.
The innermost circle represents the Earth’s orbit, divided
into 12 parts, answering to her monthly motion; the greatest Fig. 2.
circle is in the orbit of Jupiter, which he describes in about 12
years; and therefore the ¹/₁₂ thereof, from A to N, defines his motion, in one
of our years nearly; and the intermediate divisions, A, B, C, &c. his
monthly motion. Let us suppose the Earth to be in the point of her orbit 12,
and Jupiter in A, in his conjunction with the Sun; it is evident that from the
Earth Jupiter will be seen in the great orb, or in the point of the Heavens A,
and while the Earth is moving from 12 to 1, 2, &c. ♃ also moves from A to
B, &c. all which time he appears in the Heavens to move with a direct
motion from A to B, C, &c., until he comes in opposition to the Earth near
the point of the Heavens E, where he appears to be stationary; after which
♃ again begins to move ’ (tho’ at first with a slow pace) from E through F,
H, I to K, where again he appears to stand still, but afterwards he reassumes
his direct motion from I thro’ K, to M, &c.
From the construction of the preceding figure it appears, that when the
superior Planets are in conjunction with the Sun, their direct motion is much
quicker than at other times; and that because they really move from West to
East, while the Earth in the opposite part of the Heavens is carried the same
way, and round the same center. This motion afterwards continually

slackens until the Planet comes almost in opposition to the Sun, when the
line joining the Earth and Planet, will continue for some time nearly parallel
to itself, and so the Planet seems from the Earth to stand still; after which, it
begins to move with a slow motion backward, until it comes into a quartile
aspect with the Sun, when again it will appear to be stationary, for the
above reasons; after that it will resume its direct motion, until it comes into
a conjunction with the Sun, then it will proceed as above explained. Hence
it also appears, that the retrogradations of the superior Planets are much
slower than their direct motions, and their continuance much shorter; for the
Planet, from its last quarter, until it comes in opposition to the Sun, appears
to move the same way with the Earth, by whom it is then overtaken: After
which it begins to go backwards, but with a slow motion, because the Earth
being in the same part of the Heavens, and moving the same way that the
Planet really does, the apparent motion of the Planet backwards, must
thereby be lessened.
What has been here said concerning the motions of Jupiter, is also to be
understood of Mars and Saturn. But the retrogradations of Saturn do
oftener happen than those of Jupiter, because the Earth oftener overtakes
Saturn; and for the same reason, the regressions of Jupiter do oftener
happen than those of Mars. But the retrogradations of Mars are much
greater than those of Jupiter, whose are also much greater than those of
Saturn.
In either of the satellites of Jupiter or Saturn, these different
appearances in the neighbouring Worlds are much oftener seen than they are
by us in the primary Planets.
We never observe these different motions in the Moon, because she
turns round the Earth as her center; neither do we observe them in the Sun,
because he is the center of the Earth’s motion; whence the apparent motion
of the Sun always appears the same way round the Earth.

Of the Annual and Diurnal Motion of the Earth, and of the
increase and decrease of Days and Nights.

The Earth in her annual motion round the Sun, has her axis always in
the same direction, or parallel to itself; that is, if a line be drawn parallel to

the axis, while the Earth is in any point of her orbit, the axis in all other
positions of the Earth will be parallel to the said line. This parallelism of the
axis, and the simple motion of the Earth in the ecliptic, solves all the
phænomena of different seasons. These things are very well illustrated by
the Orrery.

Plate 3.

If you put on the lamp in the place of the Sun, you will see how one half
of our globe is always illuminated by the Sun, while the other hemisphere
remains in darkness; how Day and Night are formed by the revolution of
the Earth round her axis; for as she turns from West to East, the Sun appears
to move from East to West. And while the Earth turns in her orbit, you may

observe that her axis always points the same way, and the several seasons of
the year continually change.
To make these things plainer, we will take a view of the Earth in
different parts of her orbit.
When the Earth is in the first point of Libra (which is found by
extending a thread from the Sun, and over the Earth, to the ecliptic) we
have the Vernal Equinox, and the Sun at that time appears in the first point
of ♈ . In this position of the Earth, two Poles of the world are in the line
separating light and darkness; and as the Earth turns round her axis, just one
half of the equator, and all its parallels, will be in the light, and the other
half in the dark; and therefore the days and nights must be every where
equal.
As the Earth moves along in her orbit, you will perceive the North Pole
advances by degrees into the illuminated hemisphere, and at the same time
the South Pole recedes into darkness; and in all places to the Northward of
the equator, the days continually lengthen, while the contrary happens in the
Southern parts, until at length the Earth is arrived in Capricorn. In this
position of the Earth all the space included within the arctic circle falls
wholly within the light, and all the opposite part lying within the antarctic
circle, is quite involved in darkness. In all places between the equator and
the arctic circle, the days are now at the longest, and are gradually longer, as
the place are more remote from the equator. In the Southern hemisphere
there is a contrary effect. All the while the Earth is travelling from
Capricorn towards Aries, the North Pole gradually recedes from the light,
and the South Pole approaches nearer to it; the days in the Northern
hemisphere gradually decrease, and in the Southern hemisphere they
increase in the same proportion, until the Earth be arrived in ♈ ; then the
two Poles of the world lie exactly in the line separating light and darkness,
and the days are equal to the nights in all places of the world. As the Earth
advances towards Cancer, the North Pole gradually recedes from the light,
while the Southern one advances into it, at the same rate. In the Northern
hemisphere the days decrease, and in the Southern one they gradually
lengthen, until the Earth being arrived in Cancer, the North frigid Zone is
all involved in darkness, and the South frigid Zone falls intirely within the
light; the days every where in the Northern hemisphere are now at the
shortest, and to the Southward they are at the longest. As the Earth moves

