Astronomy Explained Upon Sir Isaac Newton’s Principles

Chap. XX Of the fixed Stars.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The antient Constellations.

			Ptolemy.	Tycho.	Hevelius.	Flamsteed.
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		15	12	23	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		35	30	49	95
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

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.

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.

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.

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.

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.

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].

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.

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 2¹⁄₂ 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.

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.

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.

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 14¹⁄₂ seconds; and is 20 minutes 17¹⁄₂ seconds longer than the true Solar Year.

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.

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.

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 3³⁄₄ days short of the Solar Year in that time.

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.

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.

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.

No	The Jewish year.		Days		No	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 Adar they added a month called Ve-Adar of 30 days.					Days in the year			365

No	The Arabic and Turkish year.		Days		No	The ancient Grecian year.		Days
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.

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.

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.

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.

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.

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.

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.

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.	March	April	May	June	July	August	Sept.	Octob.	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

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.

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	5d	8h	0m	Afternoon.
And 5h 52m multiplied by 2 make to be subtr.		11	44
Remains the mean time according to the Old Style, June	5d	9h	16m	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	18d	9h	16m	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 of the Cyc.	A.D.	January		February		March		April		May		June		July		August		Septemb.		October		Novemb.		Decemb.
		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
2	1725	3	2M	1	2A	3	3M	1	4A	1	4M	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
4	1727	11	8M	9	9A	11	9M	9	10A	9	11M	7	12A	7	0A	6	1M	4	1A	4	2M	2	3A	2	4M
																								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
7	1730	7	11A	6	0A	8	1M	6	1A	6	2M	4	3A	4	3M	2	4A	2	5M	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
10	1733	4	2A	3	3M	4	4A	3	4M	2	5A	1	6M	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
13	1736	2	5M	----		1	7M	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
15	1738	9	11M	7	12A	9	1A	8	1M	7	2A	6	3M	5	4A	4	5M	2	5A	2	6M	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
18	1741	6	3M	4	4A	6	4M	4	5A	4	5M	2	6A	2	7M	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
21	1744	3	6A	2	7M	2	8A	1	9M	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
23	1746	10	12A	9	1A	11	2M	9	3A	9	3M	7	4A	7	5M	5	6A	4	6M	3	7A	2	8M	1	9A
																								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
26	1749	7	3A	6	4M	7	5A	6	6M	5	6A	4	7M	3	8A	2	9M	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
29	1752	5	6M	3	7A	4	8M	2	9A	2	9M	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
32	1755	1	10A	----		1	11A	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
34	1757	9	4M	7	5A	9	6M	7	7A	7	7M	5	8A	5	9M	3	10A	2	10M	1	14A	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
37	1760	6	7A	5	8M	5	9A	4	10M	3	10A	2	11M	1	12A	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
40	1763	3	11M	1	12A	3	0A	2	1M	1	1A	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
42	1765	10	5A	9	6M	10	6A	9	7M	8	7A	7	8M	6	9A	5	10M	3	10A	3	11M	1	12A	1	1A
																								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
45	1768	8	8M	6	9A	7	10M	5	11A	5	11M	3	12A	3	1A	2	2M	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
48	1771	4	11M	3	0A	5	1M	3	2A	3	2M	1	3A	1	4M	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
51	1774	1	2A	----		1	4A	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
53	1776	9	9A	8	10M	8	10A	7	11M	6	12A	5	0A	5	1M	3	2A	2	2M	1	3A	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
56	1779	6	0A	5	1M	6	2A	5	3M	4	3A	3	4M	2	5A	1	6M	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
59	1782	3	3M	1	4A	3	5M	1	6A	1	6M	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
61	1784	11	9M	9	10A	10	11M	8	12A	8	0A	7	1M	6	2A	5	3M	3	3A	3	4M	1	5A	1	6M
																								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
64	1787	7	12A	6	1A	8	2M	6	3A	6	3M	4	4A	4	5M	2	6A	1	6M	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
67	1790	4	4A	3	5M	4	5A	3	6M	2	6A	1	7M	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
70	1793	1	7M	----		1	9M	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
72	1795	9	1A	8	2M	9	3A	8	4M	7	4A	6	5M	5	6A	4	7M	2	7A	2	8M	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
75	1798	6	4M	4	5A	6	6M	4	7A	4	7M	2	8A	2	9M	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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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	AD0
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.
Hundreds of Years.				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
				38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56
				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.
Years less than an Hundred.				0	100	200	300	400	500	600
				700	800	900	1000	1100	1200	1300
				1400	1500	1600	1700	1800	1900	2000
				2100	2200	2300	2400	2500	2600	2700
				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.
Years less than an Hundred.				0	100	200	300	400	500	600
				700	800	900	1000	1100	1200	1300
				1400	1500	1600	1700	1800	1900	2000
				2100	2200	2300	2400	2500	2600	2700
				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.
Years less than an Hundred.				100	200	300	400
				500	600	700	800
				900	1000	1100	1200
				1300	1400	1500	1600
				1700	1800	1900	2000
				2100	2200	2300	2400
				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
January 31 October 31	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
				1	2	3	4
Feb. 28-29 March 31 Nov. 30
	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
							1
April 30 July 31
	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
			1	2	3	4	5
August 31
	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
						1	2
Septemb. 30 Decemb. 31
	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
		1	2	3	4	5	6
May 31
	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
					1	2	3
June 30
	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