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 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 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 Almucantar and Azimuth as we hinted in the 6th Operation 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 Operation 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 Afternoon 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 imaginary Circle Parallel to the Aequator and answerable 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 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 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 Horizon 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 Particulars yet at the end we will contract the whole into half a dozen 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 inconstant in her dayly Elongation from the Sun that sometimes she spends from v. g. her Conjunction to her first Quarter 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 commonly 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 perform'd by an Instrument in a trice as the Operations commonly 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 Restrictions and in truth nothing but a down right Astronomical Calculation can really perform it yet since such a critical Exactness 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 Quarter 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 concerning 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 foresaid 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 according 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 Example 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 4th 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 because then her Elongation from the Sun would have been 4 minutes more than the aforesaid three hours 'T is in this manner you are to opperate in all cases but before 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 entring into her last Cardinal Point as for Example If she comes to her Conjunction or any other Cardinal Point at 7 in the Evening 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 Elongation of 45 minutes per diem Now had she been thus advanced 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 instead 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. between the hour Circle she is in and that in which the Sun happens 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 seeing that in her Course from one Cardinal Point to the other she seldom spends the same number of days and half days it follows as we hinted in the begining that no certain number of minutes can be allowed for her daily Elongation But if we divide 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 Elongation 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 inconvenience we obviate by allowing two minutes for each hour after 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 difference 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 Conjunction we must add always six hours to the Elongation which our Calculation or the Tables give it is because the said Elongation 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 Conjunction
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 Elongation 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 Lunar hour should be upon a Morning Hour-Circle To facilitate then this Operation least what we have already said has proved tedious we will conclude as I promis'd with a short Recapitulation or Abstract as also with the Tables of her daily Elongation 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 't will 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 informing 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 going 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 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 having 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 other 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 Supposition will be above the Horizon fourteen Hours wanting twenty 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
about 21 Degrees In like manner you must have look't on the West side of the Globe if you would have had the time of the Sun 's setting an hour later than 7 and thus you are still to operate when any other space of time is required OPERATION XIII To find the Sun's Amplitude Ortive or Occasive BY the Sun's Amplitude we mean his distance in the Horizon from the true East and West Points at his Rising or Setting so that this Operation is also a Corollary from the former for knowing on the said 10. of April the point or place where he Rises you will find the Ortive Amplitude to be Northward from East about 18 Degrees and on the other side of the Globe the Occasive Amplitude to be Northward as much from the West OPERATION XIV To find the length of the Day and Night DOuble the hour of the Sun 's Setting which on the 10. of April happens as we said about 7 at night and the Product to wit near 14 hours will be the length of the Day or double 5 the hour of his Rising and the Product 10 hours gives the length of the Night Nay if you do but consider how the Parallel of the Day is cut by the Horizon you have the whole business represented to the life at one view even as it happens in the very Heavens themselves for that part of the said Parallel above the Horizon being devided to your hand by the Hour-circles into almost 14 hours shews the Days length and consequently that part under the Horizon shewing a little more than 10 hours gives the length of the Night OPERATION XV. To find the beginning and end of the Crepusculum BY the Crepesculum is understood the Twilight which appears before the Sun 's Rising and continues after his Setting for as soon as the Sun comes within 18 Degrees of the Horizon according to the Opinion of the antient Astronomers or within 16. Deg. according to that of Tycho and some Modern ones his Rays are reflected from the Atmosphere or circumambient