THE
COPERNICUS
EXPLAIN'D: Or a BRIEF ACCOUNT of the NATURE and USE OF AN
Universal Astronomical Instrument,
FOR THE Calculation and Exhibition of
New
and
Full Moons,
and of
Eclipses,
both
Solar
and
Lunar
; with the Places
Heliocentrical
and
Geocentrical
of all the
Planets, Primary
and
Secondary,
&c.
By
WILLIAM WHISTON,
M.A. Sometime Professor of the
Mathematicks
in the University of
Cambridge.
LONDON,
Printed for the Author, in
Cross-Street, Hatton-Garden.
1715.
To the Right Honourable General STANHOPE, One of His MAJESTY's
Principal Secretaries of State
: A great
PATRON
and
Encourager
of
Learning,
and of
Undertakings
for the
Publick Good
; Particularly those of the Author for the Improvement of
Astronomy
and
Geography
THIS SMALL MANUAL IS, With all due Submission, and Gratitude, Dedicated by
The Author.
THE
COPERNICUS
EXPLAIN'D.
T HIS Astronomical Instrument (which is made agreeably to the
Copernican
System, and therefore by me named the
COPERNICUS)
consists (besides the immoveable Circle on the
utside, and the small moveable central Circle within) of ten intermediate concentrical
Annuli,
or broad circular Rings, fitted to revolve one within another; but so, as to be capable of being fix'd, by small Pins, in any situation whatsoever. Six of the Circles toward the Center are so contriv'd, that they may be taken away, upon occasion; and yet when they are put in, they are fast connected to the Frame, as well as the other, and revolve as freely as they do. There is also a Terrestrial Globe, of nine Inches Diameter, plac'd under the inner Circles, with its Hour Circle, turning along with it in its Diurnal Motion: And when those Circles are remov'd, the Globe may be so elevated and fix'd at any height, and so regulated by Screws, as to be ready for the Exhibition of those Eclipses, which the six outward Circles assist us to discover; to which last does also belong a Rule, with a Groove, containing an Angle of 5° 37′ for the Moon's Path in Eclipses. There is also a round Plate of Glass, with 12 Concentrical Circles therein, for the 12 Digits in Solar Eclipses; whose Diameter bears the same proportion to the Diameter of the Globe, that the apparent Semidiameters of the Sun and Moon put together, do really bear to the Disk of the Earth in those Eclipses. There is, besides, a Map of the Moon, with 6 Concentrical Circles, for the 12 Digits in Lunar Eclipses; whose Diameter bears the same proportion to that of the Globe, which the real Diameter of the Moon bears to the real Diameter of the Earth. There is also a dark Circle, representing that Section of the Earth's Conical Shadow, along which the Moon passes in its own Eclipses; and is so much less in proportion than the Diameter of the Globe, as is that of the real corresponding Circle to that of the Earth it self. There are also two Threads, with their Plummets, fix'd to the Center of the Instrument; of frequent use in its Operations.
THE Nature of the several Parts of this Instrument is as follows:
THE outmost, or largest Circle, which is immovable, is the
Ecliptick,
with its known Signs,
Aries, Taurus, Gemini, &c.
This Circle is divided equally, from the beginning of
Aries,
or the
Vernal Equinox,
into 360 Degrees, or 12 Signs of 30 Degrees apiece; and is the Measure and Standard of the whole Instrument. Every Planet, or Point, or Line being still fix'd, by knowing its Place along this Circle, either by the Signs, with the particular Degrees and Minutes, or by the bare number of Degrees and Minutes from the
Equinox.
THE Second Circle is for the Months and Days of the Year; which Days being, in a manner, equal, this Circle is equally divided into 365 Parts; which is the number of Days in a
Julian
common Year. Nor will the
Leap Year
cause any great trouble, though it has one more Day in
February;
since it is already allow'd for in those Astronomical Tables, whence all our Numbers have been transferr'd into this Instrument; and any Day therein, after
February,
is counted one farther than in the common Year. But here several things are to be noted;
viz.
(1.) That I suppose every Body can readily tell, in any Month of any Year, how remote every Day of it is from the beginning of that Year; and this both in common, and in Leap Years; and so can readily change one way of Computation for the other, as occasion shall require: Thus we know by the old Memorial Verses, that,
Thirty Days hath September,
April, June, and November:
February eight and twenty alone,
And all the rest have thirty and one.
Accordingly, we can tell, that
April
22
d,
the Day of the next total Eclipse of the Sun, in this common Year, is the 112
th
day of the Year: As also, that
Sept.
29
th,
or
Michaelmas
day, next Year, which is
Leap Year,
will be the 273
d
Day of that Year; and so in all other Cases whatsoever. (2.) That in case we fix any one Day of the Circle rightly to that Place in the
Ecliptick
whereto it belongs, every other Day of the same Circle will thereby be rightly plac'd also. (3.) That I have therefore set down upon this Circle, the true Place of the
Vernal Equinox,
for the past Ages, as well as for the present: So that 'tis but bringing either the particular Year of our Lord it self
since,
or any one which proceeded it
before Christ,
to the beginning of
Aries,
or the
Vernal Equinox,
and the whole Circle of Months is rightly plac'd, with respect to the
Ecliptick,
for that time. (4.) That yet if we desire to be exact, we must, in this case, consider further, what Year it is from
Leap Year
that we are concern'd with; for if it be the first after it (which the first of each Century and Score
since,
and the fourth of each Century and Score
before Christ
always are) the Position of the Numbers is right of it self, without any more consideration: But if it be the second after it, the Circle is to be turn'd one third of a Century's Motion, or one quarter of a Day forward; if it be the third, two thirds of a Century's Motion, or one half of a Day forwards, in order to its right Position; while if it be it self Leap Year, the Circle must be turned one quarter of a Day backward, in order to such a Position. (5.) Our Astronomical Centuries, Years, Months, and Days do ever commence from the Noon foregoing; so our 10
th
of
March,
in this Instrument begins at Noon
March
9
th,
and ends at Noon
March
1O
th;
and is indeed reckon'd by 24 Hours intire, from the one Noon to the other. Thus, because this is the third after
Leap Year,
I turn this second Circle onward half a day, and find, that the
Vernal Equinox
happens this Year,
March
9.
d.
18
h.
0
m.
or as we commonly reckon, on
March
10. about Six of the Clock in the Morning; and that, by consequence,
April
21.
d.
9
h.
42
m.
the time of the middle of the next great Eclipse of the Sun, corresponds ponds to the 13° of
Taurus,
in the outmost Circle of the
Ecliptick.
THE Third Circle is the Annual Elliptick Orbit of the Earth, here rightly represented by a Circle; with the unequal Divisions of the
Ellipsis,
corresponding to the inequality of the Earth's Motion. This Circle is fix'd to the due place of the Ecliptick by a small Arch, of the place of the
Perihelion
; as the Days of the Month were fix'd to the
Equinox.
