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
30 degrees I say here begins â™’ and going on 26. 22. minutes further I say thus far is the Star gone in Longitude Now here cuts the Finiter by this account the Azimuth 35 â…“ from the Limb in this Azimuth I number the Stars Latitude by the Almicantars 22.07 ½ and at the end of that number in the said Azimuth I prick the Stars place And here I see the 8th Parallel of North Declination upon the Mater cutteth him and the Meridian 51 â…“ from the Limb shewing the excess of his Right Ascension above 270. which I kept before Therefore I conclude the Right Ascension of Eniph Alpharats Anno Dom. 1600 was 321. 20 minutes and his Declination 8. deg North. Past this on fol. 102 so as it may ly open while that Chapter is Reading Another way to place the Stars in the Mater by their Declination and Horary-distance from the Meridian See hereafter Chapter 52. CHAP. XXXVI The Latitude and Declination of a Star given to find his Longitude and Right Ascension SEt your Planisphear in the second Mode of the Meridional Projection turning the Zenith Northward or Southward as the Stars Latitude hapneth to be North or South Then look where the Parallel of the Stars Latitude in the Reet cutteth the Parallel of the Stars Declination on the Mater the Azimuth cutting that intersection sheweth the Longitude of the Star and the Meridian there cutting sheweth his Right â—scension Example The Declination of Spica â™ Anno Dom. 1670. will be 9 ½ South the Latitude was always 1. 59 minutes South Now where the second Almicantar cutteth the 9 ½ Parallel of South Declination there passeth the 19th ¼ Azimuth from the Axis toward my left hand shewing Spica's Longitude ♎ 19 ¼ and the 17th Meridian from the Axis to which I add a Semi-circle because ♎ 0. is at the Center and I make 197 degrees the Right Ascension of Spica for 1670. CHAP. XXXVII The Longitude and Latitude of two Stars given to find their Distance MAke one of the Poles of the Mater to be Pole of the Ecliptique for this turn and set the Star which hath most Latitude at his distance in the Limb and turn the Zenith to him count thence by the Meridians the difference of Longitude till you come to the other side of your Triangle and in that side number either the Latitude from the Equator or his complement from the Pole at the end of this number is the other Star and the Azimuth passing from him to the Zenith shewes the distance This is done by the second Probleme of Obliquangled Triangles Book 3.15 Example In Tycho'es Tables for 1600. Aldebarans Longitude is ♊ 4.12 ½ Latitude 5. 31. min. A. Sirius Longitude ♋ 8. 35 ½ Latitude 39. 30 ½ A. Difference of Longitude 34. 23. I number therefore 39. 30 minutes ½ the Latitude of Sirius from the Equator in the Limb or the Complement thereof from the Pole all is one there I set the Zenith to stand for Sirius then because Aldebaran is distant from Sirius in Longitude 34. 23. minutes I take the 34 ½ Meridian from the Zenith and where the 5 ½ Parallel cutteth him there say I is Aldebaran and C of my Triangle and the Azimuth passing thence to the Zenith measureth the distance of the Stars 46 degrees almost CHAP. XXXVIII The Declination and Right Ascension of any two Stars given to find their distance DO here with the Right Ascension and Declination as you should do with the Longitude and Latitude by the former Chapter for the case is like and requireth the same manner of working CHAP. XXXIX The Declination of a Star or Planet and his distance from a known Star given to find his Right Ascension BEcause this Case is the converse of the precedent and soluble by the first Probleme of Obliquangled Triangles Book 3. 14. an Example or two shall suffice Past this on fol. 105 so as it may ly open while that Chapter is Reading A B the distance of Mandibulae from the Pole 87. 20 minutes I set between the Pole and Nadir in the Limb because B C will reach beyond the Finitor For A C the distance of the Stars I seek the 13th Parallel from the Pole And For B C I seek the 94. 50 minutes Almicantar counted from the Nadir that is the 5th almost above the Finitor and where the said Parallel and Almicantar cross there is Cor Caeti and C of my Triangle through it there cutteth the Azimuth 10 â…” shewing the Difference of the Right Ascension of the Stars which difference I subtract out of the Right Ascension of Mandibula because he was further East and there remaineth the Right Ascension of Cor Caeti 30. 16 minutes or rather 13 minutes And I have here also numbred by the Meridians the angle A at Mandibula 120 degr though un-required Another Example January 7. 1656 7 I observed by my Brass Quadrant of 12 inches in Radius the Meridian Altitude of Jupiter 56. 20 minutes out of which subtracting the height of the Equator here at Ecton 37. 45 minutes I found his Declination 18. 35 minutes North his distance then from Lucida Pleiadum I observed by my Cross-staff 5. 12 minutes and from Aldebaran 10.07 minutes The Complement of Decli of Lucida Pleiadum is 67.00 mi. The Complement of ♃ his Declination was observed 71. 25. And these two Complements with the distance of ♃ and Lucida Pleiadum 5. 