The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

SECT. III. Of the Moon. (Book 3)

HAving now finish'd with the Sun, wee'l make a step, if you please, to the Moon, and show you how to resolve all the useful ordinary Questions concerning her, whether we see her by Night or by Day; for 'tis equal to us whether she shines out right, and consequently casts a shade, or appears only faint and wan, by reason of thin Clouds, or by the excess of Light during the Sun's aboad above the Horizon. Let us then begin with her Almucantar and Azimuth, as being the Basis and Foundation of all Operations here relating to her; nor can there be the least difficulty in any of them▪ unless perchance in the 7th.

since they have so great a Correspondence and affinity with those already handled in the former Sections.

OPERATION I. To find the Moon's Almucantar or Height.

THIS is to be perform'd as well when she cast's a shade, as when she cast's none, by the two first ways of finding the Suns Almucantar, and therefore consult the * 1.1 second Operation in the first Section.

OPERATION II. To find the Moon's Azimuth.

THIS is also to be found by the two first ways of finding the Sun's Azimuth, treated of in the * 1.2 5th. Operation of the first▪ Section.

OPERATION. III. To find her true place on the Globe.

IF she casts no shade, her place is to be found by her Al∣mucantar and Azimuth, as we hinted in the * 1.3 6th. Ope∣ration of the first Section, since she must ever be where these two Circles intersect; But if she shines out cleer, you have nothing to do (having plac't your Globe on a Meridian Line) but to see what hour the shade of the enlightned Pole, or that of your String (passing over both Poles) mark's; for this giving you her hour-Circle (which we'l call the Lunar hour hereafter) her height or Almucantar must needs tell you in what part of the said Circle she resides. This Ope∣ration is to be well understood and readily perform'd, seeing

most that follow are as it were Corollaries from it; and for the better illustrating and explaining them, we will imagine the Moon's Place to be in the hour Circle of 2 in the After∣noon, about 43 Degrees above the Horizon.

OPERATION IV. To know the Moon's Declension from the Aequator.

THIS is only the nearest distance of her true Place from the Aequator, which your Bead or Compasses will show you to be about 12 Degrees Northward, if (according to the foregoing Example) she be 43 Degrees high, in the hour Circle of 2 in the afternoon.

OPERATION V. To find the Moon's Diurnal Parallel, and consequently how to Compose the Globe by the Moon.

BY the Moons Diurnal Parrallel I mean a real or ima∣ginary Circle Parallel to the Aequator, and answera∣ble to her present Declension, which by the former Operation we suppose to be about 12 Degrees; Having therefore this▪ Parallel you may compose the Globe by the Moon, as you do by the * 1.4 Sun.

And here you must remember, that tho' the finding of the Parallel implies at first a Meridian Line, yet the knowing how to compose thus your Globe will not be useless; for now you are no longer confin'd to one Place or Line, but may compose it where you please by the help of the said Parallel.

OPERATION. VI. To find the Moon's Bearing according to the Points of the Compasse.

THIS is to be perform'd after the way of finding the Sun's Bearing, in the * 1.5 7th. Operation of the first Section; for if you draw your String from the Zenith over the Moons present Place, the said String cuts (by our Example) the Ho∣rizon at S. W. and some few Degrees towards the South for her then Bearing.

OPERATION VII. To know what a clock it is by the Moon.

THere is no Operation treated of so intricate as this, and therefore if the Reader (who would have his Curiosity satisfy'd) has not Patience enough to descend to a little niceness, he had better▪ fall upon another Subject; but tho' we may be somewhat long at first, in laying down and explicating all Parti∣culars, yet at the end we will contract the whole into half a do∣zen Lines, and thereby make the Operation very expedit, and easy; I say, there is no Operation so intricate as this; for, the Moon by reason of her different Place in her Epicicle, is so in∣constant in her dayly Elongation from the Sun, that sometimes she spends from (v. g.) her Conjunction to her first Quar∣ter above 8 days, tho▪ at another time a great deal less than 7 will serve the turn; and to this variety and skittishness is the space also between any of her other changes liable. If then her distance from the Sun be so uncertain, and yet is the thing that must be known before her Place, or shade on the Globe can give us the hour seek▪ how strangely fallible is the usual way (as well in some Authors of Note, as in ordinary Almanacks) of finding it, to wit, the adding of as many 48 minutes to the hour she shows on a Dial, as she is days old; for the Tables, made in pursuance of this Rule, suppose her always on the 15th of her