vapours and consequently illuminates so that this light still encreases by how much the Sun approaches the said Horizon and decreases as it recedes Now to find it you are to bring the String hanging on the Zenith to the Meridian and making the Bead if you follow the latter Hypothesis to stand by the help of the Quadrant of Depression at 16 Degrees under the Horizon move it on the East side of the Globe along the Parallel of the Day i. e. that of the 10. of April till it just touches the said Parallel under the Horizon and there will be the true point of the Morning Crepusculum which the adjacent Hour-circle tells you begins about 3 in the morning In like manner if you move your Bead on the West or Eveningside of the Globe you will find it to end neer 9. OPERATION XVI To find the Sun's Depression at any time of the Night BY Depression we mean how many Degrees the Sun is then under the Horizon which is easily perform'd if you know the hour of the night by the Moon Stars Clock or the like for finding as hath been shown you what part or point of his Parallel the Sun is then in i.e. where the Hour-Circle corresponding to the time of the night and Parallel of the Day intersect draw the String from the Zenith over it and moving your Bead to it bring the said Bead to the Merid. or Quadr. of Depression and then by the help of the Degrees there reckoning from the Horizon to the Bead you have before you the required Depression OPERATION XVII To find the Sun 's Right Ascension THE Right Ascension is that Point or Degree of the Aequator cut by the Meridian or Hour Circle that runs through the Sun's place in the Ecliptic and this Degree is called the Right Ascension because in the Position termed by Astronomers and Geographers the Right Sphere which together with the Oblique and Parallel Spheres shall be farther explained in the Geographical Section it rises or Ascends with the Sun To find then the Sun 's Right Ascension a thing often of great Use you are only to take the String hanging from the Pole and lay it on the Degree of the Ecliptic possest then by the Sun that is to say upon the 1st of ♉ for the 10. of April is still our Example and the Degree of the Aequator cut by the said String is the required Right Ascension which counting from ♈ or East Point as you must always do happens to be 28 Degrees or thereabouts OPERATION XVIII To find the Ascensional Difference AS for the Ascensional Difference i. e. the Difference between the Right and Oblique Ascensions we have it here before our Eyes at a View as being that portion of the Day 's Parallel which lyes between the Sun 's Rising or Setting and the 6 a Clock Hour Circle so that if he rises on the 10. of April at almost 5. and sets near 7. we may conclude that the Ascensional Difference is about 14. Degrees for 15. make an hour But if you will be exact then lay the String from the Pole on the Point where the Sun rises or sets and when it cuts the Aequator count there the Degrees from the said String to the 6 a Clock Circle and all is done Thus then you see that when we know the Ascensional Difference we have the time of the Suns Rising and Setting for it is but adding it to 6 a Clock if the Sun be in his Northern Declension or substracting it in his Southern The END of the first Section SECT II. Of the Operations that concern Geography HAving given you a short account of the Operations immediately relating to the Sun without reflecting upon any part of the Earth but that on which we then stand wee 'l now descend to those that concern Geography where you may have a view not only of all Countries as to their Situations Extent and the like but see at one glance when you please several other things appertaining to them worth the knowing as What a Clock it is in any place imaginable what People are Rising who are going to Bed and who to Dinner as also where it is they have no Night where no Day with divers particulars of the same nature which were thought by many formerly not performable without Magic That our Instrument is Geographical no body will I dare say doubt it being the Terrestrial Globe and consequently the Epitome of the very Earth it self and besides its many other Operations it may be perchance useful in this that all Countries are here more obvious and consequently more easily found out than in any common Universal Map or Globe Nor do's it a little contribute to it and fix the Position and Order of the said Countries in our Memory that not only the Divisions and Subdivisions of the Earth are by our present Directions clear and distinct as far
their Fame among the Moderns they were Dia-Meroes Dia-Syenes Dia-Alexandrias Dia-Rhodou Dia-Romes Dia-Boristheneos and Dia-Riphoeon being all names made by the Addition of the Greek Preposition 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 i. e. per to some remarkable Town River or Place thro' which the middle of each Clime past so that the middle of the first went thro' Meroe an Ethiopian City on the Nile where according to some Queen Candace Reigned the second thro' Syene in Egypt lying just under the Tropic the third thro' Alexandria the fourth thro' the Isle of Rhodes the fifth thro' Rome the sixth thro' the mouth of Boristhenes now called Nieper by the Cossacks and the other Inhabitants and the seventh and last thro' the Riphoean Hills part of which lay according to their account in or about the Latitude of 50 Degrees and consequently corresponded with the Cimerians 'T was here then that Alfraganus and other Arabians ended Northwards who besides several smal particulars err'd not a little in making Rome and the Boristhenes only a Clime asunder when as their longest days differ at least an hour And as for the Southern Climes to wit those on the other side of the Aequinoctial they thought fit to consider them but not knowing what to call them as being ignorant for the most part of the Places they went through they added 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 i. e. Contra