happen 6 days and 16 hours or 6 Days and 20 hours and several such Fractions and Deviations from the Positive Terms prefixt by me but since the forementioned whole and half dayes will bring us to a knowledge exact enough of the hour sought for we call 6 days and 16 hours 6 dayes and a ½ only as coming neerer to it than 7 whole ones In like manner we call 6 and 20 hours 7 days and deal in this Proportion with all other number of days and hours which the Ephemerides or Almanack give us concerning the length of the requir'd Quarter And here you may be pleas'd to remember also that it would not be amiss in case you exceed much any of the foresaid terms to add or cast away sometimes a minute or a little more as you shall see Cause For if v. g. you find the Moon to be six days and 17 hours in her journey which according to our former Directions is to be reputed only six days and ½ and consequently the Elongation 55′½ you may then cast away 1′½ because of this great excess above the half day and if you should find her at another time to be 7 days and twenty houres i. e. eight days you may add for the want of the four hours a minute and make her dayly Elongation 46 instead of the forementioned 45 but here you may do as you you please for the error will not be considerable These Particulars being premis'd let us come to an Example and Suppose then that on the fifth of January finding the Moons shadow to marke two in the afternoon on your Globe for the Lunar hour you should desire to know the true or Solar hour First your Almanac can tell you not only that the Moons last Cardinal Point was v. g. her Conjunction but how many Days and Hours she spends in going from it to the next Cardinal Point for finding there her said Conjunction to be on the first day suppose at seven at night and that she comes to her first Quarter on the ninth day near the same hour you may presently conclude she is 8 whole Days in this Voyage and consequently that her Diurnal Elongation from the Sun will be 45 minutes Now because the said fifth day is the 4th of her Journey if you multiply 45 by 4 or lookin the Tables which we shall presently show you belonging to her 8 Days Journey you 'l have three hours for the time that she is behind the Sun so that the Solar or true hour must be five at night wanting four minutes for you are always carefully to substract two minutes for every hour the Moon wants of compleating her whole Days march which in the present case happens not before seven at night whereas you must have added them had the Solar hour bin nine at night because then her Elongation from the Sun would have been 4 minutes more than the aforesaid three hours 'T is in this manner you are to opperate in all cases but before we proceed take these two Memorandums with you First That by the Moon 's compleating a day's journey I mean 24 hours after the time let it happen by night or by day of her entring into her last Cardinal Point as for Example If she comes to her Conjunction or any other Cardinal Point at 7 in the Evening on v. g Munday then at 7 in the Evening on Tuesday she has compleated one day's journey and at the same hour on Wednesday two Dayes and so on till she comes to her next Cardinal Point The second Memorandum is That whereas in the late Example her Elongation from the Sun was three hours because you sought what a Clock it was on her fourth days journey from her Conjunction to her First Quarter at the Elongation of 45 minutes per diem Now had she been thus advanced in her Course from her First Quarter to her Full or from her last Quarter to her Conjunction you must have added 6 hours to the said 3 hours so that then the true hour would instead of 5 at night have been 11 and this is to be a general Rule Thus much then for the way of finding what a Clock it is at any time by the Moon and now let us make good what we have said First we see that to know the Hour by the Moon is to know the difference between the Lunar and Solar hour i. e. between the hour Circle she is in and that in which the Sun happens at the same time to be or in other Terms between the hour she marks on the Globe by her shade and that which the Sun would mark did he then appear Now seeing that in her Course from one Cardinal Point to the other she seldom spends the same number of days and half days it follows as we hinted in the begining that no certain number of minutes can be allowed for her daily Elongation But if we divide 6 hours or 360 minutes i. e. her total Elongation from one Cardinal Point to another by the Days and half days she spends in the journey the Quotient must be her Diurnal Elongation at least to sence during that Quarter Now since the Diurnal Elongation is as you see most commonly above three quarters and somtimes almost an hour the Horary one must be as I said considerable seeing in the space of every 7 hours it may amount to above a quarter more therefore this inconvenience we obviate by allowing two minutes for each hour after her compleat days journey and substracting them from what she wants of it Here I confess there may be an Error but it is hardly worth the mentioning for when she is either 8 days or 7 in her journey from one Cardinal Point to another i. e. when her Diurnal Elongation is either 45′ or 51′ and ½ the difference from 48 minutes a day or 2 minutes an hour cannot be but 3′ and ½ in a whole day nay when her Elongation is 55′ and ½ i. e. when she spends 6 days and ½ in her voyage the difference is but 7′ and ½ from the aforesaid 48 minutes nor can this happen till the end of every compleat days journey and consequently is not perceivable for the greatest part of it But since we here see where and how any error may arise it is easily remedied by an Allowance if any man thinks it worth the while to be so exact As for the Reason why if she be in her Course from her first Quarter to her Full or from her last Quarter to her Conjunction we must add always six hours to the Elongation which our Calculation or the Tables give it is because the said Elongation is only the precise time of her Departure from her last Cardinal Point whereas if she be past her first Quarter in her Journey towards her Full she is so much and six hours more i. e. so much and the six hours which happen from her Conjunction
to her first Quarter Now in rigor we should add twelve hours to the Elongation we find when she is gone from her Full towards her last Quarter but seeing she is in the Plane of the same Hour-Circle or very near it both at Full and in Conjunction therefore the bare adding the said simple Elongation will serve as well in one case as in the other for if the Full Moon at suppose 2 of the Clock at night casts really her Shadow on the Hour-Circle of 2 in the Afternoon yet there 's no need of hints the thing being so plain to prevent your mistaking Day for Night The like also is to be said of the last Quarter whose Elongation should be in truth eighteen hours but the additional six hours as we allow her after her first Quarter are sufficient since no man can be so ignorant as to take the Morning for the Evening notwithstanding the Lunar hour should be upon a Morning Hour-Circle To facilitate then this Operation least what we have already said has proved tedious we will conclude as I promis'd with a short Recapitulation or Abstract as also with the Tables of her daily Elongation let the time be what it will as we said that she spends in her Journey from one Cardinal point to the other The Abstract of the Operation in finding the true Hour by the Moon according to the late Example AS for the Almanac there are three things we see it informs us of viz. 1. The Hour when the Moon came to her last Cardinal Point 2. How many days she is going from the said Point to the next and 3. In which Days Journey she is at present Knowing then according to the late Example that the Moon will be eight days running throu ' her Quarter and that she is in the fourth Days Voyage 't will follow that the fourth day in the Table whose title is eight dayes will tell you that her present Elongation from the Sun is three hours so that the lunar-Lunar-hour being two in the afternoon the true hour must be just five at night only twice two Minutes are to be abated because she lacks 2 hours from compleating her said fourth days voyage for your Almanack according to our supposition informing you that it was seven at night when she set out from her last Cardinal Point it must be still seven at night before she compleat's any whole day's Journey during that Quarter This then is the summ of the whole Business nor need you trouble your self with any other Reflexion unless it be to add six hours as I already said to the Elongation in case she be going from her first Quarter to her Full or from her Last to her Conjunction And to conclude take notice that the hour if you see the Moon may be as well found by day as by night for her Place on the Globe which the third Operation show's how to find is always the true Lunar hour Tables of the Diurnal Elongation of the Moon from the Sun whether she goes in 6½ 7 7½ or 8 days from one Cardinal Point to the other 6. ½ Days Card. Point 0. Days from her Cardinal Point 0. Hor. 0. min. Elongation 1. Days from her Cardinal Point 0. Hor. 55. ½ min. Elongation 2. Days from her Cardinal Point 1. Hor. 51. min. Elongation 3. Days from her Cardinal Point 2. Hor. 46. ½ min. Elongation 4. Days from her Cardinal Point 3. Hor. 42. min. Elongation 5. Days from her Cardinal Point 4. Hor. 37. ½ min. Elongation 6. Days from her Cardinal Point 5. Hor. 33. min. Elongation 6½ Days from her Cardinal Point 6. Hor. 0. min. Elongation 7. Days Card. Point 0. Days from her Cardinal Point 0 Hor. 0. min. Elongation 1. Days from her Cardinal Point 0. Hor. 51. ½ min. Elongation 2. Days from her Cardinal Point 1. Hor. 43. min. Elongation 3. Days from her Cardinal Point 2. Hor. 34. ½ min. Elongation 4. Days from her Cardinal Point 3. Hor. 26. min. Elongation 5. Days from her Cardinal Point 4. Hor. 17. ½ min. Elongation 6. Days from her Cardinal Point 5. Hor. 9. min. Elongation 7. Days from her Cardinal Point 6. Hor. 0. min. Elongation 7 ½ Days Card. Point 0. Days from her Cardinal Point 0. Hor. 0. min. Elongation 1. Days from her Cardinal Point 0. Hor. 48. min. Elongation 2. Days from her Cardinal Point 1. Hor. 36. min. Elongation 3. Days from her Cardinal Point 2. Hor. 24. min. Elongation 4. Days from her Cardinal Point 3. Hor. 12. min. Elongation 5. Days from her Cardinal Point 4. Hor. 0. min. Elongation 6. Days from her Cardinal Point 4. Hor. 48. min. Elongation 7. Days from her Cardinal Point 5. Hor. 36. min. Elongation 7½ Days from her Cardinal Point 6. Hor. 0. min. Elongation 8 Days Card. Point 0. Days from her Cardinal Point 0. Hor. 0. min. Elongation 1. Days from her Cardinal Point 0. Hor. 45. min. Elongation 2. Days from her Cardinal Point 1. Hor. 30. min. Elongation 3. Days from her Cardinal Point 2. Hor. 15. min. Elongation 4. Days from her Cardinal Point 3. Hor. 0. min. Elongation 5. Days from her Cardinal Point 3. Hor. 45. min. Elongation 6. Days from her Cardinal Point 4. Hor. 30. min. Elongation 7. Days from her Cardinal Point 5. Hor. 15. min. Elongation 8. Days from her Cardinal Point 6. Hor. 0. min. Elongation These Tables are to be on the Globe in the most vacant and free parts of it OPERATION VIII To know how many hours the Moon has been up and how many she lacks of her setting as also how long she is to be that day above the Horizon THis is done by numbring the Hours or Hour Circles between the Moons place in her Parallel on the Globe and the intersections of her said Parallel with the Horizon for having found that her Parallel cuts the Horizon in the East at the five a clock hour circle and in the West at that of seven and seeing that her present Place is v. g. at that of two in the afternoon you may conclude that she has bin up nine hours wanting eighteen minutes that is eight hours and forty two minutes and will set within 5 hours wanting ten minutes or four hours and fifty minutes for the Moon goes from East to West by the Motion of the Primum Mobile or Motum Raptus two Minutes as we suppose every hour take one time with the other slower than the Sun which happens by her being too quick for the Sun in her own Motion that is to say in the Motion of the Center of her Epicicle which carries her from West to East therefore the Moon according to the present Example or Supposition will be above the Horizon fourteen Hours wanting twenty eight Minutes i. e. about thirteen hours and a half OPERATION IX To find at what at lack the Moon rises and sets BY the last Operation you are inform'd of the hours from her present station to her Rising and
