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

by James Ferguson

EXAMPLE.

	s	°	ʹ
Sun’s mean Dist. from the [[83]]Node at New Moon in April 1764	0	5	37
To which add the Equation of the Node		+	10
And it gives the Sun’s corrected Distance from the Node	0	5	47
To which cor. Dist. add the Eq. of the Sun’s mean Place	+	1	56
And it gives the Sun’s true Distance from the Node	0	7	43

Which, being at the time of New Moon, is the Argument of Latitude; and in [Table XIV], (making proportions for the 43ʹ) shews the Moon’s Latitude to be 40ʹ 9ʺ North Ascending[^[84]].

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

Seventh Element.

364. Precept. With the Moon’s Anomaly enter [Table XV], and thereby take out her true hourly Motion: then with the Sun’s Anomaly take out his true hourly Motion from the same Table: which done, subtract the Sun’s hourly Motion from the Moon’s, and the remainder will be the Moon’s true hourly Motion from the Sun; which, for the above time § [359], is 27ʹ 50ʺ.

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

Eighth and Ninth Elements.

365. Precept. Enter the XVth Table with the Sun’s Anomaly, and thereby take out his Semi-diameter; and in the same manner take out the Moon’s Semi-diameter by her Anomaly. The former of which for the above time will be found to be 16ʹ 6ʺ; the latter 14ʹ 58ʺ.

To find the Semi-diameter of the Penumbra.

Tenth Element.

366. Precept. Add the Sun’s semi-diameter to the Moon’s, and their Sum will be the Semi-diameter of the Penumbra; namely, at the above time 31ʹ 4ʺ.

[Pl. XII.]

366. Having found the proper Elements or Requisites for the Sun’s Eclipse April 1, 1764, and intending to project this Eclipse Geometrically, we shall now collect them under the eye, that they may be the more readily found as they are wanted in order for the Projection.

The proper Elements collected.

	D	H	M
367. I. The true time of Conj. or New Moon April	1	10	25
	°	ʹ	ʺ
II. The Earth’s Semi-Disc, which is equal to the Moon’s Horizontal Parallax 55ʹ 7ʺ diminished by the Sun’s Horizontal Parallax which is always 10ʺ	0	54	57
III. The Sun’s distance from the nearest Solstice, viz. ♋	77	51	0
IV. The Sun’s Declination, North	4	48	54
V. The Angle of the Moon’s vis. path with the Eclipt.	5	38	0
VI. The Moon’s true Latitude, North Ascending		40	9
VII. The Moon’s true Horary Motion from the Sun		27	50
VIII. The Sun’s Semi-diameter		16	6
IX. The Moon’s Semi-diameter		14	58
X. The Semi-diameter of the Penumbra		31	4

368. Having collected these Elements or Requisites, the following part of the work may be very much facilitated by means of a good Sector, with the use of which the reader should be so well acquainted, as to know how to open it to any given Radius, as far as it will go; and to take off the Chord or Sine of any Arc of that Radius. This is done by first taking the extent of the given Radius in your Compasses, and then opening the Sector so as the distance cross-wise between the ends of the lines of Sines or Chords at S or C, from Leg to Leg of the Sector, may be equal to that extent; then, without altering the Sector, take the Sine or Chord of the given Arc with your Compasses extended cross-wise from Leg to Leg of the Sector in these lines. But if the operator has not a Sector, he must construct these lines to such different lengths as he wants them in the projection. And lest this Treatise should fall into the hands of any person who would wish to project the Figure of a solar or lunar Eclipse, and has not a Sector to do it by, we shall shew how he may make a line of Sines or Chords to any Radius.

Fig. II.
How to make a line of Chords.
[Pl. XII.]

369. Draw the right line BCA at pleasure; and upon C as a Center, with the distance CA or CB as a Radius, describe the Semi-circle BDA; and from the Center C draw AC perpendicular to BCA. Then divide the Quadrants AD and BD each into 90 equal parts or degrees, and join the right line AD for the Chord of the Quadrant AD. This done, setting one foot of the Compasses in A, extend the other to the different divisions of the Quadrant AD; and so transfer them to the right line AD as in the Figure, and you have a line of Chords AD to the Radius CA. N. B. 60 Degrees on the Line of Chords is always equal to the Radius of the Circle it is made from; as is evident by the Figure, where the Arch E, whose Center is A, drawn from 60 on the Quadrant AD, cuts the Chord line in 60 degrees, and terminates in the Center C.

And of Sines.

Then, from the divisions or degrees of the Quadrant BD, draw lines parallel to CD, which will fall perpendicularly on the Radius BC, dividing it into a line of Sines; and it will be near enough for the present purpose, to have them to every fifth Degree, as in the Figure. And thus the young Tyro may supply himself with Chords and Sines, if he has not a Sector. But as the Sector greatly shortens the work, we shall describe the projection as done by it, so far as Signs and Chords are required.

Fig. II.
Earth’s Semi-Disc.

370. Make a Scale of any convenient length (six inches at least) as AC, and divide it into as many equal parts as the semi-diameter of the Earth’s Disc contains minutes, which in this construction of the Eclipse for London in April 1764, is 54 minutes and 57 seconds; but as it wants only 3ʺ of 55ʹ the Scale may be divided into 55 equal parts, as in the Figure. Then, with the whole length of the Scale as a Radius, setting one foot of your Compasses in C as a center, describe the Semi-circle AMB for the northern Hemisphere or Semi-disc of the Earth, as seen from the Sun at that time. Had the Place for which the Construction is made been in South Latitude, this Semi-circle would have been the Southern Hemisphere of the Earth’s Disc.

Axis of the Ecliptic.

371. Upon the center C raise the straight line CH for the Axis of the Ecliptic, perpendicular to ACB.

North Pole of the Earth.

372. Make a line of Chords to the Radius AC, and taking from thence the Chord of 23¹⁄₂ Degrees, set it off from H to g and to h, on the periphery of the Semi-disc; and draw the straight line gNh, in which the North Pole of the Disc is always found.

373. While the Sun is in Aries, Taurus, Gemini, Cancer, Leo, and Virgo, the North Pole of the Disc is illuminated; but while the Sun is in Libra, Scorpio, Sagittary, Capricorn, and Aquarius, the North Pole is hid in the obscure part behind the Disc.

374. And, whilst the Sun is in Capricorn, Aquarius, Pisces, Aries, Taurus, and Gemini, the Earth’s Axis CP lies to the right hand of the Axis of the Ecliptic CH as seen from the Sun, and to the left hand while the Sun is in the other six Signs.

Earth’s Axis.
Universal Meridian.

375. Make a line of Sines equal in length to Ng or Nh, and take off with your Compasses from it the Sine of the Sun’s distance from the nearest Solstice, which in the present case is 77° 51ʹ § [367], and set that distance to the right hand, from N to P, on the line gNh, because the Sun being in Aries § [359], the Earth’s Axis lies to the right hand of the Axis of the Ecliptic § [374]: then draw the straight line CXIIP, for the Earth’s Axis and the Universal Meridian; of both which P is the North Pole.

Path of a given Place on the Disc as seen from the Sun.

376. To draw the parallel of Latitude of any given Place (suppose London) which parallel is the visible Path of the Place On the Disc, as seen from the Sun, from the time that the Sun rises till it sets; subtract the Latitude of the Place (London) 51¹⁄₂ degrees from 90 degrees, and there remains 38¹⁄₂; which take from the Line of Chords in your Compasses, and set it from h (where the Universal Meridian CP cuts the periphery of the Semi-disc) to VI and VI; and draw the occult Line VILVI. Then, on the left hand of the Earth’s Axis, set off the Chord of the Sun’s Declination 4° 48ʹ 5ʺ § [367], from VI to D and to F; set off the same on the right hand from VI to E and to G; and draw the occult Lines DsE and FXIIG parallel to VI L VI.

Situation of the Place on the Disk from Sun-rise to Sun-set.

377. Bisect s XII in K, and through the point K draw the black Line VIKV1 parallel to the occult or dotted Line VILVI. Then, making AC the Radius or length of a Line of Lines, set off the Sine of 38¹⁄₂ degrees, the Co-Latitude of London, from K to VI and VI; and with that extent as a Radius, describe the Semi-Circle VI 7 8 9 &c. and divide it into 12 equal parts, beginning at VI. From these divisions, draw the occult Lines 7m, 8l, 9k, &c. all to the Line VIKVI, and parallel to CXIIP. Then, with KXII as a Radius, describe the Circle abcdef, round the Center K, and divide the Quadrant aXII into six equal parts, as ab, bc, cd, de, &c. Then, through these points of division b, c, d, e, and f, draw the occult Lines VIIbV, VIIIcIIII, IXdIII, &c. intersecting the former Lines 7m, 8l, 9k, 10i, &c. in the points VII, VIII, IX, X, XI, &c. which points mark the situation of London on the Earth’s Disc as seen from the Sun at these hours respectively, from six in the morning till six at night: and if the elliptic Curve VI, VII, VIII, &c. be drawn through these points, it will represent the parallel of London, or the path it seems to describe as viewed from the Sun, from Sun-rise to Sun-set. N.B. When the Sun’s Declination is North, the said Curve is the diurnal Path of London; and the opposite part VIsVI is it’s nocturnal Path behind the Disc, or in the obscure part thereof, § [338], [339]. But if the Sun’s Declination had been South, the Curve VIsVI would have been the diurnal path of London; in which case the Lines 7m, 8l, &c. must have been continued thro’ the right Line VIKVI, and their lengths beyond that line determined by dividing the Quadrant s a of the little Circle abcd into six equal parts, and drawing the parallels VIIb, VIIIc &c. through that division, in the same manner as done on the side K XII; and the Curve VII, VIII, IX, &c. would have been the nocturnal Path. It is requisite to divide the hours of the diurnal Path into quarters, as in the Diagram; and if possible into minutes also.

Axis of the Moon’s Orbit.

378. From the Line of Chords § [372] take the Angle of the Moon’s visible Path with the Ecliptic, viz. 5° 38ʹ § [367]: and note, that when the Moon’s Latitude is North Ascending, as in the present case, the Chord of this Angle must be set off to the left hand of the Axis of the Ecliptic CH, as from H to M, and the right line CM drawn for the Axis of the Moon’s Orbit: but when the Moon’s Latitude is North Descending, this Angle and Axis must be set to the right hand, or from H toward h. When the Moon’s Latitude South Ascending, the Axis of her Orbit lies the same way as when her Latitude is North Ascending; and when South Descending, the same way as when North Descending.

Path of the Penumbra’s center over the Earth.

