The vse of both the globes, celestiall, and terrestriall most plainely deliuered in forme of a dialogue. Containing most pleasant, and profitable conclusions for the mariner, and generally for all those, that are addicted to these kinde of mathematicall instrumentes. VVritten by T. Hood mathematicall lecturer in the citie of London, sometime fellow of Trinitie Colledge in Cambridge.

The vse of the Celestiall and Terrestriall Globe . M.

ALl hayle Philomathes , what newes ?

No newes Sir , but this is the cause of my comming , to haue a litle conference with you touching the Globe .

You know that my mind , & affection towards all men of honest disposition hath beene such , that I am ready to pleasure them so farre forth as I may . Say therefore briefly , what will you haue the ende of our communication .

My desire is to be instructed by you in the vse of the Globe : and that so much the rather , because lately by our painefull countryman Maister Mollineux , at the great cost and charge of that worshipfull gentleman , and ●ouer of learning M. William Sanderson , there haue bin two Globes set forth , and for so much as they are now in the handes of many with whome I haue to do , I would not be altogether ignorant in those matters .

In good time Philomathes , is this requested at my hands , for I my selfe haue beene very liberally inuited ●o him to penne a Booke , concerning the vse of both the Clobes , for the better profite of our countrymen . So ●●at your request is but an hastening forwarde of that worke , which in respect of his liberalitie I cannot but be willing to vndertake . Goe to therfore let vs come to the matter : and to the end your desire may be fully satisfied , mooue you the question , and I will answere .

Very well : First resolue me in this , what diffe●ence do you put betweene a Globe & a Sphere . Me thin●eth by the common phrase of speach there should be a difference betweene them , for I heare some men say , that they will learne the vse of the Globe , and others are desirous of the Sphere .

If you regarde the proper signification of the worde , they differ nothing but this , that the one is the Greeke worde , the other the Latine . But in their vnproper signification there is a difference betweene them , for the Greeke worde 〈◊〉〈◊〉〈◊〉〈◊〉〈◊〉 , as it is vsed vnproperly , signifieth that , which the Latine worde Globus cannot . The worde Sphere taken vnproperly betokeneth such a bodie as is rounde on the outside and hollowe within ( as that which is made of twoo rounde dishes ioyned together by the brimmes ) the which bodie the Latines properly call Orbis , an Orbe : in this sence also is the worde Globus vsed . Moreouer the word Sphaera signifieth that instrument made of brasen hoopes ( wee call it commonly a ringed Sphere ) wherwith the Astronomers deliuer vnto the nouices of that Science , the vnderstanding of things which they imagine in the heauen . In this sence wee cannot vse the worde Globe , except wee imitate the ignorant people who not knowing how to call a thing rightly , will now & then terme the ringed Sphere a Globe .

What is the proper signification of these word and how are they defined ?

A Sphere or Globe , which in truth are all on● is a round bowed Solide : such a one is the whole fram● of the world consisting of heauen and earth .

What am I to obserue in this definition , for th● better understanding of the present matter which we hau● in hande .

You are especially to note the worde ( round● and thereby to gather this , that whether the Globe be Mathematically conceaued in minde , or sensibly deliuered to the eye , it is contained and inclosed vnder one surface . Also because nothing is made rounde without a centre , therefore in the middest of the Globe wee must conceaue a poynt to be , the which wee call the centre of the Globe , from whence all the right lines drawne vnto the vtte●●ost surface of the Globe are equall . Item for somuch as the bodie cannot be made rounde without a circular motion , and there is no circular motion without some rest , and that rest cannot bee simplie within the Globe , therefore likewise in the vttermost surface of the Globe you must especially obserue the two points vpon which the Globe mooueth , and vpon which it resteth whilest it is mooued . These points are called the Poles of the Globe . In the Poles this is to be noted , they are but two , they are right opposite one to another , they are equally distant from the Centre of the Globe . And in regarde that the Globes ( which we vse ) represent some principall parte of the worlde , therfore we call these foresaid Poles , the Poles of the worlde and speaking eyther simply of the Poles , or of the Poles of the worlde , wee haue relation onely to those pointes vppon which the Globe mooueth , whereof the one is tearmed the North , the other the South pole . Last of all from the one Pole to the other wee must imagine a line to bee drawen through the Centre of the Globe , the which right line is called the axeltree of the Globe , which in the reuolution of the Globe neuer mooueth but standeth still . Thus much generally concerning those thinges which are to be noted in the Globe , so farre foorth as it is simplie called by that name . Let vs now proceede to the diuision thereof . The surface of the Globe , as wee haue hetherto spoken of it , is to be vnderstood as a blancke hauing nothing inscribed in it , yet fit to receiue any inscription : therefore according to the inscription of the Globe wee diuide it two seuerall wayes : so that the Globe is saide to be eyther Celestiall , or Terrestriall . The celestiall Globe is that which contayneth in the conuenitie thereof certaine circles of the heauen , and the fixed starres , with their Astronomicall appertinences . Of this Globe I minde God willing to intreat first , and then of the terrestriall Globe .

By your definition I perceaue that your whole discourse shal be either of the circles belonging to the Globe , or else of the Starres with their Astronomical appertenences as you call them . But before wee enter into the discourse of these matters , I must craue a worde or two with you , concerning the particularities of your definition , that by comparing it with the thing defined , and with the thing signified by the Globe , which is the heauen , I may the better vnderstand the matter . First therefore in that you say that the Globe is rounde , would you haue me by these wordes vnderstande the Heauen to be so ?

Yea that you must , & to confute that fonde opinion of Lactantius , who affirmed the Heauen to be flat , there are sundry arguments alleadged by the Learned , whereof some are probable , the other necessary , the arguments are these : First it hath pleased God in the forme of the heauen to set forth a resemblance of his eternitie , that as in this figure , so in him there is neither beginning not ending . 2 For so much as the heauen was to comprehende all corruptible things , & without it is neither time nor place , therefore it hath receiued a sphericall forme , which of all Isoperimetrall figures is most capacious , and fittest to containe . 3. If the Heauens were not rounde , but three or foure square , or of some such like figure , that monstruous absurditie which nature doth so much abhorre , that is to say an emptinesse must bee graunted . 4. This roundnes being denied , it must needs follow , that wheresoeuer , and of what sorte soeuer the situation of the earth were , the distance from it to the heauen would not be the same , so that the quantities of the same Starres & their distances would be vnequall to those that dwell in any one place of the earth .

And by your leaue Sir it seemeth so : who is he that hath not seene the full Moone to rise as bigge as a bushell , the which not withstanding being mounted higher seemeth nothing so great . Againe in a fayre day , if wee looke rounde about vs , toward each part of the Heauen , doth it not seeme further from vs neare vnto the ground , than ouer our heads ? So that if we should make our eyes iudges of the roundenes of Heauen , wee can not auerre it to be so , because the Starres appeare in seuerall quantities , and each parte of Heauen seemeth not to be of an equall distance from vs .

In deed it is somewhat which you say but most easily answered , euen by a familiar example . A man reading his booke seeth the quantity of each letter , & which way so euer he turneth himselfe keeping the booke in one distance from his sight the letters appeare of the same quantitie , but if he put on his spectacles he conceaueth the letter to be greater than it is , because the visible forme thereof is inlarged by that meanes . The like must be vnderstood in the Starres , namely that which way soeuer they mooue they would appeare of the same magnitude , were it not that neare vnto the earth , when the Sunne is readie to set , there is a dampe or miste which is vnto our sight as the spectacles are , whereby the visible forme of the Starres seene is so inlarged and dispersed , that our sight cannot comprehende them in their proper Magnitude . The like vnto this is to be perceaued in the water , which causeth any thing cast into it to seeme greater , than it would appeare in the same distaunce lying on the bare grounde . As for the seconde obiection which you make , you must vnderstand this , that the sight is not an immediate iudge of a distance assigned , but gathereth it by meanes , that is by the interposition of a certaine number of men or houses , or trees , or hilles , or some other such like thinge betwixt the eye and the thing seene . Which thinges interposed if they bee many , wee affirme the thing seene to be farre off , because reason telleth vs that they cannot be contained in a small space : contrarywise if they bee fewe wee iudge the distaunce to be the lesser . Hereupon it commeth to passe that our eye running along by the grounde and beholding so many housen , churches , hilles , and trees betweene vs and the heauen , wee iudge and affirme it to be farre from vs : but for somuch as in looking vp towarde heauen , there is nothing to be seene directly in our sight , except a cloude or two which ( as the Philosophers affirme ) cannot be aboue three miles or there aboutes distant from the earth , therefore wee thinke that parte of heauen to be nearer : so that the argument taken from the equall apparent magnitude of the starres cannot bee but true , and inferreth the roundenesse of the heauen . The. 5. argument is set from the motion of the starres , which is circular . 6. Againe the Sphericall figure is fittest to mooue , and therefore moste ●●tte for the heauen , whose motion is continuall without intermission . 7. Moreouer by the forme of the partes namely the Starres , wee inferre the forme of the whole . 8. Also this standeth with reason , that the most perfect body should haue the most perfect forme , and therefore the heauen beyng so pure and perfect that the Philosophers wanting a name for the subiect matter whereof it is made , haue called it a Quintessence , it ●equireth also the most perfect forme which is Sphericall and rounde , as may appeare by all the workes of God , where in this roundenesse is especially to bee obserued . 9. Last of all we may take an argument from our Astronomicall instruments which are most fitte being rounde and are deriued from a circle . Thus much for the forme and figure of heauen .

You say then that the heauen is most perfectly rounde : and not onelie that , but you will haue it also to bee accounted a Solide bodie . By the worde Solide we commonly vnderstand that bodie which beyng made of some massie matter is not hollow within , but whole and intire through out . Must I conceaue the heauen to be so ?

Common sence denieth that conceat . For you see the earth , the water , and whatsoeuer element else , or Elementate thing there is to be contayned within the coape of heauen , in so much that the matter of the heauen is not intire and Solide thorough out . But to the ende you may vnderstande this Soliditie aright , hearken I pray you vnto my wordes , and let the materiall Globe alone for a while . The whole worlde is diuided into two principall partes , the one Etheriall , the other Elementall . The Elementall parte compacted o● the 4. Elements , the fire , the aire , the water , and the earth is inuironed on euery side with the Etheriall parte which is the Heauen : which from the element of the fire vpwarde is Solide and hath no emptines in any place . Yet i● it not so Solide but that it is distinguished into certain● Spheres or ( as we ought properly to tearme them ) Orbes , whereof each one mooueth diuersly . These Orbes are in number . 10. as may be gathered by the motion , occultation , and parallaxe of the Starres . The 10. which is the vppermost of all is called the primum mobile , it mooueth from the East directly towarde the West vpon the poles of the world , expressed by the poles of the Globe , within the space of 24. houres , and imparting his motion to the other . 9. it carieth them with him rounde about in the same time , so that whereas we see the Sunne , the Moone , & all the Starres to rise and set within that space , it commeth to passe not by their owne proper and peculiar motion , but by the violent and swifte motion of this first mooueable . The inferior . 9. Spheres mooue from the West towarde the East not directly in a line against the other , but from the West Southwest they bende toward the East Northeast . Some of these . 9. Spheres are beautified with Starres the other haue none . The ninth Sphere hath neuer a Starre , it is vsually called the Christalline heauen ( although that name be common also to the foresayd Sphere ) because it is most cleare , and transparent , hauing no one parte thicker than an other . It maketh his proper and perfect reuolution as Ptolome affirmeth in 36000. as Albategnius writeth in 23760 as Alphonsus gathereth in 49000. yeares : the which time is thought to be Plato his great yeare , wherein he sayd ●ach thing should returne to the former estate . Of those ●pheres which are beautified with starres , some haue but ●●e starre , the other hath many : that which hath many is ●he , 8. Sphere , otherwise called the Firmament , either be●ause beyng the vttermost of all ( as antiquity iudged ) it ●●rmely keepeth in & incompasseth the rest , or else because 〈◊〉 comprehendeth those starres , whose distance one from an ●ther is firme & fixed , and not vncertaine as the other ●re , and therefore also is called the Sphere of the fixed ●tarres . This. 8. Sphere albeit it be partaker of the. 2. vppermost ( for as I sayd each vppermost Sphere imparteth his motion to all his inferiors ) yet hath it a motion properly belonging to it selfe , not perfect and absolutely ●phericall , as the other motions are but winding from ●he North to the Southward , in . 3500. yeares it reuolueth ●he same way in the same time , making his whole accesse and recesse in . 7000. yeares . This motion is called the motion of Trepidation . The other . 7. Spheres which succeede are each one decked with one onely starre called a Planet , that is by interpretation a wandring Starre ; not that it runneth at randon vncertainely , ( for the motion of them all is most certainely knowne , as may appeare by the Eclipses which are foreseene an hundred yeare before they come ) but because their distance one from an other is neuer the same beyng , sometimes nearer , and sometimes farther of , therefore are they tearmed wan●ring starres . The vppermost of these . 7. is the Sphere of Saturne , whose motion is complete in . 29. yeares . 155. ●ayes . 3. houres . 47. min. 44 sec. Iupiter next vnder him compasseth the Heauen by his proper course , in . 11. yeares , ●14 . dayes . 13. houres , 12. min. 4. sec. The Sphere of Mars finisheth his race in one yeare , 321. dayes . 16. houres . 34. min. 44. sec. The Spheres of the sunne , Venus ; and Mercurie run their course in one yeare , that is in . 365. dayes , 5. houres . 55. min. 26. sec. 10. thirds . 56. fourths . The which space of time is commonly called , a solare yeare . The Moone which is lowest of all & next to the Elementall region , maketh her reuolution in the space of . 27. dayes , 7. houres . 43. min. 7. sec. So that hereby you are to vnderstande that albeit both the heauen it selfe and the celestiall Globe be called a Solide bodie , yet there is this difference betweene them that the Globe consisteth of one peece , but the heauen of many Spheres or Orbes , and those as you haue hearde moouing sundry wayes & in diuers maners .

I doe beleeue you because , as the Prouerbe is , a learner must beleeue , but it seemeth vnpossible that the one Sphere should mooue one way , and the other an other way .

It is no more impossible for the one Sphere to mooue one way and the other an other way , than it is impossible for the Maister of a shippe to walke from the prowe to the poupe , that is from the South Northwarde , whilest the ship runneth from the North Southwarde .

Which of all these . 10. Spheres doth the celestiall Globe represent ?

It representeth especially the. 10. Sphere .

But you said before that the starres are in the 8. Sphere which is the firmament .

It is true : but because the motion of the fixed Starres following the motion of the ninth Sphere from West to East , is so slowe and so litle , that in a mans life tyme it can hardly be perceaued , therefore without any great inconuenience we may place the fixed starres in the ●●●face of the Globe , though it properly in respect of the ●●●cles represent the tenth .

Why do you in the definition of the celestiall ●●obe put in these words ( contayning in the conuexitie ) ?

Thereby is expressed an other difference betweene that which wee behold in the heauen it selfe , and on the celestiall Globe . Our eye not beyng within the Globe beholdeth euery thing described thereupon on the outside : whereas notwithstanding we see the starres on ●●e innerside of heauen .

Why doe you say certaine circles , are there any more to be vnderstoode in the heauen , than are expressed in the Globe .

Yea a great many , the which I will both name and describe vnto you as occasion serueth . But for so much as these on the Globe are sufficient for a yong be●inner or a Nouice in Astronomie , therefore there are ●o more described . Whereof one is Reall , the other are imaginarie .

What say you that some of these circles are imaginarie . What meane you thereby , would you haue vs thinke them to be deuises of an idle brayne ?

Not so , their commoditie is singular in common life beyng well vnderstood and applied to vse : but ●herefore they are called Imaginarie because they are not expreslie to be seene in the heauen , but are in minde to be conceaued .

Well , let vs now come to those thinges which you saide are principallie to be obserued in the celestiall Globe , that is the circles and the starres with their Astronomicall appurtenances .

Here I will vse a Hysteron proteron as the Rh●toricians tearme it , and will set the carte before the hors● that is I will first speake of the Starres , and then of th● Circles , for so I thinke it fittest for your instruction .

As you please Sir , but what Methode and ord●● shall wee obserue in them .

I thinke it not amisse to haue consideration 〈◊〉 these two thinges : First , of the writing which I tearme● before the Astronomicall appertenances , then of th● starres themselues .

I pray you do so . I perceaue in the Globe that b●● many of the Starres there are set downe the Character● of the Planets , sometimes one alone , as in the thighe 〈◊〉 Gemini , what doth it signifie .

The Character doth expresse the nature of th● Starre vnto which it is adioyned , according as the Character doth importe . If it be the Character of Saturne , signifieth the Starre to be of his nature : if it be the Character of Iupiter , it signifieth the starre to be of his nature , and so forth of the rest .

Sometimes there are two Characters togethe● as in the fishe .

They betoken that starre to admit the nature 〈◊〉 both the Planets .

Sometimes betweene the two Characters ther● standeth the letter P.

It signifieth the starre to be of the nature of th● Planet vnto whom the first Character doth belong , ye● partly also of the nature of the Planet , to whom the othe● Character apperteineth .

Sometimes the Characters are not ioyned with any one starre but are set downe by themselues alone , & before the Character there standeth a letter as in the Lion .

It signifieth that all those starres to whom that ●●●ter is adioyned , to be of the qualitie of that Planet , before whose Character the same letter standeth .

I finde in the Globe certaine syllables , but they make not perfect wordes : as Card , or Car. Alf. or Al●●● . Reg.

Card. or Car. signifieth Cardanus , whose stu●●● in these sciences hath beene singular , and therfore his authoritie is great , and is often alleaged not onely for the ●●gnesse of the Starres , as where it is written Reg. Car. that is to say , Cardane counteth it a princely Starre , or a ●●arre of the first magnitude . But also for their qualitie 〈◊〉 where you see it written by the bowe of Sagittarius the archer , the meaning is that Cardane accounteth that ●●arre to be of the nature of Iupiter & Mars . The like 〈◊〉 to be vnderstood of Alf. or Alfon. which signifieth Alphonsus king of Aragon , whose great trauaile and ●●st in those studies hath purchased vnto him an eternall ●●me .

Let vs now come to the Starres for I see nothing ●●s to be doubted of , what order shal be kept in discour●ng of them .

I thinke it sufficient to speake of their adiuncts , ●amely of their quantitie and qualitie .

Then you minde not to speake of the diuision of ●●e Starres into seuerall kindes , nor of the matter whereof they are made .

No , for the starres expressed in the Globe are all of one kinde , that is fixed , and differ onely in quantitie or ●ualitie , as for the matter , that belongeth not to the Astro●omer , but to the Philosopher : so that whether they be the thicker parte of their Orbe , and are to their Or● as a knot to a tree , or whether they bee made of fire are firie stones let the Philosophers looke to that . I pu●pose onely to entreate as I haue sayde of their quanti● and qualitie . The quantitie of the starres is to be consid●red eyther in their number , or in their magnitude .

How many are there in the Globe ?

There are 1025.

Are there no more in the heauen ? We say commonly that they are in number infinite .

It is without question that there are more 〈◊〉 heauen , but yet they are not infinite in number , for 〈◊〉 is written . Psalm. 147. He counteth the number 〈◊〉 the Starres and calleth them all by their names . If the● may be counted and named , they are not infinite . Ther●fore when wee say that they are infinite , our meaning 〈◊〉 that their number is exceeding great , as it appeareth . Genesis 22. vers. 12.

Why then do the Astronomers keepe an accor● of no more seing their number is so great ?

The heauen is to the Astronomer as a book therfore euen as a man looking vpon a booke lying farr● of from his sight , doth onely account those letters whic● he doth see & discerne : euen so the Astronomer , althoug● he see a great number of starres , yet maketh he accoūt●● no more then these because he can distinguish no more .

Haue there no more beene noted heretofore , o● since the time that this number was first ratified ?

Yes , for the Portugales traueling into Indi● haue brought home newes of certaine litle cloudes near vnto the South pole , & certaine stars , the which stars a● you may see are set downe by M. Mollineux in the Celestiall Globe . Some of them being comprehended within ●●e Crosse , and are commonly by our men called the Cro●ers , some of them are included in the South triangle , ●●hers are left in formed . So that their report argueth ●●at all the fixed starres were not obserued by Ptolomie ●●mselfe .

There is yet one question remaining touching the number of the starres . I obserue that in the winter the ●umber of the starres seemeth more than in Summer : that should be the reason thereof ?

You must note this that it most commonly fal●●th out so when the weather is coldest , and the nightes ●re frostie : and thereby I gather the chiefest reason , why 〈◊〉 the winter the starres appeare so many to bee this , 〈◊〉 Sommer the colde hauing no place left vnto it where●● to be , but the middle region of the ayre , where it ●axeth at that time most forceable by reason of the An●peristasis of the heate , it so engrosseth and thickeneth ●●e ayre , that the starres of the lesser magnitude beyng ●ut weake in their beames cannot pearse it , and come to ●ur sight : In winter this colde breaking the prison wher●● it was pend before , & gathered thicke together , sprea●eth it selfe and becommeth more thinne , so that the ayre beyng more purged , and the grossenes thereof being ●●ken away , yeeldeth to the starres of smaller light , a free ●nd readie passage through which they may sende there ●eames vnto our sight . An other reason is thus alleaged , 〈◊〉 winter because the ayre is more purged , the starres do ●ine very forceably , whereupon it commeth to passe that our sight may be deceaued in them , and causeth vs to ●hinke , that wee perceaue more starres than indeede wee wee doe : where as wee doe not see more starres , but onely certaine appearances of them procured by their vehement brightnes and twinckling , and by the wauering of the ayre . Let this also be an other reason : the nearer the Sunne is to the ground the more lightsome is the ayre aboue it , the more lightsome the ayre is the fewe● Starres are seene : therefore considering that in Summer the depression of the Sunne is but litle , and in winter great , whereby the ayre in the night time in Summer , is more lightened than in winter , herevpon it commeth to passe that the starres seeme fewer in Summer than in winter .

Thus much for the number of the starres : wha● is their Magnitude ?

Their Magnitude is a certaine quantitie wherby the starres differ one from an other . The seuerall Magnitudes obserued in the starres are sixe , vnto the which are adioyned certaine other which are called of the Latines Nebulosae , & Obscurae , cloudie and obscure o● darke starres . All there Magnitudes are expressed in the Globe , with seuerall formes set downe before the nose o● the Greater Beare , so that hauing an eye to those forme● you may easily learne what Magnitude any starre hath that is placed in the Globe .

How many starres are there of each seuerall Magnitude .

There are . 15. of the first Magnitude : of the second . 45. of the third . 208. of the fourth . 474. of the fift . 217. of the sixt 49. The cloudie starres are . 5. the obscure . 9. But you must still remember this , that in this account those starres are not contained which are inscribed in the Globe according to the report of the Portugals , yet their seuerall Magnitudes may be knowne by their forme .

So I suppose , but yet these which you haue now counted make but 1022. you reckoned before 1025.

It is true : but you must note this , that com●ōly in rehearsing the number of the starres , the Astro●omers omit those which are in the haire of Berenice , if ●hey be added the whole number is 1025.

Of what bignesse may the starres be ?

Some of them are 107. some . 90. some . 72. times ●igger than the earth . But of this matter I haue written ●argely in my Booke concerning the vse of the Celestiall Globe in Plano , wherein you may satisfie your selfe concerning their quantitie .

The nexte thing to be spoken of touching the ●tarres is their qualitie : what haue you to deliuer concerning that ?

This worde qualitie hath a very large signification , and may be applied almost to what soeuer is not of ●he substance of the Starres . But I will speake onely of ●heir twinckling and figure .

What is the cause why the starres do twinckle ?