to the former Denominations so that making Anti-dia Meroes serve for the first Clime Anti-dia Sienes for the second they proceeded in the same order with the Rest But now before I end I shall endeavour to solve a difficulty which startles not a few viz. how it comes to pass seeing the Climes are assigned as we mentioned by the Antients to know the length of the Summer Solstitial day in every Country that the middle of the first Clime which in rigour should lye no further from the Aequator than to encrease the day a quarter of an hour runs over Meroe where the Excess is at least an hour I answer the Antients deeming it more equal that the middle of the Clime and not the end of it should be the Point where the half hourly increment was to begin fixt the Terme à quo not in the Aequator but a quarter of an hour further and therefore Taprobane which some now think Sumatra was the place where Ptolemy commences all his Climes making thereby the middle of his first to pass per Sinum Avalitum or Mouth of the Red Sea and the middle of his second per Meroen But the Arabians thinking that for several Degrees from the Aequator all was either Sea or by reason of the Heats scarce Habitable or else judging it for their Honour to have their own Country in the first Clime began half an hour beyond Taprobane and so Dia Meroes tho the Days are there 13 hours long leads the Van in their Catalogue These few things premis'd I shall now shew you the way I take therein which I think in all respects clear and ready First I make the primary Circle of Longitude to be the Circle particularly appropriated to this use being devided and mark't according to the true distance of each Clime from the other and as to the place where they commence on our Globe I rather follow Ptolomies Astronomical than Geographical Method for besides the aforementioned excess of the Arabians should we begin but a quarter of an hour from the Aequator it makes a great space of the Earth viz. from Taprobane to the Aequator to be in no Clime at all and which is more it causes a little confusion when the length of the day is greater in every Clime than what the said Clime can justly challenge according to its Rank and Number I say as for the place where the Climes commence I rather follow Ptolomies Astronomical than Geographical way and therefore beginning at the very Aequator my first Parallel or middle of my first Clime is supposed to run over the places that enjoy 12. hours and a quarter of Day and the end of it noted on the primary Circle of Longitude or 2 a Clock Hour Circle with the Figure I. over the places that have 12. and 1 2 and thus we proceed to the Polar Circles to wit where the 24th Clime or 48th Parallel terminates so that from thence we come to the Devisions on the said Circle of Longitude which show where the days are as long as an ordinary Week where as long as a Month and where as two arriving at last at the Poles themselves where there is a constant half year of light and as much of Darkness And to give you a Remembrance of the Names of the aforesaid old Climes and that you may also see without Calculation or Trouble where the Ancients plac'd them I have set down the first Syllable of their names as Mer. Sy. Al. c. according to their respective Latitudes To find then in what Clime any place is v. g. Constantinople you are only to draw your String from the Pole over that City and mounting up the Bead thither to move it to the said Primary Circle of Longitude and 't will lye on the Clime or Paralel required But if you would know what places are suppose under the 4th Clime throu'out the World i. e. what places have their longest day just 14. hours Fix the Bead on the 4th Clime and moving it on its Noose from the Pole round the Globe you may conclude that every place it passes over has the Sun exactly so long above the Horizon when the days are at the longest and in the same manner you must proceed on the South of the Aequator to find the Countrys that lye under the 4th Southern Clime In short here we have besides what has been already said a view not onely of the strange inequallity of the Climes especially between the first and last but also of their exact distance in Degrees and consequently in Miles by help of our Table of Reduction mentioned in the first Operation of this Section But seeing we are a little fallen into Speculation 't will not be perchance improper to proceed yet further and to consider here as in a natural and fit place the Bounds and Terms of the five Zones so called from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Cingulum as enclosing the whole World within their respective Districts 'T is with the Torrid one we 'l then begin whose Bounds are the two Tropics so that the Diurnal Parallels not only remarkably distinguish it from the other Zones but shew why the several Inhabitants within this space were called by the Ancients AMPHISCII i. e. Vtrinque umbrati or men that had two shadows from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 utrinque 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra nay by the said Parallels you may find when the shade will change and be different For since by these Paths or Traces the Sun as we often hinted
