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
greatest extuberancy and this Circle being 90 Degrees from the point of the Globe which lies directly under our Zenith it must differ from the Horizon of the Globe as many Degrees as its Zenith differs from that in the Heavens therefore the way prescribed is at least speculatively true Operation II. To find the Suns Almucantar or Height THere are three distinct ways of performing this independent of the following Operations and each of great use for the first gives you the Suns height in an instant if he shines The second if you have the least glimps of him or can guess at his place in a Cloud The third if you know the hour by any good Watch Pendulum or the like whether we see the Heavens or no. I. As for the first way 't is this your Globe being level move it 'till the shade of the Pin in the Zenith falls directly upon the Meridian and then the shade of the Extuberancy i. e. that made by the swelling or bellying out of the Globe will touch the true degree in the Quadrant of Altitude reckoning from the Zenith to it And thus you will find not only the Sun's height sooner perchance than by any ordinary Quadrant but will still have it before your eyes as long as you please nothing being to be further done but to move sometimes the Globe that the shade of the said Pin may still concur with the Meridian But if your Globe be fix'd or that for some particular reason you have no mind to stir it at all draw your string from the Zenith through the shade of its Pin i. e. lay the string in the Plane of the Sun and then if you mount your Bead till it reaches the nearest part of the shade of Extuberancy it will by bringing it to the Meridian or Quadrant of Altitude lye on the true Degree reckoning as before from the Zenith to it The Reason of the Operation is this The Sun when he rises brushes the Zenith and Nadir of the Globe with his Rayes for he illuminates alwayes within some few Minutes just half of it therefore when he gets v. g. a Degree higher he must needs illuminate a Degree beyond the Zenith and so proportionably from time to time or else he would sensibly illuminate more or less of the Globe at one moment than at another which is absurd Now since the Sun in truth illuminates more than an Hemispere the Reader must remember that Ptolomy reckons this excess take one time with another to be about 26 minutes and Tycho something less therefore substract 13 minutes or half the said Excess from what the shade of Extuberancy mark 's and you have his Height with all ordinary Exactness but should you chance at any time to doubt how far the said Shade of Extuberancy which is not so discernable as that made by a Gnomon just reaches erect then a piece of stick straw quill c. or if you please rest your Finger on the Globe between the Sun and the point in dispute and where the shade of your Finger straw stick or quill is lost that will be the true Term of the shade As for the Second Way for both the former we reckon but one turn the Meridian of your Globe to the Sun as before or because we suppose him not to shine out-right direct by your Eye the said Meridian so that it lye in the same Plain with him and this you may do in a manner as well if you have the least glimps of him or can by any accident guess whereabouts he is as if you had the fore-mentioned help of the Pin's shade in the Zenith Having thus done Take your String in both hands and cross with it as exactly as you can at right Angles that part of the Meridian next your body whether it happens to be the Quad. of Alt. or that of Proportion then putting your Face close to it and moving your Ey lower and lower till by reason of the Extuberancy you can but just see the Sun or his supposed place in Heaven do but bring your String held as before to this point viz. bring your String towards you till it just takes away the Sun or his supposed place from your Ey and the degree in the Meridian on which it then lies will be counting from the Zenith the Height required for so far his raies would reach did he shine out-right The third way is when we know the Hour by any Watch Pendulum c. thus Find among the Aequin or Diurnal Parallels that belonging to the present Day which we will suppose Apr. 10. and drawing your string from the Zenith over that Point in the said Parallel where 't is cut by the Hour given i. e. by the morning 9 a Clock Circle move your Bead to the said Point and the distance from the Bead to the Horizon will be the required Height viz. about 36 degrees as you 'l find if you bring the Bead to the Meridian and count the degrees between it and the Horizon The Suns Height may be also known by its Azimuth as by Operat 5. Having therefore by any of the aforesaid waies his Height 't will upon any doubt soon appear whether it be Fore or Afternoon for as long as ever he increases in Degrees i. e. mounts higher and higher above the Horizon it wants of Noon whereas if he falls or declines 't is after Noon OPERAT. III. To Compose the Globe either by a Meridian Line or without it to the site of the World IF you have a Merid. line drawn viz. a Line lying exactly North and South place the Globe level with its Merid. directly over it i. e. place so the little Notch in the Pedestal markt S that it cover the Southern extremity of the said line and the Notch N the Northern and then the Poles and Circles on the Globe will without sensible error correspond with those in Heaven and each painted Region or Countrey on it will be turn'd towards the real one which it represents But if you have no line drawn Know the day of the Moneth and you have two quick waies to do this Operation without any forreign helps The Globe having in it smal pin-holes on the several intersections of the Merid. with the aforesaid Diurnal Parallels or to be exacter on each point of the Merid. which an imaginary Parallel of each fifth day would cut for tho' we are to suppose Parallels for every day throughout the year yet there being no sensible difference in the Sun from 5 daies to 5 days such holes will be abundantly sufficient nay the aforesaid ones from ten Dayes to ten Days may very well serve the turn in any ordinary Operation I say the Globe having holes in its Meridian at this distance put the Zenith Pin or if you think better a Needle in the Hole which most agrees with the true day of the Month and then exposing your Globe
