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diff --git a/old/60619-0.txt b/old/60619-0.txt deleted file mode 100644 index 3e335ce..0000000 --- a/old/60619-0.txt +++ /dev/null @@ -1,17799 +0,0 @@ -The Project Gutenberg EBook of Astronomy Explained Upon Sir Isaac Newton's -Principles, by James Ferguson - -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'll -have to check the laws of the country where you are located before using -this ebook. - - - -Title: Astronomy Explained Upon Sir Isaac Newton's Principles - And made easy to those who have not studied mathematics - -Author: James Ferguson - -Release Date: November 3, 2019 [EBook #60619] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK ASTRONOMY EXPLAINED *** - - - - -Produced by MFR, Sonya Schermann, and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - - - - - - Transcriber’s Note - - -This book uses a number of astronomical symbols, including signs of the -Zodiac (♈, ♉, ♊, ♋, ♌, ♍, ♎, ♏, ♐, ♑, ♒, ♓), symbols for planets (☿, ♀, -⊕, ♂, ♃, ♄) and for the sun and moon (☉, 🌑︎). If these characters do not -display correctly, you may have to use an alternative font, such as -Arial Unicode MS or DejaVu. - -When italics were used in the original book, the corresponding text has -been surrounded by _underscores_. Mixed fractions have been displayed -with a hyphen between whole number and fraction for clarity. -Superscripted characters are preceded by ^ and when more than one -character is superscripted, they are surrounded by {}. - -Some corrections have been made to the printed text. These are listed in -a second transcriber’s note at the end of the text. - - - - -[Illustration: The ORRERY, made by _JAMES FERGUSON_. - -_N. 1. The Sun, 2. Mercury, 3. Venus, 4. The Earth, 5. The Moon, 6. The -Sydereal Dial plate, 7. The Hour Circle, 8. y^e Circle for y^e. Moon’s -Age, 9. The Moon’s Orbit, 10. y^e Pointer, Shewing the Sun’s Place & Day -of the Month, 11. The Ecliptic, 12. The Handle for turning y^e whole -machine_ - -_J. Ferguson inv. et delin._ _G. Child. Sculp._ ] - - - - - ASTRONOMY - - EXPLAINED UPON - Sir ISAAC NEWTON’s - PRINCIPLES, - - AND MADE EASY - TO THOSE WHO HAVE NOT STUDIED - - MATHEMATICS. - - By JAMES FERGUSON. - - HEB. XI. 3. _The Worlds were framed by the Word of_ GOD. - JOB XXVI. 13. _By his Spirit he hath garnished the Heavens._ - - THE SECOND EDITION. - -[Illustration: decoration] - - - _LONDON_: - - Printed for, and sold by the AUTHOR, at the GLOBE, - opposite _Cecil-Street_ in the _Strand_. - MDCCLVII. - - - - - TO - - THE RIGHT HONOURABLE - - _GEORGE_ EARL of MACCLESFIELD, - - VISCOUNT _PARKER_ of EWELME in OXFORDSHIRE, - - AND - - BARON of MACCLESFIELD in CHESHIRE; - - PRESIDENT of the ROYAL SOCIETY of _LONDON_, - - MEMBER of the ROYAL ACADEMY OF SCIENCES at _PARIS_, - - OF THE - - IMPERIAL ACADEMY OF SCIENCES at _Petersburg_, - - AND ONE OF THE - - TRUSTEES of the BRITISH MUSEUM; - - DISTINGUISHED - - By his GENEROUS ZEAL for promoting every - BRANCH of USEFUL KNOWLEDGE; - - THIS - - TREATISE of ASTRONOMY - - IS INSCRIBED, - - With the MOST PROFOUND RESPECT, - - By HIS LORDSHIP’s - - MOST OBLIGED, - - And - - MOST HUMBLE SERVANT, - - _JAMES FERGUSON_. - - - - - THE - - CONTENTS. - - CHAP. I. - - _Of Astronomy in general_ Page 1 - - - CHAP. II. - - _A brief Description of the_ SOLAR SYSTEM 5 - - - CHAP. III. - - _The_ COPERNICAN _or_ SOLAR SYSTEM _demonstrated to be 31 - true_ - - - CHAP. IV. - - _The Phenomena of the Heavens as seen from different 39 - parts of the Earth_ - - - CHAP. V. - - _The Phenomena of the Heavens as seen from different 45 - parts of the Solar System_ - - - CHAP. VI. - - _The_ Ptolemean _System refuted. The Motions and Phases 50 - of Mercury and Venus explained_ - - - CHAP. VII. - - _The physical Causes of the Motions of the Planets. The 54 - Excentricities of their Orbits. The times in which - the Action of Gravity would bring them to the Sun._ - ARCHIMEDES’S _ideal Problem for moving the Earth. The - world not eternal_ - - - CHAP. VIII. - - _Of Light. It’s proportional quantities on the 62 - different Planets. It’s Refractions in Water and Air. - The Atmosphere, it’s Weight and Properties. The - Horizontal Moon_ - - - CHAP. IX. - - _The Method of finding the Distances of the Sun, Moon 73 - and Planets_ - - - CHAP. X. - - _The Circles of the Globe described. The different 78 - lengths of days and nights, and the vicissitude of - Seasons, explained. The explanation of the Phenomena - of Saturn’s Ring concluded_ - - - CHAP. XI. - - _The Method of finding the Longitude by the Eclipses of 87 - Jupiter’s Satellites: The amazing velocity of Light - demonstrated by these Eclipses_ - - - CHAP. XII. - - _Of Solar and Sidereal Time_ 93 - - - CHAP. XIII. - - _Of the Equation of Time_ 97 - - - CHAP. XIV. - - _Of the Precession of the Equinoxes_ 108 - - - CHAP. XV. - - _The Moon’s Surface mountainous: Her Phases described: 124 - Her Path, and the Paths of Jupiter’s Moons - delineated: The proportions of the Diameters of their - Orbits, and those of Saturn’s Moons to each other; - and to the Diameter of the Sun_ - - - CHAP. XVI. - - _The Phenomena of the Harvest-Moon explained by a 136 - common Globe: The Years in which the Harvest-Moons - are least and most beneficial, from 1751 to 1861. The - long duration of Moon-light at the Poles in Winter - Page_ - - - CHAP. XVII. - - _Of the ebbing and flowing of the Sea_ 147 - - - CHAP. XVIII. - - _Of Eclipses: Their Number and Period. A large 156 - Catalogue of Ancient and Modern Eclipses_ - - - CHAP. XIX. - - _The Calculation of New and Full Moons and Eclipses. 189 - The geometrical Construction of Solar and Lunar - Eclipses. The examination of ancient Eclipses_ - - - CHAP. XX. - - _Of the fixed Stars_ 230 - - - CHAP. XXI. - - _Of the Division of Time. A perpetual Table of New 248 - Moons. The Times of the Birth and Death of_ CHRIST. - _A Table of remarkable Æras or Events_ - - - CHAP. XXII. - - _A Description of the Astronomical Machinery serving to 260 - explain and illustrate the foregoing part of this - Treatise_ - - - - - _ERRATA._ - -_In the Table facing Page 31, the Sun’s quantity of matter should be - 227500. Page 40, l. last, for_ infinite _read_ indefinite. _Page 97, - l. 20, for_ this _read_ the next. _Page 164, l. 2 from the bottom, - for_ without any acceleration _read_ as above, without any - acceleration. _Page 199, l. 16 for_ XIV _read_ XV. _Page 238, l. 16, - for_ 40 _read_ 406. _Page 240, l. 15 from the bottom, for_ Tifri - _read_ Tisri, _Page 249 l. 13; from the bottom for_ XVII _read_ V. - - - - - ASTRONOMY - - EXPLAINED UPON - - Sir ISAAC NEWTON’s PRINCIPLES. - - - - - CHAP. I. - - _Of Astronomy in general._ - - -[Sidenote: The general use of Astronomy.] - -1. Of all the sciences cultivated by mankind, Astronomy is acknowledged -to be, and undoubtedly is, the most sublime, the most interesting, and -the most useful. For, by knowledge derived from this science, not only -the bulk of the Earth is discovered, the situation and extent of the -countries and kingdoms upon it ascertained, trade and commerce carried -on to the remotest parts of the world, and the various products of -several countries distributed for the health, comfort, and conveniency -of its inhabitants; but our very faculties are enlarged with the -grandeur of the ideas it conveys, our minds exalted above the low -contracted prejudices of the vulgar, and our understandings clearly -convinced, and affected with the conviction, of the existence, wisdom, -power, goodness, and superintendency of the SUPREME BEING! So that -without an hyperbole, - - “_An undevout Astronomer is mad_[1].” - -2. From this branch of knowledge we also learn by what means or laws the -Almighty carries on, and continues the admirable harmony, order, and -connexion observable throughout the planetary system; and are led by -very powerful arguments to form the pleasing deduction, that minds -capable of such deep researches not only derive their origin from that -adorable Being, but are also incited to aspire after a more perfect -knowledge of his nature, and a stricter conformity to his will. - -[Sidenote: The Earth but a point as seen from the Sun.] - -3. By Astronomy we discover that the Earth is at so great a distance -from the Sun, that if seen from thence it would appear no bigger than a -point; although it’s circumference is known to be 25,020 miles. Yet that -distance is so small, compared with the distance of the Fixed Stars, -that if the Orbit in which the Earth moves round the Sun were solid, and -seen from the nearest Star, it would likewise appear no bigger than a -point, although it is at least 162 millions of miles in diameter. For -the Earth in going round the Sun is 162 millions of miles nearer to some -of the Stars at one time of the year than at another; and yet their -apparent magnitudes, situations, and distances from one another still -remain the same; and a telescope which magnifies above 200 times does -not sensibly magnify them: which proves them to be at least 400 thousand -times farther from us than we are from the Sun. - -[Sidenote: The Stars are Suns.] - -4. It is not to be imagined that all the Stars are placed in one concave -surface, so as to be equally distant from us; but that they are -scattered at immense distances from one another through unlimited space. -So that there may be as great a distance between any two neighbouring -Stars, as between our Sun and those which are nearest to him. Therefore -an Observer, who is nearest any fixed Star, will look upon it alone as a -real Sun; and consider the rest as so many shining points, placed at -equal distances from him in the Firmament. - -[Sidenote: And innumerable.] - -5. By the help of telescopes we discover thousands of Stars which are -invisible to the naked eye; and the better our glasses are, still the -more become visible: so that we can set no limits either to their number -or their distances. The celebrated HUYGENS carries his thoughts so far, -as to believe it not impossible that there may be Stars at such -inconceivable distances, that their light has not yet reached the Earth -since it’s creation; although the velocity of light be a million of -times greater than the velocity of a cannon bullet, as shall be -demonstrated afterwards § 197, 216: and, as Mr. ADDISON very justly -observes, this thought is far from being extravagant, when we consider -that the Universe is the work of infinite power, prompted by infinite -goodness; having an infinite space to exert itself in; so that our -imaginations can set no bounds to it. - -[Sidenote: Why the Sun appears bigger than the Stars.] - -6. The Sun appears very bright and large in comparison of the Fixed -Stars, because we keep constantly near the Sun, in comparison of our -immense distance from the Stars. For, a spectator, placed as near to any -Star as we are to the Sun, would see that Star a body as large and -bright as the Sun appears to us: and a spectator, as far distant from -the Sun as we are from the Stars, would see the Sun as small as we see a -Star, divested of all its circumvolving Planets; and would reckon it one -of the Stars in numbering them. - -[Sidenote: The Stars are not enlightened by the Sun.] - -7. The Stars, being at such immense distances from the Sun, cannot -possibly receive from him so strong a light as they seem to have; nor -any brightness sufficient to make them visible to us. For the Sun’s rays -must be so scattered and dissipated before they reach such remote -objects, that they can never be transmitted back to our eyes, so as to -render these objects visible by reflection. The Stars therefore shine -with their own native and unborrowed lustre, as the Sun does; and since -each particular Star, as well as the Sun, is confined to a particular -portion of space, ’tis plain that the Stars are of the same nature with -the Sun. - -[Sidenote: They are probably surrounded by Planets.] - -8. It is no ways probable that the Almighty, who always acts with -infinite wisdom and does nothing in vain, should create so many glorious -Suns, fit for so many important purposes, and place them at such -distances from one another, without proper objects near enough to be -benefited by their influences. Whoever imagines they were created only -to give a faint glimmering light to the inhabitants of this Globe, must -have a very superficial knowledge of Astronomy, and a mean opinion of -the Divine Wisdom: since, by an infinitely less exertion of creating -power, the Deity could have given our Earth much more light by one -single additional Moon. - -9. Instead then of one Sun and one World only in the Universe, as the -unskilful in Astronomy imagine, _that_ Science discovers to us such an -inconceivable number of Suns, Systems, and Worlds, dispersed through -boundless Space, that if our Sun, with all the Planets, Moons, and -Comets belonging to it were annihilated, they would be no more missed -out of the Creation than a grain of sand from the sea-shore. The space -they possess being comparatively so small, that it would scarce be a -sensible blank in the Universe; although Saturn, the outermost of our -planets, revolves about the Sun in an Orbit of 4884 millions of miles in -circumference, and some of our Comets make excursions upwards of ten -thousand millions of miles beyond Saturn’s Orbit; and yet, at that -amazing distance, they are incomparably nearer to the Sun than to any of -the Stars; as is evident from their keeping clear of the attractive -Power of all the Stars, and returning periodically by virtue of the -Sun’s attraction. - -[Sidenote: The stellar Planets may be habitable.] - -10. From what we know of our own System it may be reasonably concluded -that all the rest are with equal wisdom contrived, situated, and -provided with accommodations for rational inhabitants. Let us therefore -take a survey of the System to which we belong; the only one accessible -to us; and from thence we shall be the better enabled to judge of the -nature and end of the other Systems of the Universe. For although there -is almost an infinite variety in all the parts of the Creation which we -have opportunities of examining; yet there is a general analogy running -through and connecting all the parts into one scheme, one design, one -whole! - -[Sidenote: As our Solar Planets are.] - -11. And then, to an attentive considerer, it will appear highly -probable, that the Planets of our System, together with their attendants -called Satellites or Moons, are much of the same nature with our Earth, -and destined for the like purposes. For, they are solid opaque Globes, -capable of supporting animals and vegetables. Some of them are bigger, -some less, and some much about the size of our Earth. They all circulate -round the Sun, as the Earth does, in a shorter or longer time according -to their respective distances from him: and have, where it would not be -inconvenient, regular returns of summer and winter, spring and autumn. -They have warmer and colder climates, as the various productions of our -Earth require: and, in such as afford a possibility of discovering it, -we observe a regular motion round their Axes like that of our Earth, -causing an alternate return of day and night; which is necessary for -labour, rest, and vegetation, and that all parts of their surfaces may -be exposed to the rays of the Sun. - -[Sidenote: The farthest from the Sun have most Moons to enlighten their - nights.] - -12. Such of the Planets as are farthest from the Sun, and therefore -enjoy least of his light, have that deficiency made up by several Moons, -which constantly accompany, and revolve about them, as our Moon revolves -about the Earth. The remotest Planet has, over and above, a broad Ring -encompassing it; which like a lucid Zone in the Heavens reflects the -Sun’s light very copiously on that Planet: so that if the remoter -Planets have the Sun’s light fainter by day than we, they have an -addition made to it morning and evening by one or more of their Moons, -and a greater quantity of light in the night-time. - -[Sidenote: Our Moon mountainous like the Earth.] - -13. On the surface of the Moon, because it is nearer us than any other -of the celestial Bodies are, we discover a nearer resemblance of our -Earth. For, by the assistance of telescopes we observe the Moon to be -full of high mountains, large valleys, and deep cavities. These -similarities leave us no room to doubt but that all the Planets and -Moons in the System are designed as commodious habitations for creatures -endowed with capacities of knowing and adoring their beneficent Creator. - -[Illustration: Plate I. - -THE SOLAR SYSTEM - -_J. Ferguson delin._ _J. Mynde Sculp._ ] - -14. Since the Fixed Stars are prodigious spheres of fire, like our Sun, -and at inconceivable distances from one another, as well as from us, it -is reasonable to conclude they are made for the same purposes that the -Sun is; each to bestow light, heat, and vegetation on a certain number -of inhabited Planets, kept by gravitation within the sphere of it’s -activity. - - -[Sidenote: Numberless Suns and Worlds.] - -15. What an august! what an amazing conception, if human imagination can -conceive it, does this give of the works of the Creator! Thousands of -thousands of Suns, multiplied without end, and ranged all around us, at -immense distances from each other, attended by ten thousand times ten -thousand Worlds, all in rapid motion, yet calm, regular, and harmonious, -invariably keeping the paths prescribed them; and these Worlds peopled -with myriads of intelligent beings, formed for endless progression in -perfection and felicity. - -16. If so much power, wisdom, goodness, and magnificence is displayed in -the material Creation, which is the least considerable part of the -Universe, how great, how wise, how good must HE be, who made and governs -the Whole! - - - - - CHAP. II. - - _A brief Description of the_ SOLAR SYSTEM. - - -[Sidenote: PLATE I. Fig. 1. - - The Solar System.] - -17. The Planets and Comets which move round the Sun as their center, -constitute the Solar System. Those Planets which are nearer the Sun not -only finish their circuits sooner, but likewise move faster in their -respective Orbits than those which are more remote from him. Their -motions are all performed from west to east, in Orbits nearly circular. -Their names, distances, bulks, and periodical revolutions, are as -follows. - - -[Sidenote: The Sun.] - -18. The SUN ☉, an immense globe of fire, is placed near the common -center, or rather in the lower[2] focus, of the Orbits of all the -Planets and Comets[3]; and turns round his axis in 25 days 6 hours, as -is evident by the motion of spots seen on his surface. His diameter is -computed to be 763,000 miles; and, by the various attractions of the -circumvolving Planets, he is agitated by a small motion round the center -of gravity of the System. All the Planets, as seen from him, move the -same way, and according to the order of Signs in the graduated Circle ♈ -♉ ♎ ♋ &c. which represents the great Ecliptic in the Heavens: but, as -seen from any one Planet, the rest appear sometimes to go backward, -sometimes forward, and sometimes to stand still; not in circles nor -ellipses, but in[4] looped curves which never return into themselves. -The Comets come from all parts of the Heavens, and move in all sorts of -directions. - -[Sidenote: PLATE I. Fig. I. The Sun. - - The Axes of the Planets, what.] - -19. Having mentioned the Sun’s turning round his axis, and as there will -be frequent occasion to speak of the like motion of the Earth and other -Planets, it is proper here to inform the young _Tyro_ in Astronomy, that -neither the Sun nor Planets have material axes to turn upon, and support -them, as in the little imperfect Machines contrived to represent them. -For the axis of a Planet is a line conceived to be drawn through it’s -center, about which it revolves as on a real axis. The extremities of -this line, terminating in opposite points of the Planet’s surface, are -called its _Poles_. That which points towards the _northern_ part of the -Heavens is called the _North Pole_; and the other, pointing towards the -_southern_ part, is called the _South Pole_. A bowl whirled from one’s -hand into the open air turns round such a line within itself, whilst it -moves forward; and such are the lines we mean, when we speak of the Axes -of the Heavenly bodies. - -[Sidenote: Their Orbits are not in the same plane with the Ecliptic. - - PLATE I. - - Their Nodes. - - Where situated.] - -20. Let us suppose the Earth’s Orbit to be a thin, even, solid plane; -cutting the Sun through the center, and extended out as far as the -Starry Heavens, where it will mark the great Circle called the -_Ecliptic_. This Circle we suppose to be divided into 12 equal parts, -called _Signs_; each Sign into 30 equal parts, called _Degrees_; each -Degree into 60 equal parts, called _Minutes_; and every Minute into 60 -equal parts, called _Seconds_: so that a Second is the 60th part of a -Minute; a Minute the 60th part of a Degree; and a Degree the 360th part -of a Circle, or 30th part of a Sign. The Planes of the Orbits of all the -other Planets likewise cut the Sun in halves; but extended to the -Heavens, form Circles different from one another, and from the Ecliptic; -one half of each being on the north side, and the other on the south -side of it. Consequently the Orbit of each Planet crosses the Ecliptic -in two opposite points, which are called the Planet’s _Nodes_. These -Nodes are all in different parts of the Ecliptic; and therefore, if the -planetary Tracks remained visible in the Heavens, they would in some -measure resemble the different rutts of waggon-wheels crossing one -another in different parts, but never going far asunder. That Node, or -Intersection of the Orbit of any Planet with the Earth’s Orbit, from -which the Planet ascends northward above the Ecliptic, is called the -_Ascending Node_ of the Planet; and the other, which is directly -opposite thereto, is called it’s _Descending Node_. Saturn’s Ascending -Node is in 21 deg. 13 min. of Cancer ♋, Jupiter’s in 7 deg. 29 min. of -the same Sign, Mars’s in 17 deg. 17 min. of Taurus ♉, Venus’s in 13 deg. -59 min. of Gemini ♊, and Mercury’s in 14 deg. 43 min. of Taurus. Here we -consider the Earth’s Orbit as the standard, and the Orbits of all the -other Planets as oblique to it. - -[Sidenote: The Planets Orbits, what.] - -21. When we speak of the Planets Orbits, all that is meant is their -Paths through the open and unresisting Space in which they move; and are -kept in, by the attractive power of the Sun, and the projectile force -impressed upon them at first: between which power and force there is so -exact an adjustment, that without any solid Orbits to confine the -Planets, they keep their courses, and at the end of every revolution -find the points from whence they first set out, much more truly than can -be imitated in the best machines made by human art. - - -[Sidenote: Mercury. - - Fig. I. - - May be inhabited. - - PLATE I.] - -22. MERCURY, the nearest Planet to the Sun, goes round him (as in the -circle marked ☿) in 87 days 23 hours of our time nearly; which is the -length of his year. But, being seldom seen, and no spots appearing on -his surface or disc, the time of his rotation on his axis, or the length -of his days and nights, is as yet unknown. His distance from the Sun is -computed to be 32 millions of miles, and his diameter 2600. In his -course, round the Sun, he moves at the rate of 95 thousand miles every -hour. His light and heat from the Sun are almost seven times as great as -ours; and the Sun appears to him almost seven times as large as to us. -The great heat on this Planet is no argument against it’s being -inhabited; since the Almighty could as easily suit the bodies and -constitutions of it’s inhabitants to the heat of their dwelling, as he -has done ours to the temperature of our Earth. And it is very probable -that the people there have such an opinion of us, as we have of the -inhabitants of Jupiter and Saturn; namely, that we must be intolerably -cold, and have very little light at so great a distance from the Sun. - -[Sidenote: Has like phases with the Moon.] - -23. This Planet appears to us with all the various phases of the Moon, -when viewed at different times by a good telescope; save only that he -never appears quite Full, because his enlightened side is never turned -directly towards us but when he is so near the Sun as to be lost to our -sight in it’s beams. And, as his enlightened side is always toward the -Sun, it is plain that he shines not by any light of his own; for if he -did, he would constantly appear round. That he moves about the Sun in an -Orbit within the Earth’s Orbit is also plain (as will be more largely -shewn by and by, § 141, _& seq._) because he is never seen opposite to -the Sun, nor above 56 times the Sun’s breadth from his center. - -[Sidenote: His Orbit and Nodes.] - -24. His Orbit is inclined seven degrees to the Ecliptic; and _that_ Node -§ 20, from which he ascends northward above the Ecliptic is in the 14th -degree of Taurus; the opposite, in the 14th degree of Scorpio. The Earth -is in these points on the 5th of _November_ and 4th of _May_, new style; -and when Mercury comes to either of his Nodes at his[5] inferior -Conjunction about these times, he will appear to pass over the disc or -face of the Sun, like a dark round spot. But in all other parts of his -Orbit his Conjunctions are invisible, because he either goes above or -below the Sun. - -[Sidenote: When he will be seen as if upon the Sun.] - -25. Mr. WHISTON has given us an account of several periods at which -Mercury may be seen on the Sun’s disc, _viz._ In the year 1782, _Nov._ -12th, at 3 h. 44 m. in the afternoon: 1786, _May_ 4th, at 6 h. 57 m. in -the forenoon: 1789, _Dec._ 6th, at 3 h. 55 m. in the afternoon; and -1799, _May_ 7th, at 2 h. 34 m. in the afternoon. There will be several -intermediate Transits, but none of them visible at _London_. - - -[Sidenote: Fig. I. - - Venus.] - -26. VENUS, the next Planet in order, is computed to be 59 millions of -miles from the Sun; and by moving at the rate of 69 thousand miles every -hour in her Orbit (as in the circle marked ♀), she goes round the Sun in -224 days 17 hours of our time nearly; in which, though it be the full -length of her year, she has only 9-1/4 days, according to BIANCHINI’s -observations; so that in her, every day and night together is as long as -24-1/3 days and nights with us. This odd quarter of a day in every year -makes every fourth year a leap-year to Venus; as the like does to our -Earth. Her diameter is 7906 miles; and by her diurnal motion the -inhabitants about her Equator are carried 43 miles every hour: besides -the 69,000 above-mentioned. - -[Sidenote: Her Orbit lies between the Earth and Mercury.] - -27. Her Orbit includes that of Mercury within it; for at her greatest -Elongation, or apparent distance from the Sun, she is 96 times his -breadth from his centre; which is almost double of Mercury’s. Her Orbit -is included by the Earth’s; for if it were not, she might be seen as -often in Opposition to the Sun as in Conjunction with him; but she was -never seen 90 degrees, or a fourth part of a Circle, from the Sun. - -[Sidenote: She is our morning and evening Star by turns.] - -28. When Venus appears west of the Sun she rises before him in the -morning, and is called the _Morning Star_: when she appears east of the -Sun she shines in the evening after he sets, and is then called the -_Evening Star_: being each in it’s turn for 290 days. It may perhaps be -surprising at first, that Venus should keep longer on the east or west -of the Sun than the whole time of her Period round him. But the -difficulty vanishes when we consider that the Earth is all the while -going round the Sun the same way, though not so quick as Venus: and -therefore her relative motion to the Earth must in every Period be as -much slower than her absolute motion in her Orbit, as the Earth during -that time advances forward in the Ecliptic; which is 220 degrees. To us -she appears through a telescope in all the various shapes of the Moon. - -29. The Axis of Venus is inclined 75 degrees to the Axis of her Orbit; -which is 51-1/2 degrees more than our Earth’s Axis is inclined to the -Axis of the Ecliptic: and therefore the variation of her seasons is much -greater than of ours. The North Pole of her Axis inclines toward the -20th degree of Aquarius, our Earth’s to the beginning of Cancer; and -therefore the northern parts of Venus have summer in the Signs where -those of our Earth have winter, and _vice versâ_. - -[Sidenote: Remarkable appearances.] - -30. The [6]artificial day at each Pole of Venus is as long as 112-1/2 -[7]natural days on our Earth. - -[Sidenote: Her Tropics and polar Circles, how situated.] - -31. The Sun’s greatest Declination on each side of her Equator amounts -to 75 degrees; therefore her[8] Tropics are only 15 degrees from her -Poles; and her [9]Polar Circles as far from her Equator. Consequently, -the Tropics of Venus are between her Polar Circles and her Poles; -contrary to what those of our Earth are. - -[Sidenote: The Sun’s daily Course.] - -32. As her annual Revolution contains only 9-1/4 of her days, the Sun -will always appear to go through a Sign, or twelfth Part of her Orbit, -in little more that three quarters of her natural day, or nearly in -18-3/4 of our days and nights. - -[Sidenote: And great declination.] - -33. Because her day is so great a part of her year, the Sun changes his -Declination in one day so much, that if he passes vertically, or -directly over head of any given place on the Tropic, the next day he -will be 26 degrees from it: and whatever place he passes vertically over -when in the Equator, one day’s revolution will remove him 36-1/4 degrees -from it. So that the Sun changes his Declination every day in Venus -about 14 degrees more at a mean rate, than he does in a quarter of a -year on our Earth. This appears to be providentially ordered, for -preventing the too great effects of the Sun’s heat (which is twice as -great on Venus as on the Earth) so that he cannot shine perpendicularly -on the same places for two days together; and by that means, the heated -places have time to cool. - -[Sidenote: To determine the points of the Compass at her Poles.] - -34. If the inhabitants about the North Pole of Venus fix their South, or -Meridian Line, through that part of the Heavens where the Sun comes to -his greatest Height, or North Declination, and call those the East and -West points of their Horizon, which are 90 degrees on each side from -that point where the Horizon is cut by the Meridian Line, these -inhabitants will have the following remarkables. - -[Sidenote: Surprising appearances at her Poles;] - -The Sun will rise 22-1/2 degrees[10] north of the East, and going on -112-1/2 degrees, as measured on the plane of the [11]Horizon, he will -cross the Meridian at an altitude of 12-1/2 degrees; then making an -entire revolution without setting, he will cross it again at an altitude -of 48-1/2 degrees; at the next revolution he will cross the Meridian as -he comes to his greatest height and declination, at the altitude of 75 -degrees; being then only 15 degrees from the Zenith, or that point of -the Heavens which is directly over head: and thence he will descend in -the like spiral manner; crossing the Meridian first at the altitude of -48-1/2 degrees; next at the altitude of 12-1/2 degrees; and going on -thence 112-1/2 degrees, he will set 22-1/2 degrees north of the West; so -that, after having been 4-5/8 revolutions above the Horizon, he descends -below it to exhibit the like appearances at the South Pole. - -35. At each Pole, the Sun continues half a year without setting in -summer, and as long without rising in winter; consequently the polar -inhabitants of Venus have only one day and one night in the year; as it -is at the Poles of our Earth. But the difference between the heat of -summer and cold of winter, or of mid-day and mid-night, on Venus, is -much greater than on the Earth: because in Venus, as the Sun is for half -a year together above the Horizon of each Pole in it’s turn, so he is -for a considerable part of that time near the Zenith; and during the -other half of the year, always below the Horizon, and for a great part -of that time at least 70 degrees from it. Whereas, at the Poles of our -Earth, although the Sun is for half a year together above the Horizon, -yet he never ascends above, nor descends below it, more than 23-1/2 -degrees. When the Sun is in the Equinoctial, or in that Circle which -divides the northern half of the Heavens from the southern, he is seen -with one half of his Disc above the Horizon of the North Pole, and the -other half above the Horizon of the South Pole; so that his center is in -the Horizon of both Poles: and then descending below the Horizon of one, -he ascends gradually above that of the other. Hence, in a year, each -Pole has one spring, one harvest, a summer as long as them both, and a -winter equal in length to the other three seasons. - -[Sidenote: At her polar Circles;] - -36. At the Polar Circles of Venus, the seasons are much the same as at -the Equator, because there are only 15 degrees betwixt them, § 31; only -the winters are not quite so long, nor the summers so short: but the -four seasons come twice round every year. - -[Sidenote: At her Tropics;] - -37. At Venus’s Tropics, the Sun continues for about fifteen of our weeks -together without setting in summer; and as long without rising in -winter. Whilst he is more than 15 degrees from the Equator, he neither -rises to the inhabitants of the one Tropic, nor sets to those of the -other: whereas, at our terrestrial Tropics he rises and sets every day -of the year. - -38. At Venus’s Tropics, the Seasons are much the same as at her Poles; -only the summers are a little longer, and the winters a little shorter. - -[Sidenote: At her Equator.] - -39. At her Equator, the days and nights are always of the same length; -and yet the diurnal and nocturnal Arches are very different, especially -when the Sun’s declination is about the greatest: for then, his meridian -altitude may sometimes be twice as great as his midnight depression, and -at other times the reverse. When the Sun is at his greatest Declination, -either North or South, his rays are as oblique at Venus’s Equator, as -they are at _London_ on the shortest day of winter. Therefore, at her -Equator there are two winters, two summers, two springs, and two autumns -every year. But because the Sun stays for some time near the Tropics, -and passes so quickly over the Equator, every winter there will be -almost twice as long as summer: the four seasons returning twice in that -time, which consists only of 9-1/4 days. - -40. Those parts of Venus which lie between the Poles and Tropics, and -between the Tropics and Polar Circles, and also between the Polar -Circles and Equator, partake more or less of the Phenomena of these -Circles, as they are more or less distant from them. - -[Sidenote: Great difference of the Sun’s amplitude at rising and - setting.] - -41. From the quick change of the Sun’s declination it happens, that when -he rises due east on any day, he will not set due west on that day, as -with us; for if the place where he rises due east be on the Equator, he -will set on that day almost west-north-west; or about 18-1/2 degrees -north of the west. But if the place be in 45 degrees north latitude, -then on the day that the Sun rises due east he will set north-west by -west, or 33 degrees north of the west. And in 62 degrees north latitude -when he rises in the east, he sets not in that revolution, but just -touches the Horizon 10 degrees to the west of the north point; and -ascends again, continuing for 3-1/4 revolutions above the Horizon -without setting. Therefore, no place has the forenoon and afternoon of -the same day equally long, unless it be on the Equator or at the Poles. - -[Sidenote: The longitude of places easily found in Venus.] - -42. The Sun’s altitude at noon, or any other time of the day, and his -amplitude at rising and setting, being so different at places on the -same parallels of latitude, according to the different longitudes of -those places, the longitude will be almost as easily found on Venus as -the latitude is found on the Earth: which is an advantage we can never -enjoy, because the daily change of the Sun’s declination is by much too -small for that purpose. - -[Sidenote: Her Equinoxes shift a quarter of a day forward every year.] - -43. On this Planet, wherever the Sun crosses the Equator in any year, he -will have 9 degrees of declination from that place on the same day and -hour next year; and will cross the Equator 90 degrees farther to the -west; which makes the time of the Equinox a quarter of a day (almost -equal to six of our days) later every year. Hence, although the spiral -in which the Sun’s motion is performed, be of the same sort every year, -yet it will not be the very same, because the Sun will not pass -vertically over the same places till four annual revolutions are -finished. - -[Sidenote: Every fourth year a leap-year to Venus. - - PLATE I.] - -44. We may suppose that the inhabitants of Venus will be careful to add -a day to some particular part of every fourth year; which will keep the -same seasons to the same days. For, as the great annual change of the -Equinoxes and Solstices shifts the seasons a quarter of a day every -year, they would be shifted through all the days of the year in 36 -years. But by means of this intercalary day, every fourth year will be a -leap-year; which will bring her time to an even reckoning, and keep her -Calendar always right. - -[Sidenote: When she will appear on the Sun.] - -45. Venus’s Orbit is inclined 3-1/2 degrees to the Earth’s; and crosses -it in the 14th degree of Gemini and of Sagittarius; and therefore, when -the Earth is about these points of the Ecliptic at the time that Venus -is in her inferiour conjunction, she will appear like a spot on the Sun, -and afford a more certain method of finding the distances of all the -Planets from the Sun than any other yet known. But these appearances -happen very seldom; and will only be thrice visible at _London_ for -three hundred years to come. The first time will be in the year 1761, -_June_ the 6th, at 5 hours 55 minutes in the morning. The second 1996, -_June_ the 9th, at 2 hours 13 minutes in the afternoon. And the third in -the year 2004, _June_ the 6th, at 7 hours 18 minutes in the forenoon. -Excepting such Transits as these, she shews the same appearances to us -regularly every eight years; her Conjunctions, Elongations, and Times of -rising and setting being very nearly the same, on the same days, as -before. - -[Sidenote: She may have a Moon although we cannot see it.] - -46. Venus may have a Satellite or Moon, although it be undiscovered by -us: which will not appear very surprising, if we consider how -inconveniently we are placed for seeing it. For it’s enlightened side -can never be fully turned towards us but when Venus is beyond the Sun; -and then, as Venus appears little bigger than an ordinary Star, her Moon -may be too small to be perceptible at such a distance. When she is -between us and the Sun, her full Moon has it’s dark side towards us; and -then, we cannot see it any more than we can our own Moon at the time of -Change. When Venus is at her greatest Elongation, we have but one half -of the enlightened side of her Full Moon towards us; and even then it -may be too far distant to be seen by us. But if she has a Moon, it may -certainly be seen with her upon the Sun, in the year 1761, unless it’s -Orbit be considerably inclined to the Ecliptic: for if it should be in -conjunction or opposition at that time, we can hardly imagine that it -moves so slow as to be hid by Venus all the six hours that she will -appear on the Sun’s Disc. - - -[Sidenote: The Earth. - - Fig. I. - - It’s diurnal and annual motion.] - -47. The EARTH is the next Planet above Venus in the System. It is 81 -millions of miles from the Sun, and goes round him (as in the circle ⊕) -in 365 days 5 hours 49 minutes, from any Equinox or Solstice to the same -again: but from any fixed Star to the same again, as seen from the Sun, -in 365 days 6 hours and 9 minutes; the former being the length of the -Tropical year, and the latter the length of the Sidereal. It travels at -the rate of 58 thousand miles every hour, which motion, though 120 times -swifter than that of a cannon ball, is little more than half as swift as -Mercury’s motion in his Orbit. The Earth’s diameter is 7970 miles; and -by turning round it’s Axis every 24 hours from West to East, it causes -an apparent diurnal motion of all the heavenly Bodies from East to West. -By this rapid motion of the Earth on it’s Axis, the inhabitants about -the Equator are carried 1042 miles every hour, whilst those on the -parallel of _London_ are carried only about 580, besides the 58 thousand -miles by the annual motion above-mentioned, which is common to all -places whatever. - -[Sidenote: Inclination of it’s Axis.] - -48. The Earth’s Axis makes an angle of 23-1/2 degrees with the Axis of -it’s Orbit; and keeps always the same oblique direction; inclining -towards the same fixed Stars[12] throughout it’s annual course; which -causes the returns of spring, summer, autumn, and winter; as will be -explained at large in the tenth Chapter. - -[Sidenote: A proof of it’s being round.] - -49. The Earth is round like a globe; as appears, 1. from it’s shadow in -Eclipses of the Moon; which shadow is always bounded by a circular line -§ 314. 2. From our seeing the masts of a ship whilst the hull is hid by -the convexity of the water. 3. From it’s having been sailed round by -many navigators. The hills take off no more from the roundness of the -Earth in comparison, than grains of dust do from the roundness of a -common Globe. - -[Sidenote: It’s number of square miles.] - -50. The seas and unknown parts of the Earth (by a measurement of the -best Maps) contain 160 million 522 thousand and 26 square miles; the -inhabited parts 38 million 990 thousand 569: _Europe_ 4 million 456 -thousand and 65; _Asia_ 10 million 768 thousand 823; _Africa_ 9 million -654 thousand 807; _America_ 14 million 110 thousand 874. In all, 199 -million 512 thousand 595; which is the number of square miles on the -whole surface of our Globe. - -[Sidenote: The proportion of land and sea. - - PLATE I.] - -51. Dr. LONG, in the first volume of his Astronomy, pag. 168, mentions -an ingenious and easy method of finding nearly what proportion the land -bears to the sea; which is, to take the papers of a large terrestrial -globe, and after separating the land from the sea with a pair of -scissars, to weigh them carefully in scales. This supposes the globe to -be exactly delineated, and the papers all of equal thickness. The Doctor -made the experiment on the papers of Mr. SENEX’s seventeen inch globe; -and found that the sea papers weighed 349 grains, and the land only 124: -by which it appears that almost three fourth parts of the surface of our -Earth between the Polar Circles are covered with water, and that little -more than one fourth is dry land. The Doctor omitted weighing all within -the Polar Circles; because there is no certain measurement of the land -there, so as to know what proportion it bears to the sea. - - -[Sidenote: The Moon.] - -52. The MOON is not a Planet, but only a Satellite or Attendant of the -Earth, moving round the Earth from Change to Change in 29 days 12 hours -and 44 minutes; and going round the Sun with it every year. The Moon’s -diameter is 2180 miles; and her distance from the Earth 240 thousand. -She goes round her Orbit in 27 days 7 hours 43 minutes, moving about -2290 miles every hour; and turns round her Axis exactly in the time that -she goes round the Earth, which is the reason of her keeping always the -same side towards us, and that her day and night taken together is as -long as our lunar month. - -[Sidenote: Her Phases.] - -53. The Moon is an opaque Globe like the Earth, and shines only by -reflecting the light of the Sun: therefore whilst that half of her which -is toward the Sun is enlightened, the other half must be dark and -invisible. Hence, she disappears when she comes between us and the Sun; -because her dark side is then toward us. When she is gone a little way -forward, we see a little of her enlightened side; which still increases -to our view, as she advances forward, until she comes to be opposite to -the Sun; and then her whole enlightened side is towards the Earth, and -she appears with a round, illumined Orb; which we call the _Full Moon_: -her dark side being then turned away from the Earth. From the Full she -seems to decrease gradually as she goes through the other half of her -course; shewing us less and less of her enlightened side every day, till -her next change or conjunction with the Sun, and then she disappears as -before. - -[Sidenote: A proof that she shines not by her own light. - - Fig. I.] - -54. The continual changing of the Moon’s phases or shapes demonstrates -that she shines not by any light of her own: for if she did, being -globular, we should always see her with a round full Orb like the Sun. -Her Orbit is represented in the Scheme by the little circle _m_, upon -the Earth’s Orbit ⊕: but it is drawn fifty times too large in proportion -to the Earth’s; and yet is almost too small to be seen in the Diagram. - -[Sidenote: One half of her always enlightened.] - -55. The Moon has scarce any difference of seasons; her Axis being almost -perpendicular to the Ecliptic. What is very singular, one half of her -has no darkness at all; the Earth constantly affording it a strong light -in the Sun’s absence; while the other half has a fortnight’s darkness -and a fortnight’s light by turns. - -[Sidenote: Our Earth is her Moon.] - -56. Our Earth is a Moon to the Moon, waxing and waneing regularly, but -appearing thirteen times as big, and affording her thirteen times as -much light, as she does to us. When she changes to us, the Earth appears -full to her; and when she is in her first quarter to us, the Earth is in -it’s third quarter to her; and _vice versâ_. - -57. But from one half of the Moon, the Earth is never seen at all: from -the middle of the other half, it is always seen over head; turning round -almost thirty times as quick as the Moon does. From the line which -limits our view of the Moon, or all round what we call her edges, only -one half of the Earth’s side next her is seen; the other half being hid -below the Horizon. To her, the Earth seems to be the biggest Body in the -Universe; for it appears thirteen times as big as she does to us. - -[Sidenote: A Proof of the Moon’s having no Atmosphere;] - -58. The Moon has no such Atmosphere, or body of air surrounding her as -we have: for if she had, we could never see her edge so well defined as -it appears; but there would be a sort of a mist or haziness round her, -which would make the Stars look fainter, when they were seen through it. -But observation proves, that the Stars which disappear behind the Moon -retain their full lustre until they seem to touch her very edge, and -then vanish in a moment. This has been often observed by Astronomers, -but particularly by CASSINI[13] of the Star γ in the breast of Virgo, -which appears single and round to the bare eye; but through a refracting -Telescope of 16 feet appears to be two Stars so near together, that the -distance between them seems to be but equal to one of their apparent -diameters. The Moon was observed to pass over them on the 21st of -_April_ 1720, _N. S._ and as her dark edge drew near to them, it caused -no change in their colour or Situation. At 25 min. 14 sec. past 12 at -night, the most westerly of these Stars was hid by the dark edge of the -Moon; and in 30 seconds afterward, the most easterly Star was hid: each -of them disappearing behind the Moon in an instant, without any -preceding diminution of magnitude or brightness; which by no means could -have been the case if there were an Atmosphere round the Moon; for then, -one of the Stars falling obliquely into it before the other, ought by -refraction to have suffered some change in its colour, or in it’s -distance from the other Star which was not yet entered into the -Atmosphere. But no such alteration could be perceived though the -observation was performed with the utmost attention to that particular; -and was very proper to have made such a discovery. The faint light, -which has been seen all around the Moon, in total Eclipses of the Sun, -has been observed, during the time of darkness, to have it’s center -coincident with the center of the Sun; and is therefore much more likely -to arise from the Atmosphere of the Sun than from that of the Moon; for -if it were the latter, it’s center would have gone along with the -Moon’s. - -[Sidenote: Nor Seas. - - She is full of caverns and deep pits.] - -59. If there were seas in the Moon, she could have no clouds, rains, nor -storms as we have; because she has no such Atmosphere to support the -vapours which occasion them. And every one knows, that when the Moon is -above our Horizon in the night time, she is visible, unless the clouds -of our Atmosphere hide her from our view; and all parts of her appear -constantly with the same clear, serene, and calm aspect. But those dark -parts of the Moon, which were formerly thought to be seas, are now found -to be only vast deep cavities, and places which reflect not the Sun’s -light so strongly as others, having many caverns and pits whose shadows -fall within them, and are always dark on the sides next the Sun; which -demonstrates their being hollow: and most of these pits have little -knobs like hillocks standing within them, and casting shadows also; -which cause these places to appear darker than others which have fewer, -or less remarkable caverns. All these appearances shew that there are no -seas in the Moon; for if there were any, their surfaces would appear -smooth and even, like those on the Earth. - -[Sidenote: The Stars always visible to the Moon.] - -60. There being no Atmosphere about the Moon, the Heavens in the day -time have the appearance of night to a Lunarian who turns his back -toward the Sun; and when he does, the Stars appear as bright to him as -they do in the night to us. For, it is entirely owing to our Atmosphere -that the Heavens are bright about us in the day. - -[Sidenote: The Earth a Dial to the Moon.] - -61. As the Earth turns round it’s Axis, the several continents, seas, -and islands appear to the Moon’s inhabitants like so many spots of -different forms and brightness, moving over it’s surface; but much -fainter at some times than others, as our clouds cover them or leave -them. By these spots the Lunarians can determine the time of the Earth’s -diurnal motion, just as we do the motion of the Sun: and perhaps they -measure their time by the motion of the Earth’s spots; for they cannot -have a truer dial. - -[Sidenote: PLATE I. - - How the Lunarians may know the length of their year.] - -62. The Moon’s Axis is so nearly perpendicular to the Ecliptic, that the -Sun never removes sensibly from her Equator: and the[14] obliquity of -her Orbit, which is next to nothing as seen from the Sun, cannot cause -any sensible declination of the Sun from her Equator. Yet her -inhabitants are not destitute of means for determining the length of -their year, though their method and ours must differ. For we can know -the length of our year by the return of our Equinoxes; but the -Lunarians, having always equal day and night, must have recourse to -another method; and we may suppose, they measure their year by observing -the Poles of our Earth; as one always begins to be enlightened, and the -other disappears, at our Equinoxes; they being conveniently situated for -observing great tracks of land about our Earth’s Poles, which are -entirely unknown to us. Hence we may conclude, that the year is of the -same absolute length both to the Earth and Moon, though very different -as to the number of days: we having 365-1/4 natural days, and the -Lunarians only 12-7/19; every day and night in the Moon being as long as -29-1/2 on the Earth. - -[Sidenote: And the longitudes of their places.] - -63. The Moon’s inhabitants on the side next the Earth may as easily find -the longitude of their places as we can find the latitude of ours. For -the Earth keeping constantly, or very nearly so, over one Meridian of -the Moon, the east or west distances of places from that Meridian are as -easily found, as we can find our distance from the Equator by the -Altitude of our celestial Poles. - - -[Sidenote: Mars. - - Fig. I.] - -64. The Planet MARS is next in order, being the first above the Earth’s -Orbit. His distance from the Sun is computed to be 123 millions of -miles; and by travelling at the rate of 47 thousand miles every hour, as -in the circle ♂, he goes round the Sun in 687 of our days and 17 hours; -which is the length of his year, and contains 667-1/4 of his days; every -day and night together being 40 minutes longer than with us. His -diameter is 4444 miles, and by his diurnal rotation the inhabitants -about his Equator are carried 556 miles every hour. His quantity of -light and heat is equal but to one half of ours; and the Sun appears but -half as big to him as to us. - -[Sidenote: His Atmosphere and Phases.] - -65. This Planet being but a fifth part so big as the Earth, if any Moon -attends him, she must be very small, and has not yet been discovered by -our best telescopes. He is of a fiery red colour, and by his Appulses to -some of the fixed Stars, seems to be surrounded by a very gross -Atmosphere. He appears sometimes gibbous, but never horned; which both -shews that his Orbit includes the Earth’s within it, and that he shines -not by his own light. - -66. To Mars, our Earth and Moon appear like two Moons, a bigger and a -less; changing places with one another, and appearing sometimes horned, -sometimes half or three quarters illuminated, but never full; nor at -most above a quarter of a degree from each other, although they are 240 -thousand miles asunder. - -[Sidenote: PLATE I. - - How the other Planets appear to Mars.] - -67. Our Earth appears almost as big to Mars as Venus does to us, and at -Mars it is never seen above 48 degrees from the Sun; sometimes it -appears to pass over the Disc of the Sun, and so do Mercury and Venus: -but Mercury can never be seen from Mars by such eyes as ours, unassisted -by proper instruments; and Venus will be as seldom seen as we see -Mercury. Jupiter and Saturn are as visible to Mars as to us. His Axis is -perpendicular to the Ecliptic, and his Orbit is 2 degrees inclined to -it. - - -[Sidenote: Jupiter. - - Fig. I.] - -68. JUPITER, the biggest of all the Planets, is still higher in the -System, being about 424 millions of miles from the Sun: and going at the -rate of 25 thousand miles every hour in his Orbit, as in the circle ♃ -finishes his annual period in eleven of our years 314 days and 18 hours. -He is above 1000 times as big as the Earth, for his diameter is 81,000 -miles; which is more than ten times the diameter of the Earth. - -[Sidenote: The number of days in his year.] - -69. Jupiter turns round his Axis in 9 hours 56 minutes; so that his year -contains 10 thousand 464 days; and the diurnal velocity of his -equatoreal parts is greater than the swiftness with which he moves in -his annual Orbit; a singular circumstance, as far as we know. By this -prodigious quick Rotation, his equatoreal inhabitants are carried 25 -thousand 920 miles every hour (which is 920 miles an hour more than an -inhabitant of our Earth moves in twenty-four hours) besides the 25 -thousand above-mentioned, which is common to all parts of his surface, -by his annual motion. - -[Sidenote: His Belts and spots.] - -70. Jupiter is surrounded by faint substances, called _Belts_, in which -so many changes appear, that they are generally thought to be clouds: -for some of them have been first interrupted and broken, and then have -vanished entirely. They have sometimes been observed of different -breadths, and afterwards have all become nearly of the same breadth. -Large spots have been seen in these Belts; and when a Belt vanishes, the -contiguous spots disappear with it. The broken ends of some Belts have -been generally observed to revolve in the same time with the spots; only -those nearer the Equator in somewhat less time than those near the -Poles; perhaps on account of the Sun’s greater heat near the Equator, -which is parallel to the Belts and course of the spots. Several large -spots, which appear round at one time, grow oblong by degrees, and then -divide into two or three round spots. The periodical time of the spots -near the Equator is 9 hours 50 minutes, but of those near the Poles 9 -hours 56 minutes. _See Dr._ SMITH_’s Optics_, § 1004 _& seq._ - -[Sidenote: He has no change of seasons;] - -71. The Axis of Jupiter is so nearly perpendicular to his Orbit, that he -has no sensible change of seasons; which is a great advantage, and -wisely ordered by the Author of Nature. For, if the Axis of this Planet -were inclined any considerable number of degrees, just so many degrees -round each Pole would in their turn be almost six of our years together -in darkness. And, as each degree of a great Circle on Jupiter contains -706 of our miles at a mean rate, it is easy to judge what vast tracts of -land would be rendered uninhabitable by any considerable inclination of -his Axis. - -[Sidenote: But has four Moons.] - -72. The Sun appears but 1/28 part so big to Jupiter as to us; and his -light and heat are in the same small proportion, but compensated by the -quick returns thereof, and by four Moons (some bigger and some less than -our Earth) which revolve about him: so that there is scarce any part of -this huge Planet but what is during the whole night enlightened by one -or more of these Moons, except his Poles, whence only the farthest Moons -can be seen, and where their light is not wanted, because the Sun -constantly circulates in or near the Horizon, and is very probably kept -in view of both Poles by the Refraction of Jupiter’s Atmosphere, which, -if it be like ours, has certainly refractive power enough for that -purpose. - -[Sidenote: Their periods round Jupiter. - - Their grand period.] - -73. The Orbits of these Moons are represented in the Scheme of the Solar -System by four small circles marked 1. 2. 3. 4. on Jupiter’s Orbit ♃; -but are drawn fifty times too large in proportion to it. The first Moon, -or that nearest to Jupiter, goes round him in 1 day 18 hours and 36 -minutes of our time; and is 229 thousand miles distant from his center: -The second performs it’s revolution in three days 13 hours and 15 -minutes, at 364 thousand miles distance: The third in 7 days three hours -and 59 minutes, at the distance of 580 thousand miles: And the fourth, -or outermost, in 16 days 18 hours and 30 minutes, at the distance of one -million of miles from his center. The Periods of these Moons are so -incommensurate to one another, that if ever they were all in a right -line between Jupiter and the Sun, it will require more than -3,000,000,000,000 years from that time to bring them all into the same -right line again, as any one will find who reduces all their periods -into seconds, then multiplies them into one another, and divides the -product by 432; which is the highest number that will divide the product -of all their periodical times, namely 42,085,303,376,931,994,955,904 -seconds, without a remainder. - -[Sidenote: Parallax of their Orbits, and distances from Jupiter. - - PLATE I. - - How he appears to his nearest Moon.] - -74. The Angles under which the Orbits of Jupiter’s Moons are seen from -the Earth, at it’s mean distance from Jupiter, are as follow: The first, -3ʹ 55ʺ; the second, 6ʹ 14ʺ; the third, 9ʹ 58ʺ; and the fourth, 17ʹ 30ʺ. -And their distances from Jupiter, measured by his semidiameters, are -thus: The first, 5-2/3; the second, 9; the third. 14-23/60; and the -fourth, 25-18/60[15]. This Planet, seen from it’s nearest Moon, appears -1000 times as large as our Moon does to us; waxing and waneing in all -her monthly shapes, every 42-1/2 hours. - -[Sidenote: Two grand discoveries made by the Eclipse of Jupiter’s - Moons.] - -75. Jupiter’s three nearest Moons fall into his shadow, and are eclipsed -in every Revolution: but the Orbit of the fourth Moon is so much -inclined, that it passeth by Jupiter, without falling into his shadow, -two years in every six. By these Eclipses, Astronomers have not only -discovered that the Sun’s light comes to us in eight minutes; but have -also determined the longitudes of places on this Earth with greater -certainty and facility than by any other method yet known; as shall be -explained in the eleventh Chapter. - -[Sidenote: The great difference between the Equatoreal and Polar diameters - of Jupiter. - - The difference little in those of our Earth.] - -76. The difference between the Equatoreal and Polar diameters of Jupiter -is 6230 miles; for his equatoreal diameter is to his polar as 13 to 12. -So that his Poles are 3115 miles nearer his center than his Equator is. -This results from his quick motion round his Axis; for the fluids, -together with the light particles, which they can carry or wash away -with them, recede from the Poles which are at rest, towards the Equator -where the motion is quickest, until there be a sufficient number -accumulated to make up the deficiency of gravity occasioned by the -centrifugal force, which always arises from a quick motion round an -axis: and when the weight is made up so, as that all parts of the -surface press equally heavy toward the center, there is an -_equilibrium_, and the equatoreal parts rise no higher. Our Earth being -but a very small Planet, compared to Jupiter, and it’s motion on it’s -Axis being much slower, it is less flattened of course; for the -difference between it’s equatoreal and polar diameters is only as 230 to -229, or 35 miles. - -[Sidenote: Place of his Nodes.] - -77. Jupiter’s Orbit is 1 degree 20 minutes inclined to the Ecliptic. His -North Node is in the 7th degree of Cancer, and his South Node in the 7th -degree of Capricorn. - - -[Sidenote: Saturn. - - Fig. I.] - -78. SATURN, the remotest of all the Planets, is about 777 millions of -miles from the Sun; and, travelling at the rate of 18 thousand miles -every hour, as in the circle marked ♄, performs his annual circuit in 29 -years 167 days and 5 hours of our time; which makes only one year to -that Planet. His diameter is 67,000 miles; and therefore he is near 600 -times as big as the Earth. - -[Sidenote: Fig. V. - - His Ring. - - PLATE I.] - -79. He is surrounded by a thin broad Ring, as an artificial Globe is by -its Horizon. This Ring appears double when seen through a good -telescope, and is represented by the figure in such an oblique view as -it is generally seen. It is inclined 30 degrees to the Ecliptic, and is -about 21 thousand miles in breadth; which is equal to it’s distance from -Saturn on all sides. There is reason to believe that the Ring turns -round it’s Axis, because, when it is almost edge-wise to us, it appears -somewhat thicker on one side of the Planet than on the other; and the -thickest edge has been seen on different sides at different times. But -Saturn having no visible spots on his body, whereby to determine the -time of his turning round his Axis, the length of his days and nights, -and the position of his Axis, are unknown to us. - -[Sidenote: His five Moons. - - Fig. I.] - -80. To Saturn, the Sun appears only 1/90th part so big as to us; and the -light and heat he receives from the Sun are in the same proportion to -ours. But to compensate for the small quantity of sun-light, he has five -Moons, all going round him on the outside of his Ring, and nearly in the -same plane with it. The first, or nearest Moon to Saturn, goes round him -in 1 day 21 hours 19 minutes; and is 140 thousand miles from his center: -The second, in two days 17 hours 40 minutes; at the distance of 187 -thousand miles: The third, in 4 days 12 hours 25 minutes; at 263 -thousand miles distance: The fourth, in 15 days 22 hours 41 minutes; at -the distance of 600 thousand miles: And the fifth, or outermost, at one -million 800 thousand miles from Saturn’s center, goes round him in 79 -days 7 hours 48 minutes. Their Orbits in the Scheme of the Solar System -are represented by the five small circles, marked 1. 2. 3. 4. 5. on -Saturn’s Orbit; but these, like the Orbits of the other Satellites, are -drawn fifty times too large in proportion to the Orbits of their Primary -Planets. - -[Sidenote: His Axis probably inclined to his Ring.] - -81. The Sun shines almost fifteen of our years together on one side of -Saturn’s Ring without setting, and as long on the other in it’s turn. So -that the Ring is visible to the inhabitants of that Planet for almost -fifteen of our years, and as long invisible by turns, if it’s Axis has -no Inclination to it’s Ring: but if the Axis of the Planet be inclined -to the Ring, suppose about 30 degrees, the Ring will appear and -disappear once every natural day to all the inhabitants within 30 -degrees of the Equator, on both sides, frequently eclipsing the Sun in a -Saturnian day. Moreover, if Saturn’s Axis be so inclined to his Ring, it -is perpendicular to his Orbit; and thereby the inconvenience of -different seasons to that Planet is avoided. For considering the length -of Saturn’s year, which is almost equal to thirty of ours, what a -dreadful condition must the inhabitants of his Polar regions be in, if -they be half of that time deprived of the light and heat of the Sun? -which must not be their case alone, if the Axis of the Planet be -perpendicular to the Ring, but also the Ring must hide the Sun from vast -tracks of land on each side of the Equator for 13 or 14 of our years -together, on the south side and north side by turns, as the Axis -inclines to or from the Sun: the reverse of which inconvenience is -another good presumptive proof of the Inclination of Saturn’s Axis to -it’s Ring, and also of his Axis being perpendicular to his Orbit. - -[Sidenote: How the Ring appears to Saturn and to us. - - In what Signs Saturn appears to lose his Ring; and in what - Signs it appears most open to us.] - -82. This Ring, seen from Saturn, appears like a vast luminous Arch in -the Heavens, as if it did not belong to the Planet. When we see the Ring -most open, it’s shadow upon the Planet is broadest; and from that time -the shadow grows narrower, as the Ring appears to do to us; until, by -Saturn’s annual motion, the Sun comes to the plane of the Ring, or even -with it’s edge; which being then directed towards us, becomes invisible -on account of it’s thinness; as shall be explained more largely in the -tenth Chapter, and illustrated by a figure. The Ring disappears twice in -every annual Revolution of Saturn, namely, when he is in the 19th degree -both of Pisces and of Virgo. And when Saturn is in the middle between -these points, or in the 19th degree either of Gemini or of Sagittarius, -his Ring appears most open to us; and then it’s longest diameter is to -it’s shortest as 9 to 4. - -[Sidenote: No Planet but Saturn can be seen from Jupiter; nor any from - Jupiter besides Saturn.] - -83. To such eyes as ours, unassisted by instruments, Jupiter is the only -Planet that can be seen from Saturn; and Saturn the only Planet that can -be seen from Jupiter. So that the inhabitants of these two Planets must -either see much farther than we do, or have equally good instruments to -carry their sight to remote objects, if they know that there is such a -body as our Earth in the Universe: for the Earth is no bigger seen from -Jupiter than his Moons are seen from the Earth; and if his large body -had not first attracted our sight, and prompted our curiosity to view -him with the telescope, we should never have known any thing of his -Moons; unless by chance we had directed the telescope toward that small -part of the Heavens where they were at the time of observation. And the -like is true of the Moons of Saturn. - -[Sidenote: Place of Saturn’s Nodes.] - -84. The Orbit of Saturn is 2-1/2 degrees inclined to the Ecliptic, or -Orbit of our Earth, and intersects it in the 21st degree of Cancer and -of Capricorn; so that Saturn’s Nodes are only 14 degrees from Jupiter’s, -§ 77. - -[Sidenote: The Sun’s light much stronger on Jupiter and Saturn than is - generally believed. - - All our heat depends not on the Sun’s rays.] - -85. The quantity of light, afforded by the Sun of Jupiter, being but -1/28th part, and to Saturn only 1/90th part, of what we enjoy; may at -first thought induce us to believe that these two Planets are entirely -unfit for rational beings to dwell upon. But, that their light is not so -weak as we imagine, is evident from their brightness in the night-time; -and also, that when the Sun is so much eclipsed to us as to have only -the 40th part of his Disc left uncovered by the Moon, the decrease of -light is not very sensible: and just at the end of darkness in Total -Eclipses, when his western limb begins to be visible, and seems no -bigger than a bit of fine silver wire, every one is surprised at the -brightness wherewith that small part of him shines. The Moon when Full -affords travellers light enough to keep them from mistaking their way; -and yet, according to Dr. SMITH[16], it is equal to no more than a 90 -thousandth part of the light of the Sun: that is, the Sun’s light is 90 -thousand times as strong as the light of the Moon when Full. -Consequently, the Sun gives a thousand times as much light to Saturn as -the Full Moon does to us; and above three thousand times as much to -Jupiter. So that these two Planets, even without any Moons, would be -much more enlightened than we at first imagine; and by having so many, -they may be very comfortable places of residence. Their heat, so far as -it depends on the force of the Sun’s rays, is certainly much less than -ours; to which no doubt the bodies of their inhabitants are as well -adapted as ours are to the seasons we enjoy. And if we consider, that -Jupiter never has any winter, even at his Poles; which probably is also -the case with Saturn, the cold cannot be so intense on these two Planets -as is generally imagined. Besides, there may be something in their -nature or soil much warmer than in that of our Earth: and we find that -all our heat depends not on the rays of the Sun; for if it did, we -should always have the same months equally hot or cold at their annual -returns. But it is far otherwise, for _February_ is sometimes warmer -than _May_, which must be owing to vapours and exhalations from the -Earth. - - -[Sidenote: It is highly probable that all the Planets are inhabited. - - PLATE I.] - -86. Every person who looks upon, and compares the Systems of Moons -together, which belong to Jupiter and Saturn, must be amazed at the vast -magnitude of these two Planets, and the noble attendance they have in -respect of our little Earth: and can never bring himself to think, that -an infinitely wise Creator should dispose of all his animals and -vegetables here, leaving the other Planets bare and destitute of -rational creatures. To suppose that he had any view to our Benefit, in -creating these Moons and giving them their motions round Jupiter and -Saturn; to imagine that he intended these vast Bodies for any advantage -to us, when he well knew that they could never be seen but by a few -Astronomers peeping through telescopes; and that he gave to the Planets -regular returns of days and nights, and different seasons to all where -they would be convenient; but of no manner of service to us, except only -what immediately regards our own Planet the Earth; to imagine, I say, -that he did all this on our account, would be charging him impiously -with having done much in vain: and as absurd, as to imagine that he has -created a little Sun and a Planetary System within the shell of our -Earth, and intended them for our use. These considerations amount to -little less than a positive proof that all the Planets are inhabited: -for if they are not, why all this care in furnishing them with so many -Moons, to supply those with light which are at the greater distances -from the Sun? Do we not see, that the farther a Planet is from the Sun, -the greater Apparatus it has for that purpose? save only Mars, which -being but a small Planet, may have Moons too small to be seen by us. We -know that the Earth goes round the Sun, and turns round it’s own Axis, -to produce the vicissitudes of summer and winter by the former, and of -day and night by the latter motion, for the benefit of its inhabitants. -May we not then fairly conclude, by parity of reason, that the end and -design of all the other Planets is the same? and is not this agreeable -to that beautiful harmony which reigns over the Universe? Surely it is: -and raises in us the most magnificent ideas of the SUPREME BEING, who is -every where, and at all times present; displaying his power, wisdom, and -goodness among all his creatures! and distributing happiness to -innumerable ranks of various beings! - - -[Sidenote: Fig. II. - - How the Sun appears to the different Planets.] - -87. In Fig. 2d, we have a view of the proportional breadth of the Sun’s -face or disc, as seen from the different Planets. The Sun is represented -N^o 1, as seen from Mercury; N^o 2, as seen from Venus; N^o 3, as seen -from the Earth; N^o 4, as seen from Mars; N^o 5, as seen from Jupiter; -and N^o 6, as seen from Saturn. - -[Sidenote: Fig. III. - - Fig. IV.] - -Let the circle _B_ be the Sun as seen from any Planet, at a given -distance; to another Planet, at double that distance, the Sun will -appear just of half that breadth, as _A_; which contains only one fourth -part of the area or surface of _B_. For, all circles, as well as square -surfaces, are to one another as the squares of their diameters. Thus, -the square _A_ is just half as broad as the square _B_; and yet it is -plain to sight, that _B_ contains four times as much surface as _A_. -Hence, in round numbers, the Sun appears 7 times larger to Mercury than -to us, 90 times larger to us than to Saturn, and 630 times as large to -Mercury as to Saturn. - -[Sidenote: Fig. V. - - Proportional bulks and distances of the Planets. - - PLATE I.] - -88. In Fig. 5th, we have a view of the bulks of the Planets in -proportion to each other, and to a supposed globe of two foot diameter -for the Sun. The Earth is 27 times as big as Mercury, very little bigger -than Venus, 5 times as big as Mars; but Jupiter is 1049 times as big as -the Earth, Saturn 586 times as big, exclusive of his Ring; and the Sun -is 877 thousand 650 times as big as the Earth. If the Planets in this -Figure were set at their due distances from a Sun of two feet diameter, -according to their proportional bulks, as in our System, Mercury would -be 28 yards from the Sun’s center; Venus 51 yards 1 foot; the Earth 70 -yards 2 feet; Mars 107 yards 2 feet; Jupiter 370 yards 2 feet; and -Saturn 760 yards two feet. The Comet of the year 1680, at it’s greatest -distance, 10 thousand 760 yards. In this proportion, the Moon’s distance -from the center of the Earth would be only 7-1/2 inches. - -[Sidenote: An idea of their distances.] - -89. To assist the imagination in conceiving an idea of the vast -distances of the Sun, Planets, and Stars, let us suppose, that a body -projected from the Sun should continue to fly with the swiftness of a -cannon ball; _i. e._ 480 miles every hour; this body would reach the -Orbit of Mercury, in 7 years 221 days; of Venus, in 14 years 8 days; of -the Earth, in 19 years 91 days; of Mars, in 29 years 85 days; of -Jupiter, in 100 years 280 days; of Saturn, in 184 years 240 days; to the -Comet of 1680, at it’s greatest distance from the Sun, in 2660 years; -and to the nearest fixed Stars in about 7 million 600 thousand years. - -[Sidenote: Why the Planets appear bigger and less at different times.] - -90. As the Earth is not the center of the Orbits in which the Planets -move, they come nearer to it and go farther from it and at different -times; on which account they appear bigger and less by turns. Hence, the -apparent magnitudes of the Planets are not always a certain rule to know -them by. - -[Sidenote: Fig. I.] - -91. Under Fig. 3, are the names and characters of the twelve Signs of -the Zodiac, which the Reader should be perfectly well acquainted with; -so as to know the characters without seeing the names. Every Sign -contains 30 degrees, as in the Circle bounding the Solar System; to -which the characters of the Signs are set in their proper places. - - -[Sidenote: The Comets.] - -92. The COMETS are solid opaque bodies, with long transparent trains or -tails, issuing from that side which is turned away from the Sun. They -move about the Sun, in very excentric ellipses; and are of a much -greater density than the Earth; for some of them are heated in every -Period to such a degree, as would vitrify or dissipate any substance -known to us. Sir ISAAC NEWTON computed the heat of the Comet which -appeared in the year 1680, when nearest the Sun, to be 2000 times hotter -than red-hot iron, and that being thus heated, it must retain it’s heat -until it comes round again, although it’s Period should be more than -twenty thousand years; and it is computed to be only 575. The method of -computing the heat of bodies, keeping at any known distance from the -Sun, so far as their heat depends on the force of the Sun’s rays, is -very easy; and shall be explained in the eighth Chapter. - -[Sidenote: PLATE I. - - Fig. I. - - They prove that the Orbits of the Planets are not solid. - - The Periods only of three are known. - - They prove the Stars to be at immense distances.] - -93. Part of the Paths of three Comets are delineated in the Scheme of -the Solar System, and the years marked in which they made their -appearance. It is believed, that there are at least 21 Comets belonging -to our System, moving in all sorts of directions: and all those which -have been observed, have moved through the ethereal Regions and the -Orbits of the Planets without suffering the least sensible resistance in -their motions; which plainly proves that the Planets do not move in -solid Orbs. Of all the Comets, the Periods of the above-mentioned three -only are known with any degree of certainty. The first of these Comets -appeared in the years 1531, 1607, and 1682; and is expected to appear -again in the year 1758, and every 75th year afterwards. The second of -them appeared in 1532 and 1661, and may be expected to return in 1789 -and every 129th year afterwards. The third, having last appeared in -1680, and it’s Period being no less than 575 years, cannot return until -the year 2225. This Comet, at it’s greatest distance, is about 11 -thousand two hundred millions of miles from the Sun; and at it’s least -distance from the Sun’s center, which is 490,000 miles, is within less -than a third part of the Sun’s semi-diameter from his surface. In that -part of it’s Orbit which is nearest the Sun, it flies with the amazing -swiftness of 880,000 miles in an hour; and the Sun, as seen from it, -appears an hundred degrees in breadth; consequently, 40 thousand times -as large as he appears to us. The astonishing length that this Comet -runs out into empty Space, suggests to our minds an idea of the vast -distance between the Sun and the nearest fixed Stars; of whose -Attractions all the Comets must keep clear, to return periodically, and -go round the Sun; and it shews us also, that the nearest Stars, which -are probably those that seem the largest, are as big as our Sun, and of -the same nature with him; otherwise, they could not appear so large and -bright to us as they do at such an immense distance. - -[Sidenote: Inferences drawn from the above phenomena.] - -94. The extreme heat, the dense atmosphere, the gross vapours, the -chaotic state of the Comets, seem at first sight to indicate them -altogether unfit for the purposes of animal life, and a most miserable -habitation for rational beings: and therefore [17]some are of opinion -that they are so many hells for tormenting the damned with perpetual -vicissitudes of heat and cold. But, when we consider, on the other hand, -the infinite power and goodness of the Deity; the latter inclining, and -the former enabling him to make creatures suited to all states and -circumstances; that matter exists only for the sake of intelligence; and -that wherever we find it, we always find it pregnant with life, or -necessarily subservient thereto; the numberless species, the astonishing -diversity of animals in earth, air, water, and even on other animals; -every blade of grass, every tender leaf, every natural fluid, swarming -with life; and every one of these enjoying such gratifications as the -nature and state of each requires: when we reflect moreover that some -centuries ago, till experience undeceived us, a great part of the Earth -was judged uninhabitable; the Torrid Zone by reason of excessive heat, -and the two Frigid Zones because of their intollerable cold; it seems -highly probable, that such numerous and large masses of durable matter -as the Comets are, however unlike they be to our Earth, are not -destitute of beings capable of contemplating with wonder, and -acknowledging with gratitude the wisdom, symmetry, and beauty of the -Creation; which is more plainly to be observed in their extensive Tour -through the Heavens, than in our more confined Circuit. If farther -conjecture is permitted, may we not suppose them instrumental in -recruiting the expended fuel of the Sun; and supplying the exhausted -moisture of the Planets? However difficult it may be, circumstanced as -we are, to find out their particular destination, this is an undoubted -truth, that wherever the Deity exerts his power, there he also manifests -his wisdom and goodness. - - -[Sidenote: This System very ancient, and demonstrable.] - -95. THE SOLAR SYSTEM here described is not a late invention; for it was -known and taught by the wise _Samian_ philosopher PYTHAGORAS, and others -among the ancients; but in latter times was lost, ’till the 15th -century, when it was again restored by the famous _Polish_ philosopher -NICHOLAUS COPERNICUS, who was born at _Thorn_ in the year 1473. In this, -he was followed by the greatest mathematicians and philosophers that -have since lived; as KEPLER, GALILEO, DESCARTES, GASSENDUS, and Sir -ISAAC NEWTON; the last of whom has established this System on such an -everlasting foundation of mathematical and physical demonstration, as -can never be shaken: and none who understand him can hesitate about it. - -[Sidenote: The Ptolemean System absurd.] - -96. In the _Ptolemean System_ the Earth was supposed to be fixed in the -Center of the Universe; and that the Moon, Mercury, Venus, the Sun, -Mars, Jupiter, and Saturn moved round the Earth: above the Planets, this -Hypothesis placed the Firmament of Stars, and then the two Crystalline -Spheres; all which were included in and received motion from the _Primum -Mobile_, which constantly revolved about the Earth in 24 hours, from -East to West. But as this rude Scheme was found incapable to stand the -test of art and observation, it was soon rejected by all true -philosophers; notwithstanding the opposition and violence of blind and -zealous bigots. - -[Sidenote: The Tychonic System, partly true and partly false.] - -97. The _Tychonic System_ succeeded the _Ptolemean_, but was never so -generally received. In this the Earth was supposed to stand still in the -Center of the Universe or Firmament of Stars, and the Sun to revolve -about it every 24 hours; the Planets, Mercury, Venus, Mars, Jupiter, and -Saturn, going round the Sun in the times already mentioned. But some of -TYCHO’s disciples supposed the Earth to have a diurnal motion round it’s -Axis, and the Sun with all the above Planets to go round the Earth in a -year; the Planets moving round the Sun in the foresaid times. This -hypothesis, being partly true and partly false, was embraced by few; and -soon gave way to the only true and rational System, restored by -COPERNICUS and demonstrated by Sir ISAAC NEWTON. - -98. To bring the foregoing particulars at once in view, with several -others which follow, concerning the Periods, Distances, Bulks, _&c._ of -the Planets, the following Table is inserted. - - A TABLE - - Of the PERIODS, REVOLUTIONS, MAGNITUDES, &c. of the PLANETS. - - +--------+------------+-------------+--------+--------+-------------+ - |Sun and |Annual | Diurnal |Diameter| Mean |Mean distance| - |Planets.|period | rotation | in |diam. as|from the Sun | - | |round | on it’s |English |seen fr.| in English | - | |the Sun. | Axis. |miles. |the Sun.| miles. | - +--------+------------+-------------+--------+--------+-------------+ - |Sun | ---- |25d. 6h. | 763000 | ---- | ---- | - |Mercury | 87^d 23^h|Unknown. | 2600 | 20ʺ | 32,000,000 | - |Venus | 224^d 17^h|24d. 8h. | 7906 | 30ʺ | 59,000,000 | - |Earth | 365^d 6^h| 1d. 0h. | 7970 | 21ʺ | 81,000,000 | - |Moon | 365^d 6^h|29d. 12-3/4h.| 2180 | 6ʺ | 81,000,000 | - |Mars | 686^d 23^h|24h. 40m. | 4444 | 11ʺ | 123,000,000 | - |Jupiter | 4332^d 12^h| 9h. 56m. | 81000 | 37ʺ | 424,000,000 | - |Saturn |10759^d 7^h|Unknown. | 67000 | 16ʺ | 777,000,000 | - +--------+------------+-------------+--------+--------+-------------+ - - +--------+------------+--------+---------+---------+---------+----------+ - |Sun and |Excentricity| Axis |Orbit |Place of |Place of |Proportion| - |Planets.| of it’s |inclined|inclined |it’s |it’s |of | - | | Orbit |to |to |Aphelion.|Ascending|Diameters.| - | |in miles. |Orbit. |Ecliptic.| |Node. | | - +--------+------------+--------+---------+---------+---------+----------+ - |Sun | ---- | 8° 0ʹ| ---- | ---- | ---- | 10000 | - |Mercury | 6,720,000 | Unkn. | 6° 54ʹ |♐ 13° 8ʹ|♉ 14° 43ʹ| 34-1/10 | - |Venus | 413,000 | 75° 0ʹ| 3° 20ʹ |♒ 4° 20ʹ|♊ 13° 59ʹ| 103-1/2 | - |Earth | 1,377,000 | 23° 29ʹ| 0° 0ʹ |♑ 8° 1ʹ| ---- | 104-1/2 | - |Moon | 13,000 | 2° 10ʹ| 5° 8ʹ | ---- |Variable.| 28-1/2 | - |Mars |11,439,000 | 0° 0ʹ| 1° 52ʹ |♍ 0° 32ʹ|♉ 17° 17ʹ| 58-1/6 | - |Jupiter |20,352,000 | 0° 0ʹ| 1° 20ʹ |♎ 9° 10ʹ|♋ 7° 29ʹ|1061-2/3 | - |Saturn |42,735,000 | Unkn. | 2° 30ʹ |♐ 27° 50ʹ|♋ 21° 13ʹ| 878-1/9 | - +--------+------------+--------+---------+---------+---------+----------+ - - +--------+----------+--------+----------+----------+--------+-------+--------+ - |Sun and |Proportion|Prop. of|Proportion|Proportion|Propor. |Hourly |Hourly | - |Planets.|of |Gravity |of | of |quantity|motion |motion | - | |Bulk. |on the |Density. |Light |of |in it’s|of it’s | - | | |surface.| |& Heat. |Matter. |Orbit. |Equator.| - +--------+----------+--------+----------+----------+--------+-------+--------+ - |Sun |877650 |24 |25-1/2 |45000 |227500 | ---- |3818 | - |Mercury |1/27 |Unkn. |Unkn. |6-1/2 |Unkn. |95000 |Unkn. | - |Venus |1 |Unkn. |Unkn. |1-3/4 |Unkn. |69000 |43 | - |Earth |1 |1 |100 |1 |1 |58000 |1042 | - |Moon |1/50 |34/100 |123-1/2 |1 ± |1/40 | 2290 |9-1/2 | - |Mars |1/5 |Unkn. |Unkn. |3/7 |Unkn. |47000 |556 | - |Jupiter | 1049 |2 |19 |1/28 |220 |25000 |25920 | - |Saturn |586 |1-1/2 |15 |1/90 |94 |18000 |Unkn. | - +--------+----------+--------+----------+----------+--------+-------+--------+ - - +--------+------------------+------------------------+-------------+ - |Sun and | Square miles in |Cubic miles in solidity.|Would fall to| - |Planets.| surface. | | the Sun in| - | | | | | - | | | | | - +--------+------------------+------------------------+-------------+ - |Sun | 1,828,911,000,000|232,577,115,137,000,000 | days h. | - |Mercury | 21,236,800| 9,195,534,500 | 15 13 | - |Venus | 691,361,300| 258,507,832,200 | 39 17 | - |Earth | 199,852,860| 265,404,598,080 | 14 10 | - |Moon | 14,898,750| 5,408,246,000 | 64 10 | - |Mars | 62,038,240| 45,969,335,840 | 121 0 | - |Jupiter | 20,603,970,000| 278,153,595,000,000 | 290 0 | - |Saturn | 14,102,562,000| 155,128,182,000,000 | 767 0 | - | | | | If the | - | | | | projectile | - | | | | force was | - | | | | destroyed. | - +--------+------------------+------------------------+-------------+ -If the Moon’s projectile force was destroyed, she would fall to the -Earth in 4 days 21 hours. - - +---------+--------------++---------+--------------+ - |Jupiter’s|Periods round || Saturn’s|Periods round | - | Moons. | Jupiter. || Moons. | Saturn. | - |---------+--------------||---------+--------------+ - | N^o | D. H. M. || N^o | D. H. M. | - |---------+--------------||---------+--------------+ - | 1 | 1 18 36 || 1 | 1 21 19 | - | 2 | 3 13 15 || 2 | 2 17 40 | - | 3 | 7 3 59 || 3 | 4 12 25 | - | 4 | 16 18 30 || 4 | 15 22 41 | - +---------+--------------+| 5 | 79 7 48 | - +---------+--------------+ - - - - - CHAP. III. - - _The_ COPERNICAN SYSTEM _demonstrated to be true_. - - -[Sidenote: Of matter and motion.] - -99. Matter is of itself inactive, and indifferent to motion or rest. A -body at rest can never put itself in motion; a body in motion can never -stop nor move slower of itself. Hence, when we see a body in motion we -conclude some other substance must have given it that motion; when we -see a body fall from motion to rest we conclude some other body or cause -stopt it. - -100. All motion is naturally rectilineal. A bullet thrown by the hand, -or discharged from a cannon would continue to move in the same direction -it received at first, if no other power diverted its course. Therefore, -when we see a body moving in a curve of whatever kind, we conclude it -must be acted upon by two powers at least: one to put it in motion, and -another drawing it off from the rectilineal course which it would -otherwise have continued to move in. - -[Sidenote: Gravity demonstrable.] - -101. The power by which bodies fall towards the Earth is called -_Gravity_ or _Attraction_. By this power in the Earth it is, that all -bodies, on whatever side, fall in lines perpendicular to it’s surface. -On opposite parts of the Earth bodies fall in opposite directions, all -towards the centre where the force of gravity is as it were accumulated. -By this power constantly acting on bodies near the Earth they are kept -from leaving it altogether; and those on its surface are kept thereto on -all sides, so that they cannot fall from it. Bodies thrown with any -obliquity are drawn by this power from a straight line into a curve, -until they fall to the Ground: the greater the force by which they are -thrown, the greater is the distance they are carried before they fall. -If we suppose a body carried several miles above the Earth, and there -projected in an horizontal direction, with so great a velocity that it -would move more than a semidiameter of the Earth, in the time it would -take to fall to the Earth by gravity; in that case, if there were no -resisting medium in the way, the body would not fall to the Earth at -all; but continue to circulate round the Earth, keeping always the same -path, and returning to the point from whence it was projected, with the -same velocity as at first. - -[Sidenote: Projectile force demonstrable.] - -102. We find the Moon moves round the Earth in an Orbit nearly circular. -The Moon therefore must be acted on by two powers or forces; one which -would cause her to move in a right line, another bending her motion from -that line into a curve. This attractive power must be seated in the -Earth; for there is no other body within the Moon’s Orbit to draw her. -The attractive power of the Earth therefore extends to the Moon; and, in -combination with her projectile force, causes her to move round the -Earth in the same manner as the circulating body above supposed. - -[Sidenote: The Sun and Planets attract each other.] - -103. The Moons of Jupiter and Saturn are observed to move round their -primary Planets: therefore there is such a power as gravity in these -Planets. All the Planets move round the Sun, and respect it for their -centre of motion: therefore the Sun must be endowed with attracting -force, as well as the Earth and Planets. The like may be proved of the -Comets. So that all the bodies or matter in the Solar System are -possessed of this power; and perhaps so is all matter whatsoever. - -104. As the Sun attracts the Planets with their Satellites, and the -Earth the Moon, so the Planets and Satellites re-attract the Sun, and -the Moon the Earth: action and re-action being always equal. This is -also confirmed by observation; for the Moon raises tides in the ocean, -the Satellites and Planets disturb one another’s motions. - -105. Every particle of matter being possessed of an attracting power, -the effect of the whole must be in proportion to the number of -attracting particles: that is, to the quantity of matter in the body. -This is demonstrated from experiments on pendulums: for, if they are of -equal lengths, whatever their weights be, they always vibrate in equal -times. Now, if one be double the weight of another, the force of gravity -or attraction must be double to make it oscillate with the same -celerity: if one is thrice the weight or quantity of matter of another, -it requires thrice the force of gravity to make it move with the same -celerity. Hence it is certain, that the power of gravity is always -proportional to the quantity of matter in bodies, whatever their bulks -or figures are. - -106. Gravity also, like all other virtues or emanations issuing from a -centre, decreases as the square of the distance increases: that is, a -body at twice the distance attracts another with only a fourth part of -the force; at four times the distance, with a sixteenth part of the -force. This too is confirmed from observation, by comparing the distance -which the Moon falls in a minute from a right line touching her Orbit, -with the space which bodies near the Earth fall in the same time: and -also by comparing the forces which retain Jupiter’s Moons in their -Orbits. This will be more fully explained in the seventh Chapter. - -[Sidenote: Gravitation and projection exemplified.] - -107. The mutual attraction of bodies may be exemplified by a boat and a -ship on the Water, tied by a rope. Let a man either in ship or boat pull -the rope (it is the same in effect at which end he pulls, for the rope -will be equally stretched throughout,) the ship and boat will be drawn -towards one another; but with this difference, that the boat will move -as much faster than the ship as the ship is heavier than the boat. -Suppose the boat as heavy as the ship, and they will draw one another -equally (setting aside the greater resistance of the Water on the bigger -body) and meet in the middle of the first distance between them. If the -ship is a thousand or ten thousand times heavier than the boat, the boat -will be drawn a thousand or ten thousand times faster than the ship; and -meet proportionably nearer the place from which the ship set out. Now, -whilst one man pulls the rope, endeavouring to bring the ship and boat -together, let another man, in the boat, endeavour to row her off -sidewise, or at right Angles to the rope; and the former, instead of -being able to draw the boat to the ship, will find it enough for him to -keep the boat from going further off; whilst the latter, endeavouring to -row off the boat in a straight line, will, by means of the other’s -pulling it towards the ship, row the boat round the ship at the rope’s -length from her. Here, the power employed to draw the ship and boat to -one another represents the mutual attraction of the Sun and Planets, by -which the Planets would fall freely towards the Sun with a quick motion; -and would also in falling attract the Sun towards them. And the power -employed to row off the boat represents the projectile force impressed -on the Planets at right Angles, or nearly so, to the Sun’s attraction; -by which means the Planets move round the Sun, and are kept from falling -to it. On the other hand, if it be attempted to make a heavy ship go -round a light boat, they will meet sooner than the ship can get round; -or the ship will drag the boat after it. - - -108. Let the above principles be applied to the Sun and Earth; and they -will evince, beyond a possibility of doubt, that the Sun, not the Earth, -is the center of the System; and that the Earth moves round the Sun as -the other Planets do. - -[Sidenote: The absurdity of supposing the Earth at rest.] - -For, if the Sun moves about the Earth, the Earth’s attractive power must -draw the Sun towards it from the line of projection so, as to bend it’s -motion into a curve; and the Earth being at least 169 thousand times -lighter than the Sun, by being so much less as to it’s quantity of -matter, must move 169 thousand times faster toward the Sun than the Sun -does toward the Earth; and consequently would fall to the Sun in a short -time if it had not a very strong projectile motion to carry it off. The -Earth therefore, as well as every other Planet in the System, must have -a rectilineal impulse to prevent its falling into the Sun. To say, that -gravitation retains all the other Planets in their Orbits without -affecting the Earth, which is placed between the Orbits of Mars and -Venus, is as absurd as to suppose that six cannon bullets might be -projected upwards to different heights in the Air, and that five of them -should fall down to the ground; but the sixth, which is neither the -highest nor the lowest, should remain suspended in the Air without -falling; and the Earth move round about it. - -109. There is no such thing in nature as a heavy body moving round a -light one as its centre of motion. A pebble fastened to a mill-stone by -a string, may by an easy impulse be made to circulate round the -mill-stone: but no impulse can make a mill-stone circulate round a loose -pebble, for the heaviest would undoubtedly carry the lightest along with -it wherever it goes. - -110. The Sun is so immensely bigger and heavier than the Earth[18], that -if he was moved out of his place, not only the Earth, but all the other -Planets if they were united into one mass, would be carried along with -the Sun as the pebble would be with the mill-stone. - -[Sidenote: The harmony of the celestial motions. - - The absurdity of supposing the Stars and Planets to move round - the Earth.] - -111. By considering the law of gravitation, which takes place throughout -the Solar System, in another light, it will be evident that the Earth -moves round the Sun in a year; and not the Sun round the Earth. It has -been shewn (§ 106) that the power of gravity decreases as the square of -the distance increases: and from this it follows with mathematical -certainty, that when two or more bodies move round another as their -centre of motion, the squares of their periodic times will be to one -another in the same proportion as the cubes of their distances from the -central body. This holds precisely with regard to the Planets round the -Sun, and the Satellites round the Planets; the relative distances of all -which, are well known. But, if we suppose the Sun to move round the -Earth, and compare its period with the Moon’s by the above rule, it will -be found that the Sun would take no less than 173,510 days to move round -the Earth, in which case our year would be 475 times as long as it now -is. To this we may add, that the aspects of increase and decrease of the -Planets, the times of their seeming to stand still, and to move direct -and retrograde, answer precisely to the Earth’s motion; but not at all -to the Sun’s without introducing the most absurd and monstrous -suppositions, which would destroy all harmony, order, and simplicity in -the System. Moreover, if the Earth is supposed to stand still, and the -Stars to revolve in free spaces about the Earth in 24 hours, it is -certain that the forces by which the Stars revolve in their Orbits are -not directed to the Earth, but to the centres of the several Orbits: -that is, of the several parallel Circles which the Stars on different -sides of the Equator describe every day: and the like inferences may be -drawn from the supposed diurnal motion of the Planets, since they are -never in the Equinoctial but twice, in their courses with regard to the -starry Heavens. But, that forces should be directed to no central body, -on which they physically depend, but to innumerable imaginary points in -the axe of the Earth produced to the Poles of the Heavens, is an -hypothesis too absurd to be allowed of by any rational creature. And it -is still more absurd to imagine that these forces should increase -exactly in proportion to the distances from this axe; for this is an -indication of an increase to infinity: whereas the force of attraction -is found to decrease in receding from the fountain from whence it flows. -But, the farther that any Star is from the quiescent Pole the greater -must be the Orbit which it describes; and yet it appears to go round in -the same time as the nearest Star to the Pole does. And if we take into -consideration the two-fold motion observed in the Stars, one diurnal -round the Axis of the Earth in 24 hours, and the other round the Axis of -the Ecliptic in 25920 years § 251, it would require an explication of -such a perplexed composition of forces, as could by no means be -reconciled with any physical Theory. - - -[Sidenote: Objections against the Earth’s motion answered.] - -112. There is but one objection of any weight that can be made to the -Earth’s motion round the Sun; which is, that in opposite points of the -Earth’s Orbit, it’s Axis which always keeps a parallel direction would -point to different fixed Stars; which is not found to be fact. But this -objection is easily removed by considering the immense distance of the -Stars in respect of the diameter of the Earth’s Orbit; the latter being -no more than a point when compared to the former. If we lay a ruler on -the side of a table, and along the edge of the ruler view the top of a -spire at ten miles distance; then lay the ruler on the opposite side of -the table in a parallel situation to what it had before, and the spire -will still appear along the edge of the ruler; because our eyes, even -when assisted by the best instruments are incapable of distinguishing so -small a change. - -113. Dr. BRADLEY, our present Astronomer Royal, has found by a long -series of the most accurate observations, that there is a small apparent -motion of the fixed Stars, occasioned by the aberration of their light, -and so exactly answering to an annual motion of the Earth, as evinces -the same, even to a mathematical demonstration. Those who are qualified -to read the Doctor’s modest Account of this great discovery may consult -the _Philosophical Transactions_, N^o 406. Or they may find it treated -of at large by Drs. SMITH[19], LONG[20], DESAGULIERS[21], RUTHERFURTH, -Mr. MACLAURIN[22], and M. DE LA CAILLE[23]. - -[Sidenote: Why the Sun appears to change his place.] - -114. It is true that the Sun seems to change his place daily, so as to -make a tour round the starry Heavens in a year. But whether the Earth or -Sun moves, this appearance will be the same; for, when the Earth is in -any part of the Heavens, the Sun will appear in the opposite. And -therefore, this appearance can be no objection against the motion of the -Earth. - -115. It is well known to every person who has sailed on smooth Water, or -been carried by a stream in a calm, that however fast the vessel goes he -does not feel its progressive motion. The motion of the Earth is -incomparably more smooth and uniform than that of a ship, or any machine -made and moved by human art: and therefore it is not to be imagined that -we can feel it’s motion. - - -[Sidenote: The Earth’s motion on it’s Axis demonstrated.] - -116. We find that the Sun, and those Planets on which there are visible -spots, turn round their Axes: for the spots move regularly over their -Disks[24]. From hence we may reasonably conclude that the other Planets -on which we see no spots, and the Earth which is likewise a Planet, have -such rotations. But being incapable of leaving the Earth, and viewing it -at a distance; and it’s rotation being smooth and uniform, we can -neither see it move on it’s Axis as we do the Planets, nor feel -ourselves affected by it’s motion. Yet there is one effect of such a -motion which will enable us to judge with certainty whether the Earth -revolves on it’s Axis or not. All Globes which do not turn round their -Axes will be perfect spheres, on account of the equality of the weight -of bodies on their surfaces; especially of the fluid parts. But all -Globes which turn on their Axes will be oblate spheroids; that is, their -surfaces will be higher, or farther from the centre, in the equatoreal -than in the polar Regions: for, as the equatoreal parts move quickest, -they will recede farther from the Axis of motion, and enlarge the -equatoreal diameter. That our Earth is really of this figure is -demonstrable from the unequal vibrations of a pendulum, and the unequal -lengths of degrees in different latitudes. Since then, the Earth is -higher at the Equator than at the Poles, the sea, which naturally runs -downward, or towards the places which are nearest the centre, would run -towards the polar Regions, and leave the equatoreal parts dry, if the -centrifugal force of these parts did not raise and carry the waters -thither. The Earth’s equatoreal diameter is 35 miles longer than its -Axis. - -[Sidenote: All bodies heavier at the Poles than they would be at the - Equator.] - -117. Bodies near the Poles are heavier than those towards the Equator, -because they are nearer the Earth’s centre, where the whole force of the -Earth’s attraction is accumulated. They are also heavier because their -centrifugal force is less on account of their diurnal motion being -slower. For both these reasons, bodies carried from the Poles toward the -Equator, gradually lose of their weight. Experiments prove that a -pendulum, which vibrates seconds near the Poles vibrates slower near the -Equator, which shews that it is lighter or less attracted there. To make -it oscillate in the same time, ’tis found necessary to diminish it’s -length. By comparing the different lengths of pendulums swinging seconds -at the Equator and at _London_, it is found that a pendulum must be -2-169/1000 lines shorter at the Equator than at the Poles. A line is a -twelfth part of an inch. - -[Sidenote: How they might lose all their weight.] - -118. If the Earth turned round it’s Axis in 84 minutes 43 seconds, the -centrifugal force would be equal to the power of gravity at the Equator; -and all bodies there would entirely lose their weight. If the Earth -revolved quicker they would all fly off, and leave it. - -[Sidenote: The Earth’s motion cannot be felt.] - -119. One on the Earth can no more be sensible of it’s undisturbed motion -on it’s Axis, than one in the cabin of a ship on smooth Water can be -sensible of her motion when she turns gently and uniformly round. It is -therefore no argument against the Earth’s diurnal motion that we do not -feel it: nor is the apparent revolutions of the celestial bodies every -day a proof of the reality of these motions; for whether we or they -revolve, the appearance is the very same. A person looking through the -cabin windows of a ship as strongly fancies the objects on land to go -round when the ship turns, as if they were actually in motion. - - -[Sidenote: To the different Planets the Heavens appear to turn round on - different Axes.] - -120. If we could translate ourselves from Planet to Planet, we should -still find that the Stars would appear of the same magnitudes, and at -the same distances from each other, as they do to us here; because the -width of the remotest Planet’s Orbit bears no sensible proportion to the -distance of the Stars. But then, the Heavens would seem to revolve about -very different Axes; and consequently, those quiescent Points which are -our Poles in the Heavens would seem to revolve about other points, -which, though apparently in motion to us on Earth would be at rest as -seen from any other Planet. Thus, the Axis of Venus, which lies almost -at right Angles to the Axis of the Earth, would have it’s motionless -Poles in two opposite points of the Heavens lying almost in our -Equinoctial, where the motion appears quickest because it is performed -in the greatest Circle. And the very Poles, which are at rest to us, -have the quickest motion of all as seen from Venus. To Mars and Jupiter -the Heavens appear to turn round with very different velocities on the -same Axis, whose Poles are about 23-1/2 degrees from ours. Were we on -Jupiter we should be at first amazed at the rapid motion of the Heavens; -the Sun and Stars going round in 9 hours 56 minutes. Could we go from -thence to Venus we should be as much surprised at the slowness of the -heavenly motions: the Sun going but once round in 584 hours, and the -Stars in 540. And could we go from Venus to the Moon we should see the -Heavens turn round with a yet slower motion; the Sun in 708 hours, the -Stars in 655. As it is impossible these various circumvolutions in such -different times and on such different Axes can be real, so it is -unreasonable to suppose the Heavens to revolve about our Earth more than -it does about any other Planet. When we reflect on the vast distance of -the fixed Stars, to which 162,000,000 of miles is but a point, we are -filled with amazement at the immensity of their distance. But if we try -to frame an idea of the extreme rapidity with which the Stars must move, -if they move round the Earth in 24 hours, the thought becomes so much -too big for our imagination, that we can no more conceive it than we do -infinity or eternity. If the Sun was to go round the Earth in a day, he -must travel upwards of 300,000 miles in a minute: but the Stars being at -least 10,000 times as far as the Sun from us, those about the Equator -must move 10,000 times as quick. And all this to serve no other purpose -than what can be as fully and much more simply obtained by the Earth’s -turning round eastward as on an Axis, every 24 hours, causing thereby an -apparent diurnal motion of the Sun westward, and bringing about the -alternate returns of day and night. - -[Illustration: Pl. II.] - - -[Sidenote: Objections against the Earth’s diurnal motion answered.] - -121. As to the common objections against the Earth’s motion on it’s -Axis, they are all easily answered and set aside. That it may turn -without being seen or felt to do so, has been already shewn, § 119. But -some are apt to imagine that if the Earth turns eastward (as it -certainly does if it turns at all) a ball fired perpendicularly upward -in the air must fall considerably westward of the place it was projected -from. This objection, which at first seems to have some weight, will be -found to have none at all when we consider that the gun and ball partake -of the Earth’s motion; and therefore the ball being carried