A perfect and easie Treatise of the vse of the coelestiall Globe written as well for an Introduction of such as bee yet vnskilfull in the studie of Astronomie as the practise of our Countriemen which bee exercised in the Art of Nauigation Compiled by Charles Turnbull And set out with as much plainnes as the Author could to the end it might of euery man be vnderstood Psalm xix The heauens declare the glorie of God and the firmament sheweth the worke of his handes Day vnto day vttereth the same and night vnto night teacheth knowledge ¶ Imprinted at London for Symon Waterson INSIGNISSIMO VIRO AC OMNI VIRtutum genere clarissimo Magistro Henrico Nocllo Carolus Turnbullus salutem ac foelicitatem perpetuam comprecatur CVM antiquissimorum scriptorum singularem industriam in studijs Mathematicis iam ante seriùs accuratiúsque cognouerim recentium quorundam deprauatam lectionem summa cura summáque diligentia viderim obseruauerim ne infestus error damnum inferret grauius curaui vir insignissime ea faciliùs explicare quae si fideliter discantur omnis erroris tollent difficultatem Eorum verò te patronum esse volui vt meo exemplo ad eadem vota multos inuitem tanquam indicem te in florentissimo hoc regno non solùm tanti negotij virum celeberrimum sed omnium regiarum virtutum laudúmque patronum Itaque minusculam opus hoc Aâ—… qualecunque sit quod scio quam sit indignum tibi dedico vt qui imposterum non solum obseruationes astronomicas elaboratas magis minúsque vsitatas siue sint theorica siue horalogica sed opticas quoque qua sunt geometriae communis praecepta vt tempus postulat sis receptarus Quibus vt es spiritus nobilissimi ita mirificè quoque delectaris Vnum hoc interim precibus etiam atque etiam obsecrans vt qua humanitate erga me semper vsus es cum maxime possis eadem iam indies confirmata magis libertissime quoque velis patrocinari Vale. To the Reader MEn which are more desirous of publique Fame and Renow ne then studious of coÌ„mon profit with great curiositie set a glasse vpoÌ„ such things as being discouered would shew dismeÌ„bred mishapen As for my selfe I seeke no higher dignitie then to be reported to set forth a trueth and therefore without any wrested cloquence I make bold to offer the vse of the Globe to the exquisite vewe of your curious eyes though farre inferiour as I suspect to some mens expectation to the end such grosse enormities might bee amended as often times in diuers haue bene discouered Who for want of right conceat of things by them attempted haue in the ayer built such fortresses as haue without assalts wounded their louing enemies But happely such men wil now retire and arme them selues better against the next assault lest they be like to the dogs in the capitall of Rome which were placed to the end that if by night spoylers should ariue they might sound a warning For true it is that by night these barke out false Allaromes at their enimies but if by day they barke likewise at friends I hope ye wil iudge them worthy to haue their legs broken which things I leaue to your gentle interpretation Nothing misdoubting but if in this tract either anything bee escaped contrarie to my will or omitted not satisfying your expectation ye wil aequally suffer the same For if ye receaue the fruites of my labor and care of your commoditie I require no more Wherefore my trauaile I bequeath to your discreet consideration and your selues to the protection of almightie God Farewell DEFINITIONS to be praemised necessarie for the vnderstanding of the Globe THe Sphaere or Globe is a perfect round sollide bodie contained vnder one superficies or face in whose middle is a point from which point all lines that are drawne to the superficies and face of the same are aequall the one to the other The Center of the Sphaere is the middle point of the same The Axe of the Sphaere is a right line passing from one side of the same by his Center to the contrary side about which line the Sphaere is caried but the line it self standeth still The Poles of the Sphere be the endes of his Axe The Pole of any Circle is a point without the compasse of the same and yet is aequally distant from all points of the circuit or borders of the Circle whose Pole it is from which the same Circle is drawne OF THE NAME of the Sphaere and his diuers and sundrie kindes of diuisions together with the motion of ech one in his kinde THE NAME OF the Sphaere is taken either generally or particularly Generally and so it is said to containe all perfect round bodies whether they be sollide or not whether contained vnder one onely Superficies or moe And so may euery Orbe be called a Sphaere But if wee take the worde Sphaera in his particular and proper signification then nothing is a Sphaere but a perfect round bodie being sollide contained vnder one c. as the former definition declared This Sphaere is diuided either according to his substaunce or according to certaine properties and affections which he is capable of According to his substance he is diuided into two parts the one Elementall the other Aethercall The Elementall containeth the fower Elements Fire Ayre Water and Earth and is subiect to alterations by reason of their effectual working The Aethercall compasseth in round the Elementall part in his hollownesse and is lightsome by nature