from hence towards Libra, the North Pole gradually approaches the light,
and the other recedes from it; and in all places to the Northward of the
equator, the days now lengthen, while in the opposite hemisphere they
gradually shorten, until the Earth has gotten into ♎; in which position the
days and nights will again be of equal length in all parts of the world.
You might have observed that in all positions of the Earth, one half of
the equator was in the light, and the other half in darkness; whence under
the equator, the days and nights are always of the same length: And all the
while the Earth was going from ♎ towards ♈ , the North Pole was
constantly illuminated, and the South Pole all the while in darkness; and for
the other half year, the contrary. Sometimes there is a semicircle exactly
facing the Sun, fixed over the middle of the Earth, which may be called the
horizon of the disk: This will do instead of the lamp, if that half of the Earth
which is next the Sun be considered, as being the illuminated hemisphere,
and the other half, to be that which lies in darkness.
The great circle ♈, ♉, ♊ &c. represent the Earth’s annual
orbit; and the four lesser circles ESQC, the ecliptic, upon the Plate 4.
surface of the Earth, coinciding with the great ecliptic in the
Heavens. These four lesser figures represent the Earth in the four cardinal
points of the ecliptic, P being the North Pole of the equator, and p the North
Pole of the ecliptic; SPC, the solstitial colure which is always parallel to the
great solstitial colure ♋ ☉ ♑ in the Heavens; EPQ the equinoctial colure.
The other circles passing thro’ P, are meridians at two hours distance from
one another; the semicircle EÆQ is the Northern half of the equator; the
parallel circle touching the ecliptic in S, is the tropic of Cancer; the dotted
circle, the parallel of London, and the small circle, touching the Pole of the
ecliptic, is the Arctic Circle. The shaded part, which is always opposite to
the Sun, is the obscure hemisphere, or that which lies in darkness; and that
which is next the Sun, is the illuminated hemisphere.
If we suppose the Earth in ♎ , she will then see the Sun in ♈ (which
makes our vernal equinox) and in this position the circle bounding light and
darkness, which here is SC, passes thro’ the Poles of the World, and bisects
all the parallels of the equator; and therefore the diurnal and nocturnal
arches, or the length of the days and nights, are equal in all places of the
world.

But while the Earth in her annual course, moves through ♏, ♐, to ♑,
the line SC, keeping still parallel to itself, or to the place where it was at
first, the Pole P will, by this motion, gradually advance into the illuminated
hemisphere; and also the diurnal arches of the parallels gradually increase,
and consequently the nocturnal ones decrease in the same proportion, until
the Earth has arrived into ♑; in which position the Pole P, and all the space
within the arctic circle, fall wholly within the illuminated hemisphere, and
the diurnal arches of all the parallels that are without this circle, will exceed
the nocturnal arches more or less, as the places are nearer to, or farther off
from it, until the distance from the Pole is as far as the equator, where both
these arches are always equal.
Again, while the Earth is moving from ♑ through ♒, ♓, to ♈, the Pole
P begins to incline to the line, distinguishing light and darkness, in the same
proportion that before it receded from it; and consequently the diurnal
arches gradually lessen, until the Earth has arrived into ♈ where the Pole P
will again fall on the horizon, and so cause the days and nights to be every
where equal. But when the Earth has passed ♈, while she is going thro’ ♉,
and ♊, &c. the Pole P will begin to fall in the obscure hemisphere, and so
recede gradually from the light, until the Earth is arrived in ♋ ; in which
position not only the Pole, but all the space within the arctic circle, are
involved in darkness, and the diurnal arches of all the parallels, without the
arctic circle, are equal to the nocturnal arches of the same parallels, when
the Earth was in the opposite point ♑ ; and it is evident that the days are
now at the shortest, and the nights the longest. But when the Earth has past
this point, while she is going through ♌ and ♏ , the Pole P will again
gradually approach the light, and so the diurnal arches of the parallels
gradually lengthen, until the Earth is arrived in ♎; at which time the days
and nights will again be equal in all places of the World, and the Pole itself
just see the Sun.

Plate 4.

Here we only considered the phænomena belonging to the Northern
parallels; but if the Pole P be made the South Pole, then all the parallels of
latitude will be parallels of South latitude, and the days, every where, in any
position of the Earth, will be equal to the nights of those who lived in the
opposite hemisphere, under the same parallels.

Of the Phases of the Moon, and of her Motion in her Orbit.

The orbit of the Moon makes an angle with the plane of the ecliptic, of
above 5¼ degrees, and cuts it into two points, diametrically opposite (after

the same manner as the equator and the ecliptic cut each other
upon the globe, in ♈ and ♎) which points are called the Nodes; Nodes.
and a right line joining these points, and passing through
the center of the Earth, is called the Line of the Nodes. Dragon’s Head.
That node where the Moon begins to ascend Northward
above the plane of the ecliptic, is called the Ascending Dragon’s Tail.
Node, and the Head of the Dragon, and is thus
commonly marked [Symbol]. The other node from Retrograde Motion
whence the Moon, descends to the Southward of the of the Nodes.
ecliptic, is called the Descending Node, and the
Dragon’s Tail, and is thus marked [Symbol]. The line of nodes continually
shifts itself from East to West, contrary to the order of the signs; and with
this retrograde motion, makes one revolution round the Earth, in the space
of about 19 years.
The Moon describes its orbit round the Earth in the
Space of 27 days and 7 hours, which space of time is Periodical Month.
called a Periodical Month; yet from one conjunction to
the next, the Moon spends 29 days and a half, which is Synodical Month.
called a Synodical Month; because while the Moon in
her proper Orbit finishes her course, the Earth advances near a whole sign
in the ecliptic; which space the Moon has still to describe, before she will
be seen in conjunction with the Sun.
When the Moon is in conjunction with the Sun, note her place in the
ecliptic; then turning the handle, you will find that 27 days and 7 hours will
bring the Moon to the same place; and after you have made 2¼ revolutions
more, the Moon will be exactly betwixt the Sun and the Earth.
The Moon all the while keeps in her orbit, and so the wire
that Supports her continually rises or falls in a socket, as she Phases of
the Moon.
changes her latitude; the black cap shifts itself, and so shews the
phases of the Moon, according to her age, or how much of her enlightened
part is seen from the Earth. In one synodical month, the line of the nodes
moves about 1½ degree from West to East, and so makes one entire
revolution in 19 years.
Let AB be an arch of the Earth’s orbit, and when the Earth is in T, let the
Moon be in N, in conjunction with the Sun in S, while the Moon is