forward with -the air as quick as the Earth and air turn, must fall down again on the -same place. A stone let fall from the top of a main-mast, if it meets -with no obstacle, falls on the deck as near the foot of the mast when -the ship sails as when it does not. And if an inverted bottle, full of -liquor, be hung up to the cieling of the cabin, and a small hole be made -in the cork to let the liquor drop through on the floor, the drops will -fall just as far forward on the floor when the ship sails as when it is -at rest. And gnats or flies can as easily dance among one another in a -moving cabin as in a fixed chamber. As for those scripture expressions -which seem to contradict the Earth’s motion, this general answer may be -made to them all, _viz._ ’tis plain from many instances that the -Scriptures were never intended to instruct us in Philosophy or -Astronomy; and therefore, on those subjects, expressions are not always -to be taken in the strictest sense; but for the most part as -accommodated to the common apprehensions of mankind. Men of sense in all -ages, when not treating of the sciences purposely, have followed this -method: and it would be in vain to follow any other in addressing -ourselves to the vulgar, or bulk of any community. _Moses_ calls the -Moon A GREAT LUMINARY (as it is in the Hebrew) as well as the Sun: but -the Moon is known to be an opaque body, and the smallest that -Astronomers have observed in the Heavens and shines upon us not by any -inherent light of it’s own, but by reflecting the light of the Sun. If -_Moses_ had known this, and told the _Israelites_ so, they would have -stared at him; and considered him rather as a madman than as a person -commissioned by the Almighty to be their leader. - - - - - CHAP. IV. - - _The Phenomena of the Heavens as seen from different parts of the - Earth._ - - -[Sidenote: We are kept to the Earth by gravity. - - PLATE II. Fig. I. - - Antipodes. - - Axis of the World. It’s Poles. Fig. II.] - -122. We are kept to the Earth’s surface on all sides by the power of -it’s central attraction; which, laying hold of all bodies according to -their densities or quantities of matter without regard to their bulks, -constitutes what we call their _weight_. And having the sky over our -heads, go where we will, and our feet towards the centre of the Earth, -we call it _up_ over our heads, and _down_ under our feet: although the -same right line which is _down_ to us, if continued through and beyond -the opposite side of the Earth, would be _up_ to the inhabitants on the -opposite side. For, the inhabitants _n_, _i_, _e_, _m_, _s_, _o_, _q_, -_l_ stand with their feet toward the Earth’s centre _C_; and have the -same figure of sky _N_, _l_, _E_, _M_, _S_, _O_, _Q_, _L_ over their -heads. Therefore, the point _S_ is as directly upward to the inhabitant -_s_ on the south Pole as _N_ is to the inhabitant _n_ on the North Pole: -so is _E_ to the inhabitant _e_, supposed to be on the north end of -_Peru_; and _Q_ to the opposite inhabitant _q_ on the middle of the -island _Sumatra_. Each of these observers is surprised that his opposite -or _Antipode_ can stand with his head hanging downwards. But let either -go to the other, and he will tell him that he stood as upright and firm -on the place where he was as he now stands where he is. To all these -observers the Sun, Moon, and Stars seem to turn round the points _N_ and -_S_ as the Poles of the fixed Axis _NCS_; because the Earth does really -turn round the mathematical line _nCs_ as round an Axis of which _n_ is -the North Pole and _s_ the South Pole. The Inhabitant _U_ (Fig. II.) -affirms that he is on the uppermost side of the Earth, and wonders how -another at _L_ can stand on the undermost side with his head hanging -downwards. But _U_ in the mean time forgets that in twelve hours time he -will be carried half round with the Earth; and then be in the very -situation that _L_ now is, although as far from him as before. And yet, -when _U_ comes there, he will find no difference as to his manner of -standing; only he will see the opposite half of the Heavens, and imagine -the Heavens to have gone half round him. - - -[Sidenote: How our Earth might have an upper and an under side.] - -123. When we see a globe hung up in a room we cannot help imagining it -to have an upper and an under side, and immediately form a like idea of -the Earth; from whence we conclude, that it is as impossible for persons -to stand on the under side of the Earth as for pebbles to lie on the -under side of a common Globe, which instantly fall down from it to the -ground; and well they may, because the attraction of the Earth, being -too strong for the attraction of the Globe, pulls them away. Just so -would be the case with our Earth, if it were placed near a Globe much -bigger than itself, such as Jupiter: for then it would really have an -upper and an under side with respect to that large Globe; which, by it’s -Attraction, would pull away every thing from the side of the Earth next -to it; and only those on the top of the opposite or upper side could -keep upon it. But there is no larger Globe near enough our Earth to -overcome it’s central attraction; and therefore it has no such thing as -an upper and an under side: for all bodies on or near it’s surface, even -to the Moon, gravitate towards it’s center. - -[Sidenote: PLATE II.] - -124. Let any man imagine that the Earth and every thing but himself is -taken away, and he left alone in the midst of indefinite Space; he could -then have no idea of _up_ or _down_; and were his pockets full of gold, -he might take the pieces one by one, and throw them away on all sides of -him, without any danger of losing them; for the attraction of his body -would bring them all back by the ways they went, and _he_ would be -_down_ to every one of them. But then, if a Sun or any other large body -were created, and placed in any part of Space several millions of miles -from him, he would be attracted towards it, and could not save himself -from falling _down_ to it. - - -[Sidenote: Fig. I. - - One half of the Heavens visible to an inhabitant on any part - of the Earth. - - Phenomena at the Poles. - - PLATE II.] - -125. The Earth’s bulk is but a point, as that at _C_, compared to the -Heavens; and therefore every inhabitant upon it, let him be where he -will, as at _n_, _e_, _m_, _s_, &c. sees one half of the Heavens. The -inhabitant _n_, on the North Pole of the Earth, constantly sees the -Hemisphere _ENQ_; and having the North Pole _N_ of the Heavens just over -his head, his [25]Horizon coincides with the Celestial Equator _ECQ_. -Therefore all the Stars in the Northern Hemisphere _ENC_, between the -Equator and North Pole, appear to turn round the line _NC_, moving -parallel to the Horizon. The Equatoreal Stars keep in the Horizon, and -all those in the Southern Hemisphere _ESQ_ are invisible. The like -Phenomena are seen by the observer _s_ on the South Pole, with respect -to the Hemisphere _ESQ_; and to him the opposite Hemisphere is always -invisible. Hence, under either Pole, only one half of the Heavens is -seen; for those parts which are once visible never set, and those which -are once invisible never rise. But the Ecliptic _YCX_ or Orbit which the -Sun appears to describe once a year by the Earth’s annual motion, has -the half _YC_ constantly above the Horizon _ECQ_ of the North Pole _n_; -and the other half _CX_ always below it. Therefore whilst the Sun -describes the northern half _YC_ of the Ecliptic he neither sets to the -North Pole nor rises to the South; and whilst he describes the southern -half _CX_ he neither sets to the South Pole nor rises to the North. The -same things are true with respect to the Moon; only with this -difference, that as the Sun describes the Ecliptic but once a year, he -is for half that time visible to each Pole in it’s turn, and as long -invisible; but as the Moon goes round the Ecliptic in 27 days 8 hours, -she is only visible for 13 days 16 hours, and as long invisible to each -Pole by turns. All the Planets likewise rise and set to the Poles, -because their Orbits are cut obliquely in halves by the Horizon of the -Poles. When the Sun (in his apparent way from _X_) arrives at _C_, which -is on the 20th of _March_, he is just rising to an observer at _n_ on -the North Pole, and setting to another at _s_ on the South Pole. From -_C_ he rises higher and higher in every apparent Diurnal revolution -’till he comes to the highest point of the Ecliptic _y_, on the 21st of -_June_, and then he is at his greatest Altitude, which is 23-1/2 -degrees, or the Arc _Ey_, equal to his greatest North declination; and -from thence he seems to descend gradually in every apparent -Circumvolution, ’till he sets at _C_ on the 23d of _September_; and then -he goes to exhibit the like Appearances at the South Pole for the other -half of the year. Hence the Sun’s apparent motion round the Earth is not -in parallel Circles, but in Spirals; such as might be represented by a -thread wound round a Globe from Tropic to Tropic; the Spirals being at -some distance from one another about the Equator, but gradually nearer -to each other as they approach nearer to the Tropics. - -[Sidenote: Phenomena at the Equator. - - Fig. I.] - -126. If the observer be any where on the Terrestrial Equator _eCq_, as -suppose at _e_, he is in the Plane of the Celestial Equator; or under -the Equinoctial _ECQ_; and the Axis of the Earth _nCs_ is coincident -with the Plane of his Horizon, extended out to _N_ and _S_, the North -and South Poles of the Heavens. As the Earth turns round the line _NCS_, -the whole Heavens _MOLl_ seem to turn round the same line, but the -contrary way. It is plain that this observer has the Poles constantly in -his Horizon, and that his Horizon cuts the Diurnal paths of all the -Celestial bodies perpendicularly and in halves. Therefore the Sun, -Planets, and Stars rise every day, and ascend perpendicularly above the -Horizon for six hours, and passing over the Meridian, descend in the -same manner for the six following hours; then set in the Horizon, and -continue twelve hours below it. Consequently at the Equator the days and -nights are equally long throughout the year. When the observer is in the -situation _e_, he sees the Hemisphere _SEN_; but in twelve hours after, -he is carried half round the Earth’s Axis to _q_, and then the -Hemisphere _SQN_ becomes visible to him; and _SEN_ disappears, being hid -by the Convexity of the Earth. Thus we find that to an observer at -either of the Poles one half of the Sky is always visible, and the other -half never seen; but to an observer on the Equator the whole Sky is seen -every 24 hours. - -The Figure here referred to, represents a Celestial globe of glass, -having a Terrestrial globe within it; after the manner of the Glass -Sphere invented by my generous friend Dr. LONG, _Lowndes_’s Professor of -Astronomy in _Cambridge_. - -[Sidenote: Remark.] - -127. If a Globe be held sidewise to the eye, at some distance, and so -that neither of it’s Poles can be seen, the Equator _ECQ_ and all -Circles parallel to it, as _DL_, _yzx_, _abX_, _MO_, &c. will appear to -be straight lines, as projected in this Figure; which is requisite to be -mentioned here, because we shall have occasion to call them Circles in -the following Article[26]. - -[Sidenote: Phenomena between the Equator and Poles. - - The Circles of perpetual Apparition and Occultation.] - -128. Let us now suppose that the observer has gone from the Equator e -towards the North Pole _n_, and that he stops at _i_, from which place -he then sees the Hemisphere _MElNL_; his Horizon _MCL_ having shifted as -many [27]Degrees from the Celestial poles _N_ and _S_ as he has -travelled from under the Equinoctial _E_. And as the Heavens seem -constantly to turn round the line _NCS_ as an Axis, all those Stars -which are as far from the North Pole _N_ as the observer is from under, -the Equinoctial, namely the Stars north of the dotted parallel _DL_, -never set below the Horizon; and those which are south of the dotted -parallel _MO_ never rise above it. Hence, the former of these two -parallel Circles is called _the Circle of perpetual Apparition_, and the -latter _the Circle of perpetual Occultation_: but all the Stars between -these two Circles rise and set every day. Let us imagine many Circles to -be drawn between these two, and parallel to them; those which are on the -north side of the Equinoctial will be unequally cut by the Horizon -_MCL_, having larger portions above the Horizon than below it; and the -more so, as they are nearer to the Circle of perpetual Apparition; but -the reverse happens to those on the south side of the Equinoctial, -whilst the Equinoctial is divided in two equal parts by the Horizon. -Hence, by the apparent turning of the Heavens, the northern Stars -describe greater Arcs or Portions of Circles above the Horizon than -below it; and the greater as they are farther from the Equinoctial -towards the Circle of perpetual Apparition; whilst the contrary happens -to all Stars south of the Equinoctial: but those upon it describe equal -Arcs both above and below the Horizon, and therefore they are just as -long above as below it. - -[Sidenote: PLATE II.] - -129. An observer on the Equator has no Circle of perpetual Apparition or -Occultation, because all the Stars, together with the Sun and Moon, rise -and set to him every day. But, as a bare view of the Figure is -sufficient to shew that these two Circles _DL_ and _MO_ are just as far -from the Poles _N_ and _S_ as the observer at _i_ (or one opposite to -him at _o_) is from the Equator _ECQ_; it is plain, that if an observer -begins to travel from the Equator towards either Pole, his Circle of -perpetual Apparition rises from that Pole as from a Point, and his -Circle of perpetual Occultation from the other. As the observer advances -toward the nearer Pole, these two Circles enlarge their diameters, and -come nearer one another, until he comes to the Pole; and then they meet -and coincide in the Equator. On different sides of the Equator, to -observers at equal distances from it, the Circle of perpetual Apparition -to one is the Circle of perpetual Occultation to the other. - - -[Sidenote: Why the Stars always describe the same parallel of motion, - and the Sun a different.] - -130. Because the Stars never vary their distances from the Equinoctial, -so as to be sensible in an age, the lengths of their diurnal and -nocturnal Arcs are always the same to the same places on the Earth. But -as the Earth goes round the Sun every year in the Ecliptic, one half of -which is on the north side of the Equinoctial and the other half on it’s -south side, the Sun appears to change his place every day, so as to go -once round the Circle _YCX_ every year § 114. Therefore whilst the Sun -appears to advance northward, from having described the Parallel _abX_ -touching the Ecliptic in _X_ the days continually lengthen and the -nights shorten, until he comes to _y_ and describes the Parallel _yzx_, -when the days are at the longest and the nights at the shortest: for -then, as the Sun goes no farther northward, the greatest portion that is -possible of the diurnal Arc _yz_ is above the Horizon of the inhabitant -_i_; and the smallest portion _zx_ below it. As the Sun declines -southward from _y_ he describes smaller diurnal and greater nocturnal -Arcs, or Portions of Circles, every day; which causeth the days to -shorten and nights to lengthen, until he arrives again at the Parallel -_abX_; which having only the small part _ab_ above the Horizon _MCL_, -and the great part _bX_ below it, the days are at the shortest and the -nights at the longest; because the Sun recedes no farther south, but -returns northward as before. It is easy to see that the Sun must be in -the Equinoctial _ECQ_ twice every year, and then the days and nights are -equally long; that is, 12 hours each. These hints serve at present to -give an idea of some of the Appearances resulting from the motions of -the Earth; which will be more particularly described in the tenth -Chapter. - - -[Sidenote: Fig. I. - - Parallel, Oblique, and Right sphere, what.] - -131. To an observer at either Pole, the Horizon and Equinoctial are -coincident; and the Sun and Stars seem to move parallel to the Horizon: -therefore, such an observer is said to have a Parallel position of the -Sphere. To an observer any where between the Poles and Equator, the -Parallels described by the Sun and Stars are cut obliquely by the -Horizon, and therefore he is said to have an Oblique position of the -Sphere. To an observer any where on the Equator, the Parallels of -Motion, described by the Sun and Stars are cut perpendicularly, or at -Right angles, by the Horizon; and therefore he is said to have a Right -position of the Sphere. And these three are all the different ways that -the Sphere can be posited to all people, on the Earth. - - - - - CHAP. V. - -_The Phenomena of the Heavens as seen from different Parts of the Solar - System._ - - -132. So vastly great is the distance of the starry Heavens, that if -viewed from any part of the Solar System, or even many millions of miles -beyond it, its appearance would be the very same to us. The Sun and -Stars would all seem to be fixed on one concave surface, of which the -Spectator’s eye would be the centre. But the Planets, being much nearer -than the Stars, their appearances will vary considerably with the place -from which they are viewed. - -133. If the spectator is at rest without their Orbits, the Planets will -seem to be at the same distance as the Stars; but continually changing -their places with respect to the Stars, and to one another: assuming -various phases of increase and decrease like the Moon. And, -notwithstanding their regular motions about the Sun, will sometimes -appear to move quicker, sometimes slower, be as often to the west as to -the east of the Sun; and at their greatest distances seem quite -stationary. The duration, extent, and points in the Heavens where these -digressions begin and end, would be more or less according to the -respective distances of the several Planets from the Sun: but in the -same Planet they would continue invariably the same at all times; like -pendulums of unequal lengths oscillating together, the shorter move -quick and go over a small space, the longer move slow and go over a -large space. If the observer is at rest within the Orbits of the -Planets, but not near the common center, their apparent motions will be -irregular, but less so than in the former case. Each of the several -Planets will appear bigger and less by turns, as they approach nearer or -recede farther from the observer; the nearest varying most in their -size. They will also move quicker or slower with regard to the fixed -Stars, but will never be retrograde or stationary. - -134. Next, let a spectator in motion view the Heavens: the same apparent -irregularities will be observed, but with some variation resulting from -his own motion. If he is on a Planet which has a rotation on it’s Axis, -not being sensible of his own motion he will imagine the whole Heavens, -Sun, Planets, and Stars to revolve about him in the same time that his -Planet turns round, but the contrary way; and will not be easily -convinced of the deception. If his Planet moves round the Sun, the same -irregularities and aspects as above will appear in the motions of the -Planets: only, the times of their being direct, stationary and -retrograde will be accelerated or retarded as they concur with, or are -contrary to his motion: and the Sun will seem to move among the fixed -Stars or Signs, directly opposite to those in which his Planet moves; -changing it’s place every day as he does. In a word, whether our -observer be in motion or at rest, whether within or without the Orbits -of the Planets, their motions will seem irregular, intricate and -perplexed, unless he is in the center of the System; and from thence, -the most beautiful order and harmony will be observed. - -[Sidenote: The Sun’s center the only point from which the true motions - and places of the Planets could be seen.] - -135. The Sun being the center of all the Planets motions, the only place -from which their motions could be truly seen, is the Sun’s center; where -the observer being supposed not to turn round with the Sun (which, in -this case, we must imagine to be a transparent body) would see all the -Stars at rest, and seemingly equidistant from him. To such an observer -the Planets would appear to move among the fixed Stars, in a simple, -regular, and uniform manner; only, that as in equal times they describe -equal Areas, they would describe spaces somewhat unequal, because they -move in elliptic Orbits § 155. Their motions would also appear to be -what they are in fact, the same way round the Heavens; in paths which -cross at small Angles in different parts of the Heavens, and then -separate a little from one another § 20. So that, if the solar -Astronomer should make the Path or Orbit of any one Planet a standard, -and consider it as having no obliquity § 201, he would judge the paths -of all the rest to be inclined to it; each Planet having one half of -it’s path on one side, and the other half on the opposite side of the -standard Path or Orbit. And if he should ever see all the Planets start -from a conjunction with each other[28]; Mercury would move so much -faster than Venus as to overtake her again (though not in the same point -of the Heavens) in a quantity of time almost equal to 145 of our days -and nights; or, as we commonly call them, _Natural Days_, which include -both the days and nights: Venus would move so much faster than the Earth -as to overtake it again in 585 natural days: the Earth so much faster -than Mars as to overtake him again in 778 such days: Mars is much faster -than Jupiter as to overtake him again in 817 such days: and Jupiter so -much faster than Saturn as to overtake him again in 7236 days, all of -our time. - -[Sidenote: The judgment that a solar Astronomer would probably make - concerning the distances and bulks of the Planets.] - -136. But as our solar Astronomer could have no idea of measuring the -courses of the Planets by our days, he would very probably take the -period of Mercury, which is the quickest moving Planet, for a measure to -compare the periods of the others by. As all the Stars would appear -quiescent to him, he would never think that they had any dependance upon -the Sun; but could naturally imagine that the Planets have, because they -move round the Sun. And it is by no means improbable, that he would -conclude those Planets whose periods are quickest to move in Orbits -proportionably less than those do which make slower circuits. But being -destitute of a method for finding their Parallaxes, or, more properly -speaking, as they could have no Parallax to him, he could never know any -thing of their real distances or magnitudes. Their relative distances he -might perhaps guess at by their periods, and from thence infer something -of truth concerning their relative bulks, by comparing their apparent -bulks with one another. For example, Jupiter appearing bigger to him -than Mars, he would conclude it to be much bigger in fact; because it -appears so, and must be farther from him, on account of it’s longer -period. Mercury would seem bigger than the Earth; but by comparing it’s -period with the Earth’s, he would conclude that the Earth is much -farther from him than Mercury, and consequently that it must be really -bigger though apparently less; and so of the rest. And, as each Planet -would appear somewhat bigger in one part of it’s Orbit than in the -opposite, and to move quickest when it seems biggest, the observer would -be at no loss to determine that all the Planets move in Orbits of which -the Sun is not precisely in the center. - - -[Sidenote: The Planetary motions very irregular as seen from the Earth. - - PLATE III.] - -137. The apparent magnitudes of the Planets continually change as seen -from the Earth, which demonstrates that they approach nearer to it, and -recede farther from it by turns. From these Phenomena, and their -apparent motions among the Stars, they seem to describe looped curves -which never return into themselves, Venus’s path excepted. And if we -were to trace out all their apparent paths, and put the figures of them -together in one diagram, they would appear so anomalous and confused, -that no man in his senses could believe them to be representations of -their real paths; but would immediately conclude, that such apparent -irregularities must be owing to some Optic illusions. And after a good -deal of enquiry, he might perhaps be at a loss to find out the true -cause of these inequalities; especially if he were one of those who -would rather, with the greatest justice, charge frail man with -ignorance, than the Almighty with being the author of such confusion. - -[Sidenote: Those of Mercury and Venus represented. - - Fig. I.] - -138. Dr. LONG, in his first volume of _Astronomy_, has given us figures -of the apparent paths of all the Planets separately from CASSINI; and on -seeing them I first thought of attempting to trace some of them by a -machine[29] that shews the motions of the Sun, Mercury, Venus, the Earth -and Moon, according to the _Copernican System_. Having taken off the -Sun, Mercury, and Venus, I put black-lead pencils in their places, with -the points turned upward; and fixed a circular sheet of paste-board so, -that the Earth kept constantly under it’s center in going round the Sun; -and the paste-board kept its parallelism. Then, pressing gently with one -hand upon the paste-board to make it touch the three pencils, with the -other hand I turned the winch which moves the whole machinery: and as -the Earth, together with the pencils in the places of Mercury and Venus, -had their proper motions round the Sun’s pencil, which kept at rest in -the center of the machine, all the three pencils described a diagram -from which the first Figure of the third Plate is truly copied in a -smaller size. As the Earth moved round the Sun, the Sun’s pencil -described the dotted Circle of Months, whilst Mercury’s pencil drew the -curve with the greatest number of loops, and Venus’s that with the -fewest. In their inferiour conjunctions they come as much nearer the -Earth, or within the Circle of the Sun’s apparent motion round the -Heavens, as they go beyond it in their superiour conjunctions. On each -side of the loops they appear Stationary; in that part of each loop next -the Earth retrograde; and in all rest of their paths direct. - -[Illustration: Plate III. _J. Ferguson delin._ _J. Mynde Sc._] - -[Sidenote: PLATE III.] - -If _Cassini_’s Figures of the paths of the Sun, Mercury and Venus were -put together, the Figure as above traced out, would be exactly like -them. It represents the Sun’s apparent motion round the Ecliptic, which -is the same every year; Mercury’s motion for seven years; and Venus’s -for eight; in which time Mercury’s path makes 23 loops, crossing itself -so many times, and Venus’s only five. In eight years Venus falls so -nearly into the same apparent path again, as to deviate very little from -it in some ages; but in what number of years Mercury and the rest of the -Planets would describe the same visible paths over again, I cannot at -present determine. Having finished the above Figure of the paths of -Mercury and Venus, I put the Ecliptic round them as in the Doctor’s -Book; and added the dotted lines from the Earth to the Ecliptic for -shewing Mercury’s apparent or geocentric motion therein for one year; in -which time his path makes three loops, and goes on a little farther; -which shews that he has three inferiour, and as many superiour -conjunctions with the Sun in that time, and also that he is six times -Stationary, and thrice Retrograde. Let us now trace out his motion for -one year in the Figure. - -[Sidenote: Fig. I.] - -Suppose Mercury to be setting out from _A_ towards _B_ (between the -Earth and left-hand corner of the Plate) and as seen from the Earth his -motion will then be direct, or according to the order of the Signs. But -when he comes to _B_, he appears to stand still in the 23d degree of ♏ -at _F_, as shewn by the line _BF_. Whilst he goes from _B_ to _C_, the -line _BF_ goes backward from _F_ to _E_, or contrary to the order of -Signs; and when he is at _C_ he appears Stationary at _E_; having gone -back 11-1/2 degrees. Now, suppose him Stationary on the first of -_January_ at _C_, on the tenth thereof he will appear in the Heavens as -at 20, near _F_; on the 20th he will be seen as at _G_; on the 31st at -_H_; on the 10th of _February_ at _I_; on the 20th at _K_; and on the -28th at _L_; as the dotted lines shew, which are drawn through every -tenth day’s motion in his looped path, and continued to the Ecliptic. On -the 10th of _March_ he appears at _M_; on the 20th at _N_; and on the -31st at _O_. On the 10th of _April_ he appears Stationary at _P_; on the -20th he seems to have gone back again to _O_; and on the 30th he appears -Stationary at _Q_ having gone back 11-1/2 degrees. Thus Mercury seems to -go forward 4 Signs 11 Degrees, or 131 Degrees; and to go back only 11 or -12 Degrees, at a mean rate. From the 30th of _April_ to the 10th of -_May_, he seems to move from _Q_ to _R_; and on the 20th he is seen at -_S_, going forward in the same manner again, according to the order of -letters; and backward when they go back; which, ’tis needless to explain -any farther, as the reader can trace him out so easily through the rest -of the year. The same appearances happen in Venus’s motion; but as she -moves slower than Mercury, there are longer intervals of time between -them. - -Having already § 120. given some account of the apparent diurnal motions -of the Heavens as seen from the different Planets, we shall not trouble -the reader any more with that subject. - - - - - CHAP. VI. - - _The_ Ptolemean _System refuted. The Motions and Phases of Mercury and - Venus explained._ - - -139. The _Tychonic System_ § 97, being sufficiently refuted by the 109th -Article, we shall say nothing more about it. - -140. The _Ptolemean System_ § 96, which asserts the Earth to be at rest -in the Center of the Universe, and all the Planets with the Sun and -Stars to move round it, is evidently false and absurd. For if this -hypothesis were true, Mercury and Venus could never be hid behind the -Sun, as their Orbits are included within the Sun’s: and again, these two -Planets would always move direct, and be as often in Opposition to the -Sun as in Conjunction with him. But the contrary of all this is true: -for they are just as often behind the Sun as before him, appear as often -to move backwards as forwards, and are so far from being seen at any -time in the side of the Heavens opposite to the Sun, that they were -never seen a quarter of a circle in the Heavens distant from him. - -[Sidenote: Appearances of Mercury and Venus.] - -141. These two Planets, when viewed with a good telescope, appear in all -the various shapes of the Moon; which is a plain proof that they are -enlightened by the Sun, and shine not by any light of their own: for if -they did, they would constantly appear round as the Sun does; and could -never be seen like dark spots upon the Sun when they pass directly -between him and us. Their regular Phases demonstrate them to be -Spherical bodies; as may be shewn by the following experiment. - -[Sidenote: Experiment to prove they are round.] - -Hang an ivory ball by a thread, and let any Person move it round the -flame of a candle, at two or three yards distance from your Eye: when -the ball is beyond the candle, so as to be almost hid by the flame, it’s -enlightened side will be towards you, and appear round like the Full -Moon: When the ball is between you and the candle, it’s enlightened side -will disappear, as the Moon does at the Change: When it is half way -between these two positions, it will appear half illuminated, like the -Moon in her Quarters: But in every other place between these positions, -it will appear more or less horned or gibbous. If this experiment be -made with a circular plate which has a flat surface, you may make it -appear fully enlightened, or not enlightened at all; but can never make -it seem either horned or gibbous. - -[Sidenote: PLATE II. - - Experiment to represent the motions of Mercury and Venus.] - -142. If you remove about six or seven yards from the candle, and place -yourself so that it’s flame may be just about the height of your eye, -and then desire the other person to move the ball slowly round the -candle as before, keeping it as near of an equal height with the flame -as he possibly can, the ball will appear to you not to move in a circle, -but rather to vibrate backward and forward like a pendulum; moving -quickest when it is directly between you and the candle, and when -directly beyond it; and gradually slower as it goes farther to the right -or left side of the flame, until it appears at the greatest distance -from the flame; and then, though it continues to move with the same -velocity, it will seem to stand still for a moment. In every Revolution -it will shew all the above Phases § 141; and if two balls, a smaller and -a greater, be moved in this manner round the candle, the smaller ball -being kept nearest the flame, and carried round almost three times as -often as the greater, you will have a tolerably good representation of -the apparent Motions of Mercury and Venus; especially, if the bigger -ball describes a circle almost twice as large in diameter as the circle -described by the lesser. - -[Sidenote: Fig. III. - - The elongations or digressions of Mercury from the Sun. - - PLATE II.] - -143. Let _ABCDE_ be a part or segment of the visible Heavens, in which -the Sun, Moon, Planets, and Stars appear to move at the same distance -from the Earth _E_. For there are certain limits, beyond which the eye -cannot judge of different distances; as is plain from the Moon’s -appearing to be no nearer to us than the Sun and Stars are. Let the -circle _fghiklmno_ be the Orbit in which Mercury _m_ moves round the Sun -_S_, according to the order of the letters. When Mercury is at _f_, he -disappears to the Earth at _E_, because his enlightened side is turned -from it; unless he be then in one of his Nodes § 20, 25; in which case, -he will appear like a dark spot upon the Sun. When he is at _g_ in his -Orbit, he appears at _B_ in the Heavens, westward of the Sun _S_, which -is seen at _C_: when at _h_, he appears at _A_, at his greatest western -elongation or distance from the Sun; and then seems to stand still. But, -as he moves from _h_ to _i_, he appears to go from _A_ to _B_; and seems -to be in the same place when at _i_ as when he was at _g_, only not near -so big: at _k_ he is hid from the Earth _E_ by the Sun _S_; being then -in his superiour Conjunction. In going from _k_ to _l_, he appears to -move from _C_ to _D_; and when he is at _n_, he appears stationary at -_E_; being seen as far east from the Sun then, as he was west from him -at _A_. In going from _n_ to _o_ in his Orbit, he seems to go back again -in the Heavens, from _E_ to _D_; and is seen in the same place (with -respect to the Sun) at _o_ as when he was at _l_; but of a larger -diameter at _o_, because he is then nearer the Earth _E_: and when he -comes to _f_, he again passes by the Sun, and disappears as before. In -going from _n_ to _h_ in his Orbit, he seems to go backward in the -Heavens from _E_ to _A_; and in going from _h_ to _n_, he seems to go -forward from _A_ to _E_. As he goes on from _f_ a little of his -enlightened side at _g_ is seen from _E_; at _h_ he appears half full, -because half of his enlightened side is seen; at _i_, gibbous, or more -than half full; and at _k_ he would appear quite full, were he not hid -from the Earth _E_ by the Sun _S_. At _l_ he appears gibbous again; at -_n_ half decreased, at _o_ horned, and at _f_ new like the Moon at her -Change. He goes sooner from his eastern station at _n_ to his western -station at _h_ than from _h_ to _n_ again; because he goes through less -than half his Orbit in the former case, and more in the latter. - -[Sidenote: Fig. III. - - The Elongations and Phases of Venus. - - The greatest Elongations of Mercury and Venus.] - -144. In the same Figure, let _FGHIKLMN_ be the Orbit in which Venus _v_ -moves round the Sun _S_, according to the order of the letters: and let -_E_ be the Earth as before. When Venus is at _F_ she is in her inferiour -Conjunction; and disappears like the New Moon because her dark side is -toward the Earth. At _G_ she appears half enlightened to the Earth, like -the Moon in her first quarter: at _h_ she appears gibbous; at _I_, -almost full; her enlightened side being then nearly towards the Earth: -at _K_, she would appear quite full to the Earth _E_; but is hid from it -by the Sun _S_: at _L_, she appears upon the decrease, or gibbous; at -_M_, more so; at _N_, only half enlightened; and at _F_ she disappears -again. In moving from _N_ to _G_, she seems to go backward in the -Heavens; and from _G_ to _N_, forward: but, as she describes a much -greater portion of her Orbit in going from _G_ to _N_ than from _N_ to -_G_, she appears much longer direct than retrograde in her motion. At -_N_ and _G_ she appears stationary; as Mercury does at _n_ and _h_. -Mercury, when stationary seems to be only 28 degrees from the Sun; and -Venus when so, 47; which is a demonstration that Mercury’s Orbit is -included within Venus’s, and Venus’s within the Earth’s. - -[Sidenote: Morning and Evening Star, what.] - -145. Venus, from her superiour Conjunction at _K_ to her inferiour -Conjunction at _F_ is seen on the east side of the Sun _S_ from the -Earth. _E_; and therefore she shines in the Evening after the Sun sets, -and is called _the Evening Star_: for, the Sun being then to the -westward of Venus, he must set first. From her inferiour Conjunction to -her superiour, she appears on the west side of the Sun; and therefore -rises before him, for which reason she is called _the Morning Star_. -When she is about _N_ or _G_, she shines so bright, that bodies cast -shadows in the night-time. - -[Sidenote: PLATE II. - - The stationary places of the Planets variable.] - -146. If the Earth kept always at _E_, it is evident that the Stationary -places of Mercury and Venus would always be in the same points of the -Heavens where they were before. For example; whilst Mercury _m_ goes -from _h_ to _n_, according to the order of the letters, he appears to -describe the arc _ABCDE_ in the Heavens, direct: and whilst he goes from -_n_ to _h_, he seems to describe the same arc back again, from _E_ to -_A_, retrograde: always at _n_ and _h_ he appears stationary at the same -points _E_ and _A_ as before. But Mercury goes round his Orbit, from _f_ -to _f_ again, in 88 days; and yet there are 116 days from any one of his -Conjunctions, or apparent Stations, to the same again: and the places of -these Conjunctions and Stations are found to be about 114 degrees -eastward from the points of the Heavens where they were last before; -which proves, that the Earth has not kept all that time at _E_, but has -had a progressive motion in it’s Orbit from _E_ to _t_. Venus also -differs every time in the places of her Conjunctions and Stations; but -much more than Mercury; because, as Venus describes a much larger Orbit -than Mercury does, the Earth advances so much the farther in it’s annual -path before Venus comes round again. - -[Sidenote: The Elongations of all Saturn’s inferiour Planets as seen - from him.] - -147. As Mercury and Venus, seen from the Earth, have their respective -Elongations from the Sun, and Stationary places; so has the Earth, seen -from Mars; and Mars, seen from Jupiter; and Jupiter, seen from Saturn. -That is, to every superiour Planet, all the inferiour ones have their -Stations and Elongations; as Venus and Mercury have to the Earth. As -seen from Saturn, Mercury never goes above 2-1/2 degrees from the Sun; -Venus 4-1/3; the Earth 6; Mars 9-1/2; and Jupiter 33-1/4: so that -Mercury, as seen from the Earth, has almost as great a Digression or -Elongation from the Sun, as Jupiter seen from Saturn. - -[Sidenote: A proof of the Earth’s annual motion.] - -148. Because the Earth’s Orbit is included within the Orbits of Mars, -Jupiter, and Saturn, they are seen on all sides of the Heavens; and are -as often in Opposition to the Sun as in Conjunction with him. If the -Earth stood still, they would always appear direct in their motions, -never retrograde nor stationary. But they seem to go just as often -backward as forward; which, if gravity be allowed to exist, affords a -sufficient proof of the Earth’s annual motion. - -[Sidenote: Fig. III. - - PLATE II. - - General Phenomena of a superiour Planet to an inferiour.] - -149. As Venus and the Earth are superiour Planets to Mercury, they shew -much the same Appearances to him that Mars and Jupiter do to us. Let -Mercury _m_ be at _f_, Venus _v_ at _F_, and the Earth at _E_; in which -situation Venus hides the Earth from Mercury; but, being in opposition -to the Sun, she shines on Mercury with a full illumined Orb; though, -with respect to the Earth, she is in conjunction with the Sun and -invisible. When Mercury is at _f_, and Venus at _G_, her enlightened -side not being directly towards him, she appears a little gibbous; as -Mars does in a like situation to us: but, when Venus is at _I_, her -enlightened side is so much towards Mercury at _f_, that she appears to -him almost of a round figure. At _K_, Venus disappears to Mercury at -_f_, being then hid by the Sun; as all our superiour Planets are to us, -when in conjunction with the Sun. When Venus has, as it were, emerged -out of the Sun beams, as at _L_, she appears almost full to Mercury at -_f_; at _M_ and _N_, a little gibbous; quite full at _F_, and largest of -all; being then in opposition to the Sun, and consequently nearest to -Mercury at _f_; shining strongly on him in the night, because her -distance from him then is somewhat less than a fifth part of her -distance from the Earth, when she appears roundest to it between _I_ and -_K_, or between _K_ and _L_, as seen from the Earth _E_. Consequently, -when Venus is opposite to the Sun as seen from Mercury, she appears more -than 25 times as large to him as she does to us when at the fullest. Our -case is almost similar with respect to Mars, when he is opposite to the -Sun; because he is then so near the Earth, and has his whole enlightened -side towards it. But, because the Orbits of Jupiter and Saturn are very -large in proportion to the Earth’s, these two Planets appear much less -magnified at their Oppositions or diminished at their Conjunctions than -Mars does, in proportion to their mean apparent Diameters. - - - - - CHAP. VII. - - _The physical Causes of the Motions of the Planets. The Excentricities - of their Orbits. The Times in which the Action of Gravity would bring -them to the Sun._ ARCHIMEDES_’s ideal Problem for moving the Earth. The - World not eternal._ - - -[Sidenote: Gravitation and Projection. - - Fig. IV. - - PLATE II. - - Circular Orbits. - - Fig. IV.] - -150. From the uniform projectile motion of bodies in straight lines, and -the universal power of attraction, arises the curvilineal motions of all -the Heavenly bodies. If the body _A_ be projected along the right line -_ABX_, in open Space, where it meets with no resistance, and is not -drawn aside by any other power, it will for ever go on with the same -velocity, and in the same direction. For, the force which moves it from -_A_ to _B_ in any given time, will carry it from _B_ to _X_ in as much -more time; and so on, there being nothing to obstruct or alter it’s -motion. But if, when this projectile force has carried it, suppose to -_B_, the body _S_ begins to attract it, with a power duly adjusted, and -perpendicular to it’s motion at _B_, it will then be drawn from the -straight line _ABX_, and forced to revolve about _S_ in the Circle -_BYTU_. When the body _A_ comes to _U_, or any other part of it’s Orbit, -if the small body _u_, within the sphere of _U_’s attraction, be -projected as in the right line _Z_, with a force perpendicular to the -attraction of _U_, then _u_ will go round _U_ in the Orbit _W_, and -accompany it in it’s whole course round the body _S_. Here, _S_ may -represent the Sun, _U_ the Earth, and _u_ the Moon. - - -151. If a Planet at _B_ gravitates, or is attracted, toward the Sun, so -as to fall from _B_ to _y_ in the time that the projectile force would -have carried it from _B_ to _X_, it will describe the curve _BY_ by the -combined action of these two forces, in the same time that the -projectile force singly would have carried it from _B_ to _X_, or the -gravitating power singly have caused it to descend from _B_ to _y_; and -these two forces being duly proportioned, and perpendicular to one -another, the Planet obeying them both, will move in the circle -_BYTU_[30]. - -[Sidenote: Elliptical Orbits. - - PLATE II.] - -152. But if, whilst the projectile force carries the Planet from _B_ to -_b_, the Sun’s attraction (which constitutes the Planet’s gravitation) -should bring it down from _B_ to I, the gravitating power would then be -too strong for the projectile force; and would cause the Planet to -describe the curve _BC_. When the Planet comes to _C_, the gravitating -power (which always increases as the square of the distance from the Sun -_S_ diminishes) will be yet stronger for the projectile force; and by -conspiring in some degree therewith, will accelerate the Planet’s motion -all the way from _C_ to _K_; causing it to describe the arcs _BC_, _CD_, -_DE_, _EF_, &c. all in equal times. Having it’s motion thus accelerated, -it gains so much centrifugal force, or tendency to fly off at _K_ in the -line _Kk_, as overcomes the Sun’s attraction: and the centrifugal force -being too great to allow the Planet to be brought nearer the Sun, or -even to move round him in the Circle _Klmn_, &c. it goes off, and -ascends in the curve _KLMN_, &c. it’s motion decreasing as gradually -from _K_ to _B_ as it increased from _B_ to _K_, because the Sun’s -attraction acts now against the Planet’s projectile motion just as much -as it acted with it before. When the Planet has got round to _B_, it’s -projectile force is as much diminished from it’s mean state about _G_ or -_N_, as it was augmented at _K_; and so, the Sun’s attraction being more -than sufficient to keep the Planet from going off at _B_, it describes -the same Orbit over again, by virtue of the same forces or laws. - - -[Sidenote: Fig. IV. - - The Planets describe equal Areas in equal times.] - -153. A double projectile force will always balance a quadruple power of -gravity. Let the Planet at _B_ have twice as great an impulse from -thence towards _X_, as it had before: that is, in the same length of -time that it was projected from _B_ to _b_, as in the last example, let -it now be projected from _B_ to _c_; and it will require four times as -much gravity to retain it in it’s Orbit: that is, it must fall as far as -from _B_ to 4 in the time that the projectile force would carry it from -_B_ to _c_; otherwise it could not describe the curve _BD_, as is -evident by the Figure. But, in as much time as the Planet moves from _B_ -to _C_ in the higher part of it’s Orbit, it moves from _I_ to _K_ or -from _K_ to _L_ in the lower part thereof; because, from the joint -action of these two forces, it must always describe equal areas in equal -times, throughout it’s annual course. These Areas are represented by the -triangles _BSC_, _CSD_, _DSE_, _ESF_, &c. whose contents are equal to -one another, quite round the Figure. - -[Sidenote: A difficulty removed.] - -154. As the Planets approach nearer the Sun, and recede farther from -him, in every Revolution; there may be some difficulty in conceiving the -reason why the power of gravity, when it once gets the better of the -projectile force, does not bring the Planets nearer and nearer the Sun -in every Revolution, till they fall upon and unite with him. Or why the -projectile force, when it once gets the better of gravity, does not -carry the Planets farther and farther from the Sun, till it removes them -quite out of the sphere of his attraction, and causes them to go on in -straight lines for ever afterward. But by considering the effects of -these powers as described in the two last Articles, this difficulty will -be removed. Suppose a Planet at _B_ to be carried by the projectile -force as far as from _B_ to _b_, in the time that gravity would have -brought it down from _B_ to 1: by these two forces it will describe the -curve _BC_. When the Planet comes down to _K_, it will be but half as -far from the Sun _S_ as it was at _B_; and therefore, by gravitating -four times as strongly towards him, it would fall from _K_ to _V_ in the -same length of time that it would have fallen from _B_ to 1 in the -higher part of it’s Orbit, that is, through four times as much space; -but it’s projectile force is then so much increased at _K_, as would -carry it from _K_ to _k_ in the same time; being double of what it was -at _B_, and is therefore too strong for the tendency of the gravitating -power, either to draw the Planet to the Sun, or cause it to go round him -in the circle _Klmn_, &c. which would require it’s falling from _K_ to -_w_, through a greater space than gravity can draw it whilst the -projectile force is such as would carry it from _K_ to _k_: and -therefore the Planet ascends in it’s Orbit _KLMN_, decreasing in it’s -velocity for the cause already assigned in § 152. - - -[Sidenote: The Planetary Orbits elliptical. - - Their Excentricities.] - -155. The Orbits of all the Planets are Ellipses, very little different -from Circles: but the Orbits of the Comets are very long Ellipses; the -lower focus of them all being in the Sun. If we suppose the mean -distance (or middle between the greatest and least) of every Planet and -Comet from the Sun to be divided into 1000 equal parts, the -Excentricities of their Orbits, both in such parts and in _English_ -miles, will be as follows. Mercury’s, 210 parts, or 6,720,000 miles; -Venus’s, 7 parts, or 413,000 miles; the Earth’s, 17 parts, or 1,377,000 -miles; Mars’s, 93 parts, or 11,439,000 miles; Jupiter’s, 48 parts, or -20,352,000 miles; Saturn’s, 55 parts, or 42,735,000 miles. Of the -nearest of the three forementioned Comets, 1,458,000 miles; of the -middlemost, 2,025,000,000 miles; and of the outermost, 6,600,000,000. - -[Sidenote: The above laws sufficient for motions both in circular and - elliptic Orbits.] - -156. By the above-mentioned laws § 150 _& seq._ bodies will move in all -kinds of Ellipses, whether long or short, if the spaces they move in be -void of resistance. Only, those which move in the longer Ellipses, have -so much the less projectile force impressed upon them in the higher -parts of their Orbits; and their velocities, in coming down towards the -Sun, are so prodigiously increased by his attraction, that their -centrifugal forces in the lower parts of their Orbits are so great as to -overcome the Sun’s attraction there, and cause them to ascend again -towards the higher parts of their Orbits; during which time, the Sun’s -attraction acting so contrary to the motions of those bodies, causes -them to move slower and slower, until their projectile forces are -diminished almost to nothing; and then they are brought back again by -the Sun’s attraction, as before. - -[Sidenote: In what times the Planets would fall to the Sun by the power - of gravity.] - -157. If the projectile forces of all the Planets and Comets were -destroyed at their mean distances from the Sun, their gravities would -bring them down so, as that Mercury would fall to the Sun in 15 days 13 -hours; Venus in 39 days 17 hours; the Earth or Moon in 64 days 10 hours; -Mars in 121 days; Jupiter in 290; and Saturn in 767. The nearest Comet -in 13 thousand days; the middlemost in 23 thousand days; and the -outermost in 66 thousand days. The Moon would fall to the Earth in 4 -days 20 hours; Jupiter’s first Moon would fall to him in 7 hours, his -second in 15, his third in 30, and his fourth in 71 hours. Saturn’s -first Moon would fall to him in 8 hours; his second in 12, his third in -19, his fourth in 68 hours, and the fifth in 336. A stone would fall to -the Earth’s center, if there were an hollow passage, in 21 minutes 9 -seconds. Mr. WHISTON gives the following Rule for such Computations. -“[31]It is demonstrable, that half the Period of any Planet, when it is -diminished in the sesquialteral proportion of the number 1 to the number -2, or nearly in the proportion of 1000 to 2828, is the time that it -would fall to the Center of it’s Orbit.” This proportion is, when a -quantity or number contains another once and a half as much more. - - -[Sidenote: The prodigious attraction of the Sun and Planets.] - -158. The quick motions of the Moons of Jupiter and Saturn round their -Primaries, demonstrate that these two Planets have stronger attractive -powers than the Earth has. For, the stronger that one body attracts -another, the greater must be the projectile force, and consequently the -quicker must be the motion of that other body, to keep it from falling -to it’s primary or central Planet. Jupiter’s second Moon is 124 thousand -miles farther from Jupiter than our Moon is from us; and yet this second -Moon goes almost eight times round Jupiter whilst our Moon goes only -once round the Earth. What a prodigious attractive power must the Sun -then have, to draw all the Planets and Satellites of the System towards -him; and what an amazing power must it have required to put all these -Planets and Moons into such rapid motions at first! Amazing indeed to -us, because impossible to be effected by the strength of all the living -Creatures in an unlimited number of Worlds, but no ways hard for the -Almighty, whose Planetarium takes in the whole Universe! - -[Sidenote: ARCHIMEDES’s Problem for raising the Earth.] - -159. The celebrated ARCHIMEDES affirmed he could move the Earth if he -had a place to stand on to manage his machinery[32]. This assertion is -true in Theory, but, upon examination, will be found absolutely -impossible in fact, even though a proper place and materials of -sufficient strength could be had. - -The simplest and easiest method of moving a heavy body a little way is -by a lever or crow, where a small weight or power applied to the long -arm will raise a great weight on the short one. But then, the small -weight must move as much quicker than the great weight as the latter is -heavier than the former; and the length of the long arm of the lever to -the length of the short arm must be in the same proportion. Now, suppose -a man pulls or presses the end of the long arm with the force of 200 -pound weight, and that the Earth contains in round Numbers -4,000,000,000,000,000,000,000 or 4000 Trillions of cubic feet, each at a -mean rate weighing 100 pound; and that the prop or center of motion of -the lever is 6000 miles from the Earth’s center: in this case, the -length of the lever from the _Fulcrum_ or center of motion to the moving -power or weight ought to be 12,000,000,000,000,000,000,000,000 or 12 -Quadrillions of miles; and so many miles must the power move, in order -to raise the Earth but one mile, whence ’tis easy to compute, that if -ARCHIMEDES or the power applied could move as swift as a cannon bullet, -it would take 27,000,000,000,000 or 27 Billions of years to raise the -Earth one inch. - -If any other machine, such as a combination of wheels and screws, was -proposed to move the Earth, the time it would require, and the space -gone through by the hand that turned the machine, would be the same as -before. Hence we may learn, that however boundless our Imagination and -Theory may be, the actual operations of man are confined within narrow -bounds; and more suited to our real wants than to our desires. - - -[Sidenote: Hard to determine what Gravity is.] - -160. The Sun and Planets mutually attract each other: the power by which -they do so we call _Gravity_. But whether this power be mechanical or -no, is very much disputed. We are certain that the Planets disturb one -another’s motions by it, and that it decreases according to the squares -of the distances of the Sun and Planets; as light, which is known to be -material, likewise does. Hence Gravity should seem to arise from the -agency of some subtile matter pressing towards the Sun and Planets, and -acting, like all mechanical causes, by contact. But on the other hand, -when we consider that the degree or force of Gravity is exactly in -proportion to the quantities of matter in those bodies, without any -regard to their bulks or quantity of surface, acting as freely on their -internal as external parts, it seems to surpass the power of mechanism; -and to be either the immediate agency of the Deity, or effected by a law -originally established and imprest on all matter by him. But some affirm -that matter, being altogether inert, cannot be impressed with any Law, -even by almighty Power: and that the Deity must therefore be constantly -impelling the Planets toward the Sun, and moving them with the same -irregularities and disturbances which Gravity would cause, if it could -be supposed to exist. But, if a man may venture to publish his own -thoughts, (and why should not one as well as another?) it seems to me no -greater absurdity, to suppose the Deity capable of superadding a Law, or -what Laws he pleases, to matter, than to suppose him capable of giving -it existence at first. The manner of both is equally inconceivable to -us; but neither of them imply a contradiction in our ideas: and what -implies no contradiction is within the power of Omnipotence. Do we not -see that a human creature can prepare a bar of steel so as to make it -attract needles and filings of iron; and that he can put a stop to that -power or virtue, and again call it forth again as often as he pleases? -To say that the workman infuses any new power into the bar, is saying -too much; since the needle and filings, to which he has done nothing, -re-attract the bar. And from this it appears that the power was -originally imprest on the matter of which the bar, needle, and filings -are composed; but does not seem to act until the bar be properly -prepared by the artificer: somewhat like a rope coiled up in a ship, -which will never draw a boat or any other thing towards the ship, unless -one end be tied to it, and the other end to that which is to be hauled -up; and then it is no matter which end of the rope the sailors pull at, -for the rope will be equally stretched throughout, and the ship and boat -will move towards one another. To say that the Almighty has infused no -such virtue or power into the materials which compose the bar, but that -he waits till the operator be pleased to prepare it by due position and -friction, and then, when the needle or filings are brought pretty near -the bar, the Deity presses them towards it, and withdraws his hand -whenever the workman either for use, curiosity or whim, does what -appears to him to destroy the action of the bar, seems quite ridiculous -and trifling; as it supposes God not only to be subservient to our -inconstant wills, but also to do what would be below the dignity of any -rational man to be employed about. - -161. That the projectile force was at first given by the Deity is -evident. For, since matter can never put itself into motion, and all -bodies may be moved in any direction whatsoever; and yet all the Planets -both primary and secondary move from west to east, in planes nearly -coincident; whilst the Comets move in all directions, and in planes so -different from one another; these motions can be owing to no mechanical -cause of necessity, but to the free choice and power of an intelligent -Being. - -162. Whatever Gravity be, ’tis plain that it acts every moment of time: -for should it’s action cease, the projectile force would instantly carry -off the Planets in straight lines from those parts of their Orbits where -Gravity left them. But, the Planets being once put into motion, there is -no occasion for any new projectile force, unless they meet with some -resistance in their Orbits; nor for any mending hand, unless they -disturb one another too much by their mutual attractions. - -[Sidenote: The Planets disturb one another’s motion. - - The consequences thereof.] - -163. It is found that there are disturbances among the Planets in their -motions, arising from their mutual attractions when they are in the same -quarter of the Heavens; and that our years are not always precisely of -the same length[33]. Besides, there is reason to believe that the Moon -is somewhat nearer the Earth now than she was formerly; her periodical -month being shorter than it was in former ages. For, our Astronomical -Tables, which in the present Age shew the times of Solar and Lunar -Eclipses to great precision, do not answer so well for very ancient -Eclipses. Hence it appears, that the Moon does not move in a medium void -of all resistance, § 174; and therefore her projectile force being a -little weakened, whilst there is nothing to diminish her gravity, she -must be gradually approaching nearer the Earth, describing smaller and -smaller Circles round it in every revolution, and finishing her Period -sooner, although her absolute motion with regard to space be not so -quick now as it was formerly: and therefore, she must come to the Earth -at last; unless that Being, which gave her a sufficient projectile force -at the beginning, adds a little more to it in due time. And, as all the -Planets move in spaces full of æther and light, which are material -substances, they too must meet with some resistance. And therefore, if -their gravities are not diminished, nor their projectile forces -increased, they must necessarily approach nearer and nearer the Sun, and -at length fall upon and unite with him. - -[Sidenote: The World not eternal.] - -164. Here we have a strong philosophical argument against the eternity -of the World. For, had it existed from eternity, and been left by the -Deity to be governed by the combined actions of the above forces or -powers, generally called Laws, it had been at an end long ago. And if it -be left to them it must come to an end. But we may be certain that it -will last as long as was intended by it’s Author, who ought no more to -be found fault with for framing so perishable a work, than for making -man mortal. - - - - - CHAP. VIII. - - _Of Light. It’s proportional quantities on the different Planets. It’s - Refractions in Water and Air. The Atmosphere; it’s weight and - properties. The Horizontal Moon._ - - -[Sidenote: The amazing smallness of the particles of light.] - -165. Light consists of exceeding small particles of matter -issuing from a luminous body; as from a lighted candle such -particles of matter continually flow in all directions. Dr. -NIEWENTYT[34] computes, that in one second of time there flows -418,660,000,000,000,000,000,000,000,000,000,000,000,000,000 particles of -light out of a burning candle; which number contains at least -6,337,242,000,000 times the number of grains of sand in the whole Earth; -supposing 100 grains of sand to be equal in length to an inch, and -consequently, every cubic inch of the Earth to contain one million of -such grains. - -[Sidenote: The dreadful effects that would ensue from their being - larger.] - -166. These amazingly small particles, by striking upon our eyes, excite -in our minds the idea of light: and, if they were so large as the -smallest particles of matter discernible by our best microscopes, -instead of being serviceable to us, they would soon deprive us of sight -by the force arising from their immense velocity, which is above 164 -thousand miles every second[35], or 1,230,000 times swifter than the -motion of a cannon bullet. And therefore, if the particles of light were -so large, that a million of them were equal in bulk to an ordinary grain -of land, we durst no more open our eyes to the light than suffer sand to -be shot point blank against them. - -[Sidenote: How objects become visible to us. - - PLATE II.] - -167. When these small particles, flowing from the Sun or from a candle, -fall upon bodies, and are thereby reflected to our eyes, they excite in -us the idea of that body by forming it’s picture on the retina[36]. And -since bodies are visible on all sides, light must be reflected from them -in all directions. - -[Sidenote: The rays of Light naturally move in straight lines. - - A proof that they hinder not one another’s motions.] - -168. A ray of light is a continued stream of these particles, flowing -from any visible body in straight lines. That they move in straight, and -not in crooked lines, unless they be refracted, is evident from bodies -not being visible if we endeavour to look at them through the bore of a -bended pipe; and from their ceasing to be seen by the interposition of -other bodies, as the fixed Stars by the interposition of the Moon and -Planets, and the Sun wholly or in part by the interposition of the Moon, -Mercury, or Venus. And that these rays do not interfere, or jostle one -another out of their ways, in flowing from different bodies all around, -is plain from the following Experiment. Make a little hole in a thin -plate of metal, and set the plate upright on a table, facing a row of -lighted candles standing by one another; then place a sheet of paper or -pasteboard at a little distance from the other side of the plate, and -the rays of all the candles, flowing through the hole, will form as many -specks of light on the paper as there are candles before the plate, each -speck as distinct and large, as if there were only one candle to cast -one speck; which shews that the rays are no hinderance to each other in -their motions, although they all cross in the hole. - - -[Sidenote: Fig. XI. - - In what proportion light and heat decrease at any given - distance from the Sun. - - PLATE II.] - -169. Light, and therefore heat so far as it depends on the Sun’s rays (§ -85, towards the end) decreases in proportion to the squares of the -distances of the Planets from the Sun. This is easily demonstrated by a -Figure which, together with it’s description, I have taken from Dr. -SMITH’s Optics[37]. Let the light which flows from a point _A_, and -passes through a square hole _B_, be received upon a plane _C_, parallel -to the plane of the hole; or, if you please, let the figure _C_ be the -shadow of the plane _B_; and when the distance _C_ is double of _B_, the -length and breadth of the shadow _C_ will be each double of the length -and breadth of the plane _B_; and treble when _AD_ is treble of _AB_; -and so on: which may be easily examined by the light of a candle placed -at _A_. Therefore the surface of the shadow _C_, at the distance _AC_ -double of _AB_, is divisible into four squares, and at a treble -distance, into nine squares, severally equal to the square _B_, as -represented in the Figure. The light then which falls upon the plane -_B_, being suffered to pass to double that distance, will be uniformly -spread over four times the space, and consequently will be four times -thinner in every part of that space, and at a treble distance it will be -nine times thinner, and at a quadruple distance sixteen times thinner, -than it was at first; and so on, according to the increase of the square -surfaces _B_, _C_, _D_, _E_, built upon the distances _AB_, _AC_, _AD_, -_AE_. Consequently, the quantities of this rarefied light received upon -a surface of any given size and shape whatever, removed successively to -these several distances, will be but one quarter, one ninth, one -sixteenth of the whole quantity received by it at the first distance -_AB_. Or in general words, the densities and quantities of light, -received upon any given plane, are diminished in the same proportion as -the squares of the distances of that plane, from the luminous body, are -increased: and on the contrary, are increased in the same proportion as -these squares are diminished. - -[Sidenote: Why the Planets appear dimmer when viewed thro’ telescopes - than by the bare eye.] - -170. The more a telescope magnifies the disks of the Moon and Planets, -they appear so much dimmer than to the bare eye; because the telescope -cannot magnify the quantity of light, as it does the surface; and, by -spreading the same quantity of light over a surface so much larger than -the naked eye beheld, just so much dimmer must it appear when viewed by -a telescope than by the bare eye. - - -[Sidenote: Fig. VIII. - - Refraction of the rays of light.] - -171. When a ray of light passes out of one medium[38] into another, it -is refracted, or turned out of it’s first course, more or less, as it -falls more or less obliquely on the refracting surface which divides the -two mediums. This may be proved by several experiments; of which we -shall only give three for example’s sake. 1. In a bason _FGH_ put a -piece of money as _DB_, and then retire from it as to _A_, till the edge -of the bason at _E_ just hides the money from your sight: then, keeping -your head steady, let another person fill the bason gently with water. -As he fills it, you will see more and more of the piece _DB_; which will -be all in view when the bason is full, and appear as if lifted up to -_C_. For, the ray _AEB_, which was straight whilst the bason was empty, -is now bent at the surface of the water in _E_, and turned out of it’s -rectilineal course into the direction _ED_. Or, in other words, the ray -_DEK_, that proceeded in a straight line from the edge _D_ whilst the -bason was empty, and went above the eye at _A_, is now bent at _E_; and -instead of going on in the rectilineal direction _DEK_, goes in the -angled direction _DEA_, and by entering the eye at _A_ renders the -object _DB_ visible. Or, 2dly, place the bason where the Sun shines -obliquely, and observe where the shadow of the rim _E_ falls on the -bottom, as at _B_: then fill it with water, and the shadow will fall at -_D_; which proves, that the rays of light, falling obliquely on the -surface of the water, are refracted, or bent downwards into it. - -172. The less obliquely the rays of light fall upon the surface of any -medium, the less they are refracted; and if they fall perpendicularly -thereon, they are not refracted at all. For, in the last experiment, the -higher the Sun rises, the less will be the difference between the places -where the edge of the shadow falls, in the empty and full bason. And, -3dly, if a stick be laid over the bason, and the Sun’s rays be reflected -perpendicularly into it from a looking-glass, the shadow of the stick -will fall upon the same place of the bottom, whether the bason be full -or empty. - -173. The denser that any medium is, the more is light refracted in -passing through it. - - -[Sidenote: The Atmosphere. - - The Air’s compression and rarity at different heights.] - -174. The Earth is surrounded by a thin fluid mass of matter, called the -_Air_, or _Atmosphere_, which gravitates to the Earth, revolves with it -in it’s diurnal motion, and goes round the Sun with it every year. This -fluid is of an elastic or springy nature, and it’s lowermost parts being -pressed by the weight of all the Air above them, are squeezed the closer -together; and are therefore densest of all at the Earth’s surface, and -gradually rarer the higher up. “It is well known[39] that the Air near -the surface of our Earth possesses a space about 1200 times greater than -water of the same weight. And therefore, a cylindric column of Air 1200 -foot high is of equal weight with a cylinder of water of the same -breadth and but one foot high. But a cylinder of Air reaching to the top -of the Atmosphere is of equal weight with a cylinder of water about 33 -foot high[40]; and therefore if from the whole cylinder of Air, the -lower part of 1200 foot high is taken away, the remaining upper part -will be of equal weight with a cylinder of water 32 foot high; -wherefore, at the height of 1200 feet or two furlongs, the weight of the -incumbent Air is less, and consequently the rarity of the compressed Air -is greater than near the Earth’s surface in the ratio of 33 to 32. And -having this ratio we may compute the rarity of the Air at all heights -whatsoever, supposing the expansion thereof to be reciprocally -proportional to its compression; and this proportion has been proved by -the experiments of Dr. _Hooke_ and others. The result of the computation -I have set down in the annexed Table, in the first column of which you -have the height of the Air in miles, whereof 4000 make a semi-diameter -of the Earth; in the second the compression of the Air or the incumbent -weight; in the third it’s rarity or expansion, supposing gravity to -decrease in the duplicate ratio of the distances from the Earth’s -center. And the small numeral figures are here used to shew what number -of cyphers must be joined to the numbers expressed by the larger -figures, as 0.^{17}1224 for 0.000000000000000001224, and 26956^{15} for -26956000000000000000. - - +-----------------------------------------+ - | AIR’s | - | _________________/\ _________________ | - | / \ | - | Height. Compression. Expansion. | - +-----------+---------------+-------------+ - | 0 | 33 | 1 | - | 5 | 17.8515 | 1.8486 | - | 10 | 9.6717 | 3.4151 | - | 20 | 2.852 | 11.571 | - | 40 | 0.2525 | 136.83 | - | 400 | 0.^{17}1224 | 26956^{15} | - | 4000 | 0.^{105}4465 | 73907^{102} | - | 40000 | 0.^{192}1628 | 26263^{189} | - | 400000 | 0.^{210}7895 | 41798^{207} | - | 4000000 | 0.^{212}9878 | 33414^{209} | - | Infinite. | 0.^{212}6041 | 54622^{209} | - +-----------+---------------+-------------+ - -From this Table it appears that the Air in proceeding upwards is -rarefied in such manner, that a sphere of that Air which is nearest the -Earth but of one inch diameter, if dilated to an equal rarefaction with -that of the Air at the height of ten semi-diameters of the Earth, would -fill up more space than is contained in the whole Heavens on this side -the fixed Stars, according to the preceding computation of their -distance[41].” And it likewise appears that the Moon does not move in a -perfectly free and un-resisting medium; although the air at a height -equal to her distance, is at least 34000^{190} times thinner than at the -Earth’s surface; and therefore cannot resist her motion so as to be -sensible in many ages. - - -[Sidenote: It’s weight how found. - - PLATE II.] - -175. The weight of the Air, at the Earth’s surface, is found by -experiments made with the air-pump; and also by the quantity of mercury -that the Atmosphere balances in the barometer; in which, at a mean -state; the mercury stands 29-1/2 inches high. And if the tube were a -square inch wide, it would at that height contain 29-1/2 cubic inches of -mercury, which is just 15 pound weight; and so much weight of air every -square inch of the Earth’s surface sustains; and every square foot 144 -times as much, because it contains 144 square inches. Now as the Earth’s -surface contains about 199,409,400 square miles, it must be of no less -than 5,559,215,016,960,000 square feet; which, multiplied by 2016, the -number of pounds on every foot, amounts to 11,207,377,474,191,360,000; -or 11 trillion 207 thousand 377 billion 474 thousand 191 million and 360 -thousand pounds, for the weight of the whole Atmosphere. At this rate, a -middle sized man, whose surface may be about 14 square feet, is pressed -by 28,224 pound weight of Air all round; for fluids press equally up and -down and on all sides. But, because this enormous weight is equal on all -sides, and counterbalanced by the spring of the internal Air in our -blood vessels, it is not felt. - -[Sidenote: A common mistake about the weight of the Air.] - -176. Oftentimes the state of the Air is such that we feel ourselves -languid and dull; which is commonly thought to be occasioned by the -Air’s being foggy and heavy about us. But that the Air is then too -light, is evident from the mercury’s sinking in the barometer, at which -time it is generally found that the Air has not sufficient strength to -bear up the vapours which compose the Clouds: for, when it is otherwise, -the Clouds mount high, the Air is more elastic and weighty about us, by -which means it balances the internal spring of the Air within us, braces -up our blood-vessels and nerves, and makes us brisk and lively. - -[Sidenote: Without an Atmosphere the Heavens would always appear dark, - and we should have no twilight.] - -177. According to [42]Dr. KEILL, and other astronomical writers, it is -entirely owing to the Atmosphere that the Heavens appear bright in the -day-time. For, without an Atmosphere, only that part of the Heavens -would shine in which the Sun was placed: and if an observer could live -without Air, and should turn his back towards the Sun, the whole Heavens -would appear as dark as in the night, and the Stars would be seen as -clear as in the nocturnal sky. In this case, we should have no twilight; -but a sudden transition from the brightest sunshine to the blackest -darkness immediately after sun-set; and from the blackest darkness to -the brightest sun-shine at sun-rising; which would be extremely -inconvenient, if not blinding, to all mortals. But, by means of the -Atmosphere, we enjoy the Sun’s light, reflected from the aerial -particles, before he rises and after he sets. For, when the Earth by its -rotation has withdrawn the Sun from our sight, the Atmosphere being -still higher than we, has his light imparted to it; which gradually -decreases until he has got 18 degrees below the Horizon; and then, all -that part of the Atmosphere which is above us is dark. From the length -of twilight, the Doctor has calculated the height of the Atmosphere (so -far as it is dense enough to reflect any light) to be about 44 miles. -But it is seldom dense enough at two miles height to bear up the Clouds. - - -[Sidenote: It brings the Sun in view before he rises, and keeps him in - view after he sets.] - -178. The Atmosphere refracts the Sun’s rays so, as to bring him in sight -every clear day, before he rises in the Horizon; and to keep him in view -for some minutes after he is really set below it. For, at some times of -the year, we see the Sun ten minutes longer above the Horizon than he -would be if there were no refractions: and about six minutes every day -at a mean rate. - -[Sidenote: Fig. IX. - - PLATE II.] - -179. To illustrate this, let _IEK_ be a part of the Earth’s surface, -covered with the Atmosphere _HGFC_; and let _HEO_ be the[43] sensible -Horizon of an observer at _E_. When the Sun is at _A_, really below the -Horizon, a ray of light _AC_ proceeding from him comes straight to _C_, -where it falls on the surface of the Atmosphere, and there entering a -denser medium, it is turned out of its rectilineal course _ACdG_, and -bent down to the observer’s eye at _E_; who then sees the Sun in the -direction of the refracted ray _edE_, which lies above the Horizon, and -being extended out to the Heavens, shews the Sun at _B_ § 171. - -[Sidenote: Fig. IX.] - -180. The higher the Sun rises, the less his rays are refracted, because -they fall less obliquely on the surface of the Atmosphere § 172. Thus, -when the Sun is in the direction of the line _EfL_ continued, he is so -nearly perpendicular to the surface of the Earth at _E_, that his rays -are but very little bent from a rectilineal course. - -[Sidenote: The quantity of refraction.] - -181. The Sun is about 32-1/4 min. of a deg. in breadth, when at his mean -distance from the Earth; and the horizontal refraction of his rays is -33-3/4 min. which being more than his whole diameter, brings all his -Disc in view, when his uppermost edge rises in the Horizon. At ten deg. -height the refraction is not quite 5 min. at 20 deg. only 2 min. 26 -sec.; at 30 deg. but 1 min. 32 sec.; between which and the Zenith, it is -scarce sensible: the quantity throughout, is shewn by the annexed table, -calculated by Sir ISAAC NEWTON. - - +-------------------------------------------------+ - | | - | 182. _A_ TABLE _shewing the Refractions | - | of the Sun, Moon, and Stars; | - | adapted to their apparent Altitudes_. | - | | - +-------+---------++----+---------++----+---------+ - | Appar.| Refrac- ||Ap. | Refrac- ||Ap. | Refrac- | - | Alt. | tion. ||Alt.| tion. ||Alt.| tion. | - +-------+---------++----+---------++----+---------+ - | D. M. | M. S. || D. | M. S. || D. | M. S. | - +-------+---------++----+---------++----+---------+ - | 0 0 | 33 45 || 21 | 2 18 || 56 | 0 36 | - | 0 15 | 30 24 || 22 | 2 11 || 57 | 0 35 | - | 0 30 | 27 35 || 23 | 2 5 || 58 | 0 34 | - | 0 45 | 25 11 || 24 | 1 59 || 59 | 0 32 | - | 1 0 | 23 7 || 25 | 1 54 || 60 | 0 31 | - +-------+---------++----+---------++----+---------+ - | 1 15 | 21 20 || 26 | 1 49 || 61 | 0 30 | - | 1 30 | 19 46 || 27 | 1 44 || 62 | 0 28 | - | 1 45 | 18 22 || 28 | 1 40 || 63 | 0 27 | - | 2 0 | 17 8 || 29 | 1 36 || 64 | 0 26 | - | 2 30 | 15 2 || 30 | 1 32 || 65 | 0 25 | - +-------+---------++----+---------++----+---------+ - | 3 0 | 13 20 || 31 | 1 28 || 66 | 0 24 | - | 3 30 | 11 57 || 32 | 1 25 || 67 | 0 23 | - | 4 0 | 10 48 || 33 | 1 22 || 68 | 0 22 | - | 4 30 | 9 50 || 34 | 1 19 || 69 | 0 21 | - | 5 0 | 9 2 || 35 | 1 16 || 70 | 0 20 | - +-------+---------++----+---------++----+---------+ - | 5 30 | 8 21 || 36 | 1 13 || 71 | 0 19 | - | 6 0 | 7 45 || 37 | 1 11 || 72 | 0 18 | - | 6 30 | 7 14 || 38 | 1 8 || 73 | 0 17 | - | 7 0 | 6 47 || 39 | 1 6 || 74 | 0 16 | - | 7 30 | 6 22 || 40 | 1 4 || 75 | 0 15 | - +-------+---------++----+---------++----+---------+ - | 8 0 | 6 0 || 41 | 1 2 || 76 | 0 14 | - | 8 30 | 5 40 || 42 | 1 0 || 77 | 0 13 | - | 9 0 | 5 22 || 43 | 0 58 || 78 | 0 12 | - | 9 30 | 5 6 || 44 | 0 56 || 79 | 0 11 | - | 10 0 | 4 52 || 45 | 0 54 || 80 | 0 10 | - +-------+---------++----+---------++----+---------+ - | 11 0 | 4 27 || 46 | 0 52 || 81 | 0 9 | - | 12 0 | 4 5 || 47 | 0 50 || 82 | 0 8 | - | 13 0 | 3 47 || 48 | 0 48 || 83 | 0 7 | - | 14 0 | 3 31 || 49 | 0 47 || 84 | 0 6 | - | 15 0 | 3 17 || 50 | 0 45 || 85 | 0 5 | - +-------+---------++----+---------++----+---------+ - | 16 0 | 3 4 || 51 | 0 44 || 86 | 0 4 | - | 17 0 | 2 53 || 52 | 0 42 || 87 | 0 3 | - | 18 0 | 2 43 || 53 | 0 40 || 88 | 0 2 | - | 19 0 | 2 34 || 54 | 0 39 || 89 | 1 1 | - | 20 0 | 2 26 || 55 | 0 38 || 90 | 0 0 | - +-------+---------++----+---------++----+---------+ - -[Sidenote: PLATE II. - - The inconstancy of Refractions. - - A very remarkable case concerning refraction.] - -183. In all observations, to have the true altitude of the Sun, Moon, or -Stars, the refraction must be subtracted from the observed altitude. But -the quantity of refraction is not always the same at the same altitude; -because heat diminishes the air’s refractive power and density, and cold -increases both; and therefore no one table can serve precisely for the -same place at all seasons, nor even at all times of the same day; much -less for different climates: it having been observed that the horizontal -refractions are near a third part less at the Equator than at _Paris_, -as mentioned by Dr. SMITH in the 370th remark on his Optics, where the -following account is given of an extraordinary refraction of the -sun-beams by cold. “There is a famous observation of this kind made by -some _Hollanders_ that wintered in _Nova Zembla_ in the year 1596, who -were surprised to find, that after a continual night of three months, -the Sun began to rise seventeen days sooner than according to -computation, deduced from the Altitude of the Pole observed to be 76°: -which cannot otherwise be accounted for, than by an extraordinary -quantity of refraction of the Sun’s rays, passing thro’ the cold dense -air in that climate. KEPLER computes that the Sun was almost five -degrees below the Horizon when he first appeared; and consequently the -refraction of his rays was about nine times greater than it is with us.” - -184. The Sun and Moon appear of an oval figure as _FCGD_, just after -their rising, and before their setting: the reason is, that the -refraction being greater in the Horizon than at any distance above it, -the lowermost limb _G_ appears more elevated than the uppermost. But -although the refraction shortens the vertical Diameter _FG_, it has no -sensible effect on the horizontal Diameter _CD_, which is all equally -elevated. When the refraction is so small as to be imperceptible, the -Sun and Moon appear perfectly round, as _AEBF_. - - -[Sidenote: Our imagination cannot judge rightly of the distance of - inaccessible objects.] - -185. We daily observe, that the objects which appear most distinct are -generally those which are nearest to us; and consequently, when we have -nothing but our imagination to assist us in estimating of distances, -bright objects seem nearer to us than those which are less bright, or -than the same objects do when they appear less bright and worse defined, -even though their distance in both cases be the same. And as in both -cases they are seen under the same angle[44], our imagination naturally -suggests an idea of a greater distance between us and those objects -which appear fainter and worse defined than those which appear brighter -under the same Angles; especially if they be such objects as we were -never near to, and of whose real Magnitudes we can be no judges by -sight. - -[Sidenote: Nor always of those which are accessible.] - -186. But, it is not only in judging of the different apparent Magnitudes -of the same objects, which are better or worse defined by their being -more or less bright, that we may be deceived: for we may make a wrong -conclusion even when we view them under equal degrees of brightness, and -under equal Angles; although they be objects whose bulks we are -generally acquainted with, such as houses or trees: for proof of which, -the two following instances may suffice. - -[Sidenote: The reason assigned. - - PLATE II.] - -First, When a house is seen over a very broad river by a person standing -on low ground, who sees nothing of the river, nor knows of it -beforehand; the breadth of the river being hid from him, because the -banks seem contiguous, he loses the idea of a distance equal to that -breadth; and the house seems small, because he refers it to a less -distance than it really is at. But, if he goes to a place from which the -river and interjacent ground can be seen, though no farther from the -house, he then perceives the house to be at a greater distance than he -imagined; and therefore fancies it to be bigger than he did at first; -although in both cases it appears under the same Angle, and consequently -makes no bigger picture on the retina of his eye in the latter case than -it did in the former. Many have been deceived, by taking a red coat of -arms, fixed upon the iron gate in _Clare-Hall_ walks at _Cambridge_, for -a brick house at a much greater distance[45]. - -[Sidenote: Fig. XII.] - -Secondly, In foggy weather, at first sight, we generally imagine a small -house, which is just at hand, to be a great castle at a distance; -because it appears so dull and ill defined when seen through the Mist, -that we refer it to a much greater distance than it really is at; and -therefore, under the same Angle, we judge it to be much bigger. For, the -near object _FE_, seen by the eye _ABD_, appears under the same Angle -_GCH_, that the remote object _GHI_ does: and the rays _GFCN_ and _HECM_ -crossing one another at _C_ in the pupil of the eye, limit the size of -the picture _MN_ on the retina; which is the picture of the object _FE_, -and if _FE_ were taken away, would be the picture of the object _GHI_, -only worse defined; because _GHI_, being farther off, appears duller and -fainter than _FE_ did. But if a Fog, as _KL_, comes between the eye and -the object _FE_, it appears dull and ill defined like _GHI_; which -causes our imagination to refer _FE_ to the greater distance _CH_, -instead of the small distance _CE_ which it really is at. And -consequently, as mis-judging the distance does not in the least diminish -the Angle under which the object appears, the small hay-rick _FE_ seems -to be as big as _GHI_. - - -[Sidenote: Fig. IX. - - Why the Sun and Moon appear biggest in the Horizon.] - -187. The Sun and Moon appear bigger in the Horizon than at any -considerable height above it. These Luminaries, although at great -distances from the Earth, appear floating, as it were, on the surface of -our Atmosphere _HGFfeC_, a little way beyond the Clouds; of which, those -about _F_, directly over our heads at _E_, are nearer us than those -about _H_ or _e_ in the Horizon _HEe_. Therefore, when the Sun or Moon -appear in the Horizon at _e_, they are not only seen in a part of the -Sky which is really farther from us than if they were at any -considerable Altitude, as about _f_; but they are also seen through a -greater quantity of Air and Vapours at _e_ than at _f_. Here we have two -concurring appearances which deceive our imagination, and cause us to -refer the Sun and Moon to a greater distance at their rising or setting -about _e_, than when they are considerably high as at _f_: first, their -seeming to be on a part of the Atmosphere at _e_, which is really -farther than _f_ from a spectator at _E_; and secondly, their being seen -through a grosser medium when at _e_ than when at _f_; which, by -rendering them dimmer, causes us to imagine them to be at a yet greater -distance. And as, in both cases, they are seen[46] much under the same -Angle, we naturally judge them to be biggest when they seem farthest -from us; like the above-mentioned house § 186, seen from a higher -ground, which shewed it to be farther off than it appeared from low -ground; or the hay-rick, which appeared at a greater distance by means -of an interposing Fog. - -[Sidenote: Their Diameters are not less on the Meridian than in the - Horizon.] - -188. Any one may satisfy himself that the Moon appears under no greater -Angle in the Horizon than on the Meridian, by taking a large sheet of -paper, and rolling it up in the form of a Tube, of such a width, that -observing the Moon through it when she rises, she may, as it were, just -fill the Tube; then tie a thread round it to keep it of that size; and -when the Moon comes to the Meridian, and appears much less to the eye, -look at her again through the same Tube, and she will fill it just as -much, if not more, than she did at her rising. - -189. When the full Moon is in _perigeo_, or at her least distance from -the Earth, she is seen under a larger Angle, and must therefore appear -bigger than when she is Full at other times: and if that part of the -Atmosphere where she rises be more replete with vapours than usual, she -appears so much the dimmer; and therefore we fancy her to be still the -bigger, by referring her to an unusually great distance; knowing that no -objects which are very far distant can appear big unless they be really -so. - -[Illustration: Plate IIII. _J. Ferguson delin._ _J. Mynde Sculp._] - - - - - CHAP. IX. - - _The Method of finding the Distances of the Sun, Moon, and Planets._ - - -[Sidenote: PLATE IV.] - -190. Those who have not learnt how to take the [47]Altitude of any -Celestial Phenomenon by a common Quadrant, nor know any thing of Plain -Trigonometry, may pass over the first Article of this short Chapter, and -take the Astronomer’s word for it, that the distances of the Sun and -Planets are as stated in the first Chapter of this Book. But, to every -one who knows how to take the Altitude of the Sun, the Moon, or a Star, -and can solve a plain right-angled Triangle, the following method of -finding the distances of the Sun and Moon will be easily understood. - -[Sidenote: Fig I.] - -Let _BAG_ be one half of the Earth, _AC_ it’s semi-diameter, _S_ the -Sun, _m_ the Moon, and _EKOL_ a quarter of the Circle described by the -Moon in revolving from the Meridian to the Meridian again. Let _CRS_ be -the rational Horizon of an observer at _A_, extended to the Sun in the -Heavens, and _HAO_ his sensible Horizon; extended to the Moon’s Orbit. -_ALC_ is the Angle under which the Earth’s semi-diameter _AC_ is seen -from the Moon at _L_, which is equal to the Angle _OAL_, because the -right lines _AO_ and _CL_ which include both these Angles are parallel. -_ASC_ is the Angle under which the Earth’s semi-diameter _AC_ is seen -from the Sun at _S_, and is equal to the Angle _OAf_ because the lines -_AO_ and _CRS_ are parallel. Now, it is found by observation, that the -Angle _OAL_ is much greater than the Angle _OAf_; but _OAL_ is equal to -_ALC_, and _OAf_ is equal to _ASC_. Now, as _ASC_ is much less than -_ALC_, it proves that the Earth’s semi-diameter _AC_ appears much -greater as seen from the Moon at _L_ than from the Sun at _S_: and -therefore the Earth is much farther from the Sun than from the Moon[48]. -The Quantities of these Angles are determined by observation in the -following manner. - -[Sidenote: The Moon’s horizontal Parallax, what. - - The Moon’s distance determined.] - -Let a graduated instrument as _DAE_, (the larger the better) having a -moveable Index and Sight-holes, be fixed in such a manner, that it’s -plane surface may be parallel to the Plan of the Equator, and it’s edge -_AD_ in the Meridian: so that when the Moon is in the Equinoctial, and -on the Meridian at _E_, she may be seen through the sight-holes when the -edge of the moveable index cuts the beginning of the divisions at o, on -the graduated limb _DE_; and when she is so seen, let the _precise_ time -be noted. Now, as the Moon revolves about the Earth from the Meridian to -the Meridian again in 24 hours 48 minutes, she will go a fourth part -round it in a fourth part of that time, _viz._ in 6 hours 12 minutes, as -seen from _C_, that is, from the Earth’s center or Pole. But as seen -from _A_, the observer’s place on the Earth’s surface, the Moon will -seem to have gone a quarter round the Earth when she comes to the -sensible Horizon at _O_; for the Index through the sights of which she -is then viewed will be at _d_, 90 degrees from _D_, where it was when -she was seen at _E_. Now, let the exact moment when the Moon is seen at -_O_ (which will be when she is in or near the sensible Horizon) be -carefully noted[49], that it may be known in what time she has gone from -_E_ to _O_; which time subtracted from 6 hours 12 minutes (the time of -her going from _E_ to _L_) leaves the time of her going from _O_ to _L_, -and affords an easy method for finding the Angle _OAL_ (called _the -Moon’s horizontal Parallax_, which is equal to the Angle _ALC_) by the -following Analogy: As the time of the Moon’s describing the arc _EO_ is -to 90 degrees, so is 6 hours 12 minutes to the degrees of the Arc _DdE_, -which measures the Angle _EAL_; from which subtract 90 degrees, and -there remains the Angle _OAL_, equal to the Angle _ALC_, under which the -Earth’s Semi-diameter _AC_ is seen from the Moon. Now, since all the -Angles of a right-lined Triangle are equal to 180 degrees, or to two -right Angles, and the sides of a Triangle are always proportional to the -Sines of the opposite Angles, say, by the _Rule of Three_, as the Sine -of the Angle _ALC_ at the Moon _L_ is to it’s opposite side _AC_ the -Earth’s Semi-diameter, which is known to be 3985 miles, so is Radius, -_viz._ the Sine of 90 degrees, or of the right Angle _ACL_ to it’s -opposite side _AL_, which is the Moon’s distance at _L_ from the -observer’s place at _A_ on the Earth’s surface; or, so is the Sine of -the Angle _CAL_ to its opposite side _CL_, which is the Moon’s distance -from the Earth’s centre, and comes out at a mean rate to be 240,000 -miles. The Angle _CAL_ is equal to what _OAL_ wants of 90 degrees. - -[Sidenote: The Sun’s distance cannot be yet so exactly determined as the - Moon’s; - - How near the truth it may soon be determined.] - -191. The Sun’s distance from the Earth is found the same way, but with -much greater difficulty; because his horizontal Parallax, or the Angle -_OAS_ equal to the Angle _ASC_, is so small as, to be hardly -perceptible, being only 10 seconds of a minute, or the 360th part of a -degree. But the Moon’s horizontal Parallax, or Angle _OAL_ equal to the -Angle _ALC_, is very discernible; being 57ʹ 49ʺ, or 3469ʺ at it’s mean -state; which is more than 340 times as great as the Sun’s: and -therefore, the distances of the heavenly bodies being inversely as the -Tangents of their horizontal Parallaxes, the Sun’s distance from the -Earth is at least 340 times as great as the Moon’s; and is rather -understated at 81 millions of miles, when the Moon’s distance is -certainly known to be 240 thousand. But because, according to some -Astronomers, the Sun’s horizontal Parallax is 11 seconds, and according -to others only 10, the former Parallax making the Sun’s distance to be -about 75,000,000 of miles, and the latter 82,000,000; we may take it for -granted, that the Sun’s distance is not less than as deduced from the -former, nor more than as shewn by the latter: and every one who is -accustomed to make such observations, knows how hard it is, if not -impossible, to avoid an error of a second; especially on account of the -inconstancy of horizontal Refractions. And here, the error of one -second, in so small an Angle, will make an error of 7 millions of miles -in so great a distance as that of the Sun’s; and much more in the -distances of the superiour Planets. But Dr. HALLEY has shewn us how the -Sun’s distance from the Earth, and consequently the distances of all the -Planets from the Sun, may be known to within a 500th part of the whole, -by a Transit of Venus over the Sun’s Disc, which will happen on the 6th -of _June_, in the year 1761; till which time we must content ourselves -with allowing the Sun’s distance to be about 81 millions of miles, as -commonly stated by Astronomers. - -[Sidenote: The Sun proved to be much bigger than the Moon.] - -192. The Sun and Moon appear much about the same bulk: And every one who -understands Geometry knows how their true bulks may be deduced from the -apparent, when their real distances are known. Spheres are to one -another as the Cubes of their Diameters; whence, if the Sun be 81 -millions of miles from the Earth, to appear as big as the Moon, whose -distance does not exceed 240 thousand miles, he must, in solid bulk, be -42 millions 875 thousand times as big as the Moon. - -193. The horizontal Parallaxes are best observed at the Equator; 1. -Because the heat is so nearly equal every day, that the Refractions are -almost constantly the same. 2. Because the parallactic Angle is greater -there as at _A_ (the distance from thence to the Earth’s Axis being -greater,) than upon any parallel of Latitude, as _a_ or _b_. - - -[Sidenote: The relative distances of the Planets from the Sun are known - to great precision, though their real distances are not well - known.] - -194. The Earth’s distance from the Sun being determined, the distances -of all the other Planets from him are easily found by the following -analogy, their periods round him being ascertained by observation. As -the square of the Earth’s period round the Sun is to the cube of it’s -distance from him, so is the square of the period of any other Planet to -the cube of it’s distance, in such parts or measures as the Earth’s -distance was taken; see § 111. This proportion gives us the relative -mean distances of the Planets from the Sun to the greatest degree of -exactness; and they are as follows, having been deduced from their -periodical times, according to the law just mentioned, which was -discovered by KEPLER and demonstrated by Sir ISAAC NEWTON. - - - _Periodical Revolution to the same fixed Star in days and decimal parts - of a day._ - - Of Mercury Venus The Earth Mars Jupiter Saturn - - 87.9692 224.6176 365.2564 686.9785 4332.514 10759.275 - - _Relative mean distances from the Sun._ - - 38710 72333 100000 152369 520096 954006 - - _From these numbers we deduce, that if the Sun’s horizontal Parallax be 10ʺ, - the real mean distances of the Planets from the Sun in English miles are_ - - 31,742,200 59,313,060 82,000,000 124,942,580 426,478,720 782,284,920 - - _But if the Sun’s Parallax be 11ʺ their distances are no more than_ - - 29,032,500 54,238,570 75,000,000 114,276,750 390,034,500 715,504,500 - - Errors in distance a rising from the mistake of 1ʺ in the Sun’s Parallax - - 2,709,700 5,074,490 7,000,000 10,665,830 36,444,220 66,780,420 - -195. These last numbers shew, that although we have the relative -distances of the Planets from the Sun to the greatest nicety, yet the -best observers have not hitherto been able to ascertain their true -distances to within less than a twelfth part of what they really are. -And therefore, we must wait with patience till the 6th of _June_, A. D. -1761; wishing that the Sky may then be clear to all places where there -are good Astronomers and accurate instruments for observing the Transit -of Venus over the Sun’s Disc at that time: as it will not happen again, -so as to be visible in Europe, in less than 235 years after. - -[Sidenote: Why the celestial Poles seem to keep still in the same points - of the Heavens, notwithstanding the Earth’s motion round the - Sun.] - -196. The Earth’s Axis produced to the Stars, being carried [50]parallel -to itself during the Earth’s annual revolution, describes a circle in -the Sphere of the fixed Stars equal to the Orbit of the Earth. But this -Orbit, though very large in itself, if viewed from the Stars, would -appear no bigger than a point; and consequently, the circle described in -the Sphere of the Stars by the Axis of the Earth produced, if viewed -from the Earth, must appear but as a point; that is, it’s diameter -appears too little to be measured by observation: for Dr. BRADLEY has -assured us, that if it had amounted to a single second, or two at most, -he should have perceived it in the great number of observations he has -made, especially upon γ _Dragonis_; and that it seemed to him very -probable that the annual Parallax of this Star is not so great as a -single second: and consequently, that it is above 400 thousand times -farther from us than the Sun. Hence the celestial poles seem to continue -in the same points of the Heavens throughout the year; which by no means -disproves the Earth’s annual motion, but plainly proves the distance of -the Stars to be exceeding great. - -[Sidenote: The amazing velocity of light. - - PLATE IV.] - -197. The small apparent motion of the Stars § 113, discovered by that -great Astronomer, he found to be no ways owing to their annual Parallax -(for it came out contrary thereto) but to the Aberration of their light, -which can result from no known cause besides that of the Earth’s annual -motion; and as it agrees so exactly therewith, it proves beyond dispute -that the Earth has such a motion: for this Aberration compleats all it’s -various Phenomena every year; and proves that the velocity of star-light -is such as carries it through a space equal to the Sun’s distance from -us in 8 minutes 13 seconds of time. Hence, the velocity of light is -[51]10 thousand 210 times as great as the Earth’s velocity in it’s -Orbit; which velocity (from what we know already of the Earth’s distance -from the Sun) may be affected to be at least between 57 and 58 thousand -miles every hour: and supposing it to be 58000, this number multiplied -by the above 10210, gives 592 million 180 thousand miles for the hourly -motion of light: which last number divided by 3600, the number of -seconds in an hour, shews that light flies at the rate of more than 164 -thousand miles every second of time, or swing of a common clock -pendulum. - - - - - CHAP. X. - - _The Circles of the Globe described. The different lengths of days and - nights, and the vicissitudes of seasons, explained. The explanation of - the Phenomena of Saturn’s Ring concluded._ (See § 81 and 82.) - - -[Sidenote: Circles of the Sphere. - - Fig. II - - Equator, Tropics, Polar Circles, and Poles. - - Fig. II. - - Earth’s Axis. - - PLATE IV. - - Meridians.] - -198. If the reader be hitherto unacquainted with the principal circles -of the Globe, he should now learn to know them; which he may do -sufficiently for his present purpose in a quarter of an hour, if he sets -the ball of a terrestrial Globe before him, or looks at the Figure of -it, wherein these circles are drawn and named. The _Equator_ is that -great circle which divides the northern half of the Earth from the -southern. The _Tropics_ are lesser circles parallel to the Equator, and -each of them is 23-1/2 degrees from it; a degree in this sense being the -360th part of any great circle which divides the Earth into two equal -parts. The _Tropic of Cancer_ lies on the north side of the Equator, and -the _Tropic of Capricorn_ on the south. The _Arctic Circle_ has the -_North Pole_ for it’s center, and is just as far from the north Pole as -the Tropics are from the Equator: and the _Antarctic Circle_ (hid by the -supposed convexity of the Figure) is just as far from the _South Pole_, -every way round it. These Poles are the very north and south points of -the Globe: and all other places are denominated _northward_ or -_southward_ according to the side of the Equator they lie on, and the -Pole to which they are nearest. The Earth’s _Axis_ is a straight line -passing through the center of the Earth, perpendicular to the Equator, -and terminating in the Poles at it’s surface. This, in the real Earth -and Planets is only an imaginary line; but in artificial Globes or -Planets it is a wire by which they are supported, and turned round in -_Orreries_, or such like machines, by wheel-work. The circles 12. 1. 2. -3. 