represent the Illumination and the other the Obscurity you may perform this Operation at any time whether the aforesaid 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 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 Quarter 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 illuminated 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 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 consequences 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 being again New In the next Place it will happen that the obscure part of the Globe is 140 Degrees broad for both parts or portions making up the apparent Hemisphere the said obscur'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 Discus 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 Waining or Declining one And here also remember that as to the measuring the aforesaid Portions of the Moons Discus represented on your Globe you may do it by the Horizon if she illuminates 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 Lunula 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 SECT IV. Shewing the Proportion between Perpendiculars and their Shades SEeing there is the same proportion between all Shades and their Perpendiculars at least to sense and seeing the several Almucantars of the two great Luminaries are the chief Cause of the lengthning or shortning of them I have here adjoin'd a few by Operations even in Altimetry it self as belonging naturally to our Globe since it not only shows us several ways of finding from time to time the said Almucantars but gives us also at the same instant without trouble as appears by the ensuing Operations the above-mentioned Proportion and consequently the height of all things Perpendicular to the Horizon OPERATION I. How to find the Proportion between the Perpendicular and its Shade COnsider the Northern or back part of the Globes Meridian which we will call hereafter the Quadrant of Proportion and which is not only devided like the Southern or fore-part into Degrees but markt also in relation to the affair in hand with several Figures of which that next the Zenith is 17 and the remotest 188. And by the way you must take notice that when you see a Cross behind any Figure it signifies half an Integer more so that 17 + is 17 Degrees and a half 26 + is 26 and a half c. When you would therefore Operate Turn the Southern or fore-part of the Meridian towards the Sun 'till they be both in the same Plane i. e. 'till the shade of the Pin in the Zenith falls directly upon the Quadrant of Proportion and what Figure soever suppose 25 the shade of Extuberancy cuts that will be the then Proportion between Perpendiculars and their Shades for here you may take notice that we ever suppose the Shade to be 100. Nay if finding by any of the former ways the Sun's height to be suppose 14 Degrees you rectify your Bead to 76 Degrees or the Complement of it you need only clap back your String that is to say draw it from the Zenith over the Devisions of the afore-mention'd Quadrant and then the Figures under the Bead to wit 25 will shew you the required Proportion In short take but the Suns Height any how and reckon from the Zenith as many Degrees on
onely a glimpse or faint sight of the Sun then stand the Globe being Compos'd on the obumbrated or other side of it and letting your String hang down on that side also aim or look along it with one by towards the Sun and role the String gently with your finger backwards or forwards till it lies exactly in the same Plane as the Sun does or if the Clouds suffer you not clearly to see him till it lies in the Plane of its supposed Place and the Degree under your String reckoning the contrary way that is to say from the Northern or back part of the Meridian is the requir'd Azimuth Therefore by the by if the Sun shines out 't is but drawing the String through the Shade of the Zenith-pin and it will reckoning thus answer the Question 3dly Having taken the Sun's Height and having found it to be suppose 36 deg bring the String to the Merid. and by the help of the Degr. in the Quad. of Alt. Mount the Bead above the Horizon 36 deg which Operation we shall frequently call hereafter Rectifying your Bead to the Sun's height I say having taken the Suns height and Rectifi'd your Bead to it put your Ring or Noose on the Zenith and move your String till your Bead lies exactly on the Parallel of the Day Which we will alwayes in our Examples or for the most part at least suppose to be that of the 10th of April and the said String will cut the Horizon at 58 Degrees Eastward or thereabouts for his then true Azimuth And here you may remember That as the Height gives the Azimuth so the Azimuth once known gives the Height for your string being on the true Azimuth if you mount your Bead to the Parallel of the Day it will show you in the Meridian the requir'd Height Fourthly Supposing that on the 10th of April the hour given be 9 in the Morning draw your String from the Zenith over the Point where the Parallel of the Day and the 9 a Clock hour-Circle intersect and it will fall on the 58 Degree in the Horizon Eastwardly of the Meridian for the then Azimuth OPERATION VI. To find the Sun's Declension Parallel and Place on the Globe at all times BY the Sun's Declension is meant his Northerly and Southerly distance from the Aequator therefore if you know the day of the Moneth to be the 10th of April you have his Parallel because 't is mark'd with the said day Now since the Colurus Aequinoctiorum or 6 a clock Hour Circle is as we said gradually divided from the Aequator to the Poles and that the said Parallel passes almost throu ' its 12th Degree you have his Declension as also his Place in his Parallel if you have his Almucantar or Azimuth as you will find by the second or following way If now you know not the day of the Moneth Take the Sun 's Almucantar and Azimuth by some of the foregoing wayes and Rectifying your Bead to the Height draw your String from the Zenith on the Horizon according to the Azimuth found and your Bead will lie on his true Place and consequently show his Declension and Parallel for as his Declension is as we said his Distance from the Aequator so his Parallel is a Circle described from the Pole according to his Declination And pray observe well this second Way for tho' it be not extremely necessary in Relation to the Sun yet it is of singular use when you come to the Moon and Stars whose Declensions depend not on the day of the Moneth OPERATION VII To find the Sun 's Bearing i. e. in what part of the Heavens he lies according to the Points of the Compass HAving found by the foregoing Operation on the 10th of April the Sun 's true Place in his Parallel to be suppose there where the 9 a Clock