The continuall motion of the aire : in which ●here are two motions to be considered : the one is pro●●er to the aire , which is vpward in a right line : the other is vnproper receaued from the Heauens . For as the Heauen is caried about in the space of 24. houres , so doth it ●ead with it what soeuer is moueable within it , whereby ●t commeth to passe , that the forme of the Starres appea●ing in it is greatly distracted , so that it seemeth to vs to ●●ast forth sparkles , which we call the twinckling thereof . This may easily be confirmed by the water which running on swiftly causeth the Starres which are by reflexiō●eene in it , to twinckle much more than they doe in the aire , by reason that it is a grosser bodie , and the motio● thereof is to vs more sensible than the motion of the aire

If the motion of the aire be the cause of th● twinckling of the Starres , why should not the Plane●● twinckle as well as they ?

The reason why the Planets do not twinckle i● their nearenesse vnto vs , whereby it commeth to pass● that their beame is lesser troubled and distorted .

Doth the twinckling of the Starres signifie any thing ?

It doth signifie the motion of the ayre generallie : but if it bee more than vsuall it signifieth winde Thus much concerning that matter , now followeth the figure of the Starres . The figure is eyther common o● peculiar . The common figure considered in euery one is the roundenesse , for this wee holde that the figure of euerie Starre is rounde , and not three or foure square : of this there are sundrie argumentes . First , our sence which iudgeth the Starres to be rounde : agayne the most noble bodie as I saide before requireth the most noble forme : the most excellent bodies are the heauenly bodies : therefore they craue a rounde figure for that of all other is counted most excellent . To conclude the Moone geueth vs a most certaine argument of this roundenesse : for she doth not onely appeare so at the full , but at all other times shee receaueth her light circularly from the Sunne .

Yet that is not alwayes so , for in the firste quarter and the thirde her light is parted with a right line .

The reason of that is yeelded by the Maisters of Perspectiue , who truely affirme that euery great circle in Sphericall bodie standing full before our sight , ●●emeth to be a right line , This therefore shall serue for 〈◊〉 confirmation of the common figure belonging to euery Starre , which is their roundenesse . The peculiar fig●re is that which is considered but in some , and is call●d a Constellation .

What is a Constellation ?

A Constellation is a certaine number of starres r●presenting by there place , & order ( after a certaine sort ) the forme of some naturall , or artificiall thing . It is otherwise called an Asterisme , forme or figure .

Are all the stars inclosed within these constellations .

You may easily see by the Globe they are not : there are . 108. exempted by the ancient Astronomers which the called ( informes ) vnformed , yet of later time . 6. of thē●●ue beene reduced into the figure of Antinous , and ●●ree into the haire of Berenice .

Why were the starres brought into constellations ?

For instructions sake : things cannot be taught ●ithout names : to giue a name to euery one , had beene both troublesome for the Maister and for the Scholler : ●●oublesome for the Maister to deuise , troublesome for the Scholler to remember . As the merchant therefore ca●eth all his billes of one kinde into one boxe : & out of ●●at boxe can fetch them as occasion serueth : euen so the ●stronomers haue reduced many starres into one Con●●llation , that thereby they may tell the better where to ●●eke them , and being founde how to expresse them .

Why did they bring them into these figures and into none other .

There be . 3. seuerall reasons which induced thē●ereunto . First these figures expresse some propertie of the Starres , as those of the Ramme to be hote , & drie , so● so is the Ramme : Andromeda chained betokeneth imprisonment . The head of Medusa cut of signifieth th● losse of that member . Orion with his terrible , & threaning gesture importeth tempest , and terrible weather : th● Serpent , the Scorpion , and the Dragon , signifie poiso● the Bull insinuateth a melancholie passion , the Beare i●ferreth crueltie &c. Secondly some of the Starres if no● precisely , yet after a certaine sorte do represent such a figure , and therefore that figure was assigned them : as fo● example the Crowne both North and South , the Sco●pion , and the Triangle partly represent the figure whic● they haue . The thirde cause was the continuance of th● memorie of some notable man , who either in regarde 〈◊〉 their singular paines taken in Astronomie , or in regard of some other notable deede , had well deserued of mankinde , as Hercules , Perseus , &c.

Are these constellations of any antiquitie , & wh●● was the first author of them ?

I neuer reade who was the first author of eac● particular constellation , we receaue them of Ptolomee and he receaued them of the Platonickes , so that the●● antiquity is great . Thyestes the brother of Atreus is sai● to haue inuented the constellation of the Ramme : More ouer in the 38. chapter of Iob , there is mention made o● the Pleiades Orion , and Arcturus & Mazzaroth which some interprete the 12. signes : Iob liued in th● time of Abraham as Siderocrates maketh mention in his Booke , De commensurandis locorum distantijs .

How many constellations are there , and which are they ?

There are 48. besides the Crosse & the South ●●●angle , which are newly added in the last Globes . In the ●orth parte there are . 21. namely . 1. Vrsa minor , the les●● Beare . 2. Vrsa maior , the greater Beare . 3. Draco , the Dragon . 4. Cepheus . 5. Bootes or Arctophylax . 6. Corona Borea , the North crowne . 7. Engonasis , the ●●eeler . 8. Lyra , the Harpe . 9. Olor , the swanne . 10. Cass●peia . 11. Perseus . 12. Heniochus or Auriga , the ●●●●ter . 13. Serpentarius , the man holding the Serpent . 〈◊〉 Serpens , the Serpent . 15. Sagitta , the Arrow . 16. A●●ila , the Eagle . 17. Delphinus , the Dolphine . 18. Equis●ctio , the lesse Horse . 19. Pegasus , the winged Horse . 〈◊〉 Andromeda . 21. Triangulus , the Triangle .

In the Zodiacke of the 8. Sphere or firmament there 〈◊〉 12. according to the number of the Signes . 1. Aries , ●●e Ramme . 2. Taurus , the Bull. 3. Gemini , the Twinnes . 〈◊〉 Cancer , the Crabbe . 5. Leo , the Lion . 6. Virgo , the ●●rgin . 7. Libra , the Ballance . 8. Scorpius , the Scorpion . 〈◊〉 Sagittarius , the Archer . 10. Capricornus , the Goate . 〈◊〉 Aquarius , the Waterman . 12. Pisces , the Fishes .

In the South parte there are . 15. 1. Cetus , the Whale . 〈◊〉 Orion . 3. Fluuius , the Riuer . 4. Lepus , the Hare . 5. Ca●●● maior , the greater Dogge . 6. Canis minor , the le●●●r Dogge . 7. Argo nauis , the Ship . 8. Hydra , the Snake . 〈◊〉 Crater , the Cup. 10. Coruus , the Crowe . 11. Ceutau●is , the Centaure . 12. Lupus , the Wolfe . 13. Lar , or Ara , ●●e Altar . 14. Corona Austrina , the South Garlande . 〈◊〉 . Piscis Notius , the South Fish .

Yet me thinketh there be 2. which you haue not ●●amed , that is Antinous and Berenices hayre .

Those two were diuised since , and therefore are ●ot vsually counted in the number of the Constellations ●ut are reckoned among the informed Starres , as I said ●efore .

Doe all Astronomers retaine these constellation and his number ?

No , some count but. 44. some . 46. some . 52. some 72. But by the chiefest Astronomers the foresaid number is retained .

Of which of all these Starres ought I to take notice especially ?

It is good to know them all , or at leastwi●● those which are of the first , second , and thirde Magnitude . But you must especially bee acquainted with th● lesser Beare : for the Starre which is in the ende o● her tayle is called the Pole Starre , by reason of th● nearenesse thereof vnto the Pole , it is also called th● North Starre , and for the excellent vse , which it hat● in Cosmographie , it is called simplie the Starre . An● the North pole in respect of the nearenesse of the lesse● Beare , is called the pole Arcticke ( for Arctos amon● the Grecians signifieth a Beare ) and the South pole because it is opposite , and right against the pole Arcticke● called the pole Antarcticke .

I coulde wishe ( if it were not troublesome ) th●● you would deliuer to mee the poeticall reasons of these constellations because it is very pleasant .

It shall not neede if you desire them , you m●● finde them set foorth at large in that litle booke whic● I named before called the vse of the Celestiall Globe 〈◊〉 Plano .

Well then let them passe , and let vs now● come to the Circles of the Globe , and in them I woul● gladly learne these two thinges , what they are , and wha● vse they haue .

With a good will : but first you must no● ●he manifolde signification of the worde , otherwise ●ou may mistake your selfe greatly . The worde Cir●le is taken sometimes properly , sometimes vnproper●y . Properly a Circle is a rounde plane as Ramus ●efineth it , or according to Euclide , it is a plaine figure contained vnder one Line , which is called a Cir●umference , vnto the which all righte lines drawen from the Center are equall one to an other . In this ●ence wee neuer simplie vse the worde Circle , speaking ●f the Celestiall Globe , but wee vtter it periphrastical●e in this manner , the plane of the Equinoctiall Circle , the plane of the Horizon , or Horizontall circle , &c. The worde Circle taken vnproperly , signifieth eyther a circumference which is a crooked line without breadth , or else it signifieth a surface , in both these significations , the worde Circle is vsed in the Celesti●ll Globe : be they perfectlie rounde or no , wherevpon we make this diuision of the Circles in the Globe : The Circles are eyther perfectlie rounde or vnperfectlie round .

Is it possible that there should be a circle in the Globe that is not perfectly rounde ?

Doe you not see in the Globe a space contained and inclosed on each sides with prickes , which hath certaine diuisions and goeth not on directly , and euen as the other circles doe .

Yes , it passeth by the bowe of the Archer , and from thence ascendeth to the Eagle , and so continueth to the Swanne , and to Cassiopeia , and downe to the Archer , compassing the whole heauen round about : what may that circle be ?

It is that great white circle which is really to be seene in heauen , by the Grecians it is called Galaxia by the Latines Lactea via , or Lacteus circulus , and by vs expressing word for word , it is called the milke waie● The best opinion touching this circle is this , that it is the parte of the firmament , neither so thinne as the othe● partes thereof , nor yet so thicke as the Starres thēselues● If it were so thinne as the other partes of heauen the● could it not retaine any light , but the light would passe through it , and not be seene : if it were as thicke as the Starres then would the light be so doubled in it , that i● would glister , and shine as the Starres themselues doe but beyng neither so thinne as the one , nor so thicke as the other , it becommeth of that whitenes which we see If you desire to reade the poeticall fables or other discourses touching this circle , you shall haue them also in my booke of the Globe in Plano .

What vse hath this circle in the heauen ?

First , it limiteth the tropicall points whereof w● shall speake hereafter : Secondly , it is an argument vnto vs to prooue , that the Starres mooue not in the firmament , as fishes in the sea , or as birdes in the aire : For if that were so , it is most certaine that the Starres which are in this Circle at this present , would presently shifte the same , and passe aut of it into some other place of the 8. Sphere which neuer falleth so out : but common experience witnesseth this , that the Starres which are now in the milke way , haue beene in it euer heretofore , and wee shall see them still continue therein , so long as the heauen indureth . Thus much for the vnperfect reall circle which is but one . Let vs now come to the perfect circles of the Globe , which are not really to be seene but in imagination to be conceaued , vpon which the principall vse of ●●e Globe dependeth : A perfect rounde circle is that ●hich lieth vniformally betweene his termes . In these ●ircles this is first to be noted , that vnto euery one of ●●em belongeth Poles , and Graduation either expressed 〈◊〉 vnderstood . The Poles of a circle are . 2. points concea●ed in the surface of the Globe , equally distant from eue●● parte of that circle whose Poles they are sayd to be . Graduation is the diuiding of a circle in to certaine parts , wherof euery one is called a degree . The parts wherinto ●uery circle of the Globe either is actually or imaginarily vnderstood to be diuided are . 360. Therefore a degree in nothing else but the. 360. part of a circle So that when as we speake simply of a degree either of heauen or earth , or generally of a degree of any circle , it is not to be vnder●●ood as a thing , that may be limited , and set downe by any certaine measure , as by passes , or yardes , or miles , or inches , or such like quantities , because it is not of a cer●●ine greatnesse euery where , but as the circle is greater or lesser , so doth the degree increase or decrease , and is ●ide to be the. 360. parte of it , be it of what quantitie soeuer .

I praye you let vs wade a litle farther into this matter , tell me what was the reason why a circle was diuided into these partes and not into any more or lesse ?

The reason is this . The Cosmographer whether he haue to deale with heauen or earth , hath many occasions to diuide a circle into sundry partes , therfore it be●ooued him to choose such a number in the diuision of a circle , as might most conueniently be diuided by many diuisors : now for somuch as there could no number be founde of so small a quantitie , that might be diuided by so many diuisers as this number . 360. may be ( for it ma● be diuided by . 1.2.3.4.5.6.8.9.10.12.15.18.20.24.30.36.40.45.60.72.90.120.180 . ) therefore they made 〈◊〉 speciall choyse of this number , reiecting the custome● Eratosthenes and Hipparchus , whoe were wont to diuide a circle into . 83. partes . Neither doe the Cosmographers onely graduate a circle , diuiding it into simple degrees , but they goe on farther and parte a degree into 60. minutes , a minute into . 60. secondes , a seconde into 60. thirdes , a thirde in . 60. fourthes , and so forth vntill they come to tenthes beyonde which number they do● not lightly passe .

Then I gather by your wordes , that a minut● is nothing else but the. 60. parte of a degree , and a second is the. 60. parte of a minute , and a thirde is the 60. parte of a seconde , and a fourth is the. 60. parte o● a thirde , &c. But why did they choose this number . 60.

The Cosmographer was induced to choose this number . 60. by the same reason whereby hee wa● mooued to choose the foresayd number . 360. As in diuiding of a circle so likewise in diuiding a degree , a minute , a seconde , &c. He thought it most conuenient to take such a number as beyng but small might be diuided into most partes , and therefore to auoide the tediousnesse of greater diuisions , he choose . 60. rather than any other , because there is none of so small a quantitie , that will admitte so many partitions for these number● may diuide it . 1.2.3.5.6.10.12.15.20.30 . Thus much concerning the significations of the worde circle , and the common accidents thereof , which are Poles and Graduation , now I will proceede to their seuerall kinds . The perfect rounde circles imaginarily conceaued in the ●eauen , and adscribed with the Globe , are eyther great ●t litle . A great circle is that which cutteth the Globe ●nto two equall peeces . As touching the Poles of the ●reat circles this rule is generall , that if . 2. great circles ●ut one an other at Right angles , the Poles of the one ●ircle are in the other : also , if . 2. great circles cut one ●n other at oblique angles , the Poles of the one are di●●ant from the Poles of the other , so farre , as the grea●er declination or distance of the one circle is from the other . A great circle is eyther mooueable or fixed . A mooueable circle is that , which mooueth with the motion of the Globe . A mooueable circle , eythe lieth betweene the Poles of the Globe , or passeth thorough them : The moueable circles , which lie betweene the Poles , are . 2. whereof the one lieth iust betweene them in the very middest , and is called the Equinoctiall ●or Equator . So that the Equinoctiall may bee defined to bee a great mooueable circle of the Globe , lying iust in the middest betweene the. 2. Poles of the world : The other circle lyeth not iust betweene the. 2. Poles , but leaneth towarde eyther of them , and is called the Eclipticke , so that the Eclipticke may be defined to be a great mooueable circle , leaning towarde each pole of the worlde , alwaies cutting the Equinoctiall at oblique angles . The two points wherein it cutteth , the Equinoctiall are called the Equinoctiall pointes , and the two points wherin it swarueth most of all from the Equinoctiall , are called the Solstitiall points , or Tropicall points , the reason wherof I will declare hereafter . The moueable circles passing through the Poles of the Globe are . 2. and they cut themselues at Right angles in the Poles : the one is called the Equinoctiall colour , the other is the Solstitiall colour . The Equinoctiall colour is a moueable great circle draw by the Poles of the world & the equinoctial points . The Solstitiall colour is a moueable great circle , passing thorough the Poles of the worlde , and the Solstitiall points , A great fixed circle , is a circle which followeth not the motion of the Globe , but standeth still whilest it turneth about . The fixed circles are . 2. cutting one another a● right angles , namely the Horizon , and the Meridian . The Horizon is a great fixed circle of the Globe , diuiding the parte of the heauen which is seene , from tha● parte of the heauen which is not seene . The Meridia● is a great fixed circle of the Globe , cutting the Horizon at right angles . Thus are all the perfect great circles expressed in the Globe . A litle circle is that which diuideth the Globe into 2. equall peeces , and are all equally distant to the equator : The litle circles of the Globe eyther touche the Eclipticke , or are seuered from it . Those which touch the Eclipticke , are called Tropickes . A Tropicke is a litle circle in the Globe , parallell to the Equinoctiall , touching the Eclipticke in the Tropicall point . Those litle circles , which touche not the Eclipticke , are called Polare circles : A Polare circle is a litle circle in the Globle Parallell to the Equinoctiall , passing by the Poles of the Eclipticke . Thus haue you the briefe definitions of the vsuall circles of the Globe , the other circles shal be defined as occasion serueth .

I pray you , now let vs draw neare to that , which I so greatly desire , that is the vse of the Globe .

The vse of the Celestiall Globe is eyther simple or mixte . The simple vse of the Globe , is when we worke and performe , a conclusion by the Globe it selfe , without the helpe of any forraine instrument : and that either by ●●ch circle alone , or by two or more of them taken to●●ather . The mixt vse of the Globe is that , which be●●e the Globe requireth the vse of forraine instruments . And for somuch as these seuerall vses of the Globe can●●t so be distinguished one from another , but that of ●●cessitie now and then they must goe ioyntly together , I thinke it not a misse therefore before I goe any further , to make you acquainted with the instruments .

Doe so I pray you , and I will mooue such que●●●ons concerning them , as I shall thinke conuenient for my instruction .

The instruments are these : First a paire of Calaber compasses , whose feet must be bent inward according a● you see in the figure . A. The second is a Square with a ●●ūmet line , made in such forme as you see the figure B. The third is an houre circle as wee call it , with his In●ex , expressed in the figures C. and D. The fourth is a thinne ruler of brasse , bowed according to the conuexi●ie of the Globe , & diuided into the. 90. degree , made fast at the. 90. degree to a litle buttone of brasse , this instrument is called , the Quadrant of Altitude , and is expressed in the figure . E. The fifth is an halfe circle of brasse called a circle of Position , as in the figure F. The sixte i● an Index , which wee call a Sphericall Gnomon , the fourme whereof is expressed in the figure G. The seuenth . is a Needle touched with the Loade stone .

To what end serue the Calaber compasses ?

With them wee take the distance of any two things what soeuer propounded vpon the Globle , as of two Starres , or of any circle from a Starre : or of . 2. circles one from an other .

In what manner shall I take the two starres , and how shall I inferre their distance .

Stretch the one foote of your compasse fro● the centre of the one Starre , vnto the centre of the other , then applie the feete of your compares to the ●quator , the degrees of the Equator contained between● the feete of your compasses , expresse the distance of th● two Starres .

But what is that distance ?

It is their distance onely in degrees , for we● cannot simplie expresse it otherwise , yet if you desire for your pleasure sake to knowe what number of mile● any two starres in the Globe are distant , one from an other , note these my wordes and you shall know it . Th● Astronomers considering the huge quantitie of the starres compared with the Globe of the earth , haue concluded the compasse of the firmament to be in the outside 1017562500. miles , and each degree to containe 2826562 ½ . Therefore knowing how many degrees any . 2 Starres are distant one from an other , if you multiplie the number of degrees by the number of miles answereable to each degree , you shall finde the distance in miles , the centers of the. 2. starres beyng supposed to be in the conuexitie of the firmament .

I pray you giue me leaue to haue a litle more conference with you concerning the taking of the distance of any two Starres , or what soeuer thinges else vpon the Globe . You say , that I must stretch the one foote of my compasses from the centre of the one starre vnto the centre of the other , and afterwarde applie my compasses to the Equator , the degrees of the Equator contayned betweene their feete expresse how many degrees the two Starres assigned are distant one from an ●●her . I take this rule to be certaine and true , when the ●●e foote of the compasses beyng set in the beginning of ●egree , the other foote lighteth iuste in the ende of the ●●●e , or of some other degree . But put case that the f●●te of the compasses should fall betweene the beginning , and ende of a degree , what shall I then say ?

You must pronounce the Starre to be distant ( besides the whole degrees ) so many minutes , as are contained betweene the beginning of the last degree , and the ●●●der foote of your compasses .

But how shall I know how many minutes they are ?

This question was conueniently mooued by you Philomathes , & giueth me occasion to deliuer vnto you a rule , whereby not vpon the Globe onley , but vpon your Astrolabe also , or any such like Mathematical instrument , you may find out , how many minutes there are cut 〈◊〉 aboue the whole degrees , in this manner . When the ●●ote of your compasses lighteth betweene the beginning ●●end of any degree , make a pricke , where the said foote lighteth : then take the distance betweene the beginning of the last degree , & the pricke , & count it ( beginning at which degree you please , and noting well where you began ) in the Equator . 60. times . The number of the degrees comprehended betweene the place where you first began your account , & the place wherin you finished the s●●e , expresse the number of minutes contained in the foresaid space . As for example put case that the space contained betweene the beginning of some one degree , and the pricke made in the same degree , being counted . 60. times in the Equator do runne ouer . 30. whole degrees of t●e saide circle , then must you pronounce , that space to comprehende . 30. minutes . If beyng counted . 60. times reacheth but vnto . 15. degrees , then doth the saide spa●● containe . 15. minutes , if it ouerrunne . 45. degrees , the● doth it answere to 45. minutes , &c.

I vnderstand you well . But againe suppose tha● the space contained betweene the beginning of the la●● degree , and the pricke therein be so litle , that I cann●● take it with my compasses , because ( as it may fall ou● their feete will not come close enough together : Ho● shall I then know , how many minutes are contained 〈◊〉 that small space .

When it happeneth so , that you cannot take th● space betweene the beginning of the degree & the pric●● then take that space which is contained betweene th● pricke , and the latter ende of the degree . Count that . 60. times in the Equator marking how many degrees yo● doe runne ouer , subducte the number of those degre●● from . 60. the remainder sheweth you , how many minute were comprised in the small space aforesaid . This also to be noted , that as you finde out the minutes , so ma● you finde the secondes and thirds , &c. of a degree . Fo● if ( the small space aforesaid beyng counted . 60. times i● the Equator ) the foote of your compasses doth not ligh● precisely vpon the ende of some degree , then take th● space betweene the last pricke made with you compasse● and the beginning of that degree , wherein that pricke 〈◊〉 made , count it . 60. times in the Equator , as you did th● other before , the number of the degrees , which you runn● ouer , expresse the secondes , &c.

In this thing also I conceaue your meaning , le● vs proceede . Is there any thing to be obserued in taking the distance betweene two circles of the Globe , o● betweene some poynt assigned in the Globe , and a ●●rcle ?

Yea , that there is , for you must take heed of this , that setting the one foote of your compasses in the one ●●rcle , you doe but touch the other circle with the other ●●ote : for the distance betweene two circles assigned , or betweene a point , or starre , and any circle is the shortest extention that may be : no the shortest extention frō●●rcle to circle , or from point to point is , when the feete ●f your compasse ( standing in the one circle ) cut not the other in two seuerall places , but touche it in one onely .

To what vse serueth the Plummet line ?

It serueth to set the Globe vpright , which in ●ome conclusions is necessarily required .

Vnto what parte of the Globe must it be applied ?

It is most conueniently applied to the Horizon .

Vnto how many places of the Horizon must I ●pplie it ?

You must applie it vnto . 3. seuerall places at the ●east , for setting it but in two you may chaunce to be deceaued .

The third instrument which you spake of is the houre circle , of what quantitie is it to be made ?

The quantity according to the vsuall manner is at your owne pleasure , respect beyng had to the quantitie of the Globe . The greater Globe may abide a greater houre circle , the lesser Globe a lesser , yet I would wishe you rather to exceede in the quantitie , that faile therein , because we take this for a generall rule in any Mathematicall instrument , that the greater it is the more precisenesse and pleasure is in the vse thereof .

Of what fashion would you haue it ?

Of this fashion which here you see in the fi●●gure C. But of what fashion soeuer it is made , it must b● so contriued that it may be taken of and on , from th● Globe at your discretion .