and vnchaungeable and containeth ten Sphaeres The first and highest from the earth being called the first moueable containeth in his hollownesse al the other and by his natural motion is moued directly from the East to the West and so to East againe in the space of 24. howers continually and carieth about with him by violence al the other Sphaeres The next vnder this is the ninth Sphaere called the Christall heauen and by his naturall motion is caried from West toward East but very slowly in many yeares passing but one degree and this motion hath caused the Starres to alter their LoÌ„gitudes The third Sphaere is the Firmament or Sphaere of the fixed Starres whose motion by nature is vpon two little Circles the one being described about the head of Aries and the other of Libra which motion is called the motion of Trepidation The other seauen Sphaeres be of the seauen Planets the highest of Saturne which moueth by nature from West toward East and that in 30. yeares one perfect reuolution The next of Iupiter moouing froÌ„ West to East by nature and that in twelue yeares The other of Mars making his reuolutioÌ„ from West toward East in two yeares Vnder Mars is the Sunne moouing by nature from West toward East making one perfect reuolution in 365. daies and 6. howers almost Vnder the Sunne is Venus and then Mercurie moouing from West to East about the
same time as the Sunne The last is the Moone making one perfect reuolution from West toward East in 27. daies 7. howers 43′ 7″ yet all these are caried by violence of the first moueable from East to West as is before saide OF THE CIRcles of the Sphaere of Heauen and of their names and how they be made AStronomers to the end they might shewe the motions of Heauen and the straūge and wonderful conclusions of the Coelestiall bodies haue imagined certaine Circles in the bodie of the first Sphaere or first mooueable and principally ten whereof some be greater Circles of the Sphaere so called because the Center of these Circles is also the Center of Heauen euery such Circle diuideth the whole Sphaere into two aequall parts Of this sort be sixe the Aequinoctiall Zodiack Horizon Meridian and two Colures Some bee lesser Circles of the Sphaere so called because they haue not the Center of the world for their Center neither diuide the whole Sphaere aequally Of this kinde be fower the Tropicke of Cancer the Tropicke of Capricorne the Articke and Antarticke The Aequinoctiall called the aequator or girdle of Heauen is a great Circle of the Sphaere diuiding the Sphaere into two aequal parts and is aequally distant from ech Pole of the worlde And tooke his name of the aequator either because it is aequally in the middle of Heauen as Euclide saith in his Opticks or for that the Sunne comming to this Circle maketh the day and night aequall it is diuided in 360. aequall parts which parts are called degrees His Axe is the Axe of the world and Poles the Poles of the world The Zodiack is a great Circle of the Sphaere which crosseth the Aequinoctiall in two points the one being the head of Aries the other of Libra and swarneth from him in all other points leaning toward ech Pole of the world in the point of his greatest swarning 23. degrees 30. minutes This Zodiack is of breadth 12. degrees and of length that is to say in compas 360. degrees and according to his length is diuided into 12. aequal parts which are called the 12. signes Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricornus Aquarius and Pisces And ech signe contayneth of length 30. degrees in the midle bredth of the Zodiack we imagine a Circle to passe which we call the Ecliptick Circle or line For that that when the Sunne and Moone bee both vnder this line in a Diameter then the Moone is Eclipsed Vnder this Circle the Sunne mooueth dayly without declining any waies the quantity of one degree very neere in ech day the rest of the Planets are found some times on one side the Ecliptick some time on the other This Zodiack taketh his name of a greeke word signifying a liuing creature or as the Latens will is called Signifer for that that it beareth the 12. Signes the Axe of the Zodiack and the Ecliptick is all one being a line diuers from the axe of the world and the Poles bee two points alwayes so much distant from the Poles of the world as the greatest declination of the Ecliptick commeth vnto A Colure doth generally signifie any Circle passing by the Poles of the worlde and hath his name of his vnperfect shewing himselfe in the motion of heauen But now by the name of Colures we vnderstād two great Circles the one going frō the Poles of the worlde by the points where the Aequinoctiall and Zodiack cut them selues which be called the Aequinoctiall points and is called the Aequinoctiall Colure The other passeth from the Poles of the worlde by those points of the Ecliptick which swarue most of all others from the Aequinoctiall line which points are called the Solsticiall points and this is called the Solsticial Colure And here be you to know that these foure greater Circles which we haue defined be still the same through the whole worlde and are sayd to be moueable Circles for so much as in the motion of heauen they be also mooued of which some are moueable perfectly as the Aequinoctiall and Zodiack for they in the