379. Take the Moon’s Latitude, 40ʹ 9ʺ § [367], from the Scale CA, and set it from C to T on the Axis of the Ecliptic; and through T, at right Angles to the Axis of the Moon’s Orbit CM, draw the straight Line RTS; which is the Moon’s Path, or Line that the center of her shadow and Penumbra describes in going over the Earth’s Disc. The Point T in the Axis of the Ecliptic is the Place where the true Conjunction of the Sun and Moon falls, according to the Tables; and the Point W, in the Axis of the Moon’s Orbit, is that where the center of the Penumbra approaches nearest to the center of the Earth’s Disc, and consequently the middle of the general Eclipse.

It’s Place on the Earth’s Disc shewn for every minute of it’s Transit.

380. Take the Moon’s true Horary Motion from the Sun 27ʹ 50ʺ § [367], from the Scale CA with your Compasses (every division of the Scale being a minute of a Degree) and with that extent make marks in the Line of the Moon’s Path RTS: then divide each of these equal spaces by dots into 60 equal parts or horary minutes, and set the hours to every 60th minute, in such a manner that the dot; signifying the precise minute of New Moon by the Tables, may fall in the Point T where the Axis of the Ecliptic cuts the Line of the Moon’s Path; which, in this Eclipse, is the 25th minute past ten in the Forenoon: and then the other marks will shew the places on the Earth’s Disc where the center of the Penumbra is, at the hours and minutes denoted by them, during its transit over the Earth.

Middle of the Eclipse.
It’s Phases.

381. Apply one side of a Square to the Line of the Moon’s Path, and move the Square backward or forward until the other side cuts the same hour and minute both in the Path of the Place (London, in this Construction) and Path of the Moon; and that minute, cut at the same time in both Paths, will be the precise minute of visible Conjunction of the Sun and Moon at London, and therefore the time of greatest obscuration, or middle of the Eclipse at London; which time, in this Projection, falls at t, 34 minutes past 10 in the Moon’s Path; and at u, 34 minutes past 10 in the Path of London. Then, upon the Point u as a center, describe the Circle zYy whose Radius uy is equal to the Sun’s semi-diameter 16ʹ 6ʺ § [367], taken from the Scale CA: And upon the Point t as a center, describe the Circle Hy whose Radius is equal to the Moon’s semi-diameter 14ʹ 58ʺ § [367], taken from the same Scale. The Circle zYy represents the Disc of the Sun as seen from the Earth, and the Circle Hy the Disc of the Moon. The portion of the Sun’s Disc cut off by the Moon’s shews the Quantity of the Eclipse at the time of greatest obscuration: and if a right Line as yz be drawn across the Sun’s Disc through t and u, the minute of greatest obscuration in both Paths, and divided into 12 equal parts, it will shew what number of Digits are then eclipsed. If these two Circles do not touch one another, the Eclipse will not be visible at the given Place.

It’s beginning and ending.

382. Lastly, take the Semi-diameter of the Penumbra 31ʹ 4ʺ § [367], from the Scale CA with your Compasses; and setting one foot in the Moon’s Path, to the left hand of the Axis of the Ecliptic, direct the other toward the Path of London; and carry this extent backwards or forwards until both Points of the Compasses fall into the same instants of time in both Paths: which will denote the time of the beginning of the Eclipse: then, do the same on the right hand of the Axis of the Ecliptic, and where both Points mark the same instants in both Paths, they will shew at what time the Eclipse ends. These trials give the Points R in the Moon’s Path and r in the Path of London, namely 9 minutes past 9 in the Morning for the beginning of the Eclipse at London, April 1, 1764: t and u for the middle or greatest obscuration, at 35 minutes past 10; when the Eclipse will be barely annular on the Sun’s lower-most edge, and only two thirds of a Digit left free on his upper-most edge: and for the end of the Eclipse, S in the Moon’s Path and x in the Path of London, at 4 minutes past 12 at Noon.

In this Construction it is supposed that the Equator, Tropics, Parallel of London, and Meridians through every 15th degree of Longitude are projected in visible Lines on the Earth’s Disc, as seen from the Sun at almost an infinite distance; that the Angle under which the Moon’s diameter is seen, during the time of the Eclipse, continues invariably the same; that the Moon’s motion is uniform, and her Path rectilineal, for that time. But all these suppositions do not exactly agree with the truth; and therefore, supposing the Elements § [367], given by the Tables to be perfectly accurate, yet the time and phases of the Eclipse deduced from it’s Construction will not answer exactly to what passeth in the Heavens; but may be two or three minutes wrong though done with the utmost care. Moreover, the Paths of all Places of considerable Latitude go nearer the center of the Disc as seen from the Moon than these Constructions make them; because the Earth’s Disc is projected as if the Earth were a perfect sphere, although it is known to be a spheroid. Consequently, the Moon’s shadow will go farther North in places of northern Latitude, and farther South in places of southern Latitude than these projections answer to. Hence we may venture to predict that this Eclipse will be more annular at London (that is, the annulus will be somewhat broader on the southern Limb of the Sun) than the Diagram shews it.

383. Having shewn how to compute the times and project the phases of a Solar Eclipse, we now proceed to those of the Lunar. And it has been already mentioned § [317], that when the Full Moon is within 12 degrees of either of her Nodes, she must be eclipsed. We shall now enquire whether or no the Moon will be eclipsed May 18, 1761, N. S. at 32 minutes past 10 at Night. See page [193].

[Table IV.]
[Table VI.]

	s	°	ʹ
Sun from Node at Full Moon in March 1761	9	25	27
Add his distance for two Lunations, to bring it into May	2	1	20
And his distance at Full Moon in that month is	11	26	47

Subtract this from a Circle, or 12 Signs, and there will remain 3° 13ʹ; which is all that the Sun wants of coming round to the Ascending Node; and the Moon being then opposite to the Sun, must be just as near the Descending Node: consequently, far within the limit of an Eclipse.

384. Knowing then that the Moon will be eclipsed in May 1761, we must find her true distance from the Node at that time, by applying the proper Equations as taught § [363], and then find her true Latitude as taught in that article.

[Table IV.]
[Table XIII.]
[Table XII.]

	s	°	ʹ
Sun’s mean distance from the Node at F. Moon in May 1761	11	26	47
Add the Equation of the Node, for the Sun’s Anomaly 10s 18° 15ʹ[[85]]		+	6
Sun’s mean distance from the Node corrected	11	26	53
Add the Equation of the Sun’s mean Place	+	1	15
Sun’s true distance from the Ascending Node	11	28	8
To which add 6 Signs, See § [363]	6
The sum is the Moon’s true distance from the same Node	5	28	8

[Pl. XII.]

Or the Argument of her Latitude; which in [Table XIV], gives the Moon’s true Latitude, viz. 9ʹ 56ʺ North Descending.

385. Having by the foregoing precepts § [355] found the true time of Opposition of the Sun and Moon in a lunar Eclipse, with the Moon’s Anomaly enter [Table XV] and take out her horizontal Parallax, also her true horary Motion and Semi-diameter: and likewise those of the Sun by his Anomaly, as already taught § [364] & seq. Then add the Sun’s horizontal Parallax, which is always 10 Seconds, to the Moon’s horizontal Parallax, and from their sum subtract the Sun’s Semi-diameter; the remainder will be the Semi-diameter of that part of the Earth’s shadow which the Moon goes through.

386. From the Sum of the Semi-diameters of the Moon and Earth’s Shadow, subtract the Moon’s Latitude; the remainder is the parts deficient. Then, as the Semi-diameter of the Moon is to 6 Digits, so are the parts deficient to the Digits eclipsed.

387. If the parts deficient be more than the Moon’s Diameter, the Eclipse will be total with continuance; if less, it will not be total; if equal, it will be total, but without continuance.

388. Now collect the Elements for projecting this Eclipse.

	ʹ	ʺ
Moon’s horizontal Parallax	55	32
Sun’s horizontal Parallax (always)		10
The Sum of both Parallaxes	55	42
From which subtract the Sun’s Semi-diameter	15	54
Remains the Semi-diameter of the Earth’s Shadow	39	48
Semidiameter of the Moon	15	2
Sum of the two last	54	50
Moon’s Latitude subtract	9	56
Remains the parts deficient	45	0
Moon’s horary motion	30	46
Sun’s horary motion subtract	2	24
Remains the Moon’s horary motion from the Sun	28	22

To project a lunar Eclipse.
Fig. III.

389. This done, make a Scale of any convenient length as W, whereof each division is a minute of a degree; and take from it in your Compasses 54 Minutes 50 Seconds, the Sum of Semi-diameters of the Moon and Earth’s shadow; and with that extent as a Radius, describe that Circle OVLG round C as a Center.

From the same Scale take 39 Minutes 48 Seconds, the Semi-diameter of the Earth’s shadow, and therewith as a Radius, describe the Circle UUUU for the Earth’s shadow, round C as a Center. Subtract the Moon’s Semi-diameter from the Semi-diameter of the Shadow, and with the difference 24 Minutes 46 seconds as a Radius, taken from the Scale W, describe the Circle YZ round the Center C.

Draw the right line AB through the Center C for the Ecliptic, and cross it at right Angles with the line EG for the Axis of the Ecliptic.

Because the Moon’s Latitude in this Eclipse is North Descending, § [384], set off the Angle of her visible Path with the Ecliptic 5 Degrees 38 Minutes (Page [202].) from E to V; and draw VCv for the Axis of the Moon’s Orbit. Had the Moon’s Latitude been North Ascending, this Angle must have been set off from E to f. N. B. When the Moon’s Latitude is South Ascending, the Axis of her Orbit lies the same way as when she has North Ascending Latitude; and when her Latitude is North Descending, the Axis of her Orbit lies the same way as when her Latitude is South Descending.

Take the Moon’s true Latitude 9ʹ 56ʺ in your Compasses from the Scale W, and set it off from C to F on the Axis of the Ecliptic because the Moon is north of the Ecliptic; (had she been to the South of it, her Latitude must have been set off the contrary way, as from C towards v:) and through F, at right Angles to the Axis of the Moon’s Orbit VCv, draw the right line LMHNO for the Moon’s Orbit, or her Path through the Earth’s shadow. N. B. When the Moon’s Latitude is North Ascending, or North Descending, she is above the Ecliptic: but when her Latitude is South Ascending, or South Descending, she is below it.

Take the Moon’s true horary motion from the Sun, viz. 28 Minutes 22 Seconds, from the Scale W in your Compasses; and with that extent make marks in the line of the Moon’s Path LMHNO: then divide each of these equal spaces into 60 equal parts or minutes of time: and set the hours to them as in the Figure, in such a manner that the precise time of Full Moon, as shewn by the Tables, may fall in the Axis of the Ecliptic at F, where the line of the Moon Path cuts it.