Age to be at Full, which may happen (as I now mention'd) not only much sooner, but also much later, so that most common∣ly her true Age and the said Tables are at variance; nay, when they agree, there can be no Reliance on them, seeing that if (v. g.) at 6 they show tolerably what a clock it is, yet by 12 there may happen an Error of near a Quarter, by reason that she is every moment at a new distance from the Sun, and at one also which presently becomes very sensible. Thus therefore we see that there must be Exceptions and Restrictions in any one Rule that appertains to this business; nor is it to be per∣form'd by an Instrument in a trice, as the Operations common∣ly are belonging to the Stars, that have a Regular motion, or to the Sun, whose Extravagance is not soon perceptible; I say, thus we see that there must be here Exceptions and Restricti∣ons, and in truth nothing but a down right Astronomical Cal∣culation can really perform it; yet since such a critical Exact∣ness in the hour is never necessary in our ordinary affairs, I shall propose this method, which will at least come always very near the Mark.

When you desire to know what a clock it is by the Moon,* 1.6 take an Almanac (for if you would only have her true Age, you must recur to one, or to something analogical) and reckon therein how many dayes there are in the present Quarter from one Change to the other, i. e. from New Moon to her First Quar∣ter, or from her first Quarter to her Full, and so on; for I call any of these four Aspects a Cardinal Point, or Change, and the whole time between one Change and the other a Quarter; I say, Reckon how many Days there are, in the then Quarter, and you will find either 6½, or 7, or 7½, or 8▪ so that if the number be 6½, her Elongation from the Sun is 55 Minutes and ½, per Diem, if 7 Days 51′½, if 7 days and half, 48′; and lastly if 8 Dayes, 48′. I mean not nevertheless that from Change to Change there maynot sometimes happen 6 days and 16 hours or 6 Days and 20 hours, and several such Fractions and Deviations from the Positive Terms prefixt by me: but since the forementioned whole and half dayes will bring us to a knowledge exact enough of the hour sought for, we call 6 days and 16 hours 6 dayes and a ½ only, as coming neerer to it than 7 whole ones; In like manner, we call 6, and 20 hours 7 days, and deal in this Proportion with all other number of days

and hours which the Ephemerides or Almanack give us concer∣ning the length of the requir'd Quarter.

And here you may be pleas'd to remember also, that it* 1.7 would not be amiss, in case you exceed much any of the fore∣said terms, to add or cast away sometimes a minute or a little more, as you shall see Cause; For if (v. g.) you find the Moon to be six days and 17 hours in her journey (which ac∣cording to our former Directions is to be reputed only six days and ½; and consequently the Elongation 55′½, you may then cast away 1′½, because of this great excess above the half day; and if you should find her at another time to be 7 days and twenty houres, i. e. eight days, you may add for the want of the four hours a minute, and make her dayly Elongation, 46 instead of the forementioned 45; but here you may do as you you please, for the error will not be considerable.

These Particulars being premis'd, let us come to an Exam∣ple;* 1.8 and Suppose then that on the fifth of January, finding the Moons shadow to marke two in the afternoon on your Globe for the Lunar hour, you should desire to know the true, or Solar hour.

First your Almanac can tell you not only that the Moons last Cardinal Point, was (v. g.) her Conjunction, but how many Days and Hours she spends in going from it to the next Cardinal Point; for finding there her said Conjunction to be on the first day (suppose) at seven at night, and that she comes to her first Quarter on the ninth day, near the same hour, you may presently conclude she is 8 whole Days in this Voyage, and consequently that her Diurnal Elongation from the Sun will be 45 minutes. Now because the said fifth day is the 4^th of her Journey, if you multiply 45 by 4, or lookin the Tables (which we shall presently show you) belonging to her 8 Days Journey, you'l have three hours for the time that she is behind the Sun, so that the Solar or true hour must be five at night, wanting four minutes; for you are always carefully to substract two minutes for every hour the Moon wants of compleating her whole Days march, which in the present case happens, not before seven at night; whereas you must have added them, had the Solar hour bin nine at night, be∣cause then her Elongation from the Sun would have been 4 mi∣nutes more than the aforesaid three hours.

