Chapter XIX: Part 19

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_.