Lastly, Take the Moon’s Semi-diameter 15 Minutes 2 Seconds from the Scale W in your Compasses, and therewith as a Radius describe the Circles P, Q, R, S, and T on the Centers L, M, H, N, and O; the Circles P and T just touching the Earth’s Shadow UU, but no part of them within it; the Circles Q and S all within it, but touching at its edges; and the Circle R in the middle of the Moon’s Path through the shadow. So the Circle P shall be the Moon touching the shadow at the moment the Eclipse begins; the Circle Q the Moon just immersed into the shadow at the moment she is totally eclipsed; the Circle R the Moon at the greatest obscuration, in the middle of the Eclipse; the Circle S the Moon just beginning to be enlightened on her western limb at the end of total darkness; and the Circle T the Moon quite clear of the Earth’s shadow at the moment the Eclipse ends. The moments of time marked at the points L, M, H, N and O answer to these Phenomena: and according to this small projection are as follow. The beginning of the Eclipse at 8 Hours 36 Minutes P. M. The total immersion at 9 Hours 42 Minutes. The middle of the Eclipse at 10 Hours 26 Minutes. The end of total darkness at 11 Hours 12 Minutes. And the end of the Eclipse at 12 Hours 18 Minutes; but the Figure is too small to admit of precision.

The examination of antient Eclipses.

390. By computing the times of New and Full Moons, together with the distance of the Sun and Moon from the Nodes; and knowing that when the Sun is within 17 Degrees of either Node at New Moon he must be eclipsed; and when the Moon is within 12 Degrees of either Node at Full she cannot escape an Eclipse; and that there can be no Eclipses without these limits; ’tis easy to examine whether the accounts of antient Eclipses recorded in history be true. I shall take the liberty to examine two of those mentioned in the foregoing catalogue, namely, that of the Moon at Babylon on the 19th of March in the 721st year before Christ; and that of the Sun at Athens, on the 20th of March, in the 424th year before Christ.

The time of Full Moon for the former of these Eclipses is already calculated, Page [198], and the time of New Moon for the latter, Page [196], both to the Old Style; so that we have nothing now to do but find the Sun’s distance from the Nodes the same way as we did the Anomalies; and if the Full Moon in March 721 years before Christ was within 12 degrees of either Node, she was then eclipsed; and if the Sun, at the time of New Moon in March 424 years before Christ was within 17 degrees of either Node, he must have been eclipsed at that time.

EXAMPLE I.
To find the distance of the Sun and Moon from the Nodes, at the time of Full Moon in March, the year before Christ 721, O. S.

The years 720 added to 1780 make 2500, or 25 Centuries.

	Sun from Node
	s	°	ʹ
To the mean time of Full Moon in March 1780, Table III.	10	3	1
Add the distance for 1 Lunation [See N. B. Page [195], and Example III, Page [198]]	1	0	40
Sum	11	3	41
From which subtract the Sun’s distance from the Node for 2500 years, Table V	5	4	11
Remains the Sun’s distance from the Node, March 19, 721 years before Christ	5	29	30
To which add 6 Signs for the Moon’s distance, because she was then in opposition to the Sun	6	0	0
The Sum is the Moon’s dist. from the Ascend. Node	11	29	30

That is, she was within half a degree of coming round to it again; and therefore, being so near, she must have been totally, and almost centrally eclipsed.

EXAMPLE II
To find the Suns distance from the Node at the Time of New Moon in March, the year before Christ 424, O. S.

The years 423 added to 1777 make 2200, or 22 Centuries.

	Sun from Node
	s	°	ʹ
At the mean time of New Moon in March 1777, Tab. I.	8	23	33
From which subtract the Sun’s distance from the Node for 2200 years, Table V	3	6	0
Remains the Sun’s distance from the Ascending Node, March 21, 424 years before Christ	5	17	33
Which, taken from 6 Signs, the distance of the Nodes from each other	6	0	0
Leaves the Sun’s distance at that time from the Descending Node, Descending viz.	0	12	27

Which being less than 17 degrees, shews that the Sun was then eclipsed. And as from these short Calculations we find those two antient Eclipses taken at a venture, to be truly recorded; it is natural to imagine that so are all the rest in the catalogue.

Here follow Astronomical Tables, for calculating the Times of New and Full Moons and Eclipses.

Table I. The mean time of New Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the times of all the New Moons in March for 100 years, Old Style.

Years of Christ.	Mean time of New Moon in March.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s distance from the Node.			The Sun’s Longitude from Aries.			The Node’s Longitude from Aries.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
1701	27	13	45	9	8	23	0	28	5	7	23	15	0	16	3	4	22	48
1702	16	22	34	8	27	39	11	7	53	8	1	17	0	5	20	4	4	3
1703	6	7	23	8	16	55	9	17	41	8	9	20	11	24	37	3	15	17
1704	24	4	55	9	4	30	8	23	18	9	18	3	0	13	0	2	24	57
1705	13	13	44	8	23	54	7	3	6	9	26	6	0	2	17	2	6	11
1706	2	22	32	8	13	48	5	12	54	10	4	9	11	21	34	1	17	25
1707	21	20	5	9	2	17	4	18	31	11	12	52	0	9	57	0	27	5
1708	10	4	54	8	21	10	2	28	19	11	20	55	11	29	14	0	8	19
1709	29	2	26	9	9	48	2	3	56	0	29	38	0	17	37	11	17	59
1710	18	11	16	8	28	32	0	13	44	1	7	40	0	6	54	10	29	14
1711	7	20	5	8	17	27	10	23	33	1	15	43	11	26	11	10	10	28
1712	25	17	36	9	5	8	9	29	10	2	24	26	0	14	34	9	20	8
1713	15	2	25	8	25	48	8	8	58	3	2	29	0	3	50	9	1	21
1714	4	11	14	8	14	52	6	16	46	3	10	32	11	23	7	8	12	35
1715	23	8	46	9	3	37	5	24	22	4	19	15	0	11	30	7	22	15
1716	11	17	35	8	21	26	4	4	11	4	27	18	0	0	47	7	3	29
1717	1	2	23	8	11	58	2	13	59	5	5	20	11	20	4	6	14	44
1718	19	23	56	9	0	31	1	19	36	6	14	3	0	8	27	5	24	24
1719	9	8	45	8	19	47	11	29	24	6	22	6	11	27	43	5	5	37
1720	27	6	17	9	8	9	11	5	1	8	0	49	0	16	6	4	15	17
1721	16	15	6	8	27	25	9	14	49	8	8	52	0	5	23	3	26	31
1722	5	23	55	8	16	41	7	24	38	8	16	55	11	24	40	3	7	45
1723	24	21	27	9	5	3	7	0	15	9	25	38	0	13	4	2	17	26
1724	13	6	16	8	24	19	5	10	3	10	3	41	0	2	22	1	28	41
1725	2	15	4	8	13	45	3	19	51	10	11	43	11	21	39	1	9	56
1726	21	12	37	9	1	57	2	25	28	11	20	26	0	10	3	0	19	37
1727	10	21	26	8	21	13	1	5	16	11	28	29	11	29	20	0	0	51
1728	28	18	58	9	9	35	0	10	53	1	7	13	0	17	43	11	10	30
1729	18	3	47	8	28	51	10	20	41	1	15	15	0	7	0	10	21	45
1730	7	12	36	8	18	7	9	0	29	1	23	18	11	26	17	10	2	59
1731	26	10	8	9	6	29	8	6	6	3	2	1	0	14	40	9	12	39
1732	14	18	57	8	25	45	6	15	54	3	10	3	0	3	57	8	23	54
1733	4	3	45	8	14	49	4	25	43	3	18	6	11	23	14	8	5	7
1734	23	1	18	9	3	25	4	1	20	4	26	49	0	11	37	7	14	48
1735	12	10	7	8	22	39	2	11	8	5	4	52	0	0	54	6	26	1
1736	30	7	39	0	11	1	1	16	45	6	13	35	0	19	17	6	5	42
1737	19	16	28	9	0	1	11	26	33	6	21	38	0	8	34	5	16	56
1738	9	1	17	8	19	33	10	6	21	6	29	42	11	27	51	4	28	9
1739	27	22	49	9	7	55	9	11	58	8	8	24	0	16	14	4	7	50
1740	16	7	38	8	27	11	7	21	46	8	16	27	0	5	30	3	19	3
1741	5	16	26	8	16	27	6	1	34	8	24	30	11	24	47	3	0	16
1742	24	13	59	9	4	49	5	7	11	10	3	12	0	13	10	2	9	58
1743	13	22	48	8	24	5	3	16	59	10	11	15	0	2	27	1	21	12
1744	2	7	36	8	13	21	1	26	48	10	19	18	11	21	44	1	2	25
1745	21	5	9	9	1	43	1	2	25	11	28	0	0	10	7	0	12	7
1746	10	13	58	8	20	59	11	12	13	0	6	3	11	29	44	11	23	20
1747	29	11	30	9	9	21	10	17	50	1	14	45	0	17	47	11	3	2
1748	17	20	19	8	28	37	8	27	38	1	22	49	0	7	4	10	14	15
1749	7	5	8	8	17	53	7	7	26	2	0	53	11	26	21	9	25	28
1750	26	2	40	9	6	15	6	13	3	3	9	35	0	14	44	9	5	9
1751	15	11	29	8	25	32	4	22	51	3	17	38	0	4	1	8	16	23
1752	3	20	17	8	14	47	3	2	39	3	25	41	11	23	18	7	27	37
1753	22	17	50	9	3	10	2	8	16	5	4	24	0	11	41	7	7	17
1754	12	2	39	8	22	26	0	18	4	5	12	27	0	0	59	6	18	32
1755	1	11	27	8	11	41	10	27	52	5	20	30	11	20	16	5	29	45
1756	19	9	0	9	0	4	10	3	30	6	29	13	0	8	39	5	9	27
1757	8	17	49	8	19	20	8	13	18	7	10	15	11	27	56	4	20	41
1758	27	15	21	9	7	42	7	18	55	8	15	58	0	16	19	4	0	21
1759	17	0	10	8	26	58	5	28	43	8	24	1	0	5	36	3	11	36
1760	5	8	58	8	16	13	4	8	31	9	2	4	11	24	53	2	22	49
1761	24	6	31	9	4	35	3	14	8	10	10	47	0	13	16	2	2	29
1762	13	15	19	8	23	52	1	23	56	10	18	51	0	2	33	1	13	44
1763	3	0	8	8	13	7	0	3	44	10	26	53	11	21	50	0	24	57
1764	20	21	41	9	1	29	11	9	21	0	5	36	0	10	13	0	4	37
1765	10	6	30	8	20	46	9	19	9	0	13	38	11	29	30	11	15	52
1766	29	4	2	9	9	8	8	24	46	1	22	21	0	17	53	10	25	32
1767	18	12	51	8	28	24	7	4	35	2	0	24	0	7	10	10	6	47
1768	6	21	39	8	17	39	5	14	23	2	8	27	11	26	27	9	18	1
1769	25	19	12	9	6	2	4	20	0	3	17	0	0	14	50	8	27	41
1770	15	4	1	8	25	17	2	29	48	3	25	12	0	4	7	8	8	56
1771	4	12	49	8	14	33	1	9	36	4	3	16	11	23	24	7	20	8
1772	22	10	22	9	2	56	0	15	13	5	11	49	0	11	47	6	29	48
1773	11	19	10	8	22	11	10	25	1	5	20	1	0	1	4	6	11	3
1774	1	3	59	8	11	27	9	4	49	5	28	4	11	20	21	5	22	17
1775	20	1	32	8	29	50	8	10	26	7	6	4	0	8	44	5	1	57
1776	8	10	20	8	19	5	6	20	14	7	14	50	11	28	1	4	13	12
1777	27	7	53	9	7	27	5	25	51	8	23	23	0	16	24	3	22	52
1778	16	16	42	8	26	43	4	5	40	9	1	36	0	5	41	3	4	6
1779	6	1	30	8	15	59	2	15	28	9	9	39	11	24	58	2	15	19
1780	23	23	3	9	4	21	1	21	5	10	18	22	0	13	21	1	24	59
1781	13	7	52	8	23	37	0	0	53	10	26	24	0	2	38	1	6	14
1782	2	16	40	8	12	53	10	10	41	11	4	27	11	21	54	0	17	27
1783	21	14	13	9	1	15	9	16	18	0	13	10	0	10	17	11	27	7
1784	9	23	2	8	20	32	7	26	6	0	21	13	11	29	34	11	8	22
1785	28	20	35	9	8	54	7	1	43	1	29	56	0	17	57	10	18	2
1786	18	5	23	8	28	9	5	11	31	2	7	59	0	7	14	9	29	16
1787	7	14	11	8	17	25	3	21	19	2	16	2	11	26	31	9	10	29
1788	25	11	44	9	5	47	2	26	56	3	24	45	0	14	54	8	20	9
1789	14	20	33	8	25	3	1	6	45	4	2	47	0	4	11	8	1	25
1790	4	5	21	8	14	19	11	16	33	4	10	50	11	23	28	7	12	38
1791	23	2	54	9	2	41	10	22	10	5	19	33	0	11	51	6	22	18
1792	11	11	43	8	21	57	9	1	58	5	27	56	0	1	7	6	3	32
1793	0	20	31	8	11	12	7	11	45	6	5	39	11	20	24	5	14	45
1794	19	18	4	8	29	35	6	17	23	7	14	22	0	8	48	4	24	27
1795	9	2	52	8	18	51	4	27	11	7	22	25	11	28	6	4	5	41
1796	27	0	25	9	7	13	4	2	48	9	1	8	0	16	29	3	15	21
1797	16	9	14	8	26	29	2	12	36	9	9	10	0	5	46	2	26	36
1798	5	18	2	8	15	44	0	22	24	9	17	13	11	25	3	2	7	50
1799	24	15	35	9	4	6	11	28	1	10	25	56	0	13	26	1	17	30
1800	13	0	24	8	23	23	10	7	49	11	3	59	0	2	43	0	28	44

