Meridians of the Mater and shall be so divided by the Parallels of the Mater as the Meridians are divided by them But my advice is that you divide your Ecliptique the first way and you may use this for proof of your work at last 3 The rest of the lineaments of the Reet are the Azimuths to be drawn as the Meridians of the Mater and the Almicanters to be drawn as the Parallels Onely you shall need to draw but half the Almicanters and the Azimuths but half way leaving one half of your Reet viz. E C B D blank and void of them In drawing these Azimuths and Almicanters you shall be carefull to skip over the border of the Ecliptique leaving it fair that the graduations thereof with their figures set to every tenth degr and the characters of the Signes may be more distinctly seen Also you shall do well if you make a border to the Axtree line on the Northside that is toward D and let this border be of the same breadth from A to B the breadth not exceeding one fifth of an inch in a Reet of a foot Diameter upon which border you may make a scale of degrees setting figuresin it to every tenth Almicanter This will be a great strength and Ornament to your Reet Below the Horizon C D likewise you shall make a Limb or border for the Horizon to receive his graduations this may be a quarter or three tenths of an inch broad where the Reet is a foot in Diameter and upon this border you shall set figures at every tenth Azimuths and shall number them both wayes from the Center and from the Meridian 4 You shall inscribe so many of the fixed Stars as your Reet may well receive Which to do you must know their Right Ascensions or Culminations and also their Declinations for which purpose I have given you a Table of 110 of the more notable fixed Stars which may best be inserted in your Reet with their Right Ascensions and Declinations calculated to the year of our Lord 1671. which may serve for 40 years before and after without any considerable error To inscribe them you shall first number the Right Ascension of the Star from ♈ 0 that is from D upon the Limb of the Reet toward B and at the end of that number fix your Label which by this time should be made and pinned on the Center then from the Limb count inwards upon the Label the Stars Declination and at the end of that number make a prick in your Reet close to the edge of the Label there is the Stars place Then with your Graver you shall make there the shape of a Star with 4 5 or 6 points according as the magnitude of the Star deserves and let one point be longer then the rest and let it point outward from the Center if the Stars Declination be North but inward toward the Center if his Declination be South and let the end of his long point called Apex be in the very true place of the Star But if your Label be yet unmade then take the measure of the Stars Declination with your Compasses upon any of the four Semidiameters of the Reet measuring it from the Limb inwards then lay a ruler from the Center to the Right Ascention of the Star and where the ruler cuts the Limb of the Reet there set one foot of your Compasses opened as before and with the other make a prick toward the Center close to the edge of your ruler and there is the Stars place in your Reet 5 Lastly you shall cut out all the spaces of this Reet which may be spared remembring alwaies that you leave uncut the borders of the Ecliptique Horizon and Axtree line and be very carefull that you cut not into the Center of your Reet but leave breadth sufficient about the Center to hold the Center-pin which must joyn Mater Reet and Label together This remembred you shall cut out two third parts of the spaces of the Almicanters beginning from the Horizon C D and cutting out the breadth of two degrees after which you shall leave the breadth of one degree and then cut our again the breadth of two degrees and so forward But for the greater strength and ornament of your Reet and for ease in numbring the Azimuths you shall at every 15th Azimuth leave a string of the breadth of one degree whole from the Horizon to the Pole A or at every thirtieth Azimuth leave such a string going quite through and at every other fifteenth the string may be cut off when it comes within ten degr of the Pole because there the spaces of the Azimuths be very narrow and close together And where among those Almicanters and Azimuths you have any Star you must contrive to leave him standing and to set by him his name or some figure by which you may know him again But you are to content your self with four Stars on this side the Horizon because you will want convenient room On the other side you may have more and room also to writ their names upon strings or branches left for that purpose which you may contrive into some voluntary lettess-work wherein you shall not much regard uniformity of the Quadrants but to make the Reet as open as you can provided you leave it of sufficient strength Paste this on fol. 17. so as it may by open while the first 7. Chapters are reading To cut out the Reet in pastbord is much easier if you be provided of sharp knives and chesills fitted for your purpose A Table of the Right Ascensions and Declinations of 110 of the more notable fixed Stars calculated from Tycho his Tables rectified for the year of our Lord 1671.  As mi. D. mi.   Andromeda her Head 357. 54. 27. 18. N. 2. Mirach Girdle 12. 49. 33. 55. N. 2. Foot Alamath 25. 57 40. 44. N. 2. Perseus his side Algenib 44. 16. 48. 36. N. 2. Meadusaes head Algol 41. 46. 39. 39. N. 3. Henerichus right shoulder 85. 53. 44. 56. N. 2. Left shoulder Alhabot 73. 07. 45. 37. N. 1. Left elbow 69. 29. 43. 15. N. 4. The Kids 69. 57. 40. 33. N. 4. The Kids 70. 51. 40. 42. N. 4. The great Wain The Wheels 160. 18. 58. 08. N 2. The great Wain The Wheels 160. 48. 63. 32. N 2. The great Wain The Wheels 173. 59. 55. 33. N 2. The great Wain The Wheels 179. 48. 58. 51. N 2. The Horses 189. 53. 57. 47. N. 2. The Horses 197. 37. 56. 41. N. 2. The Horses 203. 37. 51. 00. N. 2. The little rain the Pole Star 07. 53. 87. 34. N. 2. Last Wheel 231. 14. 73. 15. N 3. Dragons tongue 254. 36. 54. 55. N. 4. Head first 260. 46. 52. 34. N. 3. Head last Ras Aben. 267. 15. 51. 36. N. 3. Tail 167. 15. 71. 05. N. 3. Bootes Arcturus 210. 13. 20. 58. N. 1. Engonasi's Head 254. 12. 14. 50. N. 3 Ophiucus Head 259. 55.