describing her orbit NAFD, the Earth will describe the arch of her orbit T t;
and when the Earth has got into the point t, the Moon will be in the point of
her orbit n, having made one compleat revolution round the Earth. But the
Moon, before she comes in conjunction with the Sun, must again describe
the arch n o; which arch is similar to T t, because the lines FN, f n, are
parallel; and because, while the Moon describes the arch n o, the Earth
advances forward in the ecliptic; the arch described by the Moon, after she
has finished her periodical month, before she makes a synodical month,
must be somewhat greater than n o. To determine the mean length of a
synodical month, find the diurnal motion of the Moon (or the space she
describes round the Earth in one day) and likewise the diurnal motion of the
Earth; then the difference betwixt the two motions, is the apparent motion
of the Moon round the Earth in one day; then it will be, as this differential
arch is to a whole circle; so is one day to that space of time wherein the
Moon appears to describe a compleat circle round the Earth, which is about
29½ days. But this is not always a true Lunation, for the motion of the
Moon is sometimes faster, and sometimes slower, according to the position
of the Earth in her orbit.
In one synodical month the Moon has all manner of aspects with the
Sun and Earth, and because she is opaque, that face of hers will only appear
bright which is towards the Sun, while the opposite remains in darkness.
But the inhabitants of the Earth can only see that face of the Moon which is
turned towards the Earth; and therefore, according to the various positions
of the Moon, in respect of the Sun and Earth, we observe different portions
of her illuminated face, and so a continual change in her[7] Phases.
Let S be the Sun, RTV an arch of the Earth’s orbit, T the Earth, and the
circle ABCD, &c. the Moon’s orbit, in which she turns round the Earth in
the space of a month; and let A, B, C, &c. be the centers of the Moon in
different parts of her orbit.
Now if with the lines S A, S B, &c. we join the centers of the Sun and
Moon, and at right angles to these draw the lines H O; the said lines H O
will be the circles that separate the illuminated part of the Moon from the
dark and obscure. Again, if we conceive another line I L to be drawn at right
angles to the lines TA, TB, &c. passing from the center of the Earth to the
Moon, the said line I L will divide the visible hemisphere of the Moon, or

that which is turned towards us, from the invisible, or that which is turned
from us; and this circle may be called the Circle of Vision.
Now it is manifest, that whenever the Moon is in the
position A, or in that point of her orbit which is opposite to the Full
Moon.
Sun, the circle of vision, and the circle bounding light and
darkness, do coincide, and all the illuminated face of the Moon
is turned towards the Earth, and is visible to us; and in this Half Moon.
position the Moon is said to be full. But when the Moon arrives
to B, all her illuminated face is then not towards the Earth, there
New
being a part of it, HBI, not to be seen by us; and then her visible Moon.
face is deficient from a circle, and appears of a gibbous form, as
in B. Fig. 3. Again when she arrives to C, the two forementioned circles cut
each other at right angles, and then we observe a half Moon, as in C, Fig. 3.
And again the illuminated face of the Moon is more and more turned from
the Earth, until she comes to the Point E, where the circle of vision, and that
bounding light and darkness, do again coincide. Here the Moon disappears,
the illuminated part being wholly turned from the Earth; and she is now said
to be in Conjunction with the Sun, because she is in the same direction from
the Earth that the Sun is in, which position we call a New Moon. When the
Moon is arrived to F, she again assumes a horned figure, but her horns
(which before the change were turned Westward) have now changed their
position, and look Eastward. When she has arrived to a quadrate aspect at
G, she will appear bissected, like a half Moon, afterwards she will still grow
bigger, until at last she comes to A, where again she will appear in her full
splendor.
The same appearances which we observe in the Moon are likewise
observed by the Lunarians in the Earth, our Earth seeing a Moon to them,
as their Moon is to us; and we are observed by them to be carried round in
the space of time that they are really carried round the Earth. But the same
phases of the Earth and Moon happen when they are in contrary position;
for when the Moon is in conjunction to us, the Earth is then in opposition to
the Moon, and the Lunarians have then a full Earth, as we in a similar
position have a full Moon. When the Moon comes in opposition to the Sun,
the Earth, seen from the Moon, will appear in conjunction with her, and in
that position the Earth will disappear; afterwards she will assume a horned

figure, and so shew the same phases to the inhabitants of the Moon as she
does to us.

Of the Eclipses of the Sun and Moon.

An Eclipse is that deprivation of light in a Planet, when
another is interposed betwixt it and the Sun. Thus, an eclipse of Eclipse.
the Sun is made by the interposition of the Moon at her
conjunction, and an eclipse of the Moon is occasioned by the shadow of the
Earth falling upon the Moon, when she is in opposition to the Sun.
Let S be the Sun, T the Earth, and ABC its shadow; now if
the Moon, when she is in opposition to the Sun, should come Fig. 4..
into the conical space ABC, she will then be deprived of the
solar light, and so undergo an eclipse. Lunar
Eclipse.
In the same manner, when the shadow of the Moon falls
upon the Earth (which can never happen but when the Moon is Solar
in conjunction with the Sun) that part upon which the shadow Eclipse.
falls will be involved in darkness, and the Sun eclipsed. But
because the Moon is much less than the Earth, the shadow of the Fig. 5.
☽ cannot cover the whole Earth, but only a part of it. Let S be
the Sun, T the Earth, ABC the Moon’s orbit, and L the Moon in conjunction
with the Sun: Here the shadow of the Moon falls only upon the part DE of
the Earth’s surface, and there only the Sun is intirely hid: but there are other
parts EF, DG, on each side of the shadow, where the inhabitants are
deprived of part of the Solar rays, and that more or less, according to their
distance from the shadow. Those who live at H and I will see half of the
Sun eclipsed, but in the spaces FM, GN, all the Sun’s body will be visible,
without any eclipse. From the preceding figure it appears, that an eclipse of
the Sun does not reach a great way upon the superficies of the Earth; but the
whole body of the Moon may sometimes be involved in the Earth’s shadow.
Although the Moon seen from the Earth, and the Earth seen
from the Moon, are each alternately, once a month, in Fig. 6.
conjunction with the Sun; yet, by reason of the inclination of the
Moon’s orbit to the ecliptic, the Sun is not eclipsed every new Moon, nor
the Moon at every full. Let T be the Earth, DTE an arch of the ecliptic,
ALBF, the Moon’s orbit, having the Earth T, in its center; and let AGBG be