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

Years of Christ.	Mean time of New Moon in March.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s distance from the Node.			The Sun’s Longitude from Aries.			The Node’s Longitude from Aries.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
1753	4	5	6	7	4	2	1	12	27	4	3	44	11	12	35	7	8	50
1754	23	2	39	8	22	26	0	18	4	5	12	27	0	0	59	6	18	32
1755	12	11	27	8	11	41	10	27	52	5	20	29	11	20	16	5	29	45
1756	30	9	0	9	0	3	10	3	29	6	29	12	0	8	39	5	9	27
1757	19	17	49	8	19	19	8	13	17	7	7	15	11	27	56	4	20	41
1758	9	2	37	8	8	35	6	23	5	7	15	18	11	17	13	4	1	54
1759	28	0	9	8	26	58	5	28	43	8	24	1	0	5	36	3	11	36
1760	16	8	58	8	16	14	4	8	31	9	2	4	11	24	53	2	22	49
1761	5	7	47	8	5	29	2	18	19	9	10	9	11	14	10	2	4	1
1762	24	15	19	8	23	52	1	23	56	10	18	51	0	2	33	1	13	44
1763	14	0	8	8	13	7	0	3	44	10	26	53	11	21	50	0	24	57
1764	2	8	57	8	2	23	10	13	32	11	4	57	11	11	7	0	6	10
1765	21	6	30	8	20	46	9	19	9	0	13	38	11	29	30	11	15	52
1766	10	15	18	8	10	1	7	28	58	0	21	41	11	18	47	10	27	5
1767	29	12	51	8	28	23	7	4	35	2	0	23	0	7	10	10	6	47
1768	17	21	39	8	17	39	5	14	23	2	8	26	11	26	27	9	18	1
1769	7	6	28	8	6	55	3	24	11	2	16	29	11	15	44	8	29	15
1770	26	4	1	8	25	18	2	29	48	3	25	11	0	4	7	8	8	56
1771	15	12	49	8	14	33	1	9	36	4	3	16	11	23	24	7	20	8
1772	3	21	38	8	3	49	11	19	24	4	11	19	11	12	41	7	1	22
1773	22	19	10	8	22	11	10	25	1	5	20	1	0	1	4	6	11	3
1774	12	3	59	8	11	27	9	4	49	5	28	4	11	20	21	5	22	17
1775	1	12	48	8	0	43	7	14	37	6	6	7	11	9	38	5	3	30
1776	19	10	20	8	19	5	6	20	14	7	14	50	11	28	1	4	13	12
1777	8	19	9	8	8	21	5	0	2	7	22	53	11	17	18	3	24	25
1778	27	16	42	8	26	43	4	5	40	9	1	36	0	5	41	3	4	6
1779	17	1	30	8	15	59	2	15	28	9	9	39	11	24	58	2	15	19
1780	5	10	19	8	5	15	0	25	16	9	17	42	11	14	15	1	26	32
1781	24	7	52	8	23	37	0	0	53	10	26	24	0	2	38	1	6	14
1782	13	16	40	8	12	53	10	10	41	11	4	27	11	21	54	0	17	27
1783	3	1	29	8	2	8	8	20	29	11	12	30	11	11	11	11	28	40
1784	20	23	2	8	20	32	7	26	6	0	21	13	11	29	34	11	8	22
1785	10	7	50	8	9	47	6	5	54	0	29	16	11	18	51	10	19	35
1786	29	5	23	8	28	9	5	11	31	2	7	59	0	7	14	9	29	16
1787	18	14	11	8	17	25	3	21	19	2	16	2	11	26	31	9	10	29
1788	6	23	0	8	6	41	2	1	7	2	24	5	11	15	48	8	21	43
1789	25	20	33	8	25	3	1	6	45	4	2	47	0	4	11	8	1	25
1790	15	5	21	8	14	19	11	16	33	4	10	50	11	23	28	7	12	38
1791	4	14	10	8	3	34	9	26	21	4	18	53	11	12	44	6	23	51
1792	22	11	43	8	21	57	9	1	58	5	27	36	0	1	7	6	3	32
1793	11	20	31	8	11	12	7	11	45	6	5	39	11	20	24	5	14	45
1794	1	6	20	8	0	29	5	21	34	6	13	42	11	9	22	4	7	15
1795	20	2	52	8	18	51	4	27	11	7	22	25	11	28	6	4	5	41
1796	8	11	41	8	8	6	3	6	59	8	0	28	11	17	23	3	16	54
1797	27	9	14	8	26	29	2	12	36	9	9	10	0	5	46	2	26	36
1798	16	18	2	8	15	44	0	22	24	9	17	13	11	25	3	2	7	50
1799	6	2	51	8	5	0	11	2	12	9	25	16	11	14	20	1	19	3
1800	25	0	24	8	23	23	10	7	49	11	3	59	0	2	43	0	28	44

Table III. The mean time of Full Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the time of all the Full Moons in March for 100 years, Old Style.