Projection The Concurrent Circles meeting in the Poles A and B are Meridians Those Meridians are 180 in number and divide the Equator C D into 360. degrees because every one of them cutteth it twice that is once in each Hemisphear By these are numbred the Right Ascensions of the Stars and Planets and the hours and minutes of Day and Night for every 15 of these Meridians numbred from the Limb is an hour Circle as hath been shewed Book 1.6 they are numbred from D to C that is from Septentrio to Meridies 1.2.3 c. for the Morning hours and back again from C to D in like manner for the Afternoon the Axeltree line A B falling out to be the six a clock line both ways By those Meridians also are numbred the Longitudes of Towns and Countries in Geography The Circles or Semicircles crossing these Meridians are the Parallels of Declination they are lesser Circles whose propertie it is to divide the Sphear into unequal parts In the midst of them lies the Equator C D being here a straight line and cutting the Axtree-line A B at Right Angles in the Center E the Parallels are greatest near the Equator and from thence they lessen toward the Poles they are 180 in number i. e. 90 on each side the Equator save that the two extream Parallels are reduced to two points in the Poles By these Parallels are numbred the Declinations of the Stars in Astronomie and the Latitudes of Towns and Countries in Geography And this name and use have the Circles of the Mater always in the Meridional Projection The Ecliptick always standeth for it self when it is used which is onely in the first Mode of this Projection But the Circles of the Reet have divers names and uses in the divers Modes of this Projection which here follow 1 The first mode of the Meridional Projection The point A of the Reet in which the Concurrent Arches meet is called the Vertex of the Reet Set the Vertex of the Reet to the Latitude of your place so shall the Vertex be Zenith and the Concurrent Arches there meeting shall be Azimuths called also Vertical Circles and Circles of Position passing from Zenith to Nadir and dividing the Horizon into 360 degr as the Meridians on the Mater pass from Pole to Pole and divide the Equinoctial The Semicircles crossing these Azimuths shall be Almicanters or Circles of Altitude The Diameter crossing the Axeltree of the Reet at Right Angles shall be the Horizon or Finiter whose Graduations are set to him in a border below the Center and from him are the Almicanters reckoned upward to the Zenith The Azimuths may be reckoned from the North or South Semicircles of the Meridian or from the Axtree line of the Reet which is the East or West Azimuth commonly called the Prime Vertical When I bid you set the Vertex of the Reet to the Latitude of your place you must first know what your Latitude is It is the nearest distance of your place from the Terrestrial Equinoctial numbred in degrees and minutes of a great Circle The Latitude of London is 31 degr 32 min. North. The Latitude of Ecton or Northampton is 52 degr 15 minutes or very near And how to get the Latitude of those or any other place shall be shewed Book 4.11 The Latitude had number the degrees thereof upon the Ring from C or Meridies where the Equator cutteth the Meridian toward A or Oriens which in this Projection is the North Pole because we in England have North Latitude At the end of this number see for London 51. degrees 32. minutes from the Equator Northward set the Vertex of the Reet so this Vertex representeth the Zenith or point in the Heaven which is just over your head in which point all the Azimuths meet and through which also passeth the Meridian of your place which here is represented by the outmost Circle of the Mater or the innermost Circle of the Ring Now is the upper Semicircle of your Meridian divided into four notable parts From the Zenith Southward to the Equator is the Latitude 51. degrees 32 minutes from thence to the Horizon is the complement of the Latitude 38. degrees 28. minutes making up a Quadrant againe from the Zenith Northerly to the Pole is the complement of Latitude 38. degr 28. minutes as before and from thence to the North of the Horizon is the Elevation of the Pole above your Horizon which is always equall to the Latitude of your place for where in a right Sphear the Polesly in the Horizon and have on Elevation there the Equator passeth through the Zenith and if you go from such a Country Northward till the Pole be Elevated one degree the Equator shall there decline from your Zenith one degree Southward because the Equator keeps always the distance of 90 degrees from the Poles And this distance of the Zenith of your place from the Equator is called by Geographers Latitude and is always equal to the Elevation of your Pole So that it is all one whether you set the Vertex 51. degrees 32. min. above the Equator or set the North point of the Horizon 51. degrees 32. minutes below the North Pole Now the Vertex of the Reet set to the Latitude and consequently the