another circle coinciding with the ecliptic, and A, B, the nodes, or the two
points where the Moon’s orbit and the ecliptic cut each other. A the
ascending node, and B the descending node. The angle GAL equal to GBL
is the inclination of the Moon’s orbit to the ecliptic, being about 5¼
degrees. Now a spectator from the Earth at T, will observe the Sun to move
in the circle AGBC, and the Moon in her orbit ALBF; whence it is evident,
that the Sun and Moon can never be seen in a direct line, from the center of
the Earth, but when the Moon is in one of the nodes A or B; and then only
will the Sun appear centrally eclipsed. But if the conjunction of the Moon
happens when she is any where within the distance A c of the nodes, either
North or South, the Sun will then be eclipsed, more or less, according to the
distance from the node A, or B. If the conjunction happens when the Moon
is in b, the Sun will be then one half eclipsed; and if it happens when she is
in c, the Moon’s limb will just touch the Sun’s disk, without hiding any part
of it.
The shadow of the Earth at the place where the Moon’s orbit intersects
it, is three times as large as the Moon’s diameter, as in Fig. 4. and therefore
it often happens that eclipses of the Moon are total, when they are not
central: And for the same reason the Moon may sometimes be totally
eclipsed for three hours together; whereas total eclipses of the Sun can
scarcely ever exceed four minutes.
The eclipses of the Sun and Moon are very well explained by the
Orrery: Thus having put the lamp in the place of the Sun, and the little
Earth and the little Moon in their proper places, instead of the larger ones,
let the room wherein the instrument stands be darkened; then turning the
handle about, you will see when the conjunction of the Moon happens.
When she is in or near one of the nodes, her shadow will fall upon the
Earth, and so deprive that part upon which it falls of the light of the Sun: If
the conjunction happens when the Moon is not near one of the nodes, the
light of the lamp will fall upon the Earth, either above or below the Moon,
according to her latitude at that time. In like manner, when the full Moon
happens near one of the nodes, the shadow of the Earth will fall upon the
Moon; and if the Moon’s latitude be but small, her whole face will be
involved in darkness. At other times, when the full Moon happens when she
is not near one of her nodes, the shadow of the Earth will pass either above

or below the Moon, and so by that means the Moon will escape being
eclipsed.

Of the Eclipses of the Satellites of Jupiter.

The apparent diameters of the inferior Planets are so small, that when
they pass betwixt us and the Sun, they only appear like small spots upon the
Sun’s surface, without depriving us of any sensible quantity of his light. The
shadow of the Earth likewise terminates before it reaches any of the
superior Planets, so that they are never eclipsed by us; and the Earth when
she is in conjunction with the Sun, only appears like a black spot upon his
surface.
But Jupiter and his Moons mutually eclipse each other, as our Earth and
Moon do; as also doth Saturn and his Moons. The satellites of Jupiter
become twice hid from us, in one circulation round ♃; viz. once behind the
body of Jupiter, i. e. when they are in the right line joining the centers of
the Earth and ♃; and again they become invisible when they enter the
shadow of Jupiter, which happens when they are at their Full, as seen from
♃, at which times they also suffer eclipses; which eclipses happen to them
after the same manner as they do to our Moon, by the interposition of the
Earth betwixt her and the Sun.
Let S be the Sun, ABT the Earth’s orbit; and C ♃ D, an arch
of Jupiter’s orbit, in which let Jupiter be in the point ♃; and let Fig. 7.
CFDH be the orbit of one of Jupiter’s satellites, which we will
here suppose to be the farthest from him. These satellites, while they move
thro’ the inferior parts of their orbs, viz. from D thro’ H, I, to C, seem from
the Earth and the Sun to have a retrograde motion; but when they are in the
superior part of their orbit, they are then seen to move from West to East,
according to their true motion. Now while they describe the superior part of
their orbits, they will be twice hid from the Earth, once in the shadow of ♃,
and once behind his body. If Jupiter be more Westerly than the Sun, that is,
when the Earth is in A, they will be first hid in the shadow F, and afterwards
behind the body of ♃ in G: But when the Earth is in B, then they are first
hid behind ♃’s body in E, and afterwards fall into the shadow F. While the
satellites describe the inferior parts of their orbit, they only once disappear,

which may be either in I or H, according to the position of the Earth, in
which places they cannot be distinguished from the body of Jupiter.

Plate 5.

When the satellites seen from ♃ are in conjunction with the Sun, their
shadows will then fall upon ♃, and some part of his body be involved in
darkness, to which part the Sun will be totally eclipsed.
By observing the eclipses of Jupiter’s satellites, it was first discovered
that light is not propogated instantaneously, though it moves with an
incredible swiftness: For if light came to us in an instant, an observer in T
will see an eclipse of one of the satellites, at the same time that another in K
would. But it has been found by observations, that when the Earth is in K,
at her nearest distance from Jupiter, these eclipses happen much sooner
than when she is in T. Now having the difference of time betwixt these
appearances in K and T, we may find the length of time the light takes in
passing from K to T, which space is equal to the diameter of the Earth’s
annual orb. By these kinds of observations it has been found, that light
reaches from the Sun to us in the space of eleven minutes of time, which is
at least at the rate of 100,000 miles in a second.

FINIS.