THE Fourth Circle contains the Menstrual Orbit of the Moon, with its Periodical Revolution about the Earth; both in 360 Parts, and in 27 Days, 7 Hours, and 43 Minutes. The actual Divisions are here made for the mean State of the Orbit, which is variable; but Points are set at every five Degrees (to be thence supply'd at every Degree, and proportionably in other Cases) according to its several Degrees of Eccentricity. Upon the inner large part of this Circle there is also a Spiral Line, with the progressive mean Motion of the Moon's
Apogee
for a Century; with every one of the Months, and almost Days Motion also; That so when we have fix'd, by a proper Table, the mean Place of the
Apogee,
for the beginning of any Century, we may thereby find its mean Place to any time in the same Century also, without any other Assistance whatsoever.
THE Fifth Circle contains, along its spiral, the mean Motion of the Moon's Nodes; and particularly, of the Ascending Node whence the Numbers begin, for an intire Century, with its Months and Days; that so when we have, by a proper Table, once fix'd that Node right for the beginning of any Century, we may, as before, be hereby enabled to place it right at any time in the same Century, without any other assistance: Only we must here note, that the Motion of the Nodes being retrograde, the Numbers on this Circle are counted backward.
THE Sixth Circle contains, in a spiral, the mean Motion of the Moon for the several Days in the Year, number'd at length: And the Moon's mean Motion for the distinct Years of the Century are put at the utmost edge of the Circle, for our future Benefit in this Case also.
THUS far I have describ'd the largest and principal Circles, intended for the Discovery of the New and Full Moons; and especially for the Calculation of Eclipses, both Solar and Lunar.
AS to those six lesser Circles that follow to the Center, they need little Explication, being all of a piece; and are indeed nothing but broad
Annuli,
or Rings, to contain the Orbits of such of the Primary Planets as could be put upon them; with the Orbits of all the Secondary Planets, both those about
Saturn,
and those about
Jupiter,
in their due Proportions; that so, when the Sun is suppos'd in the Center, the Orbits of the Primary Planets may alone be made use of; when
Saturn
is there His; and when
Jupiter
is there His
Satellites
may alone be contemplated. Only we must here note several things, for the better understanding of this Part of our Instrument. (1.) Because
Saturn
and
Jupiter
's Orbits were too large for these inner Circles, they are represented by small Spheres, on the second and sixth larger Circles before describ'd; because
Saturn
's Motion is only about 12 Degrees in a Year, or one in a Month; as also
Jupiter
's only about 30 Degrees in a Year, or 2½ in a Month; there is no great necessity for these distinct Orbits, with their Motions, to be engrav'd upon these Circles; especially because of the Confusion it would introduce there. (2.) These Orbits are here Circular, or accommodated to the Planets mean Distances from the Sun; but so, that the present Places of the
Aphelia
and
Perihelia
are noted on the utmost edge of the whole Instrument, and the quantity of their several constant Eccentricities are also noted where their Orbits begin; that so the little Sphere representing each Planet, may be ever plac'd nearer to or farther from the Center, as its real Distance shall require; only the Eccentricities of the
Earth
's and
Venus
's Orbits are too small to be here sensible. (3.) These Orbits are all represented in the Plain of the Ecliptick, as it was here necessary to do: But then the present Places of the Ascending and Descending Nodes being set down at the utmost Edge, each Planet's Inclination to the Ecliptick, and Latitude on the Earth, may be nearly discover'd for this Age at the same time; I mean this, in case we observe the quantity of the several Angles of Inclination, which those Orbits make with the Ecliptick, which are as follows:
 
°
′
Saturn
02
30
Jupiter
01
20
Mars
01
52
Venus
03
24
Mercury
06
54
(4.) The seeming Motions of these
Aphelia
and Nodes in the Ecliptick, is only a Degree in 72 Years: 'Tis therefore but allowing to these
Aphelia
and Nodes that Motion of one Degree in 72 Years forwards, and their Places in the Ecliptick are known for all Ages. (5.) When
Saturn
's Secondary Planets are concern'd, the Sun is to be suppos'd in its proper Place of the Ecliptick, at the distance of 294 Feet from the Center of the Instrument: In which Case these Orbits are in true Proportions, with regard thereto. And when
Jupiter
's are concern'd, it is to be suppos'd, in the like place, at 16
Feet distance, for the same purposes. At which Points, if a Lamp be plac'd, and this Instrument be mov'd in a kind of Circular Orbit about it, we shall have a just and natural Representation of the Revolution of these Primary Planets, with their Satellites, about the Sun, both in their Annual and Menstrual Motions.
I COME now to shew the particular Uses of this Instrument: And shall do it in the Solution of the following PROBLEMS.
PROB. I.
LEMMA.
To Rectifie the first moveable Circle, or that of the Months and Days, to any Moment of Time, past, present, or to come.
TURN this Circle till the given Year, exactly corresponds to the
beginning of Aries,
in the outmost Circle; but so, that for the second Year after
Leap Year
you turn it farther one third; for the third Year two thirds of a Century's Motion
forwards
; and for the
Leap Year
one third
backwards,
beyond that beginning of
Aries.
Thus, if you would Rectifie this Circle to the time of the great Solar Eclipse this Year, which is the third after Bissextile, you would put a Point that is a little beyond
1701,
two thirds of a Century's Motion backwarder than the beginning of
Aries;
by which means this Circle will be entirely Rectify'd to the time.
PROB. II.
LEMMA.
To Rectifie the second moveable Circle, or that of the
Earth's Annual Orbit,
with its true
Anomaly
on it, to any time past, present, or to come.
THIS is readily done, by bringing its beginning to the time assign'd in the Arch; and is so easie and obvious, as to need no farther Explication. Only it must be noted, that this Place of the
Perihelion,
with regard to the Earth, is the Place of the
Aphelion,
with regard to the Sun; or the Place where when the Sun is, the Earth is most remote from it, whence every
Anomaly
is to be begun.
Thus if you add to
3 s. 7 d. 40 m.
the Place of the
Perihelion,
at the Commencement of this Century, or
1701,
those
12 m.
which is its Motion in
14
Years; you will have
3 s. 7 d. 52 m.
for the Place of the
Perihelion
at that time. To which if you bring the beginning of this Circle, you will have this whole Circle, with the Earth's true
Anomaly,
or Place thereon, exactly rectify'd to the time of that Eclipse.
PROB. III.
LEMMA.
To Rectifie the third moveable Circle, which is that of the Moon's
Apogee,
with its true
Anomaly,
or Place upon it, to any time, past, present, or to come.
