on the Meridian till the graduated edge cut the degree of the Ecliptick the Sun is in Then I examine on the Meridian what degree the upper end of the Quadrant of Altitude touches which in this example I find is 38½ degrees Therefore I substract 38½ from 51½ Londons Latitude and there remains 13. Then counting on the Meridian 13. degrees backwards from the Place where the Quadrant of Altitude touched the Meridian I come to 25½ on the Meridian Northwards Therefore I say In the North Latitude of 25½ degrees and in the Longitude of London which is in Africa in the Kingdom of Numidia the Sun May 10. at 53. minutes past 8. a clock in the Morning hath the same Altitude above the Horizon it hath here at London The Quadrant of Altitude thus applyed to the East point of the Horizon makes right angles with all points on the Meridian even as all the Meridians proceeding from the Pole do with the Equator therefore the Quadrant being applyed both to the East point and the Suns Place projects a line to intersect the Meridian Perpendicularly in equal degrees from which intersection the Sun hath at the same time equal Heighth be the degrees few or many for those 5. degrees to the Northwards of this intersection have the Sun in the same heighth that they 5 degrees to the Southwards have it and those 10 20 30. degrees more or less to the Northwards have the Sun in the same heighth that they have that are 10 20. 30. degrees more or less to the Southwards So that this Prob. may be performed another way more easily with your Compasses Thus Having first rectified the Globe and Hour Index Turn about the Globe till the Hour Index point to the Hour of the Day Then pitch one foot of your Compasses in the Suns Place and extend the other to the degree of Latitude on the Meridian which in this example is 51½ degrees North then keeping the first foot of your Compasses on the degree of the Sun turn about the other foot to the Meridian and it will fall upon 25½ as before Blaew commenting upon this Probleme takes notice how grosly they ere that think they can find the heighth of the Pole at any Hour of the Day by the Suns height because they do not consider that it is impossible to find the Hour of the Day unless they first know the height of the Pole PROB. XLVIII To find the length of the Longest and Shortest Artificial Day or Night THe Artificial Day is that space of Time which the Sun is above the Horizon of any Place and the Artificial Night is that space of Time which the Sun is under the Horizon of any Place They are measured in the Hour Circle by Hours and Minutes There is a constant unequallity of proportion in the Length of these Daies and Nights which is caused both by the alteration of the Suns Declination and the difference of the Poles Elevation Those that inhabite on the North side the Equator have their longest Day when the Sun enters ♋ and those that inhabite on the South side the Equator have their longest Day when the Sun enters ♑ But to know how long the longest Day is in any North or South Elevation Raise the North or South Pole according to the Elevation of the Place and bring ♋ for North Elevation or ♑ for South Elevation to the Meridian and the Index of the Hour Circle to 12. Then turn the Globe about till ♋ for North Elevation or ♑ for South Elevation come to the West side the Horizon and the number of Hours and minutes pointed at on the Hour Circle doubled is the number of Hours and minutes of the Longest Day The length of the Night to that Day is found by substracting the length of the day from 24. for the remainder is the length of the Night The shortest Day in that Latitude is the length of the shortest Night found as before And the longest Night is of the same length with the longest Day Example I would know the length of the longest Day at London Therefore I Elevate the North Pole 51½ degrees and bring ♋ to the Meridian and the Index of the Hour Circle to 12. Then I turn ♋ to the Western side the Horizon and find the Index point at 8. hours 18. minutes which being doubled makes 16. hours 36. minutes for the length of the longest Day here at London PROB. XLIX To find how much the Pole is Raised or Depressed where the longest Day is an Hour longer or shorter then it is in your Habitation REctifie the Globe to the Latitude of your Place and make a prick at that point of the Tropick which is at the Meridian I mean at the Tropick of ♋ if your Habitation be on the North side the Equator or ♑ if your Habitation be on the South side the Equator And if you would know where the longest Day is just an hour longer then it is at your Habitation turn the Globe to the Westward till 7½ degrees of the Equato◠pass through the Meridian and make there another prick on the Tropick Then turn about the Globe till the first prick come to the Horizon and move the Meridian through the notches of the Horizon till the second prick on the Tropick come to the Horizon so shall the arch of the Meridian contained between the Elevation of your Place and the Degree of the Meridian at the Horizon be the number of Degrees that the Pole is Elevated higher then it is in your Latitude Example I would know in what Latitude the longest Day is an Hour longer then it is at London Therefore I Rectifie the Globe to 51½ deg and where the Meridian cuts the Tropick of ♋ I make a prick then I note what degree of the Equator is at the Meridian and from that degree on the Equator count 7½ degrees to the Eastwards and bring those 7½ degrees to the Meridian also and again where the Meridian cuts the Tropick of ♋ I make another prick so shall 7½ degrees of the Tropick be contained between those 〈◊〉 pricks Then I turn the Globe about till the first prick comes to the Horizon and with a Quill thrust between the Meridian and the Ball I fasten the Globe in this position Afterwards I move the Meridian through the 〈◊〉 of the Horizon till the second prick rises up to the Horizon and then I find 56½ degrees of the Meridian cut by the Superficies of the Horizon Therefore I say In the Latitude of 56½ degrees the longest Day is an Hour longer then it is here at London But if you would know in what Latitude the Dayes are an Hour shorter you must make your second prick 7½ degrees to the Westwards of the first and after you have brought the first prick to the Horizon you must depress the Pole till the second prick descends to the Horizon so shall the degree of the Meridian at the Horizon shew in
thereof mark it well first with your Compass observing diligently upon which Point thereof it lieth And secondly you must there take the heigth of the Sun or of the Pole-star as you were taught Prob. 13. of the second Book that you may know in what Point your Ship is and that point you must call the First Point which being so done your Ship may sail on her Course all that day till the day following without losing her Way and the next day mark the Land again and see upon what Point it lieth and then take your heigth and with it cast your Point of Traverse once again and that you may call your second Point Then take a pair of Compasses and placing one foot upon the First Point and the other upon the Rhumb towards which the Land did Bear when you Cast your First Point set also one foot of another pair of Compasses in the second Point and the other foot upon the Rhumb upon which the Land lay when you cast your second Point and these two Compasses thus opened you must move by their Rhumbs till those two feet of both Compasses do meet together which were moved from the foresaid two Points and where they do so meet together there may you say is the Land which you Discovered which Land you may point out with the In lets and Out-lets or Capes and other Signes which you saw thereupon And by the graduation you may see the Latitude thereof that thereby you may find it if a any time after you go to seek for it PROB. XVIII Seeing two known Points or Capes of Land as you sail 〈◊〉 long how to know the distance of your Ship from them PItch one foot of one pair of Compasses upon one of the two foresaid Capes and the other foot upon the Rhumâ— which in this Compass pointeth towards that Cape 〈◊〉 in like manner shall you do with another pair of Compasses placing one foot thereof upon the other known Cape 〈◊〉 the other foot upon the Rhumb which stretcheth towards 〈◊〉 said second Cape and moving the two Compasses so opened by these two Rhumbs off from the Land the very same Point where the two feet which came from the two Capes do meet you may affirm to be the very Point where your Ship is And then measuring by the degrees of the Equinoctial you may see what distance there is from the said Point to either of the foresaid Capes or to any other place which you think good for it is a very easie matter if you know the point where your Ship is PROB. XIX Of Tides and how by help of the Globe you may in general judge of them DIvide the Equinoctial into 30 equal parts as was directed in Prob. 54. of the last Book These 30. equal parts represent the 30. daies of the Moons Age. Then on the North and South point of the Compass in the outmost Verge of the Horizon Write with red Ink 12. From the North Eastward viz. at the Point North and by East Write 11 ¼ At the next point to that the same way viz. North North East Write 10 ½ At the next viz. North East and by North Write 9 ¾ And so forward to every point of the Compass rebating of the last hour ¾ till you come to 12. in the South where you must begin again to mark that Semi-Circle also in the same order you did the last In this Circle is then represented the Points of the Compass the Sun and Moon passeth by every Day and the Figures annexed represent the twice 12. hours of Day and Night Having thus prepared your Globe and Horizon you may by having the Moons Age and the point of the Compass on which the Moon maketh full Sea at any Place given find at what Hour of Day or Night it shall be high Tide in the same Place Thus It is a known Rule that a North and South Moon makes high water at Margarate Therefore Bring the first point of ♈ to the North or South point in the Horizon and Elevate the North Pole into the Zenith Then count in the Equinoctial the Daies of the Moons Age numbred in red figures and the Hour and minutes written in red figures annexed to the names of the Windes that stands against the Moons Age shall be the Hour of High Tide on that Day or Night at Margarate The End of the Third Book The Fourth BOOK Shewing the Practical Use of the GLOBES Applying them to the Solution of Astrological Problemes PRAEFACE THe Practise of Astrology is grounded upon a two-fold Doctrine The first for erecting a Figure of Heaven placing the Planets in it finding what Aspects they bear each other and in what Places they are constituted c. and this we call the Astronomical part of Astrology The second is how to judge of the events of things by the Figure erected and this is indeed the only Astrological part The first of these I shall briefly handle because what therein is proposed may be performed by the Globe both with speed ease delight and demonstration The second I shall not meddle with but refer you to the whole Volumnes already written upon that Subject PROB. I. To Erect a Figure of the 12 Houses of Heaven BEfore you erect a Figure of the 12 Houses of Heaven it will be requisite you place the Planets ☊ and ☋ according to their Longitude and Latitude upon the Globe as was directed in Prob. 55. of the second Book for then as you divide the Houses of your Figure by the Circle of Position you may by inspection behold in what Houses the Planets are scituated and also see what fixed Stars they are applying to or separating from But to the matter There is disagreement between the Ancient and Modern Astrologers about erecting a Figure of Heaven M r Palmer in his Book of Spherical Problemes Chap. 48. mentions four several waies and the Authors that used them whereof one of them is called the Rational way used by Râ—giomontanus and now generally practised by all the Astrologers of this Age. This way the face of Heaven is divided into twelve parts which are called the twelve Houses of Heaven numbered from the Ascendent or angle at East downwards with 1 2 3 c As in the following Figure In a Direct Sphear viz. under the Equator these twelve Houses are twelve equal parts but in an Oblique Sphear they are unequal parts and that more or less according to the quantity of the Sphears obliquity These twelve Houses are divided by 12. Semi-Circles of Position which are Semi-Circles passing from the two intersections of the Horizon and Meridian through any Star degree or point in the Heavens The degrees and minutes of the Ecliptick upon the Cusps of these four Houses that is upon the beginning of these Houses are found all at once only by bringing the Rising degree of the Ecliptick to the Horizon for the Horizon represents the Cusp of the Ascendent and then shall
the Night and Day 42 Prob. 8. To find the Hour of Sun Set. 42 Prob. 9. To find how long it is Twilight in the Morning and Evening 43 Prob. 10. The Suns Place given to find its Amplitude And also to know upon what point of the Compass it Riseth 44 Prob. 11 The Hour of the Day given to find the Height of the Sun 45 Prob. 12. The Altitude of the Sun and Day of the Moneth given to find the Hour of the Day fol. 46 Prob. 13. How to know whether it be Before or After Noon 47 How to take Altitudes by the Quadrant Astrolabe and Cross-staff 47 To take Altitudes by the Astrolabe 50 To take Altitudes by the Cross-staff 51 Prob. 14. To observe with the Globe the Altitude of the Sun 52 Prob. 15. To find the Elevation of the Poleâ— by the Meridian Altitude of the Sun and Day of the Moneth given 53 Prob. 16. To take the Altitude of any Star above the Horizon by the Globe 54 Prob. 17. By the Meridian Altitude of any Star given to find the Height of the Pole 54 Prob. 18. Another way to find the Height of the Pole by the Globe if the Place of the Sun be given and also to find the Hour of the Day and Azimuth and Almicanter of the Sun 56 Prob. 19. To observe by the Globe the Distance of two Stars 57 Prob. 20. How you may learn to give a guess at the number of degrees that any two Stars are distant from one another or the number of degrees of Altitude the Sun or any Star is Elevated above the Horizon only by looking up to Heaven without any Instrument 58 Prob. 21. The Day of the Moneth and Altitude of any Star given to find the Hour of the Night 59 Prob. 22. The Place of the Sun and Hour of the Day given to find its Azimuth in any Latitude assigned 60 Prob. 23. The Place of the Sun and Hour of the Day given to find the Almicantar of the Sun 61 Prob. 24. The Place of the Sun given to find what Hour it comes to the East or West and what Almicantar it then shall have 61 Prob. 25. To know at any time what a clock it is in any other Part of the Earth 62 Prob. 26. To find the Right Ascension of the Sun or Stars 63 Prob. 27. To find the Declination of the Sun or Stars 64 A Table of the Right Ascensions and Declinations of 100. Select fixed Stars Calculated by Tycho Brahe for the Years 1600 and 1670. As also their Difference of Right Ascensions and Declinations in 70. Years 65 Prob. 28. The Place of the Sun or any Star given to find the Right Descension and the Oblique Ascension and the Oblque Descension fol. 71 Prob. 29. Any Place on the Terrestrial Globe being given to find its Antipodes 72 Prob. 30. To find the Perecij of any given Place by the Terrestrial Globe 73 Prob. 31. To find the Antecij of any given Place upon the Terrestrial Globe 73 Prob. 32. To find the Longitude and Latitude of the Stars by the Coelestial Globe 73 Prob. 33. To find the Distance between any two Places on the Terrestrial Globe 74 Prob. 34. To find by the Terrestrial Globe upon what point of the Compass any 〈◊〉 Places are scituate one from another 75 Prob. 35. To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars 76 Prob. 36. To find by the Coelestial Globe the Acronical Rising and Setting of the Stars 77 Prob. 37. To find by the Coelestial Globe the Heliacal Rising and Setting of the Stars 78 Prob. 38. To find the Diurnal and Nocturnal Arch of the Sun or Stars in any given Latitude 79 Prob. 39. To find the Azimuth and Almicantar of any Star 81 Prob. 40. To find the Hour of the Night by observing two known Stars in one Azimuth or Almicantar 81 Prob. 41. The Hour given that any Star in Heaven comes to the Meridian to know thereby the Place of the Sun and by consequence the Day of the Moneth though it were lost 82 Prob. 42. The Day of the Moneth given to find in the Circle of Letters on the Plain of the Horizon the Day of the Week 83 Prob. 43. The Azimuth of any Star given to find its Hour in any given Latitude 84 Prob. 44. How you may learn to know all the Stars in Heaven by the Coelestial Globe 84 Prob. 45. How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in Astronomy and Geography 89 Prob. 46. To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sâ—â— is 91 Prob. 47. To find in what different Places of the Earth the Sun hath the same Altitude at the same time 92 Prob. 48. To find the length of the Longest and shortest Artificial Day or Night 95 Prob. 49. To find how much the Pole is Raised or Depressed where the longest Day is an Hour longer or shorter then it is in your Habitation 96 Prob. 50. The Suns Place given to find what alteration of Declination he must have to make the Day an Hour longer or shorter And in what number of Daies it will be 97 Prob. 51. Of the difference of Civil and Natural Daies commonly called the Equation of Civil Daies And how it may be found by the Globe 99 Prob. 52. How to find the Hour of the Night when the Moon shines on a Sun Dyal by help of the Globe 101 Prob. 53. To find the Dominical Letter the Prime Epact Easter Day and the rest of the Moveable Feasts for ever 102 Prob. 54. The Age of the Moon given to find her place in the Ecliptick according to her mean motion 104 Prob. 55. Having the Longitude and Latitude or Right Ascension and Declination of any Planet or Comet to place it on the Globe to correspond with its place in Heaven 105 The Contents Of the Third Book Prob. 1. THe Suns Amplitude and difference of Ascension given to find the Height of the Pole and Declination of the Sun 108 Prob. 2. The Suns Declination and Amplitude given to find the Poles Elevation 108 Prob. 3. The Suns Declination and Hour at East given to find the Heigth of the Pole 109 Prob. 4. The Declination of the Sun and his Altitude at East given to find the Heigth of the Pole 110 Prob. 5. By the Suns Declination and Azimuth at 6 of the Clock given to find the Heigth of the Pole and Almicantar at 6. 11â— Prob. 6. By the Hour of the Night and a known Star Observed Rising or Setting to find the Heigth of the Pole fol. 112 Prob. 7. Two Places given in the same Latitude to find the Difference of Longitude 112 Prob. 8. Two Places given in the same Longitude to find the difference of Latitude 113 Prob. 9. Course and Distance between two Places given to find their
the number of degrees that the Sun Moon or any Star is distant from the Equinoctial towards either Pole and hath a double Denomination viz. North Declination and South Declination for if the Sun Moon or Star swarve towards the North Pole they are said to have North Declination if towards the South Pole South Declination The Right Ascension is the number of degrees of the Equinoctial accounted from the first point of Aries which comes to the Meridian with the Sun Moon or Star or any other point in Heaven proposed The Oblique Ascension is the number of degrees of the Equinoctial which comes to the East side of the Horizon with the Sun Moon or any Star The Oblique Descension is the degrees of the Equinoctial which comes to the West side of the Horizon with the Sun Moon or any Star The Ascensional Difference is the number of degrees after subtraction of the Oblique Ascension from the 〈◊〉 〈◊〉 â—scension So many degrees as you are said to sail towards the Pole you are said to Raise the Pole and so many degrees as you sail from the Pole you are said to Depress the Pole Course is the point of the Compass you sail upon as if you sail East-wards it is an Easterly Course if West a Westerly Course c. Distance is the number of leagues you have sailed from any Place upon any Course A Zone is a space of Earth contained between two Parrallels The ancient Geographers made five Zones in the Earth Two Frozen Two Temperate and one Burnt Zone The two Frozen Zones are those parts of the Globe comprehended between the North Pole and the Arctick Circle and the South Pole and the Antarctick Circle by the Ancients called inhabitable because the Sun being alwaies far remote from them shoots its beams Obliquely upon them which Oblique beams are so very weak that all their Summer is but a continued Winter and the Winter as they thought impossible to be at all indured The Temperate Zones are the space of Earth contained between the Arctick Circle and the Tropick of ♋ and the Antarctick Circle and the Tropick of ♑ by the Ancients called Temperate and Habitable because they are composed of a sweet Mediocrity between outragious Heat and extremity of Cold. The Burnt Zone is the space of Earth contained between the Tropick of ♋ and the Tropick of ♑ called by the Ancients Unhabitable because in regard the Sun never moves out of this Zone but darts its Beames perpendicularly upon it they imagined the Air was so unsufferable Hot that it was impossible for any to inhabite in this Zone So that as you see they held the two Temperate Zones only habitable and the two Frozen Zones and one Burnt Zone altogether unpossible to be inhabited But their Successors either animated by industry or compeld by necessity have apparently confuted that Assertion for at this time many thousands can witness that their bloods are not so greasie as to be melted in the Scortching heat of the one or so watry as to be congealed in the Icy frosts of the other The Ancients have yet otherwise divided the Earth into four and twenty Northern Climates and four and twenty Southern Climates so that in all there is eight and forty Climates The Climates are altered according to the half hourly increasing of the longest daies for in the Latitude where the longest daies are increased half an hour longer then they are at the Equator viz. longer then 12 hours the first Climate begins and in the Latitude where they are increased an whole hour longer then in the Equator the second Climate begins where the daies are increased three half hours longer then in the Equator the third Climate begins and so onwards the Climates alter according as the longest day increases half an hour till you come to find the longest day 24 hours long Now the Ancients in those times knowing no more then nine Habitable Climates gave names only to nine The first they called Dia Meroes after the name of a famous Inland Iland which is scituate about the middle of that Climate and is now called Gueguere The second Climate they called Dia Syenes after the name of an eminent Citty in Egypt lying about the midst of that Climate The third Dia Alexanderas after the name of the Metropolitan Citty of Egypt The fourth Dia Rhodes The fifth Dia Romes The sixth Dia Ponton The seventh Dia Boristheneos The eighth Dia Ripheos The ninth Dia Daniam These names belong only to the Climates on the North side of the Equator But those on the South side in regard of the smal Discoveries those Ages had on that side the Equator were distinguisht only by the addition of the word Anti to the same Southerly Climate as the first Southern Climate which is that Climate that lies as many degrees to the South-ward as the first doth to the North-ward they called Anti Meroes The second Anti Syenes The third Anti Alexanderas and so on to the ninth In every Climate is included two Parallels which are of the same nature with the Climates save only that as the Climates alter by the half hourly increasing of the longest day the Parallels alter by the quarter hourly increasing of the longest day Furthermore in respect of the Horizon we find the Sphear constituted into a threefold Position as first into a Direct Sphear Secondly a Parallel Sphear Thirdly an Oblique Sphear A Direct Sphear hath both the Poles of the World in the Horizon and the Equinoctial transiting the Zenith In a Direct Sphear all the Circles Parallel to the Equator make right angles with the Horizon and are also divided into two equal parts by the Horizon and in a Direct Sphear the Sun Moon and Stars are alwaies twelve hours above the Horizon and twelve hours under the Horizon and consequently make twelve hours Day and twelve hours Night It is called a Direct Sphear because all the Celestial Bodies as Sun Moon and Stars c. by the Diurnal Motion of the Primum Mobile ascend directly above and descend directly below the Horizon They that inhabite under the Equator have the Sphear thus posited as in the Iland Borneo Sumaira Celebes St. Thomas a great part of Africk Peru in the West-Indies c. as you may see by the Globe it self if you move the Brasen Meridian through the notch in the Horizon till the Poles thereof touch the Horizon As in this Figure A Parallel Sphear hath one Pole of the VVorld in the Zenith the other in the Nadir and the Equinoctial line in the Horizon In a Parallel Sphear all the Circles Parallel to the Equinoctial are also Parallel to the Horizon and in a Parallel Sphear from the 10th of March to the 11th of September the Sun being then in the Northorly Signes and consequently on the North side the Horizon there is six Moneths Day
every common Year so that in a Revolution of 4. Years one Day is gained which is added to February and therefore February hath every fourth or Leap Year 29. Daies PROBLEME IIII. To find the Day of the Moneth the Place of the Sun being given AS in the last Probleme it was your task to find on the Horizon the Day of the Moneth first so now you must first seek the Signe and degree the Sun is in and against it in the Circle of Moneths you shall see the Day of the Moneth As against ♉ 29. you have May 10. PROBLEME V. The Place of the Sun given to find its Declination HAving by the third Probleme found the Suns Place on the Plain of the Horizon you must seek the same degree in the Ecliptick on the Globe then bring that degree to the Brazen Meridian and the number of degrees intercepted between the Equinoctial and the degree just-over the degree of the Ecliptick the Sun is in is the Declination of the Sun for that Day and bears its Denomination of North or South according to its Position either on the North or South side the Equinoctial Example By the third Probleme aforesaid of May 10. I find ♉ 29. the Suns Place Therefore I seek in the Ecliptick Line on the Globe for ♉ 29. and bring it to the East side of the Brazen Meridian which is the graduated side and over ♉ 29. I find on the Brazen Meridian 20. deg 5. min. numbred from the Equinoctial and because ♉ is on the North side the Equinoctial therefore I say The Sun hath May 10. North Declination 20. degrees 5. min. PROBLEME VI. The Place of the Sun given to find its Meridian Altitude THe Globe rectified Bring the degree of the Sun to the Meridian or which is all one the degree of the Ecliptick the Sun is in and the number of degrees contained between the Horizon and the Suns Place in the Meridian is the number of degrees that the Sun is Elevated above the Horizon at Noon or which is all one the Meridian Altitude of the Sun Example To know what Meridian Altitude the Sun hath here at London May 10. I bring the Suns Place found by the third Probleme to the Meridian and count on the Meridian the number of degrees contained between the Horizon and the degree just over the Suns Place which in this Example I find to be 58½ Therefore I say the Suns Meridian Altitude May 10. is here at London 58½ degrees PROBL. VII The Suns Place given to find the Hour of Sun Rising and the length of the Night and Day THe Globe and Hour Index rectified Seek the degree the Sun is in on the Globe and bring that degree to the Eastern Side of the Horizon and the Index of the Hour Circle will point at the Hour of Sun Rising Example To know the Hour of Sun Rising here at London May 10. The Suns Place as before is ♉ 29. Therefore the Globe being rectified as before I seek ♉ 29. degrees on the Globe and bring that degree to the East Side of the Horizon and looking on the Index of the Hour Circle I find it point at 4. a clock and â…™ part of an hour more towards 5 therefore I say May 10. the Sun rises here at London at â…™ which is 12. minutes after 4 a clock in the Morning If you double 4 hours 12. minutes it gives you the length of the Night 8 hours 24. minutes And if you substract the length of the Night 8. hours 24. minutes from 24. hours the length of Day and Night it leaves the length of the Day 15. hours 36. minutes PROB. VIII To find the Hour of Sun Set. TUrn the Place of the Sun to the West side of the Horizon and the Index of the Hour Circle shews on the Hour-Circle the hour of Sun set which on the 10th of May aforesaid is 〈◊〉 parts of an hour after 〈◊〉 7. a clock at Night Viz. the Sun Sets at 48. minutes past 7. a clock PROB. IX To find how long it is Twilight in the Morning and Evening TWilight is that promiscuous and doubtfull light which appears before the Rising of the Sun in the Morning and continues after the setting of the Sun in the Evening It is made by the extension of the Suns beams into the Vapours of the Air when the Sun is less then 18. deg below the Horizon for the Sun ere it Rises and after it Sets shoots forth its Beams through the Air and so illuminates the Vapours of the Air which illumination does by degrees enlighten the Horizon and spreads through the Zenith even into the West ere the Sun Rises and also continues above the Horizon afteâ— the Sun sets Now though it be Twilight when the Sun is 18. degrees below the Horizon yet the duration of Twilight is alterable both in respect of Time and Place for at such Time at the Sun is farthest distant from any Place the Twilight shall be greater then when it is neerest And in respect of Place All Places that have great Latitude from the Equator have longer Twilight than those that are neerer to the Equator for as Authors say under the Equator there is no Twilight when again in many Climes both Northward and Southward the Nights are indeed no Nights but only as it were a little over-spread with a cloudy Shade and is either increased or diminished according to the â—autation of Meoâ—erological Causes Therefore to know the beginning of Twilight in the Morning here at London May 10 you must having the Globe rectified turn the degree of the Ecliptick which is opposite to the Place of the Sun till it be elevated 18. degrees in the Quadrant of Altitude above the Horizon in the West So shall the Index of the Hour-Circle point at the Hour that Twilight begins Then subtract the Hour and Minute that Twilight begins from the Hour and Minute of Sun Rising if in the Morning or substract the Hour of Sun sett from the Hour of Twilight if at Night and the remainder is the length of Twilight Example The Globe Quadrant and Hour-Index being rectified as before and the Suns place given ♉ 29. I seek the opposite degree on the Globe after this manner I bring ♉ 29. to the Meridian and observe what degree of the Ecliptik the opposite part of the Meridian cuts and because I find it cuts â™ 29. therefore I say â™ 29. is opposite to ♉ 29. Having found the opposite degree I bring it into the West and also the Quadrant of Altitude and joyn â™ 29. to 18. degrees accounted upwards on the Quadrant so shall ♉ 29. be depressed 18. degrees in the East Side the Horizon Then looking what Hour the Hour-Index points at in the Hour-Circle I find it to be 1. Hor. 8. Min. which shews that Twilight begins at 8. Minutes past 1. a clock in the Morning And if you substract 1. Hour 8. Minutes from 4. Hours 11. Minutes the time