Where must this houre circle stande ?

It must stande vppon the Meridian , so th●● the axeltree of the Globe come iust through the cente● of it , and the circumference of it be equally distant from the Pole . Also you must obserue this : some Globe are so fastened to their Meridian , that the axeltree commeth iust through the middest of the thickenesse of th● Meridian : Other Globes haue their axeltree fastene● to the right , other to the left side of the Meridian : the●●fore when soeuer you set the houre circle on the Meridian , you must so place it that the line of , 12. a clocke both aboue , and beneath , be answereable directly to that part●● of the Meridian , vnto which the axeltree of the Globe i● fastened .

Doe you like this fashion of the Index ?

Yea : yet if it were but halfe the length of th● Diameter it were sufficient : but howsoeuer you make it , you must take heede that the points of it be iust in a right line , with the centre of the houre circle .

What is the vse of the houre circle with his Index ?

The particular vse thereof shall appeare better hereafter in seuerall examples . The generall vse is whensoeuer there is my question made of time , or the partes thereof , as of a day , or houre , when the Sunne riseth , and setteth , &c.

What say you concerning the quadrant of altitude ?

The vse of this quadrant and where it must ●●nde , shall be declared herafter in the particular propo●ions .

What would you haue noted in the circle of position ?

The breadth of it is at your pleasure , the compasse of it is the halfe of the Horizon : But in my conceit it were much better if it were of such a Diameter , that the innerside standing vpright vpon the Horizon it may fall euen with the outside of the Meridian , for so it might be made fast to the Horizon , & the conclusions whereunto it serueth might be wrought the better , if there were added vnto it a small squire of brasse which might mooue vp and downe vpon it alwaies at right angles .

What is to be said touching the Spherical Gno●●●on , of what length would you haue it made ?

As it is vsually made the length thereof is ne●er limited . What length soeuer it haue you must take●●ed of this one thing , that it be so framed , that it may rise alwaies at right angles from the Globe .

How shall I finde that ?

Finde some place in your Globe where two great circles meete togeather , as for example the pointe where the Equator , and the Eclipticke cut one an other : set one foote of your Compasses in their intersection and extend the other at your pleasure , making therewith ●or 4. priuie markes in the circles that cut one another on each side of there intersection one . Then set your Sphericall Gnomon on this foresaide intersection , and keepe it fast , that it stirreth not , afterwardes set the one foote of your compasses in one of these priuie markes , & ●●tend the other foote to the top of your Gnomon , if the foote of your compasses thus extended , will reach fro● the toppe of the Gnomon vnto all the other markes , it 〈◊〉 a certaine argument that it is perpendicular to yo●● Globe .

The last instrument which you speake of is a n●●dle touched with the Loade stone . How would you ha●● it made , and where should it stande ?

Each man may follow his fancie , yet for my se●● I would haue the boxe made so square as might be , breadth answereable to the Horizon of the Globe , the bottome of the boxe I would haue the. 32. pointes the compasse , with certaine subdiuisions as occasion sho●● serue eyther more or lesser : also I would haue a li●● drawne according to the variation of the Compasse , would not haue it fastened to any certaine place of t●● Globe , but applied onely to the Southside of the Glo●● so close as may be , vnto the East or Westside of the M●ridian as occasion requireth . Thus much for the inst●●ments belonging to the Globe . Now you may take wh●●● course you please for the circles and their vse , eyther si●●plie alone , or ioyntly together , or as they craue the hel● of these instruments .

I must needes confesse mine ignorance in the 〈◊〉 matters to be great , and therefore I am willing to ta●● the more payne , I pray you giue me leaue to aske , wh●●● I thinke good and I will take the Globe vnto me , and b●ginne with the Equator following from one to one , v● till I haue runne them ouer all . You say that the Equator is a great circle lying iust in the middest betweene th● two Poles : therefore first I conclude this , that the Po●● of the world are the Poles of the Equator : as for the d●grees of the Equator , I see that they are . 360. and that the number goeth on continually from one to . 360. beginning ●hat point of the Globe where the Eclipticke crossing ●●oth bende towarde the North pole .

You say true : These degrees for distinction sake from the degrees of other circles the Grecians doe call ●●●vot , the Latines Tempora , that is times : because by them the seuerall times of the day , and night are limited , 〈◊〉 when soeuer there is any question made of any time be it a day , or the partes thereof , it may well be resolued by the degrees of the Equator , yet the houre circle wherof wee spake before doth serue for that purpose .

What is the reason of this name ?

It is so called because when the Sunne is vnder this circle the day , and night are of an equall length .

By your leaue Sir , why doe you say ( vnder this ●●cle ) in common phrase of speach wee say , that the ●●nne is in the Equinoctiall , and in the Eclipticke , and in 〈◊〉 Meridian , &c.

It is true that wee say so , but in these kinde of speaches wee vse the worde ( in ) for vnderneath , or right against . I tolde you before , that these circles , which are described in the Globe , are especially to be conceaued in the. 10. Sphere , and considering that the Sunne is in the. 7. Sphere beneath , therefore wee cannot trulie say that he 〈◊〉 in the Equator , &c. But when wee say so , our meaning it this , that he is vnderneath , or right against some one 〈◊〉 there circles , so that a right line drawne from the cen●●● of the worlde , through the centre of the Sunne , and continued vp to the. 10. Sphere , would light vpon that circle in the which the sunne is said to be . Wherefore to ●eturne to my former speach , when soeuer the Sunne is 〈◊〉 ( that is to say vnderneath ) this circle , the day , and the night through out the worlde are equall , wheresoeu● the Sunne riseth , & setteth within the space of . 24. houre and therefore it is called the Equator . The Grecia● call it 〈◊〉〈◊〉〈◊〉〈◊〉〈◊〉 , which worde for worde may be teamed the Equidiall , but the Latines following the pleasantnesse of the worde , haue chosen rather the Equin●ctiall , deriuing the name from the night , & not from t● day , as the Grecians doe . This circle is also tearmed 〈◊〉 girdle of the world , in regarde that it possesseth the mi●dle place betweene the poles , as a girdle on the body a man . The seafaring men for the excellent vse there doe call it the Line .

In that this circle lieth in the middest betwe●● the two Poles , what haue I to note thereby .

Hereby the Globe is diuided into . 2. half● which we call Hemispheres , wherof the one is the No● Hemisphere from the Equator to the Northpole , the oth●● is the South . Item the Equator lying as it doth , is the b●ginning of all declination , whensoeuer therfore you sh● heare hereafter of the declination of the Starres , of 〈◊〉 declination of the Sunne , or of the signes , it must be coū●●● from this circle , and whatsoeuer is precisely in , or vn● this circle hath no declination . Last of all , in that the 〈◊〉 quator lieth iust in the middest betweene the two Pol●● of the worlde , wee are to note this , that it must need mooue vniformally according to the motion of the heauen , at no time faster than at an other , but looke how many degrees thereof arise , & set in one houre , so many degrees arise , and set in euery other houre : as you you selfe may prooue hereafter , and therfore as I said it is th● measure , and rule of all time . Thus much concerning th● Equator simply considered in it selfe .

In the Eclipticke ( for that is the next ) me thin●●th there doe many doubtes arise . You defined it to be a greate mooueable circle of the Globe , cutting the Equinoctiall at oblique angles , and declining from it 2● . d. 30 m. towarde each pole of the worlde . Therefore by your generall rules set downe before concerning the Poles of the great circles , I maie conclude , that the poles of the Eclipticke are . 23. d. 30 m. from the poles of the world . But what is the chiefest ende of the Eclipticke ?

The chiefest vse of this circle is to lay foorth vnto vs the proper motion of the Sunne , for euen as you see the Eclipticke line to trauerse the heauen obliquely , and to decline bothe to the North , & to the South poles , euen so dothe the Sunne keepe his course neuer waruing from this line , but going on euery day from the West to the Eastwarde , almost one degree of this cir●● , that is to say . 59. m. 8. sec. 19 , thirds , 37. fourths . He fi●●sheth his course within the space of . 365. daies , 5. houres 〈◊〉 min. 26. sec. 10. thirds , 56. fourths , which is the length of a yeare . Also this circle is the beginning of all Latitude , so that whatsoeuer is distant from this circle , either toward the one pole , or toward the other , is said to haue a Latitude , as you shall see hereafter , and whatsoeuer is in or vnder it hath no Latitude .

Then belike the Sunne neuer hath any Latitude , for , as you said euen now , the Sunne neuer swarueth from the Ecliptike line .

You say true : this circle also serueth for the Longitude of all Starres , or what soeuer else is called in question in the heauen , the which Longitude how it is to be founde I will declare vnto you hereafter : It serueth also for the Eclipses of the Sunne , or Moone , as you may gather by the name , for there is no Eclipse , but wh●● the Sunne or Moone are bothe precisely in , or very near vnto this circle . To conclude , whensoeuer there is an question mooued of the rising , or setting , or any other thing else concerning the Sunne , wee must haue recou●● to this circle , because it representeth as I saide euen not the progresse of the Sunne , and there is no day , but th● Sunne possesseth one degree , or an other of this circle the which degree must alwaies be sought out whenseuer there is any conclusion to be wrought concerni●● the Sunne , or the place of the Sunne .

Are the degrees of the circle as many as the d●grees of the Equator ?

I told you before that euery circle of the Glob●● is either expresly diuided into 360. degrees , or else it is 〈◊〉 be vnderstood to be so diuided . But herein is a differē●● the degrees of the Equator go on continually from . 1. 〈◊〉 360. but the degrees of the Eclipticke doe not , for they 〈◊〉 c●●tinue but vnto . 30. and then beginne againe .

What is the reason of that proceeding ?

That the yeare and the Eclipticke might be a●swereable one to an other , as the yeare is diuided into . 〈◊〉 moneths , and euery moneth vsually hath . 30. daies , so th● Eclipticke is diuided into . 12. partes , whereof euerie on is called a signe , and euery signe containeth . 30. degrees .

What is a signe ?

A signe is taken properly or vnproperly : Properly a signe is the twelfth parte of the Eclipticke . So tha● if wee drawe a line from the center of the worlde to th● Eclipticke , what soeuer Planet , or Starre falleth precisely vpon that line , is saide to be in such or such a signe a● that line tendeth vnto .

What is a signe vnproperly taken ?

If you marke my wordes , I will easily deliuer the whole matter vnto you but you must plucke vp your vnderstanding , for that whereof I speake is not to be seene but to be conceaued in the Globe . First therefore imagine , that in the surface of the Globe there were two circles drawen parallell to the Eclipticke , the one on the one side therof . 6. degrees distant from it , the other on the other side according to the same distance , so that from the one circle to the other there were . 12. degrees . These circles thus drawne must inclose within them a surface .

I vnderstande you : in the ringed Sphere I remember it is called the Zodiacke , and it is parted into . 12. equall peeces , whereof euery parte is called a signe consayning in breadth . 12. degrees , and in length thirtie , and ●esembleth that figure which the Geometricians call a Parallelogramme .

That is one signification of a figure . Then imagine that from the. 4. corners of this Parallelogramme there were drawne downe to the centre of the Globe ( which representeth the centre of the worlde ) a right line , so that they met altogether in one point , these lines with the Parallelogramme aforesaid must needes inclose a solide figure like a Pyrarnis : this is the second signification of a signe , and whatsoeuer is within the compasse of this pyramidicall figure , is saide to be in such or such a signe according as the denomination of the base doth importe . Thirdly , imagine that from the Poles of the Eclipticke there were drawen . 6. great circles diuiding the Eclipticke into . 12. equall partes , betweene each two halfe circles next adioyning there must needes be inclosed a surface like vnto that of the Globe , which 〈◊〉 contayned betweene the Equator , and the Eclipticke , the which are in number . 12. and each of them is called a signe 〈◊〉 whatsoeuer therefore is contayned from the one pole of the Eclipticke to the other within any of these surfaces , is sayde to bee in such or such a signe as the denomination of each parte of the Eclipticke doth inferre , contayned in any one surface . Last of all , if from each side of this surface you imagine . 2. halfe circles to bee put into the Globe , so that they may concurre togeather in the axeltree , those halfe circles togeather with this crooked surface , will comprehende a Solide bodie , not vnlike vnto the twelfth parte of an apple beyng diuided equallie : of these bodies their wil be twelue , whereof euerie one is called a signe : and hereby it commeth to passe that what soeuer is within the worlde may bee referred to some signe . Thus much for the signification of the worde .

Yet me thinketh you haue omitted one signification : for I haue hearde these Constellations which are set foorth vpon the Globe called by the name of the twelue signes .

You say true and commonly in sunne Dials , you shall see the 12. signes painted according to these const●●lations , but they are most vnproperly termed so : and in the vse of the Globe you must especiallie take heede that when there is mention made of any signe , you haue not recourse to these constellations but to the equal partition of the Eclipticke which are properly called the signes .

What other thing is to be noted in the signes ?

Their expression , and their diuision . The signes are expressed two manner of wayes , eyther by Characters , or else by names , bothe of them are diligently to bee obserued for their vse is manifolde . Their names and Characters are these : 1. Aries , the Ramme . ♈ . ● . Taurus , the Bull. ♉ 3. Gemini , the Twinnes . ♊ . ● . Cancer , the Crabbe . ♋ . 5. Leo , the Lion . ♌ . 6. Virgo , the Virgin ♍ . 7. Libra , the Ballance . ♎ . 8. Scorpio , the Scorpion . ♏ 9. Sagittarius , the Archer . ♐ . 10. Capricornus , the Goate . ♑ . 11. Aquarius , the Waterman . ♒ . 12. Pisces , the Fishes . ♓ . Euery signe as you see excepting one , receaueth his name from some liuing ●aeature , and therefore that broade circle in the ringed Sphere , which you mentioned before ( the which also is to be vnderstood in the Globe ) is called the Zodiacke by the Grecians , who in their language call a liuing creature Zoon and Zodion . Yet some will haue it so called of Zoe life , because the Sunne passing to and fro in it , procureth life vnto liuing creatures .

What is the reason why they chose these names and none other ?

Names are best taken from familiar thinges , wherewith wee are best acquainted : For somuch therefore as the effectes of the Sunne in the course of the yeare are greatlie correspondent so certayne properties founde in these common things , therefore the Astronomers thought it good to intitle the signes by their names . As for example : wee know the Ramme to be of nature hotte and drie , carrying his chiefe credite in his forehead , such is the effect of the Sunne in this signe . Therein he beginneth to make shewe of his heat , & with his heat he inferreth a drinesse , as may be seene by the Marche winds , which then begin to blow when the Sunne entreth into this signe . The second signe is the Bull , whose force is more than the Rammes , and his complection is Melancholicke , euen so is the heate of the Sunne augmented , and that melancholike humor beginneth to abounde . The thirde signe is Gemini the twinnes , which expresseth the doubled force of the Sunne , and the naturall inclination of each liuing thing vnto copulation at that time of the yeare . The fourth signe which is the Crabbe , expresseth the returne of the Sunne , and his going backewarde as it were : for the Sunne after he is come to the head of this signe declineth no more from the Equator , but returneth againe nearer and nearer to that circle and here vpon the head of this signe is called the Tropicall point , and that tropicke which toucheth the Eclipticke in that point , is called the tropicke of Cancer . Moreouer forsomuch as the Lion of all other creatures is the strongest , and the hottest , and neuer freed of an ague , therefore the sift signe is called the Lion , to signifie the mighty strength that is in the heat of the Sunne , & the subiection of our bodies vnto feuers at that time of the yeare . The sixte signe is the Virgin , which signifieth that the Sunne in that signe bringeth forth no new thing , but hasteneth euery thing forwarde to a ripenesse : euen as the Virgin of her selfe is barren , but groweth euery day riper and riper , as the course of nature doth require . The Ballance which is the seuenth signe doth import the equalitie , and equall passing of the day and night , which are then of one length , when the Sunne entreth into this signe , so that the head of this signe & Aries are the Equinoctiall points . The eight signe , which is the Scorpion , signifieth that euen as , if you take not heede of the faire countenaunce of that beast , you may be priuilie , and at vnawares smitten with his stinge , so also if you take not heede to your selfe , at that time when the Sunne possesseth this signe , his faire shew in the morning may so deceaue you , that you may be ouertaken with a colde not thought on before night : Likewise the pearcing colde of the frost and snowe falling in the moneth of Nouember is resembled by the arrowe of the Archer which is the ninth signe . The tenth signe is the Goate : the Sunne comming vnto this signe declineth no farther from the Equator , but beginneth then to clime , and mount alofte in respect of vs , that dwell to the Northwarde of that circle , whereupon that tropicall circle which toucheth the Eclipticke line in the head of Capricorne , is called the tropicke of Capricorne : This mounting and climing of the Sunne , the Astronomers haue thought good to expresse by the figure of this beast , which of all other of that binde climeth most high , and is by nature Melancholicke answeareable to the season of the yeare . The Waterman in the. 11. signe , who putteth vs in minde of that aboundance of humors which raigne at that time . Last of all the Fishes ●●●ng the. 12. signe , do admonish vs that when the Sunne is 〈◊〉 his signe , the rayne is vsually so plentifull that euery thing may swimme therein , as the fishes in the Sea . There are other reasons of these names taken from the course of the vitall blood , and other humors felte in mans bodie when the Moone possesseth the foresaide signes , the which for breuitie sake I omit .

But are these reasons generall and may they go for currant , as well on the other side as on this side the Equinoctiall ?

Not so : but for somuch as Astronomie was bredde on the Northside of the world , the Astronomers therefore haue applied their reasons especially vnto that parte . So that when wee are in that parte of the world which is beyonde the Equator , wee must vnderstand the contrarie to that , which wee saie , whilest wee are or this side , as for example , wee saie the springe beginne●● when the Sunne entreth Aries , and the Summer whe● he entreth into Cancer , but to them it falleth out contrariwise , and the beginning of the Spring must be ascribed vnto Libra , and the Summer vnto Capricorne : &c as hereafter you shall heare more at large .

Why is the first place among the signes ascribe to Aries ?

The Astronomers alleadge certaine reason for it , which must be receaued fauourablie , because the are not necessarie , though sufficient to perswade a we willing minde : the reasons are these : 1. The Sunne comming vnto this signe , each thing beginneth to florish , and that season is most fittest for th● generation of all thinges , therefore it carrieth the preh●minence . 2. The North parte of the worlde hath a dignitie aboue the South , in respect of the creation and the bi●● of our Sauiour , & whatsoeuer excellent thing hath been since the worlde was made . 3. The Astronomers inhabiting the North parte o● the worlde , haue giuen the first place vnto this signe , because it is the first of all those a which leane from the E●quinoctiall Northwarde . 4. Last of all , there be that affirme that the Sunne ▪ when he was created , possessed this signe , and in that respect it ought to haue a dignitie aboue the other .

I praye you , now tell me are the signes all of on●● kinde , or are they seuerally diuided and distinguished one ●●●m an other ?

They are not all of one kinde , but are diuided by their place and their qualitie . By their place they are distinguished foure seuerall wayes , which are not to be neglected because they haue much vse in Astronomie . First , in respect of their place some signes are saide to be Northerne , other are called Southerne . The Northerne signes are those which decline towarde the North pole : as ♈ . ♉ . ♊ . ♋ . ♌ . ♍ . The Southerne signes are those which decline to the Southwarde : as 〈◊〉 ♏ . ♐ . ♑ . ♒ . ♓ . Secondly , the signe in respect of their place are saide to bee opposite : as ♈ . to ♎ . ♉ . 〈◊〉 ♏ . ♊ . to ♐ . ♋ . to ♑ . ♌ . to ♒ . ♍ . to ♓ .

Thirdly , some signes are named Cardinall , some Equinoctiall some Tropicall , & Solstitiall . The Cardinal signes 〈◊〉 ♈ . ♋ ♎ . ♑ . so called because they are the mayne ●ointes , and as were the thinges whereupon the foure quarters of the yeare are turned rounde , and haue egresse and regresse . For the Sunne comming to the head of ♈ . the spring beginneth , and the signes from thence to the head of Cancer , are called the Vernall signes , or the signes of the spring time , namely ♈ . ♉ . ♊ . When the Sunne commeth to the head of ♋ . the Summer commeth in , and the three signes from thence , that is ♋ . ♌ . 〈◊〉 appertaine to that season . The Haruest displayeth it selfe when the Sunne entreth into and ♎ . and these three signes ♎ . ♏ . ♐ . are called Autumnall signes , and are appropriate to that season . The winter beginneth when the Sunne toucheth the head of Capricorne , and these signes ♑ . ♒ . ♓ . are attributed to that quarter of the ●●●re . The Equinoctiall signes are ♈ . & ♎ . because the Sunne in those two points onely , and no more touche●● the Equinoctiall line ( as you may perceaue by the Glob●● and then onely are the dayes and nights equall . The tr●picall and Solstitiall signes are all one , namely ♋ a●● ♑ . yet diuersly denominated because of sundry effec● which fall out in them . For somuch as the head of 〈◊〉 and. ♑ . are the limites and boundes of the Sunne eyth●● comming to the Northward towarde vs , or declini●● from vs to the Southwards , so that he passeth not bey●●● them , but returneth presently towarde the Equator , th●●●fore these signes are called the tropicall signes ( as I pa●●ly noted before ) and the head of eyther signe is calle● tropicall point . These signes and points are called a●● Solstitiall , because as the water , when it is a full sea , 〈◊〉 neare a full sea , doth flow or ebbe so slowlie , that 〈◊〉 thinke it to stande still , and therefore call it a still wa●● euen so the Sunne comming to these points is said to sla●● ( though his motion be continuall without ceassing ) 〈◊〉 that his declination from , or towarde the Equinocti●● can hardly be discerned for the smalnesse thereof . T●● signes also are diuersly distinguished according to th● qualitie , but it is not for me in this place to reckon the● because they belong to Iudiciall Astronomie , which c●●leth some of them Masculine , some Feminine , some ●●●urnall , some Nocturnall , some Mooueable , some Fix●● some Common , &c. The qualities whereby the sig●● are vsually distinguished are either Elementall or Hum●rall . So that the signes are diuided according to the. 4. ●●●ments , and humors raigning in our bodies . The elem●●tall qualities are such as are in the elements , as heate 〈◊〉 colde , moisture , and drinesse . The fire is hote and drie , 〈◊〉 are some signes , & are therefore called firie , as ♈ . ♌ 〈◊〉〈◊〉 which because they are but. 3. in number , are called 〈◊〉 the firie triplicitie . The ayre is moyst and hot , so 〈◊〉 ♊ . ♎ . ♒ . which make the ayrie triplicitie . The water is colde and moist , so are ♋ . ♏ . ♓ . making the wa●●●● triplicitie . The earth is drie & colde , so are ♉ . ♍ . ♑ . ●●ich make the earthly triplicitie . The humorall qualities are such , as are in the. 4. humors of our bodies , and are answereable to the qualities of the. 4. Elements . The first ●●mor is choler , which is hot & drie like the fire , where●● on the firie signes are called also cholerick . Bloud an●●ereth in qualitie to the aire , which is hot and moist , ●●●rfore the airie signes are also Sanguine . The water & 〈◊〉 me agree in qualitie , being both cold & moist , so that 〈◊〉 watrie signes are called flegmaticke . Melancholie and 〈◊〉 earth are drie , & cold , the earthly signes therefore are ●●●ed Melancholicke . And to the intent that you may ●●st easily carrie these qualities of the signes in memorie 〈◊〉 this : Choose . 4. fingers of your hand , and call the first 〈◊〉 , the second earth , the thirde aire , the fourth water : ●●en in beginning at ♈ count the. 12. signes vpon your foure ●●●gers , so shall you finde which are firie and cholericke that is hot and drie , which earthly and melancholicke , that is drie and colde : &c.

There arise in this place . 2. doubtes wherein I would gladly be resolued : First the Philosophers haue 〈◊〉 downe this as a principle , that in heauen there is nei●●er heate nor colde , in what respect then are the signes ●●de to be of these qualities . Secondly the naturall pla●●●g of the Elements is this , the fire is first and the ayre su●ceedeth , & then the water , the earth it self is last of all , what is therefore the reason of this disorderly placing of ●●e signes , why are the earthly signes in the second place ?