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
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
your said Quadrant of Proportion and the Figures at the end of your Account will give the Proportion sought for Now if the Shade of Extuberancy or the Bead marks not even Degrees for the Sun's Height but for Examples sake 13 30′ and consequently falls between the Figures of 23 and 25 in the Quadrant of Proportion you had best to avoid all Calculation and Allowance expect a Moment longer for then the Sun's Height being even and without Fraction you may operate as before OPERATION II. How to find the height of a Tower by the Globe THIS Operation appears at first Sight to be a Corollary of the former for finding as I showd you that the Shade of Extuberancy falls in the Quadrant of Proportion on the number v. g 25 and that the said number represents a Perpendicular do but measure the shade of any Tower and you will soon have its height seeing that as 100 is to 25 i. e. as 100 is to the number found on the said Quadrant so is the Shade of the Tower which being measur'd wee 'l suppose 80 yards long to a fourth number viz. to 20 the required height OPERATION III. How by the help of your Globe to measure any Tower or height and yet not to seem to use any Instrument in the Operation THIS Operation may perchance a little surprise some and yet it differs not in reality from the former that showing you how to measure a height by your Globe upon the place and this how to do it privately To perform then the Operation you must choose when you are alone any of the aforesaid Numbers on the Quadrant of Proportion as suppose 25 and seeing that belongs to the 14th Degree from the Zenith rectify your Bead to the Complement i. e. to the 76th from the Zenith in the said Quadrant this being done move your String hanging on the Zenith's Pin till your Bead touches the Parallel of the Day which we now suppose to be the tenth of May and the Hour-Circle that meets with it there to wit that of six in the morning or six in the afternoon tells you that at those hours on that day of the Month the perpendicular will be the fourth part of the Shade i. e. as twenty five to an hundred so that having discours'd with some body of the possibility of measuring heights without an Instrument repair with him to any convenient place about the foresaid times of the day and when you find by your Watch that 't is exactly six do but measure the Shade and you will have the required height And by the way take notice that as it is in your power to choose what proportion you please and the more odd and exotic it happens if you can quickly reduce it the better it is for then People will not perchance so soon comprehend the Operation I say as you can choose your Proportion so you may choose the Hour also for if your Bead be rectify'd to the chosen Proportion according to the foregoing Example and Instructions and brought to the hour pitcht upon suppose 3 in the afternoon the Parallel to wit that of the fifth of February which meets with the the said Bead and Hour-Circle tells you that then the Proportion will thus happen nay you may choose what day and hour you please if you will be content with the casual Proportion or number which the Bead when rectify'd as we mentioned falls upon OPERATION IV. How to find the Hour by your Stick YOUR Stick being divided into ten equal parts and each part by Pricks into as many equal Subdevisions you must operate thus Rectify your Bead on the tenth v. g. of April to the Sun's Meridian Altitude and if you then move your String on the Pin of the Zenith to the Quadrant of Proportion the Bead will lye for Example on 87 so that having writ this on Paper with the figures of 12 above it draw your String from the Zenith over the next Hour-Circle on which hand you please I mean either over that of 11. or 1. and where your String cuts it on the said Parallel of the day there place your Bead and 't will lye v. g. on 93 in the said Quardrant of Proportion noting then 93 in your paper under the hours of 11. and 1. proceed then in this manner from Hour-Circle to Hour-Circle 'till you come to 6 for after the Sun is within an hour of his Rising or Setting you may easily guests what time of Day 't is besides shadows are then so long that they are troublesome to measure I say proceed in this manner to 6 and a Table like that in the Margin will show you the hour not only during that day but during five or six successively without any considerable Errors for you have nothing to do but to erect your Stick as perpendicularly as you can and to measure its Shade with it so that finding the length of the said Shade to be suppose 200 i. e. twice as long as the Stick your Paper will tell you that when this proportion happens 't is either eight in the morning or four in the afternoon OPERATION V. How to to take an