Pole mounted to his due Elevation your Planisphear is in a right mode and posture speedily to resolve all questions concerning the Diurnall motion as the Suns longitude Declination Right Ascension the Ascensionall differences with the Semidiurnall Arch or length of the day the Suns Altitude Azimuth and Amplitude the hour and minute of the day the beginnings endings and duration of twilight and such like and that with so great facility that having onely the Longitude of the Sun with the Ephemeris on the Ring shall give you for asking and therewith either the Altitude Azimuth or Houre one of them you may see all the rest at the first view without changing the posture of your Instrument as shall appear in the fourth book 2 The second Mode of the Meridional Projection Set the Zenith or Vertex of the Reet to the North Pole of the Ecliptick or which is all one set the Horizon line of the Reet in the Ecliptick line of the Mater so the Azimuth shall in this posture become Circles of Longitude and the Almicanters Circles of Latitude And in this Mode your Planisphear is fitted to resolve all Questions of the Longitude Latitude Right Ascension and Declination of the Stars 3 The third Mode of the Meridional Projection Number the Altitude of Culmen Caeli that is the Southing point of the Ecliptick in the Ring from the North Pole toward Meridies if the Ascendant be a North Signe or toward Septentrio if the Ascendant be a South Signe To the end of this numeration palce the Finiter Reckon also upon the Finiter from the Center toward Septentrie the Amplitude of the Ascendant the Meridian cutting there gives you
find in the next rule 2. Another way Mark what is the Right Ascension of the point proposed being counted from the next Equinoctial point as of ♉ 9 degr the Right Ascension is 36.36 min. count so many degrees in the Arctick circle from the Axeltree at the end of this number is the Pole of the Ecliptick Lay the Label to him and you shall make a Quadrantal Triangle whose Sides shall be equal to the Angles of the former Triangle which was made of the Longitude Declination and Right Ascension of the point proposed for the Right Angle you have a Radius or Quadrant of the Axis for the Angle of the greatest Declination between the Equator and Ecliptick 23 ½ you have the arch of a Meridian between the Pole of the Equator and the Pole of the Ecliptick for the angle sought you have the arch of the Label between the Pole of the Ecliptick and the Center 71.20 minutes as before the least angle of this Quadrantal Triangle is at the Center and you shall find his measure in the Limb 14.32 minutes that is the measure of the least Side of the former Triangle viz. the Declination of the point proposed Here you see If the Declination had been given you should have set it in the Limb between the Pole and the Label and so had you made the same Quadrantal Triangle and might have found on the Label between the Arctick Circle and the Center the measure of the angle sought and likewise in the Arctick Circle between the Label and the Axtree-line the Right Aseension though it be more then was required The reason hereof you may learn from Book 3.7 CHAP. X. To find the point of the Ecliptick in which the Longitude and Right Ascension have greatest difference Move the Label on the Polar circle till you find the degrees of the Label between the Polar circle and the Limb to be equal to the degr of the Limb between the Label and the Pole so have you a Rectangled aeqaicrurall Triangle made by the Limb Label and the Meridian 46 ¼ like to that in the second Variety Book 3.10 Here the angle B at the Pole between the 46 ¼ Meridian and the Limb is equal to the Longitude of the point sought 46¼ and either Leg is equal to the Declination thereof 16 ¼ Therefore I conclude that when the Sun is 46 ¼ in Longitude that is in ♉ 16 ¼ then his Longitude hath furthest out run the Right Ascension Subtract now the Right Ascension of ♉ 16 ¼ which is 43 ¾ out of the Longitude 46 ¼ there remains 2 deg ½ which being converted into Time is 10 min. the greatest inequality of Ascension in a Right Sphear CHAP. II. To find the Latitude of your Place or the Elevation of the Pole above your Horizon by the Meridional Altitude and Declination of the Sun Meridional Projection GEographers call the distance of a place from the nearest point of the Equator upon Earth the Latitude of that Place as the Latitude of London is 51 deg 32 min. from the Equator Northward the Latitude of St Thomas Island upon the coast of Africk is 0 deg 0 min. because the middle of that Island lyeth under the Equator And because the Latitude of your Place and the Elevation of the Pole above your Horizon are alwaies equal therefore the Elevation of the Pole is oft called Latitude of the Place or Latitude simply and so for brevity sake we shall often call it But when we speak of the Latitude of the Moon or Stars you must understand Astronomers thereby mean their distance from the neerest point of the Ecliptick To find the Latitude of your Place get the Suns Declination by the 6 or 7th and his Meridian Altitude by the second of this Book Then find the parallel of the Suns Declination North or South as the Declination is and where it toucheth the Limb here Meridian there is the point where you observed the Sun at Noon set the South end of the Finiter so many degr below this point as the Meridian Altitude had then is your Finiter set to your Latitude and you shall find the measure of it between the Equator and the Zenith which is properly the Latitude and the same measure shall you find between the North point of the Finiter and the North Pole where it is more