4, _&c._ are Meridians to all places they pass through; and we must -suppose thousands more to be drawn, because every place that is ever so -little to the east or west of any other place, has a different Meridian -from that other place. All the Meridians meet in the Poles; and whenever -the Sun’s center is passing over any Meridian, in his apparent motion -round the Earth, it is mid-day or noon to all places on that Meridian. - -[Sidenote: Zones.] - -199. The _broad Space_ lying between the Tropics, like a girdle -surrounding the Globe, is called the _torrid Zone_, of which the Equator -is in the middle, all around. The _Space_ between the Tropic of Cancer -and Arctic Circle is called the _North temperate Zone_. _That_ between -the Tropic of Capricorn and the Antarctic Circle, the _South temperate -Zone_. And the two _circular Spaces_ bounded by the Polar Circles are -the two _Frigid Zones_; denominated _north_ or _south_, from that Pole -which is in the center of the one or the other of them. - - -200. Having acquired this easy branch of knowledge, the learner may -proceed to make the following experiment with his terrestrial ball; -which will give him a plain idea of the diurnal and annual motions of -the Earth, together with the different lengths of days and nights, and -all the beautiful variety of seasons, depending on those motions. - -[Sidenote: Fig. III. - - A pleasant experiment shewing the different lengths of days - and nights, and the variety of seasons. - - Summer Solstice.] - -Take about seven feet of strong wire, and bend it into a circular form, -as _abcd_, which being viewed obliquely, appears elliptical as in the -Figure. Place a lighted candle on a table, and having fixed one end of a -silk thread _K_, to the north pole of a small terrestrial Globe _H_, -about three inches diameter, cause another person to hold the wire -circle so that it may be parallel to the table, and as high as the flame -of the candle _I_, which should be in or near the center. Then, having -twisted the thread as towards the left hand, that by untwisting it may -turn the Globe round eastward, or contrary to the way that the hands of -a watch move; hang the Globe by the thread within this circle, almost -contiguous to it; and as the thread untwists, the Globe (which is -enlightened half round by the candle as the Earth is by the Sun) will -turn round it’s Axis, and the different places upon it will be carried -through the light and dark Hemispheres, and have the appearance of a -regular succession of days and nights, as our Earth has in reality by -such a motion. As the Globe turns, move your hand slowly so as to carry -the Globe round the candle according to the order of the letters _abcd_, -keeping it’s center even with the wire circle; and you will perceive, -that the candle being still perpendicular to the Equator will enlighten -the Globe from pole to pole in it’s motion round the circle; and that -every place on the Globe goes equally through the light and the dark, as -it turns round by the untwisting of the thread, and therefore has a -perpetual Equinox. The Globe thus turning round represents the Earth -turning round it’s Axis; and the motion of the Globe round the candle -represents the Earth’s annual motion round the Sun, and shews, that if -the Earth’s Orbit had no inclination to it’s Axis, all the days and -nights of the year would be equally long, and there would be no -different seasons. But now, desire the person who holds the wire to hold -it obliquely in the position _ABCD_, raising the side ♋ just as much as -he depresses the side ♑, that the flame may be still in the plane of the -circle; and twisting the thread as before, that the Globe may turn round -it’s Axis the same way as you carry it round the candle; that is, from -west to east, let the Globe down into the lowermost part of the wire -circle at ♑, and if the circles be properly inclined, the candle will -shine perpendicularly on the Tropic of Cancer, and the _frigid Zone_, -lying within the _arctic_ or _north polar Circle_, will be all in the -light, as in the Figure; and will keep in the light let the Globe turn -round it’s Axis ever so often. From the Equator to the north polar -Circle all the places have longer days and shorter nights; but from the -Equator to the south polar Circle just the reverse. The Sun does not set -to any part of the north frigid Zone, as shewn by the candle’s shining -on it so that the motion of the Globe can carry no place of that Zone -into the dark: and at the same time the _south frigid Zone_ is involved -in darkness, and the turning of the Globe brings none of it’s places -into the light. If the Earth were to continue in the like part of it’s -Orbit, the Sun would never set to the inhabitants of the north frigid -Zone, nor rise to those of the south. At the Equator it would be always -equal day and night; and as the places are gradually more and more -distant from the Equator, towards the arctic Circle, they would have -longer days and shorter nights, whilst those on the south side of the -Equator would have their nights longer than their days. In this case -there would be continual summer on the north side of the Equator, and -continual winter on the south side of it. - -[Illustration: Plate V. - -_J. Ferguson delin._ _J. Mynde Sc._] - -[Sidenote: PLATE IV. - - Autumnal Equinox.] - -But as the Globe turns round it’s Axis, move your hand slowly forward so -as to carry the Globe from _H_ towards _E_, and the boundary of light -and darkness will approach towards the north Pole, and recede towards -the south Pole; the northern places will go through less and less of the -light, and the southern places through more and more of it; shewing how -the northern days decrease in length, and the southern days increase, -whilst the Globe proceeds from _H_ to _F_. When the Globe is at _E_, it -is at a mean state between the lowest and highest parts of it’s Orbit; -the candle is directly over the Equator, the boundary of light and -darkness just reaches to both the Poles, and all places on the Globe go -equally through the light and dark Hemispheres, shewing that the days -and nights are then equal at all places of the Earth, the Poles only -excepted; for the Sun is then setting to the north Pole, and rising to -the south Pole. - -[Sidenote: Winter Solstice.] - -Continue moving the Globe forward, and as it goes through the quarter -_A_, the north Pole recedes still farther into the dark Hemisphere, and -the south Pole advances more into the light, as the Globe comes nearer -to ♋; and when it comes there at _F_, the candle is directly over the -Tropic of Capricorn, the days are at the shortest, and nights at the -longest, in the northern Hemisphere, all the way from the Equator to the -arctic Circle; and the reverse in the southern Hemisphere from the -antarctic Circle; within which Circles it is dark to the north frigid -Zone and light to the south. - -[Sidenote: Vernal Equinox.] - -Continue both motions, and as the Globe moves through the quarter _B_, -the north Pole advances toward the light, and the south Pole recedes as -fast from it; the days lengthen in the northern Hemisphere, and shorten -in the southern; and when the Globe comes to _G_ the candle will be -again over the Equator (as when the Globe was at _E_) and the days and -nights will again be equal as formerly: and the north Pole will be just -coming into the light, the south Pole going out of it. - - -Thus we see the reason why the days lengthen and shorten from the -Equator to the polar Circles every year; why there is no day or night -for several turnings of the Earth, within the polar Circles; why there -is but one day and one night in the whole year at the Poles; and why the -days and nights are equally long all the year round at the Equator, -which is always equally cut by the circle bounding light and darkness. - - -[Sidenote: Remark. - - Fig. III. - - PLATE V.] - -201. The inclination of an Axis or Orbit is merely relative, because we -compare it with some other Axis or Orbit which we consider as not -inclined at all. Thus, our Horizon being level to us whatever place of -the Earth we are upon, we consider it as having no inclination; and yet, -if we travel 90 degrees from that place, we shall then have an Horizon -perpendicular to the former; but it will still be level to us. And, if -this Book be held so that the [52]Circle _ABCD_ be parallel to the -Horizon, both the Circle _abcd_, and the Thread or Axis _K_ will be -inclined to it. But if Book or Plate be held, so that the Thread be -perpendicular to the Horizon, then the Orbit _ABCD_ will be inclined to -the Thread, and the Orbit _abcd_ perpendicular to it, and parallel to -the Horizon. We generally consider the Earth’s annual Orbit as having no -inclination, and the Orbits of all the other Planets as inclined to it § -20. - - -202. Let us now take a view of the Earth in it’s annual course round the -Sun, considering it’s Orbit as having no inclination; and it’s Axis as -inclining 23-1/2 degrees from a line perpendicular to it’s Orbit, and -keeping the same oblique direction in all parts of it’s annual course; -or, as commonly termed, keeping always parallel to itself § 196. - -[Sidenote: Fig. I. - - A concise view of the seasons.] - -Let _a_, _b_, _c_, _d_, _e_, _f_, _g_, _h_ be the Earth in eight -different parts of it’s Orbit, equidistant from one another; _Ns_ it’s -Axis, _N_ the north Pole, _s_ the south Pole, and _S_ the Sun nearly in -the center of the Earth’s Orbit § 18. As the Earth goes round the Sun -according to the order of the letters _abcd_, &c. it’s Axis _Ns_ keeps -the same obliquity, and is still parallel to the line _MNs_. When the -Earth is at _a_, it’s north Pole inclines toward the Sun, and brings all -the northern places more into the light than at any other time of the -year. But when the Earth is at _e_ in the opposite time of the year, the -north Pole declines from the Sun, which occasions the northern places to -be more in the dark than in the light; and the reverse at the southern -places, as is evident by the Figure, which I have taken from Dr. LONG’s -Astronomy. When the Earth is either at _c_ or _g_, it’s Axis inclines -not either to or from the Sun, but lies sidewise to him; and then the -Poles are in the boundary of light and darkness; and the Sun, being -directly over the Equator, makes equal day and night at all places. When -the Earth is at _b_ it is half way between the Summer Solstice and -Harvest Equinox; when it is at _d_ it is half way from the Harvest -Equinox to the Winter Solstice; at _f_ half way from the Winter Solstice -to the Spring Equinox: and at _h_ half way from the Spring Equinox to -the Summer Solstice. - -[Sidenote: Fig. II. - - PLATE V. - - The Ecliptic. - - The seasons shewn in another view of the Earth, and it’s Orbit.] - -203. From this oblique view of the Earth’s Orbit, let us suppose -ourselves to be raised far above it, and placed just over it’s center -_S_, looking down upon it from it’s north pole; and as the Earth’s Orbit -differs but very little from a Circle, we shall have it’s figure in such -a view represented by the Circle _ABCDEFGH_. Let us suppose this Circle -to be divided into 12 equal parts called _Signs_, having their names -affixed to them; and each Sign into 30 equal parts called _Degrees_, -numbered 10, 20, 30, as in the outermost Circle of the Figure, which -represents the great Ecliptic in the Heavens. The Earth is shewn in -eight different positions in this Circle, and in each position _Æ_ is -the Equator, _T_ the Tropic of Cancer, the _dotted Circle_ the parallel -of _London_, _U_ the arctic or north polar Circle, and _P_ the north -Pole where all the Meridians or hour Circles meet § 198. As the Earth -goes round the Sun the north Pole keeps constantly towards one part of -the Heavens, as it keeps in the Figure towards the right hand side of -the Plate. - -[Sidenote: Vernal Equinox.] - -When the Earth is at the beginning of Libra, namely on the 20th of -_March_, in this Figure (as at _g_ in Fig. I.) the Sun _S_ as seen from -the Earth appears at the beginning of Aries in the opposite part of the -Heavens[53], the north Pole is just coming into the light, the Sun is -vertical to the Equator; which, together with the Tropic of Cancer, -parallel of _London_, and arctic Circle, are all equally cut by the -Circle bounding light and darkness, coinciding with the six o’clock hour -Circle, and therefore the days and nights are equally long at all -places: for every part of the Meridian _ÆTLa_ comes into the light at -six in the morning, and revolving with the Earth according to the order -of the hour-letters, goes into the dark at six in the evening. There are -24 Meridians or hour-Circles drawn on the Earth in this Figure, to shew -the time of Sun rising and setting at different Seasons of the Year. - -[Sidenote: Fig. II.] - -As the Earth moves in the Ecliptic according to the order of the letters -_ABCD_, &c. through the Signs Libra, Scorpio, and Sagittarius, the north -Pole comes more and more into the light; the days increase as the nights -decrease in length, at all places north of the Equator _Æ_; which is -plain by viewing the Earth at _b_ on the 5th of _May_, when it is in the -15th degree of Scorpio[54], and the Sun as seen from the Earth appears -in the 15th degree of Taurus. For then, the Tropic of Cancer _T_ is in -the light from a little after five in the morning till almost seven in -the evening; the parallel of _London_ from half an hour past four till -half an hour past seven; the polar Circle _U_ from three till nine; and -a large track round the north Pole _P_ has day all the 24 hours, for -many rotations of the Earth on it’s Axis. - -[Sidenote: Summer Solstice.] - -When the Earth comes to _c_, at the beginning of Capricorn, and the Sun -as seen from the Earth appears at the beginning of Cancer, on the 21st -of _June_, as in this Figure, it is in the position _a_ in Fig. I; and -it’s north Pole inclines toward the Sun, so as to bring all the north -frigid Zone into the light, and the northern parallels of Latitude more -into the light than the dark from the Equator to the polar Circles; and -the more so as they are farther from the Equator. The Tropic of Cancer -is in the light from five in the morning till seven at night, the -parallel of _London_ from a quarter before four till a quarter after -eight; and the polar Circle just touches the dark, so that the Sun has -only the lower half of his Disc hid from the inhabitants on that Circle -for a few minutes about midnight, supposing no inequalities in the -Horizon and no Refractions. - -[Sidenote: Autumnal Equinox. - - Winter Solstice.] - -A bare view of the Figure is enough to shew, that as the Earth advances -from Capricorn toward Aries, and the Sun appears to move from Cancer -toward Libra, the north Pole recedes toward the dark, which causes the -days to decrease, and the nights to increase in length, till the Earth -comes to Aries, and then they are equal as before; for the boundary of -light and darkness cut the Equator and all it’s parallels equally, or in -halves. The north pole then goes into the dark, and continues therein -until the Earth goes half way round it’s Orbit; or, from the 23d of -_September_ till the 20th of _March_. In the middle between these times, -_viz._ on the 22d of _December_, the north Pole is as far as it can be -in the dark, which is 23-1/2 degrees, equal to the inclination of the -Earth’s Axis from a perpendicular to it’s Orbit: and then, the northern -parallels are as much in the dark as they were in the light on the 21 of -_June_; the winter nights being as long as the summer days, and the -winter days as short as the summer nights. It is needless to multiply -words on this subject, as we shall have occasion to mention the seasons -again in describing the _Orrery_, § 439. Only this must be noted, that -all that has been said of the northern Hemisphere, the contrary must be -understood of the southern; for on different sides of the Equator the -seasons are contrary, because, when the northern Hemisphere inclines -toward the Sun the southern declines from him. - - -[Sidenote: The Phenomena of Saturn’s Ring. - - PLATE V.] - -204. As Saturn goes round the Sun, his obliquely posited ring, like our -Earth’s Axis, keeps parallel to itself, and is therefore turned edgewise -to the Sun twice in a Saturnian year, which is almost as long as 30 of -our years § 81. But the ring, though considerably broad, is too thin to -be seen when it is turned round edgewise to the Sun, at which time it is -also edgewise to the Earth; and therefore it disappears once in every -fifteen years to us. As the Sun shines half a year on the north pole of -our earth, then disappears to it, and shines as long on the south pole; -so, during one half of Saturn’s year the Sun shines on the north side of -his ring, then disappears to it, and shines as long on it’s south side. -When the Earth’s Axis inclines neither to nor from the Sun, but sidewise -to him, he instantly ceases to shine on one pole, and begins to -enlighten the other; and when Saturn’s Ring inclines neither to nor from -the Sun, but sidewise to him, he ceases to shine on the one side of it, -and begins to shine upon the other. - -[Sidenote: Fig. III.] - -Let _S_ be the Sun, _ABCDEFGH_ Saturn’s Orbit, and _IKLMNO_ the Earth’s -Orbit. Both Saturn and the Earth move according to the order of the -letters, and when Saturn is at _A_ his ring is turned edgewise to the -Sun _S_, and he is then seen from the Earth as if he had lost his ring, -let the Earth be in any part of it’s Orbit whatever, except between _N_ -and _O_; for whilst it describes that space, Saturn is apparently so -near the Sun as to be hid in his beams. As Saturn goes from _A_ to _C_ -his ring appears more and more open to the Earth: at _C_ the ring -appears most open of all; and seems to grow narrower and narrower as -Saturn goes from _C_ to _E_; and when he comes to _E_, the ring is again -turned edgewise both to the Sun and Earth: and as neither of it’s sides -are illuminated, it is invisible to us, because it’s edge is too thin to -be perceptible: and Saturn appears again as if he had lost his ring. But -as he goes from _E_ to _G_, his ring opens more and more to our view on -the under side; and seems just as open at _G_ as it was at _C_; and may -be seen in the night-time from the Earth in any part of it’s Orbit, -except about _M_, when the Sun hides the Planet from our view. As Saturn -goes from _G_ to _A_ his ring turns more and more edgewise to us, and -therefore it seems to grow narrower and narrower; and at _A_ it -disappears as before. Hence, while Saturn goes from _A_ to _E_ the Sun -shines on the upper side of his ring, and the under side is dark; but -whilst he goes from _E_ to _A_ the Sun shines on the under side of his -ring, and the upper side is dark. - -[Sidenote: Fig. I and III.] - -It may perhaps be imagined that this Article might have been placed more -properly after § 81 than here: but when the candid reader considers that -all the various Phenomena of Saturn’s Ring depend upon a cause similar -to that of our Earth’s seasons, he will readily allow that they are best -explained together; and that the two Figures serve to illustrate each -other. - -[Sidenote: PLATE VI. - - The Earth nearer the Sun in winter than in summer. - - Why the weather is coldest when the Earth is nearest the Sun.] - -205. The Earth’s Orbit being elliptical, and the Sun constantly keeping -in it’s lower Focus, which is 1,377,000 miles from the middle point of -the longer Axis, the Earth comes twice so much, or 2,754,000 miles -nearer the Sun at one time of the year than at another: for the Sun -appearing under a larger Angle in our winter than summer, proves that -the Earth is nearer the Sun in winter, (_see the Note on Art. 185_.) But -here, this natural question will arise, Why have we not the hottest -weather when the Earth is nearest the Sun? In answer it must be -observed, that the excentricity of the Earth’s Orbit, or 1 million 377 -miles bears no greater proportion to the Earth’s mean distance from the -Sun than 17 does to 1000; and therefore, this small difference of -distance cannot occasion any great difference of heat or cold. But the -principal cause of this difference is, that in winter the Sun’s rays -fall so obliquely upon us, that any given number of them is spread over -a much greater portion of the Earth’s surface where we live; and -therefore each point must then have fewer rays than in summer. Moreover, -there comes a greater degree of cold in the long winter nights, than -there can return of heat in so short days; and on both these accounts -the cold must increase. But in summer the Sun’s rays fall more -perpendicularly upon us, and therefore come with greater force, and in -greater numbers on the same place; and by their long continuance, a much -greater degree of heat is imparted by day than can fly off by night. - -[Sidenote: Fig. II.] - -206. That a greater number of rays fall on the same place, when they -come perpendicularly, than when they come obliquely on it, will appear -by the Figure. For, let _AB_ be a certain number of the Sun’s rays -falling on _CD_ (which, let us suppose to be _London_) on the 22d of -_June_: but, on the 22d of _December_, the line _CD_, or _London_; has -the oblique position _Cd_ to the same rays; and therefore scarce a third -part of them falls upon it, or only those between _A_ and _e_; all the -rest _eB_ being expended on the space _dP_, which is more than double -the length of _CD_ or _Cd_. Besides, those parts which are once heated, -retain the heat for some time; which, with the additional heat daily -imparted, makes it continue to increase, though the Sun declines toward -the south: and this is the reason why _July_ is hotter than _June_, -although the Sun has withdrawn from the summer Tropic; as we find it is -generally hotter at three in the afternoon, when the Sun has gone toward -the west, than at noon when he is on the Meridian. Likewise, those -places which are well cooled require time to be heated again; for the -Sun’s rays do not heat even the surface of any body till they have been -some time upon it. And therefore we find _January_ for the most part -colder than _December_, although the Sun has withdrawn from the winter -Tropic, and begins to dart his beams more perpendicularly upon us, when -we have the position _CF_. An iron bar is not heated immediately upon -being put into the fire, nor grows cold till some time after it has been -taken out. - - - - - CHAP. XI. - - _The Method of finding the Longitude by the Eclipses of Jupiter’s - Satellites: The amazing Velocity of Light demonstrated by these - Eclipses._ - - -[Sidenote: First Meridian, and Longitude of places, what.] - -207. Geographers arbitrarily choose to call the Meridian of some -remarkable place _the first Meridian_. There they begin their reckoning; -and just so many degrees and minutes as any other place is to the -eastward or westward of that Meridian, so much east or west Longitude -they say it has. A degree is the 360th part of a Circle, be it great or -small; and a minute the 60th part of a degree. The _English_ Geographers -reckon the Longitude from the Meridian of the Royal Observatory at -_Greenwich_, and the _French_ from the Meridian of _Paris_. - -[Sidenote: PLATE V. - - Fig. II. - - Hour Circles. - - An hour of time equal to 15 degrees of motion.] - -208. If we imagine twelve great Circles, one of which is the Meridian of -any given place, to intersect each other in the two Poles of the Earth, -and to cut the Equator _Æ_ at every 15th degree, they will be divided by -the Poles into 24 Semicircles which divide the Equator into 24 equal -parts; and as the Earth turns on it’s Axis, the planes of these -Semicircles come successively after one another every hour to the Sun. -As in an hour of time there is a revolution of 15 degrees of the -Equator, in a minute of time there will be a revolution of 15 minutes of -the Equator, and in a second of time a revolution of 15 seconds. There -are two tables annexed to this Chapter, for reducing mean solar time -into degrees and minutes of the terrestrial Equator; and also for -converting degrees and parts of the Equator into mean solar time. - -209. Because the Sun enlightens only one half of the Earth at once, as -it turns round it’s Axis he rises to some places at the same moments of -absolute Time that he sets to others; and when it is mid-day to some -places, it is mid-night to others. The XII on the middle of the Earth’s -enlightened side, next the Sun, stands for mid-day; and the opposite XII -on the middle of the dark side, for mid-night. If we suppose this Circle -of hours to be fixed in the plane of the Equinoctial, and the Earth to -turn round within it, any particular Meridian will come to the different -hours so, as to shew the true time of the day or night at all places on -that Meridian. Therefore, - -[Sidenote: And consequently to 15 degrees of Longitude. - - Lunar Eclipses useful in finding the Longitude.] - -210. To every place 15 degrees eastward from any given Meridian, it is -noon an hour sooner than on that Meridian; because their Meridian comes -to the Sun an hour sooner: and to all places 15 degrees westward it is -noon an hour later § 208, because their Meridian comes an hour later to -the Sun; and so on: every 15 degrees of motion causing an hour’s -difference in time. Therefore they who have noon an hour later than we, -have their Meridian, that is, their Longitude 15 degrees westward from -us; and they who have noon an hour sooner than we, have their Meridian -15 degrees eastward from ours: and so for every hour’s difference of -time 15 degrees difference of Longitude. Consequently, if the beginning -or ending of a Lunar Eclipse be observed, suppose at _London_, to be -exactly at mid-night, and in some other place at 11 at night, that place -is 15 degrees westward from the Meridian of _London_: if the same -Eclipse be observed at one in the morning at another place, that place -is 15 degrees eastward from the said Meridian. - -[Sidenote: Eclipses of Jupiter’s Satellites much better for that - purpose.] - -211. But as it is not easy to determine the exact moment either of the -beginning or ending of a Lunar Eclipse, because the Earth’s shadow -through which the Moon passes is faint and ill defined about the edges; -we have recourse to the Eclipses of Jupiter’s Satellites, which -disappear so instantaneously as they enter into Jupiter’s shadow, and -emerge so suddenly out of it, that we may fix the phenomenon to half a -second of time. The first or nearest Satellite to Jupiter is the most -advantageous for this purpose, because it’s motion is quicker than the -motion of any of the rest, and therefore it’s immersions and emersions -are more frequent. - - -[Sidenote: How to solve this important problem. - - PLATE V.] - -212. The _English_ Astronomers have made Tables for shewing the times of -the Eclipses of Jupiter’s Satellites to great precision, for the -Meridian of _Greenwich_. Now, let an observer, who has these Tables with -a good Telescope and a well-regulated Clock at any other place of the -Earth, observe the beginning or ending of an Eclipse of one of Jupiter’s -Satellites, and note the precise moment of time that he saw the -Satellite either immerge into, or emerge out of the shadow, and compare -that time with the time shewn by the Tables for _Greenwich_; then, 15 -degrees difference of Longitude being allowed for every hour’s -difference of time, will give the Longitude of that place from -_Greenwich_, as above § 210; and if there be any odd minutes of time, -for every minute a quarter of a degree, east or west must be allowed, as -the time of observation is before or after the time shewn by the Tables. -Such Eclipses are very convenient for this purpose at land, because they -happen almost every day; but are of no use at sea, because the rolling -of the ship hinders all nice telescopical observations. - -[Sidenote: Fig. II. - - Illustrated by an example.] - -213. To explain this by a Figure, let _J_ be Jupiter, _K_, _L_, _M_, _N_ -his four Satellites in their respective Orbits 1, 2, 3, 4; and let the -Earth be at _f_ (suppose in _November_, although that month is no -otherways material than to find the Earth readily in this scheme, where -it is shewn in eight different parts of it’s Orbit.) Let _Q_ be a place -on the Meridian of _Greenwich_, and _R_ a place on some other Meridian. -Let a person at _R_ observe the instantaneous vanishing of the first -Satellite _K_ into Jupiter’s shadow, suppose at three o’clock in the -morning; but by the Tables he finds the immersion of that Satellite to -be at midnight at _Greenwich_: he can then immediately determine, that -as there are three hours difference of time between _Q_ and _R_, and -that _R_ is three hours forwarder in reckoning than _Q_, it must be 45 -degrees of east Longitude from the Meridian of _Q_. Were this method as -practicable at sea as at land, any sailor might almost as easily, and -with equal certainty, find the Longitude as the Latitude. - -[Sidenote: Fig. II. - - We seldom see the beginning and end of the same Eclipse of - any of Jupiter’s Moons.] - -214. Whilst the Earth is going from _C_ to _F_ in it’s Orbit, only the -immersions of Jupiter’s Satellites into his shadow are generally seen; -and their emersions out of it while the Earth goes from _G_ to _B_. -Indeed, both these appearances may be seen of the second, third, and -fourth Satellite when eclipsed, whilst the Earth is between _D_ and _E_, -or between _G_ and _A_; but never of the first Satellite, on account of -the smallness of it’s Orbit and the bulk of Jupiter; except only when -Jupiter is directly opposite to the Sun; that is, when the Earth is at -_g_: and even then, strictly speaking, we cannot see either the -immersions or emersions of any of his Satellites, because his body being -directly between us and his conical shadow, his Satellites are hid by -his body a few moments before they touch his shadow; and are quite -emerged from thence before we can see them, as it were, just dropping -from him. And when the Earth is at _c_, the Sun being between it and -Jupiter hides both him and his Moons from us. - -In this Diagram, the Orbits of Jupiter’s Moons are drawn in true -proportion to his diameter; but, in proportion to the Earth’s Orbit they -are drawn 81 times too large. - -[Sidenote: PLATE VI. - - Jupiter’s conjunctions with the Sun, or oppositions to him, - are every year in different parts of the Heavens.] - -215. In whatever month of the year Jupiter is in conjunction with the -Sun, or in opposition to him, in the next year it will be a month later -at least. For whilst the Earth goes once round the Sun, Jupiter -describes a twelfth part of his Orbit. And therefore, when the Earth has -finished it’s annual period from being in a line with the Sun and -Jupiter, it must go as much forwarder as Jupiter has moved in that time, -to overtake him again: just like the minute hand of a watch, which must, -from any conjunction with the hour hand, go once round the dial-plate -and somewhat above a twelfth part more, to overtake the hour hand again. - - -[Sidenote: The surprising velocity of light.] - -216. It is found by observation, that when the Earth is between the Sun -and Jupiter, as at _g_, his Satellites are eclipsed about 8 minutes -sooner than they should be according to the Tables: and when the Earth -is at _B_ or _C_, these Eclipses happen about 8 minutes later than the -Tables predict them. Hence it is undeniably certain, that the motion of -light is not instantaneous, since it takes about 16-1/2 minutes of time -to go through a space equal to the diameter of the Earth’s Orbit, which -is 162 millions of miles in length: and consequently the particles of -light fly about 164 thousand 494 miles every second of time, which is -above a million of times swifter than the motion of a cannon bullet. And -as light is 16-1/2 minutes in travelling across the Earth’s Orbit, it -must be 8-1/4 minutes in coming from the Sun to us: therefore, if the -Sun were annihilated we should see him for 8-1/4 minutes after; and if -he were again created he would be 8-1/4 minutes old before we could see -him. - -[Sidenote: Fig. V. - - Illustrated by a Figure.] - -217. To illustrate this progressive motion of light, let _A_ and _B_ be -the Earth in two different parts of it’s Orbit, whose distance is 81 -millions of miles, equal to the Earth’s distance from the Sun _S_. It is -plain, that if the motion of light were instantaneous, the Satellite 1 -would appear to enter into Jupiter’s shadow _FF_ at the same moment of -time to a spectator in _A_ as to another in _B_. But by many years -observations it has been found, that the immersion of the Satellite into -the shadow is seen 8-1/4 minutes sooner when the Earth is at _B_, than -when it is at _A_. And so, as Mr. ROMER first discovered, the motion of -light is thereby proved to be progressive, and not instantaneous, as was -formerly believed. It is easy to compute in what time the Earth moves -from _A_ to _B_; for the chord of 60 degrees of any Circle is equal to -the Semidiameter of that Circle; and as the Earth goes through all the -360 degrees of it’s Orbit in a year, it goes through 60 of those degrees -in about 61 days. Therefore, if on any given day, suppose the first of -_June_, the Earth is at _A_, on the first of _August_ it will be at _B_: -the chord, or straight line _AB_, being equal to _DS_ the Radius of the -Earth’s Orbit, the same with _AS_ it’s distance from the Sun. - -218. As the Earth moves from _D_ to _C_, through the side _AB_ of it’s -Orbit, it is constantly meeting the light of Jupiter’s Satellites -sooner, which occasions an apparent acceleration of their Eclipses: and -as it moves through the other half _H_ of it’s Orbit, from _C_ to _D_, -it is receding from their light, which occasions an apparent retardation -of their Eclipses, because their light is then longer ere it overtakes -the Earth. - -219. That these accelerations of the immersions of Jupiter’s Satellites -into his shadow, as the Earth approaches towards Jupiter, and the -retardations of their emersions out of his shadow, as the Earth is going -from him, are not occasioned by any inequality arising from the motions -of the Satellites in excentric Orbits, is plain, because it affects them -all alike, in whatever parts of their Orbits they are eclipsed. Besides, -they go often round their Orbits every year, and their motions are no -way commensurate to the Earth’s. Therefore, a Phenomenon not to be -accounted for from the real motions of the Satellites, but so easily -deducible from the Earth’s motion, and so answerable thereto, must be -allowed to result from it. This affords one very good proof of the -Earth’s annual motion. - -220. TABLES for converting mean solar TIME into Degrees and Parts of the - terrestrial EQUATOR; and also for converting Degrees and Parts of the - EQUATOR into mean solar Time. - - +---------------------------------------------+ - | TABLE I. For converting Time into | - | Degrees and Parts of the Equator. | - +-----+-------+-----+---------+-----+---------+ - | | | *M. | D. M. | *M. | D. M. | - |Hours|Degrees| S. | M. S. | S. | M. S. | - | | | T. | S. T. | T. | S. T. | - +-----+-------+-----+---------+-----+---------+ - | 1 | 15 | 1 | 0 15 | 31 | 7 45 | - | 2 | 30 | 2 | 0 30 | 32 | 8 0 | - | 3 | 45 | 3 | 0 45 | 33 | 8 15 | - | 4 | 60 | 4 | 1 0 | 34 | 8 30 | - | 5 | 75 | 5 | 1 15 | 35 | 8 45 | - +-----+-------+-----+---------+-----+---------+ - | 6 | 90 | 6 | 1 30 | 36 | 9 0 | - | 7 | 105 | 7 | 1 45 | 37 | 9 15 | - | 8 | 120 | 8 | 2 0 | 38 | 9 30 | - | 9 | 135 | 9 | 2 15 | 39 | 9 45 | - | 10 | 150 | 10 | 2 30 | 40 | 10 0 | - +-----+-------+-----+---------+-----+---------+ - | 11 | 165 | 11 | 2 45 | 41 | 10 15 | - | 12 | 180 | 12 | 3 0 | 42 | 10 30 | - | 13 | 195 | 13 | 3 15 | 43 | 10 45 | - | 14 | 210 | 14 | 3 30 | 44 | 11 0 | - | 15 | 225 | 15 | 3 45 | 45 | 11 15 | - +-----+-------+-----+---------+-----+---------+ - | 16 | 240 | 16 | 4 0 | 46 | 11 30 | - | 17 | 255 | 17 | 4 15 | 47 | 11 45 | - | 18 | 270 | 18 | 4 30 | 48 | 12 0 | - | 19 | 285 | 19 | 4 45 | 49 | 12 15 | - | 20 | 300 | 20 | 5 0 | 50 | 12 30 | - +-----+-------+-----+---------+-----+---------+ - | 21 | 315 | 21 | 5 15 | 51 | 12 45 | - | 22 | 330 | 22 | 5 30 | 52 | 13 0 | - | 23 | 345 | 23 | 5 45 | 53 | 13 15 | - | 24 | 360 | 24 | 6 0 | 54 | 13 30 | - | 25 | 375 | 25 | 6 15 | 55 | 13 45 | - +-----+-------+-----+---------+-----+---------+ - | 26 | 390 | 26 | 6 30 | 56 | 14 0 | - | 27 | 405 | 27 | 6 45 | 57 | 14 15 | - | 28 | 420 | 28 | 7 0 | 58 | 14 30 | - | 29 | 435 | 29 | 7 15 | 59 | 14 45 | - | 30 | 450 | 30 | 7 30 | 60 | 15 0 | - +-----+-------+-----+---------+-----+---------+ - - +---------------------------------------------------+ - | TABLE II. For converting Degrees and | - | Parts of the Equator into Time. | - +-----+--------+-----+--------+-------+-----+-------+ - | *D. | H. M. | *D. | H. M. | | | | - | M. | M. S. | M. | M. S. |Degrees|Hours|Minutes| - | S. | S. T. | S. | S. T. | | | | - +-----+--------+-----+--------+-------+-----+-------+ - | 1 | 0 4 | 31 | 2 4 | 70 | 4 | 40 | - | 2 | 0 8 | 32 | 2 8 | 80 | 5 | 20 | - | 3 | 0 12 | 33 | 2 12 | 90 | 6 | 0 | - | 4 | 0 16 | 34 | 2 16 | 100 | 6 | 40 | - | 5 | 0 20 | 35 | 2 20 | 110 | 7 | 20 | - +-----+--------+-----+--------+-------+-----+-------+ - | 6 | 0 24 | 36 | 2 24 | 120 | 8 | 0 | - | 7 | 0 28 | 37 | 2 28 | 130 | 8 | 40 | - | 8 | 0 32 | 38 | 2 32 | 140 | 9 | 20 | - | 9 | 0 36 | 39 | 2 36 | 150 | 10 | 0 | - | 10 | 0 40 | 40 | 2 40 | 160 | 10 | 40 | - +-----+--------+-----+--------+-------+-----+-------+ - | 11 | 0 44 | 41 | 2 44 | 170 | 11 | 20 | - | 12 | 0 48 | 42 | 2 48 | 180 | 12 | 0 | - | 13 | 0 52 | 43 | 2 52 | 190 | 12 | 40 | - | 14 | 0 56 | 44 | 2 56 | 200 | 13 | 20 | - | 15 | 1 0 | 45 | 3 0 | 210 | 14 | 0 | - +-----+--------+-----+--------+-------+-----+-------+ - | 16 | 1 4 | 46 | 3 4 | 220 | 14 | 40 | - | 17 | 1 8 | 47 | 3 8 | 230 | 15 | 20 | - | 18 | 1 12 | 48 | 3 12 | 240 | 16 | 0 | - | 19 | 1 16 | 49 | 3 16 | 250 | 16 | 40 | - | 20 | 1 20 | 50 | 3 20 | 260 | 17 | 20 | - +-----+--------+-----+--------+-------+-----+-------+ - | 21 | 1 24 | 51 | 3 24 | 270 | 18 | 0 | - | 22 | 1 28 | 52 | 3 28 | 280 | 18 | 40 | - | 23 | 1 32 | 53 | 3 32 | 290 | 19 | 20 | - | 24 | 1 36 | 54 | 3 36 | 300 | 20 | 0 | - | 25 | 1 40 | 55 | 3 40 | 310 | 20 | 40 | - +-----+--------+-----+--------+-------+-----+-------+ - | 26 | 1 44 | 56 | 3 44 | 320 | 21 | 20 | - | 27 | 1 48 | 57 | 3 48 | 330 | 22 | 0 | - | 28 | 1 52 | 58 | 3 52 | 340 | 22 | 40 | - | 29 | 1 56 | 59 | 3 56 | 350 | 23 | 20 | - | 30 | 2 0 | 60 | 4 0 | 360 | 24 | 0 | - +-----+--------+-----+--------+-------+-----+-------+ - -These are the Tables mentioned in the 208th Article, and are so easy -that they scarce require any farther explanation than to inform the -reader, that if, in Table I. he reckons the columns marked with -Asterisks to be minutes of time, the other columns give the equatoreal -parts or motion in degrees and minutes; if he reckons the Asterisk -columns to be seconds, the others give the motion in minutes and seconds -of the Equator; if thirds, in seconds and thirds: And if in Table II. he -reckons the Asterisk columns to be degrees of motion, the others give -the time answering thereto in hours and minutes; if minutes of motion, -the time is minutes and seconds; if seconds of motion, the corresponding -time is given in seconds and thirds. An example in each case will make -the whole very plain. - - - EXAMPLE I. | EXAMPLE II. - | - In 10 hours 15 minutes 24 | In what time will 153 degrees - seconds 20 thirds, _Qu._ How | 51 minutes 5 seconds of the - much of the Equator revolves | Equator revolve through the - through the Meridian? | Meridian? - | - | - Deg. M. S. | H. M. S. T. - Hours 10 150 0 0 | Deg. { 150 10 0 0 0 - Min. 15 3 45 0 | { 3 12 0 0 - Sec. 24 6 0 | Min. 51 3 24 0 - Thirds 20 5 | Sec. 5 20 - ------------ | ------------ - _Answer_ 153 51 5 | _Answer_ 10 15 24 20 - - - - - CHAP. XII. - - _Of Solar and Sidereal Time._ - - -[Sidenote: Sidereal days shorter than solar days, and why.] - -221. The fixed Stars appear to go round the Earth in 23 hours 56 minutes -4 seconds, and the Sun in 24 hours: so that the Stars gain three minutes -56 seconds upon the Sun every day, which amounts to one diurnal -revolution in a year; and therefore, in 365 days as measured by the -returns of the Sun to the Meridian, there are 366 days as measured by -the Stars returning to it: the former are called _Solar Days_, and the -latter _Sidereal_. - -[Sidenote: PLATE III.] - -The diameter of the Earth’s Orbit is but a physical point in proportion -to the distance of the Stars; for which reason, and the Earth’s uniform -motion on it’s Axis, any given Meridian will revolve from any Star to -the same Star again in every absolute turn of the Earth on it’s Axis, -without the least perceptible difference of time shewn by a clock which -goes exactly true. - -If the Earth had only a diurnal motion, without an annual, any given -Meridian would revolve from the Sun to the Sun again in the same -quantity of time as from any Star to the same Star again; because the -Sun would never change his place with respect to the Stars. But, as the -Earth advances almost a degree eastward in it’s Orbit in the time that -it turns eastward round its Axis, whatever Star passes over the Meridian -on any day with the Sun, will pass over the same Meridian on the next -day when the Sun is almost a degree short of it; that is, 3 minutes 56 -seconds sooner. If the year contained only 360 days as the Ecliptic does -360 degrees, the Sun’s apparent place, so far as his motion is equable, -would change a degree every day; and then the sidereal days would be -just four minutes shorter than the solar. - -[Sidenote: Fig. II.] - -Let _ABCDEFGHIKLM_ be the Earth’s Orbit, in which it goes round the Sun -every year, according to the order of the letters, that is, from west to -east, and turns round it’s Axis the same way from the Sun to the Sun -again every 24 hours. Let _S_ be the Sun, and _R_ a fixed Star at such -an immense distance that the diameter of the Earth’s Orbit bears no -sensible proportion to that distance. Let _Nm_ be any particular -Meridian of the Earth, and _N_ a given point or place upon that -Meridian. When the Earth is at _A_, the Sun _S_ hides the Star _R_, -which would always be hid if the Earth never removed from _A_; and -consequently, as the Earth turns round it’s Axis, the point _N_ would -always come round to the Sun and Star at the same time. But when the -Earth has advanced, suppose a twelfth part of it’s Orbit from _A_ to -_B_, it’s motion round it’s Axis will bring the point _N_ a twelfth part -of a day or two hours sooner to the Star than to the Sun; for the Angle -_NBn_ is equal to the Angle _ASB_: and therefore, any Star which comes -to the Meridian at noon with the Sun when the Earth is at _A_, will come -to the Meridian at 10 in the forenoon when the Earth is at _B_. When the -Earth comes to _C_ the point _N_ will have the Star on it’s Meridian at -8 in the morning, or four hours sooner than it comes round to the Sun; -for it must revolve from _N_ to _n_, before it has the Sun in it’s -Meridian. When the Earth comes to _D_, the point _N_ will have the Star -on it’s Meridian at six in the morning, but that point must revolve six -hours more from _N_ to _n_, before it has mid-day by the Sun: for now -the Angle _ASD_ is a right Angle, and so is _NDn_; that is, the Earth -has advanced 90 degrees in it’s Orbit, and must turn 90 degrees on its -Axis to carry the point _N_ from the Star to the Sun: for the Star -always comes to the Meridian when _Nm_ is parallel to _RSA_; because -_DS_ is but a point in respect of _RS_. When the Earth is at _E_, the -Star comes to the Meridian at 4 in the morning; at _F_, at two in the -morning; and at _G_, the Earth having gone half round it’s Orbit, _N_ -points to the Star _R_ at midnight, being then directly opposite to the -Sun; and therefore, by the Earth’s diurnal motion the Star comes to the -Meridian 12 hours before the Sun. When the Earth is at _H_, the Star -comes to the Meridian at 10 in the evening; at _I_ it comes to the -Meridian at 8, that is, 16 hours before the Sun; at _K_ 18 hours before -him; at _L_ 20 hours; at _M_ 22; and at _A_ equally with the Sun again. - -A TABLE, shewing how much of the Celestial Equator passes over the - Meridian in any part of a mean SOLAR DAY; and how much the FIXED STARS - gain upon the mean SOLAR TIME every Day, for a Month. - - - +-----+-----------+-----+------------+-----+------------+ - | Time| Motion. | Time| Motion. |Time | Motion. | - | | | | | | | - +-----+-----------+-----+------------+-----+------------+ - |Hours| D. M. S. | *M. | D. M. S. | *M. | D. M. S. | - | | | S. | M. S. T. | S. | M. S. T. + - | | | T. | S. T. ʺʺ | T. | S. T. ʺʺ | - +-----+-----------+-----+------------+-----+------------+ - | 1 | 15 2 28 | 1 | 0 15 2 | 31 | 7 46 16 | - | 2 | 30 4 56 | 2 | 0 30 5 | 32 | 8 1 19 | - | 3 | 45 7 24 | 3 | 0 45 7 | 33 | 8 16 21 | - | 4 | 60 9 51 | 4 | 1 0 10 | 34 | 8 31 24 | - | 5 | 75 12 19 | 5 | 1 15 12 | 35 | 8 46 26 | - +-----+-----------+-----+------------+-----+------------+ - | 6 | 90 14 47 | 6 | 1 30 15 | 36 | 9 1 29 | - | 7 | 105 17 15 | 7 | 1 45 17 | 37 | 9 16 31 | - | 8 | 120 19 43 | 8 | 2 0 20 | 38 | 9 31 34 | - | 9 | 135 22 11 | 9 | 2 15 22 | 39 | 9 46 36 | - | 10 | 150 24 38 | 10 | 2 30 25 | 40 | 10 1 39 | - +-----+-----------+-----+------------+-----+------------+ - | 11 | 165 27 6 | 11 | 2 45 27 | 41 | 10 16 41 | - | 12 | 180 29 34 | 12 | 3 0 30 | 42 | 10 31 43 | - | 13 | 195 32 2 | 13 | 3 15 32 | 43 | 10 46 46 | - | 14 | 210 34 30 | 14 | 3 30 34 | 44 | 11 1 48 | - | 15 | 225 36 58 | 15 | 3 45 37 | 45 | 11 16 51 | - +-----+-----------+-----+------------+-----+------------+ - | 16 | 240 39 26 | 16 | 4 0 39 | 46 | 11 31 53 | - | 17 | 255 41 53 | 17 | 4 15 41 | 47 | 11 46 56 | - | 18 | 270 44 21 | 18 | 4 30 44 | 48 | 12 1 58 | - | 19 | 285 46 49 | 19 | 4 45 47 | 49 | 12 17 1 | - | 20 | 300 49 17 | 20 | 5 0 49 | 50 | 12 32 3 | - +-----+-----------+-----+------------+-----+------------+ - | 21 | 315 51 45 | 21 | 5 15 52 | 51 | 12 47 6 | - | 22 | 330 54 13 | 22 | 5 30 54 | 52 | 13 2 8 | - | 23 | 345 56 40 | 23 | 5 45 57 | 53 | 13 17 11 | - | 24 | 360 59 8 | 24 | 6 0 59 | 54 | 13 32 13 | - | 25 | 376 1 36 | 25 | 6 16 2 | 55 | 13 47 16 | - +-----+-----------+-----+------------+-----+------------+ - | 26 | 391 4 4 | 26 | 6 31 4 | 56 | 14 2 18 | - | 27 | 406 6 32 | 27 | 6 46 7 | 57 | 14 17 21 | - | 28 | 421 9 0 | 28 | 7 1 9 | 58 | 14 32 23 | - | 29 | 436 11 28 | 29 | 7 16 11 | 59 | 14 47 26 | - | 30 | 451 13 56 | 30 | 7 31 14 | 60 | 15 2 28 | - +-----+-----------+-----+------------+-----+------------+ - - Accelerations - of the - Fixed Stars. - +----+----------+ - | D. | H. M. S. | - +----+----------+ - | 1 | 0 3 56 | - | 2 | 0 7 52 | - | 3 | 0 11 48 | - | 4 | 0 15 44 | - | 5 | 0 19 39 | - +----+----------+ - | 6 | 0 23 35 | - | 7 | 0 27 31 | - | 8 | 0 31 27 | - | 9 | 0 35 23 | - | 10 | 0 39 19 | - +----+----------+ - | 11 | 0 43 15 | - | 12 | 0 47 11 | - | 13 | 0 51 7 | - | 14 | 0 55 3 | - | 15 | 0 58 58 | - +----+----------+ - | 16 | 1 2 54 | - | 17 | 1 6 50 | - | 18 | 1 10 46 | - | 19 | 1 14 42 | - | 20 | 1 18 38 | - +----+----------+ - | 21 | 1 22 34 | - | 22 | 1 26 30 | - | 23 | 1 30 26 | - | 24 | 1 34 22 | - | 25 | 1 38 17 | - +----+----------+ - | 26 | 1 42 13 | - | 27 | 1 46 9 | - | 28 | 1 50 5 | - | 29 | 1 54 1 | - | 30 | 1 57 57 | - +----+----------+ - -[Sidenote: PLATE III. - - An absolute Turn of the Earth on it’s Axis never finishes a - solar day. - - Fig. II.] - -222. Thus it is plain, that an absolute turn of the Earth on it’s Axis -(which is always completed when the same Meridian comes to be parallel -to it’s situation at any time of the day before) never brings the same -Meridian round from the Sun to the Sun again; but that the Earth -requires as much more than one turn on it’s Axis to finish a natural -day, as it has gone forward in that time; which, at a mean state is a -365th part of a Circle. Hence, in 365 days the Earth turns 366 times -round it’s Axis; and therefore, as a turn of the Earth on it’s Axis -compleats a sidereal day, there must be one sidereal day more in a year -than the number of solar days, be the number what it will, on the Earth, -or any other Planet. One turn being lost with respect to the number of -solar days in a year, by the Planet’s going round the Sun; just as it -would be lost to a traveller, who, in going round the Earth, would lose -one day by following the apparent diurnal motion of the Sun: and -consequently, would reckon one day less at his return (let him take what -time he would to go round the Earth) than those who remained all the -while at the place from which he set out. So, if there were two Earths -revolving equably on their Axes, and if one remained at _A_ until the -other travelled round the Sun from _A_ to _A_ again, _that_ Earth which -kept it’s place at _A_ would have it’s solar and sidereal days always of -the same length; and so, would have one solar day more than the other at -it’s return. Hence, if the Earth turned but once round it’s Axis in a -year, and if _that_ turn was made the same way as the Earth goes round -the Sun, there would be continual day on one side of the Earth, and -continual night on the other. - -[Sidenote: To know by the Stars whether a Clock goes true or not.] - -223. The first part of the preceding Table shews how much of the -celestial Equator passes over the Meridian in any given part of a mean -solar day, and is to be understood the same way as the Table in the -220th article. The latter part, intitled, _Accelerations of the fixed -Stars_, affords us an easy method of knowing whether or no our clocks -and watches go true: For if, through a small hole in a window-shutter, -or in a thin plate of metal fixed to a window, we observe at what time -any Star disappears behind a chimney, or corner of a house, at a little -distance; and if the same Star disappears the next night 3 minutes 56 -seconds sooner by the clock or watch; and on the second night, 7 minutes -52 seconds sooner; the third night 11 minutes 48 seconds sooner; and so -on, every night, as in the Table, which shews this difference for 30 -natural days, it is an infallible Sign that the machine goes true; -otherwise it does not go true; and must be regulated accordingly: and as -the disappearing of a Star is instantaneous, we may depend on this -information to half a second. [Illustration: Pl. VI. - -_J. Ferguson inv. et delin._ _J. Mynde Sc._] - - - - - CHAP. XIII. - - _Of the Equation of Time._ - - -[Sidenote: The Sun and Clocks equal only on four days of the year.] - -224. The Earth’s motion on it’s Axis being perfectly uniform, and equal -at all times of the year, the sidereal days are always precisely of the -same length; and so would the solar or natural days be, if the Earth’s -orbit were a perfect Circle, and it’s Axis perpendicular to it’s orbit. -But the Earth’s diurnal motion on an inclined Axis, and it’s annual -motion in an elliptic orbit, cause the Sun’s apparent motion in the -Heavens to be unequal: for sometimes he revolves from the Meridian to -the Meridian again in somewhat less than 24 hours, shewn by a well -regulated clock; and at other times in somewhat more: so that the time -shewn by an equal going clock and a true Sun-dial is never the same but -on the 15th of _April_, the 16th of _June_, the 31st of _August_, and -the 24th of _December_. The clock, if it goes equally and true all the -year round, will be before the Sun from the 24th of _December_ till the -15th of _April_; from that time till the 16th of _June_ the Sun will be -before the clock; from the 16th of _June_ till the 31st of _August_ the -clock will be again before the Sun; and from thence to the 24th of -_December_ the Sun will be faster than the clock. - -[Sidenote: Use of the Equation Table.] - -225. The Tables of the Equation of natural days, at the end of the next -Chapter, shew the time that ought to be pointed out by a well regulated -clock or watch every day of the year at the precise moment of solar -noon; that is, when the Sun’s centre is on the Meridian, or when a true -Sun-dial shews it to be precisely Twelve. Thus, on the 5th of _January_ -in Leap-year, when the Sun is on the Meridian, it ought to be 5 minutes -51 seconds past twelve by the clock; and on the 15th of _May_, when the -Sun is on the Meridian, the time by the clock should be but 55 minutes -57 seconds past eleven; in the former case, the clock is 5 minutes 51 -seconds beforehand with the Sun; and in the latter case, the Sun is 4 -minutes 3 seconds faster than the clock. The column at the right hand of -each month shews the daily difference of this equation, as it increases -or decreases. But without a Meridian Line, or a Transit-Instrument fixed -in the plane of the Meridian, we cannot set a Sun-dial true. - - -[Sidenote: How to draw a Meridian Line.] - -226. The easiest and most expeditious way of drawing a Meridian Line is -this: Make four or five concentric Circles, about a quarter of an inch -from one another, on a flat board about a foot in breadth; and let the -outmost Circle be but little less than the board will contain. Fix a pin -perpendicularly in the center, and of such a length that it’s whole -shadow may fall within the innermost Circle for at least four hours in -the middle of the day. The pin ought to be about an eighth part of an -inch thick, with a round blunt point. The board being set exactly level -in a place where the Sun shines, suppose from eight in the morning till -four in the afternoon, about which hours the end of the shadow should -fall without all the Circles; watch the times in the forenoon, when the -extremity of the shortening shadow just touches the several Circles, and -_there_ make marks. Then, in the afternoon of the same day, watch the -lengthening shadow, and where it’s end touches the several Circles in -going over them, make marks also. Lastly, with a pair of compasses, find -exactly the middle point between the two marks on any Circle, and draw a -straight line from the center to that point; which Line will be covered -at noon by the shadow of a small upright wire, which should be put in -the place of the pin. The reason for drawing several Circles is, that in -case one part of the day should prove clear, and the other part somewhat -cloudy, if you miss the time when the point of the shadow should touch -one Circle, you may perhaps catch it in touching another. The best time -for drawing a Meridian Line in this manner is about the middle of -summer; because the Sun changes his Declination slowest and his Altitude -fastest in the longest days. - -If the casement of a window on which the Sun shines at noon be quite -upright, you may draw a line along the edge of it’s shadow on the floor, -when the shadow of the pin is exactly on the Meridian Line of the board: -and as the motion of the shadow of the casement will be much more -sensible on the Floor, than that of the shadow of the pin on the board, -you may know to a few seconds when it touches the Meridian Line on the -floor, and so regulate your clock for the day of observation by that -line and the Equation Tables above-mentioned § 225. - - -[Sidenote: Equation of natural days explained.] - -227. As the Equation of time, or difference between the time shewn by a -well regulated Clock and a true Sun-dial, depends upon two causes, -namely, the obliquity of the Ecliptic, and the unequal motion of the -Earth in it, we shall first explain the effects of these causes -separately considered, and then the united effects resulting from their -combination. - -[Sidenote: PLATE VI. - - The first part of the Equation of time.] - -228. The Earth’s motion on it’s Axis being perfectly equable, or always -at the same rate, and the [55]plane of the Equator being perpendicular -to it’s Axis, ’tis evident that in equal times equal portions of the -Equator pass over the Meridian; and so would equal portions of the -Ecliptic if it were parallel to or coincident with the Equator. But, as -the Ecliptic is oblique to the Equator, the equable motion of the Earth -carries unequal portions of the Ecliptic over the Meridian in equal -times, the difference being proportionate to the obliquity; and as some -parts of the Ecliptic are much more oblique than others, those -differences are unequal among themselves. Therefore, if two Suns should -start either from the beginning of Aries or Libra, and continue to move -through equal arcs in equal times, one in the Equator, and the other in -the Ecliptic, the equatoreal Sun would always return to the Meridian in -24 hours time, as measured by a well regulated clock; but the Sun in the -Ecliptic would return to the Meridian sometimes sooner, and sometimes -later than the equatoreal Sun; and only at the same moments with him on -four days of the year; namely, the 20th of _March_, when the Sun enters -Aries; the 21st of _June_, when he enters Cancer; the 23d of -_September_, when he enters Libra; and the 21st of _December_, when he -enters Capricorn. But, as there is only one Sun, and his apparent motion -is always in the Ecliptic, let us henceforth call him the real Sun, and -the other which is supposed to move in the Equator the fictitious; to -which last, the motion of a well regulated clock always answers. - -[Sidenote: Fig. III.] - -Let _Z_♈_z_♎ be the Earth, _ZFRz_ it’s Axis, _abcde_ &c. the Equator, -_ABCDE_ &c. the northern half of the Ecliptic from ♈ to ♎ on the side of -the Globe next the eye, and _MNOP_ &c. the southern half on the opposite -side from ♎ to ♈. Let the points at _A_, _B_, _C_, _D_, _E_, _F_, &c. -quite round from ♈ to ♈ again bound equal portions of the Ecliptic, gone -through in equal times by the real Sun; and those at _a_, _b_, _c_, _d_, -_e_, _f_, &c. equal portions of the Equator described in equal times by -the fictitious Sun; and let _Z_♈_z_ be the Meridian. - -As the real Sun moves obliquely in the Ecliptic, and the fictitious Sun -directly in the Equator, with respect to the Meridian, a degree, or any -number of degrees, between ♈ and _F_ on the Ecliptic, must be nearer the -Meridian _Z_♈_z_, than a degree, or any corresponding number of degrees -on the Equator from ♈ to _f_; and the more so, as they are the more -oblique: and therefore the true Sun comes sooner to the Meridian whilst -he is in the quadrant ♈ _F_, than the fictitious Sun does in the -quadrant ♈ _f_; for which reason, the solar noon precedes noon by the -Clock, until the real Sun comes to _F_, and the fictitious to _f_; which -two points, being equidistant from the Meridian, both Suns will come to -it precisely at noon by the Clock. - -Whilst the real Sun describes the second quadrant of the Ecliptic -_FGHIKL_ from ♋ to ♎; he comes later to the Meridian every day, than the -fictitious Sun moving through the second quadrant of the Equator from -_f_ to ♎; for the points at _G_, _H_, _I_, _K_, and _L_ being farther -from the Meridian than their corresponding points at _g_, _h_, _i_, _k_, -and _l_, they must be later of coming to it: and as both Suns come at -the same moment to the point ♎, they come to the Meridian at the moment -of noon by the Clock. - -In departing from Libra, through the third quadrant, the real Sun going -through _MNOPQ_ towards ♑ at _R_, and the fictitious Sun through _mnopq_ -towards _r_, the former comes to the Meridian every day sooner than the -latter, until the real Sun comes to ♑, and the fictitious to _r_, and -then they both come to the Meridian at the same time. - -Lastly, as the real Sun moves equably through _STUVW_, from ♑ towards ♈; -and the fictitious Sun through _stuvw_, from _r_ towards ♈, the former -comes later every day to the Meridian than the latter, until they both -arrive at the point ♈, and then they make noon at the same time with the -clock. - - -[Sidenote: A Table of the Equation of Time depending on the Sun’s place - in the Ecliptic. - - PLATE VI.] - -229. The annexed Table shews how much the Sun is faster or slower than -the clock ought to be, so far as the difference depends upon the -obliquity of the Ecliptic; of which the Signs of the first and third -quadrants are at the head of the Table, and their Degrees at the left -hand; and in these the Sun is faster than the Clock: the Signs of the -second and fourth quadrants are at the foot of the Table, and their -degrees at the right hand; in all which the Sun is slower than the -Clock: so that entering the Table with the given Sign of the Sun’s place -at the head of the Table, and the Degree of his place in that Sign at -the left hand; or with the given Sign at the foot of the Table, and -Degree at the right hand; in the Angle of meeting is the number of -minutes and seconds that the Sun is faster or slower than the clock: or -in other words, the quantity of time in which the real Sun, when in that -part of the Ecliptic, comes sooner or later to the Meridian than the -fictitious Sun in the Equator. Thus, when the Sun’s place is ♉ Taurus 12 -degrees, he is 9 minutes 49 seconds faster than the clock; and when his -place is ♋ Cancer 18 degrees, he is 6 minutes 2 seconds slower. - - +---------------------------------------------+ - | _Sun faster than the Clock in_ | - +---------+--------+--------+--------+--------+ - | | ♈ | ♉ | ♊ | 1st Q. | - | | ♎ | ♏ | ♐ | 3d Q. | - + +--------+--------+--------+--------+ - | Degrees | ʹ ʺ | ʹ ʺ | ʹ ʺ | Deg. | - +---------+--------+--------+--------+--------+ - | 0 | 0 0 | 8 24 | 8 46 | 30 | - | 1 | 0 20 | 8 35 | 8 36 | 29 | - | 2 | 0 40 | 8 45 | 8 25 | 28 | - | 3 | 1 0 | 8 54 | 8 14 | 27 | - | 4 | 1 19 | 9 3 | 8 1 | 26 | - | 5 | 1 39 | 9 11 | 7 49 | 25 | - | 6 | 1 59 | 9 18 | 7 35 | 24 | - | 7 | 2 18 | 9 24 | 7 21 | 23 | - | 8 | 2 37 | 9 31 | 7 6 | 22 | - | 9 | 2 56 | 9 36 | 6 51 | 21 | - | 10 | 3 16 | 9 41 | 6 35 | 20 | - | 11 | 3 34 | 9 45 | 6 19 | 19 | - | 12 | 3 53 | 9 49 | 6 2 | 18 | - | 13 | 4 11 | 9 51 | 5 45 | 17 | - | 14 | 4 29 | 9 53 | 5 27 | 16 | - | 15 | 4 47 | 9 54 | 5 9 | 15 | - | 16 | 5 4 | 9 55 | 4 50 | 14 | - | 17 | 5 21 | 9 55 | 4 31 | 13 | - | 18 | 5 38 | 9 54 | 4 12 | 12 | - | 19 | 5 54 | 9 52 | 3 52 | 11 | - | 20 | 6 10 | 9 50 | 3 32 | 10 | - | 21 | 6 26 | 9 47 | 3 12 | 9 | - | 22 | 6 41 | 9 43 | 2 51 | 8 | - | 23 | 6 55 | 9 38 | 2 30 | 7 | - | 24 | 7 9 | 9 33 | 2 9 | 6 | - | 25 | 7 23 | 9 27 | 1 48 | 5 | - | 26 | 7 36 | 9 20 | 1 27 | 4 | - | 27 | 7 49 | 9 13 | 1 5 | 3 | - | 28 | 8 1 | 9 5 | 0 43 | 2 | - | 29 | 8 13 | 8 56 | 0 22 | 1 | - | 30 | 8 24 | 8 46 | 0 0 | 0 | - +---------+--------+--------+--------+--------+ - | 2d Q. | ♍ | ♌ | ♋ | Deg. | - | 4th Q. | ♓ | ♒ | ♑ | | - +---------+--------+--------+--------+--------+ - | _Sun slower than the Clock in_ | - +---------------------------------------------+ - -[Sidenote: Fig. III.] - -230. This part of the Equation of time may perhaps be somewhat difficult -to understand by a Figure, because both halves of the Ecliptic seem to -be on the same side of the Globe; but it may be made very easy to any -person who has a real Globe before him, by putting small patches on -every tenth or fifteenth degree both of the Equator and Ecliptic; and -then, turning the ball slowly round westward, he will see all the -patches from Aries to Cancer come to the brazen Meridian sooner than the -corresponding patches on the Equator; all those from Cancer to Libra -will come later to the Meridian than their corresponding patches on the -Equator; those from Libra to Capricorn sooner, and those from Capricorn -to Aries later: and the patches at the beginnings of Aries, Cancer, -Libra, and Capricorn, being also on the Equator, shew that the two Suns -meet there, and come to the Meridian together. - -[Sidenote: A machine for shewing the sidereal, the equal, and the solar - Time. - - PLATE VI.] - -231. Let us suppose that there are two little balls moving equably round -a celestial Globe by clock-work, one always keeping in the Ecliptic, and -gilt with gold, to represent the real Sun; and the other keeping in the -Equator, and silvered, to represent the fictitious Sun: and that whilst -these balls move once, round the Globe according to the order of Signs, -the Clock turns the Globe 366 times round it’s Axis westward. The Stars -will make 366 diurnal revolutions from the brasen Meridian to it again; -and the two balls representing the real and fictitious Sun always going -farther eastward from any given Star, will come later than it to the -Meridian every following day; and each ball will make 365 revolutions to -the Meridian; coming equally to it at the beginnings of Aries, Cancer, -Libra, and Capricorn: but in every other point of the Ecliptic, the gilt -ball will come either sooner or later to the Meridian than the silvered -ball, like the patches above-mentioned. This would be a pretty-enough -way of shewing the reason why any given Star, which, on a certain day of -the year, comes to the Meridian with the Sun, passes over it so much -sooner every following day, as on that day twelvemonth to come to the -Meridian with the Sun again; and also to shew the reason why the real -Sun comes to the Meridian sometimes sooner, sometimes later, than it is -noon by the clock; and, on four days of the year, at the same time; -whilst the fictitious Sun always comes to the Meridian when it is twelve -at noon by the clock. This would be no difficult task for an artist to -perform; for the gold ball might be carried round the Ecliptic by a wire -from it’s north Pole, and the silver ball round the Equator by a wire -from it’s south Pole, with a few wheels to each; which might be easily -added to my improvement of the celestial Globe, described in N^o 483 of -the _Philosophical Transactions_; and of which I shall give a -description in the latter part of this Book, from the 3d Figure of the -3d plate. - -[Sidenote: Fig. III.] - -232. ’Tis plain that if the Ecliptic were more obliquely posited to the -Equator, as the dotted Circle ♈_x_♎, the equal divisions from ♈ to _x_ -would come still sooner to the Meridian _Z0_♈ than those marked _A_, -_B_, _C_, _D_, and _E_ do: for two divisions containing 30 degrees, from -♈ to the second dott, a little short of the figure 1, come sooner to the -Meridian than one division containing only 15 degrees from ♈ to _A_ -does, as the Ecliptic now stands; and those of the second quadrant from -_x_ to ♎ would be so much later. The third quadrant would be as the -first, and the fourth as the second. And it is likewise plain, that -where the Ecliptic is most oblique, namely about Aries and Libra, the -difference would be greatest: and least about Cancer and Capricorn, -where the obliquity is least. - - -[Sidenote: The second part of the Equation of Time. - - PLATE VI.] - -234. Having explained one cause of the difference of time shewn by a -well-regulated Clock and a true Sun-dial; and considered the Sun, not -the Earth, as moving in the Ecliptic; we now proceed to explain the -other cause of this difference, namely, the inequality of the Sun’s -apparent motion § 205, which is slowest in summer, when the Sun is -farthest from the Earth, and swiftest in winter when he is nearest to -it. But the Earth’s motion on it’s Axis is equable all the year round, -and is performed from west to east; which is the way that the Sun -appears to change his place in the Ecliptic. - -235. If the Sun’s motion were equable in the Ecliptic, the whole -difference between the equal time as shewn by a Clock, and the unequal -time as shewn by the Sun, would arise from the obliquity of the -Ecliptic. But the Sun’s motion sometimes exceeds a degree in 24 hours, -though generally it is less: and when his motion is slowest any -particular Meridian will revolve sooner to him than when his motion is -quickest; for it will overtake him in less time when he advances a less -space than when he moves through a larger. - -236. Now, if there were two Suns moving in the plane of the Ecliptic, so -as to go round it in a year; the one describing an equal arc every 24 -hours, and the other describing sometimes a less arc in 24 hours, and at -other times a larger; gaining at one time of the year what it lost at -the opposite; ’tis evident that either of these Suns would come sooner -or later to the Meridian than the other as it happened to be behind or -before the other: and when they were both in conjunction they would come -to the Meridian at the same moment. - -[Sidenote: Fig. IV.] - -237. As the real Sun moves unequably in the Ecliptic, let us suppose a -fictitious Sun to move equably in it. Let _ABCD_ be the Ecliptic or -Orbit in which the real Sun moves, and the dotted Circle _abcd_ the -imaginary Orbit of the fictitious Sun; each going round in a year -according to the order of letters, or from west to east. Let _HIKL_ be -the Earth turning round it’s Axis the same way every 24 hours; and -suppose both Suns to start from _A_ and _a_, in a right line with the -plane of the Meridian _EH_, at the same moment: the real Sun at _A_, -being then at his greatest distance from the Earth, at which time his -motion is slowest; and the fictitious Sun at _a_, whose motion is always -equable because his distance from the Earth is supposed to be always the -same. In the time that the Meridian revolves from _H_ to _H_ again, -according to the order of the letters _HIKL_, the real Sun has moved -from _A_ to _F_; and the fictitious with a quicker motion from _a_ to -_f_, through a larger arc: therefore, the Meridian _EH_ will revolve -sooner from _H_ to _h_ under the real Sun at _F_, than from _H_ to _k_ -under the fictitious Sun at _f_; and consequently it will be noon by the -Sun-dial sooner than by the Clock. - -[Sidenote: PLATE VI.] - -As the real Sun moves from _A_ towards _C_, the swiftness of his motion -increases all the way to _C_, where it is at the quickest. But -notwithstanding this, the fictitious Sun gains so much upon the real, -soon after his departing from _A_, that the increasing velocity of the -real Sun does not bring him up with the equally moving fictitious Sun -till the former comes to _C_, and the latter to _c_, when each has gone -half round it’s respective orbit; and then being in conjunction, the -Meridian _EH_ revolving to _EK_ comes to both Suns at the same time, and -therefore it is noon by them both at the same moment. - -But the increased velocity of the real Sun, now being at the quickest, -carries him before the fictitious; and therefore, the same Meridian will -come to the fictitious Sun sooner than to the real: for whilst the -fictitious Sun moves from _c_ to _g_, the real Sun moves through a -greater arc from _C_ to _G_: consequently the point _K_ has it’s -fictitious noon when it comes to _k_, but not it’s real noon till it -comes to _l_. And although the velocity of the real Sun diminishes all -the way from _C_ to _A_, and the fictitious Sun by an equable motion is -still coming nearer to the real Sun, yet they are not in conjunction -till the one comes to _A_ and the other to _a_; and then it is noon by -them both at the same moment. - -And thus it appears, that the real noon by the Sun is always later than -the fictitious noon by the clock whilst the Sun goes from _C_ to _A_, -sooner whilst he goes from _A_ to _C_, and at these two points the Sun -and Clock being equal, it is noon by them both at the same moment. - - -[Sidenote: Apogee, Perigee, and Apsides, what. - - Fig. IV.] - -238. The point _A_ is called _the Sun’s Apogee_, because when he is -there he is at his greatest distance from the Earth; the point _C_ his -_Perigee_, because when in it he is at his least distance from the -Earth: and a right line, as _AEC_, drawn through the Earth’s center, -from one of these points to the other, is called _the line of the -Apsides_. - -[Sidenote: Mean Anomaly, what.] - -239. The distance that the Sun has gone in any time from his Apogee (not -the distance he has to go to it though ever so little) is called _his -mean Anomaly_, and is reckoned in Signs and Degrees, allowing 30 Degrees -to a Sign. Thus, when the Sun has gone suppose 174 degrees from his -Apogee at _A_, he is said to be 5 Signs 24 Degrees from it, which is his -mean Anomaly: and when he is gone suppose 355 degrees from his Apogee, -he is said to be 11 Signs 25 Degrees from it, although he be but 5 -Degrees short of _A_ in coming round to it again. - -240. From what was said above it appears, that when the Sun’s Anomaly is -less than 6 Signs, that is, when he is any where between _A_ and _C_, in -the half _ABC_ of his orbit, the true noon precedes the fictitious; but -when his Anomaly is more than 6 Signs, that is, when he is any where -between _C_ and _A_, in the half _CDA_ of his Orbit, the fictitious noon -precedes the true. When his Anomaly is 0 Signs 0 Degrees, that is, when -he is in his Apogee at _A_; or 6 Signs 0 Degrees, which is when he is in -his Perigee at _C_; he comes to the Meridian at the moment that the -fictitious Sun does, and then it is noon by them both at the same -instant. - - +----------------------------------------------------------+ - | _Sun faster than the Clock if his Anomaly be_ | - +----+--------+-------+-------+-------+-------+-------+----+ - | |0 Signs | 1 | 2 | 3 | 4 | 5 | | - | D. +--------+-------+-------+-------+-------+-------+ | - | | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | | - +----+--------+-------+-------+-------+-------+-------+----+ - | 0 | 0 0 | 3 48 | 6 39 | 7 45 | 6 47 | 3 57 | 30 | - | 1 | 0 8 | 3 55 | 6 43 | 7 45 | 6 43 | 3 50 | 29 | - | 2 | 0 16 | 3 2 | 6 47 | 7 45 | 6 39 | 3 43 | 28 | - | 3 | 0 24 | 4 9 | 6 51 | 7 45 | 6 35 | 3 35 | 27 | - | 4 | 0 32 | 4 16 | 6 54 | 7 45 | 6 30 | 3 28 | 26 | - | 5 | 0 40 | 4 22 | 6 58 | 7 44 | 6 26 | 3 20 | 25 | - | 6 | 0 48 | 4 29 | 7 1 | 7 44 | 6 21 | 3 13 | 24 | - | 7 | 0 56 | 4 35 | 7 5 | 7 43 | 6 16 | 3 5 | 23 | - | 8 | 1 3 | 4 42 | 7 8 | 7 42 | 6 11 | 2 58 | 22 | - | 9 | 1 11 | 4 48 | 7 11 | 7 41 | 6 6 | 2 50 | 21 | - | 10 | 1 19 | 4 54 | 7 14 | 7 40 | 6 1 | 2 42 | 20 | - | 11 | 1 27 | 5 0 | 7 17 | 7 38 | 5 56 | 2 35 | 19 | - | 12 | 1 35 | 5 6 | 7 20 | 7 37 | 5 51 | 2 27 | 18 | - | 13 | 1 43 | 5 12 | 7 22 | 7 35 | 5 45 | 2 19 | 17 | - | 14 | 1 50 | 5 18 | 7 25 | 7 34 | 5 40 | 2 11 | 16 | - | 15 | 1 58 | 5 24 | 7 27 | 7 32 | 5 34 | 2 3 | 15 | - | 16 | 2 6 | 5 30 | 7 29 | 7 30 | 5 28 | 1 55 | 14 | - | 17 | 2 13 | 5 35 | 7 31 | 7 28 | 5 22 | 1 47 | 13 | - | 18 | 2 21 | 5 41 | 7 33 | 7 25 | 5 16 | 1 39 | 12 | - | 19 | 2 28 | 5 46 | 7 35 | 7 23 | 5 10 | 1 31 | 11 | - | 20 | 2 36 | 5 52 | 7 36 | 7 20 | 5 4 | 1 22 | 10 | - | 21 | 2 43 | 5 57 | 7 38 | 7 18 | 4 58 | 1 14 | 9 | - | 22 | 2 51 | 6 2 | 7 39 | 7 15 | 4 51 | 1 6 | 8 | - | 23 | 2 58 | 6 7 | 7 41 | 7 12 | 4 45 | 0 58 | 7 | - | 24 | 3 6 | 6 12 | 7 42 | 7 9 | 4 38 | 0 50 | 6 | - | 25 | 3 13 | 6 16 | 7 43 | 7 5 | 4 31 | 0 41 | 5 | - | 26 | 3 20 | 6 21 | 7 43 | 7 2 | 4 25 | 0 33 | 4 | - | 27 | 3 27 | 6 26 | 7 44 | 6 58 | 4 18 | 0 25 | 3 | - | 28 | 3 34 | 6 30 | 7 44 | 6 55 | 4 11 | 0 17 | 2 | - | 29 | 3 41 | 6 34 | 7 45 | 6 51 | 4 4 | 0 8 | 1 | - | 30 | 3 48 | 6 39 | 7 45 | 6 47 | 3 57 | 0 0 | 0 | - +----+--------+-------+-------+-------+-------+-------+----+ - | |11 Signs| 10 | 9 | 8 | 7 | 6 | D. | - +----+--------+-------+-------+-------+-------+-------+----+ - | _Sun slower than the Clock if his Anomaly be_ | - +----------------------------------------------------------+ - -[Sidenote: A Table of the Equation of Time, depending on the Sun’s - Anomaly.] - -241. The annexed Table shews the Variation, or Equation of time -depending on the Sun’s Anomaly, and arising from his unequal motion in -the Ecliptic; as the former Table § 229 shews the Variation depending on -the Sun’s place, and resulting from the obliquity of the Ecliptic: this -is to be understood the same way as the other, namely, that when the -Signs are at the head of the Table, the Degrees are at the left hand; -but when the Signs are at the foot of the Table the respective Degrees -are at the right hand; and in both cases the Equation is in the Angle of -meeting. When both the above-mentioned Equations are either faster or -slower, their sum is the absolute Equation of Time; but when the one is -faster, and the other slower, it is their difference. Thus, suppose the -Equation depending on the Sun’s place, be 6 minutes 41 seconds too slow, -and the Equation depending on the Sun’s Anomaly, be 4 minutes 20 seconds -too slow, their Sun is 11 minutes 1 second too slow. But if the one had -been 6 minutes 41 seconds too fast, and the other 4 minutes 20 seconds -too slow, their difference had been 2 minutes 21 seconds too fast, -because the greater quantity is too fast. - -242. The obliquity of the Ecliptic to the Equator, which is the first -mentioned cause of the Equation of Time, would make the Sun and Clocks -agree on four days of the year; which are, when the Sun enters Aries, -Cancer, Libra, and Capricorn: but the other cause, now explained, would -make the Sun and Clocks equal only twice in a year; that is, when the -Sun is in his Apogee and Perigee. Consequently, when these two points -fall in the beginnings of Cancer and Capricorn, or of Aries and Libra, -they concur in making the Sun and Clocks equal in these points. But the -Apogee at present is in the 9th degree of Cancer, and the Perigee in the -9th degree of Capricorn; and therefore the Sun and Clocks cannot be -equal about the beginning of these Signs, nor at any time of the year, -except when the swiftness or slowness of Equation resulting from one -cause just balances the slowness or swiftness arising from the other. - -243. The last Table but one, at the end of this Chapter, shews the Sun’s -place in the Ecliptic at the noon of every day by the clock, for the -second year after leap-year; and also the Sun’s Anomaly to the nearest -degree, neglecting the odd minutes of a degree. Their use is only to -assist in shewing the method of making a general Equation Table from the -two fore-mentioned Tables of Equation depending on the Sun’s Place and -Anomaly § 229, 241; concerning which method we shall give a few examples -presently. The following Tables are such as might be made from these -two; and shew the absolute Equation of Time resulting from the -combination of both it’s causes; in which the minutes, as well as -degrees, both of the Sun’s Place and Anomaly are considered. The use of -these Tables is already explained, § 225; and they serve for every day -in leap-year, and the first, second, and third years after: For on most -of the same days of all these years the Equation differs, because of the -odd six hours more than the 365 days of which the year consists. - - -[Sidenote: Examples for making Equation Tables.] - -EXAMPLE I. On the 15th of _April_ the Sun is in the 25th degree of ♈ -Aries, and his Anomaly is 9 Signs 15 Degrees; the Equation resulting -from the former is 7 minutes 23 seconds of time too fast § 229; and from -the latter, 7 minutes 27 seconds too slow, § 241; the difference is 4 -seconds that the Sun is too slow at the noon of that day; taking it in -gross for the degrees of the Sun’s Place and Anomaly, without making -proportionable allowance for the odd minutes. Hence, at noon the -swiftness of the one Equation balancing so nearly the slowness of the -other, makes the Sun and Clocks equal on some part of that day. - - -EXAMPLE II. On the 16th of _June_, the Sun is in the 25th degree of ♊ -Gemini, and his Anomaly is 11 Signs 16 Degrees; the Equation arising -from the former is 1 minute 48 seconds too fast; and from the latter 1 -minute 50 seconds too slow; which balancing one another at noon to 2 -seconds, the Sun and Clocks are again equal on that day. - - -EXAMPLE III. On the 31st of _August_ the Sun’s place is 7 degrees 52 -minutes of ♍ Virgo (which we shall call the 8th degree, as it is so -near) and his Anomaly is 2 Signs 0 Degrees; the Equation arising from -the former is 6 minutes 41 seconds too slow; and from the latter 6 -minutes 39 seconds too fast; the difference being only 2 seconds too -slow at noon, and decreasing towards an equality will make the Sun and -Clocks equal in the afternoon of that day. - - -EXAMPLE. IV. On the 23d of _December_ the Sun’s place is 1 degree 41 -minutes (call it 2 degrees) of ♑ Capricorn, and his Anomaly is 5 Signs -23 Degrees; the Equation for the former is 43 seconds too slow, and for -the latter 58 seconds too fast; the difference is 15 seconds too fast at -noon; which decreasing will come to an equality, and so make the Sun and -Clocks equal in the evening of that day. - - -And thus we find, that on some part of each of the above-mentioned four -days, the Sun and Clocks are equal; but if we work examples for all -other days of the year we shall find them different. And, - -[Sidenote: Remark.] - -244. On those days which are equidistant from any Equinox or Solstice, -we do not find that the Equation is as much too fast or too slow, on the -one side, as it is too slow or too fast on the other. The reason is, -that the line of the Apsides § 238, does not, at present, fall either -into the Equinoctial or Solsticial points § 242. - - -[Sidenote: The reason why Equation Tables are but temporary.] - -245. If the line of the Apsides, together with the Equinoctial and -Solsticial points, were immoveable, a general Equation Table might be -made from the preceding Equation Tables, which would always keep true, -because these Tables themselves are permanent. But, with respect to the -fixed Stars, the line of the Apsides moves forwards 12 seconds of a -degree every year, and the above points 50 seconds backward. So that if -in any given year, the Equinoctial points, and line of the Apsides were -coincident, in 100 years afterward they would be separated 1 degree 43 -minutes 20 seconds; and consequently in 5225.8 years they would be -separated 90 degrees, and could not meet again, so that the same -Equinoctial point should fall again into the Apogee in less than 20,903 -years: and this is the shortest Period in which the Equation of Time can -be restored to the same state again, with respect to the same seasons of -the year. - - - - - CHAP. XIV. - - _Of the Precession of the Equinoxes._ - - -246. It has been already observed, § 116, that by the Earth’s motion on -it’s Axis, there is more matter accumulated all round the equatoreal -parts than any where else on the Earth. - -The Sun and Moon, by attracting this redundancy of matter, bring the -Equator sooner under them in every return towards it than if there was -no such accumulation. Therefore, if the Sun sets out, as from any Star, -or other fixed point in the Heavens, the moment he is departing from the -Equinoctial or either Tropic, he will come to the same again before he -compleats his annual course, so as to arrive at the same fixed Star or -Point from whence he set out. - -When the Sun arrives at the same [56]Equinoctial or Solstitial Point, he -finishes what we call the _Tropical Year_, which, by long observation, -is found to contain 365 days 5 hours 48 minutes 57 seconds: and when he -arrives at the same fixed Star again, as seen from the Earth, he -compleats the _Sidereal Year_; which is found to contain 365 days 6 -hours 9 minutes 14-1/2 seconds. The _Sidereal Year_ is therefore 20 -minutes 17-1/2 seconds longer than the Solar or Tropical year, and 9 -minutes 14-1/2 seconds longer than the Julian or Civil year, which we -state at 365 days 6 hours: so that the Civil year is almost a mean -betwixt the Sidereal and Tropical. - -[Sidenote: PLATE VI.] - -247. As the Sun describes the whole Ecliptic, or 360 degrees, in a -Tropical year, he moves 59ʹ 8ʺ of a degree every day; and consequently -50ʺ of a degree in 20 minutes 17-1/2 seconds of time: therefore, he will -arrive at the same Equinox or Solstice when he is 50ʺ of a degree short -of the same Star or fixed point in the Heavens from which he set out in -the year before. So that, with respect to the fixed Stars, the Sun and -Equinoctial points fall back (as it were) 30 degrees in 2160 years; -which will make the Stars appear to have gone 30 deg. forward, with -respect to the Signs of the Ecliptic in that time: for the same Signs -always keep in the same points of the Ecliptic, without regard to the -constellations. - - +------------------------------------------------------------------+ - | _A_ TABLE _shewing the Precession of the Equinoctial | - | Points in the Heavens, both in Motion and Time; | - | and the Anticipation of the Equinoxes on Earth_. | - +--------+--------------------------------------++-----------------+ - | | Precession of the Equinoctial || Anticipation of | - | | Points in the Heavens. || the Equinoxes | - | Julian +----------------+---------------------++ on the Earth. | - | years. | Motion. | Time. || | - | +----------------+---------------------++-----------------+ - | | S. ° ʹ ʺ | Days H. M. S. || D. H. M. S. | - +--------+----------------+--------------------++------------------+ - | 1 | 0 0 0 50 | 0 0 20 17-1/2 || 0 0 11 3 | - | 2 | 0 0 1 40 | 0 0 40 35 || 0 0 22 6 | - | 3 | 0 0 2 30 | 0 1 0 52-1/2 || 0 0 33 9 | - | 4 | 0 0 3 20 | 0 1 21 10 || 0 0 44 12 | - | 5 | 0 0 4 10 | 0 1 41 27-1/2 || 0 0 55 15 | - +--------+----------------+---------------------++-----------------+ - | 6 | 0 0 5 0 | 0 2 1 45 || 0 1 6 18 | - | 7 | 0 0 5 50 | 0 2 22 2-1/2 || 0 1 17 21 | - | 8 | 0 0 6 40 | 0 2 42 20 || 0 1 28 24 | - | 9 | 0 0 7 30 | 0 3 2 37-1/2 || 0 1 39 27 | - | 10 | 0 0 8 20 | 0 3 22 55 || 0 1 50 30 | - +--------+----------------+---------------------++-----------------+ - | 20 | 0 0 16 40 | 0 6 45 50 || 0 3 41 0 | - | 30 | 0 0 25 0 | 0 10 8 45 || 0 5 31 30 | - | 40 | 0 0 33 20 | 0 13 31 40 || 0 7 22 0 | - | 50 | 0 0 41 40 | 0 16 54 35 || 0 9 12 30 | - | 60 | 0 0 50 0 | 0 20 17 30 || 0 11 3 0 | - +--------+----------------+---------------------++-----------------+ - | 70 | 0 0 58 20 | 0 23 40 25 || 0 12 53 30 | - | 80 | 0 1 6 40 | 1 3 3 20 || 0 14 44 0 | - | 90 | 0 1 15 0 | 1 6 26 15 || 0 16 34 30 | - | 100 | 0 1 23 20 | 1 9 49 10 || 0 18 25 0 | - | 200 | 0 2 46 40 | 2 19 38 20 || 1 12 50 0 | - +--------+----------------+---------------------++-----------------+ - | 300 | 0 4 10 0 | 4 5 27 30 || 2 7 15 0 | - | 400 | 0 5 33 20 | 5 15 16 40 || 3 1 40 0 | - | 500 | 0 6 56 40 | 7 1 5 50 || 3 20 5 0 | - | 600 | 0 8 20 0 | 8 10 55 0 || 4 14 30 0 | - | 700 | 0 9 43 20 | 9 20 44 10 || 5 8 55 0 | - +--------+----------------+---------------------++-----------------+ - | 800 | 0 11 6 40 | 11 6 33 20 || 6 3 20 0 | - | 900 | 0 12 29 0 | 12 16 22 30 || 6 21 45 0 | - | 1000 | 0 13 53 20 | 14 2 11 40 || 7 16 10 0 | - | 2000 | 0 27 46 40 | 28 4 23 20 || 15 8 20 0 | - | 3000 | 1 11 40 0 | 42 6 35 0 || 23 0 30 0 | - +--------+----------------+---------------------++-----------------+ - | 4000 | 1 25 33 20 | 56 8 46 40 || 30 16 40 0 | - | 5000 | 2 9 26 40 | 70 10 58 20 || 38 8 50 0 | - | 6000 | 2 23 20 0 | 84 13 10 0 || 46 1 0 0 | - | 7000 | 3 7 13 20 | 98 15 21 40 || 53 17 10 0 | - | 8000 | 3 21 6 40 | 112 17 33 20 || 61 9 20 0 | - +--------+----------------+---------------------++-----------------+ - | 9000 | 4 5 0 0 | 126 19 45 0 || 69 1 30 0 | - | 10000 | 4 18 53 20 | 140 21 56 40 || 76 17 40 0 | - | 20000 | 9 7 46 40 | 281 19 53 20 || 153 11 20 0 | - | 25920 | 12 0 0 0 | 365 6 0 0 || 198 21 36 0 | - +--------+----------------+---------------------++-----------------+ - -[Sidenote: Fig. IV.] - -To explain this by a Figure, let the Sun be in conjunction with a fixed -Star at _S_, suppose in the 30th degree of ♉, on the 20th day of _May_ -1756. Then, making 2160 revolutions through the Ecliptic _VWX_, at the -end of so many Sidereal years, he will be found again at _S_: but at the -end of so many Julian years, he will be found at _M_, short of _S_: and -at the end of so many Tropical years, he will be found short of _M_, in -the 30th deg. of Taurus at _T_, which has receded back from _S_ to _T_ -in that time, by the Precession of the Equinoctial points ♈ _Aries_ and -♎ _Libra_. The Arc _ST_ will be equal to the amount of the Precession of -the Equinox in 2160 years, at the rate of 50ʺ of a degree, or 20 min. -17-1/2 sec. of time, annually: this, in so many years, makes 30 days, -10-1/2 hours; which is the difference between 2160 Sidereal and Tropical -years: And the Arc _MT_ will be equal to the space moved through by the -Sun in 2160 times 11 min. 3 sec. or 16 days, 13 hours 48 minutes, which -is the difference between 2160 Julian and Tropical years. - -248. From the shifting of the Equinoctial points, and with them all the -Signs of the Ecliptic, it follows that those Stars which in the infancy -of astronomy were in _Aries_ are now got into _Taurus_; those of -_Taurus_ into _Gemini_, &c. Hence likewise it is, that the Stars which -rose or set at any particular season of the year, in the time of HESIOD, -EUDOXUS, VIRGIL, PLINY, &c. by no means answer at this time to their -descriptions. The preceding table shews the quantity of this shifting -both in the heavens and on the earth, for any number of years to 25,920; -which compleats the grand celestial period: within which any number and -its quantity is easily found; as in the following example, for 5763 -years; which at the Autumnal Equinox, A. D. 1756, is thought to be the -age of the world. So that with regard to the fixed Stars, the -Equinoctial points in the heavens, have receded 2^s 20° 2ʹ 30ʺ since the -creation; which is as much as the Sun moves in 81^d 5^h 0^m 52^s. And -since that time, or in 5763 years, the Equinoxes with us have fallen -back 44^d 5^h 21^m 9^s; hence, reckoning from the time of the _Julian_ -Equinox, _A. D._ 1756, _viz._ _Sept._ 12th, it appears that the Autumnal -Equinox at the creation was on the 26th of _October_. - - +---------+----------------------------------++----------------+ - | | Precession of the Equinoctial || Anticipation | - | | Points in the Heavens. || of the | - | Julian +-----------------+----------------+| Equinoxes on | - | years. | Motion. | Time. || the Earth. | - | +-----------------+----------------++----------------+ - | | S. ° ʹ ʺ | D. H. M. S. || D. H. M. S. | - +---------+-----------------+----------------++----------------+ - | 5000 | 2 9 26 40 | 70 10 58 20 || 38 8 50 0 | - | 700 | 0 9 43 20 | 9 20 44 10 || 5 8 55 0 | - | 60 | 0 0 50 0 | 0 20 17 30 || 0 11 3 0 | - | 3 | 0 0 2 30 | 0 1 0 52 || 0 0 33 9 | - +---------+-----------------+----------------++----------------+ - | 5763 | 2 20 2 30 | 81 5 0 52 || 44 5 21 9 | - +---------+-----------------+----------------++----------------+ - - -[Sidenote: The anticipation of the Equinoxes and Seasons. - - PLATE VI.] - -249. The anticipation of the Equinoxes, and consequently of the seasons, -is by no means owing to the Precession of the Equinoctial and Solsticial -points in the Heavens, (which can only affect the apparent motions, -places and declinations of the fixed Stars) but to the difference -between the Civil and Solar year, which is 11 minutes 3 seconds; the -Civil year containing 365 days 6 hours, and the Solar year 365 days 5 -hours 48 minutes 57 seconds. The following table shews the length, and -consequently the difference of any number of Sidereal, Civil, and Solar -years from 1 to 10,000. - -[Sidenote: The reason for altering the Style.] - -250. The above 11 minutes 3 seconds, by which the Civil or Julian year -exceeds the Solar, amounts to 11 days in 1433 years: and so much our -seasons have fallen back with respect to the days of the months, since -the time of the _Nicene_ Council in _A.D._ 325, and therefore in order -to bring back all the Fasts and Festivals to the days then settled, it -was requisite to suppress 11 nominal days. And that the same seasons -might be kept to the same times of the year for the future, to leave out -the Bissextile day in _February_ at the end of every century of years -not divisible by 4; reckoning them only common years, as the 17th, 18th -and 19th centuries, _viz._ the years 1700, 1800, 1900, _&c._ because a -day intercalated every fourth year was too much, and retaining the -Bissextile-day at the end of those Centuries of years which are -divisible by 4, as the 16th, 20th and 24th Centuries; _viz._ the years -1600, 2000, 2400, _&c._ Otherwise, in length of time the seasons would -have been quite reversed with regard to the months of the years; though -it would have required near 23,783 years to have brought about such a -total change. If the Earth had made exactly 365-1/4 diurnal rotations on -its axis, whilst it revolved from any Equinoctial or Solstitial point to -the same again, the Civil and Solar years would always have kept pace -together; and the style would never have needed any alteration. - - -[Sidenote: The Precession of the Equinoctial Points.] - -251. Having already mentioned the cause of the Precession of the -Equinoctial points in the heavens, § 246, which occasions a flow -deviation of the earth’s axis from its parallelism, and thereby a change -of the declination of the Stars from the Equator, together with a slow -apparent motion of the Stars forward with respect to the Signs of the -Ecliptic; we shall now describe the Phenomena by a Diagram. - -[Sidenote: Fig. V.] - -Let _NZSVL_ be the Earth, _SONA_ its Axis produced to the starry -Heavens, and terminating in _A_, the present north Pole of the Heavens, -which is vertical to _N_ the north Pole of the Earth. Let _EOQ_ be the -Equator, _T_♋_Z_ the Tropic of Cancer, and _VT_♑ the Tropic of -Capricorn: _VOZ_ the Ecliptic, and _BO_ its Axis, both which are -immoveable among the Stars. But, as [57]the Equinoctial points recede in -the Ecliptic, the Earth’s Axis _SON_ is in motion upon the Earth’s -center _O_, in such a manner as to describe the double Cone _NOn_ and -_SOs_, round the Axis of the Ecliptic _BO_, in the time that the -Equinoctial points move quite round the Ecliptic, which is 25,920 years; -and in that length of time, the north Pole of the Earth’s Axis produced, -describes the Circle _ABCDA_ in the starry Heavens, round the Pole of -the Ecliptic, which keeps immoveable in the center of that Circle. The -Earth’s Axis being 23-1/2 degrees inclined to the Axis of the Ecliptic, -the Circle _ABCDA_, described by the north Pole of the Earth’s Axis -produced to _A_, is 47 degrees in diameter, or double the inclination of -the Earth’s Axis. In consequence of this, the point _A_, which at -present is the North Pole of the Heavens, and near to a Star of the -second magnitude in the tail of the constellation called _the Little -Bear_, must be deserted by the Earth’s Axis; which moving backwards a -degree every 72 years, will be directed towards the Star or Point _B_ in -6480 years hence: and in double of that time, or 12,960 years, it will -be directed towards the Star or Point _C_; which will then be the North -Pole of the Heavens, although it is at present 8-1/2 degrees south of -the Zenith of _London L_. The present position of the Equator _EOQ_ will -then be changed into _eOq_, the Tropic of Cancer _T_♋_Z_ into _Vt_♋, and -the Tropic of Capricorn _VT_♑ into _t_♑_Z_; as is evident by the Figure. -And the Sun, in the same part of the Heavens where he is now over the -earthly Tropic of Capricorn, and makes the shortest days and longest -nights in the Northern Hemisphere, will then be over the earthly Tropic -of Cancer, and make the days longest, and nights shortest. So that it -will require 12,960 years yet more, or 25,920 from the present time, to -bring the North Pole _N_ quite round, so as to be directed toward that -point of the Heavens which is vertical to it at present. And then, and -not till then, the same Stars which at present describe the Equator, -Tropics, polar Circles, and Poles, by the Earth’s diurnal motion, will -describe them over again. - - _A_ TABLE _shewing the Time contained in any number of Sidereal, Julian, - and Solar Years, from 1 to 10000_. - - +------------------------------------++--------------++------------------------+ - | Sidereal Years. || Julian Years.|| Solar Years. | - +-------+---------+----+----+--------++---------+----++---------+--------------+ - | Years | Days | H. | M. | S. || Days | H. || Days | H. | M. | S. | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | | Contain | | | || Contain | || Contain | | | | - | 1 | 365 | 6 | 9 | 14-1/2 || 365 | 6 || 365 | 5 | 48 | 57 | - | 2 | 730 | 12 | 18 | 29 || 730 | 12 || 370 | 11 | 37 | 54 | - | 3 | 1095 | 18 | 27 | 43-1/2 || 1095 | 18 || 1095 | 17 | 26 | 51 | - | 4 | 1461 | 0 | 36 | 58 || 1461 | 0 || 1460 | 23 | 15 | 48 | - | 5 | 1826 | 6 | 46 | 12-1/2 || 1826 | 6 || 1826 | 5 | 4 | 45 | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 6 | 2191 | 12 | 55 | 27 || 2191 | 12 || 2191 | 10 | 53 | 42 | - | 7 | 2556 | 19 | 5 | 41-1/2 || 2556 | 18 || 2556 | 16 | 42 | 39 | - | 8 | 2922 | 1 | 13 | 56 || 2922 | 0 || 2921 | 22 | 31 | 36 | - | 9 | 3287 | 7 | 23 | 10-1/2 || 3287 | 6 || 3287 | 4 | 20 | 33 | - | 10 | 3652 | 13 | 32 | 25 || 3652 | 12 || 3652 | 10 | 9 | 30 | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 20 | 7305 | 3 | 4 | 50 || 7305 | 0 || 7304 | 20 | 19 | 0 | - | 30 | 10957 | 16 | 37 | 15 || 10957 | 12 || 10957 | 6 | 28 | 30 | - | 40 | 14610 | 6 | 9 | 40 || 14610 | 0 || 14609 | 16 | 38 | 0 | - | 50 | 18262 | 19 | 42 | 5 || 18262 | 12 || 18262 | 2 | 47 | 30 | - | 60 | 21915 | 9 | 14 | 30 || 21915 | 0 || 21914 | 12 | 57 | 0 | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 70 | 25567 | 22 | 46 | 55 || 25567 | 12 || 25566 | 23 | 6 | 30 | - | 80 | 29220 | 12 | 19 | 20 || 25220 | 0 || 29219 | 9 | 16 | 0 | - | 90 | 32873 | 1 | 51 | 45 || 32872 | 12 || 32871 | 19 | 25 | 30 | - | 100 | 36525 | 15 | 24 | 10 || 36525 | || 36524 | 5 | 35 | | - | 200 | 73051 | 6 | 48 | 20 || 73050 | || 73048 | 11 | 10 | | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 300 | 109576 | 22 | 12 | 30 || 109575 | || 109572 | 16 | 45 | | - | 400 | 146102 | 13 | 36 | 40 || 146100 | || 146096 | 22 | 20 | | - | 500 | 182628 | 5 | 0 | 50 || 182625 | || 182621 | 3 | 55 | | - | 600 | 219153 | 20 | 25 | || 219150 | || 219145 | 9 | 30 | | - | 700 | 255679 | 11 | 49 | 10 || 255675 | || 255669 | 15 | 5 | | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 800 | 292205 | 3 | 13 | 20 || 292200 | || 292193 | 20 | 10 | | - | 900 | 328730 | 18 | 37 | 30 || 328725 | || 328718 | 2 | 15 | | - | 1000 | 365256 | 10 | 1 | 40 || 365250 | || 365242 | 7 | 50 | | - | 2000 | 730512 | 20 | 3 | 20 || 730500 | || 730484 | 15 | 40 | | - | 3000 | 1095769 | 6 | 5 | || 1095750 | || 1095726 | 23 | 30 | | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 4000 | 1461025 | 16 | 6 | 40 || 1461000 | || 1460969 | 7 | 20 | | - | 5000 | 1826282 | 2 | 8 | 20 || 1826250 | || 1826211 | 15 | 10 | | - | 6000 | 2191538 | 12 | 10 | || 2191500 | || 2191453 | 14 | 40 | | - | 7000 | 2556794 | 22 | 11 | 40 || 2556750 | || 2556696 | 6 | 50 | | - | 8000 | 2922051 | 8 | 13 | 20 || 2922000 | || 2921938 | 14 | 40 | | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - | 9000 | 3287037 | 18 | 15 | || 3287250 | || 3287180 | 22 | 30 | | - | 10000 | 3652564 | 4 | 16 | 40 || 3652500 | || 3652423 | 6 | 20 | | - +-------+---------+----+----+--------++---------+----++---------+----+----+----+ - +----------------------------------------------------------------------------------------+ - | A TABLE shewing the Sun’s true Place, and Distance from his Apogee, | - | for the second Year after Leap-year. | - +----+-------------+-------------+-------------+-------------+-------------+-------------+ - | | January | February | March | April | May | June | - + +------+------+------+------+------+------+------+------+------+------+------+------+ - | |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s | - | |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. | - + +------+------+------+------+------+------+------+------+------+------+------+------+ - |Days|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 1 |11♑ 7| 6 2|12♒ 39| 7 3|10♓ 53| 8 0|11♈ 40| 9 1|10♉ 57|10 0|10♊ 46|11 1| - | 2 |12 8| 6 3|13 40| 7 4|11 53| 8 1|12 39| 9 2|11 55|10 1|11 44|11 2| - | 3 |13 9| 6 4|14 41| 7 5|12 53| 8 2|13 38| 9 3|12 53|10 2|12 41|11 3| - | 4 |14 10| 6 5|15 42| 7 6|13 53| 8 3|14 37| 9 4|13 51|10 3|13 38|11 4| - | 5 |15 11| 6 6|16 43| 7 7|14 53| 8 4|15 36| 9 5|14 49|10 4|14 35|11 5| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 6 |16 12| 6 7|17 43| 7 8| 5 53| 8 5|16 35| 9 6|15 47|10 5|15 33|11 6| - | 7 |17 14| 6 8|18 44| 7 9|16 53| 8 6|17 34| 9 7|16 45|10 6|16 30|11 7| - | 8 |18 15| 6 9|19 45| 7 10|17 53| 8 7|18 33| 9 8|17 43|10 7|17 28|11 8| - | 9 |19 16| 6 10|20 46| 7 11|18 53| 8 8|19 32| 9 9|18 41|10 8|18 25|11 9| - | 10 |20 17| 6 11|21 46| 7 12|19 53| 8 9|20 30| 9 10|19 39|10 9|19 22|11 10| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 11 |21 18| 6 12|22 47| 7 13|20 52| 8 10|21 29| 9 11|20 37|10 10|20 20|11 11| - | 12 |22 19| 6 13|23 47| 7 14|21 52| 8 11|22 28| 9 12|21 34|10 11|21 17|11 12| - | 13 |23 21| 6 14|24 48| 7 15|22 52| 8 12|23 26| 9 13|22 32|10 12|22 14|11 13| - | 14 |24 22| 6 15|25 48| 7 16|23 52| 8 13|24 25| 9 14|23 30|10 13|23 11|11 14| - | 15 |25 23| 6 16|26 49| 7 17|24 51| 8 14|25 24| 9 15|24 28|10 14|24 8|11 15| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 16 |26 24| 6 17|27 49| 7 18|25 51| 8 15|26 22| 9 16|25 26|10 15|25 6|11 16| - | 17 |27 25| 6 18|28 50| 7 19|26 51| 8 16|27 21| 9 17|26 23|10 16|26 3|11 17| - | 18 |28 26| 6 19|29 50| 7 20|27 50| 8 17|28 19| 9 18|27 21|10 17|27 0|11 18| - | 19 |29 27| 6 20| ♓ 51| 7 21|28 50| 8 18|29 18| 9 19|28 19|10 18|27 58|11 18| - | 20 | ♒ 28| 6 21| 1 51| 7 22|29 49| 8 19| ♉ 16| 9 20|29 16|10 19|28 55|11 19| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 21 | 1 29| 6 22| 2 51| 7 23| ♈ 49| 8 20| 1 15| 9 21| ♊ 15|10 20|29 52|11 20| - | 22 | 2 30| 6 23| 3 52| 7 24| 1 48| 8 21| 2 13| 9 22| 1 11|10 21| ♋ 49|11 21| - | 23 | 3 31| 6 24| 4 52| 7 25| 2 47| 8 22| 3 11| 9 23| 2 9|10 22| 1 46|11 22| - | 24 | 4 32| 6 25| 5 52| 7 26| 3 47| 8 23| 4 10| 9 24| 3 6|10 23| 2 44|11 23| - | 25 | 5 33| 6 26| 6 52| 7 27| 4 46| 8 24| 5 8| 9 25| 4 4|10 24| 3 41|11 24| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 26 | 6 34| 6 27| 7 53| 7 28| 5 45| 8 25| 6 6| 9 26| 5 2|10 25| 4 38|11 25| - | 27 | 7 35| 6 28| 8 53| 7 29| 6 45| 8 26| 7 4| 9 27| 5 59|10 26| 5 35|11 26| - | 28 | 8 36| 6 29| 9 53| 8 0| 7 44| 8 27| 8 3| 9 28| 6 56|10 27| 6 32|11 27| - | 29 | 9 37| 7 0| | | 8 43| 8 28| 9 1| 9 29| 7 54|10 28| 7 30|11 28| - | 30 |10 38| 7 1| | | 9 42| 8 29| 9 59| 9 29| 8 51|10 29| 8 27|11 29| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 31 |11 39| 7 2| | |10 41| 9 0| | | 9 48|11 0| | | - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - +----------------------------------------------------------------------------------------+ - | A TABLE shewing the Sun’s true Place, and Distance from his Apogee, | - | for the second Year after Leap-year. | - +----+-------------+-------------+-------------+-------------+-------------+-------------+ - | | July | August | September | October | November | December | - + +------+------+------+------+------+------+------+------+------+------+------+------+ - | |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s |Sun’s | - | |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. |Place.|Anom. | - + +------+------+------+------+------+------+------+------+------+------+------+------+ - |Days|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.|D. M.|S. D.| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 1 | 9♋ 24| 0 0| 8♌ 59| 1 0| 8♍ 51| 2 1| 8♎ 10| 3 1| 9♏ 0| 4 2| 9♐ 18| 5 1| - | 2 |10 21| 0 1| 9 57| 1 1| 9 49| 2 2| 9 9| 3 2| 10 0| 4 3|10 19| 5 2| - | 3 |11 18| 0 2|10 54| 1 2|10 47| 2 3|10 8| 3 3| 11 0| 4 4|11 20| 5 3| - | 4 |12 15| 0 3|11 52| 1 3|11 45| 2 4|11 8| 3 4| 12 1| 4 5|12 21| 5 4| - | 5 |13 13| 0 4|12 49| 1 4|12 43| 2 5|12 7| 3 5| 13 1| 4 6|13 22| 5 5| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 6 |14 10| 0 5|13 47| 1 5|13 42| 2 6|13 6| 3 6| 14 1| 4 7|14 23| 5 6| - | 7 |15 7| 0 6|14 44| 1 6|14 40| 2 7|14 6| 3 7| 15 2| 4 8|15 24| 5 7| - | 8 |16 4| 0 7|15 42| 1 7|15 39| 2 8|15 5| 3 8| 16 2| 4 9|16 25| 5 8| - | 9 |17 1| 0 8|16 39| 1 8|16 37| 2 9|16 4| 3 9| 17 2| 4 10|17 26| 5 9| - | 10 |17 59| 0 8|17 37| 1 9|17 35| 2 10|17 4| 3 10| 18 3| 4 11|18 27| 5 10| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 11 |18 56| 0 9|18 35| 1 10|18 34| 2 11|18 3| 3 11| 19 3| 4 12|19 28| 5 11| - | 12 |19 53| 0 10|19 32| 1 11|19 32| 2 12|19 3| 3 12| 20 4| 4 13|20 29| 5 12| - | 13 |20 50| 0 11|20 30| 1 12|20 31| 2 13|20 2| 3 13| 21 4| 4 14|21 30| 5 13| - | 14 |21 47| 0 12|21 28| 1 13|21 29| 2 14|21 2| 3 14| 22 5| 4 15|22 31| 5 14| - | 15 |22 45| 0 13|22 25| 1 14|22 28| 2 15|22 2| 3 15| 23 5| 4 16|23 32| 5 15| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 16 |23 42| 0 14|23 23| 1 15|23 27| 2 16|23 1| 3 16| 24 6| 4 17|24 33| 5 16| - | 17 |24 39| 0 15|24 21| 1 16|24 25| 2 17|24 1| 3 17| 25 7| 4 18|25 34| 5 17| - | 18 |25 36| 0 16|25 19| 1 17|25 24| 2 18|25 1| 3 18| 26 7| 4 19|26 35| 5 18| - | 19 |26 34| 0 17|26 17| 1 18|26 23| 2 19|26 0| 3 19| 27 8| 4 20|27 36| 5 19| - | 20 |27 31| 0 18|27 14| 1 19|27 21| 2 20|27 0| 3 20| 28 9| 4 21|28 38| 5 20| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 21 |28 28| 0 19|28 12| 1 20|28 20| 2 21|28 0| 3 21| 29 9| 4 22|29 39| 5 21| - | 22 |29 26| 0 20|29 10| 1 21|29 19| 2 22|29 0| 3 22| ♐ 10| 4 23| ♑ 40| 5 22| - | 23 | ♌ 23| 0 21| ♍ 8| 1 22| ♎ 18| 2 23| ♏ 0| 3 23| 1 11| 4 24| 1 41| 5 23| - | 24 | 1 20| 0 22| 1 6| 1 23| 1 17| 2 24| 1 0| 3 24| 2 12| 4 25| 2 42| 5 24| - | 25 | 2 18| 0 23| 2 4| 1 24| 2 16| 2 25| 2 0| 3 25| 3 12| 4 26| 3 44| 5 25| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 26 | 3 15| 0 24| 3 2| 1 25| 3 15| 2 26| 3 0| 3 26| 4 13| 4 27| 4 45| 5 26| - | 27 | 4 12| 0 25| 4 0| 1 26| 4 14| 2 27| 4 0| 3 27| 5 14| 4 28| 5 46| 5 27| - | 28 | 5 10| 0 26| 4 58| 1 27| 5 13| 2 28| 5 0| 3 28| 6 15| 4 29| 6 47| 5 28| - | 29 | 6 7| 0 27| 5 56| 1 28| 6 12| 2 29| 6 0| 3 29| 7 16| 4 29| 7 48| 5 29| - | 30 | 7 5| 0 28| 6 54| 1 29| 7 11| 3 0| 7 0| 4 0| 8 17| 5 0| 8 49| 6 0| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 31 | 8 2| 0 29| 7 52| 2 0| | | 8 0| 4 1| | | 9 51| 6 1| - +----+------+------+------+------+------+------+------+------+------+------+------+------+ - +----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +----------------------------------------------------------------------------------------+ - | The Bissextile, or Leap-year. | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - |Days|January |Dif.|February|Dif.| March |Dif.| April |Dif.| May |Dif.| June |Dif.| - | +--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - |----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Inc.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 4 0| |12 14 5| |12 12 36| |12 3 48| |11 56 47| |11 57 22| | - | | | 28 | | 7 | | 13 | | 18 | | 7 | | 9 | - | 2 |12 4 28| |12 14 12| |12 12 23| |12 3 30| |11 56 40| |11 57 31| | - | | | 28 | | 7 | | 13 | | 19 | | 7 | | 9 | - | 3 |12 4 56| |12 14 19| |12 12 10| |12 3 11| |11 56 33| |11 57 40| | - | | | 28 | | 6 | | 14 | | 18 | | 6 | | 10 | - | 4 |12 5 24| |12 14 25| |12 11 56| |12 2 53| |11 56 27| |11 57 50| | - | | | 27 | | 5 | | 14 | | 18 | | 6 | | 10 | - | 5 |12 5 51| |12 14 30| |12 11 42| |12 2 35| |11 56 21| |11 58 0| | - +----+--------+ 27 +--------+ 4 +--------+ 14 +--------+ 18 +--------+ 5 +--------+ 11 | - | 6 |12 6 18| |12 14 34| |12 11 28| |12 2 17| |11 56 16| |11 58 11| | - | | | 26 | | 3 | | 15 | | 17 | | 4 | | 11 | - | 7 |12 6 44| |12 14 37| |12 11 13| |12 2 0| |11 56 12| |11 58 22| | - | | | 26 | | 3 | | 15 | | 17 | | 4 | | 11 | - | 8 |12 7 10| |12 14 40| |12 10 58| |12 1 43| |11 56 8| |11 58 33| | - | | | 25 | | 2 | | 16 | | 17 | | 4 | | 11 | - | 9 |12 7 35| |12 14 42| |12 10 42| |12 1 26| |11 56 4| |11 58 44| | - | | | 25 | | 1 | | 16 | | 17 | | 3 | | 12 | - | 10 |12 8 0| |12 14 43| |12 10 46| |12 1 9| |11 56 1| |11 58 56| | - +----+--------+ 24 +--------+Dec.+--------+ 16 +--------+ 16 +--------+ 2 +--------+ 12 + - | 11 |12 8 24| |12 14 44| |12 10 10| |12 0 53| |11 55 59| |11 59 8| | - | | | 23 | | 1 | | 17 | | 16 | | 1 | | 12 | - | 12 |12 8 47| |12 14 43| |12 9 53| |12 0 37| |11 55 58| |11 59 20| | - | | | 23 | | 1 | | 17 | | 16 | | 1 | | 12 | - | 13 |12 9 10| |12 14 42| |12 9 36| |12 0 21| |11 55 57| |11 59 32| | - | | | 22 | | 2 | | 17 | | 15 | |Inc.| | 12 | - | 14 |12 9 32| |12 14 40| |12 9 19| |12 0 6| |11 55 56| |11 59 44| | - | | | 22 | | 3 | | 17 | | 15 | | 1 | | 13 | - | 15 |12 9 54| |12 14 37| |12 9 2| |11 59 51| |11 55 57| |11 59 57| | - +----+--------+ 21 +--------+ 4 +--------+ 18 +--------+ 15 +--------+ 1 +--------+ 13 + - | 16 |12 10 15| |12 14 33| |12 8 44| |11 59 36| |11 55 58| |12 0 10| | - | | | 20 | | 4 | | 18 | | 15 | | 1 | | 13 | - | 17 |12 10 35| |12 14 29| |12 8 26| |11 59 21| |11 55 59| |12 0 23| | - | | | 19 | | 5 | | 18 | | 14 | | 2 | | 12 | - | 18 |12 10 54| |12 14 24| |12 8 8| |11 59 7| |11 56 1| |12 0 35| | - | | | 19 | | 5 | | 18 | | 13 | | 2 | | 13 | - | 19 |12 10 13| |12 14 19| |12 7 50| |11 58 54| |11 56 3| |12 0 48| | - | | | 18 | | 6 | | 18 | | 13 | | 3 | | 13 | - | 20 |12 10 31| |12 14 13| |12 7 32| |11 58 41| |11 56 6| |12 1 1| | - +----+--------+ 17 +--------+ 7 +--------+ 18 +--------+ 13 +--------+ 3 +--------+ 13 + - | 21 |12 11 48| |12 14 6| |12 7 14| |11 58 28| |11 56 9| |12 1 14| | - | | | 17 | | 8 | | 19 | | 12 | | 4 | | 13 | - | 22 |12 12 5| |12 13 58| |12 6 55| |11 58 16| |11 56 13| |12 1 27| | - | | | 16 | | 8 | | 19 | | 12 | | 5 | | 13 | - | 23 |12 12 21| |12 13 50| |12 6 36| |11 58 4| |11 56 18| |12 1 40| | - | | | 15 | | 9 | | 19 | | 12 | | 5 | | 13 | - | 24 |12 12 36| |12 13 41| |12 6 17| |11 57 52| |11 56 23| |12 1 53| | - | | | 14 | | 9 | | 19 | | 11 | | 6 | | 13 | - | 25 |12 12 50| |12 13 32| |12 5 58| |11 57 41| |11 56 29| |12 2 6| | - +----+--------+ 13 +--------+ 10 +--------+ 18 +--------+ 10 +--------+ 6 +--------+ 12 + - | 26 |12 13 3| |12 13 22| |12 5 40| |11 57 31| |11 56 35| |12 2 18| | - | | | 12 | | 11 | | 19 | | 10 | | 7 | | 13 | - | 27 |12 13 15| |12 13 11| |12 5 21| |11 57 21| |11 56 42| |12 2 31| | - | | | 12 | | 11 | | 19 | | 9 | | 7 | | 12 | - | 28 |12 13 27| |12 13 0| |12 5 2| |11 57 12| |11 56 49| |12 2 43| | - | | | 11 | | 12 | | 18 | | 9 | | 7 | | 12 | - | 29 |12 13 38| |12 12 48| |12 4 44| |11 57 3| |11 56 56| |12 2 55| | - | | | 10 | | 12 | | 19 | | 8 | | 8 | | 12 | - | 30 |12 13 48| | | |12 4 25| |11 56 55| |11 57 4| |12 3 7| | - +----+--------+ 9 +--------+----+--------+ 19 +--------+ 8 +--------+ 9 +--------+ 11 + - | 31 |12 13 57| | | |12 4 6| | | |11 57 13| | | | - | | | 8 | | | | 18 | | | | 9 | | | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - Incr. 9ʹ 57ʺ Incr. 0ʹ 39ʺ Decr. 8ʹ 30ʺ Decr. 6ʹ 53ʺ Decr. 0ʹ 50ʺ Incr. 5ʹ 45ʺ - Decr. 1 56 Incr. 1 17 - +-----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +-----------------------------------------------------------------------------------------+ - | The Bissextile, or Leap-year. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| - | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. | H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 3 18| |12 5 46| | 11 59 33| |11 49 28| |11 43 49| |11 49 42| | - | | | 11 | | 4 | | 19 | | 18 | | 1 | | 24 | - | 2 |12 3 29| |12 5 42| | 11 59 14| |11 49 10| |11 43 48| |11 50 6| | - | | | 11 | | 5 | | 19 | | 18 | |Inc.| | 24 | - | 3 |12 3 40| |12 5 37| | 11 58 55| |11 48 52| |11 43 49| |11 50 30| | - | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | - | 4 |12 3 51| |12 5 32| | 11 58 36| |11 48 34| |11 43 50| |11 50 55| | - | | | 11 | | 6 | | 19 | | 18 | | 2 | | 25 | - | 5 |12 4 2| |12 5 26| | 11 58 17| |11 48 16| |11 43 52| |11 51 20| | - +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + - | 6 |12 4 12| |12 5 20| | 11 57 57| |11 47 59| |11 43 55| |11 51 46| | - | | | 10 | | 7 | | 20 | | 17 | | 4 | | 26 | - | 7 |12 4 22| |12 5 13| | 11 57 37| |11 47 42| |11 43 59| |11 52 12| | - | | | 9 | | 8 | | 20 | | 16 | | 5 | | 26 | - | 8 |12 4 31| |12 5 5| | 11 57 17| |11 47 26| |11 44 4| |11 52 38| | - | | | 9 | | 8 | | 20 | | 15 | | 6 | | 28 | - | 9 |12 4 40| |12 4 57| | 11 56 57| |11 47 11| |11 44 10| |11 53 6| | - | | | 8 | | 9 | | 21 | | 15 | | 6 | | 27 | - | 10 |12 4 48| |12 4 48| | 11 56 36| |11 46 56| |11 44 16| |11 53 33| | - +----+--------+ 8 +--------+ 9 +---------+ 21 +--------+ 15 +--------+ 7 +--------+ 28 + - | 11 |12 4 56| |12 4 39| | 11 56 15| |11 46 41| |11 44 23| |11 54 1| | - | | | 8 | | 10 | | 21 | | 15 | | 8 | | 29 | - | 12 |12 5 4| |12 4 29| | 11 55 54| |11 46 26| |11 44 31| |11 54 30| | - | | | 7 | | 10 | | 21 | | 14 | | 9 | | 29 | - | 13 |12 5 11| |12 4 19| | 11 55 33| |11 46 12| |11 44 40| |11 54 59| | - | | | 7 | | 11 | | 21 | | 13 | | 10 | | 29 | - | 14 |12 5 18| |12 4 8| | 11 55 12| |11 45 59| |11 44 50| |11 55 28| | - | | | 6 | | 12 | | 21 | | 13 | | 11 | | 29 | - | 15 |12 5 24| |12 3 56| | 11 54 51| |11 45 46| |11 45 1| |11 55 57| | - +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 12 +--------+ 12 +--------+ 29 + - | 16 |12 5 30| |12 3 44| | 11 54 30| |11 45 34| |11 45 13| |11 56 26| | - | | | 5 | | 12 | | 20 | | 11 | | 13 | | 30 | - | 17 |12 5 35| |12 3 32| | 11 54 10| |11 45 23| |11 45 26| |11 56 56| | - | | | 5 | | 13 | | 21 | | 11 | | 13 | | 30 | - | 18 |12 5 40| |12 3 19| | 11 53 49| |11 45 12| |11 45 39| |11 57 26| | - | | | 4 | | 13 | | 21 | | 11 | | 14 | | 30 | - | 19 |12 5 44| |12 3 6| | 11 53 28| |11 45 1| |11 45 53| |11 57 56| | - | | | 4 | | 14 | | 21 | | 10 | | 15 | | 30 | - | 20 |12 5 48| |12 2 52| | 11 53 7| |11 44 51| |11 46 8| |11 58 26| | - +----+--------+ 3 +--------+ 14 +---------+ 21 +--------+ 9 +--------+ 16 +--------+ 30 | - | 21 |12 5 51| |12 2 38| | 11 52 46| |11 44 42| |11 46 24| |11 58 56| | - | | | 2 | | 15 | | 21 | | 9 | | 16 | | 30 | - | 22 |12 5 53| |12 2 23| | 11 52 25| |11 44 33| |11 46 40| |11 59 26| | - | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | - | 23 |12 5 55| |12 2 8| | 11 52 5| |11 44 25| |11 46 57| |11 59 56| | - | | | 2 | | 16 | | 20 | | 7 | | 18 | | 30 | - | 24 |12 5 57| |12 1 52| | 11 51 45| |11 44 18| |11 47 15| |12 0 26| | - | | | 1 | | 16 | | 20 | | 7 | | 19 | | 30 | - | 25 |12 5 58| |12 1 36| | 11 51 25| |11 44 11| |11 47 34| |12 0 56| | - +----+--------+ 1 +--------+ 17 +---------+ 20 +--------+ 6 +--------+ 20 +--------+ 30 + - | 26 |12 5 59| |12 1 19| | 11 51 5| |11 44 5| |11 47 54| |12 1 26| | - | | |Dec.| | 17 | | 20 | | 5 | | 20 | | 30 | - | 27 |12 5 58| |12 1 2| | 11 50 45| |11 44 0| |11 48 14| |12 1 56| | - | | | 1 | | 17 | | 20 | | 4 | | 21 | | 29 | - | 28 |12 5 57| |12 0 45| | 11 50 25| |11 43 56| |11 48 35| |12 2 25| | - | | | 2 | | 17 | | 19 | | 3 | | 22 | | 29 | - | 29 |12 5 55| |12 0 28| | 11 50 6| |11 43 53| |11 48 57| |12 2 54| | - | | | 2 | | 18 | | 19 | | 2 | | 22 | | 29 | - | 30 |12 5 53| |12 0 10| | 11 49 47| |11 43 51| |11 49 19| |12 3 23| | - +----+--------+ 3 +--------+ 18 +---------+ 19 +--------+ 1 +--------+ 23 +--------+ 29 + - | 31 |12 5 50| |11 59 52| | | |11 43 50| | | |12 3 52| | - | | | 4 | | 19 | | | | 1 | | | | | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - Incr. 2ʹ 41ʺ Decr. 5ʹ 54ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 38ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 10ʺ - Decr. 0 8 Incr. 5 30 - +-----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +-----------------------------------------------------------------------------------------+ - | The Bissextile, or Leap-year. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| - | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. | H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 3 18| |12 5 46| | 11 59 33| |11 49 28| |11 43 49| |11 49 42| | - | | | 11 | | 4 | | 19 | | 18 | | 1 | | 24 | - | 2 |12 3 29| |12 5 42| | 11 59 14| |11 49 10| |11 43 48| |11 50 6| | - | | | 11 | | 5 | | 19 | | 18 | |Inc.