Angle in Altimetry by the Globe THIS Operation is to be perform'd like that of finding the height of the Sun and Moon when they shine not out as I formerly show'd you that is to say you must place your Globe Horizontal and having turned the Meridian towards the Tower move your Eye along the said Meridian till the Extuberancy of the Globe permits you only to see the top of the Tower and then bring but your String which we suppose you hold in both hands cross the Meridian towards you till it just takes away the sight of the said Top and the Degree which your String then lies on counting from the Zenith is that of the required Angle to wit of the Angle which is ordinarily taken by any Quadrant Jacobs Staff c. OPERATION VI. How to make and figure the Quadrant of Proportion as also the Demonstration of the foregoing Operations IT appears plainly by the Scheme here before us that the Shade AB being Radius the Perpendicular CB is Tangent of A v. g. 14. the Degrees of the Suns height as also that the Perpendicular CB being Radius the Shade AB is Tangent of the Complement of the said height therefore if the Radius being 100 you mark from the Zenith to the Horizon each Degree of your Quadrant of Proportion with Figures according to the value of their respective Tangents you must necessarily perform the late Operations that give us the height of things the hour of the Day c. For if your Bead be rectify'd from the Horizon of your Globe to 76 the Complement of the Suns height it will be distant from the Zenith just as many Degrees as the Sun is high to wit 14 and consequently being moved to the Quadrant of Proportion which is figur'd we see from the
Species there are two sorts here viz. one of plain and simple Pricks the other of small Astricks alternatively plac'd so that 't is but observing of what Species the Prick next a Star is as suppose an Astrisk and then following with your Eye a File or Arch of Astrisks 'till you come to the Horizon for the Figures at their termination there give you the requir'd Azimuth Thus then the confusion which the several Almucantars and Azimuths would make were they all describ'd on the Plane is avoided seeing the Plane is now less fill'd than if the Almucantars were only exprest on it for disjoyn'd Pricks circularly plac'd occupy not the room of a continued Circle and yet each Row or Circle of the said Pricks perform both the forementioned Offices How to operate by the Projection or Pedestal FIRST the Reader must remember that I call Rectifying the first Plane the placing and adjusting it so that all the Stars may appear above and below the Horizon as they then really do in the Heavens themselves which Operation being a main and principal matter for all the other are in Truth but so many Deductions or Corollaries I will now begin with it nor is there any thing here requir'd but the height of some Star in view as the Lion's Heart or the like which you may find by the Globe as you do the Sun 's or Moons height as I mentioned before Now for cleerness sake let us suppose this Star to be about 45 Degrees high Westwardly and then if you move your Plane till the said Star lyes thus under a Prick of this height you have without ever moving more the Plane the several following Operations at a time First You see all the Stars that are then above the Horizon and below it for all the painted ones within the Circle HRST on the second Plane represent the real ones then in sight and the rest those that are below the Horizon Secondly You see what Stars are Rising what are Setting what are Culminating and what are in their Lowest Depression Thirdly If you look after any particular Star suppose the Lion's Heart by seeing him on the West-side of PS the Meridian of the said second Plane you are sure he is not only in a Declining state but also by following the Prick next him to the Horizon according to its Species that his Azimuth is 45 Degrees Fourthly You will see his Bearing to be about S. W. if you follow the Azimuthal Arch to the Nautical Characters there Fifthly You see that the Hour of the Night is 10 by observing under what Hour-Line the 10th of April i. e. the day of the Month the Suns place in the Ecliptick lyes Sixthly By any real or imaginary Hour Line that runs over the said Star you find his Right Ascension to be near 148 Degrees for thus the said Hour Line cuts the Limb. Seventhly By his being behind the Sun about 8 hours as appears by the Hour Lines that pass over the Star and the Suns place you have the difference of their Right Ascensions which amounts to about 120 Degrees Eighthly Which is the most surprising and not performable even by a Coelestial Globe you no sooner see these things in relation to this or any other particular Star but at the same time also even without touching your Projection you have them in relation to all the Stars in general for when the First Plane is rectify'd we have besides the Hour the Heighths Azimuths Bearings Right Ascensions c. of all the other Stars above the Horizon Concerning the other Operations they are more restrain'd as being peculiar to the Star you enquire after for if you would know when the Lions Heart Sets which for continuation's sake we will call the ninth Operation do but move your first Plane till the said Star touches the Horizon and the imaginary Hour Line that passeth over the Sun's place in the Ecliptic show's you that 't will be then about 3 and a quarter in the morning 10ly By the Figures about the Horizon you will see at the same time that his Occasive Amplitude is near 23 Degrees Northward and his then Bearing by the Nautecal Caracters to be WNW or