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Title: Astronomy Explained Upon Sir Isaac Newton's Principles - And made easy to those who have not studied mathematics
Author: Ferguson, James
Language: English
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                           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





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