LOOK in the proper Table for the place of the Moon's
Apogee,
at the beginning of the Century assign'd, and accordingly fix it: Count along the Spiral that is upon it the Years, Months, and part of a Month of that Century, and lay one of your Threads over that Place; then remove the
Apogee
to that Thread; this will exactly shew its mean Place. After this, observe how far the Sun is from the
Apogee
or
Perigee,
and whether it have lately gone past, or is going towards one of 'em, and turn the Circle accordingly forward or backward one third of that Distance. For in the former Case that quantity is to be substracted from, in the other added to the former Place, in order to have the true Place. I mean this only as we reckon 45
d.
for the Limit: And remember, that the fame Equation is to be substracted, or added, for any Number that is equally distant from that Limit; as for 40 and 50, 60 and 30, 70 and 20, 80 and 10, and so in all other Cases whatsoever. Only observe, that if nearest the Limit you take considerably less, and remotest from it a very little more than one third, you will still more exactly Rectifie this Circle.
Thus if you look for
A.D. 1701.
you will find the mean Place of the
Apogee
then to be
11s 8° 18′
and if you turn the Circle forward to
Apr. 22.
you will have the mean Place of the
Apogee
then. And if by turning still forwards, you add the third part of the Sun's Distance, or
7°
to the former Place, you will have the true Place of the
Apogee
at that time,
viz. 6 s. 27 d. 23 m.
PROB. IV.
LEMMA.
To Rectifie the fourth moveable Circle; which is that of the Moon's
Nodes,
for any time, past, present, or to come.
LOOK in the proper Table for the Place of the
Ascending Node,
at the beginning of the assign'd Century, and there fix it. Count along the Spiral thereon backwards, the Years, Months, and part of a Month of that Century, and lay your Thread over that Place: Then bring the beginning of the Spiral, or Ascending Node, to the Thread; which will give you the mean Place of that Node. Then turn the Circle forward a 20th part of the Sun's distance from either Node, if it have lately pass'd it; or a 20th part backward, if it have not yet pass'd it: This will fix the Nodes to their true Places at that time. I mean this also as we reckon here 45° the Limit; and remember, that the Equation is to be substracted or added for any Number that is equally distant from that Limit: Only Observe, that if nearest that Limit you take considerably less, and remotest from it somewhat more than 1/20, you will still more exactly Rectifie this Circle.
Thus, If you look for
A.D. 1701.
you will find the mean Place of the Ascending Node to be
4s 27° 24′.
Then turn the Circle backward to
Apr. 22d,
and you will have the mean Place of that Node there. And if by turning still backward, you substract a
20
th part of the Sun's distance, or
27
,
you will have the true Place of the Node at that time,
viz. 7 s. 21 d. 9 m.
PROB. V.
LEMMA.
To Rectifie the fifth moveable Circle; which is that of the mean Motion of the
Moon
it self, for every Day of a
Julian
Year, for any time, past, present, or to come.
LOOK in the proper Table for the
Mean Place of the Moon,
at the beginning of the Century assign'd, and there fix the Circle. Then look along the outward Edge of this Circle for the compleat number of Years of that Century, and laying your Thread exactly over that Year, remove the Circle so far. Then count along the Spiral upon it, the number of Days and Parts till the time assign'd; over which laying your Thread, remove the Circle so far. This rectifies the Circle of the Moon's Mean Motion for that time.
Thus if you look for
A.D. 1701.
you will find the Mean Place of the Moon to be
10 s. 15d. 20 m.
whither bring the beginning of the Circle accordingly. Lay then a Thread over the Number
14,
and bring the former Place thereto: Then is this Circle intirely rectify'd at that time.
Note, That the Moon's Motion in Hours is not distinguish'd here on the Spiral; because it may be better estimated on the Ecliptick it self.
Note farther, That when you go upwards, as in the Years before the Christian
Aera,
contrary to what is usual, you add the Mean Motions of the Node, and substract those of the Apogee and Moon it self to and from the Epocha, to prepare the Numbers for the Instrument. But then, if you thereupon chuse proper Numbers for the beginning of each Century before, as well as after the beginning of the Christian
Aera,
you will have no farther Difficulties in the use of the Instrument it self. Thus, if for the beginning of the
431
st Year before
Christ,
you take
500
Years backwards for the Epocha of the Century; and
69
compleat Years after it for the beginning of the Year it self, you will have no farther difficulty in the use of this Instrument in that case.
Note also, That the three last of these Circles will as well serve for a Century backwards as forwards, from any Root, or Epocha. I mean, if the known number
of Degrees for any number of Years backwards in the Century, be taken on the side of the Epocha contrary to that it belong'd to, if the Years had been forwards; as every one will easily find upon the least Consideration and Trial.
Note farther, That to make this Instrument as ready as possible for the present Century, the Epochae of the Places of the Moon's Apogee and Ascending Node, and of the Moon it self, at the beginning of it are noted by the following Marks upon the outmost Circle,
☉ ☊ ☽ ,
with Points at the opposite Places at the same time: And the like Marks may be made for any other Century, as occassion shall require.
Note lastly, That our Time is here always the Mean or Equal Time; which the more curious may correct by the known Equation-Table: But since this last is little more than a quarter of an Hour different from the other at the utmost, and almost always much less, it is rather too nice to deserve much Consideration in such an Instrument.
PROB. VI.
To find the
Sun
's True Place in the Ecliptick, for any time, past, present, or to come.
REctifie the two outmost moveable Circles. Look what Sign, Degree, and part of a Degree corresponds to the Time assign'd. Lay your two Threads over the first of
Aries,
and over that Place; and count the
same Number
along the Earth's Orbit, which you find belongs to that Number on the Ecliptick. This corresponds to the True Place of the Sun in the Ecliptick for that time.
Thus, if you look for
21 h. 42 m.
upon the Ecliptick on
Apr. 22
d. you will find over against it about
43 d. 30 m.
This reckon'd along the Earth's Orbit, reaches from
260 d. 10 m.
which is over against the Equinox, to
302 d. 35 m.
over against which last Number stands
12 d. 15 m.
of
Taurus;
which is therefore the Sun's True Place in the Ecliptick at that time.
PROB. VII.
To find the
Moon
's True Place in the Ecliptick, for any time, past, present, or to come.
REctifie the third and fifth moveable Circles. Lay one of your Threads over the Moon's Mean Place, and the other over the Moon's Apogee. Count along the Moon's Orbit the
same Number
which is intercepted between the Threads on the Ecliptick. A Thread laid over that Place, corresponds with the Moon's True Place in the Ecliptick.