properly called the Elevation of the Pole Example June 20 1651. I observed the Meridian Altitude of the Sun here at Ecton four miles Eastward from Northampton 60 degr 59 min. the Longitude of the Sun was then ♋ 8 degr 19 min. ½ his Declination 23 degr 14 min. Northward Therefore having found in the Limb the point where the Parallel 23 degr 14 min. toucheth above the Equator I put the South end of the Finiter 60 degr 59 min. below that point toward the South Pole which done I see the North Pole Elevated above the Finiter 52 degr 15 min. and the Zenith of my Horizon likewise to be removed from the Equator Northward 52 degr 15 min. which is the Latitude of Ecton Note that you may best observe the Latitude when the Sun is near the Summer Tropick for then you shall not be troubled with Refraction and then the Declination varyeth slowly which varyeth almost one minute every hour near the Equinoctial CHAP. XII To do the same by the Meridian Altitudes of the Stars about the Poles MAny of the Stars near the Northern Pole may be seen with us twice in the Meridian in one Winters Night that is one while above the Pole and 12 hours after again below the Pole As for Example the Pole-star called Alrucabe about December 18 will be in the Meridian above the Pole at 6 of the clock at Night and at 6 next morning he will be in the Meridian below the Pole Observe both the Meridian Altitudes and add them together half that sum is the Elevation of the Pole Example I observed at Ecton the greatest Altitude of the Pole-star to be 54 deg 45 min. and his least Altitude 49 degr 45 min. the sum is 104 deg 30 min. the half 52 degr 15 min. the Latitude of Ecton and here I have gotten also the Pole-stars distance from the Pole and consequently his Declination which is the complement thereof for the Latitude being subducted from the greater Altitude leaves the Stars distance from the Pole 2 degr 30 min. and consequently shewes his Declination to be 87 degr 30 min. which is 39 min. more then Gemma Frisius observed it Anno Dom. 1547. for in our age the Pole-star approcheth about 1 min. nearer the Pole in every 3 years Note that these Stars which are distant from the Pole less then the Latitude and more then the complement thereof have their less Meridian Altitude in the North part of the Meridian and their greater Meridian Altitude in the Southern part of the Meridian beyond the Zenith Wherefore for them you shall take the complement of
the degrees between the Ascendent and Mid-heaven otherwise count from the Defcendent to Mid-heaven Number these degrees on the Label from the Center and where they end make a prick which prick if you put upon the Parallel of the Altitude of Culmen Caeli you shall have in the Limb between the Finitor and the Label the measure of the lesser angle which taken out of 180 degrees leaveth the greater angle This is done by Probleme 2. Rectang And note that the lesser angle and the Altitude of the Nonagesimus gradus be alwayes equal Example March 29. 1652. 10. hours 32. minutes a. m. ♓ 25 ½ was in Culmine the Meridian Altitude thereof is 36. Between Culmen and the Descendent I find 61 ½ therefore I prick the degree 61 ½ from the Center in the Label and when I have turned that prick to the 36. Almicantar the Label shewes in the Limb of the Reet 42 degrees for the lesser angle of the Ecliptique with the Horizon exactly 41. 58 minutes which also is the Altitude of the Nonagesimus gradus the greater angle is 138 degrees 2 minutes Another way In the Equinoctial Projection lay the Label on the Nonagesimus gradus and observe his Declination on the Label and his Horary distance from the Meridian Then in the Meridional Projection and his first mode observe where that Declination and Horary distance meet on the Mater and the Almicantar touching the same point sheweth the Altitude of Nonagesimus gradus which is equal to the angle sought Example In the former Case where ♓ 25 ½ was in our Meridian ♈ 24. was Nonagesimus gradus the Label laid to it shewed me his Declination 9 ½ almost North and his Horary distance from the Meridian in the Limb 26. 20 minutes then the Fimtor being set to the Latitude I seek the Intersection of the 9 ½ Parallel of North Declination with the 26 ⅓ Meridian from the Limb and there toucheth the 42 Almicantar shewing the Altitude of Nonagesimus gradus and the quantity of the lesser angle sought as before And there cometh unasked also the 36 ⅓ Azimuth being the Azmuth of the Nonagesimus gradus which is alwayes equal to the Amplitude of the Ascendent Other wayes See Chapter 56. and 57. CHAP. LVI The Ascendent and his Amplitude and the Altitude of Culmen Caeli given so to represent the Ecliptique that you may presently find not onely the Altitude of the Nonagesimus gradus but the Altitude and Azimuth of every degree of the Ecliptique at one view SEt your Planisphear in the third Mode of the Meridional Projection that is If the Ascendent be a North Signe move the Finitor from Meridies toward the North Pole till the North Pole be elevated above the Finitor according to the elevation of Culmen Caeli but if the Ascendent be a South Signe move the other end of the Finitor from Septentrio toward the North Pole till the Pole have the Elevation of Culmen Caeli Then number the Amplitude of the Ascendent upon the Finitor from the Center to your left hand toward Septentrio and take the Meridian that crosseth there for the Eastern arch of the Ecliptique and his match so much distant from the Axtree towards Meridies shall be the Western arch so do the Azimuths and Almicantars of the Reet shew at once the Altitude and Azimuth of every degree of the Ecliptique Example March 29. 