Years of Christ.	Mean time of Full Moon in March.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s distance from the Node.			The Sun’s Longitude from Aries.			The Node’s Longitude from Aries.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
1701	12	19	23	8	23	56	6	15	11	7	7	55	0	1	30	4	23	35
1702	2	4	12	8	13	6	4	24	59	7	15	57	11	20	47	4	4	48
1703	21	1	45	9	1	28	4	0	35	8	24	40	0	9	10	3	14	30
1704	9	10	33	8	19	57	2	10	24	9	2	43	11	28	27	2	25	43
1705	28	8	6	9	8	27	1	16	0	10	11	26	0	16	50	2	5	25
1706	17	16	54	8	28	11	11	25	48	10	19	29	0	6	7	1	16	38s
1707	7	1	43	8	17	44	10	5	37	10	27	32	11	25	24	0	27	51
1708	24	23	16	9	5	43	9	11	14	0	6	15	0	13	47	0	7	33
1709	14	8	4	8	25	15	7	21	2	0	14	18	0	3	4	11	18	46
1710	3	16	54	8	13	59	6	0	50	0	22	21	11	22	21	11	0	0
1711	22	14	27	9	2	0	5	6	27	2	1	3	0	10	44	10	9	42
1712	10	23	14	8	20	35	3	16	16	2	9	6	0	0	1	9	20	55
1713	29	20	47	9	10	21	2	21	52	3	17	48	0	18	23	9	0	35
1714	19	5	36	8	29	25	1	1	40	3	25	53	0	7	40	8	11	48
1715	8	14	24	8	19	4	11	11	28	4	3	56	11	26	57	7	23	1
1716	26	11	57	9	5	59	0	17	5	5	12	38	0	15	20	7	2	43
1717	15	20	45	8	26	31	18	26	53	5	20	41	0	4	37	6	13	56
1718	5	5	34	8	15	58	7	6	42	5	28	44	11	23	54	5	25	10
1719	24	3	7	9	4	20	6	12	18	7	7	26	0	12	17	5	4	52
1720	12	11	55	8	23	36	4	22	7	7	15	29	0	1	34	4	16	5
1721	1	20	44	8	12	52	3	1	55	7	23	32	11	20	51	3	27	18
1722	20	18	17	9	1	14	2	7	32	9	2	15	0	9	14	3	6	59
1723	10	3	5	8	20	30	0	17	21	9	10	18	11	28	31	2	18	12
1724	28	0	38	9	8	52	11	22	57	10	19	0	0	16	55	1	27	55
1725	17	9	26	8	28	18	10	2	45	10	27	3	0	6	12	1	9	9
1726	6	18	15	8	17	24	8	12	34	11	5	6	11	25	30	0	20	23
1727	25	15	48	9	5	46	7	18	10	0	13	49	0	13	53	0	0	5
1728	14	0	36	8	25	2	5	27	59	0	21	52	0	3	10	11	11	18
1729	3	9	25	8	14	18	4	7	47	0	29	55	11	22	27	10	22	32
1730	22	6	58	9	2	40	3	13	23	2	8	38	0	10	50	10	2	13
1731	11	15	46	8	21	56	1	23	12	2	16	41	0	0	7	9	13	26
1732	29	13	19	9	10	18	0	28	48	3	25	23	0	18	30	8	23	8
1733	18	22	7	8	29	22	11	8	37	4	3	26	0	7	47	8	4	21
1734	8	6	56	8	18	50	9	18	26	4	11	29	11	27	4	7	15	34
1735	27	4	29	9	7	12	8	24	2	5	20	12	0	15	27	6	25	15
1736	15	13	17	8	26	29	7	3	51	5	28	15	0	4	44	6	6	29
1737	4	22	6	8	15	44	5	13	39	6	6	18	11	24	1	5	17	42
1738	23	19	39	9	4	6	4	19	15	7	15	1	0	12	24	4	27	24
1739	13	4	27	8	23	22	2	29	4	7	23	4	0	1	41	4	8	37
1740	1	13	16	8	12	38	1	8	52	8	1	7	11	20	57	3	19	50
1741	20	10	48	9	1	0	0	14	28	9	9	49	0	9	20	2	29	30
1742	9	19	37	8	20	16	10	24	17	9	17	52	11	28	37	2	10	44
1743	28	17	10	9	8	38	9	29	53	10	26	35	0	17	0	1	20	26
1744	17	1	58	8	27	54	8	9	42	11	4	38	0	6	17	1	1	39
1745	6	10	47	8	17	10	6	19	31	11	12	41	11	25	34	0	12	52
1746	25	8	19	9	5	32	5	25	7	0	21	24	0	13	57	11	22	34
1747	14	17	8	8	24	48	4	4	56	0	29	27	0	3	14	11	3	47
1748	3	1	57	8	14	4	2	14	44	1	7	30	11	22	31	10	15	0
1749	21	23	30	9	2	26	1	20	20	2	16	12	0	10	54	9	24	42
1750	11	8	18	8	21	42	0	0	9	2	24	15	0	0	11	9	5	59
1751	30	5	51	9	10	5	11	5	45	4	2	58	0	18	34	8	15	37
1752	18	14	39	8	29	20	9	15	33	4	11	1	0	7	51	7	26	50
1753	7	23	18	7	18	35	7	25	21	4	19	4	11	27	8	7	8	4
1754	26	21	1	9	6	59	7	0	58	7	27	47	0	15	32	6	17	45
1755	16	5	49	8	26	14	5	10	46	6	5	49	0	4	49	5	29	0
1756	4	14	38	8	15	30	3	20	35	6	13	52	11	24	6	5	10	14
1757	23	12	11	9	3	53	2	26	12	7	25	35	0	12	29	4	19	54
1758	12	20	59	8	23	8	1	5	59	8	0	38	0	1	46	4	1	9
1759	2	5	47	8	12	25	11	15	48	8	8	41	11	21	3	3	12	22
1760	20	3	20	9	0	46	10	21	25	9	17	24	0	9	26	2	22	2
1761	9	12	9	8	20	2	9	1	13	9	25	27	11	28	43	2	3	16
1762	28	9	41	9	8	25	8	6	50	11	4	11	0	17	6	1	12	57
1763	17	18	30	8	27	40	6	16	38	11	12	13	0	6	23	0	24	11
1764	6	3	19	8	16	56	4	26	26	11	20	16	11	25	40	0	5	24
1765	25	0	52	9	5	19	4	2	3	0	28	58	0	14	3	11	15	5
1766	14	9	40	8	24	34	2	11	52	1	7	1	0	3	20	10	26	20
1767	7	18	29	8	13	50	0	21	41	1	15	4	11	22	37	10	7	34
1768	21	16	1	9	2	12	11	27	17	2	23	47	0	11	0	9	17	14
1769	11	0	50	8	21	28	10	7	9	3	1	49	0	0	17	8	28	28
1770	0	9	39	8	10	44	8	16	57	3	9	52	11	19	54	8	9	42
1771	19	7	11	8	29	6	7	22	30	4	18	36	0	7	57	7	19	21
1772	7	16	0	8	18	22	6	2	18	4	26	39	11	27	14	7	0	35
1773	26	13	32	9	6	44	5	7	55	6	5	21	0	15	37	6	10	16
1774	15	22	21	8	26	0	3	17	43	6	13	24	0	4	54	5	21	31
1775	5	7	10	8	15	16	1	27	31	6	21	27	11	24	11	5	2	44
1776	23	4	42	9	3	38	1	3	8	8	0	10	0	12	34	4	12	25
1777	12	13	31	8	22	54	11	12	56	8	8	13	0	1	51	8	23	30
1778	1	22	20	8	12	10	9	22	45	8	16	16	11	21	8	3	4	52
1779	20	19	52	9	0	32	8	28	22	9	24	59	0	9	31	2	14	32
1780	9	4	41	8	19	48	7	8	10	10	3	1	11	28	48	1	25	47
1781	28	2	14	9	8	9	6	13	47	11	11	44	0	17	11	1	5	27
1782	19	11	2	8	27	28	4	23	34	11	19	47	0	6	27	0	6	41
1783	6	19	51	8	16	44	3	3	23	11	27	50	11	25	44	11	27	54
1784	24	17	24	9	5	4	2	9	0	1	6	35	0	14	7	11	7	35
1785	14	2	12	8	24	20	0	18	48	1	14	36	0	3	24	10	18	48
1786	3	11	1	8	13	36	10	28	37	1	22	39	11	22	41	10	0	2
1787	22	8	33	9	1	57	10	4	13	3	1	22	0	11	4	9	9	42
1788	10	17	22	8	21	14	8	14	2	3	9	25	0	0	21	8	20	57
1789	29	14	55	9	9	36	7	19	39	4	18	7	0	18	44	8	0	38
1790	18	23	43	8	28	52	5	29	27	4	26	10	0	8	1	7	11	51
1791	8	8	32	8	18	8	4	9	15	5	4	13	11	27	17	6	23	4
1792	26	6	5	9	6	20	3	14	52	6	12	56	0	15	40	6	2	45
1793	15	14	53	8	25	46	1	24	40	6	20	59	0	4	58	5	13	59
1794	4	23	42	8	15	2	0	4	29	6	29	2	11	24	15	4	25	13
1795	23	21	14	9	3	14	11	10	5	8	7	45	0	12	39	4	4	54
1796	12	6	3	8	22	39	9	19	53	8	15	48	0	1	56	3	16	8
1797	1	14	52	8	11	55	7	29	42	8	23	50	11	21	13	2	27	23
1798	20	12	24	9	0	7	7	5	18	10	2	33	0	9	36	2	7	3
1799	9	21	13	8	19	33	5	15	6	10	10	36	11	28	53	1	18	18
1800	27	18	46	9	7	46	4	20	43	11	19	19	0	17	16	0	27	57

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

Years of Christ.	Mean time of Full Moon in March.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s distance from the Node.			The Sun’s Longitude from Aries.			The Node’s Longitude from Aries.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
1753	18	23	18	7	18	35	7	25	21	4	19	4	11	27	8	7	8	4
1754	8	8	17	7	7	53	6	5	10	4	27	7	11	16	26	6	19	18
1755	27	5	49	8	26	14	5	10	46	6	5	49	0	4	49	5	29	0
1756	15	14	38	8	15	30	3	20	35	6	13	52	11	24	6	5	10	14
1757	4	23	27	8	4	36	2	0	23	6	21	55	11	13	23	4	21	27
1758	23	20	59	8	23	8	1	5	59	8	0	38	0	1	46	4	1	9
1759	13	5	47	8	12	25	11	15	48	8	8	41	11	21	3	3	12	22
1760	1	14	36	8	1	41	9	25	37	8	16	44	11	10	20	2	23	35
1761	20	12	9	8	20	2	9	1	13	9	25	27	11	28	43	2	3	16
1762	9	20	57	8	9	19	7	11	2	10	3	31	11	18	0	1	14	29
1763	28	18	30	8	27	40	6	16	38	11	12	13	0	6	23	0	24	11
1764	17	3	19	8	16	56	4	26	26	11	20	16	11	25	40	0	5	24
1765	6	12	8	8	6	13	3	6	15	11	28	19	11	14	57	11	16	38
1766	25	9	40	8	24	34	2	11	52	1	7	1	0	3	20	10	26	20
1767	18	18	29	8	13	50	0	21	41	1	15	4	11	22	37	10	7	33
1768	3	3	17	8	3	6	11	1	29	1	23	7	11	11	54	9	18	46
1769	22	0	50	8	21	28	10	7	5	3	1	49	0	0	17	8	28	28
1770	11	9	39	8	15	45	8	16	54	3	9	52	11	19	34	8	9	42
1771	30	7	11	8	29	6	7	22	30	4	18	36	0	7	57	7	19	21
1772	18	16	0	8	18	22	6	2	18	4	26	39	11	27	14	7	0	35
1773	8	0	48	8	7	38	4	12	7	5	4	42	11	16	31	6	11	49
1774	26	22	21	8	26	0	3	17	43	6	13	24	0	4	54	5	21	31
1775	16	7	10	8	15	16	1	27	31	6	21	27	11	24	11	5	2	44
1776	4	15	58	8	4	32	0	7	20	6	29	30	11	13	28	4	13	58
1777	23	13	31	8	22	54	11	12	56	8	8	13	0	1	51	3	23	39
1778	12	22	20	8	12	10	9	22	45	8	16	16	11	21	8	3	4	52
1779	2	7	8	8	1	26	8	2	34	8	24	19	11	10	25	2	16	5
1780	20	4	41	8	19	48	7	8	10	10	3	1	11	28	48	1	25	47
1781	9	13	30	8	9	4	5	17	59	10	11	4	11	18	5	1	7	0
1782	28	11	2	8	27	28	4	23	34	11	19	47	0	6	27	0	16	41
1783	17	19	51	8	16	44	3	3	23	11	27	50	11	25	44	11	27	54
1784	6	4	40	8	5	59	1	13	12	0	5	53	11	15	1	11	9	7
1785	25	2	12	8	24	20	0	18	48	1	14	36	0	3	24	10	18	48
1786	14	11	1	8	13	36	10	28	37	1	22	39	11	22	41	10	0	2
1787	3	19	49	8	2	52	9	8	25	2	0	42	11	11	58	9	11	15
1788	21	17	22	8	21	14	8	14	2	3	9	25	0	0	21	8	20	57
1789	11	2	11	8	10	30	6	23	51	3	17	28	11	19	38	8	2	10
1790	29	23	43	8	28	52	5	29	27	4	26	10	0	8	1	7	11	51
1791	19	8	32	8	18	8	4	9	15	5	4	13	11	27	17	6	23	4
1792	7	17	21	8	7	24	2	19	4	5	12	16	11	16	34	6	4	17
1793	26	14	53	8	25	46	1	24	40	6	20	59	0	4	58	5	13	59
1794	15	23	42	8	15	2	0	4	29	6	29	2	11	24	15	4	25	13
1795	5	8	30	8	4	18	10	14	17	7	7	5	0	13	32	4	6	26
1796	23	6	3	8	22	39	9	19	53	8	15	48	0	1	56	3	16	8
1797	12	14	52	8	11	55	7	29	42	8	23	50	11	21	13	2	27	23
1798	1	23	40	8	1	11	6	9	30	9	1	53	11	10	30	2	8	36
1799	20	21	13	8	19	33	5	15	6	10	10	36	11	28	53	1	18	18
1800	10	6	2	8	8	50	3	24	55	10	18	39	11	18	10	0	29	31