thereabouts 11. By the imaginary Hour-line that then passes over the said Star viz. that of about 7 and a quarter you have half the time of his constant aboad above the Horizon and consequently know that from his Rising to his Setting there are about 14 hours and an half 12. By reason that the imaginary Hour-line of about 7 and a quarter passes over the Star as we said at his Setting it follows that it 's Ascensional difference i. e. the difference between its Right and Oblique Ascension is about an Hour and a quarter or 18 Degrees 13. By the Degree of the Ecliptic that Sets with the Star which is the 26 of ♌ and by the opposite Degree which then Rises viz. the 26. of ♒ you see that on the 8th of August he Sets Achronically and on the 2. of February Cosmically 14. Remove the said Plane till the said Star brushes the Horizon on the East-side and by the precedent method mutatis mutandis you will find when he Rises what his Ortive Amplitude is how he then Bears how long he is under the Horizon when he Rises Cosmically and when Achronically 15. By placing the point of a Pin or Needle on the Class over the Lions Heart and then moving the first Plane till the divided 6 a Clock Hour-line PE lyes just under the said point the Divisions there will show its Declination to be about 13 Degrees and 33 Minutes The like you may do with your Compasses for if you take the Distance between the Pole and Star and measure it on PE you have what you seek for Many other Operations are performable by the Projection touching the Stars but since these are the most material ones and since I have not time to treat more fusely I leave the rest to be found out by my Reader himself who may easily do it if he understands either the Caelestial Globe or any Instrument belonging to the Stars And here he is to remember that knowing but the Hour at any time let him put the Suns place or day of the Month under the Hour-line that corresponds with it and the Projection will be rectified and consequently having a true view of the then posture of the Heavens he may opperate as before In the next place if he knows but the Suns place in the Ecliptic of the first Plane and opperates with the said place as if it were a Star he may find out the former Operations in relation to the Sun it self that is to say he may at that moment know his Height Azimuth Bearing Amplitude c. 16. If you would know the Stars in the Heavens you may also do it by the help of this Projection for your first Plane being rectified it gives you as I said the true
what part of the Ecliptic the Parallel of the Day passes 5. The Suns Declination by considering throu ' what Degree of the Aequinoctial Colure the Parallel of the Day passes 6. The Sun's Azimuth and Bearing by considering what Degree of the Horizon and what Nautical Character are cut by the shade of the String hanging from the Zenith 7. The time of the Sun 's Rising and Setting by considering on what hour circle the Parallel of the Day and Horizon intersect on the East and West sides of the Globe 8. The length of the Day and Night by considering how many Hour-Circles cross that part of the Diurnal Parallel which is above the Horizon for they show the length of the Day as the Hour-Circles that cross the part under the Horizon do the length of the Night 9. The Sun 's Ascensional Difference by considering the Hour-Circles on the Parallel of the Day between the 6 a clock Hour-Circle and the intersection of the said Parallel with the Horizon 10. The Sun's Amplitude by considering how many Degrees in the Horizon the Sun rises from the true East Point or sets from true West 11. Where 't is Day or Night over all the World by considering the illuminated and obscur'd parts of the Globe for the one show's ever where 't is Day and the other where 't is Night 12. Where they enjoy nothing but Day and where nothing but Night by considering the Illumination and Obscuration about the Poles for a Circle describ'd about the illuminated Pole to the nearest shade of Extuberancy shows that all the Inhabitants within that Circle have nothing but Day and that all they that dwell within the like Circle about the obscur'd Pole have nothing but Night 13. Where the Sun is Rising and Setting all the World over by considering the preceeding and following shade of Extuberancy for the first show's the people to whom the Sun then is Rising and the other to whom the Sun is then Setting 14. How many hours any place wants of day or night by considering first a Parallel to run over the Place propos'd and then by reckoning the number of Hours between the said place and the preceeding and following shade of Extuberancy the one bringing with it Day and the other Night 15. What a clock 't is all the World over by considering according to the little Polar Figures the Hour-Circle that passes over any place and adding to the time thus found if it be in the afternoon as many hours as are past since Midday with you or substracting if it be in the Morning as many Hours as you want of Midday Now for the last kind of Conveniences which this Globe Challenges to it self to wit Those independent of the Operations they are 4. 1. For First It takes up little or no room wheresoever it stands the bottom of the Pedestal not being ordinarily much bigger than the foot of a large hour-glass whereas other Globes are cumbersom and embarras any Table or Place on which you set them 2. It is wholly expos'd to our Eye as well below as above the Horizon whereas the Frame Meridian and the other Appendices of common Globes always hide more than half of them 3 It is as cheap as a single ordinary Globe and yet performs the Operations of the Terrestrial and Celestial ones 4. It never declines from its Position whereas other Globes by moving on their Poles encline presently more or less to this or that side of the Meridian and Horizon so that besides their usual grating all the Operations become sensibly false FINIS Decemb. 