AN INDEX OF THE
Astronomical Terms
Made Use of in this BOOK.

cronical Rising and Setting of the Stars
A
Almacanthers
Page 96

63
Altitudes ib.
——— Meridian Altitude 63
Amplitude 62
Amphiscians 91
Annual Motion 7
Antœci 92
Antarctic Circle 53
——— Pole ib.
Antipodes 93
Arctic Circle 52
Arctic Pole 53
Ascension 68
——— Right ib.
——— Oblique 69
Ascensional Difference ib.
Ascians 91
——— Heteroscians ib.
Asterisms 36
Atmosphere 81
Axis 43
——— of the World 49
Azimuth 61

Babylonish Hours 71

Bissextile 78

Circle 42
——— Great Circles ib.
——— Parallel, or lesser Circles 43
——— Secondary Circles ib.
Circles of the Sphere 47
Climates 93
Colures 53
——— Equinoctial Colure ib.
——— Solstitial Colure 54
Comets 29
Conjunction 11, 207
Constellations 36
Cosmical rising and setting of the Stars 96
Crepusculum 83
Day, Natural and Artificial 69
Declination 52
Diurnal Motion 7
Diurnal Arch 68

Eclipses 208
——— Solar ib.
——— Lunar ib.
Eclipses of Jupiter’s Satellites 212
Ecliptic 53
Egyptian Year 75
Elongation 18
Equator, or Equinoctial 48
Equinoctial Points 53
——— Precession of 55
——— Vernal and Autumnal 70
Excentricity 4

Galaxy, or Milky Way 38
Geocentric Place 19
Globe 42
——— Terrestrial 43
——— Celestial 44
Gregorian Account 80

Heliacal rising and setting of the Stars 96
Heliocentric Place 19
Hemisphere 42
——— Northern and Southern 49
Heteroscians 91
Horizon 58
——— Sensible ib.
——— Rational 59
Hour Circles 50

Italian Hours 72

Jewish Hours ib.
Julian Account 79

Latitude, in Astronomy 56
——— in Geography 84
Longitude in Astronomy 56
——— in Geography 87

Meridian 50, 61

Nadir 61
Nodes 3, 202
Nocturnal Arch 68

Orbit 3

Parallel of the Earth’s Semidiameter 23
——— of the Earth’s Annual Orb 20
Periœci 92
Periscians 91
Periodical Month 74, 202
Phases of the Moon 201
Planets 1
——— Inferior and Superior 14
Planetary Hours 72
Poles 42
——— of the World 49
——— of the Ecliptic 56
Polar Circles 52
Points of the Compass 60
——— Cardinal Points 59
Primary Planets 5

Retrograde Motion of the Planets 187
——— of the Nodes 202

Secondary Planets 5
Sidereal Year 74
Signs of the Zodiac 54
——— Northern and Southern ib.
Solstices 71
——— Summer and Winter Solstices ib.
Solstitial Points 53
Sphere 42
——— Parallel and Right 67
——— Oblique 68
Stationary 186
Style Old 79
——— New Style 80
Synodical Month 74, 202

Tropics (of Cancer and Capricorn) 52
Twilights 83

Vertical Circles 61
——— Prime Vertical 62

Zenith 61
Zenith Distance 63
Zones, Torrid, Temperate, and Frigid 90

THE END

Directions to the Binder.
The great Orrery to face the Title.
Plate I. Page 2
Plate II. 28
The Globes 35
Plate III. 194
Plate IV. 200
Plate V. 214

A CATALOGUE
Of Mathematical, Philosophical,
and Optical Instruments,

MADE and SOLD by

BENJAMIN COLE,

At his Shop, the Sign of the Orrery, No. 136,
in Fleet street, London.
l. s. d.
ariety of pocket cases of Drawing
from 3l. 3s. to 20 0 0
V Instruments, in Silver,
Ditto, in Brass, from 5s. to 5 5 0
Magazine Cases, in Silver, from 12l. to 150 0 0
Ditto, in Brass, from 5l. to 50 0 0
Circular Compasses to describe a Circle from 3s. to 0 7 6
as small as a pin’s head,
Long Hand Drawing-pens, from 1s. to 0 5 0
Compasses in Brass, with shifting points, from 2s. 6d. to 1 1 0
as the Ink and Black Lead points,
Plain Compasses, from 6d. to 0 5 0
Beam Compasses, for drawing large from 12. to 3 0 0
circles,
Proportionable Compasses, from 1l. 1s. to 5 5 0
Triangular Compasses, from 14s. to 0 18 0
from 1l. 11s. 5 5 0
Elliptical Compasses, for Ovals,
6d. to
Hair Compasses 0 7 6
Bows for drawing curved lines, from 4s. to 0 10 6
Sets of Feather-edge Scales, in Brass, from 12s. to 1 16 0
Ivory, or Wood,
Plain ditto, or Plotting ditto, in ditto, from 8d. to 0 18 0
Gunter’s 2 feet, and 1 foot Scales, in from 2s. to 2 2 0
Brass or Wood,
Protractors of all sorts, from 1s. 6d. to 1 16 0
Parallel Rules, from 6 to 36 inches, from 2s. 6d. to 1 16 0
Cross-bar ditto, in Brass, Ivory, or Wood, from 10s. 6d. to 3 0 0
from 4½ inches, to 3 feet,
Sectors, in ditto, from 2s. 6d. to 4 14 6
Theodolites, from 3l. 3s. to 6 6 0