'Tis in this manner you are to opperate in all cases; but be¦fore* 1.9 we proceed, take these two Memorandums with you. First, That by the Moon's compleating a day's journey, I mean 24 hours after the time (let it happen by night or by day) of her en∣tring into her last Cardinal Point; as for Example, If she comes to her Conjunction, or any other Cardinal Point, at 7 in the Eve∣ning on (v. g) Munday, then at 7 in the Evening on Tuesday, she has compleated one day's journey, and at the same hour on Wednesday two Dayes, and so on till she comes to her next Cardinal Point. The second Memorandum is, That whereas (in the late Example) her Elongation from the Sun was three hours (because you sought what a Clock it was on her fourth days journey from her Conjunction to her First Quarter, at the Elon∣gation of 45 minutes per diem.) Now had she been thus advan∣ced in her Course from her First Quarter to her Full, or from her last Quarter to her Conjunction, you must have added 6 hours to the said 3 hours, so that then the true hour would (in∣stead of 5 at night) have been 11; and this is to be a general Rule.

Thus much then for the way of finding what a Clock it is at* 1.10 any time by the Moon, and now let us make good what we have said. First we see, that to know the Hour by the Moon, is to know the difference between the Lunar and Solar hour, i. e. be∣tween the hour Circle she is in, and that in which the Sun hap∣pens (at the same time) to be; or, in other Terms between the hour she marks on the Globe by her shade, and that which the Sun would mark did he then appear; Now see∣ing that in her Course from one Cardinal Point to the other, she seldom spends the same number of days and half days, it fol∣lows (as we hinted in the begining) that no certain number of minutes, can be allowed for her daily Elongation; But if we di∣vide 6 hours, or 360 minutes (i. e. her total Elongation from one Cardinal Point to another) by the Days and half days she spends in the journey, the Quotient must be her Diurnal Elon∣gation (at least to sence) during that Quarter. Now since the Diurnal Elongation is, as you see most commonly above three quarters, and somtimes almost an hour, the Horary one must be (as I said) considerable, seeing in the space of every 7 hours it may amount to above a quarter more; therefore this incon∣venience we obviate by allowing two minutes for each hour af∣ter

her compleat days journey, and substracting them from what she wants of it.

Here I confess there may be an Error, but it is hardly worth* 1.11 the mentioning; for when she is either 8 days, or 7, in her journey from one Cardinal Point to another; i. e. when her Diurnal Elongation is either 45′, or 51′ and ½, the difference from 48 minutes a day (or 2 minutes an hour) cannot be but 3′ and ½ in a whole day: nay, when her Elongation is 55′ and ½ i. e. when she spends 6 days and ½ in her voyage, the diffe∣rence is but 7′ and ½ from the aforesaid 48 minutes; nor can this happen till the end of every compleat days journey, and consequently is not perceivable for the greatest part of it. But since we here see where and how any error may arise, it is easily remedied by an Allowance, if any man thinks it worth the while to be so exact.

As for the Reason why, if she be in her Course from her* 1.12 first Quarter to her Full, or from her last Quarter to her Con∣junction, we must add always six hours to the Elongation, which our Calculation or the Tables give, it is, because the said Elon∣gation is only the precise time of her Departure from her last Cardinal Point, whereas if she be past her first Quarter in her Journey towards her Full, she is so much and six hours more, i. e. so much and the six hours, which happen from her Conjun∣ction to her first Quarter. Now in rigor we should add twelve hours to the Elongation we find, when she is gone from her Full, towards her last Quarter, but seeing she is in the Plane of the same Hour-Circle or very near it, both at Full and in Conjunction, therefore the bare adding the said simple Elon∣gation will serve as well in one case as in the other; for if, the Full Moon (at suppose 2 of the Clock at night) casts really her Shadow on the Hour-Circle of 2 in the Afternoon, yet there's no need of hints (the thing being so plain) to prevent your mistaking Day for Night. The like also is to be said of the last Quarter, whose Elongation should be in truth eighteen hours, but the additional six hours (as we allow her after her first Quarter) are sufficient, since no man can be so ignorant as to take the Morning for the Evening, notwithstanding the Lu∣nar hour should be upon a Morning Hour-Circle. To facilitate then this Operation (least what we have already said has pro∣ved tedious) we will conclude (as I promis'd) with a short Reca∣pitulation▪

or Abstract, as also with the Tables of her daily Elon∣gation, let the time be what it will (as we said) that she spends in her Journey from one Cardinal point to the other.