28. 1672. A Catalogue of GLOBES Coelestial and Terrestrial Spheres Maps Sea-Plats Mathematical Instruments and Books with their prizes made and sold by Joseph Moxon on Ludgate-Hill at the Sign of Atlas GLOBES 26 Inches the Diameter The price 20 l. the pair GLOBES near 15 Inches Diameter The price 4 l. GLOBES 8 Inches Diameter The price 2 l. GLOBES 6 Inches Diameter The price 1 l. 10 s. CONCAVE HEMISPHERES of the Starry Orb which serves for a Case to a Terrestrial Globe of 3 Inches Diameter made portable for the Pocket Price 15 s. SPHERES according to the Copernican Hypothesis both General and Particular 20 Inches Diameter Price of the General 5 l. of the Particular 6 l. of both together 10 l. SPHERES according to the Ptolomaick System 14 Inches Diameter Price 3 l. SPHERES according to the Ptolomaick System 8 Inches Diameter Price 1 l. 10 s. Gunter's Quadrant 13 Inches Radius printed on Paper and pasted on a Board with a Nocturnal on the back-side Price 5 s. Gunter's Quadrant 4 Inches Radius printed on Paper and pasted on Brass with a Nocturnal on the backside and a Wooden Case covered with Lether sit for it A new Invention contrived for the Pocket Price 6 s. A large Map of the World 10 Foot long and 7 Foot deep pasted on Cloth and coloured Price 2 l. A Map of all the World 4 Foot long and 3 Foot deep pasted on Cloth and coloured Price 10 s. in Sheets 2 s. 6 d. A Map of the English Empire in America describing all Places inhabited there by the English Nation as well on the Islands as on the Continent Price 15 s. Six Scriptural Maps 1. Of all the Earth and how after the Flood it was divided among the Sons of Noah 2. Of Paradise or the Garden of Eden with the Countries circumjacent inhabited by the Patriarchs 3. The 40 years travel of the Children of Israel throug the Wilderness 4. Of Canaan or the Holy Land and how it was divided among the twelve Tribes of Israel and travelled through by our Saviour and his Apostles 5. The Travels of St. Paul and others of the Apostles in their propagating the Gospel 6. Jerusalem as it stood in our Saviours time with a Book of explanations to these Maps entituled Sacred Geography Price of the Maps 6 s. useful to be bound up with Bibles price of the Book 1 s. 6 d. A Sea Plat or Map of all the World according to Mercator in two large Royal Sheets of Paper set forth by Mr. Edward Wright and newly corrected by Joseph Moxon c. Price 2 s. Sea-Plats for Sailing to all parts of the World Price 6 d. the Sheet The famous City of Batavia in the East Indies built and inhabited by the Dutch curiously Engraved and Printed on four large Sheets of Royal Paper Price 2 s. 6 d. A small Map of all the World with Descriptions on one Sheet Price 6 d. BOOKS A Tutor to Astronomy and Geography or the Use of both the GLOBES Celestial and Terrestrrial by Joseph Moxon A Member of the Royal Society and Hydrographer to the Kings most Excellent Majesty Price 5 s. The Vse of the Copernican Spheres teaching to salve the Phaenomena by them as easily as by the Ptolomaick Spheres by Joseph Moxon c. Price 4 s. Wright's Correction of Errors in the Art of
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
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
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
the Day But by Construction all the hour-lines are thus drawn on the Cieling and consequently are exactly over the supposed ones on the Floor Ergo the Reflext Ray from G must as truly show you the Hour above as the Direct Ray below for both Rayes are ever in the same Plane Nor is there to be any real Difference in the Operation tho' the Chamber-window should look another way for you are only to remember that whilst it enjoys the least Point of South the Center of your Dial is without the Chamber when it looks full East or West 't is in the side or edges of it and when it verges Northward 't is altogether within so that in a full Southern Aspect the said Center will be most abroad and in a full Northern one the Contrary all which plainly appears to any one that will consider an Horizontal Dial truly plac'd having a Perpendicular for its Stile if he draws over the Hour-lines a Line that shall represent the aforesaid side of your Chamber according to its Position and Site OPERATION XXXIII To make a compound Dial to wit one containing several useful Operations INnumerable are the ingenious Dials that may be invented but since we have been long enough on this Subject either for my Reader 's Speculation or Curiosity I will now conclude and that with a Recapitulation or summing up of much of what we have already said by showing the Fabrick of a Compound Dial that is to say one that contains many useful Operations besides the Hour for nothing rubs up the Memory more efficatiously or makes us more Masters of our Rules than a Practical Example The said Dial shows as follows 1. The Hour with us at all times 2. The Hour in what other Countries you please 3. The Sun's Place in each Sign 4. The Day of the Month. 