12 minutes make a Triangle soluble by the first Probleme of Obliquangled Triangles whereby you may find the angle of the difference of Right Ascension of Lucida Pleiadum and ♃ is 2. 56 minutes which added to the Right Ascension of Lucida Pleiadum because ♃ was East-ward maketh 54. 44 minutes the Right Ascension of Jupiter CHAP. XL. The Latitude of a Star or Planet and his distance from a known Star given to find his Longitude DO here with the Longitude and Latitude as you were taught to do with the Right Ascension and Declination in the former Chapter CHAP. XLI To find the distance of two Stars by their Altitudes and their difference of Azimuth observed at the same time THe Complements of the Altitudes are the distances of the Stars from the Zenith Set one of the Stars at the Pole and set the Zenith as much from him in the Limb as the Complement of his Altitude comes to then considering what difference of Azimuth the Stars had take the Azimuth of like distance from the Limb beginning from that side of the Limb where the Pole aforesaid is and in that Azimuth reckon from the Finitor the Altitude of the other Star or the Complement of his Altitude from the Zenith all is one at the end thereof is C and the other Star and the Meridian that passeth from him to the Pole shewes the distance of the Stars This case is so like that of Chapter 37. that he who knowes one may know the other also CHAP. XLII To find the Angles of
London from Jerusalem CHAP. LXX The Latitude and distance of two Places given to find the difference of Longitude THe Triangle will stand as in the former Chapter there by two sides and the angle comprehended you sought the third side by Probleme 2. Obliquangled Triangles here by three sides given you seek an angle by Probleme 1 Obliquangled Triangles Make the Pole Pole and set the Zenith to the Latitude of one of the places as you did London Chapter 69. 38. 28 minutes from the Pole then number the Complement of the Latitude of the other place from the Pole by the Parallels and the distance of the two places from the Zenith by the Almicantars and where the last Parallel and last Almicantar meet is C of your Triangle see Book 3. 14. Now count how many Meridians there be between C and the Limb so many degrees is the angle at the Pole sought for the difference of Longitude Example Having the distance of London from the Pole 38. 28 minutes and of Jerusalem from the Pole 58. 5 minutes and the distance of London from Jerusalem 2300. common English Miles of which 60. make a degree I set the Zenith for London 38. 28 minutes from the Pole in the Limb then because Jerusalem is distant from the Pole 58. 5 minutes I go to the 58th Parallel from the Pole and lay one finger or the point of a bodkin on him and because London is distant from Jerusalem 38 degrees 20 minutes I count from the Zenith to the Almicantar 38. 20 minutes now where this Almicantar crosseth the Parallel last found there is C of the Triangle and the place of Jerusalem and you may see that you must cross 46. Meridians before you can go thence to the Zenith in the Limb which sheweth that the angle at the Pole for the difference of Longitude is 46. CHAP. LXXI To find what degree of the Ecliptique Culminates in another Country at any time proposed if the difference of Longitude be known IN the Equinoctial Projection Bring the Suns place to the hour proposed by help of the Label and in the Noon-line you see presently what degree Culminates in your Country as Chapter 46 is shewed Now to know this for another Town set the Label so many degrees from the Noon-line as the difference of Longitude requires and that Eastward if the place proposed be East or Westward if it bear West and so the Label shall cut the degree of Culmination for the place proposed Example If it be demanded what degree is Culminating at Jerusalem March 10. at 10. a clock before noon I will set the Suns place ♈ 0. to the hour and I see upon the Noon line which is our Meridian there Culminates ♒ 28 almost Now for the Meridian of Jerusalem I must lay the Label 46 degrees Eastward that is from Meridies towards Oriens and look what Star or degree of the Ecliptique is then cut by the Label that is then Culminating in the Meridian at Jerusalem as here I find ♈ 17 ½ for in this Projection the Label lay him where you will is a Meridian CHAP. LXXII To find what a Clock it is in another Country by knowing the hour at Home and the difference of Longitude THis is done easily enough without an Instrument for if you turn the difference of Longitude into hours and minutes and add the same to your hours for any place which lies Eastward or subtract the same for any place which lies Westward you shall make the hour of the place Example The difference of Longitude between London and Jerusalem is 46. or being converted into time 3 hours 4 minutes therefore adding this to the time at London I say when it is noon at London it is 4 minutes past 3 a clock after noon at Jerusalem and when it is 2 a clock at London it is 5. and 4 minutes at Jerusalem If you will do it by the Planisphear you shall do it in the Equinoctial Projection thus Whereas the Limb of your Rect is graduated into 360 degrees if you distinguish the hours also at every 15th