Tab. V. The first mean Conjunction of the Sun and Moon after a compleat Century, beginning with March, for 5000 years 10 days 7 hours 56 minutes (in which time there are just 61843 mean Lunations) with the mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, and the mean Long. of the Sun and Node from the beginning of the sign Aries, at the times of all those mean Conjunctions.

Centuries of Julian Years.	First Conjunction after a Century.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s distance from the Node.			The Sun’s Longitude from Aries.			The Node’s Longitude from Aries.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
100	4	8	11	0	3	21	8	15	22	4	19	27	0	5	2	4	14	25
200	8	16	22	0	6	42	5	0	44	9	8	55	0	10	4	8	28	51
300	13	0	33	0	10	3	1	16	6	1	28	22	0	15	6	1	13	16
400	17	8	43	0	13	24	10	1	28	6	17	49	0	20	8	5	27	41
500	21	16	54	0	16	46	6	16	50	11	7	16	0	25	10	10	12	6
600	26	1	5	0	20	7	3	2	12	3	26	44	1	0	12	2	26	32
700	0	20	32	11	24	22	10	21	45	7	15	31	0	6	7	7	9	24
800	5	4	43	11	27	43	7	7	7	0	4	58	0	11	9	11	23	49
900	9	12	54	0	1	4	3	22	29	4	24	25	0	16	12	4	8	13
1000	13	21	5	0	4	25	0	7	51	9	13	53	0	21	14	8	22	39
1100	18	5	16	0	7	46	8	23	13	2	3	20	0	26	16	1	7	4
1200	22	13	26	0	11	7	5	8	35	6	22	47	1	1	18	5	21	29
1300	26	21	37	0	14	28	1	23	57	11	12	15	1	6	20	10	5	55
1400	1	17	4	11	18	43	9	13	30	3	1	2	0	12	15	2	18	47
1500	6	1	15	11	22	4	5	28	52	7	20	29	0	17	17	7	3	12
1600	10	9	26	11	25	25	2	14	14	0	9	56	0	22	19	11	17	37
1700	14	17	37	11	28	46	10	29	36	4	29	23	0	27	22	4	2	2
1800	19	1	48	0	2	8	7	14	58	9	18	51	1	2	24	8	16	27
1900	23	9	58	0	5	29	4	0	20	2	8	18	1	7	26	1	0	52
2000	27	18	9	0	8	50	0	15	42	6	27	45	1	12	28	5	15	17
2100	2	13	36	11	13	5	8	5	15	10	16	32	0	18	24	9	28	8
2200	6	21	47	11	16	26	4	20	37	3	6	0	0	23	26	2	12	34
2300	11	5	58	11	19	47	1	5	59	7	25	27	0	28	28	6	26	59
2400	15	14	9	11	23	8	9	21	21	0	14	54	1	3	30	11	11	24
2500	19	22	20	11	26	29	6	6	43	5	4	11	1	8	32	3	25	49
2600	24	6	31	11	29	50	2	22	4	9	23	49	1	13	35	8	10	14
2700	28	14	41	0	3	11	11	17	26	2	13	16	1	18	37	0	24	39
2800	3	10	8	11	7	26	6	26	59	6	2	3	0	24	31	5	7	33
2900	7	18	19	11	10	47	3	12	21	10	21	30	0	29	33	9	21	58
3000	12	2	30	11	14	8	11	27	43	3	10	58	1	4	35	2	6	23
3100	16	10	41	11	17	30	8	13	5	8	10	25	1	9	37	6	20	48
3200	20	18	52	11	20	51	4	28	27	0	19	52	1	14	39	11	5	13
3300	25	3	3	11	24	11	1	13	49	5	9	20	1	19	41	3	19	39
3400	29	11	14	11	27	32	9	29	11	9	28	47	1	24	43	8	4	4
3500	4	6	41	11	1	47	5	18	44	1	17	34	1	0	41	0	16	53
3600	8	14	52	11	4	58	2	4	6	6	7	1	1	5	42	5	1	19
3700	12	23	3	11	8	9	10	19	28	10	26	28	1	10	43	9	15	45
3800	17	7	14	11	11	20	7	4	50	3	15	55	1	15	45	2	0	10
3900	21	15	25	11	14	31	4	20	12	8	5	22	1	20	47	6	14	35
4000	25	23	36	11	17	42	1	5	34	0	24	49	1	25	49	10	29	0
4100	0	19	3	10	22	56	8	25	7	4	13	36	1	0	45	3	12	51
4200	5	3	14	10	26	17	5	10	29	9	3	3	1	6	47	7	6	16
4300	9	11	25	10	29	37	1	25	51	1	12	30	1	11	48	11	25	39
4400	13	19	36	11	2	58	10	11	13	6	1	57	1	16	51	4	10	4
4500	18	3	46	11	6	18	6	26	35	10	21	24	1	21	53	8	29	31
4600	22	11	57	11	9	39	3	11	15	3	10	51	1	26	55	1	13	56
4700	26	20	7	11	12	59	11	27	19	8	0	16	2	1	57	5	28	19
4800	1	15	34	10	17	14	7	16	52	11	19	4	1	7	53	10	11	11
4900	5	23	45	10	20	35	4	2	14	4	8	30	1	12	55	2	25	35
5000	10	7	56	10	23	56	0	17	36	8	27	57	1	17	57	7	10	0

Table VI. The mean Anomaly of the Sun and Moon, the Sun’s mean distance from the Ascending Node, with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, for 13 mean Lunations.

Lunations.	Mean Lunations.			The Sun’s mean Anomaly.			The Moon’s mean Anomaly.			The Sun’s motion from the Node.			The Sun’s mean Motion.			The Node’s retrograde Motion.
	D.	H.	M.	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ	s	°	ʹ
1	29	12	44	0	29	6	0	25	49	1	0	40	0	29	6	0	1	34
2	59	1	28	1	28	13	1	21	38	2	1	20	1	28	13	0	3	8
3	88	14	12	2	27	19	2	17	27	3	2	1	2	27	19	0	4	41
4	118	2	56	3	26	26	3	13	16	4	2	41	3	26	26	0	6	15
5	147	15	4	4	25	32	4	9	5	5	3	21	4	25	32	0	7	49
6	177	4	24	5	24	38	5	4	54	6	4	1	5	24	38	0	9	23
7	206	17	8	6	23	44	6	0	43	7	4	42	6	23	45	0	10	57
8	236	5	52	7	22	50	6	26	32	8	5	22	7	22	51	0	12	31
9	265	18	36	8	21	57	7	22	21	9	6	2	8	21	58	0	14	4
10	295	7	21	9	21	3	8	18	10	10	6	42	9	21	4	0	15	38
11	324	20	5	10	20	9	9	13	59	11	7	22	10	20	10	0	17	12
12	354	8	49	11	19	16	10	9	48	0	8	3	11	19	17	0	18	46
13	383	21	33	0	18	22	11	5	37	1	8	43	0	18	23	0	20	20

The first, second, third, and fourth Tables may be continued, by means of the sixth, to any length of time: for, by adding 12 Lunations to the mean time of the New or Full Moon which happens next after the 11th day of March, and then, casting out 365 days in common years, and 366 days in leap-years, we have the mean time of New or Full Moon in March the following year. But when the mean New or Full Moon happens on or before the 11th of March, there must be 13 Lunations added to carry it to March again. The Anomalies, Sun’s distance from the Node, and Longitude of the Sun, are found the same way, by adding them for 12 or 13 Lunations. But the retrograde Motion of the Node for these Lunations must be subtracted from it’s longitude from Aries in March, to have it’s Longitude or Place in the March following.

