Chapter I: Part 1

Transcriber’s Notes:

Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
Small capitals have been converted to SOLID capitals.
Old or antiquated spellings have been preserved.
Typographical errors have been silently corrected.

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.

The great encouragement Mr. WRIGHT has 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_.

SECT. I. _Of the Order and Periods of the Primary 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_ Venus ibid.
——— _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 computed_ ibid.
——— _How the relative Distance of the Planets from the
Sun are determined_ 18
——— _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 Diurnal Revolutions of the Planets_ 28
——— _Of Comets_ 29

SECT. II. _Of the Fixed Stars_ 32

——— _That the fixed Stars are luminous Bodies, at immense
Distances from us_ ibid.
——— _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.

_The Geometrical Definition of a Globe, and of the principal
Use of the Artificial Globes_ 42

_That there will be the same prospect of the Fixed Stars,
whether the Spectator be placed in the Sun, or on the
Earth_ 45

SECT. I. _An Explanation of the Circles of the Sphere,
and of some Astronomical Terms arising therefrom_ 47
——— _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
composed of Land and Water_ ibid.
——— _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
Latitude and Longitude being given to find the Place_ ibid.
PROB. II. _To find the Difference of Latitude
betwixt any two given places_ 106
PROB. III. _To find the Difference of Longitude
betwixt any two given places_ ibid.
PROB. IV. _Any Place being given; to find all those places
that are in the same Latitude with the said place_ 107
PROB. V. _The Day of the Month being given; to find
the Sun’s place in the Ecliptic, and his Declination_ 108
PROB. VI. _To rectify the Globe for the Latitude,
Zenith, and Sun’s place_ 109
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_ 110
PROB. VIII. _To find the Angle of a Position of Places;
or the angle formed by the Meridian of one place,
and a great circle passing through both the places_ 111
PROB. IX. _To find the_ Antœci, Periœci, _and_
Antipodes, _to any given place_ 113
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) at any other place_ 114
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_ 115
PROB. XII. _A place being given in the_ Torrid
Zone; _to find those two Days in which the Sun will
be Vertical to the same_ 116
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_ ibid.
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_ 117
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_ 119
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_ 121
PROB. XVII. _To shew by the Globe, at one View,
the Length of the Days and Nights, at any particular
place, at all times of the Year_ 128
PROB. XVIII. _The Latitude of any place, not
exceeding 69½ Degrees, and the Day of the Month being
given; to the time of Sun-rising and Setting, and the
length of the Day and Night_ 136
PROB. XIX. _To find the length of the longest and shortest
Day and Night in any given place, not exceeding 66½
Degrees of Latitude_ 137
PROB. XX. _To find in what Latitude the longest Day is,
of any given length less than 24 Hours_ 139
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_ 140
PROB. XXII. _To find in what Latitude the longest Day is,
of any given length, less than 182 natural Days_ 141
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_ 142
PROB. XXIV. _To find the time when total Darkness
ceases, or when the Twilight continues from Sun-setting
to Sun-rising, in any given place_ 144
PROB. XXV. _The Day of the Month being given; to
find those places of the_ Frigid Zones, _where the Sun
begins to shine constantly without setting; and also
those places where he begins to be totally absent_ 146
PROB. XXVI. _The Latitude, the Sun’s Place, and his
Altitude being given; to find the Hour of the Day,
and Sun’s Azimuth from the Meridian_ 149
PROB. XXVII. _The Latitude, Hour of the Day, and
the Sun’s Place being given; to find the Sun’s Altitude_ 150
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 his Azimuth, at any
Hour of the Night_ 151
PROB. XXIX. _The Latitude of the Sun’s Place, and his
Azimuth being given; to find his Altitude, and the
Hour_ 152
PROB. XXX. _The Latitude, the Sun’s Altitude, and his
Azimuth being given; to find his Place on the Ecliptic,
and the Hour_ ibid.
PROB. XXXI. _The Declination, and Meridian Altitude
of the Sun, or of any Star being given; to find the
Latitude of the Place_ 153
PROB. XXXII. _The Day and Hour of a Lunar Eclipse
being known; to find all those Places upon the Globe
in which the same will be visible_ 154
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_ Babylonish, Italic,
_and_ Jewish, _or_ Judaical _Hour_ 155
PROB. XXXIV. _To find the Right Ascension and
Declination of the Sun, or any Fixed Star_ 156
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, 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_ 159
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_ 162
PROB. XXXVIII. _The Latitude and the Day of the
Month being given; to find the Hour when any known Star
will be on the Meridian, and also the time of its
Rising and Setting_ 165
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_ 166
PROB. XL. _The Day of the Month and the Azimuth, of any
known Star being given; to find the Hour of the Night_ 167
PROB. XLI. _Two known Stars, having the same
Azimuth, or the same Height, being given; to find the
Hour of the Night_ 168
PROB. XLII. _The Latitude, Day of the Month, and
the Altitude of any known Star being given; to find
the Hour of the Night_ 169
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_ 171
PROB. XLIV. _Having the Latitude of the Place; to find
the time when a Star rises and sets_ Heliacally 172
PROB. XLV. _To find the Place of any Planet upon
the Globe, 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 Day in the Year_ 173
PROB. XLVI. _To find all that space upon the Earth where
an Eclipse of one of the Satellites of_ Jupiter _will
be visible_ 175