degree beginning at the Zenith which shall be 12 and numbring thence in the Limb of your Reet to your right hand or Westward 1 2 3 c. then shall you need to do no more but set the Zenith to the difference of Longitude East or West from your Meridian as the strange place happeneth to be situate for then the Label laid to the hour of your Country in the Limb of the Mater shall shew the hour of the other Country in the Limb of the Reet And so the Zenith being laid to 60 degrees Westward which is the Meridian of the Isle of Barbados the Label laid to Meridies shall cut in the Limb of the Reet 8 of the clock before noon which sheweth me that when it is noon with us it is at Barbados but eight in the morning The end of the Fourth Book CHAP. LXXIII The Longitude and Latitude of one Place known and the Rumb and distance of a second Place to find both the Longitude and Latitude of the second Place SEt the Zenith to the Latitude of the first Place then seek the Azimuth which serveth for the Rumb of the second Place and in that Azimuth count his distance from the Zenith where this distance ends there is the second Place whole Latitude is shewn you by the Parallel which cutteth him and the Meridian cutting there also shews his Longitude Example Let Z be London and because Jerusalem beareth from London almost S b E or 77 ½ from South Eastward therefore I choose the Azimuth 77 ½ Z K. therein I number Jerusalems distance from London Z I 2300. miles or minutes that is 38. 20. minutes Now in the Triangle Z P I I may find P I the complement of Jerusalems Latitude 58. 05. minutes and Z P I the difference of Longitude 46 which must be added to the Longitude of London to make the Longitude of Jerusalem CHAP. LXXIV The Latitudes and Distance of two Places given to find the Rumb and the difference of Longitude COunt in the Meridian from P the Pole the complement of the Latitude of the first place and thereto set Z the Zenith Count also from P the complement of the Latitude of the second place and lay your finger on the Parallel at which your number ends Count also from Z the distance of the places in Degrees and Minutes and note the Almicantar at which this number ends where this Almicantar crosseth the aforesaid Parallel there is C of your Triangle but here marked I Look what Azimuth cutteth here it sheweth the Rumb and the Meridian that cutteth here if you count his distance from the Limb shews the difference of the Longitude of the places This is so plain from Chapter 69 70 and 73 that it needeth no example The same Scheam serveth these 4 Chapters The end of the Fourth Book The Fifth Book Shewing the way to resolve all GNOMONICAL
to take your points in the Tropiques at the largest distance as I have here done if there be room enough on the Cieling But because it often happens that part of your Dyal falls beside the Cieling and the plain of the Cieling and of the Walls is often interrupted and made Irregular by Beams Wal-plates Corrishes Wainscot Chimney-peeces and such like bodyes I will â—hew you one absolute device to carry on your Hour lines over all Extend the thred for any Hour line to the Tropique of Cancer â—n the Cieling as you where taught before and fix it there and extend another thred in like manner to the Tropique of Copricorn where ever it shall happen as perhaps beyond the middle beam or quite beyond the Cieling upon the Wall and fix that thred also Then place your Ey so behind these threds that one of them may cover the other and at the same instant where the upper line to your Sight or Imagination cuts the Cieling Beams Wall or any Regular or Irregular body above the end of the lower line there shall the Hour line pass from Tropique to Tropique direct any By-stander to make marks as many as you shall need and by these marks draw the Hour line according to your desire If the arch of the Horizon between the Tropiques be within view of your Window you shall draw the same on the Wall to bound the Parallels the Horizons Altitude you know is nothing and therefore he will be a level line and the Suns Azimuth when he riseth commonly called Amplitude and Ortive Latitude is in Cancer 40.40 minutes East Northward and in Capricorn as much Southward and these will be reflected to the contrary coasts on the Dyal The end of the Fifth Book A breif Description Of a CROSS-STAFF THe Cross-staff consisteth of two Rules joyned by a socket or else pinned in the form of a Romane T and three Sights or more The longer Ruler is called Radius Index and the Yard as A B of which I call A the neer end B the further end The breadth would be ¾ of an inch the depth an inch and half the length 70 or 80. inches and every of those inches would be divided by Parallels and Diagonal lines into 100. equal parts The shorter Ruler E F is called the Transom it would be half an inch or three quarters both in breadth and depth and in length about 2. foot for the Sights there if I may advise you would never be set above 20 inches asunder This Transom would be divided into whole inches onely beginning in the midst at B in the visual line ☉ B. and numbred to 10 both wayes The Sights C and D must have sockets at the bottom through which the Transom must