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

Days.	March.	April.	May.	June.	July.	August.	September.	October.	November.	December.	January.	February.
1	1	32	62	93	123	154	185	215	246	276	307	338
2	2	33	63	94	124	155	186	216	247	277	308	339
3	3	34	64	95	125	156	187	217	248	278	309	340
4	4	35	65	96	126	157	188	218	249	279	310	341
5	5	36	66	97	127	158	189	219	250	280	311	342
6	6	37	67	98	128	159	190	220	251	281	312	343
7	7	38	68	99	129	160	191	221	252	282	313	344
8	8	39	69	100	130	161	192	222	253	283	314	345
9	9	40	70	101	131	162	193	223	254	284	315	346
10	10	41	71	102	132	163	194	224	255	285	316	347
11	11	42	72	103	133	164	195	225	256	286	317	348
12	12	43	73	104	134	165	196	226	257	287	318	349
13	13	44	74	105	135	166	197	227	258	288	319	350
14	14	45	75	106	136	167	198	228	259	289	320	351
15	15	46	76	107	137	168	199	229	260	290	321	352
16	16	47	77	108	138	169	200	230	261	291	322	353
17	17	48	78	109	139	170	201	231	262	292	323	354
18	18	49	79	110	140	171	202	232	263	293	324	355
19	19	50	80	111	141	172	203	233	264	294	325	356
20	20	51	81	112	142	173	204	234	265	295	326	357
21	21	52	82	113	143	174	205	235	266	296	327	358
22	22	53	83	114	144	175	206	236	267	297	328	359
23	23	54	84	115	145	176	207	237	268	298	329	360
24	24	55	85	116	146	177	208	238	269	299	330	361
25	25	56	86	117	147	178	209	239	270	300	331	362
26	26	57	87	118	148	179	210	240	271	301	332	363
27	27	58	88	119	149	180	211	241	272	302	333	364
28	28	59	89	120	150	181	212	242	273	303	334	365
29	29	60	90	121	151	182	213	243	274	304	335	366
30	30	61	91	122	152	183	214	244	275	305	336	—
31	31	—	92	—	153	184	—	245	—	306	337	—

Table VIII. The Moon’s annual Equation.

Sun’s Ano.	Subtract						Sun’s Ano.
	0	1	2	3	4	5
	S.	S.	S.	S.	S.	S.
D.	M.	M.	M.	M.	M.	M.	D.
0	0	11	18	22	19	11	30
1	0	11	19	22	19	11	29
2	1	11	19	22	18	10	28
3	1	11	19	22	18	10	27
4	1	12	19	22	18	10	26
5	2	12	19	22	18	9	25
6	2	12	19	21	18	9	24
7	3	13	20	21	17	9	23
8	3	13	20	21	17	8	22
9	3	13	20	21	17	8	21
10	4	14	20	21	17	8	20
11	4	14	20	21	16	7	19
12	4	14	20	21	16	7	18
13	5	14	20	21	16	6	17
14	5	15	20	21	16	6	16
15	5	15	21	21	15	6	15
16	6	15	21	21	15	5	14
17	6	15	21	21	15	5	13
18	6	16	21	21	15	5	12
19	7	16	21	20	14	4	11
20	7	16	21	20	14	4	10
21	7	16	21	20	14	3	9
22	8	17	21	20	13	3	8
23	8	17	21	20	13	3	7
24	9	17	21	20	13	2	6
25	9	17	21	20	13	2	5
26	9	18	21	20	12	2	4
27	10	18	21	19	12	1	3
28	10	18	21	19	12	1	2
29	10	18	22	19	11	0	1
30	11	18	22	19	11	0	0
Sun’s Ano.	11	10	9	8	7	6	Sun’s Ano.
	S.	S.	S.	S.	S.	S.
	Add

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

Sun’s Anom.	Add						Sun’s Anom.
	0	1	2	3	4	5
	S.	S.	S.	S.	S.	S.
°	ʹ	ʹ	ʹ	ʹ	ʹ	ʹ	°
0	0	10	17	20	17	10	30
1	0	10	17	20	17	10	29
2	1	11	17	20	17	9	28
3	1	11	18	20	17	9	27
4	1	11	18	20	17	9	26
5	2	12	18	20	17	9	25
6	2	12	18	20	16	8	24
7	2	12	18	20	16	8	23
8	3	12	18	20	16	8	22
9	3	12	19	20	16	7	21
10	3	13	19	20	16	7	20
11	4	13	19	20	15	7	19
12	4	13	19	20	15	6	18
13	4	13	19	19	15	6	17
14	5	14	19	19	15	6	16
15	5	14	19	19	14	5	15
16	5	14	19	19	14	5	14
17	6	14	19	19	14	5	13
18	6	15	19	19	14	4	12
19	6	15	20	19	13	4	11
20	7	15	20	19	13	4	10
21	7	15	20	19	13	3	9
22	7	16	20	19	13	3	8
23	8	16	20	19	12	3	7
24	8	16	20	18	12	2	6
25	8	16	20	18	12	2	5
26	9	16	20	18	11	1	4
27	9	17	20	18	11	1	3
28	9	17	20	18	11	1	2
29	10	17	20	18	10	0	1
30	10	17	20	17	10	0	0
Sun’s Anom.	11	10	9	8	7	6	Sun’s Anom.
	S.	S.	S.	S.	S.	S.
	Subtract

Table X. The Moon’s elliptic Equation.

Moon’s Ano.	Add												Moon’s Ano.
	0		1		2		3		4		5
	Signs		Signs		Signs		Signs		Signs		Signs
°	H.	M.	H.	M.	H.	M.	H.	M.	H.	M.	H.	M.	°
0	0	0	4	49	8	8	9	2	7	32	4	14	30
1	0	10	4	57	8	12	9	1	7	27	4	6	29
2	0	20	5	5	8	16	9	0	7	22	3	58	28
3	0	30	5	13	8	20	8	59	7	17	3	50	27
4	0	40	5	21	8	24	8	58	7	12	3	42	26
5	0	50	5	29	8	28	8	57	7	6	3	34	25
6	1	0	5	37	8	31	8	55	7	0	3	26	24
7	1	10	5	45	8	34	8	53	6	54	3	18	23
8	1	20	5	53	8	37	8	51	6	48	3	10	22
9	1	30	6	1	8	40	8	49	6	42	3	2	21
10	1	40	6	9	8	43	8	47	6	36	2	53	20
11	1	50	6	16	8	45	8	44	6	30	2	45	19
12	2	0	6	23	8	47	8	41	6	24	2	37	18
13	2	10	6	30	8	49	8	38	6	18	2	29	17
14	2	20	6	37	8	51	8	35	6	11	2	21	16
15	2	30	6	44	8	53	8	32	6	4	2	12	15
16	2	40	6	51	8	55	8	29	5	57	2	3	14
17	2	50	6	58	8	57	8	26	5	50	1	54	13
18	3	0	7	4	8	59	8	23	5	43	1	45	12
19	3	10	7	10	9	0	8	20	5	36	1	36	11
20	3	19	7	16	9	1	8	16	5	29	1	27	10
21	3	28	7	22	9	2	8	12	5	22	1	19	9
22	3	37	7	28	9	2	8	8	5	15	1	11	8
23	3	46	7	33	9	3	8	4	5	8	1	3	7
24	3	55	7	38	9	3	8	0	5	1	0	54	6
25	4	4	7	43	9	4	7	56	4	54	0	45	5
26	4	13	7	48	9	4	7	52	4	46	0	36	4
27	4	22	7	53	9	4	7	47	4	38	0	27	3
28	4	31	7	58	9	3	7	42	4	30	0	18	2
29	4	40	8	3	9	3	7	37	4	22	0	9	1
30	4	49	8	8	9	2	7	32	4	14	0	0	0
Moon’s Ano.	11		10		9		8		7		6		Moon’s Ano.
	Signs		Signs		Signs		Signs		Signs		Signs
	Subtract

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

Sun’s Anom.	Subtract												Sun’s Anom.
	0		1		2		3		4		5
	Signs		Signs		Signs		Signs		Signs		Signs
°	H.	M.	H.	M.	H.	M.	H.	M.	H.	M.	H.	M.	°
0	0	0	1	44	3	2	3	32	3	5	1	48	30
1	0	4	1	47	3	3	3	32	3	3	1	45	29
2	0	7	1	50	3	5	3	32	3	2	1	42	28
3	0	11	1	53	3	7	3	32	3	0	1	38	27
4	0	14	1	57	3	9	3	32	2	58	1	35	26
5	0	18	2	0	3	10	3	31	2	56	1	31	25
6	0	22	2	3	3	12	3	31	2	54	1	28	24
7	0	25	2	6	3	14	3	31	2	52	1	24	23
8	0	29	2	8	3	16	3	30	2	50	1	21	22
9	0	32	2	11	3	17	4	30	2	48	1	17	21
10	0	36	2	14	3	18	3	30	2	45	1	14	20
11	0	40	2	17	3	19	3	29	2	43	1	11	19
12	0	43	2	20	3	20	3	29	2	40	1	7	18
13	0	47	2	22	3	21	3	28	2	37	1	4	17
14	0	50	2	25	3	22	3	27	2	35	1	0	16
15	0	54	2	28	3	23	3	26	2	32	0	56	15
16	0	57	2	30	3	24	3	25	2	29	0	52	14
17	1	0	2	32	3	25	3	24	2	26	0	49	13
18	1	4	2	35	3	26	3	23	2	23	0	45	12
19	1	7	2	38	3	27	3	22	2	21	0	41	11
20	1	11	2	40	3	28	3	21	2	18	0	38	10
21	1	14	2	43	3	28	3	20	2	15	0	34	9
22	1	17	2	45	3	29	3	19	2	12	0	30	8
23	1	21	2	47	3	29	3	18	2	10	0	26	7
24	1	24	2	49	3	30	3	17	2	7	0	23	6
25	1	28	2	51	3	30	3	15	2	4	0	19	5
26	1	31	2	54	3	31	3	13	2	1	0	15	4
27	1	34	2	57	3	31	3	11	1	58	0	11	3
28	1	38	2	59	3	31	3	9	1	55	0	7	2
29	1	41	3	1	3	32	3	7	1	52	0	4	1
30	1	44	3	2	3	32	3	5	1	48	0	0	0
Sun’s Anom.	11		10		9		8		7		6		Sun’s Anom.
	Signs		Signs		Signs		Signs		Signs		Signs
	Add

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

Sun’s Anom.	Subtract												Sun’s Anom.
	0		1		2		3		4		5
	Signs		Signs		Signs		Signs		Signs		Signs
°	°	ʹ	°	ʹ	°	ʹ	°	ʹ	°	ʹ	°	ʹ	°
0	0	0	0	57	1	40	1	56	1	42	0	59	30
1	0	2	0	59	1	41	1	56	1	41	0	57	29
2	0	4	1	0	1	42	1	56	1	40	0	56	28
3	0	6	1	1	1	43	1	56	1	39	0	54	27
4	0	8	1	2	1	44	1	56	1	38	0	52	26
5	0	10	1	4	1	45	1	56	1	36	0	50	25
6	0	12	1	6	1	45	1	56	1	35	0	48	24
7	0	14	1	7	1	46	1	55	1	34	0	46	23
8	0	16	1	9	1	47	1	55	1	33	0	44	22
9	0	18	1	10	1	48	1	55	1	32	0	42	21
10	0	20	1	12	1	48	1	54	1	30	0	41	20
11	0	22	1	14	1	49	1	54	1	29	0	39	19
12	0	24	1	15	1	50	1	54	1	28	0	37	18
13	0	26	1	17	1	51	1	53	1	26	0	35	17
14	0	28	1	18	1	51	1	53	1	25	0	33	16
15	0	30	1	20	1	52	1	52	1	23	0	31	15
16	0	31	1	21	1	52	1	52	1	22	0	29	14
17	0	33	1	22	1	53	1	51	1	21	0	27	13
18	0	35	1	24	1	53	1	51	1	19	0	25	12
19	0	37	1	25	1	54	1	50	1	18	0	23	11
20	0	39	1	27	1	54	1	49	1	16	0	21	10
21	0	41	1	28	1	55	1	49	1	14	0	19	9
22	0	43	1	29	1	55	1	48	1	13	0	17	8
23	0	45	1	30	1	55	1	47	1	11	0	14	7
24	0	46	1	32	1	56	1	46	1	10	0	12	6
25	0	48	1	33	1	56	1	46	1	8	0	10	5
26	0	50	1	34	1	56	1	45	1	6	0	8	4
27	0	52	1	35	1	56	1	45	1	5	0	6	3
28	0	54	1	36	1	56	1	44	1	3	0	4	2
29	0	55	1	38	1	56	1	43	1	1	0	2	1
30	0	57	1	40	1	56	1	42	0	59	0	0	0
Sun’s Anom.	11		10		9		8		7		6		Sun’s Anom.
	Signs		Signs		Signs		Signs		Signs		Signs
	Add

Table XIII. Equation of the Moon’s Nodes.