l. s. d.
Ditto, with Vertical arch, Spirit Levels, from 10l. 10s. 21 0 0
Telescope, &c. to
Plain Tables, from 3l. 3s. to 5 5 0
Circumferentors, the principal Instrument from 1l. 16s. to 3 13 6
for Surveying in the West-Indies,
Gunter’s four pole chains, from 6s. to 0 12 0
Spirit Levels of all sorts, from 5s. to 12 12 0
Pentographia, for the ready and exact
reduction or copying of
Schemes, Drawings, Prints, &c. 4 14 6
from 4l. 14s. 6 6 0
Measuring Wheels for Surveying,
6d. to
Hadley’s Quadrants, with Diagonal 1 14 0
Divisions
Ditto, with a Nonius, from 2l. 2s. to 3 13 6
from 3l. 13s. 6 6 0
Ditto, all in Brass,
6d. to
Davies’s Quadrant, from 12s. to 1 1 0
Cole’s ditto, from 18s. to 1 5 0
Sutton’s ditto 0 6 0
Gunter’s ditto, from 3s. 6d. to 1 1 0
Horizontal Sun Dials, for all Latitudes, from 5s. to 10 0 0
Ring Dials, from 10s. 6d. to 21 0 0
Azimuth Compasses, from 5l. 5s. to 10 0 0
Amplitude ditto, from 1l. 7s. to 5 5 0
Mariner’s Compasses, either for the from 7s. 6d. to 3 13 0
Cabin, or Binacle,
Pocket Compasses, from 1s. to 1 11 6
Large Orreries, from 50l. to 250 0 0
Armillary Spheres, from 12l. to 50 0 0
Seventeen inch Globes 6 6 0
Fifteen inch ditto 5 5 0
Twelve inch ditto 3 3 0
Nine inch ditto 2 2 0

l. s. d.
Six inch ditto 1 16 0
Three inch ditto, in a case, from 8s. to 0 10 0
Large double Barrell’d standing air 25 0 0
pumps
Apparatus to ditto, from 3l. 3s. to 12 12 0
Double Barrell’d table air pumps, with from 5l. 15s. 20 0 0
their apparatus, 6d. to
Single Barrell’d ditto 2 12 6
Apparatus to ditto 2 2 0
Electrical Machines, in Brass, with from 5l. 5s. to 13 13 0
apparatus, box, &c.
Barometers, from 1l. 1s. to 1 16 0
from 1. 11s. 6d. 2 12 6
Ditto & Thermometer, in one frame,
to
Barometer, Thermometer, and from 2l 12s. 6d. 3 13 6
Hydrometer, all in one frame, to
Farenheit’s Thermometers, in mahogany from 1l. 5s. to 1 11 6
cases,
Pocket ditto, in black cases, from 12s. to 1 1 0
Spirit Thermometers, on box scales, for 0 10 6
hot-houses
Hydrometers, in Ivory, from 4s. to 0 5 6
Ditto, in copper, with weights, &c. for from 1l. 1s. to 1 5 0
proving Spirits,
Hydrostatic Balance, with apparatus, &c. 1 15 0
Speaking Trumpets, from 10s. to 1 11 6
Hearing ditto, from 7s. 6d. to 1 1 0
Reflecting Telescopes, from 1l. 16s. to 50 0 0
Refracting ditto, of various lengths, with from 7s. 6d. to 6 6 0
four or six glasses,
from 3l. 13s. 7 7 0
Double reflecting Microscopes,
6d. to
Solar ditto, in Brass, from 4l. 4s. to 6 6 0
Wilson’s pocket ditto, from 1l. 5s. to 2 12 6

l. s. d.
from 2l. 12s. 3 13 6
Opake ditto,
6d. to
Cloth ditto, from 3s. 6d. to 0 7 6
Flower ditto, from 3s. 6d. to 0 5 0
Diagonal Machines for viewing prints, from 16s. to 1 11 6
Large Book Camera Obscura, from 4l. 4s. to 5 5 0
Box Camera Obscura, from 10s. 6d. to 2 2 0
Scioptric Ball and Socket, in Wood 0 7 6
Opera Glasses, from 5s. to 2 12 6
Prospect ditto, from 8d. to 0 10 6
Magic Lanthorn, without objects, from 1l. 1s. to 1 7 0
Magic Lanthorn sliders, with objects, from 5s. to 0 10 6
Mirrors, convex or concave, of all sizes, from 10s. 6d. to 16 16 0
in black frames,
Prisms, from 6s. to 1 1 0
Reading Glasses set in a variety of from 2s. 6d. to 2 12 6
curious frames,
Watchmaker’s Glasses, in frames, from 1s. to 0 10 6
Concave ditto, for short sighted persons, from 1s.6d. to 2 2 0
Spectacles ground on brass tools, and set from 1s. to 1 7 0
in silver, tortoise shell, horn, &c.
Achromatic, Opera, and Prospect glasses, from 1l. 1s. to 1 16 0
Achromatic Telescopes of any length, at 1l. 1s. each foot.
Gauging Rules, Carpenter’s Rules, and all other kind of Rules,
at the usual Prices.

The Eleventh Edition of Harris on the Globes, with the
Description and Use of the Orrery, 3s. 6d.
The Use of the Sector and plain Scale explained, 1s.
The Use of Hadley’s Quadrant explained, 6d.
A fine Print of the Orrery, on imperial paper, 2s.
A smaller ditto, 6d.

Variety of other Instruments too tedious to mention, are
made and sold at the above place: Where any Gentleman, by
Letter, or other Directions, may depend on being as
faithfully served as if present. And as I have been long in the
Wholesale part of the Business, Merchants, &c. may be sure
of being supplied on the Best Terms. As also by M. Allison,
at Falmouth.

FOOTNOTES:
[1] By the Orbit of a Planet is commonly understood the Tract or Ring,
described by its Center round the Sun, but by the Plane of the Orbit is meant a
flat Surface extended every way thro’ the Orbit infinitely.
[2] N. B. According to Biachini’s Observations, Venus’s axis inclines 75 degrees
from the perpendicular to the plane of the Ecliptic (which is 51½ deg. more than
the axis of our Earth) her Tropics are only 15 deg. from her Poles, and her Polar
Circles at the same distance from her Equator; so that the Sun’s greatest
Declination on each side of her Equator is 75 deg. by which she must undergo a
much greater variety of seasons than we do on our Earth.
[3] ☌ Is a mark commonly used for conjunction; thus ☌ with the ☉, is to be read
conjunction with the Sun.
[4] Prob. VI.
[5] Prob. XIII.
[6] The insensible change in the Longitude, Right Ascension, and Declination of
the Fixed Stars, made by their slow motion, parallel to the ecliptic (being but 1
degree in 72 years) is not worth notice in this place.
[7] Phases of the Moon are those different appearances we observe in her,
according to her position in respect to the Sun and Earth.