The Abstract of the Operation in finding the true Hour by the Moon according to the late Example.

AS for the Almanac, there are three things (we see) it informs us of, viz. 1. The Hour when the Moon came to her last Cardinal Point. 2. How many days she is going from the said Point to the next; and, 3. In which Days Journey she is at present. Knowing then, according to the late Example that the Moon will be eight days running throu' her Quarter, and that she is in the fourth Days Voyage; 'twill follow that the fourth day in the Table (whose title is eight dayes) will tell you that her present Elongation from the Sun is three hours; so that the Lunar-hour being two in the afternoon, the true hour must be just five at night; only twice two Minutes are to be abated, because she lacks 2 hours from compleating her said fourth days voyage; for your Almanack▪ (according to our supposition) in∣forming you that it was seven at night when she set out from her last Cardinal Point, it must be still seven at night before she compleat's any whole day's Journey during that Quarter.

This then is the summ of the whole Business, nor need you trouble your self with any other Reflexion unless it be to add six hours (as I already said) to the Elongation, in case she be go∣ing from her first Quarter to her Full, or from her Last to her Conjunction. And to conclude take notice, that the hour (if you see the Moon,) may be as well found by day as by night, for her Place on the Globe (which the third * 1.13 Operation show's how to find) is always the true Lunar hour.

Tables of the Diurnal Elongation of the Moon from the Sun, whether she goes in 6½, 7, 7½, or 8 days, from one Cardinal Point to the other.

6. ½ Days
Card. Point.
0. Days from her Cardinal Point.	0. Hor. 0. min. Elongation.
1. Days from her Cardinal Point.	0. Hor. 55. ½ min. Elongation.
2. Days from her Cardinal Point.	1. Hor. 51. min. Elongation.
3. Days from her Cardinal Point.	2. Hor. 46. ½ min.Elongation.
4. Days from her Cardinal Point.	3. Hor. 42. min. Elongation.
5. Days from her Cardinal Point.	4. Hor. 37. ½ min. Elongation.
6. Days from her Cardinal Point.	5. Hor. 33. min. Elongation.
6½ Days from her Cardinal Point.	6. Hor. 0. min. Elongation.

7. Days.
Card. Point.
0. Days from her Cardinal Point.	0 Hor. 0. min. Elongation.
1. Days from her Cardinal Point.	0. Hor. 51. ½ min.Elongation.
2. Days from her Cardinal Point.	1. Hor. 43. min. Elongation.
3. Days from her Cardinal Point.	2. Hor. 34. ½ min. Elongation.
4. Days from her Cardinal Point.	3. Hor. 26. min. Elongation.
5. Days from her Cardinal Point.	4. Hor. 17. ½ min. Elongation.
6. Days from her Cardinal Point.	5. Hor. 9. min. Elongation.
7. Days from her Cardinal Point.	6. Hor. 0. min. Elongation.

7 ½ Days.
Card. Point.
0. Days from her Cardinal Point.	0. Hor. 0. min.Elongation.
1. Days from her Cardinal Point.	0. Hor. 48. min.Elongation.
2. Days from her Cardinal Point.	1. Hor. 36. min. Elongation.
3. Days from her Cardinal Point.	2. Hor. 24. min. Elongation.
4. Days from her Cardinal Point.	3. Hor. 12. min. Elongation.
5. Days from her Cardinal Point.	4. Hor. 0. min. Elongation.
6. Days from her Cardinal Point.	4. Hor. 48. min. Elongation.
7. Days from her Cardinal Point.	5. Hor. 36. min. Elongation.
7½. Days from her Cardinal Point.	6. Hor. 0. min. Elongation.