Hour Circle cuts it say over this Point your String from the Zenith and 't will fall at the Horizon a little beyond the Character of SEbE for his Bearing according to the Points of the Compass OPERATION VIII To find when the Sun comes to true East or West or any other Bearing HAving found the Parallel of the Day viz. that of the 10th of April and put your String over the Zenith bring it straight to the East point that is to say to the point of the Globe where the Horizon and 6 a clock Circle intersect and you will find the said String to cut the said Parallel about 20 minutes before 7 in the Morning which is the exact time of the Sun 's then coming to full East Now if the String be laid on the Western Intersection 't will cut the said Parallel at 20 minutes or thereabouts after 5 in the Evening for the time of the Sun 's coming to full West In like manner if you would know when he come's v. g. to S. W. you are only to draw your String as before over that Bearing and you will find by the Intersection of your said string and Parallel that at a quarter past 2 of the Clock in the Afternoon or thereabouts he will have that Bearing OPERATION IX To find what Signs and Degrees of it the Sun is in at any time SEEK out the Parallel of the Day viz. that of the 10th of April and you will find it to cross the Ecliptic in two places to wit at the first of Taurus and the first of Leo Now because in April the Sun is still Ascending that is to say the Dayes encrease you may conclude that the first of Taurus is his then true place in the Ecliptick for were he in Leo he would descend toward the Aequator and consequently shorten the Dayes OPERATION X. To find the hour of the Day by the Sun together with a second way of composing the Globe and finding the Globe and finding the Day of the Moneth MANY are the wayes to perform this Operation as to the Hour But now wee 'l insist on four only each of which has some peculiar Propriety belonging to it for the First gives us the Hour by the help of the Natural Stile the Second by an Artificial one the Third without any Stile at all and the Fourth together with the said hour the Contemplation of several pleasing Operations at a time and among the rest this of Composing the Globe by the Shade I. Having Compos'd your Globe and thus wee 'l suppose it in each of the following wayes look among the Hour Circles which are as we said distinguish'd near the Polar Circles with little Roman Figures and the shade of the North-Pole or Axis of the World which we may justly call the Natural Stile will during the Sun's Northern Latitude as well as the shade of the South Pole in his Southern shew you the Hour And thus you may find it for a while by the Ordinary Globes in Circulo Horario when they are once set or Compos'd which
carry away the Bell some St. Nicholas but others St. Vincent as appears by Hondius's Globe Now Langrenius in his begins from St. Mary and St. Michael in the Azores Johnsonius in his Universal Map counts from Corvo and Flores whereas the Learned Dudley the late Titular Duke of Northumberland gives the honour to Pico and has as much reason for it as the rest Nor is there less do about the Canaries for the French fix it at Ferro several of the Hollanders at Teneriffa and many other Nations at Palma which is the Place I would willingly choose since the great Ptolomy thought fit at last to assign it there were it as convenient for my present purpose as St. Vincent 'T is St. Vincent then I here pitch upon for this Meridian to pase throu ' because it differs in Longitude from London within less than 20 Minutes of just 30 Degrees or 2 Hours so that the 2 a Clock Circle will represent it within almost a Minute in time without need of drawing a Particular one and the said Meridian is as I told you in the beginning distinguished from the rest by Pricks which being distant from each other a quarter of a Degree are useful on several occasions Having thus fixt our Grand Meridian or first Longitude that of other Places follow 's with ease for if you would know the Longitude of Constantinople draw but your String from the Pole over it and it will cut the Aequator neer the 62. Degree for the Longitude required as you may readily percieve by the lower little Aequinoctial Figures OPERATION III. How to find out any Place the Longitude and Latitude being given THis Operation is not only usefull for the finding out of Towns express'd on the Globe when you cannot guess whereabout they are situated but also for the placing them truly in case they should chance not to be set down Suppose then Constantinople were the Town sought for and that you found its Latitude to be 43 g. 5′ and Longitude 61 g. 46′ in some book or Geographical Table I say supposing this you have nothing to do after having mounted your Bead by the help of the devided Colurus 43 g. 5′ above the Aequator but to move your String on its Noose from the Pole to 61. 46. in the said Aequator and Constantinople will be just under your Bead and if in case of Omission it should not you may then if you please marke it out your self for that is its exact place But by the way if the Geographical Tables agree not with the Longitude of your Globe as telling you that v. g. Constantinople has but 54 g. 36′ you are then to look from whence the said Tables begin and finding their Commencement suppose at Palma and that Palma according to the former Operation has by your Globe 7 g. 10′ of Longitude you must add this number to your Tables and then you will agree OPERATION IV. To find the situation of any Place according to the Angle of Position or Points of the Compass DRaw the String from the Zenith over v. g. Constantinople and 't will cut the Horizon about 5 Degrees beyond E b S Eastward for the true situation of the said Town from your Habitation according to the Points of the Compass OPERATION V. To find in what Clime or Parallel any Place lies BEfore we can here well come to Operation there are some few Particulars to be