she shines out right and consequently casts a shade or appears only faint and wan by reason of thin Clouds or by the excess of Light during the Sun's aboad above the Horizon Let us then begin with her Almucantar and Azimuth as being the Basis and Foundation of all Operations here relating to her nor can there be the least difficulty in any of them unless perchance in the 7th since they have so great a Correspondence and affinity with those already handled in the former Sections OPERATION I. To find the Moon 's Almucantar or Height THIS is to be perform'd as well when she cast's a shade as when she cast's none by the two first ways of finding the Suns Almucantar and therefore consult the second Operation in the first Section OPERATION II. To find the Moon 's Azimuth THIS is also to be found by the two first ways of finding the Sun's Azimuth treated of in the 5th Operation of the first Section OPERATION III. To find her true place on the Globe IF she casts no shade her place is to be found by her Almucantar and Azimuth as we hinted in the 6th Operation of the first Section since she must ever be where these two Circles intersect But if she shines out cleer you have nothing to do having plac't your Globe on a Meridian Line but to see what hour the shade of the enlightned Pole or that of your String passing over both Poles mark 's for this giving you her hour-Circle which we 'l call the Lunar hour hereafter her height or Almucantar must needs tell you in what part of the said Circle she resides This Operation is to be well understood and readily perform'd seeing most that follow are as it were Corollaries from it and for the better illustrating and explaining them we will imagine the Moon 's Place to be in the hour Circle of 2 in the Afternoon about 43 Degrees above the Horizon OPERATION IV. To know the Moon 's Declension from the Aequator THIS is only the nearest distance of her true Place from the Aequator which your Bead or Compasses will show you to be about 12 Degrees Northward if according to the foregoing Example she be 43 Degrees high in the hour Circle of 2 in the afternoon OPERATION V. To find the Moon 's Diurnal Parallel and consequently how to Compose the Globe by the Moon BY the Moons Diurnal Parrallel I mean a real or imaginary Circle Parallel to the Aequator and answerable to her present Declension which by the former Operation we suppose to be about 12 Degrees Having therefore this Parallel you may compose the Globe by the Moon as you do by the Sun And here you must remember that tho' the finding of the Parallel implies at first a Meridian Line yet the knowing how to compose thus your Globe will not be useless for now you are no longer confin'd to one Place or Line but may compose it where you please by the help of the said Parallel OPERATION VI. To find the Moon 's Bearing according to the Points of the Compasse THIS is to be perform'd after the way of finding the Sun's Bearing in the 7th Operation of the first Section for if you draw your String from the Zenith over the Moons present Place the said String cuts by our Example the Horizon at S. W. and some few Degrees towards the South for her then Bearing OPERATION VII To know what a clock it is by the Moon THere is no Operation treated of so intricate as this and therefore if the Reader who would have his Curiosity satisfy'd has not Patience enough to descend to a little niceness he had better fall upon another Subject but tho' we may be somewhat long at first in laying down and explicating all Particulars yet at the end we will contract the whole into half a dozen Lines and thereby make the Operation very expedit and easy I say there is no Operation so intricate as this for the Moon by reason of her different Place in her Epicicle is so inconstant in her dayly Elongation from the Sun that sometimes she spends from v. g. her Conjunction to her first Quarter above 8 days tho at another time a great deal less than 7 will serve the turn and to this variety and skittishness is the space also between any of her other changes liable If then her distance from the Sun be so uncertain and yet is the thing that must be known before her Place or shade on the Globe can give us the hour seek how strangely fallible is the usual way as well in some Authors of Note as in ordinary Almanacks of finding it to wit the adding of as many 48 minutes to the hour she shows on a Dial as she is days old for the Tables made in pursuance of this Rule suppose her always on the 15th of her Age to be at Full which may happen as I now mention'd not only much sooner but also much later so that most commonly her true Age and the said Tables are at variance nay when they agree there can be no Reliance on them seeing that if v. g. at 6 they show tolerably what a clock it is yet by 12 there may happen an Error of near a Quarter by reason that she is every moment at a new distance from the Sun and at one also which presently becomes very sensible Thus therefore we see that there must be Exceptions and Restrictions in any one Rule that appertains to this business nor is it to be perform'd by an Instrument in a trice as the Operations commonly are belonging to the Stars that have a Regular motion or to the Sun whose Extravagance is not soon perceptible I say thus we see that there must be here Exceptions and Restrictions and in truth nothing but a down right Astronomical Calculation can really perform it yet since such a critical Exactness in the hour is never necessary in our ordinary affairs I shall propose this method which will at least come always very near the Mark. When you desire to know what a clock it is by the Moon take an Almanac for if you would only have her true Age you must recur to one or to something analogical and reckon therein how many dayes there are in the present Quarter from one Change to the other i. e. from New Moon to her First Quarter or from her first Quarter to her Full and so on for I call any of these four Aspects a Cardinal Point or Change and the whole time between one Change and the other a Quarter I say Reckon how many Days there are in the then Quarter and you will find either 6½ or 7 or 7½ or 8 so that if the number be 6½ her Elongation from the Sun is 55 Minutes and ½ per Diem if 7 Days 51′½ if 7 days and half 48′ and lastly if 8 Dayes 48′ I mean not nevertheless that from Change to Change there maynot sometimes
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
Mary and St. Michael 2 Isles of the Azores for truly thus it suits best according to my Tables with the 2 a Clock Circle as his Lordship would have it do An Advertisement BEcause there are several who either want time or Patience to go throu ' the whole Treatise I here present the Reader with a Catalogue of the Operations which are most pleasing and suitable to the fancy and humour of such and which they may easily in a day or two learn especially if they have a Master to help them 1. TO set the Globe level pag. 4. 2. To compose the Globe p. 8. 3. To know the day of the Month. p. 9. 4. To take the Suns height above our Horizon when he shines out clear and also when he shines dimly and is overclouded p. 5. and 6. 5. To find the Suns Azimuth and Bearing p. 10 and 12. 6. To know the Hour several ways p. 13. 7. To know at what hour the Sun rises or sets p. 16. 8. To know what a Clock 't is all the World over p. 31. 9. To find where 't is day and where 't is night all the World over p. 33. 10. To find where at that moment they have nothing but Day and where nothing but Night as also when this happens in any place subject to this Alteration p. 33. 11. To find the Sun 's present Height and Depression all the World over if he shines p. 37. 12. To find where the Sun is rising and setting all the World over p. 34. 13. To find what people have then the Sun Vertical or over their heads p. 35. 14. To know where they are rising where they are going to Dinner where to Supper and where to Bed all the World over p. 35. 15. To find 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 and want of morning and consequently the Babilonish and Italian Hour all the World over p. 36. 16. To know the Judaic Hour p. 39. 17. To find in what Clime any Place lyes p. 26. 18. To know in any Lunar Eclipse what Countries see it wholly what in part and what not at all as also the true hour which each people see her at in her several Affections with her continual Height Azimuth and Bearing all the while p. 59. 19. To represent the several Phases of the Moon p. 61. 20. To find the Proportion between any Perpendicular and it's shade p. 65. 21. To take the height of a Tower by the Globe p. 66. 22. To do it seemingly without any Instrument p. 66. 23. To know the Hour by your Stick p. 67. 24. To learn presently how to make all the 5 Dials of a Cube to wit that on its Horizontal that on its direct South that on its direct North that on its direct East and that on its direct West Plane tho' a man be never so unacquainted with Mathematics 25. To represent at any time the posture of the Heavens in relation to the appearing Fixt Stars and consequently to find the present Hour with the Height Azimuth and Bearing of any Star as also the time of its Rising Setting and continuance both above and below the Horizon p. 138. The General Heads 1. THE Figure or Delineation of this Globe as also an account of it and the occasion of its Invention together with a Catalogue of the Operations fittest for those that cannot run over the whole Treatise are contain'd in the unfigur'd or preceeding pages 2. The Introduction begins pag. 1. 3. The first Section solving the Questions which relate to the Sun in our Elevation p. 4. 4. The second Section resolving the Operations that concern Geography and the Sun all the World over p. 20. 5. The third Section concerning the Moon p. 48. 6. The Fourth Section relating to Perpendiculars and their Shades p. 64. 7. The Fifth Section treating of Dialling p. 70. The Figure of the Globe fitted for a Garden or open Portico p. 121. Geometrical Problems necessary for Dialling p. 122. 8. The Vse of the Line of Lines and Line of Sines on the Sector p. 125. 127. 9. The sixth Section solving both by the Globe and Pedestal all the usual Questions which relate to the Stars p. 129. 135. The Explication of the Letters c. on Sch. 1. P. The North Pole of the World N. The Northern Polar Circle Z. The Zenith E E. The Ecliptic ♋ ♋ The Tropic of Cancer Jun. 1. The Parallel of that day May 1. The Parallel of that day Apr. 1. The Parallel of that day AE AE The Aequator Mar. 1. The Parallel of that day Feb. 1. The Parallel of that day Jan. 1. The Parallel of that day ♑ ♑ The Tropic of Capricorn H H. The Horizon S. The Southern Polar Circle P The South Pole N. The Nadir Z H. The Quadrant of Altitude N. The Quadrant of Depression Z H. The Quadrant of Proportion P AE P. The Meridian of the Place or Solstitial Colure LL The Meridian of the World ♈ P. P. The Aequinoctial Colure XII I. II. c. The Hour Circles or particular Meridians THE Introduction THIS Globe whose several Operations we are here describing neither hangs in a Frame nor is moved about as the ordinary ones are but stands stable and immobil on its Pedestal which makes it not only to represent the Earth more naturally according to the common Hypothesis but renders it also more expedite and useful as shall be fully shewn in the Conclusion or last Chapter for then after a view of the whole Treatise every body will the better comprehend all the new Operations it performs and all the particular Advantages it can any ways challenge to its self But here my Reader must remember that though I endeavour all along even in the most ordinary things to be clear and easy yet unless he has formerly read Hewes Bleau or rather Moxons Book on the Globes I cannot promise him I shall always be understood without the help of a Master for I have not time to descend to all the Definitions and minute Explanations which those that are wholly unacquainted with Astronomical or Geographical Principles may perchance expect As for the Circles here describ'd there are some common to all Globes as the Aequator the Ecliptick the Coluri the ordinary Circles of Longitude the Tropics and the Polar Circles and some also particular to this Globe only as the Horizon the Meridian of the Place and 16 Parallels to the Aequator all within the said Tropics Now that these Circles in general may be the sooner found and comprehended by any new Beginner there are Capital Letters in the Great Figure or Delineation of the Globe in Scheme the first which sufficiently distinguish them for the Aequator is markt with AE the Ecliptic with E the Polar Circles with N. and S. The Circles of Longitude with the Roman Figures
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
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
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