pass so that the Sights may be set to any division of the Transom The Vanes or tops of those Sights must have onely two edges on their sides visible to your ey namely those edges which touch the Transom and the two other edges must be pared away The middle Sight at B would have half his head cut away and a shoulder left as in the Figure and a tenon at the bottom fitted to a mortess made in the middle of the Transom that you may stick him in and take him out when you please for to this mortess you shall do well to fit two other moveable Sights very narrow for observing the Diameter of the Moon or the distance of Stars which are very neer one may be about half an inch broad and the other about a quarter This Cross-staff is exactly made by Mr. Anthony Thomson in Hosier lane London When you would use this Staff you shall first set the Sights of the Transom to like inches as at 10 and 10. if the angle be great or at 5 and 5. as in the Figure they are placed alwayes set them at whole inches and at like numbers on both sides from the middle of the Transom and choose to place those Sights so that your Ey-sight may be far distant from them in observing for so you may the more distinctly observe the minutes and seconds of the angle inquired Then resting the further end of the Index upon a Wall or some device fitted for that purpose put the neer end over your right shoulder and setting your Ey to the Ey-hole slip the Index backward or forward till you see the objects by the sides of the Sights of the Transom and mark what number the backside of the Ey-sight cutteth upon the Index for that shall give you the angle sought in this manner Example The Sights of the Transom being set at 5 and 5 that is 10. inches asunder I observed two Steeples by their edges and the Ey-sight then cut upon the Index 6625. that is inches 66 ¼ from the Transom I say therefore As C B 500. to B G 6625. so C B Radius or 100000. to B G the Co-tangent of half the angle Here I have no more to do then to divide 662500000. by 500. or 6625000. by 5. which is an easy work and the Quotient 1325000. is the Co-tangent of 4. degrees 18. minutes 57. seconds 43. thirds for half the angle Note here that if the Sights had stood at 10 and 10. then had the number 6625. been the very Co-tangent of half the angle and remembring that your Radius on the Transom hath but 1000 actual parts go to the Canon and cutting off so many places as may leave the Radius there but 1000. you shall find your number 6625 to be the Co-tangent of 8. 35 minutes Note also that you may observe the angle between the middle Sight and one of the other and then you find the Co-tangent of the whole angle to that Radius to which your Sight is set on the Transom as to the Radius 200. 300. or any other even hundred to 1000. Note further that you must evermore observe neer the tops of your Sights that the visual lines may run above the Transom as much as the Ey is placed above the plain of it He that will may have room to set several Scales of degrees and minutes to several Radiusses as one to the Radius 300. another to 500. another to 700. by which the very degrees and minutes may be presently had without recourse to the Tables To me the Scale of equal parts is in stead of all The Commodities of this disposition of the Staff are these 1. It is better managed when it rests upon the shoulder and the Ey-sight being made to move while the Transom and his Sights stand Fixed shall save you much labour of coursing up and down from one end of the Staff to the â—â—â—er in observing 2. The Ey-sight being made to shew the angle by the length of the Co-tangents shall alwayes give you large differences insomuch that if your Staff be but 6. foot long you may observe to Seconds and Thirds in lesser angles and till you come beyond 20. degrees your Sight shall seldom move
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
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
him in his proper lines Go to the Mater of your Planisphear and take him there in the first Projection There number 60 the Suns Longitude in the Ecliptick line of the Mater from the Center outward Where 60 endeth there is C of your Triangle and the Meridian that meets you there is C A the arch of Declination follow him to the Equator and you shall find by his graduation he is 20 degr 12 min. Long. thence turn in the Equator to the Center and you make B A the Right Ascension 57 degr 48 min. so have you the true picture of your Triangle in his proper place Observe your Triangle now and you may see A is a right angle for at such angle all the Meridians cut the Equator B is 23 ½ for such an angle the Ecliptick dayly maketh with the Equator as the arch in the Limb comprehended between them shewes Now take for given any of the three Sides and you have the rest Take the Longitude for given and be it 60 degr as before or 70 degr or what you will and you may find the Declination and Right Ascension as before Let the Right Ascension be given then setting a needles point in the end thereof A you may thence in a Meridian trace out the Declination C A to the Ecliptick and the Longitude B C thence to the Center every Side being divided into his whole