5. The time of the Sun 's Rising and Setting 6. The Sun's Amplitude 7. The Sun's Height 8. The Sun's Azimuth 9. The Sun 's Bearing according to the Points of the Compass 10. The Proportion between Perpendiculars and their Shadows and consequently the height of any Tower or the like To make then this Dial you must first describe an Horizontal as in Sch. 41. about a Foot in Diameter and let B the Center of the Plane be the Point where an Erect or Vpright Stile according to our Directions in the first Horizontal shews you with its Top the Hour Now because the Shade of an Vpright Stile unless it be very short will presently fall out of the Plane as well in the Morning as toward Night therefore it will be convenient to have your Cock or Stile made so that AB the Perpendicular or fore-part of it as in Scheme 42. should stand at B the said Center of the Plane to represent this upright Stile and its Angle AOB at O the Center of the Dial or Point from whence all the Hour-lines are drawn for thus the side OA making with the Meridian line at O the Angle of the Elevation represents the Axis of the World and consequently casts its shadow on the Hour-lines as the usual Cocks of all Horizontal Dials do 2. Having chosen all the Places which you desire from time to time to know what a Clock it is at consider well your Globe and find under what Hour-Circles the said Places lye as for Example suppose Rome lies under the 11 a Clock Hour-Circle Constantinople under that of 10 Aleppo 9 c. Place therefore the said Towns towards the Limb of your Dial under the corresponding Hour-lines and you will constantly know the time of the Day in the said Places for calling it always Noon at each Place you seek after you have nothing to do but to count the Hours from thence to the shade of the Stile as v. g. If it be 4 a Clock with you in the afternoon and you would know the Hour at Aleppo let Aleppo be 12 and counting from thence 1. 2. 3. c. 'till you come to the Hour of the Day I mean the Hour then shown you by the Shade you will find it to be 7 a Clock there for Aleppo is you see three hours Eastward of you now had the Hour with you been 4 in the morning you must have counted backwards as 11 10 9 8 and consequently you would have found it there 8 in the morning In this manner then you must operate all along 3ly and 4ly Find by your Globe exactly the Sun's height every hour at his Entrance into each Sign then take by the help of your Sector AB the Erect Stile in Scheme 42. being Radius the Tangent Complements of the Heights and putting one Foot of your Compasses on your Dial at B make Pricks or Marks in each corresponding Hour-line accordingly that is to say if the Sun be high suppose 50 Degrees at 12 of the Clock when he enters ♉ or ♠then take the Tangent of 40 and prick that distance in the Meridian line viz. From B to f and if his height at 1 and 11 a Clock be v. g. 48 degrees take the Tangent of 42 and prick that distance in the 11 and 1 a Clock lines viz. from B to h and g and when you have gone thus over all the Hour-lines no sooner will the Sun come into ♉ or ♠but the Shade of the Point or Apex of the Stile AB will fall every hour on the aforesaid Pricks and consequently show you the Suns place in the Ecliptic In like manner you must do with the rest of the Signs and then with the 10th Degree of every Sign placing still the Character of each Sign about the Limb of your Dial near the last mark or Prick belonging to it This being done see by your Globe what day of the month corresponds with each Sign and what with their Subdivisions and if you mark this as the said 41th Scheme shows you on both sides of the Meridian then the said Pricks will by the help of the Shade of the top of AB show you also the day of the month I mention here Pricks not only as an easier way but a better way than Lines for besides the great difficulty of drawing them they embarras and confound a Dial very much especially if there be many of them whereas the said Pricks are never out of an Hour-line and consequently take up no new room Now to avoid Confusion and Mistakes I would have the said Pricks of 3 sorts at least for if one Row were v. g. Astericks and another Crosses and a 3d Plain Pricks you would then know at first sight to what Sign or Day of the month any of them belongs 5ly Instead of troubling you with deviding the Circle GKLT the upper part of the Border of the Dial for the finding out the time of the Suns Rising and Setting you need only consult the Days of the Month on your Globe first when He rises earliest Secondly when He rises at 4 a
the very Circles and Arches are describ'd on it Sch. 4. as it represents for the said Pricks and Asterisks are ever to be in their intersections And by way the Instrument maker may if he pleases make use of Pricks and no Asterisks on the real Transparent Plane of the Pedestal for they will upon second thoughts perform better the Operation The Conclusion HAVING thus finish'd all the Operations that at present occur I shall now end with what I promis'd in the Beginning to wit with showing the Reader the particular Advantages of this Globe which are of four kinds For First it does several Operations not performable by the Ordinary Globes 2ly It does even the Operations which the other perform much easier and quicker 3ly It performs many at a view which are to be done by the other for the most part successively Lastly It has several by-advantages and conveniences belonging to it by it's Make independent of the Operations As to the Operations not performable by any other Globe they are 1. The placing of it self Level or Horizontal 2. The Composing of it self to the Position of the Heavens 3. The showing of the Hour even several wayes and this not only at Home but at the same time also in all Places of the World 4. The knowing how much any place wants of Day if it be Night there or of Night if Day there and consequently the Babilonish and Italian Hour without any