The ancient Astronomers , men of great exper●ence , and paines , obseruing the sundry changes and alt●rations of all things here vpon earth , noted that the Su●● and other planets comming to certaine places of the he●uen , did moue some of these inferior bodies more th●● othersome , and stirred vp their qualities more or lesse● or otherwise diminished them . The qualities , whose au●mentation , diminution , & alteration they especially o●serued , were these beforenamed , because they were mo●● subiect to common sense . And considering that as black a●● white , so heate and cold , drynes and moisture cannot 〈◊〉 in one , and the same subiect being contraries : therefo●● they affirmed certain places to be hot , others to be col●● some to be moist , and some to be dry , not actually as th● elements are , but vertually by their vertue and powe● From this experience I might draw an answere to yo●● second question , that because they obserued in ♉ . whic● is the second signe , the earthly qualities , that is drougth● and coldnes , therfore they placed the signes as they b● Yet I pray you also note this in the elements , there are 〈◊〉 qualities one intensiue & predominant , which is the chi●fest of the two , the other is remisse : as in the fire the pr●domināt quality is the heat , the remisse qualitie is the di●●nes , these elements are changed one into another , not a●● all aduentures , but successiuely from one to another thi● naturall change is fitly expressed by the placing of the n●● signes . The fire which is intensiue hot cannot becom● moist immediatly , but it is always dry , yet may it lose hi● heate and become cold and dry , which are the qualitie● of the earth . The first signe therefore being firie , the second is earthly , to signifie this naturall alteration . Againe the aire is intensiue moist , and remissiue hot , therefore it cannot be dry , but it may lose his heate , and be●ome cold , as the water is , and therefore those 2. signes succeede one an other . I might deriue also a reason of this disorder from the seuerall aspects of the signes , which is not to be neglected in the eclipticke , for in this circle they are to be accounted .

What meane you by that word , aspect , which you say , is to be obserued in the signes ?

An aspect is a position of the signes ( it is a ●hing incident also to the planets ) in a determinate di●●ance of the ecliptick line , from whence they may as it ●ere beholde one another .

Hour many aspects are there ?

Hauing regard vnto the Planets , there are fiue ●spects , for they may be right vnder one an other , or else ●hey may be in one and the same great circle drawne from the poles of the eclipticke through the center of ●ach Planet : this aspect is called coniunction , and is expressed with this character ☌ . the other aspects are sextile , quadrature , trine , and opposition : these 4. are only in the signes , for the signes are not said to haue coniunction . Sextile is an aspect of the signes ( or planets ) when they are distant one from an other the sixt part of the eclipticke that is 60. degrees , as ♈ . and ♊ . ♉ . and ♋ . &c. it is expressed thus . * . Quadrature is an aspect of the signes when they are distant one from an other 90. degrees , which is the fourth part of the eclipticke , as ♈ . and ♋ . or ♋ and ♎ . it is thus expressed □ . Trine , which ●s also called trigonall , or triangular , is an aspect of the signes , when they are distant one from an other the third part of the eclipticke , which is 120. degrees , as ♈ and ♌ the character of this aspect is this △ . Opposition is an aspect of the Signes when they are distant . 180. degrees , which is halfe the Eclipticke , so that the one signe is in the one ende of the Diameter , and the other signe in the other ende : as ♈ . and ♎ . or ♋ . and ♑ . this aspect is expressed thus ☍ .

What is the reason that the quintile is exempted ?

If you marke it , there is no aspect hetherto named , but the number , which giueth the denomination thereto , will exactly diuide . 12. for so much therefore as 5. from whence the quintile aspect , if there were any such , is to receaue his denomination cannot diuide . 12 exactly , therefore that aspect is excluded by the Astronomers . Thus much for the quantitie , that is the number of the aspects .

If there be any thing to be saide , touching their qualitie , I pray you let me heare it , it cannot be much besides the text .

The qualitie of the aspects is eyther certaine or vncertaine . The certaine is eyther good or badde bothe of them are either perfect or meane . The perfect good aspect is the trine because the signes , which beholde one an other in that aspect , agree in bothe their qualities : as ♈ . and ♑ . are both hot and drie : as ♉ . and ♍ . are both drie and colde , &c. The meane good aspect is the Sextile , because the signes placed in that aspect do in qualitie partly agree , and partly disagree : as ♈ . and ♊ . agree in heate , but the one is drie the other moiste , yet are they not directly opposite . The badde aspects are the Quadrature and the opposition . The vncertaine aspect is the coniunction for it is sometimes good , sometimes badde , according to the Planets which meete together . Out of the consideration of these aspects ariseth that disorderly placing of the Signes which was mentioned before . The Astronomers perceauing the contrarietie which fell out ●implie nowe and then in the quartile aspecte , that the Signes , which were so placed , did oppugne one the other sometimes in bothe the qualities , as ♈ . and ♋ . whereof the one is fierie , the other watrie , they could not dispose of the signes in that order as the elements are placed , for by that meanes the first signe should ne●er haue oppugned the fourth in both qualities , but they should alwaies haue agreed in the one , which thing was contrarie to their obseruation . Thus haue I briefelie run thourough those things which are simplie to be respected in the eclipticke . Let vs now proceede to the Colures .

What is the reason of that name ?

Colurus properlie signifieth Cauda Mancus , maimed in the taile , for these circles ( excepting one position and situation of the sphere whereof I will speake hereafter ) do alwayes appeare vnperfect . Their office is this , to distinguish the. 12. Signes , according as they are answerable to the foure seasons of the yeare , for you see them to diuide the Zodiacke into foure partes , whereof the one containeth the Vernall signes , the other the sommer signes , &c. Moreouer , the Solstitiall colure passing through the head of ♋ . affordeth vs alwaies the two poles of the eclipticke in this manner . If you turne the head of ♋ toward you , this is a certaine rule , that looke now farre the head of Cancer is aboue the equator , so farre is the north pole of the eclipticke beyond the north pole of the world , and the south pole of the eclipticke is so farre on this side the South pole of the world . If you turne the head of Capricorne toward you , it falleth out contrarywise .

I perceaue it well , for then the north pole of the eclipticke is on this side the north pole of the world , and the south pole of the eclipticke is beyond the south pole of the world so farre as the head of Capricorne is distant from the equator . Where are the poles of the 2. Colures ?

There is no great vse of them in the Globe , yet if you desire to knowe where they be , the former generall rules will leade you to them : you shall finde the poles of the equinoctiall colure to be in the intersections of the equinoctiall , and the solstitiall colure : and the poles of the solstitiall colure to be in the intersections of the equinoctiall colure , and the equator 〈◊〉 selfe . The graduation of the colures in the celestial Globes vsuallie is omitted , but in M. Mollineux his Globe , the equinoctiall colure is gratuated from the equator toward each pole of the world the solstitiall colure is gratuated from the eclipticke toward each pole thereof , to the intent that the Globe may be readie both for the declination and latitude of the Starres . Let vs now come to the Horizon . Wherein you must first vnderstand , that the breadth which is geuen to the Horizon , or any other circle else generally belonging to the Globe , is not giuen vnto it as an Horizon ( for simplie as it is an Horizon , or a circle of the sphere , it is a line without any breadth ) but the breadth is allowed it for the degrees and other things necessarie for the vse of the Globe .

I vnderstand you well , but I pray you expresse vnto me particularlie what things these are that are inscribed in the Horizon , and what vse they haue ?

There are inscribed in the Horizon the 12. s●●nes , the 12. moneths of the yeare , and the 32. windes ( which are commonlie called the points of the Compasse ) both in english and latine .

Nay by your leaue Sir . I am not yet fully satis●●ed , I minde to goe more particularlie to the matter . What degrees are those which are set in the inner side of the Horizon ?

They are the degrees of the 12. signes , and the numbers that stand next vnto them are the numbers of the degrees of each seuerall signe from 10. to 10. In the third space next vnto the Horizon are set the names of the twelue signes with their characters , the name standeth at the beginning , the character at the ende of each signe .

But what meaneth the character which is in the ●iddest of euery signe ?

It signifieth that the signe is the house of that planet , vnto whome the character doth belong , as for example , Aries is the house of Mars , Taurus is the house of Venus , &c.

What is the reason why the first signe is set in the east point of the Horizon , and from thence successiuely they goe about by the North ?

That is done to helpe the memorie of the nouice in Astronomie , all the signes from the east , counting about by the North to the West , are those which before I counted the Northern signes , the other are the Southern signes . The partitions which follow the names of the 12. signes , are the dayes of each seuerall moneth : next vnto them succeede the number of the dayes belonging to each moneth .

But what meane the letters set vpon each seu●rall daie .

They are seuen letters of the alphabet answ●rable to the seuen dayes of the weeke : the letters a● iterated according as the dayes of the yeere doe requi●● Of these letters , that which is appropriate to the Su●daie , is called the Dominicall letter for that yeare .

Whie ? is not euerie yeare the same letter appropriate vnto the Sundaie ? these letters keepe alwaie the same dayes of the moneth , for A serueth contin● allie the first of Ianuarie , B the second , C the third , & ●

It is true that the letters are answerable 〈◊〉 those dayes , yet doth the Dominicall letter change eu●●rie yeare , and in the leape yeare there is two Domi●●call letters . The reason why they change is this , there●● in the yeare one day more than 52. weekes , as you m●● perceaue by the letters , for the last of December , and th● first of Ianuarie are marked with one letter . If the● were iust 52. weekes , the Dominicall letter could neue● change , for then if the first day in the yeare were Su●day , the last day would be Saturday , and the first day 〈◊〉 the next yeare continuallie would be Sunday againe , an● A would still be the Dominicall letter . But in respect 〈◊〉 the odde day it falleth so out in euery common yeare that the yeare beginneth and endeth with the same day ▪ as if the first of Ianuary be Sunday , the last of Decembe● that yeare is Sunday also , the first of the next yeare being Monday , the Dominicall letter must needes change , and being A , it becommeth G , thus much shall suffice for that matter .

In that space where the number of the dayes are expressed , I note certaine letters to be written , name●●● K. N. and I. to what vse serue they ?

They signifie the manner which the ancient 〈◊〉 manes obserued , in expressing the dayes of euerie ●●oneth . They did not count their dayes from one to 30 or 31. as wee doe , but they diuided their moneth into three seuerall partes , which were Kalends , Nones , and Ides , according as the three foresayd letters doe import . The first day of euery moneth was called the Kalends , and therefore the letter K. is applied vnto it throughout the horizon . The other dayes of the Kalends , were they more , or lesse , did not succeede in the same moneth , but did goe before in the former moneth , and were counted backward . As for example , the Kalends of Ianuarie did not follow the first of Ianuarie , but went before in the moneth of December in this manner : the last of December which is the 31. day , they called the day before the Kalends : the 30. of December was the third of the Kalends of Ianuarie , the 29. of December was the fourth 〈◊〉 the Kalends of Ianuarie , and so they counted them to the 14. of the moneth of December , which was the 19. of the Kalends of Ianuarie . Which moneth had more Kalends , and which had lesse , may be gathered easily out of the horizon by the place of the letters . Also you may finde which moneth had more Nones , and which had l●sse . The number of the Ides in euery moneth was e●●●all , namely 8.

But were the Nones and the Ides counted backward as the Kalends were ?

Yea , for where you see the letter N stand , that was the first of the Nones . As for example , the 5. of Ianuarie was the first of the Nones of Ianuarie , the last of the Nones was the 2. of Ianuarie , so that the Romanes account was contrarie to ours . Likewise , the 13 of Ianuarie was the first of the Ides , the last of the Ides wa● the sixt of Ianuarie . These things are to be regarded especiallie by the learned sort , that they may be skilfu● in the account of the ancient Romanes .

The next space which followeth containeth th● names of the moneths . I pray you let me haue a wo●● or two with you concerning them , because not bein● skilfull in the Latine Authors , I cannot satisfie my sel●● in many things , which I would gladlie knowe . Tell 〈◊〉 I pray you hath this number of moneths bene continuall , I speake of the Romanes .

No , for Romulus the first King of Rom● counted but 10. moneths to the yeare , according to th●● time which a woman beareth her child in her wombe Numa Pompilius succeeding him , added other tw● moneths , namely Ianuarie , and Februarie , so that he●● by he made the moneths of the yeare answerable to t●● 12. signes . This number of the moneths hath continue still .

Hath the order of them bene all one from th● beginning .

Romulus , who was the first author of th● yeare , began it at the moneth of March , in the honour● Mars his father . Numa Pompilius adding two othe● moneths , made Ianuarie the first , and Februarie the la●● moneth of the yeare , because it was consecrated to th● infernall gods . The Decemuiri afterwards ioyned Ianuarie and Februarie together , and made Februarie th● second moneth of the yeare .

What is the reason of their vnequall quantitie ?

It was not possible that they should all be 〈◊〉〈◊〉 quantitie , because of the motion of the Sun making 〈◊〉 seuerall dayes of the yeare , if the Sunne had gone ●●●iselie euerie daie one degree of the Eclipticke , then ●●●ht euerie moneth of the yeare haue had iust 30. da●es , but considering that there is fiue dayes more in th● yeare than there are degrees in the Eclipticke , it is 〈◊〉 possible , but that fiue moneths must haue one odde ●ai● more .

But now there are 7. moneths which haue 31. ●●●es , and one moneth hath but 28.

It is so : first there were but fiue moneths that had 31. dayes , but Iulius Caesar tooke one daye 〈◊〉 Februarie to put to Iulie , that as he thought him●●●● inferior to no man , so his moneth should haue as ●●●y dayes as anie other . Augustus Caesar succee●●●g him , and beeing as ambitious as his predecessor , ●●h drewe an other daie from Februarie , and ioyned it 〈◊〉 his moneth August , to the ende that it might not be ●●●rior to Iulie in the number of dayes .

Haue these names of the moneths continued ●●●m the first beginning ?

No. For the moneth of Iulie , because it was the fift from March , was called in olde time Quintilis , and August beeing the sixt , was called Sextilis . More●●er , Domitianus Germanicus Emperour of Rome , ●●●nged the name of September , and called it Ger●●●nicus , because in that moneth he ouerthrewe the G●rmanes . Hee changed also the name of October , and called it Domitianus after his owne name , but after his decease , those two moneths receaued their ●uncient names againe .

What is the reason of these names ?

The moneth of Ianuarie hath his name of 〈◊〉 latine word Ianua , which signifieth a gate , a dore , o● entrie , because it is the first entrance into the yeare . 〈◊〉 else it receaueth his name from Ianus the two fa●● God , to whome this moneth was consecrated . Feb●arie receaued his name from the word Februus , wh● was the infernall God , otherwise called Pluto , to who●● in this moneth the Romanes did sacrifice : or else of ●●brua , which were sacrifices , and ceremonies for p●●ging of soules , which in this moneth especially they ●●fred to the Gods beneath . Some deriue it from the w●● Febris , an ague , because in this moneth they were so●● what rife . Marche receaueth his name from Mars●● father of Romulus , and God of warre , as the Roma● accounted him , and in this moneth they began th● warlike prouision . Aprill , this moneth was conse●●ted to Venus the mother of Aeneas , from whome 〈◊〉 Romanes fet their discent . The Grecians called her 〈◊〉 phrodite , to signifie , that she was bred of the foame● the sea , which is by them called aphros , and from the●● they fet the name of this moneth , striking out the● calling it Aprill as it were Aphrill . But Varro think● it more conuenient to deriue the name from the La●● word aperio , which signifieth to open , because the ea●● beginneth then to be free from the binding force of 〈◊〉 frost , and to send forth the grasse and other fruites . 〈◊〉 moneth of May hath his name deriued sundry way● Some will haue it taken from the word Maius , that 〈◊〉 Iupiter . Others deriue it from the Goddesse Maiest●● daughter ( as the poets will haue ) of Honour , and Re●●rence , because in this moneth the first worship of the●● ●●ds began . Others take the name from Maia , the 〈◊〉 of Vulcane , vnto whome , Vulcans high Priest 〈◊〉 sacrifice in the Kalends of May , which is the first of 〈◊〉 moneth . Others say , this moneth was so called of ●●●ia the daughter of Atlas , and mother of Mercury 〈◊〉 of Merchants , because in this moneth the Mer●●●ts offred sacrifice to Mercurie , and Maia . Last of 〈◊〉 me affirme , that in this moneth Romulus diuided 〈◊〉 people of Rome in maiores , & minores , that is , 〈◊〉 the elder , and yonger sort . Hinc sua maiores tri●●●e vocabula Maio. So that this moneth receaued 〈◊〉 ●ame from the maiores , that is , the elder sorte . 〈◊〉 hath his name also deriued from sundrie things , ●●e fetch the name from Iunius Brutus , by whome , ●●quinius , and the name of the Kings were expulsed ●●me . Others deriue the name from Iuno Moneta , 〈◊〉 whome for her good admonition , and counsaile in ●●●ng the fearefull earthquake at Rome , the Romances ●●cated a Chappell the first of this moneth : so that the ●●●eth was called Iunonius , and afterwards Iunius , to ●●de the length of the word . Others call it Iune a ●●●endo of ioyning , because in this moneth the Ro●●es and Sabines were ioyned together in one citie . ●●ers take it from Iuuenta the Goddesse of youth , 〈◊〉 wife of Hercules . Ouid writeth thus , Iunius a ●●●num nomine dictus adest , that as May was deri●● from the maiores , that is , the elder sort , so Iune ●●ld be deriued from the minores , that is , the yonger 〈◊〉 Iulie is deriued from Iulius Caesar , who was borne 〈◊〉 is moneth : it was first called Quintilis as I sayde ●●re . August taketh his denomination from Augu●●● because in that moneth he greatlie augmented the Empire of Rome , and came three times triumphing 〈◊〉 the Citie . September is so called , because it is Septi●●● a Vere , the seuenth from the spring time , at which 〈◊〉 as I noted before the auncient Romanes began t●● moneths . Likewise October is the eight , Nouem●●● the ninth , December the tenth from the Spring . T●● you heare the reason why euerie Moneth is called by 〈◊〉 name . The great space which is next to the name●● the moneths containe the names of certaine daies the which those that are written in the greater Rom● letters , are the names of the festiuall daies obserued 〈◊〉 the Church of England .

What is the generall vse of placing the sig●● and the moneths in the Horizon ?

They serue to this purpose , the daye b● giuen to finde the place of the Sunne in the Ecliptic that is , what signe of the Eclipticke , and what degre●● euery signe he doth possesse , with his entrance into 〈◊〉 signe : and contrarywise , the degree which the Su● possesseth being knowen , and the signe to finde the 〈◊〉 of the moneth , the which things are very necessari● the vse of the Globe . For many questions cannot e●● be answered , except the place of the Sunne be know● The day therefore of the moneth being found out in 〈◊〉 Horizon , the degree which standeth right against 〈◊〉 day is the place of the Sunne . But considering that in 〈◊〉 Leape yeare there is a day more than in the other th● yeares that went before it , and that day is put in 〈◊〉 wayes immediatly after the 24. of Februarie , theref●●● in that yeare after the foresayde 24. day of Februa●● if you seeke the place of the Sunne , you shall adde 〈◊〉 daye more than the number of the daye is in w●● ●●u seeks the place of the Sunne . As for example . If ●●u seeke it the eyght and twentith of Februarie , you 〈◊〉 all take the fyrste of Marche : and if you seeke it 〈◊〉 fyrste of Marche , you shall take the seconde of ●●rche , &c. For so shall you come nearest to the ●●●th .

Why then doth not this table affoord the pre●●●● place of the Sunne ?

No , but it is done to helpe the nouice in ●●●ronomie , vntill hee attaine vnto farther know●●ge in that Arte , and this is sufficient for him , be●●●se in common practise hee shall neuer by sense finde ●●ifference betweene this , and the exact place of the ●●nne .

What meane the names of the moneths that ●●owe , howe chanceth it that they are twise set ●●wne ?

The first of them is the new reformed Al●●nacke of the Romanes proclaimed by Gregorie Pope 〈◊〉 Rome . The other is that which our Countreyman 〈◊〉 . hath lately set forth , contayning the true compu●●on and reduction of the moneths to their first and ●●●cient seates , the which were therefore set downe in 〈◊〉 Horizon belonging to this Globe , that thereby ●●●ght be seene the difference that is betweene our Ka●●●dar , and that of the new stile , and also that wee may ●●●dily keepe an account according to our owne , and ●●●ir Kalendar .

I praye you geue mee some instructions touching thys matter : for I see some Globes that haue ●●●yr Horizon described after the newe Romane Al●●●nacke ( namely , those Globes which were made at Amsterdame , by Ieames Floris ) the which tro●bleth me many times , because I cannot reduce them 〈◊〉 our account .

You see this , that the newe Romane Alm●nacke preuenteth our 10. dayes , and the other preue●teth our 15. dayes , one rule applied orderlie to th●● bothe shall be your direction in them : in this mann●● If the day of the moneth be assigned according to 〈◊〉 account , and you hauing none other Horizon butt t●● which is made after the new stile , would notwithsta●ding know what degree and signe the Sunne possesse● adde tenne dayes vnto the number of the day propou●ded , and seeke that out in the horizon the degree of 〈◊〉 signe which is correspondent to that day is the place 〈◊〉 the Sunne . As for example , the 11. of August I desire 〈◊〉 know the place of the Sunne by the Horizon made aft● the new stile . I adde 10. to the number of the daie it m●keth 21. which number I seeke in the Horizon , and rig● against it I finde the 27. degree and 30. min. of ♌ .

But put case the question were propounded co●cerning the 24. of August , if I should put 10. to th● number , it maketh 34. how shall I make answere he●● considering that August hath not so manie daies ?

If the two numbers added together excee●● the number of the daies belonging to the moneth ass●●ned , take the daies of the moneth assigned from the t●tall summe , the number remayning is the dayes of th● moneth following , as in your example 24. and 10. ma●● 34. August hath but 31. dayes , take them from 34. the 〈◊〉 mainder 3. referreth me to the third of September : th● degree answering vnto that daie is the place of the Su● Contrary wise , if you knowe what degree of the Eclip●●●ke the Sunne possesseth , and by the Horizon of the ●●●w stile you would know what day of the moneth it is 〈◊〉cording to our account , first seeke in the sayd Horizon 〈◊〉 day opposite to that degree , and if it be possible , sub●●●ct 10. from the number , the remainder giueth the day 〈◊〉 the moneth according to our account : as for ex●●●ple , if against the degree of the Sunne you finde the 〈◊〉 day of any moneth , the day vpon which the Sunne ●●ssesseth that degree according to our account , is the 11. 〈◊〉 of the same moneth .

But put case I cannot subduct tenne from the ●●●mber of the day which standeth against the degree ●●●gned ?

Then adde that number to the number of the ●●●es belonging to the moneth next before it , and sub●●ct 10. from the totall summe , the remainder is the 〈◊〉 of the moneth immediatlie going before , according ●●●our account . As for example , the day answering to 〈◊〉 degree of the Sunne in the Horizon of the new stile , ●●●he sixt of August , forsomuch as I cannot subduct 10. ●●●m this number , therefore I adde it vnto the 31. dayes 〈◊〉 Iulie , the totall summe is 37. from whence I take 10. 〈◊〉 remainder is the 27. of Iulie , vpon which day the ●●●ne possesseth the same degree ( namely , the 13. d. 5. m. 〈◊〉 ♌ ) which he possessed the sixt of August according 〈◊〉 he new account . This that I haue sayd touching the 〈◊〉 Romane Kalendar , may be sayd of the other next ●●●oyning to it , taking the number 15. for 10. To con●●●de , this is a generall rule for you to note , that what ●●gree soeuer in the Horizon you finde the Sunne to ●●ssesse the same degree , must be sought out in the E●●●ticke : the which degree wee call manie times simplie the Sunne , sometimes wee call it the place of the Sunn● and therefore whensoeuer wee saie bring the Sunne● the Meridian , or bring the place of the Sunne to 〈◊〉 Meridian , &c. our meaning is , that you should bri●● the degree of the eclipticke which the Sunne possesse●● to the Meridian , or to the Horizon .