of Sun Rising found by the 7th Probleme it leaves 3. Hours 3. Minutes for the length of Twilight And if you double 1. Hour 8. Minutes the beginning of Twilight it makes 2. Hours 16. Minutes for the intermission of Time between Twilight in the Evening and Twilight in the Morning So that May 10. absolute Night is but 2. Hours 16. Minutes long here at London The reason why you bring the degree opposite to the Suns Place to the West is because the Quadrant containing but 90. degrees will reach no lower then the Horizon but this Probleme requires it to reach 18. degrees beneath it therefore by this help you have the Proposition Answered as well as if the Quadrant did actually reach 18. degrees below the Horizon This shift you may have occasion to make in some other Problemes If you would know when Twilight ends after Sun set you shall find it by bringing the degree of the Ecliptick opposite to the Place of the Sun to 18. degrees of the Quadrant of Altitude on the East side the Horizon for then shall the Index of the Hour-Circle point at 10. Hours 52. Minutes which shews that it continues Twilight till 52. Minutes past 10. a clock at Night May 10. here at London PROB. X. The Suns Place given to find its Amplitude And also to know upon what point of the Compass it Riseth THe Globe c. rectified Bring the Suns Place to the East Side the Horizon and the number of degrees intercepted between the East point of the Horizon and the Suns Place is the number of degrees of Amplitude that the Sun hath at its Rising and bears its denomination either of North or South according to its inclination to either point in the Horizon Or if you would know upon what point of the Compass the Sun Rises Look but in the Circle of Winds and against the Place of the Sun you have the name of the point of the Compass upon which the Sun Riseth Examples of both May 10. the Suns Place is ♉ 29. Thereâ—â—re â— the Globe being rectified I bring ♉ 29. to the East side the Horizon and find it touch against 33 degrees 20. Minutes from the East point towards the North Therefore I say the Sun hath North Amplitude 33 degrees 20. Minutes And to know upon what point of the Compass the Sun rises I keep the Globe to its Position and look in the Circle of Winds in the outmost verge of the Horizon and find the Suns Place against the Wind named North East and by East Therefore I say May 10. here at London the Sun riseth upon the North East and by East point of the Compass PROBL. XI The Hour of the Day given to find the Heigth of the Sun THe Globe c. Rectified Turn about the Globe till the Index of the Hour-Circle point in the Hour-Circle to the Hour of the Day Then bring the Quadrant of Altitude to the Suns Place in the Ecliptick and the degree on the Quadrant which touches the Suns Place shall be the number of degrees of the Suns Altitude Example May 10. here at London At 53. Minutes past 8. a clock in the Morning I would know the Heigth of the Sun above the Horizon Therefore I turn about the Globe till the Index of the Hour-Circle come to 53 Minutes past 8. a clock which is almost 9. in the Hour-Circle And keeping the Globe to this Position I bring the Quadrant of Altitude to the Suns place viz. 〈◊〉 29. found by the third Probleme and because the Suns Place touches upon 40. degrees of the Quadrant therefore I say May 10. 53. Minutes past 8. a clock in the Morning here at London The Sun is just 40. degrees above the Horizon or which is all one hath 40. degrees of Altitude PROB. XII The Altitude 〈◊〉 Sun and Day of the Moneth given to find the Hour of the Day AN Hour is the 24th part of a Day and a Night or the space of time that 15. degrees of the Equator takes up in passing through the Meridian for the whole Equator which contains 360. degrees passes through the Meridian in 24. Hours therefore 15. degrees which is the 24th part of 360 pass through in one Hour These Hours are Vulgarly divided into halfs quarters and half quarters but Mathematically into Minutes Seconds Thirds Fourths c. A Minute is the 60th part of an Hour so that 60 minutes make an Hour 30 half an Hour 15. a quarter of an Hour A Second is the 60th part of a Minute a third is the 60th part of a Second a Fourth is the 60th part of a Third and so you may run on to Fifths Sixths Sevenths c. if you please 12. of these Hours make a Day and 12. more make a Night so that Day and Night contain 24. hours as aforesaid which are Volgarly numbred from Noon with 1 2 3 to 12 at Night and then begin again with 1 2 3 till 12 at Noon But by Astronomers they are Numbred from Noon with 1 2 3 c. to 12. at Night and so forward to 13 14 15 till 24 which is just full Noon the next Day Yet in this Treatise I shall mention the Hours as they are Vulgarly coâ—â—ted viz. from 〈◊〉 after noon to 12. at Night and call the Hours after Midnight by 1 2 3 4 c. in the Morning to 12. at Noon again the next Day But to the operation The Globe c. Rectified Bring the Place of the Son to the Number of degrees of Altitude accounted upon the Quadrant of Altitude and the Hour-Index shall point at the Hour in the Hour-Circle yet herein respect must be had to the Fore or After noons Elevation as shall be shewed in the next Probleme Example May 10. The Sun is elevated 40. degrees above the Horizon here at London Therefore having found the Place of the Sun by the third Probleme to be â—29 I move the Globe and Quadrant till I can joyn the 29. degree of 〈◊〉 to the 40. deg upon the Quadrant of Altitude and then looking on the Hour-Circle I find the Index point at 53. Minutes past 8. a clock for the Fore noon Elevation and at 3. hours 7. Minutes for the After noons Elevation Therefore if it be Fore-noon I say It is 53. Minutes past 8. a clock in the Morning But if it be After noon I say It is 7. Minutes past 3. a clock in the After noon PROB. XIII How to know whether it be Before or After Noon HAving made one Observation you must make a Second a little while after the First and if the Sun increase in Altitude it is Before Noon but if it decrease in Altitude it is After Noon Example The Sun was at 8. hor. 53. Min. elevated 40. degr above the Horizon A little while after suppose for examples sake aquarter of an hour viz. at 9. hor. 8. Min. I observe again the heigth of the Sun and find it 42. degrees high
as I can so as the Spherick Gnomon may cast no shadow yet if it do and the shadow fall towards the North Pole then I elevate the North Pole more till the shadow fals just in the middle of it self but if the shadow fall downwards towards the South Pole then I depress the North Pole If the shadow fall on the East side I turn the Globe on its Axis more to the West and if the shadow fall to the West I turn the Globe more into the East and the degree of the Meridian which the North point of the Horizon touches is the degree of the Poles Elevation which in this Example is 51½ the Latitude of the City of London By this Operation you have also given the Hour of the Day in the Hour-Circle if you keep the Globe unmoved and the Azimuth and Almicantar if you apply but the Quadrant of Altitude to the Place of the Sun as by the 22 and 23. Problemes PROB. XIX To observe by the Globe the Distance of two Stars YOu must pitch upon two Stars in the Meridian and observe the Altitude of one of them first and afterwards the Altitude of the other Then substract the lesser Altitude from the greater and the remainder shall be the distance required Example March 7. at 11. a clock at Night here at London I see in the Meridian the two Stars in the foremost Wheels of the Waggon in the Constellation of the Great Bear called by Sea-men the Pointers because they alwaies point towards the Pole-Star Therefore to observe the distance between these two Stars I first observe as by the last Probleme the Altitude of the most Northern to be 77. degree 59. minutes and set down that number of Degrees and minutes with a Pen and Ink on a Paper or with a peece of Chalk or a Pencil on a Board and afterwards I observe the Altitude of the other Star which is under it as I did the first to be 83. deg 21. min. and set that number of degrees and minutes also down under the other number of degrees and minutes Then by substracting the lesser from the greater I find the remainder to be 5. degrees 22. min. which is the distance of the two Stars in the Great Bear called the Pointers PROB. XX. How you may learn to give a guess at the number of degrees that any two Stars are distant from one another or the number of degrees of Altitude the Sun or any Star is elevated above the Horizon only by looking up to Heaven without any Instrument BEtween the Zenith and the Horizon is comprehended an Arch of a Circle containing 90. degrees so that if you see any Star in or neer the Zenith you may know that Star is 90. or neer 90. degrees high and by so much as you may conceive it wants of the Zenith so much you may guess it wants of 90. degrees above the Horizon By this Rule you may guess at an Arch of Heaven containing 90. degrees or at an Arch of Heaven containing 45. degrees if by your imagination you divide the whole Arch into two equal parts for then shall each of them contain 45. degrees And if by your imagination you divide the Arch of 90. into 3. equal parts each division shall contain an Arch of 30. degrees c. But this way is a little too rude for guessing at Stars elevated but few degrees or for Stars distant but few degrees from one another Therefore that you may learn to guess more precisely at Distances in Heaven you may either with a Quadrant Astrolabe or the Globe find the exact distance of any two known Stars that are but few degrees asunder and by a little revolving the distance of those Stars in your fancy you may at length so imprint their distance in your memory that you may readily guess the distance of other Stars by the distance of them Example You may find either by the Globe Quadrant or Asâ—rotabe for they all agree 3. degrees comprehended between the first Star in Orions Girdle and the last therefore by a little 〈◊〉 nating upon that distance you may imprint it in your fancy for 3. degrees and so make it applicable to other Stars either of the same distance or more or less And the Pointers by the last Probleme are distant from one another 5. degrees and almost an half These are alwaies above our Horizon and therefore may alwaies stand as a Scale for five and an half degrees So that by these for 5½ degrees and those in Orions Girdle for 3. degrees and others observed either of greater or lesser distance you may according to your own Judgement shape a guess if not exactly yet pretty neer the matter of Truth when you come to other Stars Thus you may exercise your fancy upon Stars found to be 10. or 15. degrees asunder or more or less and with a few experiments of this nature enure your Judgement to guess distances and enable your memory to retain your Judgement This way of guessing will be exact enough for finding the Hour of the Night by the Stars for most common Uses or the Hour of the Day by guessing at the Altitude of the Sun if after you have guessed at the Altitude you shall work as was taught by Prob. 12. for the Hour of the Day and as shall be taught in the next Probleme for the Hour of the Night PROB. XXI The Day of the Moneth and Altitude of any Star given to find the Hour of the Night THe Globe Quadrant and Hour Index rectified Bring the Star on the Globe to the same number of Degrees on the Quadrant of Altitude that it hath in Heaven So shall the Index of the Hour-Circle point in the Hour-Circle at the Hour of the Night Example March 10. the Altitude of Arcturus is 35. degrees above the Horizon here at London Therefore having the Globe Quadrant and Hour Index rectified I bring Arcturus on the Globe to 35. degrees on the Quadrant of Altitude And then looking in the Hour-Circle I find the Index point at 10. a clock which is the Hour of the Night PROB. XXII The Place of the Sun and Hour of the Day given to find its Azimuth in any Latitude assigned THe Globe c. rectified to your Latitude Turn the Globe till the Index of the Hour-Circle come to the given hour and bring the Quadrant of Altitude to the Place of the Sun so shall the number of degrees contained between the East point of the Horizon and the degree cut by the Quadrant of Altitude on the Horizon be the number of degrees of the Suns Azimuth at that time Example May 10. at 53. minutes past 8. a clock in the Morning I would know the Azimuth of the Sun Therefore the Globe being first rectified I turn about the Globe till the Index of the Hour-Circle point to 53. minutes past 8. a clock or which is all one within half a quarter of an hour of 9 then I move
the Quadrant of Altitude to the degree the Sun is in that Day and there let it remain till I see how many degrees is contained between the North point and the Quadrant which in this Example is 108. deg 25. min. And because this distance from the North exceeds 90. degrees therefore I substract 90. degrees from the whole and the remains is 18. degrees 25. min. for the Azimuthal distance of the Sun from the East point towards the South But if it had wanted of 90. degrees from the North point then should the Complement of 90. have been the Azimuthal distance of the Sun from the East point PROB. XXIII The Place of the Sun and hour of the Day given to find the Almicantar of the Sun THe Almicantars of the Sun is upon the matter the same thing with the Altitude of the Sun only with this distinction The Almicantars are Circles parallel to the Horizon discribed by the degree of the Quadrant of Altitude upon the Zenith as its Center by turning the Quadrant round about the Globe till it comes again to its first Place But the Altitude is an Arch of the Vertical Circle comprehended between the Horizon and any point of the Globe assigned Their agreement consists in this When the Sun or any Star haâ—â— any known Almicantar they are said to have the same number of degrees of Altitude As if the Sun be in the 20th Almicantar he hath 20 degrees of Altitude if in the 30th Almicantar he hath 30. degrees of Altitude c. Now because the Operation is the same for finding the Altitude and Almicantar I shall refer you to the 11th Probleme which shews you how to find the Altitude or Heighth and by consequence the Almicantar PROB. XXIV The Place of the Sun given to find what Hour it comes to the East or West and what Almicantar it then shall have THe Globe Quadrant and Hour Index rectified Bring the Quadrant of Altitude to the East point in the Horizon if you would know what hour it comes to the East or to the West point if you would know what hour it comes to the West Then turn about the Globe till the place of the Sun come to the Quadrant of Altitude and the Index of the Hour Circle shall point at the hour of the Day which on the Day aforesaid will be 7. hor. 7 min. in the Morning that the Sun commeth to the East and 4 hor. 53. min. after noon that the Sun commeth to the West And if you then count the number of degrees from the Horizon upwards on the Quadrant of Altitude it will shew you the Almicantar of the Sun for that time which will both Morning and Evening be 15 deg 30. min. as was taught you by the last Probleme PROB. XXV To know at any time what a clock it is in any other Part of the Earth THe difference of Time is reckoned by the access and progress of the Sun for the Sun gradually circumvolving the Earth in 24. hours doth by reason of the Earths rotundity enlighten but half 〈…〉 at one and the same moment of Time as shall be shewed hereafter so that hereby it comes to pass that when with us here in England it is 6. a clock in the Morning with those that have 90. degrees of Longitude to the Westward of us it is yet Midnight with those that have 180. degrees of Longitude from us it is Evening And with those that have 90. degrees of Longitude to the Eastwards it is Noon So that those to the Eastward have their Day begin sooner then ours But to the Westward their Day begins after ours Therefore that you may know what Hour it is in any Place of the Earth of what distance soever it be you must first Bring the Place of your own Habitation to the Meridian and the Index of the Hour Circle to 12. on the Hour Circle Then bring the other Place to the Meridian and the Arch of the Hour Circle comprehended between the hour 12. and the Index is the difference in Time between the two Places Example London in England and Surat in the East Indies First I bring London to the Meridian and turn the Index of the Hour-Circle to 12 then I turn the Globe Westward because London â—s Westward of Surat till Surat come to the Meridian and see at what Hour the Index of the Hour Circle points which in this Example is 5. hor. 54. minutes And because Surat lies to the Eastward of us so many degrees therefore as was said before their Day begins so much before ours So that when here at London it is 6. a clock in the Morning at Surat it will be 11. a clock 54. minutes when with us it is 12. a clock with them it will be 5 a clock 54. minutes afternoon If you would know the difference of Time between London and Jamaica Working as before you may find 5. hor. 15. min. But Jamaica is to the West of London therefore their Day begins 5. hor. 15. min. after ours so that when with us it is Noon with them it will be but three quarters of an hour past 6. a clock in the Morning and when with them it is Noon with us it will be one quarter past 5. a clock after Noon c. Or you may yet otherwise know the difference of Time if you divide the number of Degrees of the Equinoctial that pass through the Meridian while the Globe is moved from the first Place to the second by 15. so shall the product give you the difference of hours and minutes between the two Places as you will find if you try either of these Examples or any other PROB. XXVI To find the Right Ascension of the Sun or Stars THe Right Ascension of any point on the Globe is found by bringing the point proposed to the Meridian and counting the number of degrees comprehended between the Vernal Colure and the Meridian Example for the Sun June 1. I would know the Right Ascension of the Sun His Place found as by the third Probleme is ♊ 20. Therefore I bring ♊ 20. to the Meridian and then the Meridian cuts the Equinoctial in 79. degrees 15. minutes accounted from the Vernal point ♈ Therefore I say the Right Ascension of the Sun June 1. is 79. deg 15. Minutes Example for a Star I take Capella alias Hircus the Goat on Auriga's sholder and bring it to the Meridian and find the Meridian cut the Equinoctial counting as before from the Vernel point ♈ in 73. degrees 58. minutes Therefore I say the Right Ascension of Hircus is 73. degrees 58. min. Do the like for any other point of the Globe proposed PROB. XXVII To find the Declination of the Sun or Stars THe Declination of any point on the Globe is found by bringing the point proposed to the Meridian and counting the number of degrees comprehended on the Meridian between the Equinoctial and the point proposed and bears its Denomination
never above 29. degrees distant from the Sun Thirdly The Planets may be known from fixed Stars by their Azimuths and Altitudes observed as hath been taught before for if when you have taken the Azimuth and Altitude of the Star in Heaven you doubt to be a Planet and you find not on the Globe in the same Azimuth and Altitude a Star appearing to be of the same Magnitude that that in Heaven appears to be you may conclude that that in Heaven is a Planet Yet notwithstanding it may happen that a Planet may be in the same degree of Longitude and Latitude in the Zodiack that some eminent fixed Star is in as in the degree and minute of Longitude and Latitude that Cor Leonis or the Bulls Ey or Scorpions heart is in and so may eclipse that Star by being placed between us and it But that happens very seldom and rarely but if you doubt it you may apply your self to some other of the precedent and subsequent Rules here set down for knowing Planets from fixed Stars The fourth way is by shifting their Places for the Planets having a continual motion do continually alter their Places as ♂ moves about half a degree in a day ♀ a whole degree but ♃ and ♄ move very slowly ♃ not moving above 5. minutes and ♄ seldom above 2. minutes Yet by their motions alone the Planets may be known to be Planets if you will precisely observe their distance from any known fixed Star in or near the Ecliptick as on this Night and the next Night after observe whether they retain the same distance they had the Night before which if they do then are they fixed Stars but if they do not then are they Planets yet this Caâ—â—on is to be given you in this Rule also That the Planets sometimes are said to be Stationary as not altering 1. minute in Place forwards or backwards in 6. or 7. daies together Therefore if you find cause to doubt whether your Star be a Planet or a fixed Star you may for the help of your understanding confer with some of the former Rules unless you are willing to wait 8 or 9 daies longer and so by observation of its motion resolve your self Or Fifthly you may apply your self to an Ephemeris for that Year and see if on that day you find any Planet in the degree and minute of the Zodiack you see the Star you question in Heaven and if there be no Planet in that degree of the Zodiack you may conclude it is no Planet but a fixed Star PROB. XLV How to hang the Terrestrial Globe in such a position that by the Suns shining upon it you may with great delight at once behold the demonstration of many Principles in Astronomy and Geography TAke the Terrestrial Ball out of the Horizon and fasten a thred on the Brazen Meridian to the degree of the Latitude of your Place by this thred hang the Globe in a place where the Suns Beams may have a free access to it Then direct the Poles of the Globe to their proper Poles in Heaven the North Pole to the North and the South Pole to the South and with a thred fastned to either Pole brace the Globe so that it do not turn from his position then bring your Habitation to the Meridian so shall your Terrestrial Globe be Rectified to correspond in all respects with the Earth it self even as in Prob. 44. the Celestial Globe doth the Poles of the Globe to the Poles of the World the Meridian of the Globe to the Meridian of the World and the several Regions on the Globe made Correspondent to the same Regions on the Earth So that with great delight you may behold 1. How the counterfeit Earth like the true one will have one Hemisphear Sun shine light and the other shadowed and as it were dark By the shining Hemisphear you may see that it is Day in all Places that are scituate under it for on them the Sun doth shine and that it is Night at the same time in those Places that are situate in the shadowed Hemisphear for on them the Sun doth not shine and therefore they remain in darkness 2. If in the middle of the enlightned Hemisphear you set a Spherick Gnomon Perpendicularly it will project no shadow but shews that the Sun is just in the Zenith of that Place that is directly over the heads of the Inhabitants of that Place and the point that the Spherick Gnomon stands on being removed to the Meridian shews the Declination of the Sun on the Meridian for that Day 3. If you draw a Meridian line from one Pole to the other in all Places under that line it is Noon in those Places scituate to the West it is Morning for with them the Sun is East and in those Places scituate to the East it is Evening for with them the Sun is West 4 Note the degree of the Equator where the enlightned Hemisphear is parted from the shadowed for the number of degrees of the Equator intercepted between that degree and the Meridian of any Place converted into Hours by accounting for every 15. degrees 1. Hour shews if the Sun be Eastwards of that Place how long it will be ere the Sun Rises Sets or comes to the Meridian of that Place or if the Sun be Westward of that Place how long it is since the Sun Rose or Set or was at the Meridian of that Place 5. The Inhabitants of all Places between the enlightned and shadowed Hemisphear behold the Sun in the Horizon Those Westwards of the Meridian Semi-Circle drawn through the middle of the enlightned Hemisphear behold the Sun Rising Those in the East see it Setting 6. So many degrees as the Sun reaches beyond either the North or South Pole so many degrees is the Declination of the Sun either Northwards or Southwards and in all those Places comprehended in a Circle described at the termination of the Sun-shine about that Pole it is alwaies Day till the Sun decrease in Declination for the Sun goes not below their Horizon as you may see by turning the Globe about upon its Axis and a the opposite Pole at the same distance the Sun-shine not reaching thither it will be alwaies Night till the Sun decrease in Declination because the Sun Rises not above their Horizon 7. If you let the Globe hang steddy you may see on the East side of the Globe in what Places it grows Night and on the West side the Globe how by little and little the Sun encroaches upon it and therefore there makes it Day 8. If you make of Paper or Parchment a narrow Girdle to begirt the Globe just in the Equinoctial and divide it into 24. equal parts to represent the 24. hours of Day and Night and mark it in order with I II III c. to XII and then begin again with I II III c. to the other XII you may by placing one of the XII s. upon