carry away the Bell some St. Nicholas but others St. Vincent as appears by Hondius's Globe Now Langrenius in his begins from St. Mary and St. Michael in the Azores Johnsonius in his Universal Map counts from Corvo and Flores whereas the Learned Dudley the late Titular Duke of Northumberland gives the honour to Pico and has as much reason for it as the rest Nor is there less do about the Canaries for the French fix it at Ferro several of the Hollanders at Teneriffa and many other Nations at Palma which is the Place I would willingly choose since the great Ptolomy thought fit at last to assign it there were it as convenient for my present purpose as St. Vincent 'T is St. Vincent then I here pitch upon for this Meridian to pase throu ' because it differs in Longitude from London within less than 20 Minutes of just 30 Degrees or 2 Hours so that the 2 a Clock Circle will represent it within almost a Minute in time without need of drawing a Particular one and the said Meridian is as I told you in the beginning distinguished from the rest by Pricks which being distant from each other a quarter of a Degree are useful on several occasions Having thus fixt our Grand Meridian or first Longitude that of other Places follow 's with ease for if you would know the Longitude of Constantinople draw but your String from the Pole over it and it will cut the Aequator neer the 62. Degree for the Longitude required as you may readily percieve by the lower little Aequinoctial Figures OPERATION III. How to find out any Place the Longitude and Latitude being given THis Operation is not only usefull for the finding out of Towns express'd on the Globe when you cannot guess whereabout they are situated but also for the placing them truly in case they should chance not to be set down Suppose then Constantinople were the Town sought for and that you found its Latitude to be 43 g. 5′ and Longitude 61 g. 46′ in some book or Geographical Table I say supposing this you have nothing to do after having mounted your Bead by the help of the devided Colurus 43 g. 5′ above the Aequator but to move your String on its Noose from the Pole to 61. 46. in the said Aequator and Constantinople will be just under your Bead and if in case of Omission it should not you may then if you please marke it out your self for that is its exact place But by the way if the Geographical Tables agree not with the Longitude of your Globe as telling you that v. g. Constantinople has but 54 g. 36′ you are then to look from whence the said Tables begin and finding their Commencement suppose at Palma and that Palma according to the former Operation has by your Globe 7 g. 10′ of Longitude you must add this number to your Tables and then you will agree OPERATION IV. To find the situation of any Place according to the Angle of Position or Points of the Compass DRaw the String from the Zenith over v. g. Constantinople and 't will cut the Horizon about 5 Degrees beyond E b S Eastward for the true situation of the said Town from your Habitation according to the Points of the Compass OPERATION V. To find in what Clime or Parallel any Place lies BEfore we can here well come to Operation there are some few Particulars to be consider'd and first what a Clime is which is no hard thing to conceive since most know that after the Vernal Equinox our Days not only exceed 12 houres but that every neerer Countrey to the Pole has days of greater Length than the Remoter Nor are there many ignorant that when our Days that live on this side of the Line increase theirs on the other side decrease proportionably and when theirs encrease ours decrease so that no People are at a Constancy but they that dwell exactly between both Poles to wit under the Aequator This Diversity was thought by the Ancients a thing so fit to be known that they invented the Devision of the Earth into Climes so that as soon they heard a Countrey named they presently besides the fond Reflections concerning the Temperament of the Air Ingeniety of men c. knew the length of its longest Day and consequently how much any other Place exceeded or came short of that length For suppose the first Northern-Clime were to pass over all the Places on this side of the Aequator whose longest Day is 12 hours and 1 2 and the second Clime those of 13 hours and so on towards the Pole by a half hourly Increment what difficulty could there be to resolve immediately the Question when we once know the Clime or having the length of the longest Day to find out the very Clime it self I Wonder therefore that so ingenious a man as 〈◊〉 should seem to assert that this Devision is useless it being as easy to find the longest Day as the Clime whereas were Climes in esteem and fashion the Memory would as soon conceive and remember in which of them any Countrey lay as now it does it's Bounds the manner of its situation and the like and if so one may quickly judge whether they are useless and whether it be possible that the length aforesaid can be known by any other means so universally and at so easy a rate A Clime then generally speaking is a space contained between two Circles Parallel to the Aequator having the Places thro' which they pass differing as to the length of their longest Days half an hour and this space takes the name of Clime from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Inclinare vel Deflectere for the greater our Deflection is from the Aequator or Right Sphere the longer our Summer Solstitial Day will be Nor were the Antients content with this large Devision of the Earth but subdevided it into Parallels so that Places differing a quarter of an Hour were reckon'd to be under such and such Parallels which some call Artificial from their relation to the Artificial Day to distinguish them from all others that occur As for the Antiquity of Climes 't is immemorial nor could there be many in the beginning by reason of the small extent of the known parts of the World For tho' Ptolemy reckons about 10 that is to say 21 Parallels as making them to reach as far as Thule yet Homer Ovid and other Poets so possess'd men with the Fancy that from the Cimerians Northward there was nothing by reason of the hideous vapours and exhalations but a dubious and creperous light that even Pliny and after him the Arabians insisted only on seven looking on all Countries that lay farther as not worth perchance the taking notice of As for the seven in vogue with them and mention'd also very particularly by our Countryman Sacro-bosco whose credit and great Repute has perchance not a little kept up
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
passes from Tropic to Tropic 't is evident that sometimes he must be on the Northside and sometimes on the Southside of all that live here which must then needs alter the shadow And as for knowing the time of this change we are only to consult the days of the Month on each Parallel for that which passes over the Heads of the propos'd Inhabitants shews that from that time to the 11. of June or the Sun 's coming to Cancer and so till he comes again to be Vertical their shade will be full South at noon whereas from his said Vertical station to the 11. of December when that he enters into Capricorn and so till he comes again to them their shadow will be directly North. From this Torrid and hot Residence we 'l now run to the other Extream viz. to the two Frozen Zones which lying from each Polar Circle to the very Poles themselves are sufficiently distinguish'd from the rest Now since the longest day within these Limits is at least 24. hours in length as we show'd you even now in treating of the Climes and since the Sun in this space of time compasses the World it must follow that here he runs round the Inhabitants which gave the name of PERISCII to them that is to say Circum Vmbrati or surrounded with their shadow from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Circum 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra As for the two remaining Zones they are the Temperate ones bounded by the Tropic's and Polar Circles Nor do the Inhabitants of this moderate and more excellent position want an appellation from the property of their shadow also for never having the Sun but on one side of them as still setting before he gets round and unable to pass as he could in the Torrid Zone over their Heads by reason he has no excursion beyond the Tropics it must needs follow that their shade who live in the Northern Zone will ever fall North and theirs in the Southern South so that they were called HETEROSCII i. e. Habentes alteram solum Vmbram or People having but one kind of shadow from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 alter 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vmbra So much then for the Climes and Zones together with their various inhabitants and now we will proceed to the Operations that follow OPERATION VI. To know what a Clock 't is at any time in any place of the World THere is no Operation perchance in the whole Treatise more diverting and pleasant than this nor scarce any more readily perform'd after a very little Reflection even in the most difficult Cases For having Compos'd your Globe if it be then 12. a Clock with you the standing Hour Circles or Meridians already described will by the Common or little Figures which lye within or upon the Roman ones that surround the Polar Circles shew you exactly the Hour wheresoever you cast your Eye That is to say that 't is about 2. of the Clock at Constantinople 3 at Aleppo c. But now if it be not 12. with you but v. g. 3 in the afternoon when you desire to know the then hour at Constantinople add the said 3 a Clock to the Figure 2. which you see lyes as I now mention'd on the Meridian or Hour-Circle that runs near that City and 't will tell you that 't is about 5 a Clock there and thus you must always do unless the time of the Day with you and the Figure that lies on the Meridian of the place in question make a greater number than 12 for then the Hour sought for is what remains above 12 as for Example if it be 11 with you then this with 2 i. e. the Figure near the Meridian of Constantinople making 13 do but cast away 12 and you may conclude it there 1 in the Afternoon There are several other ways of performing this Operation as finding the Difference of Longitude between you and the Place in Dispute and so adding or substracting it as need requires from the true time of the Day Or else by calling it always Mid day there where the Hour Circle that shews your then true time of the Day which by our Example is 3 in the Afternoon crosses for by counting from thence to the Meridian of the Place in question either forwards or backwards as 1 2 3 4 or 11 10 9 8 c. according as the said Place lies East or West from 3 and all is done I say there are several ways to perform this Operation but seeing the first is the most clear and expedite I solely insist on it and now because you may be perchance running over with your Eye the whole Globe and considering how one Situation or Country differs from another in time 't will not be amiss to tell you that there are 3 Places that have more particular Relation to your Dwelling or Habitation than any other The first is that which lies opposite to you in your own Parallel whose Inhabitants are called by the Antients PERIAECI or Circumcolae from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Circum 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 habito and though by the Word all People are comprehended that dwell any where in the said Parallel yet Geographers commonly mean those by it that are thus Diametrically situated These then live in the same Zone and in the same Clime and cast the same kind of Shade with you These enjoy your proportion of Heat and Cold your Seasons of the Year your Encrease of Days and Nights and in short all things else of this kind saving that your Hours are opposite their six in the Evening being your six in the Morning and your Noon their Midnight The Second Place lyes under your very Meridian or 12 a Clock Hour Circle which makes your Hours and theirs the same but by being 51 g 30′ on the other side of the Aequator it happens that tho you all agree in the Temperament of your Zones number of Climes in the Casting a Shadow on one side onely and the like yet their Zone and Clime are Southern their Shade falls toward that Pole their Summer is your Winter and your Spring their Autumn so that from this contrariety they are named ANTAECI or Adversicolae from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 contra 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Habito The Last is the Nadir or Point on which the Globe stands whose Inhabitants are called ANTIPODES i. e. opposita habentes vestigia or men that walk Feet to Feet with you from 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Contra 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Pedes These imply even by the vulgar acception of the word the height of Opposition and since they are the very Antaeci of our Periaeci participating thereby of whatever was opposite to you in either of the former Places it is no wonder that you enjoy together neither Day nor Night nor Season of the Year nor any thing else of this Nature OPERATION VII To
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
