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
I wonder none of those who writ of their Uses take notice of I say for a while for it will only serve your Turn there from March to September II. Your String hanging by one End on the North Pole hold it straight by the other some little distance from the Globe and moving it on the Noose till its shade touch or cover the Apex of the South-Pole 't will show you among the aforesaid Polar Roman Figures the true Hour even to a minute for the Shadow of the String which we call an Artificial Stile because 't is Independent and Forrein to the Globe cutting at that Instant the Aequator and Polar Circles gives you in each place the Degrees of the hours and consequently the minutes since the 4th part of a Degree is an exact minute in time III. Look where the shade of Extuberancy cut 's on the Aequator and the great Roman Figures which are there for that purpose will give you without a Stile or more adoe the exact hour on what side soever of the Globe you stand for you must remember that the Extuberancy casts on the Aequator two shades the one still Preceding or going before the Sun and the other Following him Now if this shade be dubious your Finger as I show'd you before will help you it being the constant Remedy on all Occasions of this Nature IV. As now you find the Hour by your String hanging on the Pole so this Fourth way is to show it you in case it had hung on the Zenith nor have you more to do than to hold it by the end as before and to move it on its Noose 'till its shade concurrs and agrees with that of the Pin in the Zenith or for more Assurance till the Strings shade fall's so on the upper part of the Pillar or Fulcrum that it would cover the very Nadir were it not hid and then where the said String it self or its shade cuts the Parallel of the Day there will be the true hour according to the Roman Figures of the Polar Circles This way I would have you well observe for from hence I shall hereafter lead you to the Contemplation as I hinted before of several pleasing and useful Operations at one glance or view and to give you a little Taste at present I will here shew you the Second way of Composing the Globe by the shade Having for Expedition's sake turned the North-pole of the Globe as near as you can guess to that of the World Hold up your String with one hand to the Sun in the manner now prescribed That is to say 'till the String hanging from the Zenith casts its shade on the Nadir then move the Globe with your other hand and making by a proportionable motion of the String its shade to pass still throu ' the said two points observe when it cuts the Parallel of the day at the like hour with that which the shade of the illuminated Pole indicates and your Globe will be composed or to express this in fewer words Move thus the Globe till the shade of the string and the shade of the illuminated Pole agree in the Hour Nay fixing your String in the Zenith as before and fastning a Thred on the North-pole do but hold up both to the Sun till the shade of the String passes the Nadir and that of the Thred the South Pole if any body then moves your Globe about till the two shades passing still throu ' the foresaid Points intersect on the Parallel of the Day you have your intent for the Sun being you see in the Planes of the Thred and String he must be in their Intersection i. e. in the Parallel of the Day but 't is impossible for him as we show'd you to be in the plane of that Parallel on the true side of the Meridian except the Globe be Compos'd for the corresponding Circles of the Globe and Heavens can never else agree therefore the Operation is true and if so let the Globe be but on a Meridian Line or any way else Compos'd and the Agreement of the hour in both places or the Intersection of these two shades shews the Sun's Parallel and consequently the Day of the moneth So much then for this second way of composing the Globe and finding the Day of the Month which first came into my thoughts by reflecting on the Projection of that great man Mr. Oughtred who would have bin the Wonder of this Age had he bin as ambitious and forward as he was throughly learned OPERATION XI To find the Hour of the Day when the Sun shines not TO perform this Operation we must suppose you know either the Suns Almucantar Azimuth or Bearing and by the way you may find these tho he shine's not I say you must suppose either his Almucantar Azimuth or Bearing for they giving you his Place in his Parallel the next Hour Circle to his said place shews you the time of the Day for if v. g. in the forenoon on the 10th of April you know that the Sun is 36 degrees high Rectify your Bead but to that height and moving the String from the Zenith your said Bead will touch the Parallel of the Day at 9 of the Clock In like manner if you know the morning Azimuth to be suppose 58 degrees draw your String from the Zenith over the said Degrees in the Horizon and 't will also cut the Parallel of the day at 9. Or if the Sun 's Bearing be for Example a little more than SEbE the laying of your String from the Zenith on that Character in the Horizon shows you on the Parallel of the day that 't is 9 as before OPERATION XII To know when the Sun rises and sets FIND the Parallel of the Day to wit that of the 10th of April and where it cuts the Horizon on the East-side of the Globe there the Suns place at his Rising will be so that the time of the day appears by the next Hour Circle to be a very little past 5 in the morning and if you cast your eye in the Intersection of the said Circle on the West you 'l find the hour to be almost 7 in the Evening This being so here follow 's a very pleasant and useful Operation as a Corallary viz. How to find at what time of the year and at what Declension the Sun rises or sets an Hour or any other space of time either early or later than it does at the proposing of the Question for if you observe but what Parallel intersects with the Horizon on the 4 a Clock morning hour-circle which is an hour earlier than when it rises on the 10. of April you will find it an Imaginary Parallel which the next real or mark't one shews to be the Parallel for the 14. of May and 12. of July and consequently by the Devisions of the Aequinoctial Colure that the then Declension is
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
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