what Elevation of the Pole the Daies shall be an Hour shorter By this Probleme may be found the Alteration of Climates for as was said in the Definition of Climates Book 1. fol. 28. Climates alter according to the half-hourly increasing of the Longest Day therefore the Latitude of 56½ degrees having its Daies increased an whole Hour is distant from the Latitude of London by the space of two Climates PROB. L. The Suns Place given to find what alteration of Declination be must have to make the Day an Hour longer or shorter And in what number of Daâ—es it will be REctifie the Globe to the Latitude of the Place and bâ—ing the Suns place to the East side the Horizon and note against what degree of the Horizon it is then bring one of the Colures to intersect the Horizon in that degree of the Horizon and at the point of Intersection make a prick in the Colure and observe what degree of the Equator is then at the Meridian Then turn the Globe Westward if the Daies shorten but Eastwards if they lengthen till 7½ degrees of the Equator pass through the Meridian and where the Horizon intersects the same Colure make another prick in the Colure Afterwards bring the Colure to the Meridian and count the number of degrees between the two pricks for so many degrees must the Suns Declination alter to lengthen or shorten the Day an Hour Example The Suns Place is ♉ 10. I would know how much he must alter his Declination before the Day is an Hour longer here at London Therefore I rectifie the Globe to the Latitude of London and bring ♉ 10. to the East side the Horizon and find it against 24½ degrees from the East point therefore I bring one of the Colures to this 24½ degrees and close by the edge of the Horizon I make a prick with black lead in the Colure then keeping the Globe in this position I look what degree of the Equator is then at the Meridian and find 250¼ and because the Daies lengthen I turn the Globe Eastwards till 7½ degrees from the foresaid 250¼ pass through the Meridian then keeping the Globe in this position I make another prick in the Colure and bringing this Colure to the Meridian I find a little more then 5 degrees of the Meridian contained between the two pricks therefore I say when the Sun is in ♉ 10. degrees he must alter his Declination a little more then 5 degrees to make the Day an Hour longer Now to know in what number of Daies he shall alter this Declination you must find the Declination of the two pricks on the Colure as you found the Suns Declination by Prob. 5. and the Arch of the Ecliptick that passes through the Meridian while the Globe is turned from the first pricks Declination to the second pricks Declination is the number of Ecliptical degrees that the Sun is to pass while he alters this Declination and the degree of the Ecliptick then at the Meridian is with respect had to the Quarter of the Year the place the Sun shall have when its Declination shall be altered so much as to make the Day an Hour longer Thushaving the Suns first place given and its second place found you may by finding those two places on the Plain of the Horizon also find the number of Daies comprehended between them as you are taught by the fourth Probleme This Probleme thus wrought for different Times of the Year will shew the falacy of that Vulgar Rule which makes the Day to be lengthned or shortned an Hour in every Fifteen Daies when as the lengthning or shortning of Daies keeps no such equality of proportion for when the Sun is neer the Equinoctial points the Daies lengthen or shorten very fast but when he is neer the Tropical points very slowly PROB. LI. Of the Difference of Civil and Natural Daies commonly called the Equation of Civil Daies And how it may be found by the Globe THe Civil Day is that space of Time containing just 24. Hours reckoned from 12 a clock on one Day to 12 a clock the next Day in which space of Time the Equinoctial makes upon the Poles of the World a Diurnal Revolution The Natural Day is that space of Time wherein the Sun moveth from the Meridian of any Place to the same Meridian again These Daies are at one time of the Year longer then at another and at all Times longer then the Civil Daies There is but smal discrepancy between them yet some there is made by a two-fold Cause For first The Suns Apparent motion is different from his true motion He being much slower in his Apogeum then he is in his Perigeum For when the Sun is in his Apogeum he scarce moves 58 minutes from West to East in a Civil Day but when he is in his Perigeum he moves above 61 minutes in a Civil Day and therefore increases his Right Ascension more in equal Time The second Cause is the difference of Right Ascensions answerable to equal parts of the Ecliptick for about ♋ and ♑ the differences of Right Ascensions are far greater then about ♈ and ♎ for about ♈ and ♎ the Right Ascension of 10. degrees is but 9. degrees 11. minutes but about ♋ and ♑ the Right Ascension of 10 degrees will be found to be 10. degrees 53. minutes as by the Globe will appear But because of the smalness of the Globes graduation you cannot actually distinguish to parts neer enough for the solution of this Probleme if you should enquire the difference in length of two single Daies it will be requisite to take some number of Daies together Suppose 20. Therefore find by Prob. 3. the Places of the Sun for the beginning and ending of those Daies you would compare and find the Right Ascensions answerable to each place in the Ecliptick and also the differences of Right Ascensions answerable to the Suns motion in each number of Daies Then compare the differences of Right Ascensions together and by substracting the lesser from the greater you will have the number of degrees and minutes of the Equator that have passed through the Meridian more in one number of Daies then in the other number of Daies which degrees of the Equator converted into Time is the number of minutes that the one number of Daies is longer then the other number of Daies Example I would know what difference of Time there is in the length of the first 20. Daies of December and the first 20 Daies of March I find by Prob. 3. the Suns place December 1 is 〈◊〉 19. 45. at the end of 20 Daies viz. on the 21 Day his place is 〈◊〉 10. 11. The Suns place March 1. is ♓ 21. 16. at the 20. Daies end viz. March 21 his place is ♈ 11. 3. I find by Prob. 26. the Right Ascension answerable to â™ 19. 45 is 258. 10. ♑ 10. 11 280. 25. ♓ 21. 16 352. 00. ♈ 11. 3 9. 40. and
the difference of Right Ascensions contained between the first Day in each Moneth and the 21 of the same Moneth by substracting the lesser from the greater is for 258. 10. And for 352. 00. 280. 25. 9. 40. 22. 15 17. 40. But note because the Vernal Colure where the degrees of Right Ascension begin and end their account is intercepted is the Arch of the Suns motion from the first to the 21. of March therefore instead of substracting the lesser number of degrees of Right Ascension from the greater viz. 9. 40 from 35. 2. I do for finding the difference of the Right Ascensional arch of the Suns motion in those 20 Daies sustract the foresaid 352 degrees from 360 and the remains is 8. which is the difference of Right Ascension from ♓ 21 16. to the Equinoctial Colure to which 8 adding 9 degrees 40 minutes the Right Ascension from the Equinoctial Colure to ♈ 11. 3. it makes 17 degrees 40. minutes for the difference of Right Ascensions between ♓ 21 16. and ♈ 11. 3 Then I find the difference of this Difference of Right Ascension by substracting the less from the greater viz. 17. 40. from 22. 15. and the remains is 4. degrees 35. minutes for the number of degrees and minutes of the Equator that pass through the Meridian in the first 20 Daies in the Moneth of December more then in the first 20 Daies of the Moneth of March which 4. degrees 35. minutes converted into Time gives 19. minutes that is a quarter of an Hour and 4 minutes that the first 20 Daies of December aforesaid are longer then the first 20 Daies of March. PROB. LII How to find the Hour of the Night when the Moon shines on a Sun Dyal by help of the Globe REctifie the Globe and find by Prob. 54. or an Ephemeris the Moons place at Noon Bring it to the Meridian and the Index of the Hour Circle to 12. and turn about the Globe till the Index of the Hour Circle points to the same Hour the shade of the Moon falls on on the Sun Dyal Then by Prob. 3. find the Suns place at Noon and see how many degrees of Right Ascension are contained between the Suns place and the degree of the Equator at the Meridian when the Index of the Hour Circle is brought to the Hour the Moon shines on in the Sun Dyal for those number of degrees converted into Time shall be the Time from Noon or the Hour of the Night Only note Respect must be had to the motion of the Moon from West to East for so swift is her mean motion that it is accounted to be above 12. degrees in 24. Hours that is 6 degrees in 12 Hours 3 degrees in 6 Hours c. and this also converted into Time as aforesaid you must add proportionably to the Time found from Noon and the sum shall give you the true Hour of the Night Example Here at London I desired to know the Hour of the Night January 6. this present Year 1658. The Moons place found by an Ephemeris or for want of an Ephemeris by Prob. 54. is in ♊ 21. degree 22 minutes Therefore I rectified the Globe to Londons Latitude and brought ♊ 21. 22. minutes to the Meridian and the Index of the Hour Circle to 12. then by Prob. 3. I found the Suns place in ♑ 26. degrees 46. minutes and by Prob. 26. I found his Right Ascension to be 300 degrees Then I turned about the Globe till the Index of the Hour Circle pointed at 10 Hours and at the degree of the Equator at the Meridian I made a prick then I counted the number of degrees of the Equater contained between the foresaid 300 deg and this prick and found them 111¼ degrees which converted into Time by allowing 15 degrees for an Hour gives 7 hours 25 minutes Time from Noon which if the Moons motion were not to be considered should be the immediate Hour of the Night But by the Rule aforesaid the Moons motion from West to East in 7 hours 25 minutes is 3 degrees 42 minutes and this 3 degrees 42 minutes being converted into Time is 14 minutes more which being added to 7 hours 25 minutes make 7 hours 39 minutes for the true Hour of the Night PROB. LIII To find the Dominical Letter the Prime Epact Easter Day and the rest of the Moveable Feasts for ever THough these Problemes cannot be performed by the Globe because of the several changes and irregular accounts that their Rules are framed upon yet because they are of frequent and Vulgar use and for that the solution of many other Questions will have dependency on the knowledge these Therefore I have thought fit here to inserte this Table of M r Palmers by which you may find them All. I shall not insist upon the Reasons of the several changes of Letters and Numbers Himself having already very learnedly handled that subject in his Book of the Catholick Planisphear Book 1. Chapter 11. to which I refer you Neither shall I need to give you any other Instructions for finding what is here proposed then what himself hath given in his fourth Book Chapter 66 and part of 67. Therefore take it as he there delivers it An Example shall serve here instead of a Rule For the Year 1657. I would know all these wherefore I seek the Year 1657. in the Table of the Suns Cycle and over against it I find 14. for the Year of the Cycle of the Sun and D for the Dominical Letter And note here that every Leap-year hath 2 Dominical Letters as 1660 hath A G and the first viz. A serveth that Year till February 25 and the second G for the rest of the Year And note that these Letters go alwayes backwards when you count forwards as B A then G F c. not F G and then A B as you may see by the Table To find the Age of the Moon Remember first that the Epact begins with March which must be here accounted the first Moneth Then if you add to the Epact the number of the Moneth current and the number of the day of the Moneth current the sum or the excess above 30 is the Moons age Example January 20. 1656. According to the accompt of the Church of England who begin the Year with March 25. which was the Equinoctial day about Christ time the Epact is 14. January is the 11 th Moneth and the 20 th day is proposed now add 14. 11. and 20. together they make 45. out of which I take 30. and there remains 15 the Moons age PROB. LIV. The Age of the Moon given to find her place in the Ecliptick according to her mean motion THis Probleme may be performed exact enough for Common uses by the Globe but in regard it only shews the Moons place in the Ecliptick according to her meat motion it will often fail you some few degrees of her true Place The work is thus First set figures
the Meridian cut the degree of the Ecliptick on the Cusp of the tenth House The Western Semi-Circle of the Horizon shall cut the degree of the Ecliptick on the Cusp of the Seventh House and the Semi-Circle of the Meridian under the Horizon shall cut the degree of the Ecliptick on the Cusp of the fourth House If you have the day of the Moneth you may by Prob. 3. of the second Book find the Suns Place and if you have the Hour of the Day you may by first rectifying the Globe as by Prob. 2. of the same Book turn about the Globe till the Index of the Hour-Circle point to the same Hour in the Hour-Circle and you will then at the Eastern Semi-Circle of the Horizon have the degree of the Ecliptick that is Rising and by Consequence as aforesaid all the Cardinal points in their respective places Now to find what degree of the Ecliptick occupies the Cusps of the other eight Houses of Heaven Do thus The Globe rectified as aforesaid Move the Semi-Circle of Position upwards till 30 degrees of the Equator shall be contained between it and the Eastern Semi-Circle of the Horizon so shall the Semi-Circle of Position cut in the Ecliptick the degree and minute of the Ecliptick on the Cusp of the twelfth House and its opposite degree and minute in the Ecliptick shall be the Cusp of the sixth House for you must note that if you have but the degree and minute of the Ecliptick upon the Cusps of six of the Houses the opposite degrees and minutes of the Ecliptick shall immediately possess the Cusp of every opposite House Then move the Circle of Position over 30. degrees more of the Equinoctial so shall the degree of the Ecliptick cut by the Circle of Position be the degree of the Ecliptick upon the Cusp of the eleventh House and its opposite degree in the Ecliptick shall be upon the Cusp of the fifth House The degree of the Ecliptick upon the Cusp of the tenth and fourth Houses was found as before Then remove the Circle of Position to the Western side of the Meridian and let it fall towards the Horizon till 30. degrees of the Equator are contained between the Meridian and it so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cuâ—p of the Ninth House and the opposite degree of the Ecliptick shall be upon the Cusp of the third House Let the Semi-Circle of Position fall yet lower till it pass over 30. degrees more of the Equator so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cusp of the eighth House and the opposite degree of the Ecliptick shall be upon the Cusp of the second House The degrees of the Ecliptick on the Cusp of the seventh House and Ascendent were found as before Example I would erect a Figure of Heaven for July 27. 5. hours oâ— minutes Afternoon 1658. in the Latitude of London viz. 51½ degrees North Latitude I first place the Planets ☊ and ☋ on the Globe as by Prob. 55. of the Second Book was directed yet not exactly as I find them in the Ephemeris for that shews only their place in the Ecliptick at Noon Therefore I consider how many degrees or minutes each Planets motion is in a whole Day or 24. Hours by substracting the Ecliptical degrees and minutes of the Planets place that Day at Noon from the Ecliptical degrees and minutes of the Planets place the next Day at Noon or contrarily if the Planet be Retrograde for the remains of those degrees and minutes is the motion of the Planet that Day Therefore proportionably to that motion I place the Planet forward in the Ecliptick or backward if it be Retrograde As if the Sun should move forward 1 degree that is 60 minutes in a whole Day or 24 Hours then in 12 hours he should move 30 minutes in 6 hours 15 minutes in 4 hours 10 minutes in 1 hour 2½ minutes and so proportionably for any other space of Time which I consider before I place the Planets on the Globe PROB. II. To Erect a Figure of Heaven according to Campanus REgiomontanus as aforesaid makes the beginning of every House to be the Semi Circle drawn by the side of the Semi Circle of Position according to the succession of every 30 th degree of the Equator from the Horizon But Camp 〈◊〉 make it to be the Semi-Circle drawn by the side of the Semi-Circle 〈◊〉 Position according to the succession of every 30 th degree of 〈◊〉 Prime Verticle or East Azimuth which is represented by the Quadrant of Altitude placed at the East point The four Cardinals are the same both according to Regiomontanus and Campanus but the other eight Houses differ Therefore when you would find them according to Campanus Rectifie the Globe and Quadrant of Altitude and bring the lower end 〈◊〉 the Quadrant of Altitude to the East point in the Horizon Then count from the Horizon upwards 30 degrees oâ— the Quadrant 〈◊〉 Altitude and bringing the Circle of Position to those 30 degreeâ— examine where the Circle of Position cuts the Ecliptick which 〈◊〉 the aforesaid time is in 〈◊〉 29. 40 for that degree and minute upon the Cusp of the twelfth House and its opposite degree 〈◊〉 minute in the Ecliptick viz. ♉ 29. 40. is upon the Cusp of 〈◊〉 sixth House Lift up the Circle of Position 30 degrees highâ— upon the Quadrant of Altitude viz. to 60 degrees and 〈◊〉 Circle of Position will cut the Ecliptick in 〈◊〉 15. degrees for the Cusp of the eleventh House and its opposite degree and minute in the Ecliptick viz. ♉ 15. is upon the Cusp of the first House The degree and minute of the Ecliptick on the Cusp 〈◊〉 the Tenth and Fourth Houses is at the Meridian Then transfering the Circle of Position to the West side of the Meridian and the Quadrant of Altitude to the West point in the Horizon Let the Semi-Circle of Position fall 30 degrees from the Meridian on the Quadrant of Altitude and it will cut in the Ecliptick ♎ 16 degrees for the Cusp of the ninth House and its opposite degree and minute in the Ecliptick viz. ♈ 16. is upon the Cusp of the third House Let fall the Circle of Position 30 degrees lower on the Quadrant of Altitude and it will cut the Ecliptick in 〈◊〉 2 degrees for the Cusp of the eight House and its opposite degree viz. ♓ 2. degrees is on the Cusp of the second House The Cusps of the Seventh and Ascendent is the same with Regiomontanus viz. 〈◊〉 27. 47 and â™ 27. 47. The Figure follows PROB. III. To find the length of a Planetary Hour AStrologers divide the Artificial day be it long or short into 12 equal parts and the Night into 12 equal parts These parts they call Planetary Hours The first of these Planetary Hours takes its
denomination from the Planetary Day and the rest â—re named orderly from that Planet according to the succession of the Planetary Orbs As if it be Munday that is the Moons day as by Prob. 42 of the second â—ook the Planet reigning the first Hour shall beâ—â— the Planet ruling the second Hour shall be ♄ the third Planetary Hour shall be 〈◊〉 the fourth 〈◊〉 the fifth ☉ the sixth ♀ the seventh Thee begin again with 〈◊〉 for the eight Planetary 〈◊〉 for the ninth and so through the whole Day and Night till the Sun Rise again the next Day The length of this Planetary Hour is found by the Globe thus The Globe rectified Bring the Suns place to the East side the Horizon and make a prick at the degree of the Equator that comes to the Horizon with it Then remove the Suns place to the Meridian and count the number of degrees of the Equator comprehended between that prick and the degree now at the Horizon and divide that number of degrees and minutes by 6. because there is 6 Planetary Hâ—urs past since Noon and the Qâ—â—tient shall shew the number of dâ—gâ—â—â—s and minutes that pass through the Meridian in one Planetary Hour Example Jâ—ly 27. 1658. I would know the length of the Planetary 〈◊〉 here at Lonaon I Rectifie the Globe and bring the Sun place viz ♌ 〈◊〉 50. to the Eastern side the Horizon and find 115 degrees of the Equator come to the Horizon with it to this 115 degrees I make a prick Then I turn the Suns place to the Meridian and find 22â— degrees of the Equator at the Horizon Therefore I either count the number of degrees between the pricks and the degree of the Equator at the horizon or else subâ—â—râ—ct the 〈◊〉 from the greater but both waies I find 111 degâ—ees of the Equator to pass through the Meridian or the Horizon in six Planetary Hours Therefore dividing 111. by 6. I 〈◊〉 〈◊〉 degrees â—0 minutes of the Equator to pass through the Mâ—â—â—â—â—an in one Planetary Hour which 18. degrees 30 minutes reduced into Time yeelds 72. minutes by accounting for every 15. degrees one Hour for 1. degree 4. minutes and for half a degree 〈◊〉 minutes of Time and so proportionably so that the leâ—gâ—h of a Planetary Hour July 27 is 1 coâ—â—on Hour and â—4 minute here at London PROB. IV. The length of a Planetary Hour known to find what Planet Reigneth any green Hour of the Day or Night THe Globe Rectified as in the last Probleme Turn about the Globe till the Index of the Hour Circle points to the Hour of the Day in the Hour Circle Then count the number of degrees comprehended between the degree of the Equator at the Horizon and the prick in the Equator made as in the last Probleme and reduce that number of degrees into minutes of Time by reâ—koning 4. minutes of Time for every degree of the Equator Reduce also the number of degrees and minutes that pass through the Meridian in one Planetary Hour into minutes by allowing as aforesaid 4. minutes for every degree and then divide the 〈◊〉 〈◊〉 by the second and the Quotient shall be the number of 〈◊〉 〈◊〉 since Sun Rising Having the number of Planetary Hours since Sun Rising Râ—ckon the first Planetary Hâ—ur by the â—ame of that Planet that bears the denomination of the Day the second Planetary Hour by the Planet succeeding that in order â—he thâ—â—d by the next in order and so for all the rest 〈◊〉 you câ—me to the last Planet viz. 〈◊〉 and then begin again with 〈◊〉 and so 〈◊〉 〈◊〉 c. 〈◊〉 you have 〈◊〉 so many Planets as there are Planetary Hours siâ—ce Mâ—â—â—â—ing and that Planet the number ends on shall be the Planet Reigning that Planetary Hour Example July 27. 1658. aforesaid I would know what Planet Rules at 5 a clock past Noon The length of the Planetary Hour this Day â—ound by â—he last Probleme is 1. hour 14. minutes Therefore the Globe Rectified I bring the Index of the Hour Circle to the Hour of the Day viz. 5 a clock in the Hour-Circle and then count the number of degrees between the Prick made as by the last Probleme and the degree of the Equator at the Horizoâ— and find them 187. which I reduce into minutes by allowiâ—g for every degree 4 minutes and that gives 748 minutes This 〈◊〉 minuâ—es I divide by the minutes contained in one Planetary Hour this Day viz. by 72. and find 10. hours 8. minutes which shews there are 10. Planetary Hours and 8. minutes past and gon since Sun Rising Therefore ♂ being the Planet after whose name the Day is called viz. Dia Martis ♂ is as aforesaid the Ruler of the first Planetary Hour From him I count the Planet succeding which is ☉ for the second Hour from ☉ I count the Planet succeding which is ♀ for the third Hour and so on to ♀ and ☽ and then I begin the Round again with ♄ ♃ ♂ and ☉ till I come again to ♀ which is the tenth Planetary Hour since Sun Rising and the minutes remaining being 8. shews that there is 8. minutes past since she began to Reign PROB. V. To find Part of Fortune by the Globe COunt the number of degrees and minutes contained between the Suns place and the Moons place begining at the Suns place and counting according to the succession of Signes till you come to the Moons place and having found that number of degrees and minutes add them to the number of degrees and minutes Ascending reckoned from the first point of ♈ If the sum exceed 360 east away 360 and the remainder shall be the number of degrees and minutes from the first point in 〈◊〉 in which Part of Forâ—â—ne falls But if it do not exceed 360 you have already the number of degrees and minutes from the first point of ♈ in which you must place Part of Fortune Example I would find the place of Part of Fortune for the time of ouâ— Figure I seek the two pricks representing ☉ and 〈◊〉 and find ☉ in ♌ 14. 9. and ☽ in â™ 19. 44. therefore counting from the Suns place to the Moons place according to the succession of Signes I find 95. degrees 35. minutes contained between them This 95. degrees 35. minutes I add to 267. degrees 47. minutes the degree and minute contained between the first point of ♈ and the Ascendent and they make together 363. degrees 22. minutes This exceeds 360. therefore I cast away 360. and the remains are 3 degrees 22. minutes for the place in the Ecliptick of Part of Fortune reckoned from the first point of ♈ Therefore this character â™ which represents Part of Fortune I set in its proper place of the Figure as I did the Planets PROB. VI. To find in what Circle of Position any Star or any degree of the Ecliptick is CIrcles of Position are numbred from the Horizon upwards upon the Quadrant of Altitude
that shadow shall be a Meridian liâ—e Secondly on the backside the Clinatory discribe a Circle and draw a line through the Center to both sides the Circumference cross this line with an other line at Râ—ght Angles in the Center so shall the Circle be divided into four equal parts These four parts you must maâ—k with East West North South and divide each of them into 90. degrees In the Center of this Plain erect a straight wyer prependicularly when you would find a Meridian line examine by the tenth Prob. of the second Book the Amplitude of the Suns Rising or Setting from the East or West points and waiting the just Rising or Setting that Day turn the Instrument about till the shadow of the wyer falls upon the same degree from the East or West the Amplitude is of for then the North and South line in the Instrument will be the same with the North and South line in Heaven Thirdly by the Suns Azimuth Find the Azimuth of the Sun by Prob. 22. of the second Book and at the same instant turn the Instrument till the shadow of the wyer fall upon the degree on the Instrument opposite to the degree of the Suns Azimuth so shall the Meridional line of the Instrument agree with the Meridional line in Heaven You may the same way work by the Azimuth of any Star Only whereas the shadow of the wyer should fall upon the opposite degree aforesaid Now you must place a Sight or Perpendicular upon that opposite degree and turn the Instrument about till the wyer at the Center the Sight in the opposite degree of the Stars Azimuth and the Star in Heaven come into one straight line so shall the Meridian line of the Instrument agree with the Meridional line in Heaven Fourthly It may be found by any Star observed in the Meridian if two Perpendiculars be erected in the Meridian line of your Instrument for then by turning the Instrument till the two Perpendiculars and the Star come into a straight line the Meridian line of your Instrument will be the same with the Meridian line in Heaven See more waies in Mr. Palmer on the Planisphear Book 4. Chap. 9 If your Plain either Recline or Incline apply one of the sides of your Clinatory Parallel to one of the Semi-diameters of the Quadrant to the Plain in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant for then the number of degrees of the Quadrant comprehended between the side of the Quadrant Parallel to the Plain and the Plumb-line shall be the number of degrees of Reclination if thâ— Center of the Quadrant points upwards or Inclination if thâ— Center points downwards If your Reclining or Inclining Plain Decline draw upon it a line Parallel to the Horizon which you may do by applying the back-side of the Clinatory and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Semi-diameters for then you may by the upper side of the Clinatory draw an Horizontal line if the Plain Incline or by the under side if it Recline If it neither Incline or Recline you may drawâ— an Horizontal line both by the upper and under sides of the Clinatory Having drawn the Horizontal line apply the North 〈◊〉 â— of the Clinatory to it and if the North end of the Needle 〈◊〉 directly towards the Plain it is then a South Plain If the 〈◊〉 point of the Needle points directly from the Plain it is a Norâ—â— plain but if it points towards the East it is an East Plain if towards the West a West Plain If it do not point directly 〈◊〉 East West North or South then so many degrees as the 〈◊〉 declines from any of these four points to any of the other of 〈◊〉 four points so many degrees is the Declination of the Plain 〈◊〉 respect as aforesaid had to the Variation of the Compass Or if you find the Azimuth of the Sun by its Altitude observed just when its beams are coming on or going off youâ— Plain that Azimuth shall be the Azimuth of your Plain Or you may erect a wyer Perpendicularly on your Plain and wait till the shadow of that wyer comes to be Perpendicular with the Horizon which you may examine by applying a Plumb-line to it for then the shadow of the Plumb-line and the shadow of the Perpendicular will be in one then taking the Altitude of the Sun you may by Prob. 22. of the second Book find its Azimuth and thereby know in what Azimuth the Plain of your Dyal lies for the Azimuth your Plain lies in is distant from the Azimuth of the Sun just 90. degrees PROB. I. How by one position of the Globe to find the distances of the Hour-lines on all manner of Plains YOu may have Meridian lines drawn from Pole to Pole through every 15. degrees of the Equinoctial to represent the Horary motion of the Sun both Day and Night and when the Pole of the Globe is Elevated to the height of the Pole in any Place and one of these Meridian lines be brought to the Brazen Meridian all the rest of the Meridian lines shall cut any Circle which you intend shall represent the Plain of a Dyal in the number of degrees on the same Circle that each respective Hour-line is distant from the Noon-line point in the same Circle Thus if you should enquire the distance of the Hour-lines upon an Horizontal Plain in Londons Latitude The Pole of the Globe as aforesaid must be Elevated 51½ degrees and one of the Meridian lines you may chuse the Vernal Colure be brought to the Brazen Meridian which being done you are only to examine in the Horizon Because it is an Horizontal Plain at what distance from the Meridian which in Horizontals is the Noon-line the several Meridians drawn on the Globe intersect the Horizon for that distance in degrees shall be the distance on a Circle divided into 360. degrees that each respective Hour-line must have from the Meridian or a Noon line chosen in the same Circle and lines drawn from the Center of that Circle through those degrees shall be the Hour lines of an Horizontal Plain If your Plain be not Direct but declines East or West 〈◊〉 must number the Declination Eastwards or Westwards reâ—pectively in the degrees of the Horizon and the Quadrant 〈◊〉 Altitude screwed to the Zenith as aforesaid bring the lower end of the Quadrant of Altitude to the said degrees of Declination and the number of degrees cut by the Meridians in the Quadrant of Altitude numbred downwards is the number of degrees that the Hour-lines are distant from the Noon line in a Circle of 360 degrees And lines drawn from the Center of that Circle through those degrees be the Hour lines of half the Day And if you turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon
be numbred so that what so ever decimal degree of the Equator you light on at the Meridian or else where you will find its number from that Colure already set down to your hand without either adding to or substracting from it Bring this Colure therefore to the Meridian and the Index of the Hour Circle to 12. in the Hour Circle Then turn the Globe Westwards and so oft as 15 degrees of the Equator passes through the Meridian so oft you must examine what degrees of the Horizon the Vernal Colure cuts and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E beginning your account or reckoning at B towards D and markt with Pricks through which Pricks you must draw lines from the Center A and those lines shall be the Hour lines after noon Then bring the Colure to the Meridian again to find the Fore-noon Hour-lines and turn the Globe Eastwards and so oft as 15 degrees of the Equator passes through the Meridian so oft you must examine what degrees of the Horizon the Vernal Colure cuts and those degrees and minutes so cut by the Vernal Colure must be found in the Circle C B D E begining your reckoning from B towards C and markt with Pricks through which Pricks you must draw lines from the Center A and those lines shall be the Fore-noon Hour-lines These Hour-lines must be markt from the Meridian line viz. the line A B which is the 12 a clock line towards D with I II III c. till you have numbred to the Hour of Sun set found by Prob. 7. of the second Book the longest Day and from the Meridian line towards C with XI X. IX c. till you have numbred to Sun Rising the longest Day The Stile must be placed in the Center and Elevated so many degrees above the Plane as the Pole is elevated above the Horizon of the Place Example of the whole I would make an Horizontal Dyal for Londons Latitude Therefore I E evate the North Pole 51½ degrees above the Horizon and bring the Vernal Colure to the Meridian and the Index of the Hour Circle to 12 on the Hour Circle And turning the Globe Westwards till the Index points to 1 a clock or till 15 deg of the Equator pass through the Meridian I find the Colure cut the Hori in 11. 4 from the Meridian 2 24. 15 3 38. 4 4 53. â—6 5 71. 6 6 90. These are the distances of the Hour lines from Noon till 6 at Night and to these distances on the Plane counting from B towards D I make pricks and from the Center I draw lines through these Pricks and these lines are the Hour lines from 12 to 6 Afternoon But the Sun in the longest Day shines till past 8 at Night as you may find by Prob. 48. of the second Book therefore here wants the two Evening Hour lines which though they may be found after the same way I found the former viz. by continuing the turning of the Globe Westwards yet that I may the sooner reduce my work to the Plane I Count the number of degrees between the 6 a clock line and the 5 a clock line in the Circle on the Plane for the same number of degrees counted from D towards E is the distance of the 7 a clock Hour line from the 6 a clock Hour line and the number of degrees contained between the 6 a clock Hour line and the 4 a clock Hour line is the distance of the 8 a clock Hour line from the 6 a clock Hour-line Or I need not draw the 7 and 8 a clock Hour lines till I have drawn the forenoon Hour lines for then by laying the edge of a Ruler that will reach through the opposite side of the Plane to the Morning 7 and 8 a clock Hour lines I may by the side of that Ruler draw lines from the Center through the opposite side of the Plane and those lines shall be the 7 and 8 a clock Hour lines Afternoon Having thus all the Afternoon Hour lines I bring the Vernal Colure to the Meridian again so shall the Index again point to 12. Therefore as before I turned the Globe Westwards so now turning it Eastwards till the Index points to 11 a clock or till 15 deg of the Equator pass through the Meridian I find the Colure cut the Hori in 11. 40 from the Meridian 10 24. 15 9 38. 4 8 53. 36 7 71. 6 6 90. These are the distances of the Hour lines from Noon to 6. a clock in the Morning and these distances I seek in the Circle of the Plain counting from the Noon line B towards C and mark them with Pricks through which pricks as before I draw lines from the Center to the outside the Plane and those lines shall be the Hour lines Or having the distance of all the Afternoon Hour-lines I have also the distance of all the forenoon Hour lines from the Meridian as you may see by comparing the two former Tables For the 1 a clock Hour line Afternoon is equidistant from the Meridian or Noon line with the 11 a clock Hour line before Noon viz. they are both 11 degrees 40 minutes distant from the Noon line and the 2 a clock Hour line Afternoon is from the Noon line equidistant with the 10 a clock Hour line Beforenoon for they are both 24. degrees 15. minutes distant from the Meridian or Noon line and so all the other Morning Hour lines are distant from the Noon line by the same space that the same number of Afternoon Hour lines told from the Meridian on the contrary side the Noon line are distant from the Meridian Whence it follows that since as aforesaid the same number of Hour lines after 6 at Night and before 6 in the Morning have the same distance from the 6 a clock line that the same number of Hour lines before 6 at Night and after 6 in the Morning have from the 6 a clock line and since the same number of Hour lines before Noon are equidistant from the Meridian or Noon line by the same space of degrees that the same number of Hour lines Afternoon are It follows I say that having found the distance of the six Hour lines either before or after Noon you have also given the distance of all the other Hour lines If you will have the half Hour lines placed on your Dyal you must turn the Globe till the Index points to every half Hour in the Hour Circle as well as to the whole and examine the degrees of the Horizon cut by the Vernal Colure as you did for the whole Hours and in like manner transfer them to your Plane Having thus drawn all the Hour lines I count from the Noon line 51½ degrees the Elevation of the Pole here at London and from the Center A I draw a straight line as A F through these 51½ degrees for the Gnomon or Style
difference in Longitude and Latitude 113 Prob. 10. To find how many Miles are contained in a Degree of any Parallel 114 Prob. 11. The Rhumb you have sailed upon and the Latitudes you departed from and are arived to given to find the Difference of Longitude and the number of Leagues you have Sailed 114 Prob. 12. The Longitudes and Latitudes of two Places given to find Course and Great Circle distance between them 116 Prob. 13. The Latitude you departed from and the Latitude you are arrived to and the number of Lagues you have sailed given to find the Rhumb you have sailed on and difference of Longitude 116 Prob. 14. To find by the Globe the Variation of the Needle commonly called the Variation of the Compass 117 Prob. 15. To keep a Journal by the Globe 118 Prob. 16. To Steer in the Night by the Stars 119 Prob. 17. How to platt on the Globe a New Land never before Discovered 119 Prob. 18. Seeing two known points or Capes of Land as you sail along how to know the distance of your Ship from them 120 Prob. 19. Of Tides and how by help of the Globe you may in general judge of them 121 The Contents Of the Fourth Book Prob 1. To Erect a Figure of the 12 Houses of Heaven 123 Prob. 2. â—o Erect a Figure of Heaven according to Campanus 128 Prob. 3. To find the length of a Planetary Hour 129 Prob. 4. The length of a Planetary Hour known to find what Planet Reigneth any given Hour of the Day or Night fol. 131 Prob. 5. To find Part of Fortune by the Globe 132 Prob. 6. To find in what Circle of Position any Star or any degree of the Ecliptick is 133 Prob. 7. To find the Right Ascensions the Oblique Ascensions and the Declinations of the Planets 133 Prob. 8. How to Direct a Figure by the Globe 134 Prob. 9. Of Revolutions and how they are found by the Globe 135 Prob. 10. How a Figure of Heaven may be erected by the Revolution thus found 135 The Contents Of the Fifth Book Prob. 1. HOw by one position of the Globe to find the distance of the Hour lines on all manner of Planes fol. 143 Prob. 2. To make an Equinoctial Dyal 147 Prob. 3. To make an Horizontal Dyal 149 Prob. 4. To make an Erect Direct South Dyal 153 Prob. 5. To make an Erect Direct North Dyal 156 Prob. 6. To make an Erect Direct East Dyal 156 Prob. 7. To make an Erect Direct West Dyal 159 Prob. 8. To make a Polar Dyal 159 Prob. 9. To make Erect South Dyals Declining Eastwards or Westwards 160 Prob. 10. To make a North Erect Dyal declining Eastwards or Westwards 163 Prob. 11. To make Direct Reelining or Inclining Dyals 164 Prob. 12. To make Declining Reclining or Declining Inclining Dyals 164 Prob. 13. To make a Dyal upon a Declining Inclining Plane 168 Prob. 14. To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal shall be Horizontal 171 Prob. 15. To make a Dyal on the â—eâ—ling of a Room where the Direct Beams of the Sun never come 175 Prob. 16. To make a Dyal upon a solid Ball or Globe that shall shew the Hour of the Day without a Gnomon 178 Prob. 17. To make a Dyal upon a Glass Globe whose Axis shall cast a shadow upon the Hour of the Day 180 The Contents Of the Sixth Book Of the Parts and Kindes of Spherical Triangles fol. 183 Prob. 1. The Legs of a Right Angled Spherical Triangle given to find the Hypothenusa and the two other Angles 184 Prob. 2. A Leg and the Hypothenusa given to find the Rest. 187 Prob. 3. The Hypothenusa and an Angle given to find the Rest. 187 Prob. 4. A Leg and Angle adjoyning given to find the Rest. 188 Prob. 5. A Leg and the Angle opposite given to find the Rest. 188 Prob. 6. The Angle given to find the Sides 189 Prob. 7. Oblique Triangles The three Sides given to find the Angles 190 Prob. 8. Two Sides and the Angle contained between them given to find the Rest. 193 Prob. 9. Two Sides and an Angle opposite to one of them given to find the Rest. 194 Prob. 10. Two Angles and the Side comprehended between them given to find the Rest. 194 Prob. 11. Two Angles and a Side opposite to one of them given to find the Rest. 195 Prob. 12. Three Angles given to find the Sides 196 Prob. 13. How to let fall a Perpendicular that shall divide any Oblique Spherical Triangle into two Right Angled Spherical Triangles 198 The Poetical Stories of the Constellations in Heaven 200 The First BOOK Being the first RUDIMENTS of Astronomy Geography Or A Description of the Lines Circles and other Parts of the GLOBE PRAEFACE THe Students of all Arts and Sciences have ever proposed a Maxime whereon as on an allowed Truth the whole Science hath dependance and by so much the more demonstrable that Maxime is so much the more of Excellency the Science may claim This of Astronomy and Geography comes not behind any for herein we shall only admit with the Ancients that the Form of the visible World is Spherical Neither shall we beg our Ascertion any farther then Occular Appearance will demonstrate every Mans Ey being his Judge if he be either on a Plain field or at Sea where nothing can hinder a free inspection of the Horizon Vpon good grounds therefore they ascerted the Spherical form of the Whole and also concluded the Parts to be Round I meane very intire Subsistence as the Stars Planets and the Earth In the Celestial Bodies as the Stars and Planets this is also visible and therefore un-controullable But that the Earth is Round proves with the unskilfull matter of dispute they frequently objecting with S. Austine the words of the Scripture which say He hath stretched forth the corners of the Earth not considering whether those words were spoken as alluding to the amplitude of Gods Omnipotence or that the Corners were meant Capes of Land which indeed are stretched forth into the Sea But that the Earth is Round is proved by divers certain and infallible Reasons As first By the Navigations of our Age Divers able and honest Mariners having Sailed and continued an Easterly Course have at length arrived without turning back to the same place from whence they set forth witness Magellanicus Sr. Francis Drake Tho. Cavendish Oliver vander Noort W. Schouten c. Secondly By the length of degrees in every Parallel for it is found by Dayly observation that the degrees of every Parallel upon the Earth hold the same proportion to the degrees of the Equinoctial as the degrees of the same Parallel upon an Artificial Globe or Sphear do to the degrees of the greatest Circle of the same This Argument alone is sufficient yet take one more from Visible Appearance And that is this The shadow which the Earth and Water together make in the Eclipse of
Moon or Stars c. and for the finding the Azimuth and Amplitude c. VI. Of the Quadrant of Altitude The Quadrant of Altitude is a thin brass plate divided into 90. degrees and marked upwards with 10 20 30 40 c. to 90. It is rivetted to a Brass Nut which is fitted to the Meridian and hath a Screw in it to screw upon any degree of the Meridian When it is used it is screwed to the Zenith It s use is for measuring the Altitudes finding Amplitudes and Azimuths and discribing Almicantaraths It would sometimes stand you in good steed if the Plate were longer by the bredth of the Horizon then 90. degrees for then that length being turned back will serve you instead of an Index when the Nut is screwed to the Zenith to cut either the degrees or Daies of either Style or the Points of the Compass in any of those Circles concentrical to the innermost edge of the Horizon which the Ey cannot so well judge at VII Of the Hour Circle and its Index The Hour Circle is a smal Brasen Circle fitted on the Meridian whose Center is the Pole of the world It is divided into the 24 hours of the Day and Night and each hour is again divided into halfs and quarters which in a Revolution of the Globe are all pointed at with an Index which to that purpose is fitted on the Axis of the Globe The use of the hour Circle is for shewing the Time of the several mutations and Configurations of Celestial Appearances VIII Of the Nautical Compass or Box and Needle Just under the East point of the Horizon upon the undermost Plane is sometimes fixed a Nautical Compass whose North and South line must be Parallel to the North and South line of the Horizon The use of it is for setting the Angles of the Globe correspondent to the Angles of the World IX Of the Semi-Circle of Position This is a Semi-Circle made of Brass and divided into 180. degrees numbred from the Equinoctial on either side with 10 20 30 c. to 90. at the two ends there is an Axis which is fitted into the two hole of two smal studs fixed in the North and South points of the upper Plane of the Horizon upon this Axis it is moved up and down according to the intent of your operation The use of this Circle of Position is for the finding the twelve Astrological Houses of Heaven and also for finding the Circle of Position of any Star or Point in Heaven Thus much may serve for the lineaments Circumjacent to the body of the Globe The next discourse shall be CHAP. II. Of the Circles Lines c. discribed upon the Superficies of the Globe beginning with the Terrestrial Globe and I. Of the Equator THe Equator is a great Circle encompassing the very middle of the Globe between the two Poles thereof and divides it into two equal parts the one the North part and the other the South part It is as all great Circles are divided into 360. equal parts which are called Degrees Upon this Circle the Longitude is numbred from East to West and from this Circle both waies viz. North and South the Latitude is reckoned It is called the Equator because when the Sun comes to this line which is twice in one year to wit on the tenth of March and the eleventh of June the Daies and Nights are equated and both of one length II. Of the Meridians There are infinite of Meridians for all places lying East or West from one another have several Meridians but the Meridians delineated upon the Terrestrial Globe are in number 36. so that between two Meridians is contained ten degrees of the Equator From the first of these Meridians which is divided into twice 90 degrees accounted from the Equator towards either Pole is the beginning of Longitude which upon our English Globes is at the Ile Gratiosa one of the Iles of the Azores and numbred in the Equator Eastwards with 10 20 30 c. to 360. round about the Globe till it end where it began They are called Meridians because they divide the Day into two equal parts for when the Sun comes to the Meridian of any Place it is then Midday or full Noon III. Of the Parallels As the Meridians are infinite so are the Parallels and as the Meridian lines delineated upon the Globe are drawn through no more then every tenth degree of the Equator so are the Parallels also delineated but upon every tenth degree of the Meridian lest the Globe should be too much filled with superfluity of lines which might obscure the smal names of Places The Parallel Circles run East and West round about the Globe even as the Equator only the Equator is a great Circle and these are every one less then other diminishing gradually till they end in the Pole The Parallels are numbred upon the Meridian with 10 20 30 c. to 90. beginning in the Equator and ending in the Pole They are called Parallels because they are Parallel to the Equator IIII. Of the Ecliptick Tropicks and Polar Circles These Circles though they are delineated upon the Terrestrial Globe yet they are most proper to the Celestial and therefore when I come to the Celestial Globe I shall define them unto V. Of the Rhumbs The Rhumbs are neither Circles nor straight lines but Helispherical or Spiral lines They proceed from the point where we stand and wind about the Globe till they come to the Pole where at last they loose themselves They represent the 32 winds of the Compass Their use is to shew the bearing of any two places one from another that is to say upon what point of the Compass any shoar or Land lies from another There are many of them described upon the Globe for the better directing the ey from one shoar to the other when you seek after the bearing of any two Lands Some of them where there is room for it have the figure of the Nautical Card drawn about the Center or common intersection and have as all other Cards have for the distinction of the North point a Flowerdeluce pictured thereon They were first called Rumbs by the Portugals and since used by Latine Authors and therefore that name is continued by all Writers that have occasion to speak of them VI. Of the Lands Seas Ilands c. Described upon the Terrestrial Globe The Land described upon the Globe is bounded with an irregular line which runs turning and winding into Creeks and Angles even as the shoar which it represents doth For the better distinction of Lands c this line is cullered close by one side thereof with divers Cullers as with red yellow green c. these cullers distinguish one part of the Continent from the other and also one Iland from another That side of the line which incompasses the Cullers is the bounds of the Land the other side of the line which is
left bare without Cullers is the limits of the Water The Land is either Continents or Ilands A Continent is a great quantity of Land not interlaced or separated by the Sea in which many Kingdomes and Principalities are contained as Europe Asia Affrica America An Island is a part of the Earth environed round with Waters as Britain Java S. Laurence Isle Barmudas c. These again are sub-divided into Peninsula Istmus Promontorium A Peninsula is almost an Island that is a track of Land which being almost encompassed round with Water is joyned to the firm Land by some little Istmus as Molacca in the East-Indies c. An Istmus is a little narrow neck of Land which joyneth any Peninsula to the Continent as the Straits of Dariene in Peru and Corinth in Greece Promontorium is some high Mountain which shooteth it self into the Sea the utmost end of which is called a Cape as that great Cape of Good Hope and Cape Verde in Africa The Water is either Ocean Sea Straits Creeks or Rivers The Ocean is that generall collection of all Waters which invironeth the whole Earth on every side The Sea is a part of the Ocean to which we cannot come but through some Strait as Mare Mediterraneum Mare Balticum and the like These two take their names either from the adjacent places as the Brittish Ocean the Atlantick Sea c. or from the first discovere as Mare Magellanicum Davis and Forbishers Staits c. Or from some remarkable accident as Mare Rubrum from the red colour of the Sands Mare Aegeum Pontus Euxinus and the like A Strait is a part of the Ocean restrained within narrow bounds and opening a way to the Sea as the Straits of Gibralter Hellespont c. A Creek is a crooked shoar thrusting out as it were two armes to imbrace the Sea as Sinus Adriaticus Sinus Persicus c. A River is a small branch of the Sea flowing into the Land as Thames Tiber Rhine Nilus c. Now that these Lands Ilands Towns Seas Rivers c. may at the first search be found upon the Globe all Geographers have placed them thereon according to Longitude and Latitude VII Longitude The Longitude is an Arch of the Equator comprehended between the first Meridian and the Meridian of the Place you inquire after It is numbred on the Equator from the West to the Eastwards with 10 20 30 to 360. degrees till it end where it began VIII Latitude The Latitude is an Arch of the Meridian comprehended between the Equator and the place enquired after It is numbred on the Meridian from the Equator both waies viz. North and South till it come to the Poles or 90 degrees Thus much may serve for the description of the Terestrial Globe I therefore come to treat of the Celestial CHAP. III. Of the Celestial Globe or the Eighth Sphear represented by the Celestial Globe its motion and of the Circles Lines Images Stars c. described thereon I. Of the eighth Sphear THe eighth Sphear which is the starry Heaven is represented by the Celestial Globe because upon the Convexity of it all the Stars and visible appearances are placed according to the order that they are situated in the concavity of the eighth Sphear It is called the eighth Sphear because between it and us are contained seven other Heavens or Sphears as 1. the Moon 2. Mercury 3. Venus 4. the Sun 5. Mars 6. Jupiter 7. Saturn and eighthly the starry Heaven The antients have made the Systeme of the world to consist of 2 other Sphears called the Chiristiline Heaven and the Primum Mobile or first Mover as in the following figure is represented A figure wherein may be seen the Composition of the whole frame of the World II. Of the Motion of the eighth Sphear There hath bin attributed to the eighth Sphear a twofold motion the one called its Diurnal Motion which is made from East to West upon the Poles and Axis of the World And the other called its Second motion which is made from West to East upon the Poles and Axis of the Ecliptick The Diurnal motion is caused by the violent Motion of the Primum Mobile for in 24 hours it carries along with it not only the eighth Heaven or Orb of fixed Stars but the Orbs of the Sun the Moon and all the rest of the Planets It is called the Diurnal Motion because it is finished in one Day The second Motion is unproperly attributed to the eighth Sphear it being indeed the Motion of the Equinoctiall tho Authors sometimes carelesly mention the one insteed of the other Therefore in the next Section where I treat of the Equinoctial I shall at large explain unto you the nature of this mis-called Second Motion III. Of the Equinoctial The Equinoctial upon the Celestial Globe is the same line formerly called the Equator upon the Terrestrial only with this difference that the Equator remains fixt upon the Terrestrial Globe but the Equinoctial upon the Celestial Globe is moveable or at least must be imagined to move contrary to the Diurnal motion from West to East upon the Poles of the Ecliptick I say imagined to move because in the Heavens it doth really move tho on a material Globe it would be inconvenient to make a moveable Equinoctial and therefore it hath one fixed which for this and the next age will sufficiently serve without much deviation from the truth it self Now that the difference between the Equator upon the Terrestrial Globe and the Equinoctial upon the Celestial may be proved and the motion of the Equinoctial be the better understood I shall only bring this example All places that were formerly under the Equator do and will keep the same Longitude and remain still under the Equator as may be proved by comparing the Ancient and modern Geographers together but those Stars that were formerly under the Equinoctial do not keep the same Longitude nor remain under the Equinoctial because the Equinoctial as aforesaid hath a motion from West to East upon the Poles of the Ecliptick But the Stars being fixed in their one Sphear like knots in wood and therefore move not are by the Precession of the Equinox left behind the Equinoctial Colure and so are caused to alter their Longitude as by comparing the Observations of ancient and modern 〈◊〉 together it will appear for about 346 years before Christ the first Star in the Rams horn was by the Egyptian and Grecian Astronomers observed to be in the Equinoctial Colure and 57 years ago when Tycho observed it was found to be in 27 degrees 37 minutes of ♈ So that in about 2000 years it is moved forwards 28 degrees and will according to Tycho's opinion finish its Revolution in 25412 years According to which motion I have Calculated this following Table for finding the Degrees and Minutes of the Equinoctial motion answerable to any number of years within the said Revolution ye deg m years deg m. 1