Sun’s Ano.	Subtract						Sun’s Ano.
	0	1	2	3	4	5
	S.	S.	S.	S.	S.	S.
°	ʹ	ʹ	ʹ	ʹ	ʹ	ʹ	°
0	0	5	8	10	8	5	30
1	0	5	8	10	8	5	29
2	0	5	8	10	8	5	28
3	0	5	8	10	8	4	27
4	1	5	8	10	8	4	26
5	1	5	8	10	8	4	25
6	1	6	9	10	8	4	24
7	1	6	9	9	8	4	23
8	1	6	9	9	8	4	22
9	1	6	9	9	7	3	21
10	2	6	9	9	7	3	20
11	2	6	9	9	7	3	19
12	2	6	9	9	7	3	18
13	2	6	9	9	7	3	17
14	2	7	9	9	7	3	16
15	2	7	9	9	7	3	15
16	2	7	9	9	7	2	14
17	3	7	9	9	7	2	13
18	3	7	9	9	6	2	12
19	3	7	9	9	6	2	11
20	3	7	9	9	6	2	10
21	3	7	9	9	6	2	9
22	4	7	9	9	6	1	8
23	4	8	9	9	6	1	7
24	4	8	9	9	6	1	6
25	4	8	9	9	6	1	5
26	4	8	10	9	5	1	4
27	4	8	10	9	5	1	3
28	4	8	10	8	5	0	2
29	5	8	10	8	5	0	1
30	5	8	10	8	5	0	0
Sun’s Ano.	11	10	9	8	7	6	Sun’s Ano.
	S.	S.	S.	S.	S.	S.
	Add

The above titles, Add and Subtract, are right when the Equation is applied to the Sun’s mean distance from the Node; but when it is applied to the mean place of the Node, the titles must be changed.

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

Argument of Latit.
Moon fr. the Node.	Sig. 0 N. A.
	Sig. 6 S. D.
°	°	ʹ	ʺ	°
0	0	0	0	30
1	0	5	15	29
2	0	10	30	28
3	0	15	44	27
4	0	20	59	26
5	0	26	13	25
6	0	31	26	24
7	0	36	39	23
8	0	41	51	22
9	0	47	2	21
10	0	52	13	20
11	0	57	23	19
12	1	2	31	18
13	1	7	38	17
14	1	12	44	16
15	1	17	49	15
16	1	22	52	14
17	1	27	53	13
18	1	32	54	12
N. D. Sig. 5				Moon fr. the Node.
S. A. Sig. 11
Argument of Latit.

This Table extends no farther than the limits of Eclipses. N. A. signifies North Ascending Lat. S. A. South Ascending; N. D. North Descending; and S. D. South Descending.

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

Anomaly of the Sun and Moon.		Moon’s Horizontal Parallax.		Sun’s Semidiameter.		Moon’s Semidiamet.		Moon’s horary Mot.		Sun’s horary Mot.		Anomaly of the Sun and Moon.
s	°	ʹ	ʺ	ʹ	ʺ	ʹ	ʺ	ʹ	ʺ	ʹ	ʺ	s	°
0	0	54	59	15	50	14	54	30	10	2	23	12	0
	6	54	59	15	50	14	55	30	12	2	23		24
	12	55	0	15	50	14	56	30	15	2	23		18
	18	55	4	15	51	14	57	30	18	2	23		12
	24	55	11	15	51	14	58	30	26	2	23		6
1	0	55	20	15	52	14	59	30	34	2	23	11	0
	6	55	30	15	53	15	1	30	44	2	24		24
	12	55	40	13	54	15	4	30	55	2	24		18
	18	55	51	15	55	15	8	31	9	2	24		12
	24	56	0	15	56	15	12	31	23	2	25		6
2	0	56	11	15	58	15	17	31	40	2	25	10	0
	6	56	24	15	59	15	22	31	58	2	26		24
	12	56	41	16	1	15	26	32	17	2	27		18
	18	57	12	16	2	15	30	32	39	2	27		12
	24	57	30	16	4	15	36	33	11	2	28		6
3	0	57	49	16	6	15	41	33	23	2	28	9	0
	6	58	10	16	8	15	46	33	47	2	29		24
	12	58	31	16	9	15	52	34	11	2	29		18
	18	58	52	16	11	15	58	34	34	2	29		12
	24	59	11	16	13	16	3	34	58	2	30		6
4	0	59	30	16	14	16	9	35	22	2	30	8	0
	6	59	52	16	15	16	14	35	45	2	31		24
	12	60	9	16	17	16	19	36	0	2	31		18
	18	60	26	16	19	16	24	36	20	2	32		12
	24	60	40	16	20	16	28	36	40	2	32		6
5	0	60	54	16	21	16	31	37	0	2	32	7	0
	6	61	4	16	21	16	34	37	10	2	33		24
	12	61	11	16	22	16	37	37	19	2	33		18
	18	61	16	16	22	16	38	37	28	2	33		12
	24	61	20	16	23	16	39	37	36	2	33		6
6	0	61	24	16	23	16	39	37	40	2	33	6	0

The gradual increase or decrease of the above numbers being so small, it is sufficient to have them to every sixth degree; the proportions for the intermediate degrees being easily made by sight.

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

	Years of Christ beginning	Sun’s mean Longitude from Aries.				Sun’s mean Anomaly.
		s	°	ʹ	ʺ	s	°	ʹ
O.S.	1	9	7	53	10	6	29	54
	1301	9	17	42	30	6	16	58
	1401	9	18	27	50	6	15	59
	1501	9	19	13	10	6	14	59
	1601	9	19	58	30	6	13	59
	1701	9	20	43	50	6	12	59
N.S.	1753	9	10	16	52	6	1	38
	1801	9	9	39	39	6	0	10
Old Style to the beginning of A. D. 1753; then New Style	Years of Christ compleat	Sun’s mean Motion.				Sun’s mean Anomaly.
		s	°	ʹ	ʺ	s	°	ʹ
	1	11	29	45	40	11	29	45
	2	11	29	31	20	11	29	29
	3	11	29	17	0	11	29	14
	4	0	0	1	49	11	29	58
	5	11	29	47	29	11	29	42
	6	11	29	33	9	11	29	27
	7	11	29	18	49	11	29	11
	8	0	0	3	38	11	29	55
	9	11	29	49	18	11	29	40
	10	11	29	34	58	11	29	24
	11	11	29	20	38	11	29	9
	12	0	0	5	26	11	29	53
	13	11	29	51	7	11	29	37
	14	11	29	36	47	11	29	22
	15	11	29	22	27	11	29	7
	16	0	0	7	15	11	29	50
	17	11	29	52	55	11	29	35
	18	11	29	38	35	11	29	20
	19	11	29	24	16	11	29	4
	20	0	0	9	4	11	29	48
	40	0	0	18	8	11	29	36
	60	0	0	27	12	11	29	24
	80	0	0	36	16	11	29	12
	100	0	0	45	20	11	29	0
	200	0	1	30	40	11	28	1
	300	0	2	16	0	11	27	1
	400	0	3	1	20	11	26	1
	500	0	3	46	40	11	25	2
	600	0	4	32	0	11	24	2
	700	0	5	17	20	11	23	2
	800	0	6	2	40	11	22	3
	900	0	6	48	0	11	21	3
	1000	0	7	33	20	11	20	3
	2000	0	15	6	40	11	10	7
	3000	0	22	40	0	11	0	10
	4000	1	0	13	20	10	20	13
	5000	1	7	46	40	10	10	16
	6000	1	15	20	0	10	0	19
	Months	Sun’s mean Motion.				Sun’s mean Anomaly.
		s	°	ʹ	ʺ	s	°	ʹ
	Jan.	0	0	0	0	0	0	0
	Feb.	1	0	33	18	1	0	33
	Mar.	1	28	9	11	1	28	9
	Apr.	2	28	42	30	2	28	42
	May.	3	28	16	40	3	28	17
	June	4	28	49	58	4	28	50
	July	5	28	24	8	5	28	24
	Aug.	6	28	57	26	6	28	57
	Sep.	7	29	30	44	7	29	30
	Oct.	8	29	4	54	8	29	4
	Nov.	9	29	38	12	9	29	37
	Dec.	10	29	12	22	10	29	11

Days.	Sun’s mean Motion and Anomaly.
	s	°	ʹ	ʺ
1	0	0	59	8
2	0	1	58	17
3	0	2	57	25
4	0	3	56	33
5	0	4	55	42
6	0	5	54	50
7	0	5	53	58
8	0	7	53	7
9	0	8	52	15
10	0	9	51	23
11	0	10	50	32
12	0	11	49	40
13	0	12	48	48
14	0	13	47	57
15	0	14	47	5
16	0	15	46	13
17	0	16	45	22
18	0	17	44	30
19	0	18	43	38
20	0	19	42	47
21	0	20	41	55
22	0	21	41	3
23	0	22	40	12
24	0	23	39	20
25	0	24	38	28
26	0	25	37	37
27	0	26	36	45
28	0	27	35	53
29	0	28	35	2
30	0	29	34	10
31	1	0	33	18

In Leap-years, after February, add one Day and one Day’s motion.