Do these degrees of the signes continuallie a●swere to the same dayes of the moneth ?

No , but they may serue the turne 24. yeare , 〈◊〉 30. without great inconuenience . That they doe 〈◊〉 keepe the same dayes of the moneth , you may see● the entrance of the Sunne into the equinoctiall poin● and into the solstitiall points : for the vernall eq●noctiall at the Incarnation of Christ , was the 25. 〈◊〉 March , and the sommer solstice was the 24. of Iu●●● The Nicene Councell found the vernall equinoctiall 〈◊〉 be the 21. of March , and now it is the eleuenth of 〈◊〉 sayd moneth . The reason of this difference is , in 〈◊〉 Iulius Caesars Almanack which wee follow , presupp●seth the yeare to be 365. dayes and 6. houres , which ●●ing greater than the yeare of the Sunne , it comm●● hereby to passe , that the Solare yeare preuenteth 〈◊〉 yeare of Iulius Caesar , and draweth by litle and 〈◊〉 nearer vnto the first day of the moneth , so that in 〈◊〉 to come the entrance of the Sunne into the head of ●●ries , which is the equinoctiall point , will be the first 〈◊〉 March , if there be not a correction vsed . In the oth●● spaces that followe are set the names of the wind●● which commonlie wee call the 32. points of the comp●● both in english and latine , to the intent that not only 〈◊〉 learned , but the ignorant also might haue vse of them 〈◊〉 the latine names the author thought good to follo● 〈◊〉 . Lemnius , both in respect of the learning of the ●ame , and also because the names which are vsed by ●hers sauour rather of the Italian speach , than of the ●●cient Romane tong . The vse of them is excellent as ●●al be declared hereafter , both for the place of the rising and setting of the fixed starres , and the Sunne , and also for their coasting round about the heauen .

This is one thing that I would faine be resolued 〈◊〉 , why in saying the compasse as the mariners tearme 〈◊〉 they begin at the North point , and so goe on from ●●ence Eastward , were it not as good to begin at the ●●ast where the Sunne alwaies riseth ?

In deede if the Sunne did alwaies rise full East , 〈◊〉 were conuenient the compasse should begin there : ●ut they follow the Sunne , and for so much as the vt●rmost rising of the Sunne is at the North point of the ●●orizon , and beyond that he cannot rise , as you shall see ●●ereafter , therefore they begin there . Thus much con●●erning those things which are described vpon the Ho●●zon of the Globe , whereof the points of the compasse ●ust be vnderstood in the Horizon of heauen , and be●●des them certain degrees : for the quarter from the East to the South , from the West to the South , also from the East to the North , and from the West to the North , is to be vn●●●ood to be deuided into 90. degrees , the number of which ●●egrees is not vsually expressed , because the degrees of ●●e signes next vnto the Globe may easily supply them . The reason why each quarter must be vnderstood to be ●●us diuided , is the difference which is between the lear●ed & the common mariner . The common mariner seing a star or the Sun to rise and set , vsually nameth the point ●f the compasse vpon the which it appeared , as , that it riseth East , Northeast , or East , and by South . The l●●ned Astronomer he counteth how many degrees th● rise from the East , and how many degrees they set fro● the West , as that the Sunne riseth 22. degrees 30. min●● the Northward , or 11. degrees ¼ . to the South wa●● Therefore that you may quicklie vnderstand them both 〈◊〉 you must accustome your selfe to turne the degrees 〈◊〉 each quarter into the points of the Compasse , and co●trary wise the points of the compasse into degrees , 〈◊〉 this manner . The whole circle is diuided into 360. ●●grees , therefore the 32 points of the compasse , and 〈◊〉 360. degrees are equall , the quarter of the circle cont●neth 90. degrees , and 8. points of the compasse , eu●● point of the compasse therefore containeth 11 degr●● two points containe 22. degr. ½ . three points conta●● 33. degrees . ¾ . foure points containe 45. degrees . N●● demaund what you thinke good concerning the Ho●●zon , as it is to be conceaued in the heauen .

I haue diuers things to aske concerning 〈◊〉 circle , I will fet them out of the definition : which 〈◊〉 this . The Horizon is a great fixed circle of the Glo●● diuiding that part of the heauen which is seene , f●●●● that part of the heauen which is not seene . First tell 〈◊〉 what is the reason of the name ?

You obserue this , that when you stande 〈◊〉 plaine champion countrie , where there is nothing 〈◊〉 hinder your sight , that round about you there seeme●● circle to be described , which is a representation of 〈◊〉 circle whereof wee speake : beyond this circle you● 〈◊〉 nothing , neither doth your sight passe it , but end●● there , whereupon the Grecians haue called it the Ho●●zon , of the word 〈◊〉〈◊〉〈◊〉〈◊〉〈◊〉 , which is finio , to ende , the ●●●●●●es also call if finitor , that is the ender , because it limi●●h our sight .

You say it is a fixed circle : what meaneth that ?

My meaning is , that it neuer stirreth nor mo●●●h , as it may be proued by a most certaine argument ●●ken from the poles thereof in this manner . The Horizon , as you may perceiue by the Globe , cutteth the meridian at right angles , the poles therefore of the Horizon ( by that generall rule which I gaue you at the first ) must ●●edes be in the Meridian , the one of them is that point 〈◊〉 the Meridian , or that point of the heauen which is ●●●ht ouer our head , and is called the Zenith , the other is ●●e point right vnder our feete , and is called the Nadir : 〈◊〉 then the poles be the points directlie aboue , and di●●ctlie beneath vs where wee stande , and no pole can ●●me nearer to his circle in one place than in an other , ●●t is alwayes equallie distant on euerie side from it , it must needes followe , that so long as wee stand still , the Horizon must be fixed , for if it should rise vpward , it ●ust come nearer , if it should moue downeward , it ●ust fall farther from the verticall point which is our ●●nith , and the pole of that circle .

What then ? doth the Horizon moue when wee moue ?

Not so : but that Horizon standeth still , and ●●u transport your selfe into another , so that you are ●●yd to change your Horizon .

Are there then so many Horizons ?

Herein is the difference betweene the other circles of the Globe before named , and the Horizon , they are but one in the heauen , as one equator , one e●●ipticke , &c. But the Horizons are infinite , not to be numbred , euery man hath his Horizon in truth , yea a● many points as there can be conceaued , in the halfe 〈◊〉 the heauen so many Horizons are to be vnderstoode though not sensiblie to be discerned in a small space for the sensible alteration of our Horizon can hard●● be perceaued in 400. furlongs , which amount vnto 〈◊〉 miles .

You say that the Horizon diuideth the heauen , b● how doth it diuide it into equall , or into vnequall parts

It is a great circle , therefore it diuideth it in●● equall partes .

When I looke round about me standing in 〈◊〉 plaine champion feeld , doe I see iust the one halfe of th● heauen ?

Here you must vnderstand , that the Horizo● is taken two seuerall wayes , the one is called rationall 〈◊〉 naturall , because it is the true horizon represented by 〈◊〉 horizon of the globe , and not by sence , but by geomet●● call reason , to be comprehended to diuide the heau●● equallie . The other is sensible and apparent : that i● it is that space of the land and sea which our eye sig●● beholdeth , and from thence runneth on vnto the he●uen . And for so much as the centre of the Horizon is 〈◊〉 our sight , the which is farre distant from the centre 〈◊〉 the world , through which the diameter of the true Horizon doth passe , therefore reason telleth vs this , tha● it cannot be so great as the other is , and consequently 〈◊〉 cannot diuide the heauen into two equall parts : ye● considering that the Globe of the earth in respect of th● heauen is insensible , so that our sight cannot make● sensible distinction betweene each Horizon , therefore although our reason affirme an vnequalitie , wee acc●●nt them equall .

Haue you any thing else to be added touching 〈◊〉 Horizon ?

As the equinoctiall is the beginning of all declin●●ion , and the ecliptick is the beginning of all latitude i●●he celestiall globe , so is the Horizon the beginning of all eleuation , altitude , or height . Whatsoeuer is in the Horizon hath no eleuation , whatsoeuer is aboue it , hath a● eleuation more or lesse , as hereafter you shall heare . ●●s the beginning also of all depression . In it are coun●●d the amplitude of euery thing , that riseth or setteth in the heauen , and the seuerall coasting of the Sun or stars , which is called the Azimuth or verticall circles , &c. But 〈◊〉 vs now come to the Meridian . You see that it cutteth the Horizon at right angles , and standeth so vpon 〈◊〉 that it leaneth neither to the one hand nor to the o●●er , therefore the poles of it must needes be in the Ho●●zon , in the East and West points thereof . In it are con●●ined the poles of the world , and the poles of the Horizon , which I called before the Zenith , and the Nadir . The degrees thereof are 360. not continued as the degrees of the equator , but are counted from 1. to 90. for so it is most conuenient for the raysing of the pole , and the equator aboue the Horizon . The vse of it simplie considered in it selfe , is the diuiding of the heauen into two equall partes , whereof the one is the East , and the ●ther the West . Whatsoeuer is toward the rising of the Sunne , is the East , whatsoeuer is toward his setting is the West part of the world , and by it the day is distinguished equally . From it ( as you heard before ) wee begin to account the points of the compasse , and the variation thereof .

Are the Meridians manie in number , or 〈◊〉 there no more than one , as wee see in the Globe ?

The Meridians are not so many as the Ho●●rons in number , yet are they so many , that wee m●● tearme them infinite in respect . Which way soeuer yo● goe the Horizon differeth , because your verticall po●●● differeth , but the Meridian differeth only betweene 〈◊〉 East and West . If you goe North , or South , your Me●dian continuallie is the same , because your Zenith , 〈◊〉 verticall point is alwaies in the selfesame line : so th●● the Meridians in truth are so manie in number as the● are points betweene the South and North part of th● Globe , as you see it diuided by the Meridian , though 〈◊〉 sence they cannot be discerned . Notwithstanding , w●● commonlie count those that are of one Shire , or Ci●●● or Towne , to be vnder one Meridian , because the se●sible distinction of one Meridian is not perceaued scare●ly in 300. furlongs , which are 37. miles ½ . Thus mu●● touching the great circles of the Globe , as they are simplie considered by themselues , now of them iointly on● with an other , and first generallie without respect ha●● vnto any certaine position of the Sphere . Here the●● things do offer themselues to be considered , 1. the equall diuision of the great circles by the Horizon , 2. th● vniforme motion of the equator , 3. the declination , 4. the longitude , 5. the latitude , 6. the foure cardinall points o● the world , 7. the goodnes of the Globe . Howsoeuer the Globe is situated in the Horizon , be the pole higher o● lower from it , or iust in the same , the great circles of the Globe are equallie diuided by the Horizon , except they be conicident , and hid therewith .

May they then be hid with the Horizon ?

Yea , there is none of them excepting the Meri●●an , but in some position of the Sphere it may be iust in ●●e Horizon , and couered with it : as thus for example . 〈◊〉 the two poles of the Globe be in the Horizon , the two ●●●ures interchangeablie are in the Horizon . If the pole 〈◊〉 rased 66. degrees 30. min ▪ aboue the Horizon , the E●●●pticke is sometimes couered therewith , namely , when th●t tropicall point , which is next to the pole eleuated , ●●mmeth to the North side of the Meridian . Last of all ●●en the pole is in the Zenith equallie distinct on euerie ●●e from the Meridian , then is the equator continuallie in the Horizon . What is to be noted thereby I will de●●●re vnto you hereafter , only marke you my words at 〈◊〉 time . Otherwise the great circles are equally diuided 〈◊〉 the Horizon : whereby you shall note this touching 〈◊〉 equator , that whensoeuer the Sunne commeth vnto ●●●t circle , the day and the night is of an equall length . ●●●o concerning the Eclipticke you see this , that there 〈◊〉 alwayes sixe signes aboue , and sixe beneath ( sauing 〈◊〉 that verie moment of time , which I spake of euen ●●w ) and therefore when any signe doth rise , the opposi●● signe doth alwayes set , as if ♈ arise , ♎ doth set , if ♋ 〈◊〉 , ♑ doth arise . And contrary wise , the second thing to be noted , is the vniforme rising and setting of the equa●●● ▪ which ( howsoeuer the Globe be set ) riseth and set●●●● neither faster nor slower at any one time more than 〈◊〉 ●n other , whereupon as I sayd before it is the measure of all time , the intire reuolution of it is the measure of ●4 . houres , and the rising of euerie 15. degrees is the m●● sure of an houre .

How shall I induce my selfe to beleeue this vniforme motion of the equator ?

First , the situation of the equator in the middes● of the globe betweene the two poles , may moue you t● beleeue it : euen as therefore the motion of the heauen is certaine & doth not moue but equally , so doth the 〈◊〉 quinoctiall moue also . Secondly , it maketh the same angl● with the Horizon in any certaine position of the Sphe●● without alteration , which thing the ecliptick doth not ▪

How shall I know that ?

Raise the the pole of the globe as high as yo● please aboue the Horizon , as for example 50. degree● The angle which the equator maketh with the horizo● will be 40. broad , as you may perceiue by the degrees 〈◊〉 the meridian intercepted between them bothe . The turne the globe round , and that angle will still continu● of the same quantitie : but the angle which the eclptic● maketh with the horizon will varie diuerslie . Last of 〈◊〉 the vniforme rising and setting of the equator , may 〈◊〉 perceiued by the houre circle , for if you place it as yo● were taught before , and apply the index vnto twelue● clocke , and then marke what degree of the equator is 〈◊〉 the East or West side of the meridian , in mouing 〈◊〉 globe , vntill the Index light vpon one a clocke , you sh●● finde 15. degrees of the equator to rise , and to set , and consequently it will fall out from houre to houre . A● heere I must put you in minde of one thing , that for 〈◊〉 much as the equator is the measure of time , the you● students in Astronomy ought diligently to endeuor th● selues to be cunning , and ready to conuert the degree minutes , seconds , &c. of the equator , into parts of tim● and contrarywise the parts of time into degrees of the ●quator , the which thing is most easy vnto them that 〈◊〉 skilfull in the rule of proportion , for if 15. degr. do ye● houre , they may easily infer what 30. or 40. degr. &c. ●●l yeeld : and againe , if 1. houre giue 15. degr. what shal 2.3 . or 4. houres yeeld , &c. The third thing which cra●eth no certaine position of the Sphere is the declinatio● , a thing to be noted by all students in Astronomie . Declination is the distance of any thing in the celestiall Globe from the equator measured by the degrees of a great circle drawen from the poles of the world .

But what great circle is that , by whose degrees the declination is to be measured ?

It is that great circle which is drawen from the poles of the world through the center of that thing whose declination I would know by the globe . But for so much as it were an infinite and an impossible worke to drawe through euery point assigned a circle , therfore wee make 〈◊〉 meridian the common instrument to finde the declination . So that whether wee seeke the declination ●●●ny starre in the heauen , or whether we seeke the de●●●ation of any point assigned in the eclipticke ( which ●●●earmed also the declination of the Sunne , because the ●●●ne alwayes possesseth one degree or other of the e●●pticke ) this is your rule : If you bring the starre or any assigned degree of the eclipticke vnto the meridian , the degrees of the meridian intercepted between the equator , & the asigned star or degree , expresse the declination .

You say that I must bring the starre or degree as●●●ned to the meridian , but is it no matter vnto which ●ide of the meridian I bring it ?

Yes , it is a great matter . Here therefore you must call to minde that which I told you before , concerning the applying of the houre circle vnto the meridian . If the ●●elcree of the globe come through the midst of the meridian , or be aplied to the right or left side of the merid●an , the starre or degree assigned , whose declination yo● would know , must be aplied to the Meridian accordin●ly , either to the middest , to the right or left side there●● ▪

You sayd before , that the equator was the b●ginning of all declination , and whatsoeuer is vnder th● circle , hath no declination , whereupon I may infer●● this , that the heads of ♈ and ♎ haue no declination .

It is true : but what point soeuer is either 〈◊〉 the one side , or the other of the equator , it hath a dec●●nation according to the denomination of the pole ●●ward which it declineth .

Then all declination is either Northern or So●therne , whether it be of the Sunne or Starres . But wh● is the greatest quantitie that they may haue ?

The termes and limits of the declination as y●● haue heard is the equator , and the thing propounde● whose declination you would know . The greatest dec●●●nation therefore of any thing propounded , cannot 〈◊〉 more than 90. degrees , because nothing can be farth●● distant from the equator than 90 degrees , the po●● therefore haue the greatest declination , and whatsoe●● it is that commeth nearest vnto them , hath a gre●● declination than that which is farther off from the●● whatsoeuer is nearest the equator , hath the least decli●●tion . The chiefest regard of the greatest declination is 〈◊〉 the eclipticke , wherein 2. points haue greater declinati●● than all the rest , namely , the heads of ♋ and ♑ , whi●● decline according to the latter obseruations 23. d. 28. 〈◊〉

Why hath there bene a difference found in tha●

As there hath bene a difference found in th● declination of the fixed starres by reason of the moti●● 〈◊〉 the ninth Sphere , so in regard of the motion of trepi●●tion belonging to the eight Sphere , the Sunne doth ●●●nge his greatest declination . Ptolemee founde the ●●atest declination to be 23. d. 51. min 20. s . Io. Regio●●●ntanus auouched it to be 23. d. 30. min. Copernicus pronounced it to be 23. d. 28. m. All the other points of 〈◊〉 eclipticke are of a lesser declination , according as they are nearer to the equinoctiall , and in them this is a generall rule , that those points of the eclipticke which 〈◊〉 opposite , or equallie distant from the equinoctiall points haue equall declination , as ♉ and ♏ . being opposite , item ♉ and ♓ . or ♉ and ♍ . which are of equall ●●stance from the equinoctiall points , haue equall declination .

Hetherto you haue made the Meridian the ●●mmon measurer of the declination : but may I not ●●de it otherwise ?

Yes you may finde it by your compasses more ●●ecisely in this manner : set one foote of your com●●sses in any starre propounded , or in any degree of the ●clipticke , whose declination you desire , and turne the other foote of them to the equator , or any other circle parallell vnto the equator , putting the said foote out , or pulling it in , vntill you do but touch the circle . Then app●●e your compasses to the equinoctiall line , and obserue the number of degrees intercepted betweene them , for they expresse the declination .

What commoditie doth the knowledge of the declination bring ?

First , it helpeth vs to finde the heigth of the pole , as I will teach you hereafter when I speake of the ●eigth of the starres and Sunne . Secondly , it bringeth vs to the knowledge of the place of the Sunne . Last of a●● it bringeth forth the day of the moneth .

Tell mee the declination being knowen ( as s● example , suppose I know the Sunne to decline 11. de●● 30. m. ) how shall I finde the place of the Sunne ?

Forsomuch as 4. meane points of the ecliptio● haue equall declination ( as I said euen now ) there m●●● therefore consideration be had of the time of the yea●● as , whether the Sunne be supposed to haue this declin●tion in the spring , or in the sommer , &c. For the dec●●nation propounded , must be sought out only in that p●●● of the eclipticke which is correspondent to the seaso● then is your rule this : if the quarter of the ecliptick 〈◊〉 swerable to the season propounded , be applied to 〈◊〉 meridian , the degree of the eclipticke , which falleth 〈◊〉 vnder the assigned declination , is the place of the Sun●● so if it be spring time , the Sunne declining 11. d. 30. 〈◊〉 must needes possesse the head of ♉ . if it be sommer , 〈◊〉 possesseth the head of ♍ &c.

Hereby me thinketh I could answere the 〈◊〉 proposition my selfe .

Let me see : the declination of the Sunne be●● giuen , how can you finde the day of the moneth ?

If the degree which the Sun possesseth being fo●● out by the former proposition , be sought for afterwa●● in the horizon of the Globe , the day of the mon● which standeth right against it , is the day required , 〈◊〉 for example , the Sunne in the Spring time declineth 〈◊〉 d. 30. m. by the former proposition I finde his place to 〈◊〉 the head of ♉ . vnto the which in the horizon of t●● globe I finde the ende of the tenth of Aprill to answe● ▪

You saie true : the fourth thing which craue●● 〈◊〉 certaine position of the Globe is the Longitude : this ●ay belong to any point assigned in the Globe , but generally wee seeke the longitude either of the Starres , or of the degrees of the eclipticke , wherby also wee count ●●e longitude of the Sunne . The beginning of longi●●de is the head of ♉ , the circle wherein it is counted ●nd measured is the eclipticke . The extremitie or ende of the longitude in respect of the Starres which are distant from the eclipticke toward either pole thereof , is ●●at point of the eclipticke , vpon which , that great ●●cle lighteth , which is drawne from the poles of the ●●lipticke through the centre of the starre . But in re●●●ct of the eclipticke it selfe , or in regard of any starre , 〈◊〉 the sunne supposed to be in the eclipticke , the end or ●●●it of longitude is that degree , which the sunne or starre is supposed to possesse . Hereupon wee define the ●●●gitude thus . The longitude is an arcke of the eclip●●●ke , contained according to the naturall succession of the signes betweene the head of ♈ , and that great circle , ●hich is drawne from the poles of the eclipticke , through the point assigned in the Globe . Heere you must note this , that forsomuch as the head of ♈ is the beginning of all longitude , therefore whatsoeuer is contained vnder the halfe of that great circle , which is ●●●wen from the one pole of the eclipticke through that ●●int vnto the other , hath no longitude at all . The other ●●ints assigned in the globe , may increase in longitude ●●to 360. degrees , than the which there can be no greate● , because they are the degrees of the whole eclipticke .

You say , that the longitude is an arcke of the eclipticke , but how shall I expresse it : as for example . 〈◊〉 I be demaunded of the Longitude of the Starre called the Lions hart , what shall I say , that it is an ar●●● of the eclipticke , & c ? me thinketh that were somewh●● absurd .

If you should answere so your answere we●● true : but for your instruction note this , that when 〈◊〉 be demanded of the Longitude of the Sunne or starr● wee make answere two seuerall waies , sometimes by 〈◊〉 degrees of the signe vpon which the great circle falle● which is drawen from the poles of the eclipticke throu●● the centre therof : so wee say , that the Longitude of 〈◊〉 Lions hart is the 23. d. 43. m. of Leo. Sometimes 〈◊〉 answere by the continuall succession of the degrees co●tained in the arcke of the eclipticke , for wee say the Lio● hart hath Longitude 143. d. 43. m.

But the degrees of the eclipticke are not 〈◊〉 downe in continuall succession vpon the Globe .

It is true , and therefore the Longitude vp●● the Globe is not found , but according to the signes , 〈◊〉 their degrees . Yet if for euerie whole signe you co●● 30. degrees , and vnto that summe adde the odde degre● and minutes remayning , if there be anie , the totall is 〈◊〉 Longitude according to the continuall succession , as 〈◊〉 example , the Lions hart is in the 23. d. 43. m. of Leo. ●●fore Leo there are 4. whole signes , therefore I take fo● times 30. which make 120. vnto which I adde the o●● degrees , and minutes remayning , which are 23. d. 43. 〈◊〉 the totall summe 143. d. 43. m. is the Longitude , acco●ding to the continuall succession of the degrees .

You sayd , that in finding the declination , 〈◊〉 meridian circle is a fit and conuenient instrument : 〈◊〉 what shall wee haue to finde the longitude .

It were conuenient for this purpose and for 〈◊〉 latitude whereof I am to speake , to haue a semicircle ●●●de fast to each pole of the eclipticke when occasion ●●●uld serue , diuided into 180. degrees , so that the quar●●●●rom the eclipticke to each pole should containe 90. ●●●erwise you must vse the quadrant of altitude , ap●●●ng the 90. degree thereof vnto the pole of the eclip●●●●e , and bringing the edge of the quadrant through 〈◊〉 centre of the starre . But if you could so order the ●●●ter that the Globe might be taken off from the me●●●●an , and the poles of the eclipticke fastened thereto ●●●he poles of the equator are , then were it most com●●dious for this purpose , and for the finding of the la●●●●de of the starres , which is the fift generall thing to be ●●●ed in the vse of the Globe , without any certaine po●●●n regarded .