| | 24 | - | 3 |12 3 40| |12 5 37| | 11 58 55| |11 48 52| |11 43 49| |11 50 30| | - | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | - | 4 |12 3 51| |12 5 32| | 11 58 36| |11 48 34| |11 43 50| |11 50 55| | - | | | 11 | | 6 | | 19 | | 18 | | 2 | | 25 | - | 5 |12 4 2| |12 5 26| | 11 58 17| |11 48 16| |11 43 52| |11 51 20| | - +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + - | 6 |12 4 12| |12 5 20| | 11 57 57| |11 47 59| |11 43 55| |11 51 46| | - | | | 10 | | 7 | | 20 | | 17 | | 4 | | 26 | - | 7 |12 4 22| |12 5 13| | 11 57 37| |11 47 42| |11 43 59| |11 52 12| | - | | | 9 | | 8 | | 20 | | 16 | | 5 | | 26 | - | 8 |12 4 31| |12 5 5| | 11 57 17| |11 47 26| |11 44 4| |11 52 38| | - | | | 9 | | 8 | | 20 | | 15 | | 6 | | 28 | - | 9 |12 4 40| |12 4 57| | 11 56 57| |11 47 11| |11 44 10| |11 53 6| | - | | | 8 | | 9 | | 21 | | 15 | | 6 | | 27 | - | 10 |12 4 48| |12 4 48| | 11 56 36| |11 46 56| |11 44 16| |11 53 33| | - +----+--------+ 8 +--------+ 9 +---------+ 21 +--------+ 15 +--------+ 7 +--------+ 28 + - | 11 |12 4 56| |12 4 39| | 11 56 15| |11 46 41| |11 44 23| |11 54 1| | - | | | 8 | | 10 | | 21 | | 15 | | 8 | | 29 | - | 12 |12 5 4| |12 4 29| | 11 55 54| |11 46 26| |11 44 31| |11 54 30| | - | | | 7 | | 10 | | 21 | | 14 | | 9 | | 29 | - | 13 |12 5 11| |12 4 19| | 11 55 33| |11 46 12| |11 44 40| |11 54 59| | - | | | 7 | | 11 | | 21 | | 13 | | 10 | | 29 | - | 14 |12 5 18| |12 4 8| | 11 55 12| |11 45 59| |11 44 50| |11 55 28| | - | | | 6 | | 12 | | 21 | | 13 | | 11 | | 29 | - | 15 |12 5 24| |12 3 56| | 11 54 51| |11 45 46| |11 45 1| |11 55 57| | - +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 12 +--------+ 12 +--------+ 29 + - | 16 |12 5 30| |12 3 44| | 11 54 30| |11 45 34| |11 45 13| |11 56 26| | - | | | 5 | | 12 | | 20 | | 11 | | 13 | | 30 | - | 17 |12 5 35| |12 3 32| | 11 54 10| |11 45 23| |11 45 26| |11 56 56| | - | | | 5 | | 13 | | 21 | | 11 | | 13 | | 30 | - | 18 |12 5 40| |12 3 19| | 11 53 49| |11 45 12| |11 45 39| |11 57 26| | - | | | 4 | | 13 | | 21 | | 11 | | 14 | | 30 | - | 19 |12 5 44| |12 3 6| | 11 53 28| |11 45 1| |11 45 53| |11 57 56| | - | | | 4 | | 14 | | 21 | | 10 | | 15 | | 30 | - | 20 |12 5 48| |12 2 52| | 11 53 7| |11 44 51| |11 46 8| |11 58 26| | - +----+--------+ 3 +--------+ 14 +---------+ 21 +--------+ 9 +--------+ 16 +--------+ 30 | - | 21 |12 5 51| |12 2 38| | 11 52 46| |11 44 42| |11 46 24| |11 58 56| | - | | | 2 | | 15 | | 21 | | 9 | | 16 | | 30 | - | 22 |12 5 53| |12 2 23| | 11 52 25| |11 44 33| |11 46 40| |11 59 26| | - | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | - | 23 |12 5 55| |12 2 8| | 11 52 5| |11 44 25| |11 46 57| |11 59 56| | - | | | 2 | | 16 | | 20 | | 7 | | 18 | | 30 | - | 24 |12 5 57| |12 1 52| | 11 51 45| |11 44 18| |11 47 15| |12 0 26| | - | | | 1 | | 16 | | 20 | | 7 | | 19 | | 30 | - | 25 |12 5 58| |12 1 36| | 11 51 25| |11 44 11| |11 47 34| |12 0 56| | - +----+--------+ 1 +--------+ 17 +---------+ 20 +--------+ 6 +--------+ 20 +--------+ 30 + - | 26 |12 5 59| |12 1 19| | 11 51 5| |11 44 5| |11 47 54| |12 1 26| | - | | |Dec.| | 17 | | 20 | | 5 | | 20 | | 30 | - | 27 |12 5 58| |12 1 2| | 11 50 45| |11 44 0| |11 48 14| |12 1 56| | - | | | 1 | | 17 | | 20 | | 4 | | 21 | | 29 | - | 28 |12 5 57| |12 0 45| | 11 50 25| |11 43 56| |11 48 35| |12 2 25| | - | | | 2 | | 17 | | 19 | | 3 | | 22 | | 29 | - | 29 |12 5 55| |12 0 28| | 11 50 6| |11 43 53| |11 48 57| |12 2 54| | - | | | 2 | | 18 | | 19 | | 2 | | 22 | | 29 | - | 30 |12 5 53| |12 0 10| | 11 49 47| |11 43 51| |11 49 19| |12 3 23| | - +----+--------+ 3 +--------+ 18 +---------+ 19 +--------+ 1 +--------+ 23 +--------+ 29 + - | 31 |12 5 50| |11 59 52| | | |11 43 50| | | |12 3 52| | - | | | 4 | | 19 | | | | 1 | | | | | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - Incr. 2ʹ 41ʺ Decr. 5ʹ 54ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 38ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 10ʺ - Decr. 0 8 Incr. 5 30 - - +-----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +-----------------------------------------------------------------------------------------+ - | The first after Leap-year. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| - | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. | H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 3 15| |12 5 48| |11 59 38 | |11 49 33| |11 43 49| |11 49 36| | - | | | 12 | | 4 | | 19 | | 19 | | 0 | | 24 | - | 2 |12 3 27| |12 5 44| |11 59 19 | |11 49 14| |11 43 49| |11 50 0| | - | | | 11 | | 5 | | 19 | | 19 | |Inc.| | 24 | - | 3 |12 3 38| |12 5 39| |11 59 0 | |11 48 55| |11 43 49| |11 50 24| | - | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | - | 4 |12 3 49| |12 5 34| |11 58 41 | |11 48 37| |11 43 50| |11 50 49| | - | | | 10 | | 6 | | 20 | | 17 | | 2 | | 25 | - | 5 |12 3 59| |12 5 28| |11 58 21 | |11 48 20| |11 43 52| |11 51 14| | - +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + - | 6 |12 4 9| |12 5 22| |11 58 1 | |11 48 3| |11 43 55| |11 51 40| | - | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | - | 7 |12 4 19| |12 5 15| |11 57 41 | |11 47 46| |11 43 58| |11 52 6| | - | | | 10 | | 7 | | 20 | | 17 | | 4 | | 27 | - | 8 |12 4 29| |12 5 8| |11 57 21 | |11 47 29| |11 44 2| |11 52 33| | - | | | 9 | | 8 | | 20 | | 16 | | 5 | | 27 | - | 9 |12 4 38| |12 5 0| |11 57 1 | |11 47 13| |11 44 7| |11 53 0| | - | | | 8 | | 9 | | 20 | | 15 | | 6 | | 27 | - | 10 |12 4 46| |12 4 51| |11 56 41 | |11 46 58| |11 44 13| |11 53 27| | - +----+--------+ 8 +--------+ 9 +---------+ 20 +--------+ 15 +--------+ 7 +--------+ 28 + - | 11 |12 4 54| |12 4 42| |11 56 21 | |11 46 43| |11 44 20| |11 53 35| | - | | | 8 | | 10 | | 21 | | 14 | | 8 | | 28 | - | 12 |12 5 2| |12 4 32| |11 56 0 | |11 46 29| |11 44 28| |11 54 23| | - | | | 8 | | 10 | | 21 | | 13 | | 9 | | 29 | - | 13 |12 5 10| |12 4 22| |11 55 39 | |11 46 16| |11 44 37| |11 54 52| | - | | | 7 | | 11 | | 21 | | 13 | | 10 | | 29 | - | 14 |12 5 17| |12 4 11| |11 55 18 | |11 46 3| |11 44 47| |11 55 21| | - | | | 6 | | 11 | | 21 | | 13 | | 11 | | 29 | - | 15 |12 5 23| |12 4 0| |11 54 57 | |11 45 50| |11 44 58| |11 55 50| | - +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 13 +--------+ 12 +--------+ 30 + - | 16 |12 5 29| |12 3 48| |11 54 36 | |11 45 37| |11 45 10| |11 56 19| | - | | | 5 | | 12 | | 21 | | 12 | | 13 | | 30 | - | 17 |12 5 34| |12 3 36| |11 54 15 | |11 45 25| |11 45 23| |11 56 49| | - | | | 5 | | 13 | | 21 | | 11 | | 13 | | 30 | - | 18 |12 5 39| |12 3 23| |11 53 54 | |11 45 14| |11 45 36| |11 57 19| | - | | | 4 | | 13 | | 21 | | 11 | | 14 | | 30 | - | 19 |12 5 43| |12 3 10| |11 53 33 | |11 45 3| |33 45 50| |11 57 49| | - | | | 4 | | 14 | | 21 | | 10 | | 14 | | 30 | - | 20 |12 5 47| |12 2 56| |11 53 12 | |11 44 53| |11 46 4| |11 58 19| | - +----+--------+ 4 +--------+ 14 +---------+ 21 +--------+ 10 +--------+ 15 +--------+ 30 + - | 21 |12 5 51| |12 2 42| |11 52 51 | |11 44 43| |11 46 19| |11 58 49| | - | | | 3 | | 15 | | 20 | | 9 | | 16 | | 30 | - | 22 |12 5 54| |12 2 17| |11 52 31 | |11 44 34| |11 46 35| |11 59 19| | - | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | - | 23 |12 5 56| |12 2 12| |11 52 11 | |11 44 26| |11 46 52| |11 59 49| | - | | | 1 | | 16 | | 21 | | 7 | | 18 | | 30 | - | 24 |12 5 57| |12 1 56| |11 51 50 | |11 44 19| |11 47 10| |12 0 19| | - | | | 1 | | 16 | | 21 | | 6 | | 19 | | 30 | - | 25 |12 5 58| |12 1 40| |11 51 29 | |11 44 13| |11 47 29| |12 0 49| | - +----+--------+Dec.+--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + - | 26 |12 5 59| |12 1 24| |11 51 9 | |11 44 7| |11 47 48| |12 1 19| | - | | | 1 | | 17 | | 20 | | 5 | | 20 | | 30 | - | 27 |12 5 58| |12 1 7| |11 50 40 | |11 44 2| |11 48 8| |12 1 49| | - | | | 1 | | 17 | | 19 | | 4 | | 21 | | 29 | - | 28 |12 5 57| |12 1 50| |11 50 30 | |11 43 58| |11 48 29| |12 2 18| | - | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | - | 29 |12 5 55| |12 1 32| |11 50 11 | |11 43 55| |11 48 51| |12 2 47| | - | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | - | 30 |12 5 53| |12 0 14| |11 49 52 | |11 43 52| |11 49 13| |12 3 16| | - +----+--------+ 2 +--------+ 18 +---------+ 19 +--------+ 2 +--------+ 23 +--------+ 29 + - | 31 |12 5 51| |11 59 56| | | |11 43 50| | | |12 3 45| | - | | | 3 | | 18 | | | | 1 | | | | 29 | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - Incr. 2ʹ 43ʺ Decr. 5ʹ 52ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 43ʺ Decr. 0ʹ 0ʺ Incr. 14ʹ 9ʺ - Decr. 0 8 Incr. 5 24 - +----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +----------------------------------------------------------------------------------------+ - | The second after Leap-year. | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - |Days| January|Dif.|February|Dif.| March |Dif.| April |Dif.| May |Dif.| June |Dif.| - | +--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Inc.| |Dec.| |Dec.| |Inc.| - | 1 |12 4 14| |12 14 9| |12 12 42| |12 3 56| |11 56 50| |11 57 16| | - | | | 28 | | 7 | | 13 | | 18 | | 8 | | 9 | - | 2 |12 4 42| |12 14 16| |12 12 20| |12 3 38| |11 56 42| |11 57 25| | - | | | 28 | | 6 | | 13 | | 18 | | 7 | | 10 | - | 3 |12 5 10| |12 14 22| |12 12 16| |12 3 20| |11 56 35| |11 57 35| | - | | | 27 | | 5 | | 13 | | 18 | | 6 | | 10 | - | 4 |12 5 37| |12 14 27| |12 12 3| |12 3 2| |11 56 29| |11 57 45| | - | | | 27 | | 5 | | 14 | | 18 | | 6 | | 10 | - | 5 |12 6 4| |12 14 32| |12 11 49| |12 2 44| |11 56 23| |11 57 55| | - +----+--------+ 27 +--------+ 4 +--------+ 14 +--------+ 18 +--------+ 5 +--------+ 10 + - | 6 |12 6 30| |12 14 36| |12 11 35| |12 2 26| |11 56 18| |11 58 5| | - | | | 26 | | 3 | | 15 | | 17 | | 5 | | 11 | - | 7 |12 6 56| |12 14 39| |12 11 20| |12 2 9| |11 56 23| |11 58 16| | - | | | 26 | | 2 | | 15 | | 17 | | 4 | | 11 | - | 8 |12 7 22| |12 14 41| |12 11 5| |12 1 52| |11 56 9| |11 58 27| | - | | | 25 | | 2 | | 15 | | 17 | | 3 | | 11 | - | 9 |12 7 47| |12 14 43| |12 10 50| |12 1 35| |11 56 6| |11 58 38| | - | | | 24 | | 1 | | 16 | | 17 | | 3 | | 12 | - | 10 |12 8 11| |12 14 44| |12 10 34| |12 1 18| |11 56 3| |11 58 50| | - +----+--------+ 24 +--------+Dec.+--------+ 16 +--------+ 17 +--------+ 2 +--------+ 12 + - | 11 |12 8 35| |12 14 44| |12 10 18| |12 1 1| |11 56 1| |11 59 2| | - | | | 23 | | 1 | | 17 | | 16 | | 2 | | 12 | - | 12 |12 8 58| |12 14 43| |12 10 1| |12 0 45| |11 55 59| |11 59 14| | - | | | 22 | | 2 | | 17 | | 16 | | 2 | | 12 | - | 13 |12 9 20| |12 14 41| |12 9 44| |12 0 29| |11 55 57| |11 59 26| | - | | | 22 | | 3 | | 17 | | 16 | | 1 | | 12 | - | 14 |12 9 42| |12 14 38| |12 9 27| |12 0 13| |11 55 56| |11 59 38| | - | | | 21 | | 3 | | 17 | | 15 | |Inc.| | 12 | - | 15 |12 10 3| |12 14 35| |12 9 10| |11 59 58| |11 55 56| |11 59 50| - +----+--------+ 21 +--------+ 4 +--------+ 18 +--------+ 15 +--------+ 1 +--------+ 13 + - | 16 |12 10 24| |12 14 31| |12 8 52| |11 59 43| |11 55 57| |12 0 3| | - | | | 20 | | 4 | | 18 | | 14 | | 1 | | 13 | - | 17 |12 10 44| |12 14 27| |12 8 34| |11 59 29| |11 55 58| |12 0 16| | - | | | 19 | | 5 | | 18 | | 14 | | 2 | | 13 | - | 18 |12 11 3| |12 14 22| |12 8 16| |11 59 15| |11 56 0| |12 0 29| | - | | | 18 | | 6 | | 18 | | 14 | | 2 | | 13 | - | 19 |12 11 21| |12 14 16| |12 7 58| |11 59 1| |11 56 2| |12 0 42| | - | | | 18 | | 7 | | 18 | | 14 | | 3 | | 13 | - | 20 |12 11 39| |12 14 9| |12 7 40| |11 58 47| |11 56 5| |12 0 55| | - +----+--------+ 17 +--------+ 7 +--------+ 18 +--------+ 13 +--------+ 3 +--------+ 13 + - | 21 |12 11 56| |12 14 2| |12 7 22| |11 58 34| |11 56 8| |12 1 8| | - | | | 16 | | 8 | | 18 | | 12 | | 3 | | 13 | - | 22 |12 12 12| |12 13 54| |12 7 4| |11 58 22| |11 56 11| |12 1 21| | - | | | 15 | | 9 | | 19 | | 12 | | 4 | | 13 | - | 23 |12 12 27 |12 13 45| |12 6 45| |11 58 10| |11 56 15| |12 1 34| | - | | | 15 | | 9 | | 19 | | 12 | | 5 | | 13 | - | 24 |12 12 42| |12 13 36| |12 6 26| |11 57 58| |11 56 20| |12 1 47| | - | | | 14 | | 10 | | 19 | | 11 | | 6 | | 12 | - | 25 |12 12 56| |12 13 26| |12 6 7| |11 57 47| |11 56 26| |12 1 59| | - +----+--------+ 13 +--------+ 10 +--------+ 19 +--------+ 11 +--------+ 6 +--------+ 13 + - | 26 |12 13 9| |12 13 16| |12 5 48| |11 57 36| |11 56 32| |12 2 12| | - | | | 12 | | 11 | | 19 | | 10 | | 6 | | 13 | - | 27 |12 13 21| |12 13 5| |12 5 29| |11 57 26| |11 56 38| |12 2 25| | - | | | 11 | | 11 | | 19 | | 10 | | 7 | | 12 | - | 28 |12 13 32| |12 12 54| |12 5 10| |11 57 16| |11 56 45| |12 2 37| | - | | | 10 | | 12 | | 19 | | 9 | | 7 | | 12 | - | 29 |12 13 42| | | |12 4 51| |11 57 7| |11 56 52| |12 2 49| | - | | | 10 | | | | 18 | | 9 | | 8 | | 12 | - | 30 |12 13 52| | | |12 4 33| |11 56 58| |11 57 0| |12 3 1| | - +----+--------+ 9 +--------+----+--------+ 18 +--------+ 8 +--------+ 8 +--------+ 11 + - | 31 |12 14 1| | | |12 4 15| | | |11 57 8| | | | - | | | 8 | | | | 18 | | | | 8 | | | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - Incr. 9ʹ 47ʺ Incr. 0ʹ 35ʺ Decr. 8ʹ 27ʺ Decr. 6ʹ 58ʺ Decr. 0ʹ 54ʺ Incr. 5ʹ 45ʺ - Decr. 1 50 Incr. 1 12 - +-----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +-----------------------------------------------------------------------------------------+ - | The second after Leap-year. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| - | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. |H. M. S. | S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 3 12| |12 5 48| |11 59 43 | |11 49 37| |11 43 49| |11 49 30| | - | | | 12 | | 4 | | 19 | | 19 | | 1 | | 23 | - | 2 |12 3 24| |12 5 44| |11 59 24 | |11 49 18| |11 43 48| |11 49 53| | - | | | 11 | | 4 | | 19 | | 18 | |Inc.| | 24 | - | 3 |12 3 35| |12 5 40| |11 59 5 | |11 49 0| |11 43 49| |11 50 17| | - | | | 11 | | 5 | | 19 | | 18 | | 1 | | 25 | - | 4 |12 3 46| |12 5 35| |11 58 46 | |11 48 42| |11 43 50| |11 50 42| | - | | | 11 | | 5 | | 20 | | 18 | | 2 | | 25 | - | 5 |12 3 57| |12 5 30| |11 58 26 | |11 48 24| |11 43 52| |11 51 7| | - +-------------+ 10 +--------+ 6 +---------+ 20 +--------+ 17 +--------+ 3 +--------+ 26 + - | 6 |12 4 7| |12 5 24| |11 58 6 | |11 48 7| |11 43 55| |11 51 33| | - | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | - | 7 |12 4 17| |12 5 17| |11 57 46 | |11 47 50| |11 43 58| |11 51 59| | - | | | 9 | | 7 | | 20 | | 17 | | 4 | | 26 | - | 8 |12 4 26| |12 5 10| |11 57 26 | |11 47 33| |11 44 2| |11 52 25| | - | | | 9 | | 8 | | 21 | | 16 | | 5 | | 27 | - | 9 |12 4 35| |12 5 2| |11 57 5 | |11 47 17| |11 44 7| |11 52 52| | - | | | 9 | | 9 | | 20 | | 16 | | 6 | | 28 | - | 10 |12 4 44| |12 4 53| |11 56 45 | |11 47 1| |11 44 13| |11 53 20| | - +----+--------+ 8 +--------+ 9 +---------+ 21 +--------+ 15 +--------+ 7 +--------+ 28 + - | 11 |12 4 52| |12 4 44| |11 56 24 | |11 46 46| |11 44 20| |11 53 48| | - | | | 8 | | 9 | | 21 | | 14 | | 8 | | 28 | - | 12 |12 5 0| |12 4 35| |11 56 3 | |11 46 32| |11 44 28| |11 54 16| | - | | | 8 | | 10 | | 21 | | 14 | | 9 | | 28 | - | 13 |12 5 8| |12 4 25| |11 55 42 | |11 46 18| |11 44 37| |11 54 44| | - | | | 7 | | 11 | | 20 | | 13 | | 9 | | 29 | - | 14 |12 5 15| |12 4 13| |11 55 22 | |11 46 5| |11 44 46| |11 54 13| | - | | | 6 | | 11 | | 20 | | 13 | | 10 | | 29 | - | 15 |12 5 21| |12 4 3| |11 55 2 | |11 45 52| |11 44 56| |11 55 42| | - +----+--------+ 6 +--------+ 12 +---------+ 21 +--------+ 13 +--------+ 11 +--------+ 29 + - | 16 |12 5 27| |12 3 51| |11 54 41 | |11 45 39| |11 45 7| |11 56 11| | - | | | 6 | | 12 | | 21 | | 12 | | 12 | | 30 | - | 17 |12 5 33| |12 3 39| |11 54 20 | |11 45 27| |11 45 19| |11 56 41| | - | | | 5 | | 12 | | 21 | | 11 | | 13 | | 30 | - | 18 |12 5 38| |12 3 27| |11 53 59 | |11 45 16| |11 45 32| |11 57 11| | - | | | 4 | | 13 | | 20 | | 10 | | 14 | | 30 | - | 19 |12 5 42| |12 3 14| |11 53 39 | |11 45 6| |11 45 46| |11 57 41| | - | | | 4 | | 14 | | 21 | | 10 | | 15 | | 30 | - | 20 |12 5 46| |12 3 0| |11 53 18 | |11 44 56| |11 46 1| |11 58 11| | - +----+--------+ 3 +--------+ 14 +---------+ 21 +--------+ 10 +--------+ 15 +--------+ 30 + - | 21 |12 5 49| |12 2 46| |11 52 57 | |11 44 46| |11 46 16| |11 58 41| | - | | | 3 | | 15 | | 20 | | 9 | | 16 | | 30 | - | 22 |12 5 52| |12 2 31| |11 52 37 | |11 44 37| |11 46 32| |11 59 11| | - | | | 2 | | 15 | | 21 | | 8 | | 17 | | 30 | - | 23 |12 5 54| |12 2 16| |11 52 16 | |11 44 29| |11 46 49| |11 59 41| | - | | | 2 | | 15 | | 21 | | 7 | | 18 | | 30 | - | 24 |12 5 56| |12 2 1| |11 51 55 | |11 44 22| |11 47 7| |12 0 11| | - | | | 2 | | 16 | | 21 | | 7 | | 18 | | 30 | - | 25 |12 5 58| |12 1 45| |11 51 34 | |11 44 15| |11 47 25| |12 0 41| | - +----+--------+ 1 +--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + - | 26 |12 5 59| |12 1 29| |11 51 14 | |11 44 9| |11 47 44| |12 1 11| | - | | |Dec.| | 17 | | 20 | | 5 | | 20 | | 30 | - | 27 |12 5 58| |12 1 12| |11 50 54 | |11 44 4| |11 48 4| |12 1 41| | - | | | 1 | | 17 | | 20 | | 5 | | 21 | | 30 | - | 28 |12 5 57| |12 0 55| |11 50 34 | |11 43 59| |11 48 25| |12 2 11| | - | | | 1 | | 18 | | 19 | | 4 | | 21 | | 29 | - | 29 |12 5 56| |12 0 37| |11 50 15 | |11 43 55| |11 48 46| |12 2 40| | - | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | - | 30 |12 5 54| |12 0 19| |11 49 56 | |11 43 52| |11 49 8| |12 3 9| | - +----+--------+ 3 +--------+ 18 +---------+ 19 +--------+ 2 +--------+ 22 +--------+ 29 + - | 31 |12 5 51| |12 0 1| | | |11 43 50| | | |12 3 38| | - | | | 3 | | 18 | | | | 1 | | | | 29 | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - Incr. 2ʹ 46ʺ Decr. 5ʹ 47ʺ Decr. 9ʹ 47ʺ Decr. 5ʹ 47ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 8ʺ - Decr. 0 8 Incr. 5 19 - +----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +----------------------------------------------------------------------------------------+ - | The third after Leap-year. | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - |Days| January|Dif.|February|Dif.| March |Dif.| April |Dif.| May |Dif.| June |Dif.| - | +--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Inc.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 4 7| |12 14 6| |12 12 44| |12 4 1| |11 56 52| |11 57 15| | - | | | 28 | | 7 | | 12 | | 18 | | 8 | | 9 | - | 2 |12 4 35| |12 14 13| |12 12 32| |12 3 43| |11 56 44| |11 57 24| | - | | | 28 | | 7 | | 13 | | 18 | | 7 | | 9 | - | 3 |12 5 3| |12 14 20| |12 12 19| |12 3 25| |11 56 37| |11 57 33| | - | | | 27 | | 6 | | 13 | | 18 | | 7 | | 9 | - | 4 |12 5 30| |12 14 26| |12 12 6| |12 3 7| |11 56 30| |11 57 42| | - | | | 27 | | 5 | | 14 | | 18 | | 6 | | 10 | - | 5 |12 5 57| |12 14 31| |12 11 52| |12 2 49| |11 56 24| |11 57 52| | - +----+--------+ 27 +--------+ 4 +--------+ 14 +--------+ 18 +--------+ 5 +--------+ 10 + - | 6 |12 6 24| |12 14 35| |12 11 38| |12 2 31| |11 56 19| |11 58 2| | - | | | 26 | | 3 | | 14 | | 18 | | 5 | | 11 | - | 7 |12 6 50| |12 14 38| |12 11 24| |12 2 13| |11 56 14| |11 58 13| | - | | | 25 | | 2 | | 15 | | 18 | | 4 | | 11 | - | 8 |12 7 15| |12 14 41| |12 11 9| |12 1 55| |11 56 10| |11 58 24| | - | | | 25 | | 1 | | 16 | | 17 | | 4 | | 11 | - | 9 |12 7 40| |12 14 43| |12 10 53| |12 1 38| |11 56 6| |11 58 35| | - | | | 25 | | 1 | | 16 | | 17 | | 3 | | 11 | - | 10 |12 8 5| |12 14 44| |12 10 37| |12 1 21| |11 56 3| |11 58 46| | - +----+--------+ 24 +--------+Dec.+--------+ 16 +--------+ 16 +--------+ 2 +--------+ 12 + - | 11 |12 8 29| |12 14 44| |12 10 21| |12 1 5| |11 56 1| |11 58 58| | - | | | 23 | | 1 | | 16 | | 16 | | 2 | | 12 | - | 12 |12 8 52| |12 14 43| |12 10 5| |12 0 49| |11 55 59| |11 59 10| | - | | | 23 | | 2 | | 17 | | 16 | | 2 | | 12 | - | 13 |12 9 15| |12 14 41| |12 10 48| |12 0 33| |11 55 57| |11 59 22| | - | | | 22 | | 2 | | 17 | | 16 | | 1 | | 12 | - | 14 |12 9 37| |12 14 39| |12 9 31| |12 0 17| |11 55 56| |11 59 34| | - | | | 21 | | 3 | | 17 | | 15 | |Inc.| | 13 | - | 15 |12 9 58| |12 14 36| |12 9 14| |12 0 2| |11 55 56| |11 59 47| | - +----+--------+ 21 +--------+ 4 +--------+ 17 +--------+ 15 +--------+ 1 +--------+ 13 + - | 16 |12 10 19| |12 14 32| |12 8 57| |11 59 47| |11 55 57| |12 0 0| | - | | | 20 | | 4 | | 18 | | 15 | | 1 | | 13 | - | 17 |12 10 39| |12 14 28| |12 8 39| |11 59 32| |11 55 58| |12 0 13| | - | | | 19 | | 5 | | 18 | | 14 | | 1 | | 13 | - | 18 |12 10 58| |12 14 23| |12 8 21| |11 59 18| |11 55 59| |12 0 26| | - | | | 18 | | 6 | | 18 | | 14 | | 2 | | 13 | - | 19 |12 11 16| |12 14 17| |12 8 3| |11 59 4| |11 56 1| |12 0 39| | - | | | 18 | | 7 | | 18 | | 14 | | 2 | | 13 | - | 20 |12 11 34| |12 14 10| |12 7 45| |11 58 50| |11 56 3| |12 0 52| | - +----+--------+ 17 +--------+ 7 +--------+ 18 +--------+ 13 +--------+ 3 +--------+ 13 + - | 21 |12 11 51| |12 14 3| |12 7 27| |11 58 37| |11 56 6| |12 1 5| | - | | | 16 | | 8 | | 19 | | 13 | | 4 | | 12 | - | 22 |12 12 7| |12 13 55| |12 7 8| |11 58 24| |11 56 10| |12 1 17| | - | | | 16 | | 8 | | 19 | | 12 | | 4 | | 13 | - | 23 |12 12 23| |12 13 47| |12 6 49| |11 58 12| |11 56 14| |12 1 30| | - | | | 15 | | 9 | | 19 | | 12 | | 5 | | 13 | - | 24 |12 12 38| |12 13 38| |12 6 30| |11 58 0| |11 56 19| |12 1 43| | - | | | 14 | | 9 | | 19 | | 11 | | 5 | | 13 | - | 25 |12 12 52| |12 13 29| |12 6 11| |11 57 49| |11 56 24| |12 1 56| | - +----+--------+ 13 +--------+ 10 +--------+ 18 +--------+ 11 +--------+ 6 +--------+ 13 + - | 26 |12 13 5| |12 13 19| |12 5 53| |11 57 38| |11 56 30| |12 2 9| | - | | | 12 | | 11 | | 19 | | 10 | | 6 | | 13 | - | 27 |12 13 17| |12 13 8| |12 5 34| |11 57 28| |11 56 36| |12 2 22| | - | | | 11 | | 12 | | 19 | | 10 | | 7 | | 12 | - | 28 |12 13 28| |12 12 56| |12 5 15| |11 57 18| |11 56 43| |12 2 34| | - | | | 11 | | 12 | | 18 | | 9 | | 7 | | 12 | - | 29 |12 13 39| | | |12 4 57| |11 57 9| |11 56 50| |12 2 46| | - | | | 10 | | | | 19 | | 9 | | 8 | | 12 | - | 30 |12 13 49| | | |12 4 38| |11 57 0| |11 56 58| |12 2 58| | - +----+--------+ 9 +--------+----+--------+ 19 +--------+ 8 +--------+ 8 +--------+ 12 + - | 31 |12 13 58| | | |12 4 19| | | |11 57 6| | | | - | | | 8 | | | | 18 | | | | 9 | | | - +----+--------+----+--------+----+--------+----+--------+----+--------+----+--------+----+ - Incr. 9ʹ 51ʺ Incr. 0ʹ 38ʺ Decr. 8ʹ 25ʺ Decr. 7ʹ 1ʺ Decr. 0ʹ 56ʺ Incr. 5ʹ 43ʺ - Decr. 1 48 Incr. 1 10 - +-----------------------------------------------------------------------------------------+ - | A TABLE of the Equation of natural Days, shewing what Time it ought to | - | be by the Clock when the Sun is on the Meridian. | - +-----------------------------------------------------------------------------------------+ - | The third after Leap-year. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - |Days| July |Dif.| August |Dif.|September|Dif.| October|Dif.|November|Dif.|December|Dif.| - | +--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | |H. M. S.| S. |H. M. S.| S. |H. M. S. | S. |H. M. S.| S. |H. M. S.| S. |H. M. S.| S. | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - | | |Inc.| |Dec.| |Dec.| |Dec.| |Dec.| |Inc.| - | 1 |12 3 10| |12 5 49| |11 59 47 | |11 49 42| |11 43 49| |11 49 25| | - | | | 11 | | 4 | | 19 | | 18 | | 1 | | 23 | - | 2 |12 3 21| |12 5 45| |11 59 28 | |11 49 24| |11 43 48| |11 49 48| | - | | | 11 | | 4 | | 19 | | 18 | |Inc.| | 24 | - | 3 |12 3 32| |12 5 41| |11 59 9 | |11 49 6| |11 43 48| |11 50 12| | - | | | 11 | | 5 | | 19 | | 18 | | 1 | | 24 | - | 4 |12 3 43| |12 5 36| |11 58 50 | |11 48 48| |11 43 49| |11 50 36| | - | | | 11 | | 5 | | 19 | | 18 | | 2 | | 25 | - | 5 |12 3 54| |12 5 31| |11 58 31 | |11 48 30| |11 43 51| |11 51 1| | - +----+--------+ 10 +--------+ 6 +---------+ 20 +--------+ 18 +--------+ 2 +--------+ 25 + - | 6 |12 4 4| |12 5 25| |11 58 11 | |11 48 12| |11 43 53| |11 51 26| | - | | | 10 | | 7 | | 20 | | 17 | | 3 | | 26 | - | 7 |12 4 14| |12 5 18| |11 57 51 | |11 47 55| |11 43 56| |11 52 52| | - | | | 10 | | 7 | | 20 | | 16 | | 4 | | 27 | - | 8 |12 4 24| |12 5 11| |11 57 31 | |11 47 39| |11 44 0| |11 52 19| | - | | | 9 | | 7 | | 20 | | 16 | | 5 | | 27 | - | 9 |12 4 33| |12 5 4| |11 57 11 | |11 47 23| |11 44 5| |11 52 46| | - | | | 9 | | 8 | | 20 | | 16 | | 6 | | 27 | - | 10 |12 4 42| |12 4 56| |11 56 51 | |11 47 7| |11 44 11| |11 53 13| | - +----+--------+ 8 +--------+ 8 +---------+ 20 +--------+ 15 +--------+ 7 +--------+ 28 + - | 11 |12 4 50| |12 4 48| |11 56 31 | |11 46 52| |11 44 18| |11 53 41| | - | | | 8 | | 9 | | 21 | | 15 | | 8 | | 28 | - | 12 |12 4 58| |12 4 37| |11 56 10 | |11 46 37| |11 44 26| |11 54 9| | - | | | 8 | | 10 | | 21 | | 14 | | 8 | | 28 | - | 13 |12 5 6| |12 4 27| |11 55 49 | |11 46 23| |11 44 34| |11 54 37| | - | | | 7 | | 10 | | 21 | | 14 | | 9 | | 29 | - | 14 |12 5 13| |12 4 17| |11 55 28 | |11 46 9| |11 44 43| |11 55 6| | - | | | 6 | | 11 | | 21 | | 13 | | 10 | | 30 | - | 15 |12 5 19| |12 4 6| |11 55 7 | |11 45 56| |11 44 53| |11 55 36| | - +----+--------+ 6 +--------+ 12 +---------+ 20 +--------+ 12 +--------+ 11 +--------+ 29 + - | 16 |12 5 25| |12 3 54| |11 54 47 | |11 45 44| |11 45 4| |11 56 6| | - | | | 6 | | 12 | | 21 | | 12 | | 12 | | 30 | - | 17 |12 5 31| |12 3 42| |11 54 26 | |11 45 32| |11 45 16| |11 56 36| | - | | | 5 | | 13 | | 21 | | 12 | | 13 | | 30 | - | 18 |12 5 36| |12 3 29| |11 54 5 | |11 45 20| |11 45 29| |11 57 6| | - | | | 5 | | 13 | | 21 | | 11 | | 14 | | 29 | - | 19 |12 5 41| |12 3 16| |11 53 44 | |11 45 9| |11 45 43| |11 57 35| | - | | | 4 | | 13 | | 21 | | 10 | | 14 | | 30 | - | 20 |12 5 45| |12 3 3| |11 53 23 | |11 44 59| |11 45 57| |11 58 5| | - +----+--------+ 4 +--------+ 14 +---------+ 20 +--------+ 9 +--------+ 15 +--------+ 30 + - | 21 |12 5 49| |12 2 49| |11 53 3 | |11 44 50| |11 46 12| |11 58 34| | - | | | 3 | | 15 | | 21 | | 9 | | 16 | | 30 | - | 22 |12 5 52| |13 2 34| |11 52 42 | |11 44 41| |11 46 28| |11 59 4| | - | | | 3 | | 15 | | 21 | | 9 | | 17 | | 30 | - | 23 |12 5 55| |12 2 19| |11 52 21 | |11 44 32| |11 46 45| |11 59 34| | - | | | 2 | | 15 | | 20 | | 8 | | 17 | | 30 | - | 24 |12 5 57| |12 2 4| |11 52 1 | |11 44 24| |11 47 2| |12 0 4| | - | | | 1 | | 16 | | 21 | | 7 | | 18 | | 30 | - | 25 |12 5 58| |12 1 48| |11 51 40 | |11 44 17| |11 47 20| |12 0 34| | - +----+--------+ 1 +--------+ 16 +---------+ 20 +--------+ 6 +--------+ 19 +--------+ 30 + - | 26 |12 5 59| |12 1 32| |11 51 20 | |11 44 11| |11 47 39| |12 1 4| | - | | |Dec.| | 16 | | 20 | | 5 | | 20 | | 30 | - | 27 |12 5 58| |12 1 16| |11 51 0 | |11 44 6| |11 47 59| |12 1 34| | - | | | 1 | | 17 | | 20 | | 5 | | 20 | | 30 | - | 28 |12 5 57| |12 0 59| |11 50 40 | |11 44 1| |11 48 19| |12 2 4| | - | | | 1 | | 17 | | 20 | | 4 | | 21 | | 29 | - | 29 |12 5 56| |12 0 42| |11 50 20 | |11 43 57| |11 48 40| |12 2 33| | - | | | 2 | | 18 | | 19 | | 3 | | 22 | | 29 | - | 30 |12 5 54| |12 0 24| |11 50 1 | |11 43 54| |11 49 2| |12 3 2| | - +----+--------+ 2 +--------+ 18 +---------+ 19 +--------+ 3 +--------+ 23 +--------+ 29 + - | 31 |12 5 52| |12 0 6| | | |11 43 51| | | |12 3 31| | - | | | 3 | | 19 | | | | 2 | | | | 29 | - +----+--------+----+--------+----+---------+----+--------+----+--------+----+--------+----+ - Incr. 2ʹ 48ʺ Decr. 5ʹ 43ʺ Decr. 9ʹ 46ʺ Decr. 5ʹ 51ʺ Decr. 0ʹ 1ʺ Incr. 14ʹ 6ʺ - Decr. 0 7 Incr. 5 14 - - - - - CHAP. XV. - -_The Moon’s surface mountainous: Her Phases described: Her path, and the -paths of Jupiter’s Moons delineated: The proportions of the Diameters of - their Orbits, and those of Saturn’s Moons, to each other; and to the - Diameter of the Sun._ - - -[Sidenote: PL. VII. - - The Moon’s surface mountainous.] - -252. By looking at the Moon with an ordinary telescope we perceive that -her surface is diversified with long tracts of prodigious high mountains -and deep cavities. Some of her mountains, by comparing their height with -her diameter (which is 2180 miles) are found to be three times higher -than the highest hills on our Earth. This ruggedness of the Moon’s -surface is of great use to us, by reflecting the Sun’s light to all -sides: for if the Moon were smooth and polished like a looking-glass, or -covered with water, she could never distribute the Sun’s light all -round; only in some positions she would shew us his image, no bigger -than a point, but with such a lustre as would be hurtful to our eyes. - -[Sidenote: Why no hills appear on her edge.] - -253. The Moon’s surface being so uneven, many have wondered why her edge -appears not jagged, as well as the curve bounding the light and dark -places. But if we consider, that what we call the edge of the Moon’s -Disc is not a single line set round with mountains, in which case it -would appear irregularly indented, but a large Zone having many -mountains lying behind one another from the observer’s eye, we shall -find that the mountains in some rows will be opposite to the vales in -others; and so fill up the inequalities as to make her appear quite -round: just as when one looks at an orange, although it’s roughness be -very discernible on the side next the eye, especially if the Sun or a -Candle shines obliquely on that side, yet the line terminating the -visible part still appears smooth and even. - -[Illustration: Plate VII. - -_J. Ferguson delin._ _J. Mynde Sculp._] - -[Sidenote: The Moon has no twilight. - - Fig. I.] - -254. As the Sun can only enlighten that half of the Earth which is at -any moment turned towards him, and being withdrawn from the opposite -half leaves it in darkness; so he likewise doth to the Moon: only with -this difference, that the Earth being surrounded by an Atmosphere, and -the Moon having none, we have twilight after the Sun sets; but the Lunar -Inhabitants have an immediate transition from the brightest Sun-shine to -the blackest darkness § 177. For, let _tkrsw_ be the Earth, and _A_, -_B_, _C_, _D_, _E_, _F_, _G_, _H_ the Moon in eight different parts of -her Orbit. As the Earth turns round its Axis, from west to east, when -any place comes to _t_ the twilight begins there, and when it revolves -from thence to _r_ the Sun _S_ rises; when the place comes to _s_ the -Sun sets, and when it comes to _w_ the twilight ends. But as the Moon -turns round her Axis, which is only once a month, the moment that any -point of her surface comes to _r_ (see the Moon at _G_) the Sun rises -there without any previous warning by twilight; and when the same point -comes to _s_ the Sun sets, and that point goes into darkness as black as -at midnight. - -[Sidenote: The Moon’s Phases.] - -255. The Moon being an opaque spherical body, (for her hills take off no -more from her roundness than the inequalities on the surface of an -orange takes off from its roundness) we can only see that part of the -enlightened half of her which is towards the Earth. And therefore, when -the Moon is at _A_, in conjunction with the Sun _S_, her dark half is -towards the Earth, and she disappears as at _a_, there being no light on -that half to render it visible. When she comes to her first Octant at -_B_, or has gone an eighth part of her orbit from her Conjunction, a -quarter of her enlightened side is towards the Earth, and she appears -horned as at _b_. When she has gone a quarter of her orbit from between -the Earth and Sun to _C_, she shews us one half of her enlightened side -as at _c_, and we say, she is a quarter old. At _D_ she is in her second -Octant, and by shewing us more of her enlightened side she appears -gibbous as at _d_. At _E_ her whole enlightened side is towards the -Earth, and therefore she appears round as at _e_, when we say, it is -Full Moon. In her third Octant at _F_, part of her dark side being -towards the Earth, she again appears gibbous, and is on the decrease, as -at _f_. At _G_ we see just one half of her enlightened side, and she -appears half decreased, or in her third Quarter, as at _g_. At _H_ we -only see a quarter of her enlightened side, being in her fourth Octant, -where she appears horned as at _h_. And at _A_, having compleated her -course from the Sun to the Sun again, she disappears; and we say, it is -New Moon. Thus in going from _A_ to _E_ the Moon seems continually to -increase; and in going from _E_ to _A_, to decrease in the same -proportion; having like Phases at equal distances from _A_ or _E_, but -as seen from the Sun _S_, she is always Full. - -[Sidenote: The Moon’s Disc not always quite round when full.] - -256. The Moon appears not perfectly round when she is Full in the -highest or lowest part of her Orbit, because we have not a direct view -of her enlightened side at that time. When Full in the highest part of -her orbit, a small deficiency appears on her lower edge; and the -contrary when Full in the lowest part of her Orbit. - -[Sidenote: The Phases of the Earth and Moon contrary.] - -257. ’Tis plain by the Figure, that when the Moon changes to the Earth, -the Earth appears Full to the Moon; and _vice versâ_. For when the Moon -is at _A_, _New_ to the Earth, the whole enlightened side of the Earth -is towards the Moon: and when the Moon is at _E_, _Full_ to the Earth, -it’s dark side is towards her. Hence a _New Moon_ answers to a _Full -Earth_, and a _Full Moon_ to a _New Earth_. The _Quarters_ are also -reversed to each other. - -[Sidenote: An agreeable Phenomenon.] - -258. Between the third Quarter and Change, the Moon is frequently -visible in the forenoon, even when the Sun shines; and then she affords -us an opportunity of seeing a very agreeable appearance, wherever we -find a globular stone above the level of the eye, as suppose on the top -of a gate. For, if the Sun shines on the stone, and we place ourselves -so as the upper part of the stone may just seem to touch the point of -the Moon’s lowermost horn, we shall then see the enlightened part of the -stone exactly of the same shape with the Moon; horned as she is, and -inclining the same way to the Horizon. The reason is plain; for the Sun -enlightens the stone the same way as he does the Moon: and both being -Globes, when we put ourselves into the above situation, the Moon and -stone have the same position to our eyes; and therefore we must see as -much of the illuminated part of the one as of the other. - -[Sidenote: The nonagesimal Degree, what.] - -259. The position of the Moon’s Cusps, or a right line touching the -points of her horns, is very differently inclined to the Horizon at -different hours of the same days of her age. Sometimes she stands, as it -were, upright on her lower horn, and then such a line is perpendicular -to the Horizon: when this, happens, she is in what the Astronomers call -_the Nonagesimal Degree_; which is the highest point of the Ecliptic -above the Horizon at that time, and is 90 degrees from both sides of the -Horizon where it is then cut by the Ecliptic. But this never happens -when the Moon is on the Meridian, except when she is at the very -beginning of Cancer or Capricorn. - -[Sidenote: How the inclination of the Ecliptic may be found by the - position of the Moon horns. - - PL. VII.] - -260. The inclination of that part of the Ecliptic to the Horizon in -which the Moon is at any time when horned, may be known by the position -of her horns; for a right line touching their points is perpendicular to -the Ecliptic. And as the Angle that the Moon’s orbit makes with the -Ecliptic can never raise her above, nor depress her below the Ecliptic, -more than two minutes of a degree, as seen from the Sun; it can have no -sensible effect upon the position of her horns. Therefore, if a Quadrant -be held up, so as one of it’s edges may seem to touch the Moon’s horns, -the graduated side being kept towards the eye, and as far from the eye -as it can be conveniently held, the arc between the Plumb-line and that -edge of the Quadrant which seems to touch the Moon’s horns will shew the -inclination of that part of the Ecliptic to the Horizon. And the arc -between the other edge of the Quadrant and Plumb-line will shew the -inclination of the Moon’s horns to the Horizon at that time also. - -[Sidenote: Fig. I. - - Why the Moon appears as big as the Sun.] - -261. The Moon generally appears as large as the Sun; for the Angle -_vkA_, under which the Moon is seen from the Earth, is the same with the -Angle _LkM_, under which the Sun is seen from it. And therefore the Moon -may hide the Sun’s whole Disc from us, as she sometimes does in solar -Eclipses. The reason why she does not eclipse the Sun at every Change -shall be explained afterwards. If the Moon were farther from the Earth -as at _a_, she could never hide the whole of the Sun from us; for then -she would appear under the Angle _NkO_, eclipsing only that part of the -Sun which lies between _N_ and _O_: were she still further from the -Earth, as at _X_, she would appear under the small Angle _TkW_, like a -spot on the Sun, hiding only the part _TW_ from our sight. - -[Sidenote: A proof of the Moon’s turning round her Axis.] - -262. The Moon turns round her Axis in the time that she goes round her -orbit; which is evident from hence, that a spectator at rest, without -the periphery of the Moon’s orbit, would see all her sides turned -regularly towards him in that time. She turns round her Axis from any -Star to the same Star again in 27 days 8 hours; from the Sun to the Sun -again in 29-1/2 days: the former is the length of her sidereal day, and -the latter the length of her solar day. A body moving round the Sun -would have a solar day in every revolution, without turning on it’s -Axis; the same as if it had kept all the while at rest, and the Sun -moved round it: but without turning round it’s Axis it could never have -one sidereal day, because it would always keep the same side towards any -given Star. - -[Sidenote: Her periodical and synodical Revolution.] - -263. If the Earth had no annual motion, the Moon would go round it so as -to compleat a Lunation, a sidereal, and a solar day, all in the same -time. But, because the Earth goes forward in it’s orbit while the Moon -goes round the Earth in her orbit, the Moon must go as much more than -round her orbit from Change to Change in compleating a solar day as the -Earth has gone forward in it’s orbit during that time, _i. e._ almost a -twelfth part of a Circle. - - -[Sidenote: Familiarly represented. - - A Table shewing the times that the hour and minute hands of a - watch are in conjunction. - - A machine for shewing the motions of the Sun and Moon. - - PL. VII.] - -264. The Moon’s periodical and synodical revolution may be familiarly -represented by the motions of the hour and minute hands of a watch round -it’s dial-plate, which is divided into 12 equal parts or hours, as the -Ecliptic is divided into 12 Signs, and the year into 12 months. Let us -suppose these 12 hours to be 12 months, the hour hand the Sun, and the -minute hand the Moon; then will the former go round once in a year, and -the latter once in a month; but the Moon, or minute hand must go more -than round from any point of the Circle where it was last conjoined with -the Sun, or hour hand, to overtake it again: for the hour hand being in -motion, can never be overtaken by the minute hand at that point from -which they started at their last conjunction. The first column of the -annexed Table shews the number of conjunctions which the hour and minute -hand make whilst the hour hand goes once round the dial-plate; and the -other columns shew the times when the two hands meet at every -conjunction. Thus, suppose the two hands to be in conjunction at XII, as -they always are; then, at the first following conjunction it is 5 -minutes 27 seconds 16 thirds 21 fourths 49-1/11 fifths past I where they -meet; at the second conjunction it is 10 minutes 54 seconds 32 thirds 43 -fourths 38-1/2 fifths past II; and so on. This, though an easy -illustration of the motions of the Sun and Moon, is not precise as to -the times of their conjunctions; because, while the Sun goes round the -Ecliptic, the Moon makes 12-1/3 conjunctions with him; but the minute -hand of a watch or clock makes only 11 conjunctions with the hour hand -in one period round the dial-plate. But if, instead of the common -wheel-work at the back of the dial-plate, the Axis of the minute hand -had a pinion of 6 leaves turning a wheel of 40, and this last turning -the hour hand, in every revolution it makes round the dial-plate the -minute hand would make 12-1/3 conjunctions with it; and so would be a -pretty device for shewing the motions of the Sun and Moon; especially, -as the slowest moving hand might have a little Sun fixed on it’s point, -and the quickest a little Moon. Besides, the plate, instead of hours and -quarters, might have a Circle of months, with the 12 Signs and their -Degrees; and if a plate of 29-1/2 equal parts for the days of the Moon’s -age were fixed to the Axis of the Sun-hand, and below it, so as the Sun -always kept at the 1/2 day of that plate, the Moon-hand would shew the -Moon’s age upon that plate for every day pointed out by the Sun-hand in -the Circle of months; and both Sun and Moon would shew their places in -the Ecliptic: for the Sun would go round the Ecliptic in 365 Days and -the Moon in 27-1/3 days, which is her periodical revolution; but from -the Sun to the Sun again, or from Change to Change, in 29-1/2 days, -which is her synodical revolution. - - +-----+-------------------------------+ - |Conj.| H. M. S. ʺʹ ʺʺ v p^{ts}. | - +-----+-------------------------------+ - | 1 | I 5 27 16 21 49-1/11 | - | 2 | II 10 54 32 43 38-2/11 | - | 3 | III 16 21 49 5 27-3/11 | - | 4 | IIII 21 49 5 27 16-4/11 | - | 5 | V 27 16 21 49 5-5/11 | - | 6 | VI 32 43 38 10 54-6/11 | - | 7 | VII 38 10 54 32 43-7/11 | - | 8 | VIII 43 38 10 54 32-8/11 | - | 9 | IX 49 5 27 16 21-9/11 | - | 10 | X 54 32 43 38 10-10/11| - | 11 | XII 0 0 0 0 0 | - +-----+-------------------------------+ - - -[Sidenote: The Moon’s motion thro’ open space described.] - -265. If the Earth had no annual motion, the Moon’s motion round the -Earth, and her track in absolute space, would be always the same[58]. -But as the Earth and Moon move round the Sun, the Moon’s real path in -the Heavens is very different from her path round the Earth: the latter -being in a progressive Circle, and the former in a curve of different -degrees of concavity, which would always be the same in the same parts -of the Heavens, if the Moon performed a compleat number of Lunations in -a year. - -[Sidenote: An idea of the Earth’s path and the Moon’s.] - -266. Let a nail in the end of the axle of a chariot-wheel represent the -Earth, and a pin in the nave the Moon; if the body of the chariot be -propped up so as to keep that wheel from touching the ground, and the -wheel be then turned round by hand, the pin will describe a Circle both -round the nail and in the space it moves through. But if the props be -taken away, the horses put to, and the chariot driven over a piece of -ground which is circularly convex; the nail in the axle will describe a -circular curve, and the pin in the nave will still describe a circle -round the progressive nail in the axle, but not in the space through -which it moves. In this case, the curve described by the nail will -resemble in miniature as much of the Earth’s annual path round the Sun, -as it describes whilst the Moon goes as often round the Earth as the pin -does round the nail: and the curve described by the nail will have some -resemblance of the Moon’s path during so many Lunations. - -[Sidenote: Fig. II. - - PL. VII.] - -Let us now suppose that the Radius of the circular curve described by -the nail in the axle is to the Radius of the Circle which the pin in the -nave describes round the axle as 337-1/2 to 1; which is the proportion -of the Radius or Semidiameter of the Earth’s Orbit to that of the -Moon’s; or of the circular curve _A_ 1 2 3 4 5 6 7 _B_ &c. to the little -Circle _a_; and then, whilst the progressive nail describes the said -curve from _A_ to _E_, the pin will go once round the nail with regard -to the center of it’s path, and in doing so, will describe the curve -_abcde_. The former will be a true representation of the Earth’s path -for one Lunation, and the latter of the Moon’s for that time. Here we -may set aside the inequalities of the Moon’s Moon, and also the Earth’s -moving round it’s common center of gravity and the Moon’s: all which, if -they were truly copied in this experiment, would not sensibly alter the -figure of the paths described by the nail and pin, even though they -should rub against a plain upright surface all the way, and leave their -tracks visible. And if the chariot should be driven forward on such a -convex piece of ground, so as to turn the wheel several times round, the -track of the pin in the nave would still be concave toward the center of -the circular curve described by the pin in the Axle; as the Moon’s path -is always concave to the Sun in the center of the Earth’s annual Orbit. - -[Sidenote: Proportion of the Moon’s Orbit to the Earth’s.] - -In this Diagram, the thickest curve line _ABCD_, with the numeral -figures set to it, represents as much of the Earth’s annual Orbit as it -describes in 32 days from west to east; the little Circles at _a_, _b_, -_c_, _d_, _e_ shew the Moon’s Orbit in due proportion to the Earth’s; -and the smallest curve _abcdef_ represents the line of the Moon’s path -in the Heavens for 32 days, accounted from any particular New Moon at -_a_. The machine, Fig. 5th is for delineating the Moon’s path, and will -be described, with the rest of my Astronomical machinery, in the last -Chapter. The Sun is supposed to be in the center of the curve _A 1 2 3 4 -5 6 7 B_ &c. and the small dotted Circles upon it represent the Moon’s -Orbit, of which the Radius is in the same proportion to the Earth’s path -in this scheme, that the Radius of the Moon’s Orbit in the Heavens bears -to the Radius of the Earth’s annual path round the Sun; that is, as -240,000 to 81,000,000, or as 1 to 337-1/2. - -[Sidenote: Fig. II.] - -When the Earth is at _A_ the New Moon is at _a_; and in the seven days -that the Earth describes the curve _1 2 3 4 5 6 7_, the Moon in -accompanying the Earth describes the curve _ab_; and is in her first -Quarter at _b_ when the Earth is at _B_. As the Earth describes the -curve _B 8 9 10 11 12 13 14_ the Moon describes the curve _bc_; and is -opposite to the Sun at _c_, when the Earth is at _C_. Whilst the Earth -describes the curve _C 15 16 17 18 19 20 21 22_ the Moon describes the -curve _cd_; and is in her third Quarter at _d_ when the Earth is at _D_. -Once more, whilst the Earth describes the curve _D 23 24 25 26 27 28 29_ -the Moon describes the curve _de_; and is again in conjunction at _e_ -with the Sun when the Earth is at _E_, between the 29th and 30th day of -the Moon’s age, accounted by the numeral Figures from the New Moon at -_A_. In describing the curve _abcde_, the Moon goes round the -progressive Earth as really as if she had kept in the dotted Circle _A_, -and the Earth continued immoveable in the center of that Circle. - -[Sidenote: The Moon’s motion always concave towards the Sun.] - -And thus we see, that although the Moon goes round the Earth in a -Circle, with respect to the Earth’s center, her real path in the Heavens -is not very different in appearance from the Earth’s path. To shew that -the Moon’s path is concave to the Sun, even at the time of Change, it is -carried on a little farther into a second Lunation, as to _f_. - -[Sidenote: How her motion is alternately retarded and accelerated.] - -267. The Moon’s absolute motion from her Change to her first Quarter, or -from _a_ to _b_, is so much slower than the Earth’s, that she falls 240 -thousand miles (equal to the Semidiameter of her Orbit) behind the Earth -at her first Quarter in _b_, when the Earth is in _B_; that is, she -falls back a space equal to her distance from the Earth. From that time -her motion is gradually accelerated to her Opposition or Full at _c_, -and then she is come up as far as the Earth, having regained what she -lost in her first Quarter from _a_ to _b_. From the Full to the last -Quarter at _d_ her motion continues accelerated, so as to be just as far -before the Earth at _D_, as she was behind it at her first Quarter in -_b_. But, from _d_ to _e_ her motion is retarded so, that she loses as -much with respect to the Earth as is equal to her distance from it, or -to the Semidiameter of her Orbit; and by that means she comes to _e_, -and is then in conjunction with the Sun as seen from the Earth at _E_. -Hence we find, that the Moon’s absolute motion is slower than the -Earth’s from her third Quarter to her first; and swifter than the -Earth’s from her first Quarter to her third: her path being less curved -than the Earth’s in the former case, and more in the latter. Yet it is -still bent the same way towards the Sun; for if we imagine the concavity -of the Earth’s Orbit to be measured by the length of a perpendicular -line _Cg_, let down from the Earth’s place upon the straight line _bgd_ -at the Full of the Moon, and connecting the places of the Earth at the -end of the Moon’s first and third Quarters, that length will be about -640 thousand miles; and the Moon when New only approaching nearer to the -Sun by 240 thousand miles than the Earth is, the length of the -perpendicular let down from her place at that time upon the same -straight line, and which shews the concavity of that part of her path, -will be about 400 thousand miles. - - -[Sidenote: A difficulty removed. - - PL. VII.] - -268. The Moon’s path being concave to the Sun throughout, demonstrates -that her gravity towards the Sun, at her conjunction, exceeds her -gravity towards the Earth. And if we consider that the quantity of -matter in the Sun is almost 230 thousand times as great as the quantity -of matter in the Earth, and that the attraction of each body diminishes -as the square of the distance from it increases, we shall soon find, -that the point of equal attraction where these two powers would be -equally strong, is about 70 thousand miles nearer the Earth than the -Moon is at her Change. It may now appear surprising that the Moon does -not abandon the Earth when she is between it and the Sun, because she is -considerably more attracted by the Sun than by the Earth at that time. -But this difficulty vanishes when we consider, that the Moon is so near -the Earth in proportion to the Earth’s distance from the Sun, that she -is but very little more attracted by the Sun at that time than the Earth -is; and whilst the Earth’s attraction is greater upon the Moon than the -difference of the Sun’s attraction upon the Earth and her (and that it -is always much greater is demonstrable) there is no danger of the Moon’s -leaving the Earth; for if she should fall towards the Sun, the Earth -would follow her almost with equal speed. The absolute attraction of the -Earth upon a drop of falling rain is much greater than the absolute -attraction of the particles of that drop upon each other, or of it’s -center upon all parts of it’s circumference; but then the side of the -drop next the Earth is attracted with so very little more force than -it’s center, or even it’s opposite side; that the attraction of the -center of the drop upon it’s side next the Earth is much greater than -the difference of force by which the Earth attracts it’s nearer surface -and center: on which account the drop preserves it’s round figure, and -might be projected about the Earth by a strong circulating wind so as to -be kept from falling to the Earth. It is much the same with the Earth -and Moon in respect to the Sun; for if we should suppose the Moon’s -Orbit to be filled with a fluid Globe, of which all the parts would be -attracted towards the Earth in it’s center, but the whole of it much -more attracted by the Sun; one part of it could not fall to the Sun -without the other, and a sufficient projectile force would carry the -whole fluid Globe round the Sun. A ship, at the distance of the Moon, -sailing round the Earth on the surface of the fluid Globe, could no more -be taken away by the Sun when it is on the side next him, than the Earth -could be taken away from it when it is on the opposite side; which could -never happen unless the Earth’s projectile motion were stopt; and if it -were stopt, the Ship with the whole fluid Globe, Earth and all together, -would as naturally fall to the Sun as a drop of rain in calm air falls -to the Earth. Hence we may see, that the Earth is in no more danger of -being left by the Moon at the Change, than the Moon is of being left by -the Earth at the Full: the diameter of the Moon’s Orbit being so small -in comparison of the Sun’s distance, that the Moon is but little more or -less attracted than the Earth at any time. And as the Moon’s projectile -force keeps her from falling to the Earth, so the Earth’s projectile -force keeps it from falling to the Sun. - - -[Sidenote: Fig. III.] - -269. All the curves which Jupiter’s Satellites describe, are different -from the path described by our Moon, although these Satellites go round -Jupiter, as the Moon goes round the Earth. Let _ABCDE_ &c. be as much of -Jupiter’s Orbit as he describes in 18 days from _A_ to _T_; and the -curves _a_, _b_, _c_, _d_ will be the paths of his four Moons going -round him in his progressive motion. - -[Sidenote: The absolute Path of Jupiter and his Satellites delineated. - - Fig. III.] - -Now let us suppose all these Moons to set out from a conjunction with -the Sun, as seen from Jupiter. When Jupiter is at _A_ his first or -nearest Moon will be at _a_, his second at _b_, his third at _c_, and -his fourth at _d_. At the end of 24 terrestrial hours after this -conjunction, Jupiter has moved to _B_, his first Moon or Satellite has -described the curve _a1_, his second the curve _b1_, his third _c1_, and -his fourth _d1_. The next day when Jupiter is at _C_, his first -Satellite has described the curve _a2_ from its conjunction, his second -the curve _b2_, his third the curve _c2_, and his fourth the curve _d2_, -and so on. The numeral Figures under the capital letters shew Jupiter’s -place in his path every day for 18 days, accounted from _A_ to _T_; and -the like Figures set to the paths of his Satellites, shew where they are -at the like times. The first Satellite, almost under _C_, is stationary -at + as seen from the Sun; and retrograde from + to _2_: at _2_ it -appears stationary again, and thence it moves forward until it has past -_3_, being twice stationary, and once retrograde between _3_ and _4_. -The path of this Satellite intersects itself every 42-1/2 hours of our -time, making such loops as in the Diagram at _2._ _3._ _5._ _7._ _9._ -_10._ _12._ _14._ _16._ _18_, a little after every Conjunction. The -second Satellite _b_, moving slower, barely crosses it’s path every 3 -days 13 hours; as at _4._ _7._ _11._ _14._ _18_, making only five loops -and as many conjunctions in the time that the first makes ten. The third -Satellite _c_ moving still slower, and having described the curve _c 1. -2. 3. 4. 5. 6. 7_, comes to an Angle at _7_ in conjunction with the Sun -at the end of 7 days 4 hours; and so goes on to describe such another -curve _7. 8. 9. 10. 11. 12. 13. 14_, and is at _14_ in it’s next -conjunction. The fourth Satellite _d_ is always progressive, making -neither loops nor angles in the Heavens; but comes to it’s next -conjunction at _e_ between the numeral figures _16_ and _17_, or in 16 -days 18 hours. In order to have a tolerably good figure of the paths of -these Satellites, I took the following method. - -[Sidenote: Fig. IV. - - PL. VII. - - How to delineate the paths of Jupiter’s Moons. - - And Saturn’s.] - -Having drawn their Orbits on a Card, in proportion to their relative -distances from Jupiter, I measured the radius of the Orbit of the fourth -Satellite, which was an inch and a tenth part; then multiplied this by -424 for the radius of Jupiter’s Orbit, because Jupiter is 424 times as -far from the Sun’s center as his fourth Satellite is from his center; -and the product thence arising was 466-4/10 inches. Then taking a small -cord of this length, and fixing one end of it to the floor of a long -room by a nail, with a black lead pencil at the other end I drew the -curve _ABCD_ &c. and set off a degree and an half thereon, from _A_ to -_T_; because Jupiter moves only so much, whilst his outermost Satellite -goes once round him, and somewhat more; so that this small portion of so -large a circle differs but very little from a straight line. This done, -I divided the space _AT_ into 18 equal parts, as _AB_, _BC_, &c. for the -daily progress of Jupiter; and each part into 24 for his hourly -progress. The Orbit of each Satellite was also divided into as many -equal parts as the Satellite is hours in finishing it’s synodical period -round Jupiter. Then drawing a right line through the center of the Card, -as a diameter to all the 4 Orbits upon it, I put the card upon the line -of Jupiter’s motion, and transferred it to every horary division -thereon, keeping always the said diameter-line on the line of Jupiter’s -path; and running a pin through each horary division in the Orbit of -each Satellite as the card was gradually transferred along the Line -_ABCD_ etc. of Jupiter’s motion, I marked points for every hour through -the Card for the Curves described by the Satellites as the primary -planet in the center of the Card was carried forward on the line: and so -finished the Figure, by drawing the lines of each Satellite’s motion, -through those (almost innumerable) points: by which means, this is -perhaps as true a Figure of the paths of these Satellites as can be -desired. And in the same manner might those for Saturn’s Satellites be -delineated. - -[Sidenote: The grand Period of Jupiter’s Moons.] - -270. It appears by the scheme, that the three first Satellites come -almost into the same line or position every seventh day; the first being -only a little behind with the second, and the second behind with the -third. But the period of the fourth Satellite is so incommensurate to -the periods of the other three, that it cannot be guessed at by the -diagram when it would fall again into a line of conjunction with them, -between Jupiter and the Sun. And no wonder; for supposing them all to -have been once in conjunction, it will require 3,087,043,493,260 years -to bring them in a conjunction again: See § 73. - -[Sidenote: Fig. IV. The proportions of the Orbits of the Planets and - Satellites.] - -271. In Fig. 4th we have the proportions of the Orbits of Saturn’s five -Satellites, and of Jupiter’s four, to one another, to our Moon’s Orbit, -and to the Disc of the Sun. _S_ is the Sun; _M m_ the Moon’s Orbit (the -Earth supposed to be at _E_;) _J_ Jupiter; _1._ _2._ _3._ _4_ the Orbits -of his four Moons or Satellites; _Sat_ Saturn; and _1._ _2._ _3._ _4._ -_5_ the Orbits of his five Moons. Hence it appears, that the Sun would -much more than fill the whole Orbit of the Moon; for the Sun’s diameter -is 763,000 miles, and the diameter of the Moon’s Orbit only 480,000. In -proportion to all these Orbits of the Satellites, the Radius of Saturn’s -annual Orbit would be 21-1/4 yards, of Jupiter’s orbit 11-2/3, and of -the Earth’s 2-1/4, taking them in round numbers. - -272. The annexed table shews at once what proportion the Orbits, -Revolutions, and Velocities, of all the Satellites bear to those of -their primary Planets, and what sort of curves the several Satellites -describe. For, those Satellites whose velocities round their primaries -are greater than the velocities of their primaries in open space, make -loops at their conjunctions § 269; appearing retrograde as seen from the -Sun whilst they describe the inferior parts of their Orbits, and direct -whilst they describe the superior. This is the case with Jupiter’s first -and second Satellites, and with Saturn’s first. But those Satellites -whose velocities are less than the velocities of their primary planets -move direct in their whole circumvolutions; which is the case of the -third and fourth Satellites of Jupiter, and of the second, third, -fourth, and fifth Satellites of Saturn, as well as of our Satellite the -Moon: But the Moon is the only Satellite whose motion is always concave -to the Sun. There is a table of this sort in _De la Caile_’s Astronomy, -but it is very different from the above, which I have computed from our -_English_ accounts of the periods and distances of these Planets and -Satellites. - - +------------+-----------------+----------------+----------------------+ - | | Proportion of | Proportion of | Proportion of | - | | the Radius of | the Time of | the Velocity of | - | The | the Planet’s | the Planet’s | each Satellite | - | Satellites | Orbit to the | Revolution to | to the Velocity | - | | Radius of the | the Revolution | of its primary | - | | Orbit of each | of each | Planet. | - | | Satellite. | Satellite. | | - +------------+-----------------+----------------+----------------------+ - | of Saturn | | | | - | 1 | As 5322 to 1 | As 5738 to 1 | As 5738 to 5322 | - | 2 | 4155 1 | 3912 1 | 3912 4155 | - | 3 | 2954 1 | 2347 1 | 2347 2954 | - | 4 | 1295 1 | 674 1 | 674 1295 | - | 5 | 432 1 | 134 1 | 134 432 | - +------------+-----------------+----------------+----------------------+ - | of Jupiter | | | | - | 1 | As 1851 to 1 | As 2445 to 1 | As 2445 to 1851 | - | 2 | 1165 1 | 1219 1 | 1219 1165 | - | 3 | 731 1 | 604 1 | 604 731 | - | 4 | 424 1 | 258 1 | 258 424 | - +------------+-----------------+----------------+----------------------+ - | The Moon | As 337-1/2 to 1 | As 12-1/3 to 1 | As 12-1/3 to 337-1/2 | - +------------+-----------------+----------------+----------------------+ - - - - - CHAP. XVI. - - _The Phenomena of the Harvest-Moon explained by a common Globe: The - years in which the Harvest-Moons are least and most beneficial from -1751, to 1861. The long duration of Moon-light at the Poles in winter._ - - -[Sidenote: No Harvest-Moon at the Equator.] - -273. It is generally believed that the Moon rises about 48 minutes later -every day than on the preceding; but this is true only with regard to -places on the Equator. In places of considerable Latitude there is a -remarkable difference, especially in the harvest time; with which -Farmers were better acquainted than Astronomers till of late; and -gratefully ascribed the early rising of the Full Moon at that time of -the year to the goodness of God, not doubting that he had ordered it so -on purpose to give them an immediate supply of moon-light after sun-set -for their greater conveniency in reaping the fruits of the earth. - -[Sidenote: But remarkable according to the distance of places from it.] - -In this instance of the harvest-moon, as in many others discoverable by -Astronomy, the wisdom and beneficence of the Deity is conspicuous, who -really ordered the course of the Moon so, as to bestow more or less -light on all parts of the earth as their several circumstances and -seasons render it more or less serviceable. About the Equator, where -there is no variety of seasons, and the weather changes seldom, and at -stated times, Moon-light is not necessary for gathering in the produce -of the ground; and there the moon rises about 48 minutes later every day -or night than on the former. At considerable distances from the Equator, -where the weather and seasons are more uncertain, the autumnal Full -Moons rise very soon after sun-set for several evenings together. At the -polar circles, where the mild season is of very short duration, the -autumnal Full Moon rises at Sun-set from the first to the third quarter. -And at the Poles, where the Sun is for half a year absent, the winter -Full moons shine constantly without setting from the first to the third -quarter. - -[Sidenote: The reason of this.] - -It is soon said that all these Phenomena are owing to the different -Angles made by the Horizon and different parts of the Moon’s orbit; and -that the Moon can be full but once or twice in a year in those parts of -her orbit which rise with the least angles. But to explain this subject -intelligibly we must dwell much longer upon it. - -[Sidenote: PLATE III.] - -274. The [59]plane of the Equinoctial is perpendicular to the Earth’s -Axis: and therefore, as the Earth turns round its Axis, all parts of the -Equinoctial make equal Angles with the Horizon both at rising and -setting; so that equal portions of it always rise or set in equal times. -Consequently, if the Moon’s motion were equable, and in the Equinoctial, -at the rate of 12 degrees from the Sun every day, as it is in her orbit, -she would rise and set 48 minutes later every day than on the preceding: -for 12 degrees of the Equinoctial rise or set in 48 minutes of time in -all Latitudes. - -[Sidenote: Fig. III.] - -275. But the Moon’s motion is so nearly in the Ecliptic that we may -consider her at present as moving in it. Now the different parts of the -Ecliptic, on account of its obliquity to the Earth’s Axis, make very -different Angles with the Horizon as they rise or set. Those parts or -Signs which rise with the smallest Angles set with the greatest, and -_vice versâ_. In equal times, whenever this Angle is least, a greater -portion of the Ecliptic rises than when the Angle is larger; as may be -seen by elevating the pole of a Globe to any considerable Latitude, and -then turning it round its Axis in the Horizon. Consequently, when the -Moon is in those Signs which rise or set with the smallest Angles, she -rises or sets with the least difference of time; and with the greatest -difference in those Signs which rise or set with the greatest Angles. - -[Sidenote: Fig. III. - - The different Angles made by the Ecliptic and Horizon.] - -But, because all who read this Treatise may not be provided with Globes, -though in this case it is requisite to know how to use them, we shall -substitute the Figure of a Globe; in which _FUP_ is the Axis, ♋_TR_ the -Tropic of Cancer, _LT_♑ the Tropic of Capricorn, ♋_EU_♑ the Ecliptic -touching both the Tropics which are 47 degrees from each other, and _AB_ -the Horizon. The Equator, being in the middle between the Tropics, is -cut by the Ecliptic in two opposite points, which are the beginnings of -♈ Aries and ♎ Libra. _K_ is the Hour circle with its Index, _F_ the -North pole of the Globe elevated to the Latitude of _London_[60], namely -51-1/2 degrees above the Horizon; and _P_ the South Pole depressed as -much below it. Because of the oblique position of the Sphere in this -Latitude, the Ecliptic has the high elevation _N_♋ above the Horizon, -making the Angle _NU_♋ of 62 degrees with it when ♋ Cancer is on the -Meridian, at which time ♎ Libra rises in the East. But let the Globe be -turned half round its Axis, till ♑ Capricorn comes to the Meridian and ♈ -Aries rises in the East, and then the Ecliptic will have the low -elevation _NL_ above the Horizon making only an Angle _NUL_ of 15 -degrees, with it; which is 47 degrees less than the former Angle, equal -to the distance between the Tropics. - -[Sidenote: Least and greatest, when.] - -276. The smallest Angle made by the Ecliptic and Horizon is when Aries -rises, at which time Libra sets: the greatest when Libra rises, at which -time Aries sets. From the rising of Aries to the rising of Libra (which -is twelve [61]Sidereal hours) the angle increases; and from the rising -of Libra to the rising of Aries it decreases in the same proportion. By -this article and the preceding, it appears that the Ecliptic rises -fastest about Aries and slowest about Libra. - - +------+-----------+--------+---------+ - | | Signs | Rising | Setting | - | | | Diff. | Diff. | - | Days | +--------+---------+ - | | Degrees | H. M. | H. M. | - +------+-----------+--------+---------+ - | 1 | ♋ 13 | 1 5 | 0 50 | - | 2 | 26 | 1 10 | 0 43 | - | 3 | ♌ 10 | 1 14 | 0 37 | - | 4 | 23 | 1 17 | 0 32 | - | 5 | ♍ 6 | 1 16 | 0 28 | - | 6 | 19 | 1 15 | 0 24 | - | 7 | ♎ 2 | 1 15 | 0 20 | - | 8 | 15 | 1 15 | 0 18 | - | 9 | 28 | 1 15 | 0 17 | - | 10 | ♏ 12 | 1 15 | 0 22 | - | 11 | 25 | 1 14 | 0 30 | - | 12 | ♐ 8 | 1 13 | 0 39 | - | 13 | 21 | 1 10 | 0 47 | - | 14 | ♑ 4 | 1 4 | 0 56 | - | 15 | 17 | 0 46 | 1 5 | - | 16 | ♒ 1 | 0 40 | 1 8 | - | 17 | 14 | 0 35 | 1 12 | - | 18 | 27 | 0 30 | 1 15 | - | 19 | ♓ 10 | 0 25 | 1 16 | - | 20 | 23 | 0 20 | 1 17 | - | 21 | ♈ 7 | 0 17 | 1 16 | - | 22 | 20 | 0 17 | 1 15 | - | 23 | ♉ 3 | 0 20 | 1 15 | - | 24 | 16 | 0 24 | 1 15 | - | 25 | 29 | 0 30 | 1 14 | - | 26 | ♊ 13 | 0 40 | 1 13 | - | 27 | 26 | 0 50 | 1 7 | - | 28 | ♋ 9 | 1 0 | 1 58 | - +------+-----------+--------+---------+ - - -[Sidenote: Quantity of this Angle at London.] - -277. On the Parallel of _London_, as much of the Ecliptic rises about -Pisces and Aries in two hours as the Moon goes through in six days: and -therefore whilst the Moon is in these Signs, she differs but two hours -in rising for six days together; that is, 20 minutes later every day or -night than on the preceding. But in fourteen days afterwards, the Moon -comes to Virgo and Libra; which are the opposite Signs to Pisces and -Aries; and then she differs almost four times as much in rising; namely, -one hour and about fifteen minutes later every day or night than the -former, whilst she is in these Signs; for by § 275 their rising Angle is -at least four times as great as that of Pisces and Aries. The annexed -Table shews the daily mean difference of the Moon’s rising and setting -on the Parallel of _London_, for 28 days; in which time the Moon -finishes her period round the Ecliptic, and gets 9 degrees into the same -Sign from the beginning of which she set out. So it appears by the -Table, that while the Moon is in ♍ and ♎ she rises an hour and a quarter -later every day than the former; and differs only 24, 20, 18 or 17 -minutes in setting. But, when she comes to ♓ and ♈, she is only 20 or 17 -minutes later of rising; and an hour and a quarter later in setting. - -278. All these things will be made plain by putting small patches on the -Ecliptic of a Globe, as far from one another as the Moon moves from any -Point of the celestial Ecliptic in 24 hours, which at a mean rate is -[62]13-1/6 degrees; and then in turning the globe round, observe the -rising and setting of the patches in the Horizon, as the Index points -out the different times in the hour circle. A few of these patches are -represented by dots at _0_ _1_ _2_ _3_ &c. on the Ecliptic, which has -the position _LUI_ when Aries rises in the East; and by the dots _0_ _1_ -_2_ _3_, &c. when Libra rises in the East, at which time the Ecliptic -has the position _EU_♑: making an angle of 62 degrees with the Horizon -in the latter case, and an angle of no more than 15 degrees with it in -the former; supposing the Globe rectified to the Latitude of _London_. - -279. Having rectified the Globe, turn it until the patch at _0_, about -the beginning of ♓ Pisces on the half _LUI_ of the Ecliptic, comes to -the Eastern side of the Horizon; and then keeping the ball steady, set -the hour Index to XII, because _that_ hour may perhaps be more easily -remembred than any other. Then, turn the Globe round westward, and in -that time, suppose the patch _0_ to have moved thence to _1_, 13-1/6 -degrees, whilst the Earth turns once round its Axis, and you will see -that _1_ rises only about 20 minutes later than _0_ did on the day -before. Turn the Globe round again, and in that time suppose the same -patch to have moved from _1_ to _2_; and it will rise only 20 minutes -later by the hour-index than it did at _1_ on the day or turn before. At -the end of the next turn, suppose the patch to have gone from _2_ to _3_ -at _U_, and it will rise 20 minutes later than it did at _2_. And so on -for six turns, in which time there will scarce be two hours difference: -Nor would there have been so much if the 6 degrees of the Sun’s motion -in that time had been allowed for. At the first Turn the patch rises -south of the East, at the middle Turn due East, and at the last Turn -north of the East. But these patches will be 9 hours of setting on the -western side of the Horizon, which shews that the Moon will be so much -later of setting in that week in which she moves through these two -Signs. The cause of this difference is evident; for Pisces and Aries -make only an Angle of 15 degrees with the Horizon when they rise; but -they make an Angle of 62 degrees with it when they set § 275. As the -Signs Taurus, Gemini, Cancer, Leo, Virgo, and Libra rise successively, -the Angle increases gradually which they make with the Horizon; and -decreases in the same proportion as they set. And for that reason, the -Moon differs gradually more in the time of her rising every day whilst -she is in these Signs, and less in her setting: After which, through the -other six Signs, _viz._ Scorpio, Sagittary, Capricorn, Aquarius, Pisces, -and Aries, the rising difference becomes less every day, until it be at -the least of all, namely, in Pisces and Aries. - -280. The Moon goes round the Ecliptic in 27 days 8 hours; but not from -Change to Change in less than 29 days 12 hours: so that she is in Pisces -and Aries at least once in every Lunation, and in some Lunations twice. - -[Sidenote: Why the Moon is always Full in different Signs. - - Her periodical and synodical Revolution exemplified.] - -281. If the Earth had no annual motion, the Sun would never appear to -shift his place in the Ecliptic. And then every New Moon would fall in -the same Sign and degree of the Ecliptic, and every Full Moon in the -opposite: for the Moon would go precisely round the Ecliptic from Change -to Change. So that if the Moon was once Full in Pisces, or Aries, she -would always be Full when she came round to the same Sign and Degree -again. And as the Full Moon rises at Sun-set (because when any point of -the Ecliptic sets the opposite point rises) she would constantly rise -within two hours of Sun-set during the week in which she were Full. But -in the time that the Moon goes round the Ecliptic from any conjunction -or opposition, the Earth goes almost a Sign forward; and therefore the -Sun will seem to go as far forward in that time, namely 27-1/2 degrees: -so that the Moon must go 27-1/2 degrees more than round; and as much -farther as the Sun advances in that interval, which is 2-1/15 degrees, -before she can be in conjunction with, or opposite to the Sun again. -Hence it is evident, that there can be but one conjunction or opposition -of the Sun and Moon in a year in any particular part of the Ecliptic. -This may be familiarly exemplified by the hour and minute hands of a -watch, which are never in conjunction or opposition in that part of the -dial-plate where they were so last before. And indeed if we compare the -twelve hours on the dial-plate to the twelve Signs of the Ecliptic, the -hour-hand to the Sun and the minute-hand to the Moon, we shall have a -tolerably near resemblance in miniature to the motions of our great -celestial Luminaries. The only difference is, that whilst the Sun goes -once round the Ecliptic the Moon makes 12-1/3 conjunctions with him: but -whilst the hour-hand goes round the dial-plate the minute-hand makes -only 11 conjunctions with it; because the minute hand moves slower in -respect of the hour-hand than the Moon does with regard to the Sun. - -[Sidenote: The Harvest and Hunter’s Moon.] - -282. As the Moon can never be full but when she is opposite to the Sun, -and the Sun is never in Virgo and Libra but in our autumnal months, ’tis -plain that the Moon is never full in the opposite Signs, Pisces and -Aries, but in these two months. And therefore we can have only two Full -Moons in the year, which rise so near the time of Sun-set for a week -together as above-mentioned. The former of these is called the _Harvest -Moon_, and the latter the _Hunter’s Moon_. - -[Sidenote: Why the Moon’s regular rising is never perceived but in - Harvest.] - -283. Here it will probably be asked, why we never observe this -remarkable rising of the Moon but in harvest, since she is in Pisces and -Aries at least twelve times in the year besides; and must then rise with -as little difference of time as in harvest? The answer is plain: for in -winter these Signs rise at noon; and being then only a Quarter of a -Circle distant from the Sun, the Moon in them is in her first Quarter: -but when the Sun is above the Horizon the Moon’s rising is neither -regarded nor perceived. In spring these Signs rise with the Sun because -he is then in them; and as the Moon changeth in them at that time of the -year, she is quite invisible. In summer they rise about mid-night, and -the Sun being then three Signs, or a Quarter of a Circle before them, -the Moon is in them about her third Quarter; when rising so late, and -giving but very little light, her rising passes unobserved. And in -autumn, these Signs being opposite to the Sun, rise when he sets, with -the Moon in opposition, or at the Full, which makes her rising very -conspicuous. - - -284. At the Equator, the North and South Poles lie in the Horizon; and -therefore the Ecliptic makes the same Angle southward with the Horizon -when Aries rises as it does northward when Libra rises. Consequently, as -the Moon at all the fore-mentioned patches rises and sets nearly at -equal Angles with the Horizon all the year round; and about 48 minutes -later every day or night than on the preceding, there can be no -particular Harvest Moon at the Equator. - -285. The farther that any place is from the Equator, if it be not beyond -the Polar Circle, the Angle gradually diminishes which the Ecliptic and -Horizon make when Pisces and Aries rise; and therefore when the Moon is -in these Signs she rises with a nearly proportionable difference later -every day than on the former; and is for that reason the more remarkable -about the Full, until we come to the Polar Circles, or 66 degrees from -the Equator; in which Latitude the Ecliptic and Horizon become -coincident, every day for a moment, at the same sidereal hour (or 3 -minutes 56 seconds sooner every day than the former) and the very next -moment one half of the Ecliptic containing Capricorn, Aquarius, Pisces, -Aries, Taurus, and Gemini rises, and the opposite half sets. Therefore, -whilst the Moon is going from the beginning of Capricorn to the -beginning of Cancer, which is almost 14 days, she rises at the same -sidereal hour; and in autumn just at Sun-set, because all that half of -the Ecliptic in which the Sun is at that time sets at the same sidereal -hour, and the opposite half rises: that is, 3 minutes 56 seconds, of -mean solar time, sooner every day than on the day before. So whilst the -Moon is going from Capricorn to Cancer she rises earlier every day than -on the preceding; contrary to what she does at all places between the -polar Circles. But during the above fourteen days, the Moon is 24 -sidereal hours later in setting; for the six Signs which rise all at -once on the eastern side of the Horizon are 24 hours in setting on the -western side of it: as any one may see by making chalk-marks at the -beginning of Capricorn and of Cancer, and then, having elevated the Pole -66-1/2 degrees, turn the Globe slowly round it’s Axis, and observe the -rising and setting of the Ecliptic. As the beginning of Aries is equally -distant from the beginning of Cancer and of Capricorn, it is in the -middle of that half of the Ecliptic which rises all at once. And when -the Sun is at the beginning of Libra, he is in the middle of the other -half. Therefore, when the Sun is in Libra and the Moon in Capricorn, the -Moon is a Quarter of a Circle before the Sun; opposite to him, and -consequently full in Aries, and a Quarter of a Circle behind him when in -Cancer. But when Libra rises Aries sets, and all that half of the -Ecliptic of which Aries is the middle. And therefore, at that time of -the year the Moon rises at Sun-set from her first to her third Quarter. - -[Sidenote: The Harvest Moons regular on both sides of the Equator.] - -286. In northern Latitudes, the autumnal Full Moons are in Pisces and -Aries; and the vernal Full Moons in Virgo and Libra: in southern -Latitudes just the reverse because the seasons are contrary. But Virgo -and Libra rise at as small Angles with the Horizon in southern Latitudes -as Pisces and Aries do in the northern; and therefore the Harvest Moons -are just as regular on one side of the Equator as on the other. - -287. As these Signs which rise with the least Angles set with the -greatest, the vernal Full Moons differ as much in their times of rising -every night as the autumnal Full Moons differ in their times of setting; -and set with as little difference as the autumnal Full Moons rise: the -one being in all cases the reverse of the other. - -[Sidenote: The Moon’s Nodes.] - -288. Hitherto, for the sake of plainness, we have supposed the Moon to -move in the Ecliptic, from which the Sun never deviates. But the orbit -in which the Moon really moves is different from the Ecliptic: one half -being elevated 5-1/3 degrees above it, and the other half as much -depressed below it. The Moon’s orbit therefore intersects the Ecliptic -in two points diametrically opposite to each other: and these -intersections are called the _Moon’s Nodes_. So the Moon can never be in -the Ecliptic but when she is in either of her Nodes, which is at least -twice in every course from Change to Change, and sometimes thrice. For, -as the Moon goes almost a whole Sign more than round her Orbit from -Change to Change; if she passes by either Node about the time of Change, -she will pass by the other in about fourteen days after, and come round -to the former Node two days again before the next Change. That Node from -which the Moon begins to ascend northward, or above the Ecliptic, in -northern Latitudes, is called the _Ascending Node_; and the other the -_Descending Node_, because the Moon, when she passes by it, descends -below the Ecliptic southward. - -289. The Moon’s oblique motion with regard to the Ecliptic causes some -difference in the times of her rising and setting from what is already -mentioned. For whilst she is northward of the Ecliptic, she rises sooner -and sets later than if she moved in the Ecliptic: and when she is -southward of the Ecliptic she rises later and sets sooner. This -difference is variable even in the same Signs, because the Nodes shift -backward about 19-2/3 degrees in the Ecliptic every year; and so go -round it contrary to the order of Signs in 18 years 225 days. - -290. When the Ascending Node is in Aries, the southern half of the -Moon’s Orbit makes an Angle of 5-1/3 degrees less with the Horizon than -the Ecliptic does, when Aries rises in northern Latitudes: for which -reason the Moon rises with less difference of time whilst she is in -Pisces and Aries than there would be if she kept in the Ecliptic. But in -9 years and 112 days afterward, the Descending Node comes to Aries; and -then the Moon’s Orbit makes an Angle 5-1/3 degrees greater with the -Horizon when Aries rises, than the Ecliptic does at that time; which -causes the Moon to rise with greater difference of time in Pisces and -Aries than if she moved in the Ecliptic. - -291. To be a little more particular, when the Ascending Node is in -Aries, the Angle is only 9-2/3 degrees on the parallel of _London_ when -Aries rises. But when the Descending Node comes to Aries, the Angle is -20-1/3 degrees; this occasions as great a difference of the Moon’s -rising in the same Signs every 9 years, on the parallel of _London_, as -there would be on two parallels 10-2/3 degrees from one another, if the -Moon’s course were in the Ecliptic. The following Table shews how much -the obliquity of the Moon’s Orbit affects her rising and setting on the -parallel of _London_ from the 12th to the 18th day of her age; supposing -her to be Full at the autumnal Equinox; and then, either in the -Ascending Node, highest part of her Orbit, Descending Node, or lowest -part of her Orbit. _M_ signifies morning, _A_ afternoon; and the line at -the foot of the Table shews a week’s difference in rising and setting. - - +--------+---------------+---------------+---------------+---------------+ - | | Full in her | In the | Full in her | In the lowest | - | | Ascending | highest part | Descending | part of her | - | | node. | of her Orbit. | node. | Orbit. | - | Moon’s +---------------+-------+-------+-------+-------+-------+-------+ - | Age | Rises | Sets | Rises | Sets | Rises | Sets | Rises | Sets | - | | at | at | at | at | at | at | at | at | - | | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | - +--------+-------+-------+-------+-------+-------+-------+-------+-------+ - | | _A_ | _M_ | _A_ | _M_ | _A_ | _M_ | _A_ | _M_ | - | 12 | 5 15 | 3 20 | 4 30 | 3 15 | 4 32 | 3 40 | 5 16 | 3 0 | - | 13 | 5 32 | 4 25 | 4 50 | 4 45 | 5 15 | 4 20 | 6 0 | 4 15 | - | 14 | 5 48 | 5 30 | 5 15 | 6 0 | 5 45 | 5 40 | 6 20 | 5 28 | - | 15 | 6 5 | 7 0 | 5 42 | 7 20 | 6 15 | 6 56 | 6 45 | 6 32 | - | 16 | 6 20 | 8 15 | 6 2 | 8 35 | 6 46 | 8 0 | 7 8 | 7 45 | - | 17 | 6 36 | 9 12 | 6 26 | 9 45 | 7 18 | 9 15 | 7 30 | 9 15 | - | 18 | 6 54 | 10 30 | 7 0 | 10 40 | 8 0 | 10 20 | 7 52 | 10 0 | - +--------+-------+-------+-------+-------+-------+-------+-------+-------+ - | Dif. | 1 39 | 7 10 | 2 30 | 7 25 | 3 28 | 6 40 | 2 36 | 7 0 | - +--------+-------+-------+-------+-------+-------+-------+-------+-------+ - -This Table was not computed, but only estimated as near as could be done -from a common Globe, on which the Moon’s Orbit was delineated with a -black lead pencil. It may at first sight appear erroneous; since as we -have supposed the Moon to be full in either Node at the autumnal -Equinox, she ought by the Table to rise just at six o’clock, or at -Sun-set, on the 15th day of her age; being in the Ecliptic at that time. -But it must be considered, that the Moon is only 14-1/4 days old when -she is Full; and therefore in both cases she is a little past the Node -on the 15th day, being above it at one time, and below it at the other. - -[Sidenote: The period of the Harvest Moons.] - -292. As there is a compleat revolution of the Nodes in 18-2/3 years, -there must be a regular period of all the Varieties which can happen in -the rising and setting of the Moon during that time. But this shifting -of the Nodes never affects the Moon’s rising so much, even in her -quickest descending Latitude, as not to allow us still the benefit of -her rising nearer the time of Sun-set for a few days together about the -Full in Harvest, than when she is Full at any other time of the year. -The following Table shews in what years the Harvest-Moons are least -beneficial as to the times of their rising, and in what years most, from -1751 to 1861. The column of years under the letter _L_ are those in -which the Harvest-Moons are least of all beneficial, because they fall -about the Descending Node: and those under _M_ are the most of all -beneficial, because they fall about the Ascending Node. In all the -columns from _N_ to _S_ the Harvest-Moons descend gradually in the Lunar -Orbit, and rise to less heights above the Horizon. From _S_ to _N_ they -ascend in the same proportion, and rise to greater heights above the -Horizon. In both the columns under _S_ the Harvest-Moons are in the -lowest part of the Moon’s Orbit, that is, farthest South of the -Ecliptic; and therefore stay shortest of all above the Horizon: in the -columns under _N_ just the reverse. And in both cases, their rising, -though not at the same times, are nearly the same with regard to -difference of time, as if the Moon’s Orbit were coincident with the -Ecliptic. - - +------------------------------------------------------------+ - | | - | _Years in which the Harvest-Moons are least beneficial._ | - | | - | N L S | - | 1751 1752 1753 1754 1755 1756 1757 1758 1759 | - | 1770 1771 1772 1773 1774 1775 1776 1777 1778 | - | 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 | - | 1807 1808 1809 1810 1811 1812 1813 1814 1815 | - | 1826 1827 1828 1829 1830 1831 1832 1833 1834 | - | 1844 1845 1846 1847 1848 1849 1850 1851 1852 | - | | - | _Years in which they are most beneficial._ | - | | - | S M N | - | 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 | - | 1779 1780 1781 1782 1783 1784 1785 1786 1787 | - | 1798 1799 1800 1801 1802 1803 1804 1805 1806 | - | 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 | - | 1835 1836 1837 1838 1839 1840 1841 1842 1843 | - | 1853 1854 1855 1856 1857 1858 1859 1860 1861 | - +------------------------------------------------------------+ - -[Sidenote: PL. VIII.] - -293. At the Polar Circles, when the Sun touches the Summer Tropic, he -continues 24 hours above the Horizon; and 24 hours below it when he -touches the Winter Tropic. For the same reason the Full Moon neither -rises in Summer, nor sets in Winter, considering her as moving in the -Ecliptic. For the Winter Full Moon being as high in the Ecliptic as the -Summer Sun, must therefore continue as long above the Horizon; and the -Summer Full Moon being as low in the Ecliptic as the Winter Sun, can no -more rise than he does. But these are only the two Full Moons which -happen about the Tropics, for all the others rise and set. In Summer the -Full Moons are low, and their stay is short above the Horizon, when the -nights are short, and we have least occasion for Moon-light: in Winter -they go high, and stay long, above the Horizon when the nights are long, -and we want the greatest quantity of Moon-light. - -[Sidenote: The long continuance of Moon-light at the Poles. - - Fig. V.] - -294. At the Poles, one half of the Ecliptic never sets, and the other -half never rises: and therefore, as the Sun is always half a year in -describing one half of the Ecliptic, and as long in going through the -other half, ’tis natural to imagine that the Sun continues half a year -together above the Horizon of each Pole in it’s turn, and as long below -it; rising to one Pole when he sets to the other. This would be exactly -the case if there were no refraction: but by the Atmosphere’s refracting -the Sun’s rays, he becomes visible some days sooner § 183, and continues -some days longer in sight than he would otherwise do: so that he appears -above the Horizon of either Pole before he has got below the Horizon of -the other. And, as he never goes more than 23-1/2 degrees below the -Horizon of the Poles, they have very little dark night: it being -twilight there as well as at all other places till the Sun be 18 degrees -below the Horizon, § 177. The Full Moon being always opposite to the -Sun, can never be seen while the Sun is above the Horizon, except when -the Moon falls in the northern half of her Orbit; for whenever any point -of the Ecliptic rises the opposite point sets. Therefore, as the Sun is -above the Horizon of the north Pole from the 20th of _March_ till the -23d of _September_, it is plain that the Moon, when Full, being opposite -to the Sun, must be below the Horizon during that half of the year. But -when the Sun is in the southern half of the Ecliptic he never rises to -the north Pole, during which half of the year, every Full Moon happens -in some part of the northern half of the Ecliptic, which never sets. -Consequently, as the polar Inhabitants never see the Full Moon in -Summer, they have her always in the Winter, before, at, and after the -Full, shining for 14 of our days and nights. And when the Sun is at his -greatest depression below the Horizon, being then in Capricorn, the Moon -is at her First Quarter in Aries, Full in Cancer, and at her Third -Quarter in Libra. And as the beginning of Aries is the rising point of -the Ecliptic, Cancer the highest, and Libra the setting point, the Moon -rises at her First Quarter in Aries, is most elevated above the Horizon, -and Full in Cancer, and sets at the beginning of Libra in her Third -Quarter, having continued visible for 14 diurnal rotations of the Earth. -Thus the Poles are supplied one half of the winter time with constant -Moon-light in the Sun’s absence; and only lose sight of the Moon from -her Third to her First Quarter, while she gives but very little light; -and could be but of little, and sometimes of no service to them. A bare -view of the Figure will make this plain; in which let _S_ be the Sun, -_e_ the Earth in Summer when it’s north Pole _n_ inclines toward the -Sun, and _E_ the Earth in Winter, when it’s north Pole declines from -him. _SEN_ and _NWS_ is the Horizon of the north Pole, which is -coincident with the Equator; and, in both these positions of the Earth, -♈♋♎♑ is the Moon’s Orbit, in which she goes round the Earth, according -to the order of the letters _abcd_, _ABCD_. When the Moon is at _a_ she -is in her Third Quarter to the Earth at _e_, and just rising to the -north Pole _n_; at _b_ she changes, and is at the greatest height above -the Horizon, as the Sun likewise is; at _c_ she is in her First Quarter, -setting below the Horizon; and is lowest of all under it at _d_, when -opposite to the Sun, and her enlightened side toward the Earth. But then -she is full in view to the south Pole _p_; which is as much turned from -the Sun as the north Pole inclines towards him. Thus in our Summer, the -Moon is above the Horizon of the north Pole whilst she describes the -northern half of the Ecliptic ♈♋♎, or from her Third Quarter to her -First; and below the Horizon during the progress through the southern -half ♎♑♈; highest at the Change, most depressed at the Full. But in -winter, when the Earth is at _E_, and it’s north Pole declines from the -Sun, the New Moon at _D_ is at her greatest depression below the Horizon -_NWS_, and the Full Moon at _B_ at her greatest height above it; rising -at her First Quarter _A_, and keeping above the Horizon till she comes -to her Third Quarter _C_. At a mean state she is 23-1/2 degrees above -the Horizon at _B_ and _b_, and as much below it at _D_ and _d_, equal -to the inclination of the Earth’s Axis _F_. _S_♋ and _S_♑ are, as it -were, a ray of light proceeding from the Sun to the Earth; and shews -that when the Earth is at _e_, the Sun is above the Horizon, vertical to -the Tropic of Cancer; and when the Earth is at _E_, he is below the -Horizon, vertical to the Tropic of Capricorn. - -[Illustration: Plate VIII. - -_J. Ferguson delin._ _J. Mynde Sculp._] [Illustration: Plate IX. - -_J. Ferguson delin._ _J. Mynde Sculp._] - - - - - CHAP. XVII. - - _Of the ebbing and flowing of the Sea._ - - -[Sidenote: The cause of the Tides discovered by KEPLER. - - PLATE IX. - - Their Theory improved by Sir ISAAC NEWTON.] - -295. The cause of the Tides was discovered by KEPLER, who, in his -_Introduction to the Physics of the Heavens_, thus explains it: “The Orb -of the attracting power, which is in the Moon, is extended as far as the -Earth; and draws the waters under the torrid Zone, acting upon places -where it is vertical, insensibly on confined seas and bays, but sensibly -on the ocean whose beds are large, and the waters have the liberty of -reciprocation; that is, of rising and falling.” And in the 70th page of -his _Lunar Astronomy_——“But the cause of the Tides of the Sea appears to -be the bodies of the Sun and Moon drawing the waters of the Sea.” This -hint being given, the immortal Sir ISAAC NEWTON improved it, and wrote -so amply on the subject, as to make the Theory of the Tides in a manner -quite his own; by discovering the cause of their rising on the side of -the Earth opposite to the Moon. For KEPLER believed that the presence of -the Moon occasioned an impulse which caused another in her absence. - -[Sidenote: Explained on the Newtonian principles. - - Fig. I. - - Fig. I.] - -296. It has been already shewn § 106, that the power of gravity -diminishes as the square of the distance increases; and therefore the -waters at _Z_ on the side of the Earth _ABCDEFGH_ next the Moon _M_ are -more attracted than the central parts of the Earth _O_ by the Moon, and -the central parts are more attracted by her than the waters on the -opposite side of the Earth at _n_: and therefore the distance between -the Earth’s center and the waters on it’s surface under and opposite to -the Moon will be increased. For, let there be three bodies at _H_, _O_, -and _D_: if they are all equally attracted by the body _M_, they will -all move equally fast toward it, their mutual distances from each other -continuing the same. If the attraction of _M_ is unequal, then that body -which is most strongly attracted will move fastest, and this will -increase it’s distance from the other body. Therefore, by the law of -gravitation, _M_ will attract _H_ more strongly than it does _O_, by -which, the distance between _H_ and _O_ will be increased: and a -spectator on _O_ will perceive _H_ rising higher toward _Z_. In like -manner, _O_ being more strongly attracted than _D_, it will move farther -towards _M_ than _D_ does: consequently, the distance between _O_ and -_D_ will be increased; and a spectator on _O_, not perceiving his own -motion, will see _D_ receding farther from him towards _n_: all effects -and appearances being the same whether _D_ recedes from _O_ or _O_ from -_D_. - -[Sidenote: PLATE IX.] - -297. Suppose now there is a number of bodies, as _A_, _B_, _C_, _D_, -_E_, _F_, _G_, _H_ placed round _O_, so as to form a flexible or fluid -ring: then, as the whole is attracted towards _M_, the parts at _H_ and -_D_ will have their distance from _O_ increased; whilst the parts at _B_ -and _F_, being nearly at the same distance from _M_ as _O_ is, these -parts will not recede from one another; but rather, by the oblique -attraction of _M_, they will approach nearer to _O_. Hence, the fluid -ring will form itself into an ellipse _ZIBLnKFNZ_, whose longer Axis -_nOZ_ produced will pass through _M_, and it’s shorter Axis _BOF_ will -terminate in _B_ and _F_. Let the ring be filled with bodies, so as to -form a flexible or fluid sphere round _O_; then, as the whole moves -toward _M_, the fluid sphere being lengthned at _Z_ and _n_, will assume -an oblong or oval form. If _M_ is the Moon, _O_ the Earth’s center, -_ABCDEFGH_ the Sea covering the Earth’s surface, ’tis evident by the -above reasoning, that whilst the Earth by it’s gravity falls toward the -Moon, the Water directly below her at _B_ will swell and rise gradually -towards her: also, the Water at _D_ will recede from the center -[strictly speaking, the center recedes from _D_] and rise on the -opposite side of the Earth: whilst the Water at _B_ and _F_ is -depressed, and falls below the former level. Hence, as the Earth turns -round it’s Axis from the Moon to the Moon again in 24-3/4 hours, there -will be two tides of flood and two of ebb in that time, as we find by -experience. - -[Sidenote: Fig. II.] - -298. As this explanation of the ebbing and flowing of the Sea is deduced -from the Earth’s constantly falling toward the Moon by the power of -gravity, some may find a difficulty in conceiving how this is possible -when the Moon is Full, or in opposition to the Sun; since the Earth -revolves about the Sun, and must continually fall towards it, and -therefore cannot fall contrary ways at the same time: or if the Earth is -constantly falling towards the Moon, they must come together at last. To -remove this difficulty, let it be considered, that it is not the center -of the Earth that describes the annual orbit round the Sun; but the -[63]common center of gravity of the Earth and Moon together: and that -whilst the Earth is moving round the Sun, it also describes a Circle -round that centre of gravity; going as many times round it in one -revolution about the Sun as there are Lunations or courses of the Moon -round the Earth in a year: and therefore, the Earth is constantly -falling towards the Moon from a tangent to the Circle it describes round -the said common center of gravity. Let _M_ be the Moon, _TW_ part of the -Moon’s Orbit, and _C_ the center of gravity of the Earth and Moon: -whilst the Moon goes round her Orbit, the center of the Earth describes -the Circle _ged_ round _C_, to which Circle _gak_ is a tangent: and -therefore, when the Moon has gone from _M_ to a little past _W_, the -Earth has moved from _g_ to _e_; and in that time has fallen towards the -Moon, from the tangent at _a_ to _e_; and so round the whole Circle. - -[Sidenote: PLATE IX.] - -299. The Sun’s influence in raising the Tides is but small in comparison -of the Moon’s: For though the Earth’s diameter bears a considerable -proportion to it’s distance from the Moon, it is next to nothing when -compared with the distance of the Sun. And therefore, the difference of -the Sun’s attraction on the sides of the Earth under and opposite to -him, is much less than the difference of the Moon’s attraction on the -sides of the Earth under and opposite to her: and therefore the Moon -must raise the Tides much higher than they can be raised by the Sun. - - -[Sidenote: Why the Tides are not highest when the Moon is on the Meridian. - - Fig. I.] - -300. On this Theory so far as we have explained it, the Tides ought to -be highest directly under and opposite to the Moon; that is, when the -Moon is due north and south. But we find, that in open Seas, where the -water flows freely, the Moon _M_ is generally past the north and south -Meridian as at _p_ when it is high water at _Z_ and at _n_. The reason -is obvious; for though the Moon’s attraction was to cease altogether -when she was past the Meridian, yet the motion of ascent communicated to -the water before that time would make it continue to rise for some time -after; much more must it do so when the attraction is only diminished: -as a little impulse given to a moving ball will cause it still move -farther than otherwise it could have done. And as experience shews, that -the day is hotter about three in the afternoon, than when the Sun is on -the Meridian, because of the increment made to the heat already -imparted. - -[Sidenote: Nor always answer to her being at the same distance from it.] - -301. The Tides answer not always to the same distance of the Moon from -the Meridian at the same places; but are variously affected by the -action of the Sun, which brings them on sooner when the Moon is in her -first and third Quarters, and keeps them back later when she is in her -second and fourth: because, in the former case, the Tide raised by the -Sun alone would be earlier than the Tide raised by the Moon; and in the -latter case later. - - -[Sidenote: Spring and neap Tides. - - PLATE IX. - - Fig. VI.] - -302. The Moon goes round the Earth in an elliptic Orbit, and therefore -she approaches nearer to the Earth than her mean distance, and recedes -farther from it, in every Lunar Month. When she is nearest: she attracts -strongest, and so rises the Tides most; the contrary happens when she is -farthest, because of her weaker attraction. When both Luminaries are in -the Equator, and the Moon in _Perigeo_, or at her least distance from -the Earth, she raises the Tides highest of all, especially at her -Conjunction and opposition; both because the equatoreal parts have the -greatest centrifugal force from their describing the largest Circle, and -from the concurring actions of the Sun and Moon. At the Change, the -attractive forces of the Sun and Moon being united, they diminish the -gravity of the waters under the Moon, which is also diminished on the -other side, by means of a greater centrifugal force. At the full, whilst -the Moon raises the Tide under and opposite to her, the Sun acting in -the same line, raises the Tide under and opposite to him; whence their -conjoint effect is the same as at the Change; and in both cases, -occasion what we call _the Spring Tides_. But at the Quarters the Sun’s -action on the waters at _O_ and _H_ diminishes the Moon’s action on the -waters at _Z_ and _N_; so that they rise a little under and opposite to -the Sun at _O_ and _H_, and fall as much under and opposite to the Moon -at _Z_ and _N_; making what we call _the Neap Tides_, because the Sun -and Moon then act cross-wise to each other. But, strictly speaking, -these Tides happen not till some time after; because in this, as in -other cases, § 300, the actions do not produce the greatest effect when -they are at the strongest, but some time afterward. - -[Sidenote: Not greatest at the Equinoxes, and why.] - -303. The Sun being nearer the Earth in Winter than in Summer, § 205, is -of course nearer to it in _February_ and _October_ than in _March_ and -_September_: and therefore the greatest Tides happen not till some time -after the autumnal Equinox, and return a little before the vernal. - -[Sidenote: The Tides would not immediately cease upon the annihilation - of the Sun and Moon.] - -The Sea being thus put in motion, would continue to ebb and flow for -several times, even though the Sun and Moon were annihilated, or their -influence should cease: as if a bason of water were agitated, the water -would continue to move for some time after the bason was left to stand -still. Or like a Pendulum, which having been put in motion by the hand, -continues to make several vibrations without any new impulse. - - -[Sidenote: The lunar day, what. - - The Tides rise to unequal heights in the same day, and why. - - PLATE IX. - - Fig. III, IV, V. - - Fig. III. - - Fig. IV. - - Fig. V.] - -304. When the Moon is in the Equator, the Tides are equally high in both -parts of the lunar day, or time of the Moon’s revolving from the -Meridian to the Meridian again, which is 24 hours 48 minutes. But as the -Moon declines from the Equator towards either Pole, the Tides are -alternately higher and lower at places having north or south Latitude. -For one of the highest elevations, which is that under the Moon, follows -her towards the same Pole, and the other declines towards the opposite; -each describing parallels as far distant from the Equator, on opposite -sides, as the Moon declines from it to either side; and consequently, -the parallels described by these elevations of the water are twice as -many degrees from one another, as the Moon is from the Equator; -increasing their distance as the Moon increases her declination, till it -be at the greatest, when the said parallels are, at a mean state, 47 -degrees from one another: and on that day, the Tides are most unequal in -their heights. As the Moon returns toward the Equator, the parallels -described by the opposite elevations approach towards each other, until -the Moon comes to the Equator, and then they coincide. As the Moon -declines toward the opposite Pole, at equal distances, each elevation -describes the same parallel in the other part of the lunar day, which -it’s opposite elevation described before. Whilst the Moon has north -declination, the greatest Tides in the northern Hemisphere are when she -is above the Horizon; and the reverse whilst her declination is south. -Let _NESQ_ be the Earth, _NCS_ it’s Axis, _EQ_ the Equator, _T_♋ the -Tropic of Cancer, _t_♑ the Tropic of Capricorn, _ab_ the arctic Circle, -_cd_ the Antarctic, _N_ the north Pole, _S_ the south Pole, _M_ the -Moon, _F_ and _G_ the two eminences of water, whose lowest parts are at -_a_ and _d_ (Fig. III.) at _N_ and _S_ (Fig. IV.) and at _b_ and _c_ -(Fig. V.) always 90 degrees from the highest. Now when the Moon is in -her greatest north declination at _M_, the highest elevation _G_ under -her, is on the Tropic of Cancer _T_♋, and the opposite elevation _F_ on -the Tropic of Capricorn _t_♑; and these two elevations describe the -Tropics by the Earth’s diurnal rotation. All places in the northern -Hemisphere _ENQ_ have the highest Tides when they come into the position -_b_♋_Q_, under the Moon; and the lowest Tides when the Earth’s diurnal -rotation carries them into the position _aTE_, on the side opposite to -the Moon; the reverse happens at the same time in the southern -Hemisphere _ESQ_, as is evident to sight. The Axis of the Tides _aCd_ -has now it’s Poles _a_ and _d_ (being always 90 degrees from the highest -elevations) in the arctic and antarctic Circles; and therefore ’tis -plain, that at these Circles there is but one Tide of Flood, and one of -Ebb, in the lunar day. For, when the point _a_ revolves half round to -_b_, in 12 lunar hours, it has a Tide of Flood; but when it comes to the -same point _a_ again in 12 hours more, it has the lowest ebb. In seven -days afterward, the Moon _M_ comes to the equinoctial Circle, and is -over the Equator _EQ_, when both Elevations describe the Equator; and in -both Hemispheres, at equal distances from the Equator, the Tides are -equally high in both parts of the lunar day. The whole Phenomena being -reversed when the Moon has south declination to what they were when her -declination was north, require no farther description. - -[Sidenote: Fig. VI. - - When both Tides are equally high in the same day, they arrive - at unequal intervals of Time; and _vice versa_.] - -305. In the three last-mentioned Figures, the Earth is orthographically -projected on the plane of the Meridian; but in order to describe a -particular Phenomenon we now project it on the plane of the Ecliptic. -Let _HZON_ be the Earth and Sea, _FED_ the Equator, _T_ the Tropic of -Cancer, _C_ the arctic Circle, _P_ the north Pole, and the Curves _1_, -_2_, _3_, _&c._ 24 Meridians, or hour Circles, intersecting each other -in the Poles; _AGM_ is the Moon’s orbit, _S_ the Sun, _M_ the Moon, _Z_ -the Water elevated under the Moon, and _N_ the opposite equal Elevation. -As the lowest parts of the Water are always 90 degrees from the highest, -when the Moon is in either of the Tropics (as at _M_) the Elevation _Z_ -is on the Tropic of Capricorn, and the opposite Elevation _N_ on the -Tropic of Cancer, the low-water Circle _HCO_ touches the polar Circles -at _C_; and the high-water Circle _ETP6_ goes over the Poles at _P_, and -divides every parallel of Latitude into two equal segments. In this case -the Tides upon every parallel are alternately higher and lower; but they -return in equal times: the point _T_, for example, on the Tropic of -Cancer (where the depth of the Tide is represented by the breadth of the -dark shade) has a shallower Tide of Flood at _T_ than when it revolves -half round from thence to _6_, according to the order of the numeral -Figures; but it revolves as soon from _6_ to _T_ as it did from _T_ to -_6_. When the Moon is in the Equinoctial, the Elevations _Z_ and _N_ are -transferred to the Equator at _O_ and _H_, and the high and low-water -Circles are got into each other’s former places; in which case the Tides -return in unequal times, but are equally high in both parts of the lunar -day: for a place at _1_ (under _D_) revolving as formerly, goes sooner -from _1_ to _11_ (under _F_) than from _11_ to _1_, because the parallel -it describes is cut into unequal segments by the high-water Circle -_HCO_: but the points 1 and 11 being equidistant from the Pole of the -Tides at _C_, which is directly under the Pole of the Moon’s orbit -_MGA_, the Elevations are equally high in both parts of the day. - -306. And thus it appears, that as the Tides are governed by the Moon, -they must turn on the Axis of the Moon’s orbit, which is inclined 23-1/2 -degrees to the Earth’s Axis at a mean state: and therefore the Poles of -the Tides must be so many degrees from the Poles of the Earth, or in -opposite points of the polar Circles, going round these Circles in every -lunar day. ’Tis true that according to Fig. IV. when the Moon is -vertical to the Equator _ECQ_, the Poles of the Tides seem to fall in -with the Poles of the World _N_ and _S_: but when we consider that _FHG_ -is under the Moon’s orbit, it will appear, that when the Moon is over -_H_, in the Tropic of Capricorn, the north Pole of the Tides, (which can -be no more than 90 degrees from under the Moon) must be at _c_ in the -arctic Circle, not at _N_; the north Pole of the Earth; and as the Moon -ascends from _H_ to _G_ in her orbit, the north Pole of the Tides must -shift from _c_ to _a_ in the arctic Circle; and the South Pole as much -in the antarctic. - -It is not to be doubted, but that the Earth’s quick rotation brings the -poles of the Tides nearer to the Poles of the World, than they would be -if the Earth were at rest, and the Moon revolved about it only once a -month; for otherwise the Tides would be more unequal in their heights, -and times of their returns, than we find they are. But how near the -Earth’s rotation may bring the Poles of it’s Axis and those of the Tides -together, or how far the preceding Tides may affect those which follow, -so as to make them keep up nearly to the same heights, and times of -ebbing and flowing, is a problem more fit to be solved by observation -than by theory. - - -[Sidenote: To know at what times we may expect the greatest and least - Tides.] - -307. Those who have opportunity to make observations, and choose to -satisfy themselves whether the Tides are really affected in the above -manner by the different positions of the Moon; especially as to the -unequal times of their returns, may take this general rule for knowing, -when they ought to be so affected. When the Earth’s Axis inclines to the -Moon, the northern Tides, if not retarded in their passage through -Shoals and Channels, nor affected by the Winds, ought to be greatest -when the Moon is above the Horizon, least when she is below it; and -quite the reverse when the Earth’s Axis declines from her: but in both -cases, at equal intervals of time. When the Earth’s Axis inclines -sidewise to the Moon, both Tides are equally high, but they happen at -unequal intervals of time. In every Lunation the Earth’s Axis inclines -once to the Moon, once from her, and twice sidewise to her, as it does -to the Sun every year; because the Moon goes round the Ecliptic every -month, and the Sun but once in a year. In Summer, the Earth’s Axis -inclines towards the Moon when New; and therefore the day-tides in the -north ought to be highest, and night-tides lowest about the Change: at -the Full the reverse. At the Quarters they ought to be equally high, but -unequal in their returns; because the Earth’s Axis then inclines -sidewise to the Moon. In winter the Phenomena are the same at Full-Moon -as in Summer at New. In Autumn the Earth’s Axis inclines sidewise to the -Moon when New and Full; therefore the Tides ought to be equally high, -and unequal in their returns at these times. At the first Quarter the -Tides of Flood should be least when the Moon is above the Horizon, -greatest when she is below it; and the reverse at her third Quarter. In -Spring, Phenomena of the first Quarter answer to those of the third -Quarter in Autumn; and _vice versa_. The nearer any time is to either of -these seasons, the more the Tides partake of the Phenomena of these -seasons; and in the middle between any two of them the Tides are at a -mean state between those of both. - -[Sidenote: Why the Tides rise higher in Rivers than in the Sea.] - -308. In open Seas, the Tides rise but to very small heights in -proportion to what they do in wide-mouthed rivers, opening in the -Direction of the Stream of Tide. For, in Channels growing narrower -gradually, the water is accumulated by the opposition of the contracting -Bank. Like a gentle wind, little felt on an open plain, but strong and -brisk in a street; especially if the wider end of the street be next the -plain, and in the way of the wind. - -[Sidenote: The Tides happen at all distances of the Moon from the - Meridian at different places, and why.] - -309. The Tides are so retarded in their passage through different Shoals -and Channels, and otherwise so variously affected by striking against -Capes and Headlands, that to different places they happen at all -distances of the Moon from the Meridian; consequently at all hours of -the lunar day. The Tide propagated by the Moon in the _German_ ocean, -when she is three hours past the Meridian, takes 12 hours to come from -thence to _London_ bridge; where it arrives by the time that a new Tide -is raised in the ocean. And therefore when the Moon has north -declination, and we should expect the Tide at _London_ to be greatest -when the Moon is above the Horizon, we find it is least; and the -contrary when she has south declination. At several places ’tis high -water three hours before the Moon comes to the Meridian; but that Tide -which the Moon pushes as it were before her, is only the Tide opposite -to that which was raised by her when she was nine hours past the -opposite Meridian. - -[Sidenote: The Water never rises in Lakes.] - -310. There are no Tides in Lakes, because they are generally so small -that when the Moon is vertical she attracts every part of them alike, -and therefore by rendering all the water equally light, no part of it -can be raised higher than another. The _Mediterranean_ and _Baltic_ Seas -suffer very small elevations, because the Inlets by which they -communicate with the ocean are so narrow, that they cannot, in so short -a time, receive or discharge enough to raise or sink their surfaces -sensibly. - - -[Sidenote: The Moon raises Tides in the Air. - - Why the Mercury in the Barometer is not affected by the aerial - Tides.] - -311. Air being lighter than Water, and the surface of the Atmosphere -being nearer to the Moon than the surface of the Sea, it cannot be -doubted that the Moon raises much higher Tides in the Air than in the -Sea. And therefore many have wondered why the Mercury does not sink in -the Barometer when the Moon’s action on the particles of Air makes them -lighter as she passes over the Meridian. But we must consider, that as -these particles are rendered lighter, a greater number of them is -accumulated, until the deficiency of gravity be made up by the height of -the column; and then there is an _equilibrium_, and consequently an -equal pressure upon the Mercury as before; so that it cannot be affected -by the aerial Tides. - - - - - CHAP. XVIII. - -_Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and - Modern Eclipses._ - - -[Sidenote: A shadow, what.] - -312. Every Planet and Satellite is illuminated by the Sun; and casts a -shadow towards that point of the Heavens which is opposite to the Sun. -This shadow is nothing but a privation of light in the space hid from -the Sun by the opake body that intercepts his rays. - -[Sidenote: Eclipses of the Sun and Moon, what.] - -313. When the Sun’s light is so intercepted by the Moon, that to any -place of the Earth the Sun appears partly or wholly covered, he is said -to undergo an Eclipse; though properly speaking, ’tis only an Eclipse of -that part of the Earth where the Moon’s shadow or [64]Penumbra falls. -When the Earth comes between the Sun and Moon, the Moon falls into the -Earth’s shadow; and having no light of her own, she suffers a real -Eclipse from the interception of the Sun’s rays. When the Sun is -eclipsed to us, the Moon’s Inhabitants on the side next the Earth (if -any such there be) see her shadow like a dark spot travelling over the -Earth, about twice as fast as its equatoreal parts move, and the same -way as they move. When the Moon is in an Eclipse, the Sun appears -eclipsed to her, total to all those parts on which the Earth’s shadow -falls, and of as long continuance as they are in the shadow. - -[Illustration: Plate X. - -_J. Ferguson delin._ _J. Mynde Sculp._] - -[Sidenote: A proof that the Earth and Moon are globular bodies.] - -314. That the Earth is spherical (for the hills take off no more from -the roundness of the Earth, than grains of dust do from the roundness of -a common Globe) is evident from the figure of its shadow on the Moon; -which is always bounded by a circular line, although the Earth is -incessantly turning its different sides to the Moon, and very seldom -shews the same side to her in different Eclipses, because they seldom -happen at the same hours. Were the Earth shaped like a round flat plate, -its shadow would only be circular when either of its sides directly -faced the Moon; and more or less elliptical as the Earth happened to be -turned more or less obliquely towards the Moon when she is eclipsed. The -Moon’s different Phases prove her to be round § 254; for, as she keeps -still the same side towards the earth, if that side were flat, as it -appears to be, she would never be visible from the third Quarter to the -first; and from the first Quarter to the third, she would appear as -round as when we say she is Full: because at the end of her first -Quarter the Sun’s light would come as suddenly on all her side next the -Earth, as it does on a flat wall, and go off as abruptly at the end of -her third Quarter. - -[Sidenote: And that the Sun is much bigger than the Earth, and the Moon - much less.] - -315. If the Earth and Sun were equally big, the Earth’s shadow would be -infinitely extended, and all of the same breadth; and the Planet Mars, -in either of its nodes and opposite to the Sun, would be eclipsed in the -Earth’s shadow. Were the Earth bigger than the Sun, it’s shadow would -increase in breadth the farther it was extended, and would eclipse the -great Planets Jupiter and Saturn, with all their Moons, when they were -opposite to the Sun. But as Mars in opposition never falls into the -Earth’s shadow, although he is not then above 42 millions of miles from -the Earth, ’tis plain that the Earth is much less than the Sun; for -otherwise it’s shadow could not end in a point at so small a distance. -If the Sun and Moon were equally big, the Moon’s shadow would go on to -the Earth with an equal breadth, and cover a portion of the Earth’s -surface more than 2000 miles broad, even if it fell directly against the -Earth’s center, as seen from the Moon: and much more if it fell -obliquely on the Earth: but the Moon’s shadow is seldom 150 miles broad -at the Earth, unless when it falls very obliquely on the Earth, in total -Eclipses of the Sun. In annular Eclipses, the Moon’s real shadow ends in -a point at some distance from the Earth. The Moon’s small distance from -the Earth, and the shortness of her shadow, prove her to be less than -the Sun. And, as the Earth’s shadow is large enough to cover the Moon, -if her diameter was three times as large as it is (which is evident from -her long continuance in the shadow when she goes through it’s center) -’tis plain, that the Earth is much bigger than the Moon. - -[Sidenote: The primary Planets never eclipse one another. - - PLATE X.] - -316. Though all opake bodies on which the Sun shines have their shadows, -yet such is the bulk of the Sun, and the distances of the Planets, that -the primary Planets can never eclipse one another. A Primary can eclipse -only it’s secondary, or be eclipsed by it; and never but when in -opposition or conjunction with the Sun. The primary Planets are very -seldom in these positions, but the Sun and Moon are so every month: -whence one may imagine that these two Luminaries should be eclipsed -every month. But there are few Eclipses in respect of the number of New -and Full Moons; the reason of which we shall now explain. - -[Sidenote: Why there are so few Eclipses. - - The Moon’s Nodes. - - Limits of Eclipses.] - -317. If the Moon’s Orbit were coincident with the Plane of the Ecliptic, -in which the Earth always moves and the Sun appears to move, the Moon’s -shadow would fall upon the Earth at every Change, and eclipse the Sun to -some parts of the Earth. In like manner the Moon would go through the -middle of the Earth’s shadow, and be eclipsed at every Full; but with -this difference, that she would be totally darkened for above an hour -and half; whereas the Sun never was above four minutes totally eclipsed -by the interposition of the Moon. But one half of the Moon’s Orbit, is -elevated 5-1/3 degrees above the Ecliptic, and the other half as much -depressed below it: consequently, the Moon’s Orbit intersects the -Ecliptic in two opposite points called _the Moon’s Nodes_, as has been -already taken notice of § 288. When these points are in a right line -with the center of the Sun at New or Full Moon, the Sun, Moon, and Earth -are all in a right line; and if the Moon be then New, her shadow falls -upon the Earth; if Full the Earth’s shadow falls upon her. When the Sun -and Moon are more than 17 degrees from either of the Nodes at the time -of Conjunction, the Moon is then too high or too low in her Orbit to -cast any part of her shadow upon the Earth. And when the Sun is more -than 12 degrees from either of the Nodes at the time of Full Moon, the -Moon is too high or too low in her Orbit to go through any part of the -Earth’s shadow: and in both these cases there will be no Eclipse. But -when the Moon is less than 17 degrees from either Node at the time of -Conjunction, her shadow or Penumbra falls more or less upon the Earth, -as she is more or less within this limit. And when she is less than 12 -degrees from either Node at the time of opposition, she goes through a -greater or less portion of the Earth’s shadow, as she is more or less -within this limit. Her Orbit contains 360 degrees; of which 17, the -limit of solar Eclipses on either side of the Nodes, and 12 the limit of -lunar Eclipses, are but small portions: and as the Sun commonly passes -by the Nodes but twice in a year, it is no wonder that we have so many -New and Full Moons without Eclipses. - -[Sidenote: Fig. I. - - PLATE X. - - Line of the Nodes.] - -To illustrate this, let _ABCD_ be the _Ecliptic_, _RSTU_ a Circle lying -in the same Plane with the Ecliptic, and _VWXY_ the _Moon’s Orbit_, all -thrown into an oblique view, which gives them an elliptical shape to the -eye. One half of the Moon’s Orbit, as _VWX_, is always below the -Ecliptic, and the other half _XYV_ above it. The points _V_ and _X_, -where the Moon’s Orbit intersects the Circle _RSTU_, which lies even -with the Ecliptic, are the _Moon’s Nodes_; and a right line as _XEV_ -drawn from one to the other, through the Earth’s center, is the _Line of -the Nodes_, which is carried almost parallel to itself round the Sun in -a year. - -If the Moon moved round the Earth in the Orbit _RSTU_, which is -coincident with the Plane of the Ecliptic, her shadow would fall upon -the Earth every time she is in conjunction with the Sun; and at every -opposition she would go through the Earth’s shadow. Were this the case, -the Sun would be eclipsed at every Change, and the Moon at every Full, -as already mentioned. - -But although the Moon’s shadow _N_ must fall upon the Earth at _a_, when -the Earth is at _E_, and the Moon in conjunction with the Sun at _i_, -because she is then very near one of her Nodes; and at her opposition -_n_ she must go through the Earth’s shadow _I_, because she is then near -the other Node; yet, in the time that she goes round the Earth to her -next Change, according to the order of the letters _XYVW_, the Earth -advances from _E_ to _e_, according to the order of the letters _EFGH_, -and the line of the Nodes _VEX_ being carried nearly parallel to itself, -brings the point _f_ of the Moon’s Orbit in conjunction with the Sun at -that next Change; and then the Moon being at _f_ is too high above the -Ecliptic to cast her shadow on the Earth: and as the Earth is still -moving forward, the Moon at her next opposition will be at _g_, too far -below the Ecliptic to go through any part of the Earth’s shadow; for by -that time the point _g_ will be at a considerable distance from the -Earth as seen from the Sun. - -[Sidenote: Fig. I and II.] - -When the Earth comes to _F_, the Moon in conjunction with the Sun _Z_ is -not at _k_, in a Plane coincident with the Ecliptic, but above it at _Y_ -in the highest part of her Orbit: and then the point _b_ of her shadow -_O_ goes far above the Earth (as in Fig. II, which is an edge view of -Fig. I.) The Moon at her next opposition is not at _o_ (Fig I) but at -_W_ where the Earth’s shadow goes far above her, (as in Fig. II.) In -both these cases the line of the Nodes _VFX_ (Fig. I.) is about 90 -degrees from the Sun, and both Luminaries as far as possible from the -limits of Eclipses. - -[Sidenote: PLATE X.] - -When the Earth has gone half round the Ecliptic from _E_ to _G_, the -line of the Nodes _VGX_ is nearly, if not exactly, directed towards the -Sun at _Z_; and then the New Moon _l_ casts her shadow _P_ on the Earth -_G_; and the Full Moon _p_ goes through the Earth’s shadow _L_; which -brings on Eclipses again, as when the Earth was at _E_. - -When the Earth comes to _H_ the New Moon falls not at _m_ in a plane -coincident with the Ecliptic _CD_, but at _W_ in her Orbit below it: and -then her shadow _Q_ (see Fig. II) goes far below the Earth. At the next -Full she is not at _q_ (Fig. I) but at _Y_ in her orbit 5-1/3 degrees -above _q_, and at her greatest height above the Ecliptic _CD_; being -then as far as possible, at any opposition, from the Earth’s shadow _M_ -(as in Fig. II.) - -So, when the Earth is at _E_ and _G_, the Moon is about her Nodes at New -and Full; and in her greatest _North_ and _South Declination_, (or -Latitude as it is generally called) from the Ecliptic at her Quarters: -but when the Earth is at _F_ or _H_, the Moon is in her greatest _North_ -and _South Declination_ from the Ecliptic at New and Full, and in the -_Nodes_ about her Quarters. - -[Sidenote: The Moon’s ascending and descending Node. - - Her North and South Latitude.] - -318. The point _X_ where the Moon’s Orbit crosses the Ecliptic is called -_the Ascending Node_, because the Moon ascends from it above the -Ecliptic: and the opposite point of intersection _V_ is called _the -Descending Node_, because the Moon descends from it below the Ecliptic. -When the Moon is at _Y_ in the highest point of her Orbit, she is in her -greatest _North Latitude_; and when she is at _W_ in the lowest point of -her Orbit, she is in her greatest _South Latitude_. - -[Sidenote: The Nodes have a retrograde motion. - - Fig. I. - - Which brings on the Eclipses sooner every year than they would - be if the Nodes had not such a motion.] - -319. If the line of the Nodes, like the Earth’s Axis, was carried -parallel to itself round the Sun, there would be just half a year -between the conjunctions of the Sun and Nodes. But the Nodes shift -backward, or contrary to the Earth’s annual motion, 19-1/3 degrees every -year; and therefore the same Node comes round to the Sun 19 days sooner -every year than on the year before. Consequently, from the time that the -ascending Node _X_ (when the Earth is at _E_) passes by the Sun as seen -from the Earth, it is only 173 days (not half a year) till the -descending Node _V_ passes by him. Therefore, in whatever time of the -year we have Eclipses of the Luminaries about either Node, we may be -sure that in 173 days afterward we shall have Eclipses about the other -Node. And when at any time of the year the line of the Nodes is in the -situation _VGX_, at the same time next year it will be in the situation -_rGs_; the ascending Node having gone backward, that is, contrary to the -order of Signs from _X_ to _s_, and the descending Node from _V_ to _r_; -each 19-1/3 degrees. At this rate the Nodes shift through all the Signs -and degrees of the Ecliptic in 18 years and 225 days; in which time -there would always be a regular period of Eclipses, if any compleat -number of Lunations were finished without a fraction. But this never -happens, for if the Sun and Moon should start from a conjunction with -either of the Nodes in any point of the Ecliptic, whilst the same Node -is going round to that point again the Earth performs 18 annual -revolutions about the Sun and 222 Degrees (or 7 Signs 12 Degrees) over; -and the Moon 230 Lunations or Courses from Change to Change and 85 -Degrees (or 2 Signs 25 Degrees) over; so that the Sun will be 138 -Degrees from the same Node when it comes round, and the Moon 85 Degrees -from the Sun. Hence, the period of Eclipses and revolution of the Nodes -are completed in different times. - -[Sidenote: A period of Eclipses. - - The defects of it.] - -320. In 18 years 10 days 7 hours 43 minutes after the Sun Moon and Nodes -have been in a line of conjunction, they come very near to a conjunction -again: only, if the conjunction from which you reckon falls in a -leap-year, the return of the conjunction will be one day later. -Therefore, if to the [65]mean time of any Eclipse of the Sun or Moon in -leap-year, you add 18 years 11 days 7 hours 43 minutes; or in a common -year a day less, you will have the mean time of that Eclipse returned -again for some ages; though not always visible, because the 7 hours 43 -minutes may shift a solar Eclipse into the night, and a lunar Eclipse -into the day. In this period there are just 223 Lunations, and the Sun -is again within half a degree of the same Node, but short of it. -Therefore, although this period will serve tolerably well for some ages -to examine Eclipses by, it cannot hold long; because half a degree from -the Node sets the Moon 2-1/2 minutes of a degree from the Ecliptic. And -as the Moon’s mean distance from the Earth is equal to 60 Semidiameters -of the Earth, every minute of a degree at that distance is equal to 60 -geographical miles, or one degree on the Earth; consequently 2-1/2 -minutes of declination from the Ecliptic in the Moon’s Orbit, is equal -to 150 such miles, or 2-1/2 degrees on the Earth. Consequently, if the -Moon be passing by her ascending Node at the end of this period, her -shadow will go 150 miles more southward on the Earth than it did at the -beginning thereof. If the Moon be passing by her descending Node, her -shadow will go 150 miles more northward: and in either case, in 500 -years the shadow will have too great a Latitude to touch the Earth. So -that any Eclipse of the Sun, which begins (for example) to touch the -Earth at the south Pole (and that must be when the Moon is 17 degrees -past her descending Node) will advance gradually northward in every -return for about a thousand years, and then go off at the north Pole; -and cannot take such another course again in less than 11,683 years. - -This falling back of the Sun and Moon in every period, with respect to -the Nodes, will occasion those Eclipses which happen about the ascending -Node to go more southerly in each return; and those which happen about -the descending Node to go more northerly: for the farther the Moon is -short of the ascending Node, within the limits of Eclipses, the farther -she is south of the Ecliptic; and on the contrary, the more she is short -of the descending Node, the farther she is northward of the Ecliptic. - -[Sidenote: From Mr. G. SMITH’s dissertation on Eclipses, printed at - _London_, by E. CAVE, in the year 1748.] - -321. “To illustrate this a little farther, we shall examine some of the -most remarkable circumstances of the returns of the Eclipse which -happened _July 14, 1748_, about noon: This Eclipse, after traversing the -voids of space from the Creation, at last began to enter the _Terra -Australis Incognita_, about 88 years after the Conquest, which was the -last of King STEPHEN’s reign; every [66]_Chaldean_ period it has crept -more northerly, but was still invisible in _Britain_ before the year -1622; when on the 30th of _April_ it began to touch the south parts of -_England_ about 2 in the afternoon; its central appearance rising in the -_American_ South Seas, and traversing _Peru_ and the _Amazon_’s country, -through the _Atlantic_ ocean into _Africa_, and setting in the -_Æthiopian_ continent, not far from the beginning of the Red Sea. - -“Its next visible period was after three _Chaldean_ revolutions in 1676, -on the first of _June_, rising central in the _Atlantic_ ocean, passing -us about 9 in the morning, with four [67]Digits eclipsed on the under -limb; and setting in the gulf of _Cochinchina_ in the _East-Indies_. - -“It being now near the Solstice, this Eclipse was visible the very next -return in 1694, in the evening; and in two periods more, which was in -1730, on the 4th of _July_, was seen above half eclipsed just after -Sun-rise, and observed both at _Wirtemberg_ in _Germany_, and _Pekin_ in -_China_, soon after which it went off. - -“Eighteen years more afforded us the Eclipse which fell on the 14th of -_July 1748_. - -“The next visible return will happen on _July 25, 1766_, in the evening, -about four Digits eclipsed; and after two periods more, on _August_ -16th, 1802, early in the morning, about five Digits, the center coming -from the north frozen continent, by the capes of _Norway_, through -_Tartary_, _China_, and _Japan_, to the _Ladrone_ islands, where it goes -off. - -“Again, in 1820, _August 26_, betwixt one and two, there will be another -great Eclipse at _London_, about 10 Digits; but happening so near the -Equinox, the center will leave every part of _Britain_ to the West, and -enter _Germany_ at _Embden_, passing by _Venice_, _Naples_, _Grand -Cairo_, and set in the gulf of _Bassora_ near that city. - -“It will be no more visible till 1874, when five Digits will be -obscured, the center being now about to leave the Earth on _September -28_. In 1892 the Sun will go down eclipsed at _London_, and again in -1928 the passage of the center will be in the _expansum_, though there -will be two Digits eclipsed at _London_, _October_ the 31st of that -year; and about the year 2090 the whole Penumbra will be wore off; -whence no more returns of this Eclipse can happen till after a -revolution of 10 thousand years. - -“From these remarks on the intire revolution of this Eclipse, we may -gather, that a thousand years, more or less (for there are some -irregularities that may protract or lengthen this period 100 years) -complete the whole terrestrial Phenomena of any single Eclipse: and -since 20 periods of 54 years each, and about 33 days, comprehend the -intire extent of their revolution, ’tis evident that the times of the -returns will pass through a circuit of one year and ten months, every -_Chaldean_ period being ten or eleven days later, and of the equable -appearances about 32 or 33 days. Thus, though this Eclipse happens about -the middle of _July_, no other subsequent Eclipse of this period will -return to the middle of the same month again; but wear constantly each -period 10 or 11 days forward, and at last appear in Winter, but then it -begins to cease from affecting us. - -“Another conclusion from this revolution may be drawn, that there will -seldom be any more than two great Eclipses of the Sun in the interval of -this period, and these follow sometimes next return, and often at -greater distances. That of 1715 returned again in 1733 very great; but -this present Eclipse will not be great till the arrival of 1820, which -is a revolution of four _Chaldean_ periods: so that the irregularities -of their circuits must undergo new computations to assign them exactly. - -“Nor do all Eclipses come in at the south Pole: _that_ depends -altogether on the position of the lunar Nodes, which will bring in as -many from the _expansum_ one way as the other; and such Eclipses will -wear more southerly by degrees, contrary to what happens in the present -case. - -“The Eclipse, for example, of 1736, in _September_, had its center in -the _expansum_, and set about the middle of its obscurity in _Britain_; -it will wear in at the north Pole, and in the year 2600, or thereabouts, -go off into the _expansum_ on the south side of the Earth. - -“The Eclipses therefore which happened about the Creation are little -more than half way yet of their etherial circuit; and will be 4000 years -before they enter the Earth any more. This grand revolution seems to -have been entirely unknown to the antients. - -[Sidenote: Why our present Tables agree not with antient observations.] - -“322. It is particularly to be noted, that Eclipses which have happened -many centuries ago, will not be found by our present Tables to agree -exactly with antient observations, by reason of the great Anomalies in -the lunar motions; which appears an incontestable demonstration of the -non-eternity of the Universe. For it seems confirmed by undeniable -proofs, that the Moon now finishes her period in less time than -formerly, and will continue by the centripetal law to approach nearer -and nearer the Earth, and to go sooner and sooner round it: nor will the -centrifugal power be sufficient to compensate the different gravitations -of such an assemblage of bodies as constitute the solar system, which -would come to ruin of itself, without some new regulation and adjustment -of their original motions[68]. - -[Sidenote: THALES’s Eclipse.] - -“323. We are credibly informed from the testimony of the antients, that -there was a total Eclipse of the Sun predicted by THALES to happen in -the fourth year of the 48th [69]_Olympiad_, either at _Sardis_ or -_Miletus_ in _Asia_, where THALES then resided. That year corresponds to -the 585th year before CHRIST; when accordingly there happened a very -signal Eclipse of the Sun, on the 28th of _May_, answering to the -present 10th of that month[70], central through _North America_, the -south parts of _France_, _Italy_, &c. as far as _Athens_, or the Isles -in the _Ægean_ Sea; which is the farthest that even the _Caroline_ -Tables carry it; and consequently make it invisible to any part of -_Asia_, in the total character; though I have good reasons to believe -that it extended to _Babylon_, and went down central over that city. We -are not however to imagine, that it was set before it past _Sardis_ and -the _Asiatic_ towns, where the predictor lived; because an invisible -Eclipse could have been of no service to demonstrate his ability in -Astronomical Sciences to his countrymen, as it could give no proof of -its reality. - -[Sidenote: THUCYDIDES’s Eclipse.] - -“324. For a farther illustration, THUCYDIDES relates, that a solar -Eclipse happened on a Summer’s day in the afternoon, in the first year -of the _Peloponnesian_ war, so great that the Stars appeared. _Rhodius_ -was victor in the _Olympic_ games the fourth year of the said war, being -also the fourth of the 87th _Olympiad_, on the 428th year before CHRIST. -So that the Eclipse must have happened in the 431st year before CHRIST; -and by computation it appears, that on the 3d of _August_ there was a -signal Eclipse which would have past over _Athens_, central about 6 in -the evening, but which our present Tables bring no farther than the -antient _Syrtes_ on the _African_ coast, above 400 miles from _Athens_; -which suffering in that case but 9 Digits, could by no means exhibit the -remarkable darkness recited by this historian; the center therefore -seems to have past _Athens_ about 6 in the evening, and probably might -go down about _Jerusalem_, or near it, contrary to the construction of -the present Tables. I have only obviated these things by way of caution -to the present Astronomers, in re-computing antient Eclipses; and refer -them to examine the Eclipse of _Nicias_, so fatal to the _Athenian_ -fleet[71]; that which overthrew the _Macedonian_ Army[72] _&c._” So far -Mr. SMITH. - -[Sidenote: The number of Eclipses.] - -325. In any year, the number of Eclipses of both Luminaries cannot be -less than two, nor more than seven; the most usual number is four, and -it is very rare to have more than six. For the Sun passes by both the -Nodes but once a year, unless he passes by one of them in the beginning -of the year; and if he does, he will pass by the same Node again a -little before the year be finished; because, as these points move 19 -degrees backward every year, the Sun will come to either of them 173 -days after the other § 319. And when either Node is within 17 degrees of -the Sun at the time of New Moon, the Sun will be eclipsed. At the -subsequent opposition the Moon will be eclipsed in the other Node; and -come round to the next conjunction again ere the former Node be 17 -degrees past the Sun, and will therefore eclipse him again. When three -Eclipses fall about either Node, the like number generally falls about -the opposite; as the Sun comes to it in 173 days afterward: and six -Lunations contain but four days more. Thus, there may be two Eclipses of -the Sun and one of the Moon about each of her Nodes. But when the Moon -changes in either of the Nodes, she cannot be near enough the other Node -at the next Full to be eclipsed; and in six lunar months afterward she -will change near the other Node: in these cases there can be but two -Eclipses in a year, and they are both of the Sun. - -[Sidenote: Two periods of Eclipses.] - -326. A longer, and consequently more exact period than the -above-mentioned § 320, for comparing and examining Eclipses which happen -at long intervals of time, is 57 _Julian_ years 324 days 21 hours 41 -minutes and 35 seconds; in which time there are just 716 mean Lunations, -and the Sun is again within 5 minutes of the same Node as before. But a -still better period is 557 years 21 days 18 hours 30 minutes 12 seconds; -in which time there are 6890 mean Lunations; and the Sun and Node meet -again so nearly as to be but 11 seconds distant. - -[Sidenote: An account of the following catalogue of Eclipses.] - -327. We shall subjoin a catalogue of Eclipses recorded in history, from -721 years before CHRIST to _A. D._ 1485; of computed Eclipses from 1485 -to 1700; and of all the Eclipses visible in _Europe_ from 1700 to 1800. -From the beginning of the catalogue to _A.D._ 1485 the Eclipses are -taken from STRUYK’s _Introduction to universal Geography_, as that -indefatigable author has, with much labour, collected them from -_Ptolemy_, _Thucydides_, _Plutarch_, _Calvisius_, _Xenophon_, _Diodorus -Siculus_, _Justin_, _Polybius_, _Titus Livius_, _Cicero_, _Lucanus_, -_Theophanes_, _Dion Cassius_, and many others. From 1485 to 1700 the -Eclipses are taken from _Ricciolus_’s _Almagest_: and from 1700 to 1800 -from _L’art de verifier les Dates_[73]. Those from _Struyk_ have all the -places mentioned where they were observed: Those from the _French_ -authors, _viz._ the religious _Benedictines_ of the Congregation of St. -_Maur_, are fitted to the Meridian of _Paris_: And concerning those from -_Ricciolus_, that author gives the following account. - -Because it is of great use for fixing the Cycles or Revolutions of -Eclipses, to have at hand, without the trouble of calculation, a list of -successive Eclipses for many years, computed by authors of -_Ephemerides_, although from Tables not perfect in all respects, I shall -for the benefit of Astronomers give a summary collection of such. The -authors I extract from are, an anonymous one who published _Ephemerides_ -from 1484 to 1506 inclusive; _Jacobus Pflaumen_ and _Jo. Stæflerinus_, -to the Meridian of _Ulm_, from 1507 to 1534: _Lucas Gauricus_, to the -Latitude of 45 degrees, from 1534 to 1551: _Peter Appian_, to the -Meridian of _Leysing_, from 1538 to 1578: _Jo. Stæflerus_ to the -Meridian of _Tubing_, from 1543 to 1554: _Petrus Pitatus_, to the -Meridian of _Venice_ from 1544 to 1556: _Georgius-Joachimus Rheticus_, -for the year 1551: _Nicholaus Simus_, to the Meridian of _Bologna_, from -1552 to 1568: _Michael Mæstlin_, to the Meridian of _Tubing_, from 1557 -to 1590: _Jo. Stadius_, to the Meridian of _Antwerp_, from 1554 to 1574: -_Jo. Antoninus Maginus_, to the Meridian of _Venice_, from 1581 to 1630: -_David Origan_, to the Meridian of _Franckfort_ on the _Oder_, from 1595 -to 1664: _Andrew Argol_, to the Meridian of _Rome_, from 1630 to 1700: -_Franciscus Montebrunus_, to the Meridian of _Bologna_, from 1461 to -1660: Among which, _Stadius_, _Mæstlin_, and _Maginus_, used the -_Prutenic_ Tables; _Origan_ the _Prutenic_ and _Tychonic_; _Montebrunus_ -the _Lansbergian_, as likewise those of _Duret_. Almost all the rest the -_Alphonsine_. - -But, that the places may readily be known for which these Eclipses were -computed, and from what Tables, consult the following list, in which the -years _inclusive_ are also set down. - - From 1485 to 1506 The place and author unknown. - 1507 1553 _Ulm_ in _Suabia_, from the _Alphonsine_. - 1554 1576 _Antwerp_, from the _Prutenic_. - 1577 1585 _Tubing_, from the _Prutenic_. - 1586 1594 _Venice_, from the _Prutenic_. - 1595 1600 _Franckfort_ on _Oder_, from the _Prutenic_. - 1601 1640 _Franckfort_ on _Oder_, from the _Tychonic_. - 1641 1660 _Bologna_, from the _Lansbergian_. - 1661 1700 _Rome_, from the _Tychonic_. - -So far RICCIOLUS. - -_N. B._ The Eclipses marked with an Asterisk are not in RICCIOLUS’s -catalogue; but are supplied from _L’art de verifier les Dates_. - -From the beginning of the catalogue to _A. D._ 1700, the time is -reckoned from the noon of the day mentioned to the noon of the following -day; but from 1700 to 1800 the time is set down according to our common -way of reckoning. Those marked _Pekin_ and _Canton_ are Eclipses from -the _Chinese_ chronology according to STRUYK; and throughout the Table -this mark ☉ signifies _Sun_, and this 🌑︎ _Moon_. - - STRUYK’s Catalogue of ECLIPSES. - - +------+--------------------+-----+----------+---------+----------+ - | Bef. | Eclipses of the Sun| | M. & D. | Middle | Digits | - | Chr. | and Moon seen at | | | H. M. | eclipsed | - +------+--------------------+-----+----------+---------+----------+ - | 721 | Babylon | 🌑︎ | Mar. 19 | 10 34 | Total | - | 720 | Babylon | 🌑︎ | Mar. 8 | 11 56 | 1 5 | - | 720 | Babylon | 🌑︎ | Sept. 1 | 10 18 | 5 4 | - | 621 | Babylon | 🌑︎ | Apr. 21 | 18 22 | 2 36 | - | 523 | Babylon | 🌑︎ | July 16 | 12 47 | 7 24 | - | 502 | Babylon | 🌑︎ | Nov. 19 | 12 21 | 1 52 | - | 491 | Babylon | 🌑︎ | Apr. 25 | 12 12 | 1 44 | - | 431 | Athens | ☉ | Aug. 3 | 6 35 | 11 0 | - | 425 | Athens | 🌑︎ | Oct. 9 | 6 45 | Total | - | 424 | Athens | ☉ | Mar. 20 | 20 17 | 9 0 | - | 413 | Athens | 🌑︎ | Aug. 27 | 10 15 | Total | - | 406 | Athens | 🌑︎ | Apr. 15 | 8 50 | Total | - | 404 | Athens | ☉ | Sept. 2 | 21 12 | 8 40 | - | 403 | Pekin | ☉ | Aug. 28 | 5 53 | 10 40 | - | 394 | Gnide | ☉ | Aug. 13 | 22 17 | 11 0 | - | 383 | Athens | 🌑︎ | Dec. 22 | 19 6 | 2 1 | - | 382 | Athens | 🌑︎ | June 18 | 8 54 | 6 15 | - | 382 | Athens | 🌑︎ | Dec. 12 | 10 21 | Total | - | 364 | Thebes | ☉ | July 12 | 23 51 | 6 10 | - | 357 | Syracuse | ☉ | Feb. 28 | 22 -- | 3 33 | - | 357 | Zant | 🌑︎ | Aug. 29 | 7 29 | 4 21 | - | 340 | Zant | ☉ | Sept. 14 | 18 -- | 9 0 | - | 331 | Arbela | 🌑︎ | Sept. 20 | 10 9 | Total | - | 310 | Sicily Island | ☉ | Aug. 14 | 20 5 | 10 22 | - | 219 | Mysia | 🌑︎ | Mar. 19 | 14 5 | Total | - | 218 | Pergamos | 🌑︎ | Sept. 1 | rising | Total | - | 217 | Sardinia | ☉ | Feb. 11 | 1 57 | 9 6 | - | 203 | Frusini | ☉ | May 6 | 2 52 | 5 40 | - | 202 | Cumis | ☉ | Oct. 18 | 22 24 | 1 0 | - | 201 | Athens | 🌑︎ | Sept. 22 | 7 14 | 8 58 | - | 200 | Athens | 🌑︎ | Mar. 19 | 13 9 | Total | - | 200 | Athens | 🌑︎ | Sept. 11 | 14 48 | Total | - | 198 | Rome | ☉ | Aug. 6 | ---- | ---- | - | 190 | Rome | ☉ | Mar. 13 | 18 -- | 11 0 | - | 188 | Rome | ☉ | July 16 | 20 38 | 10 48 | - | 174 | Athens | 🌑︎ | Apr. 30 | 14 33 | 7 1 | - | 168 | Macedonia | 🌑︎ | June 21 | 8 2 | Total | - | 141 | Rhodes | 🌑︎ | Jan. 27 | 10 8 | 3 26 | - | 104 | Rome | ☉ | July 18 | 22 0 | 11 52 | - | 63 | Rome | 🌑︎ | Oct. 27 | 6 22 | Total | - | 60 | Gibralter | ☉ | Mar. 16 | setting | Central | - | 54 | Canton | ☉ | May 9 | 3 41 | Total | - | 51 | Rome | ☉ | Mar. 7 | 2 12 | 9 0 | - | 48 | Rome | 🌑︎ | Jan. 18 | 10 0 | Total | - | 45 | Rome | 🌑︎ | Nov. 6 | 14 -- | Total | - | 36 | Rome | ☉ | May 19 | 3 52 | 6 47 | - | 31 | Rome | ☉ | Aug. 20 | setting | Gr. Ecl. | - | 29 | Canton | ☉ | Jan. 5 | 4 2 | 11 0 | - | 28 | Pekin | ☉ | June 18 | 23 48 | Total | - | 26 | Canton | ☉ | Oct. 23 | 4 16 | 11 15 | - | 24 | Pekin | ☉ | April 7 | 4 11 | 2 0 | - | 16 | Pekin | ☉ | Nov. 1 | 5 13 | 2 8 | - | 2 | Canton | ☉ | Feb. 1 | 20 8 | 11 42 | - +------+--------------------+-----+----------+---------+----------+ - +------+--------------------+-----+----------+---------+----------+ - | Aft. | Eclipses of the Sun| | M. & D. | Middle | Digits | - | Chr. | and Moon seen at | | | H. M. | eclipsed | - +------+--------------------+-----+----------+---------+----------+ - | 1 | Pekin | ☉ | June 10 | 1 10 | 11 43 | - | 5 | Rome | ☉ | Mar. 28 | 4 13 | 4 45 | - | 14 | Panonia | 🌑︎ | Sept. 26 | 17 15 | Total | - | 27 | Canton | ☉ | July 22 | 8 56 | Total | - | 30 | Canton | ☉ | Nov. 13 | 19 20 | 10 30 | - | 40 | Pekin | ☉ | Apr. 30 | 5 50 | 7 34 | - | 45 | Rome | ☉ | July 31 | 22 1 | 5 17 | - | 46 | Pekin | ☉ | July 21 | 22 25 | 2 10 | - | 46 | Rome | 🌑︎ | Dec. 31 | 9 52 | Total | - | 49 | Pekin | ☉ | May 20 | 7 16 | 10 8 | - | 53 | Canton | ☉ | Mar. 8 | 20 42 | 11 6 | - | 55 | Pekin | ☉ | July 12 | 21 50 | 6 40 | - | 56 | Canton | ☉ | Dec. 25 | 0 28 | 9 20 | - | 59 | Rome | ☉ | Apr. 30 | 3 8 | 10 38 | - | 60 | Canton | ☉ | Oct. 13 | 3 31 | 10 30 | - | 65 | Canton | ☉ | Dec. 15 | 21 50 | 10 23 | - | 69 | Rome | 🌑︎ | Oct. 18 | 10 43 | 10 49 | - | 70 | Canton | ☉ | Sept. 22 | 21 13 | 8 26 | - | 71 | Rome | 🌑︎ | Mar. 4 | 8 32 | 6 0 | - | 95 | Ephesus | ☉ | May 21 | ---- | 1 0 | - | 125 | Alexandria | 🌑︎ | April 5 | 9 16 | 1 44 | - | 133 | Alexandria | 🌑︎ | May 6 | 11 44 | Total | - | 134 | Alexandria | 🌑︎ | Oct. 20 | 11 5 | 10 19 | - | 136 | Alexandria | 🌑︎ | Mar. 5 | 15 56 | 5 17 | - | 237 | Bologna | ☉ | Apr. 12 | ---- | Total | - | 238 | Rome | ☉ | April 1 | 20 20 | 8 45 | - | 290 | Carthage | ☉ | May 15 | 3 20 | 11 20 | - | 304 | Rome | 🌑︎ | Aug. 31 | 9 36 | Total | - | 316 | Constantinople | ☉ | Dec. 30 | 19 53 | 2 18 | - | 334 | Toledo | ☉ | July 17 | at noon | Central | - | 348 | Constantinople | ☉ | Oct. 8 | 19 24 | 8 0 | - | 360 | Ispahan | ☉ | Aug. 27 | 18 0 | Central | - | 364 | Alexandria | 🌑︎ | Nov. 25 | 15 24 | Total | - | 401 | Rome | 🌑︎ | June 11 | ---- | Total | - | 401 | Rome | 🌑︎ | Dec. 6 | 12 15 | Total | - | 402 | Rome | 🌑︎ | June 1 | 8 43 | 10 2 | - | 402 | Rome | ☉ | Nov. 10 | 20 33 | 10 30 | - | 447 | Compostello | ☉ | Dec. 23 | 0 46 | 1 -- | - | 451 | Compostello | 🌑︎ | April 1 | 16 34 | 19 52 | - | 451 | Compostello | 🌑︎ | Sept. 26 | 6 30 | 0 2 | - | 458 | Chaves | ☉ | May 27 | 23 16 | 18 53 | - | 462 | Compostello | 🌑︎ | Mar. 1 | 13 2 | 11 11 | - | 464 | Chaves | ☉ | July 19 | 19 1 | 10 15 | - | 484 | Constantinople | ☉ | Jan. 13 | 19 53 | 0 0 | - | 486 | Constantinople | ☉ | May 19 | 1 10 | 5 15 | - | 497 | Constantinople | ☉ | Apr. 18 | 6 5 | 17 57 | - | 512 | Constantinople | ☉ | June 28 | 23 8 | 1 50 | - | 538 | England | ☉ | Feb. 14 | 19 -- | 8 23 | - | 540 | London | ☉ | June 19 | 20 15 | 8 -- | - | 577 | Tours | 🌑︎ | Dec. 10 | 17 28 | 6 46 | - | 581 | Paris | 🌑︎ | April 4 | 13 33 | 6 42 | - | 582 | Paris | 🌑︎ | Sept. 17 | 12 41 | Total | - | 590 | Paris | 🌑︎ | Oct. 18 | 6 30 | 9 25 | - | 592 | Constantinople | ☉ | Mar. 18 | 22 6 | 10 0 | - | 603 | Paris | ☉ | Aug. 12 | 3 3 | 11 20 | - | 622 | Constantinople | 🌑︎ | Febr. 1 | 11 28 | Total | - | 644 | Paris | ☉ | Nov. 5 | 0 30 | 9 53 | - | 680 | Paris | 🌑︎ | June 17 | 12 30 | Total | - | 683 | Paris | 🌑︎ | April 16 | 11 30 | Total | - | 693 | Constantinople | ☉ | Oct. 4 | 23 54 | 11 54 | - | 716 | Constantinople | 🌑︎ | Jan. 13 | 7 -- | Total | - | 718 | Constantinople | ☉ | June 3 | 1 15 | Total | - | 733 | England | ☉ | Aug. 13 | 20 -- | 11 1 | - | 734 | England | 🌑︎ | Jan. 23 | 14 -- | Total | - | 752 | England | 🌑︎ | July 30 | 13 -- | Total | - | 753 | England | ☉ | June 8 | 22 -- | 10 35 | - | 753 | England | 🌑︎ | Jan. 23 | 13 -- | Total | - | 760 | England | ☉ | Aug. 15 | 4 -- | 8 15 | - | 760 | London | 🌑︎ | Aug. 30 | 5 50 | 10 40 | - | 764 | England | ☉ | June 4 | at noon | 7 15 | - | 770 | London | 🌑︎ | Feb. 14 | 7 12 | Total | - | 774 | Rome | 🌑︎ | Nov. 22 | 14 37 | 11 58 | - | 784 | London | 🌑︎ | Nov. 1 | 14 2 | Total | - | 787 | Constantinople | ☉ | Sept. 14 | 20 43 | 9 47 | - | 796 | Constantinople | 🌑︎ | Mar. 27 | 16 22 | Total | - | 800 | Rome | 🌑︎ | Jan. 15 | 9 0 | 10 17 | - | 807 | Angoulesme | ☉ | Feb. 10 | 21 24 | 9 42 | - | 807 | Paris | 🌑︎ | Feb. 25 | 13 43 | Total | - | 807 | Paris | 🌑︎ | Aug. 21 | 10 20 | Total | - | 809 | Paris | ☉ | July 15 | 21 33 | 8 8 | - | 809 | Paris | 🌑︎ | Dec. 25 | 8 -- | Total | - | 810 | Paris | 🌑︎ | June 20 | 8 -- | Total | - | 810 | Paris | ☉ | Nov. 30 | 0 12 | Total | - | 810 | Paris | 🌑︎ | Dec. 14 | 8 -- | Total | - | 812 | Constantinople | ☉ | May 14 | 2 13 | 9 -- | - | 813 | Cappadocia | ☉ | May 3 | 17 5 | 10 35 | - | 817 | Paris | 🌑︎ | Feb. 5 | 5 42 | Total | - | 818 | Paris | ☉ | July 6 | 18 -- | 6 55 | - | 820 | Paris | 🌑︎ | Nov. 23 | 6 26 | Total | - | 824 | Paris | 🌑︎ | Mar. 18 | 7 55 | Total | - | 828 | Paris | 🌑︎ | June 30 | 15 -- | Total | - | 828 | Paris | 🌑︎ | Dec. 24 | 13 45 | Total | - | 831 | Paris | 🌑︎ | April 30 | 6 19 | 11 8 | - | 831 | Paris | ☉ | May 15 | 23 -- | 4 24 | - | 831 | Paris | 🌑︎ | Oct. 24 | 11 18 | Total | - | 832 | Fulda | 🌑︎ | Apr. 18 | 9 0 | Total | - | 840 | Paris | ☉ | May 4 | 23 22 | 9 20 | - | 841 | Paris | ☉ | Oct. 17 | 18 58 | 5 24 | - | 842 | Paris | 🌑︎ | Mar. 29 | 14 38 | Total | - | 843 | Paris | 🌑︎ | Mar. 19 | 7 1 | Total | - | 861 | Paris | 🌑︎ | Mar. 29 | 15 7 | Total | - | 878 | Paris | 🌑︎ | Oct. 14 | 16 -- | Total | - | 878 | Paris | ☉ | Oct. 29 | 1 -- | 11 14 | - | 883 | Arracta | 🌑︎ | July 23 | 7 44 | 11 -- | - | 889 | Constantinople | ☉ | April 3 | 17 52 | 9 23 | - | 891 | Constantinople | ☉ | Aug. 7 | 23 48 | 10 30 | - | 901 | Arracta | 🌑︎ | Aug. 2 | 15 7 | Total | - | 904 | London | 🌑︎ | May 31 | 11 47 | Total | - | 904 | London | 🌑︎ | Nov. 25 | 9 0 | Total | - | 912 | London | 🌑︎ | Jan. 6 | 15 12 | Total | - | 926 | Paris | 🌑︎ | Mar. 31 | 15 17 | Total | - | 934 | Paris | ☉ | Apr. 16 | 4 30 | 11 36 | - | 939 | Paris | ☉ | July 18 | 19 45 | 10 7 | - | 955 | Paris | 🌑︎ | Sept. 4 | 11 18 | Total | - | 961 | Rhemes | ☉ | May 16 | 20 13 | 9 18 | - | 970 | Constantinople | ☉ | May 7 | 18 38 | 11 22 | - | 976 | London | 🌑︎ | July 13 | 15 7 | Total | - | 985 | Messina | ☉ | July 20 | 3 52 | 4 10 | - | 989 | Constantinople | ☉ | May 28 | 6 54 | 8 40 | - | 990 | Fulda | 🌑︎ | Apr. 12 | 10 22 | 9 5 | - | 990 | Fulda | 🌑︎ | Oct. 6 | 15 4 | 11 10 | - | 990 | Constantinople | ☉ | Oct. 21 | 0 45 | 10 5 | - | 995 | Augsburgh | 🌑︎ | July 14 | 11 27 | Total | - | 1009 | Ferrara | 🌑︎ | Oct. 6 | 11 38 | Total | - | 1010 | Messina | ☉ | Mar. 18 | 5 41 | 9 12 | - | 1016 | Nimeguen | 🌑︎ | Nov. 16 | 16 39 | Total | - | 1017 | Nimeguen | ☉ | Oct. 22 | 2 8 | 6 -- | - | 1020 | Cologne | 🌑︎ | Sept. 4 | 11 38 | Total | - | 1023 | London | ☉ | Jan. 23 | 23 29 | 11 -- | - | 1030 | Rome | 🌑︎ | Feb. 20 | 11 43 | Total | - | 1031 | Paris | 🌑︎ | Feb. 9 | 11 51 | Total | - | 1033 | Paris | 🌑︎ | Dec. 8 | 11 11 | 9 17 | - | 1034 | Milan | 🌑︎ | June 4 | 9 8 | Total | - | 1037 | Paris | ☉ | Apr. 17 | 20 45 | 10 45 | - | 1039 | Auxerre | ☉ | Aug. 21 | 23 40 | 11 5 | - | 1042 | Rome | 🌑︎ | Jan. 8 | 16 39 | Total | - | 1044 | Auxerre | 🌑︎ | Nov. 7 | 16 12 | 10 1 | - | 1044 | Cluny | ☉ | Nov. 21 | 22 12 | 11 -- | - | 1056 | Nuremburg | 🌑︎ | April 2 | 12 9 | Total | - | 1063 | Rome | 🌑︎ | Nov. 8 | 12 16 | Total | - | 1074 | Augsburgh | 🌑︎ | Oct. 7 | 10 13 | Total | - | 1080 | Constantinople | 🌑︎ | Nov. 29 | 11 12 | 9 36 | - | 1082 | London | 🌑︎ | May 14 | 10 32 | 10 2 | - | 1086 | Constantinople | ☉ | Feb. 16 | 4 7 | Total | - | 1089 | Naples | 🌑︎ | June 25 | 6 6 | Total | - | 1093 | Augsburgh | ☉ | Sept. 22 | 22 35 | 10 12 | - | 1096 | Gemblours | 🌑︎ | Feb. 10 | 16 4 | Total | - | 1096 | Augsburgh | 🌑︎ | Aug. 6 | 8 21 | Total | - | 1098 | Augsburgh | ☉ | Dec. 25 | 1 25 | 10 12 | - | 1099 | Naples | 🌑︎ | Nov. 30 | 4 58 | Total | - | 1103 | Rome | 🌑︎ | Sept. 17 | 10 18 | Total | - | 1106 | Erfurd | 🌑︎ | July 17 | 11 28 | 11 54 | - | 1107 | Naples | 🌑︎ | Jan. 10 | 13 16 | Total | - | 1109 | Erfurd | ☉ | May 31 | 1 30 | 10 20 | - | 1110 | London | 🌑︎ | May 5 | 10 51 | Total | - | 1113 | Jerusalem | ☉ | Mar. 18 | 19 0 | 9 12 | - | 1114 | London | 🌑︎ | Aug. 17 | 15 5 | Total | - | 1117 | Trier | 🌑︎ | June 15 | 13 26 | Total | - | 1117 | Trier | 🌑︎ | Dec. 10 | 12 51 | Total | - | 1118 | Naples | 🌑︎ | Nov. 29 | 15 46 | 4 11 | - | 1121 | Trier | 🌑︎ | Sept. 27 | 16 47 | Total | - | 1122 | Prague | 🌑︎ | Mar. 24 | 11 20 | 3 49 | - | 1124 | Erfurd | 🌑︎ | Feb. 1 | 6 43 | 8 39 | - | 1124 | London | ☉ | Aug. 10 | 23 29 | 9 58 | - | 1132 | Erfurd | 🌑︎ | March 3 | 8 14 | Total | - | 1133 | Prague | 🌑︎ | Feb. 20 | 16 41 | 3 23 | - | 1135 | London | 🌑︎ | Dec. 22 | 20 11 | Total | - | 1142 | Rome | 🌑︎ | Feb. 11 | 14 17 | 8 30 | - | 1143 | Rome | 🌑︎ | Feb. 1 | 6 36 | Total | - | 1147 | Auranches | ☉ | Oct. 25 | 22 38 | 7 20 | - | 1149 | Bary | 🌑︎ | Mar. 25 | 13 54 | 5 29 | - | 1151 | Eimbeck | 🌑︎ | Aug. 28 | 12 4 | 4 29 | - | 1153 | Augsburgh | ☉ | Jan. 26 | 0 42 | 11 -- | - | 1154 | Paris | 🌑︎ | June 26 | 16 1 | Total | - | 1154 | Paris | 🌑︎ | Dec. 21 | 8 30 | 4 42 | - | 1155 | Auranches | 🌑︎ | June 10 | 8 45 | 0 53 | - | 1160 | Rome | 🌑︎ | Aug. 18 | 7 53 | 6 49 | - | 1161 | Rome | 🌑︎ | Aug. 7 | 8 15 | Total | - | 1162 | Erfurd | 🌑︎ | Feb. 1 | 6 40 | 5 56 | - | 1162 | Erfurd | 🌑︎ | July 27 | 12 30 | 4 11 | - | 1163 | Mont Cassin. | ☉ | July 3 | 7 40 | 2 0 | - | 1164 | Milan | 🌑︎ | June 6 | 10 0 | Total | - | 1168 | London | 🌑︎ | Sept. 18 | 14 0 | Total | - | 1172 | Cologne | 🌑︎ | Jan. 11 | 13 31 | Total | - | 1176 | Auranches | 🌑︎ | April 25 | 7 2 | 8 6 | - | 1176 | Auranches | 🌑︎ | Oct. 19 | 11 20 | 8 53 | - | 1178 | Cologne | 🌑︎ | March 5 | setting | 7 52 | - | 1178 | Auranches | 🌑︎ | Aug. 29 | 13 52 | 5 31 | - | 1178 | Cologne | ☉ | Sept. 12 | -- -- | 10 51 | - | 1179 | Cologne | 🌑︎ | Aug. 18 | 14 28 | Total | - | 1180 | Auranches | ☉ | Jan. 28 | 4 14 | 10 34 | - | 1181 | Auranches | ☉ | July 13 | 3 15 | 3 48 | - | 1181 | Auranches | 🌑︎ | Dec. 22 | 8 58 | 4 40 | - | 1185 | Rhemes | ☉ | May 1 | 1 53 | 9 0 | - | 1186 | Cologne | 🌑︎ | April 5 | 6 -- | Total | - | 1186 | Franckfort | ☉ | April 20 | 7 19 | 4 0 | - | 1187 | Paris | 🌑︎ | Mar. 25 | 16 17 | 8 42 | - | 1187 | England | ☉ | Sept. 3 | 21 54 | 8 6 | - | 1189 | England | 🌑︎ | Feb. 2 | 10 -- | 9 -- | - | 1191 | England | ☉ | June 23 | 0 20 | 11 32 | - | 1192 | France | 🌑︎ | Nov. 20 | 14 -- | 6 -- | - | 1193 | France | 🌑︎ | Nov. 10 | 5 27 | Total | - | 1194 | London | ☉ | April 22 | 2 15 | 6 49 | - | 1200 | London | 🌑︎ | Jan. 2 | 17 2 | 4 35 | - | 1201 | London | 🌑︎ | June 17 | 15 4 | Total | - | 1204 | England | 🌑︎ | April 15 | 12 39 | Total | - | 1204 | Saltzburg | 🌑︎ | Oct. 10 | 6 32 | Total | - | 1207 | Rhemes | ☉ | Feb. 27 | 10 50 | 10 20 | - | 1208 | Rhemes | 🌑︎ | Feb. 2 | 5 10 | Total | - | 1211 | Vienna | 🌑︎ | Nov. 21 | 13 57 | Total | - | 1215 | Cologne | 🌑︎ | Mar. 16 | 15 35 | Total | - | 1216 | Acre | ☉ | Feb. 18 | 21 15 | 11 36 | - | 1216 | Acre | 🌑︎ | March 5 | 9 38 | 7 4 | - | 1218 | Damietta | 🌑︎ | July 9 | 9 46 | 11 31 | - | 1222 | Rome | 🌑︎ | Oct. 22 | 14 28 | Total | - | 1223 | Colmar | 🌑︎ | April 16 | 8 13 | 11 0 | - | 1228 | Naples | ☉ | Dec. 27 | 9 55 | 9 19 | - | 1230 | Naples | ☉ | May 13 | 17 -- | Total | - | 1230 | London | 🌑︎ | Nov. 21 | 13 21 | 9 34 | - | 1232 | Rhemes | ☉ | Oct. 15 | 4 29 | 4 25 | - | 1245 | Rhemes | ☉ | July 24 | 17 47 | 6 -- | - | 1248 | London | 🌑︎ | June 7 | 8 49 | Total | - | 1255 | London | 🌑︎ | July 20 | 9 47 | Total | - | 1255 | Constantinople | ☉ | Dec. 30 | 2 52 | Annul. | - | 1258 | Augsburgh | 🌑︎ | May 18 | 11 17 | Total | - | 1261 | Vienna | ☉ | Mar. 31 | 22 40 | 9 8 | - | 1262 | Vienna | 🌑︎ | March 7 | 5 50 | Total | - | 1262 | Vienna | 🌑︎ | Aug. 30 | 14 39 | Total | - | 1263 | Vienna | 🌑︎ | Feb. 24 | 6 52 | 6 29 | - | 1263 | Augsburgh | ☉ | Aug. 5 | 3 24 | 11 17 | - | 1263 | Vienna | 🌑︎ | Aug. 20 | 7 35 | 9 7 | - | 1265 | Vienna | 🌑︎ | Dec. 23 | 16 25 | Total | - | 1267 | Constantinople | ☉ | May 24 | 23 11 | 11 40 | - | 1270 | Vienna | ☉ | Mar. 22 | 18 47 | 10 40 | - | 1272 | Vienna | 🌑︎ | Aug. 10 | 7 27 | 8 53 | - | 1274 | Vienna | 🌑︎ | Jan. 23 | 10 39 | 9 25 | - | 1275 | Lauben | 🌑︎ | Dec. 4 | 6 20 | 4 29 | - | 1276 | Vienna | 🌑︎ | Nov. 22 | 15 -- | Total | - | 1277 | Vienna | 🌑︎ | May 18 | -- -- | Total | - | 1279 | Franckfort | ☉ | Apr. 12 | 6 55 | 10 6 | - | 1280 | London | 🌑︎ | Mar. 17 | 12 12 | Total | - | 1284 | Reggio | 🌑︎ | Dec. 23 | 16 11 | 9 13 | - | 1290 | Wittemburg | ☉ | Sept. 4 | 19 37 | 10 30 | - | 1291 | London | 🌑︎ | Feb. 14 | 10 2 | Total | - | 1302 | Constantinople | 🌑︎ | Jan. 14 | 10 25 | Total | - | 1307 | Ferrara | ☉ | April 2 | 22 18 | 0 54 | - | 1309 | London | 🌑︎ | Feb. 24 | 17 44 | Total | - | 1309 | Lucca | 🌑︎ | Aug. 21 | 10 32 | Total | - | 1310 | Wittemburg | ☉ | Jan. 31 | 2 2 | 10 10 | - | 1310 | Torcello | 🌑︎ | Feb. 14 | 4 8 | 10 20 | - | 1310 | Torcello | 🌑︎ | Aug. 10 | 15 33 | 7 16 | - | 1312 | Wittemburg | ☉ | July 4 | 19 49 | 3 23 | - | 1312 | Plaisance | 🌑︎ | Dec. 14 | 7 19 | Total | - | 1313 | Torcello | 🌑︎ | Dec. 3 | 8 58 | 9 34 | - | 1316 | Modena | 🌑︎ | Oct. 1 | 14 55 | Total | - | 1321 | Wittemburg | ☉ | June 25 | 18 1 | 11 17 | - | 1323 | Florence | 🌑︎ | May 20 | 15 24 | Total | - | 1324 | Florence | 🌑︎ | May 9 | 6 3 | Total | - | 1324 | Wittemburg | ☉ | Apr. 23 | 6 35 | 8 8 | - | 1327 | Constantinople | 🌑︎ | Aug. 31 | 18 26 | Total | - | 1328 | Constantinople | 🌑︎ | Feb. 25 | 13 47 | 11 -- | - | 1330 | Florence | 🌑︎ | June 30 | 15 10 | 7 34 | - | 1330 | Constantinople | ☉ | July 16 | 4 5 | 10 43 | - | 1330 | Prague | 🌑︎ | Dec. 25 | 15 49 | Total | - | 1331 | Prague | ☉ | Nov. 29 | 20 26 | 7 41 | - | 1331 | Prague | 🌑︎ | Dec. 14 | 18 -- | 11 -- | - | 1333 | Wittemburg | ☉ | May 14 | 3 -- | 10 18 | - | 1334 | Cesena | 🌑︎ | Apr. 19 | 10 33 | Total | - | 1341 | Constantinople | 🌑︎ | Nov. 23 | 12 23 | Total | - | 1341 | Constantinople | ☉ | Dec. 8 | 22 15 | 6 30 | - | 1342 | Constantinople | 🌑︎ | May 20 | 14 27 | Total | - | 1344 | Alexandria | ☉ | Oct. 6 | 18 40 | 8 55 | - | 1349 | Wittemburg | 🌑︎ | June 30 | 12 20 | Total | - | 1354 | Wittemburg | ☉ | Sept. 16 | 20 45 | 8 43 | - | 1356 | Florence | 🌑︎ | Feb. 16 | 11 43 | Total | - | 1361 | Constantinople | ☉ | May 4 | 22 15 | 8 54 | - | 1367 | In China | 🌑︎ | Jan. 16 | 8 27 | Total | - | 1389 | Eugibin | 🌑︎ | Nov. 3 | 17 5 | Total | - | 1396 | Augsburg | ☉ | Jan. 11 | 0 16 | 6 22 | - | 1396 | Augsburg | 🌑︎ | June 21 | 11 10 | Total | - | 1399 | Forli | ☉ | Oct. 29 | 0 43 | 9 -- | - | 1406 | Constantinople | 🌑︎ | June 1 | 13 -- | 10 31 | - | 1406 | Constantinople | ☉ | June 15 | 18 1 | 11 38 | - | 1408 | Forli | ☉ | Oct. 18 | 21 47 | 9 32 | - | 1409 | Constantinople | ☉ | Apr. 15 | 3 1 | 10 48 | - | 1410 | Vienna | 🌑︎ | Mar. 20 | 13 13 | Total | - | 1415 | Wittemburg | ☉ | June 6 | 6 43 | Total | - | 1419 | Franckfort | ☉ | Mar. 25 | 22 5 | 1 45 | - | 1421 | Forli | 🌑︎ | Feb. 17 | 8 2 | Total | - | 1422 | Forli | 🌑︎ | Feb. 6 | 8 26 | 11 7 | - | 1424 | Wittemburg | ☉ | June 26 | 3 57 | 11 20 | - | 1431 | Forli | ☉ | Feb. 12 | 2 4 | 1 39 | - | 1433 | Wittemburg | ☉ | June 17 | 5 -- | Total | - | 1438 | Wittemburg | ☉ | Sept. 18 | 20 59 | 8 7 | - | 1442 | Rome | 🌑︎ | Dec. 17 | 3 56 | Total | - | 1448 | Tubing | ☉ | Aug. 28 | 22 23 | 8 53 | - | 1450 | Constantinople | 🌑︎ | July 24 | 7 19 | Total | - | 1457 | Vienna | 🌑︎ | Sept. 3 | 11 17 | Total | - | 1460 | Austria | 🌑︎ | July 3 | 7 31 | 5 23 | - | 1460 | Austria | ☉ | July 17 | 17 32 | 11 19 | - | 1460 | Vienna | 🌑︎ | Dec. 27 | 13 30 | Total | - | 1461 | Vienna | 🌑︎ | June 22 | 11 50 | Total | - | 1461 | Rome | 🌑︎ | Dec. 17 | -- -- | Total | - | 1462 | Viterbo | 🌑︎ | June 11 | 15 -- | 7 38 | - | 1462 | Viterbo | ☉ | Nov. 21 | 0 10 | 2 6 | - | 1464 | Padua | 🌑︎ | Apr. 21 | 12 43 | Total | - | 1465 | Rome | ☉ | Sept. 20 | 5 15 | 8 46 | - | 1465 | Rome | 🌑︎ | Oct. 4 | 5 12 | Total | - | 1469 | Rome | 🌑︎ | Jan. 27 | 7 9 | Total | - | 1485 | Norimburg | ☉ | Mar. 16 | 3 53 | 11 -- | - +------+--------------------+-----+----------+---------+----------+ - - The following ECLIPSES are all taken from RICCIOLUS, except those marked - with an Asterisk, which are from _L’Art de verifier les Dates_. - - +------+-----+----------+----------+----------+ - | Aft. | | M. & D. | Middle | Digits | - | Chr. | | | H. M. | eclipsed | - +------+-----+----------+----------+----------+ - | 1486 | 🌑︎ | Feb. 18 | 5 41 | Total | - | 1486 | ☉ | Mar. 5 | 17 43 | 9 0 | - | 1487 | 🌑︎ | Feb. 7 | 15 49 | Total | - | 1487 | ☉ | July 20 | 2 6 | 7 0 | - | 1488 | 🌑︎ | Jan. 28 | 6 -- | * | - | 1488 | ☉ | July 8 | 17 30 | 4 0 | - | 1489 | 🌑︎ | Dec. 7 | 17 41 | Total | - | 1490 | ☉ | May 19 | Noon | * | - | 1490 | 🌑︎ | June 2 | 10 6 | Total | - | 1490 | 🌑︎ | Nov. 26 | 18 25 | Total | - | 1491 | ☉ | May 8 | 2 19 | 9 0 | - | 1491 | 🌑︎ | Nov. 15 | 18 -- | * | - | 1492 | ☉ | Apr. 26 | 7 -- | * | - | 1492 | ☉ | Oct. 20 | 23 -- | * | - | 1493 | 🌑︎ | April 1 | 14 0 | Total | - | 1493 | ☉ | Oct. 10 | 2 40 | 8 0 | - | 1494 | ☉ | Mar. 7 | 4 12 | 4 0 | - | 1494 | 🌑︎ | Mar. 21 | 14 38 | Total | - | 1494 | 🌑︎ | Sept. 14 | 19 45 | Total | - | 1495 | 🌑︎ | Mar. 10 | 16 -- | * | - | 1495 | ☉ | Aug. 19 | 17 -- | * | - | 1496 | 🌑︎ | Jan. 29 | 14 -- | * | - | 1497 | 🌑︎ | Jan. 18 | 6 38 | Total | - | 1497 | ☉ | July 29 | 3 2 | 3 0 | - | 1499 | 🌑︎ | June 22 | 17 -- | * | - | 1499 | ☉ | Aug. 23 | 18 -- | * | - | 1499 | 🌑︎ | Nov. 17 | 10 -- | * | - | 1500 | ☉ | Mar. 27 | In the | Night | - | 1500 | 🌑︎ | Apr. 11 | At | Noon | - | 1500 | 🌑︎ | Oct. 5 | 14 2 | 10 0 | - | 1501 | 🌑︎ | May 2 | 17 49 | Total | - | 1502 | ☉ | Sept. 30 | 19 45 | 10 0 | - | 1502 | 🌑︎ | Oct. 15 | 12 20 | 2 0 | - | 1503 | 🌑︎ | Mar. 12 | 9 -- | * | - | 1503 | ☉ | Sept. 19 | 22 -- | * | - | 1504 | 🌑︎ | Feb. 29 | 13 36 | Total | - | 1504 | ☉ | Mar. 16 | 3 -- | * | - | 1505 | 🌑︎ | Aug. 14 | 8 18 | Total | - | 1506 | 🌑︎ | Feb. 7 | 15 -- | * | - | 1506 | ☉ | July 20 | 3 11 | 2 0 | - | 1506 | 🌑︎ | Aug. 3 | 10 -- | * | - | 1507 | ☉ | Jan. 12 | 19 -- | * | - | 1508 | ☉ | Jan. 2 | 4 -- | * | - | 1508 | ☉ | May 29 | 6 -- | * | - | 1508 | 🌑︎ | June 12 | 17 40 | Total | - | 1509 | 🌑︎ | June 2 | 11 11 | 7 0 | - | 1509 | ☉ | Nov. 11 | 22 -- | * | - | 1510 | 🌑︎ | Oct. 16 | 19 -- | * | - | 1511 | 🌑︎ | Oct. 6 | 11 50 | Total | - | 1512 | 🌑︎ | Sept. 25 | 3 56 | Total | - | 1513 | ☉ | Mar. 7 | 0 30 | 6 0 | - | 1513 | ☉ | Aug. 30 | 1 -- | * | - | 1515 | 🌑︎ | Jan. 29 | 15 18 | Total | - | 1516 | 🌑︎ | Jan. 19 | 6 0 | Total | - | 1516 | 🌑︎ | July 13 | 11 37 | Total | - | 1516 | ☉ | Dec. 23 | 3 47 | 3 0 | - | 1517 | ☉ | June 18 | 16 -- | * | - | 1517 | 🌑︎ | Nov. 27 | 19 -- | * | - | 1518 | 🌑︎ | May 24 | 11 19 | 9 11 | - | 1518 | ☉ | June 7 | 17 56 | 11 0 | - | 1519 | ☉ | May 28 | 1 -- | * | - | 1519 | ☉ | Oct. 23 | 4 33 | 6 0 | - | 1519 | 🌑︎ | Nov. 6 | 6 24 | Total | - | 1520 | 🌑︎ | May 2 | 7 -- | * | - | 1520 | ☉ | Oct. 11 | 5 22 | 3 | - | 1520 | 🌑︎ | Oct. 25 | 19 -- | * | - | 1520 | 🌑︎ | Mar. 21 | 17 -- | * | - | 1521 | ☉ | April 6 | 19 -- | * | - | 1521 | ☉ | Sept. 30 | 3 -- | * | - | 1522 | 🌑︎ | Sept. 5 | 12 17 | Total | - | 1523 | 🌑︎ | Mar. 1 | 8 26 | Total | - | 1523 | 🌑︎ | Aug. 25 | 15 24 | Total | - | 1524 | ☉ | Feb. 4 | 1 -- | * | - | 1524 | 🌑︎ | Aug. 16 | 16 -- | * | - | 1525 | ☉ | Jan. 23 | 4 -- | * | - | 1525 | 🌑︎ | July 4 | 10 10 | Total | - | 1525 | 🌑︎ | Dec. 29 | 10 46 | Total | - | 1526 | 🌑︎ | Dec. 18 | 10 30 | Total | - | 1527 | ☉ | Jan. 2 | 3 -- | * | - | 1527 | 🌑︎ | Dec. 7 | 10 -- | * | - | 1528 | ☉ | May 17 | 20 -- | * | - | 1529 | 🌑︎ | Oct. 16 | 20 23 | 11 55 | - | 1530 | ☉ | Mar. 28 | 18 23 | 8 24 | - | 1530 | 🌑︎ | Oct. 6 | 12 11 | Total | - | 1531 | 🌑︎ | April 1 | 7 -- | * | - | 1532 | ☉ | Aug. 30 | 0 49 | 3 35 | - | 1533 | 🌑︎ | Aug. 4 | 11 50 | Total | - | 1533 | ☉ | Aug. 19 | 17 -- | * | - | 1534 | ☉ | Jan. 14 | 1 42 | 5 45 | - | 1534 | 🌑︎ | Jan. 29 | 14 25 | Total | - | 1535 | ☉ | June 30 | Noon | * | - | 1535 | 🌑︎ | July 14 | 8 -- | * | - | 1535 | ☉ | Dec. 24 | 2 -- | * | - | 1536 | ☉ | June 18 | 2 2 | 8 0 | - | 1536 | 🌑︎ | Nov. 27 | 6 21 | 10 15 | - | 1537 | 🌑︎ | May 24 | 8 3 | Total | - | 1537 | ☉ | June 7 | 7 -- | * | - | 1537 | 🌑︎ | Nov. 16 | 14 56 | Total | - | 1538 | 🌑︎ | May 13 | 14 24 | 3 0 | - | 1538 | 🌑︎ | Nov. 6 | 5 31 | 3 37 | - | 1539 | ☉ | Apr. 18 | 4 33 | 9 0 | - | 1540 | ☉ | April 6 | 17 15 | Total | - | 1541 | 🌑︎ | Mar. 11 | 16 34 | Total | - | 1541 | ☉ | Aug. 21 | 0 56 | 3 0 | - | 1542 | 🌑︎ | Mar. 1 | 8 46 | 1 38 | - | 1542 | ☉ | Aug. 10 | 17 -- | * | - | 1543 | 🌑︎ | July 15 | 16 -- | * | - | 1544 | 🌑︎ | Jan. 9 | 18 13 | Total | - | 1544 | ☉ | Jan. 23 | 21 16 | 11 17 | - | 1544 | 🌑︎ | July 4 | 8 31 | Total | - | 1544 | 🌑︎ | Dec. 28 | 18 27 | Total | - | 1545 | ☉ | June 8 | 20 48 | 3 45 | - | 1545 | 🌑︎ | Dec. 17 | 18 -- | * | - | 1546 | ☉ | May 30 | 5 -- | * | - | 1546 | ☉ | Nov. 22 | 23 -- | * | - | 1547 | 🌑︎ | May 4 | 10 27 | 8 0 | - | 1547 | 🌑︎ | Oct. 28 | 4 56 | 11 34 | - | 1547 | ☉ | Nov. 12 | 2 9 | 9 30 | - | 1548 | ☉ | April 8 | 3 -- | * | - | 1548 | 🌑︎ | Apr. 22 | 11 24 | Total | - | 1549 | 🌑︎ | Apr. 11 | 15 19 | 2 0 | - | 1549 | 🌑︎ | Oct. 6 | 6 -- | * | - | 1550 | ☉ | Mar. 16 | 20 -- | * | - | 1551 | 🌑︎ | Feb. 20 | 8 21 | Total | - | 1551 | ☉ | Aug. 31 | 2 0 | 1 52 | - | 1553 | ☉ | Jan. 12 | 22 54 | 1 22 | - | 1553 | ☉ | July 10 | 7 -- | * | - | 1553 | 🌑︎ | July 24 | 16 0 | 0 31 | - | 1554 | ☉ | June 29 | 6 -- | * | - | 1554 | 🌑︎ | Dec. 8 | 13 7 | 10 12 | - | 1555 | 🌑︎ | June 4 | 15 0 | Total | - | 1555 | ☉ | Nov. 13 | 19 -- | * | - | 1556 | ☉ | Nov. 1 | 18 0 | 9 41 | - | 1556 | 🌑︎ | Nov. 16 | 12 44 | 6 55 | - | 1557 | ☉ | Oct. 20 | 20 -- | * | - | 1558 | 🌑︎ | April 2 | 11 0 | 9 50 | - | 1558 | ☉ | Apr. 18 | 1 -- | * | - | 1559 | 🌑︎ | Apr. 16 | 4 50 | Total | - | 1560 | 🌑︎ | Mar. 11 | 15 40 | 4 13 | - | 1560 | ☉ | Aug. 21 | 1 0 | 6 22 | - | 1560 | 🌑︎ | Sept. 4 | 7 -- | * | - | 1561 | ☉ | Feb. 13 | 19 -- | * | - | 1562 | ☉ | Feb. 3 | 5 -- | * | - | 1562 | 🌑︎ | July 15 | 15 50 | Total | - | 1563 | ☉ | Jan. 22 | 19 -- | * | - | 1563 | ☉ | June 20 | 4 50 | 8 38 | - | 1563 | 🌑︎ | July 5 | 8 4 | 11 34 | - | 1565 | ☉ | Mar. 7 | 12 53 | ------ | - | 1565 | 🌑︎ | May 14 | 16 -- | * | - | 1565 | 🌑︎ | Nov. 7 | 12 46 | 11 46 | - | 1566 | 🌑︎ | Oct. 28 | 5 38 | Total | - | 1567 | ☉ | April 8 | 23 4 | 9 34 | - | 1567 | 🌑︎ | Oct. 17 | 13 43 | 2 40 | - | 1568 | ☉ | Mar. 28 | 5 -- | * | - | 1569 | 🌑︎ | Mar. 2 | 15 18 | Total | - | 1570 | 🌑︎ | Feb. 20 | 5 46 | Total | - | 1570 | 🌑︎ | Aug. 15 | 9 17 | Total | - | 1571 | ☉ | Jan. 25 | 4 -- | * | - | 1572 | ☉ | Jan. 14 | 19 -- | * | - | 1572 | 🌑︎ | June 25 | 9 0 | 5 26 | - | 1573 | ☉ | June 28 | 18 -- | * | - | 1573 | ☉ | Nov. 24 | 4 -- | * | - | 1573 | 🌑︎ | Dec. 8 | 6 51 | Total | - | 1574 | ☉ | Nov. 13 | 3 50 | 5 21 | - | 1575 | ☉ | May 19 | 8 -- | * | - | 1575 | ☉ | Nov. 2 | 5 -- | * | - | 1576 | 🌑︎ | Oct. 7 | 9 45 | ------ | - | 1577 | 🌑︎ | April 2 | 8 33 | Total | - | 1577 | 🌑︎ | Sept. 26 | 13 4 | Total | - | 1578 | 🌑︎ | Sept. 15 | 13 4 | 2 20 | - | 1579 | ☉ | Feb. 15 | 5 41 | 8 36 | - | 1579 | ☉ | Aug. 20 | 19 0 | * | - | 1580 | 🌑︎ | Jan. 31 | 10 7 | Total | - | 1581 | 🌑︎ | Jan. 19 | 9 22 | Total | - | 1581 | 🌑︎ | July 15 | 17 51 | Total | - | 1582 | 🌑︎ | Jan. 8 | 10 29 | 0 53 | - | 1582 | ☉ | June 19 | 17 5 | 7 5 | - | 1583 | 🌑︎ | Nov. 28 | 21 51 | Total | - | 1584 | ☉ | May 9 | 18 20 | 3 36 | - | 1584 | 🌑︎ | Nov. 17 | 14 15 | Total | - | 1585 | ☉ | Apr. 29 | 7 53 | 11 7 | - | 1585 | 🌑︎ | May 13 | 5 2 | 6 54 | - | 1586 | 🌑︎ | Sept. 27 | 8 -- | * | - | 1586 | ☉ | Oct. 12 | Noon | * | - | 1587 | 🌑︎ | Sept. 16 | 9 28 | 10 2 | - | 1588 | ☉ | Feb. 26 | 1 23 | 1 3 | - | 1588 | 🌑︎ | Mar. 12 | 14 14 | Total | - | 1588 | 🌑︎ | Sept. 4 | 17 30 | Total | - | 1589 | ☉ | Aug. 10 | 18 -- | * | - | 1589 | ☉ | Aug. 25 | 8 1 | 3 54 | - | 1590 | ☉ | Feb. 4 | 5 -- | * | - | 1590 | 🌑︎ | July 16 | 17 4 | 3 54 | - | 1590 | ☉ | July 30 | 19 57 | 10 27 | - | 1591 | 🌑︎ | Jan. 9 | 6 21 | 9 40 | - | 1591 | 🌑︎ | July 6 | 5 8 | Total | - | 1591 | ☉ | July 20 | 4 2 | 1 0 | - | 1591 | 🌑︎ | Dec. 29 | 16 11 | Total | - | 1592 | 🌑︎ | June 24 | 10 13 | 8 58 | - | 1592 | 🌑︎ | Dec. 18 | 7 24 | 5 54 | - | 1593 | ☉ | May 30 | 2 30 | 2 38 | - | 1594 | ☉ | May 19 | 14 58 | 10 23 | - | 1594 | 🌑︎ | Oct. 28 | 19 15 | 9 40 | - | 1595 | ☉ | April 9 | Ter. de | Fuego | - | 1595 | 🌑︎ | Apr. 24 | 4 12 | Total | - | 1595 | ☉ | May 7 | 22 -- | * | - | 1595 | ☉ | Oct. 3 | 2 4 | 5 18 | - | 1595 | 🌑︎ | Oct. 18 | 20 47 | Total | - | 1596 | ☉ | Mar. 28 | In | Chili | - | 1596 | 🌑︎ | Apr. 12 | 8 52 | 6 4 | - | 1596 | ☉ | Sept. 21 | In | China | - | 1596 | 🌑︎ | Oct. 6 | 21 15 | 3 33 | - | 1597 | ☉ | Mar. 17 | St. Pet. | Isle | - | 1597 | ☉ | Sept. 11 | Picora | 9 49 | - | 1598 | 🌑︎ | Feb. 20 | 18 12 | 10 55 | - | 1598 | ☉ | Mar. 6 | 22 12 | 11 57 | - | 1598 | 🌑︎ | Aug. 16 | 8 15 | Total | - | 1598 | ☉ | Aug. 31 | Magel. | 8 34 | - | 1599 | 🌑︎ | Feb. 10 | 17 21 | Total | - | 1599 | ☉ | July 22 | 4 31 | 4 18 | - | 1599 | 🌑︎ | Aug. 6 | ------ | Total | - | 1600 | ☉ | Jan. 15 | Java | 11 48 | - | 1600 | 🌑︎ | Jan. 30 | 6 40 | 2 58 | - | 1600 | ☉ | July 10 | 2 10 | 5 39 | - | 1601 | ☉ | Jan. 4 | Ethiop. | 9 40 | - | 1601 | 🌑︎ | June 15 | 6 18 | 4 52 | - | 1601 | ☉ | June 29 | China | 4 29 | - | 1601 | 🌑︎ | Dec. 9 | 7 6 | 10 53 | - | 1601 | ☉ | Dec. 24 | 2 46 | 9 52 | - | 1602 | ☉ | May 21 | Greenl. | 2 41 | - | 1602 | 🌑︎ | June 4 | 7 18 | Total | - | 1602 | ☉ | June 19 | N. Gra. | 5 43 | - | 1602 | ☉ | Nov. 13 | Magel. | 3 -- | - | 1602 | 🌑︎ | Nov. 28 | 10 2 | Total | - | 1603 | ☉ | May 10 | China | 11 21 | - | 1603 | 🌑︎ | May 24 | 11 41 | 7 59 | - | 1603 | ☉ | Nov. 3 | Rom. I. | 11 17 | - | 1603 | 🌑︎ | Nov. 18 | 7 31 | 3 26 | - | 1604 | ☉ | Apr. 29 | Arabia | 9 32 | - | 1604 | ☉ | Oct. 22 | Peru | 6 49 | - | 1605 | 🌑︎ | April 3 | 9 19 | 11 49 | - | 1605 | ☉ | Apr. 18 | Madag. | 5 31 | - | 1605 | 🌑︎ | Sept. 27 | 4 27 | 9 26 | - | 1605 | ☉ | Oct. 12 | 2 32 | 9 24 | - | 1606 | ☉ | Mar. 8 | Mexico | 6 0 | - | 1606 | 🌑︎ | Mar. 24 | 11 17 | Total | - | 1606 | ☉ | Sept. 2 | Magel. | 6 40 | - | 1606 | 🌑︎ | Sept. 16 | 15 6 | Total | - | 1607 | ☉ | Feb. 25 | 21 48 | 1 13 | - | 1607 | 🌑︎ | Mar. 13 | 6 36 | 1 22 | - | 1607 | ☉ | Sept. 5 | 15 40 | 4 7 | - | 1608 | ☉ | Feb. 15 | at the | Antipo. | - | 1608 | 🌑︎ | July 27 | 0 30 | 1 53 | - | 1608 | ☉ | Aug. 9 | 4 39 | 0 40 | - | 1609 | 🌑︎ | Jan. 19 | 15 21 | 10 32 | - | 1609 | ☉ | Feb. 4 | Fuego | 5 22 | - | 1609 | 🌑︎ | July 16 | 12 8 | Total | - | 1609 | ☉ | July 30 | Canada | 4 10 | - | 1609 | ☉ | Dec. 26 | 19 -- | 5 50 | - | 1610 | 🌑︎ | Jan. 9 | 1 31 | Total | - | 1610 | ☉ | June 20 | Java | 10 46 | - | 1610 | 🌑︎ | July 5 | 16 58 | 11 13 | - | 1610 | ☉ | Dec. 15 | Cyprus | 4 50 | - | 1610 | 🌑︎ | Dec. 29 | 16 47 | 4 23 | - | 1611 | ☉ | June 10 | Califor. | 11 30 | - | 1612 | 🌑︎ | May 14 | 10 38 | 7 22 | - | 1612 | ☉ | May 29 | 23 38 | 7 14 | - | 1612 | 🌑︎ | Nov. 8 | 3 22 | 9 49 | - | 1612 | ☉ | Nov. 22 | Magel. | 9 0 | - | 1613 | ☉ | Apr. 20 | Magel | lanica | - | 1613 | 🌑︎ | May 4 | 0 35 | Total | - | 1613 | ☉ | May 19 | East | Tartary | - | 1613 | ☉ | Oct. 13 | South | Amer. | - | 1613 | 🌑︎ | Oct. 28 | 4 19 | Total | - | 1614 | ☉ | April 8 | N. Gui. | 8 44 | - | 1614 | 🌑︎ | Apr. 23 | 17 36 | 5 25 | - | 1614 | ☉ | Oct. 3 | 0 57 | 5 2 | - | 1614 | 🌑︎ | Oct. 17 | 4 38 | 4 56 | - | 1615 | ☉ | Mar. 29 | Goa | 10 38 | - | 1615 | ☉ | Sept. 22 | Salom | Isle | - | 1616 | 🌑︎ | Mar. 3 | 1 58 | Total | - | 1616 | ☉ | Mar. 17 | Mexico | 6 47 | - | 1616 | 🌑︎ | Aug. 26 | 15 33 | Total | - | 1616 | ☉ | Sept. 10 | Magel. | 10 33 | - | 1617 | ☉ | Feb. 5 | Magel | lanica | - | 1617 | 🌑︎ | Feb. 20 | 1 49 | Total | - | 1617 | ☉ | Mar 6 | 22 -- | * | - | 1617 | ☉ | Aug. 1 | Biarmia | | - | 1617 | 🌑︎ | Aug. 16 | 8 22 | Total | - | 1618 | ☉ | Jan. 26 | Magel | lanica | - | 1618 | 🌑︎ | Feb. 9 | 3 29 | 2 57 | - | 1618 | ☉ | July 21 | Mexico | ------ | - | 1619 | ☉ | Jan. 15 | Califor | nia | - | 1619 | 🌑︎ | June 26 | 12 40 | 3 10 | - | 1619 | ☉ | July 11 | Africa | 11 39 | - | 1619 | 🌑︎ | Dec. 20 | 15 53 | 10 47 | - | 1620 | ☉ | May 31 | Arctic | Circle | - | 1620 | 🌑︎ | June 14 | 13 47 | Total | - | 1620 | ☉ | June 29 | Magel. | 7 20 | - | 1620 | 🌑︎ | Dec. 9 | 6 39 | Total | - | 1620 | ☉ | Dec. 23 | Magel | lanica | - | 1621 | ☉ | May 20 | 14 54 | 10 44 | - | 1621 | 🌑︎ | June 3 | 19 42 | 9 53 | - | 1621 | ☉ | Nov. 13 | Magel | lanica | - | 1621 | 🌑︎ | Nov. 28 | 15 43 | 3 38 | - | 1622 | ☉ | May 10 | C. Verd | 11 52 | - | 1622 | ☉ | Nov. 2 | Malac | ca In. | - | 1623 | 🌑︎ | Apr. 14 | 7 19 | 10 54 | - | 1623 | ☉ | Apr. 29 | ------ | ------ | - | 1623 | 🌑︎ | Oct. 8 | 0 22 | 8 35 | - | 1623 | ☉ | Oct. 23 | Califor. | 10 46 | - | 1624 | ☉ | May 18 | N. Zem. | 6 0 | - | 1624 | 🌑︎ | Apr. 3 | 7 9 | Total | - | 1624 | ☉ | Apr. 17 | Antar. | Circle | - | 1624 | ☉ | Sept. 12 | Magel | lanica | - | 1624 | 🌑︎ | Sept. 26 | 8 55 | Total | - | 1625 | ☉ | Mar. 8 | Florida | | - | 1625 | 🌑︎ | Mar. 23 | 14 11 | 2 11 | - | 1625 | ☉ | Sept. 1 | St. Pete | r’s Isl. | - | 1625 | 🌑︎ | Sept. 16 | 11 41 | 5 6 | - | 1626 | ☉ | Feb. 25 | Madag. | 8 27 | - | 1626 | 🌑︎ | Aug. 7 | 7 48 | 0 25 | - | 1626 | ☉ | Aug. 21 | In | Mexico | - | 1627 | 🌑︎ | Jan. 30 | 11 38 | 10 21 | - | 1627 | ☉ | Feb. 15 | Magel | lanica | - | 1627 | 🌑︎ | July 27 | 9 4 | Total | - | 1627 | ☉ | Aug. 11 | Tenduc | 10 0 | - | 1628 | ☉ | Jan. 6 | Tenduc | 5 40 | - | 1628 | 🌑︎ | Jan. 20 | 10 11 | Total | - | 1628 | ☉ | July 1 | C Good | Hope | - | 1628 | 🌑︎ | July 16 | 11 26 | Total | - | 1628 | ☉ | Dec. 25 | In | England | - | 1629 | 🌑︎ | Jan. 9 | 1 36 | 4 27 | - | 1629 | ☉ | June 21 | Ganges | 11 25 | - | 1629 | ☉ | Dec. 14 | Peru | 10 14 | - | 1630 | 🌑︎ | May 25 | 17 56 | 6 0 | - | 1630 | ☉ | June 10 | 7 47 | 9 8 | - | 1630 | 🌑︎ | Nov. 19 | 11 24 | 9 27 | - | 1630 | ☉ | Dec. 3 | N. Gui. | 10 10 | - | 1631 | ☉ | Apr. 30 | Antar. | Circle | - | 1631 | 🌑︎ | May 15 | 8 15 | Total | - | 1631 | ☉ | Oct. 24 | C Good | Hope | - | 1631 | 🌑︎ | Nov. 8 | 12 0 | Total | - | 1632 | ☉ | Apr. 19 | C Good | Hope | - | 1632 | 🌑︎ | May 4 | 1 24 | 6 35 | - | 1632 | ☉ | Oct. 13 | Mexico | 8 37 | - | 1632 | 🌑︎ | Oct. 27 | 12 23 | 5 31 | - | 1633 | ☉ | April 8 | 5 14 | 4 30 | - | 1633 | ☉ | Oct. 3 | Maldiv. | Total | - | 1634 | 🌑︎ | Mar. 14 | 9 35 | 11 18 | - | 1634 | ☉ | Mar. 28 | Japan | 10 19 | - | 1634 | 🌑︎ | Sept. 7 | 5 0 | Total | - | 1634 | ☉ | Sept. 22 | C.G.H. | 9 54 | - | 1635 | ☉ | Feb. 17 | Antar. | Circle | - | 1635 | 🌑︎ | Mar. 3 | 9 26 | Total | - | 1635 | ☉ | Mar. 18 | Mexico | 0 16 | - | 1635 | ☉ | Aug. 12 | Iceland | 5 0 | - | 1635 | 🌑︎ | Aug. 27 | 16 4 | Total | - | 1636 | ☉ | Feb. 6 | In | Peru | - | 1636 | 🌑︎ | Feb. 20 | 11 34 | 3 23 | - | 1636 | ☉ | Aug. 1 | Tartary | 11 20 | - | 1636 | 🌑︎ | Aug. 16 | 4 34 | 1 25 | - | 1637 | ☉ | Jan. 26 | Camboya | | - | 1637 | ☉ | July 21 | Jucutan | | - | 1637 | 🌑︎ | Dec. 31 | 0 44 | 10 45 | - | 1638 | ☉ | Jan. 14 | Persia | 9 45 | - | 1638 | 🌑︎ | June 25 | 20 17 | Total | - | 1638 | ☉ | July 11 | Magellan | 9 5 | - | 1638 | ☉ | Dec. 5 | Magellan | 2 10 | - | 1638 | 🌑︎ | Dec. 20 | 15 16 | Total | - | 1639 | ☉ | Jan. 4 | Tartary | 0 30 | - | 1639 | ☉ | June 1 | 5 59 | 10 40 | - | 1639 | 🌑︎ | June 15 | 2 41 | 11 9 | - | 1639 | ☉ | Nov. 24 | Magel. | 11 0 | - | 1639 | 🌑︎ | Dec. 9 | 11 57 | 3 46 | - | 1640 | ☉ | May 20 | N. Spa. | 10 30 | - | 1640 | ☉ | Nov. 13 | Peru | 10 36 | - | 1641 | 🌑︎ | Apr. 25 | 1 2 | 9 49 | - | 1641 | ☉ | May 9 | Peru | 10 16 | - | 1641 | 🌑︎ | Oct. 18 | 8 19 | 6 31 | - | 1641 | ☉ | Nov. 2 | 18 46 | ------ | - | 1642 | ☉ | Mar. 30 | Estotl. | 4 0 | - | 1642 | 🌑︎ | Apr. 14 | 14 31 | Total | - | 1642 | ☉ | Sept. 25 | Magel | lan | - | 1642 | 🌑︎ | Oct. 7 | 16 45 | Total | - | 1643 | ☉ | Mar. 19 | 13 53 | ------ | - | 1643 | 🌑︎ | April 3 | 21 10 | 3 9 | - | 1643 | ☉ | Sept. 12 | 17 0 | ------ | - | 1643 | 🌑︎ | Sept. 27 | 7 38 | 6 0 | - | 1644 | ☉ | Mar. 8 | 6 20 | ------ | - | 1644 | ☉ | Aug. 31 | 18 10 | ------ | - | 1645 | 🌑︎ | Feb. 10 | 7 45 | 8 52 | - | 1645 | ☉ | Feb. 26 | Rom. I. | 10 46 | - | 1645 | 🌑︎ | Aug. 7 | 2 4 | Total | - | 1645 | ☉ | Aug. 21 | 0 35 | 4 40 | - | 1646 | ☉ | Jan. 16 | Str. of | Anian. | - | 1646 | 🌑︎ | Jan. 30 | 18 11 | Total | - | 1646 | ☉ | July 12 | 6 57 | ------ | - | 1646 | 🌑︎ | July 27 | 6 2 | Total | - | 1647 | ☉ | Jan. 5 | 12 10 | ------ | - | 1647 | 🌑︎ | Jan. 20 | 9 43 | 4 47 | - | 1647 | ☉ | July 2 | 0 9 | ------ | - | 1647 | ☉ | Dec. 25 | 13 38 | ------ | - | 1648 | 🌑︎ | June 5 | 0 55 | 4 28 | - | 1648 | ☉ | June 20 | 13 28 | ------ | - | 1648 | 🌑︎ | Nov. 29 | 19 17 | 7 40 | - | 1648 | ☉ | Dec. 13 | 21 48 | ------ | - | 1649 | 🌑︎ | May 25 | 15 20 | Total | - | 1649 | ☉ | June 9 | Arct. C. | 4 0 | - | 1649 | ☉ | Nov. 4 | 2 10 | 5 19 | - | 1649 | 🌑︎ | Nov. 18 | 19 56 | Total | - | 1650 | ☉ | Apr. 30 | 5 54 | ------ | - | 1650 | 🌑︎ | May 15 | 8 37 | 7 57 | - | 1650 | ☉ | Oct. 24 | 17 17 | ------ | - | 1650 | 🌑︎ | Nov. 7 | 20 29 | 5 3 | - | 1651 | ☉ | Apr. 19 | Tuber. | ------ | - | 1651 | ☉ | Oct. 14 | 2 15 | ------ | - | 1652 | 🌑︎ | Mar. 24 | 16 52 | 8 50 | - | 1652 | ☉ | April 7 | 22 40 | 9 59 | - | 1652 | 🌑︎ | Sept. 17 | 7 27 | 9 49 | - | 1652 | ☉ | Oct. 2 | 5 2 | ------ | - | 1653 | ☉ | Feb. 27 | -- -- | ------ | - | 1653 | 🌑︎ | Mar. 13 | 17 9 | Total | - | 1653 | ☉ | Aug. 22 | -- -- | ------ | - | 1653 | 🌑︎ | Sept. 6 | 23 45 | Total | - | 1654 | ☉ | Feb. 16 | 9 10 | ------ | - | 1654 | 🌑︎ | Mar. 2 | 19 25 | 3 14 | - | 1654 | ☉ | Aug. 11 | 22 24 | 2 28 | - | 1654 | 🌑︎ | Aug. 27 | 11 49 | 1 53 | - | 1655 | ☉ | Feb. 6 | 2 37 | 4 20 | - | 1655 | ☉ | Aug. 1 | 14 19 | ------ | - | 1655 | 🌑︎ | Aug. 16 | 16 -- | * | - | 1656 | 🌑︎ | Jan. 11 | 9 4 | 10 0 | - | 1656 | 🌑︎ | July 6 | 3 17 | Total | - | 1656 | ☉ | July 21 | 11 48 | ------ | - | 1656 | 🌑︎ | Dec. 30 | 23 30 | Total | - | 1657 | ☉ | June 11 | 11 20 | ------ | - | 1657 | 🌑︎ | June 25 | 9 35 | Total | - | 1657 | ☉ | Dec. 4 | 20 0 | ------ | - | 1657 | 🌑︎ | Dec. 20 | 7 47 | 3 9 | - | 1658 | ☉ | May 31 | 16 0 | ------ | - | 1658 | 🌑︎ | June 14 | 22 58 | ------ | - | 1658 | 🌑︎ | Nov. 9 | 13 56 | 0 10 | - | 1658 | ☉ | Nov. 24 | 11 36 | ------ | - | 1659 | 🌑︎ | May 6 | 8 34 | 8 5 | - | 1659 | ☉ | May 20 | 17 4 | ------ | - | 1659 | 🌑︎ | Oct. 29 | 16 16 | 5 52 | - | 1659 | ☉ | Nov. 14 | 4 25 | 9 51 | - | 1660 | 🌑︎ | Apr. 24 | 21 58 | Total | - | 1660 | ☉ | Oct. 3 | 22 34 | ------ | - | 1660 | 🌑︎ | Oct. 18 | 0 32 | Total | - | 1660 | ☉ | Nov. 2 | 13 48 | ------ | - | 1661 | ☉ | Mar. 29 | 22 32 | ------ | - | 1661 | 🌑︎ | Apr. 14 | 4 28 | ------ | - | 1661 | ☉ | Sept. 23 | 1 36 | 11 19 | - | 1661 | 🌑︎ | Oct. 7 | 14 51 | 7 4 | - | 1662 | ☉ | Mar. 19 | 15 8 | ------ | - | 1662 | ☉ | Apr. 12 | 1 8 | ------ | - | 1663 | ☉ | Feb. 21 | 16 11 | 3 14 | - | 1663 | ☉ | Mar. 9 | 5 47 | ------ | - | 1663 | 🌑︎ | Aug. 18 | 8 45 | Total | - | 1663 | ☉ | Sept. 1 | 8 8 | ------ | - | 1664 | ☉ | Jan. 27 | 20 40 | ------ | - | 1664 | 🌑︎ | Feb. 11 | 3 16 | ------ | - | 1664 | ☉ | July 22 | 14 48 | ------ | - | 1664 | ☉ | Aug. 20 | 22 10 | ------ | - | 1665 | 🌑︎ | Jan. 30 | 18 47 | 4 34 | - | 1665 | ☉ | July 12 | 7 48 | ------ | - | 1665 | 🌑︎ | July 26 | 13 31 | 0 10 | - | 1666 | ☉ | Jan. 4 | 21 33 | ------ | - | 1666 | ☉ | July 1 | 19 0 | 11 10 | - | 1667 | 🌑︎ | June 5 | Noon | ------ | - | 1667 | ☉ | July 21 | 2 32 | ------ | - | 1667 | ☉ | Nov. 15 | 11 30 | ------ | - | 1668 | ☉ | May 10 | Setting | ------ | - | 1668 | 🌑︎ | May 25 | 16 26 | 9 32 | - | 1668 | ☉ | Nov. 4 | 2 53 | 9 50 | - | 1668 | 🌑︎ | Nov. 18 | 3 54 | 6 45 | - | 1669 | ☉ | Apr. 29 | 18 18 | ------ | - | 1669 | ☉ | Oct. 24 | 10 13 | ------ | - | 1670 | ☉ | Apr. 19 | 7 0 | ------ | - | 1670 | ☉ | Sept. 10 | 19 0 | ------ | - | 1670 | 🌑︎ | Sept. 28 | 15 43 | 9 7 | - | 1670 | ☉ | Oct. 13 | 12 5 | ------ | - | 1671 | ☉ | April 8 | 23 29 | ------ | - | 1671 | ☉ | Sept. 2 | 21 25 | ------ | - | 1671 | 🌑︎ | Sept. 18 | 7 44 | Total | - | 1672 | ☉ | Feb. 28 | 3 38 | ------ | - | 1672 | 🌑︎ | Mar. 13 | 3 17 | ------ | - | 1672 | ☉ | Aug. 22 | 6 43 | ------ | - | 1672 | 🌑︎ | Sept. 6 | 18 54 | ------ | - | 1673 | ☉ | Feb. 16 | 7 29 | ------ | - | 1673 | ☉ | Aug. 11 | 21 44 | ------ | - | 1674 | 🌑︎ | Jan. 21 | 18 22 | 11 21 | - | 1674 | ☉ | Feb. 5 | 9 4 | ------ | - | 1674 | 🌑︎ | July 17 | 9 40 | Total | - | 1675 | 🌑︎ | Jan. 11 | 8 29 | Total | - | 1675 | ☉ | Jan. 25 | 10 36 | ------ | - | 1675 | 🌑︎ | July 6 | 16 31 | Total | - | 1676 | ☉ | June 10 | 21 26 | 4 34 | - | 1676 | 🌑︎ | June 25 | 6 26 | ------ | - | 1676 | ☉ | Dec. 4 | 20 52 | ------ | - | 1677 | ☉ | Nov. 24 | 12 5 | ------ | - | 1677 | 🌑︎ | May 16 | 16 25 | 8 15 | - | 1678 | 🌑︎ | May 6 | 5 30 | ------ | - | 1678 | 🌑︎ | Oct. 29 | 9 17 | Total | - | 1679 | ☉ | Apr. 10 | 21 0 | ------ | - | 1679 | 🌑︎ | Apr. 25 | 11 53 | 5 47 | - | 1680 | ☉ | Mar. 29 | 23 22 | ------ | - | 1680 | ☉ | Sept. 22 | 7 57 | ------ | - | 1681 | 🌑︎ | Mar. 4 | Noon | ------ | - | 1681 | ☉ | Mar. 10 | 13 43 | ------ | - | 1681 | 🌑︎ | Aug. 28 | 15 22 | 10 35 | - | 1681 | ☉ | Sept. 11 | 15 43 | ------ | - | 1682 | 🌑︎ | Feb. 21 | 12 28 | Total | - | 1682 | 🌑︎ | Aug. 17 | 18 56 | Total | - | 1683 | ☉ | Jan. 27 | 1 35 | 10 30 | - | 1683 | 🌑︎ | Feb. 9 | 3 39 | ------ | - | 1683 | 🌑︎ | Aug. 6 | 20 36 | ------ | - | 1684 | ☉ | Jan. 16 | 6 34 | ------ | - | 1684 | 🌑︎ | June 26 | 15 18 | 1 35 | - | 1684 | ☉ | July 12 | 3 26 | Total | - | 1684 | 🌑︎ | Dec. 21 | 11 18 | 9 45 | - | 1685 | ☉ | Jan. 4 | 16 0 | ------ | - | 1685 | 🌑︎ | June 16 | 6 0 | ------ | - | 1685 | 🌑︎ | Dec. 10 | 11 26 | Total | - | 1686 | ☉ | May 21 | 17 9 | ------ | - | 1686 | 🌑︎ | June 6 | Noon | ------ | - | 1686 | 🌑︎ | Nov. 29 | 12 22 | Total | - | 1687 | ☉ | May 11 | 1 -- | * | - | 1687 | 🌑︎ | May 26 | 14 -- | * | - | 1687 | 🌑︎ | Apr. 15 | 7 4 | 6 49 | - | 1688 | ☉ | Apr. 29 | 16 27 | ------ | - | 1688 | 🌑︎ | Oct. 9 | Noon | ------ | - | 1688 | ☉ | Oct. 25 | 19 40 | ------ | - | 1689 | 🌑︎ | April 4 | 7 42 | Total | - | 1689 | 🌑︎ | Sept. 28 | 15 46 | Total | - | 1690 | ☉ | Mar. 10 | -- -- | ------ | - | 1690 | 🌑︎ | Mar. 24 | 11 14 | 5 43 | - | 1690 | ☉ | Sept. 3 | -- -- | ------ | - | 1690 | 🌑︎ | Sept. 18 | 2 42 | ------ | - | 1691 | ☉ | Feb. 27 | 17 30 | ------ | - | 1691 | ☉ | Aug. 23 | 5 51 | ------ | - | 1692 | 🌑︎ | Feb. 2 | 3 20 | ------ | - | 1692 | ☉ | Feb. 16 | 17 31 | ------ | - | 1692 | 🌑︎ | July 27 | 16 9 | Total | - | 1693 | 🌑︎ | Jan. 21 | 17 25 | Total | - | 1693 | 🌑︎ | July 17 | Noon | ------ | - | 1694 | 🌑︎ | Jan. 11 | Noon | ------ | - | 1694 | ☉ | June 22 | 4 22 | 6 22 | - | 1694 | 🌑︎ | July 6 | 13 51 | 0 47 | - | 1695 | ☉ | May 11 | 6 3 | ------ | - | 1695 | 🌑︎ | May 28 | Noon | ------ | - | 1695 | 🌑︎ | Nov. 20 | 8 0 | 6 55 | - | 1695 | ☉ | Dec. 5 | 17 7 | ------ | - | 1696 | 🌑︎ | May 16 | 12 45 | Total | - | 1696 | ☉ | May 30 | 12 56 | ------ | - | 1696 | 🌑︎ | Nov. 8 | 17 30 | Total | - | 1696 | ☉ | Nov. 23 | 17 32 | ------ | - | 1697 | ☉ | Apr. 20 | 14 32 | ------ | - | 1697 | 🌑︎ | May 5 | 18 27 | ------ | - | 1697 | 🌑︎ | Oct. 29 | 8 44 | 8 54 | - | 1698 | ☉ | Apr. 10 | 9 13 | ------ | - | 1698 | ☉ | Oct. 3 | 15 29 | ------ | - | 1699 | 🌑︎ | Mar. 15 | 8 14 | 9 7 | - | 1699 | ☉ | Mar. 30 | 22 0 | ------ | - | 1699 | 🌑︎ | Sept. 8 | 23 22 | ------ | - | 1699 | ☉ | Sept. 23 | 22 38 | 9 58 | - | 1700 | 🌑︎ | Mar. 4 | 20 11 | ------ | - | 1700 | 🌑︎ | Aug. 29 | 1 42 | ------ | - +------+-----+----------+----------+----------+ - -The Eclipses from STRUYK were observed: those from RICCIOLUS calculated: -the following from _L’Art de verifier les Dates_, are only those which -are visible in _Europe_ for the present century: those which are total -are marked with a _T_; and _M_ signifies Morning, _A_ Afternoon. - - Visible ECLIPSES from 1700 to 1800. - - +------+-----+----------+------------+ - | Aft. | | Months | Time of | - | Chr. | | and | the Day | - | | | Days. | or Night. | - +------+-----+----------+------------+ - | 1701 | 🌑︎ | Feb. 22 | 11 A. | - | 1703 | 🌑︎ | Jan. 3 | 7 M. | - | 1703 | 🌑︎ | June 29 | 1 M. _T._ | - | 1703 | 🌑︎ | Dec. 23 | 7 M. _T._ | - | 1704 | 🌑︎ | Dec. 11 | 7 M. | - | 1706 | 🌑︎ | Apr. 28 | 2 M. | - | 1706 | ☉ | May 12 | 10 M. | - | 1706 | 🌑︎ | Oct. 21 | 7 A. | - | 1707 | 🌑︎ | Apr. 17 | 2 M. _T._ | - | 1708 | 🌑︎ | April 5 | 6 M. | - | 1708 | ☉ | Dec. 14 | 8 M. | - | 1708 | 🌑︎ | Sept. 29 | 9 A. | - | 1709 | ☉ | Mar. 11 | 2 A. | - | 1710 | 🌑︎ | Feb. 13 | 11 A. | - | 1710 | ☉ | Feb. 28 | 1 A. | - | 1711 | ☉ | July 15 | 8 A. | - | 1711 | 🌑︎ | July 29 | 6 A. _T._ | - | 1712 | 🌑︎ | Jan. 23 | 8 A. | - | 1713 | 🌑︎ | June 8 | 6 A. | - | 1713 | 🌑︎ | Dec. 2 | 4 M. | - | 1715 | ☉ | May 3 | 9 M. _T._ | - | 1715 | 🌑︎ | Nov. 11 | 5 M. | - | 1717 | 🌑︎ | Mar. 27 | 3 M. | - | 1717 | 🌑︎ | May 20 | 6 A. | - | 1718 | 🌑︎ | Sept. 9 | 8 A. _T._ | - | 1719 | 🌑︎ | Aug. 29 | 9 A. | - | 1721 | 🌑︎ | Jan. 13 | 3 A. | - | 1722 | 🌑︎ | June 29 | 3 M. | - | 1722 | ☉ | Dec. 8 | 3 A. | - | 1722 | 🌑︎ | Dec. 22 | 4 A. | - | 1724 | ☉ | May 22 | 7 A. _T._ | - | 1724 | 🌑︎ | Nov. 1 | 4 M. | - | 1725 | 🌑︎ | Oct. 21 | 7 A. | - | 1726 | ☉ | Sept. 25 | 6 A. | - | 1726 | 🌑︎ | Oct. 11 | 5 M. | - | 1727 | ☉ | Sept. 15 | 7 M. | - | 1729 | 🌑︎ | Feb. 13 | 9 A. _T._ | - | 1729 | 🌑︎ | Aug. 9 | 1 M. | - | 1730 | 🌑︎ | Feb. 4 | 4 M. | - | 1731 | 🌑︎ | June 20 | 2 M. | - | 1732 | 🌑︎ | Dec. 1 | 10 A. _T._ | - | 1733 | ☉ | May 13 | 7 A. | - | 1733 | 🌑︎ | May 28 | 7 A. | - | 1735 | 🌑︎ | Oct. 2 | 1 M. | - | 1736 | 🌑︎ | Mar. 26 | 12 A. _T._ | - | 1736 | 🌑︎ | Sept. 20 | 3 M. _T._ | - | 1736 | ☉ | Oct. 4 | 6 A. | - | 1737 | ☉ | Mar. 1 | 4 A. | - | 1737 | 🌑︎ | Sept. 9 | 4 M. | - | 1738 | ☉ | Aug. 15 | 11 M. | - | 1739 | 🌑︎ | Jan. 24 | 11 A. | - | 1739 | ☉ | Aug. 4 | 5 A. | - | 1739 | ☉ | Dec. 30 | 9 M. | - | 1740 | 🌑︎ | Jan. 13 | 11 A. _T._ | - | 1741 | 🌑︎ | Jan. 1 | 12 A. | - | 1743 | 🌑︎ | Nov. 2 | 3 M. _T._ | - | 1744 | 🌑︎ | Aug. 26 | 9 A. | - | 1746 | 🌑︎ | Aug. 30 | 12 A. | - | 1747 | 🌑︎ | Feb. 14 | 5 M. _T._ | - | 1748 | ☉ | July 25 | 11 M. | - | 1748 | 🌑︎ | Aug. 8 | 12 A. | - | 1749 | 🌑︎ | Dec. 23 | 8 A. | - | 1750 | ☉ | Jan. 8 | 9 M. | - | 1750 | 🌑︎ | June 19 | 9 A. _T._ | - | 1750 | 🌑︎ | Dec. 13 | 7 M. | - | 1751 | 🌑︎ | June 9 | 2 M. | - | 1751 | 🌑︎ | Dec. 2 | 10 A. | - | 1752 | ☉ | May 13 | 8 A. | - | 1753 | 🌑︎ | Apr. 17 | 7 A. | - | 1753 | ☉ | Oct. 26 | 10 M. | - | 1755 | 🌑︎ | Mar. 28 | 1 M. | - | 1757 | 🌑︎ | Feb. 4 | 6 M. | - | 1757 | 🌑︎ | July 30 | 12 A. | - | 1758 | 🌑︎ | Jan. 24 | 7 M. _T._ | - | 1758 | ☉ | Dec. 30 | 7 M. | - | 1759 | ☉ | June 24 | 7 A. | - | 1759 | ☉ | Dec. 19 | 2 A. | - | 1760 | 🌑︎ | May 29 | 9 A. | - | 1760 | ☉ | June 13 | 7 M. | - | 1760 | 🌑︎ | Nov. 22 | 9 A. | - | 1761 | 🌑︎ | May 18 | 11 A. _T._ | - | 1762 | 🌑︎ | May 8 | 4 M. | - | 1762 | ☉ | Oct. 17 | 8 M. | - | 1762 | 🌑︎ | Nov. 1 | 8 A. | - | 1763 | ☉ | Apr. 13 | 8 M. | - | 1764 | ☉ | Apr. 1 | 10 M. | - | 1764 | 🌑︎ | Apr. 16 | 1 M. | - | 1765 | ☉ | Mar. 21 | 2 A. | - | 1765 | ☉ | Aug. 16 | 5 A. | - | 1766 | 🌑︎ | Feb. 24 | 7 A. | - | 1766 | ☉ | Aug. 5 | 7 A. | - | 1768 | 🌑︎ | Jan. 4 | 5 M. | - | 1768 | 🌑︎ | June 30 | 4 M. _T._ | - | 1768 | 🌑︎ | Dec. 23 | 4 A. _T._ | - | 1769 | ☉ | June 4 | 8 M. | - | 1769 | 🌑︎ | Dec. 13 | 7 M. | - | 1770 | ☉ | Nov. 17 | 10 M. | - | 1771 | 🌑︎ | Apr. 28 | 2 M. | - | 1771 | 🌑︎ | Oct. 23 | 5 A. | - | 1772 | 🌑︎ | Oct. 11 | 6 A. _T._ | - | 1772 | ☉ | Oct. 26 | 10 M. | - | 1773 | ☉ | Mar. 23 | 5 M. | - | 1773 | 🌑︎ | Sept. 30 | 7 A. | - | 1774 | ☉ | Mar. 12 | 10 M. | - | 1776 | 🌑︎ | July 31 | 1 M. _T._ | - | 1776 | ☉ | Aug. 14 | 5 M. | - | 1777 | ☉ | Jan. 9 | 5 A. | - | 1778 | ☉ | June 24 | 4 A. | - | 1778 | 🌑︎ | Dec. 4 | 6 M. | - | 1779 | 🌑︎ | May 30 | 5 M. _T._ | - | 1779 | ☉ | June 14 | 8 M. | - | 1779 | 🌑︎ | Nov. 23 | 8 A. | - | 1780 | ☉ | Oct. 27 | 6 A. | - | 1780 | 🌑︎ | Nov. 12 | 4 M. | - | 1781 | ☉ | Apr. 23 | 6 A. | - | 1781 | ☉ | Oct. 17 | 8 M. | - | 1782 | 🌑︎ | Apr. 12 | 7 A. | - | 1783 | 🌑︎ | Mar. 18 | 9 A. _T._ | - | 1783 | 🌑︎ | Sept. 10 | 11 A. _T._ | - | 1784 | 🌑︎ | Mar. 7 | 3 M. | - | 1785 | ☉ | Feb. 9 | 1 A. | - | 1787 | 🌑︎ | Jan. 3 | 12 A. _T._ | - | 1787 | ☉ | Jan. 19 | 10 M. | - | 1787 | ☉ | June 15 | 5 A. | - | 1787 | 🌑︎ | Dec. 24 | 3 A. | - | 1788 | ☉ | June 4 | 9 M. | - | 1789 | 🌑︎ | Nov. 2 | 12 A. | - | 1790 | 🌑︎ | Apr. 28 | 12 A. _T._ | - | 1790 | 🌑︎ | Oct. 23 | 1 M. _T._ | - | 1791 | ☉ | April 3 | 1 A. | - | 1791 | 🌑︎ | Oct. 12 | 3 M. | - | 1792 | ☉ | Sept. 16 | 11 M. | - | 1793 | 🌑︎ | Feb. 25 | 10 A. | - | 1793 | ☉ | Sept. 5 | 3 A. | - | 1794 | ☉ | Jan. 31 | 4 A. | - | 1794 | 🌑︎ | Feb. 14 | 11 A. _T._ | - | 1794 | ☉ | Aug. 25 | 5 A. | - | 1795 | 🌑︎ | Feb. 4 | 1 M. | - | 1795 | ☉ | July 16 | 9 M. | - | 1795 | 🌑︎ | July 31 | 8 A. | - | 1797 | ☉ | June 25 | 8 A. | - | 1797 | 🌑︎ | Dec. 4 | 6 M. | - | 1798 | 🌑︎ | May 27 | 7 A. _T._ | - | 1800 | 🌑︎ | Oct. 2 | 11 A. | - +------+-----+----------+------------+ - - 328. _A List of Eclipses, and historical Events, which happened about - the same Times, from_ RICCIOLUS. - -[Sidenote: Historical Eclipses.] - - Before CHRIST. - | | - 754 | _July_ 5 | But according to an old Calendar this Eclipse of - | | the Sun was on the 21st of _April_, on which day the - | | Foundations of _Rome_ were laid if we may believe - | | _Taruntius Firmanus_. - | | - 721 | _March_ 19 | A total Eclipse of the Moon. The _Assyrian_ - | | Empire at an end; the _Babylonian_ established. - | | - 585 | _May_ 28 | An Eclipse of the Sun foretold by THALES, by - | | which a peace was brought about between the - | | _Medes_ and _Lydians_. - | | - 523 | _July_ 16 | An Eclipse of the Moon, which was followed - | | by the death of CAMBYSES. - | | - 502 | _Nov._ 19 | An Eclipse of the Moon, which was followed - | | by the slaughter of the _Sabines_, and death of - | | _Valerius Publicola_. - | | - 463 | _April_ 30 | An Eclipse of the Sun. The _Persian_ war, and the - | | falling off of the _Persians_ from the _Egyptians_. - | | - 431 | _April_ 25 | An Eclipse of the Moon, which was followed - | | by a great famine at _Rome_; and the beginning of - | | the _Peloponnesian_ war. - | | - 431 | _August_ 3 | A total Eclipse of the Sun. A Comet and Plague - | | at _Athens_[74]. - | | - 413 | _Aug._ 27 | A total Eclipse of the Moon. _Nicias_ with his - | | ship destroyed at _Syracuse_. - | | - 394 | _Aug._ 14 | An Eclipse of the Sun. The _Persians_ beat by - | | _Conon_ in a sea engagement. - | | - 168 | _June_ 21 | A total Eclipse of the Moon. The next day - | | _Perseus_ King of _Macedonia_ was conquered by - | | _Paulus Emilius_. - - After CHRIST. - | | - 59 | _April_ 30 | An Eclipse of the Sun. This is reckoned among - | | the prodigies, on account of the murther of - | | _Agrippinus_ by _Nero_. - | | - 237 | _April_ 12 | A total Eclipse of the Sun. A sign that the reign - | | of the _Gordiani_ would not continue long. A sixth - | | persecution of the Christians. - | | - 306 | _July_ 27 | An Eclipse of the Sun. The Stars were seen, - | | and the Emperor _Constantius_ died. - | | - 840 | _May_ 4 | A dreadful Eclipse of the Sun. And _Lewis_ the - | | Pious died within six months after it. - | | - 1009 | ---- | An Eclipse of the Sun. And _Jerusalem_ taken by - | | the _Saracens_. - | | - 1133 | _Aug._ 2 | A terrible Eclipse of the Sun. The Stars were - | | seen. A schism in the church, occasioned by there - | | being three Popes at once. - -[Illustration: Plate XI. - -_J. Ferguson delin._ _J. Mynde Sculp._] - -[Sidenote: The superstitious notions of the antients with regard to - Eclipses. - - PLATE XI.] - -329. I have not cited one half of RICCIOLUS’s list of potentous -Eclipses; and for the same reason that he declines giving any more of -them than what that list contains: namely, that ’tis most disagreeable -to dwell any longer on such nonsense, and as much as possible to avoid -tiring the reader: the superstition of the antients may be seen by the -few here copied. My author farther says, that there were treatises -written to shew against what regions the malevolent effects of any -particular Eclipse was aimed: and the writers affirmed, that the effects -of an Eclipse of the Sun continued as many years as the Eclipse lasted -hours; and that of the Moon as many months. - -[Sidenote: Very fortunate once for CHRISTOPHER COLUMBUS.] - -330. Yet such idle notions were once of no small advantage to -CHRISTOPHER COLUMBUS; who, in the year 1493, was driven on the island of -_Jamaica_, where he was in the greatest distress for want of provisions, -and was moreover refused any assistance from the inhabitants; on which -he threatened them with a plague, and that in token of it there should -be an Eclipse: which accordingly fell on the day he had foretold, and so -terrified the Barbarians, that they strove who should be first in -bringing him all sorts of provisions; throwing them at his feet, and -imploring his forgiveness. RICCIOLUS’s _Almagest_, Vol. I. 1. v. c. ii. - -[Sidenote: Why there are more visible Eclipses of the Moon than of the - Sun.] - -331. Eclipses of the Sun are more frequent than of the Moon, because the -Sun’s ecliptic limits are greater than the Moon’s § 317: yet we have -more visible Eclipses of the Moon than of the Sun, because Eclipses of -the Moon are seen from all parts of that Hemisphere of the Earth which -is next her, and equally great to each of these parts; but the Sun’s -Eclipses are visible only to that small portion of the Hemisphere next -him whereon the Moon’s shadow falls; as shall be explained by and by at -large. - -[Sidenote: Fig. I. - - Total and annular Eclipses of the Sun. - - PLATE XI.] - -332. The Moon’s Orbit being elliptical, and the Earth in one of its -focuses, she is once at her least distance from the Earth, and once at -her greatest in every Lunation. When the Moon changes at her least -distance from the Earth, and so near the Node that her dark shadow falls -on the Earth, she appears big enough to cover the whole [75]Disc of the -Sun from that part on which her shadow falls; and the Sun appears -totally eclipsed there, as at _A_, for some minutes: But when the Moon -changes at her greatest distance from the Earth, and so near the Node -that her dark shadow is directed towards the Earth, her diameter -subtends a less angle than the Sun’s; and therefore she cannot hide his -whole Disc from any part of the Earth, nor does her shadow reach it at -that time; and to the place over which the point of her shadow hangs, -the Eclipse is annular as at _B_; the Sun’s edge appearing like a -luminous ring all around the body of the Moon. When the Change happens -within 17 degrees of the Node, and the Moon at her mean distance from -the Earth, the point of her shadow just touches the Earth, and she -eclipseth the Sun totally to that small spot whereon her shadow falls; -but the darkness is not of a moment’s continuance. - -[Sidenote: The longest duration of total Eclipses of the Sun.] - -333. The Moon’s apparent diameter when largest exceeds the Sun’s when -least only 1 minute 38 seconds of a degree: And in the greatest Eclipse -of the Sun that can happen at any time and place, the total darkness -continues no longer than whilst the Moon is going 1 minute 38 seconds -from the Sun in her Orbit; which is about 3 minutes and 13 seconds of an -hour. - -[Sidenote: To how much of the Earth the Sun may be totally or partially - eclipsed at once.] - -334. The Moon’s dark shadow covers only a spot on the Earth’s surface, -about 180 _English_ miles broad, when the Moon’s diameter appears -largest and the Sun’s least; and the total darkness can extend no -farther than the dark shadow covers. Yet the Moon’s partial Shadow or -Penumbra may then cover a circular space 4900 miles in diameter, within -all which the Sun is more or less eclipsed as the places are less or -more distant from the Center of the Penumbra. When the Moon changes -exactly in the Node, the Penumbra is circular on the Earth at the middle -of the general Eclipse; because at that time it falls perpendicularly on -the Earth’s surface: But at every other moment it falls obliquely, and -will therefore be elliptical; and the more so, as the time is longer -before or after the middle of the general Eclipse; and then, much -greater portions of the Earth’s surface are involved in the Penumbra. - -[Sidenote: Duration of general and particular Eclipses. - - The Moon’s dark shadow. - - And Penumbra.] - -335. When the Penumbra first touches the Earth the general Eclipse -begins: when it leaves the Earth the general Eclipse ends: from the -beginning to the end the Sun appears eclipsed in some part of the Earth -or other. When the Penumbra touches any place the Eclipse begins at that -place, and ends when the Penumbra leaves it. When the Moon changes in -the Node, the Penumbra goes over the center of the Earth’s Disc as seen -from the Moon; and consequently, by describing the longest line possible -on the Earth, continues the longest upon it; namely, at a mean rate, 5 -hours 50 minutes: more, if the Moon be at her greatest distance from the -Earth, because she then moves slowest; less, if she be at her least -distance, because of her quicker motion. - -[Sidenote: Fig. II.] - -336. To make the last five articles and several other Phenomena plainer, -let _S_ be the Sun, _E_ the Earth, _M_ the Moon, and _AMP_ the Moon’s -Orbit. Draw the right line _Wc 12_ from the western edge of the Sun at -_W_, touching the western edge of the Moon at _c_ and the Earth at _12_: -draw also the right line _Vd 12_ from the eastern edge of the Sun at -_V_, touching the eastern edge of the Moon at _d_ and the Earth at _12_: -the dark space _ce 12 d_ included between those lines is the Moon’s -shadow, ending in a point at _12_ where it touches the Earth; because in -this case the Moon is supposed to change at _M_ in the middle between -_A_ the Apogee, or farthest point of her Orbit from the Earth, and _P_ -the Perigee, or nearest point to it. For, had the point _P_ been at _M_, -the Moon had been nearer the Earth; and her dark shadow at _e_ would -have covered a space upon it about 180 miles broad, and the Sun would -have been totally darkened as at _A_ (Fig I) with some continuance: but -had the point _A_ (Fig. II) been at _M_, the Moon would have been -farther from the Earth, and her shadow would have ended in a point about -_e_, and therefore the Sun would have appeared as at _B_ (Fig. I) like a -luminous ring all around the Moon. Draw the right lines _WXdh_ and -_VXcg_, touching the contrary sides of the Sun and Moon, and ending on -the Earth at _a_ and _b_: draw also the right line _SXM 12_, from the -center of the Sun’s Disc, through the Moon’s center, to the Earth at -_12_; and suppose the two former lines _WXdh_ and _VXcg_ to revolve on -the line _SXM 12_ as an Axis, and their points _a_ and _b_ will describe -the limits of the Penumbra _TT_ on the Earth’s surface, including the -large space _a0b12a_; within which the Sun appears more or less eclipsed -as the places are more or less distant from the verge of the Penumbra -_a0b_. - -[Sidenote: Digits, what.] - -Draw the right line _y 12_ across the Sun’s Disc, and parallel to the -plane of the Moon’s Orbit; divide this line into twelve equal parts, as -in the Figure, for the twelve [76]Digits of the Sun’s diameter: and at -equal distances from the center of the Penumbra _TT_ to its edge on the -Earth, or from _12_ to _0_, draw twelve concentric Circles, as marked -with the numeral Figures _1_ _2_ _3_ _4_ &c. and remember that the -Moon’s motion in her Orbit _AMP_ is from west to east, as from _s_ to -_t_. Then, - -[Sidenote: The different phases of a solar Eclipse. - - PLATE XI. - - Fig. III.] - -To an observer on the Earth at _b_, the eastern limb of the Moon at _d_ -seems to touch the western limb of the Sun at _W_, when the Moon is at -_M_; and the Sun’s Eclipse begins at _b_; appearing as at _A_ in Fig. -III at the left hand; but at the same moment of absolute time to an -observer at _a_ in Fig. II the western edge of the Moon at _c_ leaves -the eastern edge of the Sun at _V_, and the Eclipse ends, as at the -right hand _C_ of Fig. III. At the very same instant, to all those who -live on the Circle marked _1_ on the Earth _E_ in Fig. II, the Moon _M_ -cuts off or darkens a twelfth part of the Sun _S_, and eclipses him one -Digit, as at _1_ in Fig. III: to those who live on the Circle marked _2_ -in Fig. II the Moon cuts off two twelfth parts of the Sun, as at _2_ in -Fig. III: to those on the Circle _3_, three parts; and so on to the -center at _12_ in Fig. II, where the Sun is centrally eclipsed as at _B_ -in the middle of Fig. III: under which Figure there is a scale of hours -and minutes, to shew at a mean state how long it is from the beginning -to the end of a central Eclipse of the Sun on the parallel of _London_; -and how many Digits are eclipsed at any particular time from the -beginning at _A_ to the middle at _B_, or the end at _C_. Thus in 16 -minutes from the beginning, the Sun is two Digits eclipsed; in an hour -and five minutes, 8 Digits; and in an hour and thirty-seven minutes, 12 -Digits. - -[Sidenote: Fig. II. - - The Velocity of the Moon’s shadow on the Earth. - - Fig. IV.] - -337. By Fig. II it is plain, that the Sun is totally or centrally -eclipsed but to a small part of the Earth at any time; because the dark -conical shadow _e_ of the Moon _M_ falls but on a small part of the -Earth: and that the partial Eclipse is confined at that time to the -space included by the Circle _a 0 b_, of which only one half can be -projected in the Figure, the other half being supposed to be hid by the -convexity of the Earth _E_: and likewise, that no part of the Sun is -eclipsed to the large space _YY_ of the Earth, because the Moon is not -between the Sun and that part of the Earth: and therefore to all that -part the Eclipse is invisible. The Earth turns eastward on its Axis, as -from _g_ to _h_, which is the same way that the Moon’s shadow moves; but -the Moon’s motion is much swifter in her Orbit from _s_ to _t_: and -therefore, altho’ Eclipses of the Sun are of longer duration on account -of the Earth’s motion on its Axis, than they would be if that motion was -stopt, yet in 3 minutes and 13 seconds of time, the Moon’s swifter -motion carries her dark shadow quite over any place that its center -touches at the time of greatest obscuration. The motion of the shadow on -the Earth’s Disc is equal to the Moon’s motion from the Sun, which is -about 30-1/2 minutes of a degree every hour at a mean rate; but so much -of the Moon’s Orbit is equal to 30-1/2 degrees of a great Circle on the -Earth, § 320; and therefore the Moon’s shadow goes 30-1/2 degrees or -1830 geographical miles on the Earth in an hour, or 30-1/2 miles in a -minute, which is almost four times as swift as the motion of a -cannon-ball. - -[Sidenote: PLATE XI. - - Fig. IV. - - Phenomena of the Earth as seen from the Sun or New Moon - at different times of the year.] - -338. As seen from the Sun or Moon, the Earth’s Axis appears differently -inclined every day of the year, on account of keeping its parallelism -throughout its annual course. Let _E_, _D_, _O_, _N_, be the Earth at -the two Equinoxes and the two Solstices; _N S_ its Axis, _N_ the North -Pole, _S_ the South Pole, _Æ Q_ the Equator, _T_ the Tropic of Cancer, -_t_ the Tropick of Capricorn, and _ABC_ the Circumference of the Earth’s -enlightened Disc as seen from the Sun or New Moon at these times. The -Earth’s Axis has the position _NES_ at the vernal Equinox, lying towards -the right hand, as seen from the Sun or New Moon; its Poles _N_ and _S_ -being then in the Circumference of the Disc; and the Equator and all its -parallels seem to be straight lines, because their planes pass through -the observer’s eye looking down upon the Earth from the Sun or Moon -directly over _E_, where the Ecliptic _FG_ intersects the Equator _Æ_. -At the Summer Solstice, the Earth’s Axis has the position _NDS_; and -that part of the Ecliptic _FG_ in which the Moon is then New, touches -the Tropic of Cancer _T_ at _D_. The North Pole _N_ at that time -inclining 23-1/2 degrees towards the Sun, falls so many degrees within -the Earth’s enlightened Disc, because the Sun is then vertical to _D_, -23-1/2 degrees north of the Equator _ÆQ_; and the Equator with all its -parallels seem elliptic curves bending downward, or towards the South -Pole as seen from the Sun: which Pole, together with 23-1/2 degrees all -round it, is hid behind the Disc in the dark Hemisphere of the Earth. At -the autumnal Equinox the Earth’s Axis has the position _NOS_, lying to -the left hand as seen from the Sun or New Moon, which are then vertical -to _O_, where the Ecliptic cuts the Equator _ÆQ_. Both Poles now lie in -the circumference of the Disc, the North Pole just going to disappear -behind it, and the South Pole just entering into it; and the Equator -with all its parallels seem to be straight lines, because their planes -pass through the observer’s eye, as seen from the Sun, and very nearly -so as seen from the Moon. At the Winter Solstice the Earth’s Axis has -the position _NNS_; when its South Pole _S_ inclining 23-1/2 degrees -toward the Sun falls 23-1/2 degrees within the enlightened Disc, as seen -from the Sun or New Moon which are then vertical to the Tropic of -Capricorn _t_, 23-1/2 degrees south of the Equator _ÆQ_; and the Equator -with all its parallels seem elliptic curves bending upward; the North -Pole being as far hid behind the Disc in the dark Hemisphere, as the -South Pole is come into the light. The nearer that any time of the year -is to the Equinoxes or Solstices, the more it partakes of the Phenomena -relating to them. - -[Sidenote: PLATE XI. - - Various positions of the Earth’s Axis, as seen from the Sun - at different times of the year.] - -339. Thus it appears, that from the vernal equinox to the autumnal, the -North Pole is enlightened; and the Equator and all its parallels appear -Semi-ellipses as seen from the Sun, more or less curved as the time is -nearer to or farther from the Summer Solstice; and bending downwards or -towards the South Pole; the reverse of which happens from the autumnal -Equinox to the vernal. A little consideration will be sufficient to -convince the reader, that the Earth’s Axis inclines towards the Sun at -the Summer Solstice; from the Sun at the Winter Solstice; and sidewise -to the Sun at the Equinoxes; but towards the right hand, as seen from -the Sun at the vernal Equinox; and towards the left hand at the -autumnal. From the Winter to the Summer Solstice, the Earth’s Axis -inclines more or less to the right hand, as seen from the Sun; and the -contrary from the Summer to the Winter Solstice. - -[Sidenote: How these positions affect solar Eclipses.] - -340. The different positions of the Earth’s Axis, as seen from the Sun -at different times of the year, affect solar Eclipses greatly with -regard to particular places; yea so far as would make central Eclipses -which fall at one time of the year invisible if they fell at another, -even though the Moon should always change in the Nodes and at the same -hour of the day: of which indefinitely various affections, we shall only -give Examples for the times of the Equinoxes and Solstices. - -[Sidenote: Fig. IV.] - -In the same Diagram, let _FG_ be part of the Ecliptic, and _IK_ _ik_ -_ik_ _ik_ part of the Moon’s Orbit; both seen edgewise, and therefore -projected into right lines; and let the intersections _N_, _O_, _D_, _E_ -be one and the same Node at the above times, when the Earth has the -forementioned different positions; and let the spaces included by the -Circles _P_, _p_, _p_, _p_ be the Penumbra at these times, as its center -is passing over the center of the Earth’s Disc. At the Winter Solstice, -when the Earth’s Axis has the position _NNS_, the center of the Penumbra -_P_ touches the Tropic of Capricorn _t_ in _N_ at the middle of the -general Eclipse; but no part of the Penumbra touches the Tropic of -Cancer _T_. At the Summer Solstice, when the Earth’s Axis has the -position _NDS_ (_iDk_ being then part of the Moon’s Orbit whose Node is -at _D_) the Penumbra _p_ has its center on the Tropic of Cancer _T_ at -the middle of the general Eclipse, and then no part of it touches the -Tropic of Capricorn _t_. At the autumnal Equinox the Earth’s Axis has -the position _NOS_ (_iOk_ being then part of the Moon’s Orbit) and the -Penumbra equally includes part of both Tropics _T_ and _t_ at the middle -of the general Eclipse: at the vernal Equinox it does the same, because -the Earth’s Axis has the position _NES_: But, in the former of these two -last cases, the Penumbra enters the Earth at _A_, north of the Tropic of -Cancer _T_, and leaves it at _m_, south of the Tropic of Capricorn _t_; -having gone over the Earth obliquely southward, as its center described -the line _AOm_: whereas in the latter case the Penumbra touches the -Earth at _n_, south of the Equator _ÆQ_, and describing the line _nEq_ -(similar to the former line _AOm_ in open space) goes obliquely -northward over the Earth, and leaves it at _q_, north of the Equator. - -In all these circumstances, the Moon has been supposed to change at noon -in her descending Node: had she changed in her ascending Node, the -Phenomena would have been as various the contrary way, with respect to -the Penumbra’s going northward or southward over the Earth. But because -the Moon changes at all hours, as often in one Node as the other, and at -all distances from them both at different times as it happens, the -variety of the Phases of Eclipses are almost innumerable, even at the -same places, considering also how variously the same places are situated -on the enlightened Disc of the Earth, with respect to the Penumbra’s -motion, at the different hours that Eclipses happen. - -[Sidenote: How much of the Penumbra falls on the Earth at different - distances from the Nodes.] - -341. When the Moon changes 17 degrees short of her descending Node, the -Penumbra _P_ 18 just touches the northern part of the Earth’s Disc, near -the North Pole _N_; and, as seen from that place the Moon appears to -touch the Sun, but hides no part of him from sight. Had the Change been -as far short of the ascending Node, the Penumbra would have touched the -southern part of the Disc near the South Pole _S_. When the Moon changes -12 degrees short of the descending Node, more than a third part of the -Penumbra _P 12_ falls on the northern parts of the Earth at the middle -of the general Eclipse: had she changed as far past the same Node, as -much of the other side of the Penumbra about _P_ would have fallen on -the southern part of the Earth; all the rest in the _expansum_, or open -space. When the Moon changes 6 degrees from the Node, almost the whole -Penumbra _P6_ falls on the Earth at the middle of the general Eclipse. -And lastly, when the Moon changes in the Node, the Penumbra _PN_ takes -the longest course possible on the Earth’s Disc; its center falling on -the middle thereof, at the middle of the general Eclipse. The farther -the Moon changes from either Node within 17 degrees of it, the shorter -is the Penumbra’s continuance on the Earth, because it goes over a less -portion of the Disc, as is evident by the Figure. - -[Sidenote: The Earth’s diurnal motion lengthens the duration of solar - Eclipses, which fall without the polar Circles.] - -342. The nearer that the Penumbra’s center is to the Equator at the -middle of the general Eclipse, the longer is the duration of the Eclipse -at all those places where it is central; because, the nearer that any -place is to the Equator, the greater is the Circle it describes by the -Earth’s motion on its Axis: and so, the place moving quicker keeps -longer in the Penumbra whose motion is the same way with that of the -place, tho’ faster as has been already mentioned § 337. Thus, (see the -Earth at _D_ and the Penumbra at _12_) whilst the point _b_ in the polar -Circle _abcd_ is carried from _b_ to _c_ by the Earth’s diurnal motion, -the point _d_ on the Tropick of Cancer _T_ is carried a much greater -length from _d_ to _D_: and therefore, if the Penumbra’s center goes one -time over _c_ and another time over _D_, the Penumbra will be longer in -passing over the moving place _d_ than it was in passing over the moving -place _b_. Consequently, central Eclipses about the Poles are of the -shortest duration; and about the Equator of the longest. - -[Sidenote: And shortens the duration of some which fall within these - Circles.] - -343. In the middle of Summer the whole frigid Zone included by the polar -Circle _abcd_ is enlightened; and if it then happens that the Penumbra’s -center goes over the north Pole, the Sun will be eclipsed much the same -number of Digits at _a_ as at _c_; but whilst the Penumbra moves -eastward over _c_ it moves westward over _a_, because with respect to -the Penumbra, the motions of _a_ and _c_ are contrary: for _c_ moves the -same way with the Penumbra towards _d_, but _a_ moves the contrary way -towards _b_; and therefore the Eclipse will be of longer duration at _c_ -than at _a_. At _a_ the Eclipse begins on the Sun’s eastern limb, but at -_c_ on his western: at all places lying without the polar Circles, the -Sun’s Eclipses begin on his western limb, or near it, and end on or near -his eastern. At those places where the Penumbra touches the Earth, the -Eclipse begins with the rising Sun, on the top of his western or -uppermost edge; and at those places where the Penumbra leaves the Earth, -the Eclipse ends with the setting Sun, on the top of his eastern edge -which is then the uppermost, just at its disappearing in the Horizon. - -[Sidenote: The Moon has no Atmosphere.] - -344. If the Moon were surrounded by an Atmosphere of any considerable -Density, it would seem to touch the Sun a little before the Moon made -her appulse to his edge, and we should see a little faintness on that -edge before it were eclipsed by the Moon: But as no such faintness has -been observed, at least so far as I ever heard, it seems plain, that the -Moon has no such Atmosphere as that of the Earth. The faint ring of -light surrounding the Sun in total Eclipses, called by CASSINI _la -Chevelure du Soleil_, seems to be the Atmosphere of the Sun; because it -has been observed to move equally with the Sun, not with the Moon. - -[Sidenote: PLATE XI.] - -345. Having been so prolix concerning Eclipses of the Sun, we shall drop -that subject at present, and proceed to the doctrine of lunar Eclipses; -which, being more simple, may be explained in less time. - -[Sidenote: Eclipses of the Moon. - - Fig. II.] - -That the Moon can never be eclipsed but at the time of her being Full, -and the reason why she is not eclipsed at every Full, have been shewn -already § 316, 317. Let _S_ be the Sun, _E_ the Earth, _RR_ the Earth’s -shadow, and _B_ the Moon in opposition to the Sun: in this situation the -Earth intercepts the Sun’s light in its way to the Moon; and when the -Moon touches the Earth’s shadow at _v_ she begins to be eclipsed on her -eastern limb _x_, and continues eclipsed until her western limb _y_ -leaves the shadow at _w_: at _B_ she is in the middle of the shadow, and -consequently in the middle of the Eclipse. - -[Sidenote: Why the Moon is visible in a total Eclipse.] - -346. The Moon when totally eclipsed, is not invisible if she be above -the Horizon and the Sky be clear; but appears generally of a dusky -colour like tarnished copper, which some have thought to be the Moon’s -native light. But the true cause of her being visible is the scattered -beams of the Sun, bent into the Earth’s shadow by going through the -Atmosphere; which, being more dense near the Earth than at considerable -heights above it, refracts or bends the Sun’s rays more inward § 179, -the nearer they are passing by the Earth’s surface, than those rays -which go through higher parts of the Atmosphere, where it is less dense -according to its height, until it be so thin or rare as to lose its -refractive power. Let the Circle _fghi_, concentric to the Earth, -include the Atmosphere whose refractive power vanishes at the heights -_f_ and _i_; so that the rays _Wfw_ and _Viv_ go on straight without -suffering the least refraction: But all those rays which enter the -Atmosphere between _f_ and _k_, and between _i_ and _l_, on opposite -sides of the Earth, are gradually more bent inward as they go through a -greater portion of the Atmosphere, until the rays _Wk_ and _Vl_, -touching the Earth at _m_ and _n_, are bent so as to meet at _q_, a -little short of the Moon; and therefore the dark shadow of the Earth is -contained in the space _moqpn_ where none of the Sun’s rays can enter: -all the rest _RR_, being mixed by the scattered rays which are refracted -as above, is in some measure enlightened by them; and some of those rays -falling on the Moon give her the colour of tarnished copper, or of iron -almost red hot. So that if the Earth had no Atmosphere, the Moon would -be as invisible in total Eclipses as she is when New. If the Moon were -so near the Earth as to go into its dark shadow, suppose about _po_, she -would be invisible during her stay in it; but visible before and after -in the fainter shadow _RR_. - -[Sidenote: PLATE XI. - - Why the Sun and Moon are sometimes visible when the Moon is - totally eclipsed.] - -347. When the Moon goes through the center of the Earth’s shadow she is -directly opposite to the Sun: yet the Moon has been often seen totally -eclipsed in the Horizon when the Sun was also visible in the opposite -part of it: for, the horizontal refraction being almost 34 minutes of a -degree § 181, and the diameter of the Sun and Moon being each at a mean -state but 32 minutes, the refraction causes both Luminaries to appear -above the Horizon when they are really below it § 179. - -[Sidenote: Fig. V. - - Duration of central Eclipses of the Moon.] - -348. When the Moon is Full at 12 degrees from either of her Nodes, she -just touches the Earth’s shadow but enters not into it. Let _GH_ be the -Ecliptic, _ef_ the Moon’s Orbit where she is 12 degrees from the Node at -her Full; _cd_ her Orbit where she is 6 degrees from the Node, _ab_ her -Orbit where she is Full in the Node, _AB_ the Earth’s shadow, and _M_ -the Moon. When the Moon describes the line _ef_ she just touches the -shadow but does not enter into it; when she describes the line _cd_ she -is totally though not centrally immersed in the shadow; and when she -describes the line _ab_ she passes by the Node at _M_ in the center of -the shadow, and takes the longest line possible, which is a diameter, -through it: and such an Eclipse being both total and central is of the -longest duration, namely, 3 hours 57 minutes 6 seconds from the -beginning to the end, if the Moon be at her greatest distance from the -Earth: and 3 hours 37 minutes 26 seconds, if she be at her least -distance. The reason of this difference is, that when the Moon is -farthest from the Earth she moves slowest; and when nearest to it, -quickest. - -[Sidenote: Digits.] - -349. The Moon’s diameter, as well as the Sun’s, is supposed to be -divided into twelve equal parts called _Digits_; and so many of these -parts as are darkened by the Earth’s shadow, so many Digits is the Moon -eclipsed. All that the Moon is eclipsed above 12 Digits, shew how far -the shadow of the Earth is over the body of the Moon, on that edge to -which she is nearest at the middle of the Eclipse. - -[Sidenote: Why the beginning and end of a lunar Eclipse is so difficult - to be determined by observation.] - -350. It is difficult to observe exactly either the beginning or ending -of a lunar Eclipse, even with a good Telescope; because the Earth’s -shadow is so faint, and ill defined about the edges, that when the Moon -is either just touching or leaving it, the obscuration of her limb is -scarce sensible; and therefore the nicest observers can hardly be -certain to four or five seconds of time. But both the beginning and -ending of solar Eclipses are visibly instantaneous; for the moment that -the edge of the Moon’s Disc touches the Sun’s, his roundness seems a -little broke on that part; and the moment she leaves it he appears -perfectly round again. - -[Sidenote: The use of Eclipses in Astronomy, Geography, and Chronology.] - -351. In Astronomy, Eclipses of the Moon are of great use for -ascertaining the periods of her motions; especially such Eclipses as are -observed to be alike in all circumstances, and have long intervals of -time between them. In Geography, the Longitudes of places are found by -Eclipses, as already shewn in the eleventh chapter: but for this purpose -Eclipses of the Moon are more useful than those of the Sun, because they -are more frequently visible, and the same lunar Eclipse is of equal -largeness and duration at all places where it is seen. In Chronology, -both solar and lunar Eclipses serve to determine exactly the time of any -past event: for there are so many particulars observable in every -Eclipse, with respect to its quantity, the places where it is visible -(if of the Sun) and the time of the day or night; that ’tis impossible -there can be two Eclipses in the course of many ages which are alike in -all circumstances. - -[Sidenote: The darkness at our SAVIOUR’s crucifixion supernatural.] - -352. From the above explanation of the doctrine of Eclipses it is -evident, that the darkness at our SAVIOUR’s crucifixion was -supernatural. For he suffered on the next day after eating his last -Passover-Supper, on which day it was impossible that the Moon’s shadow -could fall on the Earth, for the _Jews_ kept the Passover at the time of -Full Moon: nor does the darkness in total Eclipses of the Sun last four -minutes in any place § 333, whereas the darkness at the crucifixion -lasted three hours, _Matt._ xxviii. 