consider'd and first what a Clime is which is no hard thing to conceive since most know that after the Vernal Equinox our Days not only exceed 12 houres but that every neerer Countrey to the Pole has days of greater Length than the Remoter Nor are there many ignorant that when our Days that live on this side of the Line increase theirs on the other side decrease proportionably and when theirs encrease ours decrease so that no People are at a Constancy but they that dwell exactly between both Poles to wit under the Aequator This Diversity was thought by the Ancients a thing so fit to be known that they invented the Devision of the Earth into Climes so that as soon they heard a Countrey named they presently besides the fond Reflections concerning the Temperament of the Air Ingeniety of men c. knew the length of its longest Day and consequently how much any other Place exceeded or came short of that length For suppose the first Northern-Clime were to pass over all the Places on this side of the Aequator whose longest Day is 12 hours and 1 2 and the second Clime those of 13 hours and so on towards the Pole by a half hourly Increment what difficulty could there be to resolve immediately the Question when we once know the Clime or having the length of the longest Day to find out the very Clime it self I Wonder therefore that so ingenious a man as 〈◊〉 should seem to assert that this Devision is useless it being as easy to find the longest Day as the Clime whereas were Climes in esteem and fashion the Memory would as soon conceive and remember in which of them any Countrey lay as now it does it's Bounds the manner of its situation and the like and if so one may quickly judge whether they are useless and whether it be possible that the length aforesaid can be known by any other means so universally and at so easy a rate A Clime then generally speaking is a space contained between two Circles Parallel to the Aequator having the Places thro' which they pass differing as to the length of their longest Days half an hour and this space takes the name of Clime from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Inclinare vel Deflectere for the greater our Deflection is from the Aequator or Right Sphere the longer our Summer Solstitial Day will be Nor were the Antients content with this large Devision of the Earth but subdevided it into Parallels so that Places differing a quarter of an Hour were reckon'd to be under such and such Parallels which some call Artificial from their relation to the Artificial Day to distinguish them from all others that occur As for the Antiquity of Climes 't is immemorial nor could there be many in the beginning by reason of the small extent of the known parts of the World For tho' Ptolemy reckons about 10 that is to say 21 Parallels as making them to reach as far as Thule yet Homer Ovid and other Poets so possess'd men with the Fancy that from the Cimerians Northward there was nothing by reason of the hideous vapours and exhalations but a dubious and creperous light that even Pliny and after him the Arabians insisted only on seven looking on all Countries that lay farther as not worth perchance the taking notice of As for the seven in vogue with them and mention'd also very particularly by our Countryman Sacro-bosco whose credit and great Repute has perchance not a little kept up
draw but your String over his then Place and it will cut the Parallel at the true Judaical time of the Night These Vnequal Hours were also called Planetary by the Ancients who allowed to each a Planet to govern it so that the first hour suppose on Saturday belonging to Saturn if you go on still in the usual Coelestial Order as 't is exprest in the Margent and consequently assign Jupiter to the second hour Mars to the third c. the 25th i. e. the first hour of Sunday will happen to the Sun's Lot and the first of Munday to the Moon 's and so forward and thus you may see how it came to pass that the dayes of the week succeeded in the present order and not according to that of the Planets in the Heavens that is to say why Dies Lunae or Munday and not Dies Veneris or Fryday immediately follows Sunday I shall now end this Discourse after I have told you that if we English-men think these Computations strange they that use them wonder as much at ours nay each man pretends some particular Convenience and Advantage by his Method For first an Italian says that without breaking ones Brains no body can tell our way when the Day-ends so that idle men who usually hate computing do often couzen themselves and take false measures in their Affairs for continues he if they chance to get up at 8 of the Clock in Winter they fancy a whole day even St. Barnabas's before them when as this Hour or early rising to Him is 16 of the Clock which informs him at the very instant there are but 8 hours to Night The Caldean on the other side urges that Morning being the most precious part of the Day is fittest to be nicely known and tho' his Hour gives him not presently the Distance to the Evening yet it so alarms him as to what relates to the Morning that he cannot make the least slip therein without being at the same moment conscious of his failure Lastly the Jew approving both Reasons highly triumphs in his way for he no sooner looks he says upon his Dial but sees there not only what hours are past but also what remain and are yet behind But notwithstanding all these shews and pretences of Reasons our Account is so far from coming short of any that in reality it surpasses all for we not only know exactly what we want every moment of Noon a thing of mighty Concern but can appoint positive hours all the Year long for any Employment whether private or publick whilst these other ways by reason of the Suns inconstancy in Rising and Setting have all orderly and set times as when to Dine when to Sup when to Rise when to go to Bed c. still mutable and fleeting OPERATION XV. How to make the Globe Universal THis Operation is quite