Distance between Rome and the shade of Extuberancy and 't will give you in any great Circle about 22 Degrees for his Height there at that moment And the reason of it is because when the Sun i. e. the Place where he is Vertical is distant 90 Degrees from Rome then Rome sees him in his Horizon and as soon as he gets above the Horizon v. g. 22 Degrees his Rayes will illuminate beyond Rome 22 Degrees for else there would not be always 90 Degrees from the Place where the Sun is Verticale to the Confines of the shade and Light or utmost Extent of his Rayes but the distance from Rome to the nearest part of the shade of Extuberancy is the distance of his Illumination beyond Rome ergo 'tis his true Height In like manner if it be Night at any Place on your Globe and you desire to know how much the Sun is there depress'd or under the Horizon take the Distance as before between the said place and the nearest Term of the shade of Extuberancy and that for the former reason will be the required Depression As for the finding out of all Places that have the Sun suppose 22 Degrees above their Horizon you are only to lay the Plummet end of your String or Foot of your Compasses on the middle of the Coast of Malabar where we now suppose the Sun to be Vertical and making your Bead or the other Foot of your said Compasses to lye on Rome describe an imaginary Circle and then all People under the said Circle will have the Sun 22 Degrees high since they are all distant from him like Rome and thus you must operate in all other Cases OPERATION XIV To know what a Clock 't is with you the Italian Babilonish and Judaic way YOU are first to know that as England France Spain Denmark Sweden most part of Germany and many other Places follow the Astronomical account in their Diurnal Computation of time with this only difference that the Astronomers begin at Noon and so go on from 1 to 24 whereas the aforesaid Nations begin at Mid-night dividing the whole Natural Day into twice twelve hours I say as these Nations begin their Account at Mid-Night so the Italians do theirs at Sun-set continuing to 24 without interruption after the Athenian manner of old which is also now usually observed in Bohemia Austria Silesia c. On the contrary some Places in Germany and particularly Noremberg still follows the antient Babilonian or Caldean Way as commencing their 24 hours from Sun-rising therefore the difficulty and seeming Confusion of counting by either of these 2 last wayes proceeds from the Sun's inconstancy in its Rising and Setting for when he is in the Aequinoctial our Globe show's us the hour as soon after their manner as our own As for example if you would then know what hour 't is with you the Babilonian way Hold up your String against the Sun and moove it on it's Noose from the Pole till the shade fall on the contrary Pole i. e. look what a clock 't is the second Way and where the shade of the String cuts the Aequator the Roman Figures there will give you the true Babilonish Hour Or which is all one see what a clock 't is by the shade of Extuberancy or 3d way and finding the said shade to fall suppose on the 9 a clock hour-circle in the Aequator as the then true hour after our English Fashion do but cast your Eye on the Polar Circles and the said 9 a clock hour-circle will cut there at the Roman Figure 3. so that you may conclude it then 3 a clock the Babilonian way Nor does the Italian manner materially differ from this for 't is but adding 12 hours to the 3 found as before and then 15 will be the true hour after that account Now if you would know the hour when the Sun is out of the Aequator as for example on the 10th of April consider the Parallel of the Day which giving you at first sight about one hour for the Ascensional Difference as I show'd you in the former Section do but add this hour to the three found as we now show'd you and 't will give you four for the true Babilonian hour whereas if you substract it from 3 i. e. from the aforefaid 15. you have the true Italian hour and thus you are to proceed in all other cases Only remember that when the Sun is in his Southern Declension the Substraction of his Ascentional Difference gives the Babilonian and the Addition of it the Italian hour But if you would have yet an easier way of performing this consult the 12th Operation and the distance in time there from Day gives you the Babilonian and the distance from Night the Italian hour As for the Jews they devided the day always into 12. equal parts which they called hours as appears by our Saviours demand Are there not 12 hours in the Day therefore when the Sun is in the Aequator as it happened about the time of the Passion this and the Babilonish way are the same for then the 3d. hour is 9 a Clock with us and our 3 in the afternoon is their 9th hour so that at 6 our way or at 12 theirs the Sun Sets and the Night begins which they also devided into 12 equal parts I say this is the same as the Babilonish way when the Sun is at or about the Aequator and consequently easy but afterwards by reason of the strange inequallity of both Day and Night the Computation must be troublesom especially if we use Reduction the common prescribed way on the Globe for the Summer days with us contain above 16 of our hours and the Winter ones not half so many and yet both kind of Days are to be devided into 12 equal parts or hours Nor were the Jews the only people that reckon'd thus for the manner was in use among the Romans as we see by Persius his Drunkards who lay a Bed to digest their Wine Quinta dum line a tangitur Vmbra Nay the Greeks followed it also and had Machines or Clocks as Achilles Tatius tell us which could notwithstanding the forementioned strange inequality of Dayes measure their Time But this seemingly odd and exotic account may very exactly and expeditely be perform'd by our Globe for if the Globe-maker devides each diurnal Parallel by distinct specks or pricks into twenty four parts that is to say if he devides that part of each Parallel above the Horizon into 12 equal ones and that below it into the like number you have nothing to do but to hold up your String against the Sun and if you move it from the Pole on its Noose 'till its shade passes over the contrary Pole then upon what prick soever the shade falls that will be the requir'd hour and in like manner if you know the Sun's Depression
draw but your String over his then Place and it will cut the Parallel at the true Judaical time of the Night These Vnequal Hours were also called Planetary by the Ancients who allowed to each a Planet to govern it so that the first hour suppose on Saturday belonging to Saturn if you go on still in the usual Coelestial Order as 't is exprest in the Margent and consequently assign Jupiter to the second hour Mars to the third c. the 25th i. e. the first hour of Sunday will happen to the Sun's Lot and the first of Munday to the Moon 's and so forward and thus you may see how it came to pass that the dayes of the week succeeded in the present order and not according to that of the Planets in the Heavens that is to say why Dies Lunae or Munday and not Dies Veneris or Fryday immediately follows Sunday I shall now end this Discourse after I have told you that if we English-men think these Computations strange they that use them wonder as much at ours nay each man pretends some particular Convenience and Advantage by his Method For first an Italian says that without breaking ones Brains no body can tell our way when the Day-ends so that idle men who usually hate computing do often couzen themselves and take false measures in their Affairs for continues he if they chance to get up at 8 of the Clock in Winter they fancy a whole day even St. Barnabas's before them when as this Hour or early rising to Him is 16 of the Clock which informs him at the very instant there are but 8 hours to Night The Caldean on the other side urges that Morning being the most precious part of the Day is fittest to be nicely known and tho' his Hour gives him not presently the Distance to the Evening yet it so alarms him as to what relates to the Morning that he cannot make the least slip therein without being at the same moment conscious of his failure Lastly the Jew approving both Reasons highly triumphs in his way for he no sooner looks he says upon his Dial but sees there not only what hours are past but also what remain and are yet behind But notwithstanding all these shews and pretences of Reasons our Account is so far from coming short of any that in reality it surpasses all for we not only know exactly what we want every moment of Noon a thing of mighty Concern but can appoint positive hours all the Year long for any Employment whether private or publick whilst these other ways by reason of the Suns inconstancy in Rising and Setting have all orderly and set times as when to Dine when to Sup when to Rise when to go to Bed c. still mutable and fleeting OPERATION XV. How to make the Globe Universal THis Operation is quite beyond both my Proposal and Design for I really intend nothing but a Dial according to a Determin'd Elevation fraught with several easy and natural Performances as well divertising as useful And if a man cannot be content with one for his Study or Garden unless it may serve for Jerusalem also he must not only quarrel with Mr. Oughtred's excellent Projection and all particular Analems Quadrants and the like but with Stoffler's Astrolabe an Instrument received with mighty applause by all Besides 't is forty to one especially since there are as we already see so many Vniversal Operations performable by our Globe tho fixt for a particular Place if there chance a case in seven years that would move one to wish the Elevation changed Yet least this might happen the Instrument Maker will prepare a thin Brass Circle gradually devided like the Horizon and of the same bigness therefore if the new Elevation were suppose for Rome open but your Compasses at 90 Degrees in any of the great Circles or take the same distance with your String and Bead and having designed by your said Compasses or String any two Points thus distant from Rome clap over your new Horizon so that it s devided edge rests on the said two Points or in short let Rome be the Pole of the Brass Circle and 't will cut all the Equinoctial Parallels as if the Globe had been made for that City and consequently you will soon have there the Suns Rising Setting Amplitude Ascensional Difference c. Moreover the Circle being exactly made will stick of it self or at least by the help of any scrap of Paper between so that if at any time you set but the Plumet-end of your String on Rome you may then hold it down with one Finger and operate as you would do from your own Zenith But since I am fallen upon this needless affair and since the Operation is in effect the changing of the fixt and standing Site of our Globe 't will be perchance not amiss to inform you if you are not already well verst in the Sphere that there are three different and distinct Positions of it which you will better comprehend if you consider your self in these three Places Sch. 1 Suppose first that you were under one of the Poles and for Example sake the Northern one it must needs follow that that Pin on your Globe will not only be useful there in relation to the several Operations that must as we show'd you be done from the Polar Pin but from that of the Zenith also because now 't is the Zenith there and therefore the South-Pole being the Nadir all Circles must lye as they are represented in Scheme the first Seeing then that the Horizon is a great Circle and always 90 Degrees from both Zenith and Nadir it will necessarily happen that the Horizon and Aequator must concur so that the Aequator describ'd on the Globe will serve for an Horizon in this Position of the Sphere which is called by Geographers the Parallel one because by reason of the concurrence aforesaid all the Heavenly Bodies according to their Diurnal motion i. e. according to the motion of the Primum Mobile parallel to the Horizon so that the Sun cannot Set during the six Months of his Northern Declension nor rise during the six of his Southern for his Rising and Setting imply the cutting or intercepting of some part of his daily Road or Track by the Horizon Nor want the Stars here their particular Properties also for being carried daily on the Poles of the World and consequently moving parallel to the Aequator all that are above the Horizon cannot go under it nor the others emerge unless some by their proper motion after a long series of time change that Order Having then in this Sphere the Zenith and Horizon whatsoever is performable by your own Zenith and Horizon may be here mutatis mutandis perform'd after the same manner Sch. 2. Sch. 3. As for the oblique Sphere which is the third and last Position and here express'd by the third Scheme we are in it you