Transcriber’s Notes:

The cover image was created by the transcriber, and is in the public domain.
Illustrations were moved so as not to break up paragraphs.
Antiquated spellings were not corrected.
Typographical errors have been silently corrected.

*** END OF THE PROJECT GUTENBERG EBOOK THE
DESCRIPTION AND USE OF THE GLOBES AND THE ORRERY ***

Updated editions will replace the previous one—the old editions will be
renamed.

Creating the works from print editions not protected by U.S. copyright law
means that no one owns a United States copyright in these works, so the
Foundation (and you!) can copy and distribute it in the United States
without permission and without paying copyright royalties. Special rules,
set forth in the General Terms of Use part of this license, apply to copying
and distributing Project Gutenberg™ electronic works to protect the
PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a
registered trademark, and may not be used if you charge for an eBook,
except by following the terms of the trademark license, including paying
royalties for use of the Project Gutenberg trademark. If you do not charge
anything for copies of this eBook, complying with the trademark license is
very easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project Gutenberg
eBooks may be modified and printed and given away—you may do
practically ANYTHING in the United States with eBooks not protected by
U.S. copyright law. Redistribution is subject to the trademark license,
especially commercial redistribution.

START: FULL LICENSE

THE FULL PROJECT GUTENBERG™ LICENSE
PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work (or any
other work associated in any way with the phrase “Project Gutenberg”), you
agree to comply with all the terms of the Full Project Gutenberg License
available with this file or online at www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing
Project Gutenberg electronic works

1.A. By reading or using any part of this Project Gutenberg electronic work,
you indicate that you have read, understand, agree to and accept all the
terms of this license and intellectual property (trademark/copyright)
agreement. If you do not agree to abide by all the terms of this agreement,
you must cease using and return or destroy all copies of Project Gutenberg
electronic works in your possession. If you paid a fee for obtaining a copy
of or access to a Project Gutenberg electronic work and you do not agree to
be bound by the terms of this agreement, you may obtain a refund from the
person or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be used on
or associated in any way with an electronic work by people who agree to be
bound by the terms of this agreement. There are a few things that you can
do with most Project Gutenberg electronic works even without complying
with the full terms of this agreement. See paragraph 1.C below. There are a
lot of things you can do with Project Gutenberg electronic works if you
follow the terms of this agreement and help preserve free future access to
Project Gutenberg electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation”
or PGLAF), owns a compilation copyright in the collection of Project
Gutenberg electronic works. Nearly all the individual works in the
collection are in the public domain in the United States. If an individual
work is unprotected by copyright law in the United States and you are

located in the United States, we do not claim a right to prevent you from
copying, distributing, performing, displaying or creating derivative works
based on the work as long as all references to Project Gutenberg are
removed. Of course, we hope that you will support the Project Gutenberg
mission of promoting free access to electronic works by freely sharing
Project Gutenberg works in compliance with the terms of this agreement for
keeping the Project Gutenberg name associated with the work. You can
easily comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg License when you
share it without charge with others.

1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are in a
constant state of change. If you are outside the United States, check the
laws of your country in addition to the terms of this agreement before
downloading, copying, displaying, performing, distributing or creating
derivative works based on this work or any other Project Gutenberg work.
The Foundation makes no representations concerning the copyright status
of any work in any country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other immediate
access to, the full Project Gutenberg License must appear prominently
whenever any copy of a Project Gutenberg work (any work on which the
phrase “Project Gutenberg” appears, or with which the phrase “Project
Gutenberg” is associated) is accessed, displayed, performed, viewed, copied
or distributed:

This eBook is for the use of anyone anywhere in the United States
and most other parts of the world at no cost and with almost no
restrictions whatsoever. You may copy it, give it away or re-use it
under the terms of the Project Gutenberg™ License included with
this eBook or online at www.gutenberg.org. If you are not located in
the United States, you will have to check the laws of the country
where you are located before using this eBook.

1.E.2. If an individual Project Gutenberg electronic work is derived from
texts not protected by U.S. copyright law (does not contain a notice
indicating that it is posted with permission of the copyright holder), the
work can be copied and distributed to anyone in the United States without
paying any fees or charges. If you are redistributing or providing access to a
work with the phrase “Project Gutenberg” associated with or appearing on
the work, you must comply either with the requirements of paragraphs
1.E.1 through 1.E.7 or obtain permission for the use of the work and the
Project Gutenberg trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg electronic work is posted with the
permission of the copyright holder, your use and distribution must comply
with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed
by the copyright holder. Additional terms will be linked to the Project
Gutenberg License for all works posted with the permission of the
copyright holder found at the beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg License
terms from this work, or any files containing a part of this work or any
other work associated with Project Gutenberg.

1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without prominently
displaying the sentence set forth in paragraph 1.E.1 with active links or
immediate access to the full terms of the Project Gutenberg License.

1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including any
word processing or hypertext form. However, if you provide access to or
distribute copies of a Project Gutenberg work in a format other than “Plain
Vanilla ASCII” or other format used in the official version posted on the
official Project Gutenberg website (www.gutenberg.org), you must, at no
additional cost, fee or expense to the user, provide a copy, a means of
exporting a copy, or a means of obtaining a copy upon request, of the work
in its original “Plain Vanilla ASCII” or other form. Any alternate format
must include the full Project Gutenberg License as specified in paragraph
1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying, performing,
copying or distributing any Project Gutenberg works unless you comply
with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing access to
or distributing Project Gutenberg electronic works provided that:

• You pay a royalty fee of 20% of the gross profits you derive from the
use of Project Gutenberg works calculated using the method you
already use to calculate your applicable taxes. The fee is owed to the
owner of the Project Gutenberg trademark, but he has agreed to donate
royalties under this paragraph to the Project Gutenberg Literary
Archive Foundation. Royalty payments must be paid within 60 days
following each date on which you prepare (or are legally required to
prepare) your periodic tax returns. Royalty payments should be clearly
marked as such and sent to the Project Gutenberg Literary Archive
Foundation at the address specified in Section 4, “Information about
donations to the Project Gutenberg Literary Archive Foundation.”