beyond both my Proposal and Design for I really intend nothing but a Dial according to a Determin'd Elevation fraught with several easy and natural Performances as well divertising as useful And if a man cannot be content with one for his Study or Garden unless it may serve for Jerusalem also he must not only quarrel with Mr. Oughtred's excellent Projection and all particular Analems Quadrants and the like but with Stoffler's Astrolabe an Instrument received with mighty applause by all Besides 't is forty to one especially since there are as we already see so many Vniversal Operations performable by our Globe tho fixt for a particular Place if there chance a case in seven years that would move one to wish the Elevation changed Yet least this might happen the Instrument Maker will prepare a thin Brass Circle gradually devided like the Horizon and of the same bigness therefore if the new Elevation were suppose for Rome open but your Compasses at 90 Degrees in any of the great Circles or take the same distance with your String and Bead and having designed by your said Compasses or String any two Points thus distant from Rome clap over your new Horizon so that it s devided edge rests on the said two Points or in short let Rome be the Pole of the Brass Circle and 't will cut all the Equinoctial Parallels as if the Globe had been made for that City and consequently you will soon have there the Suns Rising Setting Amplitude Ascensional Difference c. Moreover the Circle being exactly made will stick of it self or at least by the help of any scrap of Paper between so that if at any time you set but the Plumet-end of your String on Rome you may then hold it down with one Finger and operate as you would do from your own Zenith But since I am fallen upon this needless affair and since the Operation is in effect the changing of the fixt and standing Site of our Globe 't will be perchance not amiss to inform you if you are not already well verst in the Sphere that there are three different and distinct Positions of it which you will better comprehend if you consider your self in these three Places Sch. 1 Suppose first that you were under one of the Poles and for Example sake the Northern one it must needs follow that that Pin on your Globe will not only be useful there in relation to the several Operations that must as we show'd you be done from the Polar Pin but from that of the Zenith also because now 't is the Zenith there and therefore the South-Pole being the Nadir all Circles must lye as they are represented in Scheme the first Seeing then that the Horizon is a great Circle and always 90 Degrees from both Zenith and Nadir it will necessarily happen that the Horizon and Aequator must concur so that the Aequator describ'd on the Globe will serve for an Horizon in this Position of the Sphere which is called by Geographers the Parallel one because by reason of the concurrence aforesaid all the Heavenly Bodies according to their Diurnal motion i. e. according to the motion of the Primum Mobile parallel to the Horizon so that the Sun cannot Set during the six Months of his Northern Declension nor rise during the six of his Southern for his Rising and Setting imply the cutting or intercepting of some part of his daily Road or Track by the Horizon Nor want the Stars here their particular Properties also for being carried daily on the Poles of the World and consequently moving parallel to the Aequator all that are above the Horizon cannot go under it nor the others emerge unless some by their proper motion after a long series of time change that Order Having then in this Sphere the Zenith and Horizon whatsoever is performable by your own Zenith and Horizon may be here mutatis mutandis perform'd after the same manner Sch. 2. Sch. 3. As for the oblique Sphere which is the third and last Position and here express'd by the third Scheme we are in it you
must know our selves and so are all other People and Places of the World that are in neither of the two former ones for take any point not under the Poles or the Aequator for your Zenith and 't will be impossible to describe an Horizon or Circle 90 Degrees from it which cuts not the Aequator and all its Parallels obliquely 'T is this Obliquity then that gives name to the Position and 't is this that makes the great inequalities in days and nights for if the Horizon has a greater portion of one Diurnal Parallel above it than of another as it must needs have by its slanting 't will follow when the Sun is in such a Parallel that the Day will be longer than when the portion was less and consequently since more of one Parallel is under the Horizon than of another that one Night is shorter than another and seeing the nearer the Pole is to the Horizon the more equally it cuts the said Parallels and the further it is from it the greater the inequality happens to be 't is no wonder that by how much the greater the Elevation is by so much the longer the Days are and when the whole Horizon falls below some of the Parallels that then during the Sun's aboad there the Inhabitants have no night at all therefore it follows that if a Star be neerer the Pole than is the Latitude of a Place it can never set in that Place Yet notwithstanding this strange inequality and disproportion of Day and Night all People in all Positions by that time the Sun finishes his annual Course make them even and thereby enjoy an equal share of both for if under the Pole the Sun be six months above the Horizon he is as long under it and if we and the Rest that live in the Oblique Sphere have Summer Days of a mighty length our Winter Nights are of the same Dimension therefore it follows that at the long Run the Inhabitants under the Aequator or in the Right Sphere who have always 12 hours of Day and as much of Night cannot boast of having more of the Suns Company than they that live in the two other and consequently that the assertion is true 'T is in the Oblique Sphere then that the above-mentioned