must know our selves and so are all other People and Places of the World that are in neither of the two former ones for take any point not under the Poles or the Aequator for your Zenith and 't will be impossible to describe an Horizon or Circle 90 Degrees from it which cuts not the Aequator and all its Parallels obliquely 'T is this Obliquity then that gives name to the Position and 't is this that makes the great inequalities in days and nights for if the Horizon has a greater portion of one Diurnal Parallel above it than of another as it must needs have by its slanting 't will follow when the Sun is in such a Parallel that the Day will be longer than when the portion was less and consequently since more of one Parallel is under the Horizon than of another that one Night is shorter than another and seeing the nearer the Pole is to the Horizon the more equally it cuts the said Parallels and the further it is from it the greater the inequality happens to be 't is no wonder that by how much the greater the Elevation is by so much the longer the Days are and when the whole Horizon falls below some of the Parallels that then during the Sun's aboad there the Inhabitants have no night at all therefore it follows that if a Star be neerer the Pole than is the Latitude of a Place it can never set in that Place Yet notwithstanding this strange inequality and disproportion of Day and Night all People in all Positions by that time the Sun finishes his annual Course make them even and thereby enjoy an equal share of both for if under the Pole the Sun be six months above the Horizon he is as long under it and if we and the Rest that live in the Oblique Sphere have Summer Days of a mighty length our Winter Nights are of the same Dimension therefore it follows that at the long Run the Inhabitants under the Aequator or in the Right Sphere who have always 12 hours of Day and as much of Night cannot boast of having more of the Suns Company than they that live in the two other and consequently that the assertion is true 'T is in the Oblique Sphere then that the above-mentioned Brazen Horizon is chiefly intended but as I said in the beginning 't is forty to one so many Universal Operations being perform'd by the Globe in its set Posture that in 7 years a man lights on a Question that could invite him to change it were it moveable as other Globes are so that having show'd you that in case of Necessity it may be in effect altered even without stirring it from its Pedestal I shall proceed OPERATION XVI How to take the Elevation of the Pole in any place whatsoever SUppose you were in a strange Place and that your Globe being one that had bin fitted for London you desire to know the present Elevation Expose your Globe to the Sun on a Meridian Line with the Pin or Needle in the Hole on the Parallel of the 10 of April or true day of the Moneth and observing at 12 a clock when the Sun comes into the Plain of the Globes Meridian that the shade of the said Needle or Pin loses not it self as it would do were the Sun directly opposite to it for so it had hapn'd at London or in any place in the Latitude of 51 e 30′ I say having thus expos'd your Globe and observing this move your Pin or Needle from Hole to Hole or from one Degree of the Meridian to the other 'till it's shade be wholly lost and finding the said Needle or Pin on the Parallel suppose of June 11th which is about 11. 30′ higher then it 's proper place to wit the Parallel of the 10th of April you may conclude that your present Elevation is 63 degrees i. e. 11. 30′ higher than the Globe's whereas had you bin oblig'd to move your Needle or Pin so many Degrees lower than the 10th of April your Elevation had bin but 40. The Demonstration is obvious for since the Earth is round as nothing perchance proves it better than the Experience we have that as so many miles suppose 60 elevates or depresses the Pole one Degree so just 60 Miles more elevates or depresses it another I say since the World is round and that the Degrees of the Globe answer to its Degrees it must follow that the difference between the Pins situation now on the Globe and where it would have stood on it at London is the true difference of the two Elevations OPERATION XVII How to know in what Elevation the Sun Rises or Sets an hour or any other space of time earlier or later than he do's in the Globes Elevation IF the Sun rising at London on the 10th of April about 5 and setting about 7 you would know in what Elevation or Latitude he then rises for examples sake at 4 and sets at 8 take the distance of 90 Degrees with your String or Compasses in any great Circle and placing one end of your String or one foot of your Compasses where the Parallel of the day intersects with the Hour-Circle of either 4 in the morning or 8 at night observe where or at what point the other end of your said String or other foot of your said Compasses touches in the Meridian or 12 a Clock Circle of the Globe and you will find it to be at or about 8 Degrees and 30 Minutes beyond the Zenith towards the North Pole so that the Elevation required is greater than your own by those 8 Degrees and 30 minutes that is to say the Elevation is that of 60 or thereabout whereas had your String or Compasses touch't 8. ° 30 ′ on the other side of your Zenith the required Elevation would have been less than your own so many Degrees i. e. it would have been that of 43 Degrees or thereabout This appears true by placing your Brazen Horizon or by describing an imaginary one over the two points made by the Intersection of the Parallel of the Day and Hour-Circles of 4 in the morning and 8 in the evening for in the Elevation belonging to such an Horizon 't is evident that the Sun rises at 4 and sets at 8. Now the Pole of every Circle being 90 Degrees from it and the Point in the Meridian being 90 Degrees from the aforementioned Intersection it follows that the said Point in the Meridian is the Zenith or Pole of this new Horizon and consequently by being distant from the Aequator 60 Degrees that so many Degrees is the Latitude or Elevation required The END of the second Section SECT III. Of the Moon HAving now finish'd with the Sun wee 'l make a step if you please to the Moon and show you how to resolve all the useful ordinary Questions concerning her whether we see her by Night or by Day for 't is equal to us whether
Setting which hapning in the Example to be about eight hours and fourty two Minutes for the one and four hours and fifty minutes for the other it must follow having found the true hour to be within four minutes of five at Night that she rose about eight and fourteen minutes in the Morning and will set at nine and fourty six minutes at Night OPERATION X. To find how long the Moon shines every night HAving found by the precedent Operation that the Moon sets at 9 and 46 minutes at night and that the Sun by the 12th of the first Section sets the same day suppose the 8th of February at 5 in the Evening 't will follow that she shines four hours and 46 minutes OPERATION XI To find when the Moon comes to South and consequently when t is high water at London Bridge HAving found by the third Operation the Moons place to be in the 2 a Clock Circle you thereby see that she is past the South 2 hours and 4. minutes Now since it is always High-water at the Bridge three hours after her coming to South and since the Solar or true hour is according to our Example 5 at Night it follows 't was High-water at 4 minutes before 6. and consequently 't will be high water again at the same hour next morning and 24 minutes for from one Tide to the other there are always about 12 hours and 24 minutes OPERATION XII To know in any Eclips of the Moon what Countries see it wholly what in part and what not at all PLACE your Globe on a Meridian Line or otherwise Compose it and when you percieve the Moon to begin to enter into the shade of the Earth consider as you do when you seek by the Suns Rays where 't is day and night what part of the Globe is illuminated and what not for since she appears to all Countries that lie in the Light and is hid from those in the Shade you have not only a view of what people see her in her then condition but may till her total immersion perceive by her illumination how the Countries that lye in or near the Following shade of Extuberancy loose every moment the sight of her and consequently who they are that took leave of her in the beginning of her Eclips who when she came to half of it and who when wholly obscur'd with infinite more Reflections of this nature On the other side you may find how some that lay in the preceding shade of Extuberancy saw nothing of her at first but now begin to discover her in her Angony and if you draw on the Globe a little Circle with Chalk or the like in the Confines of the obscurity and light just as she begins to be wholly in the shadow you will discern by the space between the said Chalk and the new shade of extuberancy at her Emersion what people never saw her tho she were above their Horizon Infinite are the Reflexions as I said of this nature but these are sufficient to show you how to make more your self so that now I will end after I have remembred you that the Sun being by his Opposition in the same hour Circle with the Moon especially in all Central Eclipses nay he is so as to sense for some time both before and after such Eclipses I say the Sun being so you may therefore not only by the bare shade of the String or that of the illuminated Pole know what a Clock it is from time to time in the Polar Circles but in the Aequator also by the shade of Extuberancy which performs the observations above mentioned and thus by the very same shade you find not only what People see the Eclipse either in whole or in part as we now told you but at what hour it appears to each of them and how long as also the Duration of her Decrease and Encrease in light together with the time of her total Obscurity moreover this very shade gives you her Height and Azimuth all along as you may see in the Operations that concern them OPERATION XIII To represent the several Phases or Shapes of the Moon by the Globe THIS is rather a Speculation than an Operation Nor should I have mentioned it were it not that several who know something in Mathematics cannot comprehend the Cause of the Moon 's continual Metamorphosis or Change that is to say why she should be now more now less illuminated and that also in so different a shape and manner To comprehend therefore this Expose your Globe elevated on a Stand or a Table as high as your Eye to the Sun or Moon and place your self so before it as to see the whole illuminated half for as to sense the illuminated and shady parts of all Spheres are as we formerly mentioned equal Having then a while consider'd this great Circle made by the Limb or Extremity of the illumination remove your station a little on the one side as for Example towards the righthand and you will find the illuminated part to appear Gibbous or Oval I mean not so broad as long because so much of it is hid from you as you can now discover of obscurity From hence go yet farther side-wise and the visible part of the Globe will be Dicotomous or party per pale that is to say the light and shade will become equal After this make another Proportionable step and all that is illuminated will appear Horned or Lunular and the obscure part Gibbous But if you remove to the point opposite to your first Station you will see nothing besides a dark and shadow'd Hemisphere whereas should you proceed further in the same Order you would perceive Light on the other side first Lunular then Dicotomous next Gibbous and lastly totally predominant Now as the Globe is always half illuminated whether we see little or much of the illumination so it happens with the Moon who being in Conjunction appears all dark to us because her illuminated half is towards the Sun and opposite to us but as soon as she gets from him and consequently is no longer in the same Plane with him and our Eye we must needs have a view of some part of the Illumination seeing she can only appear wholly obscure when she is thus before the Sun The said Illumination also since she is Spherical must seem as on the Globe the more Horned the less it is and then blunter and blunter according to her Encrease or Elongation till at last she becomes Dicotomous afterwards Gibbous and lastly Full for by being at her greatest distance from the Sun or in Opposition with him which causes our Eye to be in the middle or between them 't is impossible she should appear otherwise than all Light And here you may be pleased to take notice that if you compass your Globe with a String or Thred that passes throu ' the Zenith and Nadir and let one half of the describ'd Circle
is not then able tho' up to shine upon it 't were needless as we said to express more Hour lines 'T is the Describing also of the Plane with your String that brings us to the knowledge of the second part of this Operation I mean the knowing at all times when the Sun comes on and goes off any Plane for having describ'd one Declining v. g. 20 Degrees Eastward do but observe what Diurnal Parallels and Hour-circles intersect on the Edges of your Plane and you have your Intent for you will by this means see that tho' the Sun rises for example sake on the 11 of June before 4 the first hour circle which intersects with this Parallel on the Edges of the Plane is that of a Quarter before six whereas about the beginning of May he is there at half an hour past five and on the 10 of April at or near 5. Now if you consider in the same manner the West-side of the Globe you will see from time to time at what hour he goes off it and thus you may do let the Plane be what it will Here therefore it evidently appears if you should erect at any time suppose about the 10th of April a Perpendiculur stile on an Horizontal Plane and draw every Hour a Line along the Shade of the said stile why such a Dial will be false as only telling you the true Hour twice in the year to wit on the 10th of April and about the 10th of August viz. on the days on which the Sun run's in the same Diurnal Parallel I say all this now evidently appears since every Line thus drawn on an Horizontal Plane except the Meridian or 12 a clock line is no Hour line but an Azimuthal Section I mean the Section of the said Plane with a Circle that then passes over your head throu ' the body of the Sun so that if one of these Lines should Bear suppose almost SE and be figur'd with 10 in the morning Draw but your String from the Zenith over that Bearing or Point of the Compass in the Horizon of your Globe and it will truly represent the said shade or Line on your Plane for it show's it to be 10 of the Clock on the Parallel belonging to the said 10th of April But since your String cuts also on your Globe v. g. the Tropic of ♑ at a little before 9 and the