Thus, if you look for
111 d. 21 h. 42 m.
on the fifth moveable Circle, you will find it is distant from the Moon's Apogee, along the Ecliptick, about
192 d. 40 m.
which Number, taken in the Moon's own Orbit, on the third moveable Circle, corresponds to
12 d. 15 m.
of
Taurus,
the True Place of the Moon at that time. But it is here to be noted, that when the Moon's Apogee is either in Conjunction or Opposition with the Sun, the Eccentricity of the Moon's Orbit is
the greatest; and the Points or Marks nearest the Apogee are the true ones: (which is nearly the Case in this Example, and accordingly made use of in it) and when it is in the Octants, that Excentricity is in a Mean, and the Lines and Numbers themselves are right; but when it is in the Quadratures, the Points or Marks nearest the Perigee are the true Places: And so in all other intermediate Positions whatsoever. Which Circumstances being consider'd, and proportionably allow'd for in all Cases, this Problem will be exactly solv'd.
PROB. VIII.
To find the True
Conjunctions
and
Oppositions
of the Sun and Moon, with the
New
and
Full Moons,
for any time, past, present, or to come.
REctifie the first, second, third and fifth moveable Circles, as before directed. After that find the True Places of the Sun and Moon for the time given, as before. If they are either the same, or directly opposite, you have the time already; if not, carry your Threads that lie over the two Places respectively, along their own Orbits, forwards or backwards; so that you carry the Moon's 13 Degrees and a quarter to the Sun's one; or a Day's Motion of one, to a Days Motion of the other; and so all along proportionally,
i.e.
somewhat above half a Degree to an Hour, till the Moon's Place overtakes the Sun's. For that Place where they are coincident, gives you the Conjunction or Opposition, with the New or Full Moon.
Thus, If you look for the Sun's Place at Noon,
Apr. 21.
which is, Astronomically,
21
compleat Days in that Month, you will find it about
11 d. 20 m.
in
Taurus.
And if, in like manner, you look for the True Place of the Moon at the same time, you will find it about
28 d. 40 m.
in
Aries:
Whence if you carry both the Threads so far as corresponds to
21 h. 42 m.
you will perceive that the Moon does there overtake the Sun; which shews, that at that very time, or
Apr. 22 d.
about a quarter before Ten in the Morning, the Sun and Moon will be in Conjunction, and it will be New Moon. But Observe, that if you do not at all know before-hand, at what time of any Month the Conjunction or Opposition will fall, you must find the distinct Places of the Sun and Moon at the beginning of the Month, and so go
downwards, as to the Days, as well as Hours, and parts of an Hour, till they are coincident; as has been just now directed; and you will thereby find the Day, Hour and part of an Hour of the next Conjunction or Opposition. You may also if you please, find the True Places of the Sun and Moon, to that last time, over again, as before directed; especially where there is a design to examin an Eclipse at the same time; for the greater Accuracy. But Note, that if you only intend to find the time of Conjunction or Opposition, in order to an Eclipse, you need not examin any Month or Days, but only such as are near one of the Nodes, or within the Limits of such Eclipses; which Limits will be stated under the next Problem.
PROB. IX.
To find whether there will be either a
Solar,
or a
Lunar Eclipse,
at any
Conjunction
or
Opposition,
for any time past, present, or to come.
ALL the Circles first rectify'd, and the Time and Place of the True Conjunction or Opposition found, as already directed, Lay one of your Threads over that Place, and the other over the nearest Node. If that Distance be less than 16 Degrees and an half, and it be a Conjunction, there will be an Eclipse of the Sun somewhere: If it be greater, there will be no Eclipse. If that Distance be less than 10
d.
38
m.
and it be an Opposition, there will be an Eclipse of the Moon: If it be more, there will be no Eclipse.
Thus, it happening this Year
1715.
that the Sun and Moon are in Conjunction, about a quarter before Ten o' Clock, on the next
22 d
of
April,
and that at
8 d.
distance from the Descending Node; it is evident there will at that time happen an Eclipse of the Sun. And there happening an Opposition
October 31st,
about a quarter past
4
in the Morning, within
7
Degrees and an half of the same Node, 'tis evident there will then be an Eclipse of the Moon also.
Note here, that several other Circumstances of Eclipses, may be discover'd by the Solution of this Problem. Thus, because the Conjunction for the next Solar Eclipse happens
before
the Moon has reach'd its Descending Node, 'tis plain, it must belong to the Northern Parts more than to the Southern. Because it is in a sort of a Mean Distance between that descending Node and the Limit, it will be a great and Total Eclipse, and the greatest in the Northern Temperate Zone. Because it happens near the
Aphelion
of the Earth, and near the
Perigee
of the Moon, when the apparent Diameters of the Sun is smaller, and of the Moon greater than usual, it will not be Annular, but Total, and that for some few Minutes also; I mean along that Line, which the Center of the
Penumbra
describes upon the Earth. And because the Solar Eclipse this Year happens here in the Daytime, and the Lunar in the Night, they will both be visible; I mean, in
case the Cloud cause no interruption. So that these Circumstances do not need Particular Problems for their Solution.
PROB. X.
To Rectifie the Globe, and its Hour Circle, for the
Exhibition
of Eclipses.
BRing
London
to the graduated side of the Meridian, and turn the Hour Circle till 12 o' Clock is pointed to by its Index: Then turn the Globe, with its Hour Circle, so far forward or backward, as the right Ascension belonging to the Distance of the Place of the Conjunction, from the beginning of
Cancer
or
Capricorn,
does require; reckoning still 15 Degrees to an Hour, and 1 Degree to 4 Minutes. Hold the Globe in that Position, and bring 12 in the Hour Circle, to the graduated edge of the Meridian again, and there fix it fast, to move with the Globe all along afterward. By this means the Index will tell you the true time, as it is counted at the Meridian of
London,
during the whole time of the Eclipse. And Note, that the Distance from
Cancer
or
Capricorn
it self, if increas'd or diminished one 13
th
part, or one Degree in 13, according as the Position of the Sun and Moon shall require, will nearly give the Right Ascension; reckoning the Limit 45, as under the 3
d
and 4
th
Problems, and increasing or diminishing the Equation as there also. But Note, that this Distance it self will never err 2
d.
30
m.
or 10 Minutes in time, from the Truth; nay, will usually be much nearer the same, even without any Allowance for that Correction at all.
Thus if you bring
London
to the graduated edge of the Meridian and the Hour of
12
to the Index; and remove the Globe, with its Hour Circle, backward from East to West
50
Degrees,
i.e. 3
Hours
20
Minutes; and then turn the Hour of
12
to the Index again, and there fix it, you will have the Globe, with its Hour Circle, rectify'd for the time of the next Total Eclipse of the Sun, and every part of it will agree to that Hour which the Index shews on the Hour Circle.
PROB. XI.
In any
Solar
Eclipse, consider'd in general, and with regard to the whole enlightened Disk of the Earth, to find when and where it will begin and end; whether it will be any where total, or every where only partial; and, if partial, how many Digits will any where be Eclipsed; with the other general Circumstances of the same.