15. and overspread at least all the -land of _Judea_. - - - - - CHAP. XIX. - - _The Calculation of New and Full Moons and Eclipses. The geometrical - Construction of Solar and Lunar Eclipses. The examination of antient - Eclipses._ - - -353. To construct an Eclipse of the Sun, we must collect these ten -Elements or Requisites from the following Astronomical Tables. - -[Sidenote: Requisites for a solar Eclipse.] - -I. The true time of conjunction of the Sun and Moon: to know at what -conjunctions the Sun must be eclipsed; and to the times of those -conjunctions, - -II. The Moon’s horizontal parallax, or angle which the semi-diameter of -the Earth subtends as seen from the Moon. - -III. The Sun’s true place, and distance from the solstitial colure to -which he is then nearest, either in coming to it or going from it. - -IV. The Sun’s declination. - -V. The angle of the Moon’s visible path with the Ecliptic. - -VI. The Moon’s Latitude or Declination from the Ecliptic. - -VII. The Moon’s true hourly motion from the Sun. - -VIII. The Angle of the Sun’s semi-diameter as seen from the Earth. - -IX. The Angle of the Moon’s semi-diameter as seen from the Earth. - -X. The semi-diameter of the Penumbra. - - -And for an Eclipse of the Moon, the following Elements. - -[Sidenote: Requisites for a lunar Eclipse.] - -I. The true time of opposition of the Sun and Moon; and for that time, - -II. The Moon’s horizontal parallax. - -III. The Sun’s semi-diameter. - -IV. The semi-diameter of the Earth’s shadow. - -V. The Moon’s semi-diameter. - -VI. The Moon’s Latitude. - -VII. The Moon’s true hourly motion from the Sun. - -VIII. The Angle of the Moon’s visible path with the Ecliptic. - - -These Elements are easily found from the following Tables and Precepts, -by the common Rules of Arithmetic. - - -_Note_, 60 minutes make a Degree, 30 degrees a Sign, and 12 Signs a -Circle. A Sign is marked thus ^s, a Degree thus °, and a Minute thus ʹ. - -When you exceed 12 Signs, always reject them and set down the remainder. -When the number of Signs to be subtracted is greater than the number you -subtract from, add 12 Signs to that which you subtract from; and then -you will have a remainder to set down. - -[Sidenote: How the Signs are reckoned.] - -354. As we fix arbitrarily upon the beginning of the Sign _Aries_ to -reckon from, when we speak of the places of the Sun, Moon, and Nodes; we -call _Aries_ 0 Signs, _Taurus_ 1 Sign, _Gemini_ 2 Signs, _Cancer_ 3 -Signs, _&c._ So, when the Sun is in the 10th degree of Aries, we say his -Place or Longitude is 0 Signs 10 Degrees, because he is only 10 Degrees -from the beginning of Aries: if he is in the 5th, 10th, _&c._ Degree of -Taurus, we say his Place or Longitude is 1 Sign, 5, 10, _&c._ Degrees: -and so on, till he comes quite round again. But in reckoning the -Anomalies of the Sun and Moon, and their distance from the Nodes, we -only consider the number of Signs and Degrees the Luminaries are gone -past their Apogee or Nodes; not how far they have to go to these points, -were the distance ever so little. The Sun, Moon, and Apogee move -according to the order of Signs, but the Nodes contrary. We shall now -give the Precepts and Examples for the above Requisites in their due -order. - - - _To calculate the time of New and Full Moon._ - -[Sidenote: First Element or Requisite.] - -355. PRECEPT I. For any proposed year in the 18th Century, take out the -mean time of the New Moon in _March_ from Table I., and the mean time of -Full Moon from Table III., for the _Old Stile_; or from Tables II and IV -for _New Stile_; with the mean Anomalies of the Sun and Moon for these -times, and set them by themselves. Then, from Table VI, take out as many -Lunations as the proposed Month is after _March_, with the days, hours, -and minutes belonging to them; and also the mean Anomalies of the Sun -and Moon for these Lunations. - -II. Add the days, hours, and minutes of these Lunations to the time of -New or Full Moon in _March_, and the Anomalies for the Lunations to the -Anomalies for _March_: the sums give the hours and minutes of the mean -New or Full Moon required, and the mean Anomalies of the Sun and Moon -for that time. - -III. Then, with the number of days enter Table VII, under the given -Month, and right against this number, in the left hand column you have -the day of New or Full Moon; which set before the hours and minutes -above-mentioned. - -IV. But, (as it will sometimes happen) if the number of days fall short -of all those under the given Month, add one Lunation with its Anomalies -from Table VI to the foresaid sums; so you will have a new sum of days -wherewith to enter the 7th Table under the given Month, where you are -sure to find that sum the second time, if the first falls short. - -V. With the Signs and Degrees of the Sun’s Anomaly enter Table VIII, -_The Moon’s annual Equation_, and take out the minutes of time of that -Equation by the Anomaly; remembring, that if the Signs are at the head -of the Table, the degrees are at the left hand, in which case the -Equation found in the Angle of meeting must be subtracted from the mean -time of New or Full Moon, as the title _Subtract_, at the head of the -Table directs: but if the Signs are at the foot of the Table their -degrees are in the right-hand column, and the Equation where the Signs -and Degrees meet in the Table is to be added to the mean time, as the -title _Add_, at the foot of the Table directs; which Equation, so -applied, gives the mean time of New or Full Moon corrected. - -VI. With the Signs and Degrees of the Sun’s Anomaly enter Table IX, -_Equation of the Moon’s mean Anomaly_, and take out the Equation -thereof; adding it to the mean Anomaly or subtracting it therefrom, as -the titles at the head or foot of the Table direct; and it gives the -mean Anomaly corrected. Then, with the Sun’s Anomaly enter Table XII, -_Equation of the Sun’s mean Place_, and take out that Equation, applying -it to the Moon’s corrected Anomaly as the titles direct; and it will -give the Moon’s Anomaly equated[77]. _N. B._ In all these Equations, -care must be taken to make proper allowance for the odd minutes of -Anomaly; the Tables having the Equations only for compleat Degrees. - -VII. With the Moon’s equated Anomaly enter Table X, _The Moon’s elliptic -Equation_, and take out that Equation in the same manner as the -preceding: adding it to the former corrected time if the Signs be at the -head of the Table, or subtracting it if they be at the foot, as the -Table directs; and this gives the mean time equated. - -VIII. Lastly, enter Table XI, _The Sun’s Equation at New and Full Moon_, -with the Sun’s Anomaly, and take out the Sun’s Equation in the same -manner as the others; adding it to, or subtracting it from the former -equated time, as the titles direct: and by this last Equation you have -the true time of New or Full Moon, agreeing with well regulated Clocks -and Watches. But to make it agree with true Sun-Dials, the Equation of -time must be applied as taught § 225. - - - EXAMPLE I. - - _To find the time of New Moon in_ April 1764, _N. S._ - - +------------------------------------+----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +----------+-------------+-------------+ - | Tab. II. Mean time of New Moon | | | | - | in _March_ | 2 8 57 | 8 2 23 | 10 13 32 | - | Add, for Lunation, from Tab. VI. | 29 12 44 | 0 29 6 | 0 25 49 | - | | -------- | ---------- | ---------- | - | Mean New Moon and Anomaly | 31 21 41 | 0 1 29 | 11 9 21 | - | To which Time add the Moon’s | +-------------+ | - | Ann. Equ. Tab. VIII. | + 0 22 | Equ. Moon’s Anom. - 20 | - | And it gives the Mean time | -------- | ---------- | - | corrected | 31 22 3 | Anom. cor. 11 9 1 | - | From which subtract the Moon’s | | Sun’s Equat. + 1 56 | - | elliptic Equ. Tab. X. | - 3 10 | ---------- | - | | -------- | Moon’s Ano. 11 10 57 | - | And it gives the Mean time equated | 31 18 53 +---------------------------+ - | To which add the Sun’s Equation, | | h. m. | - | Tab. XI. | + 3 32 | Moon’s ann. Equ. 0 22 add | - | And it gives the true time | -------- | Her ellipt. Equ. 3 10 sub.| - | of Conjunction | 31 22 25 | Sun’s Equation 3 32 add | - | +----------+---------------------------+ - | | - | Which true time answers to the first of _April_, at 25 minutes past 10 in | - | the forenoon: for, as the Astronomical Day begins at Noon, then 22 | - | hours 25 min. after the Noon of _March 31_, is _April 1_, at 10 hours | - | 25 min. in the Forenoon. | - +---------------------------------------------------------------------------+ - - - EXAMPLE II. - - _To find the time of Full Moon in_ May 1761, _N. S._ - - +------------------------------------+----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +----------+-------------+-------------+ - | Mean time of Full Moon in _March_ | 20 12 9 | 8 20 2 | 9 1 13 | - | Add, for two Lunations | 59 1 28 | 1 28 13 | 1 21 38 | - | | -------- | ---------- | ---------- | - | The several sums are | 79 13 37 | 10 18 15 | 10 22 51 | - | +----------+-------------+ | - | The days, in Tab. VII, answer to | | Equ. Moon’s Anom. - 13 | - | _May 18_ | 18 13 37 | ---------- | - | Moon’s annual Equation add | + 14 | Anom. cor. 10 22 38 | - | | -------- | Sun’s Equat. + 1 15 | - | Mean time corrected | 18 13 51 | ---------- | - | Moon’s elliptic Equation subtract | - 5 38 | Moon’s Ano. 10 23 53 | - | | -------- +---------------------------+ - | Mean time equated | 18 8 13 | h. m. | - | Sun’s Equation add | + 2 19 | Moon’s ann. Equ. 0 14 add | - | | -------- | Her ellipt. Equ. 5 38 sub.| - | True time of Opposition, _May_ | 18 10 32 | Sun’s Equation 2 19 add | - | +----------+---------------------------+ - | Namely, the 18th day, at 32 minutes past 10 at night. | - +---------------------------------------------------------------------------+ - -The Leap-years are allowed for in the Tables, so as to give no Trouble -in these Calculations. - -_To compute the time of New and Full Moon in a given year and month, of -any particular Century, between the Christian Æra[78] and 18th Century._ - -PRECEPT I. Find the like year of the 18th Century in Table I., for New -Moon, or Table III., for Full Moon; and take out the New or Full Moon in -_March_ for that year, with the Anomalies of the Sun and Moon. - -II. From Table V, take as many compleat Centuries, as when subtracted -from the above year of the 18th Century, will answer to the given year; -and take out the Conjunctions and Anomalies of these Centuries. - -III. Subtract the Conjunctions and Anomalies of these Centuries from -those of the New or Full Moon in _March_ above taken out, and the -remainders will shew the mean time of New or Full Moon in _March_ the -given year, with the Anomalies of the Sun and Moon at that time. Then, -work in all respects for the true time of the proposed New or Full Moon, -as taught by the Precepts already given § 355. - - - EXAMPLE I. - - _To find the time of New Moon in_ July 1581, _O. S._ - -From 1781 subtract 200 years, and there remains 1581. - - +-----------------------------------+-----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +-----------+-------------+-------------+ - | Table I. Mean time of New Moon | | | | - | in _March 1781_ | 13 7 52 | 8 23 37 | 0 0 53 | - | Tab. V. Conj. and Anom. for 200 | | | | - | years subtract | 8 16 22 | 0 6 42 | 5 0 44 | - | | --------- | ---------- | ---------- | - | Remain the Conj. and Anom. for | | | | - | _March 1581_ | 4 15 30 | 8 16 55 | 7 0 9 | - | Tab. VI. Add, for five Lunations, | | | | - | to bring it to _July_ | 147 15 40 | 4 25 32 | 4 9 5 | - | | --------- | ---------- | ---------- | - | The sums are | 152 7 10 | 1 12 27 | 11 9 14 | - | +-----------+-------------+ | - | The Days in Tab. VII. answer | | Equ. Moon’s Anom. + 13 | - | to _July_ 30th | 30 7 10 | ----------- | - | Sum of the three Equations | | Anom. cor. 11 9 27 | - | subtract | - 7 9 | Sun’s Equat. - 1 16 | - | | --------- | ----------- | - |True time of Conjunction, _July_ | 30 0 1 | Moon’s Ano. 11 8 11 | - | +-----+-----+---------------------------+ - | Which is the 30th day, at one minute | Moon’s ann. Eq. 0^h 14^m sub. | - | past noon, as shewn by well | Her ellipt. Equ. 3 35 sub. | - | regulated Clocks or Watches | Sun’s Equation 3 20 sub. | - | | ------------- | - | | Sum 7 9 sub. | - +-----------------------------------------+---------------------------------+ - - - EXAMPLE II. - - _To find the time of Full Moon in_ April _A. D. 30, O. S._ - - From 1730 subtract 1700, and there remains 30. - - +------------------------------------+----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +----------+-------------+-------------+ - | Tab. III. Mean time of Full Moon | | | | - | in _March 1730_ | 22 6 58 | 9 2 40 | 3 13 23 | - | Tab. V. Conj. and Anom. for 1700 | | | | - | years subtract | 14 17 37 | 11 28 46 | 10 29 36 | - | | -------- | ---------- | ---------- | - | Rem. the Opposition and Anom. in | | | | - | _March_ A. D. 30 | 7 13 21 | 9 3 54 | 4 13 47 | - | Tab. V. Add, for one Lunation, to | | | | - | bring it into _April_ | 29 12 44 | 0 29 6 | 0 25 49 | - | | -------- | ---------- | ---------- | - | The sums are | 37 2 5 | 10 3 0 | 5 9 36 | - | +----------+-------------+ | - | The Days in Tab. VII. answer to | | Equ. Moon’s Anom. - 17 | - | _April 6_ | 6 2 5 | ---------- | - | To which add the sum of the three | | Anom. cor. 5 9 19 | - | Equations | 6 1 | Sun’s Equat. + 1 35 | - | | -------- | ---------- | - | True time of Opposition | | Moon’s Ano. 5 10 54 | - | _April_ A. D. 30 | 6 8 6 | | - | +-----+----+---------------------------+ - | Which is the 6th day, at 6 minutes past | Moon’s ann. Eq. 0^h 18^m add | - | 8 in the Evening. And thus, the time | Her ellipt. Equ. 2 46 add | - | of New or Full Moon may be found for | Sun’s Equat. 2 57 add | - | any given year and month after the | ------------- | - | Christian Æra. | Sum 6 1 add | - +------------------------------------------+--------------------------------+ - -[Sidenote: Remark.] - -_N. B._ Sometimes it happens that the days annexed to the Centuries in -Table V are more in number than the days on which the New or Full Moon -happens in _March_ the year of the 18th Century, with which the -computation begins; as in the third following Example, _viz._ for the -Full Moon in _March_ the year before CHRIST 721: in which case, a -Lunation and it’s Anomalies must be added, from Table VI, to the days -and Anomalies of the New or Full Moon in _March_; and then, subtraction -can be made: and having gained a remainder, work in all respects as -taught in § 355. - - -_To find the time of New or Full Moon in any given year and month before - the Christian Æra._ - -356. PRECEPT I. Find a year of the 18th Century, which added to the -given number of years before CHRIST, diminished by one, shall make a -number of whole Centuries. - -II. Find this number of Centuries in Table V, and subtract the Time and -Anomalies answering to it from the Time and Anomalies answering to the -mean New or Full Moon in _March_ the year of the 18th Century thus -found; and they will give the mean time of New or Full Moon in _March_ -the given year before CHRIST, with the Anomalies answering thereto. -Whence the true time of that New or Full Moon may be had by the Precepts -already delivered § 355. - -III. The Tables are calculated for the Meridian of _London_: therefore, -in computing for any place westward of _London_, four minutes of time -must be subtracted from the time shewn by the Tables, for every degree -the place is westward; and added for every degree it is eastward. See § -210. - - - EXAMPLE I. - - _To find the time of New Moon at_ London _and_ Athens _in_ March, _the - year before Christ 424._ - - The years 423 added to 1777 make 2200, or 22 Centuries. - - +------------------------------------+----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +----------+-------------+-------------+ - | Tab. I. Mean New Moon in _March_ | | | | - | A. D. 1777 | 27 7 53 | 9 7 27 | 5 25 51 | - | From which subtract 2200 years | | | | - | in Tab. V. | 6 21 47 | 11 16 26 | 4 20 37 | - | | -------- | ---------- | ---------- | - | Mean Conj. and Anom. in _March_ | | | | - | before Chr. 424 | 20 10 6 | 9 21 1 | 1 5 14 | - | Which with, the total of the three | +-------------+ | - | Equations added | 9 20 | Equ. Moon’s Anom. - 19 | - | | -------- | ---------- | - | Gives the true time of Conjunction | 20 19 26 | Anom. cor. 1 4 55 | - | +----------+ Sun’s Equat. + 1 48 | - | Which was the 21st day of _March_, at | --------- | - | 26 minutes past 7 in the morning at | Moon’s Ano. 1 6 43 | - | _London_: and if 1 hour 35 minutes +---+---------------------------+ - | be added for _Athens_, which is 23° 52ʹ | Moon’s ann. Eq. 0^h 20^m add | - | east of the meridian of _London_, we | Her ellipt. Equ. 5 43 add | - | have the time at _Athens_; namely, | Sun’s Equation 3 17 add | - | 1 minute past 9 in the morning. | Total 9 20 add | - +-------------------------------------------+-------------------------------+ - - - EXAMPLE II. - - _To find the time of Full Moon in_ October, _the year before Christ - 4030_. - - The years 1771 added to 4029 make 5800, or 58 Centuries. - - +-----------------------------------+-----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +-----------+-------------+-------------+ - | Tab. III. From the mean Full Moon | | | | - | in _March 1771_ | 19 7 11 | 8 29 6 | 7 22 30 | - | +-----------+-------------+-------------+ - | Tab. V. Subtr. the numbers for | | | | - | 5800 years { 5000 | 10 7 56 | 10 23 56 | 0 17 36 | - | { 800 | 5 4 43 | 11 27 43 | 7 7 7 | - | | --------- | ---------- | ---------- | - | Which collected make | 15 12 39 | 10 21 39 | 7 24 43 | - | | --------- | ---------- | ---------- | - | Rem. the mean Full Moon _&c._ | | | | - | _March_ before Chr. 4030 | 3 18 32 | 10 7 27 | 11 27 47 | - | To which add eight Lunations to | | | | - | carry it to _October_ | 236 5 52 | 7 22 50 | 6 26 32 | - | | --------- | ---------- | ---------- | - | And the several sums will be | 240 0 24 | 6 0 17 | 6 24 19 | - | +-----------+-------------+-------------+ - | Which, for Full Moon day, | | | - | Tab. VII, is _October 26_ | 26 0 24 | h. m. | - | Moon’s ellipt. Equation subtr. | | | - | there being none besides | 3 28 | Moon’s Ann. Eq. 0 0 add | - | | --------- | Moon’s ellipt. | - | Rem. the true time of Full Moon, | | Eq. 3 28 sub. | - | _October_ | 25 20 56 | Sun’s Equation 0 0 add | - | +-----------+ --------- | - | Which is the 26th day, at 8 hours | Total 3 28 sub. | - | 26 minutes in the forenoon[79]. | | - +-----------------------------------------------+---------------------------+ - -[Sidenote: Age of the world uncertain.] - -By the method prescribed § 248 it will be found, that the Autumnal -Equinox in the year before CHRIST 4030, fell on the 26th of _October_; -as this Example shews the Full Moon to have been on the same day: and by -working as hereafter taught, it will appear that the Dominical Letter -was then _G_, which shews the 26th of _that October_ to have been on a -_Friday_; namely our sixth day of the week, but the _Ante-Mosaic_ fifth -day. And as, according to _Genesis_, chap. i. ver. 14. the Sun and Moon -were created on the fourth day of the week, those who are of opinion -that the world was made at the time of the Autumnal Equinox, and that -the Moon at her first appearance was in full lustre, opposite to the -Sun, or nearly so, may perhaps look upon this as a Criterion for -ascertaining the year of the creation; since it shews the Moon to have -been Full the next day after she was made: and this is only 9 years -sooner than _Rheinholt_ makes it, and 11 years later than according to -_Lange_. Whereas, they who maintain that the world was created in the -4007th year before CHRIST, with the Sun on the Autumnal Equinoctial -Point, _October 26_, and the Moon then Full; will find, if they compute -by the best Tables extant, that the Moon was New, instead of being Full, -on that day. - -If it could be proved from the writings of _Moses_ that the Sun was -created on the point of the Autumnal Equinox, and the Moon in -opposition; as well as it can be proved that these Luminaries were made -(or according to some, did not shine out till) on the fourth day of the -creation-week, there would be _Data_ enough for ascertaining the age of -the world: for supposing the Moon to have been Full on an Equinoctial -Day, which was the fourth day of the week, it would require many -thousands of years to bring these three characters together again. For, -the soonest in which the Moon returns to be New or Full on the same days -of the Months as before, is 19 years wanting an hour and half, but then -the days of the week return not to the same days of the months in less -than 28 years, in which time the Moon has gone through one Course of -Lunations, and 9 years over; therefore a co-incidence of the Full Moon -and day of the Week and Month cannot happen in that time, and if we -multiply 19 by 28, which is the nearest co-incidence of these three -characters, namely 532 years; the Moon’s falling back an hour and half -every 19 years will amount to 42 hours in so many years; and the Equinox -will have anticipated five days. From all which we may venture to say, -that 200000 years would not be sufficient to bring all these -circumstances together again. - - - EXAMPLE III. - -_To find the time of Full Moon at_ Babylon _in_ March, _the year before - Christ 721_. - - The years 720 added to 1780 make 2500, or 25 Centuries. - - +------------------------------------+----------+-------------+-------------+ - | | | Sun’s Anom. | Moon’s Ano. | - | | D. H. M. +-------------+-------------+ - | | | s ° ʹ | s ° ʹ | - | +----------+-------------+-------------+ - | Tab. I. To the mean F. Moon and | | | | - | Anom. in _Mar. 1780_ | 9 4 41 | 8 19 48 | 7 8 10 | - | Add one Lunation and it’s | | | | - | Anomalies from Tab. VI[80] | 29 12 44 | 0 29 6 | 0 25 49 | - | | -------- | ---------- | ---------- | - | The several sums are | 38 17 25 | 9 18 54 | 8 3 59 | - | Fr. which subt. the Days & Anom. | | | | - | of 2500 years, Tab. V | 19 22 20 | 11 26 19 | 6 6 43 | - | | -------- | --------- | ---------- | - | Rem. the mean time and Anom. of | | | | - | F.M. in _Mar. b.C. 721_ | 18 19 5 | 9 22 25 | 1 27 16 | - | To which add the sum of the | +-------------+ | - | three Equations | + 11 36 | Equ. Moon’s Anom. - 18 | - | | -------- | Anom. cor. 1 26 48 | - | And it gives the true time of | | Sun’s Equat. + 1 47 | - | Full Moon, _Mar. b.C. 721_ | 18 6 41 | ---------- | - | +------+---+ Moon’s Anom. 1 28 35 | - | Which was the 19th day, at 41 minutes +-------------------------------+ - | past 6 in the evening, at _London_; | Moon’s ann. Eq. 0^h 20^m add | - | to which time, if[81] 2 hours 51 | Her ellipt. Equ. 8 1 add | - | minutes be added, we shall have | Sun’s Equation 3 15 add | - | the time at _Babylon_, namely, | Sum 11 36 add | - | 9 hours 51 minutes. | | - +-------------------------------------------+-------------------------------+ - -357. To know whether the Sun will be eclipsed or no, at the time of any -given New Moon; collect the Sun’s distance from the Node at that time, -and if it be less than 17 degrees he will be eclipsed, otherwise not. - - - EXAMPLE. - - _For the time of New Moon in_ April 1764. - - Sun from Node - s ° ʹ -Table II, mean New Moon in _March 1764, New Stile_, 11 4 57 -Table VI, add for 1 Lunation to carry it to _April_ 1 0 40 - -------- -Sun’s distance from the Node at New Moon in _April_ 0 5 37 - -------- - -Which, being within the above limit, the Sun must be eclipsed: and -therefore, we proceed to find the rest of the Elements for computing -this Eclipse. - - - _To find the Moons Horizontal Parallax, or the Angle of the Earth’s - semi-diameter as seen from the Moon._ - -[Sidenote: Second Element.] - -358. PRECEPT. Having found the Moon’s mean Anomaly for the above time, -by the first and second Precepts of § 355, enter the XVth Table with the -signs and degrees of that Anomaly, and thereby take out the Moon’s -Horizontal Parallax: only note, that this is given but to every 6th -degree of Anomaly in the Table, because it is very easy to make proper -allowance by sight. So the Moon’s Horizontal Parallax _April_ the 1st -1764, at 10 hours 25 minutes in the Forenoon, answering to her mean -Anomaly at that time (namely 11^s 9° 21ʹ) is 55ʹ 7ʺ; which, diminished -by 10ʺ, the Sun’s constant Horizontal Parallax, gives for the -semi-diameter of the Earth’s Disc 54ʹ 57ʺ. - - - _To find the Sun’s true Place, and his distance from the nearest - Solstice._ - -[Sidenote: Third Element.] - -359. PRECEPT I. We are to consider, that the beginning of Aries and of -Libra, which are the Equinoctial Points, are equidistant from the -beginning of Cancer and of Capricorn, which are the Solstitial Points. -Hence, when we know in what Sign and Degree the Sun is, we can easily -find his distance from the nearest Solstice. Now, to find the Sun’s -Place, or Longitude from Aries, _April_ the 1st, 1764, at 10 hours 21 -minutes in the Forenoon; being the equated time of New Moon. - -PRECEPT II. This being to the time of New Moon, take out the Sun’s mean -Place and Anomaly from Table II. for that time, and the Equation of his -mean Place from Table XII by his Anomaly; adding the Equation to his -mean Place or subtracting it from the same, as the Table directs, will -give his true Place. - - - EXAMPLE. - - +----------------------------------------------+-------------+------------+ - | | Sun’s Long. | Sun’s mean | - | | from Aries. | Anomaly. | - | +-------------+------------+ - | | s ° ʹ | s ° ʹ | - | Table I. To the Sun’s mean Place and +-------------+------------+ - | Anomaly at the mean time of New Moon | | | - | in _March 1764_, N. S. | 11 17 7 | 8 2 23 | - | Add the same from Tab. VI. for one Lunation, | | | - | to carry it to _April_ | 0 29 6 | 0 29 6 | - | | --------- | ---------- | - | Mean Place and Anomaly at the time of New | | | - | Moon in _April_ | 0 10 13 | 9 1 29 | - | To which place add the Sun’s Equation | +------------+ - | from Tab. XII. | 1 56 | Equal | - | | --------- | 1° 56ʹ | - | And it gives the Sun’s true place | 0 12 9 | Additive. | - | +-------------+------------+ - | Which is Aries 12° 9ʹ; and this, when taken from three Signs, or the | - | beginning of Cancer, leaves 2 signs 17 deg. 51 min., or 77° 51ʹ for | - | the Sun’s distance from the then nearest Solstice. | - +-------------------------------------------------------------------------+ - -360. But because the Sun’s true Place is often wanted when the Moon is -neither New nor Full, we shall next shew how it may be found for any -given moment of time: though this be digressing from our present -purpose. - - -In Table XVI find the nearest lesser year to that in which the Sun’s -Place is sought; and take out the Sun’s mean Longitude and Anomaly -answering thereto; to which add his mean motion and Anomaly for the -compleat residue of the years, with the month, day, hour, and minute, -all taken from the same Table, and you have the Sun’s mean Longitude and -Anomaly for the given time. Then, from Table XII take out the Sun’s -Equation by means of his Anomaly (making proportions for the odd minutes -of Anomaly) which Equation being added to or subtracted from the Sun’s -mean Longitude from Aries, as the titles in the Table direct, gives his -true Place, or Longitude from the beginning of Aries, reckoned according -to the order of the Signs § 354. - - - EXAMPLE. - -_To find the Sun’s true Place_ April _30th, A. D. 1757, at 18 minutes 40 - seconds past 10 in the morning_. - - +---------------------------------------------+-------------+-------------+ - | | Sun’s Long. | Sun’s Anom. | - | The year next less than 1757 in the Table +-------------+-------------+ - | is 1753, at the beginning of which, the | s ° ʹ ʺ | s ° ʹ | - | Sun’s mean Longitude from the beginning +-------------+-------------+ - | of Aries, and his mean Anomaly, is | 9 10 16 52 | 6 1 38 | - | To which add his mean Mot. and Anom. for | | | - | four years to make 1757 | 0 0 1 49 | 11 29 58 | - | { _April_ | 2 28 42 30 | 2 28 42 | - | { days 29 | 0 28 35 2 | 0 28 35 | - | And likewise his mean Mot. and { hours 22 | 0 54 13 | 0 54 | - | Anom. for { min. 18 | 0 44 | 1 | - | { sec. 49 | 2 | 0 | - | | ----------- |-------------+ - | Sun’s mean Longitude and Anomaly for the | | | - | given time is | 1 8 31 12 | 9 29 48 | - | To which add the Equation of the Sun’s | | | - | mean Place | 1 40 14 +-------------+ - | | ----------- | Sun’s Eq. | - | And it gives his true Place, _viz._ | | 1° 40ʹ 14ʺ | - | ♉ Taurus 10° 11ʹ 26ʺ | 1 10 11 26 | | - +---------------------------------------------+-------------+-------------+ - -N. B. _In leap-years after_ February, _the Sun’s mean Motion and Anomaly -must be taken out for the day next after the given one._ - -361. _To calculate the Sun’s true Place for any time in a given year -before the first year of_ CHRIST: subtract the mean Motions and -Anomalies for the compleat hundreds next above the given year; to the -remainder add those for the residue of years, months, _&c._ and then -work in all respects as above taught. - - - EXAMPLE. - -_To find the Suns true Place_ May _the 28th at 4 hours 3 min. 42 sec. in - the afternoon, the year before Christ 585, which was a Leap year_[82]. - - +---------------------------------------------+-------------+-------------+ - | | Sun’s Long. | Sun’s Anom. | - | +-------------+-------------+ - | | s ° ʹ ʺ | s ° ʹ | - | From the Sun’s mean Longitude and Anomaly +-------------+-------------+ - | at the beginning of the year Christ 1 | 9 7 53 10 | 6 29 54 | - | Subtract his mean Motion and Anomaly for | | | - | 600 years | 0 4 32 0 | 11 24 2 | - | + ----------- | ---------- | - | And the remainder, or radix, is | 9 3 21 10 | 7 5 52 | - | To which add what 585 wants of 600, | | | - | _viz._ 15 years | 11 29 22 27 | 11 29 7 | - | { _May_ | 3 28 16 40 | 3 28 17 | - | { days 28 Bissextile | 0 28 35 2 | 0 28 35 | - | And also those of { hours 4 | 0 9 51 | 0 10 | - | { min. 3 | 0 7 | ---------- | - | { sec. 42 | 2 | 0 2 1 | - | | ----------- | Sun’s Anom. | - | Sun’s mean Long. _May_ 28th, at 4 hour | +-------------+ - | 3 min. 24 sec. afternoon | 1 29 45 19 | | - | Equation of the Sun’s mean Place subtract | 2 2 | 2ʹ 22ʺ | - | | ----------- | Sun’s Equat.| - | Rem. his true Place for the same time, | | subtract. | - | _viz._ ♉ Taurus 29° 43ʹ 17ʺ | 1 29 43 17 | | - +---------------------------------------------+-------------+-------------+ - -_N. B._ As the Longitudes or Places of all the visible Stars in the -Heavens are well known, we have an easy method of finding the Sun’s true -Place in the Ecliptic: for the Sun is directly opposite to that Point of -the Ecliptic which comes to the Meridian at mid-night. - - - _To find the Sun’s Declination._ - -[Sidenote: Fourth Element.] - -362. PRECEPT. Enter Table XVII with the Signs and Degrees of the Sun’s -Place; and making proportions, take out his Declination answering -thereto. If the Signs are at the head of the Table, the Degrees are at -the left hand; but if the Signs are at the foot of the Table, the -Degrees are at the right hand. So, the Sun’s Declination answering to -his true Place (found by § 359 to be 0^s 12° 9ʹ) is 4 degrees 48 minutes -54 seconds, making allowance for the 9ʹ that his Place exceeds 12°. - - - _To find the Angle of the Moon’s visible Path with the Ecliptic._ - -[Sidenote: Fifth Element.] - -PRECEPT. This we may state at 5 degrees 38 minutes, as near enough for -the purpose; since it is never above 8 minutes of a degree more or less. - - - _To find the Moon’s Latitude._ - -[Sidenote: Sixth Element.] - -363. PRECEPT. Having found the Sun’s distance from the Ascending Node by -§ 357, at the mean time of New Moon, and his Anomaly for that time by § -359, find the Equation of the Node in Table XIII, by the Sun’s Anomaly, -and the Equation of the Sun’s mean Place in Table XII by his Anomaly: -these two Equations applied (as the titles direct) to the Sun’s mean -distance from the Ascending Node, give his true distance from it, and -also the Moon’s true distance at the time of Change: but when the Moon -is Full, this distance must be increased by the addition of 6 Signs, -which will then be the Moon’s true distance from the same Node. - -The Moon’s true distance from the Ascending Node is called the _Argument -of the Moon’s Latitude_; with the Signs of which, at the head of Table -XIV, and Degrees at the left hand, or with the Signs at the foot of the -Table and Degrees at the right hand, take out the Moon’s Latitude: which -is _North Ascending_, _North Descending_, _South Ascending_, or _South -Descending_, according to the letters _NA_, _ND_, _SA_ or _SD_, annexed -to the Signs of the said Argument. - -[Illustration: Plate XII. - -_The Geometrical Construction of Solar and Lunar Eclipses._ - -_J. Ferguson delin._ _J. Mynde Sculp._] - - - EXAMPLE. - - s ° ʹ - Sun’s mean Dist. from the [83]Node at New Moon in _April 1764_ 0 5 37 - To which add the Equation of the Node + 10 - ---------- - And it gives the Sun’s corrected Distance from the Node 0 5 47 - To which cor. Dist. add the Eq. of the Sun’s mean Place + 1 56 - ---------- - And it gives the Sun’s true Distance from the Node 0 7 43 - -Which, being at the time of New Moon, is the _Argument of Latitude_; and -in Table XIV, (making proportions for the 43ʹ) shews the Moon’s Latitude -to be 40ʹ 9ʺ _North Ascending_[84]. - - - _To find the Moon’s true hourly Motion from the Sun._ - -[Sidenote: Seventh Element.] - -364. PRECEPT. With the Moon’s Anomaly enter Table XV, and thereby take -out her true hourly Motion: then with the Sun’s Anomaly take out his -true hourly Motion from the same Table: which done, subtract the Sun’s -hourly Motion from the Moon’s, and the remainder will be the Moon’s true -hourly Motion from the Sun; which, for the above time § 359, is 27ʹ 50ʺ. - - - _To find the Semi-diameters of the Sun and Moon as seen from the Earth - at the above-mentioned time._ - -[Sidenote: Eighth and Ninth Elements.] - -365. PRECEPT. Enter the XVth Table with the Sun’s Anomaly, and thereby -take out his Semi-diameter; and in the same manner take out the Moon’s -Semi-diameter by her Anomaly. The former of which for the above time -will be found to be 16ʹ 6ʺ; the latter 14ʹ 58ʺ. - - - _To find the Semi-diameter of the Penumbra._ - -[Sidenote: Tenth Element.] - -366. PRECEPT. Add the Sun’s semi-diameter to the Moon’s, and their Sum -will be the Semi-diameter of the Penumbra; namely, at the above time 31ʹ -4ʺ. - -[Sidenote: Pl. XII.] - -366. Having found the proper Elements or Requisites for the Sun’s -Eclipse _April 1, 1764_, and intending to project this Eclipse -Geometrically, we shall now collect them under the eye, that they may be -the more readily found as they are wanted in order for the Projection. - -[Sidenote: The proper Elements collected.] - - D H M - - 367. I. The true time of Conj. or New Moon _April_ 1 10 25 - - ° ʹ ʺ - - II. The Earth’s Semi-Disc, which is equal to the - Moon’s Horizontal Parallax 55ʹ 7ʺ diminished by - the Sun’s Horizontal Parallax which is always 10ʺ 0 54 57 - - III. The Sun’s distance from the nearest Solstice, - _viz._ ♋ 77 51 0 - - IV. The Sun’s Declination, North 4 48 54 - - V. The Angle of the Moon’s vis. path with the - Eclipt. 5 38 0 - - VI. The Moon’s true Latitude, North Ascending 40 9 - - VII. The Moon’s true Horary Motion from the Sun 27 50 - - VIII. The Sun’s Semi-diameter 16 6 - - IX. The Moon’s Semi-diameter 14 58 - - X. The Semi-diameter of the Penumbra 31 4 - -368. Having collected these Elements or Requisites, the following part -of the work may be very much facilitated by means of a good Sector, with -the use of which the reader should be so well acquainted, as to know how -to open it to any given Radius, as far as it will go; and to take off -the Chord or Sine of any Arc of that Radius. This is done by first -taking the extent of the given Radius in your Compasses, and then -opening the Sector so as the distance cross-wise between the ends of the -lines of Sines or Chords at _S_ or _C_, from Leg to Leg of the Sector, -may be equal to that extent; then, without altering the Sector, take the -Sine or Chord of the given Arc with your Compasses extended cross-wise -from Leg to Leg of the Sector in these lines. But if the operator has -not a Sector, he must construct these lines to such different lengths as -he wants them in the projection. And lest this Treatise should fall into -the hands of any person who would wish to project the Figure of a solar -or lunar Eclipse, and has not a Sector to do it by, we shall shew how he -may make a line of Sines or Chords to any Radius. - -[Sidenote: Fig. II. - - How to make a line of Chords. - - Pl. XII.] - -369. Draw the right line _BCA_ at pleasure; and upon _C_ as a Center, -with the distance _CA_ or _CB_ as a Radius, describe the Semi-circle -_BDA_; and from the Center _C_ draw _AC_ perpendicular to _BCA_. Then -divide the Quadrants _AD_ and _BD_ each into 90 equal parts or degrees, -and join the right line _AD_ for the Chord of the Quadrant _AD_. This -done, setting one foot of the Compasses in _A_, extend the other to the -different divisions of the Quadrant _AD_; and so transfer them to the -right line _AD_ as in the Figure, and you have a line of Chords _AD_ to -the Radius _CA_. _N. B._ 60 Degrees on the Line of Chords is always -equal to the Radius of the Circle it is made from; as is evident by the -Figure, where the Arch _E_, whose Center is _A_, drawn from 60 on the -Quadrant _AD_, cuts the Chord line in 60 degrees, and terminates in the -Center _C_. - -[Sidenote: And of Sines.] - -Then, from the divisions or degrees of the Quadrant _BD_, draw lines -parallel to _CD_, which will fall perpendicularly on the Radius _BC_, -dividing it into a line of Sines; and it will be near enough for the -present purpose, to have them to every fifth Degree, as in the Figure. -And thus the young _Tyro_ may supply himself with Chords and Sines, if -he has not a Sector. But as the Sector greatly shortens the work, we -shall describe the projection as done by it, so far as Signs and Chords -are required. - - -[Sidenote: Fig. II. - - Earth’s Semi-Disc.] - -370. Make a Scale of any convenient length (six inches at least) as -_AC_, and divide it into as many equal parts as the semi-diameter of the -Earth’s Disc contains minutes, which in this construction of the Eclipse -for _London_ in _April 1764_, is 54 minutes and 57 seconds; but as it -wants only 3ʺ of 55ʹ the Scale may be divided into 55 equal parts, as in -the Figure. Then, with the whole length of the Scale as a Radius, -setting one foot of your Compasses in _C_ as a center, describe the -Semi-circle _AMB_ for the northern Hemisphere or Semi-disc of the Earth, -as seen from the Sun at that time. Had the Place for which the -Construction is made been in South Latitude, this Semi-circle would have -been the Southern Hemisphere of the Earth’s Disc. - -[Sidenote: Axis of the Ecliptic.] - -371. Upon the center _C_ raise the straight line _CH_ for the Axis of -the Ecliptic, perpendicular to _ACB_. - -[Sidenote: North Pole of the Earth.] - -372. Make a line of Chords to the Radius _AC_, and taking from thence -the Chord of 23-1/2 Degrees, set it off from _H_ to _g_ and to _h_, on -the periphery of the Semi-disc; and draw the straight line _gNh_, in -which the North Pole of the Disc is always found. - -373. While the Sun is in Aries, Taurus, Gemini, Cancer, Leo, and Virgo, -the North Pole of the Disc is illuminated; but while the Sun is in -Libra, Scorpio, Sagittary, Capricorn, and Aquarius, the North Pole is -hid in the obscure part behind the Disc. - -374. And, whilst the Sun is in Capricorn, Aquarius, Pisces, Aries, -Taurus, and Gemini, the Earth’s Axis _CP_ lies to the right hand of the -Axis of the Ecliptic _CH_ as seen from the Sun, and to the left hand -while the Sun is in the other six Signs. - -[Sidenote: Earth’s Axis. - - Universal Meridian.] - -375. Make a line of Sines equal in length to _Ng_ or _Nh_, and take off -with your Compasses from it the Sine of the Sun’s distance from the -nearest Solstice, which in the present case is 77° 51ʹ § 367, and set -that distance to the right hand, from _N_ to _P_, on the line _gNh_, -because the Sun being in Aries § 359, the Earth’s Axis lies to the right -hand of the Axis of the Ecliptic § 374: then draw the straight line -_C_XII_P_, for the Earth’s Axis and the Universal Meridian; of both -which _P_ is the North Pole. - -[Sidenote: Path of a given Place on the Disc as seen from the Sun.] - -376. To draw the parallel of Latitude of any given Place (suppose -_London_) which parallel is the visible Path of the Place On the Disc, -as seen from the Sun, from the time that the Sun rises till it sets; -subtract the Latitude of the Place (_London_) 51-1/2 degrees from 90 -degrees, and there remains 38-1/2; which take from the Line of Chords in -your Compasses, and set it from _h_ (where the Universal Meridian _CP_ -cuts the periphery of the Semi-disc) to VI and VI; and draw the occult -Line VI_L_VI. Then, on the left hand of the Earth’s Axis, set off the -Chord of the Sun’s Declination 4° 48ʹ 5ʺ § 367, from VI to _D_ and to -_F_; set off the same on the right hand from VI to _E_ and to _G_; and -draw the occult Lines _DsE_ and _F_XII_G_ parallel to VI _L_ VI. - -[Sidenote: Situation of the Place on the Disk from Sun-rise to Sun-set.] - -377. Bisect _s_ XII in _K_, and through the point _K_ draw the black -Line VI_K_V1 parallel to the occult or dotted Line VI_L_VI. Then, making -_AC_ the Radius or length of a Line of Lines, set off the Sine of 38-1/2 -degrees, the Co-Latitude of _London_, from _K_ to VI and VI; and with -that extent as a Radius, describe the Semi-Circle VI 7 8 9 &c. and -divide it into 12 equal parts, beginning at VI. From these divisions, -draw the occult Lines 7_m_, 8_l_, 9_k_, &c. all to the Line VI_K_VI, and -parallel to _C_XII_P_. Then, with _K_XII as a Radius, describe the -Circle _abcdef_, round the Center _K_, and divide the Quadrant _a_XII -into six equal parts, as _ab_, _bc_, _cd_, _de_, &c. Then, through these -points of division _b_, _c_, _d_, _e_, and _f_, draw the occult Lines -VII_b_V, VIII_c_IIII, IX_d_III, &c. intersecting the former Lines 7_m_, -8_l_, 9_k_, 10_i_, &c. in the points VII, VIII, IX, X, XI, &c. which -points mark the situation of _London_ on the Earth’s Disc as seen from -the Sun at these hours respectively, from six in the morning till six at -night: and if the elliptic Curve VI, VII, VIII, &c. be drawn through -these points, it will represent the parallel of _London_, or the path it -seems to describe as viewed from the Sun, from Sun-rise to Sun-set. -_N.B._ When the Sun’s Declination is North, the said Curve is the -diurnal Path of _London_; and the opposite part VI_s_VI is it’s -nocturnal Path behind the Disc, or in the obscure part thereof, § 338, -339. But if the Sun’s Declination had been South, the Curve VI_s_VI -would have been the diurnal path of _London_; in which case the Lines -7_m_, 8_l_, &c. must have been continued thro’ the right Line VI_K_VI, -and their lengths beyond that line determined by dividing the Quadrant -_s a_ of the little Circle _abcd_ into six equal parts, and drawing the -parallels VII_b_, VIII_c_ &c. through that division, in the same manner -as done on the side _K_ XII; and the Curve VII, VIII, IX, &c. would have -been the nocturnal Path. It is requisite to divide the hours of the -diurnal Path into quarters, as in the Diagram; and if possible into -minutes also. - -[Sidenote: Axis of the Moon’s Orbit.] - -378. From the Line of Chords § 372 take the Angle of the Moon’s visible -Path with the Ecliptic, _viz._ 5° 38ʹ § 367: and note, that when the -Moon’s Latitude is _North Ascending_, as in the present case, the Chord -of this Angle must be set off to the left hand of the Axis of the -Ecliptic _CH_, as from _H_ to _M_, and the right line _CM_ drawn for the -Axis of the Moon’s Orbit: but when the Moon’s Latitude is _North -Descending_, this Angle and Axis must be set to the right hand, or from -_H_ toward _h_. When the Moon’s Latitude _South Ascending_, the Axis of -her Orbit lies the same way as when her Latitude is _North Ascending_; -and when _South Descending_, the same way as when _North Descending_. - -[Sidenote: Path of the Penumbra’s center over the Earth.] - -379. Take the Moon’s Latitude, 40ʹ 9ʺ § 367, from the Scale _CA_, and -set it from _C_ to _T_ on the Axis of the Ecliptic; and through _T_, at -right Angles to the Axis of the Moon’s Orbit _CM_, draw the straight -Line _RTS_; which is the Moon’s Path, or Line that the center of her -shadow and Penumbra describes in going over the Earth’s Disc. The Point -_T_ in the Axis of the Ecliptic is the Place where the true Conjunction -of the Sun and Moon falls, according to the Tables; and the Point _W_, -in the Axis of the Moon’s Orbit, is that where the center of the -Penumbra approaches nearest to the center of the Earth’s Disc, and -consequently the middle of the general Eclipse. - -[Sidenote: It’s Place on the Earth’s Disc shewn for every minute of it’s - Transit.] - -380. Take the Moon’s true Horary Motion from the Sun 27ʹ 50ʺ § 367, from -the Scale _CA_ with your Compasses (every division of the Scale being a -minute of a Degree) and with that extent make marks in the Line of the -Moon’s Path _RTS_: then divide each of these equal spaces by dots into -60 equal parts or horary minutes, and set the hours to every 60th -minute, in such a manner that the dot; signifying the precise minute of -New Moon by the Tables, may fall in the Point _T_ where the Axis of the -Ecliptic cuts the Line of the Moon’s Path; which, in this Eclipse, is -the 25th minute past ten in the Forenoon: and then the other marks will -shew the places on the Earth’s Disc where the center of the Penumbra is, -at the hours and minutes denoted by them, during its transit over the -Earth. - -[Sidenote: Middle of the Eclipse. - - It’s Phases.] - -381. Apply one side of a Square to the Line of the Moon’s Path, and move -the Square backward or forward until the other side cuts the same hour -and minute both in the Path of the Place (_London_, in this -Construction) and Path of the Moon; and _that_ minute, cut at the same -time in both Paths, will be the precise minute of visible Conjunction of -the Sun and Moon at _London_, and therefore the time of greatest -obscuration, or middle of the Eclipse at _London_; which time, in this -Projection, falls at _t_, 34 minutes past 10 in the Moon’s Path; and at -_u_, 34 minutes past 10 in the Path of _London_. Then, upon the Point -_u_ as a center, describe the Circle _zYy_ whose Radius _uy_ is equal to -the Sun’s semi-diameter 16ʹ 6ʺ § 367, taken from the Scale _CA_: And -upon the Point _t_ as a center, describe the Circle _Hy_ whose Radius is -equal to the Moon’s semi-diameter 14ʹ 58ʺ § 367, taken from the same -Scale. The Circle _zYy_ represents the Disc of the Sun as seen from the -Earth, and the Circle _Hy_ the Disc of the Moon. The portion of the -Sun’s Disc cut off by the Moon’s shews the Quantity of the Eclipse at -the time of greatest obscuration: and if a right Line as _yz_ be drawn -across the Sun’s Disc through _t_ and _u_, the minute of greatest -obscuration in both Paths, and divided into 12 equal parts, it will shew -what number of Digits are then eclipsed. If these two Circles do not -touch one another, the Eclipse will not be visible at the given Place. - -[Sidenote: It’s beginning and ending.] - -382. Lastly, take the Semi-diameter of the Penumbra 31ʹ 4ʺ § 367, from -the Scale _CA_ with your Compasses; and setting one foot in the Moon’s -Path, to the left hand of the Axis of the Ecliptic, direct the other -toward the Path of _London_; and carry this extent backwards or forwards -until both Points of the Compasses fall into the same instants of time -in both Paths: which will denote the time of the beginning of the -Eclipse: then, do the same on the right hand of the Axis of the -Ecliptic, and where both Points mark the same instants in both Paths, -they will shew at what time the Eclipse ends. These trials give the -Points _R_ in the Moon’s Path and _r_ in the Path of _London_, namely 9 -minutes past 9 in the Morning for the beginning of the Eclipse at -_London_, _April 1, 1764_: _t_ and _u_ for the middle or greatest -obscuration, at 35 minutes past 10; when the Eclipse will be barely -annular on the Sun’s lower-most edge, and only two thirds of a Digit -left free on his upper-most edge: and for the end of the Eclipse, _S_ in -the Moon’s Path and _x_ in the Path of _London_, at 4 minutes past 12 at -Noon. - -In this Construction it is supposed that the Equator, Tropics, Parallel -of _London_, and Meridians through every 15th degree of Longitude are -projected in visible Lines on the Earth’s Disc, as seen from the Sun at -almost an infinite distance; that the Angle under which the Moon’s -diameter is seen, during the time of the Eclipse, continues invariably -the same; that the Moon’s motion is uniform, and her Path rectilineal, -for that time. But all these suppositions do not exactly agree with the -truth; and therefore, supposing the Elements § 367, given by the Tables -to be perfectly accurate, yet the time and phases of the Eclipse deduced -from it’s Construction will not answer exactly to what passeth in the -Heavens; but may be two or three minutes wrong though done with the -utmost care. Moreover, the Paths of all Places of considerable Latitude -go nearer the center of the Disc as seen from the Moon than these -Constructions make them; because the Earth’s Disc is projected as if the -Earth were a perfect sphere, although it is known to be a spheroid. -Consequently, the Moon’s shadow will go farther North in places of -northern Latitude, and farther South in places of southern Latitude than -these projections answer to. Hence we may venture to predict that this -Eclipse will be more annular at _London_ (that is, the annulus will be -somewhat broader on the southern Limb of the Sun) than the Diagram shews -it. - - -383. Having shewn how to compute the times and project the phases of a -Solar Eclipse, we now proceed to those of the Lunar. And it has been -already mentioned § 317, that when the Full Moon is within 12 degrees of -either of her Nodes, she must be eclipsed. We shall now enquire whether -or no the Moon will be eclipsed _May 18, 1761, N. S._ at 32 minutes past -10 at Night. See page 193. - -[Sidenote: Table IV. - - Table VI.] - - s ° ʹ - Sun from Node at Full Moon in _March 1761_ 9 25 27 - Add his distance for two Lunations, to bring it into _May_ 2 1 20 - --------- - And his distance at Full Moon in that month is 11 26 47 - -Subtract this from a Circle, or 12 Signs, and there will remain 3° 13ʹ; -which is all that the Sun wants of coming round to the Ascending Node; -and the Moon being then opposite to the Sun, must be just as near the -Descending Node: consequently, far within the limit of an Eclipse. - -384. Knowing then that the Moon will be eclipsed in _May 1761_, we must -find her true distance from the Node at that time, by applying the -proper Equations as taught § 363, and then find her true Latitude as -taught in that article. - - -[Sidenote: Table IV. - - Table XIII. - - Table XII.] - - s ° ʹ - Sun’s mean distance from the Node at F. Moon in _May 1761_ 11 26 47 - Add the Equation of the Node, for the Sun’s Anomaly 10^s - 18° 15ʹ[85] + 6 - -------- - Sun’s mean distance from the Node corrected 11 26 53 - Add the Equation of the Sun’s mean Place + 1 15 - -------- - Sun’s true distance from the Ascending Node 11 28 8 - To which add 6 Signs, See § 363 6 - -------- - The sum is the Moon’s true distance from the same Node 5 28 8 - -[Sidenote: Pl. XII.] - -Or the _Argument_ of her _Latitude_; which in Table XIV, gives the -Moon’s true Latitude, _viz._ 9ʹ 56ʺ North Descending. - -385. Having by the foregoing precepts § 355 found the true time of -Opposition of the Sun and Moon in a lunar Eclipse, with the Moon’s -Anomaly enter Table XV and take out her horizontal Parallax, also her -true horary Motion and Semi-diameter: and likewise those of the Sun by -his Anomaly, as already taught § 364 & _seq._ Then add the Sun’s -horizontal Parallax, which is always 10 Seconds, to the Moon’s -horizontal Parallax, and from their sum subtract the Sun’s -Semi-diameter; the remainder will be the Semi-diameter of that part of -the Earth’s shadow which the Moon goes through. - -386. From the Sum of the Semi-diameters of the Moon and Earth’s Shadow, -subtract the Moon’s Latitude; the remainder is the parts deficient. -Then, as the Semi-diameter of the Moon is to 6 Digits, so are the parts -deficient to the Digits eclipsed. - -387. If the parts deficient be more than the Moon’s Diameter, the -Eclipse will be total with continuance; if less, it will not be total; -if equal, it will be total, but without continuance. - -388. Now collect the Elements for projecting this Eclipse. - - - ʹ ʺ - Moon’s horizontal Parallax 55 32 - Sun’s horizontal Parallax (always) 10 - The Sum of both Parallaxes 55 42 - From which subtract the Sun’s Semi-diameter 15 54 - Remains the Semi-diameter of the Earth’s Shadow 39 48 - Semidiameter of the Moon 15 2 - Sum of the two last 54 50 - Moon’s Latitude subtract 9 56 - Remains the parts deficient 45 0 - Moon’s horary motion 30 46 - Sun’s horary motion subtract 2 24 - Remains the Moon’s horary motion from the Sun 28 22 - -[Sidenote: To project a lunar Eclipse. - - Fig. III.] - -389. This done, make a Scale of any convenient length as _W_, whereof -each division is a minute of a degree; and take from it in your -Compasses 54 Minutes 50 Seconds, the Sum of Semi-diameters of the Moon -and Earth’s shadow; and with that extent as a Radius, describe that -Circle _OVLG_ round _C_ as a Center. - -From the same Scale take 39 Minutes 48 Seconds, the Semi-diameter of the -Earth’s shadow, and therewith as a Radius, describe the Circle _UUUU_ -for the Earth’s shadow, round _C_ as a Center. Subtract the Moon’s -Semi-diameter from the Semi-diameter of the Shadow, and with the -difference 24 Minutes 46 seconds as a Radius, taken from the Scale _W_, -describe the Circle _YZ_ round the Center _C_. - -Draw the right line _AB_ through the Center _C_ for the Ecliptic, and -cross it at right Angles with the line _EG_ for the Axis of the -Ecliptic. - -Because the Moon’s Latitude in this Eclipse is North Descending, § 384, -set off the Angle of her visible Path with the Ecliptic 5 Degrees 38 -Minutes (Page 202.) from _E_ to _V_; and draw _VCv_ for the Axis of the -Moon’s Orbit. Had the Moon’s Latitude been North Ascending, this Angle -must have been set off from _E_ to _f_. _N. B._ When the Moon’s Latitude -is South Ascending, the Axis of her Orbit lies the same way as when she -has North Ascending Latitude; and when her Latitude is North Descending, -the Axis of her Orbit lies the same way as when her Latitude is South -Descending. - -Take the Moon’s true Latitude 9ʹ 56ʺ in your Compasses from the Scale -_W_, and set it off from _C_ to _F_ on the Axis of the Ecliptic because -the Moon is north of the Ecliptic; (had she been to the South of it, her -Latitude must have been set off the contrary way, as from _C_ towards -_v_:) and through _F_, at right Angles to the Axis of the Moon’s Orbit -_VCv_, draw the right line _LMHNO_ for the Moon’s Orbit, or her Path -through the Earth’s shadow. _N. B._ When the Moon’s Latitude is North -Ascending, or North Descending, she is above the Ecliptic: but when her -Latitude is South Ascending, or South Descending, she is below it. - -Take the Moon’s true horary motion from the Sun, _viz._ 28 Minutes 22 -Seconds, from the Scale _W_ in your Compasses; and with that extent make -marks in the line of the Moon’s Path _LMHNO_: then divide each of these -equal spaces into 60 equal parts or minutes of time: and set the hours -to them as in the Figure, in such a manner that the precise time of Full -Moon, as shewn by the Tables, may fall in the Axis of the Ecliptic at -_F_, where the line of the Moon Path cuts it. - -Lastly, Take the Moon’s Semi-diameter 15 Minutes 2 Seconds from the -Scale _W_ in your Compasses, and therewith as a Radius describe the -Circles _P_, _Q_, _R_, _S_, and _T_ on the Centers _L_, _M_, _H_, _N_, -and _O_; the Circles _P_ and _T_ just touching the Earth’s Shadow _UU_, -but no part of them within it; the Circles _Q_ and _S_ all within it, -but touching at its edges; and the Circle _R_ in the middle of the -Moon’s Path through the shadow. So the Circle _P_ shall be the Moon -touching the shadow at the moment the Eclipse begins; the Circle _Q_ the -Moon just immersed into the shadow at the moment she is totally -eclipsed; the Circle _R_ the Moon at the greatest obscuration, in the -middle of the Eclipse; the Circle _S_ the Moon just beginning to be -enlightened on her western limb at the end of total darkness; and the -Circle _T_ the Moon quite clear of the Earth’s shadow at the moment the -Eclipse ends. The moments of time marked at the points _L_, _M_, _H_, -_N_ and _O_ answer to these Phenomena: and according to this small -projection are as follow. The beginning of the Eclipse at 8 Hours 36 -Minutes _P. M._ The total immersion at 9 Hours 42 Minutes. The middle of -the Eclipse at 10 Hours 26 Minutes. The end of total darkness at 11 -Hours 12 Minutes. And the end of the Eclipse at 12 Hours 18 Minutes; but -the Figure is too small to admit of precision. - - -[Sidenote: The examination of antient Eclipses.] - -390. By computing the times of New and Full Moons, together with the -distance of the Sun and Moon from the Nodes; and knowing that when the -Sun is within 17 Degrees of either Node at New Moon he must be eclipsed; -and when the Moon is within 12 Degrees of either Node at Full she cannot -escape an Eclipse; and that there can be no Eclipses without these -limits; ’tis easy to examine whether the accounts of antient Eclipses -recorded in history be true. I shall take the liberty to examine two of -those mentioned in the foregoing catalogue, namely, that of the Moon at -_Babylon_ on the 19th of _March_ in the 721st year before CHRIST; and -that of the Sun at _Athens_, on the 20th of _March_, in the 424th year -before CHRIST. - -The time of Full Moon for the former of these Eclipses is already -calculated, Page 198, and the time of New Moon for the latter, Page 196, -both to the _Old Style_; so that we have nothing now to do but find the -Sun’s distance from the Nodes the same way as we did the Anomalies; and -if the Full Moon in _March_ 721 years before CHRIST was within 12 -degrees of either Node, she was then eclipsed; and if the Sun, at the -time of New Moon in _March_ 424 years before CHRIST was within 17 -degrees of either Node, he must have been eclipsed at that time. - - - EXAMPLE I. - -_To find the distance of the Sun and Moon from the Nodes, at the time of - Full Moon in_ March, _the year before_ CHRIST _721, O. S._ - - The years 720 added to 1780 make 2500, or 25 Centuries. - - Sun from Node - s ° ʹ - To the mean time of Full Moon in _March 1780_, Table III. 10 3 1 - Add the distance for 1 Lunation [See _N. B._ Page 195, - and Example III, Page 198] 1 0 40 - -------- - Sum 11 3 41 - From which subtract the Sun’s distance from the Node - for 2500 years, Table V 5 4 11 - -------- - Remains the Sun’s distance from the Node, _March 19_, - 721 years before CHRIST 5 29 30 - To which add 6 Signs for the Moon’s distance, because - she was then in opposition to the Sun 6 0 0 - -------- - The Sum is the Moon’s dist. from the Ascend. Node 11 29 30 - -That is, she was within half a degree of coming round to it again; and -therefore, being so near, she must have been totally, and almost -centrally eclipsed. - - - EXAMPLE II - - _To find the Suns distance from the Node at the Time of New Moon in_ - March, _the year before_ CHRIST _424, O. S._ - - The years 423 added to 1777 make 2200, or 22 Centuries. - - Sun from Node - s ° ʹ - At the mean time of New Moon in _March 1777_, Tab. I. 8 23 33 - From which subtract the Sun’s distance from the Node - for 2200 years, Table V 3 6 0 - -------- - Remains the Sun’s distance from the Ascending Node, - _March 21_, 424 years before CHRIST 5 17 33 - Which, taken from 6 Signs, the distance of the Nodes - from each other 6 0 0 - -------- - Leaves the Sun’s distance at that time from the Descending - Node, Descending _viz._ 0 12 27 - -Which being less than 17 degrees, shews that the Sun was then eclipsed. -And as from these short Calculations we find those two antient Eclipses -taken at a venture, to be truly recorded; it is natural to imagine that -so are all the rest in the catalogue. - -Here follow ASTRONOMICAL TABLES, for calculating the Times of NEW and -FULL MOONS and ECLIPSES. - - +-------------------------------------------------------------------------+ - | TABLE I. _The mean time of New Moon in_ March, _the mean Anomaly of the | - | Sun and Moon, the Sun’s mean Distance from the Ascending Node; with | - | the mean Longitude of the Sun and Node from the beginning of the Sign | - | Aries, at the times of all the New Moons in_ March _for 100 years, | - | Old Style_. | - +-------+----------+----------+----------+----------+----------+----------+ - |Years |Mean time |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - |of |of New | mean | mean |distance |Longitude |Longitude | - |CHRIST.|Moon in |Anomaly. |Anomaly. |from the |from |from | - | |_March_. | | | Node. |Aries. |Aries. | - +-------+----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +-------+----------+----------+----------+----------+----------+----------+ - | 1701 | 27 13 45 | 9 8 23 | 0 28 5 | 7 23 15 | 0 16 3 | 4 22 48 | - | 1702 | 16 22 34 | 8 27 39 | 11 7 53 | 8 1 17 | 0 5 20 | 4 4 3 | - | 1703 | 6 7 23 | 8 16 55 | 9 17 41 | 8 9 20 | 11 24 37 | 3 15 17 | - | 1704 | 24 4 55 | 9 4 30 | 8 23 18 | 9 18 3 | 0 13 0 | 2 24 57 | - | 1705 | 13 13 44 | 8 23 54 | 7 3 6 | 9 26 6 | 0 2 17 | 2 6 11 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1706 | 2 22 32 | 8 13 48 | 5 12 54 | 10 4 9 | 11 21 34 | 1 17 25 | - | 1707 | 21 20 5 | 9 2 17 | 4 18 31 | 11 12 52 | 0 9 57 | 0 27 5 | - | 1708 | 10 4 54 | 8 21 10 | 2 28 19 | 11 20 55 | 11 29 14 | 0 8 19 | - | 1709 | 29 2 26 | 9 9 48 | 2 3 56 | 0 29 38 | 0 17 37 | 11 17 59 | - | 1710 | 18 11 16 | 8 28 32 | 0 13 44 | 1 7 40 | 0 6 54 | 10 29 14 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1711 | 7 20 5 | 8 17 27 | 10 23 33 | 1 15 43 | 11 26 11 | 10 10 28 | - | 1712 | 25 17 36 | 9 5 8 | 9 29 10 | 2 24 26 | 0 14 34 | 9 20 8 | - | 1713 | 15 2 25 | 8 25 48 | 8 8 58 | 3 2 29 | 0 3 50 | 9 1 21 | - | 1714 | 4 11 14 | 8 14 52 | 6 16 46 | 3 10 32 | 11 23 7 | 8 12 35 | - | 1715 | 23 8 46 | 9 3 37 | 5 24 22 | 4 19 15 | 0 11 30 | 7 22 15 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1716 | 11 17 35 | 8 21 26 | 4 4 11 | 4 27 18 | 0 0 47 | 7 3 29 | - | 1717 | 1 2 23 | 8 11 58 | 2 13 59 | 5 5 20 | 11 20 4 | 6 14 44 | - | 1718 | 19 23 56 | 9 0 31 | 1 19 36 | 6 14 3 | 0 8 27 | 5 24 24 | - | 1719 | 9 8 45 | 8 19 47 | 11 29 24 | 6 22 6 | 11 27 43 | 5 5 37 | - | 1720 | 27 6 17 | 9 8 9 | 11 5 1 | 8 0 49 | 0 16 6 | 4 15 17 | - +-------+----------+----------+----------+------------+--------+----------+ - | 1721 | 16 15 6 | 8 27 25 | 9 14 49 | 8 8 52 | 0 5 23 | 3 26 31 | - | 1722 | 5 23 55 | 8 16 41 | 7 24 38 | 8 16 55 | 11 24 40 | 3 7 45 | - | 1723 | 24 21 27 | 9 5 3 | 7 0 15 | 9 25 38 | 0 13 4 | 2 17 26 | - | 1724 | 13 6 16 | 8 24 19 | 5 10 3 | 10 3 41 | 0 2 22 | 1 28 41 | - | 1725 | 2 15 4 | 8 13 45 | 3 19 51 | 10 11 43 | 11 21 39 | 1 9 56 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1726 | 21 12 37 | 9 1 57 | 2 25 28 | 11 20 26 | 0 10 3 | 0 19 37 | - | 1727 | 10 21 26 | 8 21 13 | 1 5 16 | 11 28 29 | 11 29 20 | 0 0 51 | - | 1728 | 28 18 58 | 9 9 35 | 0 10 53 | 1 7 13 | 0 17 43 | 11 10 30 | - | 1729 | 18 3 47 | 8 28 51 | 10 20 41 | 1 15 15 | 0 7 0 | 10 21 45 | - | 1730 | 7 12 36 | 8 18 7 | 9 0 29 | 1 23 18 | 11 26 17 | 10 2 59 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1731 | 26 10 8 | 9 6 29 | 8 6 6 | 3 2 1 | 0 14 40 | 9 12 39 | - | 1732 | 14 18 57 | 8 25 45 | 6 15 54 | 3 10 3 | 0 3 57 | 8 23 54 | - | 1733 | 4 3 45 | 8 14 49 | 4 25 43 | 3 18 6 | 11 23 14 | 8 5 7 | - | 1734 | 23 1 18 | 9 3 25 | 4 1 20 | 4 26 49 | 0 11 37 | 7 14 48 | - | 1735 | 12 10 7 | 8 22 39 | 2 11 8 | 5 4 52 | 0 0 54 | 6 26 1 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1736 | 30 7 39 | 0 11 1 | 1 16 45 | 6 13 35 | 0 19 17 | 6 5 42 | - | 1737 | 19 16 28 | 9 0 1 | 11 26 33 | 6 21 38 | 0 8 34 | 5 16 56 | - | 1738 | 9 1 17 | 8 19 33 | 10 6 21 | 6 29 42 | 11 27 51 | 4 28 9 | - | 1739 | 27 22 49 | 9 7 55 | 9 11 58 | 8 8 24 | 0 16 14 | 4 7 50 | - | 1740 | 16 7 38 | 8 27 11 | 7 21 46 | 8 16 27 | 0 5 30 | 3 19 3 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1741 | 5 16 26 | 8 16 27 | 6 1 34 | 8 24 30 | 11 24 47 | 3 0 16 | - | 1742 | 24 13 59 | 9 4 49 | 5 7 11 | 10 3 12 | 0 13 10 | 2 9 58 | - | 1743 | 13 22 48 | 8 24 5 | 3 16 59 | 10 11 15 | 0 2 27 | 1 21 12 | - | 1744 | 2 7 36 | 8 13 21 | 1 26 48 | 10 19 18 | 11 21 44 | 1 2 25 | - | 1745 | 21 5 9 | 9 1 43 | 1 2 25 | 11 28 0 | 0 10 7 | 0 12 7 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1746 | 10 13 58 | 8 20 59 | 11 12 13 | 0 6 3 | 11 29 44 | 11 23 20 | - | 1747 | 29 11 30 | 9 9 21 | 10 17 50 | 1 14 45 | 0 17 47 | 11 3 2 | - | 1748 | 17 20 19 | 8 28 37 | 8 27 38 | 1 22 49 | 0 7 4 | 10 14 15 | - | 1749 | 7 5 8 | 8 17 53 | 7 7 26 | 2 0 53 | 11 26 21 | 9 25 28 | - | 1750 | 26 2 40 | 9 6 15 | 6 13 3 | 3 9 35 | 0 14 44 | 9 5 9 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1751 | 15 11 29 | 8 25 32 | 4 22 51 | 3 17 38 | 0 4 1 | 8 16 23 | - | 1752 | 3 20 17 | 8 14 47 | 3 2 39 | 3 25 41 | 11 23 18 | 7 27 37 | - | 1753 | 22 17 50 | 9 3 10 | 2 8 16 | 5 4 24 | 0 11 41 | 7 7 17 | - | 1754 | 12 2 39 | 8 22 26 | 0 18 4 | 5 12 27 | 0 0 59 | 6 18 32 | - | 1755 | 1 11 27 | 8 11 41 | 10 27 52 | 5 20 30 | 11 20 16 | 5 29 45 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1756 | 19 9 0 | 9 0 4 | 10 3 30 | 6 29 13 | 0 8 39 | 5 9 27 | - | 1757 | 8 17 49 | 8 19 20 | 8 13 18 | 7 10 15 | 11 27 56 | 4 20 41 | - | 1758 | 27 15 21 | 9 7 42 | 7 18 55 | 8 15 58 | 0 16 19 | 4 0 21 | - | 1759 | 17 0 10 | 8 26 58 | 5 28 43 | 8 24 1 | 0 5 36 | 3 11 36 | - | 1760 | 5 8 58 | 8 16 13 | 4 8 31 | 9 2 4 | 11 24 53 | 2 22 49 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1761 | 24 6 31 | 9 4 35 | 3 14 8 | 10 10 47 | 0 13 16 | 2 2 29 | - | 1762 | 13 15 19 | 8 23 52 | 1 23 56 | 10 18 51 | 0 2 33 | 1 13 44 | - | 1763 | 3 0 8 | 8 13 7 | 0 3 44 | 10 26 53 | 11 21 50 | 0 24 57 | - | 1764 | 20 21 41 | 9 1 29 | 11 9 21 | 0 5 36 | 0 10 13 | 0 4 37 | - | 1765 | 10 6 30 | 8 20 46 | 9 19 9 | 0 13 38 | 11 29 30 | 11 15 52 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1766 | 29 4 2 | 9 9 8 | 8 24 46 | 1 22 21 | 0 17 53 | 10 25 32 | - | 1767 | 18 12 51 | 8 28 24 | 7 4 35 | 2 0 24 | 0 7 10 | 10 6 47 | - | 1768 | 6 21 39 | 8 17 39 | 5 14 23 | 2 8 27 | 11 26 27 | 9 18 1 | - | 1769 | 25 19 12 | 9 6 2 | 4 20 0 | 3 17 0 | 0 14 50 | 8 27 41 | - | 1770 | 15 4 1 | 8 25 17 | 2 29 48 | 3 25 12 | 0 4 7 | 8 8 56 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1771 | 4 12 49 | 8 14 33 | 1 9 36 | 4 3 16 | 11 23 24 | 7 20 8 | - | 1772 | 22 10 22 | 9 2 56 | 0 15 13 | 5 11 49 | 0 11 47 | 6 29 48 | - | 1773 | 11 19 10 | 8 22 11 | 10 25 1 | 5 20 1 | 0 1 4 | 6 11 3 | - | 1774 | 1 3 59 | 8 11 27 | 9 4 49 | 5 28 4 | 11 20 21 | 5 22 17 | - | 1775 | 20 1 32 | 8 29 50 | 8 10 26 | 7 6 4 | 0 8 44 | 5 1 57 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1776 | 8 10 20 | 8 19 5 | 6 20 14 | 7 14 50 | 11 28 1 | 4 13 12 | - | 1777 | 27 7 53 | 9 7 27 | 5 25 51 | 8 23 23 | 0 16 24 | 3 22 52 | - | 1778 | 16 16 42 | 8 26 43 | 4 5 40 | 9 1 36 | 0 5 41 | 3 4 6 | - | 1779 | 6 1 30 | 8 15 59 | 2 15 28 | 9 9 39 | 11 24 58 | 2 15 19 | - | 1780 | 23 23 3 | 9 4 21 | 1 21 5 | 10 18 22 | 0 13 21 | 1 24 59 | - +-------+----------+---------+----------+----------+----------+----------+ - | 1781 | 13 7 52 | 8 23 37 | 0 0 53 | 10 26 24 | 0 2 38 | 1 6 14 | - | 1782 | 2 16 40 | 8 12 53 | 10 10 41 | 11 4 27 | 11 21 54 | 0 17 27 | - | 1783 | 21 14 13 | 9 1 15 | 9 16 18 | 0 13 10 | 0 10 17 | 11 27 7 | - | 1784 | 9 23 2 | 8 20 32 | 7 26 6 | 0 21 13 | 11 29 34 | 11 8 22 | - | 1785 | 28 20 35 | 9 8 54 | 7 1 43 | 1 29 56 | 0 17 57 | 10 18 2 | - +-------+----------+---------+----------+----------+----------+----------+ - | 1786 | 18 5 23 | 8 28 9 | 5 11 31 | 2 7 59 | 0 7 14 | 9 29 16 | - | 1787 | 7 14 11 | 8 17 25 | 3 21 19 | 2 16 2 | 11 26 31 | 9 10 29 | - | 1788 | 25 11 44 | 9 5 47 | 2 26 56 | 3 24 45 | 0 14 54 | 8 20 9 | - | 1789 | 14 20 33 | 8 25 3 | 1 6 45 | 4 2 47 | 0 4 11 | 8 1 25 | - | 1790 | 4 5 21 | 8 14 19 | 11 16 33 | 4 10 50 | 11 23 28 | 7 12 38 | - +-------+----------+---------+----------+----------+----------+----------+ - | 1791 | 23 2 54 | 9 2 41 | 10 22 10 | 5 19 33 | 0 11 51 | 6 22 18 | - | 1792 | 11 11 43 | 8 21 57 | 9 1 58 | 5 27 56 | 0 1 7 | 6 3 32 | - | 1793 | 0 20 31 | 8 11 12 | 7 11 45 | 6 5 39 | 11 20 24 | 5 14 45 | - | 1794 | 19 18 4 | 8 29 35 | 6 17 23 | 7 14 22 | 0 8 48 | 4 24 27 | - | 1795 | 9 2 52 | 8 18 51 | 4 27 11 | 7 22 25 | 11 28 6 | 4 5 41 | - +-------+----------+---------+----------+----------+----------+----------+ - | 1796 | 27 0 25 | 9 7 13 | 4 2 48 | 9 1 8 | 0 16 29 | 3 15 21 | - | 1797 | 16 9 14 | 8 26 29 | 2 12 36 | 9 9 10 | 0 5 46 | 2 26 36 | - | 1798 | 5 18 2 | 8 15 44 | 0 22 24 | 9 17 13 | 11 25 3 | 2 7 50 | - | 1799 | 24 15 35 | 9 4 6 | 11 28 1 | 10 25 56 | 0 13 26 | 1 17 30 | - | 1800 | 13 0 24 | 8 23 23 | 10 7 49 | 11 3 59 | 0 2 43 | 0 28 44 | - +-------+----------+---------+----------+------------+--------+----------+ - +-------------------------------------------------------------------------+ - | TABLE II. _The mean New Moons, &c. in_ March _to the New Style_. | - +-------+----------+----------+----------+----------+----------+----------+ - |Years |Mean time |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - |of |of New | mean | mean |distance |Longitude |Longitude | - |CHRIST.|Moon in |Anomaly. |Anomaly. |from the |from |from | - | |_March_. | | | Node. |Aries. |Aries. | - +-------+----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +-------+----------+----------+----------+----------+----------+----------+ - | 1753 | 4 5 6 | 7 4 2 | 1 12 27 | 4 3 44 | 11 12 35 | 7 8 50 | - | 1754 | 23 2 39 | 8 22 26 | 0 18 4 | 5 12 27 | 0 0 59 | 6 18 32 | - | 1755 | 12 11 27 | 8 11 41 | 10 27 52 | 5 20 29 | 11 20 16 | 5 29 45 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1756 | 30 9 0 | 9 0 3 | 10 3 29 | 6 29 12 | 0 8 39 | 5 9 27 | - | 1757 | 19 17 49 | 8 19 19 | 8 13 17 | 7 7 15 | 11 27 56 | 4 20 41 | - | 1758 | 9 2 37 | 8 8 35 | 6 23 5 | 7 15 18 | 11 17 13 | 4 1 54 | - | 1759 | 28 0 9 | 8 26 58 | 5 28 43 | 8 24 1 | 0 5 36 | 3 11 36 | - | 1760 | 16 8 58 | 8 16 14 | 4 8 31 | 9 2 4 | 11 24 53 | 2 22 49 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1761 | 5 7 47 | 8 5 29 | 2 18 19 | 9 10 9 | 11 14 10 | 2 4 1 | - | 1762 | 24 15 19 | 8 23 52 | 1 23 56 | 10 18 51 | 0 2 33 | 1 13 44 | - | 1763 | 14 0 8 | 8 13 7 | 0 3 44 | 10 26 53 | 11 21 50 | 0 24 57 | - | 1764 | 2 8 57 | 8 2 23 | 10 13 32 | 11 4 57 | 11 11 7 | 0 6 10 | - | 1765 | 21 6 30 | 8 20 46 | 9 19 9 | 0 13 38 | 11 29 30 | 11 15 52 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1766 | 10 15 18 | 8 10 1 | 7 28 58 | 0 21 41 | 11 18 47 | 10 27 5 | - | 1767 | 29 12 51 | 8 28 23 | 7 4 35 | 2 0 23 | 0 7 10 | 10 6 47 | - | 1768 | 17 21 39 | 8 17 39 | 5 14 23 | 2 8 26 | 11 26 27 | 9 18 1 | - | 1769 | 7 6 28 | 8 6 55 | 3 24 11 | 2 16 29 | 11 15 44 | 8 29 15 | - | 1770 | 26 4 1 | 8 25 18 | 2 29 48 | 3 25 11 | 0 4 7 | 8 8 56 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1771 | 15 12 49 | 8 14 33 | 1 9 36 | 4 3 16 | 11 23 24 | 7 20 8 | - | 1772 | 3 21 38 | 8 3 49 | 11 19 24 | 4 11 19 | 11 12 41 | 7 1 22 | - | 1773 | 22 19 10 | 8 22 11 | 10 25 1 | 5 20 1 | 0 1 4 | 6 11 3 | - | 1774 | 12 3 59 | 8 11 27 | 9 4 49 | 5 28 4 | 11 20 21 | 5 22 17 | - | 1775 | 1 12 48 | 8 0 43 | 7 14 37 | 6 6 7 | 11 9 38 | 5 3 30 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1776 | 19 10 20 | 8 19 5 | 6 20 14 | 7 14 50 | 11 28 1 | 4 13 12 | - | 1777 | 8 19 9 | 8 8 21 | 5 0 2 | 7 22 53 | 11 17 18 | 3 24 25 | - | 1778 | 27 16 42 | 8 26 43 | 4 5 40 | 9 1 36 | 0 5 41 | 3 4 6 | - | 1779 | 17 1 30 | 8 15 59 | 2 15 28 | 9 9 39 | 11 24 58 | 2 15 19 | - | 1780 | 5 10 19 | 8 5 15 | 0 25 16 | 9 17 42 | 11 14 15 | 1 26 32 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1781 | 24 7 52 | 8 23 37 | 0 0 53 | 10 26 24 | 0 2 38 | 1 6 14 | - | 1782 | 13 16 40 | 8 12 53 | 10 10 41 | 11 4 27 | 11 21 54 | 0 17 27 | - | 1783 | 3 1 29 | 8 2 8 | 8 20 29 | 11 12 30 | 11 11 11 | 11 28 40 | - | 1784 | 20 23 2 | 8 20 32 | 7 26 6 | 0 21 13 | 11 29 34 | 11 8 22 | - | 1785 | 10 7 50 | 8 9 47 | 6 5 54 | 0 29 16 | 11 18 51 | 10 19 35 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1786 | 29 5 23 | 8 28 9 | 5 11 31 | 2 7 59 | 0 7 14 | 9 29 16 | - | 1787 | 18 14 11 | 8 17 25 | 3 21 19 | 2 16 2 | 11 26 31 | 9 10 29 | - | 1788 | 6 23 0 | 8 6 41 | 2 1 7 | 2 24 5 | 11 15 48 | 8 21 43 | - | 1789 | 25 20 33 | 8 25 3 | 1 6 45 | 4 2 47 | 0 4 11 | 8 1 25 | - | 1790 | 15 5 21 | 8 14 19 | 11 16 33 | 4 10 50 | 11 23 28 | 7 12 38 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1791 | 4 14 10 | 8 3 34 | 9 26 21 | 4 18 53 | 11 12 44 | 6 23 51 | - | 1792 | 22 11 43 | 8 21 57 | 9 1 58 | 5 27 36 | 0 1 7 | 6 3 32 | - | 1793 | 11 20 31 | 8 11 12 | 7 11 45 | 6 5 39 | 11 20 24 | 5 14 45 | - | 1794 | 1 6 20 | 8 0 29 | 5 21 34 | 6 13 42 | 11 9 22 | 4 7 15 | - | 1795 | 20 2 52 | 8 18 51 | 4 27 11 | 7 22 25 | 11 28 6 | 4 5 41 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1796 | 8 11 41 | 8 8 6 | 3 6 59 | 8 0 28 | 11 17 23 | 3 16 54 | - | 1797 | 27 9 14 | 8 26 29 | 2 12 36 | 9 9 10 | 0 5 46 | 2 26 36 | - | 1798 | 16 18 2 | 8 15 44 | 0 22 24 | 9 17 13 | 11 25 3 | 2 7 50 | - | 1799 | 6 2 51 | 8 5 0 | 11 2 12 | 9 25 16 | 11 14 20 | 1 19 3 | - | 1800 | 25 0 24 | 8 23 23 | 10 7 49 | 11 3 59 | 0 2 43 | 0 28 44 | - +-------+----------+----------+----------+----------+----------+----------+ - +-------------------------------------------------------------------------+ - | TABLE III. _The mean time of Full Moon in_ March, _the mean Anomaly | - | of the Sun and Moon, the Sun’s mean Distance from the | - | Ascending Node; with the mean Longitude of the Sun and Node | - | from the beginning of the Sign Aries, at the time of all the Full | - | Moons in_ March _for 100 years, Old Style_. | - +-------+----------+----------+----------+----------+----------+----------+ - |Years |Mean time |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - |of |of Full | mean | mean |distance |Longitude |Longitude | - |CHRIST.|Moon in |Anomaly. |Anomaly. |from the |from |from | - | |_March._ | | | Node. |Aries. |Aries. | - +-------+----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +-------+----------+----------+----------+----------+----------+----------+ - | 1701 | 12 19 23 | 8 23 56 | 6 15 11 | 7 7 55 | 0 1 30 | 4 23 35 | - | 1702 | 2 4 12 | 8 13 6 | 4 24 59 | 7 15 57 | 11 20 47 | 4 4 48 | - | 1703 | 21 1 45 | 9 1 28 | 4 0 35 | 8 24 40 | 0 9 10 | 3 14 30 | - | 1704 | 9 10 33 | 8 19 57 | 2 10 24 | 9 2 43 | 11 28 27 | 2 25 43 | - | 1705 | 28 8 6 | 9 8 27 | 1 16 0 | 10 11 26 | 0 16 50 | 2 5 25 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1706 | 17 16 54 | 8 28 11 | 11 25 48 | 10 19 29 | 0 6 7 | 1 16 38 | - | 1707 | 7 1 43 | 8 17 44 | 10 5 37 | 10 27 32 | 11 25 24 | 0 27 51 | - | 1708 | 24 23 16 | 9 5 43 | 9 11 14 | 0 6 15 | 0 13 47 | 0 7 33 | - | 1709 | 14 8 4 | 8 25 15 | 7 21 2 | 0 14 18 | 0 3 4 | 11 18 46 | - | 1710 | 3 16 54 | 8 13 59 | 6 0 50 | 0 22 21 | 11 22 21 | 11 0 0 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1711 | 22 14 27 | 9 2 0 | 5 6 27 | 2 1 3 | 0 10 44 | 10 9 42 | - | 1712 | 10 23 14 | 8 20 35 | 3 16 16 | 2 9 6 | 0 0 1 | 9 20 55 | - | 1713 | 29 20 47 | 9 10 21 | 2 21 52 | 3 17 48 | 0 18 23 | 9 0 35 | - | 1714 | 19 5 36 | 8 29 25 | 1 1 40 | 3 25 53 | 0 7 40 | 8 11 48 | - | 1715 | 8 14 24 | 8 19 4 | 11 11 28 | 4 3 56 | 11 26 57 | 7 23 1 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1716 | 26 11 57 | 9 5 59 | 0 17 5 | 5 12 38 | 0 15 20 | 7 2 43 | - | 1717 | 15 20 45 | 8 26 31 | 18 26 53 | 5 20 41 | 0 4 37 | 6 13 56 | - | 1718 | 5 5 34 | 8 15 58 | 7 6 42 | 5 28 44 | 11 23 54 | 5 25 10 | - | 1719 | 24 3 7 | 9 4 20 | 6 12 18 | 7 7 26 | 0 12 17 | 5 4 52 | - | 1720 | 12 11 55 | 8 23 36 | 4 22 7 | 7 15 29 | 0 1 34 | 4 16 5 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1721 | 1 20 44 | 8 12 52 | 3 1 55 | 7 23 32 | 11 20 51 | 3 27 18 | - | 1722 | 20 18 17 | 9 1 14 | 2 7 32 | 9 2 15 | 0 9 14 | 3 6 59 | - | 1723 | 10 3 5 | 8 20 30 | 0 17 21 | 9 10 18 | 11 28 31 | 2 18 12 | - | 1724 | 28 0 38 | 9 8 52 | 11 22 57 | 10 19 0 | 0 16 55 | 1 27 55 | - | 1725 | 17 9 26 | 8 28 18 | 10 2 45 | 10 27 3 | 0 6 12 | 1 9 9 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1726 | 6 18 15 | 8 17 24 | 8 12 34 | 11 5 6 | 11 25 30 | 0 20 23 | - | 1727 | 25 15 48 | 9 5 46 | 7 18 10 | 0 13 49 | 0 13 53 | 0 0 5 | - | 1728 | 14 0 36 | 8 25 2 | 5 27 59 | 0 21 52 | 0 3 10 | 11 11 18 | - | 1729 | 3 9 25 | 8 14 18 | 4 7 47 | 0 29 55 | 11 22 27 | 10 22 32 | - | 1730 | 22 6 58 | 9 2 40 | 3 13 23 | 2 8 38 | 0 10 50 | 10 2 13 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1731 | 11 15 46 | 8 21 56 | 1 23 12 | 2 16 41 | 0 0 7 | 9 13 26 | - | 1732 | 29 13 19 | 9 10 18 | 0 28 48 | 3 25 23 | 0 18 30 | 8 23 8 | - | 1733 | 18 22 7 | 8 29 22 | 11 8 37 | 4 3 26 | 0 7 47 | 8 4 21 | - | 1734 | 8 6 56 | 8 18 50 | 9 18 26 | 4 11 29 | 11 27 4 | 7 15 34 | - | 1735 | 27 4 29 | 9 7 12 | 8 24 2 | 5 20 12 | 0 15 27 | 6 25 15 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1736 | 15 13 17 | 8 26 29 | 7 3 51 | 5 28 15 | 0 4 44 | 6 6 29 | - | 1737 | 4 22 6 | 8 15 44 | 5 13 39 | 6 6 18 | 11 24 1 | 5 17 42 | - | 1738 | 23 19 39 | 9 4 6 | 4 19 15 | 7 15 1 | 0 12 24 | 4 27 24 | - | 1739 | 13 4 27 | 8 23 22 | 2 29 4 | 7 23 4 | 0 1 41 | 4 8 37 | - | 1740 | 1 13 16 | 8 12 38 | 1 8 52 | 8 1 7 | 11 20 57 | 3 19 50 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1741 | 20 10 48 | 9 1 0 | 0 14 28 | 9 9 49 | 0 9 20 | 2 29 30 | - | 1742 | 9 19 37 | 8 20 16 | 10 24 17 | 9 17 52 | 11 28 37 | 2 10 44 | - | 1743 | 28 17 10 | 9 8 38 | 9 29 53 | 10 26 35 | 0 17 0 | 1 20 26 | - | 1744 | 17 1 58 | 8 27 54 | 8 9 42 | 11 4 38 | 0 6 17 | 1 1 39 | - | 1745 | 6 10 47 | 8 17 10 | 6 19 31 | 11 12 41 | 11 25 34 | 0 12 52 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1746 | 25 8 19 | 9 5 32 | 5 25 7 | 0 21 24 | 0 13 57 | 11 22 34 | - | 1747 | 14 17 8 | 8 24 48 | 4 4 56 | 0 29 27 | 0 3 14 | 11 3 47 | - | 1748 | 3 1 57 | 8 14 4 | 2 14 44 | 1 7 30 | 11 22 31 | 10 15 0 | - | 1749 | 21 23 30 | 9 2 26 | 1 20 20 | 2 16 12 | 0 10 54 | 9 24 42 | - | 1750 | 11 8 18 | 8 21 42 | 0 0 9 | 2 24 15 | 0 0 11 | 9 5 59 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1751 | 30 5 51 | 9 10 5 | 11 5 45 | 4 2 58 | 0 18 34 | 8 15 37 | - | 1752 | 18 14 39 | 8 29 20 | 9 15 33 | 4 11 1 | 0 7 51 | 7 26 50 | - | 1753 | 7 23 18 | 7 18 35 | 7 25 21 | 4 19 4 | 11 27 8 | 7 8 4 | - | 1754 | 26 21 1 | 9 6 59 | 7 0 58 | 7 27 47 | 0 15 32 | 6 17 45 | - | 1755 | 16 5 49 | 8 26 14 | 5 10 46 | 6 5 49 | 0 4 49 | 5 29 0 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1756 | 4 14 38 | 8 15 30 | 3 20 35 | 6 13 52 | 11 24 6 | 5 10 14 | - | 1757 | 23 12 11 | 9 3 53 | 2 26 12 | 7 25 35 | 0 12 29 | 4 19 54 | - | 1758 | 12 20 59 | 8 23 8 | 1 5 59 | 8 0 38 | 0 1 46 | 4 1 9 | - | 1759 | 2 5 47 | 8 12 25 | 11 15 48 | 8 8 41 | 11 21 3 | 3 12 22 | - | 1760 | 20 3 20 | 9 0 46 | 10 21 25 | 9 17 24 | 0 9 26 | 2 22 2 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1761 | 9 12 9 | 8 20 2 | 9 1 13 | 9 25 27 | 11 28 43 | 2 3 16 | - | 1762 | 28 9 41 | 9 8 25 | 8 6 50 | 11 4 11 | 0 17 6 | 1 12 57 | - | 1763 | 17 18 30 | 8 27 40 | 6 16 38 | 11 12 13 | 0 6 23 | 0 24 11 | - | 1764 | 6 3 19 | 8 16 56 | 4 26 26 | 11 20 16 | 11 25 40 | 0 5 24 | - | 1765 | 25 0 52 | 9 5 19 | 4 2 3 | 0 28 58 | 0 14 3 | 11 15 5 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1766 | 14 9 40 | 8 24 34 | 2 11 52 | 1 7 1 | 0 3 20 | 10 26 20 | - | 1767 | 7 18 29 | 8 13 50 | 0 21 41 | 1 15 4 | 11 22 37 | 10 7 34 | - | 1768 | 21 16 1 | 9 2 12 | 11 27 17 | 2 23 47 | 0 11 0 | 9 17 14 | - | 1769 | 11 0 50 | 8 21 28 | 10 7 9 | 3 1 49 | 0 0 17 | 8 28 28 | - | 1770 | 0 9 39 | 8 10 44 | 8 16 57 | 3 9 52 | 11 19 54 | 8 9 42 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1771 | 19 7 11 | 8 29 6 | 7 22 30 | 4 18 36 | 0 7 57 | 7 19 21 | - | 1772 | 7 16 0 | 8 18 22 | 6 2 18 | 4 26 39 | 11 27 14 | 7 0 35 | - | 1773 | 26 13 32 | 9 6 44 | 5 7 55 | 6 5 21 | 0 15 37 | 6 10 16 | - | 1774 | 15 22 21 | 8 26 0 | 3 17 43 | 6 13 24 | 0 4 54 | 5 21 31 | - | 1775 | 5 7 10 | 8 15 16 | 1 27 31 | 6 21 27 | 11 24 11 | 5 2 44 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1776 | 23 4 42 | 9 3 38 | 1 3 8 | 8 0 10 | 0 12 34 | 4 12 25 | - | 1777 | 12 13 31 | 8 22 54 | 11 12 56 | 8 8 13 | 0 1 51 | 8 23 30 | - | 1778 | 1 22 20 | 8 12 10 | 9 22 45 | 8 16 16 | 11 21 8 | 3 4 52 | - | 1779 | 20 19 52 | 9 0 32 | 8 28 22 | 9 24 59 | 0 9 31 | 2 14 32 | - | 1780 | 9 4 41 | 8 19 48 | 7 8 10 | 10 3 1 | 11 28 48 | 1 25 47 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1781 | 28 2 14 | 9 8 9 | 6 13 47 | 11 11 44 | 0 17 11 | 1 5 27 | - | 1782 | 19 11 2 | 8 27 28 | 4 23 34 | 11 19 47 | 0 6 27 | 0 6 41 | - | 1783 | 6 19 51 | 8 16 44 | 3 3 23 | 11 27 50 | 11 25 44 | 11 27 54 | - | 1784 | 24 17 24 | 9 5 4 | 2 9 0 | 1 6 35 | 0 14 7 | 11 7 35 | - | 1785 | 14 2 12 | 8 24 20 | 0 18 48 | 1 14 36 | 0 3 24 | 10 18 48 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1786 | 3 11 1 | 8 13 36 | 10 28 37 | 1 22 39 | 11 22 41 | 10 0 2 | - | 1787 | 22 8 33 | 9 1 57 | 10 4 13 | 3 1 22 | 0 11 4 | 9 9 42 | - | 1788 | 10 17 22 | 8 21 14 | 8 14 2 | 3 9 25 | 0 0 21 | 8 20 57 | - | 1789 | 29 14 55 | 9 9 36 | 7 19 39 | 4 18 7 | 0 18 44 | 8 0 38 | - | 1790 | 18 23 43 | 8 28 52 | 5 29 27 | 4 26 10 | 0 8 1 | 7 11 51 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1791 | 8 8 32 | 8 18 8 | 4 9 15 | 5 4 13 | 11 27 17 | 6 23 4 | - | 1792 | 26 6 5 | 9 6 20 | 3 14 52 | 6 12 56 | 0 15 40 | 6 2 45 | - | 1793 | 15 14 53 | 8 25 46 | 1 24 40 | 6 20 59 | 0 4 58 | 5 13 59 | - | 1794 | 4 23 42 | 8 15 2 | 0 4 29 | 6 29 2 | 11 24 15 | 4 25 13 | - | 1795 | 23 21 14 | 9 3 14 | 11 10 5 | 8 7 45 | 0 12 39 | 4 4 54 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1796 | 12 6 3 | 8 22 39 | 9 19 53 | 8 15 48 | 0 1 56 | 3 16 8 | - | 1797 | 1 14 52 | 8 11 55 | 7 29 42 | 8 23 50 | 11 21 13 | 2 27 23 | - | 1798 | 20 12 24 | 9 0 7 | 7 5 18 | 10 2 33 | 0 9 36 | 2 7 3 | - | 1799 | 9 21 13 | 8 19 33 | 5 15 6 | 10 10 36 | 11 28 53 | 1 18 18 | - | 1800 | 27 18 46 | 9 7 46 | 4 20 43 | 11 19 19 | 0 17 16 | 0 27 57 | - +-------+----------+----------+----------+----------+----------+----------+ - +-------------------------------------------------------------------------+ - | TABLE IV. _The mean Full Moons, &c. in_ March _to the New Style_. | - +-------+----------+----------+----------+----------+----------+----------+ - |Years |Mean time |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - |of |of Full | mean | mean |distance |Longitude |Longitude | - |CHRIST.|Moon in |Anomaly. |Anomaly. |from the |from |from | - | |_March_. | | | Node. |Aries. |Aries. | - +-------+----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +-------+----------+----------+----------+----------+----------+----------+ - | 1753 | 18 23 18 | 7 18 35 | 7 25 21 | 4 19 4 | 11 27 8 | 7 8 4 | - | 1754 | 8 8 17 | 7 7 53 | 6 5 10 | 4 27 7 | 11 16 26 | 6 19 18 | - | 1755 | 27 5 49 | 8 26 14 | 5 10 46 | 6 5 49 | 0 4 49 | 5 29 0 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1756 | 15 14 38 | 8 15 30 | 3 20 35 | 6 13 52 | 11 24 6 | 5 10 14 | - | 1757 | 4 23 27 | 8 4 36 | 2 0 23 | 6 21 55 | 11 13 23 | 4 21 27 | - | 1758 | 23 20 59 | 8 23 8 | 1 5 59 | 8 0 38 | 0 1 46 | 4 1 9 | - | 1759 | 13 5 47 | 8 12 25 | 11 15 48 | 8 8 41 | 11 21 3 | 3 12 22 | - | 1760 | 1 14 36 | 8 1 41 | 9 25 37 | 8 16 44 | 11 10 20 | 2 23 35 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1761 | 20 12 9 | 8 20 2 | 9 1 13 | 9 25 27 | 11 28 43 | 2 3 16 | - | 1762 | 9 20 57 | 8 9 19 | 7 11 2 | 10 3 31 | 11 18 0 | 1 14 29 | - | 1763 | 28 18 30 | 8 27 40 | 6 16 38 | 11 12 13 | 0 6 23 | 0 24 11 | - | 1764 | 17 3 19 | 8 16 56 | 4 26 26 | 11 20 16 | 11 25 40 | 0 5 24 | - | 1765 | 6 12 8 | 8 6 13 | 3 6 15 | 11 28 19 | 11 14 57 | 11 16 38 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1766 | 25 9 40 | 8 24 34 | 2 11 52 | 1 7 1 | 0 3 20 | 10 26 20 | - | 1767 | 18 18 29 | 8 13 50 | 0 21 41 | 1 15 4 | 11 22 37 | 10 7 33 | - | 1768 | 3 3 17 | 8 3 6 | 11 1 29 | 1 23 7 | 11 11 54 | 9 18 46 | - | 1769 | 22 0 50 | 8 21 28 | 10 7 5 | 3 1 49 | 0 0 17 | 8 28 28 | - | 1770 | 11 9 39 | 8 15 45 | 8 16 54 | 3 9 52 | 11 19 34 | 8 9 42 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1771 | 30 7 11 | 8 29 6 | 7 22 30 | 4 18 36 | 0 7 57 | 7 19 21 | - | 1772 | 18 16 0 | 8 18 22 | 6 2 18 | 4 26 39 | 11 27 14 | 7 0 35 | - | 1773 | 8 0 48 | 8 7 38 | 4 12 7 | 5 4 42 | 11 16 31 | 6 11 49 | - | 1774 | 26 22 21 | 8 26 0 | 3 17 43 | 6 13 24 | 0 4 54 | 5 21 31 | - | 1775 | 16 7 10 | 8 15 16 | 1 27 31 | 6 21 27 | 11 24 11 | 5 2 44 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1776 | 4 15 58 | 8 4 32 | 0 7 20 | 6 29 30 | 11 13 28 | 4 13 58 | - | 1777 | 23 13 31 | 8 22 54 | 11 12 56 | 8 8 13 | 0 1 51 | 3 23 39 | - | 1778 | 12 22 20 | 8 12 10 | 9 22 45 | 8 16 16 | 11 21 8 | 3 4 52 | - | 1779 | 2 7 8 | 8 1 26 | 8 2 34 | 8 24 19 | 11 10 25 | 2 16 5 | - | 1780 | 20 4 41 | 8 19 48 | 7 8 10 | 10 3 1 | 11 28 48 | 1 25 47 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1781 | 9 13 30 | 8 9 4 | 5 17 59 | 10 11 4 | 11 18 5 | 1 7 0 | - | 1782 | 28 11 2 | 8 27 28 | 4 23 34 | 11 19 47 | 0 6 27 | 0 16 41 | - | 1783 | 17 19 51 | 8 16 44 | 3 3 23 | 11 27 50 | 11 25 44 | 11 27 54 | - | 1784 | 6 4 40 | 8 5 59 | 1 13 12 | 0 5 53 | 11 15 1 | 11 9 7 | - | 1785 | 25 2 12 | 8 24 20 | 0 18 48 | 1 14 36 | 0 3 24 | 10 18 48 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1786 | 14 11 1 | 8 13 36 | 10 28 37 | 1 22 39 | 11 22 41 | 10 0 2 | - | 1787 | 3 19 49 | 8 2 52 | 9 8 25 | 2 0 42 | 11 11 58 | 9 11 15 | - | 1788 | 21 17 22 | 8 21 14 | 8 14 2 | 3 9 25 | 0 0 21 | 8 20 57 | - | 1789 | 11 2 11 | 8 10 30 | 6 23 51 | 3 17 28 | 11 19 38 | 8 2 10 | - | 1790 | 29 23 43 | 8 28 52 | 5 29 27 | 4 26 10 | 0 8 1 | 7 11 51 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1791 | 19 8 32 | 8 18 8 | 4 9 15 | 5 4 13 | 11 27 17 | 6 23 4 | - | 1792 | 7 17 21 | 8 7 24 | 2 19 4 | 5 12 16 | 11 16 34 | 6 4 17 | - | 1793 | 26 14 53 | 8 25 46 | 1 24 40 | 6 20 59 | 0 4 58 | 5 13 59 | - | 1794 | 15 23 42 | 8 15 2 | 0 4 29 | 6 29 2 | 11 24 15 | 4 25 13 | - | 1795 | 5 8 30 | 8 4 18 | 10 14 17 | 7 7 5 | 0 13 32 | 4 6 26 | - +-------+----------+----------+----------+----------+----------+----------+ - | 1796 | 23 6 3 | 8 22 39 | 9 19 53 | 8 15 48 | 0 1 56 | 3 16 8 | - | 1797 | 12 14 52 | 8 11 55 | 7 29 42 | 8 23 50 | 11 21 13 | 2 27 23 | - | 1798 | 1 23 40 | 8 1 11 | 6 9 30 | 9 1 53 | 11 10 30 | 2 8 36 | - | 1799 | 20 21 13 | 8 19 33 | 5 15 6 | 10 10 36 | 11 28 53 | 1 18 18 | - | 1800 | 10 6 2 | 8 8 50 | 3 24 55 | 10 18 39 | 11 18 10 | 0 29 31 | - +-------+----------+----------+----------+----------+----------+----------+ - +----------------------------------------------------------------------------+ - | TAB. V. _The first mean Conjunction of the Sun and Moon after a compleat | - | Century, beginning with_ March, _for 5000 years 10 days 7 hours 56 | - | minutes (in which time there are just 61843 mean Lunations) with the | - | mean Anomaly of the Sun and Moon, the Sun’s mean distance from the | - | Ascending Node, and the mean Long. of the Sun and Node from the | - | beginning of the sign Aries, at the times of all those mean | - | Conjunctions_. | - +---------+-----------+----------+----------+----------+----------+----------+ - |Centuries| First |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - | of |Conjunction| mean | mean |distance |Longitude |Longitude | - |_Julian_ | after a | Anomaly. | Anomaly. |from the |from |from | - | Years. | Century. | | |Node. |Aries. |Aries. | - + +-----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +---------+-----------+----------+----------+----------+----------+----------+ - | 100 | 4 8 11 | 0 3 21 | 8 15 22 | 4 19 27 | 0 5 2 | 4 14 25 | - | 200 | 8 16 22 | 0 6 42 | 5 0 44 | 9 8 55 | 0 10 4 | 8 28 51 | - | 300 | 13 0 33 | 0 10 3 | 1 16 6 | 1 28 22 | 0 15 6 | 1 13 16 | - | 400 | 17 8 43 | 0 13 24 | 10 1 28 | 6 17 49 | 0 20 8 | 5 27 41 | - | 500 | 21 16 54 | 0 16 46 | 6 16 50 | 11 7 16 | 0 25 10 | 10 12 6 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 600 | 26 1 5 | 0 20 7 | 3 2 12 | 3 26 44 | 1 0 12 | 2 26 32 | - | 700 | 0 20 32 | 11 24 22 | 10 21 45 | 7 15 31 | 0 6 7 | 7 9 24 | - | 800 | 5 4 43 | 11 27 43 | 7 7 7 | 0 4 58 | 0 11 9 | 11 23 49 | - | 900 | 9 12 54 | 0 1 4 | 3 22 29 | 4 24 25 | 0 16 12 | 4 8 13 | - | 1000 | 13 21 5 | 0 4 25 | 0 7 51 | 9 13 53 | 0 21 14 | 8 22 39 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 1100 | 18 5 16 | 0 7 46 | 8 23 13 | 2 3 20 | 0 26 16 | 1 7 4 | - | 1200 | 22 13 26 | 0 11 7 | 5 8 35 | 6 22 47 | 1 1 18 | 5 21 29 | - | 1300 | 26 21 37 | 0 14 28 | 1 23 57 | 11 12 15 | 1 6 20 | 10 5 55 | - | 1400 | 1 17 4 | 11 18 43 | 9 13 30 | 3 1 2 | 0 12 15 | 2 18 47 | - | 1500 | 6 1 15 | 11 22 4 | 5 28 52 | 7 20 29 | 0 17 17 | 7 3 12 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 1600 | 10 9 26 | 11 25 25 | 2 14 14 | 0 9 56 | 0 22 19 | 11 17 37 | - | 1700 | 14 17 37 | 11 28 46 | 10 29 36 | 4 29 23 | 0 27 22 | 4 2 2 | - | 1800 | 19 1 48 | 0 2 8 | 7 14 58 | 9 18 51 | 1 2 24 | 8 16 27 | - | 1900 | 23 9 58 | 0 5 29 | 4 0 20 | 2 8 18 | 1 7 26 | 1 0 52 | - | 2000 | 27 18 9 | 0 8 50 | 0 15 42 | 6 27 45 | 1 12 28 | 5 15 17 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 2100 | 2 13 36 | 11 13 5 | 8 5 15 | 10 16 32 | 0 18 24 | 9 28 8 | - | 2200 | 6 21 47 | 11 16 26 | 4 20 37 | 3 6 0 | 0 23 26 | 2 12 34 | - | 2300 | 11 5 58 | 11 19 47 | 1 5 59 | 7 25 27 | 0 28 28 | 6 26 59 | - | 2400 | 15 14 9 | 11 23 8 | 9 21 21 | 0 14 54 | 1 3 30 | 11 11 24 | - | 2500 | 19 22 20 | 11 26 29 | 6 6 43 | 5 4 11 | 1 8 32 | 3 25 49 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 2600 | 24 6 31 | 11 29 50 | 2 22 4 | 9 23 49 | 1 13 35 | 8 10 14 | - | 2700 | 28 14 41 | 0 3 11 | 11 17 26 | 2 13 16 | 1 18 37 | 0 24 39 | - | 2800 | 3 10 8 | 11 7 26 | 6 26 59 | 6 2 3 | 0 24 31 | 5 7 33 | - | 2900 | 7 18 19 | 11 10 47 | 3 12 21 | 10 21 30 | 0 29 33 | 9 21 58 | - | 3000 | 12 2 30 | 11 14 8 | 11 27 43 | 3 10 58 | 1 4 35 | 2 6 23 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 3100 | 16 10 41 | 11 17 30 | 8 13 5 | 8 10 25 | 1 9 37 | 6 20 48 | - | 3200 | 20 18 52 | 11 20 51 | 4 28 27 | 0 19 52 | 1 14 39 | 11 5 13 | - | 3300 | 25 3 3 | 11 24 11 | 1 13 49 | 5 9 20 | 1 19 41 | 3 19 39 | - | 3400 | 29 11 14 | 11 27 32 | 9 29 11 | 9 28 47 | 1 24 43 | 8 4 4 | - | 3500 | 4 6 41 | 11 1 47 | 5 18 44 | 1 17 34 | 1 0 41 | 0 16 53 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 3600 | 8 14 52 | 11 4 58 | 2 4 6 | 6 7 1 | 1 5 42 | 5 1 19 | - | 3700 | 12 23 3 | 11 8 9 | 10 19 28 | 10 26 28 | 1 10 43 | 9 15 45 | - | 3800 | 17 7 14 | 11 11 20 | 7 4 50 | 3 15 55 | 1 15 45 | 2 0 10 | - | 3900 | 21 15 25 | 11 14 31 | 4 20 12 | 8 5 22 | 1 20 47 | 6 14 35 | - | 4000 | 25 23 36 | 11 17 42 | 1 5 34 | 0 24 49 | 1 25 49 | 10 29 0 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 4100 | 0 19 3 | 10 22 56 | 8 25 7 | 4 13 36 | 1 0 45 | 3 12 51 | - | 4200 | 5 3 14 | 10 26 17 | 5 10 29 | 9 3 3 | 1 6 47 | 7 6 16 | - | 4300 | 9 11 25 | 10 29 37 | 1 25 51 | 1 12 30 | 1 11 48 | 11 25 39 | - | 4400 | 13 19 36 | 11 2 58 | 10 11 13 | 6 1 57 | 1 16 51 | 4 10 4 | - | 4500 | 18 3 46 | 11 6 18 | 6 26 35 | 10 21 24 | 1 21 53 | 8 29 31 | - +---------+-----------+----------+----------+----------+----------+----------+ - | 4600 | 22 11 57 | 11 9 39 | 3 11 15 | 3 10 51 | 1 26 55 | 1 13 56 | - | 4700 | 26 20 7 | 11 12 59 | 11 27 19 | 8 0 16 | 2 1 57 | 5 28 19 | - | 4800 | 1 15 34 | 10 17 14 | 7 16 52 | 11 19 4 | 1 7 53 | 10 11 11 | - | 4900 | 5 23 45 | 10 20 35 | 4 2 14 | 4 8 30 | 1 12 55 | 2 25 35 | - | 5000 | 10 7 56 | 10 23 56 | 0 17 36 | 8 27 57 | 1 17 57 | 7 10 0 | - +---------+-----------+----------+----------+----------+----------+----------+ - +-----------------------------------------------------------------------------+ - | TABLE VI. _The mean Anomaly of the Sun and Moon, the Sun’s mean | - | distance from the Ascending Node, with the mean Longitude of the Sun | - | and Node from the beginning of the Sign Aries, for 13 mean Lunations._ | - +----------+-----------+----------+----------+----------+----------+----------+ - | | |The Sun’s |The Moon’s|The Sun’s |The Sun’s |The Node’s| - |Lunations.| Mean | mean | mean |motion | mean |retrograde| - | |Lunations. |Anomaly. | Anomaly. |from |Motion. |Motion. | - | | | | |the Node. | | | - | +-----------+----------+----------+----------+----------+----------+ - | | D. H. M. | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | s ° ʹ | - +----------+-----------+----------+----------+----------+----------+----------+ - | 1 | 29 12 44 | 0 29 6| 0 25 49 | 1 0 40 | 0 29 6 | 0 1 34 | - | 2 | 59 1 28 | 1 28 13| 1 21 38 | 2 1 20 | 1 28 13 | 0 3 8 | - | 3 | 88 14 12 | 2 27 19| 2 17 27 | 3 2 1 | 2 27 19 | 0 4 41 | - | 4 | 118 2 56 | 3 26 26| 3 13 16 | 4 2 41 | 3 26 26 | 0 6 15 | - | 5 | 147 15 4 | 4 25 32| 4 9 5 | 5 3 21 | 4 25 32 | 0 7 49 | - +----------+-----------+----------+----------+----------+----------+----------+ - | 6 | 177 4 24 | 5 24 38 | 5 4 54 | 6 4 1 | 5 24 38 | 0 9 23 | - | 7 | 206 17 8 | 6 23 44 | 6 0 43 | 7 4 42 | 6 23 45 | 0 10 57 | - | 8 | 236 5 52 | 7 22 50 | 6 26 32 | 8 5 22 | 7 22 51 | 0 12 31 | - | 9 | 265 18 36 | 8 21 57 | 7 22 21 | 9 6 2 | 8 21 58 | 0 14 4 | - | 10 | 295 7 21 | 9 21 3 | 8 18 10 | 10 6 42 | 9 21 4 | 0 15 38 | - +----------+-----------+----------+----------+----------+----------+----------+ - | 11 | 324 20 5 | 10 20 9 | 9 13 59 | 11 7 22 | 10 20 10 | 0 17 12 | - | 12 | 354 8 49 | 11 19 16 | 10 9 48 | 0 8 3 | 11 19 17 | 0 18 46 | - | 13 | 383 21 33 | 0 18 22 | 11 5 37 | 1 8 43 | 0 18 23 | 0 20 20 | - +----------+-----------+----------+----------+----------+----------+----------+ - -The first, second, third, and fourth Tables may be continued, by means -of the sixth, to any length of time: for, by adding 12 Lunations to the -mean time of the New or Full Moon which happens next after the 11th day -of _March_, and then, casting out 365 days in common years, and 366 days -in leap-years, we have the mean time of New or Full Moon in _March_ the -following year. But when the mean New or Full Moon happens on or before -the 11th of _March_, there must be 13 Lunations added to carry it to -_March_ again. The Anomalies, Sun’s distance from the Node, and -Longitude of the Sun, are found the same way, by adding them for 12 or -13 Lunations. But the retrograde Motion of the Node for these Lunations -must be subtracted from it’s longitude from Aries in _March_, to have -it’s Longitude or Place in the _March_ following. - - +----------------------------------------------------+ - | TABLE VII. _The number of Days, reckoned | - | from the beginning of_ March, _answering to | - | the Days of all the mean New and Full Moons_. | - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - |Days|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec|Jan|Feb| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 1 | 1| 32| 62| 93|123|154|185|215|246|276|307|338| - | 2 | 2| 33| 63| 94|124|155|186|216|247|277|308|339| - | 3 | 3| 34| 64| 95|125|156|187|217|248|278|309|340| - | 4 | 4| 35| 65| 96|126|157|188|218|249|279|310|341| - | 5 | 5| 36| 66| 97|127|158|189|219|250|280|311|342| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 6 | 6| 37| 67| 98|128|159|190|220|251|281|312|343| - | 7 | 7| 38| 68| 99|129|160|191|221|252|282|313|344| - | 8 | 8| 39| 69|100|130|161|192|222|253|283|314|345| - | 9 | 9| 40| 70|101|131|162|193|223|254|284|315|346| - | 10 | 10| 41| 71|102|132|163|194|224|255|285|316|347| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 11 | 11| 42| 72|103|133|164|195|225|256|286|317|348| - | 12 | 12| 43| 73|104|134|165|196|226|257|287|318|349| - | 13 | 13| 44| 74|105|135|166|197|227|258|288|319|350| - | 14 | 14| 45| 75|106|136|167|198|228|259|289|320|351| - | 15 | 15| 46| 76|107|137|168|199|229|260|290|321|352| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 16 | 16| 47| 77|108|138|169|200|230|261|291|322|353| - | 17 | 17| 48| 78|109|139|170|201|231|262|292|323|354| - | 18 | 18| 49| 79|110|140|171|202|232|263|293|324|355| - | 19 | 19| 50| 80|111|141|172|203|233|264|294|325|356| - | 20 | 20| 51| 81|112|142|173|204|234|265|295|326|357| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 21 | 21| 52| 82|113|143|174|205|235|266|296|327|358| - | 22 | 22| 53| 83|114|144|175|206|236|267|297|328|359| - | 23 | 23| 54| 84|115|145|176|207|237|268|298|329|360| - | 24 | 24| 55| 85|116|146|177|208|238|269|299|330|361| - | 25 | 25| 56| 86|117|147|178|209|239|270|300|331|362| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - | 26 | 26| 57| 87|118|148|179|210|240|271|301|332|363| - | 27 | 27| 58| 88|119|149|180|211|241|272|302|333|364| - | 28 | 28| 59| 89|120|150|181|212|242|273|303|334|365| - | 29 | 29| 60| 90|121|151|182|213|243|274|304|335|366| - | 30 | 30| 61| 91|122|152|183|214|244|275|305|336|---| - | 31 | 31| --| 92|---|153|184|---|245|---|306|337|---| - +----+---+---+---+---+---+---+---+---+---+---+---+---+ - +-----------------------------------------+ - |TABLE VIII. _The Moon’s annual Equation._| - +-----+-----------------------------+-----+ - |Sun’s| Subtract |Sun’s| - |Ano. +----+----+----+----+----+----+Ano. | - | | 0 | 1 | 2 | 3 | 4 | 5 | | - | | S. | S. | S. | S. | S. | S. | | - +-----+----+----+----+----+----+----+-----+ - | D. | M. | M. | M. | M. | M. | M. | D. | - +-----+----+----+----+----+----+----+-----+ - | 0 | 0 | 11 | 18 | 22 | 19 | 11 | 30 | - | 1 | 0 | 11 | 19 | 22 | 19 | 11 | 29 | - | 2 | 1 | 11 | 19 | 22 | 18 | 10 | 28 | - | 3 | 1 | 11 | 19 | 22 | 18 | 10 | 27 | - | 4 | 1 | 12 | 19 | 22 | 18 | 10 | 26 | - | 5 | 2 | 12 | 19 | 22 | 18 | 9 | 25 | - | 6 | 2 | 12 | 19 | 21 | 18 | 9 | 24 | - | 7 | 3 | 13 | 20 | 21 | 17 | 9 | 23 | - | 8 | 3 | 13 | 20 | 21 | 17 | 8 | 22 | - | 9 | 3 | 13 | 20 | 21 | 17 | 8 | 21 | - | 10 | 4 | 14 | 20 | 21 | 17 | 8 | 20 | - | 11 | 4 | 14 | 20 | 21 | 16 | 7 | 19 | - | 12 | 4 | 14 | 20 | 21 | 16 | 7 | 18 | - | 13 | 5 | 14 | 20 | 21 | 16 | 6 | 17 | - | 14 | 5 | 15 | 20 | 21 | 16 | 6 | 16 | - | 15 | 5 | 15 | 21 | 21 | 15 | 6 | 15 | - | 16 | 6 | 15 | 21 | 21 | 15 | 5 | 14 | - | 17 | 6 | 15 | 21 | 21 | 15 | 5 | 13 | - | 18 | 6 | 16 | 21 | 21 | 15 | 5 | 12 | - | 19 | 7 | 16 | 21 | 20 | 14 | 4 | 11 | - | 20 | 7 | 16 | 21 | 20 | 14 | 4 | 10 | - | 21 | 7 | 16 | 21 | 20 | 14 | 3 | 9 | - | 22 | 8 | 17 | 21 | 20 | 13 | 3 | 8 | - | 23 | 8 | 17 | 21 | 20 | 13 | 3 | 7 | - | 24 | 9 | 17 | 21 | 20 | 13 | 2 | 6 | - | 25 | 9 | 17 | 21 | 20 | 13 | 2 | 5 | - | 26 | 9 | 18 | 21 | 20 | 12 | 2 | 4 | - | 27 | 10 | 18 | 21 | 19 | 12 | 1 | 3 | - | 28 | 10 | 18 | 21 | 19 | 12 | 1 | 2 | - | 29 | 10 | 18 | 22 | 19 | 11 | 0 | 1 | - | 30 | 11 | 18 | 22 | 19 | 11 | 0 | 0 | - +-----+----+----+----+----+----+----+-----+ - |Sun’s| 11 | 10 | 9 | 8 | 7 | 6 |Sun’s| - |Ano. | S. | S. | S. | S. | S. | S. |Ano. | - | +----+----+----+----+----+----+ | - | | Add | | - +-----+-----------------------------+-----+ - +-----------------------------------------+ - | TABLE IX. _Equation of the Moon’s | - | mean Anomaly._ | - +-----+-----------------------------+-----+ - |Sun’s| |Sun’s| - |Anom.| Add |Anom.| - +-----+----+----+----+----+----+----+-----+ - | | 0 | 1 | 2 | 3 | 4 | 5 | | - | | S. | S. | S. | S. | S. | S. | | - +-----+----+----+----+----+----+----+-----+ - | ° | ʹ | ʹ | ʹ | ʹ | ʹ | ʹ | ° | - +-----+----+----+----+----+----+----+-----+ - | 0 | 0 | 10 | 17 | 20 | 17 | 10 | 30 | - | 1 | 0 | 10 | 17 | 20 | 17 | 10 | 29 | - | 2 | 1 | 11 | 17 | 20 | 17 | 9 | 28 | - | 3 | 1 | 11 | 18 | 20 | 17 | 9 | 27 | - | 4 | 1 | 11 | 18 | 20 | 17 | 9 | 26 | - | 5 | 2 | 12 | 18 | 20 | 17 | 9 | 25 | - | 6 | 2 | 12 | 18 | 20 | 16 | 8 | 24 | - | 7 | 2 | 12 | 18 | 20 | 16 | 8 | 23 | - | 8 | 3 | 12 | 18 | 20 | 16 | 8 | 22 | - | 9 | 3 | 12 | 19 | 20 | 16 | 7 | 21 | - | 10 | 3 | 13 | 19 | 20 | 16 | 7 | 20 | - | 11 | 4 | 13 | 19 | 20 | 15 | 7 | 19 | - | 12 | 4 | 13 | 19 | 20 | 15 | 6 | 18 | - | 13 | 4 | 13 | 19 | 19 | 15 | 6 | 17 | - | 14 | 5 | 14 | 19 | 19 | 15 | 6 | 16 | - | 15 | 5 | 14 | 19 | 19 | 14 | 5 | 15 | - | 16 | 5 | 14 | 19 | 19 | 14 | 5 | 14 | - | 17 | 6 | 14 | 19 | 19 | 14 | 5 | 13 | - | 18 | 6 | 15 | 19 | 19 | 14 | 4 | 12 | - | 19 | 6 | 15 | 20 | 19 | 13 | 4 | 11 | - | 20 | 7 | 15 | 20 | 19 | 13 | 4 | 10 | - | 21 | 7 | 15 | 20 | 19 | 13 | 3 | 9 | - | 22 | 7 | 16 | 20 | 19 | 13 | 3 | 8 | - | 23 | 8 | 16 | 20 | 19 | 12 | 3 | 7 | - | 24 | 8 | 16 | 20 | 18 | 12 | 2 | 6 | - | 25 | 8 | 16 | 20 | 18 | 12 | 2 | 5 | - | 26 | 9 | 16 | 20 | 18 | 11 | 1 | 4 | - | 27 | 9 | 17 | 20 | 18 | 11 | 1 | 3 | - | 28 | 9 | 17 | 20 | 18 | 11 | 1 | 2 | - | 29 | 10 | 17 | 20 | 18 | 10 | 0 | 1 | - | 30 | 10 | 17 | 20 | 17 | 10 | 0 | 0 | - +-----+----+----+----+----+----+----+-----+ - | | 11 | 10 | 9 | 8 | 7 | 6 | | - |Sun’s| S. | S. | S. | S. | S. | S.|Sun’s| - |Anom.+----+----+----+----+----+----+Anom.| - | | Subtract | | - +-----+-----------------------------+-----+ - +-------------------------------------------------------------+ - | TABLE X. _The Moon’s elliptic Equation._ | - +------+-----------------------------------------------+------+ - | | | | - |Moon’s| Add |Moon’s| - | +-------+-------+-------+-------+-------+-------+ | - | Ano. | 0 | 1 | 2 | 3 | 4 | 5 |Ano. | - | | Signs | Signs | Signs | Signs | Signs | Signs | | - +------+-------+-------+-------+-------+-------+-------+------+ - | ° | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | ° | - +------+-------+-------+-------+-------+-------+-------+------+ - | 0 | 0 0 | 4 49 | 8 8 | 9 2 | 7 32 | 4 14 | 30 | - | 1 | 0 10 | 4 57 | 8 12 | 9 1 | 7 27 | 4 6 | 29 | - | 2 | 0 20 | 5 5 | 8 16 | 9 0 | 7 22 | 3 58 | 28 | - | 3 | 0 30 | 5 13 | 8 20 | 8 59 | 7 17 | 3 50 | 27 | - | 4 | 0 40 | 5 21 | 8 24 | 8 58 | 7 12 | 3 42 | 26 | - | 5 | 0 50 | 5 29 | 8 28 | 8 57 | 7 6 | 3 34 | 25 | - | 6 | 1 0 | 5 37 | 8 31 | 8 55 | 7 0 | 3 26 | 24 | - | 7 | 1 10 | 5 45 | 8 34 | 8 53 | 6 54 | 3 18 | 23 | - | 8 | 1 20 | 5 53 | 8 37 | 8 51 | 6 48 | 3 10 | 22 | - | 9 | 1 30 | 6 1 | 8 40 | 8 49 | 6 42 | 3 2 | 21 | - | 10 | 1 40 | 6 9 | 8 43 | 8 47 | 6 36 | 2 53 | 20 | - | 11 | 1 50 | 6 16 | 8 45 | 8 44 | 6 30 | 2 45 | 19 | - | 12 | 2 0 | 6 23 | 8 47 | 8 41 | 6 24 | 2 37 | 18 | - | 13 | 2 10 | 6 30 | 8 49 | 8 38 | 6 18 | 2 29 | 17 | - | 14 | 2 20 | 6 37 | 8 51 | 8 35 | 6 11 | 2 21 | 16 | - | 15 | 2 30 | 6 44 | 8 53 | 8 32 | 6 4 | 2 12 | 15 | - | 16 | 2 40 | 6 51 | 8 55 | 8 29 | 5 57 | 2 3 | 14 | - | 17 | 2 50 | 6 58 | 8 57 | 8 26 | 5 50 | 1 54 | 13 | - | 18 | 3 0 | 7 4 | 8 59 | 8 23 | 5 43 | 1 45 | 12 | - | 19 | 3 10 | 7 10 | 9 0 | 8 20 | 5 36 | 1 36 | 11 | - | 20 | 3 19 | 7 16 | 9 1 | 8 16 | 5 29 | 1 27 | 10 | - | 21 | 3 28 | 7 22 | 9 2 | 8 12 | 5 22 | 1 19 | 9 | - | 22 | 3 37 | 7 28 | 9 2 | 8 8 | 5 15 | 1 11 | 8 | - | 23 | 3 46 | 7 33 | 9 3 | 8 4 | 5 8 | 1 3 | 7 | - | 24 | 3 55 | 7 38 | 9 3 | 8 0 | 5 1 | 0 54 | 6 | - | 25 | 4 4 | 7 43 | 9 4 | 7 56 | 4 54 | 0 45 | 5 | - | 26 | 4 13 | 7 48 | 9 4 | 7 52 | 4 46 | 0 36 | 4 | - | 27 | 4 22 | 7 53 | 9 4 | 7 47 | 4 38 | 0 27 | 3 | - | 28 | 4 31 | 7 58 | 9 3 | 7 42 | 4 30 | 0 18 | 2 | - | 29 | 4 40 | 8 3 | 9 3 | 7 37 | 4 22 | 0 9 | 1 | - | 30 | 4 49 | 8 8 | 9 2 | 7 32 | 4 14 | 0 0 | 0 | - +------+-------+-------+-------+-------+-------+-------+------+ - | | 11 | 10 | 9 | 8 | 7 | 6 | | - |Moon’s| Signs | Signs | Signs | Signs | Signs | Signs |Moon’s| - | +-------+-------+-------+-------+-------+-------+ | - | Ano. | Subtract | Ano. | - +------+-----------------------------------------------+------+ - +---------------------------------------------------------------+ - | TABLE XI. _The Sun’s Equation at the time of | - | New and Full Moon._ | - +-------+-----------------------------------------------+-------+ - | | Subtract | | - | Sun’s +-------+-------+-------+-------+-------+-------+ Sun’s | - | Anom. | 0 | 1 | 2 | 3 | 4 | 5 | Anom. | - | | Signs | Signs | Signs | Signs | Signs | Signs | | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | ° | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | ° | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | 0 | 0 0 | 1 44 | 3 2 | 3 32 | 3 5 | 1 48 | 30 | - | 1 | 0 4 | 1 47 | 3 3 | 3 32 | 3 3 | 1 45 | 29 | - | 2 | 0 7 | 1 50 | 3 5 | 3 32 | 3 2 | 1 42 | 28 | - | 3 | 0 11 | 1 53 | 3 7 | 3 32 | 3 0 | 1 38 | 27 | - | 4 | 0 14 | 1 57 | 3 9 | 3 32 | 2 58 | 1 35 | 26 | - | 5 | 0 18 | 2 0 | 3 10 | 3 31 | 2 56 | 1 31 | 25 | - | 6 | 0 22 | 2 3 | 3 12 | 3 31 | 2 54 | 1 28 | 24 | - | 7 | 0 25 | 2 6 | 3 14 | 3 31 | 2 52 | 1 24 | 23 | - | 8 | 0 29 | 2 8 | 3 16 | 3 30 | 2 50 | 1 21 | 22 | - | 9 | 0 32 | 2 11 | 3 17 | 4 30 | 2 48 | 1 17 | 21 | - | 10 | 0 36 | 2 14 | 3 18 | 3 30 | 2 45 | 1 14 | 20 | - | 11 | 0 40 | 2 17 | 3 19 | 3 29 | 2 43 | 1 11 | 19 | - | 12 | 0 43 | 2 20 | 3 20 | 3 29 | 2 40 | 1 7 | 18 | - | 13 | 0 47 | 2 22 | 3 21 | 3 28 | 2 37 | 1 4 | 17 | - | 14 | 0 50 | 2 25 | 3 22 | 3 27 | 2 35 | 1 0 | 16 | - | 15 | 0 54 | 2 28 | 3 23 | 3 26 | 2 32 | 0 56 | 15 | - | 16 | 0 57 | 2 30 | 3 24 | 3 25 | 2 29 | 0 52 | 14 | - | 17 | 1 0 | 2 32 | 3 25 | 3 24 | 2 26 | 0 49 | 13 | - | 18 | 1 4 | 2 35 | 3 26 | 3 23 | 2 23 | 0 45 | 12 | - | 19 | 1 7 | 2 38 | 3 27 | 3 22 | 2 21 | 0 41 | 11 | - | 20 | 1 11 | 2 40 | 3 28 | 3 21 | 2 18 | 0 38 | 10 | - | 21 | 1 14 | 2 43 | 3 28 | 3 20 | 2 15 | 0 34 | 9 | - | 22 | 1 17 | 2 45 | 3 29 | 3 19 | 2 12 | 0 30 | 8 | - | 23 | 1 21 | 2 47 | 3 29 | 3 18 | 2 10 | 0 26 | 7 | - | 24 | 1 24 | 2 49 | 3 30 | 3 17 | 2 7 | 0 23 | 6 | - | 25 | 1 28 | 2 51 | 3 30 | 3 15 | 2 4 | 0 19 | 5 | - | 26 | 1 31 | 2 54 | 3 31 | 3 13 | 2 1 | 0 15 | 4 | - | 27 | 1 34 | 2 57 | 3 31 | 3 11 | 1 58 | 0 11 | 3 | - | 28 | 1 38 | 2 59 | 3 31 | 3 9 | 1 55 | 0 7 | 2 | - | 29 | 1 41 | 3 1 | 3 32 | 3 7 | 1 52 | 0 4 | 1 | - | 30 | 1 44 | 3 2 | 3 32 | 3 5 | 1 48 | 0 0 | 0 | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | | 11 | 10 | 9 | 8 | 7 | 6 | | - | Sun’s | Signs | Signs | Signs | Signs | Signs | Signs | Sun’s | - | Anom. +-------+-------+-------+-------+-------+-------+ Anom. | - | | Add | | - +-------+-----------------------------------------------+-------+ - +---------------------------------------------------------------+ - | TABLE XII. _Equation of the Sun’s mean Place._ | - +-------+-----------------------------------------------+-------+ - | | Subtract | | - | Sun’s +-------+-------+-------+-------+-------+-------+ Sun’s | - | Anom. | 0 | 1 | 2 | 3 | 4 | 5 | Anom. | - | | Signs | Signs | Signs | Signs | Signs | Signs | | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | ° | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° ʹ | ° | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | 0 | 0 0 | 0 57 | 1 40 | 1 56 | 1 42 | 0 59 | 30 | - | 1 | 0 2 | 0 59 | 1 41 | 1 56 | 1 41 | 0 57 | 29 | - | 2 | 0 4 | 1 0 | 1 42 | 1 56 | 1 40 | 0 56 | 28 | - | 3 | 0 6 | 1 1 | 1 43 | 1 56 | 1 39 | 0 54 | 27 | - | 4 | 0 8 | 1 2 | 1 44 | 1 56 | 1 38 | 0 52 | 26 | - | 5 | 0 10 | 1 4 | 1 45 | 1 56 | 1 36 | 0 50 | 25 | - | 6 | 0 12 | 1 6 | 1 45 | 1 56 | 1 35 | 0 48 | 24 | - | 7 | 0 14 | 1 7 | 1 46 | 1 55 | 1 34 | 0 46 | 23 | - | 8 | 0 16 | 1 9 | 1 47 | 1 55 | 1 33 | 0 44 | 22 | - | 9 | 0 18 | 1 10 | 1 48 | 1 55 | 1 32 | 0 42 | 21 | - | 10 | 0 20 | 1 12 | 1 48 | 1 54 | 1 30 | 0 41 | 20 | - | 11 | 0 22 | 1 14 | 1 49 | 1 54 | 1 29 | 0 39 | 19 | - | 12 | 0 24 | 1 15 | 1 50 | 1 54 | 1 28 | 0 37 | 18 | - | 13 | 0 26 | 1 17 | 1 51 | 1 53 | 1 26 | 0 35 | 17 | - | 14 | 0 28 | 1 18 | 1 51 | 1 53 | 1 25 | 0 33 | 16 | - | 15 | 0 30 | 1 20 | 1 52 | 1 52 | 1 23 | 0 31 | 15 | - | 16 | 0 31 | 1 21 | 1 52 | 1 52 | 1 22 | 0 29 | 14 | - | 17 | 0 33 | 1 22 | 1 53 | 1 51 | 1 21 | 0 27 | 13 | - | 18 | 0 35 | 1 24 | 1 53 | 1 51 | 1 19 | 0 25 | 12 | - | 19 | 0 37 | 1 25 | 1 54 | 1 50 | 1 18 | 0 23 | 11 | - | 20 | 0 39 | 1 27 | 1 54 | 1 49 | 1 16 | 0 21 | 10 | - | 21 | 0 41 | 1 28 | 1 55 | 1 49 | 1 14 | 0 19 | 9 | - | 22 | 0 43 | 1 29 | 1 55 | 1 48 | 1 13 | 0 17 | 8 | - | 23 | 0 45 | 1 30 | 1 55 | 1 47 | 1 11 | 0 14 | 7 | - | 24 | 0 46 | 1 32 | 1 56 | 1 46 | 1 10 | 0 12 | 6 | - | 25 | 0 48 | 1 33 | 1 56 | 1 46 | 1 8 | 0 10 | 5 | - | 26 | 0 50 | 1 34 | 1 56 | 1 45 | 1 6 | 0 8 | 4 | - | 27 | 0 52 | 1 35 | 1 56 | 1 45 | 1 5 | 0 6 | 3 | - | 28 | 0 54 | 1 36 | 1 56 | 1 44 | 1 3 | 0 4 | 2 | - | 29 | 0 55 | 1 38 | 1 56 | 1 43 | 1 1 | 0 2 | 1 | - | 30 | 0 57 | 1 40 | 1 56 | 1 42 | 0 59 | 0 0 | 0 | - +-------+-------+-------+-------+-------+-------+-------+-------+ - | | 11 | 10 | 9 | 8 | 7 | 6 | | - | Sun’s | Signs | Signs | Signs | Signs | Signs | Signs | Sun’s | - | Anom. +-------+-------+-------+-------+-------+-------+ Anom. | - | | Add | | - +-------+-----------------------------------------------+-------+ - +-----------------------------------------+ - | TABLE XIII. _Equation of the | - | Moon’s Nodes._ | - +-----+-----------------------------+-----+ - | | Subtract | | - |Sun’s+----+----+----+----+----+----+Sun’s| - |Ano. | 0 | 1 | 2 | 3 | 4 | 5 |Ano. | - | | S. | S. | S. | S. | S. | S. | | - +-----+----+----+----+----+----+----+-----+ - | ° | ʹ | ʹ | ʹ | ʹ | ʹ | ʹ | ° | - +-----+----+----+----+----+----+----+-----+ - | 0 | 0 | 5 | 8 | 10 | 8 | 5 | 30 | - | 1 | 0 | 5 | 8 | 10 | 8 | 5 | 29 | - | 2 | 0 | 5 | 8 | 10 | 8 | 5 | 28 | - | 3 | 0 | 5 | 8 | 10 | 8 | 4 | 27 | - | 4 | 1 | 5 | 8 | 10 | 8 | 4 | 26 | - | 5 | 1 | 5 | 8 | 10 | 8 | 4 | 25 | - | 6 | 1 | 6 | 9 | 10 | 8 | 4 | 24 | - | 7 | 1 | 6 | 9 | 9 | 8 | 4 | 23 | - | 8 | 1 | 6 | 9 | 9 | 8 | 4 | 22 | - | 9 | 1 | 6 | 9 | 9 | 7 | 3 | 21 | - | 10 | 2 | 6 | 9 | 9 | 7 | 3 | 20 | - | 11 | 2 | 6 | 9 | 9 | 7 | 3 | 19 | - | 12 | 2 | 6 | 9 | 9 | 7 | 3 | 18 | - | 13 | 2 | 6 | 9 | 9 | 7 | 3 | 17 | - | 14 | 2 | 7 | 9 | 9 | 7 | 3 | 16 | - | 15 | 2 | 7 | 9 | 9 | 7 | 3 | 15 | - | 16 | 2 | 7 | 9 | 9 | 7 | 2 | 14 | - | 17 | 3 | 7 | 9 | 9 | 7 | 2 | 13 | - | 18 | 3 | 7 | 9 | 9 | 6 | 2 | 12 | - | 19 | 3 | 7 | 9 | 9 | 6 | 2 | 11 | - | 20 | 3 | 7 | 9 | 9 | 6 | 2 | 10 | - | 21 | 3 | 7 | 9 | 9 | 6 | 2 | 9 | - | 22 | 4 | 7 | 9 | 9 | 6 | 1 | 8 | - | 23 | 4 | 8 | 9 | 9 | 6 | 1 | 7 | - | 24 | 4 | 8 | 9 | 9 | 6 | 1 | 6 | - | 25 | 4 | 8 | 9 | 9 | 6 | 1 | 5 | - | 26 | 4 | 8 | 10 | 9 | 5 | 1 | 4 | - | 27 | 4 | 8 | 10 | 9 | 5 | 1 | 3 | - | 28 | 4 | 8 | 10 | 8 | 5 | 0 | 2 | - | 29 | 5 | 8 | 10 | 8 | 5 | 0 | 1 | - | 30 | 5 | 8 | 10 | 8 | 5 | 0 | 0 | - +-----+----+----+----+----+----+----+-----+ - | | 11 | 10 | 9 | 8 | 7 | 6 | | - |Sun’s| S. | S. | S. | S. | S. | S. |Sun’s| - |Ano. +----+----+----+----+----+----+Ano. | - | | Add | | - +-----------------------------------+-----+ - | The above titles, _Add_ and _Subtract_, | - | are right when the Equation is applied | - | to the Sun’s mean distance from the | - | Node; but when it is applied to the | - | mean place of the Node, the titles must | - | be changed. | - +-----------------------------------------+ - +------------------------+ - | TAB. XIV. _The | - | Moon’s latitude | - | in Eclipses._ | - +------------------------+ - | Argument of Latit. | - +------+-----------------+ - | Moon | | - | fr. | Sig. 0 N. A. | - | the | Sig. 6 S. D. | - | Node.