Tropic of ♋ at almost half an hour past 10 you may conclude that this will be the true time of the Day on the 11 of December and 11 of June tho' the shade of the Perpendicular stile still show's 10 a clock at the aforesaid Bearing let the Season of the year be what it will therefore a Dial thus made must be false Of several ingenious and humersome Dials HAving thus run throu ' all Planes I shall at present show you how to make use of the former Principles as to the ready Describing of several ingenious and humersome Dials for all are now in a manner but Corollaries from what we have already said and consequently easy both in Speculation and Practice OPERATION XXVI How to make a Dial on any Plane whose stile shall be an Arrow fixt casually on it EXamine what the Plane is and having found it to be suppose a Vertical one Declining 40 Degrees East-ward describe by your former Rules such a Dial on Paper with the Paper stile F x M. as in Scheme 31. exactly set and mounted then draw on the Plane an Horizontal Line H h and place on it your said Paper draught so that the 12 a clock Line FP may fall at right Angles on the said Horizontal line Lastly move your Draught along it till some part of F x or Indicating side of the stile suppose the Point A just touches the Top or most prominent Part of the Arrow and fixing there the said Draught if you draw fair Lines on your Plane under those on the Paper the said Arrow will always show you the Hour with its Top. The Reason is plain for you see by the said Top's just touching the Edge or Indicating side of the Paper-stile it has the effect of the Top of AB I mean the Top of a Perpendicular falling from the said side on the Sub-stile so that X the Top of XM both in the present Scheme and also in Scheme 18. or Example of a Declining Plane has this Effect also Now since the Top of AB or XM or of any other Perpendicular that falls from the Indicating side XF on the substile FM will perform the Office of the stile as we show'd you at large in Demonstration of the first Horizontal Dial or first Example it must necessarily follow that A the Arrow's Top do's the like OPERATION XXVII How to make a Dial to show the Hour without a stile on any Plane DEscribe as in Scheme 32. a Dial on P the given Plane and erect for the present a true stile as FAB of Paper or the like then fixing a Glass or any other transparent matter suppose G at what distance you please before the said given Plane and Parallel to it mark where A the Top of the Stile just touches the said Glass and if there you paint a little Asterisk or spot it will as often as the Sun shines describe such another Figure at suppose D by its shade on the said Plane P and move also from Hour Line to Hour Line according to the true time of the day The reason of this is also Evident for if A the top of the real Stile show's the Hour by casting a Shade as we show'd you all along on the Hour Lines then the Asterisk being there painted where the said Top touches the Glass must do the like for it is you see the Stile 's Apex or Top and consequently casts a true shade to know the Hour by This Dial serves not only for all double Windows or for Cavities that have over them any Glass or Transparent matter but shows us how to make one for any Plane that is illuminated by a Ray coming throu ' a Hole since if you describe the Planes proper Dial on Paper and move it duly as before on the said Plane 'till the Stile or if that be too short 'till a Thred drawn along its Indicating side touches the Hole it will give you marks for the drawing the fair and standing Hour-lines of your Plane which the said Ray will dayly run over in order and consequently show you from time to time the Hour for the Ray passing as you see throu ' the Hole v. g. at A and falling on the true Hour Line at D performs what A the Apex of the true Stile FAB would do OPERATION XXVIII How to describe a Dial having a Picture of a Man in it that shall Point to the Hour from time to time with his Finger THIS Dial is on several Planes of Mr. Lines his forementioned Pile
in Whitehal Garden and as no Dial can be more useful so perchance none ever struck the Fancy both of the Ignorant and Learned with a more sudden Admiration than this as I have often found by Experience both in England and elsewhere Nor truly can it but surprize one at first to think that a Picture without a Machine or Movement should have his Finger ever on the Hour and as duly attend the Sun's motion as if he were alive I say this cannot but surprize one and yet this very Dial is as easy to be made as any of the former Suppose then as in Scheme 33 that the Plane given you were that of the Vertical Cavity a b c d lying directly South describe therefore on the Glass ABCD the contrary Dial i. e. a Direct North Dial with a Paper Style truly mounted and placing the said Glass over the Plane and Paralel to it see where the Stile just touches the said Plane and at that point suppose E let the top of the Pictures Finger be painted then throwing away your Paper Stile and now by the Help of a handsome Frame or the like fixing there your Glass all its painted Hour Lines by hindring the Sun's Passage or Light will project so many Dark Lines on you Plane whilst the then true one falls directly on the Mans Finger and consequently shows you what a Clock it is For if there were a Hole that passed at E the Top of the Mans Fingers throu ' the Center of the World to our Antipodes it necessary follows by the Reasons in our former Operation that at 10 of the Clock suppose at night the Sun being then Northward must cast its Rays throu ' the said Hole or top of the Finger on the 10 a Clock Line of this North Dial on the Glass but since at 10 a Clock in the morning the Sun is in the same Plane as he was at 10 at night only his Station is contrary therefore he must now cast the Shade of the Hour Line the contrary way i. e. on the Mans Finger for in the day time the Hour-line is between the Sun and the Finger whereas in the night time the Finger or Hole is between him and the Hour-Line This Dial needs not always be made on a Glass for 't is sufficient if you raise a thin Frame aaaa in Scheme 34. on the Pillars bbbb above P your Plane as high as the Glasse's true Station or Place for then you may cross the said Frame with small Strings or Wyars which will by their interposition cast the same shade as the Hour-lines of the Glass would have done so that if the Figures belonging to the said Lines be put on the Frame at the end of each corresponding Wyar and then pierc'd the Sun Beams passing throu ' their Cavities will distinguish each very perfectly on the Plane Tho I have not time to show you all the particulars of this Learned Man's rare Invention in Dialling for most of the Dials on the aforesaid Pile may be naturally and expeditely describ'd by the help of this Globe yet I will give you two more viz. the two following ones because besides their prettiness we may have use of them as you shall see by and by OPERATION XXIX To make a Dial by which a Blind man may constantly know the Hour YOU must first get made in Brass the Armillary Hemisphere ABCDE as in Scheme 35 8 Inches suppose in Diameter representing your Globe cut throu ' the Horizon but the said Hemisphere is not to have any thing solid remaining besides the Horizon ABCE with the Pieces of the Hour Circles 1234 c that reach to it from the Nadir or rather from the Tropic of Capricorn AFC on the Northernside for the Southerly Circles are superfluous Then having plac'd the said Hemisphere directly North and South as your Globe stands when Compos'd fix G a Glass Bowl of clear water 4 Inches in Diameter i. e. half the former in the midst or center of it for the Sun's Beames passing throu ' the Water will contract in a Point and ever burn at suppose H the true Hour-Circle so that if a Blind-man puts but his Hand on the said Brazen Hour Circles he will soon find by the Heat where the Sun marks and consequently tell you the Hour for he may easily feel how far it is from the middlemost Hour Circle I mean the 12 a Clock Circle or Meridian As for the Reason of this Operation 't is presently conceiv'd for when the Sun is over against suppose the 5 a Clock Hour Circle on the South-side of the Dial he must needs be over against the same Hour on the North-side both hours making but one Circle Now since the Center of the Bowl by being in the Center of the Hemisphere is in the Plane of all the Hour Circles and since according to the nature of Refraction all Parallel Rays of the Sun passing throu ' a Sphere of Water are where they meet with the Direct Ray that passes throu ' the said Center contracted into a point viz. on the opposite side at the distance of half its Diameter or two Inches according to our present Example I say seeing this it must needs follow that at 5 of the Clock the Sun will burn on the corresponding Hour-Circle and if so then a Blind-man by feeling the Heat and finding its distance from 12 must needs be able to tell you the true time of the Day OPERATION XXX To make a Dial to show the Hour when the Sun shines not PRepare a Blew Glass Bowl as in Scheme 36th and describe on it with their Respective Figures all the Hour-Circles of the Globe or as many as you think fit then fixing it where you intend and composing it truly by your Globe if you place your self so at some Distance that a little Hole being made at each Pole to wit at P p you may see quite throu ' the Bowl 't will follow that the Hour-Circle suppose A which the Sun's Picture appears on will be the true time of the Day I call this to know what a Clock it is when the Sun shines not because now the least faint Appearance of him serves the turn tho' it be not enough to cast any shadow nay let the Sun be quite cover'd and if you can but guess by the Adjacent Brightness whereabout he is you will be able to guess the Hour without any sensible Error for the said Brightness appearing on the Bowl will be proportionably distant from the Sun 's true place there as 't is from the Sun in the Heavens 'T is clear that the Suns Picture must fall if any where on the true Hour-Circle because by Composing the Bowl according to the true Position of the Heavens the Hour-Circles of the one concur with the other and fall exactly in the same Plane therefore were your Eye in the Center of the Bowl its true
Hour Circle i. e. that which corresponds with the time of the Day would be just interpos'd between your Eye and the Sun but since the whole Axis is the common Section of the Hour-Circles let your Eye be but in any part of it the same Interposition must happen so that seeing the Suns Ray by reason of the Blew Colour penetrates not the Glass his Picture must needs be on the outside of it where the said Ray would have otherways past Now the Ray that goes from your Eye throu ' the two Holes being the Axis therefore whilst your Eye remains in this Posture it will follow that wheresoever you see the Suns Picture on the Glass there his place must be and consequently his said Picture must show the Hour OPERATION XXXI How to make an Horizontal Concave Dial by the Globe and Geometrically also COmpose so your Globe in the Concavity given suppose BAC in Scheme 37. that A the Center of the said concavity shall concurr with the Center of the said Globe then drawing your String over each necessary hour Circle on the Globe to the sides of the Concavity mark as many Points as shall be convenient for the Describing the corresponding hour Circles and the Pin AD erected in the Nadir at D as high as the said Center A I mean a Pin equal to the Semi-diameter of the Concavity will with its Top always show you the hour Tho the former way be impracticable when the Hole is less than the Globe yet it serves to illustrate and make easy the Geometrical Operation for you have nothing you see to do but to draw hour Circles within as you would without were the said Concavity a whole Sphere and then the Top of its Semi-Diameter i. e. the poynt which lyes in the Center A will perform the Stiles part for since the Sun is every Hour as we have before showd you in the same Plane of the true hour Circle and since A the Top of the Semi-Diameter being in the Center of the Concavity is part of the Axis or Common Section of all the Hour-Circles it follows that its Shadow must fall on the true Hour OPERATION XXXII How to describe Geometrically a Cieling Dial. SEeing the Glass which reflects the Suns Rayes to show us the Hour is commonly fixt in the corners and by-places of Windows the Globe can seldom be so well order'd by reason of its Bulk as to help us in the Construction of this Dial therefore I shall only give you the Geometrical way which is as I take it both short and new and because these Dials have commonly the Windows or inlets for the Sun Southerly for otherwise they will show but very few hours we 'l suppose ours also in the following Example to stand thus and afterwards you shall see the difference between such a Dial and those whose Windows have another Aspect First make on any Past-board Trencher c. an Horizontal Dial as in Scheme 38. and fix in O its Center a Thred of a good Length to wit OP then fasten the said Dial so with a Nail to a Long Masons Ruler that its Fiducial edge KL may lye upon the Meridian or 12 a Clock Line and having cemented and plac't Level a piece of Looking Glass of the bigness of a Three pence in the Window or what convenient place else you please of your Chamber which we 'l suppose to be G find by the Plumet AE the Poynt A in the Cieling WXYZ being the poynt in Scheme 39. directly over the said G and draw throu ' it a Meridian line viz. the Line AL. In the next place fix one end of a piece of Packthred on G the Center of the Glass and the other on some point of your Meridian line in such manner that it make an Angle with it of 51. 