TAKE the eleventh part of the Distance of the Place of the Conjunction from the nearest Node, for the Latitude of the Moon at the middle of the Eclipse. Remove the inner Circles; and elevate the Globe that stands beneath them, North or South, as the Case shall require. By the side Screws place it in the Center or Axis of your Circles. Lay your Rule, with its Glass of 12 Circles (then set over its middle Point) and its Lamp or Candle, so that the Node may lie in a Position suitable to that of the Moon's Orbit at that time (which is easily known from the Observations under the last Problem); and so, that the middle Point, or that under the Center of the Glass, may be directed to the Place of the Conjunction in the Ecliptick. Turn your Globe, rectify'd as before, till the Index points to the time of the True Conjunction, already found; That is very nearly the time of the middle of the general Eclipse. Then turn your Globe, and draw your Glass backwards any number of Minutes equally; so that an Hour in the Hour Circle may ever correspond to an Hour in the Path of the Moon; and till the Shadow of the edge of the Circular Glass begins to touch the nearest Place of the Globe; for that is the Time, and that the Place, when and where the general Eclipse begins. Carry both Motions forward, and observe, whether the Central bright Spot does any where touch the Globe; if it does not, the Eclipse is no where Total, and the Circles cast on the Globe will shew the number of Digits eclips'd: If it does touch, note the Time and Place when and where it does so; for that is the Time, and that the Place of the entry of the Central Shadow, or total Darkness upon the Earth. Do the like as to the Central Spot, or other edge of the Circles going off the Globe afterwards; this will, in like manner, shew the Time and Place of the end of Total Darkness, and of the whole Eclipse respectively And by this means all the other Circumstances of the general Eclipse of the Sun, may be most easily and readily discover'd and exhibited to the Eye, with the greatest Pleasure and Satisfaction.
Thus, in the next great Solar Eclipse, consider'd in general, you will find that it will begin in
17 d.
of North Latitude, and about
90 d.
westward from
London;
and this about
21 m.
after
7,
and will end in the Latitude of
40,
about
98 d.
to the East of
London;
and this at
3 m.
after
12.
That it will be a Total Eclipse for about
150
Miles in breadth, and that the Center of the
Penumbra
will go near the
Lizard
Point,
Bristol, Stamford
and
Boston;
and so by
Stockholm
and
Archangel,
into
Russia, Siberia,
and
East Tartary.
Note, that if instead of a Lamp, or Candle, you make use of the Sun it self; either by placing the Instrument so, that the Rays
may themselves fall parallel to the Axis of the Glass, or that they may be inclin'd to it by a reflecting
Speculum,
or Looking-glass, it will be better.
Note also, that if with a Pencil, put thro' the Axis of the Glass, you draw a Line; or with a sharp Pin or Needle therein, make Points upon the Globe, as you move it and the Glass together, you will have the Path-way ef the Center transferr'd upon the Globe; and may thereby exactly find all the Places where the Eclipse will be Total, or Annular, or Central; and may easily see, from the like Lines drawn, or Marks made at any number of Digits distance, how broad the Path of any kind of partial Eclipse will be also over the whole Earth; which how entertaining and useful a Sight it may be to all the Curious, I leave to their own Trial and Determination.
Note also, That the Problem, thus solv'd, includes one main part of that famous Discovery of Sir
Christopher Wren
's, Dr.
Halley
's, and Mr.
Flamsteed
's, publish'd by the last, and nam'd,
The Construction of Solar Eclipses,
without the tedious Method of Calculation. Only what they are forc'd to do with no small pains, and in no short timegeometrically, is here done with great ease and quickness and an exact imitation of the Originals in Nature, and so with a great deal more Pleasure and Satisfaction.
PROB. XII.
In a
Solar Eclipse,
consider'd in particular, and with regard to any single Place, to find when it did, or will begin and end; whether it was or will be there Total or Partial; and if Partial, how many Digits were or will be Eclipsed: With the other particular Circumstances of the same in that Place.
THIS Problem is, in effect, already solv'd, under the former Problem: It being as easie to observe when the Shadow of the edge of the Glass-Circle first touches, or last leaves any Place upon the Globe; which is the beginning and ending of the Eclipse there: when the bright erect Line crosses it, which is its middle there: How near any Circle of Digits comes to it then: Which is the number of Digits Eclipsed there: With other the like Circumstances of that Place, as it was before to observe the same for the Eclipse in general. Nor is there any occasion for farther Directions.
Thus the next great Solar Eclipse will begin here at
London, April 21.
about
8 h. 7 m.
in the Morning; its middle will be about
9 h. 13 m.
its end about
10 h. 24 m.
and it will be intirely, or very nearly Total: tho' if it be Total here, it cannot be so for much more than a single Minute of Time; as Dr.
Halley
's particular Map, fitted for this Eclipse, will easily show.
Note, that if in the Solution of this, and the foregoing Problem, you add for East, and substract for West Longitude, resolved into Time, you will have the Moment of each of these Appearances at any other Place also.
Note also, that the Problem, thus solv'd, includes the remaining part of the foremention'd famous Discovery of the
Construction of Solar Eclipses;
and that not only as done with the like greater ease, quickness and pleasure, but principally that with the same operation, and without any new trouble, it discovers every thing for
all particular Places
at once; which neither that Method of
Construction, nor any other Method of
Astronomy
whatsoever could pretend to before. And yet all this is here done only by such a close imitation of Nature, as is in it self most easie and obvious, and what one would now imagin should have come into the Thoughts of
Astronomers
first of all, before any other Contrivance whatsoever.
PROB. XIII.
In a
Lunar
Eclipse, to find whether it was or will be Total or Partial; and if Partial, how many Digits were or will be Eclipsed; which of the Lunar Spots and Mountains were or will be obscured; and when they did or will begin or end to be so: How long the Entire, or Central, or Partial Eclipse will last. With all the other Circumstances of the same.
TAKE away the Globe, and set the Dark Circle in its Place. Take also the Glass of 12 Circles away, and put the Map of the Moon, with its 6 Circles, in its Place. Then do in all things with this Map of the Moon, as you were order'd to do with the Glass-Circle Circle before. By this means you will have all those
Phaenomena
of Lunar Eclipses solv'd, with greater ease, and the like pleasure, which were before represented in the Solar. Nor is there any new difficulty in the Application. Only Note, that this Map of the Moon being too small to have the Names of its several Seas and Lands engraven on it, it will be convenient to have withal a larger Map of the Moon, with those Names, as an Explication of the other; which accordingly is here provided, and plac'd on one side of the dark Circle, which is us'd with it. And Note farther, that those who have a mind to be here very particular and exact, may use the larger Map of the Moon instead of the other, in case they join with it a dark Circle of 16 Inches and a quarter in Diameter: For the same Proportion which the Diameter of our smaller Moon of two Inches and an half, bears to that of our dark Circle of six Inches and two fifths, does the Diameter of that Circle, or of the larger Moon bear to that of a Circle of sixteen Inches and two fifths Diameter. Whence its plain, the larger Moon, and that largest Circle, will more exactly exhibit such Lunar Eclipses than the other. Tho' I believe there will be but few, who will not be satisfy'd with the smaller dark Circle; so I have not provided the larger: Which yet Mr.