Brazen Horizon is chiefly intended but as I said in the beginning 't is forty to one so many Universal Operations being perform'd by the Globe in its set Posture that in 7 years a man lights on a Question that could invite him to change it were it moveable as other Globes are so that having show'd you that in case of Necessity it may be in effect altered even without stirring it from its Pedestal I shall proceed OPERATION XVI How to take the Elevation of the Pole in any place whatsoever SUppose you were in a strange Place and that your Globe being one that had bin fitted for London you desire to know the present Elevation Expose your Globe to the Sun on a Meridian Line with the Pin or Needle in the Hole on the Parallel of the 10 of April or true day of the Moneth and observing at 12 a clock when the Sun comes into the Plain of the Globes Meridian that the shade of the said Needle or Pin loses not it self as it would do were the Sun directly opposite to it for so it had hapn'd at London or in any place in the Latitude of 51 e 30′ I say having thus expos'd your Globe and observing this move your Pin or Needle from Hole to Hole or from one Degree of the Meridian to the other 'till it's shade be wholly lost and finding the said Needle or Pin on the Parallel suppose of June 11th which is about 11. 30′ higher then it 's proper place to wit the Parallel of the 10th of April you may conclude that your present Elevation is 63 degrees i. e. 11. 30′ higher than the Globe's whereas had you bin oblig'd to move your Needle or Pin so many Degrees lower than the 10th of April your Elevation had bin but 40. The Demonstration is obvious for since the Earth is round as nothing perchance proves it better than the Experience we have that as so many miles suppose 60 elevates or depresses the Pole one Degree so just 60 Miles more elevates or depresses it another I say since the World is round and that the Degrees of the Globe answer to its Degrees it must follow that the difference between the Pins situation now on the Globe and where it would have stood on it at London is the true difference of the two Elevations OPERATION XVII How to know in what Elevation the Sun Rises or Sets an hour or any other space of time earlier or later than he do's in the Globes Elevation IF the Sun rising at London on the 10th of April about 5 and setting about 7 you would know in what Elevation or Latitude he then rises for examples sake at 4 and sets at 8 take the distance of 90 Degrees with your String or Compasses in any great Circle and placing one end of your String or one foot of your Compasses where the Parallel of the day intersects with the Hour-Circle of either 4 in the morning or 8 at night observe where or at what point the other end of your said String or other foot of your said Compasses touches in the Meridian or 12 a Clock Circle of the Globe and you will find it to be at or about 8 Degrees and 30 Minutes beyond the Zenith towards the North Pole so that the Elevation required is greater than your own by those 8 Degrees and 30 minutes that is to say the Elevation is that of 60 or thereabout whereas had your String or Compasses touch't 8. ° 30 ′ on the other side of your Zenith the required Elevation would have been less than your own so many Degrees i. e. it would have been that of 43 Degrees or thereabout This appears true by placing your Brazen Horizon or by describing an imaginary one over the two points made by the Intersection of the Parallel of the Day and Hour-Circles of 4 in the morning and 8 in the evening for in the Elevation belonging to such an Horizon 't is evident that the Sun rises at 4 and sets at 8. Now the Pole of every Circle being 90 Degrees from it and the Point in the Meridian being 90 Degrees from the aforementioned Intersection it follows that the said Point in the Meridian is the Zenith or Pole of this new Horizon and consequently by being distant from the Aequator 60 Degrees that so many Degrees is the Latitude or Elevation required The END of the second Section SECT III. Of the Moon 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 't is equal to us whether
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 minutes of five at Night that she rose about eight and fourteen minutes in the Morning and will set at nine and fourty six minutes 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 Section sets the same day suppose the 8th of February at 5 in the Evening 't will follow that she shines four hours and 46 minutes OPERATION XI To find when the Moon comes to South and consequently when t is high water at London Bridge HAving found by the 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 't was High-water at 4 minutes before 6. and consequently 't will be high water again at the same hour next morning 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 Suns Rays where 't is 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 Following 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 Confines 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 Infinite 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 especially 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 mentioned 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 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 Table 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 illumination remove your station a little on the one side as for Example towards the righthand and you will find the illuminated part to appear Gibbous or Oval I mean not so broad as long because 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 Lunular then Dicotomous next Gibbous and lastly totally predominant 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 because 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 only 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 Opposition with him which causes our Eye to be in the middle or between them 't is 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