find where 't is Day and where 't is Night all the World over COmpose your Globe and all People that live in the illuminated Hemisphere enjoy DAY at that Moment and all that live in the Obscure One NIGHT. OPERATION VIII To know where at that Moment of time the Inhabitants enjoy nothing but DAY and where nothing but NIGHT as also when the DAY and NIGHT will be thus perpetual in any place subject to this Alteration DEscribe with your Eye an Imaginary Circle about the Illuminated Pole its Radius being the Distance from the said Pole to the nearest part of the shade of Extuberancy and all places within that Circle will have then no Night and all places within the dark Circle of the like Radius round the obscur'd or obumbrated Pole will have then no Day Now if you desire to know when 't will be in this manner perpetual Day or Night at any Place between the Poles and the Polar Circles for you know 't is never perpetual Day and Night any where else you have nothing to do but to measure with your String or Compasses the Distance between the Place requir'd and the next Pole which now for Examples sake we will suppose the Northern Pole I say you have nothing to do but to measure this Distance for placing one end of your String or one Foot of your Compasses on the Interfection of the Meridian and the Aequator if you observe what Northern Parallel the other end of your String or Foot of the Compasses extended at the aforesaid Distance touches 't will shew you by touching v. g. the Parallel mark't with the 10th of April and 12th of July that it begins to be on the said 10th of April perpetual Day there and so continues until the 12th of July Now if you measure from the before mentioned Intersection towards the Southern Pole and find the End of your String or Foot of the Compasses to touch the 13th of October and 9th of January 't is certain that from the said Day in October to that of January 't will be perpetual Night there and consequently from the 12 of July to the 13th of October the Days and Nights succeed each other after the ordinary manner OPERATION IX To find where the Sun is Rising and where He is Setting all the World over COmpose your Globe and having consider'd the Confines or Extremity of the PRECEEDING and FOLLOWING Shades of Extuberancy you may conclude that to all the Inhabitants under the first the Sun is Rising and to them under the Second that He is then Setting OPERATION X. To find where the Sun is Vertical at any time i. e. what People have him just over their Heads THE Sun is always Vertical to those that lye in the middle of the Illuminated part of the Globe i. e. to those that dwell under his then present Place in his Parallel therefore as I show'd you in the first Section if you Compose your Globe and hold up your String against the Sun from the Pole till its Shade passes thro' the other or from the Zenith till it passes thro' the Nadir 't will cut the Parallel of the Day at the Suns true Place and consequently show you who they are that have him then just over their Heads which happens for Examples sake on the 10th of April about our 6 in the Morning to them that dwell about the middle of the Coast of Malabar OPERATION XI To know where they are Rising where they are at Dinner where at Supper and where going to Bed all over the World THis Operation depends on this Maxim That it is the same Hour with all People that have the same Longitude that is to say that live under the same Semi-hour Circle or Semi-Meridian therefore as the drawing of your String from the Pole over half the illuminated part of the Globe i. e. over the Sun 's present Place shows you that 't is Noon or Dinner-time with all that inhabit under the said String so the drawing it over any Place distant 6 hours Westward i. e. over so many hours towards the left hand from the Vertical point shows where 't is then all the World over 6 in the Morning or Tunc to Rise whereas had you drawn it six hours Eastward i. e. towards your Right-hand it would have shewn you where 't was six in the Evening or Supper-time and four hours further i. e. two hours short of Midnight or the point opposite to Noon where 't is 10 of Clock or Bed-time OPERATION XII How much any People if it be Day with them are past Morning or want of Evening and if it be Night with them how much they are past Evening or want of Morning IF the Place you propose has a Diurnal Parallel that runs over it then see what Point of the said Parallel the Preceding shade of Extuberancy cuts and if you count the Hour Circles or distance in time between the said Point and the proposed Place 't will give you if it be there Night how much it lack 's of Morning and the distance in time between the said Place and the Point made by the Following shade of Extuberancy gives you how much it is since Evening On the other side if it be Day there the distance between the said Place and Poynt made by the Preceding shade tells you how long 't is since Morning and the Following shade how long 't is since Evening Now if there be no Parallel that run's over or neer your said proposed Place mount your Bead to it and moving your said Bead on the Noose from the Pole it will describe a Parallel and then you may operate as before The Reason of the Operation is this The shade of Extuberancy getting every hour in the Aequator as you saw before fifteen degrees 't will proceed in the same proportion on all Parallels over which it passes therefore if the Distance between any Point in the Aequator and the Following shade be the distance in time of the said Point from Evening or Sun-set and if the distance there between any Point and the Preceding shade be the distance of the said Point from Morning or Sun-rising it follows that the distance between any Point in an Aequinoctial Parallel and these two shades of Extuberancy that cut it must be also it 's true measure or distance in time both from Morning and Evening OPERATION XIII To find the Sun's height in any Place where the Globe shews 't is Day or his Depression where it show's 't is Night as also what People throughout the World see the Sun at the same Height SUppose on the 10 of April Having compos'd your Globe and found it about 6 in the morning with you you should desire to know how high the Sun is at Rome as also all the People that then see him at that or any other determin'd height Measure by your String or Compasses the nearest