1652. 10. hours 32 min. a. m. I found ♓ 25 ½ Culminating and his Meridian Altitude by Chapter 46 36 degrees the Ascendent ♋ 24. by Chapter 47. and his Amplitude 36 ⅓ by Chapter 15 and 16. the Sun being then Eclipsed in ♈ 19. 11 minutes I would know his Altitude and Azimuth and likewise the Altitude and Azimuth of the Nonagesimus gradus To this purpose I take the North Pole for Culmen and set the Finitor 36. below him toward Meridies and from the Center toward my left hand I number on the Finitor the Amplitude of the Ascendent 36 ⅓ there cuts the twenty third Meridian from the Axis which here serveth for the Eastern arch of the Ecliptique the degree in this Ecliptique here cut by the Finitor is the Ascendent ♋ 24. thence I number in this Ecliptique South-ward 90 degrees by help of the Parallels and so I come to ♈ 24 degrees being the Nonagesimus gradus Here the 42 Almicantar toucheth the Nonagesimus gradus shewing the Altitude thereof and here also cutteth the Azimuth of the Nonagesimus gradus 36 ⅓ equal to the Amplitude of the Ascendent as it is alwayes and ought to be so as that you might have found the Nonagesimus gradus by this Azimuth with less numbring Now for the Sun he is in ♈ 19. 11 minutes that is nearer the Meridian then the Nonagesimus gradus by almost 5. degrees I count therefore 4. 49 minutes for so it is past the Nonagesimus gradus there is the Sun and the Almicantar cutting there shewes his Altitude 41 ⅔ and his Azimuth is shewn by the 29 Azimuth some what near Or if you would reckon after the order of the Signes which is easier begin at the Descendent where is ♑ 24. thence 61 ½ makes ♓ 25 ½ at the Pole for Culmen Caeli thence in the Eastern arch to the Suns place I make 85 degrees 11 minutes and 4.49 minutes further is ♈ 24. the Nonagesimus gradus CHAP. LVII To do the same another way by the Horizontal Projection very plainly TAke the Zenith for the Ascendent and set him in his place in the Limb which here is Horizon so much from Oriens as his Amplitude comes to and that toward Septentrio if it be a Northern Signe or if it be a Southern Signe toward Meridies Then number upon the Meridian line from the Limb inwards the Altitude of Culmen Caeli and the Azimuth that cutteth there shall be your Ecliptique in this Case If the Azimuths reach not the Meridian turn about the Reet and set Nadir for Ascendent Lay the Label to any degree of this Ecliptique and the degrees of the Label from that degree to the Limb shall be the Altitude thereof and between the Label and Meridies in the Limb the Azimuth thereof Example Because in the Case of the former Chapter I foresee that the Sun will be past the Nonagesimus gradus and so in the West Quadrant of the Ecliptique though he be in the East Quadrant of the Horizon therefore I set Nadir at the Amplitude of the Ascendent viz. 36 ⅓ from Oriens North-ward then in the Meridian line I number from the Limb inwards 36. for the Altitude of Culmen where I make a prick and say Here is ♓ 25 ½ Culminating and through that prick passeth the 42. Azimuth from the Limb which is now my Ecliptique and by that I see that the angle of the Ecliptique which the Horizon called the angle of the Ascendent and alwayes equal to the Altitude of Nonagesimus gradus as was said is 42 degrees and if I
follow this Azimuth to the Finitor there is Nonagesimus gradus and the Altitude thereof 42 degrees counted from the Limb here Horizon the Azimuth thereof lies in the Limb between the Finitor and the Meridian 36 ⅓ as before equal to the Amplitude of the Ascendent I number also from ♓ 25 ½ in the Meridian 23. 41 minutes to the left hand still and there I have ♈ 19. 11 minutes the Suns place which cuts on the Label 41 ⅔ for the Altitude of the Sun there and the Label at the same time cutteth in the Limb about 29. from South East-ward for the Azimuth of the Sun and after the same manner you have before you the Altitude and Azimuth of every other degree of the Ecliptique for the time proposed CHAP. LVIII To do the same by the Nonagesimal Projection if the Altitude of Nonagesimus gradus be first given instead of the Altitude of Culmen Caeli SEt your Planisphear in the Nonagesimal Projection by Book 2.3 that is make the Limb now to represent the Circle of Longitude or Azimuth for it is both which cutteth the Nonagesimus gradus and make the Equinoctial line here to be Horizon and from the Equinectial line number in the Limb the Altitude of Nonagesimus gradus and thereto set the Finitor so shall the Finitor be Ecliptique the Nonagesimus gradus at the Limb the Ascendent and Descendent at the Center and because the Equinoctial line is Horizon in this Projection therefore the Meridians become Azimuths and the Parallels Almicantars shewing the Altitude and Azimuth of every degree of the Ecliptique if you reckon as you ought in this manner Reckon in the Equinoctial line here Horizon from the Center the Amplitude of the Ascendent to the right Hand if it be a North Signe and contrarily if it be a South Signe Where this Amplitude ends is the East point from whence you shall reckon all your Azimuths Count thence to the Limb and back again if need be in the said Equinoctial line till you have made 90 degrees there is your Meridian as far distant from the Limb as the East point was from the Ascendent Follow this Meridian to the Finitor and there he shewes you Culmen Caeli and the Parallel there cutting shewes the Altitude thereof Now may you find every degree of the Ecliptique above the Horizon if you know but what Ascends or Descends or Culminates and of every such degree the Parallels shew you the Altitude and the Meridians shew his Azimuth if you begin your numbring from the East or South Azimuth Example When ♋ 24 degrees was Ascending as in the Example before used as by consequence ♈ 24. in Nonagisimo gradu ♂ was in ♉ 4. 