| | - +------+----------+------+ - | ° | ° ʹ ʺ | ° | - +------+----------+------+ - | 0 | 0 0 0 | 30 | - | 1 | 0 5 15 | 29 | - | 2 | 0 10 30 | 28 | - | 3 | 0 15 44 | 27 | - | 4 | 0 20 59 | 26 | - | 5 | 0 26 13 | 25 | - | 6 | 0 31 26 | 24 | - | 7 | 0 36 39 | 23 | - | 8 | 0 41 51 | 22 | - | 9 | 0 47 2 | 21 | - | 10 | 0 52 13 | 20 | - | 11 | 0 57 23 | 19 | - | 12 | 1 2 31 | 18 | - | 13 | 1 7 38 | 17 | - | 14 | 1 12 44 | 16 | - | 15 | 1 17 49 | 15 | - | 16 | 1 22 52 | 14 | - | 17 | 1 27 53 | 13 | - | 18 | 1 32 54 | 12 | - +------+----------+------+ - | | Moon | - | N. D. Sig. 5 | fr. | - | S. A. Sig. 11 | the | - | | Node.| - +-----------------+------+ - | Argument of Latit. | - +------------------------+ - | This Table extends | - | no farther than the | - | limits of Eclipses. | - | N. A. signifies North | - | Ascending Lat. S. A. | - | South Ascending; N. D. | - | North Descending; | - | and S. D. South | - | Descending. | - +------------------------+ - +--------------------------------------------------------+ - | TABLE XV. _The Moons Horizontal Parallax; | - | the Semidiameters and true Horary motions | - | of the Sun and Moon._ | - +--------------------------------------------------------+ - | Anomaly of the Sun and Moon. | - | +------------------------------------------------+ - | | Moon’s Horizontal Parallax. | - | | +----------------------------------------+ - | | | Sun’s Semidiameter. | - | | | +--------------------------------+ - | | | | Moon’s Semidiamet. | - | | | | +------------------------+ - | | | | | Moon’s horary Mot. | - | | | | | +----------------+ - | | | | | | Sun’s | - | | | | | | horary Mot. | - | | | | | | +---------+ - | | | | | | | Anomaly | - | | | | | | | of the | - | | | | | | | Sun and | - | | | | | | | Moon. | - +-------+-------+-------+-------+-------+------+---------+ - | ^s ° | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ʹ ʺ | ^s ° | - +-------+-------+-------+-------+-------+------+---------+ - | 0 0 | 54 59 | 15 50 | 14 54 | 30 10 | 2 23 | 12 0 | - | 6 | 54 59 | 15 50 | 14 55 | 30 12 | 2 23 | 24 | - | 12 | 55 0 | 15 50 | 14 56 | 30 15 | 2 23 | 18 | - | 18 | 55 4 | 15 51 | 14 57 | 30 18 | 2 23 | 12 | - | 24 | 55 11 | 15 51 | 14 58 | 30 26 | 2 23 | 6 | - | 1 0 | 55 20 | 15 52 | 14 59 | 30 34 | 2 23 | 11 0 | - | 6 | 55 30 | 15 53 | 15 1 | 30 44 | 2 24 | 24 | - | 12 | 55 40 | 13 54 | 15 4 | 30 55 | 2 24 | 18 | - | 18 | 55 51 | 15 55 | 15 8 | 31 9 | 2 24 | 12 | - | 24 | 56 0 | 15 56 | 15 12 | 31 23 | 2 25 | 6 | - | 2 0 | 56 11 | 15 58 | 15 17 | 31 40 | 2 25 | 10 0 | - | 6 | 56 24 | 15 59 | 15 22 | 31 58 | 2 26 | 24 | - | 12 | 56 41 | 16 1 | 15 26 | 32 17 | 2 27 | 18 | - | 18 | 57 12 | 16 2 | 15 30 | 32 39 | 2 27 | 12 | - | 24 | 57 30 | 16 4 | 15 36 | 33 11 | 2 28 | 6 | - | 3 0 | 57 49 | 16 6 | 15 41 | 33 23 | 2 28 | 9 0 | - | 6 | 58 10 | 16 8 | 15 46 | 33 47 | 2 29 | 24 | - | 12 | 58 31 | 16 9 | 15 52 | 34 11 | 2 29 | 18 | - | 18 | 58 52 | 16 11 | 15 58 | 34 34 | 2 29 | 12 | - | 24 | 59 11 | 16 13 | 16 3 | 34 58 | 2 30 | 6 | - | 4 0 | 59 30 | 16 14 | 16 9 | 35 22 | 2 30 | 8 0 | - | 6 | 59 52 | 16 15 | 16 14 | 35 45 | 2 31 | 24 | - | 12 | 60 9 | 16 17 | 16 19 | 36 0 | 2 31 | 18 | - | 18 | 60 26 | 16 19 | 16 24 | 36 20 | 2 32 | 12 | - | 24 | 60 40 | 16 20 | 16 28 | 36 40 | 2 32 | 6 | - | 5 0 | 60 54 | 16 21 | 16 31 | 37 0 | 2 32 | 7 0 | - | 6 | 61 4 | 16 21 | 16 34 | 37 10 | 2 33 | 24 | - | 12 | 61 11 | 16 22 | 16 37 | 37 19 | 2 33 | 18 | - | 18 | 61 16 | 16 22 | 16 38 | 37 28 | 2 33 | 12 | - | 24 | 61 20 | 16 23 | 16 39 | 37 36 | 2 33 | 6 | - | 6 0 | 61 24 | 16 23 | 16 39 | 37 40 | 2 33 | 6 0 | - +-------+-------+-------+-------+-------+------+---------+ - | The gradual increase or decrease of the above numbers | - | being so small, it is sufficient to have them to every | - | sixth degree; the proportions for the intermediate | - | degrees being easily made by sight. | - +--------------------------------------------------------+ - +----------------------------------+ - | TABLE XVI. _The Sun’s mean | - | Motion and Anomaly._ | - +---------+-------------+----------+ - | | Sun’s mean | Sun’s | - |Years of | Longitude | mean | - |Christ | from Aries. | Anomaly. | - |beginning+-------------+----------+ - | | ^s ° ʹ ʺ | ^s ° ʹ| - +---------+-------------+----------+ - O.S. | 1 | 9 7 53 10 | 6 29 54 | - | 1301 | 9 17 42 30 | 6 16 58 | - | 1401 | 9 18 27 50 | 6 15 59 | - | 1501 | 9 19 13 10 | 6 14 59 | - | 1601 | 9 19 58 30 | 6 13 59 | - | 1701 | 9 20 43 50 | 6 12 59 | - N.S. | 1753 | 9 10 16 52 | 6 1 38 | - | 1801 | 9 9 39 39 | 6 0 10 | - Old Style +---------+-------------+----------+ - to the | | Sun’s mean | Sun’s | - beginning |Years of | Motion. | mean | - of A. D. |Christ | | Anomaly. | - 1753; |compleat +-------------+----------+ - then | | ^s ° ʹ ʺ | ^s ° ʹ| - New Style +---------+-------------+----------+ - | 1 | 11 29 45 40 | 11 29 45 | - | 2 | 11 29 31 20 | 11 29 29 | - | 3 | 11 29 17 0 | 11 29 14 | - | 4 | 0 0 1 49 | 11 29 58 | - | 5 | 11 29 47 29 | 11 29 42 | - | 6 | 11 29 33 9 | 11 29 27 | - | 7 | 11 29 18 49 | 11 29 11 | - | 8 | 0 0 3 38 | 11 29 55 | - | 9 | 11 29 49 18 | 11 29 40 | - | 10 | 11 29 34 58 | 11 29 24 | - | 11 | 11 29 20 38 | 11 29 9 | - | 12 | 0 0 5 26 | 11 29 53 | - | 13 | 11 29 51 7 | 11 29 37 | - | 14 | 11 29 36 47 | 11 29 22 | - | 15 | 11 29 22 27 | 11 29 7 | - | 16 | 0 0 7 15 | 11 29 50 | - | 17 | 11 29 52 55 | 11 29 35 | - | 18 | 11 29 38 35 | 11 29 20 | - | 19 | 11 29 24 16 | 11 29 4 | - | 20 | 0 0 9 4 | 11 29 48 | - | 40 | 0 0 18 8 | 11 29 36 | - | 60 | 0 0 27 12 | 11 29 24 | - | 80 | 0 0 36 16 | 11 29 12 | - | 100 | 0 0 45 20 | 11 29 0 | - | 200 | 0 1 30 40 | 11 28 1 | - | 300 | 0 2 16 0 | 11 27 1 | - | 400 | 0 3 1 20 | 11 26 1 | - | 500 | 0 3 46 40 | 11 25 2 | - | 600 | 0 4 32 0 | 11 24 2 | - | 700 | 0 5 17 20 | 11 23 2 | - | 800 | 0 6 2 40 | 11 22 3 | - | 900 | 0 6 48 0 | 11 21 3 | - | 1000 | 0 7 33 20 | 11 20 3 | - | 2000 | 0 15 6 40 | 11 10 7 | - | 3000 | 0 22 40 0 | 11 0 10 | - | 4000 | 1 0 13 20 | 10 20 13 | - | 5000 | 1 7 46 40 | 10 10 16 | - | 6000 | 1 15 20 0 | 10 0 19 | - +---------+-------------+----------+ - | | Sun’s mean | Sun’s | - | | Motion. | mean | - | | | Anomaly. | - | Months +-------------+----------+ - | | ^s ° ʹ ʺ | ^s ° ʹ| - +---------+-------------+----------+ - | Jan. | 0 0 0 0 | 0 0 0 | - | Feb. | 1 0 33 18 | 1 0 33 | - | Mar. | 1 28 9 11 | 1 28 9 | - | Apr. | 2 28 42 30 | 2 28 42 | - | May. | 3 28 16 40 | 3 28 17 | - | June | 4 28 49 58 | 4 28 50 | - | July | 5 28 24 8 | 5 28 24 | - | Aug. | 6 28 57 26 | 6 28 57 | - | Sep. | 7 29 30 44 | 7 29 30 | - | Oct. | 8 29 4 54 | 8 29 4 | - | Nov. | 9 29 38 12 | 9 29 37 | - | Dec. | 10 29 12 22 | 10 29 11 | - +---------+-------------+----------+ - +-----+-------------+ - | | Sun’s mean | - | | Motion and | - | | Anomaly. | - |Days.+-------------+ - | | ^s ° ʹ ʺ | - +-----+-------------+ - | 1 | 0 0 59 8 | - | 2 | 0 1 58 17 | - | 3 | 0 2 57 25 | - | 4 | 0 3 56 33 | - | 5 | 0 4 55 42 | - | 6 | 0 5 54 50 | - | 7 | 0 5 53 58 | - | 8 | 0 7 53 7 | - | 9 | 0 8 52 15 | - | 10 | 0 9 51 23 | - | 11 | 0 10 50 32 | - | 12 | 0 11 49 40 | - | 13 | 0 12 48 48 | - | 14 | 0 13 47 57 | - | 15 | 0 14 47 5 | - | 16 | 0 15 46 13 | - | 17 | 0 16 45 22 | - | 18 | 0 17 44 30 | - | 19 | 0 18 43 38 | - | 20 | 0 19 42 47 | - | 21 | 0 20 41 55 | - | 22 | 0 21 41 3 | - | 23 | 0 22 40 12 | - | 24 | 0 23 39 20 | - | 25 | 0 24 38 28 | - | 26 | 0 25 37 37 | - | 27 | 0 26 36 45 | - | 28 | 0 27 35 53 | - | 29 | 0 28 35 2 | - | 30 | 0 29 34 10 | - | 31 | 1 0 33 18 | - +-----+-------------+ - | In Leap-years, | - | after _February_, | - | add one Day and | - | one Day’s motion. | - +-------------------+ - +----------------------+ - | Sun’s mean Motion | - | and Anomaly. | - +------+---------------+ - |Hours.| Mot. & Ano. | - | +---------------+ - | | ° ʹ ʺ | - | ʹ | ʹ ʺ ʺʹ | - | ʺ | ʺ ʺʹ ʺʺ | - +------+---------------+ - | 1 | 0 2 28 | - | 2 | 0 4 56 | - | 3 | 0 7 24 | - | 4 | 0 9 51 | - | 5 | 0 12 19 | - | 6 | 0 14 47 | - | 7 | 0 17 15 | - | 8 | 0 19 43 | - | 9 | 0 22 11 | - | 10 | 0 24 38 | - | 11 | 0 27 6 | - | 12 | 0 29 34 | - | 13 | 0 32 2 | - | 14 | 0 34 30 | - | 15 | 0 36 58 | - | 16 | 0 39 26 | - | 17 | 0 41 53 | - | 18 | 0 44 21 | - | 19 | 0 46 49 | - | 20 | 0 49 17 | - | 21 | 0 51 45 | - | 22 | 0 54 13 | - | 23 | 0 56 40 | - | 24 | 0 59 8 | - | 25 | 1 1 36 | - | 26 | 1 4 4 | - | 27 | 1 6 32 | - | 28 | 1 9 0 | - | 29 | 1 11 28 | - | 30 | 1 13 55 | - | 31 | 1 16 23 | - | 32 | 1 18 51 | - | 33 | 1 21 19 | - | 34 | 1 23 47 | - | 35 | 1 26 15 | - | 36 | 1 28 42 | - | 37 | 1 31 10 | - | 38 | 1 33 38 | - | 39 | 1 36 6 | - | 40 | 1 38 34 | - | 41 | 1 41 2 | - | 42 | 1 43 30 | - | 43 | 1 45 57 | - | 44 | 1 48 25 | - | 45 | 1 50 53 | - | 46 | 1 53 21 | - | 47 | 1 55 49 | - | 48 | 1 58 17 | - | 49 | 2 0 44 | - | 50 | 2 3 12 | - | 51 | 2 5 40 | - | 52 | 2 8 8 | - | 53 | 2 10 36 | - | 54 | 2 13 4 | - | 55 | 2 15 32 | - | 56 | 2 17 59 | - | 57 | 2 20 27 | - | 58 | 2 22 55 | - | 59 | 2 25 23 | - | 60 | 2 27 51 | - +------+---------------+ - | In Leap-years, after | - | _February_, add one | - | Day and one Day’s | - | motion. | - +----------------------+ - +----------------------------------------------+ - | TABLE XVII. _The Sun’s Declination | - | in every Degree of the Ecliptic._ | - +-----+-----------+-----------+-----------+----+ - | | ♈ ♎ | ♉ ♏ | ♊ ♐ | | - |Signs| 0 6 | 1 7 | 2 8 | | - | | Nor. Sou. | Nor. Sou. | Nor. Sou. | | - +-----+-----------+-----------+-----------+----+ - | ° | ° ʹ ʺ | ° ʹ ʺ | ° ʹ ʺ | ° | - +-----+-----------+-----------+-----------+----+ - | 0 | 0 0 0 | 11 29 33 | 20 11 16 | 30 | - | 1 | 0 23 54 | 11 50 35 | 20 23 49 | 29 | - | 2 | 0 47 48 | 12 11 26 | 20 36 0 | 28 | - | 3 | 1 11 42 | 12 32 5 | 20 47 48 | 27 | - | 4 | 1 35 34 | 12 52 31 | 20 59 13 | 26 | - | 5 | 1 59 25 | 13 12 44 | 21 10 15 | 25 | - | 6 | 2 23 14 | 13 32 54 | 21 20 53 | 24 | - | 7 | 2 47 1 | 13 52 32 | 21 31 7 | 23 | - | 8 | 3 10 45 | 14 12 5 | 21 40 58 | 22 | - | 9 | 3 34 26 | 14 31 24 | 21 50 24 | 21 | - | 10 | 3 58 4 | 14 50 28 | 21 59 25 | 20 | - | 11 | 4 21 38 | 15 9 17 | 22 8 2 | 19 | - | 12 | 4 45 8 | 15 27 51 | 22 16 14 | 18 | - | 13 | 5 8 34 | 15 46 9 | 22 24 0 | 17 | - | 14 | 5 31 55 | 16 4 11 | 22 31 21 | 16 | - | 15 | 5 55 11 | 16 21 57 | 22 38 16 | 15 | - | 16 | 6 18 21 | 16 39 26 | 22 44 45 | 14 | - | 17 | 6 41 25 | 16 56 37 | 22 50 49 | 13 | - | 18 | 7 4 23 | 17 13 31 | 22 56 26 | 12 | - | 19 | 7 27 15 | 17 30 7 | 23 1 36 | 11 | - | 20 | 7 50 0 | 17 46 15 | 23 6 20 | 10 | - | 21 | 8 12 36 | 18 2 24 | 23 10 38 | 9 | - | 22 | 8 35 5 | 18 18 3 | 23 14 29 | 8 | - | 23 | 8 57 26 | 18 33 24 | 23 17 52 | 7 | - | 24 | 9 19 39 | 18 48 25 | 23 20 49 | 6 | - | 25 | 9 41 43 | 19 3 5 | 23 23 19 | 5 | - | 26 | 10 3 37 | 19 17 26 | 23 25 22 | 4 | - | 27 | 10 25 21 | 19 31 25 | 23 26 57 | 3 | - | 28 | 10 46 56 | 19 45 3 | 23 28 5 | 2 | - | 29 | 11 8 20 | 19 58 20 | 23 28 46 | 1 | - | 30 | 11 29 33 | 20 11 16 | 23 29 0 | 0 | - +-----+-----------+-----------+-----------+----+ - | | ♓ ♍ | ♒ ♌ | ♑ ♋ | | - |Signs| 1 5 | 10 4 | 9 3 | | - | | Sou. Nor. | Sou. Nor. | Sou. Nor. | | - +-----+-----------+-----------+-----------+----+ - | If the Sun’s place be taken from the Tables | - | on pag. 114 and 115, his declination may be | - | had thereby, near enough for common use, | - | from this Table, by entering it with the | - | signs at the head and degrees at the left | - | hand; or with the signs at the foot and | - | degrees at the right hand. Thus, _March_ | - | the 5th, the Sun’s place is ♓ 14° 53ʹ | - | (call it 15°, being so near) to which | - | answers 5° 55ʹ 11ʺ of the south | - | declination. | - +---------------------------------------------+ - +---------------------------------+ - | TABLE XVIII. _Lunations | - | from 1 to 100000._ | - +--------+---------+----+----+----+ - | Lunat. | Days. | H. | M. | S. | - +--------+---------+----+----+----+ - | | Contain | | | | - | 1 | 29 | 12 | 44 | 3 | - | 2 | 59 | 1 | 28 | 6 | - | 3 | 88 | 14 | 12 | 9 | - | 4 | 118 | 2 | 56 | 13 | - | 5 | 147 | 15 | 40 | 16 | - +--------+---------+----+----+----+ - | 6 | 177 | 4 | 24 | 19 | - | 7 | 206 | 17 | 8 | 22 | - | 8 | 236 | 5 | 52 | 25 | - | 9 | 265 | 18 | 36 | 28 | - | 10 | 295 | 7 | 20 | 31 | - +--------+---------+----+----+----+ - | 20 | 590 | 14 | 41 | 3 | - | 30 | 885 | 22 | 1 | 34 | - | 40 | 1181 | 5 | 22 | 6 | - | 50 | 1476 | 12 | 42 | 37 | - | 60 | 1771 | 20 | 3 | 9 | - +--------+---------+----+----+----+ - | 70 | 2067 | 3 | 23 | 40 | - | 80 | 2362 | 10 | 44 | 12 | - | 90 | 2657 | 18 | 4 | 43 | - | 100 | 2953 | 1 | 25 | 15 | - | 200 | 5906 | 2 | 50 | 30 | - +--------+---------+----+----+----+ - | 300 | 8859 | 4 | 15 | 45 | - | 400 | 11812 | 5 | 41 | 0 | - | 500 | 14765 | 7 | 6 | 15 | - | 600 | 17718 | 8 | 31 | 30 | - | 700 | 20671 | 9 | 56 | 45 | - +--------+---------+----+----+----+ - | 800 | 23624 | 11 | 22 | 0 | - | 900 | 26577 | 12 | 47 | 15 | - | 1000 | 29530 | 14 | 12 | 30 | - | 2000 | 59061 | 4 | 25 | 0 | - | 3000 | 88591 | 18 | 37 | 30 | - +--------+---------+----+----+----+ - | 4000 | 118122 | 8 | 50 | 0 | - | 5000 | 147652 | 23 | 2 | 30 | - | 6000 | 177183 | 13 | 15 | 0 | - | 7000 | 206714 | 3 | 27 | 30 | - | 8000 | 236244 | 17 | 40 | 0 | - +--------+---------+----+----+----+ - | 9000 | 265775 | 7 | 52 | 30 | - | 10000 | 295305 | 22 | 5 | | - | 20000 | 590611 | 20 | 10 | | - | 30000 | 885917 | 18 | 15 | | - | 40000 | 1181223 | 16 | 20 | | - +--------+---------+----+----+----+ - | 50000 | 1476529 | 14 | 25 | | - | 60000 | 1771835 | 12 | 30 | | - | 70000 | 2067141 | 10 | 35 | | - | 80000 | 2362447 | 8 | 40 | | - | 90000 | 2657753 | 6 | 45 | | - | 100000 | 2953059 | 4 | 50 | | - +--------+---------+----+----+----+ - | By comparing this Table with | - | the Table on page 113, it is | - | easy to find how many Lunations | - | are contained in any given | - | number of Sidereal, Julian, and | - | Solar years, from 1 to 8000. | - +---------------------------------+ - - - - - CHAP. XX. - - _Of the fixed Stars._ - - -[Sidenote: Why the fixed Stars appear bigger when viewed by the bare eye - than when seen through a telescope.] - -391. The Stars are said to be fixed, because they have been generally -observed to keep at the same distance from each other: their apparent -diurnal revolutions being caused solely by the Earth’s turning on its -Axis. They appear of a sensible magnitude to the bare eye, because the -retina is affected not only by the rays of light which are emitted -directly from them, but by many thousands more, which falling upon our -eye-lids, and upon the aerial particles about us, are reflected into our -eyes so strongly as to excite vibrations not only in those points of the -retina where the real images of the Stars are formed, but also in other -points at some distance round about. This makes us imagine the Stars to -be much bigger than they would appear, if we saw them only by the few -rays which come directly from them, so as to enter our eyes without -being intermixed with others. Any one may be sensible of this, by -looking at a Star of the first Magnitude through a long narrow tube; -which, though it takes in as much of the sky as would hold a thousand -such Stars, yet scarce renders that one visible. - -[Sidenote: A proof that they shine by their own light.] - -The more a telescope magnifies, the less is the aperture through which -the Star is seen; and consequently the fewer rays it admits into the -eye. Now since the Stars appear less in a telescope which magnifies 200 -times than they do to the bare eye, insomuch that they seem to be only -indivisible points, it proves at once both that the Stars are at immense -distances from us, and that they shine by their own proper light. If -they shone by borrowed light they would be as invisible without -telescopes as the Satellites of Jupiter are: for these Satellites appear -bigger when viewed with a good telescope than the largest fixed Stars -do. - -[Sidenote: Their number much less than is generally imagined.] - -392. The number of Stars discoverable, in either Hemisphere, by the -naked eye, is not above a thousand. This at first may appear incredible, -because they seem to be without number: But the deception arises from -our looking confusedly upon them, without reducing them into any order. -For look but stedfastly upon a pretty large portion of the sky, and -count the number of Stars in it, you will be surprised to find them so -few. Or, if one considers how seldom the Moon meets with any Stars in -her way, although there are as many about her Path as in other parts of -the Heavens (the _Milky way_ excepted) he will soon be convinced that -the Stars are much thinner sown than he was aware of. The _British_ -catalogue, which, besides the Stars visible to the bare eye, includes a -great number which cannot be seen without the assistance of a telescope, -contains no more than 3000, in both Hemispheres. - -[Sidenote: The absurdity of supposing the Stars were made only to - enlighten our nights.] - -393. As we have incomparably more light from the Moon than from all the -Stars together, it were the greatest absurdity to imagine that the Stars -were made for no other purpose than to cast a faint light upon the -Earth: especially since many more require the assistance of a good -telescope to find them out, than are visible without that Instrument. -Our Sun is surrounded by a system of Planets and Comets; all which would -be invisible from the nearest fixed Star. And from what we already know -of the immense distance of the Stars, the nearest may be computed at -32,000,000,000,000 of miles from us which is more than a cannon bullet -would fly in 7,000,000 of years. Hence ’tis easy to prove, that the Sun -seen from such a distance, would appear no bigger than a Star of the -first magnitude. From all this it is highly probable that each Star is a -Sun to a system of worlds moving round it though unseen by us; -especially, as the doctrine of a plurality of worlds is rational, and -greatly manifests the Power, Wisdom, and Goodness of the great Creator. - -[Sidenote: Their different Magnitudes.] - -394. The Stars, on account of their apparently various magnitudes, have -been distributed into several classes or orders. Those which appear -largest are called _Stars of the first magnitude_; the next to them in -lustre, _Stars of the second magnitude_, and so on to the _sixth_, which -are the smallest that are visible to the bare eye. This distribution -having been made long before the invention of telescopes, the Stars -which cannot be seen without the assistance of these instruments are -distinguished by the name of _Telescopic Stars_. - -[Sidenote: And division into Constellations.] - -395. The antients divided the starry Sphere into particular -Constellations, or Systems of Stars, according as they lay near one -another, so as to occupy those spaces which the figures of different -sorts of animals or things would take up, if they were there delineated. -And those Stars which could not be brought into any particular -Constellation were called _unformed Stars_. - -[Sidenote: The use of this division.] - -396. This division of the Stars into different Constellations or -Asterisms, serves to distinguish them from one another, so that any -particular Star may be readily found in the Heavens by means of a -Celestial Globe; on which the Constellations are so delineated as to put -the most remarkable Stars into such parts of the figures as are most -easily distinguished. The number of the antient Constellations is 48, -and upon our present Globes about 70. On _Senex_’s Globes are inserted -_Bayer_’s Letters; the first in the Greek Alphabet being put to the -biggest Star in each Constellation, the second to the next, and so on: -by which means, every Star is as easily found as if a name were given to -it. Thus, if the Star γ in the Constellation of the _Ram_ be mentioned, -every Astronomer knows as well what Star is meant as if it were pointed -out to him in the Heavens. - -[Sidenote: The _Zodiac_.] - -397. There is also a division of the Heavens into three parts. 1. The -_Zodiac_, (ζωδιακὸς) from ζώδιον _Zodion_ an Animal, because most of the -Constellations in it, which are twelve in number, are the figures of -Animals: as _Aries_ the Ram, _Taurus_ the Bull, _Gemini_ the Twins, -_Cancer_ the Crab, _Leo_ the Lion, _Virgo_ the Virgin, _Libra_ the -Balance, _Scorpio_ the Scorpion, _Sagittarius_ the Archer, _Capricornus_ -the Goat, _Aquarius_ the Water-bearer, and _Pisces_ the Fishes. The -Zodiac goes quite round the Heavens: it is about 16 degrees broad, so -that it takes in the Orbits of all the Planets, and likewise the Orbit -of the Moon. Along the middle of this Zone or Belt is the Ecliptic, or -Circle which the Earth describes annually as seen from the Sun; and -which the Sun appears to describe as seen from the Earth. 2. All that -Region of the Heavens, which is on the north side of the Zodiac, -containing 21 Constellations. And 3. that on the south side, containing -15. - -[Sidenote: The manner of dividing it by the antients.] - -398. The antients divided the _Zodiac_ into the above 12 Constellations -or Signs in the following manner. They took a vessel with a small hole -in the bottom, and having filled it with water, suffered the same to -distil drop by drop into another Vessel set beneath to receive it; -beginning at the moment when some Star rose, and continuing until it -rose the next following night. The water fallen down into the receiver -they divided into twelve equal parts; and having two other small vessels -in readiness, each of them fit to contain one part, they again poured -all the water into the upper vessel, and strictly observing the rising -of some Star in the _Zodiac_, they at the same time suffered the water -to drop into one of the small vessels; and as soon as it was full, they -shifted it and set an empty one in it’s place. By this means, when each -vessel was full, they observed what Star of the _Zodiac_ rose; and -though not possible in one night, yet in many, they observed the rising -of twelve Stars, by which they divided the _Zodiac_ into twelve parts. - - -399. The names of the Constellations, and the number of Stars observed -in each of them by different Astronomers, are as follows. - -Key to table P = _Ptolemy._ T = _Tycho._ H = _Hevelius._ F = -_Flamsteed._ - - The antient Constellations. - P T H F - Ursa minor The Little Bear 8 7 12 24 - Ursa major The Great Bear 35 29 73 87 - Draco The Dragon 31 32 40 80 - Cepheus Cepheus 13 4 51 35 - Bootes, _Arctophilax_ 23 18 52 54 - Corona Borealis The northern Crown 8 8 8 21 - Hercules, _Engonasin_ Hercules kneeling 29 28 45 113 - Lyra The Harp 10 11 17 21 - Cygnus, _Gallina_ The Swan 19 18 47 81 - Cassiopea The Lady in her Chair 13 26 37 55 - Perseus Perseus 29 29 46 59 - Auriga The Waggoner 14 9 40 66 - Serpentarius, _Ophiuchus_ Serpentarius 29 15 40 74 - Serpens The Serpent 18 13 22 64 - Sagitta The Arrow 5 5 5 18 - Aquila, _Vultur_ The Eagle } 12 23 - } 15 71 - Antinous Antinous } 3 19 - Delphinus The Dolphin 10 10 14 18 - Equulus, _Equi sectio_ The Horse’s Head 4 4 6 10 - Pegasus, _Equus_ The Flying Horse 20 19 38 89 - Andromeda Andromeda 23 23 47 66 - Triangulum The Triangle 4 4 12 16 - Aries The Ram 18 21 27 66 - Taurus The Bull 44 43 51 141 - Gemini The Twins 25 25 38 85 - Cancer The Crab 23 15 29 83 - Leo The Lion } 30 49 95 - } 35 - Coma Berenices Berenice’s Hair } 14 21 43 - Virgo The Virgin 32 33 50 110 - Libra, _Chelæ_ The Scales 17 10 20 51 - Scorpius The Scorpion 24 10 20 44 - Sagittarius The Archer 31 14 22 69 - Capricornus The Goat 28 28 29 51 - Aquarius The Water-bearer 45 41 47 108 - Pisces The Fishes 38 36 39 113 - Cetus The Whale 22 21 45 97 - Orion Orion 38 42 62 78 - Eridanus, _Fluvius_ Eridanus, _the River_ 34 10 27 84 - Lepus The Hare 12 13 16 19 - Canis major The Great Dog 29 13 21 31 - Canis minor The Little Dog 2 2 13 14 - Argo Navis The Ship 45 3 4 64 - Hydra The Hydra 27 19 31 60 - Crater The Cup 7 3 10 31 - Corvus The Crow 7 4 9 - Centaurus The Centaur 37 35 - Lupus The Wolf 19 24 - Ara The Altar 7 9 - Corona Australis The southern Crown 13 12 - Pisces Australis The southern Fish 18 24 - - - The New Southern Constellations. - - Columba Noachi Noah’s Dove 10 - Robur Carolinum The Royal Oak 12 - Grus The Crane 13 - Phœnix The Phenix 13 - Indus The Indian 12 - Pavo The Peacock 14 - Apus, _Avis Indica_ The Bird of Paradise 11 - Apis, _Musca_ The Bee or Fly 4 - Chamæleon The Chameleon 10 - Triangulum Australis The South Triangle 5 - Piscis volans, _Passer_ The Flying Fish 8 - Dorado, _Xiphias_ The Sword Fish 6 - Toucan The American Goose 9 - Hydrus The Water Snake 10 - - - _Hevelius_’s Constellations made out of the unformed Stars. - - _Hevelius._ _Flamsteed._ - Lynx The Lynx 19 44 - Leo minor The Little Lion 53 - Asterion & Chara The Greyhounds 23 25 - Cerberus Cerberus 4 - Vulpecula & Anser The Fox and Goose 27 35 - Scutum Sobieski Sobieski’s Shield 7 - Lacerta The Lizard 10 16 - Camelopardalus The Camelopard 32 58 - Monoceros The Unicorn 19 31 - Sextans The Sextant 11 41 - -[Sidenote: The _Milky Way_.] - -400. There is a remarkable track round the Heavens, called the _Milky -Way_ from its peculiar whiteness, which is owing to a great number of -Stars scattered therein; none of which can be distinctly seen without -telescopes. This track appears single in some parts, in others double. - -[Sidenote: Lucid Spots.] - -401. There are several little whitish spots in the Heavens, which appear -magnified, and more luminous when seen through telescopes; yet without -any Stars in them. One of these is in _Andromeda_’s girdle, first -observed _A. D._ 1612, by _Simon Marius_; and which has some whitish -rays near its middle: it is liable to several changes, and is sometimes -invisible. Another is near the Ecliptic, between the head and bow of -_Sagittarius_: it is small, but very luminous. A third is on the back of -the _Centaur_, which is too far South to be seen in _Britain_. A fourth, -of a smaller size, is before _Antinous_’s right foot; having a Star in -it, which makes it appear more bright. A fifth is in the Constellation -of _Hercules_, between the Stars ζ and η, which spot, though but small, -is visible to the bare eye if the sky be clear and the Moon absent. - -[Sidenote: Cloudy Stars. - - Magellanic Clouds.] - -402. _Cloudy Stars_ are so called from their misty appearance. They look -like dim Stars to the naked eye; but through a telescope they appear -broad illuminated parts of the sky; in some of which is one Star, in -others more. Five of these are mentioned by _Ptolemy_. 1. One at the -extremity of the right hand of _Perseus_. 2. One in the middle of the -_Crab_. 3. One unformed, near the Sting of the _Scorpion_. 4. The eye of -_Sagittarius_. 5. One in the head of _Orion_. In the first of these -appear more Stars through the telescope than in any of the rest, -although 21 have been counted in the head of _Orion_, and above 40 in -that of the _Crab_. Two are visible in the eye of _Sagittarius_ without -a telescope, and several more with it. _Flamsteed_ observed a cloudy -Star in the bow of _Sagittarius_, containing many small Stars: and the -Star _d_ above _Sagittary_’s right shoulder is encompassed with several -more. Both _Cassini_ and _Flamsteed_ discovered one between the _Great_ -and _Little Dog_, which is very full of Stars visible only by the -telescope. The two whitish spots near the South Pole, called the -_Magellanic Clouds_ by Sailors, which to the bare eye resemble part of -the Milky-Way, appear through telescopes to be a mixture of small Clouds -and Stars. But the most remarkable of all the cloudy Stars is that in -the middle of _Orion’s Sword_, where seven Stars (of which three are -very close together) seem to shine through a cloud, very lucid near the -middle, but faint and ill defined about the edges. It looks like a gap -in the sky, through which one may see (as it were) part of a much -brighter region. Although most of these spaces are but a few minutes of -a degree in breadth, yet, since they are among the fixed Stars, they -must be spaces larger than what is occupied by our solar System; and in -which there seems to be a perpetual uninterrupted day among numberless -Worlds which no human art ever can discover. - -[Sidenote: Changes in the Heavens.] - -403. Several Stars are mentioned by antient Astronomers, which are not -now to be found; and others are now visible to the bare eye which are -not recorded in the antient catalogues. _Hipparchus_ observed a new Star -about 120 years before CHRIST; but he has not mentioned in what part of -the Heavens it was seen, although it occasioned his making a catalogue -of the Stars; which is the most antient that we have. - -[Sidenote: New Stars.] - -The first _New Star_ that we have any good account of, was discovered by -_Cornelius Gemma_ on the 8th of _November_ A. D. 1572, in the Chair of -Cassiopea. It surpassed _Sirius_ in brightness and magnitude; and was -seen for 16 months successively. At first it appeared bigger than -_Jupiter_ to some eyes, by which it was seen even at mid-day: afterwards -it decayed gradually both in magnitude and lustre, until _March_ 1573, -when it became invisible. - -On the 13th of _August_ 1596, _David Fabricius_ observed the _Stella -Mira_, or wonderful Star, in the _Neck_ of the _Whale_; which has been -since found to appear and disappear periodically, seven times in six -years, continuing in its greatest lustre for 15 days together; and is -never quite extinguished. - -In the year 1600, _William Jansenius_ discovered a changeable Star in -the _Neck_ of the _Swan_; which, in time became so small as to be -thought to disappear entirely, till the years 1657, 1658, and 1659, when -it recovered its former lustre and magnitude; but soon decayed, and is -now of the smallest size. - -In the year 1604 _Kepler_ and several of his friends saw a new Star near -the heel of the right foot of _Serpentarius_, so bright and sparkling -that it exceeded any thing they had ever seen before; and took notice -that it was every moment changing into some of the colours of the -rainbow, except when it was near the horizon, at which time it was -generally white. It surpassed _Jupiter_ in magnitude, which was near it -all the month of _October_, but easily distinguished from it by a steady -light. It disappeared between _October_ 1605 and the _February_ -following, and has not been seen since that time. - -In the year 1670, _July_ 15, _Hevelius_ discovered a new Star, which in -_October_ was so decayed as to be scarce perceptible. In _April_ -following it regained its lustre, but wholly disappeared in _August_. In -_March_ 1672 it was seen again, but very small; and has not been visible -since. - -In the year 1686 a new Star was discovered by _Kirch_, which returns -periodically in 404 days. - -In the year 1672, _Cassini_ saw a Star in the _Neck_ of the Bull, which -he thought was not visible in _Tycho_’s time; nor when _Bayer_ made his -Figures. - -[Sidenote: Cannot be Comets.] - -404. Many Stars, besides those above-mentioned, have been observed to -change their magnitudes: and as none of them could ever be perceived to -have tails, ’tis plain they could not be Comets; especially as they had -no parallax, even when largest and brightest. It would seem that the -periodical Stars have vast clusters of dark spots, and very slow -rotations on their Axis; by which means, they must disappear when the -side covered with spots is turned towards us. And as for those which -break out all of a sudden with such lustre, ’tis by no means improbable -that they are Suns whose Fuel is almost spent, and again supplied by -some of their Comets falling upon them, and occasioning an uncommon -blaze and splendor for some time: which indeed appears to be the -greatest use of the cometary part of any system[86]. - -[Sidenote: Some Stars change their Places.] - -Some of the Stars, particularly _Arcturus_, have been observed to change -their places above a minute of a degree with respect to others. But -whether this be owing to any real motion in the Stars themselves, must -require the observations of many ages to determine. If our solar System -changeth its Place, with regard to absolute space, this must in process -of time occasion an apparent change in the distances of the Stars from -each other: and in such a case, the places of the nearest Stars to us -being more affected than of those which are very remote, their relative -positions must seem to alter, though the Stars themselves were really -immoveable. On the other hand, if our own system be at rest, and any of -the Stars in real motion, this must vary their positions; and the more -so, the nearer they are to us, or the swifter their motions are; or the -more proper the direction of their motion is, for our perception. - -[Sidenote: The Ecliptic less oblique now to the Equator than formerly.] - -405. The obliquity of the Ecliptic to the Equinoctial is found at -present to be above a third part of a degree less than _Ptolemy_ found -it. And most of the observers after him found it to decrease gradually -down to _Tycho_’s time. If it be objected, that we cannot depend on the -observations of the antients, because of the incorrectness of their -Instruments; we have to answer, that both _Tycho_ and _Flamsteed_ are -allowed to have been very good observers: and yet we find that -_Flamsteed_ makes this obliquely 2-1/2 minutes of a degree less than -_Tycho_ did, about 100 years before him: and as _Ptolemy_ was 1324 years -before _Tycho_, so the gradual decrease answers nearly to the difference -of time between these three Astronomers. If we consider, that the Earth -is not a perfect sphere, but an oblate spheroid, having its Axis shorter -than its Equatoreal diameter; and that the Sun and Moon are constantly -acting obliquely upon the greater quantity of matter about the Equator, -pulling it, as it were, towards a nearer and nearer co-incidence with -the Ecliptic; it will not appear improbable that these actions should -gradually diminish the Angle between those Planes. Nor is it less -probable that the mutual attractions of all the Planets should have a -tendency to bring the planes of all their Orbits to a co-incidence: but -this change is too small to become sensible in many ages. - - - - - CHAP. XXI. - -_Of the Division of Time. A perpetual Table of New Moons._ _The Times of -the Birth and Death of_ CHRIST. _A Table of remarkable Æras or Events._ - - -406. The parts of time are _Seconds_, _Minutes_, _Hours_, _Days_, -_Years_, _Cycles_, _Ages_, and _Periods_. - -[Sidenote: A Year.] - -407. The original standard, or integral measure of Time, is a year; -which is determined by the Revolution of some Celestial Body in its -Orbit, _viz._ the _Sun_ or _Moon_. - -[Sidenote: Tropical Year.] - -408. The time measured by the Sun’s Revolution in the Ecliptic, from any -Equinox or Solstice to the same again, is called the _Solar_ or -_Tropical Year_, which contains 365 days 5 hours 48 minutes 57 seconds; -and is the only proper or natural year, because it always keeps the same -seasons to the same months. - -[Sidenote: Sidereal year.] - -409. The quantity of time, measured by the Sun’s Revolution, as from any -fixed Star to the same Star again, is called the _Sidereal Year_; which -contains 365 days 6 hours 9 minutes 14-1/2 seconds; and is 20 minutes -17-1/2 seconds longer than the true Solar Year. - -[Sidenote: Lunar Year.] - -410. The time measured by twelve Revolutions of the Moon, from the Sun -to the Sun again, is called the _Lunar Year_; it contains 354 days 8 -hours 48 minutes 37 seconds; and is therefore 10 days 21 hours 0 minutes -20 seconds shorter than the Solar Year. This is the foundation of the -Epact. - -[Sidenote: Civil Year.] - -411. The _Civil Year_ is that which is in common use among the different -nations of the world; of which, some reckon by the Lunar, but most by -the Solar. The Civil Solar Year contains 365 days, for three years -running, which are called _Common Years_; and then comes in what is -called the _Bissextile_ or _Leap-Year_, which contains 366 days. This is -also called the _Julian Year_ on account of _Julius Cæsar_, who -appointed the Intercalary-day every fourth year, thinking thereby to -make the Civil and Solar Year keep pace together. And this day, being -added to the 23d of _February_, which in the _Roman_ Calendar, was the -sixth of the Calends of _March_, _that_ sixth day was twice reckoned, or -the 23d and 24th were reckoned as one day; and was called _Bis sextus -dies_, and thence came the name _Bissextile_ for that year. But in our -common Almanacks this day is added at the end of _February_. - -[Sidenote: Lunar Year.] - -412. The _Civil Lunar Year_ is also common or intercalary. The common -Year consists of 12 Lunations, which contain 354 days; at the end of -which, the year begins again. The _Intercalary_, or _Embolimic_ Year is -that wherein a month was added, to adjust the Lunar Year to the Solar. -This method was used by the _Jews_, who kept their account by the Lunar -Motions. But by intercalating no more than a month of 30 days, which -they called _Ve-Adar_, every third year, they fell 3-3/4 days short of -the Solar Year in that time. - -[Sidenote: _Roman_ Year.] - -413. The _Romans_ also used the _Lunar Embolimic Year_ at first, as it -was settled by _Romulus_ their first King, who made it to consist only -of ten months or Lunations; which fell 61 days short of the Solar Year, -and so their year became quite vague and unfixed; for which reason, they -were forced to have a Table published by the High Priest, to inform them -when the spring and other seasons began. But _Julius Cæsar_, as already -mentioned, § 411, taking this troublesome affair into consideration, -reformed the Calendar, by making the year to consist of 365 days 6 -hours. - -[Sidenote: The original of the _Gregorian_, or _New Style_.] - -414. The year thus settled, is what we still make use of in _Britain_: -but as it is somewhat more than 11 minutes longer than the _Solar -Tropical Year_, the times of the Equinoxes go backward, and fall earlier -by one day in about 130 years. In the time of the _Nicene Council_ (A. -D. 325.) which was 1431 years ago, the vernal Equinox fell on the 21st -of _March_: and, if we divide 1431 by 130, it will quote 11, which is -the number of days the Equinox has fallen back since the Council of -_Nice_. This causing great disturbances, by unfixing the times of the -celebration of _Easter_, and consequently of all the other moveable -Feasts, Pope _Gregory_ the 13th, in the year 1582 ordered ten days to be -at once struck out of that year; and the next day after the fourth of -_October_ was called the fifteenth. By this means the vernal Equinox was -restored to the 21st of _March_; and it was endeavoured, by the omission -of three intercalary days in 400 years, to make the civil or political -year keep pace with the Solar for time to come. This new form of the -year is called the _Gregorian Account_ or _New Style_; which is received -in all Countries where the Pope’s Authority is acknowledged, and ought -to be in all places where truth is regarded. - -[Sidenote: Months.] - -415. The principal division of the year is into _Months_, which are of -two sorts, namely _Astronomical_ and _Civil_. The Astronomical month is -the time in which the Moon runs through the _Zodiac_, and is either -_Periodical_ or _Synodical_. The Periodical Month is the time spent by -the Moon in making one compleat Revolution from any point of the Zodiac -to the same again; which is 27^d 7^h 43^m. The Synodical Month, called a -_Lunation_, is the time contained between the Moon’s parting with the -Sun at a Conjunction, and returning to him again; which is in 29^d 12^h -44^m. The Civil Months are those which are framed for the uses of Civil -life; and are different as to their names, number of days, and times of -beginning, in several different Countries. The first month of the -_Jewish Year_ fell according to the Moon in our _August_ and -_September_, Old Style; the second in _September_ and _October_, and so -on. The first month of the _Egyptian Year_ began on the 29th of our -_August_. The first month of the _Arabic_ and _Turkish Year_ began the -16th of _July_. The first month of the _Grecian Year_ fell according to -the Moon in _June_ and _July_, the second in _July_ and _August_, and so -on, as in the following Table. - - +----+--------------------------+----++----+-----------------------+----+ - |N^o | The Jewish year. |Days||N^o | The Egyptian year. |Days| - +----+--------------------------+----++----+-----------------------+----+ - | 1 |Tisri Aug.-Sept.| 30 || 1 |Thoth August 29 | 30 | - | 2 |Marchesvan Sept.-Oct.| 29 || 2 |Paophi Septemb. 28 | 30 | - | 3 |Casleu Oct.-Nov. | 30 || 3 |Athir October 28 | 30 | - | 4 |Tebeth Nov.-Dec. | 29 || 4 |Chojac Novemb. 27 | 30 | - | 5 |Shebat Dec.-Jan. | 30 || 5 |Tybi Decemb. 27 | 30 | - | 6 |Adar Jan.-Feb. | 29 || 6 |Mechir January 26 | 30 | - | 7 |Nisan _or_ Abib Feb.-Mar. | 30 || 7 |Phamenoth Februar. 25 | 30 | - | 8 |Jiar Mar.-Apr. | 29 || 8 |Parmuthi March 27 | 30 | - | 9 |Sivan April-May | 30 || 9 |Pachon April 26 | 30 | - | 10 |Tamuz May-June | 29 || 10 |Payni May 26 | 30 | - | 11 |Ab June-July | 30 || 11 |Epiphi June 25 | 30 | - | 12 |Elul July-Aug. | 29 || 12 |Mesori July 25 | 30 | - +----+--------------------------+----++----+-----------------------+----+ - | Days in the year |354 || _Epagomenæ_ or days added | 5 | - +-------------------------------+----++----------------------------+----+ - |In the __Embolimic_ year after | || Days in the year |365 | - | _Adar_ they added a month | || | | - | called _Ve-Adar_ of 30 days. | || | | - +-------------------------------+----++----------------------------+----+ - +---+-------------------------+----++---+----------------------------+----+ - |N^o|The _Arabic_ and |Days||N^o|The ancient _Grecian_ year. |Days| - | | _Turkish_ year. | || | | | - +---+-------------------------+----++---+----------------------------+----+ - | 1 |Muharram July 16 | 30 || 1 |Hecatombæon June-July | 30 | - | 2 |Saphar August 15 | 29 || 2 |Metagitnion July-Aug. | 29 | - | 3 |Rabia I. Septemb. 13 | 30 || 3 |Boedromion Aug.-Sept. | 30 | - | 4 |Rabia II. October 13 | 29 || 4 |Pyanepsion Sept.-Oct. | 29 | - | 5 |Jomada I. Novemb. 11 | 30 || 5 |Mæmacterion Oct.-Nov. | 30 | - | 6 |Jomada II. Decemb. 11 | 29 || 6 |Posideon Nov.-Dec. | 29 | - | 7 |Rajab January 9 | 30 || 7 |Gamelion Dec.-Jan. | 30 | - | 8 |Shasban February 8 | 29 || 8 |Anthesterion Jan.-Feb. | 29 | - | 9 |Ramadan March 9 | 30 || 9 |Elapheloblion Feb.-Mar. | 30 | - |10 |Shawal April 8 | 29 ||10 |Munichion Mar.-Apr. | 29 | - |11 |Dulhaadah May 7 | 30 ||11 |Thargelion April-May | 30 | - |12 |Dulheggia June 5 | 29 ||12 |Schirrophorion May-June | 29 | - +---+-------------------------+----++---+----------------------------+----+ - | Days in the year |354 || Days in the year |354 | - +-----------------------------+----++--------------------------------+----+ - |The _Arabians_ add 11 days at the end of every year, which keep the same | - | months to the same seasons. | - +-------------------------------------------------------------------------+ - -[Sidenote: Weeks] - -416. A month is divided into four parts called _Weeks_, and a Week into -seven parts called _Days_; so that in a _Julian_ Year there are 13 such -Months, or 52 Weeks, and one Day over. The Gentiles gave the names of -the Sun, Moon, and Planets to the Days of the Week. To the first, the -Name of the _Sun_; to the second, of the _Moon_; to the third, of -_Mars_; to the fourth, of _Mercury_; to the fifth, of _Jupiter_; and to -the sixth, of _Saturn_. - -[Sidenote: Days] - -417. A Day is either _Natural_ or _Artificial_. The Natural Day contains -24 hours; the Artificial the time from Sun-rise to Sun-set. The Natural -Day is either _Astronomical_ or _Civil_. The Astronomical Day begins at -Noon, because the increase and decrease of Days terminated by the -Horizon are very unequal among themselves; which inequality is likewise -augmented by the inconstancy of the horizontal Refractions § 183: and -therefore the Astronomer takes the Meridian for the limit of diurnal -Revolutions; reckoning Noon, that is the instant when the Sun’s Center -is on the Meridian, for the beginning of the Day. The _British_, -_French_, _Dutch_, _Germans_, _Spaniards_, _Portuguese_, and -_Egyptians_, begin the Civil Day at mid-night: the antient _Greeks_, -_Jews_, _Bohemians_, _Silesians_, with the modern _Italians_, and -_Chinese_, begin it at Sun-setting: And the antient _Babylonians_, -_Persians_, _Syrians_, with the modern _Greeks_, at Sun-rising. - -[Sidenote: Hours] - -418. An _Hour_ is a certain determinate part of the Day, and is either -equal or unequal. An equal Hour is the 24th part of a mean natural Day, -as shewn by well regulated Clocks and Watches; but those Hours are not -quite equal as measured by the returns of the Sun to the Meridian, -because of the obliquity of the Ecliptic and Sun’s unequal motion in it -§ 224-245. Unequal Hours are those by which the Artificial Day is -divided into twelve Parts, and the Night into as many. - -[Sidenote: Minutes, Seconds, Thirds, and Scruples.] - -419. An Hour is divided into 60 equal parts called _Minutes_, a minute -into 60 equal parts called Seconds, and these again into 60 equal parts -called _Thirds_. The _Jews_, _Chaldeans_, and _Arabians_, divide the -Hour into 1080 equal parts called _Scruples_; which number contains 18 -times 60, so that one minute contains 18 Scruples. - -[Sidenote: Cycles, of the Sun, Moon, and Indiction.] - -420. A _Cycle_ is a perpetual round, or circulation of the same parts of -time of any sort. The _Cycle of the Sun_ is a revolution of 28 years, in -which time, the days of the months return again to the same days of the -week; the Sun’s Place to the same Signs and Degrees of the Ecliptic on -the same months and days, so as not to differ one degree in 100 years; -and the leap-years begin the same course over again with respect to the -days of the week on which the days of the months fall. The _Cycle of the -Moon_, commonly called the _Golden Number_, is a revolution of 19 years; -in which time, the Conjunctions, Oppositions, and other Aspects of the -Moon are within an hour and half of being the same as they were on the -same days of the months 19 years before. The _Indiction_ is a revolution -of 15 years, used only by the _Romans_ for indicating the times of -certain payments made by the subjects to the republic: It was -established by _Constantine_, A.D. 312. - -[Sidenote: To find the Years of these Cycles.] - -421. The year of our SAVIOUR’s Birth, according to the vulgar _Æra_, was -the 9th year of the Solar Cycle; the first year of the Lunar Cycle; and -the 312th year after his birth was the first year of the _Roman_ -Indiction. Therefore, to find the year of the Solar Cycle, add 9 to any -given year of CHRIST, and divide the sum by 28, the Quotient is the -number of Cycles elapsed since his birth, and the remainder is the Cycle -for the given year: if nothing remains, the Cycle is 28. To find the -Lunar Cycle, add 1 to the given year of CHRIST, and divide the sum by -19; the Quotient is the number of Cycles elapsed in the interval, and -the remainder is the Cycle for the given year: if nothing remains, the -Cycle is 19. Lastly, subtract 312 from the given year of CHRIST, and -divide the remainder by 15; and what remains after this division is the -Indiction for the given year: if nothing remains, the Indiction is 15. - -[Sidenote: The deficiency of the Lunar Cycle, and consequence thereof.] - -422. Although the above deficiency in the Lunar Cycle of an hour and -half every 19 years be but small, yet in time it becomes so sensible as -to make a whole Natural Day in 310 years. So that, although this Cycle -be of use, when rightly placed against the days of the month in the -Calendar, as in our _Common Prayer Books_, for finding the days of the -mean Conjunctions or Oppositions of the Sun and Moon, and consequently -the time of _Easter_; it will only serve for 310 years _Old Style_. For -as the New and Full Moons anticipate a day in that time, the Golden -Numbers ought to be placed one day earlier in the Calendar for the next -310 years to come. These Numbers were rightly placed against the days of -New Moon in the Calendar, by the Council of _Nice_, A. D. 325; but the -anticipation which has been neglected ever since, is now grown almost -into 5 days: and therefore, all the Golden Numbers ought now to be -placed 5 days higher in the Calendar for the _O.S._ than they were at -the time of the said Council; or six days lower for the _New Style_, -because at present it differs 11 days from the _Old_. - - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - |Days||Jan.|Feb.|Mar.|Apr.|May |Jun.|Jul.|Aug.|Sep.|Oct.|Nov.|Dec.| - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 1 || 9 | | 9 | 17 | 17 | 6 | | | | 11 | | 19 | - | 2 || | 17 | | | 6 | 14 | 14 | 3 | 11 | | 19 | | - | 3 || 17 | 6 | 17 | 6 | | | 3 | 11 | | 19 | 8 | 8 | - | 4 || 6 | | 6 | 14 | 14 | 3 | | | 19 | 8 | | 16 | - | 5 || | 14 | | | 3 | 11 | 11 | 19 | 8 | | 16 | | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 6 || 14 | 3 | 14 | 3 | | | 19 | | | 16 | 5 | 5 | - | 7 || 3 | | 3 | 11 | 11 | 19 | | 8 | 16 | | | 13 | - | 8 || | 11 | | | 19 | 8 | 8 | 16 | 5 | 5 | 13 | | - | 9 || 11 | 19 | 11 | 19 | | | | | | 13 | | 2 | - | 10 || | | 19 | 8 | 8 | 16 | 16 | 5 | 13 | | 2 | 10 | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 11 || 19 | 8 | | | | | 5 | 13 | 2 | 2 | 10 | | - | 12 || 8 | 16 | 8 | 16 | 16 | 5 | | | | 10 | | 18 | - | 13 || | | | | 5 | 13 | 13 | 2 | 10 | | 18 | 7 | - | 14 || 16 | 5 | 16 | 5 | | | 2 | 10 | 18 | 18 | 7 | | - | 15 || 5 | | 5 | 13 | 13 | 2 | | | | 7 | | 15 | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 16 || | 13 | | | 2 | 10 | 10 | 18 | 7 | | 15 | | - | 17 || 13 | 2 | 13 | 2 | | | 18 | 7 | | 15 | 4 | 4 | - | 18 || 2 | | 2 | 10 | 10 | 18 | | | 15 | | | 12 | - | 19 || | 10 | | | 18 | 7 | 7 | 15 | 4 | 4 | 12 | | - | 20 || 10 | 18 | 10 | 18 | | | 15 | | | 12 | 1 | 1 | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 21 || | | 18 | 7 | 7 | 15 | | 4 | 12 | | | 9 | - | 22 || 18 | 7 | | | 15 | 4 | 4 | 12 | 1 | 1 | 9 | | - | 23 || 7 | 15 | 7 | 15 | | | 12 | | | 9 | 17 | 17 | - | 24 || | | 15 | 4 | 4 | 12 | | 1 | 9 | | | 6 | - | 25 || 15 | 4 | | | 12 | | 1 | 9 | 17 | 17 | 6 | | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 26 || 4 | | 4 | 12 | | 1 | | | | 6 | | 14 | - | 27 || | 12 | | 1 | 1 | 9 | 9 | 17 | 6 | | 14 | | - | 28 || 12 | 1 | 12 | | 9 | | 17 | 6 | 14 | 14 | 3 | 3 | - | 29 || 1 | | 1 | 9 | | 17 | | | | 3 | | 11 | - | 30 || | | | | 17 | 6 | 6 | 14 | 3 | | 11 | | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - | 31 || 9 | | 9 | | | | 14 | 3 | | 11 | | 19 | - +----++----+----+----+----+----+----+----+----+----+----+----+----+ - -[Sidenote: How to find the day of the New Moon by the Golden Number.] - -423. In the annexed Table, the Golden Numbers under the months stand -against the days of New Moon in the left hand column, for the _New -Style_; adapted chiefly to the second year after leap-year as being the -nearest mean for all the four; and will serve till the year 1900. -Therefore, to find the day of New Moon in any month of a given year till -that time, look for the Golden Number of that year under the desired -month, and against it, you have the day of New Moon in the left hand -column. Thus, suppose it were required to find the day of New Moon in -_September_ 1757; the Golden Number for that year is 10, which I look -for under _September_ and right against it in the left hand column I -find 13, which is the day of New Moon in that month. _N. B._ If all the -Golden Numbers, except 17 and 6, were set one day lower in the Table, it -would serve from the beginning of the year 1900 till the end of the year -2199. The first Table after this chapter shews the Golden Number for -4000 years after the birth of CHRIST, by looking for the even hundreds -of any given year at the left hand, and for the rest to make up that -year at the head of the Table; and where the columns meet, you have the -Golden Number (which is the same both in _Old_ and _New Style_) for the -given year. Thus, suppose the Golden Number was wanted for the year -1757; I look for 1700 at the left hand of the Table, and for 57 at the -top of it; then guiding my eye downward from 57 to over against 1700, I -find 10, which is the Golden Number for that year. - -[Sidenote: A perpetual Table of the time of New Moon to the nearest - hour, for the _Old Style_.] - -424. But because the lunar Cycle of 19 years sometimes includes five -leap-years, and at other times only four, this Table will sometimes vary -a day from the truth in leap-years after _February_. And it is -impossible to have one more correct, unless we extend it to four times -19 or 76 years; in which there are 19 leap years without a remainder. -But even then to have it of perpetual use, it must be adapted to the -_Old Style_, because in every centurial year not divisible by 4, the -regular course of leap-years is interrupted in the _New_; as will be the -case in the year 1800. Therefore, upon the regular _Old Style_ plan, I -have computed the following Table of the mean times of all the New Moons -to the nearest hour for 76 years; beginning with the year of CHRIST -1724, and ending with the year 1800. - -This Table may be made perpetual, by deducting 6 hours from the time of -New Moon in any given year and month from 1724 to 1800, in order to have -the mean time of New Moon in any year and month 76 years afterward; or -deducting 12 hours for 152 years, 18 hours for 228 years; and 24 hours -for 304 years, because in that time the changes of the Moon anticipate -almost a complete natural day. And if the like number of hours be added -for so many years past, we shall have the mean time of any New Moon -already elapsed. Suppose, for example, the mean time of Change was -required for _January_ 1802; deduct 76 years and there remains 1726, -against which in the following Table under _January_ I find the time of -New Moon was on the 21st day at 11 in the evening: from which take 6 -hours and there remains the 21st day at 5 in the evening for the mean -time of Change in _January_ 1802. Or, if the time be required for _May_, -A. D. 1701, add 76 years and it makes 1777, which I look for in the -Table, and against it under _May_ I find the New Moon in that year falls -on the 25th day at 9 in the evening; to which add 6 hours, and it gives -the 26th day at 3 in the Morning for the time of New Moon in _May_, A. -D. 1701. By this addition for time past, or subtraction for time to -come, the Table will not vary 24 hours from the truth in less than 14592 -years. And if, instead of 6 hours for every 76 years, we add or subtract -only 5 hours 52 minutes, it will not vary a day in 10 millions of years. - - -Although this Table is calculated for 76 years only, and according to -the _Old Style_, yet by means of two easy Equations it may be made to -answer as exactly to the _New Style_, for any time to come. Thus, -because the year 1724 in this Table is the first year of the Cycle for -which it is made; if from any year of CHRIST after 1800 you subtract -1723, and divide the overplus by 76, the Quotient will shew how many -entire Cycles of 76 years are elapsed since the beginning of the Cycle -here provided for; and the remainder will shew the year of the current -Cycle answering to the given year of CHRIST. Hence, if the remainder be -0, you must instead thereof put 76, and lessen the Quotient by unity. - -Then, look in the left hand column of the Table for the number in your -remainder, and against it you will find the times of all the mean New -Moons in that year of the present Cycle. And whereas in 76 _Julian_ -Years the Moon anticipates 5 hours 52 minutes, if therefore these 5 -hours 52 minutes be multiplied by the above found Quotient, that is, by -the number of entire Cycles past; the product subtracted from the times -in the Table will leave the corrected times of the New Moons to the _Old -Style_; which may be reduced to the _New Style_ thus: - -Divide the number of entire hundreds in the given year of CHRIST by 4, -multiply this Quotient by 3, to the product add the remainder, and from -their sum subtract 2: this last remainder denotes the number of days to -be added to the times above corrected, in order to reduce them to the -_New Style_. The reason of this is, that every 400 years of the _New -Style_ gains 3 days upon the _Old Style_: one of which it gains in each -of the centurial years succeeding that which is exactly divisible by 4 -without remainder; but then, when you have found the days so gained, 2 -must be subtracted from their number on account of the rectifications -made in the Calendar by the Council of _Nice_, and since by Pope -_Gregory_. It must also be observed, that the additional days found as -above directed do not take place in the centurial Years which are not -multiples of 4 till _February_ 29th, _O. S._ for on that day begins the -difference between the _Styles_; till which day therefore, those that -were added in the preceding years must be used. The following Example -will make this accommodation plain. - - - _Required the mean time of New Moon in_ June, A.D. 1909, _N.S._ - - From 1909 take 1723 Years, and there rem. 186 - Which divided by 76, gives the Quotient 2 - and the remainder 34 - Then, against 34 in the Table is _June_ 5^d 8^h 0^m Afternoon. - And 5^h 52^m multiplied by 2 make to be subtr. 11 44 - ------------- - Remains the mean time according to the _Old - Style_, _June_ 5^d 9^h 16^m Morning. - Entire hundred in 1909 are 19, which divided - by 4, quotes 4 - And leaves a remainder of 3 - Which Quotient multiplied by 3 makes 12, - and the remainder added makes 15 - From which subtract 2, and there remains 13 - Which number of days added to the above - time _Old Style_, gives _June_ 18^d 9^h 16^m Morn._N.S._ - -So the mean time of New Moon in _June_ 1909 _New Style_ is the 18th day -at 16 minutes past 9 in the Morning. - -If 11 days be added to the time of any New Moon in this Table, it will -give the time thereof according to the _New Style_ till the year 1800. -And if 14 days 18 hours 22 minutes be added to the mean time of New Moon -in either _Style_, it will give the mean time of the next Full Moon -according to that _Style_. - - +---------------------------------------------------------------------------------------------+ - |_A_ TABLE _shewing the times of all the mean Changes of the Moon, to the nearest Hour, | - |through four Lunar Periods, or 76 years._ M _signifies morning_, A _afternoon_. | - +----+----+-------+------+-----+------+------+------+------+------+------+------+-------+-----+ - |Yrs | |January| |March| | May | | July | |Sept. | |Novemb.| | - |of |A.D.| |February| |April | | June | |August| |October| |Decemb.| - |the +----+------+------+------+------+------+------+------+------+------+------+------+------+ - |Cyc.| |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. | - +----+----+------+------+------+------+------+------+------+------+------+------+------+------+ - | 1 |1724|14 5A|13 5M|13 6A|12 7M|11 8A|10 8M| 9 9A| 8 10M| 6 10A| 6 11M| 4 12A| 4 1A| - | | | | | | | 1 4M| | | | | | | | - | 2 |1725| 3 2M| 1 2A| 3 3M| 1 4A| |29 6M|28 7A|27 8M|25 8A|25 9M|23 10A|23 11M| - | | | | | | |30 5A| | | | | | | | - | 3 |1726|21 11A|20 11M|21 12A|20 1A|20 1M|18 2A|18 3M|16 4A|15 5M|14 5A|13 6M|12 7A| - | | | | | | | | | | | | | | 2 4M| - | 4 |1727|11 8M| 9 9A|11 9M| 9 10A| 9 11M| 7 12A| 7 0A| 6 1M| 4 1A| 4 2M| 2 3A| | - | | | | | | | | | | | | | |31 5A| - | 5 |1728|30 6M|28 7A|29 7M|27 8A|27 8M|25 9A|25 10M|23 11A|22 11M|21 12A|20 1A|20 2M| - | 6 |1729|18 2A|17 3M|18 4A|17 4M|16 5A|15 6M|14 7A|12 7M|11 8A|11 9M| 9 0A| 9 11M| - | | | | | | | | | | | 2 5M| | | | - | 7 |1730| 7 11A| 6 0A| 8 1M| 6 1A| 6 2M| 4 3A| 4 3M| 2 4A| |30 7M|28 8A|28 9M| - | | | | | | | | | | |30 6A| | | | - | 8 |1731|26 9A|25 10M|26 10A|25 11M|24 11A|23 0A|23 1M|21 2A|20 2M|19 3A|18 4M|17 5A| - | 9 |1732|16 5M|14 6A|15 7M|13 8A|13 8M|11 9A|11 10M| 9 11A| 8 11M| 7 12A| 6 1A| 6 2M| - | | | | | | | | 1 6M| | | | | | | - | 10 |1733| 4 2A| 3 3M| 4 4A| 3 4M| 2 5A| |30 8M|28 8A|27 9M|26 10A|25 11M|24 11A| - | | | | | | | |30 7A| | | | | | | - | 11 |1734|23 0A|22 1M|23 1A|22 2M|21 2A|20 3M|19 4A|18 5M|16 5A|16 6M|14 7A|14 8M| - | 12 |1735|12 9A|11 9M|12 10A|11 11M|10 11A| 9 0A| 9 1M| 7 2A| 6 2M| 5 3A| 4 4M| 3 5A| - | | | 2 5M| | 1 7M| | | | | | | | | | - | 13 |1736| | ---- | |29 9M|28 9A|27 10M|26 11A|25 0A|23 12A|23 1A|22 2M|21 3A| | - | | |31 6A| |30 8A| | | | | | | | | | - | 14 |1737|20 3M|18 4A|20 4M|18 5A|18 5M|16 6A|16 7M|14 8A|13 8M|12 9A|11 10M|10 11A| - | | | | | | | | | | | | 2 6M| | | - | 15 |1738| 9 11M| 7 12A| 9 1A| 8 1M| 7 2A| 6 3M| 5 4A| 4 5M| 2 5A| |30 8M|29 8A| - | | | | | | | | | | | |31 7A| | | - | 16 |1739|28 9M|26 10A|28 11M|26 12A|26 0A|25 1M|24 2A|23 3M|21 3A|21 4M|19 5A|19 6M| - | 17 |1740|17 6A|16 7M|16 8A|15 9M|14 9A|13 10M|12 11A|11 0A|9 12A| 9 1A| 8 2M| 7 3A| - | | | | | | | | | 2 7M| | | | | | - | 18 |1741| 6 3M| 4 4A| 6 4M| 4 5A| 4 5M| 2 6A| |30 8M|28 9A|28 10M|26 11A|26 11M| - | | | | | | | | |31 7A| | | | | | - | 19 |1742|24 12A|23 1A|25 2M|23 3A|23 3M|21 4A|21 5M|19 6A|18 6M|17 7A|16 8M|15 9A| - | 20 |1743|14 9M|12 10A|14 11M|12 12A|12 0A|11 1M|10 2A| 9 3M| 7 3A| 7 4M| 5 5A| 5 6M| - | | | | | | 1 9M| | | | | | | | | - | 21 |1744| 3 6A| 2 7M| 2 8A| |30 10M|28 11A|28 0A|26 12A|25 1A|25 2M|23 3A|23 3M| - | | | | | |30 9A| | | | | | | | | - | 22 |1745|21 4A|20 5M|21 5A|20 6M|19 6A|18 7M|17 8A|16 8M|14 9A|14 10M|12 11A|12 0A| - | | | | | | | | | | | | | | 1 9A| - | 23 |1746|10 12A|9 1A|11 2M| 9 3A| 9 3M| 7 4A| 7 5M| 5 6A| 4 6M| 3 7A| 2 8M| | - | | | | | | | | | | | | | |31 10M| - | 24 |1747|29 10A|28 11M|29 11A|28 0A|27 12A|26 1A|26 2M|24 3A|23 3M|22 4A|21 5M|20 6A| - | 25 |1748|19 6M|17 7A|18 8M|16 9A|16 9M|14 10A|14 11M|12 12A|11 0A|11 1M| 9 2A| 9 3M| - | | | | | | | | | | 2 9M| | | | | - | 26 |1749| 7 3A| 6 4M| 7 5A| 6 6M| 5 6A| 4 7M| 3 8A| |30 10M|29 11A|28 0A|27 12A| - | | | | | | | | | |31 9A| | | | | - | 27 |1750|26 1A|25 2M|26 3A|25 4M|24 4A|23 5M|22 6A|21 7M|19 7A|19 8M|17 9A|17 10M| - | 28 |1751|15 10A|14 11M|15 11A|14 0A|13 12A|12 1A|12 2M|10 3A| 9 3M| 8 4A| 7 5M| 6 6A| - | | | | | | | 2 9M| | | | | | | | - | 29 |1752| 5 6M| 3 7A| 4 8M| 2 9A| |30 11M|29 12A|28 0A|27 1M|26 2A|25 3M|24 3A| - | | | | | | |31 10A| | | | | | | | - | 30 |1753|23 4M|21 5A|23 6M|21 7A|21 7M|19 8A|19 9M|17 10A|16 10M|15 11A|14 0A|14 1M| - | 31 |1754|12 1A|11 2M|12 3A|11 4M|10 4A| 9 5M| 8 6A| 7 7M| 5 7A| 5 8M| 3 9A| 3 10M| - | | | 1 10A| | 1 11A| | | | | | | | | | - | 32 |1755| | ---- | |29 12A|29 1A|28 2M|27 3A|25 3M|24 4A|24 5M|22 6A|22 6M| - | | |31 11M| |31 0A| | | | | | | | | | - | 33 |1756|20 7A|19 8M|19 9A|18 9M|17 10A|16 11M|15 12A|14 1A|13 1M|12 2A|11 3M|10 4A| - | | | | | | | | | | | | 1 14A| | | - | 34 |1757| 9 4M| 7 5A| 9 6M| 7 7A| 7 7M| 5 8A| 5 9M| 3 10A| 2 10M| |30 1M|29 1A| - | | | | | | | | | | | |31 0A| | | - | 35 |1758|28 2M|26 3A|28 3M|26 4A|26 4M|24 5A|24 6M|22 7A|21 7M|20 8A|19 9M|18 10A| - | 36 |1759|17 10M|15 11A|17 0A|16 1M|15 1A|14 2M|13 3A|12 2M|10 4A|10 5M| 8 6A| 8 7M| - | | | | | | | | | 1 12A| | | | | | - | 37 |1760| 6 7A| 5 8M| 5 9A| 4 10M| 3 10A| 2 11M| |30 1M|28 2A|28 3M|26 4A|26 4M| - | | | | | | | | |31 1A| | | | | | - | 38 |1761|24 5A|23 6M|24 7A|23 8M|22 9A|21 10M|20 10A|19 11M|17 11A|17 0A|16 1M|15 2A| - | 39 |1762|14 2M|12 3A|14 3M|12 4A|12 4M|10 5A|10 6M|8 7A| 7 7M| 6 8A| 5 9M| 4 10A| - +----+----+------+------+------+------+------+------+------+------+------+------+------+------+ - | | | | | | | 1 1A| | | | | | | | - | 40 |1763| 3 11M| 1 12A| 3 0A| 2 1M| |29 3A|29 4M|27 4M|26 5M|25 6A|24 7M|23 7A| - | | | | | | |31 2M| | | | | | | | - | 41 |1764|22 8M|20 9A|21 10M|19 11A|19 11M|17 12A|17 1A|16 2M|14 2A|14 3M|12 4A|12 5M| - | | | | | | | | | | | | | | 1 1A| - | 42 |1765|10 5A| 9 6M|10 6A| 9 7M| 8 7A| 7 8M| 6 9A| 5 10M| 3 10A| 3 11M| 1 12A| | - | | | | | | | | | | | | | |31 1M| - | 43 |1766|29 2A|28 3M|29 4A|28 5M|27 5A|26 6M|25 7A|24 8M|22 8A|22 9M|20 10A|20 11M| - | 44 |1767|18 11A|17 0A|19 1M|17 2A|17 2M|15 3A|15 4M|13 5A|12 6M|11 6A|10 7M| 9 8A| - | | | | | | | | | | 2 2M | | | | | - | 45 |1768| 8 8M| 6 9A| 7 10M| 5 11A| 5 11M| 3 12A| 3 1A| |30 3M|29 4A|28 5M|27 5A| - | | | | | | | | | |31 2A| | | | | - | 46 |1769|26 6M|24 7A|26 7M|24 8A|24 8M|22 9A|22 10M|20 11A|19 11M|18 12A|17 1A|17 2M| - | 47 |1770|15 2A|14 3M|15 4A|14 5M|13 5A|12 4M|11 7A|10 8M| 8 8A| 8 9M| 6 10A| 6 11M| - | | | | | | | | | 1 4M| | | | | | - | 48 |1771| 4 11M| 3 0A| 5 1M| 3 2A| 3 2M| 1 3A| |29 5M|27 6A|27 7M|25 8A|25 9M| - | | | | | | | | |30 5A| | | | | | - | 49 |1772|23 9A|22 10M|22 10A|21 11M|20 11A|19 0A|19 1M|17 2A|16 2M|15 3A|14 4M|13 5A| - | 50 |1773|12 5M|10 6A|12 7M|10 8A|10 8M| 8 9A| 8 9M| 6 10A| 5 11M| 4 12A| 3 1A| 3 2M| - | | | 1 2A| | 1 4A| | | | | | | | | | - | 51 |1774| | ---- | |29 5A|29 6M|27 7A|27 8M|25 8A|24 9M|23 10A|22 11M|21 11A| - | | |31 3M| |31 5M| | | | | | | | | | - | 52 |1775|20 0A|19 1M|20 2A|19 3M|18 3A|17 4M|16 5A|15 6M|13 6A|13 7M|11 8A|11 9M| - | | | | | | | | | | | | 1 3A| | | - | 53 |1776| 9 9A| 8 10M| 8 10A| 7 11M| 6 12A| 5 0A| 5 1M| 3 2A| 2 2M| |29 5A|29 5M| - | | | | | | | | | | | |31 4M| | | - | 54 |1777|27 6A|26 7M|27 8A|26 9M|25 9A|24 10M|23 11A|22 0A|20 12A|20 1A|19 2M|18 3A| - | 55 |1778|17 3M|15 4A|17 5M|15 6A|15 6M|13 7A|13 8M|11 9A|10 9M| 9 10A| 8 11M| 7 12A| - | | | | | | | | | |1 6M| | | | | - | 56 |1779| 6 0A| 5 1M| 6 2A| 5 3M| 4 3A| 3 4M| 2 5A| |29 7M|28 8A|27 9M|26 9A| - | | | | | | | | | |30 6A| | | | | - | 57 |1780|25 10M|23 11A|24 11M|22 12A|22 0A|21 1M|20 2A|19 3M|17 3A|17 4M|15 5A|15 6M| - | 58 |1781|13 6A|12 7M|13 8A|12 9M|11 9A|10 10M| 9 11A| 8 0A| 6 12A| 6 1A| 5 2M| 4 3A| - | | | | | | | 1 6M| | | | | | | | - | 59 |1782| 3 3M| 1 4A| 3 5M| 1 6A| |29 8M|28 9A|27 9M|25 10A|25 11M|23 12A|23 0A| - | | | | | | |30 7A| | | | | | | | - | 60 |1783|22 1M|20 2A|22 2M|20 3A|20 3M|18 4A|18 5M|16 6A|15 6M|14 7A|13 8M|12 9A| - | | | | | | | | | | | | | |1 6M| - | 61 |1784|11 9M| 9 10A|10 11M| 8 12A| 8 0A| 7 1M| 6 2A| 5 3M| 3 3A| 3 4M| 1 5A| | - | | | | | | | | | | | | | |30 6A| - | 62 |1785|29 7M|27 8A|29 9M|27 10A|27 10M|25 11A|25 0A|24 1M|22 1A|22 2M|20 3A|20 3M| - | 63 |1786|18 4A|17 5M|18 5A|17 6M|16 6A|15 7M|14 8A|13 9M|11 9A|11 10M| 9 11A| 9 0A| - | | | | | | | | | | | 1 6M| | | | - | 64 |1787| 7 12A| 6 1A| 8 2M| 6 3A| 6 3M| 4 4A| 4 5M| 2 6A| |30 8M|28 9A|28 9M| - | | | | | | | | | | |30 7A| | | | - | 65 |1788|26 10A|25 11M|25 12A|24 1A|24 1M|22 2A|22 3M|20 4M|19 4M|18 5A|17 6M|16 7A| - | 66 |1789|15 7M|13 8A|15 9M|13 10A|13 10M|11 11A|11 0A|10 1M| 8 1A| 8 2M| 6 3A| 6 4M| - | | | | | | | | 1 7M| | | | | | | - | 67 |1790| 4 4A| 3 5M| 4 5A| 3 6M| 2 6A| |30 9M|28 9A|27 10M|26 11A|25 0A|24 12A| - | | | | | | | |30 8A| | | | | | | - | 68 |1791|23 1A|22 2M|23 3A|22 4M|21 4A|20 5M|19 6A|18 7M|16 7A|16 8M|14 9A|14 10M| - | 69 |1792|12 10A|11 11M|11 12A|10 1A|10 1M| 8 2A| 8 3M| 6 4A| 5 4A| 4 5A| 3 6M| 2 7A| - | | | 1 7M| | 1 9M| | | | | | | | | | - | 70 |1793| | ---- | |29 10M|28 11A|27 0A|27 1M|25 1A|24 2M|23 3A|22 4M|21 4A| - | | |30 8A| |30 10A| | | | | | | | | | - | 71 |1794|20 5M|18 6A|20 6M|18 7A|18 7M|16 8A|16 9M|14 10A|13 10M|12 11A|11 0A|11 1M| - | | | | | | | | | | | | 2 8M| | | - | 72 |1795| 9 1A| 8 2M| 9 3A| 8 4M| 7 4A| 6 5M| 5 6A| 4 7M| 2 7A| |30 10M|29 10A| - | | | | | | | | | | | |31 9A| | | - | 73 |1796|28 11M|26 12A|27 0A|26 1M|25 1A|24 2M|23 3A|22 4M|20 4A|20 5M|18 6A|18 7M| - | 74 |1797|16 7A|15 8M|16 9A|15 10M|14 10A|13 11M|12 12A|11 1A|10 1M| 9 2A| 8 3M| 7 4A| - | | | | | | | | | 2 9M| | | | | | - | 75 |1798| 6 4M| 4 5A| 6 6M| 4 7A| 4 7M| 2 8A| |30 10M|28 11A|28 0A|27 1M|26 1A| - | | | | | | | | |31 10A| | | | | | - | 76 |1799| 25 2M|23 3A|25 4M|23 5A|23 5M|21 6A|21 6M|19 8A|18 8M|17 9A|16 10M|15 11A| - | 1 |1800|14 11A|12 12A|13 0A|12 1M|11 1A|10 2M| 9 3A| 8 4M| 6 4A| 6 5M| 4 6A| 4 7M| - +----+----+------+------+------+------+------+------+------+------+------+------+------+------+ - - The year 1800 begins a new Cycle. - -[Sidenote: _Easter_ Cycle, deficient.] - -425. The _Cycle of Easter_, also called the _Dionysian Period_, is a -revolution of 532 years, found by multiplying the Solar Cycle 28 by the -Lunar Cycle 19. If the New Moons did not anticipate upon this Cycle, -_Easter-Day_ would always be the _Sunday_ next after the first Full Moon -which succeeds the 21st of _March_. But, on account of the above -anticipation § 422, to which no proper regard was had before the late -alteration of the _Style_, the _Ecclesiastic Easter_ has several times -been a week different from the _true Easter_ within this last Century: -which inconvenience is now remedied by making the Table which used to -find Easter _for ever_, in the Common Prayer Book, of no longer use than -the Lunar difference from the _New Style_ will admit of. - -[Sidenote: Number of Direction. - - To find the true _Easter_.] - -426. The _earliest Easter possible_ is the 22d of _March_, the _latest_ -the 25th of _April_. Within these limits are 35 days, and the number -belonging to each of them is called the _Number of Direction_; because -thereby the time of Easter is found for any given year. To find the -Number of Direction, according to the _New Style_, enter Table V -following this Chapter, with the compleat hundreds of any given year at -the top, and the years thereof (if any) below an hundred at the left -hand; and where the columns meet is the Dominical Letter for the given -year. Then, enter Table I, with the compleat hundreds of the same year -at the left hand, and the years below an hundred at the top; and where -the columns meet is the Golden Number for the same year. Lastly, enter -Table II with the Dominical Letter at the left hand and Golden Number at -the top; and where the columns meet is the Number of Direction for that -year; which number, added to the 21st day of _March_ shews on what day -either of _March_ or _April_ Easter _Sunday_ falls in that year. Thus, -the Dominical Letter _New Style_ for the year 1757 is _B_ (Table V) and -the Golden Number is 10, (Table I) by which in Table II, the Number of -Direction is found to be 20; which, reckoned from the 21st of _March_, -ends on the 10th of _April_, and _that_ is _Easter Sunday_ in the year -1757. _N. B._ There are always two Dominical Letters to the leap-year, -the first of which takes place to the 24th of _February_, the last for -the following part of the year. - -[Sidenote: Dominical Letter.] - -427. _The first seven Letters of the Alphabet_ are commonly placed in -the annual Almanacks to shew on what days of the week the days of the -months fall throughout the year. And because one of those seven Letters -must necessarily stand against _Sunday_ it is printed in a capital form, -and called the _Dominical Letter_: the other six being inserted in small -characters to denote the other six days of the week. Now, since a common -_Julian Year_ contains 365 Days, if this number be divided by 7 (the -number of days in a week) there will remain one day. If there had been -no remainder, ’tis plain the year would constantly begin on the same day -of the week. But since one remains, ’tis as plain that the year must -begin and end on the same day of the week; and therefore the next year -will begin on the day following. Hence, when _January_ begins on -_Sunday_, _A_ is the Dominical or _Sunday_ Letter for that year: then, -because the next year begins on _Monday_, the _Sunday_ will fall on the -seventh day, to which is annexed the seventh Letter _G_, which therefore -will be the Dominical Letter for all that year: and as the third year -will begin on _Tuesday_, the _Sunday_ will fall on the sixth day; -therefore _F_ will be the _Sunday_ Letter for that year. Whence ’tis -evident that the _Sunday_ Letters will go annually in a retrograde order -thus, _G_, _F_, _E_, _D_, _C_, _B_, _A_. And in the course of seven -years, if they were all common ones, the same days of the week and -Dominical Letters would return to the same days of the months. But -because there are 366 days in a leap-year, if this number be divided by -7, there will remain two days over and above the 52 weeks of which the -year consists. And therefore, if the leap-year begins on _Sunday_, it -will end on _Monday_; and the next year will begin on _Tuesday_, the -first _Sunday_ whereof must fall on the sixth of _January_, to which is -annexed the Letter _F_, and not _G_ as in common years. By this means, -the leap-year returning every fourth year, the order of the Dominical -Letters is interrupted; and the Series does not return to its first -state till after four times seven, or 28 years: and then the same days -of the month return in order to the same days of the week. - -[Sidenote: To find the Dominical Letter.] - -428. _To find the Dominical Letter for any year either before or after -the Christian Æra_[87]: In Table III or IV for _Old Style_, or V for -_New Style_, look for the hundreds of years at the head of the Table, -and for the years below an hundred (to make up the given year) at the -left hand: and where the columns meet you have the Dominical Letter for -the year desired. Thus, suppose the Dominical Letter be required for the -year of CHRIST 1758, _New Style_, I look for 1700 at the head of Table -V, and for 58 at the left hand of the same Table; and in the angle of -meeting, I find _A_, which is the Dominical Letter for that year. If it -was wanted for the same year _Old Style_, it would be found by Table IV -to be _D_. But _to find the Dominical Letter for any given year before_ -CHRIST, subtract one from _that_ year and then proceed in all respects -as just now taught, to find it by Table III Thus, suppose the Dominical -Letter be required for the 585th year before the first year of CHRIST, -look for 500 at the head of Table III, and for 84 at the left hand; in -the meeting of these columns is _FE_, which were the Dominical Letters -for that year, and shews that it was a leap-year; because, leap-year has -always two Dominical Letters. - -[Sidenote: To find the Days of the Months.] - -429. _To find the day of the month answering to any day of the week, or -the day of the week answering to any day of the month; for any year past -or to come:_ Having found the Dominical Letter for the given year, enter -Table VI, with the Dominical Letter at the head; and under it, all the -days in that column to the right hand are _Sundays_, in the divisions of -the months; the next column to the right are _Mondays_; the next, -_Tuesdays_; and so on to the last column under _G_, from which go back -to the column under _A_, and thence proceed towards the right hand as -before. Thus, in the year 1757, the Dominical Letter _New Style_ is _B_, -in Table V, then in Table VI all the days under _B_ are _Sundays_ in -that year, _viz._ the 2d, 9th, 16th, 23d, and 30th of _January_ and -_October_; the 6th, 13th, 20th, and 27th of _February_, _March_ and -_November_; the 3d, 10th, and 17th, of _April_ and _July_, together with -the 31st of _July_: and so on to the foot of the column. Then, of -course, all the days under _C_ on _Mondays_, namely the 3d, 10th, _&c._ -of _January_ and _October_; and so of all the rest in that column. If -_the day of the week answering to any day of the month_ be required, it -is easily had from the same Table by the Letter that stands at the top -of the column in which the given day of the month is found. Thus, the -Letter that stands over the 28th of _May_ is _A_; and in the year 585 -before CHRIST the Dominical Letter was found to be _FE_ § 428; which -being a leap-year, and _E_ taking place from the 24th of _February_ to -the end of that year, shews by the Table that the 25th of _May_ was on a -_Sunday_; and therefore the 28th must have been on a _Wednesday_: for -when _E_ stands for _Sunday_, _F_ must stand for _Monday_, _G_ for -_Tuesday_, _A_ for _Wednesday_, _B_ for _Thursday_, _C_ for _Friday_, -and _D_ for _Saturday_. Hence, as it appears that the famous Eclipse of -the Sun foretold by THALES, by which a peace was brought about between -the _Medes_ and _Lydians_, happened on the 28th of _May_, in the 585th -year before CHRIST, it certainly fell on a _Wednesday_. - -[Sidenote: _Julian Period._] - -430. From the multiplication of the Solar Cycle of 28 years into the -Lunar Cycle of 19 years, arises the great _Julian Period_ consisting of -7980 years; which had its beginning 764 years before the supposed year -of the creation (when all the three Cycles began together) and is not -yet compleated, and therefore it comprehends all other Cycles, Periods -and Æras. There is but one year in the whole Period which has the same -numbers for the three Cycles of which it is made up: and therefore, if -historians had remarked in their writings the Cycles of each year, there -had been no dispute about the time of any action recorded by them. - -[Sidenote: To find the year of this Period. - - And the Cycles of that year.] - -431. The _Dionysian_ or vulgar Æra of _Christ_’s birth was about the end -of the year of the _Julian_ Period 4713; and consequently the first year -of his age, according to that account, was the 4714th year of the said -Period. Therefore, if to the current year of _Christ_ we add 4713, the -Sum will be the year of the _Julian_ Period. So the year 1757 will be -found to be the 6470th year of that Period. Or, to find the year of the -_Julian_ Period answering to any given year before the first year of -CHRIST, subtract the number of that given year from 4714, and the -remainder will be the year of the _Julian_ Period. Thus, the year 585 -before the first year of CHRIST (which was the 584th before his birth) -was the 4129th year of the said Period. Lastly, to find the Cycles of -the Sun, Moon, and Indiction for any given year of this Period, divide -the given year by 28, 19, and 15; the three remainders will be the -Cycles sought, and the Quotients the numbers of Cycles run since the -beginning of the Period. So in the above 4714th year of the _Julian_ -Period the Cycle of the Sun was 10, the Cycle of the Moon 2, and the -Cycle of Indiction 4; the Solar Cycle having run through 168 courses, -the Lunar 248, and the Indiction 314. - - -[Sidenote: The true Æra of CHRIST’s birth.] - -432. The vulgar Æra of CHRIST’s birth was never settled till the year -527; when _Dionysius Exiguus_, a _Roman_ Abbot, fixed it to the end of -the 4713th year of the _Julian_ Period; which was certainly four years -too late. For, our SAVIOUR was undoubtedly born before the Death of -_Herod_ the Great, who sought to kill him as soon as he heard of his -birth. And, according to the testimony of _Josephus_ (B. xvii. c. 8.) -there was an eclipse of the Moon in the time of _Herod_’s last illness: -which very eclipse our Astronomical Tables shew to have been in the year -of the _Julian_ Period 4710, _March_ 13th, 3 hours 21 minutes after -mid-night, at _Jerusalem_. Now, as our SAVIOUR must have been born some -months before _Herod_’s death, since in the interval he was carried into -_Ægypt_; the latest time in which we can possibly fix the true _Æra_ of -his birth is about the end of the 4709th year of the _Julian_ Period. -And this is four years before the vulgar _Æra_ thereof. - -[Sidenote: The time of his crucifixion.] - -In the former edition of this book, I endeavoured to ascertain the time -of CHRIST’s death; by shewing in what year, about the reputed time of -the Passion, there was a Passover Full Moon on a _Friday_: on which day -of the week, and at the time of the Passover, it is evident from _Mark_ -xv. 42. that our SAVIOUR was crucified. And in computing the times of -all the Passover Full Moons from the 20th to the 40th year of CHRIST, -after the _Jewish_ manner, which was to add 14 days to the time when the -New Moon next before the Passover was first visible at _Jerusalem_, in -order to have their day of the Passover Full Moon, I found that the only -Passover Full Moon which fell on a _Friday_, in all that time, was in -the year of the _Julian_ Period 4746, on the third day of _April_: which -year was the 33d year of CHRIST’s age, reckoning from the vulgar Æra of -his birth, but the 37th counting from the true _Æra_ thereof: and was -also the last year of the 402d Olympiad[88], in which very year -_Phlegon_ an Heathen writer tells us, _there was the most extraordinary -Eclipse of the Sun that ever was known_, and that _it was night at the -sixth hour of the day_. Which agrees exactly with the time that the -darkness at the crucifixion began, according to the three Evangelists -who mention it[89]: and therefore must have been the very same darkness, -but mistaken by _Phlegon_ for a natural Eclipse of the Sun; which was -impossible on two accounts, 1. because it was at the time of Full Moon; -and 2. because whoever takes the pains to calculate, will find that -there could be no regular and total Eclipse of the Sun that year in any -part of _Judea_, nor any where between _Jerusalem_ and _Egypt_: so that -this darkness must have been quite out of the common course of nature. - -From the co-incidence of these characters, I made no doubt of having -ascertained the true year and day of our SAVIOUR’s death. But having -very lately read what some eminent authors have wrote on the same -subject, of which I was really ignorant before; and heard the opinions -of other candid and ingenious enquirers after truth (which every honest -man will follow wherever it leads him) and who think they have strong -reasons for believing that the time of CHRIST’s death was not in the -year of the _Julian_ Period 4746, but in the year 4743; I find -difficulties on both sides, not easily got over: and shall therefore -state the case both ways as fairly as I can; leaving the reader to take -which side of the Question he pleases. - -Both Dr. _Prideaux_ and Sir _Isaac Newton_ are of opinion that -_Daniel_’s seventy weeks, consisting of 490 years (_Dan._ chap. ix. v. -23-26) began with the time when Ezra received his commission from -_Artaxerxes_ to go to _Jerusalem_, which was in the seventh year of that -King’s reign (_Ezra_ ch. vii. v. 11-26) and ended with the death of -CHRIST. For, by joining the accomplishment of that prophecy with the -expiation of Sin, those weeks cannot well be supposed to end at any -other time. And both these authors agree that this was _Artaxerxes -Longimanus_, not _Artaxerxes Mnemon_. The Doctor thinks that the last of -those annual weeks was equally divided between _John_’s ministry and -CHRIST’s. And, as to the half week, mentioned by _Daniel_ chap. ix. v. -27. Sir _Isaac_ thinks it made no part of the above seventy; but only -meant the three years and an half in which the _Romans_ made war upon -the _Jews_ from spring in _A.D._ 67 to autumn in _A.D._ 70, when a final -Period was put to their sacrifices and oblations by destroying their -city and sanctuary, on which they were utterly dispersed. Now, both by -the undoubted Canon of _Ptolemy_, and the famous Æra of _Nabonassar_, -which is so well verified by Eclipses that it cannot deceive us, the -beginning of these seventy weeks, or the seventh year of the reign of -_Artaxerxes Longimanus_, is pinned down to the year of the _Julian_ -Period 4256: from which count 490 years to the death of CHRIST, and the -same will fall in the above year of the _Julian_ Period 4746: which -would seem to ascertain the true year beyond dispute. - -But as _Josephus_’s Eclipse of the Moon in a great measure fixes our -SAVIOUR’s birth to the end of the 4713th year of the _Julian_ Period, -and a _Friday_ Passover Full Moon fixes the time of his death to the -third of _April_ in the 4746th year of that Period, the same as above by -_Daniel_’s weeks, this supposes our SAVIOUR to have been crucified in -the 37th year of his age. And as St. _Luke_ chap. iii. ver. 23. fixes -the time of CHRIST’s baptism to the beginning of his 30th year, it would -hence seem that his publick ministry, to which his baptism was the -initiation, lasted seven years. But, as it would be very difficult to -find account in all the Evangelists of more than four Passovers which he -kept at _Jerusalem_ during the time of his ministry, others think that -he suffered in the vulgar 30th year of his age, which was really the -33d; namely in the year of the _Julian_ Period 4743. And this opinion is -farther strengthened by considering that our SAVIOUR eat his last -Paschal Supper on a _Thursday_ evening, the day immediately before his -crucifixion: and that as he subjected himself to the law, he would not -break the law by keeping the Passover on the day before the law -prescribed; neither would the Priests have suffered the Lamb to be -killed for him before the fourteenth day of _Nisan_ when it was killed -for all the people, _Exod._ xii. _ver._ 6. And hence they infer that he -kept this Passover at the same time with the rest of the _Jews_, in the -vulgar 30th year of his age: at which time it is evident by calculation -that there was a Passover Full Moon on _Thursday April_ the 6th. But -this is pressed with two difficulties. 1. It drops the last half of -_Daniel_’s seventieth week, as of no moment in the prophecy; and 2. it -sets aside the testimony of _Phlegon_, as if he had mistaken almost a -whole _Olympiad_. - -Others again endeavour to reconcile the whole difference, by supposing, -that as CHRIST expressed himself only in round numbers concerning the -time he was to lie in the grave, _Matt._ xii. 40. so might St. _Luke_ -possibly have done with regard to the year of his baptism: which would -really seem to be the case when we consider, that the _Jews_ told our -SAVIOUR, sometime before his death, _Thou art not yet fifty years old_, -John vii. 57. which indeed was more likely to be said to a person near -forty than to one but just turned of thirty. And as to his eating the -above Passover on _Thursday_, which must have been on the _Jewish_ Full -Moon day, they think it may be easily accommodated to the 37th year of -his age; since, as the _Jews_ always began their day in the evening, -their _Friday_ of course began on the evening of our _Thursday_. And it -is evident, as above-mentioned, that the only _Jewish Friday_ Full Moon, -at the time of their Passover, was in the vulgar 33d, but the real 37th -year of CHRIST’s age; which was the 4746th year of the _Julian_ Period, -and the last year of the 202d _Olympiad_. - - -[Sidenote: Æras or Epochas.] - -433. As there are certain fixed points in the Heavens from which -Astronomers begin their computations, so there are certain points of -time from which historians begin to reckon; and these points or roots of -time are called _Æras_ or _Epochas_. The most remarkable _Æras_ are -those of the _Creation_, the _Greek Olympiads_, the building of _Rome_, -the _Æra_ of _Nabonassar_, the death of _Alexander_, the birth of -CHRIST, the _Arabian Hegira_, and the _Persian Jesdegird_: All which, -together with several others of less note, have their beginnings in the -following Table fixed to the years of the _Julian Period_, to the age of -the world at those times, and to the years before and after the birth of -CHRIST. - - |Julian Period.| - + + - | |Y. of the World.| - | + + + - | | |Before Christ. - | | | - 1. The creation of the world, according to _Strauchius_ | 764 | 1 | 3949 | - 2. The Deluge, or _Noah_’s Flood | 2420 | 1656 | 2293 | - 3. The _Assyrian_ Monarchy by _Nimrod_ | 2537 | 1773 | 2176 | - 4. The Birth of _Abraham_ | 2712 | 1948 | 2001| - 5. The beginning of the Kingdom of the _Argives_ | 2856 | 2092 | 1857| - 6. The begin. of the Kingdom of _Athens_ by _Cecrops_ | 3157 | 2393 | 1556 | - 7. The departure of the _Israelites_ from _Egypt_ | 3216 | 2452 | 1497 | - 8. Their entrance into _Canaan_, or the Jubilee | 3256 | 2492 | 1457 | - 9. The destruction of _Troy_ | 3529 | 2865 | 1184 | - 10. The beginning of King _David_’s reign | 3653 | 2889 | 1060 | - 11. The foundation of _Solomon_’s Temple | 3696 | 2932 | 1017 | - 12. The _Argonautic_ expedition | 3776 | 3012 | 937 | - 13. _Arbaces_, the first King of the _Medes_ | 3838 | 3074 | 175 | - 14. _Mandaucus_ the second | 3865 | 3101 | 848 | - 15. _Sosarmus_ the third | 3915 | 3151 | 798 | - 16. _Artica_ the fourth | 3945 | 3181 | 768 | - 17. _Cardica_ the fifth | 3996 | 3232 | 718 | - 18. _Phraortes_ the sixth | 4057 | 3293 | 656 | - 19. _Cyaxares_ the seventh | 4080 | 3316 | 633 | - 20. The beginning of the _Olympiads_ | 3938 | 3174 | 775 | - 21. The _Catonian_ Epocha of the building of _Rome_ | 3961 | 3197 | 752 | - 22. The Æra of _Nabonassar_ | 3967 | 3202 | 746 | - 23. The destruction of _Samaria_ | 3990 | 3226 | 723 | - 24. The _Babylonish_ captivity | 4133 | 3349 | 600 | - 25. The destruction of _Solomon_’s Temple | 4124 | 3360 | 589 | - 26. The _Persian_ monarchy founded by _Cyrus_ | 4154 | 3390 | 559 | - 27. The battle of _Marathon_ | 4224 | 3460 | 489 | - 28. The begin. of the reign of _Art. Longimanus_ | 4249 | 3485 | 464 | - 29. The beginning of _Daniel_’s 70 weeks | 4256 | 3492 | 457 | - 30. The beginning of the _Peloponnesian_ war | 4282 | 3518 | 431 | - 31. The death of _Alexander_ | 4390 | 3626 | 323 | - 32. The restoration of the _Jews_ | 4548 | 3784 | 129 | - 33. The corr. of the Calendar by _Julius Cæsar_ | 4669 | 3905 | 44 | - 34. The beginning of the reign of _Herod_ | 4673 | 3909 | 40 | - 35. The _Spanish_ Æra | 4675 | 3911 | 38 | - 36. The battle at _Actium_ | 4683 | 3919 | 30 | - 37. The taking of _Alexandria_ | 4683 | 3919 | 30 | - 38. The Epoch of the title of _Augustus_ | 4686 | 3922 | 27 | - 39. The true Æra of CHRIST’s birth | 4709 | 3945 | 4 | - 40. The death of _Herod_ | 4710 | 3946 | 3 | - 41. The _Diony_. or vulg. Æra of the birth of CHRIST | 4713 | 3949 |_AD_0 | - 42. The true year of CHRIST’s death | 4746 | 3982 | 33 | - 43. The destruction of _Jerusalem_ | 4783 | 4019 | 70 | - 44. The _Dioclesian_ persecution | 5015 | 4251 | 302 | - 45. The Epoch of _Constantine_ the Great | 5019 | 4255 | 306 | - 46. The Council of _Nice_ | 5038 | 4274 | 325 | - 47. The Epocha of the _Hegira_ | 5335 | 4571 | 622 | - 48. The Epoch of _Yesdejerd_ | 5344 | 4580 | 631 | - 49. The _Jellalæan_ Epocha | 5791 | 5027 | 1078 | - 50. The Epocha of the reformation | 6230 | 5466 | 1517 | - +------------------------------------------------------------------------+ - |TAB. I. _Shewing the Golden Number (which is the same both in the Old | - | and New Style) from the Christian Æra to A.D. 4000._ | - +------------------------------------------------------------------------+ - | Years less than an Hundred. | - +--------------++-----+-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - | || 0| 1| 2| 3|4 | 5|6 | 7| 8| 9|10|11|12|13|14|15|16|17|18| - | ||19|20|21|22|23|24|25|26|27|28|29|30|31|32|33|34|35|36|37| - | Hundreds of ||38|39|40|41|42|43|44|45|46|47|48|49|50|51|52|53|54|55|56| - | Years. ||57|58|59|60|61|62|63|64|65|66|67|68|69|70|71|72|73|74|75| - | ||76|77|78|79|80|81|82|83|84|85|86|87|88|89|90|91|92|93|94| - | ||95|96|97|98|99| | | | | | | | | | | | | | | - +--------------++==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+==+ - | 0|1900|3800|| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| - | 100|2000|3900|| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| - | 200|2100|4000||11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10| - | 300|2200| &c.||16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15| - | 400|2300| -- || 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| - +----+----+----++--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - | 500|2400| -- || 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| - | 600|2500| -- ||12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11| - | 700|2600| -- ||17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16| - | 800|2700| -- || 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| - | 900|2800| -- || 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| - +----+----+----++--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - |1000|2900| -- ||13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12| - |1100|3000| -- ||18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17| - |1200|3100| -- || 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| - |1300|3200| -- || 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| - |1400|3300| -- ||14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13| - +----+----+----++--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - |1500|3400| -- ||19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18| - |1600|3500| -- || 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| - |1700|3600| -- ||10|11|12|13|14|15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9| - |1800|3700| -- ||15|16|17|18|19| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14| - +----+----+----++--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - +--------------------------------------------------------------+ - |TAB. II. _Shewing the Number of Direction, for finding Easter | - | Sunday by the Golden Number and Dominical Letter._ | - +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - |G. N.| 1| 2| 3| 4| 5| 6| 7| 8| 9|10|11|12|13|14|15|16|17|18|19| - +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - | A |26|19| 5|26|12|33|19|12|26|19| 5|26|12| 5|26|12|33|19|12| - | B |27|13| 6|27|13|34|20|13|27|20| 6|27|13| 6|20|13|34|20| 6| - | C |28|14| 7|21|14|35|21| 7|28|21| 7|28|14| 7|21|14|28|21| 7| - | D |29|15| 8|22|15|29|22| 8|29|15| 8|29|15| 1|22|15|29|22| 8| - | E |30|16| 2|23|16|30|23| 9|30|16| 9|23|16| 2|23| 9|30|23| 9| - | F |24|17| 3|24|10|31|24|10|31|17|10|24|17| 3|24|10|31|17|10| - | G |25|18| 4|25|11|32|18|11|32|18| 4|25|18| 4|25|11|32|18|11| - +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - | This Table is adapted to the New Style. | - +--------------------------------------------------------------+ - - - TAB. III. _Shewing the Dominical Letters, Old Style, for 4200 Years - before the Christian Æra._ - - +-------------------+------------------------------------------------+ - | Before Christ | Hundreds of Years. | - +-------------------+------+------+------+------+------+------+------+ - | | 0 | 100 | 200 | 300 | 400 | 500 | 600 | - | | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | - | Years less | 1400 | 1500 | 1600 | 1700 | 1800 | 1900 | 2000 | - | than an | 2100 | 2200 | 2300 | 2400 | 2500 | 2600 | 2700 | - | Hundred. | 2800 | 2900 | 3000 | 3100 | 3200 | 3300 | 3400 | - | | 3500 | 3600 | 3700 | 3800 | 3900 | 4000 | 4100 | - +----+----+----+----+------+------+------+------+------+------+------+ - | 0 | 28 | 56 | 84 | D C | C B | B A | A G | G F | F E | E D | - +----+----+----+----+------+------+------+------+------+------+------+ - | 1 | 29 | 57 | 85 | E | D | C | B | A | G | F | - | 2 | 30 | 58 | 86 | F | E | D | C | B | A | G | - | 3 | 31 | 59 | 87 | G | F | E | D | C | B | A | - | 4 | 32 | 60 | 88 | B A | A G | G F | F E | E D | D C | C B | - +----+----+----+----+------+------+------+------+------+------+------+ - | 5 | 33 | 61 | 89 | C | B | A | G | F | E | D | - | 6 | 34 | 62 | 90 | D | C | B | A | G | F | E | - | 7 | 35 | 63 | 91 | E | D | C | B | A | G | F | - | 8 | 36 | 64 | 92 | G F | F E | E D | D C | C B | B A | A G | - +----+----+----+----+------+------+------+------+------+------+------+ - | 9 | 37 | 65 | 93 | A | G | F | E | D | C | B | - | 10 | 38 | 66 | 94 | B | A | G | F | E | D | C | - | 11 | 39 | 67 | 95 | C | B | A | G | F | E | D | - | 12 | 40 | 68 | 96 | E D | D C | C B | B A | A G | G F | F E | - +----+----+----+----+------+------+------+------+------+------+------+ - | 13 | 41 | 69 | 97 | F | E | D | C | B | A | G | - | 14 | 42 | 70 | 98 | G | F | E | D | C | B | A | - | 15 | 43 | 71 | 99 | A | G | F | E | D | C | B | - | 16 | 44 | 72 | | C B | B A | A G | G F | F E | E D | D C | - +----+----+----+----+------+------+------+------+------+------+------+ - | 17 | 45 | 73 | | D | C | B | A | G | F | E | - | 18 | 46 | 74 | | E | D | C | B | A | G | F | - | 19 | 47 | 75 | | F | E | D | C | B | A | G | - | 20 | 48 | 76 | | A G | G F | F E | E D | D C | C B | B A | - +----+----+----+----+------+------+------+------+------+------+------+ - | 21 | 49 | 77 | | B | A | G | F | E | D | C | - | 22 | 50 | 78 | | C | B | A | G | F | E | D | - | 23 | 51 | 79 | | D | C | B | A | G | F | E | - | 24 | 52 | 80 | | F E | E D | D C | C B | B A | A G | G F | - +----+----+----+----+------+------+------+------+------+------+------+ - | 25 | 53 | 81 | | G | F | E | D | C | B | A | - | 26 | 54 | 82 | | A | G | F | E | D | C | B | - | 27 | 55 | 83 | | B | A | G | F | E | D | C | - +----+----+----+----+------+------+------+------+------+------+------+ - - -TAB. IV. _Shewing the Dominical Letters, Old Style, for 4200 Years after - the Christian Æra._ - - +-------------------+------------------------------------------------+ - | After Christ | Hundreds of Years. | - +-------------------+------+------+------+------+------+------+------+ - | | 0 | 100 | 200 | 300 | 400 | 500 | 600 | - | | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | - | Years less | 1400 | 1500 | 1600 | 1700 | 1800 | 1900 | 2000 | - | than an | 2100 | 2200 | 2300 | 2400 | 2500 | 2600 | 2700 | - | Hundred. | 2800 | 2900 | 3000 | 3100 | 3200 | 3300 | 3400 | - | | 3500 | 3600 | 3700 | 3800 | 3900 | 4000 | 4100 | - +----+----+----+----+------+------+------+------+------+------+------+ - | 0 | 28 | 56 | 84 | D C | E D | F E | G F | A G | B A | C B | - +----+----+----+----+------+------+------+------+------+------+------+ - | 1 | 29 | 57 | 85 | B | C | D | E | F | G | A | - | 2 | 30 | 58 | 86 | A | B | C | D | E | F | G | - | 3 | 31 | 59 | 87 | G | A | B | C | D | E | F | - | 4 | 32 | 60 | 88 | F E | G F | A G | B A | C B | D C | E D | - +----+----+----+----+------+------+------+------+------+------+------+ - | 5 | 33 | 61 | 89 | D | E | F | G | A | B | C | - | 6 | 34 | 62 | 90 | C | D | E | F | G | A | B | - | 7 | 35 | 63 | 91 | B | C | D | E | F | G | A | - | 8 | 36 | 64 | 92 | A G | B A | C B | D C | E D | F E | G F | - +----+----+----+----+------+------+------+------+------+------+------+ - | 9 | 37 | 65 | 93 | F | G | A | B | C | D | E | - | 10 | 38 | 66 | 94 | E | F | G | A | B | C | D | - | 11 | 39 | 67 | 95 | D | E | F | G | A | B | C | - | 12 | 40 | 68 | 96 | C B | D C | E D | F E | G F | A G | B A | - +----+----+----+----+------+------+------+------+------+------+------+ - | 13 | 41 | 69 | 97 | A | B | C | D | E | F | G | - | 14 | 42 | 70 | 98 | G | A | B | C | D | E | F | - | 15 | 43 | 71 | 99 | F | G | A | B | C | D | E | - | 16 | 44 | 72 | | E D | F E | G F | A G | B A | C B | D C | - +----+----+----+----+------+------+------+------+------+------+------+ - | 17 | 45 | 73 | | C | D | E | F | G | A | B | - | 18 | 46 | 74 | | B | C | D | E | F | G | A | - | 19 | 47 | 75 | | A | B | C | D | E | F | G | - | 20 | 48 | 76 | | G F | A G | B A | C B | D C | E D | F E | - +----+----+----+----+------+------+------+------+------+------+------+ - | 21 | 49 | 77 | | E | F | G | A | B | C | D | - | 22 | 50 | 78 | | D | E | F | G | A | B | C | - | 23 | 51 | 79 | | C | D | E | F | G | A | B | - | 24 | 52 | 80 | | B A | C B | D C | E D | F E | G F | A G | - +----+----+----+----+------+------+------+------+------+------+------+ - | 25 | 53 | 81 | | G | A | B | C | D | E | F | - | 26 | 54 | 82 | | F | G | A | B | C | D | E | - | 27 | 55 | 83 | | E | F | G | A | B | C | D | - +----+----+----+----+------+------+------+------+------+------+------+ - - - TAB. V. _The Dominical Letter, New Style, for 4000 Years after the - Christian Æra._ - - +-------------------+---------------------------+ - | After Christ. | Hundreds of Years. | - +-------------------+------+------+------+------+ - | | 100 | 200 | 300 | 400 | - | | 500 | 600 | 700 | 800 | - | | 900 | 1000 | 1100 | 1200 | - | | 1300 | 1400 | 1500 | 1600 | - | | 1700 | 1800 | 1900 | 2000 | - | Years less than | 2100 | 2200 | 2300 | 2400 | - | an Hundred. | 2500 | 2600 | 2700 | 2800 | - | | 2900 | 3000 | 3100 | 3200 | - | | 3300 | 3400 | 3500 | 3600 | - | | 3700 | 3800 | 3900 | 4000 | - | +------+------+------+------+ - | | C | E | G | B A | - +----+----+----+----+------+------+------+------+ - | 1 | 29 | 57 | 85 | B | D | F | G | - | 2 | 30 | 58 | 86 | A | C | E | F | - | 3 | 31 | 59 | 87 | G | B | D | E | - | 4 | 32 | 60 | 88 | F E | A G | C B | D C | - +----+----+----+----+------+------+------+------+ - | 5 | 33 | 61 | 89 | D | F | A | B | - | 6 | 34 | 62 | 90 | C | E | G | A | - | 7 | 35 | 63 | 91 | B | D | F | G | - | 8 | 36 | 64 | 92 | A G | C B | C D | F E | - +----+----+----+----+------+------+------+------+ - | 9 | 37 | 65 | 93 | F | A | C | D | - | 10 | 38 | 66 | 94 | E | G | B | C | - | 11 | 39 | 67 | 95 | D | F | A | B | - | 12 | 40 | 68 | 96 | C B | E D | G F | A G | - +----+----+----+----+------+------+------+------+ - | 13 | 41 | 69 | 97 | A | C | E | F | - | 14 | 42 | 70 | 98 | G | B | D | E | - | 15 | 43 | 71 | 99 | F | A | C | D | - | 16 | 44 | 72 | | E D | G F | B A | C B | - +----+----+----+----+------+------+------+------+ - | 17 | 45 | 73 | | C | E | G | A | - | 18 | 46 | 74 | | B | D | F | G | - | 19 | 47 | 75 | | A | C | E | F | - | 20 | 48 | 76 | | G F | B A | D C | E D | - +----+----+----+----+------+------+------+------+ - | 21 | 49 | 77 | | E | G | B | C | - | 22 | 50 | 78 | | D | F | A | B | - | 23 | 51 | 79 | | C | E | G | A | - | 24 | 52 | 80 | | B A | D C | F E | G F | - +----+----+----+----+------+------+------+------+ - | 25 | 53 | 81 | | G | B | D | E | - | 26 | 54 | 82 | | F | A | C | D | - | 27 | 55 | 83 | | E | G | B | C | - | 28 | 56 | 84 | | D C | F E | A G | B A | - +----+----+----+----+------+------+------+------+ - - - TAB. VI. _Shewing the Days of the Months for both Styles by the - Dominical Letters._ - - +-------------+----+----+----+----+----+----+----+ - | Week Day. | A | B | C | D | E | F | G | - +-------------+----+----+----+----+----+----+----+ - | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | - | | 8 | 9 | 10 | 11 | 12 | 13 | 14 | - | January 31 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | - | October 31 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | - | | 29 | 30 | 31 |----|----|----|----| - +-------------+----|----|----| 1 | 2 | 3 | 4 | - | | 5 | 6 | 7 | 8 | 9 | 10 | 11 | - | Feb. 28-29 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | - | March 31 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | - | Nov. 30 | 26 | 27 | 28 | 29 | 30 | 31 |----| - +-------------+----+----+----+----+----+----+ 1 | - | | 2 | 3 | 4 | 5 | 6 | 7 | 8 | - | | 9 | 10 | 11 | 12 | 13 | 14 | 15 | - | April 30 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | - | July 31 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | - | | 30 | 31 |----|----|----|----|----| - +-------------+----|----| 1 | 2 | 3 | 4 | 5 | - | | 6 | 7 | 8 | 9 | 10 | 11 | 12 | - | | 13 | 14 | 15 | 16 | 17 | 18 | 19 | - | August 31 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | - | | 27 | 28 | 29 | 30 | 31 |----|----| - +-------------+----|----|----|----|----| 1 | 2 | - | | 3 | 4 | 5 | 6 | 7 | 8 | 9 | - | | 10 | 11 | 12 | 13 | 14 | 15 | 16 | - | Septemb. 30 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | - | Decemb. 