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 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.

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As may be seen by one he made for Mr. _Watt_’s Academy in _Tower-street_.

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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.

[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.]