Senex,
or Mr.
Hudson,
the exact Engraver and Framer of this Instrument, will readily procure for any that desire them But then the several Circles concern'd must be ever so adjusted, that the perpendicular of their Centers may still be the same with the Latitude of the Moon at the middle of the Eclipse; and that as measur'd by a Scale, which is so much larger than ours, as their Diameters are larger.
Thus we shall find by this Instrument, that there will be an Eclipse of the Moon this Year,
Octob. 31.
that it will not be a Total, but a Partial Eclipse; that the Digits eclips'd will be
8,
and this on the North side of the Moon's Body: That the Eclipse will begin about
2 h. 58 m.
and end about
4 h. 40 m.
in the Morning; and that Mount
Aetna
will enter the Shadow about
3 h. 8 m.
and emerge about
5 h. 17 m.
Note those that would exactly imitate Nature in these Lunar Eclipses, must let the Globe stand, and have a Lamp or Circle of Light, larger in Diameter than the Globe, through whose Shadow the Map of the Moon must pass. They ought also to have different Maps of the Moon out of
Hevelius,
to fit the different Librations of the Moon, or the small variety there is in that Face which is expos'd to us in different Eclipses. But since this Method would be much more troublesome, and but little more advantageous or entertaining, I chose the former easie way of exhibiting these Lunar Eclipses by this Instrument, leaving the other to those among the Curious, who shall think fit to bestow any extraordinary cost and trouble about it.
But Note, That the Diameters of the
Penumbra,
and of the Moon, are here still fitted to their Mean Quantity, when the Earth and Moon are about the shorter Axis of their Ellipses: So that when they are near their Aphelion and Apogee, their Perihelion and Perigee; or the Earth its Aphelion, and the Moon its Perigee; the Earth its Perihelion, and the Moon its Apogee; some small Differences will arise in the Business of Eclipses; which yet may easily be allow'd for on a little consideration. Thus the next visible Eclipse of the Sun happening somewhat near the Earth's Aphelion, and nearer the Moon's Perigee, as the Position of their Orbits at that time in this Instrument will shew; the Moon will appear a little larger, and the Sun
a little smaller than ordinary; whereby the Sun will be about
3
Minutes and
3
quarters under a total Eclipse, all along the Central Path of the Moon's Shadow, and the
12
Digits on your Glass will not include the whole. In this Case you are to suppose all the Circles
2
thirds of a Digit inlarg'd, and the Central Digit so much broader. Thus the next invisible Eclipse of the Sun,
Octob. 16.
happening somewhat near the Earth's Perihelion, and nearer the Moon's Apogee; the Moon will appear somewhat less, and the Sun somewhat greater than ordinary; so that this Eclipse will be only Annular, and not Total, and the Digits Eclipsed will not be quite
12.
In this case you are to suppose all the Circles diminish'd
2
thirds of a Digit, and the Central Digit so much narrower; and the like Allowances are to be made in the Numbers upon the Path of and perpendicular to the Moon's Shadow, in the Diameter of the Moon's Map, in the Duration of Eclipses,
&c.
which must be left to every curious Person's own estimation; only with this intimation, that these Differences from the Standards here given are ever so small, and commonly so insensible, that they may be well look'd on as almost perfectly inconsiderable in the use of this or the like Instruments.
Yet the Latitude of the Moon will sometimes well deserve an allowance; and may be corrected by taking not much above a
12
th part of the distance from the Node, near the Moon's Perigee, and almost a
10
th near its Apogee, instead of that
11
th part, which is the usual standard:
whence at this next Eclipse the real Latitude of
44 m. 10 s.
will be here represented by
41 m. 40 s.
on our Scale; and so proportionally in all Cases whatsoever.
SCHOLIUM.
Since the Computation and Exhibition of all Eclipses, past or future, is by this Instrument become now so very easie, it will be fit to examin thereby all the old Eclipses men ioned by Historians, and to compare them with Original Accounts, for the settling all Ancient Chronology and History; which Design was the very Occasion of the Contrivance of the same. In particular, it will be fit to examin hereby the very old pretended Eclipses, mention'd in the
Chinese
Records; and to see how far they will agree with the Real Eclipses of those remote Ages. Which may be also one valuable use, as to Lunar Eclipses at least, of the acute Dr.
Halley's
Tables for the Periodical Returns of Eclipses; which he has given us a Specimen of already, and which we shortly expect the Completion of from him.
PROB. XIV.
To find the
Heliocentrick
True Places of all the Primary Planets, for any time, past, present, or to come.
BY the help of the proper Tables, which are publish'd in my Astronomy, find the true Place of each Planet, as is there directed: From thence you may set them accordingly by this Instrument.
Thus for Example, Let us compute the Heliocentrick Place of
Mercury
to the Time of the next great Solar Eclipse.
See Astron. Lect. Edit. Lat. p. 302, 303. 304. Eng. p. 337, 340.
 
s.
°
′
1701
8
04
02
Years
14
1
14
06
Apr.
0
08
19
Days
21
2
25
56
h. 21
0
03
35
m. 42
0
00
07
Anom. Med.
0
26
05
Long. Hel.
8
01
15
Add. Preces. Aequinoct.
0
29
08
True Place of
Merc.
9
00
23
But because this Method is not wholly free from the trouble of Calculation, you may frequently help your self by some good
Ephemeris;
such as is annually set out by Mr.
Parker;
whence you may readily transfer the Heliocentrick Places of the Planets into your Instrument. Accordingly, by either Method, at the Time of the next Solar Eclipse the six Primary Planets Heliocentrick Places will appear to be these:
 
s.
°
′
Saturn
05
22
42
Jupiter
01
03
38
Mars
07
06
41
Earth
07
12
15
Venus
09
11
09
Mercury
09
00
23
PROB. XV.
To find the
Geocentrick
Places of any of the Primary Planets, for any time, past, present, or to come.
HAving found, as before, the
Heliocentrick
Places of the other Planets, and particularly that of the
Earth,
noted all by several small Spheres, and having allow'd for their proper Eccentricities in the sticking of those Spheres, Lay one of your Threads from the
Earth
to the Planet, and the other Thread laid parallel thereto from the Center, gives you the
Geocentrick
Place of that Planet for the time assigned.
Thus, at the forementioned Time, the five Primary Planets
Geocentrick
Places will be nearly these:
 
s.
°
′
Saturn
05
17
44
Jupiter
01
05
07
Mars
06
26
42
Venus
11
27
51
Mercury
00
16
21
PROB. XVI.
