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 ...

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, 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 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; 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 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 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 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 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 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.

Notes

• How you are to operate;
• A Memoran∣dum.
• An Example.
• Two Memo∣randums.
• The reason or demonstrati∣on of the O∣peration.
• A memoran∣dum.
• Why 6 hours must be added sometime to the Tables.
• p. 49.