30′ i. e. the Angle of the Elevation which may be easily perform'd by the application of the side of a Quadrant to the said extended Packthread and when 't is right let the Point thus found in your Meridian line be called B. Lastly take the distance between the aforesaid Points A and B and marking it suppose at C on the edge of your Ruler from O the Center or fastning of the Horizontal place so the said Rulers Fiducial edge KCL along the Meridian line on the Cieling that the point C may lye just on A and all is done for then if you draw but the Thred OP streight over each Hour-line of the Horizontal it shows you where you are to draw all the fair Lines of the required Dial. Sch. 40. As for the truth of this Dial it appears in Scheme 40. by the right Angle Triangles OGH and GHF where HF is part of HM a suppos'd Meridian line on the Floor under that in the Cieling G the Station of the Glass in the Window H the Point under the said Station as formerly A was the Point over it and to facilitate the Demonstration let us imagine GH equal to GA i. e. that the Glass lyes in the middle between the Floor and Cieling This being so suppose that GH instead of representing a Perpendicular Line in the Wall as here we conceive it had been a Perpendicular Stick and that you were to describe an Horizontal Dial on the Floor whose Stile was to be the said Stick I say supposing this you must you know to perform the Operation produce the Meridian Line MH to suppose N and fastning a String on G find in it the Point v. g. O for the Center of the Dial I mean a Point to which a String being extended from G makes with the Meridian OH the Angle of the Elevation and so draw the several Hour-lines from the said O according to their respective Angles and Distances all which is exprest at large in the third Scheme or first Horizontal Dial for there you see GH is a Perpendicular Stile showing the Hour with its top and that O is the Center of the Dial having a Line drawn to it from G making the Angle of the Elevation with the Meridian OH Now since O in our present case is a point without the Chamber and consequently the Line MH cannot be produc'd to it you must draw your Thred from G to the said Meridian Line HM within the Chamber and find in it the Point F to wit the Point where the said Thred GF makes with it an Angle equal to that of the Elevation for thereby you will have the distance of O your true Center from H as being the distance of F from H seeing the side GH is common and the Angles in both Triangles equal This being so if you put out of the Chamber an Horizontal Dial whose Center shall lye on O and its Meridian Line concurr with HF 't is but producing all its Hour-Lines on the Floor and it must necessarily follow that G the Top of the Perpendicular Stile will show you truly the time of
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
Clock Thirdly when at 4½ Fifthly when at 5 and in the like Proportion go on till the Days come to their greatest Decrease and putting the said days of the Month in Order as they are in the Scheme under the corresponding Hours on the morning side of your Dial for his Rising do the like for his Setting on the Evening side of it and you may perform the Operation with sufficient Exactness In like manner you are to proceed for the Quarters half Quarters c. if you would have them exprest 6ly To avoid also the trouble of deviding the Circle 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 according to the Suns Diurnal Increment and Decrement in Amplitude you need only find by your Globe what the said Amplitude amounts to on every of the aforementioned Days which are markt on your Dial for the Suns Rising and Setting and then put it in Figures under each Day as the Scheme shows you 7ly Open your Compasses at the Tangent of 28 Degrees AB being the Radius and putting one Foot on B describe the Circle XYZ afterwards describe another according to the Tangent of 35 Degrees then a third according to that of 40 and so on in the same Proportion as far as your Plane permits Now if you mark these Circles with the Figures of the Complement of their Degrees that is to say the Circle of 28 Degrees with the Figure 62 that of 35 with 55 that of 40 with 50 c. you will always know the height of the Sun for what Circle soever the Shade of AB touches with its Top that will be the requir'd Height and if it falls between 2 Circles 't is but considering which of them it comes nearest to and then you may guess at the Height with sufficient exactness 8ly and 9ly Devide one of these Circles viz. SEWN into Degrees and under each 11 Degree and ¼ place the several Points of the Pixidis Nauticae or Mariners Compass in the Order as they are express'd in our said Scheme and you will not only have by the Shade of AB the Suns Azimuth at all times but see also how he bears from you according to the Points of the Compass and if the Shade be at any time too short lay on it but a Ruler Label of Paper or the like and that will truly lengthen the said Shade and resolve your Question 10thly Devide AF the Northern half of the Meridian as many times as you can by the Stile or Radius AB and then each Devision into ten equal parts as you see it done in the said Scheme and by it you will know at all times the Proportion between any Perpendicular and its Shade and consequently besides many other things the height of any Tower Tree or the like for having found the Sun to be suppose 25 Degrees high and that the Circle of Altitude cuts the Linc AF in the 22 Devision if therefore you measure the Shade of your Tower and finding it for Examples sake to be 66 Yards long you have what you seek for as the said 22 is to 10 the Stiles height so is 66 the length of the Shade to 30 the height of the Tower So much then for the Construction of Dials And now let me desire all those that are pleased to follow this Geometrical way which perchance is as expedite a one and as free from blind Lines as can be not to rest satisfy'd till they fully comprehend what they do for the Mechanical way of Dialling is as soon lost as learnt it being impossible without continual Practice not to forget the Rules especially if one can make many Dials when as a man that understands the reason of the Operations by having in his Head a true Idea of the Sphere and its Projection will 20 years after without Memorandums or Notes be able reflecting but a little to make not only all Dials he formerly knew but new ones also at first fight To Conclude I here present my Reader with the Globe in a new Dress for being painted or stain'd on Marble according to Sch. 43. 't will be fit for any Garden or open Portico and least it might appear too plain the corners of its Base or Pedestal may be adorned with handsom well turn'd Branches which not only embellish the whole Machin by their Make But hold out Bowls of Glass and Wyar for use also For on the First Corner to wit That markt with A there is placed as a Rarity The blind man's Dial. On the Second markt with B. The Dial that shows the Hour when the Sun shines not which will be often very useful On the third mark't with C there is an Armillary Wyer Sphere having a Vane on the Top that continually shows on the brass Plane within graduated and Nautically Character'd from what Quarter the Wind exactly blows as also if you turn the said Vane into the Plane of the Sun his Azimuth and Bearing Besides the Sphere being an Horizontal Concave Dial shows the Hour too for the Shade of the Pin's top in the Center ever fall's on the true Hour-Circle as I show'd in the Construction of such a Dial. And by the way you must know this Branch stands not in it's true place in the Scheme I mean on the third Corner of the Base because in Perspective 't will fall on the Globe it self and consequently not appear well to the Eye in a Picture Lastly on the fourth Corner markt with D there is another Glass Bowl of the former Dimension containing orderly all the Constellations and remarkable Stars and therefore if you know the Hour it will compose the said Bowl or Globe and so represent the then position of the Heavens but tho you are Ignorant of the Hour if you see a known Star and move the Bowl on its Axis till the painted star on it lyes just between your Eye and the Real one you have the Hour and consequently may know the Globe being now Compos'd any Star or Constellation above the Horizon for the Axis of this Bowl having one end pointing directly to the North Pole and the other fixt in the Center of a Rundle containing on its Limb the Days of each Month fitted to the right Ascension of the Stars and moving also on a Plane divided into 24 equal parts figured with the hours of a Natural Day 't will follow that the Day of the Month when the Globe is Compos'd must lye on the true Hour as the true Hour move'd to the Day of the Month must Compose the Globe as is before hinted These short directions are sufficient for any Mathematician or Instrument-Maker and as for the Branch it self 't is as you see not in its true Place for the above mentioned Reason J. Moxon To the Reader HAving Courteous Reader engaged to show you the Problems and Operations on the Sector which the Noble Author supposes every one that studies the Geometrical way of Dialling to know I
describe the ProjectioÌ„ but they may serve for Sch 1 2 Pag. 135. if on the higher the Constellation are supposd to be Engravd on the lower a line was drawÌ„ froÌ„ the Center to lack hour in the limb no Almucantar or Aziâ—â—th exprest but by Pricks satisfy any ordinary curiosity on the Globe it self according to their true Longitude and Latitude for then their Declensions Parallels and right Ascensions appear in a manner at first view which must needs therefore facilitate the other Operations Of the PEDESTAL THUS you see that our Globe tho' it be a Terrestial one may in case of necessity be serviceable in relation to the very Stars but because all Operations that have the least Reflection in them seem intricate and troublesome to some I have here adjoyned for them that will be at the Expence of the best sort of these Globes a most Facile way that shall resolve in an instant all the former Questions and more for there is not only a Steriographical Projection on the Pedestal of the appearing Stars in our Horizon but one also so ordered that it obviates the inconveniences which make Stofflers admirable Astrolabe so much neglected of late for some say there is no finding a Star on it without much poring tho' we should know near what Constellation it lyes others that when we see a Star there we are still ignorant to what Constellation it belongs many quarrel at the great confusion which the Azimuths Almucuntars and other Circles exprest on it make and some again object that the numeral Figures belonging to the said Circles are oftentimes so hid by the solid part of the Rete that we cannot without a new trouble and motion perform the intended Operation I say this Projection on the Pedestal besides several other things obviates these inconveniences as you will presently see The Explanation of the Circles and Lines of the whole Projection or Pedestal THE uttermost Circle in Sch. 1 or Limb SENW of the lower or first Plane represents Circulum maximum semper latentium or if you think that too large what Parallel you please It may be conveniently nine Inches or a little more in Diameter if the Globes be a Foot and being of fine Pastboard or the like substance it is to be let into the Pedestal which is purposely made Cradle or Frame wise that it may by your hand underneath be easily turn'd round and be also taken quite out if any particular or extraordinary occasion should require it Nay the whole Pedestal may be pulled off if you think fit from the handle or Fulerum and us'd apart as a distinct Instrument 2. The great Circles described on it are only two viz. the Aequator ♈ AE ♎ ae and the Ecliptic ♈ ♋ ♎ ♑ divided into the 12 Signs with their gradual subdivisions Now since it will be no incumbrance to your Plane you may express on it also if you please the two Tropics by two fine Circles that of Cancer touching the Ecliptic at ♋ and that of Capricorn at ♑ And as for the Limb it is divided into 360 Degrees for being in Projection greater than the Aequator 't will prove more useful in all the Operations that concern such Divisions Nor are the Circles or Stars placed here as on the Globe I mean according to the Degrees of a Quadrant equally divided but Steriographically projected by half Tangents i. e. as they would appear and fall on an Aequinoctial Plane or a Plane parallel to it were our Eye in the Pole of which more hereafter as also the Centers and Radius's of each Circle when we come to the Description and Demonstration of the whole Projection and in this manner also to wit by half Tangents the Line P. E. is divided which shows the Declension of any Star Thirdly