Computation 5. The showing the Judaical Hour without any Computation 6. The showing the Sun 's true Place in the Heavens every Moment and consequently in what Countrey he is then Vertical 7. The Sun's height at any time of the Day both at home and in all other Places where the Globe show's 't is Day as also his Depression where it show's 't is Night 8. The Sun's Azimuth and Bearing 9. The Antient Geography as well as Modern 10. The Hour by the Moon with several other Operations concerning her 11. The proportion of Perpendiculars to their shades with Corollaries in relation to Altimetry and showing the Hour by your stick 12. The performing of all the accidental Requisites to Dialling as how to draw Meridian Lines and Lines Parallel to the Horizon how to find the Declension of all Planes as also their Reclination Inclination c. But here the Reader must remember that when I say none of the forementioned Operations are performable by other Globes I mean not this alwayes in a strict sence for if suppose we have the Hour of the Day given we may then as every body knows soon find by it the Sun's height or if suppose we have his Azimuth we have the Hour I say I mean not this alwayes in a strict Sence but call all these Operations not performable by other Globes since they at first require for the Operations they do somthing as hard to be found as what we seek after whereas by exposing only of this Globe to the Sun and having but the day of the Month most of the Premises present themselves to us at all times with as much facility as the very Hour it self by an Horizontal Dial. Besides the Reader must know if a Brazen graduated Semi-Circle were hung on the Poles here with an erected moveable Pin or Cursor on it there would be no need of the Holes I formerly mention'd in each Parallel of the Globe for the true Composing of it Nay this Semi-Circle omitting several other things will also give the hour by being still directly over it as often as 't is moved into the Plane of the Sun but seeing I pretend to show all the Operations here treated of even on a naked and free Globe by the sole help of a little String or Thred I hint only the said Semi-Circle that the Reader may use it if he shall judge it any time fit for his business In the second place as to the Operations common to all Globes but more easily perform'd by this take some few Examples that follow 1. If you would find suppose the Aurora by the Common Globes you must after knowing the Day of the Month or Suns place in the Ecliptic bring it to the Meridian then you must put the Index Horarius on 12 and so move the said Sun's place to the East side of the Horizon Afterwards you must find the opposit Point to the Sun's place and fixing your Quadrant of Altitude in the Zenith you must mount the said opposite Point till it meet with the 18th Degree and then the Index gives you what you seek for whereas by This Globe you have nothing to do but to depress your Bead 18 Degrees below the Horizon and to move the String on the Zenith till the said Bead touches the Parallel of the Day on the East side of the Globe for then it lyes on the requir'd Hour 2. If you would but know when the Sun rises by the other Globes you must after finding of the Sun's place lay your Index on 12 and when you have brought the said Place to the East side of the Horizon the Index will show the Hour Whereas now the * Intersection of the Parallel of the day with the Horizon performs the Operation without more a-doe 3. If you would know the Ascensional Difference by the other Globes you must first find the Right Ascension then you must find the Oblique and lastly you must substract the greater from the less whereas here the distance on the Parallel of the day which the Hour-Circles measure between the 6 a clock hour circle and the intersection of the said Parallel with the Horizon gives at a view the requir'd Ascensional Difference in time and consequently in Degrees I shall not trouble my Reader with more Instances at present leaving the rest to his own Observation and he will still find at least generally speaking That the Operations as I said common to both Globes are more easily and readily perform'd by this than by any other As to the Advantages of the third kind to wit The performing several Operations at one view which are perform'd successively by other Globes there are at least 15 that present themselves to you the Globe being compos'd as soon as ever you have made the Shade of the String hanging on the Zenith to pass throu ' the Nadir for then you have before your Eyes 1. The Hour of the Day by considering the shade of the illuminated Pole 2. The Day of the Month by considering on what Diurnal Parallel the Shade of the String marks the same Hour with that shewn by the shade of the said illuminated Pole 3. The Place where the Sun is Vertical by considering the Sun's place in his Parallel and consequently the Country under it 4. The Sun's Sign or Place in the Ecliptic by considering according to the Increment or Decrement of the Days throu '