in the North and six Moneths Night in the South and contrarily from the 11th of September to the 10th of March the Sun being then in the Southerly Signes and therefore on the South side the Horizon there is six Moneths Day in the South and six Moneths Night in the North. It is called a Parallel Sphear because the Sun Moon or Stars in a Diurnal Revolution of the Heavens neither ascend higher or descend lower but alwaies move Parallel to the Horizon The Earth is thus Posited under both the Poles viz. in 90 degrees of Latitude as may be seen by the Globe if you turn the Brasen Meridian till either of the Poles be elevated 90 degrees above the Horizon As in this figure An Oblique Sphear hath the Axis of the World neither Direct nor Parallel to the Horizon but lies aslope from it In an Oblique Sphear all the Celestial Bodies as Sun Moon or Stars c. have in respect of the Horizon Oblique and unequal Ascensions and Descensions and all the lines Parallel to the Equator make unequal Angles with the Horizon and are cut by the Horizon into unequal parts for those lines towards the elevated Pole have a greater portion of a Circle under the Horizon then above it only the Equator because it hath the same Center with the Horizon doth divide the Horizon into two equal parts and is also divided into two equal parts by the Horizon Hence is follows that when the Sun is in any part of the Ecliptick that declines towards the elevated Pole the Daies in the elevated Hemisphear shall be longer then the Nights and when the Sun is in any part of the Ecliptick that declines towards the Depressed Pole the Nights shall be longer then the Daies But when the Sun is in the Equinoctial because whether the Pole be either Raised or Depressed equal portions remain both above and under the Horizon therefore the Daies are of the same length with the Nights and the Nights with the Daies Also in an Oblique Sphear all those Stars that have as great or greater number of degrees of Declination then is the elevated Poles Complement of Latitude to 90 never set or come under the Horizon and those Stars that have the same Declination about the Depressed Pole never rise It is called an Oblique Sphear because all the Circles of the Sphear move Obliquely about the Horizon The Earth is thus Obliquely posited to all those Nations that inhabite under any degree of Latitude either North or South-wards between the Equator and either Pole as may variously be seen by the Globe when the Axis lies not on the Horizon nor the Equator is Parallel to the Horizon As in this following Figure Moreover all Places have their Antipodes Peraeci and Antaeâ—i The Antipodes of any Place is the opposite degree on the Globe As if a Perpendicular were let fall from the Place you stand on through the Center of the Earth and continued till it pass quite through the Superficies of the Earth on the other side then in the point where the Perpendicular cuts the Superficies of the Earth on the other side is the Antipodes of that Place The Inhabitants of any two Places that are in Antipodes to each other go with their Feet directly against one another and have a contrariety in the Seasons of the Year and Risings and Settings of the Sun Moon Stars and all other of the Heavenly Bodies so that when with us it is Spring with them it is Autumn when with us the Sun Rises in our Antipodes it Sets and therefore their Morning is our Evening their Noon our Midnight their Evening our Morning and their Longest Day our shortest The Periaeci of any Place is that point in the same Parallel which comes to the Meridian with the Antipodes In the Periaeci of any Place there happens not that Contrariety of Seasons in the Year that doth in the Antipodes nor in the Length of Daies for the Daies in both Places are of equal length but in the times of the Day there is the same contrariety for though their Spring be our Spring and therest of their Seasons of the year the same with ours yet their Morning is our Evening their Night our Day c. The Antaeci of any Place is the point under the same Meridian that is distant from the Equator on the South side so many degrees as your Place is distant from the Equator on the North side In the Antaeci there happens not that contrariety in the Daies as doth in the Antipodes but in the Seasons of the Year there is the same contrariety for in our Antaeci their Morning is our Morning their Noon our Noon their Night our Night but herein is the Difference their Spring is our Fall their Summer our VVinter c. and their Longest Day our shortest as in the â—ntipodes The Second Book Shewing the Practical Use of the GLOBES Applying them to the Solution of Astronomical and Geographical Problems PRAEFACE Some Advertisements in Choosing and Using the GLOBES 1. SEE the Papers be well and neatly pasted on the Globes which you may know if the Lines and Circles discribed thereon meet exactly and continue all the way even and whole the lines not swerving out or in and the Circles not breaking into several Arches nor the Papers either come short or lap over one the other 2. See that the Culler be transparent and ly not too thick on the Globe lest it hide the superficial Descriptions 3. See the Globe hang evenly between the Meridian and Horizon not inclining more to one side then the other 4. See the Globe swim as close to the Meridian and Horizon as conveniently it may lest you be too much puzzeld to find against what point of the Globe any degree of the Horizon or Meridian is 5. See the Equinoctal line be one with the Horizon when the Globe is set in a Parallel Sphear 6. See the Equinoctal line cut the East and West point of the Horizon when the Globe is set to an Oblique Sphear 7. See the Degrees marked with 90. and 00 hang exactly over the Equinoctial line of the Globe 8. See that exactly half the Meridian be above the Horizon and half under the Horizon which you may know if you bring any of the Decimal Divisions to the North Side of the Horizon and find their Complement to 90. int h South 9. See that when the Quadrant of Altitude is placed at the Zenith the Beginning of the Graduations reach just to the superficies of the Horizon 10. See that while the Index of the Hour Circle by the motion of the Globe passes from one hour to the other 15. degrees of the Equator pass through the Meridian 11. If you have a Circle of Position see the Graduations agree with those of the Horizon 12. See that your wooden Horizons be made substantial and strong for besides the Inconveniences that thin wood is subject unto in
respect of warping and shrinking I have had few Globes come to mending that have not had either broken Horizons or some other notorious fault occasioned through the sleightness of the Horizons In the Using the Globes KEep the East side of the Horizon alwaies towards you unless your Proposition requires the turning of it which East side you may know by the Word East placed on the outmost verge thereof For then have you the graduated side of the Meridian alwaies towards you the Quadrant of altitude before you and the Globe divided exactly into two equal parts So oft as I name to at of or under the Meridian or Horizon I mean the East side of the Meridian and Superficies of the Horizon because the East side of the Meridian passes through the North and South points both of the Globe and Horizon and agrees just with the middle of the Axis And the Superficies of the Horizon divideth the Globe exactly into two equal parts It you happen to use the Globes on the South side the Equator you must draw the wyers out of either Pole and change them to the contrary Poles putting the longest wyer into the South Pole And because on the other side the Equator the South Pole is elevated therefore you must elevate the South Pole of the Globe above the Horizon according to the South Latitude of your Place as shall be shewed hereafter In the working some Problems it will be required that you turn the Globe to look on the West side thereof which turning will be apt to jog the Ball so as the degree that was at the Horizon or Meridian will be moved away and thereby the Position of the Globe altered To avoid which inconvenince you may make use of a Quill thrusting the Feather end between the Ball and the Brazen Meridian and so wedge it up without wronging the Globe at all till your Proposition be answered PROBLEME I. To find the Longitude and Latitude of Places on the Terrestrial Globe SEek the Place on the Terrestrial Globe whose Longitude and Latitude you would know and bring that Place to the Brazen Meridian and see how many degrees of the Equator is cut by the Meridian from the first general Meridian which on my Globes pass through Gratiosa one of the Isles of the Azores for that number of degrees is the Longitude of the Place Example I desire to know the Longitude of London and close to the name London I find a smal mark 0 thus which smal mark is in some Globes and Maps adorned with the Picture of a Steeple c. therefore I do not bring the word London to the Meridian but that smal mark for that alwaies represents the the Town or Citty sought for And keeping the Globe steddy in this Position I examine how many degrees of the Equator are contained between the Brazen Meridian and the first general Meridian which I find to be 24. deg 00. min. Therefore I say the Longitude of London is 24. degrees 00. min. For the Latitude See on the Brazen Meridian how many degrees are contained between the Equator and the mark for London which in this Example is 51½ therefore I say London hath 51½ degrees North Latitude PROBLEME II. The Longitude and Latitude being know to Rectifie the Globe fit for use 1. WHen you rectifie the Globe to any particular Latitude you must move the Brazen Meridian through the notches of the Horizon till the same number of degrees accounted on the Meridian from the Pole about which the Hour-Circle is towards the North point in the Horizon if in North Latitude and toward the South if in South Latitude come just to the edge of the Horizon Example By the former Proposition I found the Latitude of London to be 51½ degrees North Latitude therefore I count 51½ degrees from the Pole downwards towards my right hand and turn the Meridian through the notches of the Horizon till those 51½ degrees comes exactly to the uppermost edge of the North point in the Horizon and then is the Meridian rectified to the Latitude of London 2. Next rectifie the Quadrant of altitude after this manner Screw the edge of the Nut that is even with the graduated edge of the thin Plate to 51½ degrees of the Brazen Meridian accounted from the Equinoctial on the Southern side the Horizon which is just the Zenith of London and then is your Quadrant Rectified 3. Bring the degree of the Ecliptick the Sun is in that day to the Meridian which you shall learn to know by the next Probleme and then turn the Index of the Hour Circle to the hour 12. on the South side the Hour Circle and then is your Hour Circle also rectified fit to use for that Day 4. Lastly If you will rectifie the Globe to correspond in all respects with the Position and Scituation of the Sphear you must set the four Quarters of the Horizon viz. East West North and South agreeable with the four quarters of the World which you may do by the Needle in the bottom of the Horizon for you must turn the Globe so long till the Needle point just to the Flower de luce Next you must set the Plain of the wooden Horizon parallel to the Horizon of the World which you may try by setting a common Level on the four Quaters of the Horizon And then positing the degree of the Ecliptick the Sun is in to the Height above or depth below the Horizon the Sun hath in Heaven as by the 11th Probleme your Globe is made Correspondent in all points with the frame of the Sphear for that particular Time and Latitude PROBLEME III. To find the Place of the Sun in the Ecliptick the Day of the Moneth being first known SEek the Day of the Moneth in the Circle of Moneths upon the Horizon and right against it in the Circle of Signes is the degree of the Ecliptick the Sun is in Example Imagine the Day to be given is May 10. therefore I seek on the Horizon in the Circle of Moneths for May and find the Moneths divided into so many parts as there is Daies in the Moneth which parts are marked with Arithmetical figures from the beginning of the Moneth to the end and denote the number of the Day of the Moneth that each Division represents therefore among the Divisions I seek for 10 and directly against it in the Circle of Signes I find ♉ 29. degrees Therefore I say May 10. the Suns Place is in 29. degrees of ♉ But note that if it be Leap Year instead of the 10. of May you must take the 11. of May because February having in a Leap Year 29. Daies the 29. of February must be reckoned for the first of March and the first of March for the second of March the second of March for the third of March and so throughout the year The Leap Year is caused by the six od hours more then 365. daies that are assigned to
Day of the Moneth given THe Day of the Moneth is March 20. By the 4th Prob. you may find the place of the Sun to be ♈ 10. Therefore bring the Place of the Sun to the Meridian and elevate it above the Horizon the same number of degrees it hath in Heaven so shall the arch of the Meridian comprehended between the Pole and the Horizon be the elevation of the Pole in your Place Otherwise The Day of the Moneth given is March 20. so that by the fourth Prob. you have the Suns Place ♈ 10 and by the fifth the Declination of the Sun 3. 55. North therefore the Declination being North and you on the North side the Equator you must substract 3. 55. from the Meridian Altitude 42. 25. and there remains 38 30. for the heighth of the Equinoctial above the Horizon but if your Declination had been South you must have added 3 55. to the Meridian Altitude and the Sum would have been the Elevation of the Equinoctial Having the Elevation of the Equinoctial you may easily have the Elevation of the Pole for the one is alwaies the Complement of the other to 90. Thus the Height of the Equinoctial 38. 30. subtracted from 90. leaves 51. 30. for the Elevation of the Pole here at London And thus it follows that the Latitude of any Place from the Equinoctial is alwaies equal to the Elevation of the Pole for between the Zenith and the Equinoctial is contained the Complement of the Heighth of the Equinoctial above the Horizon to 90. PROB. XVI To take the Altitude of any Star above the Horizon by the Globe THe Horizon of the Globe set parallel to the Horizon of the World as before Turn the North Pole towards the Star and when you can see the Star through the Axis the Northern notch of the Horizon will cut the degree of Elevation on the Meridian Example April 19. at 11. a clock at Night I would observe the Altitude of Spica Virgo Therefore I set the Horizon parallel to the Horizon of the World as by the Second Probleme and turn the Northern Pole till it point towards the Star Then looking in at the South Pole of the Globe through the Axis I shall see the Star and have on the Meridian the Question resolved But if it point not exactly then I move the North Pole upwards or downwards either to the right hand or to the left according as I may find occasion till I can see the Star through the Axis and then the edge of the notch in the Horizon cuts 28. degrees 57. min. on the Brazen Meridian Therefore I say April 19. at 11. a clock at Night here at London the Altitude of Spica 〈◊〉 is 30. degrees above the Horizon PROB. XVII By the Meridian Altitude of any Star given to find the Height of the Pole JOyn the Star to the Meridian and place it to the Altitude observed so shall the number of degrees intercepted between the Pole and the Horizon be the Elevation of the Pole Example Spica Virgo is observed to have 28. degrees 57. min Meridian Altitude therefore I bring Spica Virgo to the Meridian and raise it or depress it higher or lower as I find occasion till it is just 28. degrees 57. min. above the Horizon Then I count the number of degrees between the Pole and the Horizon and find them 51½ Therefore I say the Elevation of the Pole is here at London 51½ Yet note If the Star whose Altitude you observe have fewer number of degrees of Declination from the Pole then the Elevation of the Pole you may be apt to mistake in its coming to the Meridian for those Stars never set and therefore are twice Visible in the Meridian in 24. hours once above the Pole and once under the Pole If your Star have greater Altitude then the North Star it is above the Pole but if it have less it is below the Pole so that if you know but whether it be above or below it is enough for so you may accordingly raise it to the Altitude on the Meridian it hath in Heaven and joyn it to the Meridian either above or beneath the Pole as the Star is placed in Heaven and then the arch of the Meridian comprehended between the Pole and the Horizon is the Elevation of the Pole as aforesaid Otherwise Having the Meridian Altitude of the Star you must find its Declination by the 27. Probleme and if the Declination be South and you on the North side the Equator you must ad the Declination to the Meridian Altitude and the sum of both makes the Altitude of the Equinoctial But if the Declination be North and you on the North side the Equator you must substract the Declination from the Meridian Altitude as was taught by the 15. Prob. in the Example of the Sun and the remainder is the Altitude of the Equinoctial Then as was taught by the 15 Probleme aforesaid substract the Altitude of the Equinoctial from 90 the Remainder is the Elevation of the Pole in your Place Example By the last Probleme the Meridian Altitude of Spica Virgo was 28 degrees 57 min and the Declination of Spica by the 27th Probleme is found 9. degrees 33. min. South therefore because the Declination is South I ad 9. degrees 33. min. to the Meridian Altitude which makes 38. deg 30. min. for the Elevation of the Equinoctial which 38. deg 30. min. substracted from 90. leaves 51. degrees 30. min. for the Elevation of the Pole here at London PROB. XVIII Another way to find the Height of the Pole by the Globe if the Place of the Sun be given and also to find the Hour of the Day and Azimuth and Almicantar of the Sun THis must be performed by help of a Spherick Gnomon as Blaew calls it which is a small Pin or Needle fixed perpendicularly into a smal Basis with an hollow concave bottom that it may stand upon the convexity of the Globe Therefore the Horizon of the Globe being set parallel to the Horizon of the World as by the Second Probleme the Spherick Gnomon must be set exactly upon the Place of the Sun and then turning the Globe about upon its Axis either from East to West or contrarily from West to East or else by the Meridian through the notches of the Horizon till the Spherick Gnomon cast no shadow on any side thereof you have on the Meridian in the North point of the Horizon the number of degrees that the Pole is elevated above the Horizon Example Imagine the four Quarters of the Horizon of the Globe correspond with the four Quarters of the Horizon of the World and the Plain of the Horizon of the Globe is parallel to the Plain of the Horizon of the World The Suns Place is ♉ 29¼ which I find on the Globe and place the Spherick Gnomon thereon Then at a guess I move the Globe both on its Axis and by the Meridian as neer
Quadrant of Altitude the same degree on it will ly on both the Stars so shall the Index of the Hour-Circle point at the Hour of the Night PROB. XLI The Hour given that any Star in Heaven comes to the Meridian to know thereby the Place of the Sun and by consequence the Day of the Moneth though it were lost BRing the Star proposed to the Meridian and turn the Index of the Hour-Circle to the Hour given Then turn about the Globe till the Index point at the Hour of 12 for Noon and the Place of the Sun in the Ecliptick shall be cut by the Meridian Example March 7. at 11 aclock at Night the Pointers come to the Meridian of London Therefore I place the Pointers on the Caelestial Globe under the Meridian and turn the Index of the Hour-Circle to 11. past Noon afterwards I turn back the Globe till the Index point to 12. at Noon Then looking in the Ecliptick I find the Meridian cuts it in ♓ 26. 45. minutes Therefore I say when the Pointers come to the Meridian at 11. a clock at Night the Place of the Sun is ♓ 26. 45. Having thus the Place of the Sun I may find the Day of the Moneth by the fourth Probleme and so either know the Day that the Pointers come to the Meridian at 11. a clock at Night or at any other Hour given The Day of the Moneth might also be found by the Declination and the Quarter of the Ecliptick the Sun is in given For the Meridian will cut the degree of the Suns Place in the Ecliptick in the Parallel of Declination So that having respect to the Quarter of the Ecliptick you 'le find the Suns Place and having the Suns Place you may as aforesaid find the Day of the Moneth PROB. XLII The Day of the Moneth given to find in the Circle of Letters on the Plain of the Horizon the Day of the Week THe seven Daies of the Week were by the Idolatry of the ancient Roman Heathenish Times Dedicated to the Honour of seven of their Gods which we call Planets The first is the most eminent and therefore doubtless by them set in the first Place called Dia Solis or the Suns Day The second Dia Luna the Moons Day The third Dia Martis the Day of Mars by us called Tuesday The fourth Dia Mercurius Mercuries Day by us called Wednesday from Woden an Idol the Saxons Worshipt to whose Honour they Dedicated that Day and is by all those Germain Nations still called Wodensdagh The fifth Dia Jovis Jupiter or Joves Day which doubtless the Saxons from whom probably we receive it called Donder-dagh because Jupiter is the God of Thunder and we either by corruption or for shortness or both call it Thursday The sixth Dia Veneris the Day of Venus but the Saxons transferring her Honour to another of their Goddesses named Fria called it Fridagh and we from them call it Fryday The seventh is Dia Saturnis Saturus Day The same Day of the Moneth in other Years happens not on the same Day of the Week therefore the Dominical Letter for one Year is not the same it is the next Now because you cannot come to the knowledge of the Day of the Week unless you first know the Sundaies Letter therefore have I in Prob. 5â— inserted a Table of M r Palmers by which you may find the Dominical or Sundaies Letter for ever and having the Dominical Letter you may in the Circle of Letters on the Horizon find it neer the day of that Moneth and count that for Sunday the next under it for Monday the next under that for Tuesday and so in order till you come to the Day of the Moneth Example I would know what Day of the Week June 1. Anno 1658. Old Style falls on I find by the Table aforesaid the Dominical Letter is C then I look in the Calender of Old Style for June 1. and against it I find Letter E which because it is the second Letter in order from C therefore it is the second Day in order from Sunday which is Tuesday PROB. XLIII The Azimuth of any Star given to find its Hour in any given Latitude THe Hour of a Star is the number of Hours that a Star is distant from the Meridian To find which Rectifie the Globe and Quadrant of Altitude and bring the Star proposed to the Meridian and the Index of the Hour-Circle to 12. Then place the lower end of the Quadrant of Altitude to the given Azimuth in the Horizon and turn the Globe till the Star come to the graduated edge of the Quadrant of Altitude so shall the Index of the Hour-Circle point at the Hour of the Star Only this caution you must take If the Star were turned from the Meridian towards the Eastern side of the Horizon you must substract the number of Hours the Index points at from 12. and the remainder shall be the Hour of the Star But if the Star were turned from the Meridian towards the West side the Horizon the Hour the Index points at is without more adoe the Hour of the Star PROB. XLIV How you may learn to know all the Stars in Heaven by the Coelestial Globe REctifie the Globe Quadrant Hour-Index and Horizon as by Prob. 2. Then turn about the Globe till the Index of the Hour-Circle point at the Hour of the Night on the Hour-Circle Then if every Star on the Globe had a hole in the midst and your Ey were placed in the Center of the Globe you might by keeping your Ey in the Center and looking through any Star on the Globe see its Maâ—ch in Heaven that is the same Star in Heaven which that Star on the Globe represents for from the Center of the Globe there proceeds a straight line through the Star on the Globe even to the same Star in Heaven Therefore those Stars that are in the Zenith in Heaven will then be in the Zenith on the Globe those that are in the East in Heaven will be in the East on the Globe those in the West in Heaven in the West on the Globe and those Stars that are in any Altitude in Heaven will at the same time have the same Altitude on the Globe So that if you see any Star in Heaven whose Name you desire to know you need but observe its Azimuth and Altitude and in the same Azimuth and Altitude on the Globe you may find the same Star and if it be an eminent Star you will find its Name adjoyned to it Example December 10. at half an hour past 9. a clock at Night here at London I see two bright Stars at a pretty distance one from another in the South I desire to know the Names of them Therefore having the Globe rectified to the Latitude of London and the Quadrant of Altitude screwed to the Zenith the Hour-Index also Rectified and the Horizon posited Horizontally as by Prob. 2. I observe the Altitude of those Stars in
the Equinoctial under the Meridian of your Place have a continual Sun-Dyal of it and the hour of the Day given on it at once in two places one by the parting the enlightned Hemisphear from the shadowed on the Eastern side the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe Much more might be said on this Probleme But the Ingenuous Artist may of himself find out diversities of Speculations therefore I forbear PROB. XLVI To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is THis may be performed by the former Probleme in the Day time if the Sun shines but not else But to find it at all times do thus Bring the Place of your Habitation to the Meridian and the Index of the Hour-Circle to 12 Then turn the Globe Eastwards if Afternoon or Westwards if Before Noon till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is either before or After-Noon so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day Example May 10 at ¾ of an hour past 4. a clock After Noon I would know in what Place of the Earth the Sun is in the Zenith My Habitation is London Therefore I bring London to the Meridian and the Index of the Hour-Circle to 12. and because it is After Noon I turn the Globe Eastwards till the Index passes through 4 hours and 3 quarters or which is all one till 70 degrees 15 minutes of the Equator pass through the Meridian Then I find by Prob. 5. the Suns Declination is 20. degrees 5. minutes which I find upon the Meridian and in that Place just under that degree and minute on the Globe the Sun is in the Zenith which in this Example is in the North East Cape of Hispaniola Having thus found in what Place of the Earth the Sun is in the Zenith Bring that Place to the Meridian and Elevate its respective Pole according to its respective Elevation so shall all Places cut by the Horizon have the Sun in their Horizon Those to the Eastwards shall have the Sun Setting those to the Westward shall have it Rising in their Horizon those at the Intersection of the Meridian and Horizon under the Elevated Pole have the Sun in their Horizon at lowest but Rising those at the Intersection of the Meridian and Horizon under the Depressed Pole have the Sun in their Horizon at highest but Setting Thus in those Countries that are above the Horizon it is Day-light and in those but 18 degrees below the Horizon it is Twilight But in those Countries further below the Horizon it is at that time dark Night And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial have the Sun alwaies above the Horizon till the Sun have less Respective Declination then the Elevated Pole and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon till the Sun inclines more towards the Depressed Pole As you may see by turning about the Globe for in this position that portion of the Globe intercepted between the Elevated Pole and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole ascend above the Horizon PROB. XLVII To find in what different Places of the Earth the Sun hath the same Altitude at the same time FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith and bring that Place on the Globe to the Zenith and on the Meridian there screw the Quadrant of Altitude and turn it about the Horizon describing degrees of Almicantars thereby as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon those in the 20 th Almicantar shall have the Sun Elevated 20 degrees above their Horizon those in the 30 th 30. degrees c. So that you may see when the Sun is in the Zenith of any Place All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon But to find in what different Places the Sun hath the same heighth at the same time as well Before or After Noon as at Full Noon and that in Countries that have greater Latitude then the Suns greatest Declination and therefore cannot have the Sun in their Zenith requires another Operation Therefore Elevate its respective Pole according to your respective Latitude and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation and the degree of the Ecliptick the Sun is in represent the Sun Then bring the Sun to the Meridian and the Index of the Hour-Circle to 12 and turn the Globe Eastwards if Before Noon or Westwards if After Noon till the Index point to the Hour of the Day Then place the lower end of the Quadrant of Altitude to the East point of the Horizon and move the upper end by sliding the Nut over the Meridian till the edge of the Quadrant touch the place of the Sun Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place and count the number of remaining degrees on the Meridian on the contrary side the degree of the Meridian where the upper end of the Quadrant of Altitude touches the Meridian and where that number of degrees ends on the Meridian in that Latitude and your Habitations Longitude hath the Sun the same heighth at the same time Example May 10. at 53. minutes past 8. a clock in the Morning I would know in what Place the Sun shall have the same Altitude it shall have at London London's Latitude found by Prob. 1. is 51½ degrees Northwards And because the Elevation of the Pole is equal to the Latitude of the Place as was shewed Prob. 15. Therefore I Elevate the North Pole 51½ degrees so shall 51½ degrees on the Meridian be in the Zenith This 51½ degrees on the Meridian represents London The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian and the Hour Index to 12. on the Hour Circle Then I turn the Globe Eastwards because it is before Noon till the Index point at 8. hours 53 minutes on the Hour-Circle and place the lower end of the Quadrant of Altitude to the East point in the Horizon and slide the upper end either North or Southwards