31 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | - | | 31 |----|----|----|----|----|----| - +-------------+----| 1 | 2 | 3 | 4 | 5 | 6 | - | | 7 | 8 | 9 | 10 | 11 | 12 | 13 | - | | 14 | 15 | 16 | 17 | 18 | 19 | 20 | - | May 31 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | - | | 28 | 29 | 30 | 31 |----|----|----| - +-------------+----|----|----|----| 1 | 2 | 3 | - | | 4 | 5 | 6 | 7 | 8 | 9 | 10 | - | | 11 | 12 | 13 | 14 | 15 | 16 | 17 | - | June 30 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | - | | 25 | 26 | 27 | 28 | 29 | 30 | | - +-------------+----+----+----+----+----+----+----+ - - - - - CHAP. XXII. - - _A Description of the Astronomical Machinery serving to explain and - illustrate the foregoing part of this Treatise._ - - -[Sidenote: Fronting the Title Page. - - The ORRERY.] - -434. The ORRERY. This Machine shews the Motions of the Sun, Mercury, -Venus, Earth, and Moon; and occasionally, the superior Planets, Mars, -Jupiter, and Saturn may be put on; Jupiter’s four Satellites are moved -round him in their proper times by a small Winch; and Saturn has his -five Satellites, and his Ring which keeps its parallelism round the Sun; -and by a Lamp put in the Sun’s place, the Ring shews all the Phases -described in the 204th Article. - -[Sidenote: The Sun. - - The Ecliptic.] - -In the Center, No 1. represents the SUN, supported by it’s Axis -inclining almost 8 Degrees from the Axis of the Ecliptic; and turning -round in 25-1/4 days on its Axis, of which the North Pole inclines -toward the 8th Degree of Pisces in the great Ecliptic (No. 11.) whereon -the Months and Days are engraven over the Signs and Degrees in which the -Sun appears, as seen from the Earth, on the different days of the year. - -[Sidenote: Mercury.] - -The nearest Planet (No. 2) to the Sun is _Mercury_, which goes round him -in 87 days 23 hours, or 87-23/24 diurnal rotations of the Earth; but has -no Motion round its Axis in the Machine, because the time of its diurnal -Motion in the Heavens is not known to us. - -[Sidenote: Venus.] - -The next Planet in order is _Venus_ (No. 3) which performs her annual -Course in 224 days 17 hours; and turns round her Axis in 24 days 8 -hours, or in 24-1/3 diurnal rotations of the Earth. Her Axis inclines 75 -Degrees from the Axis of the Ecliptic, and her North Pole inclines -towards the 20th Degree of Aquarius, according to the observations of -_Bianchini_. She shews all the Phenomena described from the 30th to the -44th Article in Chap. I. - -[Sidenote: The Earth.] - -Next without the Orbit of Venus is the _Earth_ (No. 4) which turns round -its Axis, to any fixed point at a great distance, in 23 hours 56 minutes -4 seconds of mean solar time (221 & _seq._) but from the Sun to the Sun -again in 24 hours of the same time. No. 6 is a sidereal Dial-Plate under -the Earth; and No. 7 a solar Dial-Plate on the cover of the Machine. The -Index of the former shews sidereal, and of the latter, solar time; and -hence, the former Index gains one entire revolution on the latter every -year, as 365 solar or natural days contain 366 sidereal days, or -apparent revolutions of the Stars. In the time that the Earth makes -365-1/4 diurnal rotations on its Axis, it goes once round the Sun in the -Plane of the Ecliptic; and always keeps opposite to a moving Index (No. -10) which shews the Sun’s daily change of place, and also the days of -the months. - -The Earth is half covered with a black cap for dividing the apparently -enlightened half next the Sun, from the other half, which when turned -away from him is in the dark. The edge of the cap represents _the Circle -bounding Light and Darkness_, and shews at what time the Sun rises and -sets to all places throughout the year. The Earth’s Axis inclines 23-1/2 -Degrees from the Axis of the Ecliptic, the North Pole inclines toward -the beginning of Cancer; and keeps its parallelism throughout its annual -Course § 48, 202; so that in Summer the northern parts of the Earth -incline towards the Sun, and in the Winter from him: by which means, the -different lengths of days and nights, and the cause of the various -seasons, are demonstrated to sight. - -There is a broad Horizon, to the upper side of which is fixed a Meridian -Semi-circle in the North and South Points, graduated on both sides from -the Horizon to 90° in the Zenith, or vertical Point. The edge of the -Horizon is graduated from the East and West to the South and North -Points, and within these Divisions are the Points of the Compass. On the -lower side of this thin Horizon Plate stand out four small Wires, to -which is fixed a Twilight Circle 18 Degrees from the graduated side of -the Horizon all round. This Horizon may be put upon the Earth (when the -cap is taken away) and rectified to the Latitude of any place: and then, -by a small Wire called _the Solar Ray_, which may be put on so as to -proceed directly from the Sun’s Center towards the Earth’s, but to come -no farther than almost to touch the Horizon, the beginning of Twilight, -time of Sun-rising, with his Amplitude, Meridian Altitude, time of -Setting, Amplitude, and end of Twilight, are shewn for every day of the -year, at _that_ place to which the Horizon is rectified. - -[Sidenote: The Moon.] - -The Moon (No. 5) goes round the Earth, from between it and any fixed -point at a great distance, in 27 days 7 hours 43 minutes, or through all -the Signs and Degrees of her Orbit; which is called _her Periodical -Revolution_; but she goes round from the Sun to the Sun again, or from -Change to Change, in 29 days 12 hours 45 minutes, which is _her -Synodical Revolution_; and in that time she exhibits all the Phases -already described § 255. - -When the above-mentioned Horizon is rectified to the Latitude of any -given place, the times of the Moon’s rising and setting, together with -her Amplitude, are shewn to that place as well as the Sun’s; and all the -various Phenomena of the Harvest Moon § 273 & _seq._ made obvious to -sight. - -[Sidenote: The Nodes.] - -The Moon’s Orbit (No. 9.) is inclined to the Ecliptic, (No. 11.) one -half being above, and the other below it. The Nodes, or Points at 0 and -0 lie in the Plane of the Ecliptic, as described § 317, 318, and shift -backward through all it’s Signs and Degrees in 18-2/3 years. The Degrees -of the Moon’s Latitude, to the highest at _NL_ (North Latitude) and -lowest at _SL_ (South Latitude) are engraven both ways from her Nodes at -0 and 0; and, as the Moon rises and falls in her Orbit according to its -inclination, her Latitude and Distance from her Nodes are shewn for -every day; having first rectified her Orbit so as to set the Nodes to -their proper places in the Ecliptic: and then, as they come about at -different, and almost opposite times of the year § 319, and then point -towards the Sun, all the Eclipses may be shewn for hundreds of years -(without any new rectification) by turning the Machinery backward for -time past, or forward for time to come. At 17 Degrees distance from each -Node, on both Sides, is engraved a small Sun; and at 12 Degrees -distance, a small Moon; which shew the limits of solar and lunar -Eclipses § 317: and when, at any change, the Moon falls between either -of these Suns and the Node, the Sun will be eclipsed on the day pointed -to by the annual Index (No. 10,) and as the Moon has then North or South -Latitude, one may easily judge whether that Eclipse will be visible in -the Northern or Southern Hemisphere; especially as the Earth’s Axis -inclines towards the Sun or from him at that time. And when, at any -Full, the Moon falls between either of the little Moon’s and Node, she -will be eclipsed, and the annual Index shews the day of that Eclipse. -There is a Circle of 29-1/2 equal parts (No. 8.) on the cover of the -Machine, on which an Index shews the days of the Moon’s age. - -[Sidenote: PLATE IX. Fig. X.] - -There are two Semi-circles fixed to an elliptical Ring, which being put -like a cap upon the Earth, and the forked part _F_ upon the Moon, shews -the Tides as the Earth turns round within them, and they are led round -it by the Moon. When the different Places come to the Semi-circle -_AaEbB_, they have Tides of Flood; and when they come to the Semicircle -_CED_ they have Tides of Ebb § 304, 305; the Index on the hour Circle -(No. 7.) shewing the times of these Phenomena. - -There is a jointed Wire, of which one end being put into a hole in the -upright stem that holds the Earth’s cap, and the Wire laid into a small -forked piece which may be occasionally put upon Venus or Mercury, shews -the direct and retrograde Motions of these two Planets, with their -stationary Times and Places as seen from the Earth. - -The whole Machinery is turned by a winch or handle (No. 12,) and is so -easily moved that a clock might turn it without any danger of stopping. - -To give a Plate of the wheel-work of this Machine, would answer no -purpose, because many of the wheels lie so behind others as to hide them -from sight in any view whatsoever. - - -[Sidenote: Another ORRERY. - - PLATE VI. Fig. I.] - -435. _Another_ ORRERY. In this Machine, which is the simplest I ever -saw, for shewing the diurnal and annual motions of the Earth, together -with the motion of the Moon and her Nodes; _A_ and _B_ are two oblong -square Plates held together by four upright pillars; of which three -appear at _f_, _g_, and _g_2. Under the Plate _A_ is an endless screw on -the Axis of the handle _b_, which works in a wheel fixed on the same -Axis with the double grooved wheel _E_; and on the top of this Axis is -fixed the toothed wheel _i_, which turns the pinion _k_, on the top of -whose Axis is the pinion _k_2 which turns another pinion _b_2, and that -other turns a third, on the Axis _a_2 of which is the Earth _U_ turning -round; this last Axis inclining 23-1/2 Degrees. The supporter _X_2, in -which the Axis of the Earth turns, is fixed to the moveable Plate _C_. - -In the fixed Plate _B_, beyond _H_, is fixed the strong wire _d_, on -which hangs the Sun _T_ so as it may turn round the wire. To this Sun is -fixed the wire or solar ray _Z_, which (as the Earth _U_ turns round its -Axis) points to all the places that the Sun passes vertically over, -every day of the year. The Earth is half covered with a black cap _a_, -as in the former Orrery, for dividing the day from the night; and, as -the different places come out from below the edge of the cap, or go in -below it, they shew the times of Sun-rising and setting every day of the -year. This cap is fixed on the wire _b_, which has a forked piece _C_ -turning round the wire _d_: and, as the Earth goes round the Sun, it -carries the Cap, Wire, and solar Ray round him; so that the solar Ray -constantly points towards the Earth’s Center. - -On the Axis of the pinion _k_ is the pinion _m_, which turns a wheel on -the cock or supporter _n_, and on the Axis of this wheel nearest _n_ is -a pinion (hid from view) under the Plate _C_, which pinion turns a wheel -that carries the Moon _V_ round the Earth _U_; the Moon’s Axis rising -and falling in the socket _W_, which is fixed to the triangular piece -above _Z_; and this piece is fixed to the top of the Axis of the last -mentioned wheel. The socket _W_ is slit on the outermost side; and in -this slit the two pins near _Y_, fixed in the Moon’s Axis, move up and -down; one of them being above the inclined Plane _YX_, and the other -below it. By this mechanism, the Moon _V_ moves round the Earth _T_ in -the inclined Orbit _q_, parallel to the Plane of the Ring _YX_; of which -the Descending Node is at _X_, and the Ascending Node opposite to it, -but hid by the supporter _X_2. - -The small wheel _E_ turns the large wheels _D_ and _F_, of equal -diameters, by cat-gut strings crossing between them: and the Axis of -these two wheels are cranked at _G_ and _H_, above the Plate _B_. The -upright stems of these cranks going through the Plate _C_, carry it over -and over the fixed Plate _B_, with a motion which carries the Earth _U_ -round the Sun _T_, keeping the Earth’s Axis always parallel to itself; -or still inclining towards the left-hand of the Plate; and shewing the -vicissitudes of seasons, as described in the tenth chapter. As the Earth -goes round the Sun the pinion _k_ goes round the wheel _i_, for the Axis -of _k_ never touches the fixed Plate _B_; but turns on a wire fixed into -the Plate _C_. - -On the top of the crank _G_ is an Index _L_, which goes round the Circle -_m_2 in the time that the Earth goes round the Sun; and points to the -days of the months; which, together with the names of the seasons, are -marked in this Circle. - -This Index has a small grooved wheel _L_ fixed upon it, round which, and -the Plate _Z_, goes a cat-gut string crossing between them; and by this -means the Moon’s inclined Plane _YX_ with its Nodes is turned backward, -for shewing the times and returns of Eclipses § 319, 320. - -The following parts of this machine must be considered as distinct from -those already described. - -Towards the right hand, let _S_ be the Earth hung on the wire _e_, which -is fixed into the Plate _B_; and let _O_ be the Moon fixed on the Axis -_M_, and turning round within the cap _P_, in which, and in the Plate -_C_ the crooked wire _Q_ is fixed. On the Axis _M_ is also fixed the -Index _K_, which goes round a Circle _h_2, divided into 29-1/2 equal -parts, which are the days of the Moon’s age: but to avoid confusion in -the scheme, it is only marked with the numeral figures 1 2 3 4, for the -Quarters. As the crank _H_ carries this Moon round the Earth _S_ in the -Orbit _t_, she shews all her Phases by means of the cap _P_ for the -different days of her age, which are shewn by the Index _K_; this Index, -turning just as the Moon _O_ does, demonstrates her turning round her -Axis as she still keeps the same side towards the Earth _S_ § 262. - -[Sidenote: PL. VIII.] - -At the other end of the Plate _C_, a Moon _N_ goes round an Earth _R_ in -the Orbit _p_; but this Moon’s Axis is stuck fast into the Plate _C_ at -_S_2; so that neither Moon nor Axis can turn round; and as this Moon -goes round her Earth she shews herself all round to it; which proves, -that if the Moon was seen all round from the Earth in a Lunation, she -could not turn round her Axis. - -_N. B._ If there were only the two wheels _D_ and _F_, with a cat-gut -string over them, but not crossing between them, the Axis of the Earth -_U_ would keep its parallelism round the Sun _T_, and shew all the -seasons; as I sometimes make these Machines: and the Moon _O_ would go -round the Earth _S_, shewing her Phases as above; as likewise would the -Moon _N_ round the Earth _R_; but then, neither could the diurnal motion -of the Earth _U_ on its Axis be shewn, nor the motion of the Moon _V_ -round that Earth. - - -[Sidenote: The CALCULATOR.] - -436. In the year 1746 I contrived a very simple Machine, and described -it’s performance in a small treatise upon the Phenomena of the Harvest -Moon, published in the year 1747. I improved it soon after, by adding -another wheel, and called it _the Calculator_. It may be easily made by -any Gentleman who has a mechanical Genius. - -[Sidenote: Fig. I.] - -The great flat Ring supported by twelve pillars, and on which the twelve -Signs with their respective Degrees are laid down, is the Ecliptic; -nearly in the center of it is the Sun _S_ supported by the strong -crooked Wire _I_; and from the Sun proceeds a Wire _W_, called _the -Solar Ray_, pointing towards the center of the Earth _E_, which is -furnished with a moveable Horizon _H_, together with a brazen Meridian, -and Quadrant of Altitude. _R_ is a small Ecliptic, whose Plane -co-incides with that of the great one, and has the like Signs and -Degrees marked upon it; and is supported by two Wires _D_ and _D_, which -enter into the Plate _PP_, but may be taken off at pleasure. As the -Earth goes round the Sun, the Signs of this small Circle keep parallel -to themselves, and to those of the great Ecliptic. When it is taken off, -and the solar Ray _W_ drawn farther out, so as almost to touch the -Horizon _H_, or the Quadrant of Altitude, the Horizon being rectified to -any given Latitude, and the Earth turned round its Axis by hand, the -point of the Wire _W_ shews the Sun’s Declination in passing over the -graduated brass Meridian, and his height at any given time upon the -Quadrant of Altitude, together with his Azimuth, or point of Bearing -upon the Horizon at that time; and likewise his Amplitude, and time of -Rising and Setting by the hour Index, for any day of the year that the -annual Index _U_ points to in the Circle of Months below the Sun. _M_ is -a solar Index or Pointer supported by the Wire _L_ which is fixed into -the knob _K_: the use of this Index is to shew the Sun’s place in the -Ecliptic every day in the year; for it goes over the Signs and Degrees -as the Index _U_ goes over the months and days; or rather as they pass -under the Index _U_, in moving the cover plate with the Earth and its -Furniture round the Sun; for the Index _U_ is fixed tight on the -immoveable Axis in the Center of the Machine. _K_ is a knob or handle -for moving the Earth round the Sun, and the Moon round the Earth. - -As the Earth is carried round the Sun, its Axis constantly keeps the -same oblique direction, or parallel to itself § 48, 202, shewing thereby -the different lengths of days and nights at different times of the year, -with all the various seasons. And, in one annual revolution of the -Earth, the Moon _M_ goes 12-1/3 times round it from Change to Change, -having an occasional provision for shewing her different Phases. The -lower end of the Moon’s Axis bears by a small friction wheel upon the -inclined Plane _T_, which causes the Moon to rise above and sink below -the Ecliptic _R_ in every Lunation; crossing it in her Nodes, which -shift backward through all the Signs and Degrees of the said Ecliptic, -by the retrograde Motion of the inclined Plane _T_, in 18 years and 225 -days. On this Plane the Degrees and Parts of the Moon’s North and South -Latitude are laid down from both the Nodes, one of which, _viz._ the -Descending Node appears at 0, by _DN_ above _B_; the other Node being -hid from Sight on this Plane by the plate _PP_; and from both Nodes, at -proper distances, as in the other Orrery, the limits of Eclipses are -marked, and all the solar and lunar Eclipses are shewn in the same -manner, for any given year, within the limits of 6000, either before or -after the Christian Æra. On the plate that covers the wheel-work, under -the Sun _S_, and round the knob _K_ are Astronomical Tables, by which -the Machine may be rectified to the beginning of any given year within -these limits, in three or four minutes of time; and when once set right, -may be turned backward for 300 years past, or forward for as many to -come, without requiring any new rectification. There is a method for its -adding up the 29th of _February_ every fourth year, and allowing only 28 -days to that month for every other three: but all this being performed -by a particular manner of cutting the teeth of the wheels, and dividing -the month circle, too long and intricate to be described here, I shall -only shew how these motions may be performed near enough for common use, -by wheels with grooves and cat-gut strings round them, only here I must -put the Operator in mind that the grooves are to be made sharp (not -round) bottomed to keep the strings from slipping. - -The Moon’s Axis moves up and down in the socket _N_ fixed into the bar -_O_ (which carries her round the Earth) as she rises above or sinks -below the Ecliptic; and immediately below the inclined Plane _T_ is a -flat circular plate (between _Y_ and _T_) on which the different -Excentricities of the Moon’s Orbit are laid down; and likewise her mean -Anomaly and elliptic Equation by which her true Place may be very nearly -found at any time. Below this Apogee-plate, which shews the Anomaly, -&_c_. is a Circle _Y_ divided into 29-1/2 equal parts which are the days -of the Moon’s age: and the forked end _A_ of the Index _AB_ (Fig II) may -be put into the Apogee-part of this plate; there being just such another -Index to put into the inclined Plane _T_ at the Ascending Node; and then -the curved points _B_ of these Indexes shew the direct motion of the -Apogee, and retrograde motion of the Nodes through the Ecliptic _R_, -with their Places in it at any given time. As the Moon _M_ goes round -the Earth _E_, she shews her Place every day in the Ecliptic _R_, and -the lower end of her Axis shews her Latitude and distance from her Node -on the inclined Plane _T_, also her distance from her Apogee and -Perigee, together with her mean Anomaly, the then Excentricity of her -Orbit, and her elliptic Equation, all on the Apogee Plate, and the day -of her age in the Circle _Y_ of 29-1/2 equal parts; for every day of the -year pointed out by the annual Index _U_ in the Circle of months. - -Having rectified the Machine by the Tables for the beginning of any -year, move the Earth and Moon forward by the knob _K_, until the annual -Index comes to any given day of the month; then stop, and not only all -the above Phenomena may be shewn for that day, but also, by turning the -Earth round its Axis, the Declination, Azimuth, Amplitude, Altitude of -the Moon at any hour, and the times of her Rising and Setting, are shewn -by the Horizon, Quadrant of Altitude, and hour Index. And in moving the -Earth round the Sun, the days of all the New and Full Moons and Eclipses -in any given year are shewn. The Phenomena of the Harvest Moon, and -those of the Tides, by such a cap as that in Plate 9 Fig. 10. put upon -the Earth and Moon, together with the solution of many problems not here -related, are made conspicuous. - -[Sidenote: PL. VIII.] - -The easiest, though not the best way, that I can instruct any mechanical -person to make the wheel-work of such a machine, is as follows; which is -the way that I made it, before I thought of numbers exact enough to make -it worth the trouble of cutting teeth in the wheels. - -[Sidenote: Fig. III.] - -Fig. 3d of Plate 8 is a section of this Machine; in which _ABCD_ is a -frame of wood held together by four pillars at the corners, whereof two -appear at _AC_ and _BD_. In the lower Plate _CD_ of this Frame are three -small friction-wheels, at equal distances from each other; two of them -appearing at _e_ and _e_. As the frame is moved round, these wheels run -upon the fixed bottom Plate _EE_ which supports the whole work. - -In the Center of this last mentioned Plate is fixed the upright Axis _f_ -_FFG_, and on the same Axis is fixed the wheel _HHH_ in which are four -grooves _I_, _X_, _k_, _L_ of different Diameters. In these grooves are -cat-gut strings going also round the separate wheels _M_, _N_, _O_ and -_P_. - -The wheel _M_ is fixed on a solid Spindle or Axis, the lower pivot of -which turns at _R_ in the under Plate of the moveable frame _ABCD_; and -on the upper end of this Axis is fixed the Plate _o o_ (which is _PP_, -under the Earth, in Fig. I.) and to this Plate is fixed, at an Angle of -23-1/2 Degrees inclination, the Dial-plate below the Earth _T_; on the -Axis of which, the Index _q_ is turned round by the Earth. This Axis, -together with the Wheel _M_, and Plate _o o_, keep their parallelism in -going round the Sun _S_. - -On the Axis of the wheel _M_ is a moveable socket on which the small -wheel _N_ is fixed, and on the upper end of this socket is put on tight -(but so as it may be occasionally turned by hand) the bar _ZZ_ (_viz._ -the bar _O_ in Fig. I.) which carries the Moon _m_ round the Earth _T_, -by the Socket _n_, fixed into the bar. As the Moon goes round the Earth -her Axis rises and falls in the Socket _n_; because, on the lower end of -her Axis, which is turned inward, there is a small friction Wheel _s_ -running on the inclined Plane _X_ (which is _T_ in Fig. I.) and so -causes the Moon alternately to rise above and sink below the little -Ecliptic _VV_ (_R_ in Fig. I.) in every Lunation. - -On the Socket or hollow Axis of the Wheel _N_, there is another Socket -on which the Wheel _O_ is fixed; and the Moon’s inclined Plane _X_ is -put tightly on the upper end of this Socket, not on a square, but on a -round, that it may be occasionally set by hand without wrenching the -Wheel or Axle. - -Lastly, on the hollow Axis of the Wheel _O_ is another Socket on which -is fixed the Wheel _P_, and on the upper end of this Socket is put on -tightly the Apogee-plate _Y_, (that immediately below _T_ in Fig. I.) -all these Axles turn in the upper Plate of the moveable frame at _Q_ -which Plate is covered with the thin Plate _cc_ (screwed to it) whereon -are the fore-mentioned Tables and month Circle in Fig. I. - -The middle part of the thick fixed Wheel _HHH_ is much broader than the -rest of it, and comes out between the Wheels _M_ and _O_ almost to the -Wheel _N_. To adjust the diameters of the grooves of this fixed wheel to -the grooves of the separate Wheels _M_, _N_, _O_ and _P_, so as they may -perform their motions in the proper times, the following method must be -observed. - -The Groove of the Wheel _M_, which keeps the parallelism of the Earth’s -Axis, must be precisely of the same Diameter as the lower Groove _I_ of -the fixed Wheel _HHH_; but, when this Groove is so well adjusted as to -shew, that in ever so many annual revolutions of the Earth, its Axis -keeps its parallelism, as may be observed by the solar Ray _W_ (Fig. I.) -always coming precisely to the same Degree of the small Ecliptic _R_ at -the end of every annual revolution, when the Index _M_ points to the -like Degree in the great Ecliptic; then, with the edge of a thin File -give the Groove of the Wheel _M_ a small rub all round; and by that -means, lessening the Diameter of the Groove, perhaps about the 20th part -of a hair’s breadth, it will cause the Earth to shew the precession of -the Equinoxes; which, in many annual revolutions will begin to be -sensible as the Earth’s Axis slowly deviates from its parallelism § 246, -towards the antecedent Signs of the Ecliptic. - -The Diameter of the Groove of the Wheel _N_, which carries the Moon -round the Earth, must be to the Diameter of the Groove _X_ as a Lunation -is to a year; that is, as 29-1/2 to 365-1/4. - -The Diameter of the Groove of the Wheel _O_, which turns the inclined -Plane _X_ with the Moon’s Nodes backward, must be to the Diameter of the -Groove _k_ as 20 to 18-225/365. And, - -Lastly, the Diameter of the Groove of the Wheel _P_, which carries the -Moon’s Apogee forward, must be to the Diameter of the Groove _L_ as 70 -to 62. - -[Sidenote: PLATE IV.] - -But, after all this nice adjustment of the Grooves to the proportional -times of their respective Wheels turning round, and which seems to -promise very well in Theory, there will still be found a necessity of a -farther adjustment by hand; because proper allowance must be made for -the Diameters of the cat-gut strings: and the Grooves must be so -adjusted by hand, as, that in the time the Earth is moved once round the -Sun, the Moon must perform 12 synodical revolutions round the Earth, and -be almost 11 days old in her 13th revolution. The inclined Plane with -its Nodes must go once round backward through all the Signs and Degrees -of the small Ecliptic in 18 annual revolutions of the Earth and 225 days -over. And the Apogee-plate must go once round forward, so as its Index -may go over all the Signs and Degrees of the small Ecliptic in eight -years (or so many annual revolutions of the Earth) and 312 days over. - -_N. B._ The string which goes round the Grooves _X_ and _N_ for the -Moon’s Motion must cross between these Wheels; but all the rest of the -strings go in their respective Grooves _IM_, _kO_, and _LP_ without -crossing. - - -[Sidenote: The COMETARIUM.] - -437. The COMETARIUM. This curious Machine shews the Motion of a Comet or -excentric Body moving round the Sun, describing equal Areas in equal -times § 152, and may be so contrived as to shew such a Motion for any -Degree of Excentricity. It was invented by the late Dr. _Desaguliers_. - -[Sidenote: Fig. IV.] - -The dark elliptical Groove round the letters _abcdefghiklm_ is the Orbit -of the Comet _Y_: this Comet is carried round in the Groove according to -the order of letters, by the Wire _W_, fixed in the Sun _S_, and slides -on the Wire as it approaches nearer to or recedes farther from the Sun, -being nearest of all in the Perihelion _a_, and farthest in the Aphelion -_g_. The Areas _aSb_, _bSc_, _cSd_ &c. or contents of these several -Triangles are all equal; and in every turn of the Winch _N_ the Comet -_Y_ is carried over one of these Areas; consequently in as much time as -it moves, from _f_ to _g_, or from _g_ to _h_, it moves from _m_ to _a_, -or from _a_ to _b_; and so of the rest, being quickest of all at _a_, -and slowest at _g_. Thus, the Comet’s velocity in its Orbit continually -decreases from the Perihelion _a_ to the Aphelion _g_; and increases in -the same proportion from _g_ to _a_. - -[Sidenote: PLATE IV.] - -The elliptic Orbit is divided into 12 equal Parts or Signs with their -respective Degrees, and so is the Circle _n o p q r s t n_ which -represents a great Circle in the Heavens, and to which all the fixed -Stars in the Comet’s way are referred. Whilst the Comet moves from _f_ -to _g_ in its Orbit it appears to move only about 5 Degrees in this -Circle, as is shewn by the small knob on the end of the Wire _W_; but in -as short time as the Comet moves from _m_ to _a_, or from _a_ to _b_, -and it appears to describe the large space _tn_ or _no_ in the Heavens, -either of which spaces contains 120 Degrees or four Signs. Were the -Excentricity of its Orbit greater, the greater still would be the -difference of its Motion, and _vice versâ_. - -_ABCDEFGHIKLMA_ is a circular Orbit for shewing the equable Motion of a -Body round the Sun _S_, describing equal Areas _ASB_, _BSC_, &c. in -equal times with those of the Body _Y_ in its elliptical Orbit above -mentioned; but with this difference, that the circular Motion describes -the equal Arcs _AB_, _BC_, &c. in the same equal times that the -elliptical Motion describes the unequal Arcs _ab_, _bc_, &c. - -Now, suppose the two Bodies _Y_ and I to start from the Points _a_ and -_A_ at the same moment of time, and each having gone round its -respective Orbit, to arrive at these Points again at the same instant, -the Body _Y_ will be forwarder in its Orbit than the Body I all the way -from _a_ to _g_, and from _A_ to _G_; but I will be forwarder than _Y_ -through all the other half of the Orbit; and the difference is equal to -the Equation of the Body _Y_ in its Orbit. At the Points _a_, _A_, and -_g_, _G_, that is, in the Perihelion and Aphelion, they will be equal; -and then the Equation vanishes. This shews why the Equation of a Body -moving in an elliptic Orbit, is added to the mean or supposed circular -Motion from the Perihelion to the Aphelion, and subtracted from the -Aphelion to the Perihelion, in Bodies moving round the Sun, or from the -Perigee to the Apogee, and from the Apogee to the Perigee in the Moon’s -Motion round the Earth, according to the Precepts in the 355th Article; -only we are to consider, that when Motion is turned into Time, it -reverses the titles in the Table of _The Moon’s elliptic Equation_. - -[Sidenote: Fig. V.] - -This curious Motion is performed in the following manner. _ABC_ is a -wooden bar (in the box containing the wheel-work) above which are the -wheels _D_ and _E_; and below it the elliptic Plates _FF_ and _GG_; each -Plate being fixed on an Axis in one of its Focuses, at _E_ and _K_; and -the Wheel _E_ is fixed on the same Axis with the Plate _FF_. These -Plates have Grooves round their edges precisely of equal Diameters to -one another, and in these Grooves is the cat-gut string _gg_, _gg_ -crossing between the Plates at _h_. On _H_, the Axis of the handle or -winch _N_ in Fig. 4th, is an endless screw in Fig. 5, working in the -Wheels _D_ and _E_, whose numbers of teeth being equal, and should be -equal to the number of lines _aS_, _bS_, _cS_, &c. in Fig. 4, they turn -round their Axes in equal times to one another, and to the Motion of the -elliptic Plates. For, the Wheels _D_ and _E_ having equal numbers of -teeth, the Plate _FF_ being fixed on the same Axis with the Wheel _E_, -and the Plate _FF_ turning the equally big Plate _GG_ by a cat-gut -string round them both, they must all go round their Axes in as many -turns of the handle _N_ as either of the Wheels has teeth. - -’Tis easy to see, that the end _h_ of the elliptical Plate _FF_ being -farther from its Axis _E_ than the opposite end _i_ is, must describe a -Circle so much the larger in proportion; and therefore move through so -much more space in the same time; and for that reason the end _h_ moves -so much faster than the end _i_, although it goes no sooner round the -Center _E_. But then, the quick-moving end _h_ of the Plate _FF_ leads -about the short end _hK_ of the Plate _GG_ with the same velocity; and -the slow moving end _i_ of the Plate _FF_ coming half round as to _B_, -must then lead the long end _k_ of the Plate _GG_ as slowly about: So -that the elliptical Plate _FF_ and it’s Axis _E_ move uniformly and -equally quick in every part of its revolution; but the elliptical Plate -_GG_, together with its Axis _K_ must move very unequally in different -parts of its revolution; the difference being always inversely as the -distance of any point of the Circumference of _GG_ from its Axis at _K_: -or in other words, to instance in two points, if the distance _Kk_ be -four, five, or six times as great as the distance _Kh_, the Point _h_ -will move in that position four, five, or six times as fast as the Point -_k_ does, when the Plate _GG_ has gone half round: and so on for any -other Excentricity or difference of the Distances _Kk_ and _Kh_. The -tooth _i_ on the Plate _FF_ falls in between the two teeth at _k_ on the -Plate _GG_, by which means the revolution of the latter is so adjusted -to that of the former, that they can never vary from one another. - -On the top of the Axis of the equally moving Wheel _D_, in Fig. 5th, is -the Sun _S_ in Fig. 4th; which Sun, by the Wire _Z_ fixed to it, carries -the Ball I round the Circle _ABCD_, &c. with an equable Motion according -to the order of the letters: and on the top of the Axis _K_ of the -unequally moving Ellipsis _GG_, in Fig. 5th, is the Sun _S_ in Fig. 4th, -carrying the Ball _Y_ unequably round in the elliptical Groove _a b c -d_, &c. _N.B._ This elliptical Groove must be precisely equal and -similar to the verge of the Plate _GG_, which is also equal to that of -_FF_. - -In this manner, Machines may be made to shew the true Motion of the Moon -about the Earth, or of any Planet about the Sun; by making the -elliptical Plates of the same Excentricities, in proportion to the -Radius, as the Orbits of the Planets are whose Motions they represent: -and so, their different Equations in different parts of their Orbits may -be made plain to sight; and clearer Ideas of these Motions and Equations -acquired in half an hour, than could be gained from reading half a day -about such Motions and Equations. - - -[Sidenote: The improved CELESTIAL GLOBE. - - PLATE III. Fig. III.] - -438. The _Improved Celestial Globe_. On the North Pole of the Axis, -above the Hour Circle, is fixed an Arch _MKH_ of 23-1/2 Degrees; and at -the end _H_ is fixed an upright pin _HG_, which stands directly over the -North Pole of the Ecliptic, and perpendicular to that part of the -surface of the Globe. On this pin are two moveable Collets at _D_ and -_H_, to which are fixed the quadrantal Wires _N_ and _O_, having two -little Balls on their ends for the Sun and Moon, as in the Figure. The -Collet _D_ is fixed to the circular Plate _F_ whereon the 29-1/2 days of -the Moon’s age are engraven, beginning just under the Sun’s Wire _N_; -and as this Wire is moved round the Globe, the Plate _F_ turns round -with it. These Wires are easily turned if the Screw _G_ be slackened; -and when they are set to their proper places, the Screw serves to fix -them there so, as in turning the Ball of the Globe, the Wires with the -Sun and Moon go round with it; and these two little Balls rise and set -at the same times, and on the same points of the Horizon, for the day to -which they are rectified, as the Sun and Moon do in the Heavens. - -Because the Moon keeps not her course in the Ecliptic (as the Sun -appears to do) but has a Declination of 5-1/3 Degrees on each side from -it in every Lunation § 317, her Ball may be screwed as many Degrees to -either side of the Ecliptic as her Latitude or Declination from the -Ecliptic amounts to at any given time; and for this purpose _S_ is a -small piece of pasteboard, of which the curved edge _S_ is to be set -upon the Globe at right Angles to the Ecliptic, and the dark line over -_S_ to stand upright upon it. From this line, on the convex edge, are -drawn the 5-1/3 Degrees of the Moon’s Latitude on both sides of the -Ecliptic; and when this piece is set upright on the Globe, it’s -graduated edge reaches to the Moon on the Wire _O_, by which means she -is easily adjusted to her Latitude found by an Ephemeris. - -The Horizon is supported by two semicircular Arches, because Pillars -would stop the progress of the Balls when they go below the Horizon in -an oblique sphere. - -[Sidenote: To rectify it.] - -_To rectify the Globe._ Elevate the Pole to the Latitude of the Place; -then bring the Sun’s place in the Ecliptic for the given day to the -brasen Meridian, and set the Hour Index to XII at noon, that is, to the -upper XII on the Hour Circle; keeping the Globe in that situation, -slacken the Screw _G_, and set the Sun directly over his place on the -Meridian; which done, set the Moon’s Wire under the number that -expresses her age for that day on the Plate _F_, and she will then stand -over her place in the Ecliptic, and shew what Constellation she is in. -Lastly, fasten the Screw _G_, and laying the curved edge of the -pasteboard _S_ over the Ecliptic below the Moon, adjust the Moon to her -Latitude over the graduated edge of the pasteboard; and the Globe will -be rectified. - -[Sidenote: It’s use.] - -Having thus rectified the Globe, turn it round, and observe on what -points of the Horizon the Sun and Moon Balls rise and set, for these -agree with the points of the Compass on which the Sun and Moon rise and -set in the Heavens on the given day; and the Hour Index shews the times -of their rising and setting; and likewise the time of the Moon’s passing -over the Meridian. - -This simple Apparatus shews all the varieties that can happen in the -rising and setting of the Sun and Moon; and makes the forementioned -Phenomena of the Harvest Moon (Chap. xvi.) plain to the Eye. It is also -very useful in reading Lectures on the Globes, because a large company -can see this Sun and Moon going round, rising above and setting below -the Horizon at different times, according to the seasons of the year; -and making their appulses to different fixed Stars. But, in the usual -way, where there is only the places of the Sun and Moon in the Ecliptic -to keep the Eye upon, they are easily lost sight of, unless covered with -Patches. - -[Sidenote: The PLANETARY GLOBE. - - PL. VIII. Fig. IV.] - -439. The _Planetary Globe_. In this Machine, _T_ is a terrestrial Globe -fixed on its Axis standing upright on the Pedestal _CDE_, on which is an -Hour Circle, having its Index fixed on the Axis, which turns somewhat -tightly in the Pedestal, so that the Globe may not be liable to shake; -to prevent which, the Pedestal is about two Inches thick, and the Axis -goes quite through it, bearing on a shoulder. The Globe is hung in a -graduated brasen Meridian, much in the usual way; and the thin Plate -_N_, _NE_, _E_, is a moveable Horizon, graduated round the outer edge, -for shewing the Bearings and Amplitudes of the Sun, Moon, and Planets. -The brasen Meridian is grooved round the outer edge; and in this Groove -is a slender Semi-circle of brass, the ends of which are fixed to the -Horizon in its North and South Points: this Semi-circle slides in the -Groove as the Horizon is moved in rectifying it for different Latitudes. -To the middle of the Semi-circle is fixed a Pin which always keeps in -the Zenith of the Horizon, and on this Pin the Quadrant of Altitude _q_ -turns; the lower end of which, in all Positions, touches the Horizon as -it is moved round the same. This Quadrant is divided into 90 Degrees -from the Horizon to the zenithal Pin on which it is turned, at 90. The -great flat Circle or Plate _AB_ is the Ecliptic, on the outer edge of -which, the Signs and Degrees are laid down; and every fifth Degree is -drawn through the rest of the surface of this Plate towards its Center. -On this Plate are seven Grooves, to which seven little Balls are -adjusted by sliding Wires, so that they are easily moved in the Grooves, -without danger of starting out of them. The Ball next the terrestrial -Globe is the Moon, the next without it is Mercury, the next Venus, the -next the Sun, then Mars, then Jupiter, and lastly Saturn; and in order -to know them, they are separately stampt with the following Characters; -☽, ☿, ♀, ☉, ♂, ♃, ♄. This Plate or Ecliptic is supported by four strong -Wires, having their lower ends fixed into the Pedestal, at _C_, _D_, and -_E_, the fourth being hid by the Globe. The Ecliptic is inclined 23-1/2 -Degrees to the Pedestal, and is therefore properly inclined to the Axis -of the Globe which stands upright on the Pedestal. - -[Sidenote: To rectify it.] - -_To rectify this Machine._ Set all the planetary Balls to their -geocentric places in the Ecliptic for any given time by an Ephemeris: -then, set the North Point of the Horizon to the Latitude of your place -on the brasen Meridian, and the Quadrant of Altitude to the South Point -of the Horizon; which done, turn the Globe with its Furniture till the -Quadrant of Altitude comes right against the Sun, _viz._ to his place in -the Ecliptic; and keeping it there, set the Hour Index to the XII next -the letter _C_; and the Machine will be rectified, not only for the -following Problems, but for several others, which the Artist may easily -find out. - - - PROBLEM I. - - _To find the Amplitudes, Meridian Altitudes, and times of Rising, - Culminating, and Setting, of the Sun, Moon, and Planets._ - -[Sidenote: It’s use.] - -Turn the Globe round eastward, or according to the order of Signs; and -as the eastern edge of the Horizon comes right against the Sun, Moon, or -any Planet, the Hour Index will shew the time of it’s rising; and the -inner edge of the Ecliptic will cut it’s rising Amplitude in the -Horizon. Turn on, and as the Quadrant of Altitude comes right against -the Sun, Moon, or Planets, the Ecliptic cuts their meridian Altitudes in -the Quadrant, and the Hour Index shews the times of their coming to the -Meridian. Continue turning, and as the western edge of the Horizon comes -right against the Sun, Moon, or Planets, their setting Amplitudes are -cut in the Horizon by the Ecliptic; and the times of their setting are -shewn by the Index on the Hour Circle. - - - PROBLEM II. - -_To find the Altitude and Azimuth of the Sun, Moon, and Planets, at any - time of their being above the Horizon._ - -Turn the Globe till the Index comes to the given time in the Hour -Circle; then keep the Globe steady, and moving the Quadrant of Altitude -to each Planet respectively, the edge of the Ecliptic will cut the -Planet’s mean Altitude on the Quadrant, and the Quadrant will cut the -Planet’s Azimuth, or Point of Bearing on the Horizon. - - - PROBLEM III. - -_The Sun’s Altitude being given at any time either before or after Noon, - to find the Hour of the Day, and the Variation of the Compass, in any - known Latitude._ - -With one hand hold the edge of the Quadrant right against the Sun; and, -with the other hand, turn the Globe westward, if it be in the forenoon, -or eastward if it be in the afternoon, until the Sun’s place at the -inner edge of the Ecliptic cuts the Quadrant in the Sun’s observed -Altitude; and then the Hour Index will point out the time of the day, -and the Quadrant will cut the true Azimuth, or Bearing of the Sun for -that time: the difference between which, and the Bearing shewn by the -Azimuth Compass, shews the variation of the Compass in that place of the -Earth. - - -[Sidenote: The TRAJECTORIUM LUNARE. - - PL. VII. Fig. V.] - -440. The _Trajectorium Lunare_. This Machine is for delineating the -paths of the Earth and Moon, shewing what sort of Curves they make in -the etherial regions; and was just mentioned in the 266th Article. _S_ -is the Sun, and _E_ the Earth, whose Centers are 81 Inches distant from -each other; every Inch answering to a Million of Miles § 47. _M_ is the -Moon, whose Center is 24/100 parts of an Inch from the Earth’s in this -Machine, this being in just proportion to the Moon’s distance from the -Earth § 52. _AA_ is a Bar of Wood, to be moved by hand round the Axis -_g_ which is fixed in the Wheel _Y_. The Circumference of this Wheel is -to the Circumference of the small Wheel _L_ (below the other end of the -Bar) as 365-1/4 days is to 29-1/2; or as a Year is to a Lunation. The -Wheels are grooved round their edges, and in the Grooves is the cat-gut -string _GG_ crossing between the Wheels at _X_. On the Axis of the Wheel -_L_ is the Index _F_, in which is fixed the Moon’s Axis _M_ for carrying -her round the Earth _E_ (fixed on the Axis of the Wheel _L_) in the time -that the Index goes round a Circle of 29-1/2 equal parts, which are the -days of the Moon’s age. The Wheel _Y_ has the Months and Days of the -year all round it’s Limb; and in the Bar _AA_ is fixed the Index _I_, -which points out the Days of the Months answering to the Days of the -Moon’s age, shewn by the Index _F_, in the Circle of 29-1/2 equal parts -at the other end of the Bar. On the Axis of the Wheel _L_ is put the -piece _D_, below the Cock _C_, in which this Axis turns round; and in -_D_ are put the Pencils _e_ and _m_, directly under the Earth _E_ and -Moon _M_; so that _m_ is carried round _e_ as _M_ is round _E_. - -[Sidenote: It’s use.] - -Lay the Machine on an even Floor, pressing gently on the Wheel _Y_ to -cause its spiked Feet (of which two appear at _P_ and _P_, the third -being supposed to be hid from sight by the Wheel) enter a little into -the Floor to secure the Wheel from turning. Then lay a paper about four -foot long under the Pencils _e_ and _m_, cross-wise to the Bar: which -done, move the Bar slowly round the Axis _g_ of the Wheel _Y_; and, as -the Earth _E_ goes round the Sun _S_, the Moon _M_ will go round the -Earth with a duly proportioned velocity; and the friction Wheel _W_ -running on the Floor, will keep the Bar from bearing too heavily on the -Pencils _e_ and _m_, which will delineate the paths of the Earth and -Moon, as in Fig. 2d, already described at large, § 266, 267. As the -Index _I_ points out the Days of the Months, the Index _F_ shews the -Moon’s age on these Days, in the Circle of 29-1/2 equal parts. And as -this last Index points to the different Days in it’s Circle, the like -numeral Figures may be set to those parts of the Curves of the Earth’s -Path and Moon’s, where the Pencils _e_ and _m_ are at those times -respectively, to shew the places of the Earth and Moon. If the Pencil -_e_ be pushed a very little off, as if from the Pencil _m_, to about -1/40 part of their distance, and the Pencil _m_ pushed as much towards -_e_, to bring them to the same distances again, though not to the same -points of space; then as _m_ goes round _e_, _e_ will go as it were -round the Center of Gravity between the Earth _e_ and Moon _m_ § 298: -but this Motion will not sensibly alter the Figure of the Earth’s Path -or the Moon’s. - -If a Pin as _p_ be put through the Pencil _m_, with its head towards -that of the Pin _q_ in the Pencil _e_, its head will always keep thereto -as _m_ goes round _e_, or as the same side of the Moon is still obverted -to the Earth. But the Pin _p_, which may be considered as an equatoreal -Diameter of the Moon, will turn quite round the Point _m_, making all -possible Angles with the Line of its progress or line of the Moon’s -Path. This is an ocular proof of the Moon’s turning round her Axis. - - -[Sidenote: The TIDE DIAL. - - PLATE IX. Fig. VII. - - It’s use.] - -441. The TIDE-DIAL. The outside parts of this Machine consist of, 1. An -eight-sided Box, on the top of which at the corner is shewn the Phases -of the Moon at the Octants, Quarters, and Full. Within these is a Circle -of 29-1/2 equal parts, which are the days of the Moon’s age accounted -from the Sun at New Moon round to the same again. Within this Circle is -one of 24 hours divided into their respective Halves and Quarters. 2. A -moving elliptical Plate painted blue to represent the rising of the -Tides under and opposite to the Moon; and has the words, _High Water, -Tide falling, Low Water, Tide rising_, marked upon it. To one end of -this Plate is fixed the Moon _M_ by the Wire _W_, and goes along with -it. 3. Above this elliptical Plate is a round one, with the Points of -the Compass upon it, and also the names of above 200 places in the large -Machine (but only 32 in the Figure to avoid confusion) set over those -Points on which the Moon bears when she raises the Tides to the greatest -heights at these Places twice in every lunar day: and to the North and -South Points of this Plate are fixed two Indexes _I_ and _K_, which shew -the times of High Water in the Hour Circle at all these places. 4. Below -the elliptical Plate are four small Plates, two of which project out -from below its ends at New and Full Moon; and so, by lengthening the -Ellipse shew the Spring Tides, which are then raised to the greatest -heights by the united attractions of the Sun and Moon § 302. The other -two of these small Plates appear at low water when the Moon is in her -Quadratures, or at the sides of the elliptic Plate, to shew the Nepe -Tides; the Sun and Moon then acting cross-wise to each other. When any -two of these small Plates appear, the other two are hid; and when the -Moon is in her Octants they all disappear, there being neither Spring -nor Nepe Tides at those times. Within the Box are a few Wheels for -performing these Motions by the Handle or Winch _H_. - -[Illustration: Plate XIII. - -_J. Ferguson inv. et del._ _J. Mynde Sculp._] - -Turn the Handle until the Moon _M_ comes to any given day of her age in -the Circle of 29-1/2 equal parts, and the Moon’s Wire _W_ will cut the -time of her coming to the Meridian on that day, in the Hour Circle; the -XII under the Sun being Mid-day, and the opposite XII Mid-night: then -looking for the name of any given place on the round Plate (which makes -29-1/2 rotations whilst the Moon _M_ makes only one revolution from the -Sun to the Sun again) turn the Handle till _that_ place comes to the -word _High Water_ under the Moon, and the Index which falls among the -Afternoon Hours will shew the time of high water at that place in the -Afternoon of the given day: then turn the Plate half round, till the -same place comes to the opposite High Water Mark, and the Index will -shew the time of High Water in the Forenoon at that place. And thus, as -all the different places come successively under and opposite to the -Moon, the Indexes shew the times of High Water at them in both parts of -the day: and when the same places come to the Low Water Marks the -Indexes shew the times of Low Water. For about two days before and after -the times of New and Full Moon, the two small Plates come out a little -way from below the High Water Marks on the elliptical Plate, to shew -that the Tides rise still higher about these times: and about the -Quarters, the other two Plates come out a little from under the Low -Water Marks towards the Sun and on the opposite side, shewing that the -Tides of Flood rise not then so high, nor do the Tides of Ebb fall so -low, as at other times. - -By pulling the Handle a little way outward, it is disengaged from the -Wheel-work, and then the upper Plate may be turned round quickly by hand -so, as the Moon may be brought to any given day of her age in about a -quarter of a minute. - -[Sidenote: The inside work described. - - Fig. VIII.] - -On _AB_, the Axis of the Handle _H_, is an endless Screw _C_ which turns -the Wheel _FED_ of 24 teeth round in 24 revolutions of the Handle: this -Wheel turns another _ONG_ of 48 teeth, and on its Axis is the Pinion -_PQ_ of four leaves which turns the Wheel _LKI_ of 59 teeth round in -29-1/2 turnings or rotations of the Wheel _FED_, or in 708 revolutions -of the Handle, which is the number of Hours in a synodical revolution of -the Moon. The round Plate with the names of Places upon it is fixed on -the Axis of the Wheel _FED_; and the Elliptical or Tide-Plate with the -Moon fixed to it is upon the Axis of the Wheel _LKI_; consequently, the -former makes 29-1/2 revolutions in the time that the latter makes one. -The whole Wheel _FED_ with the endless Screw _C_, and dotted part of the -Axis of the Handle _AB_, together with the dotted part of the Wheel -_ONG_, lie hid below the large Wheel _LKI_. - -Fig. 9th represents the under side of the Elliptical or Tide-Plate -_abcd_, with the four small Plates _ABCD_, _EFGH_, _IKLM_, _NOPQ_ upon -it: each of which has two slits as _TT_, _SS_, _RR_, _UU_ sliding on two -Pins as _nn_, fixed in the elliptical Plate. In the four small Plates -are fixed four Pins at _W_, _X_, _Y_, and _Z_; all of which work in an -elliptic Groove _oooo_ on the cover of the Box below the elliptical -Plate; the longest Axis of this Groove being in a right line with the -Sun and Full Moon. Consequently, when the Moon is in Conjunction or -Opposition, the Pins _W_ and _X_ thrust out the Plates _ABCD_ and _IKLM_ -a little beyond the ends of the elliptic Plate at _d_ and _b_, to _f_ -and _e_; whilst the Pins _Y_ and _Z_ draw in the Plates _EFGH_ and -_NOPQ_ quite under the elliptic Plate to _g_ and _h_. But, when the Moon -comes to her first or third Quarter, the elliptic Plate lies across the -fixed elliptic Groove in which the Pins work; and therefore the end -Plates _ABCD_ and _IKLM_ are drawn in below the great Plate, and the -other two Plates _EFGH_ and _NOPQ_ are thrust out beyond it to _a_ and -_c_. When the Moon is in her Octants the Pins _V, X, Y, Z_ are in the -parts _o, o, o, o_ of the elliptic Groove, which parts are at a mean -between the greatest and least distances from the Center _q_, and then -all the four small Plates disappear below the great one. - - -[Sidenote: The ECLIPSAREON. - - Pl. XIII.] - -442. The ECLIPSAREON. This Piece of Mechanism exhibits the Time, -Quantity, Duration, and Progress of solar Eclipses, at all Parts of the -Earth. - -The principal parts of this Machine are, 1. A terrestrial Globe _A_ -turned round its Axis _B_ by the Handle or Winch _M_; the Axis _B_ -inclines 23-1/2 Degrees, and has an Index which goes round the Hour -Circle _D_ in each rotation of the Globe. 2. A circular Plate _E_ on the -Limb of which the Months and Days of the year are inserted. This Plate -supports the Globe, and gives its Axis the same position to the Sun, or -to a candle properly placed, that the Earth’s Axis has to the Sun upon -any day of the year § 338, by turning the Plate till the given Day of -the Month comes to the fixed Pointer or annual Index _G_. 3. A crooked -Wire _F_ which points towards the middle of the Earth’s enlightened Disc -at all times, and shews to what place of the Earth the Sun is vertical -at any given time. 4. A Penumbra, or thin circular Plate of brass _I_ -divided into 12 Digits by 12 concentric Circles, which represent a -Section of the Moon’s Penumbra, and is proportioned to the size of the -Globe; so that the shadow of this Plate, formed by the Sun, or a candle -placed at a convenient distance, with it’s Rays transmitted through a -convex Lens to make them fall parallel on the Globe, covers exactly all -those places upon it that the Moon’s Shadow and Penumbra do on the -Earth: so that the Phenomena of any solar Eclipse may be shewn by this -Machine with candle-light, almost as well as by the light of the Sun. 5. -An upright frame _HHHH_, on the sides of which are Scales of the Moon’s -Latitude or Declination from the Ecliptic. To these Scales are fitted -two Sliders _K_ and _K_, with Indexes for adjusting the Penumbra’s -Center to the Moon’s Latitude, as it is North or South Ascending or -Descending. 6. A solar Horizon _C_, dividing the enlightened Hemisphere -of the Globe from that which is in the dark at any given time, and -shewing at what places the general Eclipse begins and ends with the -rising or setting Sun. 7. A Handle _M_, which turns the Globe round it’s -Axis by wheel-work, and at the same time moves the Penumbra across the -frame by threads over the Pullies _L, L, L_, with the velocity duly -proportioned to that of the Moon’s shadow over the Earth, as the Earth -turns on its Axis. And as the Moon’s Motion is quicker or slower, -according to her different distances from the Earth, the penumbral -Motion is easily regulated in the Machine by changing one of the -Pullies. - -[Sidenote: To rectify it.] - -_To rectify the Machine for use._ The true time of New Moon and her -Latitude being known by the foregoing Precepts § 355, 363, if her -Latitude exceeds the number of minutes or divisions on the Scales (which -are on the side of the frame hid from view in the Figure of the Machine) -there can be no Eclipse of the Sun at that Conjunction; but if it does -not, the Sun will be eclipsed to some places of the Earth; and, to shew -the times and various appearances of the Eclipse at those places, -proceed in order as follows. - -_To rectify the Machine for performing by the Light of the Sun._ 1. Move -the Sliders _KK_ till their Indexes point to the Moon’s Latitude on the -Scales, as it is North and South Ascending or Descending, at that time. -2. Turn the Month Plate _E_ till the day of the given New Moon comes to -the annual Index _G_. 3. Unscrew the Collar _N_ a little on the Axis of -the Handle, to loosen the contiguous Socket on which the threads that -move the Penumbra are wound; and set the Penumbra by Hand till its -Center comes to the perpendicular thread in the middle of the frame; -which thread represents the Axis of the Ecliptic § 371. 4. Turn the -Handle till the Meridian of _London_ on the Globe comes just under the -point of the crooked Wire _F_; then stop, and turn the Hour Circle _D_ -by Hand till XII at Noon comes to its Index. 5. Turn the Handle till the -Hour Index points to the time of New Moon in the Circle _D_; and holding -it there, screw fast the Collar _N_. Lastly, elevate the Machine till -the Sun shines through the Sight-Holes in the small upright Plates _O_, -_O_, on the Pedestal; and the whole Machine will be rectified. - -_To rectify the Machine for shewing the Candle-Light_, proceed in every -respect as above, except in that part of the last paragraph where the -Sun is mentioned; instead of which place a Candle before the Machine, -about four yards from it, so as the shadow of Intersection of the cross -threads in the middle of the frame may fall precisely on that part of -the Globe to which the crooked Wire _F_ points: then, with a pair of -Compasses take the distance between the Penumbra’s Center and -Intersection of the threads; and equal to that distance set the Candle -higher or lower as the Penumbra’s Center is above or below the said -Intersection. Lastly, place a large convex Lens between the Machine and -Candle, so as the Candle may be in the Focus of the Lens, and then the -Rays will fall parallel, and cast a strong light on the Globe. - -[Sidenote: It’s use.] - -These things done, which may be sooner than expressed, turn the Handle -backward until the Penumbra almost touches the side _HF_ of the frame; -then turning it gradually forward, observe the following Phenomena. 1. -Where the eastern edge of the Shadow of the penumbral Plate _I_ first -touches the Globe at the solar Horizon, those who inhabit the -corresponding part of the Earth see the Eclipse begin on the uppermost -edge of the Sun, just at the time of its rising. 2. In that place where -the Penumbra’s Center first touches the Globe, the inhabitants have the -Sun rising upon them centrally eclipsed. 3. When the whole Penumbra just -falls upon the Globe, its western edge, at the solar Horizon, touches -and leaves the place where the Eclipse ends at Sun-rise on his lowermost -edge. Continue turning, and, 4. the cross lines in the Center of the -Penumbra will go over all those places on the Globe where the Sun is -centrally eclipsed. 5. When the eastern edge of the Shadow touches any -place of the Globe, the Eclipse begins there: when the vertical line in -the Penumbra comes to any place, then is the greatest obscuration at -that place; and when the western edge of the Penumbra leaves the place, -the Eclipse ends there; the times of all which are shewn on the Hour -Circle: and from the beginning to the end, the Shadows of the concentric -penumbral Circles shew the number of Digits eclipsed at all the -intermediate times. 6. When the eastern edge of the Penumbra leaves the -Globe at the solar Horizon _C_, the inhabitants see the Sun beginning to -be eclipsed on his lowermost edge at its setting. 7. Where the -Penumbra’s Center leaves the Globe, the inhabitants see the Sun set -centrally eclipsed. And lastly, where the Penumbra is wholly departing -from the Globe, the inhabitants see the Eclipse ending on the uppermost -part of the Sun’s edge, at the time of its disappearing in the Horizon § -343. - -_N.B._ If any given day of the year on the Plate _E_ be set to the -annual Index _G_, and the Handle turned till the Meridian of any place -comes under the point of the crooked Wire, and then the Hour Circle _D_ -set by the hand till XII comes to its Index; in turning the Globe round -by the Handle, when the said place touches the eastern edge of the Hoop -or solar Horizon _C_, the Index shews the time of Sun-setting at that -place; and when the place is just coming out from below the other edge -of the Hoop _C_, the Index shews the time that the evening Twilight ends -to it. When the place has gone through the dark part _A_, and comes -about so to touch under the back of the Hoop _C_ on the other side, the -Index shews the time that the Morning Twilight begins; and when the same -place is just coming out from below the edge of the Hoop next the frame, -the Index points out the time of Sun-rising. And thus, the times of -Sun-rising and setting are shewn at all places in one rotation of the -Globe, for any given day of the year: and the point of the crooked Wire -_F_ shews all the places that the Sun passes vertically over on that -day. - - - FINIS. - - - - - INDEX. - - - The numeral Figures refer to the Articles, and the small _n_ to the - Notes on the Articles. - - A. - - _Acceleration_ of the Stars, 221. - - _Angle_, what, 185. - - _Annual Parallax_ of the Stars, 196. - - _Anomaly_, what, 239. - - _Antients_, their superstitious notions of Eclipses, 329. - Their method of dividing the Zodiac, 398. - - _Antipodes_, what, 122. - - _Apsides_, line of, 238. - - ARCHIMEDES, his ideal Problem for moving the Earth, 159. - - _Areas_ described by the Planets, equal in times, 153. - - _Astronomy_, the great advantages arising from it both in our religious - and civil concerns, 1 Discovers the laws by which the Planets move, - and are retained in their Orbits, 2 - _Atmosphere_, the higher the thinner, 174. - It’s prodigious expansion, _ib._ - It’s whole weight on the Earth, 175. - Generally thought to be heaviest when it is lightest, 176. - Without it the Heavens would appear dark in the day-time, 177. - Is the cause of twilight, _ib._ - It’s height, _ib._ - Refracts the Sun’s rays, 178. - Causeth the Sun and Moon to appear above the Horizon when they are - really below it, _ib._ - Foggy, deceives us in the bulk and distance of objects, 185. - - _Attraction_, 101-105. - Decreases as the square of the distance increases, 106. - Greater in the larger than in the smaller Planets, 158. - Greater in the Sun than in all the Planets if put together, _ib._ - - _Axes of the Planets_, what, 19. - Their different positions with respect to one another, 120. - - _Axis of the Earth_, it’s parallelism, 302. - It’s position variable as seen from the Sun or Moon, 338. - the Phenomena thence arising, 340. - - - B. - - _Bodies_, on the Earth, lose of their weight the nearer they are to the - Equator, 117. - How they might lose all their weight, 118, - How they become visible, 167. - - - C. - - _Calculator_, (an Instrument) described, 436. - - _Calendar_, how to inscribe the Golden Numbers rightly in it for - shewing the days of New Moons, 423. - - _Cannon-Ball_, it’s swiftness, 89. - In what times it would fly from the Sun to the different Planets and - fixed Stars, _ib._ - - CASSINI, his account of a double Star eclipsed by the Moon, 58. - His Diagrams of the Paths of the Planets, 138. - - _Catalogue_ of the Eclipses, 327. - Of the Constellations and Stars, 367. - Of remarkable _Æras_ and events, 433. - - _Celestial Globe_ improved, 438. - - _Centripetal and centrifugal forces_, how they alternately overcome - each other in the motions of the Planets, 152-154. - - _Changes in the Heavens_, 403. - - _Chords_, line of, how to make, 369. - - _Circles_, of perpetual Apparition and Occultation, 128. - Of the Sphere, 198. - Contain 360 Degrees whether they be great or small, 207. - - _Civil Year_, what, 411. - - COLUMBUS (CHRISTOPHER) his story concerning an Eclipse, 330. - - _Clocks_ and _Watches_, an easy method of knowing whether they go true - or false, 223. - Why they seldom agree with the Sun if they go true, 228-245. - How to regulate them by Equation Tables and a Meridian line, 225, - 226. - - _Cloudy Stars_, 402. - - _Cometarium_ (an Instrument) described, 437. - - _Constellations_, antient, their number, 396. - The number of Stars in each, according to different Astronomers, 399. - - _Cycle_, Solar, Lunar, and _Romish_, 420. - Of _Easter_, 425. - - - D. - - _Darkness_ at our SAVIOUR’s crucifixion supernatural, 352, 432. - - _Day_, natural and artificial, what, 417. - And _Night_, always equally long at the Equator, 126. - Natural, not compleated in an absolute turn of the Earth on it’s - Axis, 222. - - _Degree_, what, 207. - - _Digit_, what, 321, _n._ - - _Direction_, (Number of) 426. - - _Distances of the Planets from the Sun_, an idea thereof, 89. - A Table thereof, 98. - How found, 190. - - _Diurnal_ and _annual Motions_ of the Earth illustrated, 200, 202. - - _Dominical Letter_, 427. - - _Double_ projectile force, a balance to a _Quadruple_ Power of Gravity, - 153. - Star covered by the Moon, 58. - - - E. - - _Earth_, it’s bulk but a point as seen from the Sun, 3 It’s Diameter, - annual Period, and Distance from the Sun, 47. - Turns round it’s Axis, _ib._ - Velocity of it’s equatoreal Parts, _ib._ - Velocity in it’s annual Orbit, _ib._ - Inclination of it’s Axis, 48. - Proof of it’s being globular, or nearly so, 49, 314. - Measurement of it’s surface, 50, 51. - Difference between it’s Equatoreal and Polar Diameters, 76. - It’s motion round the Sun demonstrated by gravity, 108, 111. - by Dr. BRADLEY’s observations, 113. - by the Eclipses of Jupiter’s Satellites, 219. - It’s diurnal motion highly probable from the absurdity that must - follow upon supposing it not to move, 111. 120. - and demonstrable from it’s figure, 116. - this motion cannot be felt, 119. - Objections against it’s motion answered, 112, 121. - It has no such thing as an upper or under side, 122. - in what case it might, 123. - The swiftness of it’s motion in it’s Orbit compared with the velocity - of light, 197. - It’s diurnal and annual motions illustrated by an easy experiment, - 200. - Proved to be less than the Sun and bigger than the Moon, 315. - - _Easter Cycle_, 425. - - _Eclipsareon_ (an Instrument) described, 442. - - _Eclipses_, of Jupiter’s Satellites, how the Longitude is found by - them, 207-218. - they demonstrate the velocity of light, 216. - Of the Sun and Moon, 312-327. - Why they happen not in every month, 316. - When they must be, 317. - Their limits, _ib._ - Their Period, 320, 326. - A dissertation on their progress, 321-324. - A large catalogue of them, 327. - Historical ones, 328. - More of the Sun than of the Moon, and why, 331. - The proper Elements for their calculation and projection, 353-390. - - _Ecliptic_, it’s Signs, their names and characters, 91. - Makes different Angles with the Horizon every hour and minute, 275. - how these Angles may be estimated by the position of the Moon’s - horns, 260. - It’s obliquity to the Equator less now than it was formerly, 405. - How it’s Signs are numbered, 354. - - _Elongations_, of the Planets, as seen by an observer at rest on the - outside of all their Orbits, 133. - Of Mercury and Venus as seen from the Earth, illustrated, 142. - it’s quantity, 143. - Of Mercury, Venus, the Earth, Mars, and Jupiter; it’s quantity as - seen from Saturn, 147. - - _Epochas_ or _Æras_, 433. - - _Equation_ of time, 224-245. - Of the Moon’s Place, 355. - Of the Sun’s Place, _ib._ - Of the Nodes, 363. - - _Equator_, day and night always equal there, 126. - Makes always the same Angle with the Horizon of the same place; the - Ecliptic not, 274, 275. - - _Equinoctial Points_ in the Heavens, their precession, 246, - a very different thing from the recession or anticipation of the - Equinoxes on Earth, the one no ways occasioned by the other, 249. - - _Excentricities_ of the Planets Orbits, 155. - - - F. - - _Fallacies_ in judging of the bulk of objects by their apparent - distance, 185; - applied to the solution of the horizontal Moon, 187. - - _First Meridian_, what, 207. - - _Fixed Stars_, why they appear of less magnitude when viewed through a - telescope than by the bare eye, 391. - Their number, 392. - Their division into different Classes and Constellations, 395-399. - - - G. - - _General Phenomena_ of a superior Planet as seen from an inferior, 149. - - _Gravity_, demonstrable, 101-104. - Keeps all bodies on the Earth to it’s surface, or brings them back - when thrown upward; and constitutes their weight, 101, 122. - Retains all the Planets in their Orbits, 103. - Decreases as the square of the distance increases, 106. - Proves the Earth’s annual motion, 108. - Demonstrated to be greater in the larger Planets than in the smaller; - and stronger in the Sun than in all the Planets together, 158. - Hard to understand what it is, 160. - Acts every moment, 162. - - _Globe_, improved celestial, 438. - - _Great Year_, 251. - - - H. - - _Harmony_ of the celestial motions, 111. - - _Harvest-Moon_, 273-293. - None at the Equator, 273. - Remarkable at the Polar Circles, 285. - In what years most and least advantageous, 292. - - _Heat_, decreases as the square of the distance from the Sun increases, - 169. - Why not greatest when the Earth is nearest the Sun, 205. - Why greater about three o’Clock in the afternoon than when the Sun is - on the Meridian, 300. - - _Heavens_, seem to turn round with different velocities as seen from - the different Planets; and on different Axes as seen from most of - them, 120. - Only one Hemisphere of them seen at once from any one Planet’s - surface, 125. - The Sun’s Center the only point from which their true Motions could - be seen, 135. - Changes in them, 403. - - _Horizon_, what, 125, _n._ - - _Horizontal-Moon_ explained, 187. - - _Horizontal Parallax_, of the Moon, 190; - of the Sun, 191; - best observed at the Equator, 193. - - _Hour-Circles_, what, 208. - - _Hour_ of time equal to 15 degrees of motion, _ib._ - How divided by the _Jews_, _Chaldeans_, and _Arabians_, 419. - - HUYGENIUS, his thoughts concerning the distance of some Stars, 5 - - I. J. - - _Inclination_ of Venus’s Axis, 29. - Of the Earth’s, 48. - Of the Axis or Orbit of a Planet only relative, 201. - - _Inhabitants_ of the Earth (or any other Planet) stand on opposite - sides with their feet toward one another, yet each thinks himself on - the upper side, 122. - - _Julian Period_, 430. - - _Jupiter_, it’s distance, diameter, diurnal and annual revolutions, - 67-69. - The Phenomena of it’s Belts, 70. - Has no difference of seasons, 71. - Has four Moons, 72, - their grand Period, 73, - the Angles which their Orbits subtend as seen from the Earth, 74, - most of them are eclipsed in every revolution, 75. - The great difference between it’s equatoreal and polar Diameters, 76. - The inclination of it’s Orbit, and place of it’s Ascending Node, 77. - The Sun’s light 3000 times as strong on it as Full Moon-light is on - the Earth, 85. - Is probably inhabited, 86. - The amazing strength required to put it in motion, 158. - The figures of the Paths described by it’s Satellites, 269. - - - L. - - _Light_, the inconceivable smallness of it’s particles, 165, - and the dreadful mischief they would do if they were larger, 166. - It’s surprising velocity, 166, - compared with the swiftness of the Earth’s annual motion, 197. - Decreases as the square of the distance from the luminous body - increases, 169. - Is refracted in passing through different Mediums, 171-173. - Affords a proof of the Earth’s annual motion, 197, 219. - In what time it comes from the Sun to the Earth, 216, - this explained by a figure, 217. - - _Limits_ of Eclipses, 317. - - _Line_, of the Nodes, what, 317; - has a retrograde motion, 319. - Of Sines and Chords, how to make, 369. - - LONG (Rev. Dr.) his method of comparing the quantity of the surface of - dry land with that of the Sea, 51. - His glass sphere, 126. - - _Longitude_, how found, 207-213. - - _Lucid Spots_ in the Heavens, 401. - - _Lunar Cycle_ deficient, 422. - - - M. - - _Magellanic Clouds_, 402. - - _Man_, of a middle size, how much pressed by the weight of the - Atmosphere, 175; - why this pressure is not felt, _ib._ - - _Mars_, it’s Diameter, Period, Distance, and other Phenomena, 64-67. - - _Matter_, it’s properties, 99. - - _Mean Anomaly_, what, 239. - - _Mercury_, it’s Diameter, Period, Distance, &c. 22. - Appears in all the shapes of the Moon, 23. - When it will be seen on the Sun, 24. - The inclination of it’s Orbit and Place of it’s Ascending Node, _ib._ - It’s Path delineated, 138. - Experiment to shew it’s Phases and apparent Motion, 142. - - _Mercury_ (Quicksilver) in the Barometer, why not affected by the - Moon’s raising Tides in the Air, 311. - - _Meridian_, first, 207. - Line, how to draw one, 226. - - _Milky Way_, what, 400. - - _Months_, _Jewish_, _Arabian_, _Egyptian_, and _Grecian_, 415. - - _Moon_, her Diameter and Period, 52. - Her phases, 53, 255. - Shines not by her own light, 54. - Has no difference of seasons, 55. - The Earth is a Moon to her, 56. - Has no Atmosphere of any visible Density, 58; - nor Seas, 59. - How her inhabitants may be supposed to measure their year, 62. - Her light compared with day-light, 85. - The excentricity of her Orbit, 98. - Is nearer the Earth now than she was formerly, 163. - Appears bigger in the Horizon than at any considerable height above - it, and why, 187; - yet is seen much under the same Angle in both cases, 188. - Her surface mountainous, 252: - if smooth she could give us no light, _ib._ - Why no hills appear round her edge, 253. - Has no Twilight, 254. - Appears not always quite round when full, 256. - Her phases agreeably represented by a globular Stone viewed in - Sun-shine when she is above the Horizon, and the observer placed - as if he saw her on the top of the Stone, 258. - Turns round her Axis, 262. - The length of her Solar and Sidereal Day, _ib._ - Her periodical and synodical revolution represented by the motions of - the hour and minute hands of a Watch, 264. - Her Path delineated, and shewn to be always concave to the Sun, - 265-268. - Her motion alternately retarded and accelerated, 267. - Her gravity toward the Sun greater than toward the Earth at her - Conjunction, and why she does not then abandon the Earth on that - account, 268. - Rises nearer the time of Sun-set when about the full in harvest for a - whole week than when she is about the full at any other time of - the year, and why, 273-284: - this rising goes through a course of increasing and - decreasing benefit to the farmers every 19 years, 292. - Continues above the Horizon of the Poles for fourteen of our natural - Days together, 293. - Proved to be globular, 314. - and to be less than the Earth, 315. - Her Nodes, 317. - ascending and descending, 318. - their retrograde motion, 319. - Her acceleration proved from antient Eclipses, 322, _n._ - Her Apogee and Perigee, 336. - Not invisible when she is totally eclipsed, and why, 346. - How to calculate her Conjunctions, Oppositions, and Eclipses, - 355-390. - How to find her age in any Lunation by the Golden Number, 423. - - _Morning_ and _Evening Star_, what, 145. - - _Motion_, naturally rectilineal, 100. - Apparent, of the Planets as seen by a spectator at rest on the - outside of all their Orbits, 133; - and of the Heavens as seen from any Planet, 154. - - - N. - - _Natural Day_, not compleated in the time that the Earth turns round - it’s Axis, 222. - - _New_ and _Full Moon_, to calculate the times of 355. - - _New Stars_, 403, - cannot be Comets, 404. - - _New Style_, it’s original, 414. - - NICIAS’s Eclipse, 328. - - _Nodes_, of the Planet’s Orbits, their places in the Ecliptic, 20. - Of the Moon’s Orbit, 317. - their retrograde motion, 319. - - _Nonagesimal Degree_, what, 259. - - _Number of Direction_, 426. - - - O. - - _Objects_, we often mistake their bulk by mistaking their distance, - 185. - Appear bigger when seen through a fog than through clear Air, and - why, _ib._ - this applied to the solution of the Horizontal Moon, 187. - - _Oblique Sphere_, what, 131. - - _Olympiads_, what, 323. _n._ - - _Orbits_ of the Planets not solid, 21. - - _Orrery_ described, 434, 435, 436. - - - P. - - _Parallax_, Horizontal, what, 190. - - _Parallel Sphere_, what, 131. - - _Path_ of the Moon, 265, 266, 267. - Of Jupiter’s Moons, 269. - - _Pendulums_, their vibrating slower at the Equator than near the Poles - proves that the Earth turns on it’s Axis, 117. - - _Penumbra_, what, 336. - It’s velocity on the Earth in Solar Eclipses, 337. - - _Period of Eclipses_, 320, 326. - - _Phases of the Moon_, 252-268. - - _Planets_, much of the same nature with the Earth, 11. - Some have Moons belonging to them, 12. - Move all the same way as seen from the Sun, but not as seen from one - another, 18. - Their Moons denote them to be inhabited, 86. - The proportional breadth of the Sun’s Disc as seen from each of them, - 87. - Their proportional bulks as seen from the Sun, 88. - An idea of their distances from the Sun, 89. - Appear bigger and less by turns, and why, 90. - Are kept in their Orbits by the power of gravity, 101, 150-158. - Their motions very irregular as seen from the Earth, 137. - The apparent motions of Mercury and Venus delineated by Pencils in an - Orrery, 138. - Elongations of all the rest as seen from Saturn, 147. - Describe equal areas in equal times, 153. - The excentricities of their Orbits, 155. - In what times they would fall to the Sun by the power of gravity, - 157. - Disturb one another’s motions, the consequence thereof, 163. - Appear dimmer when seen through telescopes than by the bare eye, the - reason of this, 170. - - _Planetary Globe_ described, 439. - - _Polar Circles_, 198. - - _Poles_, of the Planets, what, 19. - Of the world, what, 122. - Celestial, seem to keep on the same points of the Heavens all the - year, and why, 196. - - _Projectile Force_, 150; - if doubled would require a quadruple power of gravity to retain the - Planets in their Orbits, 153. - Is evidently an impulse from the hand of the ALMIGHTY, 161. - - _Precession of the Equinoxes_, 246-251. - - _Ptolemean_ System absurd, 96, 140. - - - R. - - _Rays of Light_, if not disturbed, move in straight lines, and hinder - not one another’s motions, 168. - Are refracted in passing through different mediums, 171. - - _Reflection of the Atmosphere_ causes the Twilight, 177. - - _Refraction of the Atmosphere_ bends the rays of light from straight - lines, and keeps the Sun and Moon longer in sight than they would - otherwise be, 178. - A surprising instance of this, 183. - Must be allowed for in taking the Altitudes of the celestial bodies, - _ib._ - - _Right Sphere_, 131. - - - S. - - _Satellites_; the times of their revolutions round their primary - Planets, 52, 73, 80. - Their Orbits compared with each other, with the Orbits of the primary - Planets, and with the Sun’s circumference, 271. - What sort of Curves they describe, 272. - - _Saturn_, with his Ring and Moon’s, their Phenomena, 78, 79, 82. - The Sun’s light 1000 times as strong to him as the light of the Full - Moon is to us, 85. - The Phenomena of his Ring farther explained, 204. - - _Our blessed_ SAVIOUR, the darkness at his crucifixion supernatural, - 352. - The prophetic year of his crucifixion found to agree with an - astronomical calculation, 432. - - _Seasons_, different, illustrated by an easy experiment, 200; - by a figure, 202. - - _Shadow_, what, 312. - - _Sidereal Time_, what, 221; - the number of Sidereal Days in a year exceeds the number of Solar - Days by one, and why, 222. - An easy method for regulating Clocks and Watches by it, 223. - - _Signs of the Zodiac_, their names and characters, 91, 365. - How they are numbered by Astronomers, 354. - - _Sines_, line of, how to make, 369. - - SMITH, (Rev. Dr.) his companion between Moon-light and Day-light, 85. - His demonstration that light decreases as the square of the distance - from the luminous body increases, 169. - (_Mr._ GEORGE) his Dissertation on the Progress of a Solar Eclipse, - 321-324. - - _Solar Astronomer_, the judgment he might be supposed to make - concerning the Planets and Stars, 135, 136. - - _Sphere_, parallel, oblique, and right, 131. - It’s Circles, 198. - - _Spring and Neap Tides_, 302. - - _Stars_, their vast distance from the Earth, 3, 196. - Probably not all at the same distance, 4 Shine by their own light, - and are therefore Suns 7, - probably to other worlds, 8 A demonstration that they do not move - round the Earth, 111. - Have an apparent slow motion round the Poles of the Ecliptic, and - why, 251. - A catalogue of them, 399. - _Cloudy_, 402. - New, 403. - Some of them change their places, 404. - - _Starry Heavens_ have the same appearance from any part of the Solar - System, 132. - - SUN appears bigger than the Stars, and why, 4 Turns round his Axis, 18. - His proportional breadth as seen from the different Planets, 87. - Describes unequal arcs above and below the Horizon at different - times, and why, 130. - His Center the only place from which the true motions of the Planets - could be seen, 135. - Is for half a year together visible at each Pole in it’s turn, and as - long in visible, 200, 294. - Is nearer the Earth in Winter than in Summer, 205. - Why his motion agrees so seldom with the motion of a well regulated - Clock, 224-245. - Would more than fill the Moon’s Orbit, 271. - Proved to be much bigger than the Earth, and the Earth to be bigger - than the Moon, 315. - To calculate his true place, 360. - - _Systems_, the Solar, 17-95; - the Ptolemean, 96; - the Tychonic, 97. - - - T. - - _Table_, of the Periods, Revolutions, Magnitudes, Distances, _&c._ of - the Planets, facing § 99. - Of the Air’s rarity, compression, and expansion at different heights, - 174. - Of refractions, 182. - For converting time into motion, and the reverse, 220. - For shewing how much of the celestial Equator passes over the - Meridian in any part of a mean Solar Day; and how much the Stars - accelerate upon the mean Solar time for a month, 221. - Of the first part of the Equation of time, 229; - of the second part, 241. - Of the precession of the Equinox, 247. - Of the length of Sidereal, Julian, and Tropical Years, 251. - Of the Sun’s place and Anomaly, following 251. - Of the Equation of natural Days, following 251 - Of the Conjunctions of the hour and minute hands of a Watch, 264. - Of the Curves described by the Satellites, 272. - Of the difference of time in the Moon’s rising and setting on the - parallel of - _London_ every day during her course round the Ecliptic, 277. - Of Eclipses, 327. - For calculating New and Full Moons and Eclipses, following 390. - Of the Constellations and number of the Stars, 399. - Of the _Jewish_, _Egyptian_, _Arabic_, and _Grecian_ months, 415. - For inserting the Golden Numbers right in the Calendar, 423. - Of the times of all the New Moons for 76 years, 424. - Of remarkable Æras or Events, 433. - Of the Golden Number, Number of Direction, Dominical Letter and Days - of the Months, following 433. - - THALES’s Eclipse, 323. - - THUCYDIDES’s Eclipse 324. - - _Tides_, their Cause and Phenomena, 295-311. - - _Tide-Dial_ described, 441. - - _Trajectorium Lunare_ described, 440. - - _Tropics_, 198. - - _Twilight_, none in the Moon, 254. - - _Tychonic System_ absurd, 97. - - - U. - - _Universe_, the Work of Almighty Power, 5, 161. - - _Up_ and _down_, only relative terms, 122. - - _Upper_ or _under side of the Earth_ no such thing, 123. - - - V. - - _Velocity of Light_ compared with the velocity of the Earth in it’s - annual Orbit, 197. - - _Venus_, her bulk, distance, period, length of days and nights, 26. - Shines not by her own light, _ib._ - Is our morning and evening Star, 28. - Her Axis, how situated, 29. - Her surprising Phenomena, 29-43. - The inclination of her Orbit, 45. - When she will be seen on the Sun, _ib._ - How it may probably be soon known if she has a Satellite, 46. - Appears in all the Shapes of the Moon, 23, 141. - An experiment to shew her phases and apparent motion, 141. - - _Vision_, how caused, 167. - - - W. - - _Weather_, not hottest when the Sun is nearest to us, and why, 205. - - _Weight_, the cause of it, 122. - - _World_ not eternal, 164. - - - Y. - - _Year_, 407, - Great, 251, - Tropical, 408, - Sidereal, 400, - Lunar, 410, - Civil, 411, - Bissextile, _ib._ - _Roman_, 413, - _Jewish_, _Egyptian_, _Arabic_, and _Grecian_, 415, - how long it would be if the Sun moved round the Earth, 111. - - - Z. - - _Zodiac_, what, 397. - How divided by the antients, 398. - - _Zones_, what, 199. - - - - - DIRECTIONS to the BOOKBINDER. - - - The ORRERY PLATE is to front the Title Page. - - PLATE I fronting Page 5 - II 39 - III 49 - IV 73 - V 81 - VI 97 - VII 125 - VIII 147 - IX 147 - X 157 - XI 179 - XII 203 - XIII 279 - - - - - Footnotes - -Footnote 1: - - Dr. YOUNG’s Night Thoughts. - -Footnote 2: - - If a thread be tied loosely round two pins stuck in a table, and - moderately stretched by the point of a black lead pencil carried round - by an even motion and light pressure of the hand, an oval or ellipsis - will be described; the two points where the pins are fixed being - called the _foci_ or focuses thereof. The Orbits of all the Planets - are elliptical, and the Sun is placed in or near to one of the _foci_ - of each of them: and _that_ in which he is placed, is called the - _lower focus_. - -Footnote 3: - - Astronomers are not far from the truth, when they reckon the Sun’s - center the lower focus of all the Planetary Orbits. Though strictly - speaking, if we consider the focus of Mercury’s Orbit to be in the - Sun’s center, the focus of Venus’s Orbit will be in the common center - of gravity of the Sun and Mercury; the focus of the Earth’s Orbit in - the common center of gravity of the Sun, Mercury, and Venus; the focus - of the Orbit of Mars in the common center of gravity of the Sun, - Mercury, Venus, and the Earth; and so of the rest. Yet, the focuses of - the Orbits of all the Planets, except Saturn, will not be sensibly - removed from the center of the Sun; nor will the focus of Saturn’s - Orbit recede sensibly from the common center of gravity of the Sun and - Jupiter. - -Footnote 4: - - As represented in Plate III. Fig. I. and described in § 138. - -Footnote 5: - - When he is between the Earth and the Sun in the nearer part of his - Orbit. - -Footnote 6: - - The time between the Sun’s rising and setting. - -Footnote 7: - - One entire revolution, or 24 hours. - -Footnote 8: - - These are lesser circles parallel to the Equator, and as many degrees - from it, towards the Poles, as the Axis of the Planet is inclined to - the Axis of it’s Orbit. When the Sun is advanced so far north or south - of the Equator as to be directly over either Tropic, he goes no - farther; but returns towards the other. - -Footnote 9: - - These are lesser circles round the Poles, and as far from them as the - Tropics are from the Equator. The Poles are the very north and south - points of the Planet. - -Footnote 10: - - A Degree is a 360th part of any Circle. See § 21. - -Footnote 11: - - The Limit of any inhabitant’s view, where the Sky seems to touch the - Planet all round him. - -Footnote 12: - - This is not strictly true, as will appear when we come to treat of the - Recession of the Equinoctial Points in the Heavens § 246; which - recession is equal to the deviation of the Earth’s Axis from it’s - parallelism: but this is rather too small to be sensible in an age, - except to those who make very nice observations. - -Footnote 13: - - _Memoirs d’Acad. ann. 1720._ - -Footnote 14: - - The Moon’s Orbit crosses the Ecliptic in two opposite points called - the Moon’s Nodes; so that one half of her Orbit is above the Ecliptic, - and the other half below it. The Angle of it’s Obliquity is 5-1/3 - degrees. - -Footnote 15: - - CASSINI _Elements d’Astronomie_, _Liv._ ix. _Chap._ 3. - -Footnote 16: - - Optics, Art. 95. - -Footnote 17: - - Mr. WHISTON, in his Astronomical Principles of Religion. - -Footnote 18: - - As will be demonstrated in the ninth Chapter. - -Footnote 19: - - Optics, B. I. § 1178. - -Footnote 20: - - Astronomy, B. II. §. 838. - -Footnote 21: - - Philosophy, Vol. I. p. 401. - -Footnote 22: - - Account of Sir Isaac Newton’s _Philosophical Discoveries_, B. III. c. - 2. § 3. - -Footnote 23: - - _Elements d’Astronomie_, § 381. - -Footnote 24: - - The face of the Sun, Moon, or any Planet, as it appears to the eye, is - called it’s Disc. - -Footnote 25: - - The utmost limit of a person’s view, where the Sky seems to touch the - Earth all around, is called his Horizon; which shifts as the person - changes his place. - -Footnote 26: - - The Plane of a Circle, or a thin circular Plate, being turned edgewise - to the eye appears to be a straight line. - -Footnote 27: - - A Degree is the 360th part of a Circle. - -Footnote 28: - - Here we do not mean such a conjunction, as that the nearer Planet - should hide all the rest from the observer’s sight; (for that would be - impossible unless the intersections of all their Orbits were - coincident, which they are not, _See_ § 21.) but when they were all in - a line crossing the standard Orbit at right Angles. - -Footnote 29: - - The ORRERY fronting the Title-page. - -Footnote 30: - - To make the projectile force balance the gravitating power so exactly - as that the body may move in a Circle, the projectile velocity of the - body must be such as it would have acquired by gravity alone in - falling through half the radius. - -Footnote 31: - - Astronomical Principles of Religion, p. 66. - -Footnote 32: - - Δὸς ποῦ στῶ, καὶ τὸν κόσμον κινήσω, _i. e._ Give me a place to stand - on, and I shall move the Earth. - -Footnote 33: - - If the Sun was not agitated about the common center of gravity of the - whole System, and the Planets did not act mutually upon one another, - their Orbits would be elliptical, and the areas described by them - would be exactly proportionate to the times of description § 153. But - observations prove that these areas are not in such exact proportion, - and are most varied when the greatest number of Planets are in any - particular quarter of the Heavens. When any two Planets are in - conjunction, their mutual attractions, which tend to bring them nearer - to one another, draws the inferior one a little farther from the Sun, - and the superior one a little nearer to him; by which means, the - figure of their Orbits is somewhat altered; but this alteration is too - small to be discovered in several ages. - -Footnote 34: - - Religious Philosopher, Vol. III. page 65. - -Footnote 35: - - This will be demonstrated in the eleventh Chapter. - -Footnote 36: - - A fine net-work membrane in the bottom of the eye. - -Footnote 37: - - Book I. Art. 57. - -Footnote 38: - - A medium, in this sense, is any transparent body, or that through - which the rays of light can pass; as water, glass, diamond, air; and - even a vacuum is sometimes called a Medium. - -Footnote 39: - - NEWTON’s _System of the World_, _p._ 120. - -Footnote 40: - - This is evident from pumps, since none can draw water higher than 33 - foot. - -Footnote 41: - - Namely 10000 times the distance of Saturn from the Sun; p. 94. - -Footnote 42: - - See his Astronomy, p. 232. - -Footnote 43: - - As far as one can see round him on the Earth. - -Footnote 44: - -[Sidenote: Fig. V.] - - An Angle is the inclination of two right lines, as _IH_ and _KH_, - meeting in a point at _H_; and in describing an Angle by three - letters, the middle letter always denotes the angular point: thus, the - above lines _IH_ and _KH_ meeting each other at _H_, make the Angle - _IHK_. And the point _H_ is supposed to be the center of a Circle, the - circumference of which contains 360 equal parts called degrees. A - fourth part of a Circle, called a Quadrant, as _GE_, contains 90 - degrees; and every Angle is measured by the number of degrees in the - arc it cuts off; as the angle _EHP_ is 45 degrees, the Angle _EHF_ 33, - &c: and so the Angle _EHF_ is the same with the angle _CHN_, and also - with the Angle _AHM_, because they all cut off the same arc or portion - of the Quadrant _EG_; and so likewise the Angle _EHF_ is greater than - the Angle _CHD_ or _AHL_, because it cuts off a greater arc. - - The nearer an object is to the eye the bigger it appears, and under - the greater Angle is it seen. To illustrate this a little, suppose an - Arrow in the position _IK_, perpendicular to the right line _HA_ drawn - from the eye at _H_ through the middle of the Arrow at _O_. It is - plain that the Arrow is seen under the Angle _IHK_, and that _HO_, - which is it’s distance from the eye, divides into halves both the - Arrow and the Angle under which it is seen: _viz._ the Arrow into - _IO_, _OK_, and the Angle into _IHO_ and _KHO_: and this will be the - case whatever distance the Arrow is placed at. Let now three Arrows, - all of the same length with _IK_, be placed at the distances _HA_, - _HC_, _HE_, still perpendicular to, and bisected by the right line - _HA_; then will _AB_, _CD_, _EF_, be each equal to, and represent - _IO_; and _AB_ (the same as _IO_) will be seen from _H_ under the - Angle _AHB_; but _CD_ (the same as _IO_) will be seen under the Angle - _CHD_ or _AHL_; and _EF_ (the same as _IO_) will be seen under the - Angle _EHF_, or _CHN_, or _AHM_. Also, _EF_ or _IO_ at the distance - _HE_ will appear as long as _CN_ would at the distance _HC_, or as - _AM_ would at the distance _HA_: and _CD_ or _IO_ at the distance _HC_ - will appear as long as _AL_ would at the distance _HA_. So that as an - object approaches the eye, both it’s magnitude and the Angle under - which it is seen increase; and as the object recedes, the contrary. - -Footnote 45: - - The fields which are beyond the gate rise gradually till they are just - seen over it; and the arms, being red, are often mistaken for a house - at a considerable distance in those fields. - - I once met with a curious deception in a gentleman’s garden at - _Hackney_, occasioned by a large pane of glass in the garden-wall at - some distance from his house. The glass (through which the fields and - sky were distinctly seen) reflected a very faint image of the house; - but the image seemed to be in the Clouds near the Horizon, and at that - distance looked as if it were a huge castle in the Air. Yet, the Angle - under which the image appeared, was equal to that under which the - house was seen: but the image being mentally referred a much greater - distance than the house, appeared much bigger to the imagination. - -Footnote 46: - - The Sun and Moon subtend a greater Angle on the Meridian than in the - Horizon, being nearer the Earth in the former case than the latter. - -Footnote 47: - - The Altitude of any celestial Phenomenon is an arc of the Sky - intercepted between the Horizon and the Phenomenon. In Fig. VI. of - Plate II. let _HOX_ be a horizontal line, supposed to be extended from - the eye at _A_ to _X_, where the Sky and Earth seem to meet at the end - of a long and level plain; and let _S_ be the Sun. The arc _XY_ will - be the Sun’s height above the Horizon at _X_, and is found by the - instrument _EDC_, which is a quadrantal board, or plate of metal, - divided into 90 equal parts or degrees on its limb _DPC_; and has a - couple of little brass plates, as _a_ and _b_, with a small hole in - each of them, called _Sight-Holes_, for looking through, parallel to - the edge of the Quadrant whereon they stand. To the center _E_ is - fixed one end of a thread _F_, called _the Plumb-Line_, which has a - small weight or plummet _P_ fixed to it’s other end. Now, if an - observer holds the Quadrant upright, without inclining it to either - side, and so that the Horizon at _X_ is seen through the sight-holes - _a_ and _b_, the plumb-line will cut or hang over the beginning of the - degrees at _o_, in the edge _EC_; but if he elevates the Quadrant so - as to look through the sight-holes at any part of the Heavens, suppose - to the Sun at _S_; just so many degrees as he elevates the sight-hole - _b_ above the horizontal line _HOX_, so many degrees will the - plumb-line cut in the limb _CP_ of the Quadrant. For, let the - observer’s eye at _A_ be in the center of the celestial arc _XYV_ (and - he may be said to be in the center of the Sun’s apparent diurnal - Orbit, let him be on what part of the Earth he will) in which arc the - Sun is at that time, suppose 25 degrees high, and let the observer - hold the Quadrant so that he may see the Sun through the sight-holes; - the plumb-line freely playing on the quadrant will cut the 25th degree - in the limb _CP_ equal to the number of degrees of the Sun’s Altitude - at the time of observation. _N. B._ Whoever looks at the Sun, must - have a smoaked glass before his eyes to save them from hurt. The - better way is not to look at the Sun through the sight-holes, but to - hold the Quadrant facing the eye, at a little distance, and so that - the Sun shining through one hole, the ray may be seen to fall on the - other. - -Footnote 48: - - See the Note on § 185. - -Footnote 49: - - Here proper allowance must be made for the Refraction, which being - about 34 minutes of a degree in the Horizon, will cause the Moon’s - center to appear 34 minutes above the Horizon when her center is - really in it. - -Footnote 50: - - By this is meant, that if a line be supposed to be drawn parallel to - the Earth’s Axis in any part of it’s Orbit, the Axis keeps parallel to - that line in every other part of it’s Orbit: as in Fig. I. of Plate V; - where _abcdefgh_ represents the Earth’s Orbit in an oblique view, and - _Ns_ the Earth’s Axis keeping always parallel to the line _MN_. - -Footnote 51: - - SMITH’s Optics, § 1197. - -Footnote 52: - - All Circles appear ellipses in an oblique view, as is evident by - looking obliquely at the rim of a bason. For the true figure of a - Circle can only be seen when the eye is directly over it’s center. The - more obliquely it is viewed, the more elliptical it appears, until the - eye be in the same plane with it, and then it appears like a straight - line. - -Footnote 53: - - Here we must suppose the Sun to be no bigger than an ordinary point - (as ·) because he only covers a Circle half a degree in diameter in - the Heavens; whereas in the figure he hides a whole sign at once from - the Earth. - -Footnote 54: - - Here we must suppose the Earth to be a much smaller point than that in - the preceding note marked for the Sun. - -Footnote 55: - - If the Earth were cut along the Equator, quite through the center, the - flat surface of this section would be the plane of the Equator; as the - paper contained within any Circle may be justly termed the plane of - that Circle. - -Footnote 56: - - The two opposite points in which the Ecliptic crosses the Equinoctial, - are called _the Equinoctial Points_: and the two points where the - Ecliptic touches the Tropics (which are likewise opposite, and 90 - degrees from the former) are called _the Solstitial Points_. - -Footnote 57: - - The Equinoctial Circle intersects the Ecliptic in two opposite points, - called _Aries_ and _Libra_, from the Signs which always keep in these - points: They are called the Equinoctial Points, because when the Sun - is in either of them, he is directly over the terrestrial Equator; and - then the days and nights are equal. - -Footnote 58: - - In this discourse, we may consider the Orbits of all the Satellites as - circular, with respect to their primary Planets; because the - excentricities of their Orbits are too small to affect the Phenomena - here described. - -Footnote 59: - - If a Globe be cut quite through upon any Circle, the flat surface - where it is so divided, is the plane of that circle. - -Footnote 60: - - The Figure shews the Globe as if only elevated about 40 degrees, which - was occasioned by an oversight in the drawing: but it is still - sufficient to explain the Phenomena. - -Footnote 61: - - The Ecliptic, together with the fixed Stars, make 366-1/4 apparent - diurnal revolutions about the Earth in a year; the Sun only 365-1/4. - Therefore the Stars gain 3 minutes 56 seconds upon the Sun every day: - so that a Sidereal day contains only 23 hours 56 minutes of mean Solar - time; and a natural or Solar day 24 hours. Hence 12 Sidereal hours are - 1 minute 58 seconds shorter than 12 Solar. - -Footnote 62: - - The Sun advances almost a degree in the Ecliptic in 24 hours, the same - way that the Moon moves: and therefore, the Moon by advancing 13-1/6 - degrees in that time goes little more than 12 degrees farther from the - Sun than she was on the day before. - -Footnote 63: - - This center is as much nearer the Earth’s center than the Moon’s as - the Earth is heavier, or contains a greater quantity of matter than - the Moon, namely about 40 times. If both bodies were suspended on it - they would hang in _æquilibria_. So that dividing 240,000 miles, the - Moon’s distance from the Earth’s center, by 40 the excess of the - Earth’s weight above the Moon’s, the quotient will be 6000 miles, - which is the distance of the common center of gravity of the Earth and - Moon from the Earth’s center. - -Footnote 64: - - The Penumbra is a faint kind of shadow all around the perfect shadow - of the Planet or Satellite; and will be more fully explained by and - by. - -Footnote 65: - - Which is the time that the Eclipse would be at the greatest - obscuration, if the motions of the Sun and Moon were equable, or the - same in all parts of their Orbits. - -Footnote 66: - - The above period of 18 years 11 days 7 hours 43 minutes, which was - found out by the _Chaldeans_, and by them called _Saros_. - -Footnote 67: - - A Digit is a twelfth part of the diameter of the Sun or Moon. - -Footnote 68: - - There are two antient Eclipses of the Moon, recorded by _Ptolemy_ from - _Hipparchus_, which afford an undeniable proof of the Moon’s - acceleration. The first of these was observed at _Babylon_, _December_ - the 22d, in the year before CHRIST 383: when the Moon began to be - eclipsed about half an hour before the Sun rose, and the Eclipse was - not over before the Moon set: but by our best Astronomical Tables, the - Moon was set at _Babylon_ half an hour before the Eclipse began; in - which case, there could have been no possibility of observing it. The - second Eclipse was observed at _Alexandria_, _September_ the 22d, the - year before CHRIST 201; where the Moon rose so much eclipsed, that the - Eclipse must have begun about half an hour before she rose: whereas by - our Tables the beginning of this Eclipse was not till about 10 minutes - after the Moon rose at _Alexandria_. Had these Eclipses begun and - ended while the Sun was below the Horizon, we might have imagined, - that as the antients had no certain way of measuring time, they might - have been so far mistaken in the hours, that we could not have laid - any stress on the accounts given by them. But, as in the first Eclipse - the Moon was set, and consequently the Sun risen, before it was over; - and in the second Eclipse the Sun was set, and the Moon not risen, - till some time after it began; these are such circumstances as the - observers could not possibly be mistaken in. Mr. _Struyk_ in the - following Catalogue, notwithstanding the express words of _Ptolemy_, - puts down these two Eclipses as observed at _Athens_; where they might - have been seen as above, without any acceleration of the Moon’s - motion: _Athens_ being 20 degrees West of _Babylon_, and 7 degrees - West of _Alexandria_. - -Footnote 69: - - Each _Olympiad_ began at the time of Full Moon next after the Summer - Solstice, and lasted four years, which were of unequal lengths because - the time of Full Moon differs 11 days every year: so that they might - sometimes begin on the next day after the Solstice, and at other times - not till four weeks after it. The first _Olympiad_ began in the year - of the Julian Period 3938, which was 776 years before the first year - of CHRIST, or 775 before the year of his birth; and the last - _Olympiad_, which was the 293d, began _A. D._ 393. At the expiration - of each _Olympiad_, the _Olympic Games_ were celebrated in the _Elean_ - fields, near the river _Alpheus_ in the _Peloponnesus_ (now _Morea_) - in honour of JUPITER OLYMPUS. See STRAUCHIUS’_s_ _Breviarium - Chronologium_, p. 247-251. - -Footnote 70: - - The reader may probably find it difficult to understand why Mr. SMITH - should reckon this Eclipse to have been in the 4th year of the 48th - _Olympiad_; as it was only in the end of the third year: and also why - the 28th of _May_, in the 585th year before CHRIST should answer to - the present 10th of that month. But we hope the following explanation - will remove these difficulties. - - The month of _May_ (when the Sun was eclipsed) in the 585th year - before the first year of CHRIST, which was a leap-year, fell in the - latter end of the third year of the 48th _Olympiad_; and the fourth - year of that _Olympiad_ began at the Summer Solstice following: but - perhaps Mr. SMITH begins the years of the _Olympiad_ from _January_, - in order to make them correspond more readily with _Julian_ years; and - so reckons the month of _May_, when the Eclipse happened, to be in the - fourth year of that _Olympiad_. - - The Place or Longitude of the Sun at that time was ♉ 29° 43ʹ 17ʺ, to - which same place the Sun returned (after 2300 years, _viz._) _A. D._ - 1716, on _May_, 9^d. 5^h. 6^m. after noon: so that, with respect to - the Sun’s place, the 9th of _May_, 1716 answers to the 28th of _May_ - in the 585th year before the first year of CHRIST; that is, the Sun - had the same Longitude on both those days. - -Footnote 71: - - Before CHRIST 413, _August 27_. - -Footnote 72: - - Before CHRIST 168, _June 20_. - -Footnote 73: - - STRUYK’s Eclipses are to the _Old Style_, all the rest to the _New_. - -Footnote 74: - - This Eclipse happened in the first year of the _Peloponnesian_ war. - -Footnote 75: - - Although the Sun and Moon are spherical bodies, as seen from the Earth - they appear to be circular planes, and so would the Earth if it were - seen from the Moon. The apparently flat surfaces of the Sun and Moon - are called their _Disks_ by Astronomers. - -Footnote 76: - - A Digit is a twelfth part of the diameter of the Sun and Moon. - -Footnote 77: - - This is the same with _the annual Argument of the Moon_. - -Footnote 78: - - When the _Romans_ divided the Empire, which was about 38 years before - CHRIST, _Spain_ fell to _Augustus_’s share: in memory of which, the - _Spaniards_ dated all their memorable events _ab exordio Regni - Augusti_; as Christians do from the birth of our SAVIOUR. But in - process of time, only the initial letters _AERA_ of these words were - used instead of the words themselves. And thus, according to some, - came the word _ÆRA_, which is made use of to signify a point of time - from whence historians begin to reckon. - -Footnote 79: - - When the Sun’s Anomaly is 0 signs 0 degrees, or 6 signs 0 degrees, - neither the Sun nor the Moon’s Anomaly have any Equation; which is the - case in this Example. - -Footnote 80: - - See the Remark, p. 195. - -Footnote 81: - - _Babylon_ is 42 deg. 46 min. east from the Meridian of _London_, which - is equal to 2 hours 51 min. of time nearly. See § 220. - -Footnote 82: - - Our SAVIOUR was born in a leap-year, and therefore every fourth year - both before and after is a leap-year in the _Old Stile_: but the - Tables begin with the year _next after_ that of his birth. - -Footnote 83: - - When only one of the Nodes is mentioned, it is the Ascending Node that - is meant, to which the Descending Node is exactly opposite. - -Footnote 84: - - When the Moon is North of the Ecliptic and going farther from it, her - Latitude or Declination from the Ecliptic is called _North Ascending_: - when she is North of the Ecliptic and going toward it, her Latitude is - _North Descending_: when she is South of the Ecliptic and going - farther from it, her Latitude is _South Descending_: and lastly, when - she is South of the Ecliptic and going toward it, her Latitude is - _South Ascending_. - -Footnote 85: - - See Page 193, Example II. - -Footnote 86: - - M. _Maupertuis_, in his dissertation on the figures of the Celestial - Bodies (p. 61-63) is of opinion that some Stars, by their prodigious - quick rotations on their Axes, may not only assume the figures of - oblate spheroids, but that by the great centrifugal force, arising - from such rotations, they may become of the figures of mill-stones; or - be reduced to flat circular planes, so thin as to be quite invisible - when their edges are turned towards us; as Saturn’s Ring is in such - positions. But when very excentric Planets or Comets go round any flat - Star, in Orbits much inclined to it’s Equator, the attraction of the - Planets or Comets in their perihelions must alter the inclination of - the Star; on which account it will appear more or less large and - luminous as it’s broad side is more or less turned towards us. And - thus he imagines we may account for the apparent changes of magnitude - and lustre in those Stars, and likewise for their appearing and - disappearing. - -Footnote 87: - - See this word explained in the note at the foot of page 194. - -Footnote 88: - - See the note on § 323. - -Footnote 89: - - _Matt._ xxvii. 45. _Mark_ xv. 43. _Luke_ xxiii. 44. - - - - - Transcriber’s Note - - -This book uses inconsistent spelling and hyphenation, which were -retained in the ebook version. Some corrections have been made to the -text, including correcting the errata and normalizing punctuation. -Further corrections are noted below: - - Errata: l. 15 from botton -> l. 15 from bottom - p. 9: forward in the Eliptic -> forward in the Ecliptic - p. 31: is at it were -> is as it were - p. 36, Footnote 22 moved from referring to Rutherfurth to - Maclaurin, additionally ‘Isacc Newton’ changed to ‘Isaac Newton’. - Footnote marker on Rutherfurth removed as there was no footnote - associated with it. - p. 38: on the the same Axis -> on the same Axis - Footnote 32 κοσμὸν -> κόσμον - p. 69: who were suprised to find -> who were surprised to find - p. 69: than those whch -> than those which - p. 72: than tie a thread -> then tie a thread - p. 74: is is equal to -> is equal to - p. 74: the graduaded limb -> the graduated limb - Footnote 49: bove the horizon -> above the horizon - p. 78: different lenghts -> different lengths - p. 78: from the the Equator -> from the Equator - p. 90: is not instantaneons -> is not instantaneous - p. 92: Degreees and Parts of the Equtor-> Degrees and Parts of the - Equator - p. 132: appear supprising -> appear surprising - p. 133: When Jupiter at -> When Jupiter is at - Sidenote p. 136: The reason of of this -> the reason of this - p. 140 the opposite points rises -> the opposite point rises - Sidenote p. 141: Harvest aad Hunter’s -> Harvest and Hunter’s - p. 154: espeically as to the -> especially as to the - Sidenote p. 155: aereal Tides -> aerial Tides - p. 158: the the Earth -> the Earth - p. 160: goes round him 87 days -> goes round him in 87 days - p. 161: Eclipses and revolulution -> Eclipses and revolution - p. 167: Jacobus Ptlaumen -> Jacobus Pflaumen - p. 168: set set down -> set down - p. 172 Table 2, 1st column, 6th row: 1388 -> 1488 - p. 174: duplicate entry for 1606 Sept 2. removed - p. 177: foretold by Thalls -> foretold by Thales - p. 180: the Eclipse is annualar -> the Eclipse is annular - p. 193: EAAMPLE II. -> EXAMPLE II - p. 202: these two Fquations -> these two Equations - p. 203: their Sun will be -> their Sum will be - p. 210: the page number was printed as 110 and has been corrected - p. 210: Motion and Semi diameter -> Motion and Semi-diameter - p. 232: ζωδίακος -> ζωδιακὸς - p. 232: ζῶδιον -> ζώδιον - p. 238: oblate spheriod -> oblate spheroid - p. 261 18 Degres -> 18 Degrees - Index Mercury (Quicksiver) -> Mercury (Quicksilver) - List of Plates Page number for Plate IV corrected from 15 to 97 - - - - - -End of the Project Gutenberg EBook of Astronomy Explained Upon Sir Isaac -Newton's Principles, by James Ferguson - -*** END OF THIS PROJECT GUTENBERG EBOOK ASTRONOMY EXPLAINED *** - -***** This file should be named 60619-0.txt or 60619-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/6/0/6/1/60619/ - -Produced by MFR, Sonya Schermann, and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - -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. 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