45 minutes and had but 3. or 4. minutes South Latitude I would know ♂ his Altitude and Azimuth setting go the Finitor above the Equinoctial line 42 degrees which is the Altitude of Nonagesimus gradus I say because the Nonagesimus gradus at the end of the Finitor in the Limb is ♈ 24. therefore I must count back 10. 45 minutes toward the Ascendent for Mars and there the Parallel 41 degrees with 10 minutes cutteth the Finitor for the Altitude of ♂ and the 14th Meridian East-ward from the Limb gives me his Azimuth which if I begin to reckon from the East point falleth out to be almost the 40th Azimuth from the East Mars his Latitude here is not regarded CHAP. LIX The Nonagesimus gradus and his Altitude and Azimuth given as in the former Chapter How in the same Projection to get the Altitude and Azimuth of any Planet or Star by his Longitude and Latitude YOur Palnisphear set as in the former Chapter you shall number the Longitude of the Star upon the Finitor here Ecliptique beginning at the Descendent or Nonagesimus gardus and in the Azimuth serving his Longitude count his Latitude by the Almicantars at the end of which account is the Stars place for this time The Parallel cutting there shewes his Altitude and the Meridian cutting there shewes his Azimuth if you count from the East point as you were taught in the former Chapter Example Lucida Pleiadum was in Longitude ♉ 25. 10 minutes Latitude 4 degrees 00 minutes North. Therefore from the Nonagesimus gradus ♈ 24. I number in the Finitor toward the Ascendent 31. 10 minutes and there is the Longitude of Lucida Pleiaedum in the Azimuth that cuts here I go up Northward 4 degrees and there I make a prick for Lucida Pleiadum Now the Parallel 38 ½ shewes me his Altitude and the 48th ½ Meridian from the Center shewes me that Lucida Pleiadum is gone 48 ½ in Azimuth from the Ascendent but from the East point onely 12 degrees 10 minutes CHAP. LX. The Altitude and Azimuth of any Star taken and either the Ascendent Nonagesimus gradus or Culmen Caeli known How by the same Nonagesimal Projection to find the Stars Longitude and Latitude IF you know either the Ascendent Nonagesimus gradus or Culmen Caeli you have enough to put your Planisphear in the Nonagesimal Projection by the former Chapters And your Planisphear so set you shall seek out the Meridian which standeth for the Azimuth in which you observe the Star and therein number from the Equinoctial line the Altitude observed the Azimuth and Almicantar cutting there shew the Longitude and Latitude of the Star inquired If the Azimuths reach not the place of the Star turn the Reet half round and let the Zenith and Nadir points change places and your turn is served Example Febr. 13 1657 8. I observed somewhat near that ♃ was gone West-ward from the Meridian in Azimuth 14 degrees and that his Altitude was 61 degrees Sirius was then in the Meridian by which I have the Ascendent Culmen and Nonagesimus gradus any or all of them given For when in the Equinoctial Projection I bring Sirius to the Meridian line it is all one as if I had set the Suns place to the hour of the Night by Chapter 46. and I see there Culminates with Sirius ♋ 7. 10 minutes whose Meridian Altitude by the 46. is 61. 5 minutes and I see ♎ 5 ½ ascending in my Horizon and ♈ 5 ½ descending therefore ♋ 5 ½ is Nonagesimus gradus which is 90 degrees distant both from the Ascendent and Descendent his Altitude by Chapter 55. 61. 10 minutes almost Therefore I set the Finitor 61. 10 minutes above Meridies as Chapter 58. and in the Finitor at the Limb I count ♋ 5 ½ Nonagesimus gradus thence I go inwards in the Finitor 1. 40 minutes where I come to ♋ 7. 10. the degree of Culmination this degree is cut by the 4th Meridian from the Limb whereby I learn that this 4th Meridian will be the Meridian of my place and that the Amplitude of the Nonagesimus gradus and likewise of the Ascendent is 4 degrees Now to place ♃ in the Mater I count his Azimuth first beginning from the Meridian of my
less then the tenth part of an inch for one minute And beyond 30. or 40. degrees this Instrument would not be used because the Ey cannot see both the Sights of the Transom at once without rolling from one to another whereby the Center of Vision is changed 3. Your Ey is better fixed and shadowed by this Ey-sight then when the end of the Index is placed by guess upon the Cheek-bone The inconvenience here is no more then what is found in all Cross-staffes of what form soever And that is they are subject to some errour by reason of the Eccentricity of the Ey For the visual Beams meet within the Ey at a depth uncertain and they are also refracted in the Superficies of the apple of the Ey the apple of the Ey also is not of the same convexity nor of the same breadth in all Men and it is contracted in a bright Air and dilated in a darker Air as you shall soon find if you go about to observe the Diameter of the Moon by this Instrument without correction of the Eccentricity for you shall alwayes find the apparent Diameter too great and much greater in the Night then in the Day Thus November 18. 