_The_ DESCRIPTION _of the_ ORRERY 177

_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 her Orbit_ 201
_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._

[Sidenote: _Planets._]

The Sun is placed in the midst of an immense space, wherein six opaque spherical bodies revolve about 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.

THE SOLAR SYSTEM Or the Orbits of the Planets _according to their mean distances from the Sun_.]

[Sidenote: _Nodes._]

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

[Sidenote: _Excentricity._]

The inclinations of the orbits of the Planets to the plane of the ecliptic, are as follows, _viz._ the orbit of _Mercury_ makes an 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.

[Sidenote: _Primary Planets._]

[Sidenote: _Secondary Planets._]

The six Planets above-mentioned, are called _Primaries_, or _Primary Planets_; but besides these, there are ten other lesser Planets, which are called _Secondaries_, _Moons_, or _Satellites_. These moons always accompany their respective primaries, and perform their Revolutions round them, whilst both together are 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.

[Sidenote: _Jupiter’s_ four Moons.]

_Jupiter_ has four _Moons_, or _Satellites_; the _first_, or innermost, performs its revolution in about one Day, and 18½ Hours, at the distance of 5⅔ Semidiameters of _Jupiter_, from his Center; the _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.

[Sidenote: _Saturn_ has five Moons.]

_Saturn_ has no less than five _Satellites_; the _first_, or innermost, revolves about him in 1 Day, and 21 Hours, at the distance of 4⅜ Semidiameters of ♄, from his center; the _second_ 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.

[Sidenote: _Saturn’s_ Ring.]

Besides these attendants, _Saturn_ is encompassed with a thin plain Ring, that does no where touch his body; The diameter of 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.

[Sidenote: _Annual Motion._]

[Sidenote: _Diurnal Motion._]

The motion of the primary Planets round the Sun (as also of the Satellites round their respective primaries) is called their _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_, 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.

[Sidenote: Diurnal Motion of the ♁, ♀, ♂ and ♃.]

[Sidenote: ☉ and ☽ likewise turn round their Axis.]

The _Earth_ performs its revolution round its axis in 23 Hours, 56 Minutes;[2]_Venus_, in 24 Days, 8 Hours; _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 27 Days: And the Moon, which is nearest to us of all the 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.

[Sidenote: The Planets are Opaque and Globular.]

I. The Planets are all _Opaque_ bodies, having no light but what they borrow from the Sun; for that side of them which is next towards the Sun, has always been 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.

[Sidenote: The Planets turn round the Sun.]

II. That the Earth is placed betwixt the Orbs of _Mars_ and _Venus_, and that ☿, ♀, ♂, ♃ and ♄, do all turn round the Sun, is proved from observations as follow:

[Sidenote: _Plate 2. Fig. 1. 2._]

1. Whenever _Venus_ is in conjunction with the Sun, that is, when she is in the same direction from the Earth, 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.

[Sidenote: Why _Venus_ is always either our Morning or Evening Star.]

Besides the forgoing, there is another argument to prove that _Venus_ turns round the Sun in an Orbit that is within the Earth’s, because she is always observed to keep near the Sun, and in the same quarter of the 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.

