Astronomy Explained Upon Sir Isaac Newton's Principles: And made easy to those who have not studied mathematics

By James Ferguson

The author, a Scottish astronomer named James Ferguson, wrote this guide to astronomy for a general audience according to the scientific principles laid out by Sir Issac Newton. Ferguson's love of the field is apparent from the first sentence of the book, in which he says: "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."

• Language: English
• Publisher: DigiCat
• Release date: Jun 3, 2022
• ISBN: 8596547056911

James Ferguson

James Ferguson is Associate Professor of Anthropology at the University of California, Irvine, and the author of The Anti-Politics Machine: "Development," Depoliticization, and Bureaucratic Power in Lesotho (1990). He is also coeditor, with Akhil Gupta, of Anthropological Locations: Boundaries and Grounds of a Field Science (California, 1997) and Culture, Power, Place: Explorations in Critical Anthropology (1997).

Book preview

James Ferguson

Astronomy Explained Upon Sir Isaac Newton's Principles

And made easy to those who have not studied mathematics

EAN 8596547056911

DigiCat, 2022

Contact: [e-mail]

Table of Contents

ASTRONOMY EXPLAINED UPON Sir ISAAC NEWTON’s PRINCIPLES, AND MADE EASY TO THOSE WHO HAVE NOT STUDIED MATHEMATICS.

THE CONTENTS.

ERRATA.

CHAP. I. Of Astronomy in general.

CHAP. II. A brief Description of the Solar System .

CHAP. III. The COPERNICAN SYSTEM demonstrated to be true .

CHAP. IV. The Phenomena of the Heavens as seen from different parts of the Earth.

CHAP. V. The Phenomena of the Heavens as seen from different Parts of the Solar System.

CHAP. VI. The Ptolemean System refuted. The Motions and Phases of Mercury and Venus explained.

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.

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.

CHAP. IX. The Method of finding the Distances of the Sun, Moon, and Planets.

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 § and .)

CHAP. XI. The Method of finding the Longitude by the Eclipses of Jupiter’s Satellites: The amazing Velocity of Light demonstrated by these Eclipses.

CHAP. XII. Of Solar and Sidereal Time.

CHAP. XIII. Of the Equation of Time.

CHAP. XIV. Of the Precession of the Equinoxes.

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.

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.

CHAP. XVII. Of the ebbing and flowing of the Sea.

CHAP. XVIII. Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and Modern Eclipses.

CHAP. XIX. The Calculation of New and Full Moons and Eclipses. The geometrical Construction of Solar and Lunar Eclipses. The examination of antient Eclipses.

To calculate the time of New and Full Moon.

EXAMPLE I. To find the time of New Moon in April 1764, N. S.

EXAMPLE II. To find the time of Full Moon in May 1761, N. S.

EXAMPLE I. To find the time of New Moon in July 1581, O. S.

To find the time of New or Full Moon in any given year and month before the Christian Æra.

EXAMPLE I. To find the time of New Moon at London and Athens in March, the year before Christ 424.

EXAMPLE II. To find the time of Full Moon in October, the year before Christ 4030 .

EXAMPLE III. To find the time of Full Moon at Babylon in March, the year before Christ 721 .

EXAMPLE. For the time of New Moon in April 1764.

To find the Moons Horizontal Parallax, or the Angle of the Earth’s semi-diameter as seen from the Moon.

To find the Sun’s true Place, and his distance from the nearest Solstice.

EXAMPLE.

EXAMPLE. To find the Sun’s true Place April 30th, A. D. 1757, at 18 minutes 40 seconds past 10 in the morning .

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 .

To find the Sun’s Declination.

To find the Angle of the Moon’s visible Path with the Ecliptic.

To find the Moon’s Latitude.

EXAMPLE.

To find the Moon’s true hourly Motion from the Sun.

To find the Semi-diameters of the Sun and Moon as seen from the Earth at the above-mentioned time.

To find the Semi-diameter of the Penumbra.

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.

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.

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 .

Table II. The mean New Moons, &c. in March to the New Style .