What is the Latitude ?

I told you , that as the equator was the beginning of all declination , so is the eclipticke the beginning ●●●ll latitude in the celestiall Globe . Whatsoeuer there●●● is iust vnder the eclipticke , hath no latitude , as the ●●●ne who keepeth alwayes vnderneath it . The lati●●●e then which is afforded by the celestiall Globe , is of 〈◊〉 starres that are not vnder the eclipticke , it is defined 〈◊〉 . Latitude is the distance of a starre from the eclip●●●●e measured by the degrees of a great circle drawne 〈◊〉 the poles of the eclipticke through the centre of 〈◊〉 starre propounded .

Therefore if I take the quadrant of altitude , or the halfe circle , which you spake of before , and applie it to the poles of the eclipticke , bringing it close to 〈◊〉 starre assigned , the degrees which are contained ●●●weene the eclipticke , and the starre , expresse the latitude thereof . But put case I wanted bothe of the●● might I not finde the Latitude by the Compasses ?

Yes in such manner as I taught you to fin●● the declination . If you set one foote of your compa●●● in the centre of the Starre , and take the shortest exte●tion ( as wee call it ) between the said centre and the ●cliptick , the degrees of the equator contained betwe●● the feete of your Compasses afford the Latitude , 〈◊〉 which must be pronounced to be either North or So●●● according as it leaneth to the Poles . What Starre s●●uer leaneth from the eclipticke toward the North p●●● hath North latitude , and what soeuer leaneth tow●●● the South pole , hath South latitude .

What vse hath the longitude and the latitude

They serue to finde out the Starres of the Glo●● which are easily found if I knowe these two things 〈◊〉 I applie the quadrant of altitude to the pole of the ●clipticke either North or South as the denominatio● 〈◊〉 the Latitude doth direct me , and bring the ende the●● to the degree of Longitude , the Latitude being coun●●● in the quadrant , will bring me directlie to the place● the Starre . Moreouer , wee cannot so conuenientlie 〈◊〉 the celestiall Globe , or rather wee cannot make it a●●● without the knowledge of the longitude and latitud●● the Starres .

You haue taught me how to finde out the de●●●nation longitude , and latitude of the Starres , so 〈◊〉 forth as they are inscribed in the Globe . Now put 〈◊〉 that I should finde in the heauen some Starre which 〈◊〉 not in the Globe , may I notwithstanding by the Gl●●● finde out the longitude , latitude , and declination of 〈◊〉 Starre ?

Yea that you may . Can you tell how to finde 〈◊〉 distance of Starres ?

Yea that I can , I learned it at your Lecture when 〈◊〉 read your booke concerning the vse of the crosse ●●●fe , and there it is set downe .

Then when you espie any starre in heauen not ●●●ressed in the celestiall globe , first make choise of two ●●●res in a reasonable distance from that which you espy , ●●●e any two , it maketh no great matter which , only ●●●y must not be in a right line with the starre seene , but ●●her choose them in a triangle . Secondly , take the distance of each starre from the starre newly seene : Thirdly ▪ finde out those two starres vpon your Globe , which 〈◊〉 made choise of in the heauen , then extending your ●●●passes at seuerall times , vnto so make degrees of the ●●●ator , as the seuerall distance of each starre doth re●●●re . Set the one foote of your Compasses in the one ●●●re , whose distance was first taken , and according to 〈◊〉 distance make a circumference either vpward or ●●wneward , according as the situation of the starre ●●wly found out doth admonish you . Also set the foote 〈◊〉 your Compasse in the starre whose distance was ●●●nd out at the second time , and according to that ●●●●nce make an other circle which shall crosse the for●●● in one place or an other , the intersection of those 〈◊〉 circles is the true place of the starre , whose declina●●●● , longitude and latitude may be found by the rules ●●●e sayd .

〈◊〉

I perceaue your meaning , the practise of it will be de●●●htsome , proceede now I pray you to the sixt thing 〈◊〉 ●e noted in the circles of the Globe , considered ●●tlie one with an other , without anie certayne position of the Globe , which is the finding of the four cardinall points .

This is certaine , that where the meridian cu●teth the Horizon , there are the two cardinall poin● which are called the North and South : and where t●● equator cutteth the Horizon , there are the other 〈◊〉 which are called the East and West : so that if by 〈◊〉 helpe of the needle touched with the Loade stone y●● turne the fore part of the meridian to the Southwar● the foure cardinall points will appeare , howsoeuer 〈◊〉 pole of the Globe be raised more or lesse aboue the H●rizon , so that it be not made your Zenith .

Why do you put in that caueat ?

They that dwell vnder either pole , haue 〈◊〉 equator iust in their Horizon , so that it maketh no i●tersection with the Horizon , and therefore in that ●●spect they cannot say that this place or that place is i● East or West , but which way soeuer they looke , i● South vnto them . The last generall thing to be noted 〈◊〉 the circles , is the goodnes of the materiall Globe it se●●● And heere I must tell you this , that concerning a●● Globes , which our countreyman hath made , the bo●● vpon which the printed papers are pasted , is most pe●fectly round , as by the triall I haue found them , and 〈◊〉 therefore to say it , that he may receaue commenda●●ons for his paines , and artificiall handling of the sa●● If there be a fault , it is either in the papers or in the H●rizon or meridian : which whether it be , the circles 〈◊〉 bewraie it , in this manner . If the great circles which 〈◊〉 drawne from the poles of the world , being applyed 〈◊〉 the meridian , do not precisely answere it , and fall i● vnderneath it , without bowing one way or an oth●● ●●ere is a fault in the pasting of the papers , or else the ●●ridian it selfe is crooked . The papers cannot be hol●● , the meridian may . If the equator , in the reuolution 〈◊〉 ●he Globe , do not keepe iust vnder the middle of the ●●●idian where the degrees begin , there is a fault in the 〈◊〉 be , for it is a signe , that it sincketh downe to much ●●●ard the nethermost pole , or else is raysed to high ●●●ard the vppermost pole . If the equator in the reuo●●●on of the Globe do not rise and fall iust vpon the 〈◊〉 and West point of the Horizon , there is a fault as ●●●ore , or else the papers are not pasted iust in a circle . 〈◊〉 ●he iust halfe of the meridian be not aboue and be●●●th the Horizon , there is a fault , either in the Hori●●● it selfe , which warpeth , or else in letting of the me●●●an into the Horizon , which may be remedied either ●●raysing it higher , or letting it sincke lower . If the Ho●●●on do not cut the equator into two equall peeces , ●●●re is the same fault in the Globe also , except the Ho●●●on warpe . Thus haue I deliuered as briefelie as I ●●●ld those things which are to be considered in the ●●at circles of the Globe iointlie one with an other , ●●hout regard had vnto anie certaine position of the ●●ere , it remaineth therefore now to speake of them ●●●ey require a certaine position which we commonlie 〈◊〉 the rectifying of the Globe .

What is it to rectifie the Globe ?

To rectifie the Globe is so to situate it , that it ●●●y be answerable to the heauen , so that the meridian 〈◊〉 ●he Globe , the poles and axeltree , with the Horizon , 〈◊〉 answerable to the same circles in the heauen , whe●●●r it be a right Sphere as we tearme it , or a crooked .

What meane you by a right Sphere & a crooked ?

You see this , that howsoeuer you place 〈◊〉 Globe in the Horizon , the equinoctiall either make● an angle with the Horizon , or is parallell vnto it , a● falleth iust within it . If it make an angle with the Hor●zon , the angle is either right or oblique . According 〈◊〉 this angle the Sphere is called either right or obliqu● A right Sphere is that wherein the equinoctiall and 〈◊〉 Horizon cut one an other at right angles : therefo● the poles of the equinoctiall ( which are the poles of t●● world ) are in the Horizon , and contrarywise , the poles 〈◊〉 the Horizon are in the equinoctiall , so that the equin●ctiall passeth both directly ouer our head , and vnder 〈◊〉 feete . The Horizon in regard of this concurse at rig●● angles with the equator , is called also a right Horizo● And here you are to note this diligently for your ease● vsing of the Globe , that the meridian may supply 〈◊〉 place of a right horizon , because it hath all the prope●ties thereof . For as the Horizon of a right Sphere cu●teth the equinoctiall at right angles , so doth the me●●dian , as the poles of the world are in the right Horizo● so are they in the meridian : as the right horizon di●deth all the circles of the Globe , be they great , or li●● into two equall parts , so doth the meridian : whereup●● wee take this for a generall rule , that what conclusion● euer in the vse of the Globe is to be tried by the horizo● of the right Sphere , the same may with lesser trouble 〈◊〉 tried by the meridian .

By that which you haue spoken of a right Spher●● I may easily gather what an oblique ( or as wee tearm●● it ) a crooked Sphere is , I thinke I may rightly define 〈◊〉 oblique Sphere to be that , wherein the equator make●● an oblique angle with the horizon : whereupon th● 〈◊〉 needes followe as a consequent , that one of the ●●s is alwayes aboue the horizon , and the other be●●h , either more or lesse .

You say true : and therefore this also doth insue , 〈◊〉 an oblique Sphere may admit all the degrees of ●●●parison , that is , it may be oblique , it may be more ●●●que , it may be most oblique . It is oblique when the 〈◊〉 is raised neuer so litle aboue the horizon : it is most ●●●que when the pole is raised most aboue the horizon , 〈◊〉 is , when the pole is in our Zenith , and the equi●●●tiall is coincident with the horizon . The horizon in ●●●rd of this oblique angle made with the equator , is ●●ed also an oblique horizon . Moreouer , you must ●●e this , that whether the Sphere be right or croked , ●●arre as the equinoctiall is distant from the horizon , ●●●rre is the pole of the equinoctiall distant from the 〈◊〉 of the horizon which is our Zenith . And againe , ●●arre as the Zenith is from the equator , so farre is the ●●e from the horizon . If the equinoctiall be 90. de●●es aboue the horizon , the Zenith is 90. degrees di●●t from the poles of the equator . If the equator be 〈◊〉 degrees aboue the horizon , the Zenith is 30. degrees ●●●ue the pole . If the equator and the horizon doe ●●●se one with an other , the pole and the Zenith are 〈◊〉 ●he one point .

〈◊〉 .

What am I to learne by this for mine instruction ?

Hereby you may learne how to set the quadrant ●●altitude in his due place : for if from the pole vp●ard you count so many degrees of the meridian , as 〈◊〉 contayned betweene the equator , and the horizon : 〈◊〉 otherwise , if from the equator vpward you count 〈◊〉 many degrees of the meridian , as are contayned between the pole and the Horizon , there is the 〈◊〉 place vnto which you must fasten the sayd quadran●

Let vs now returne from whence wee depar● Tell me I pray you , is it alwayes requisite that the Glo●● should be in situation iust correspondent to the fac● the heauen ?

No. In most conclusions it is only requis●●● that the pole of the Globe should be raysed accord 〈◊〉 to the pole of the heauen , for otherwise wee cannot ●●●taine to the truth of the question . But the setting of●● Globe due North and South by the helpe of the nee● or the setting of it leuell by the plommet line , are 〈◊〉 alwayes necessarie , when they are necessarie , I will 〈◊〉 you hereafter . The height of the pole must either giuen , or be sought out .

I perceaue your meaning . Now to the purp●●● concerning the vse of the circles of the Globe , when 〈◊〉 Globe requireth a certaine position , or as you calle● a rectifying , with which circle shall wee begin ?

With the Horizon , for either in that , or fro● that most of the propositions do arise . First of all let 〈◊〉 call in question the rising and setting of the Sunne 〈◊〉 Starres : the rising and setting of the Starre is to 〈◊〉 gathered by the Starre it selfe , the rising the setting 〈◊〉 the Sunne is to be gathered by the degrees of the ●clipticke .

When is a Starre , or the Sunne sayd to rise & se●●

If the centre of the Sunne or Starre commi●● from the inferior Hemisphere do mount aboue our Horizon , he is sayd to arise . If descending from the super i● Hemisphere , his centre falleth beneath our Horizon , 〈◊〉 is sayd to set . If mounting vpward , or descendi●● ●●wneward , the center doth but touch the Horizon , 〈◊〉 is sayd then neither to rise nor set , but is rising .

Goe to then , answere me to this , any eleuation 〈◊〉 ●he pole being giuen , how shall I finde by the Globe ●●at starres do arise and set , what starres neuer set , and ●●at starres neuer rise ?

Rectifie your Globe , that is , rayse the pole of 〈◊〉 Globe according to the eleuation assigned , so shall 〈◊〉 presently answere your selfe by the reuolution of 〈◊〉 Globe . If bothe the poles be in the Horizon , you ●●ll see euery starre and euery degree of the eclipticke 〈◊〉 ●rise and set . If one of the poles be in your Zenith , ●●u shall see all the starres and degrees of the eclipticke ●●●m the equator vpward neuer to set , and contrarywise ●●●se that are from the equator downeward neuer to 〈◊〉 . If the pole be raysed 66. d 30. m. you shall see all the ●●●res from the one tropicke vpward neuer to set , and ●●●m the other tropicke downeward neuer to rise , and 〈◊〉 Sunne being in the tropicke next to the pole that is ●●●uated , doth but touch the Horizon with his centre , 〈◊〉 being in all other places of the eclipticke , he doth 〈◊〉 the rise , and set . To conclude , this is a generall rule to 〈◊〉 gathered out of the declination . If the declination ●●●●er of the Sunne or Starre be lesser than the comple●●●nt of the heigth of the pole , the Sunne and Starre a●●●th and setteth . If the declination be greater , they ne●●● set , or else neuer arise . If the declination be equall , ●●ey touch the Horizon , but neuer set , or else neuer a●●●● . The next thing to be considered in the Horizon is 〈◊〉 ascension and descension of the Sunne or Starres , ●●●h the difference thereof . Ascension is the portion of 〈◊〉 equator contained ( the orderly succession of the degrees being obserued ) betweene the head of ♈ , a● the horizon , at the time of the rising of the Sunne , 〈◊〉 Starre . Descension is the portion of the equator contayned in like manner betweene the head of ♈ , and th● horizon , at the time of the setting of the Sunne 〈◊〉 Starre . Therefore whatsoeuer is in the horizon wi●● the head of ♈ , hath neither ascension or descensio● Ascension and descension is either right or crooked otherwise called oblique . Right ascension is the portio● of the equator contained betweene the head of Ari●● and the meridian , at the time of the comming of a●● either sunne or starre vnto the meridian . Descensio● may be defined in the same manner by the departi●● from the meridian .

How commeth it to passe that you define th● right ascension by the meridian and not by the ho●●zon , as you did generally define it before ?

I define it by the meridian , because I would ha●● you remember that which I tolde you before , namel● that the meridian of the Globe may very fitly supply 〈◊〉 place of the horizon in a right sphere . Therefore if y●● would know the right ascension of the sunne or starre● bring the degree of the eclipticke which the sunne p●sesseth , or else bring the starre assigned to the meridia● and there obserue what portion of the equator is co●tained betweene the head of ♈ and the meridian , 〈◊〉 that is the right ascension . Heere this is to be no●● that the right ascension and descension are alwayes on● for the same degree of the equator which commeth 〈◊〉 the meridian , the same degree goeth from the meridia● with the sunne or starre . Moreouer , there is no degre● of the eclipticke , nor no starre , but it hath a right ascen●●● , and descension , excepting those which were gene●●● excepted before , namely , those which are iust vn●●● the meridian with the head of ♈ .

By your words I gather , that the oblique ascen●●●● is the portion of the equator contained betweene 〈◊〉 head of ♈ , and the horizon of an oblique sphere , at ●●●rising of the sunne or starres . Descension also may 〈◊〉 ●efined in the same manner by the setting . So that if ●●sire to know the oblique ascension , I must bring the ●●●●ee of the eclipticke , or else the starre assigned to the ●●●●zon , and there obserue what portion of the equator ●●ntained betweene the head of ♈ and the horizon , 〈◊〉 that on the East side of the horizon is the oblique ●●●nsion , on the West side it is the descension .

You say right . And here note this , that the ●●●que ascension and descension are neuer the same . 〈◊〉 some starres and the sunne likewise haue neither ●●●ension or descension , namely , when they neither rise 〈◊〉 set .

What is the difference of ascension which you ●●●red before ?

In searching out the right and crooked as●●●sion , you shall finde this continually to be true , that of ●ne and the same signe or starre the seuerall ascensi●● neuer agree : the one is alwayes either greater , or ●●●r than another : therefore hauing found out the ●●●t and crooked ascension of any one starre , subduct 〈◊〉 lesser from the greater , the degrees of the equator ●●●ch remayne , is called the difference of ascen●●●● .

To what ende serueth this ascension , and diffe●●●ce of ascension whereof you speake ?

It serueth to diuers purposes , whereof I sh●● make mention hereafter , now let vs follow the mat●● which we haue in hand . Wee vse in the Horizon to o●serue with what degree of the eclipticke any Sta●● doth arise or set , which thing is done only by mou●● the Globe vp and downe , vntill the Starre assigned co●meth to the East or West side of the Horizon , the d●gree of the eclipticke which is then in the Horizon , 〈◊〉 the degree required .

By this meanes also I may knowe what degr●● commeth to the meridian , for if I bring the Starre p●●pounded to the meridian , the degree of the ecliptic which is vnder the meridian with the starre , is the ●●gree required . But what dothe the knowledge of 〈◊〉 auaile me ?

Hereby you may learne vpon what day of 〈◊〉 uery moneth euery Starre is to be seene rising or s●●ting , or in the meridian at midnight , in this manne● Bring the Starre propounded to the East side of the H●rizon , marke what degree of the eclipticke is in the H●rizon with it when the Sunne shall possesse the oppo●● degree , that day shall the assigned starre arise at the ●●ting of the Sunne .

But how shall I knowe that daye ?

I tolde you before , that whensoeuer there any degree of the eclipticke assigned , it must be sou● out in the Horizon , and right against it you shall fin●● the day of the moneth wherein the sunne possesseth th● degree . Take an example : the litle dogge ariseth in o● Horizon with the 5. d. 30. m. of Leo , the degree oppos● to this in the west side of the Horizon , is the 5. d. 30. m Aquarius , the sunne possesseth that degree as I perce● ●he Horizon the 16. of Januarie , therefore vpon that ●●at the setting of the Sunne the litle dogge ariseth ●●e Horizon . Contrarywise , bring any Starre to the 〈◊〉 side of the Horizon , marke the degree of the e●●●icke which commeth to the Horizon with it : ●●●n the Sunne possesseth the opposite degree , on that ●●at the rising of the Sunne the sayd Starre shall set in 〈◊〉 West . And heere is the first meanes offred to finde 〈◊〉 eleuation of the pole . This is certaine , that there is 〈◊〉 eleuation wherein one and the same Starre ariseth or ●●●eth with the same degree of the eclipticke with ●●●ch it riseth , and setteth in an other eleuation , but a Starre in each seuerall eleuation of the pole , hath ●●uerall degree of the eclipticke , with which it riseth 〈◊〉 setteth euery day . If the lesser dogge arise in one ●●e with the head of Leo , in an other place he ariseth 〈◊〉 the 10. or 20. of Leo. Therefore if you can obserue 〈◊〉 Starre rising in the Horizon when the Sunne doth 〈◊〉 or setting in the Horizon when the Sunne doth a●●●● note the day of the moneth in the Horizon , and the degree of the eclipticke answerable to that day : find out also the opposite degree , then if you noted the Starre to arise , bring the Starre to the East side of the Horizon , and raise or depresse the pole of the Globe , vntill the ●●●●re and the degree of the eclipticke fall bothe together in the Horizon , for then shall the pole of the ●●●be be at his true eleuation .

If I noted the Starre to set , I must worke this conclusion on the West side of the Globe .

It is so . Moreouer , if you note with what degree any Starre commeth to the Meridian , seeke out the opposite degree , when the Sunne possesseth that degree , then at midnight you shall see the starre in the meridian : but wee cannot from hence infer the eleuation of the pole , because euery where be the pole higher or lower , the starres continuallie come to the meridian with the selfesame degree of the eclipticke . Heere is occasion offred to deliuer vnto you the cosmicall , achronicall , and helicall rising and setting of the signes and starres , which are not to be neglected of young students , especially such as are conuersant in reading of the Poets , because in many places they can hardlie be vnderstoode , without the knowledge of these things , Cosmicall rising and setting of the starres generally taken , is their ascending and descending at any houre of the day whatsoeuer . Likewise , wee define generallie the Achronicall rising and setting of the signes and starres to be their ascending and descending in the night . But properlie they are applied to that time onlie at which the Sunne doth arise or set . Therefore the degree which the Sunne possesseth being applied to the East side of the horizon , the signe or starres which are then on the East side of the horizon with the Sunne , are said to arise Cosmicallie , and they which at the same time are in the West side of the horizon , are said to set cosmicallie . Furthermore , the degree which the Sunne possesseth , being brought to the West side of the horizon , the signe or starres that are on that side with the said degree , doe set Achronicallie ( that is by interpretation in the edge of the night ) and they on the other side arise achronicallie . Whereby this appeareth , that what signe or starres soeuer arise cosmicallie , the same doe set achronicallie , and contrarywise . Likewise what starre or signe soeuer riseth achronicallie , the same doe set cosmicallie , and contrarywise . The helicall rising of the starres is their appearance after they haue bin hidden by the beames of the sunne . The helicall setting of the starres is the hiding by the beames of the Sunne . For this you must note , that the Sunne mouing from the West to the East , doth by litle and litle gather vpon the starres which are Eastward from him , and comming neare vnto them within some 15. degrees , litle more or lesse , according to the quantitie of the starres , by his brightnes he obscureth their light , and then are they said to set helicallie . Afterwards the Sunne keeping on his course , leaueth the starres to be seene toward the West , then are they said to rise helicallie . By the Globe you shall gather the helicall rising and setting thus , turne the degree which the Sunne possesseth to the East side of the horizon , the starres which are alitle aboue it , are those which are risen helicallie , for the Sunne hath left them to be seen before his rising . Againe , turne the degree which the Sun possesseth to the West side of the horizon , the starres which are alitle aboue it , are those which are ready to set helicallie , for the Sunne will come vpon them from the West . The next thing to be noted , is the amplitude of the Sunne or starres .

Tell me what it is , how it is diuided , what vse it hath ?

The amplitude is to be consider at the instant time of the rising and setting of the Sun or starres , and not else . The amplitude is the distance of the Sunne or starres from the true East or West measured by the arcke of the horizon . Therefore you must bring the place of the Sun ( that is the degree of the ecliptick which the Sun possesseth ) or the starre assigned to the East or West side of the horizon , according as the time requireth , then marke how many degrees of the Horizon are contained betweene the Sunne , or the Starre , and the true East or West point of the Horizon , for those degree● expresse the amplitude . Amplitude is either North or South . North amplitude is the arcke of the Horizon counted from the true East or West Northward . South amplitude is to the Southward . The seafaring men kepe account as I told you before by the points of the Compasse , but it is better to obserue the amplitude by degrees . The Sunne or Starres vnder the equator haue no amplitude , because that circle alwayes riseth and setteth full East and West : for the other points of heauen this is generall , that those which haue equall declination , haue equall amplitude , be it to the North , or to the Southward . In a right Sphere the declination and amplitude of the Sunne and Starres is of one quantitie , so that knowing the one , I knowe the other : therefore if at any time in trauailing , wee finde the declination and amplitude of the Sunne or Starres to agree together , it is a certaine signe that wee are then vnder the equator , and our Zenith is iust in that circle .

Then may I inferre this also , that for so much as the meridian of a right Sphere , & the Horizon may be counted as one , if the distance of the Sunne or Starres from one Zenith be equall vnto their declination , wee are iust vnder the equinoctiall .