8 Days.
Card. Point.
0. Days from her Cardinal Point.	0. Hor. 0. min.Elongation.
1. Days from her Cardinal Point.	0. Hor. 45. min.Elongation.
2. Days from her Cardinal Point.	1. Hor. 30. min. Elongation.
3. Days from her Cardinal Point.	2. Hor. 15. min. Elongation.
4. Days from her Cardinal Point.	3. Hor. 0. min. Elongation.
5. Days from her Cardinal Point.	3. Hor. 45. min. Elongation.
6. Days from her Cardinal Point.	4. Hor. 30. min. Elongation.
7. Days from her Cardinal Point.	5. Hor. 15. min. Elongation.
8. Days from her Cardinal Point.	6. Hor. 0. min. Elongation.

These Tables are to be on the Globe in the most vacant and free parts of it.

OPERATION VIII. To know how many hours the Moon has been up, and how many she lacks of her setting, as also how long she is to be that day above the Horizon.

THis is done by numbring the Hours or Hour Circles between the Moons place in her Parallel on the Globe and the intersections of her said Parallel with the Horizon; for ha∣ving found that her Parallel cuts the Horizon in the East at the five a clock hour circle, and in the West at that of seven, and seeing that her present Place is (v. g.) at that of two in the afternoon, you may conclude that she has bin up nine hours wanting eighteen minutes, that is, eight hours and forty two minutes; and will set within 5 hours wanting ten minutes, or four hours and fifty minutes; for the Moon goes from East to West (by the Motion of the Primum Mobile or Motum Raptus) two Minutes (as we suppose) every hour (take one time with the o∣ther) slower than the Sun; which happens by her being too quick for the Sun in her own Motion, that is to say, in the Motion of the Center of her Epicicle, which carries her from West to East; therefore the Moon according to the present Example or Sup∣position will be above the Horizon fourteen Hours wanting twen∣ty eight Minutes, i. e. about thirteen hours and a half.

OPERATION IX. To find at what at lack the Moon rises and sets.

BY the last Operation you are inform'd of the hours from her present station to her Rising and Setting, which hapning in the Example to be about eight hours and fourty two Minutes for the one, and four hours, and fifty minutes for the other, it must follow, (having found the true hour to be within four mi∣nutes of five at Night) that she rose about eight and fourteen mi∣nutes in the Morning, and will set at nine and fourty six mi∣nutes at Night.

OPERATION X. To find how long the Moon shines every night.

HAving found by the precedent Operation, that the Moon sets at 9 and 46 minutes at night, and that the Sun (by the 12th. of the first * 1.14 Section) sets the same day, (suppose the 8th. of February) at 5 in the Evening, 'twill follow that she shines four hours and 46 minutes.

OPERATION XI. To find when the Moon comes to South, and consequently when tis high water at London Bridge.

HAving found by the * 1.15 third Operation the Moons place to be in the 2 a Clock Circle, you thereby see that she is past the South 2 hours and 4. minutes; Now since it is always High-water at the Bridge three hours after her coming to South, and since the Solar or true hour is (according to our Example) 5 at Night, it follows 'twas High-water at 4 minutes before 6. and conse∣quently 'twill be high water again at the same hour next morn∣ing, and 24 minutes; for from one Tide to the other there are always about 12 hours and 24 minutes.

OPERATION XII. To know in any Eclips of the Moon, what Countries see it wholly, what in part, and what not at all.

PLACE your Globe on a Meridian Line, or otherwise Compose it, and when you percieve the Moon to begin to enter into the shade of the Earth, consider (as you do when you seek by the * 1.16 Suns Rays where 'tis day and night) what part of the Globe is illuminated, and what not; for, since she appears to all Countries that lie in the Light, and is hid from those in the