to every twelth degree of the Equinoctial accounted from the Equinoctial Colure marking them with 1 2 3 4. c. to 30 which will end where you began viz. at the Equinoctial Colure again so shall the Equinoctial be divided into 30 equal parts representing the 30 Dayes of the Moons Age These figures to distinguish them from the degrees of the Equator were best be writ with Red Ink. When you would enquire the Moons Place Elevate the North Pole 90 degrees that is in the Zenith so shall the Equator ly in the Horizon Then bring the Equinoctial Colure against the Day of the Moneth in the Horizon so shall the Moons Age written in Red figures stand against the Signe and degree in the Horizon that the Moon is in at that Time Example September 28. 1658. I would know the Moons place in the Ecliptick she being then 12 Daies old Therefore I Elevate the North Pole 90 degrees above the Horizon and turn the Globe about till the Equinoctial Colure come to September 28. in the Circle of Daies on the Horizon then looking against what Signe and degree of the Ecliptick Circle in the Horizon the 12 th division in Red figures stands I find ♓ 9. which is the Signe and degree the Moon is in according to her mean Motion This Probleme may be applyed to many Uses for having the Moons Place you may find the Time of her Rising Southing Setting and Shining c. by working with her as you were taught to work with the Sun in several fore-going Problemes proper to each purpose PROB. LV. Having the Longitude and Latitude or Right Ascension and Declination of any Planet or Comet to place it on the Globe to correspond with its place in Heaven PLanets and Comets cannot be placed on the Globe so as their places will long retain correspondence with their places in Heaven Because as was said Chap. 44. they have a continual motion from West to East upon the Poles of the Ecliptick yet never-the-less you may by having their Longitude and Latitude or Right Ascension and Declination for any set Time place a Mark for them on the Globe either with Ink if your Globe be Varnisht for then you may with a wet finger wipe it off again or with Black-lead if it be not Varnisht and then you may rub it out again with a little White Bread which Mark for that Time will as effectually serve you to work by as any of the Fixed Stars placed on the Globe will do Therefore if the Longitude and Latitude of any Planet or Comet be given Do thus Elevate the North Pole if the Latitude given be North but if the Latitude given be South Elevate the South Pole 66 ½ degrees and place the Pole of the Ecliptick in the Zenith and over it screw the Quadrant of Altitude so shall the Ecliptickly in the Horizon and the Quadrant of Altitude being turned about the Horizon shall pass through all the Degrees of Longitude Then find the point of given Longitude in the Ecliptick and bring it to the Quadrant of Altitude and hold it there Then count upwards on the Quadrant of Altitude the number of degrees and minutes of given Latitude and at the point where the number ends close to the Quadrant of Altitude make a smal Prick and that Prick shall represent the Planet or Comet you were to place on the Globe If it be the Right Ascension and Declination of a Planet or Comet that is given you must find the degree and minute of Right Ascension on the Equinoctial and bring it to the Meridian and keep the Globe there steddy then find the degree and minute of Declination on the Meridian and under that degree and minute on the Globe make a Prick and that Prick shall represent the Planet or Comet as aforesaid If it be ♄ or ♃ that this Prick is to represent it may stand on the Globe sometimes a Week or a Fortnight without much difference from the Planets place in Heaven But if the Prick were to represent the other Planets you must in regard of their swift motion alter it very often especially for the Moon for so swift is her motion that in every two Hours she alters about a degree in Longitude Having thus placed this Mark on the Globe you may find out the Time of its several Positions and Aspects if you work by it as you are directed to work by the Sun in the several respective Problemes throughout this Book The End of the Second Book The Third BOOK Being the Practical Use of the GLOBES Applyed to the Solution of Problemes In the Art of NAVIGATION PRAEFACE BEcause the Art of Navigation consists aswell in the knowledge of Astronomical and Geographical Problemes as in Problemes meerly Nautical Therefore I must desire the Artist to seek in the last Book such Problemes as are only Astronomical or Geographical For my Designe is here to collect such Problemes as are only used in the Art of Navigation some few particulars excepted as for finding Latitude Longitude Course Distance c. Which though they are handled in than Book yet for their exceeding Vtility in the Art of Navigation and for that what there is given cannot alwayes be had to work by therefore in this Book I have mentioned divers other Observations which being made or had you may by the Rules proper for each Observation find what shall be proposed PROB. I. The Suns Amplitude and Difference of Ascension given to find the Heigth of the Pole and Declination of the Sun ELevate the Pole so many degrees as the Difference of the Suns Ascension is and screw the Quadrant of Altitude to the Zenith and bring the first point of ♈ to the Meridian then number on the Quadrant of Altitude upwards the complement to 90. of the Suns Amplitude and move the Quadrant of Altitude till that number of degrees cuts the Equator So shall the Quadrant cut in the Horizon the degree of the Pole Elevation and in the Equator the degree of the Suns Declination Example The difference of Ascension is 27. degrees 7. minutes Therefore I Elevate the Pole 27. degrees 7. minutes above the Horizon and screw the Quadrant of Altitude to 27. degrees 7. minutes which is in the Zenith then I bring the first point of ♈ to the Meridian and number on the Quadrant of Altitude upwards 56. degrees 40. minutes the Complement of the Suns Amplitude and bring that degree to the Equator then I see in what degree of the Horizon the Quadrant cuts the Horizon and find 51 ½ which is the Elevation of the Pole then looking in what degree of the Equator the Quadrant of Altitude cuts the Equator I find 20 degrees 5 min. which is the Declination of the Sun at the same Time PROB. II. The Suns Declination and Amplitude given to find the Poles Elevation ELevate the Pole so many degrees as the Complement of the Suns Amplitude is and screw the Quadrant of Altitude
or more in Places neer either Pole Note If you be not very curious in opening your Compasses to this smal distance you may in oft turning them about upon the Rhumb commit error in your measuring therefore when you have taken the Distance of one degree try if you neither gain or loose any thing in measuring 10 or 20. degrees of the Equinoctial by them for then your Compasses are opened to a width exact enough for your purpose PROB. XII The Longitudes and Latitudes of two Places given to find Course and Great Circle distance between them FInd on the Globe the Longitudes and Latitudes given and make pricks to either Longitude and Latitude If any Rhumb pass from one place to the other that is without more a doe the Rhumb sought But if no Rhumb pass through Take the Rhumb that runs most Parallel to the two pricks for that shall be the Rhumb or the neerest Rhumb that these two pricks Bear on An Example of this see in Prob. 34. of the Last Book And the Great Circle Distance between these two pricks you may find as by Prob 33. of the same Book PROB. XIII The Latitude you departed from and the Latitude you are arrived to and the number of Leagues you have sailed given to find the Rhumb you have sailed on and difference of Longitude MAke a prick on the Globe in the Latitude you departed from then open your Compasses to the number of Leagues you have sailed by taking for every 20. Leagues 1. degree of the Equator half a degree for 10 Leagues a quarter of a Degree for 5 Leagues and so proportionably for any other number of Leagues Place one foot of your Compasses in the prick made for the Latitude you departed from and extend the other towards the Latitude you are arived to and discribe an occult Arch Turn the Globe till this occult Arch come to the Latitude on the Meridian and where the Latitude cuts this occult arch make another prick to represent the Latitude you are arived to so shall the Rhumb passing through those two pricks or that is most Parallel to those two pricks be as in the last Prob. the Course or the Rhumb those two pricks Bears on The difference of Longitude you may find as by Prob. 11. PROB. XIV To find by the Globe the Variation of the Needle commonly called the Variation of the Compass OBserve by a Compass whose wyer is placed just under the Flower deluce what point of the Compass the Sun Rises or Sets on Morning or Evening Then examine by Prob 10. of the second Book what degree of the Horizon the Sun Rises or Sets on by the Globe also and if the Rising or Setting be the same both on the Globe and Compass there is no Variation in your Place But if there be difference between the Rising or Setting by the Compass and the Globe then is there Variation in your Place If the point the Sun Rises upon in the Compass be neerer the North point then the point the Sun Rises upon by the Globe the Variation is Westwards If the point the Sun Sets upon in the Compass be neerer the North then the point it Sets upon by the Globe the Variation is Eastwards If the point the Sun Sets upon in the Compass be further from the North point then the point the Sun Sets upon by the Globe the Variation is Westwards If the point the Sun Rises upon in the Compass be further from the North point then the point the Sun Rises upon by the Globe the Variation is Eastwards And so many degrees as there is between the point of Rising or Setting found by the Compass and the point of true Rising or Setting found by the Globe so many degrees is the Variation from the North towards the East or West point Otherwise when the Sun hath Altitude Having the Altitude of the Sun find by Prob. 22. of the second Book its Azimuth Then examine by a Compass whether the true Azimuth found by the Globe agree with the Azimuth found by a Nautical Compass If they agree there is no Variation But if the Azimuth of the Compass before Noon be neerer the North then the true Azimuth found by the Globe the Variation is Westwards If the Azimuth by the Compass Afternoon be neerer the North the Variation is Eastwards If the Azimuth by the Compass Afternoon be further from the North the Variation is Westwards If the Azimuth by the Compass before Noon be further from the North the Variation is Eastwards And this Variation shall be as aforesaid so many degrees as there is between the Azimuth Observed by the Compass and the true Azimuth Observed by the Globe PROB. XV. To keep a Journal by the Globe BY some of these foregoing Problemes you may Dayly when Observations can be made find both the Longitude and Latitude on the Globe of the Places you are arived to and also the Way the Ship hath made and make pricks on the Globe in their proper Places for every Daâ—â—s Journey so truly and 〈◊〉 naturally that if you kept your reckoning aright you may be sure you cannot miss any thing of the truth it self and that with less trouble and greater advantage then keeping a Book of every Daies Reckoning PROB. XVI To Steer in the Night by the Stars REctifie the Globe and Hour Index as by Prob. 2. of the last Book and turn about the Globe till the Index of the Hour Circle points to the Hour of the Day or Night Then turn the Globe till the Difference of Longitude between the Place you depart from and the Place you sail to pass through the Meridian and if any Star in the Latitude of the Place you sail To come to the Meridian or neer the Meridian with the degree of the difference of Longitude that Star is at that time in or neer the Zenith of that Place you sail to and by finding the same Star in Heaven as by Prob 44. of the last Book you may direct your ship towards that Star and fail as confidently saies M r Blagrave as if Mercurie were your Guide But because this Star moves from the Zenith of this Place you must often examine what Star is come to the Zenith and so often charge the Star you Steer by as the length of your Voyage may require PROB. XVII How to platt on the Globe a New Land never before Discovered THese two following Problemes are 2. Chapters of M r Wrights delivered by him as follows It may sometimes fall out in new Discoveries or when your Ship by means of a Tempest is driven out of her right Course that you shall come to the sight of some Isle Shoald or new Land whereof the Mariner is utterly ignorant And to make some relation of the same or to go unto it some other time if you desire to set it down on your Globe in the true place you may do it after this manner So soon as you have sight
placed at the East or West point of the Horizon Therefore when you would find what Circle of Position any Star or degree of the Ecliptick is in Rectifie the Globe and Quadrant of Altitude and bring the lower end of the Quadrant of Altitude to the East or West point of the Horizon and lift up the Circle of Position till it come to the Star or degree of the Ecliptick proposed and the number of degrees the Circle of Position then cuts in the Quadrant of Altitude is the number of the Circle of Position that the Star or degree of the Ecliptick is in If the Star or degree of the Ecliptick be under the Horizon turn the Globe about till 180 degrees of the Equator pass through the Meridian then will the Star or degree of the Ecliptick be above the Horizon Lift up then the Circle of Position as before to the Star or degree of the Ecliptick and the number of degrees of the Quadrant of Altitude the Circle of Position cuts on the East side is the number of Circles of Position the Star was under the Horizon on the West side Or so many degrees as the Circle of Position cuts on the Quadrant of Altitude in the West side the Horizon is the number of the Circles of Position the Star or degree of the Ecliptick was under the Horizon on the East side PROB. VII To find the Right Ascensions the Oblique Ascensions and the Declinations of the Planets EXamine the Right Ascensions and Declinations of those pricks made to represent each Planet in Prob. 1. of this Book and work by them as you were directed to work by the Sun in Prob. 26 27 28. of the second Book PROB. VIII How to Direct a Figure by the Globe TO Direct a Figure is to examine how many degrees of the Equinoctial are moved Eastwards or Westwards while any Planet or Star in one House comes to the Cusp or any other point of any other House When you would Direct any Promittor to any Hylegiacal point examine the degree of the Equator at the Meridian then turn about the Globe till the Promittor come to the Hylegiacal point and examine again the degree of the Equator at the Meridian and by substracting the lesser from the greater you will have the number of Degrees that passed through the Meridian whiles the place of the Promittor was brought to the Hyâ—â—gâ—â—cal point and that number of degrees shall be the Arch of Dâ—rection Example I would Direct the Body of the Moon in our Figure aforesaid to Medium Câ—â—â— or the tenth House I find by the Globe 20â— degrâ—es 30. minutes of the Equator at the Meridian with the â—eath House and turning the Globe till the prick made to represent the Moon come to the Meridian I find 227 degrees 20 minutes of the Equator come to the Meridian with it Therefore I 〈◊〉 the lesser from the greater viz. 2â—3 degrees 3 minutes from 227. degrees 2â— minutes and have remaining 2â— degrees 50 minutes This 〈◊〉 degrees 50. minutes shews that 23. Years 1â— Moneths must expire ere the Effects promised by the Moons present position shall opperate upon the signification of the 〈◊〉 House If the Body of the Moon had been Directed to any other point the◠〈◊〉 Meridian or Horizon you must have Elevated the Circle of 〈◊〉 〈◊〉 the point proposed and have under-propped it to that 〈◊〉 and 〈◊〉 have turned about the Globe till the prick 〈◊〉 the Moon had come to the Circle of Position and then 〈◊〉 degrees of the Equator that should have passed through the Meridian whiles this motion was making should be the number of degrees of Direction and signifie in Time as foresaid PROB. IX Of Revolutions and how they are found by the Globe BY Revolution is meant the Annual Conversion of the Sun to the same place he was in at the Radix of any Business When you would find a Revolution by the Globe first find the Right Ascension of Mâ—d Heaven at the â—â—adix of the Business as by Prob 26. of the second Book you were directed to find the Right Ascerâ—â—on of the 〈◊〉 and 〈◊〉 add 87 degrees for every Yâ—aâ— since the Radix Then substract 360 so oâ—â— as you can from the whole and the Râ—mâ—â—â—s shall be the Right Ascension oâ— Mid Hâ—aven for the Aâ—â—â—al Revoluâ—â—on Iâ— yâ—u 〈◊〉 the number of degrees of the Equator contained between the Râ—ght Aâ—cension of the Mid Hâ—aven and the Right Ascension of the Sun and convert that number of degrees 〈◊〉 Time by allowing for every 15. degrees 1 Hour of Time it will shew if the Suns place be on the Western side of the Meridian the number of Hours and minutes Afternoon the Revolution shall hâ—ppen on but if on the East side the Meridian the number of Hours and minutes Before-noon the Revolution shall happen on PROB. X. How a Figure of Heaven may be erected by the Revolution thus found SEek the degree of Right Ascension of Mid Heaven and bring it to the Meridian so shall the four Cardinal points of the Globe be the same with the four Cardinal points in Heaven at the time of the Revolution The other Hâ—â—â—ses are 〈◊〉 by the Circle of Position as in the first Probleme of this Book The End of the Fourth Book The Fifth BOOK Shewing the Practical Use of the GLOBES Applying them tâ— the Solution of Gnomonical Problems PRAEFACE DYals are of two sorts Pendent and Fixed Pendeâ— are such as are hung by the hand and turned towards the Sun that by its Beams darting througâ— smal Pin-holes made for that purpose the hour of the Daâ— may be found These are of two sorts Vniversal and Pâ—â—ticular Vniversal Dyals are those commonly called Equiâ—ocâ—â—â— or Ring-Dyals They are used by Sea-men and Trâ—vellers that often shift Latitudes Particular are such as are made and only serve for Particular Latitudes Of these sorts are the several Dyaâ—â— discribed on Quadrants Cilinders c. Fixed Dyaâ—s shall be the matter of this discourse and they are such as are made upon fixed Planes and shew the Hour of the Day by a Stile or Gnomon made Parallel to the Axiâ— of the World Of the several Kinds of Dyal Plains and how you may know them A Plain in Dyalling is that flat whereon a Dyal is discribed There is some disagreement among Older and Later Authors in the naming of Plains for some name them according to the Great Circle in Heaven they ly in and others according to the scituation of the Poles of the Plains Thus they which name them according to the Great Circle in Heaven their Plains ly in call that an Horizontal Plain which others call a Vertical Plain those Vertical which others will call Horizontal and those Polar which others call Equinoctial However they be called it matters not so you can but distinguish their kinds which with a little consideration you may easily learn to do For remembring but upon what grounds either the
Order or Later Authors gave the Plains their Names upon the same grounds you may also learn to know them I confess both waies admit of some just exception against for in the Older Rule a Plain about the Pole is called an Equinoctial Plain when as to a sudden apprehension it would sound more significant to call it a Polar Plain as Later Authors do Again Later Authors call an Horizontall Plain a Vertical Plain when as it sounds more significant to call it an Horizontal Plain as Older Authors do because it lie flat upon the Horizon But I shall give you the names according to both Rules and leave you to your liberty to accept of which you please First therefore you have an Equinoctial Plain otherwise called a Polar Plain This Plain hath two Faces upper and under These two Faces ly in the Plain of the Equinoctial the upper Face beholding the Elevated Pole the under Face the depressed Pole 2. An Horizontal Plain otherwise called a Vertical Plain it lies in the Plain of the Horizon directly beholding the Zenith Erect Plains otherwise called Horizontal Plains are the sides of Walls and these are of seven sorts viz 1. Erect Direct Vertical North or South 2. Erect Direct East or West 3. Erect Vertical Declining 4. Erect Inclining Direct 5. Erect Inclining Declining 6. Erect Reclining Direct 7. Erect Reclining Declining 3. Erect Vertical North or South Direct otherwise called Direct North or South Horizontals behold the North or South Directly and ly in the East or West Azimuth 4. Erect Direct East or West otherwise called Direct East or West Equinoctials behold the East or West Directly and lies in the Plain of the Meridian having its Poles in the Equinoctial 5. Erect Vertical Declining Plains otherwise called Declining Horizontals do not behold the North or South Directly but swerves from them so much as the Azimuth Parallel to their Plains swerves or Declines from them 6. Erect Inclining Direct Plains have the upper side of their Plains Inclining or coming towards you and their Plains do exactly behold either the East West North or South 7. Erect Reclining Direct Plains have the upper side of their Plains Reclining or falling from you and their Plains exactly beholding either the East West North or South 8. Eâ—â—ct Reclining Declining or Erect Inclining Declining Plains are those Plains which are either Inclining or Reclining but 〈◊〉 behold the East West North or South Directly but 〈◊〉 or Decline more or less from them 9. Polar Plains are Parallel to the Axis of the World and to the Mâ—ridians that cuts the East and West or North and South points of the Horizon All these kinds of Plains have two Faces the one beholding the North Pole with the same respect that the other beholds the South Pole except the Equinoctial Plain which because neither Pole is Elevated hath but one Face yet that one contains as many Hour lines as two other Faces These two Faces or Plains will receive just 24. hour lines foâ— the 24 Hour-lines of Day and Night for so much as the one side or Face wanteth or exceedeth 12. the other side shall either exceed or want of 12. Every Dyal Plain is Parallel to the Horizon of some Country or other in the World therefore a Dyal made for any Horizon in the World may be set to such a Position that it will shew you the Hour of the Day in your own Habitation At least for so long as the Sun continues upon that Planâ— All Plains may be aptly demonstrated by the Globe by setting it correspondent to all the Circles in Heaven as by Prob. 2. of the second B ok for if you imagine the Globe in that Position were prest flat into the Plain of any Circle that Flat shall represent a Dyal plain which shall be called after the name of that Circle it is prest into Thus if the Quadrant of Altitude be applyed to any degree of Azimuth and you imagine the Globe were prest flat to the edge of the Quadrant of Altitude so much as that Azimuth Declines from the East West North or South in the Horizon so much shall that flat on the Globe be said to Decline either from the East West North or South Or if you imagine the Globe were prest flat down even with the Plain of the Horizon that flat shall represent an Horizontal Plain because as was said before the Plain lies in that Circle cal'd the Horizon The Style or Gnomon is that straight wyre that casts the shadow upon the Hour of the Day it is alwaies placed Parallel to the Axis of the World There are several waies to find the scituation of all Plains but the readiest and speediest is by a Clinatory The Clinatory is made of a square board as A B C D of a good thickness and the larger the better between two of the sides is discribed on the Center A a Quadrant as E F divided into 90 equal parts or degrees which are figured with 10 20 30 to 90 and then back again with the Complements of the same numbers to 90 between the Limb and the two Semidiameters is made a Round Box into which a Magnetical Needle is fitted and a Card of the Sea Compass divided into 4 Nineties beginning their numbers at the East West North and South points of the Compass from which points the opposite sides of the Clinatory receives their Names of East West North or South Upon the Center A whereon the Quadrant was discribed is fastned a Plumb-line having a Plumbet of Lead or Brass fastned to the end of it which Plumb-line is of such length that the Plumbet may fall just into the Grove G H below the Quadrant which is for that purpose made of such a depth that the Plumbet may ride freely within it without stopping at the sides of it See the Figure annexed But admit there be Variation Having by Prob. 19. of the third Book found the number of degrees of this Variation towards the East or West count the same number of degrees from the North point in the Card either to the Eastwards or Westwards and note the degree in the Card terminating at that number for that degree shall be the North point and its opposite degree the South point 90. degrees from it either way shall be the East and West points Therefore whereas before you were directed to turn the Clinatory till the North point of the Needle point to the Flower-de-luce on the â—aid you mâ—st now turn or move the Clinatory till the North point of the Needle â—arg just over the degree of Variation thus sound and then a line drawn as aforesaid by the side of the Clinatory Paralâ—el to the Needle shall be a North and South line or to speak more properly a Meridional line You may fiâ—d a Mâ—ridian liâ—e several other waies as first If the Sun shine just at Noon hold up a Plumb-line so as the shadow of it may fall upon your Plain and