going about of heauen doe ascend by little and little till the whole Circle haue gone oure the Horison some vnperfectly moueable as the two Colures which neuer shewe the whole Circle in any crooked Sphaere the other two greater Circles which followe be called fixed for that they neuer mooue by the motion of heauen But they be changeable in euery Region The Horizon is a greater Circle diuiding the halfe of the Heauen which we see from the halfe which we see not and is called in Latine Finitor because it endeth our sight The Horizon maketh fower principal points East West North and South His Axe is a line imagined to fall from the point of heauen which is directly ouer our head where we be downe to the groūd like a plumme line and his Poles be the endes of that line called the Verticall point and point opposite to the Verticall The Meridian is also a great Circle passing from the Poles of the world by our Verticall point cutting the Horizon in the North and South points his Axe is a line going from the East point of the Horizon to the West and his Poles be the same points and these two Circles doe alwayes chaunge are diuers in euery Region for so much as the Verticall point of euery Region is diuers by the which the Meridian of necessitie must passe and is the Pole also of the Horizon OF THE LESSER Circles of the Sphaere and their names and of their making THe lesse Circles of the Sphaere in number be fower The Tropicke of Cancer the Tropicke of Capricorne and the two Artickes The Tropicke of Cancer is a lesse Circle of the Sphaere which is aequally distant from the Aequinoctial lying betwixt the Aequinoctiall and the North Pole and touching the Ecliptick in the beginning of Cancer This Circle is described by the bodie of the Sunne in the longest day of Summer at which time the Sunne is entred the solstitiall point or beginning of Cācer is called the Tropick of a Greeke word which signifieth a returning because the Sunne being brought to this point falleth in his noone height and returneth againe The Tropicke of Capricorne is a like Circle betwixt the Aequator the South pole and is described by the Sunne in the shortest day of Winter at which time the Sunne is in the beginning of Capricorne whereof it is called the Tropick of Capricorne The Articke Circle is a lesse Circle of the Sphaere described by the Northerne Pole of the Ecliptick Proclus saith it is described by the formost foote of the great beare and thereof taketh his name The Antarticke is a like Circle described by the South Pole of the Ecliptick is called Antartick of the Greeke worde which signifieth Opposition because it is opposite to the other Of the vse of the Circles of the Sphaere or Globle THE most
principall cause why Artificers inuented the Aequinoctiall was first because it is the measure of the first Heauen by a conuenient perpetual and aequal swiftnesse Secondly it measureth and limitteth the time of rising of the Signes as also the length of the Artificial daies and times of the Aequinoctials with declinations and right ascentions of Starres together with Longitudes of Regions Lastly for the exection of the twelue howsen of Heauen In like maner the Zodiack serueth for Latitudes Longitudes of Starres for distinction of the times of the yeare for the motions of all the Planers and effects of the same Not vnlike be the vses of the Colures and Meridian ech shewing the greatest declination of the Ecliptick but especially the MeridiaÌ„ which giueth as well al declinations of Starres their noone height and distinguisheth the daies and nights into two aequal parts and serueth for the Horizon of the right Sphaere It beginneth likewise and endeth all Longitudes of Regions and sheweth Latitudes and Eleuations of the Pole It helpeth to diuide the 12. howsen In like maner sundrie and diuers be the vses of the Horizon As in seperating the hidden part of Heauen from that which is seene and sheweth the place of rising and setting of any Starre how farre from East or West with his height All which points are respected of Astronomers as the Sphaere is secondarily diuided that is to say as he is a right or a crooked Sphaere which bee his properties and affections ment in the diuision afore specified By a right Sphaere is ment such a kinde of position of Heauen as that neither Pole bee râ—ised aboue ground but that ech lye in the face of the earth And such a kinde of position haue they which dwell in Bersera and the Islands of Molucca or such like Contrariwise it is sayd to bee a crooked Sphaere when any one of the Poles is raised aboue ground Such a Sphaere haue we at Oxford and London and generally all which dwell not vnder the line All which thinges for our better conceate are shewed to the eye in the materiall Globe whose names and diuisions appeare at the first vewe two things only being waied First that the mechanicall or materiall Globe which representeth the first mooueable beareth in him the fixed Starres not because the Starres bee in the first mooueable but because their motion is so litle in their own Sphaeres in many yeares that they may seeme not to haue mooued at all in a man 's his age from their places vnder which they be of the first moueable therefore they may bee supposed to stand in it Secondly the Globe representeth