You say true : in any oblique Sphere the declination and amplitude of the Sunne or Starres doth alwayes differ , for the amplitude doth exceede the declination , yet is it neuer more than 90. degrees . Where the pole is eleuated ( as you may perceiue by the Globe ) 66. d. 30. min. the amplitude of the Sunne in the tropicall points , is 90. degrees . Where the pole is in our Zenith , there is no account made of the amplitude , because there is neither rising nor setting of the starres . The vse of the amplitude is in the finding of the eleuation of the pole . Each seuerall starre in each seuerall eleuation , hath a peculiar amplitude , so also haue the seuerall degrees of the eclipticke , whose declination doth differ . Therefore the amplitude of the Sunne or starre being knowen , if you bring them to the horizon , and rayse the pole of the Globe , or depresse it , vntill the starre or Sunne come to his iust amplitude , the pole shall haue his true election .

Me thinketh contrariwise I may inferre this : the amplitude being knowen , and the pole hauing his due eleuation , to finde the degree which the Sunne possesseth : for that degree which toucheth that amplitude , ●s the degree of the eclipticke fought for .

You say well : but considering that two seue●all degrees in the North part , and two in the South haue equall declination , and therefore equall amplitude , you must in answering this question haue an eye to the ●ime of the yeare , that you may make choise of the signe which is correspondent to the season , according as it hath bin noted heretofore . Moreouer , the amplitude either of the Sunne or Starres being knowen , and the pole of the Globe being raysed as it ought to be , you may finde the variation of the compasse in this manner . Pitch your compasse in some conuenient place , take the amplitude of the Sunne , or any other starre arising or setting , then bring the degree of the eclipticke which ●he Sunne possesseth or the starre obserued , vnto the horizon of your Globe , if the amplitude found out be correspondent to that which the Globe affordeth , then hath your compasse no variation , otherwise the variation is so much , as the difference betweene the obseruation made with your compas & the Globe amounteth vnto .

But how would you haue the compasse framed , for the performance of the conclusion ?

You may take any how so euer they be made , but for the yong beginner that compare is fittest which hath the Needle set iust vnder the North and South point .

I pray you tell mee this : the pole being raised as it ought to bee , how shall I finde at what time the Sunne or any other starre ariseth .

The rediest way to performe this is by the rectifying of the index belonging to the hower circle .

How is the index to be rectifyed ?

The degree which the Sunne possesseth being brought to the Meridian of your Globe , and you● houre circle beeing fastened to the Meridian orderly , 〈◊〉 you place the index vpon 12. a clocke , then is the inde● sayd to be rectifyed . This thing you shall note diligently , that there bee no more repetition made thereof when soeuer the mention shall be made rectifying the index of your Globe . The index being rectifyed if you bring the degree of the Eclipticke which the Su● possesseth to the Horizon the index will expresse the time of his rising or setting , according as it is applyed ether to the East or West side of the Horizon . Likewise the index being rectifyed if you bring any Starr● assigned to the East or west side of the Horizon , yo● shall find the time when it ryseth or setteth .

But put case I wanted mine hours circle , and th● ●ndex , may I not find the time of the Sunnes rising and ●etting otherwise ?

Yes , you may finde it by the difference of ascen●●on as I will teach you hereafter . Thus much concer●ing those thinges which are to be obserued when the Sun or Starres are in the Horizon . Now let vs come to those thinges which are to be noted when the Sunne or ●tarres are ether aboue or beneath the Horizon . Among the which , the first to be considered is the altitude of the Sunne or Starres .

I pray you let mee haue your instruction in this ●atter , for I take it to be a thing expedient to be known , because I heare many men bragge of their cunning in taking the altitude of Sunne and Starre .

The Horizon is the beginning of all altitude height or eleuation : therefore what soeuer is in the ho●zon hath no altitude , height , or eleuation . The extremi●●e of all altitude is the Zenith , for nothing can be high●r aboue the Horizon than that point , which being 90. ●egrees aboue the Horizon is equally distant from it ●n euery side . Moreouer this you must vnderstand , ●hat from the Zenith to each seuerall point of the Ho●zon a great circle may bee drawen , which because they ●ome from the verticall point , are therefore called ver●call circles , in some one of these circles is the altitude to bee counted , whereuppon wee define the altitude to bee the distance of the Sunne or Starre from ●he Horizon , expressed by the degrees of the verticall ●●rcle , which is drawen from the Zenith through the cē●r of the Starre propounded . The instrument seruing ●or this purpose is the quadrant of altitude which must ●ee fastened as you were taught before vnto the Zenith .

How shall I finde the altitude thereby ?

Lay the quadrant of altitude vpon the place o● the Sunne , or any other degree of the eclipticke ; o● vpon any starre , and obserue the degrees contained betweene it and the horizon , for they generally express● the altitude required , the Sunne or starre being supposed to be in such or such a place of the heauen . The altitude of the Sunne or starre is either meridian , or intermeridian . The meridian altitude is the distance betweene the starre and the horizon , when the starre i● iust in the meridian , the quantitie whereof is expressed by the degrees of the meridian circle . Therefore if you bring either the Sunne or starre assigned to the meridian , you shall finde the meridian altitude thereof , the pole of the Globe being raysed to his due heigth .

Why doe you put in that caueat ?

Because as the pole riseth higher or lower , 〈◊〉 doth the meridian eleuation of Sunne or starres alte● In a right Sphere the meridian eleuation of the Sunne or starres is alwayes equall to the complement of declination : as if the Sunne decline 23. d. 30. min. his eleuation is 66. d. 30. &c. In the most oblique Sphere the meridian altitude is alwayes equall to the declination therefore where the pole is 90. degrees aboue the Horizon , you shall neuer see the Sunne mount higher that 23. d. 30. min. which is his greatest declination . In other situations of the Sphere the meridian altitude is four in this manner if the Sunne or starre decline to the po●● eleuated , the declination of the starre being added t● the eleuation of the equator , geueth the meridian altitude : as for example , if the Sunne decline 23. d. 30. min● toward the North pole , the eleuation of the equator being supposed to be 38. d. 30. m. his meridian altitude will be 62. degrees . Contrariwise , if the Sunne or starre decline from the pole eleuated , the declination being taken from the eleuation of the equator , leaueth the meridian altitude : as if the Sunne decline from the North pole 23. d. 30. m. the eleuation of the equator being supposed to be 38. d. 30. m. his meridian altitude will be but 15. degrees .

Is there any excellent thing to be gathered by the meridian altitude of the Sunne or starre .

Yea , for it bringeth vs to the eleuation of the pole , for considering that each seuerall eleuation of the pole hath a seuerall and peculiar eleuation of the Sunne or starres , therefore by it wee may knowe the eleuation of the pole . If the eleuation of the Sunne or starres be equall to the complement of their declination , then are wee iust vnder the equator , and bothe the poles are in the horizon . If the eleuation be equall to their declination , then are wee iust vnder the pole . The other eleuations of the pole are found by addition or subduction , ●n this manner . If the Sunne or starre decline toward the pole eleuated , the declination being subducted from the meridian altitude , leaueth the heigth of the equator , which is alwayes the complement of the eleuation of the pole , therefore if you take the heigth of the equator from 90. you haue the eleuation of the pole . If the Sunne or starre decline from the pole eleuated , their declination added to the meridian altitude , geueth the heigth of the equator , and consequently the heigth of the pole .

But what if the Sunne or starre haue no declination ?

Then is this a generall rule , that the Sunne o● starre is then in the equator , and therefore the Meridian altitude expresseth the height of the equator , which being subducted from 90 geueth the pole . Thus much concerning the meridian altitude of the Sunne or Starr● The intermeridian altitude is the distance of the Sunne or Starre from the Horizon , when they are in some other place of heauen , and not in the meridian : This altitude is either antemeridian or postmeridian . The antemeridian altitude is the distance of the Sunne or Starre from the Horizon at any time before noone : the post meridian altitude is the distance of the Sunne or Starr● from the Horizon after noone . And for so much as th● Sunne or Starre by their proper motion make but sma● difference in their place , so that it cannot sensibly be perceaued in the after noone a that they haue moue from that place wherin they were in the forenoone therfore we say that the antemeridian & postmeridian altitude of the Sunne or Starres is all one , this being supposed that they bee equally distant from the meridian . 〈◊〉 searching out the antemeridian or postmeridian altitude of the Sunne or Starres the rule is all one with that generall rule which I gaue you before , so that the Sunne o● Starre be supposed to be in any place aboue the Horizon bet weene it and the Meridan .

But put case that I did not suppose the Sunne or Starre to bee in any place ? may not I finde out b● the Globe their certaine and true altitude which the haue in heauen .

This you must vnderstand that some thinges ar● found out immediatly , some things mediatly by certain meanes . If the Sunne shine hee will bewray his own height by the helpe of the sphericall gnomon , but the height of the starres cannot so bee found out , for they require the knowledge of the houre or some other such like thing , as you shall perceaue hereafter .

Tell me then , how shall I finde the height of the Sunne by the sphericall gnomon .

Rectify your Globe perfectly in the open aire where the Sunne shineth , so that it may stand precisely North and South , and that the Horizon be leuel , and the pole raised as it is conuenient : set your spherical gnomon vpon the place of the sunne , on the East or West side of the globe , acording as the time requireth , and turne the globe to and fro vntill the gnomon geue no shadow : them if you fasten the globe , that it moue not , & bring the quadrant of altitude ouer the place of the sunne , the degrees therof intercepted between the place of the sunne , & the Horizon wil expres the true height of the sunne . Thus much concerning the altitude of the sun or starres .

Now teach me how I may know how long they continue aboue the Horizon .

Here you must note this , that for so much as the sunne is the efficient cause of the day , therefore to know how long he continueth aboue the horizon is to know the length of the day , which is found in seuerall manners . First thus . Bring the degree which the sunne possesseth to the East side of the horizon , then rectify the index , setting if vpon 12. a clock in the houre circle . Turn the globe about vntill the said degree come to the West side of the Horizon : the hours ( which the index runneth ouer ) expresse the continuance of the sunne aboue the Horizon : in like maner may you finde how long any starre continueth aboue the Horizon .

The second way to finde out the continuance of the Sunne or starre aboue the Horizon , is by the difference of ascension taken twise .

Why doe you take the difference of ascension ?

This you shall perceaue by the Globe , that in a right Sphere there is no point of heauen which doth not rise and set within the space of 12. houres , so that the day is neuer longer than 12. houres , neither doth any starre continue aboue the Horizon longer than that time . But in an oblique Sphere ( if the Sunne or starres be not in the equinoctiall ) the day is either longer or shorter than 12. houres . If the Sunne or starres decline toward the pole eleuated , their continuance is longer , if from that pole their continuance is shorter aboue the horizon than 12. houres , by the difference of ascension twise taken as I finde before .

But why take you this difference twise ?

The one declareth how much the Sunne or any Starre ariseth sooner or later in an oblique , than it doth in a right Sphere , the other telleth how much sooner or later it setteth , and thereupon wee frame our rule thus , if the difference of ascension of the Sunne or starre declining toward the pole eleuated be twise taken and added to 180. degrees , the totall summe conuerted into houres and partes of houres as occasion offereth , shall declare the continuance of them aboue the ground . Againe , if the difference of ascension of the Sunne or starre declining from the pole eleuated be twise taken and subducted from 180. degrees , the remainder conuerted into houres &c. declareth their continuance aboue the ground .

The length of the day being found , what may be inferred thereupon .

Many things both pleasant , and profitable in Astronomie , as the eleuation of the pole . If the day be continuallie but 12. houres long , then are wee precisely vnder the equator . If the day be 6. moneths long , then are wee directlie vnder the pole . The other eleuations are found out thus . Diuide the length of the day into two equall partes , and conuert the houres into degrees , as if the day be 16. houres long , the halfe thereof is 8. houres , which containe 120. d. From the head of Aries count these degrees in the equator to the West side of the Horizon , and set fast the last degree vnder the meridian , so that it stirre not from it : then in the equinoctiall colure count the declination of the Sunne for the day propounded either vpward or downeward from the equator , according as the place of the signe requireth . Last of all , rayse or let fall the pole of the Globe vntill the degree of declination doth touch the Horizon , so shall the pole haue his iust eleuation , the like may be done by any fixed starre . The second thing to be noted in knowing the length of the day , is the time of the Sunnes rising or setting , for if the length of the artificiall day be diuided into two partes , the one declareth the houre of his setting , the other being subducted from 12. ●ffordeth the time of his rising : as if the day be 16. houres long , he setteth at 8. and riseth at 4. a clocke . The like may be done concerning the rising and setting of the starres . The third thing is the length of the night : for the length of the day being subducted from 24. houres , yeeldeth the length of the night .

But may not these three last things be performed by the Globe it selfe ?

Yes very conueniently I taught you before how the time of the sunne his rising & setting may be found out . The length of the night is knowen in this maner ▪ Seeke out that degree of the eclipticke which is opposite to the place of the sunne : Bring it to the East side o● the horizon , set the index of the houre circle vpon 12. a clocke , turne the Globe about vntill the said degree touch the horizon in the West , the houres which the index hath passed ouer , expresse the length of the night . The fourth thing ro be gathered out of the length of the day being knowen , is the length of the planetarie houre . The planetarie houre is the twelft part of the artificiall day or night : therefore sometimes it is longer than the common houre , sometimes shorter , sometimes equal● vnto it , in a right sphere , the common houre and the planet houre , both of the day & night are equall , in an oblique sphere if the sunne dicline from the pole eleuated , the common houre of the day is lesser than the planetary houre , but the common houre of the night is greater : contrariwise if the sunne decline toward the pole eleuated , the common houre of the day is greater than the planetary houre , but the common houre of the night is lesser . The next conclusion is to finde the houre of the day by the sunne shining .

Why do you say by the sunne shining , may not the houre be found , if the shine not , or may it not bee found by the starres .

If the sunne shine , he leadeth vs vnto the knowledge of the houre by his light , but if he shine not , there must bee one thing or another granted , and geuen , o● else wee cannot come to the knowledge of any particular thing be it houre , or height , or coasting : the like is to be said of the starres whose beame being so weake , that it cannot make a shadow , inforceth vs to craue some one thing granted vnto vs , before wee can inferre any conclusion .

I perceaue your meaning , first therefore tell me what I may doe by the shining of the sunne : and then I will craue the other conclusions .

The hour of the day by the sun shining is found thus , Rectify your globe perfectly , seeke out the place of the sunne , and rectify the index , bring the place of the sunne ether to the East or West side of the meridian according as the time of the day shall aduise you , set the sphericall gnomon vpon it , and turne the globe to and froe vntill the gnomon cast to shadow , then will the index in the houre circle giue the houre of the daye . Now marke how many thinges followe vpon this worke : First , so soone as you haue found the houre , if you fasten the Globe that it stirre not , and bring the quadrant of altitude ouer the place of the sunne , you shall finde his altitude aboue the Horizon . Item the globe being fastened , and the quadrant of altitude being brought ouer the place of the Sunne , you shall finde vpon what point of the compasse he is , with his distance ether from East , West , North , or South . Item , the houre being found : you haue all the Starres aboue the Horizon at that houre . Item you may by the Globe perceaue what Starres are in your Zenith at that time . Item , if you note what point of the Eclipticke is vnder the Meridian , both aboue and beneath the Horizon , and also what point of the Eclipticke is in the East and West , you may thereby very well knowe the foure Cardinall pointes of Heauen , as wee terme them , and consequently the beginnings and endings of the 12. housen of heauen which is commonlie tearmed the erecting of a figure .

All that you haue mentioned before is easie , but I do not perceaue this last conclusion .

I will helpe your vnderstanding so well as I can . First therefore a figure , as wee take it commonlie in this sence , is the diuision of the heauen into 12. parts by certaine great circles drawen from the intersections of the meridian and the horizon , through equall partitions of the equator , diuiding the eclipticke into 12. vnequall partes . Each part of heauen thus diuided is called an house . The beginning of them is in the East , and from thence the rest are accounted vnder the horizon to the nether part of the meridian , and from thence vpward to the West , and so by the South side of the meridian to the East againe , for so the reuolution of the heauen requireth . The instrument whereby the housen are found out , is that halfe circle which we commonly call the circle of position wherof I spake before . The manner of finding them out is this . The houre being knowen by the shining of the Sunne , the 4. cardinall points doe straightway offer themselues , whereof that which is in the East is called the first house , that which is vnder the horizon in the meridian is the fourth house , that which is in the West is the seuenth house , and that in the South part of the meridian is the tenth house . These being noted seuerally according as you see in the figure following , from the point of the equator , which is vnder the meridian , you shall count 30. degrees toward the East , ouer the thirtith degree bring the circle of position , and note what point of the eclipticke it crosseth , for that is the beginning of the eleuenth house , and the degree opposite vnto that degree of the eclipticke is the beginning of the fift house . Againe , from the point of the equator , which is vnder the meridian , you shall count 60. degrees toward the East , and ouer the said 60. degree bring the circle of position , and note what point of the eclipticke it lighteth vpon , for that is the beginning of the twelfth house , and the opposite degree of the eclipticke vnder the Horizon is the beginning of the sixt house . The beginning of the ninth and eight house are found out in the same manner on the West side of the Globe , as the eleueth and twelfth house were found out on the East side . The beginning of the second house is the degree opposite to the eight house , and the degree opposite to the ninth house is the beginning of the third house .

Is there any thing else to be found out by the shadow of the sphericall gnomon .

The Sunne being in the meridian , the heigth of the pole may be found out thus . Rectifie the Globe precisely in the open aire , not regarding the eleuation of the pole of the Globe at his due heigth . If the gnomon cast a shaddow , the pole of the Globe is either higher or lower than it should be , and therefore must it be raysed , or let fall .

But how shall I knowe when I am to rayse it , and when to let it fall ?

If the shaddow runne toward the pole eleuated , you must rayse the pole of the Globe , if it runne from the pole toward the equator , you must let the pole fall .

Is there any thing to be gathered out of the former propositions , touching the variation of the compasse .

Yea , for if you remember it , I told you , that when the spherical gnomon casteth no shadow , then do wee finde not onely the houre of the day , but also the coasting of the Sunne , that is , the point of the compasse vpon which hee shineth : Compare therefore your Compsse with the Globe , and you shall easily finde , whether it doth varie yea or no , and how much the variation is , so that the Globe bee rectified precisely as it ought to be : for if the Sunne shine vppon the same point of your Compasse , vpon which the Globe signified him to bee , then hath it not variation at all , but if they differ , their difference will expresse their variation . Thus much concerning those conclusions , which may bee performed on the Globe by the shining of the Sunne , and the Sphericall Gnomon . Let vs now come to those propositions , which require a certaine supposition , or the granting of some one thing or another , and may bee performed without the sunne shining : and thus , for example . The houre being giuen to finde the height that the Sunne shall haue , at that same houre . Rectifye your index , turne the Globe either to East , or West side of the Horizon , according as the houre assigned doth require , vntill the index fall vpon the sayd houre , then fasten the Globe , and bring the quadrant of altitude ouer the place of the sunne , the degrees of it intercepted betweene the place of the Sunne , and the Horizon , expresse his height at that houre .

Here me thinketh I may reuerse the former proposition , and by the height of the sunne giuen , I may finde out the houre .

You say well , for if you rectify your index , and moue the globe to and froe as the time requireth , vntil the place of the Sunne fall vpon that degree in the quadrant of altitude , which you supposed the sunne to haue , then will the Index expresse the houre .

May I not also by the height of the starres finde the houre of the night ?

Yes , if so be you know the starres of heauen , & can compare them with your Globe .

Put case I did know them ( for afterwards I will bee bold to craue the knowledge of them ) how shall I finde the houre of the night .

Take the height of some knowen starre , rectify your index , turne the globe about vntill the same starre founde out in your globe , haue the same eleuation in the Quadrant of Altitude , which you founde him to haue in the Heauen , so shall the Index expresse the houre .

Here also I may inferre this proposition . The ●oure of the night being giuen to finde not only what ●eight the starres shall haue aboue the horizon , but also what starres are then aboue it .

You may , in this manner : rectifie your index , ●urne your Globe about , vntill the Index fall vpon the ●oure assigned , so shall you haue the starres in your Globe answerable to them which are seene in heauen : then applying your quadrant of altitude vnto them , you shall finde the height of each seuerall Starre .

Nowe marke you well how many thinges followe ●ereupon . By this meanes you may come vnto the knowledge of the starres , especially if you set the Glob● North , and South , for then the Globe will be so answerable to the heauen , that you cannot but knowe th● starres of the heauen by the starres of the Globe , fo● that starre in the Globe which in place and height 〈◊〉 answerable to the like starre in heauen , affordeth th● name and title thereof . Item , the houre being found b● the starres height , or the height being found by th● houre , as I taught you euen now , if you fasten the globe and bring the quadrant of altitude ouer the center of th● starre , you shall finde vpon what point of the compa●●● any starre is , and how many degrees it is distant fro● either of the foure cardinall points of the Horizon . ●tem , you shall finde the culminant starres , that is , tho●● starres which passe ouer your Zenith . Item , you ma● thus finde the foure cardinall points of heauen , with th● beginning of the twelue housen , and how farre th● Sunne is distant from the Horizon , according as I deliuered it before , in speaking of finding the houre of th● day by the Sunne .

But may the height of the pole be found by th● starres , as it was found by the Sunne ?

It cannot be found by the shaddowe of th● sphericall gnomon , because the beame of the starres i● so weake , that it cannot cause a shaddowe , but the meridian altitude of any starre being geuen , the height of th● pole is presently found by the Globe in this manne●● Bring the starre whose meridian altitude is knowne vnt● the meridian of the Globe , either to the North , or Sou●● side thereof , as the starre it selfe doth admonish you then rayse , or let fall the pole of your Globe , vnt● there be so many degrees of the meridian contayne● betweene the centre of the starre , and the horizon , as ●he height found out amounted vnto , so shall the pole of the Globe haue his dew eleuation .

Let vs now returne to our former purpose : you ●●id euen now that by supposition of some one thing or ●nother , many conclusions may bee performed by the Globe without the sight , or shining of the sunne , or ●●arres as you shewed it by example in supposing the ●eight of the sunne , or starres to be knowen , or the hour ●f the day , or nighte , and from thence you deriued ma●y other conclusions . Haue you anie other proposition ●ending to the same effect ?

Yea there are many , for out of any one thing al●ost all the other may arise : because there is in them a ●ertaine reciprocation , & a necessarie consequence from ●he one vnto the other : as thus . If the hour be knowen , & the height of the sunne , we may finde his place : the ●●dex being rectifyed .

That may bee easily done by the height of the ●●nne at twelue a clocke hauing consideration of the ●ason of the yeare , because in each quarter of the eclip●cke each seuerall degree hath a certaine altitude in the ●eridian . But how it should be done at any other houre ●ther before , or after noone , I do not see .

You must suppose that when your index was ●ectifyed , you did then knowe the place of the Sunne : ●ut when you went about to take his height you forgot 〈◊〉 : if therefore you desire to know it againe , turne the ●obe to and froe , vntil you bring the index to the houre ●ssigned , fixe the Globe and apply the quadrant of alti●●de to the ecliptick , that degree of the eclipticke , which ●nder the quadrant of altitude answereth to the height of the Sunne knowen , is the place of the Sunne , Which beeing founde , wee may proceede by a necessary consequence to all the former conclusions whatsoeuer . As to the point of the compasse vpon which he shineth , to his distance from the East , West , North , o● South , &c.

Then if I perfectly knowe the distaunce of the Sunne from the Easte , or Weste , together with hi● height , I may finde his place in any eleuation of the pole .

You may , hauing consideration of the time of the yeare , which is alwayes requisite in these propositions , which leade vs to the place of the Sunne For if you sette the Quadrant of altitude to the point of the Compasse , vppon which the Sunne is sayde to shine , or vppon that distaunce from the true Easte , or West , which the Sunne is sayde to haue , and turne that quarter of the ecliptick which the time of the yeare requireth , vnto the quadrant of Altitude , that degree which vnder the Quadrant answeareth to the supposed height of the Sunne , is the degree which the Sunne possesseth . Contrariwise wee may by the place of the Sunne , and the point of the compasse , vppon which hee shineth , finde the height of the Sunne .