and prolong it to the farthest extent of the Plane From this Gnomon or Style I let fall a Perpendicular upon the Noon line as F G this Perpendicular is called the Substile and this Perpendicular and its Base which is the Noon line and Hypothenusa which is the Gnomon shall make a Triangle which being erected upon the Base so as the Substile may stand Perpendicular to the Plane the Hypothenusa A F shall be the Gnomon and be Parallel to the Axis of the World and cast a shadow upon the Hour of the Day PROB. IIII. To make an Erect Direct South Dyal DRaw on your Plane an Horizontal line as C A D as was shewed in the Preface in the middle of this line as at A discribe as on a Center the Semi-Circle C B D from the Center A let fall a Perpendicular which shall divide the Semi-Circle into two Quadrants each of which Quadrants you must divide into 90 degrees Then Rectifie the Globe Quadrant of Altitude Colure and Hour Index thus Elevate the Pole of the Globe to the Latitude of your Place and screw the Quadrant of Altitude to the Zenith Then bring the Vernal Colure to the Meridian and the Index of the Hour Circle to the Hour of 12. in the Hour Circle so shall your Globe Quadrant of Altitude Colure and Hour Index be Rectified Aâ—d â—â—us you must alwaies Rectifie them for the making of most sorts of Dyals by the Globe Then to make an Erect Direct South Dyal Bring the lower end of the Quadrant of Altitude to the West point of the Horizon And turn the Globe Westwards till the Index points to all the Hours Afternoon and examine in what numbers of degrees from the Zenith the Colare cuts the Quadrant of Altitude when the Index points to each Hour for a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B which is the 12 a clock line towards D on the Plane shall be the same Hour lines the Index points at Thus in our Latitude viz. 51½ degrees the Vernal Coloure being brought to the Meridian and the Index to 12 If you turn the Globe Westwards till the Index points to 1 a clock or till 15 deg of the Equator pass through the Meridian the Colure will cut the Quadrant of Altitude in 9. 18 counted from the Zenith 2 19. 15 3 32. 5 4 48. 0 5 67. 4 6 90. And these are the distances of the Afternoon Hour lines which you must transfer to the East side of your Plane viz from B towards D and draw lines from the Center A through these distances and these lines shall be your Afternoon Hour lines Note once for all when the Colure goes off that Circle you examine the Hour distances in the Sun will shine no longer upon that Plane As in this example the Colure goes off the Quadrant of Altitude at 6 a clock therefore the Sun will not shine longer then till 6 a clock upon this Plane The Hour lines before Noon have the same distance from the Meridian that the Afternoon Hour lines have as was shewed in the last Probleme Only they must be drawn on the West side the Noon line and counted from B towards C. Otherwise You may reduce all Verticals into Horizontals if you Elevate the Pole of the Globe to the Complement of the Latitude of your Place and bring the Vernal Colure to the Meridian under the Horizon and the Index of the Hour Circle to 12 and turn the Globe Westwards for as the Index passes through every Hour on the Hour Circle the Colure shews in the Horizon the distance of the several Afternoon Hour lines from the Meridian or 12 a clock line in the Circle on your Plane numbred from B to D and lines drawn from the Center through these distances on your Plane shall be the Afternoon Hour lines of your Dyal Example Londons Latitude is 51½ degrees Its Complement to 90. is 38½ Therefore I Elevate the Pole 38½ degrees above the Horizon and bring the Vernal Colure to the Meridian under the Horizon and the Index of the Hour Circle to 12 on the Hour Circle Then Turning the Globe Westwards till the Index of the Hour Circle points to 1 a clock or till 15 deg of the Equator pass through the Meridian I find the Colure cut the Horizon in 9 18 from the Intersection of the Meridian and the Horizon as in the former Table 2 19 15 3 32 5 4 48 0 5 67 0 6 90 And these are the distances of the 6 Hour lines from the Merid. By this Example you may see that it is easie to reduce Verticals into Horizonâ—als and Horizontals into Verticals for this Erect Direct South Dyal is an Horizontal Dyal to those People that Inhabite 90 degrees from us viz. in the South Latitude of 38½ degrees Then make a Triangle whereof the Noon line shall be Base from it count the Complement of the Poles Elevation viz. 38½ degrees and through them draw the line A F from the Center A which shall be Hypotenusa Then â—et fall a Perpendicular upon the Noon line A B so is your Triangle made If this Triangle be erected Perpendicularly upon the Base or Noon line The Hypotenusa A F shall stand Parallel to the Axis of the World and cast a shadow upon the Hour of the Day PROB. V. To make an Erect Direct North Dyal IF the Erect Direct South Dyal were turned towards the North and the line C A D were turned downwards and the line marked with 7 be now marked with 5 and the line 8 with 4 the line 5 with 7 and the line 4 with 8 then have you of it a North Erect Direct Dyal All the other Hour lines in this Dyal are useless because the Sun in our Latitude shines on a North Face the longest Day only before 6 in the Morning and after 6 at Night PROB. VI. To make an Erect Direct East Dyal THese sorts of Dyals may better be demonstrated then made by the Globe unless the Axis of your Globe were accessible as in the Wyer-Globe specified in Prob. 1. Therefore when you would make an East or West Dyal or a Polar Dyal Provide a square Board as A B C D draw the straight line e f upon it Parallel to the sides A C and B D. and just in the middle between them Cross this straight line at Right Angles with another straight line as g h quite through the Board Upon this Board with a little Pitch or Wax fasten the Semi-Circle of Position so as both the Poles thereof may ly in the line g h and the middle of the Semi-Circle marked co may ly upon the line e f so shall i be the Center of the Semi-circle of Position In this Center make a smal hole through the Board fit to receive a Wyer or a Nail So may you with this Circle of Position thus fitted and the side C D applyed to a line of
Contingence elevated to the Height of the Equinoctial draw line from the Center through every 15 degrees of the Circle of Position and by continuing them intersect the line of Contiâ—gence in the points from whence the Hour lines of an East or West Dyal is to be drawn Example But because in our Latitude the Sun Rises before 4. in the Morning therefore two Hour-lines are yet wanting viz. 5 and 4 which I may find either by applying the thred first to 15 and next to 30 degrees from 0 towards g in the Semi-Circle and so marking where it cuts the Contingent line as before Or else by transfering the distance of the same number of Hour lines from the 6 a clock line already drawn on the side e 〈◊〉 to the side e g as in Prob. 2. of this Book is more fully shewed Having thus marked out on the Contingent line the distances of each Hour I draw a line Parallel to the Contingent line and draw lines from every Hour markt on the Contingent to cross the Contingent line at Right Angles and continue each line to the line Parallel to the Contingent and these lines shall be the Hour lines of an East Plane To these Hour-lines I set Figures as in the Scheam may be seen The Style D K of this Dyal as well as of others must stand Parallel to the Axis of the World it must be also Parallel to all the Hour lines and stand directly over the 6 a clock line and that so high as is the distance between the Center of the Semi-Circle of Position and the point where the 6 a clock line cuts the Contingent line Or which is all one at such a height as when it is laid flat down upon the Plane it may just reach the 3 a clock line PROB. VII To make an Erect Direct West Dyal AN Erect Direct West Dyal is the same in all respects with an Erect Direct East Dyal Only as the East shews the Fore-noon Hours the West shews the After-noon Hours Thus if you should draw the East Dyal on any transparent Plane as on Glass Horn or an Oyled Paper on the one side will appear an East Dyal and on the other a West Only the Figures as was said before must be changed for that which in the East Dyal is 11 in the West must be 1 that which in the East Dyal is 10 in the West must be 2 that which in the East Dyal is 9 in the West must be 3. c. PROB. VIII To make a Polar Dyal POlar Dyals are Horizontal Dyals under the Equinoctial They are of the same kind with East and West Dyals Only whereas East and West Dyals have but the Hour lines of half the longest Day discribed on them these have all the Hour lines of the whole Day and are marked on both sides the Noon line as in the following Figure The Style of this Dyal must stand over the Noon line Parallel to the Plane for then it will also be Parallel to the Axis of the World and its height above the Plane must be the distance between the Center i of the Semi-Circle and the point in the Contingent line cut by the Noon-line But I have inserted the Figure which alone is sufficient Instructions PROB. IX To make Erect South Dyals Declining Eastwards or Westwards DRaw on your Plane an Horizontal line and on it discribe a Semi-Circle as you were taught in Prob 4. Then Rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to the degree of Declination from the East or West point according is your Declination is Eastwards or Westwards for then the Quadrant of Altitude shall represent a Plane declining from the South Eâ—stwards or Westwards accordingly Then tuâ—n the Globe Eastwards till the Index of the Hour-Circle points to all the Hours before Noon and examine in what number of degrees from the Zenith the Colure cuts the Qâ—â—drant of Altitude when the Index points to each Hour For a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B which is the 12 a clock line towards Con the Plane shall be the same Hour-lines the Index points at Example I would make an Erect Dyal declining from the South towards the East 27. degrees The Globe Quadrant of Altitude Vernal Colure and Hour Index Rectified as before I bring the lower end of the Quadrant of Altitude to 27. degrees counted from the East point of the Horizon towards the North Then I turn the Globe East-wards till the Index points to 11 a clock or till 15. deg of the Equator pass through the Meridian and find the Colure cut the Quadrant of Altitude in 9.43 counted from the Zenith 10 19.0 9 25.57 8 35.10 7 45.56 6 60.15 5 79.45 And these are the distances of the Fore-noon Hour-lines which I seek in the West side of the Plane viz. from B towards C and through these distances I draw lines from the Center and these lines shall be the Fore-noon Hour-lines Now herein is a difference between Declining Dyals and Direct Dyals For having found the distances of the Hour lines for one half of the Day be it either for Before Noon or After Noon in a Direct Dyal you have also found the distances for the other half Day because as was said Prob. 3. Equal number of Hours have equal distance from the Noon line But in Declining Dyals it is not so Because the Sun remaining longer upon that side of the Plane which it declines to then it doth upon the contrary side there will be a greater number of Hour lines upon it and by consequence the distance of the Hour lines less then on the contrary side of the Plane Therefore for finding the After Noon Hour lines I turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to that degree of Declination that the Quadrant of Altitude was placed at when I sought the Fore Noon Hour lines viz to 27. degrees counted â—om the West towards the South and bring the Verâ—al Colure again to the Meridian and the Index as before to 12. Then turning the Globe Westwards till the Index poinâ—s to 1 a clock or till 15 degr of the Equator pass through the Meridian I find the Colure cut the Quadrant of Altitude in 11.20 counted from the Zenith 2 26.47 3 49.20 4 75.52 And these are the distances of the After Noon Hour lines which distaâ—â—â—â— I seek in the East side of the Plane viz. from B towards D as before and so drawing lines from the Center A through these distances I have all the Afternoon Hour lines also drawn on my Plane You may note that this Plane is capable to receive no more Hour lines After Noon then 4. for when the Colure goes off the Quadrant of Altitude the Sun goes
minutes Then to find all the Fore Noon Hour lines I turn the Globe East-wards till the Index points to 11 a clock or till 15 degr of the Equator pass through the Meridian and find the Colure cut the Gnomonical Semi-Circle in 15. 8 counted from the middle of the Gnomonical Semi Circle 10 18. 56 9 22. 37 8 26. 52 7 32. 37 6 42. 5 5 62. 43 And these are the distances of the Fore Noon Hour lines to which distances you may set Pricks on the West side the Semi Circle of the Plane viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian and the Index of the Hour Circle to 12. for then turning the Globe Westwaâ—s till the Index points to 1 a clock or till 15 degr of the Equator pass throug the Meridian I find the Colure cut the Gnomon Semi-Circle in 5. 45 counted from the middle of the Gnomon Semi-Circle 2 2. 54 3 20. 52 4 64. 36 Having drawn the Hour-lines I remove the Quadrant of Altitude to the degree of the Horizon opposite to the degree it was at before viz. to 30. degrees from the South Westwards which is so much as the Plane declines Eastwards But I let the Gnomonical Semi Circle stand as it did And turning about the Globe till the Colure cut the Quadrant of Altitude in 20. degrees counted from the Horizon upwards viz. the degrees of Reclination I find 18. degrees 40. minutes contained between the middle of the Gnomonical Semi Circle and the Brasen Meridian which is the distance of the Substyle from the Perpendicular And I find the Gnomonical Semi Circle cut the Colure in 13. degrees 49. minutes from the Pole which is the Height that the Style must be raised over the Substyle Therefore I prick off in the Semi Circle on the Plane the distance of the Substyle 18. degrees 40. minutes from the Perpendicular Westwards because this Plane declines Eastwards And from the Center A I draw through that prick the line A E which shall be the Substyle and from this Substyle either way I count in the Semi Circle on the Plane 13 degrees 49. minutes and there make a Prick Then from the Center A I draw through that Prick the line A F to represent the Style or Gnomon Then I let fall the Perpendiculer F G upon the Substyle A G So is a Triangle made which if it be erected Perpendicularly upon the Substyle A G the Style A F shall be Parallel to the Axis of the World and cast a shadow upon the Hour of the Day Having made this Dyal you have made four several Dyals whereof this is one And his opposite viz. North Declining Westwards 30. degrees Inclining to the Horizon 70. degrees is another The South Declining Westwards 30. degrees Reclining from the Zenith 20. degrees is another And his opposite viz. North Declining Eastwards 30. degrees Inclining to the Horizon 70. degrees is the other PROB. XIII To make a Dyal upon a Declining Inclining Plane THe Precepts for making these Dyals are delivered in the foregoing Probleme Therefore we shall at first come to an Example I would make a Dyal upon a Plane in Londons Latitude Declining from the South Westwards 25. degrees and Inclining towards the Horizon by the space of an Arch containing 14. degrees Having first discribed on the Plane a Semi Circle as was directed Prob. 4. I rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to the degree of the Planes Declination viz. to 25. degrees counted from the South Westwards and the ends of the Gnomonical Semi Circle to the degree of Azimuth the Plane lies in viz. to 25. degrees from the West Northwards and the middle of the Gnomonical Semi Circle to the degree of the Planes Inclination viz. 14. degrees counted from the Zenith downwards on the Quadrant of Altitude Then counting the degrees of the Gnomonical Semi Circle contained between the middle of the same and the Brasen Meridian I find 5. degrees 30. minutes These 5. degrees 30. minutes shews the distance of the 12 a clock line from the Perpendicular Therefore I number in the Semi Circle discribed on the Plane from the Perpendicular Westwards Because the middle of the Gnomonical Semi Circle lies Westwards on the Globe from the Meridian And for finding all the Fore-Noon Hour-distances I turn the Globe East-wards till the Index points to 11 a clock or till 15 degr of the Equa pass throug the Meridian and find the Colure cut the Gnomon Semi-Circle in 20. 5 counted from the middle of the Gnomon Semi-Circle 10 36. 57 9 56. 24 8 76. 31 And these are the distances of all the Fore Noon Hour lines to which several distances I make pricks on the West side the Semi Circle on the Plane viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian and the Index of the Hour Circle to 12. For then turning the Globe Westwards till the Index points to 1 a clock or till 15. degrees of the Equator pass through the Meridian I find the Colure cut the Gnomonical Semi-Circle in 6. 20 counted from the middle of the Gnomonical Semi Circle 2 18. 2 3 28. 45 4 39. 56 5 52. 30 6 67. 19 7 84. 13 And these are the distances of the After Noon Hour lines which I also prick down at their respective distances from the Perpendicular Eastwards viz. from B towards D on the Plane and by drawing lines from the Center A through all the Pricks I have all the Hour lines that this Plane will admit of Having made this Dyal you have also four Dyals made as well as in the former Probleme For this is one and its opposite viz. North declining Eastwards 25. degrees Reclining 76. degrees is another The South declining Eastwards 25. degrees inclining 14 degrees is another and its opposite viz. North declining Westwards 25. degrees Reclining 76. degrees is another PROB. XIV To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal shall be Horizontal IT was said in the Preface that all manner of Planes however scituate are Parallel to some Country or other on the Earth Therefore all manner of Planes are indeed Horizontal Planes and the distances of the Hour lines to be â—â—scribed on them may be found as the distances of the Hour lines of the Horizontal Dyal in Prob. 3. It rests now to learn in what place of the Earth any Plane that is not Horizontal in your Habitation shall become Horizontal And for help of your understanding herein Take these following Rules 1. If your Plane be Erect Direct North or South it shall be an Horizontal in the same Longitude at 90. degrees distance on the Meridian counted from the Zenith of your Place through the Equinoctial See an Example of this
in Prob. 3. where I have reduced an Erect Dyrect Dyal to an Horizontal Thus an Erect Plane under the Pole is an Horizontal under the Equator and an Erect Direct in 80. degrees North Latitude is in the same Longitude an Horizontal at 10. degrees South Latitude An Erect Direct in 70. degrees North Latitude is in the same Longitude an Horizontal at 20. degrees South Latitude and so to any other degrees of Latitude as aforesaid till you come to 45. degrees Latitude where an Erect is an Horizontal and an Horizontal an Erect Only as the Hour lines of the Horizontal being 〈◊〉 downwards are numbred from the right hand towards the left in the Erect Direct Dyal they are numbred from the left hand towards the Right 2. If your Plaâ—â— be Erect Declining it shall be an Horizontal Plane at that point on the Globe which is against the degree of Declination found in the Horizon But note If your Plane declines Westwards the Sun comes sooner to the Meridian of it then to the Meridian of the Place where it becomes an Horizontal Plane and that by so many Hours or minutes as the degrees of the difference of Longitude between the two Places converted into Time amounts to If it declines Eastwards the Sun comes so much later to the Meridian of it And for this Cause though the making this Dyal be the same with an Horizontal Dyal for another Place yet in Respect of Time there will be a difference between them Example I would make the South Dyal Declining East 27. degrees as in Prob. 9. by the Plane of the Horizon First I seek in what Place of the Earth it shall become an Horizontal Plane Thus I Elevate the Pole of the Globe 51½ degrees above the Horizon and bring the Vernal Colure to the Meridian then I count from the South point in the Horizon Eastwards 27. degrees and on the point on the Globe directly against those 27. degrees I make a prick for the Place where a Plane that declines 27. degrees from the South Eastwards at London shall be Horizontal or which is all one this Declining Plane at London shall ly in the Horizon of that Prick This Prick for distinction sake we shall hereafter call the Horizontal Place Then by Prob. 1. of the Second Book I examine the Latitude and Longitude of this Horizontal Place and find Latitude 33. 40. South and Longitude from the Colure 33. degrees which is the difference of Longitude between London and the Horizontal Place which being converted into Time by allowing for every 15. degrees 1. hour of Time gives 2 hours 12. minutes that the Sun comes sooner to the Meridian of the Horizontal Place then to the Meridian of the Plane at London so that when it is 12 a clock there it will be but 9. a clock 48. minutes here when 12 a clock here it will be 2 a clock 12. minutes There c. Having thus found in what Longitude from London and Latitude this Plane is Parallel to the Horizon I seek the distances of the Hour-lines upon the Planes of the Horizon Thus I Elevate the Pole of the Globe to the Height of the Pole in the Horizontal Place viz. 33. degrees 40 minutes and bring the Horizontal Place on the Globe to the Meridian and the Index of the Hour Circle to 12. Then I examine the degree of the Horizon the Colare cuts and find it 19¾ from the South Westwards This 19¾ degrees respresents the Meridian line of the Horizontal Place And also the Substylar line here at London Therefore this 19¾ degrees I count from the Perpendicular A B of the Plane and from the Center A draw the line A G through them Because from this line on the Plane all the Hour lines must be numbred and not as all along hitherto from the Perpendicular of the Plane Then turning the Globe East-wards till the Index of the Hour Circle points to 11 a clock or till 15. degr of the Equator pass through the Meridian I find the Colure cut the Horizon in 10. 2 from the Meridian 10 0. 45 9 6. 12 8 15. 25 7 26. 11 6 40. 30 5 60. 0 And these are the distances of the Forenoon Hour lines which distances I transfer by pricks to the Plane But as in Prob. 9. I sought the distances from the Perpendicular on the Plane so now in this Case as was said before I seek them from the Substyle and through these pricks I draw lines from the Center as in other Dyals and these lines shall be the Fore Noon Hour lines To find the Afternoon Hour distances I bring the Horizontal Place on the Globe again to the Meridian and the Index of the Hour Circle to 12. and turning the Globe Westwards till the Index points to 1 a clock or till 15 degr of the Equator pass through the Meridian I find the Colure cut the Horizon iâ— 31. 5 counted from the Meridian 2 46. 32 3 68. 5 4 95. 37 And these are the distances of all the Afternoon Hour lines which I also transfer to the Plane counting them from the Substyle and draw lines from the Center A through these distances and these lines shall be all the Afternoon Hour lines Then from the Substyle I count the degrees and minutes of the Latitude of the Horizontal Place viz. 33. degrees 40. minutes and through these degrees and minutes I draw the line A F from the Center A for the Style Then from the Style I let fall the Perpendicular F G upon the Substyle so is there a Triangle made which if it be erected Perpendicularly upon the Substyle A G the Style A F shall be Parallel to the Axis of the World and cast a shadow upon the Hour of the Day 3. If your Plane be a Direct Recliner Seek in the Longitude of your Place the Complement to 90. of your Planes Reclination For there a Direct Recliner becomes an Horizontal Plane 4. If your Plane be a Declining Recliner The Globe and Quadrant of Altitude Rectified Bring your Habitation on the Terrestrial Globe to the Meridian and the Quadrant of Altitude to the Declination as by the second Rule in this Probleme and count upwards on the Quadrant of Altitude the Reclination and there make a prick on the Globe by the side of the Quadrant of Altitude for at that prick on the Globe the Declining Recliner shall become an Horizontal Plane Then examine the Latitude of that prick as by Prob. 1. of the second Book and the difference of Longitude as by Prob. 9. of the third Book And convert the difference of Longitude into Time by allowing for every 15. degrees 1. hour Time for every degree 4 minutes Time and so proportionably so shall you know what Hours and Minutes the Sun comes sooner or later to the Meridian of your Habitation then to the Meridian of that Place where it becomes an Horizontal Plane Sooner if the Globe were turned Eastwards but Later if it were turned
Thus The 1 a clock Hour-line 11.40 whose Complement 90. is 78.20 2 24.15 65.45 3 38.4 51.56 4 53.36 36.24 I measure in a Quadrant of the same Radius with those arches already drawn from the Equinoctial line for the 1 a clock Hour 78.20 2 65.45 3 51.56 4 36.24 and transfer these distances to the Arches drawn on the Ceeling For then straight lines drawn through the mark in the Arch and through the mark in the Equator and prolonged both waies to a convenient length shall be the several Hour-lines a foresaid And when the Sun shines upon the Glass at Nodus its Beams shall reflect upon the Hour of the Day PROB. XVI To make a Dyal upon a solid Ball or Globe that shall shew the Hour of the Day without a Gnomon THe Equinoctial of this Globe or which is all one the middle line must be divided into 24 equal parts and marked with 1 2 3 4 c to 12. and then beginning again with 1 2 3 c. to 12. Then if you Elevate one of the Poles so many degrees above an Horizontal line as the Pole of the World is Elevated above the Horizon in your Habitation and place one of the 12 s directly to behold the North and the other to behold the South when the Sun shines on it the Globe will be divided into two halfs the one enlightened with the Sun-shine and the other shadowed and where the enlightned half is parted from the shadowed half there you shall find in the Equinoctial the Hour of the Day and that on two places on the Ball because the Equinoctial is cut in two opposite points by the light of the Sun A Dyal of this fort was made by M r John Lâ—â—k and set up on a Composite Columne at Leaden Hall Corner in London in the Majoralty of S r John Dethick Knight The Figure whereof I have inserted because it is a pretty peece of Ingenuity and may perhaps stand some Lover of Arâ— in stead either for Imitation or help of Invention PROB. XVII To make a Dyal upon a Glass Globe whose Axis shall cast a shadow upon the Hour of the Day FIrst divide the Equinoctial of your Globe into 24 equal parts and having a Semi-Circle cut out of some Brass plate or thin Wood to the same Diameter your Globe is of or a very little wider Apply this Semi-Circle to the Globe so as the upper edge of each end of the Semi Circle may touch the Poles of the Globe and the middle of the Semi Circle may at the same edge cut through some division made in the Equinoctial for then a line drawn by the edge of the Semi Circle thus posited shall be a Meridian line The same way you must draw Meridian lines through every division of the Equinoctial and set figures to them beginning with 1 2 3 4 c. to 12 and then beginning again with 1 2 3 4 c. to 12 again This Globe being made of Glass and having an Axis of Wyer passing through â—t from Pole to Pole will be an Horizontal Dyal all the World over if its Axis be set Parallel to the Axis of the World in the same Place and one of the Meridians marked 12 be set so as it may directly behold the North point in Heaven and the other the South point in Heaven for then the Axis of the Globe shall cast a shadow upon the Hour of the Day And if you divide the upper half of the Glass Globe from the under half when the Axis stands Parallel to the Axis of the World by a Circle drawn round about the Globe that Circle shall represent the Horizon and the Meridian lines drawn on the Globe shall be the Hour lines and have in the Horizontal Circle the same distance from the 12 a clock line that the same respective Hour line was found to have as by Prob. 3. of this Book But because the shadow of this Axis will not be discerned through the Glass Body therefore you may with Water and white Lead ground together lay a Ground on the Inside of the under half of the Glass to the Horizontal Circle as Looking-glass makers do their Looking Glasses with Tinfoil for then the shadow will appear Such a Glass Globe Dyal hath the Lord Robert Titchborn standing in his Garden supported by Atlas The End of the Fifth Book The Sixth BOOK Shewing the Practical Use of the GLOBES Applying them to the Solution of Spherical Triangles PRAEFACE THe Solution of Spherical Triangles is to know the length of its Sides and the width of its Angles These have already by many learned Men been taught to be performed by a Canon of Sines and Tangents and also by many Instruments some serving as Tables of Sines and Tangents such as are the Sectors Scales the Spiral line c. and others serving to represent the Globe such as be the Mathematical Jewel Astrolabium Catholicum and several other Projections of the Sphear But none hath as yet taught the Solution of Spherical Triangles by the Globe it self though it be the most natural and most demonstrative way of all and indeed ought first to be learnt before the Learner enters upon any other way To this Authors of Trigonometry agree for the most of them in their Books give Caution that the Learner be already sufficiently grounded in the Principles of the Globe For those Lines or Circles which either in Tables or other Instuments your force your Imagination to conceive represents your Line or Circle in question those Lines and Circles I say you have Actually and Naturally discribed on the Globe and therefore may at a single Operation or perhaps only by a sudden inspection have an Answer annexed according as the nature of your Question shall require and that more Copiously then by Tables of Sines and Tangents For therein you find but one Question at once resolved but by the Globe you have alwaies two resolved together Of the Parts and Kindes of Spherical Triangles THEOREMS 1. ALL Spherical Triangles are made of six parts Three Sides and three Angles The Sides are joyned together at the Angles and measured by degrees of a Great Circle from one end to the other The Angles are the distance of the two joyned sides and they are also measured by an Arch of a Circle discribed on the Angular point If any three of these parts be known the rest may be found 2. All Spherical Triangles are either Right Angled or Oblique Angled A Right Angle contains 90. degrees An Oblique Angle either more or less 3. If a Spherical Triangle have one or more Right Angles it is called a Right Angled Spherical Triangle But if it have no Right Angle it is called an Oblique Angled Spherical Triangle 4. If an Oblique Spherical Triangle have one Angle greater then a Right Angle it is called an Obtuse Angled Spherical Triangle But if it have no Angle greater it is called an Accute Angled Spherical Triangle 5. In Right