1653. I observed the Moons Diameter 32. minutes 06. seconds in the Day Time and that Night I observed it 58. minutes by reason of the dilatation of the apple of my Ey in the Night This errour may be rectified two wayes The First is by examining the observations made with your Cross-staff by some other Instrument which is not subject to like errour As for Example I have devised to fasten an arch of a Circle containing 20. or 30. degrees to the end of a Ruler of 6. or 7. foot and fit to it a Label with Sights then having observed by my Cross-staff the length of Orions Girdle I will set my other Instrument to it turning the arch toward me that I may manage the Label better and noting the difference of the observations I will find how to correct my Staff in that posture an another time and so by many observations I may frame a Table to correct the Eccentricity throughout but my Table perhaps will not serve to correct the eccentricity every Mans Ey neither will a Table made for the Night serve me in the Day The other way is most exact and certain for all Men. Make another Transom in all points like the first but shorter by half and let the divisions thereof be into half-inches this Transom must ride upon the Index with a socket between the long Transom and your Ey Now when you observe set the Sights of the short Transom to the like number of half inches as the Sights of the long Transom stand at whole inches and when you have placed your Ey-sight so that you see the Stars upon the edges of the Sights of the long Transom draw your short Transom till you see the Stars by his Sights in like manner at once then look what number is cut by the short Transom the double thereof is the Co-tangent of the angle and look what the number cut by the Ey-sight wants of that double so much is the Eccentricity of your Ey in that place This way is shewed by that Excellent Mathematician Mr Edward Wright in Chapter 15. of his Treatise of Errours in Navigation FINIS A Catalogue of Eclipses Observed since the Year of our Lord 1637. FIrst At Coventree whose Longitude is more West then London 1. degree 29. minutes of space Latitude 52. 28. minutes My especial friends Dr John Twysden and Mr Samuel Foster late Professor of Astronomy in Gresham Colleige and my self all together observed the totall and great Eclipse of the Moon which hapned in the Year 1638. on Tuesday December 11. before Noon The totall obscuration began 1. hour 07. minutes The time of emergence observed by the Altitude of Benenaes was 2. hours 41. minutes so the totall Obscuration continued 1. hour 34. minutes during the greatest part of which time the Moon was quite lost though the Skie was clear When the Moon began to recover light she was in the foremost foot of Apollo between the two Stars of the third Magnitude a line drawn between those Stars did cut off the lower part of the Moons body to ⅙ of her Diameter and setting the distance of the Stars in 12. parts the Moon had gone 7 ½ of those parts toward the Easterly Star which is in Calce Apollinis Hence I compute the apparent Longitude of the Moon at the time of emergence ♊ 29. 36. minutes 19 seconds and her apparent Latitude 0. 44. minutes South 2. At Easton Macodit whose Longitude is West from London 0. 43. minutes of space that is almost 3 minutes of Time the Latitude 52. 13. minutes Anno Dom. 1641. upon Fryday October 8. I observed the end of the totall Eclipse of the Moon when Lyra had Altitude 48. 48. minutes that is at 8 hours 38. minutes 08. seconds after Noon 3. At Ecton whose Longitude is West from London 45. minutes of space or 3. minutes of Time Latitude 52. 15. minutes Anno Dom. 1645 upon Munday Angust 11. I observed the Eclipse of the Sun ending when the Center of the Sun was in Azimuch 0. 55. minutes past the South that is 0. hours 2 ½ minutes after Noon This Eclipse Hevelius observed to end at Danizick at 1. hour 53 minutes as he writes in his Selenographia 4. At Ecton aforesaid Anno Dom. 1649. upon Wednesday May 16. before Noon I observed in the company of Mr Samuel Sillesby late Fellow of Queens Colleige in Cambridge the totall Eclipse of the Moon The beginning when the right Knee of Ophiucus was in Azimuth 7. 42. minutes past South that is 1. hour 08. minutes a.m. The totall obscuration began when the Azimuth of the said Star was 20 degrees Westward that is at 1. hour 55. minutes 44. seconds By the Medicaean Tables it should happen to be totally obscured at Uraniburg 2. hours 46. minutes 23. seconds and at Ecton 1. 53. minutes 23. seconds By Lantsbergius Tables at Ecton 1. hour 40. minutes 48. seconds 5. At Ecton Anno Dom. 1649. October 25. current Afternoon I observed by a Telescope the Eclipse of the Sun The Digits Eclipsed and the Time were as followeth Dig. H. min sec Dig. Hour 0. ⅛ 0. 41.56 4. 1.47.28 1.  49.48 3. 2.03.28 2.  59.44 2. 15.32 3. 1. 09.44 1. 22.40 4.  26.12 0. 31.04 4. ⅛ 33.32   6. At Easton Macodit Anno Domi. 1651 2. on Munday March 15. in the Morning I observed with Dr Twysden that the Moon was Eclipsed about one Digit when Alkair was in Azimuth 79. 40. minutes from the South Eastward More we could not see for Clouds 7. At Ecton Anno Dom. 1652. on Munday March 29. before Noon I observed the great Eclipse of the Sun by a Telescope and a minute-watch Rectified by the Azimuth of the Sun taken both before and