the Starres to vs in his connexitie which appeare in Heauen in the concauitie For that our eye is not in the Globe but without Furthermore in the Globe besides the aforenamed Circles bee found three others of brasse the one being a perfect Circle of a litle quantitie placed about the Pole which is eleuated is called the hower Circle whose stile is called the Index An other is a thinne rule of brasse representing one quarter of a whole Circle called the quadrant of Altitude and is alwaie to be fixed when ye vse the Globe on the middle of the halfe of your Meridian which is aboue the Horizon that is to say 90. degrees aboue the Horizon The third and last is a great halfe Circle lying at the Horizon seruing aswell for the erection of the scheme of Heauen as any Circle of position All which things being aduisedly considered of ye may proceede in the vse of the Globe As followeth HOW THE Globe is to be placed readie for his vse and practise THe placing of the Globe ought to be such that the Horizon of the Globe may stand parallele or leuied to the true Horizon and the Meridian of the Globe stand in the Superficies of the true Meridian of Heauen and the Poles of the Globe and his Axe answere exactly to the Poles and Axe of Heauen Now to the leuying of the Horizon there ought to bee at your Globe a hanging plummet and for the Meridian a Needle touched of the lode stone and touching the rectifying of the Poles and Axe of the Globe the eleuation of the Pole of heauen is first to be knowen the meanes to performe and accomplish the same being such as followe Propositio 1. To finde a Meridian line in any place appoynted SEt vp on your Horizon or some plaine leuied boarde a Gnomon of any reasonable length then at such time as the same shineth describe from the top of your Gnomon a Circle by the tippe of his shadowe and make a marke in the Circle where the shadowe ended at your obseruation which must be before noone Then marke in the afternoone at what time the ende of the shadowe returneth into the same Circle againe and make a marke at his point of falling so shall ye haue a portion of the sayde Circle inclosed betwixt the two points If then ye diuide this portion into two aequal parts and drawe a line from this middle point by the point in which the Gnomon standeth it shal be a Meridian line Propositio 2. To take the height of any Starre FRrom the point of Heauen which is directly ouer our heads being called the Verticall point or Zenith are imagined diuers Circles to fall by euery degree and minute of the Horizon all which Circles are called Verticals serue for the height of Starres for so much as the altitude of Sunne or starre is the portion of the Vâ—…ticall Circle inclosed betwixt the Center of the Sunne or Starre in the time of his obseruation and the Horizon which height is thus found Take your Astrolabe and let him hang freely by his ring then turne vp his Dioptral so long that ye see the Starre whose height yee seeke thorowe his sights for then howe many degrees and minutes are inclosed betwixt the Dioptrall and the line of your Astrolabe which is parallele to the Horizon so many hath that Starrs of height as the seauenth day of Ianuarie Anno. 1585. vnder the Meridian of Oxford at 9. of the clocke I sought the height of the Sunne taking then my Astrolabe and hanging him towarde the Sunne and raising his Dioptrall till I espyed the Sunne I found betwixt the Dioptral and the line representing the Horizon seauen degrees and 16. minutes so much was the height of the Sunne at that time Propositio 3. To take the altitude of the Pole in in any place or countrey THe altitude of the pole is the portion of the MeridiaÌ„ Circle inclosed betwixt the Pole and the Horizon and is thus found Find a Meridian line and drawe him in the Horizon by the first proposition then take the height of any fixed Starre which setteth not and that at the fore part of the night at such time as he is pointed vppon your Meridian line by the second proposition Again the next morning or any other morning take the height of
Ecliptick which is so vnder the Circle shal be called the place of that Starre And the Starre is sayd to bee vnder that Signe of whom the aforesaid point is a part The Longitude may also be taken if ye doe but fixe the Quadrant of Altitude in the Pole of the Ecliptick and stirre not at all the Meridian Circle Propositio 39. To finde the Latitude of any Starre THE Latitude of a Starre is the portion of the Circle that passeth from the Poles of the Ecliptick line by the Center of any Starre which is inclosed betwixt the Ecliptick line and the Center of the Starre and is found thus Your Circle standing in the Poles of the Zodiack as before turne the Starr vnder the said Circle for then the portion of that Circle betwixt the Starre and the Ecliptick is his Latitude And this Latitude is Northern when the Starre is North from the Ecliptick and Southerne of contrary Propositio 40. To finde what Starres be aboue ground at any time of the day or night IF ye would know it in the day time whē the Sunne shineth then take the height of the Sunne by the 2. proposition afterward finde his place by the 5. proposition lastly by help of the Quadrant of Altitude set the Sunne at his owne height Coast and then all the Starres aboue the