Word is Rendred the Nature of Things signified Discussed and where Need requires Illustrated with apt Figures and Diagrams With an Appendix exactly containing the Quantities of all sorts of Weights and Measures The Characters and meaning of the Marks Symbols or Abbreviations commonly used in Algebra And sundry other Observables By Joseph Moxon Price 2s 6d The English Globe invented by the Right Honourable the Earl of Castlemain and of which this Book shews the use containing about a Foot in Diameter are made by Joseph Moxon Price ordinary made up 40s and with the Projection described in Section 6. of this Book Price 50s At the place aforesaid you may also have all manner of Maps Sea-Plats Drafts Mathematical Books Instruments c. at the lowest Prizes FINIS * pag. 24. * p. 73. †p. 80. * p. 82. †p. 85. Of the Circles describ'd on the Globe The 4 Cardinal points of the Globe * vid. Oper 2. 5. in Sect. 2. What the Operations of the Globe are perform'd with A Memorandum How the Treatise is divided The first way A Memorandum The second way The Reason and Demonstration of the Operation The first way The Reason and Domonstration of the operation How much the Sun illuminates more than half the Earth How to know the terms of the shade of Extuberancy when the sun shines faintly The second Way The Third way To know at any time whether it be Forenoon or Afternoon * Operat 1. pag. 4. A way to Compose the Globe by the Sun * Operat 2. pag. 7. A Memorandum The first way of Composing the Globe The Demonstration The 2d way vid. Op. 10. The 1. way The Second way vid. Op. 10. The first way * Operat 3. pag. 8. The second way The Third way * vid. Oper. 2. pag. 5. A Memorandum The 4th way The first way The 2. way * Op. 2. pag. 6. †Op. 5. pag. 10 A Memorandum * Op. 3. pag. 8. The 1st way The 2. way The 3d. way * 2. pag. 6. The 4th way A Memorandum * vid. the particulars in the conclusion or last Chapter The 2d way of composing the Globe by the shade Demonstration * Op. 3. pag. 8 The 3d. way of finding the day of the month * Op. 2. pag. 6 Op. 5. pag. 10. To find when and at what declension the Sun rises or sets earlier or later accord * Op. 6. pag. 11. * Vid. Oper. 13. Sect. 2. Preliminary Considerations The grand Divisions of the Earth The Boundary between Europ and Asia The Division of each modern Country from the other The Ancient Limits of several Nations A Table of reducing Degrees into Miles What the Latitude of a Place is and how to find it What the Longitude is Of the Grand Meridian Of the most noted Places where Author 's have plac't the grand Meridian Where we fix our Grand Meridian How to find the Longitude of any place A Memorandum A preliminary Discourse of Climes What a Clime is What a Parallel is Of the Antiquity and number of Climes Of the 7 common Northern Climes Of the 7 Southern Climes Why the middle of the first Clime has 13. hours of day How the first Circle of Longitude is divided as to the Climes To find in what Clime any Place lies Of the inequality of the Climes * pag. 23. Of the 5 Zones Of the bounds of the Torrid Zone which contains the Amphiscii To find when the shade changes side here Of the bounds of the frozen Zones which contain the Periscii Of the bounds of the Temperate Zones which contain the Heteroscij First way Second way Third way Of the Periaeci Of the Antaeci Where they have no Night and where no Day When 't will be perpetual Day or Night at any Place * Op. 6. pag. 11. Where 't is Dinner-time all the World over Where 't is the time of Rising all the World over Where 't is Supper time all the World over Where 't is Bed-time all the World over The Reason or Demonstration of the Operation * Oper. 10 sec 1. pag. 14. To find the Sun's height in any place The Reason of the Operation To find the Sun's Depression To find all the Places that have the Sun at the same height How Astronomers begin their Computation of Time How the Italians How the Babilonians To find the Babilonish and Italian hour when the sun is in the Aequator * Op. 10. sec 1. pag. 14. * Op. 10. sec 1. pag. 14. To find the Italian Hour when the Sun is in the Aequator To find the hour both the said ways at any time * Op. 18. p. 19 A most ready way of finding at any time the Babilonian and Italian Hour all the world over Of the Judaic way of Computing time A most ready way to find the Judaic Hour Why the days of the Week being called by the Names of the Planets follow not each other after the order of the Planets * ♄ Saturn ♃ Jupiter ♂ Mars ☉ Sol ♀ Venus ☿ Mercury ☽ Luna The Advantage in reckoning the Italian way The Advantage in reckoning the Babylonian way Of the Parallel Sphere Oblique Sphere All Positions taking the year round enjoy an equal share of the Sun's presence * Vid. Op. 3. sec 1. pag. 8. The Demonstration How the Earth is prov'd Round The Demonstration * pag. 5. * pag 10 * pag. 11 * vid. pag. 8. 15 A Memoran * p. 12. How you are to operate A Memorandum An Example Two Memorandums The reason or demonstration of the Operation A memorandum Why 6 hours must be added sometime to the Tables * p. 49. * p. 16. * pag. 49. * Op. 7. sec 2. pag. 33. * Vid. Op. 1. 2. pag. 49. A Corollary An Example A memorandum * Sect. 1. Op. 2. p. 5. *  1. 2. 3. 4. 6.  12. 11. 10. 9. 8. 7. 6. 87. 93. 110. 140. 200. 300. 625. * Op. 2. Sect. 1. pag. 6. A preliminary Discourse * pag. 4. †pag. 5. * pag. 10 * ☞ Because every body that desires to know these and the following Problems has not perchance at hand Mr. Gunter's Book I shall add them to this Treatise as the Reader will find at the end of it J. Moxon How to find the Tangent and Secant of any degree Demonstration A Memorandum The Construction An Example How to draw the half hours quarters c. The Construction Demonstration * pag. 71. The Demonstration * pag. 4. A Memorandum * pag. 8. * pag. 73. The Construction The construction * pag. 79. How to draw a Line Paralel to the Horizon and how to place truly the draught on its Plane An easier way how to place any paper draught on its Plane A Memorandum Demonstration A Memorandum Some few things to be premis'd The Construction of an East Dial. Of a West Dial. Of the Stile and Substilar The Demonstration The Construction The Demonstration The reason of the