Shade, you have not only a view of what people see her in her then condition, but may (till her total immersion) perceive by her illumination how the Countries, that lye in or near the Fol∣lowing shade of Extuberancy, loose every moment the sight of her, and consequently, who they are that took leave of her in the beginning of her Eclips, who when she came to half of it, and who when wholly obscur'd, with infinite more Reflections of this nature. On the other side you may find, how some that lay in the preceding shade of Extuberancy saw nothing of her at first, but now begin to discover her in her Angony; and if you draw on the Globe a little Circle with Chalk or the like, in the Con∣fines of the obscurity and light, just as she begins to be wholly in the shadow, you will discern (by the space between the said Chalk and the new shade of extuberancy at her Emersion) what people never saw her, tho she were above their Horizon. Infi∣nite are the Reflexions (as I said) of this nature, but these are sufficient to show you how to make more your self; so that now I will end after I have remembred you, that the Sun being by his Opposition in the same hour Circle with the Moon, especial∣ly in all Central Eclipses, nay he is so (as to sense) for some time both before and after such Eclipses; I say, the Sun being so, you may therefore not only (by the bare shade of the String, or that of the illuminated Pole) know what a Clock it is from time to time in the Polar Circles, but in the Aequator also, by the shade of Extuberancy, which performs the observations above menti∣oned; and thus by the very same shade you find not only what People see the Eclipse, either in whole or in part, (as we now told you) but at what hour it appears to each of them, and how long; as also the Duration of her Decrease and Encrease in light, together with the time of her total Obscurity; moreover, this very shade gives you her Height and Azimuth all along, as you may see in the * 1.17 Operations that concern them.

OPERATION XIII. To represent the several Phases or Shapes of the Moon by the Globe.

THIS is rather a Speculation than an Operation, Nor should I have mentioned it, were it not that several (who know something in Mathematics) cannot comprehend the Cause of the Moon's continual Metamorphosis or Change, that is to say, why she should be now more, now less illuminated, and that also in so different a shape and manner. To comprehend therefore this, Expose your Globe (elevated on a Stand or a Ta∣ble as high as your Eye) to the Sun or Moon, and place your self so before it as to see the whole illuminated half; for (as to sense) the illuminated and shady parts of all Spheres are (as we formerly mentioned) equal. Having then a while consider'd this great Circle made by the Limb or Extremity of the illumi∣nation, remove your station a little on the one side (as for Exam∣ple towards the righthand) and you will find the illuminated part to appear Gibbous or Oval, I mean not so broad as long, be∣cause so much of it is hid from you, as you can now discover of obscurity. From hence go yet farther side-wise, and the visible part of the Globe will be Dicotomous, or party per pale, that is to say the light and shade will become equal.

After this make another Proportionable step, and all that is illuminated will appear Horned or Lunular, and the obscure part Gibbous; But if you remove to the point opposite to your first Station, you will see nothing besides a dark and shadow'd Hemisphere; whereas should you proceed further in the same Order, you would perceive Light on the other side, first Lu∣nular, then Dicotomous, next Gibbous, and lastly totally predo∣minant.

Now as the Globe is always half illuminated, whether we see little or much of the illumination, so it happens with the Moon, who being in Conjunction appears all dark to us▪ be∣cause her illuminated half is towards the Sun, and opposite to us; but as soon as she gets from him, and consequently is no longer in the same Plane with him and our Eye, we must needs

have a view of some part of the Illumination, seeing she can on∣ly appear wholly obscure when she is thus before the Sun. The said Illumination also (since she is Spherical) must seem as on the Globe the more Horned the less it is, and then blunter and blunter according to her Encrease or Elongation, till at last she becomes Dicotomous, afterwards Gibbous, and lastly Full; for by being at her greatest distance from the Sun, or in Oppo∣sition with him (which causes our Eye to be in the middle or between them) 'tis impossible she should appear otherwise than all Light: And here you may be pleased to take notice, that if you compass your Globe with a String or Thred that passes throu' the Zenith and Nadir, and let one half of the describ'd Circle represent the Illumination and the other the Obscurity, you may perform this Operation at any time, whether the a∣foresaid Luminaries shine or no.

How easy therefore is it to conceive the whole Mistery of the Moons four principal Changes, and what men mean by them.* 1.18 For first we see that as She is call'd New by an Astronomer from her being with the Sun, (i. e. as fully between our Eye and the Sun, as her then Course permits) so no sooner has he found by their several motions that she is gotten 90 Degrees or six hours from the Sun, but he says, she is in her first Quarter; and when they are asunder 180 Degrees or 12 Hours (to wit as far as ever they can be) that she is Full; and lastly, as soon as they are distant 270 Degrees or 18 hours on the same side, and 90 Degrees or six hours on the other, that she is in her last Quar∣ter; so that at their next meeting she becomes New again.