parts or degrees If the Declination be given say Because the 20th Parrallel almost must cut off C A the arch of Declination in C therefore I follow the Parallel 20 ⅕ to the place where he cutteth the Ecliptick and there comes the Meridian that serves my turn and I may go down by him to the Equator as you would go down a ladder counting the rounds or degrees as you go and so on round my Triangle and I need no more For observe it when you will in the use of this Planisphear if you can find the way to go round your Triangle you have all the Sides measured to your hand and evermore one Angle also most commonly two and the angle C onely left unknown But admit the Sun be in ♌ 0 then is his Longitude 120 degrees and he is come back from the Solstice in your Planisphear as many degr as he wanted of it before Here the Triangle is equal to the former and resolved in like manner The Declination is the same as before But the arches of Longitude and Right Ascension in the Triangle are supplements of the true Longitude and Right Ascension shewing what the Sun wants of the Longitude and Right Ascension 180 in ♎ 0. wherefore subtract the Base of the Triangle 57 degr 48 min. from a Semicircle or 180 degr and you shall leave 122 degr 12 min. the Right Ascension of ♌ 0. or number in the Equator from the Center the way in which the Right Ascension hath increased that is first to the Limb which here is Colurus Solstitiorum 90 degr then back again to A the Right angle of your Triangle and you have 32 degr 12 min. to be added thereto The Sum is 122 degr 12 min. the Right Ascension as before If you observe this Example you will easily perceive that when the Sun is past ♎ 0. the Triangle will be on the other side the Center and between ♎ and ♑ you must add to the Right Ascension and Longitude found within the Triangle 180 degr and in the last Quadrant between ♑ and ♈ where the Right Ascension again increaseth inwards you must add 270 degr to the complement of Right Ascension found in the Triangle and take the sum or else subduct the Right Ascension found in the Triangle from 360 degr and take the residue for the Right Ascension CHAP. VII To do the same in the second Projection more easily IN the second Projection where the Center is the Pole of the World and the Limb Equator you shall find the Ecliptick fairly drawn upon the Reet and distinguished into his quarters and degrees Remember now from the former chap. that the Ecliptick Equator and a Meridian must make your Triangle and know that the Label supplieth the place of the Meridians If the Longitude or Right Ascension be given lay the Label on the degree given in the Ecliptick for Longitude or in the Limb of the Reet for Right Ascension and your Triangle is made and you may presently see your desire If the Declination be given consider in what quarter of the Ecliptick the Sun is then number the Declination given upon the Label inwards and where the numbring ends make a prick on your Label then move the Label into the quarter where the Sun is and lay the prick on the Ecliptick there and your Triangle is made wherein you may see the Longitude and Right Ascension desired This needeth no Example CHAP. VIII To find the Angle at the Sun made between the Ecliptick and Meridian THis is the angle C of the former Triangle and is the onely part which cannot be found in the former posture of the Triangle neither in chap. 6 nor 7 but is easily had by conversion of the Triangle as you may remember out of the third Book Take the Triangle of chap. 6 and make the Cathetus Base for this turn and by the 1 or 2 Problemes of Rectangled Triangles you may find this angle to be 77 degr 43 min. CHAP. IX To find the said angle of the Ecliptick with the Meridian by the Longitude Declination or Right Ascension divers other wayes IN the Meridional Projection do thus If you have the Longitude given count the distance of the Sun in that Longitude from the next Equinoctial point and count so many degrees in the Arctick Circle from the Limb inwards to the end of this numbring lay the Label and between the Label and Equator you have upon the Limb the lesser angle made between the Ecliptick and Meridian the greater angle is the supplement thereof Also between the Arctick Circle and the Limb you may find the Declination on the Label which is more then was required If you have the Declination given count it on the Label inwards and make a prick where the number ends then turn this prick upon the Arctick Circle and the Label sheweth the lesser angle in the Limb as before Example I would know what angle the Meridian that cutteth the Sun in ♉ 9 degr maketh with the Ecliptick I number therefore in the Arctick Circle from the Limb inwards 39 deg and to the 39th degr I say the Label and it sheweth in the Limb the angle sought 71 degr 20 min. and in the Label the Declination of ♉ 9 degr viz. 14. 32 minutes this is a good way But that the Label at this 39th degr cutteth the Pole of the Ecliptick as Mr. Blagrave saith Book 3 40. is not true either Mr. Blagrave or the Printer here mistakes For the Pole of the Ecliptick lies 14. 24 minutes nearer the Axletree as you shall
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