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
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
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
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
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
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
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
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