OPERATION XIV. How to find how long the Moon wants of any Change, or Cardinal Point, and consequently how old she is.

I Propose not this Operation as a thing exact, but seeing it is a Corollary of the former, I thought fit to hint it; therefore pray take it▪ for better, for worse, and make of it what you can: To resolve then these Questions by the Globe, you are to expose it as before to the Moon when she shines, and move about it till you can there just describe her shape; and by the way you will

come nearer the mark, if you only consider the Lunular or lesser Portion, whether it happen to be the obscure or the il∣luminated part of her whole Discus or Orbe; I say, describe her Shape on the Globe, as neer as you can, and observe how many Degrees the breadth of the Horn'd or Lunular Portion will be in any great Circle, that crosses it in the middle at Right Angles, and that will give you taliter qualiter what you seek for, as appears more clearly by the ensuing Example.

Having observ'd, suppose, the illuminated Portion of the* 1.19 Moon to be Lunular, expose your Globe, and move about it 'till you perceive on it an illuminated Lunula proportionable to the Real one, then finding its measure by some great Circle that crosses it at right Angles, to be 40 Degrees, these consequen∣ces will follow. First if the Moon be in her Encrease, she is past being New 40 Degrees, i. e. three days and about seven hours, seeing her hourly Elongation from the Sun (is one time with another) about half a Degree and half a minute; but if she be in her Decrease, she wants so many days and hours from be∣ing again New. In the next Place it will happen that the ob∣scure part of the Globe is 140 Degrees broad; for (both parts or portions making up the apparent Hemisphere) the said ob∣scur'd Part becomes the supplement of the former 40 Degrees; so that 140′ amounting to about 279 hours, or 11 days and 15 hours, you may conclude that if she be Encreasing, she wants so much of being Full, as also that she is 50 Degrees or almost 100 hours (i. e. four Days and almost four hours) past her first Quarter; whereas if she be Decreasing, she will want eleven Days and fifteen hours from her next Conjunction, and be four days and almost 4 hours beyond her last Quarter.

As for knowing the Moons state in relation to her Waxing and Waining, you need only observe on what side of her Dis∣cus her illuminated Part stands; for if it be on the West-side of it, she is in a Waxing Condition, if on the East-side in a Wain∣ing or Declining one: And here also remember that as to the measuring the aforesaid Portions of the Moons Discus, repre∣sented on your Globe, you may do it by the Horizon, if she il∣luminates not much beyond the Zenith, or by the Aequator, when the illumination reaches to the Pole or neer it, or by the Ecliptic when it extends it self a good way further; for the said Portion of the Moons Discus is measur'd at first sight by that

great Circle which lies equally distant from each Horn of the Lu∣nula on the Globe, i. e. by that great Circle which crosses it (as we said) in the middle at Right Angles; and when no great Circle does so. you had best measure it exactly with your Compasses, seeing that on the knowledge of its breadth, the Resolution of all the former Questions depend. Many things of great use may be drawn from knowing the true proportion of the illuminated and obscure parts of the Moons Orb, but this I leave to them that have exacter Instruments than the Globe, and more time to make Deductions.

The END of the Third Section.

Notes

• * 1.1

  pag. 5.
• * 1.2

  pag▪ 10▪
• * 1.3

  pag. 11:
• * 1.4

  vid. pag. 8. & 15: A Memoran.
• * 1.5

  p. 12.
• * 1.6

  How you are to operate;
• * 1.7

  A Memoran∣dum.
• * 1.8

  An Example.
• * 1.9

  Two Memo∣randums.
• * 1.10

  The reason or demonstrati∣on of the O∣peration.
• * 1.11

  A memoran∣dum.
• * 1.12

  Why 6 hours must be added sometime to the Tables.
• * 1.13

  p. 49.
• * 1.14

  p. 16.
• * 1.15

  pag. 49.
• * 1.16

  Op. 7. sec. 2. pag. 33.
• * 1.17

  Vid. Op. 1. & 2. pag. 49.
• * 1.18

  A Corollary.
• * 1.19

  An Example.