after in the company of half a score Gentlemen and Ministers my Neighbours as followeth Di. mi. Ti. mi. sec Digits Time 0.03 9.21.12 11.00 10.35 ½ 1.00 9.27 10.00 10.42 ½ 2.00 9.31.08 9.00 10.48 ½ 3.00 9.37 8.00 10.55 4.00 9.44 7.00 11.01 5.00 9.50 6.00 11.06 ½ 6.00 9.55 5.00 11.11 ¾ 7.00 10.00 4.00 11.19 8.00 10.06 ½ 3.00 11.24 ½ 9.00 10.11.28 2.00 11.31 10.00 10.18 1.00 11.35 ½ 11.00 10.25 0.00 11 42½ 11.22 ½ 10.32.04  And though this Eclipse was so great yet we could read in the time of the greatest darkness within Dores notwithstanding that the Window was covered with a Blanket 8. At Ecton Anno Dom. 1652. on Tuesday September 7. current the Moon rose Eclipsed about 10. Digits and while 8. Digits were yet darkned all the dark part of the Moon was visible of a Dusk and Tawny colour this Eclipse ended when the double Star in Cornu ♑ wanted in Azimuth 6. 30. minutes of the South that is at 7. hours 51. minutes 52. seconds but the Moon was not free of the Penumbra till 7. minutes after 9. At Ecton Anno Dom. 1654. on Wednesday August 2. current before Noon I observed the great Eclipse of the Sun by a Telescope and a Minute-watch sufficiently Rectified by the Azimuth of the Sun in the company of many learned Men my Neighbours and friends as followeth Di. T. mi. Di. Time 0. 7.47 10 ¼ 1. 7.52 ½ 10. 9.00 2. 7.58 ½ 9. 9.09 3. 8.04 8. 9.18 4. 8.09 7. 5. 8.15 6. 9.31 6. 8.20 ¾ 5. 9.38 7. 8.28 4. 9.45 ½ 8. 8.34 3. 9.51 ¼ 9. 8.40 ½ 2. 10. 8.49 1. 10.03 ½ 10 ¼  0. 10.09 10. At Ecton Anno Dom. 1654. on Thursday August 17. I observed the Eclipse of the Moon by a Telescope and a Minute-watch Rectified by the Azimuth of the first Star in the Horn of ♑ as followeth Time After Noon mi.  9. 47 ½ I saw the Penumbra invading the Moon with my bare Ey 9. 54. I saw the Penumbra invading through my Telescope 10. 15 ½ Shadow 3 minutes deep 10. 25. Shadow 4. minutes deep Yet I could discern all the Limb. 10. 45. Shadow more then 4. minutes deep Yet the Moons Limb all seen 11. 05. Yet the darkness is more on the East side shadow is 5. minutes deep and the Limb is lost in the shadow 11. 11. All the Limb seen again and the shadow seems but 3. minutes deep and just under the Moon so that the East and West side of the are darkned alike 11. 22. The shadow little above 1. minute deep in my Glass 11. 25. The shadow half a minute deep by my Glass 11. 27. The shadow gone in my Glass But the Penumbra still covers almost ⅓ of the Moons Diameter 11. 30. The shadow is here gone in the judgement of my naked Ey but the Penumbra is seen still 11. 35. The Moon as clear as at 9.47 ½ but yet the lower quarter of the Moon is much dusker then the rest of her body 11. At Ecton Anno Dom. 1655 6. upon Tuesday January 1. afternoon I observed the Eclipse of the Moon by a Minute-watch Rectified by the Southing of the Stars Clouds often hindred but thus I observed Ho. mi.  6.43 ½ The Moon growes dusk on the East side 6.49 ½ More dusk yet all the Limb is seen 6.51 ½ Here I judge the Moon to touch the Vmbra 6.53 ½ The Limb begins to be lost in the shadow so far as I can discern both with the Telescope and without it 7.00 ½ ☽ darkned 2. Digits by estimation 7.07 ½ Almost 4. Digits 7.34 ½ Almost 7. Digits here the Clouds thicken 8.29 ½ ☽ darkned about 10. Digits yet almost all the Moon is perceivable through the shadow 8.36 ½ About 10. Digits yet almost all the Limb perceivable 9.11 ½ About 8 Digits 9.23 ½ About 5 ½ Digits 9.28 ½ About 4. Digits 9.39 ½ About 3. Digits 9.51 ½ Here I judge the end The Limb of the ☽ is all restored yet the West side of the Moon looks duskish for 3. or 4. minutes longer 12. At Ecton Anno Dom. 1657. on Munday June 15. the Moon rose Eclipsed I observed the end thereof by the Azimuth of Antares to be 16. minutes after 10. 13. At Ecton Anno Dom. 1057. on Thursday December 10. I observed the Eclipse of the Moon ending when she was apparently 34 degrees high and me thought I discerned the Penumbra till her Altitude 35. it was a thick flying mist no Star but Jupiter could be seen with us all the time of this Eclipse about one third at the most of the Moons Diameter was darkned on the North side From the first Ecliptical opposition mentioned in this Catalogue to this last is the space of a Metonique Year These Observations are faithfully reported as I made them I could have strained some of them to a better Harmony if I would have forged any thing or used my own judgement upon them but I rather leave them to the judgement of the learned Readers especially such as have accustomed themselves to Celestial Observations FINIS The Rudiments of Astronomy Put into plain Rhythmes The Constellations of the Fixed Stars THe Army of the Starry Skie Declares the Glory of God most high Seen and perceived of all Nations In eight and fortie Constellations First neer unto the Northern Pole The Dragon and two Beares do Role Whose hinder parts and Tailes contain The lesser and the greater Wain The Hair the Bear-ward and the Crown And then comes Hercules kneeling down And next below a place doth take Great Serpentarius with his Snake Under the Harp of Orpheus The Eagle and Antinous The Silver Swan her Wings doth spread Above the Dart and Dolphins head Then Pegasus comes on amain Andromeda followes in her Chain The Triangle below her stands And at her feet in Perseus hands The Gorgons Head Above are seen Her Parents Cepheus with his Queen Cassiope Not far below Heniochus his Goat doth show On his left shoulder in his hand He doth the stormy Kids command Here in the Zodiaque begins The Ram the Bull the Loving Twins The Crab the Lion and Virgin Tender The Ballance Scorpion and Bow bender Goat Waterman then Fishes twain Shall bring you round to th' Ram again Fifteen Images appear In the Southern Hemisphear The Monstrous Whale before the rest Eridanus scarce wers his brest Over the Hare Orion bright Sparkles in a Winters night Then comes the great Dog at whose tayl The famous Argo spreads her sayl Above the little Dog doth flame For whom the Latines had no name Long Hydra on her tail alow Carries the Pitcher and the Crow The Centaure holds the Wolfe by th' heel The Altar and Ixions Wheel Are never seen of us but here The Southern Fish brings up the rear The Planets UNder those fixed Stars above Seven Planets in their Orbes do move The high'st is Saturn Thirty Year He spends in Compassing his Sphear Twelve Jupiter