Horizon doe appeare in the Globe Now if it be in the night and the Starres appeare then take the height of some knowne Starre and place the same Starr at his due height in the Globe so shall ye see the same Propositio 41. To doe the same without Sunne or appearaunce of any Starre YE must knowe what it is of the clocke at that time when ye would worke this conclusion then rectifie the Index by the 14. proposition Lastly turne the Globe till the Index come on the same hower as is giuen by the clocke for then the Starres appeare as they should Propositio 42. To finde what Starres will passe directly ouer our heads in the motion of the heauen AFter that the Quadrant of Altitudes is fixed in his due place as is spoken of before so that he now doe shewe the Zenith or Verticall point then mooue about the Globe and marke what Starres passe vnder the Zenith in this motion for those bee such as goe by our heads are called sometimes Culminant starres sometimes Verticall starres and haue their cheefest vse in Astrologie Propositio 43. To knowe with what degree of the Ecliptick any Starre rised commeth to the Meridian or setteth MOue the Globe till the Starre whom ye propose ascend aboue the Horizon and then marke the degrée of the Ecliptick that riseth with him Againe mooue him to the Meridian and marke the degree of the Ecliptick so doe by him in the West side of the Horizon and ye shal haue your intent Propositio 44. To knowe the hower of any Starres rising REctifie the Index by the 14. propositiō then turne the Globe til the said Starre whose time of rising ye desire touch the East side of the Horizon for then the Index giueth his time of rising And if ye turne him to the Meridian the Index will shewe his time of comming the ther or if ye turne him to the West side of the Horizō the Index sheweth his setting Propositio 45. To find in how long time any whole signe ariseth REctifie the Index by the fowerteenth proposition then put the beginning of the signe whose time of rising ye seeke to the East part of the Horizon and marke what the Index standeth on then againe put the last degree of the sayde signe to the Horizon and see what the Index sheweth for the differēce of the two times by the Index is the time in which that signe riseth Propositio 46. To find in what coast any starre is and how many degrees from the Meridian FInde the Starres aboue ground by the 40. proposition then the Globe beeing fixed put the Quadrant of altitude to any State Then shall the foote of the Quadrant shewe in the Horizon how farre the same Starre is from East West North or South But if ye first rectifie your Index by the 14. proposition and then finde the starres aboue by the 40. propositiō Agayn at the same time marke where the Index standeth lastly put any Starre vnder the Meridian and againe note the standing of the Index the differēce of those two times shewed by the Index is the distance of that starre from the Meridian in the time of your obseruation Propositio 47. To find what Starres rise or set any day Cosmically Achronically or Helically SVch starres as bee neare to the sunne in any day and ascende aboue the Horizon a little before the appearance of the same are said to ryse helically and such Starres as set very little after the Sunne are sayd to set helically Againe such Starres as ascend together with the Sunne and such as set at the same time are sayd to rise and set cosmically Lastly such starres as set together with the Sunne and such as rise at the same time are sayde to set and rise achronically and such may bee thus found Rectifie the Index by the 14. proposition and turne the place of the Sunne to the East side of the Horizon for the starres going immediatly before the Sunne rise helically and those in the Horizon rise cosmically and they that are in the Horizon in the west doe set cosmically and such as immediatly rise after the Sunne doe sette helically Lastly turne the Sunne to the West point of the Horizon and looke what starres touch the Horizon with him such set achronically and such as are at the same time rising in the East rise Achronically Propositio 48. To knowe the hower of the night at any time by the Starres REctifie the Index by the 14. proposition then againe finde what starres bee aboue ground at the same time when yee would know the hower by the 40. proposition for then the Index will shewe the hower Propositio 49 To find the fower Cardinall points of heauen at any time of day or night THe fower Cardinall points bee the fower degrees of the Ecliptick where of one is in the East rising an other is in the South or vnder the Meridian aboue at the same time the third in the West setting and the fourth vnder the Meridian beneath ground all at one instant in the time of any geniture or motion of any question and are thus knowen If yee seeke them in the day the Sunne shining then find the starres aboue ground by the 40. proposition and with all marke the degree of the Ecliptick in the East so likewise in the South West and North for those be then the Cardinall points Againe if it be in the night then find the starres aboue by the same 40. proposition and the pointes shall likewise appeare Lastly if nether the Sunne shine or starre then knowe the hower by the clock and afterward find the starres