To find the
Mutual Aspects
of all the Primary Planets with one another, and with the
Sun
and
Moon;
their
Conjunctions, Oppositions, Trines, Quartiles
and
Sextiles,
both
Heliocentrick
and
Geocentrick,
for any time, past, present, or to come.
THIS is easily done when the Places themselves of the Primary Planets, with that of the Moon, are once found by the former Solution. Nor is there then any difficulty in noting the several Angles of distance 120°, 90° and 60°, which make the
Trine, Quartile
and
Sextile Aspect.
But this Problem looks too like the Fooleries of
Astrology,
to deserve any nicer Explication.
PROB. XVII.
To find whether any Primary Planet, with its Satellits, be Direct, Stationary or Retrograde, at any time past, present, or to come.
HAving found the
Heliocentrick
and
Geocentrick
Places of the Planets, and set small Spheres to represent 'em: From the Sphere representing any Planet lay two Rules or Threads, so as to touch the Earth's Orbit on both sides. If the Earth be considerably
without
that mixtilinear Triangle, the Planet is Direct; if considerably
within
it, it is Retrograde; if
about the Limit,
it is Stationary: or at least lately was, or soon will be so. Nor can you by this means absolutely determin, near those Limits, whether the Planet be Direct, Stationary, or Retrograde. But then, by finding its Geocentrick Place two several times within a few Days of one another, and observing whether the Planet at the latter time be farther, or in the same Place, or not so far in the Ecliptick as it was at the former time, you may entirely determin the Problem. Nor is the Case of the Inferior Planets much different from that of the Superior ones, as to this matter. Only Note, that the Rules or Threads must be laid from the Earth to touch their Orbits; which is the
Station,
or Limit of the
Direction
and
Retrogradation
of those Planets, and is call'd their
utmost Elongation
; and that the Inferior Planets Position near those Limits, are here correspondent to the Earth's Position in the Superior. Nor is this a Case of such difficulty, as to require any nicer Consideration.
Thus, at the time of the foremention'd Eclipse, we shall find by this Method, that
Saturn
and
Mars
will be Retrograde; and that
Jupiter, Venus
and
Mercury
will be direct.
PROB. XVIII.
To find the Places of the
Circum-Saturnals
and
Circum-Jovials
from their Opposition to the Sun, at any time, (since their Motions have been known) past, present, or to come.
FIND the Place of
Saturn
or
Jupiter
in the Ecliptick, for the given time, as before. Then, by the proper Tables of their Satellits Motions about them, when they shall be made; (for we have only one Set of such Tables yet publish'd, and render'd fit for our purpose; I mean those of
Cassini
for
Jupiter
's innermost) fix the beginning of their Orbits, or the small Spheres stuck there to represent those Satellits: Place also, or imagin a Lamp, or Candle, at the distance of about 160 Feet for
Saturn,
and about the same number of Feet for
Jupiter.
By this means you will have a true and noble Representation of these Systems of Secondary Planets at any time whatsoever.
PROB. XIX.
To find the Eclipses of these Secondary Planets, for any time (since their Motions have been known) past, present, or to come.
THE time of Opposition is the time of the Middle of any Eclipse; and by taking away and adding the half duration of that Eclipse, you have the time of the Immersion and Emersion. 'Tis plain therefore, that finding the Opposition, does, in effect, find the Immersions, Emersions, and intire Durations of those Eclipses also.
Note, that the time of half Duration in
Jupiter
's innermost, which is the most remarkable Satellit in this matter, is nearly
1 h. 6 m.
and so the whole Duration about
2 h. 12. m.
perpetually.
Note farther, that only one of these Appearances, the Immersion or Emersion of a Satellit, is generally visible at the same time;
viz.
the Immersion from the Conjunction of the Primary Planet with the Sun till its Opposition; and the Emersion from its Opposition till its Conjunction.
Note also, that till we have more exact and suitable Tables of the rest of these Secondary Planets, it will be proper, two Nights successively, to observe the Position of as many as we can of them; and from those Observations to fix their Places, with relation to their Primary ones, to those times. For since their Orbits, on our Instrument, gives their several Periods exactly enough; from those Periods their future Places and Positions may be found by two such Observations, for a great while; and such Positions may be with pleasure enough compar'd with a great number of other Observations afterwards. Nor do we wholly want an Astronomical Method, as to the most useful of these Secondary Planets, which is the innermost about
Jupiter;
since the Tables necessary for placing the same right, and for the Eclipses for some Years to come, tho' too large for this small Manual, are publish'd in my Astronomy, with full Directions for their use also; to which I must refer the curious Reader.
Note farther, that we are generally to look for only one of
Saturn
's Satellites; there being few Glasses that can shew us any more; and none but those of the famous
Cassini
that can discover the two innermost.
Note here, that
Jupiter
's Planets are all in or near the Plain of his Equator, which is near the Plain of the Ecliptick it self; and that they are hardly at all Eccentrical. That
Saturn
's most visible Planet, discover'd by
Hugenius,
is the fourth in order, or the outmost but one: as also that its Planets are in or near the Plain of its Ring, which is about
31
deg. inclin'd to the Ecliptick; and that they do not any of them appear to be very much Eccentrical neither.
And note, that our Terrestrial Globe may be so contriv'd, that it may be also us'd with an Horizon, as any other Terrestrial Globe may; and by consequence, those who buy its Celestial Fellow, may at the same time have a
Pair of Globes,
as well as a
Copernicus;
which will at once save almost all the Charges of one Globe; and afford a Foundation for the understanding of both the principal parts of
Astronomy
also, I mean
the Doctrine of the Sphere,
to which the Globes; and
the Theory of the Planets,
to which our
Copernicus
does immediately belong.
Note lastly, That all who purchase this
Copernicus,
and desire to have it explain'd more distinctly to them, according to the Directions in this Paper, may apply themselves to the Author; who will endeavour to make the several Parts and Uses of it easie and familiar to them.
Mar. 18. 1714/15.
Will. Whiston
ERRATA.
PAGE 2. Line 21.
read
5° 37′ p. 6. l. 10, 12.
r.
backwards; l. 15.
r.
forwards; p. 11. l. 19.24.
r.
about 160.
APPENDIX.
IN this
Appendix
I have set down those
Astronomical Tables,
which are chiefly necessary, in order to the ready Use of the present Instrument: And they are, 1. A Table of the
Mean Place
of the
Apogee,
and of the
Ascending Node
of the
Moon's Orbit,
as well as of the
Moon
it self, at the beginning of every Century for 1000 Years before, and ever since the Christian
Aera.
2. A Table of the middle of the general
Eclipses
of the
Sun,
within some Hours under or over, for above half this Century. This is deriv'd from Dr.