The Stars being all plac'd on this Plane according to their respective Right Ascensions and Declensions and by the way when you once know how to find by this Projection the Right Ascension and Declension of a Star as you will presently do by the following Instructions that concern operation you will then also know by the help of Astronomical Tables which give each Star's Right Ascension and Declension how to place them here I say the Stars being all plac't on this Plane according to their respective Right Ascensions and Declensions they are to be Marshall'd and reduc'd into Constellations and therefore you must suppose either fit Pictures drawn about them to express what they are or that the uttermost Stars of each be join'd by a fine Prick't Line which will give you perchance the most clear and just representation of them and consequently prove the easiest way for the finding them out in the Heavens But since Pictures have conveniences and great ones also for thus without consulting the written names we cannot only find presently even a far off the Constellation we seek after but know at the same time the Place of each Star in it which Place for the most part gives the Star its ordinary Name I say since Pictures have great Conveniences let them be us'd but then they must be as faintly and simply express'd as can be for deep shadows and unnecessary Flourishes both distract the Fancy and cause even the Stars that are express'd to be less conspicuous and observ'd Fourthly When the first Plane is thus garnished and plac'd in its Frame there is another of the same bigness either of Glass or Talk represented by Scheme the second to be put over it and fixt or fastned in the uttermost Molding or Ledge of the Pedestal And here be pleas'd for distinction sake to remember that by the Terms First and Second these two Planes are distinguish'd and that by Projection is meant the whole Pedestal or Astronomical Machin which as I said may be taken off and used apart as a particular Instrument Lastly the second Plane represented as I said by Scheme the second has its Limb S. E. N. W divided besides the subdivisions or Quarters into 24 equal parts by so many streight Lines drawn from the. Center P and figur'd I. II. III c. according to the hours of a natural Day As for the Circle HRST it represents the Horizon and the Circular Pricks within it give the Almucantars and Azimuths of every 10 Degrees for on the one side if you consider the said Pricks as so many Circles ascending from the Horizon towards the Zenith the Figures along the Lines PS and PN give you from the Horizon upwards the height of that Star which touches any of them On the other side if you consider them in File I mean as so many Arches passing thro' the Zenith and terminating in the Horizon their distance from PS the Southern part of the Meridian shows the Azimuth of the Star next any of them by the Figures round the Horizon and least you might not readily distinguish Arch from Arch if the Pricks were all of the same kind or
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
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 '
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
Navigation Price 8 s. New and rare Inventions of Water-works teaching how to raise Water higher than the Spring By which Invention the Perpetual Motion is proposed many hard Labours performed and varieties of Motion and Sounds produced By Isaac de Caus Engineer to King Charles the First Price 8s Practical Perspective or Perspective made easie Teaching by the Opticks how to delineate all Bodies Buildings and Landskips c. By the Catoptricks how to delineate confused Appearances so as when seen in a Mirrour or Polish'd Body of any intended Shape the Reflection shall shew a Design By the Dioptricks how to draw part of many Figures into one when seen through a Glass or Christal cut into many Faces By Joseph Moxon c. Price 7s An exact Survey of the Microcosm being an Anatomy of the Bodies of Man and Woman wherein the Skin Veins Nerves Muscles Bones Sinews and Ligaments are accurately delineated Engraven on large Copper Plates Printed and curiously pasted together so as at first sight you may behold all the parts of Man and Woman and by turning up the several Dissections of the Papers take a view of all their Inwards with Alphabetical References to the names of every Member and part of the Body Set forth in Latin by Remelinus and Michael Spaher of Tyrol and Englished by John Ireton Chyrurgeon and lastly perused and corrected by several rare Anatomists Price 14s Vignola or the Compleat Architect shewing in a plain and easy way the Rules of the five Orders in Architecture viz. Tuscan Dorick Ionick Corinthian and Composite whereby any that can but read and understand English may readily learn the Proportions that all Members in a Building have to one another Set forth by Mr. James Barrozzio of Vignola and Translated into English by Joseph Moxon c. Price 3s 6d Christiologia or a brief but true Account of the certain Year Month Day and Minute of the Birth of Jesus Christ. By John Butler B. D. and Chaplain to his Grace James Duke of Ormond c. and Rector of Lichborough in the Diocess of Peterborough Price 3s 6d A Tutor to Astrology or Astrology made easie being a plain Introduction to the whole Art of Astrology whereby the meanest Apprehension may learn to Erect a Figure and by the same to give a determinate Judgment upon any Question or Nativity whatsoever Also new Tables of Houses calculated for the Latitude of 51 degr 32 min. Also Tables of Right and Oblique Ascensions to 6 degr of Latitude Whereunto is added an Ephemeris for three years with all other necessary Tables that belong to the Art of Astrology Also how to Erect a Figure the Rational way by the Tables of Triangles more methodically than hath been yet published digested into a small Pocket Volume for the conveniency of those that erect Figures abroad By W. Eland Price 2s The Use of a Mathematical Instrument called a Quadrant shewing very plainly and easily to know the exact Height and Distance of any Steeple Tree or House c. Also to know the time of the Sun-Rising and Setting and the Length of every day in the year the Place of the Sun in the Ecliptick the Azimuth Right Ascension and Declination of the Sun with many other necessary and delightful Conclusions performed very readily Also the use of a Nocturnal whereby you may learn to know the Stars in Heaven and the Hour of the Night by them with many other delightful Operations Price 6d A brief Discourse of a Passage by the North-Pole to Japan China c. pleaded by three Experiments and Answers to all Objections that can be urged against a passage that way As 1. By a Navigation into the North Pole and two Degrees beyond it 2. By a Navigation from Japan towards the North-Pole 3. By an experiment made by the Czar of Muscovy whereby it appears that to the Northward of Nova Zembla is a free and open Sea as far as Japan China c. With a Map of all the discovered Land nearest to the Pole By Joseph Moxon c. Price 6d Regulae Trium Ordinum Literarum Typographicarum Or the Rules of the three Orders of Print-Letters viz. the Roman Italica and English Capitals and Small shewing how they are compounded of Geometrick Figures and mostly made by Rule and Compass Useful for Writing Masters Painters Carvers Masons and others that are lovers of Curiosity By Joseph Moxon c. Price 5s The Use of the Astronomical Playing Cards teaching an ordinary Capacity by them to be acquainted with all the Stars in Heaven to know their Places Colours Natures and Bignesses Also the Poetical Reasons for every Constellation Very useful pleasant and delightful for all lovers of Ingeniety By Joseph Moxon c. Price 6d The Astronomical Cards By Joseph Moxon c. Price plain 1s Coloured 1s 6d best coloured and the Stars Gilt. 5s Geographical Playing Cards wherein is exactly described all the Kingdoms of the Earth curiously engraved Price Plain 1s Coloured 2s best Coloured and Gilt 5s the Pack The Genteel House-Keepers Pastime or the Mode of Carving at the Table represented in a Pack of Playing Cards By which together with the Instructions in this Book any ordinary Capacity may easily learn how to Cut up or Carve in Mode all the most usual Dishes of Flesh Fish Fowl and Bak'd Meats and how to make the several Services of the same at the Table with the several Sawces and Garnishes proper to each Dish of Meat Set forth by several of the best Masters in the Faculty of Carving and published for publick use Price 6d Carving Cards By the best Carvers at the Lord Mayor's Table Price 1s Compendium Euclidis Curiosi Or Geometrical Operations shewing how with one single opening of the Compasses and a straight Ruler all the Propositions of Euclid's first five Books are performed Translated out of Dutch into English By Joseph Moxon c. Price 1s An Introduction to the Art of Species By Sir Jonas Moor. Price 6d Two Tables of Ranges according to the Degrees of Mounture By Henry Bond Senior Price 6d Mechanick Exercises Or the Doctrine of Handy-Works in nine Monthly Exercises The first Three viz. Numb I. Numb II. Numb III. teaching the Art of Smithing The second Three viz. Numb IV. Numb V. Numb VI. teaching the Art of Joynery The third Three viz. Numb VII Numb VIII Numb IX teaching the Art of House-Carpentery Accommodated with suitable Engraved Figures By Joseph Moxon c. Price of each Monthly Exercise 6d Mechanick Dialling Teaching any man though of an ordinary Capacity and unlearned in the Mathematicks to draw a true Sun-Dial on any Given Plane however situated only with the help of a straight Ruler and a pair of Compasses and without any Arithmetical Calculation By Joseph Moxon c. Price 1s 6d Mathematicks made Easie Or A Mathematical Dictionary Explaining the Terms of Art and Difficult Phrases used in Arithmetick Geometry Astronomy Astrology and other Mathematical Sciences Wherein the true Meaning of the
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
unequal distance of these hour-lines What a Declining Plane is The Construction * pag. 80. To describe the Morning hours of a Declining Dial. To describe the Afternoon Hours How to make the Stile and Substilar of a Declining Dial. A Memorandum The Construction The Demonstration of these 2 declining Dials A Memorandum * pag. 84. Another Demonstration * pag. 83. * pag. 73. The construction * pag. 23. * pag 8. The Construction A ready way to find the Stile and Substile of a declining Dial. Demonstration * pag. 92. The Demonstration of the Stile and Substilar * pag. 82. * vid. pag 104. * vid. pag 105. The Construction and Demonstration How to make an Horizontal Plane an Aequinoctial one The Demonstration The Geometrical Construction A Memorandum * pag. 8. The Construction The Construction and Demonstration of a declining direct Dial facing the South A Direct North reclining Plane * pag. 89. How to describe the Plane of this Reclining Dial on the Globe The Construction A Memorandum Of the Stile and Substilar * pag. 82. Another Demonstration The construction * pag. 2. First way * pag. 4. * pag. 4. The second way The first part of the Operation * pag. 89. The second part of the Operation Why every Erect Stile or perpendicular show's not always the true Hour The Construction * pag. 89. The Demonstration * pag. 94. * pag. 75. Demonstration The Advantage or use of this Dial. The Construction Demonstration Another Dial of the same nature The construction The Demonstration The Construction Demonstration The Construction The Geometrical way The Demonstration The Construction The Demonstration * pag. 73. How this Dial is to be made when the windows lye not Southward The Construction of it as to the Hour at home * pag. 73. The Construction of it as to the Hour in other places To find the Suns place and day of the Month. To find the Rising and Setting of the Sun To find the Suns Amplitude To find the Height of the Sun To find the Suns Azimuth and Bearing To find the Proportion of Perpendiculars to their Shades The description of the Branches or Embellishments in Sheme 43. * p. 111. †p. 112. * vid. p. 113. * p. 71. Of the Sector * Op. 17. Sect. 1. pag. 19. A Memorandum * p. 6. * p. 68. * Op. 5. way 2. p. 10. A Memorandum Of the first Plane and its bigness Of the Circles and Stars on it and how they are placed Of the second Plane and it's bigness * p. 6. †p. 68. * p. 132. Two Memorandums The Principle on which this Projection depends Of the Concentric Circles The general Rule for projecting the great Oblique Circles Of projecting the Ecliptic Of projecting the Horizon Of projecting the primary Vertical Of projecting the rest of the Azimuths An expedite way of finding the said Centers and Radius Lemma 1. * Eucl. 27. 1 †6. 1. Lemma 2. †Eucl. 27. 1. * 6. 1. The Ecliptic truly projected A Memorandum The way of describing G. Frisius's Meridians The way of describing G. F. hia Parallels How to describe the Circles of Altitude on the 2 Plane * p. 138 and 139. * p. ◠First kind * pag. 4. ‡ p 8. 15. * pag. 13. ‡ p. 31. * pag. 36. ‡ pag. 39. * p. 40. * p. 35. * p. 5. ‡ p. 37. * p. 10. ‡ p. 11. * p. 21. ‡ p. 51. * p. 65. * p. 70. A Memorandum * p. 8. 2d kind * p. 18. * p. 9. 3 kind * p. 14. * p. 15. * p. 35. * p. 13. * p. 11. * p. 10. 12 * p. 16. * p. 17. * p. 19. * p. 17. * p. 33. * p. 33. * p. 34. * p. 36. * p. 31. 4th kind