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 .

Table IV. The mean Full Moons, &c. in March to the New Style .

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 .

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.

Table VII. The number of Days, reckoned from the beginning of March, answering to the Days of all the mean New and Full Moons .

Table VIII. The Moon’s annual Equation.

Table IX. Equation of the Moon’s mean Anomaly.

Table X. The Moon’s elliptic Equation.

Table XI. The Sun’s Equation at the time of New and Full Moon.

Table XII. Equation of the Sun’s mean Place.

Table XIII. Equation of the Moon’s Nodes.

Tab. XIV. The Moon’s latitude in Eclipses.

Table XV. The Moons Horizontal Parallax; the Semidiameters and true Horary motions of the Sun and Moon.

Table XVI. The Sun’s mean Motion and Anomaly.

Sun’s mean Motion and Anomaly.

Table XVII. The Sun’s Declination in every Degree of the Ecliptic.

Table XVIII. Lunations from 1 to 100000.

CHAP. XX. Of the fixed Stars.

The antient Constellations.

The New Southern Constellations.

Hevelius ’s Constellations made out of the unformed Stars.

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.

Required the mean time of New Moon in June, A.D. 1909, N.S.

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 .

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.

Tab. II. Shewing the Number of Direction, for finding Easter Sunday by the Golden Number and Dominical Letter.

Tab. III. Shewing the Dominical Letters, Old Style, for 4200 Years before the Christian Æra.

Tab. IV. Shewing the Dominical Letters, Old Style, for 4200 Years after the Christian Æra.

Tab. V. The Dominical Letter, New Style, for 4000 Years after the Christian Æra.

Tab. VI. Shewing the Days of the Months for both Styles by the Dominical Letters.

CHAP. XXII. A Description of the Astronomical Machinery serving to explain and illustrate the foregoing part of this Treatise.

PROBLEM I. To find the Amplitudes, Meridian Altitudes, and times of Rising, Culminating, and Setting, of the Sun, Moon, and Planets.

PROBLEM II. To find the Altitude and Azimuth of the Sun, Moon, and Planets, at any time of their being above 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.

INDEX.

DIRECTIONS to the BOOKBINDER.

ASTRONOMY

EXPLAINED UPON

Sir ISAAC NEWTON’s

PRINCIPLES,

AND MADE EASY

TO THOSE WHO HAVE NOT STUDIED

MATHEMATICS.

Table of Contents

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.

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.

Table of Contents

ERRATA.

Table of Contents

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.

Table of Contents

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.

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.

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.

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.

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.

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.

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.

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!

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.

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.

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.

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.

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.

Table of Contents

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.

The Sun.

18. The Sun 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.

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.

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.

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.

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.

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.

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.

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.

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 9¹⁄4 days, according to Bianchini’s observations; so that in her, every day and night together is as long as 24¹⁄3 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.

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.

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 51¹⁄2 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.

Remarkable appearances.

30. The [6]artificial day at each Pole of Venus is as long as 112¹⁄2 [7]natural days on our Earth.

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.

The Sun’s daily Course.

32. As her annual Revolution contains only 9¹⁄4 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 18³⁄4 of our days and nights.

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 36¹⁄4 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.

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.

Surprising appearances at her Poles;

The Sun will rise 22¹⁄2 degrees[10] north of the East, and going on 112¹⁄2 degrees, as measured on the plane of the [11]Horizon, he will cross the Meridian at an altitude of 12¹⁄2 degrees; then making an entire revolution without setting, he will cross it again at an altitude of 48¹⁄2 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 48¹⁄2 degrees; next at the altitude of 12¹⁄2 degrees; and going on thence 112¹⁄2 degrees, he will set 22¹⁄2 degrees north of the West; so that, after having been 4⁵⁄8 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 23¹⁄2 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.

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.

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.

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 9¹⁄4 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.

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 18¹⁄2 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 3¹⁄4 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.

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.

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.

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.

When she will appear on the Sun.

45. Venus’s Orbit is inclined 3¹⁄2 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.

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