• You provide a full refund of any money paid by a user who notifies
you in writing (or by e-mail) within 30 days of receipt that s/he does
not agree to the terms of the full Project Gutenberg™ License. You
must require such a user to return or destroy all copies of the works
possessed in a physical medium and discontinue all use of and all
access to other copies of Project Gutenberg™ works.

• You provide, in accordance with paragraph 1.F.3, a full refund of any
money paid for a work or a replacement copy, if a defect in the
electronic work is discovered and reported to you within 90 days of
receipt of the work.

• You comply with all other terms of this agreement for free distribution
of Project Gutenberg™ works.

1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™
electronic work or group of works on different terms than are set forth in
this agreement, you must obtain permission in writing from the Project
Gutenberg Literary Archive Foundation, the manager of the Project

Gutenberg™ trademark. Contact the Foundation as set forth in Section 3
below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread works
not protected by U.S. copyright law in creating the Project Gutenberg™
collection. Despite these efforts, Project Gutenberg™ electronic works, and
the medium on which they may be stored, may contain “Defects,” such as,
but not limited to, incomplete, inaccurate or corrupt data, transcription
errors, a copyright or other intellectual property infringement, a defective or
damaged disk or other medium, a computer virus, or computer codes that
damage or cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except
for the “Right of Replacement or Refund” described in paragraph 1.F.3, the
Project Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all liability to
you for damages, costs and expenses, including legal fees. YOU AGREE
THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT
EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE
THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY
DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE
TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL,
PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE
NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you
discover a defect in this electronic work within 90 days of receiving it, you
can receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium with
your written explanation. The person or entity that provided you with the
defective work may elect to provide a replacement copy in lieu of a refund.
If you received the work electronically, the person or entity providing it to

you may choose to give you a second opportunity to receive the work
electronically in lieu of a refund. If the second copy is also defective, you
may demand a refund in writing without further opportunities to fix the
problem.

1.F.4. Except for the limited right of replacement or refund set forth in
paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER
WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR
FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied warranties or
the exclusion or limitation of certain types of damages. If any disclaimer or
limitation set forth in this agreement violates the law of the state applicable
to this agreement, the agreement shall be interpreted to make the maximum
disclaimer or limitation permitted by the applicable state law. The invalidity
or unenforceability of any provision of this agreement shall not void the
remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in accordance
with this agreement, and any volunteers associated with the production,
promotion and distribution of Project Gutenberg™ electronic works,
harmless from all liability, costs and expenses, including legal fees, that
arise directly or indirectly from any of the following which you do or cause
to occur: (a) distribution of this or any Project Gutenberg work, (b)
alteration, modification, or additions or deletions to any Project Gutenberg
work, and (c) any Defect you cause.

Section 2. Information about the Mission of Project
Gutenberg

Project Gutenberg is synonymous with the free distribution of electronic
works in formats readable by the widest variety of computers including
obsolete, old, middle-aged and new computers. It exists because of the

efforts of hundreds of volunteers and donations from people in all walks of
life.

Volunteers and financial support to provide volunteers with the assistance
they need are critical to reaching Project Gutenberg’s goals and ensuring
that the Project Gutenberg collection will remain freely available for
generations to come. In 2001, the Project Gutenberg Literary Archive
Foundation was created to provide a secure and permanent future for
Project Gutenberg and future generations. To learn more about the Project
Gutenberg Literary Archive Foundation and how your efforts and donations
can help, see Sections 3 and 4 and the Foundation information page at
www.gutenberg.org.

Section 3. Information about the Project Gutenberg
Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)
(3) educational corporation organized under the laws of the state of
Mississippi and granted tax exempt status by the Internal Revenue Service.
The Foundation’s EIN or federal tax identification number is 64-6221541.
Contributions to the Project Gutenberg Literary Archive Foundation are tax
deductible to the full extent permitted by U.S. federal laws and your state’s
laws.

The Foundation’s business office is located at 41 Watchung Plaza #516,
Montclair NJ 07042, USA, +1 (862) 621-9288. Email contact links and up
to date contact information can be found at the Foundation’s website and
official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project
Gutenberg Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of increasing the
number of public domain and licensed works that can be freely distributed
in machine-readable form accessible by the widest array of equipment

including outdated equipment. Many small donations ($1 to $5,000) are
particularly important to maintaining tax exempt status with the IRS.

The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United States.
Compliance requirements are not uniform and it takes a considerable effort,
much paperwork and many fees to meet and keep up with these
requirements. We do not solicit donations in locations where we have not
received written confirmation of compliance. To SEND DONATIONS or
determine the status of compliance for any particular state visit
www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we have
not met the solicitation requirements, we know of no prohibition against
accepting unsolicited donations from donors in such states who approach us
with offers to donate.

International donations are gratefully accepted, but we cannot make any
statements concerning tax treatment of donations received from outside the
United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation methods
and addresses. Donations are accepted in a number of other ways including
checks, online payments and credit card donations. To donate, please visit:
www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg
electronic works

Professor Michael S. Hart was the originator of the Project Gutenberg
concept of a library of electronic works that could be freely shared with
anyone. For forty years, he produced and distributed Project Gutenberg
eBooks with only a loose network of volunteer support.

Project Gutenberg eBooks are often created from several printed editions,
all of which are confirmed as not protected by copyright in the U.S. unless a

copyright notice is included. Thus, we do not necessarily keep eBooks in
compliance with any particular paper edition.

Most people start at our website which has the main PG search facility:
www.gutenberg.org.

This website includes information about Project Gutenberg, including how
to make donations to the Project Gutenberg Literary Archive Foundation,
how to help produce our new eBooks, and how to subscribe to our email
newsletter to hear about new eBooks.