Halley
's SAROS, or very useful Table of the first 18 Years of the same Century; and will save some trouble in the use of this Instrument, and indeed in any other method of Calculation for the same purpose; which must needs be shortened by knowing the Time so nearly as is here specified. 3. A like Table of the middle of the
Eclipses
of the
Moon,
for the same interval, and deriv'd from the same Original; as well as serving to the like purpose with the former. The rest of the Astronomical Tables, any way necessary in this Instrument, may be found at the end of my
Astronomical Lectures,
which are now published both in
Latin
and
English.
Astronomical Tables.
I. A Table of the Mean Place of the
Moon's Apogee
and
Node,
and of the
Moon
it self, in the beginning of the several Centuries, before and since the Christian
Aera.
Before Christ
Apogee
Node
Moon
s.
°
′
s.
°
′
s.
°
′
1000
9
0
15
5
19
29
9
13
39
900
0
19
26
1
6
17
7
21
30
800
4
8
37
8
22
6
5
29
20
700
7
27
49
4
7
54
4
7
10
600
11
17
0
11
23
44
2
15
1
500
3
6
11
7
9
32
0
22
51
400
7
25
22
2
25
21
9
0
41
300
10
14
33
10
11
9
9
8
32
200
2
3
45
5
26
58
7
16
23
100
5
22
56
1
12
47
5
24
13
A.D 1
9
12
7
8
28
36
4
2
3
101
1
1
18
4
14
25
2
9
53
201
4
20
29
0
0
14
0
17
43
301
8
9
40
7
16
3
10
25
34
401
11
28
52
3
1
51
9
3
24
501
3
18
3
10
17
40
7
11
15
601
7
7
14
6
3
29
5
19
5
701
10
26
25
1
19
18
3
26
56
801
2
15
37
9
5
6
2
4
46
901
6
4
48
4
20
55
0
12
37
1001
9
23
59
0
6
44
10
20
27
1101
1
13
10
7
22
33
8
27
17
1201
5
2
21
3
8
21
7
6
7
13O1
8
21
32
10
24
10
5
13
58
1401
0
10
44
6
10
59
3
22
49
1501
3
29
56
1
25
47
1
29
39
1601
7
19
7
9
11
36
0
7
29
17O1
11
8
18
4
27
24
10
15
20
II. A Table of the general
Eclipses
o
the
Sun,
within less than a Day under or over, till
Ann. Dom.
1754
A.D.
Days current at Noon.
1701
Jan.
27
Jul.
24
1702
Jan.
17
Jul.
13
1703
Jan.
6
Jul.
3
Nov.
27
Dec.
27
1704
May
2
Nov.
16
1705
May
11
Nov.
5
1706
Apr.
30
Oct.
25
1707
Mar.
22
Apr.
21
Sept.
14
Oct.
14
1708
Mar.
11
Sept.
3
1709
Feb.
28
Aug.
24
1710
Feb.
17
Aug.
13
1711
Jan.
7
Feb.
6
Jul.
4
Dec.
28
1712
Jun.
22
Dec.
17
1713
Jun.
11
Dec.
6
1714
May
2
June
1
Oct.
27
Nov.
26
1715
Apr.
22
Oct.
16
1716
Apr.
11
Oct.
4
1717
Mar.
31
Sept.
23
1718
Feb.
19
Mar.
20
Aug
14
Sept.
13
1719
Feb.
8
Aug.
4
1720
Jan.
28
Jul.
24
1721
Jan.
16
Jul.
13
1722
Jan.
6
Jun.
2
Nov.
27
1723
May
22
Nov.
16
1724
May
11
Nov.
4
1725
Apr.
2
May
1
Sept.
25
Oct.
24
1726
Mar.
22
Sept.
14
1727
Mar.
11
Sept.
4
1728
Feb.
28
Aug.
24
1729
Jan.
18
Feb.
16
Jul.
15
1730
Jan.
7
Jul.
4
Dec.
28
1731
Jun.
23
Dec.
17
1732
May
13
Jun.
11
Nov.
6
Dec.
6
1733
May
2
Oct.
26
1734
Apr.
22
Oct.
15
1735
Apr.
11
Oct.
5
1736
Feb.
29
Mar
31
Aug.
25
1737
Feb.
19
Aug.
15
1738
Feb.
8
Aug.
3
1739
Jan.
27
Jul.
23
Dec.
18
1740
Jan.
16
Jun.
4
Dec.
8
1741
Jun.
3
Nov.
28
1742
May
21
Nov.
15
1743
Apr.
12
May
11
Oct.
5
Nov.
4
1744
Apr.
2
Sept.
25
1745
Mar.
23
Sept.
15
1746
Mar.
10
Sept.
3
1747
Jan.
28
Feb.
27
Jul.
25
1748
Jan.
17
Jul.
15
1749
Jan.
8
Jul.
4
Dec.
29
1750
May
23
Jun.
21
Nov.
16
Dec.
16
1751
May
12
Nov.
5
1752
May
3
Oct.
26
1753
Apr.
23
Oct.
16
1754
Mar.
10
Apr.
10
Sept.
4
Oct.
3
III. A Table of the
Eclipses
of the
Moon,
within less than a Day under or over, till
A.D.
1754.
A.D.
Days current at Noon.
1701
Feb.
11
Aug.
7
1702
Dec.
23
1703
Jun.
18
Dec.
2
1704
Jun.
6
Nov.
30
1706
Apr.
17
Oct.
10
1707
Apr.
6
Sept,
30
1708
Mar.
25
Sept.
18
1710
Feb.
2
Jul.
29
1711
Jan.
23
Jul.
18
1712
Jan.
12
Jul.
7
1713
May
28
Nov.
21
1714
May
18
Nov.
10
1715
May
7
Oct.
31
1717
Mar.
16
Sept.
9
1718
Mar.
5
Aug.
29
1719
Feb.
23
Aug.
18
1721
Jan.
2
Jun.
28
Dec.
22
1722
Jun.
18
Dec.
11
1
24
Apr.
27
Oct.
21
1725
Apr.
16
Oct.
10
1726
Apr.
5
Sept.
30
1728
Feb.
14
Aug.
8
1729
Feb.
2
Jul.
29
1730
Jan.
23
Jul.
18
1731
Jun.
9
Dec.
2
1732
May
28
Nov.
20
1733
May
17
Nov.
10
1735
Mar.
27
Sept.
21
1736
Mar.
15
Sept.
9
1737
Mar.
6
Aug.
30
1739
Jan.
12
Jul.
8
1740
Jan.
1
Jun.
29
Dec.
22
1742
May
7
Oct.
31
1743
Apr.
26
Oct.
20
1744
Apr.
16
Oct.
11
1746
Feb.
25
Aug.
18
1747
Feb.
13
Aug.
8
1748
Feb.
2
Jul.
29
1749
Jun.
20
Dec.
13
1750
Jun.
7
Dec.
1
1751
May
28
Nov.
20
1753
Apr.
7
Oct.
2
1754
Mar.
26
Sept.
19
FINIS.