Science partly to the Gods themselves and partly to ancient Hero's which Achilles Tatius seasonably alluding unto introduceth old Aeschylus attributing to God that He shewed the risings and settings of the Stars and distinguish't Winter Summer and the other Seasons and Ovid Fathers the same wholly upon Jupiter Perque Hiemes Aestusque in aequales Autumnos Et breve Ver spatijs exegit quatuor Annum Besides it is in the Fiction that Jupiter took his Father Saturn bound him and precipitated him into Hell Now this seems to intimate that Jupiter having imposed his own name upon one of the most eminent and illustrious of the Planets gave that of his Father to another of them that was more remote situate in the deepest part of the Aetherial spaces and of the slowest progress though all this while we are not ignorant that those names were fixed upon those Planets a long time after since more anciently the Planet Jupiter was called Phaeton and that of Saturn Phoenon For we may collect very neer as much from Lucian who by Tartarus understands the immense Altitude or Profunditie of the Aetherial Region so denies that Saturn was either exil'd by Jupiter into Hell or cast into bonds as common heads were perswaded to beleeve As for Hyperion Diodorus hath a tradition that he being of the progeny of old Coelus demonstrated the courses of the Sun and Moon and therefore called the Sun Helios after the name of his Sonne and the Moon Selene after that of his Daughter Last of all comes Japetus who also was the Sonne of Coelus but performed nothing worthy commendation in the advance of his Fathers Speculations but Promotheus whom he begat was therefore imagined to have been chained on the hill Caueasus and to have his heart perpetually torn by a hungry Eagle or Vultur Because as Servius expounds the riddle with restless care and solicitude of mind he constantly excruciated himself with observing the Stars and studying their Ascensions and Declinations We shall not insist upon what follows in the same Author namely that this Prometheus was the first who introduced Astrology to the Assyrians not far from Caucasus it being more usefull for us now to observe that He was imagined to have stolen Fire from Heaven for the inanimation of Man for no other reason but because he infused this Heavenfetch't Knowledge into the breasts of men and inflamed their souls with the desire and love thereof For as to the remainder for as much as Belus was the same with Jupiter among the Assyrians as Diodorus testifies it is He rather who was accounted both the most sacred of their Dieties and the Inventor of this Sideral Science as Pliny affirms It is not needfull for us here to examine many other of the ancient Traditions accounted likewise among the Fabulous as in particular the Fable of Phaeton which hath this Mythology that in his life time he had made a considerable progress toward the discovery of the Suns Annual course but dying immaturely he left the Theory thereof imperfect That other of Bellerophon whom Interpreters maintain to have been carried up to Heaven not by a flying horse but a studious and contemplative mind eager in the the quest of Syderal mysteries That of Doedalas who indeed by thâ— same towring speculations as by the artifice of wings mounted up to the Northern part of Heaven while his less ingenious Sonne Icarus falling short in his attempt of imitating his Fathers sublime flight as not so well understanding the demonstrations of the reasons of his Theory flaggd very low in his Studies and fell from the true and apodicticall cognition of Coelestial motions and vicissitudes with many other the like recounted by Lucian as that of Endymion the favourite of the Moon of Tiresias the Prophet c. Yet one thing there is mentioned as well by Lucian as Tatius which we cannot well pass by which falling under the account of Heroicall times seems to come somwhat neer to that which is called Historicall And that is the notable Centention that arose betwixt Atreus and Thyestes about supreme dominion For when by the publike Consent and Vote of the Argives the Kingdom was to be his of the two who should give the most eminent testimony of Science it came to Atreus share to be King because though Thyestes showed them the signe Aries in Heaven for which he was honourd with a golden Ram yet had Aireus declared a thing more excellent while discoursing about the variety of the Suns rising he made it appear that the Sun and the World i. e. the Starry Orb were not carryed the same but quite contrary wayes and consequently that that part of the Heavens which was the West or Occident of the Starry Orb was the very rising or Orient of the Solary Hence that verse of Euripides 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Qui Astrorum enim contrariam ostendi viam To the same times likewise are we to refer the Institution of the Olympick Games by Hercules which after a long interruption were renewed by Iphitus For inasmuch as those sports were instituted for no other end as may be assured from Censorius but that their celebration might put men in mind of that Intercalation of a month and half that was to be made constantly every fourth Year in respect of those four times eleven or 44. Dayes by which the moâ—ion of the Moon anticipated that of the Sun and the four times six hours or one whole Day by which the circuit of the Sun exceded 365 Dayes manifest it is that Hercules could not understand this without having first exactly observed the Motions of Sun and Moon Hither also belongs that which is reported of Orpheus who must needs have attentively observed the seven Planets if it be true as Lucian averrs that he represented their Harmony by his Seven-stringed Harp which the Grecians thereupon designed in Heaven by some Stars that to this Day retain the name of Lyra. So likewise doth what Sophocles saith of Palamedes who pointed out the several Asterisms and particularly 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Vrsum volutam gelâ—dum occasum Canis And lastly what Homer recounts that in those times were well known besides Bootes and the Bear or Wain 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Pleiades atque Hyades roburque ipsum Orionis We have now struggled through the Darkness of Fabulous Times and are advanced as far as to discerne the twilight of Historicall An here the first thing we clearly perceive is that the whole controversy about the Antiquity of Astronomical Observations lies betwixt the Egyptians and the Assirians or Babylonians For as to the Grecians though some have thought they might put in also for a claim to the honour of being the Anthors of this admirable Science yet by the Verdict even of Plato himself they are to lay by the presence of Competition For sayth He the
from Ptolomy himself Further though the motions of Sun and Moon were already in some measure known he yet made that knowledge much more exact For He did not only much correct the Callippick Period formerly spoken of but also having collected a long Series of Eclipses namely from the time of those Babylonish ones in the Dayes of Mardocempades down to those observed by himself for full six hundred Years together and remarking that neither the like Eclipses did return on the same Dayes after the space of every nineteen Years nor that after some recurses of ten Novennales or ten times nine Years any such Eclipses happened at the times supposed and that the cause thereof consisted both in the various Latitude of the Moon and the anticipation of her Nodi or Knotts and her Eccentricicy by reason whereof her motions to her Apogeium were found to be sometimes slower and those to her Perigeium more speedy therefore we say He comprehended and gave Reasons for all these difficulties and composed certain Hypotheses and according to them certain Tables by which he could safely and exactly calculate and predict what Eclipses were to follow how great they were and when And this was it which Pliny remembred when having spoken of Thales and Sulpitius Gallus he comes to mention Hipparchus After these saith He Hipparchus foretold the courses of both Luminaries for six hundred Years to come comprehending the months Dayes and hours of Nations and the Scituations of Places and turns of People his age testifying that he did all these great things only as he was partaker of Natures Councels For it must be that Hipparchus besides the precise times when such or such Eclipses were to be visible to the Horizon of Rhodes or Alexandriâ— pointed forth also some Countries and principal Citties together with the Designation of the Months in use among them as also the very Days and hours when each Eclipse would happen and other praedictions succeding to Rome in the Dayes of Pliny Again it is well worthy our recital that Hipparchus labouring with long desire both to constitute Hypotheses and reduce into Tables the motions of the other Planets or five wandering Stars and yet not being able to furnish himself either from the Egyptians or from his Country men the Grecians with any competent Observations respective to those Planets for while the places of the Fixt Stars remained unknown it was impossible any such could be made and again those he had himself made were of a much shorter time than was requisite for the establishing any thing certain and permanent in that sort He therefore only digested such Observations as he had recorded by him into the best order and method he could devise and so left them for their use and improvement who should come after him in case any were found capable of understanding and advancing them And at length by good fortune it so fell out that those his Observations came into the hands of Ptolomy who comparing them with his own and finding them judicious and exact thereupon first began to erect both Hypotheses and Tables of Motions fit for those Planets yet not without much timerousness and diffidence because his Observations being but few nor of sufficient time he durst not promise himself any certainty of his Tables for any considerable space or number of Years But for more assurance let us hear his own ingenious Confession in that point The Time saith He from whence we have the Observations of the Planets set down is so vastly short in comparison of the greatness of Coelestial vicissitudes as that it renders all predictions that are for any great number of Years to come infirm and uncertain And therefore I judge that Hipparchus that zealous lover of truth considering this difficulty and withall receiving not so many true Obsertions from the Ancients as he bequeath'd to us undertook indeed the business of the Sun and Moon and demonstrated that it might be performed by equal and circular motions yet as for that of the Planets those Commentaries of his which have come into our hands clearly shews that he attempted it not but collecting all his own Observations concerning them together into one order and method for their more commodious use resigned them to the industry of after times having first demonstrated that they were not congruous to those Hypotheses which the Mathematicians of those Dayes made use of And for Others sure I am that either they demonstrated nothing at all or else only attempted the business and left it unfinisht But Hipparchus being eminently knowing in all kinds of learning conceived that he ought not as others had done before him to attempt what he should not be able to accomplish So that we see Ptolomy was the first who from true Observations reduced the Motions of the Planets into Hypotheses and Tables correspondent But before we speak more particularly of him who lived about an hundred and thirty Years after Christ forasmuch as in the space of time betwixt Hipparchus and Ptolomy these studies so florisht at Alexandria as that Julius Caesar returning thence brought along with him that Sosigenes by whose assistance he endeavoured the restitution of the Calendar and so may be thought to have propagated the Study of Astronomy among the Romans let us reflect a little upon that time and see what care they then had of Celestial matters In the first place we are to lay aside the Commemoration of Sulpitius Gallus of whom more then once afore as one that falls not under this account concerning whom we may not yet forget what Cato is induced by Cicero saying While we saw that Gallus dye that familiar friend of thy Father O Scipio who was restless in measuring Heaven and Earth I say while we saw him dying even in that Study How often did Day oppress him when he had set himself to observe and describe somthing in the Night and how often did Night oppress him when he had begun his Speculations in the Morn How was he delighted when he had a long time before predicted to us Eclipses of the Sun and Moon c. For he was a man clearly singular and in an Age when so great ignorance and neglect of good Arts tyrannized over mens minds being himself studious and inquisitive could not but have borrowed his skill either from Egypt or Greece where having obtained a Series of Eclipses and the way of deducing them through the circuit of of nineteen Years as we said afore he became able to calculate them so as Cicero relates For as to the rest how great doe you think was the ignorance and neglect nay even contempt of studies of this nature among the Romans Why truely so great as that Virgil could not dissemble it in the Poesy attributed to Anchisa according to which the Romans should indeed come to rule the World but yet should yeeld to others in learning to know the Stars and describe the Heavens Caelique
meatus Describent radio surgentia sidera dicent And Cato himself is cited by Agellius to have left in writing that it was not lawfull to write what is in a Table kept by the High Preist how often scarcity of Provision would happen how often the light of the Sun or Moon should be darkned so far saith Gellius did Cato contemne the Science of Astronomy and thought it useless either to know or fore-tell the Eclipses of Sun and Moon Furthermore though from times as high as Numa the Romans made several Intercalations yet they took all their art of that Sort from the Greeks and Pliny remarks that in France Spain and Africa there was no one man who could so much as tell the Rising of the Stars Nevertheless we are not to forget that among the Gauls was one Pythias the Philosopher as Cleomedes calls him of Masilia who about the time of Alexander of Macedon found the proportion of the Gnomon to the Solsticial shadow to be the same at Massilta as Strabo tells us Hipparchus had observed it at Byzantium who first attempted the Northern Ocean and discovered the utmost Thule in which Cleomedes cohaerently proves the Summer Tropick to be the same with the Polar or greatest of allwayes apparent ones and who as from his Book de Oceano may be inferred was excedingly curious to find out what was the Position of Heaven respective to the variety of Countries and Climates But not so soon to digress from the Romans Pliny delivers that in those first times of Romes being a Common-wealth the Invention of Dialls was very raw and imperfect for that they had only the risings and settings named out of twelve Tables That after some Years they added the Meridian and by the indication of a certaine columne the last hour nor that neither but only in clear weather even as long as till the first Punick warre Afterward they advanced so far as to make one or two Sun Dialls but not with lines exactly correspondent to the hours untill about an Age after when Q. Marcus Philippus ordered the busi ness more diligently and succesfully And because the hours of the Day remained yet uncertain in dark and cloudy weather Nasica Scipio began to divide the Hours of Day and Night equally by Water distilling from Vessel to Vessel and called it The Diall within Doores in the Year Urbis conditae DXCV. And till then saith Pliny Populi Romani indiscreta lux fuit And thus much of Hipparchus and some Astronomers betwixt him and the Prince of them all Ptolomy And of him so great is his name all we need to say is only that He was the very Founder of the Art or Science of Astronomy For though Hipparchus had indeed as it were hewn out the Stones and Beams fit for so noble a Structure and prepared good part of the Materials yet was it Ptolomy alone who put them into Order and Form and by adding many admirable Inventions of his own by infinite labour and cost erected that so famous Building worthily called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the great Co-ordination Construction or Composition which consisting of no less than thirteen Books contains all the Doctrine that could then be advanced concerning the Sun Moon and aswell the Fixt as wandering Stars And albeit one Day teacheth another and that as Himself had truely foretold there came others after him who saw good cause for the Castigation and Correction of many things delivered in that Work yet in the general the Art he had instituted remained firm and constant and was afterwards imbraced not only by the Alexandrians but also by all the Arabians Latins and others who devoted themselves to the service of Urania ever since For that the Study of her Celestial mysteries continued in great esteem and Veneration at Alexandria for some Ages after his desease may be undeniably attested not only from hence that among others both Theon and Pappus named Alexandrians were eminent therein of which the one put forth eminent Commentaries upon Ptolomies Works and the other among sundry excellent peeces of which his sixth Book of Mathematicall Collections is one observed that about four hundred Years from Christ the Obliquity of the Ecliptick was not so great as Erathosthenes Hipparchus and Ptolomy had conceived but neer upon the same we discover it to be in our Dayes we say that this is not the only Monument that is extant of the flourishing of Astronomy at Alexandria long after Prolomy had given it so great a Reputation there but there remains another as fresh and lively which is the memorialls of those Patriarchs of the Alexandrine Church to whose judgement the determination of that great dispute about the true time of Easter was thought fit to be wholly referred aswell by the Nicene Councel as by divers learned Bishops afterward and by Holy Leo himself then Pope Now among these Patriarchs were Theophilus Cyrillus and Proterius whose advice and directions were thought necessary in regard that the Controversies raised about the Celebration of Easter about the time of the Veneral Equinox about the Full-Moon next following and about constituting certain constant Rules respective to them could not be better composed than by the definitive sentence of these Prelates who Living at Alexandria where Astronomy was in such Height had the advantage of others in point of knowing those things which were requisite to the finding out of the truth But of the Arabians who in the Study of Astronomy succeded the Alexandrians and translated into their own language the Great Composition of Ptolomy which they called Almagestum the First and most worthy to be remembred was Albategnius otherwise called Mahometes Aractensis born of a Family of the Dynastae of Syria He about 800 Years after Christ made divers Celestial Observations partly at Aracta and partly at Antioch and found both that the Apogeium of the Sun since the Dayes of Ptolomy was advanced to the following Signes and that the Stars did regress toward the East one degree not in the space of a hundred Years as Ptolomy also had designed but of somwhat less than seventy as also that the Obliquity of the Ecliptick according to Pappus his Theory was less viz. above 23. degr 35. minutes with many other particulars concerning aswell the Fixt Stars as the Planets whereupon he both corrected Ptolomy in many things and composed new Tables and wrote a Book intituled De Scientia Stellarum After him within 2 or 3 Ages following succeeded Alphraganus Arzachel Almeon and other Arbians among whom as being already tainted with that superstition which had corrupted the simplicity of Astronomy with Astrological Fooleries some certain Jewes as ambitiously affecting the glory of Divination as the others intermixed themselves After them for a long time the Worship of Urania lay neglected nor did Astronomy receive any the least considerable advantage by Observators till neer about four hundred Years
erroneously that little of credit can be attributed unto them California is found to be an Iland though formerly supposed to be part of the main Continent whose North West shoar was imagined to thrust it self forth close to the Coasts of Cathaio and so make the supposed Straits of Anian The Western Shoars of the West Indies are more accurately discribed then formerly as you may see if you compare my Terrestrial Globe with the Journals of the latest Navigators And if you compare them with other Globes you will find 5 6 yea 7 degrees difference in Longitude in most Places of these Coasts Magellanica which heretofore was thought to be part of the South Continent called Terra Incognita is now also found to be an Iland All that Track of Land called Terra Incognita I have purposely omitted because as yet we have no certainty whether it be Sea or Land unless it be of some parts lately found out by the Dutch who having a convenient Port at Bantam in Java have from thence sent forth Ships Southwards where they have found several very large Countries one whereof they have called Hollandia Nova another Zelandia Nova another Anthoni van Diemans Land and divers others some whereof lies near our Antipodes as you may see by my Terrestrial Globe Again Far to the Northwards there are some New Discoveries even within 6. degrees of the Pole The Drafts to the North Eastwards I have laid down even as they were discribed by the Searchers of these Parts for a Passage into the East Indies And also the Discoveries of Baffin Capt. James and Capt. Fox our own Country men that attempted the finding a passage that way into the South Sea I also told you what difference there is in several Authors about placing their first Meridian which is the beginning of Longitude that Ptolomy placed it at the Fortunate Ilands which Mr Hues pag. 4. chap 1. in his Treatise of Globes proves to be the Ilands of Cabo Verde and not those now called the Canary Ilands because in his Time they were the furthest Places of the Discovered World towards the Setting of the Sun Others placed it at Pico in Teneriffa Others at Corvus and Flora because under that Meridian the Compass had no Variation but did then duely respect the North and South Others for the same Reason began their Longitude at St Michaels and others between the Ilands of Flores and Fayal And the Spaniards of late by reason of their great Negotiation in the West Indies have begun their Longitude at Toledo there and contrary to all others account it Westwards Therefore I seeing such diversity among all Nations and as yet a Uniformity at home chose with our own Country men to place my First Meridian at the Ile Gratiosa one of the Iles of the Azores By the different placing of this first Meridian it comes to pass that the Longitude of places are diversly set down in different Tables For those Globes or Maps that have their first Meridian placed to the Eastwards of Gratiosa have all places counted Eastward between the first Mertdian and the Meridian of Gratiosa in fewer degrees of Longitude And those Globes and Maps that have their first Meridian placed to the Westwards have all Places counted Eastwards from the Meridian of Gratiosa and their first Meridian in a greater number of degrees of Longitude and that according as the Arch of Difference is I have annexed a smal Collection out of Dr Hood which declares the Re son why such strange Figures and Forms are pictured on the Caelestial Globe and withall the Poetical Stories of e-every Constellation I also thought good to add at the latter end of this Book a smal Treatise intituled The Antiquity Progress and Augmentation of Astronomy I may without Partiallity give it the Encomium of a Pithy Pleasant and Methodical peece It was written by a Learned Author and is worthy the Perusal of all Ingenuous Lovers of these Studies Joseph Moxon Encomiastic Achrosticon Authoris IT s now since Atlas raign'd thousands of Years OF whom 't is Fabl'd Heavens hee did Uphold SO Ancient Authors write But it appeares EXcell he others did for we are told PRoject he did the Sphear and for his Skil HE had therein his Fame will Flourish still MUst we not also Praise in this our Age OUr Authors skill and Pains who doth ingage X Thousand Thanks not for this Book alone OF his But for the Globes he makes there 's none NOw extant made so perfect This is known The Contents of the First Book Chap. 1. WHat a Globe is fol. 4 2. Of the two Poles 4 3. Of the Axis 4 4. Of the Brazen Meridian 4 5. Of the Horizon 5 6. Of the Quadrant of Altitude 6 7. Of the Hour-Circle and its Index 6 8. Of the Nautical Compass or Box and Needle 7 9. Of the Semi-Circle of Position 7 Chap. 2. Of the Circles Lines c. described upon the superficies of the Globe beginning with the Terrestrial Globe and 7 1. Of the Equator 7 2. Of the Meridians 8 3. Of the Parallels 8 4. Of the Ecliptique Tropicks and Polar Circles 8 5. Of the Rhumbs 9 6. Of the Lands Seas Ilands c. Discribed upon the Terrestrial Globe 9 7. Longitude 10 8. Latitude 11 Chap. 3. Of the Celestial Globe or the Eighth Sphear represented by the Celestial Globe its motion and of the Circles Lines Images Stars c. described thereon 11 1. Of the eight Sphear 11 2. Of the Motion of the eighth Sphear 12 3. Of the Equinoctial 13 4. Of the Ecliptick 15 5. Of the Poles of the Ecliptick 15 6. Of the Axis of the Ecliptick 16 7. Of the Colures and Cardinal Points 16 8. Of the Tropick fol. 16 9. Of the Circles Arctick and Antarctick 17 10. Of the Images called Constellations drawn upon the Celestial Globe 17 11. Of the number of the Stars 19 12. Of the Scituation of the Stars 20 13. Of the Magnitudes of the Stars 20 The proportion of the Diameters of the fixed Stars Compared with the Diameter of the Earth 21 The proportions of the fixed Stars Compared with the Globe of the Earth 22 14. Of the Nature of the Stars 23 15. Of Via Lactea or the Milky way 23 The Contents Of the Second Book Prob. 1. SOme Advertisements in Choosing and Using the Globes 35 To find the Longitude and Latitude of Places on the Terrestrial Globe fol. 37 Prob. 2. The Longitude and Latitude being known to Rectifie the Globe fit for use 38 Prob. 3. To find the Place of the Sun in the Ecliptick the day of the Moneth being first known 39 Prob. 4. To find the Day of the Moneth the Place of the Sun being given 40 Prob. 5. The Place of the Sun given to find its Declination 40 Prob. 6. The Place of the Sun given to find us Meridian Altitude 41 Prob. 7. The Suns Place given to find the Hour of Sun Rising and the length of