[Sidenote: The Orbit of _Mars_ includes the Earth’s.]

[Sidenote: _Fig. 3._]

_Mars_ is observed to come in opposition, and likewise to have all other aspects with the Sun; he 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 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.

[Sidenote: _Inferior_ and _Superior Planets_.]

We have now shewn that all the Planets turn round the Sun, and that _Mercury_ and _Venus_ are included 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:

[Sidenote: The Earth does not stand still, but turns round the Sun.]

[Sidenote: _Fig. 4._]

All the Planets seen from the Earth appear to move very unequally, as sometimes to go faster, at other times slower; sometimes to go backwards, and sometimes to 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 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.

[Sidenote: The Annual and Diurnal Motions of the Planets, how computed.]

The annual periods of the Planets round the Sun are determined by carefully observing the length of time since their departure from a certain point in the Heavens, (or from a fix’d Star) until they arrive to the same again. 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.

[Sidenote: How the relative distances of the Planets from the Sun are determined.]

The relative distances of the Planets from the Sun, and likewise from each other, are determined by the following methods: First, the distance of the two inferior 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.

[Sidenote: _Fig. 5. Elongation._]

The greatest _Elongation_ of _Venus_ is found by observation to be about 48 degrees, which is the angle S 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 }

[Sidenote: _Heliocentric_ and _Geocentric Place_, what.]

The distances of the superior Planets, _viz._ ♂, ♃, and ♄, are found by comparing their true places, as they are seen from the Sun, with their apparent places, as they are 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.

[Sidenote: How the absolute distances of the Planets from the Sun are computed.]

[Sidenote: _Parallax_ of the _Earth’s Semidiameter_.]

[Sidenote: _Fig. 7._]

Hitherto we have only considered the distances of the Planets in relation to one another, without determining them by any known measure; but in order to find their absolute distances in some determinate measure, there must be something given, whose measure is known. Now the circumference of the Earth is divided into 360 degrees, and each of these degrees into 60 Geographical miles, so that the whole circumference contains 21600; and by the known proportion for finding the diameter of a circle from its circumference, the Earth’s diameter 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.

[Sidenote: How the Magnitudes of the Planets are determined.]

[Sidenote: _Fig. 8._]

The eye judgeth of the magnitudes of far distant objects, according to the quantities of the angles under which they are seen (which are called their apparent magnitudes;) and these angles appear greater or less in a certain proportion to their distances. Wherefore the distances of the Planets from the Earth, and their apparent 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.

[Sidenote: Why the Moon appears bigger than any of the Planets.]

From hence it appears, that the same body at different distances, will seem to have very different magnitudes. Thus the diameter BD will appear from the 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 | Distance in
|Sun in the space of| 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

_Moon_} Round the { D. H. M. |
} Earth. { 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_.

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_.

[Sidenote: Of _Comets_.]

The motion of Comets in the Heavens, according to the best observations hitherto made, seem to be regulated by the same immutable law that rules the Planets; for their orbits are 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.

[Sidenote: The fixed Stars are at immense distance from us.]

The fixed Stars are those bright and shining bodies, which in a clear night appear to us every where dispersed through the boundless regions of space. 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.

[Sidenote: The fixed Stars are luminous bodies like the Sun.]

It is evident from hence, that all the Stars are luminous bodies, and shine with their own proper and native light, else they could not be seen at such a great 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.

[Sidenote: The distance from us to the Sun is nothing in comparison of the vast distance of the fixed Stars.]

Although the distance betwixt us and the Sun is vastly large, when compared to the diameter of the Earth, yet it is nothing when compared with the prodigious distance of the fixed Stars; for the whole diameter of the Earth’s annual orbit, appears from the 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.

[Sidenote: As to appearance, the Earth may be consider’d as being the center of the Heavens.]

Hence it follows, that tho’ we approach nearer to some fixed Stars at one time of the year than we do at the opposite, and that by the whole length of the diameter of the Earth’s orbit; yet this distance being so small in comparison with the distance of the fixed Stars, 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.

[Sidenote: The fixed Stars are Suns.]

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, 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.

[Sidenote: The fixed Stars are at vast distance from each other.]

It is not reasonable to suppose that all the fixed Stars are placed at the same distance from us; but it is more probable that they are every where interspersed thro’ the 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.