Mee thinketh that that is easie : for if I set the Quadrant of Altitude agaynst the point of the Compasse assigned , and bring the place of the Sunne vnto it , the degrees of the Quadrant contayned betweene the place of the Sunne , and the Horrizon expresse his height .

You say true : this proposition also is performed with the same facilitie . The point of the Com●asse beeing giuen , and the place of the Sunne to find ●●e houre of the Daye , in this manner . Rectify your ●ndex , set the Quadrant of Altitude vppon the point ●f the Compasse assigned , then bring the place of the ●unne to the edge of the Quadrant , so shall the ●ndex expresse the houre .

This also is another consequent : the point of the com●asse beeing giuen , and the height of the Sunne to ●nder the time of the rising or setting : you knowe that ●●e point of the compasse , and the height of the Sunne ●ust necessarily leade vs to his place , hauing found his ●lace , rectify the Index , then bring the place of the Sunne 〈◊〉 the East side of the Horizon , so will the Index point ●ut the time of his rising : againe turne the place of the ●unne to the West side of the Horizon , and the index ●ill expresse the time of his setting .

I find it now true which you sayd before , name● that the supposition of some certaine things bringeth 〈◊〉 the consequence of all the other . For mee thinketh ●●at I my selfe knowing the point of the Compasse , and ●●e height of the Sunne , coulde easilie inferre by your ●xample the declination , the right and crooked ascen●on of the Sunne , the length of the day , or night , the ●eridian Altitude , and whatsoeuer hath beene spoken of before . For the height of the Sunne , and the point ●f the compasse , vpon which he shineth leadeth me to ●e place of the Sun , the place of the Sun being brought 〈◊〉 the meridian geueth his declination , & also his right ●cension , and his meridian altitude likewise the same ●ace being brought to the Horizon affordeth his croo●ed ascention , then keeping the place of the Sunne at the horizon , if I set the index vpon 12.2 clocke , and turne the Globe about to the West , I cannot but finde the length of the day : &c. Let vs now proccede .

Hetherto you haue heard those conclusions which may be inferred by the Globe , the Sunne or Starres being supposed to bee either in the horizon or about it : there are some which belong to the Sunne or Starres , being vnder the horizon . Among the which 3. or 4. only are vsually sought after : the other ether because they are not greatly profitable , or because they are easily performed by that which hath bin deliuered heretofore , are neglected . The first of them is to finde the depression of the Sunne at anie houre assigned : but especially at midnight .

What meaneth the depression of the Sunne ?

The depression is opposite vnto the altitude : and it is the distance of the Sunne from the horizon downward , it is found thus : Seeke out the degree of the eclipticke opposite vnto that degree , which the Sun possesseth , bring it to the South side of the meridian aboue the horizon , the degree of the meridian betweene it and the horizon expresse the depression of the Sunne at midnight . Whereby is gathered how he is vnto them which are our antipodes .

But put case I would know the depression of the Sunne at any other houre , how shall I find it ?

Bring the opposite degree vnto the meridian , rectify the index , turne the Globe about vntill the index fall vpon the same houre , fasten the Globe , & then bring the quadrant of altitude ouer the sayd degree , the portion of the quadrant betweene it , and the horizon expresse the depression of the sunne at the hour assigned . The second concerneth the dawning of the day . That is ●ound in this manner . Bring the degree of the Sunne ●o the meridian , rectify your index , then seeke out the degree of the ecliptick opposite to the degree which the Sunne possesseth , moue it toward the West side of she Horizon , and by the helpe of the quadrant of altitude ●et it 18. degrees aboue he Horizon , the houre vpon which the index falleth , expresseth the dawning of the ●ay .

I pray you tell tree this , what is the reason why ●ou bring the opposite degree to the West side of the Horizon ?

As before in seeking the depression of the Sun , ●he opposite degree being brought to the South side of ●he meridian declared how low the degree of the Sunne ●as vnder the Horizon in the North side , euen so here ●he placing of the opposite degree 18. degrees aboue the Horizon in the West , causeth the true place of the Sun ●o be 18. degrees vnder the Horizon in the East , at which ●istance the dawning doth beginne .

What if the opposite degree cannot haue 18. degrees of eleuation , but falleth vnderneath it .

Then must you conclude , that the twilighte ●ontinueth from the setting of the Sunne vntill his ri●ing .

Is the dawning of the day in all places at the same ●oure the Sunne possessing one and the same degree ?

No , for the more oblique the sphere is the daw●ing beginnineth so much the sooner , because the Sunne ●reepeth his course continually nearer to the Horizon , & ●herfore lighteneth our hemisphere so much the sooner . The third conclusion concerneth the length of the dawning , which is the time from the first breaking of the day vnto the rysing of the Sunne : the conclusion is wrough● thus , Seeke out by the former proposition the time 〈◊〉 the dawning , then seeke also the time of the Sunne ▪ rising , the difference of these two times expresse the length of the dawning , which is more or lesse according to the obliquitie of the Sphere . The fourth conclusion concerneth the length of time wherein any signe a ariseth aboue the Horizon .

What , is one signe longer arising than another I thought that as they were all equall , so the time 〈◊〉 their rising or setting was also equall : and this is certaine , that any sixe Signes arise and sette in 12. houre .

That is true , if you take them ioyntly together otherwise being taken seuerally , the one is longer a ●sing than the other : wherevpon there ariseth another distinction of ascension , which in respect of the time limited vnto each signe is said to be right or oblique without respect had to the situation of the sphere as it was before Those signes haue a right ascention , with whom the●● arise more than 30 ▪ degrees of the equator : that is to say that are longer arising than 2. houres , contrariwise if there arise with the signe fewer than 30. degrees of the equator , that is to say , if the signe arise in lesser time than 2. hours , then is that called an oblique ascention . Ether of these ascensions may be found out 2. seueral wayes : by the degree of the Equator , for that is the measure of all time , o● els mechanichally by the houre circle . By the degrees of the equator , the length of time , that is the ascention of any whole signe is found thus in any situation of the sphere Bring the hed of any signe to the East signe of the horizon , marke what degree of the equator is in the horizon with it , them moue the globe , vntil the end of the said signe cometh to the horizon , mark the degree of the equator in the horizon , subduct the lesser from the greater , the remainder conuerted into houres , and minutes if neede require expresseth the assention of the signe propounded . By the houre circle the length of time wherin any signe ariseth is thus sought out . Bring the hed of any signe to the East side of the horizon , set the index vpon 12. a clock , moue the globe west ward , vntil the end of the said signe come to the horizon , the index in the houre circle will expresse the length of time wherein the signe did arise . These are the chiefest questions moued concerning those thinges which happen vnder the horizon .

I pray you hath the circle of position no other vse then to rectifie a figure .

Yes , for it findeth that circle whereof it receaueth his name , that is the circle of position , which is but a great circle drawen from the one intersection of the horizon and meridian , vnto the other , through the centre of some star , or any point els assigned in the heauen , diuiding the sphere into 2. peeces . By it in erecting of the 12. housen , we find what notable starres , or what planets are in any of the housen . The distance of any circle of position from the meridian is found thus . The circle of position being raised from the horizon vnto any point assigned in the globe , moue the quadrant of altitude ( fixed to the Zenith ) to the east or west point of the horizon as occasion requireth : the degrees of the quadrant contained between the said circle of position & the meridian expresse the quantity of the angle which it maketh : each circle of position may supply the place of halfe an horizon , & in that respect it hath singular vse in astronomical & geographical matters , as shall be declared , if God spare me life and ability to performe that which I haue in hand . It remaineth now to speake of the lesser circles of the Globe .

But by your leaue sir , you haue sayd nothing of making the dials by the Globe : which is a matter mentioned by all Astronomers in handling the vse of the Globe .

It is true , and therefore I did omit it , because it is the matter which I haue now in hand , the which I am so much the more desirous to performe , because it hath binne earnestly required by a friend of mine , whose forwardnes in these in studies I would helpe so much as lyeth in me . Therefore let me at this instant craue pardon for that matter , vntill such time as I shall particularly discourse thereof .

Well then proceed in the vse of the lesser circlet of the celestiall Globe .

You see that the foure lesser circles of the globe diuide the whole surface thereof into 5. partes . Euery one of them is called a Zone .

What meaneth chat word Zone ?

It signifieth among the Grecians a gyrdle , or a swadling band , and therefore it is fitly applyed vnto these portions of the globe , because they in their figure represent after a manner such a thing . Of the Zones some are enclosed with one onely limit some with two : those which are inclosed with one only limit , namely with the circle arcticke , and antarcticke are the two Zones which lie about each pole , which because of their distance from the eclipticke , and place of the sunne are called cold . Not that there is ether heate or colde in heauen , but because they which dwell on earth vnder that circuit of the heauen , feele not the Sunne so forceable in his heat by reason of his obliquitie , as others doe . The other 2. Zones are limited on each side : That which is in the middest , being limited on the one side with the tropick of Cancer , on the other side with the tropicke of Capricorne , ●s called the burning Zone , because the Sunne keeping ●his course continually within it doth greatlie heate that part of the earth which is subiect vnto it . The other two being nether too neare the Sunne , nor too farre of are called temperate , because they are nether so hot as the ●one , nor so cold as the other : that which is to the Northward is limitted with the circle arcticke , & the tropick , of Cancer , the other to the Southward is enclosed with the circle antarcticke , and the tropicke of Capricorne : The breadth of each cold zone is 47. degrees : the breadth of the burning Zone is as much : each temperate Zone hath 43. degrees in breadth . As they are described on the celestiall globe , they expresse vnto vs what starres are enclosed within each seuerall Zone , which are to be no●ed , because they adde somewhat according to their nature vnto the quality of the Zone making it more hot or cold . Thus much concerning the vse of the celestiall Globe , wherein if I seeme to haue bin ouerlong , I doe therefore craue pardon , because I haue witten it for the behoofe of our countrie men , who being not throughly seen in the Latine tongue might from hence gather that in some measure , which might further their knowledge , and satisfy their desire in these kinde of matters .

The vse of the Terrestriall Globe .

WE are now come Philomathes , to the terrestriall Globe , whose vse I am so much the more desirous to teach you , by the more I find you willing to learn : follow you therefore your accustomed manner in mouing of questions , & I will endeuor my selfe to shape you answere to your demaund : for so I iudge it best for your instruction .

Seeing it is your will I should doc so , I pray you te1 me , what mean you by the terrestriall Globe , & how do you define it ?

The thing it selfe telleth vs , that we may define it to be a solide round bodie containing in the conuexity thereof the description of the land , and sea , with certaine lines necessarie thereunto .

For somuch as I haue now the definitions of the two Globes before I goe any further to the vse of this : tell me wherein the celestial and terrestriall Globe agree , and wherein they differ ?

Concerning their agreement : first you see they haue their forme common , for they are both round .

It is so : but herein mee thinketh the terrestriall globe is faulty , because it doth not represent the true forme of the earth , as the celestiall globe doth resemble the heauen , for the earth is not round .

Take heed what you say Philomathes , the roundnes of the earth both in breadth & length ii so substantially confirmed , that he is almost accounted an hereticke among the geographers that denieth it . Their arguments are set , not only from the proportion , but also from the manner of the rising & setting of the starres , & the raising & depression of the poles . Item besides the eclipse of the moone & the natural course of the water , that which appeareth to our sight in going from , or comming neere the shore , is an euident token of the foresayd roundnes .

But for all these arguments I say , that the globe doth not represent the iust forme of the earth , which being ful of hilles & dales doth greatly disagree from a perfect round . yea my sight also witnesseth such a thing , for which way soeuer I looke , both the water and the earth for the most part seemeth playne .

It is is somewhat Philomathes which you say , but there are diuers reasons which moued the Cosmographers in setting forth the terrestrial globe , to do that which they haue done , that is , to make it rounde . First because it was not necessary to make these hilles & dales , it was sufficient to expresse their place , & to say the truth it was vnpossible to set them forth as they are indeede . Secondly , the earth in regarde of the heauen doth not seeme otherwise than rounde : as you may perceaue by the shadow thereof , which in the eclipse is most sphericall , & round : thirdly , these hilles and dales in regarde of the whole earth , are but as a mole , or wart vppon a mans bodie , or the small pimples on an orange . And as for the playnes which I see , bee it either on the water or land , it aryseth of the huge circuit of the earth , which is so great , that each parte thereof which wee see , cannot but seeme vnto our sight to be a right liue .

Well then the first agreement of these 2. globe● is in their forme , they are both round , albeit the earth be not to be conceaued to be so precisely round as the heauen is . In what else doe the Globes agree ?

They haue the same poles , the same axletree , the same imaginarie circle . So that what conclusion soeuer may be performed by any of these on the celestiall Globe , the same may bee performed on the terrestriall Globe , excepting those proportions which concerne the fixed starres .

I thought that these thinges had belonged especially to the celestiall Globe .

So they doe : but they are therefore expressed in this , because the globe of the earth and water being contained within the heauen , and being in respect the centre thereof , wee may hereby gather what part thereof is subiect to any part of the heauen . Thus much concerning their agreement , their difference appeareth first in their inscription , as their seuerall titles do import , the one containing the starres of heauen , & the circles therof , the other expressing the earth and water . The second difference consisteth in the manner of the description : For as I told you , the starres which wee beholde in the concauitie of heauen are described on the conuexity of the celestiall Globe : but in the terrestriall Globe the earth is described on the outside euen as wee behold it . The third difference is in certaine circles and lines expressed in the terrestriall Globe , but not in the celestial : namely the circles of longitude and latitude , and the Rhombes .

Doe you not mistake your selfe : there are in the celestiall Globe circles of longitude and latitude , for otherwise how should wee finde the longitude and lati●ude of the starres ?

Put case it were as you say ( which is seldom or ne●er seene ) that the circles of longitude & latitude were ●escribed on the celestial globe : yet are they not the same with those of the terrestriall Globe , for the longitude & ●●titude in both these Globes is not accounted in one ●inde of circles , as I will declare vnto you , when I shall ●aue occasion to speake of the vse of this Globe . This hall suffice for the difference of the Globes which constech in these foure thinges . 1. In the generall subiect ●atter . 2. In the manner of describing the same . 3. in the ●rcles of longitude and latitude . 4. in the Rhombes . Let ●s now come to the vse of the Globe , wherein I will proceede euen as the subiect matter inscribed doth af●ord , not medling with any of the former conclusions ●t downe in the vse of the celestiall Globe , but speaking ●f those thinges only which the terrestriall Globe doth ●ade vs vnto .

Goe too then : what doe I learne by the circles of ●e Globe , first by the equator ?

It deuideth the earth into 2. peeces , the North , ●nd South : the North is that which is from the equinoc●all round about subiect to the North pole , the South that , which is from the equinoctiall round about toward the South pole .

Do you say then that al they which are betweene ●he equator and the North pole , are the northren peole , and so likewise of any seuerall place ?

Yea that I doe , what thinke you of myne assertion .

I can hardly thinke it to be true : for then why doe wee call Cape Saint Vincent the South Cape ? and why doth the Scripture call the Queene of Saba the Queen of the South , seeing they be both on this side the equator ?

You must note this , that North and South are not taken after our maner of way : neither East or West . North and South is taken three manner of wayes . One way , simply as I spake of it euen now : the other are in respect : as first for example , what soeuer is from our Zenith toward the North pole is said to be Northward , and what soeuer is from thence toward the South pole , i● sayd to be Southward : and in this respect is cape Saint Vincent called the Southcape being compared with cape sinister because it is toward the South pole in respect of this . Againe North and South are taken in respect of the eclipticke , whereupon euery starre distant from the Ecliptick toward each pole is said to haue North or South latitude according to the pole toward which it bendeth : as for example , the starre called the lesser dogge in respect of the eclipticke is sayd to haue South latitude , because it leaneth from the ecliptick toward the South pole 39. d. 10. m. yet in respect of the equator it is counted Northern because it declineth from the equator toward the North pole . 5. d. 57. m.

I vnderstand you well : what ether vse hath the equator in the terrestriall Globe .

You heard me speake in the vse of the celestiall globe of a right sphere , & of the diuers accidents belonging thereto , as that the day and night therein was alwayes of on equall length , and that the starres did rise & set in 12. houres : the equinoctiall line therefore in the terrestriall globe , expresseth , who they be that haue the right sphere and see the accid●●ts belonging thereto . As those of the ●e Iland Gilolo , of Celebes , of Borneo , of Taprobana , ●f part of Africa , and America . Moreouer the degrees ●f the Equator are the common scale of the terrestriall ●obe whereby wee knowe what distance there is from ●ace to place in this manner , set the one foote of your ●ompasse in the one place assigned , & extende the other ●ot vnto the other place : apply your compas so extened vnto the equinoctiall , the degrees intercepted betweene the feete of your compasse expresse the distance ,

In deede I finde hereby how many degrees of ●e equinoctiall are contayned betweene the feete of the ●ompasse , but how shall I expresse their distance , ether 〈◊〉 miles or leagues ?

You must expresse that according as the allow●ce is of seuerall cosmographers . Ptolomee alloweth ●nto euery degree of any great circle described on the ●●rth 500. furlongs or 62 miles & ½ . We allow 60. miles or 〈◊〉 . leagues . The French man alloweth 16. leagues and ⅔ . ●he Spaniard maketh euerie degree 17. leagues & ½ : So ●at if you multiply the number of degrees intercepted betweene the feet of your compasse by any of the foresaid ●umbers the product giueth the distance of the 2 places e●er in miles , or leagues according to the denomination of ●e multiplier . Another vse of the equator is this : in it the ●gitude of any place is found , the latitude is counted from it .

Here accordinng to your promise , I pray you in●ruct me in these thinges , that I may know readily how 〈◊〉 distinguish the longitude , & latitude of the terrestriall ●obe from them of the celestiall globe .

That wil I do so plain as I can : the longitude of the ●elestial globe beginneth at the head of Aries , in terrestriall Globe it beginneth in the equator at that great circle , which being drawen from the Pole of the World through the fortunate Ilandes ( as Ptolemee will haue it ) cutteth the equator at right angles . Againe the longitude celestiall is counted in the eclipticke the terrestriall longitude is counted in the equinoctiall . Thirdly , the celestiall longitude is counted from the head of Aries in the Eclipticke vnto that great circle which is drawen from the pole of the Eclipticke through the starre , or any point els assigned in the heauen , vnto the eclipticke : the terrestriall longitude is counted in the equator from the foresayd great circle vnto that which is drawen from the poles of the world vnto the equator , through the Citie , or any other point assigned in the terrestriall Globe . Last of all , the longitude in the celestiall Globe is found ou● by the quadrant of altitude applied to the poles of the eclipticke : in the terrestriall Globe it is found out by the meridian . In regard of these differences , wee define the terrestriall longitude to be the arcke of the equinoctiall contained betweene the great circle passing through the fortunate or Canary Ilandes , and the great circle drawe● from the poles of the world through any point assigned in the Globe : according to the degree of that arke so is the longitude assigned to be , as if the degrees be 20.30 . or 40. &c. The place or point assigned is sayd to haue 20.30 . or 40. degrees of longitude .

Giue mee leaue here to moue certaine question for myne instruction . First , why is the longitude counted in the equator , and not in the meridian from pole to pole , or in some other great circle ?

You know it is an vsuall custome when a thing is offred to vs that is both long and broade ( the dimensions being vnequall , to call that the length of the thing which is the greatest , and that dimension which is the shortest wee call the breadth . The Geographers therefore taking suruey of the world , & finding the inhabited part thereof to be more betweene East , and West , than between North and South , they gaue the name of longitude to that part following or accustomed manner in these dimensions .

In speaking of the beginning of longitude , you sayd that according to Ptolemee , it was to bee counted from the meridian of the Canarie or fortunat Ilandes : why did you put in those wordes ?

There is a diuersity in the beginning of longitude among the Cosmographers , & therefore I thought good by my words to insinuat so much vnto you , Ptolemee and the ancient Cosmographers began their account at the foresayd meridian . But the later men haue begun it at the meridian , which runneth through the Ilande of S. Michael , as you may see vppon the terrestriall Globe wherein this meridian is diuided into degrees , that it may be the better distinguished from the other .

Why did they begin at this place , and why did they account from thence Eastward ?

Ptolemee began at the forenamed meridian of the Canarie , or fortunate Ilandes , because in his time they were the furthest places of the worlde discouered toward the setting of the Sunne , & he did therfore reckon to the Eastward , because from the fortunate Ilandes to the Westward , there was not any hope of more land , out to the Eastward there was . The later age began at ●he meridian of Saint Michael , because vnder that meridian the compasse hath no variation , but respecteth duly the North and South as most men affirme , though other say it hath his iust position vnder the meridian of Corno and Flores : and others betweene the Ilandes of Flores and Faiall , which are all in the number of those Ilands that are commonly called Acores : They accounted also the longitude the same way that Ptolemee did , thinking indeede , that beyond that place there was nothing but sea . But since the world hath bin found to be habitable round about : there haue bin some that haue begun the longitude at some such certaine place as liked them best , and haue counted to the West ward : as for example , the Spaniards who trauelling much vnto the West india , haue begun their longitude at Toledo and counted it Westward .

What difference make you betweene a circle of longitude and the meridian : mee thinketh by your wordes they are confounded .

It is so , they are confounded for euery circle of longittude is a meridian , & contrariwise euery meridian is a circle of longitude , but they are distinguished by their office : so farre forth as the circle drawen through any place assigned limiteth the distance in the equinoctiall , which the said place hath from the meridian passing through the Canarie Ilandes , or any other meridian from whence the longitude is accounted , in that respect it is called a circle of longitude . But in regard that when the sunne commeth to this circle it is then high noone or midday , it is therefore called a meridian .

Are there then so many circles of longitude as there be meridians ?

Yea that there are , although vpon the globe all the circles of longitude are not expressed , as for example vpon M. Moleneux his globe they are drawen but through each tenth degree .

How is the longitude of any citie or towne assigned vpon the globe to be found out ?

The instrument seruing for this purpose is the meridian of the Globe , it supplyeth the want of all the circles of longitude which are not expressed . Therefore if you bring the citie assigned to the meridian of the globe the arcke of the equator contained betweene the said meridian , & the first meridian of longitude expresseth the longitude of the place assigned : so that the said arcke be taken and accounted according to the orderly succession of the degrees of the equator .

I pray you expresse the meaning by some example on the globe .

I will . I bring Ierusalem to the meridian , and finde betweene it and the first Meridian of longitude 72. degrees , 30. minutes of the Equator : so much I pronounce the longitude of that place to be , because the succession of the degrees of the Equator is orderly taken : againe I bring the citie of Mexice in America to the Meridian : & albeit betweene the meridian of that place and the first meridian of longitude there bee contained but 90. d. 30. m. yet must I not affirme that to be the longitude of Mexico , because counting from the first meridi●n to the meridian of Mexico I count against the orderly succession of the degrees ; therfore I must haue regard vn●o the said succession & pronounce Mexico to be from the first meridian 269. degrees , 30. minutes . But that yon may not bee deceaued in counting the longitude , let this ●e a generall rule , and easie vnto you : if the first meri●ian of longitude be on the left hand of the meridian of the Globe which is taken for the meridian of the place assigned , then beginne at the first meridian , the degrees of the shortest arcke of the Equator from the left hand towarde the right expresse the Longitude . But if the first meridian or circle of longitude be on the right hand of the meridian of the Globe then beginning at the first meridian the degrees of the greatest arcke of the equator from the right hand to the lefte , declare the longitude of the place assigned .

Mee thinketh by your wordes that the longitude of euery place must be accounted continually by degrees .

Yea , it must be so accounted , but if it be your pleasure to know how many miles or leagues &c. it is distant from the sayd first meridian : Extend the foote of your compasses , from the place assigned to the first meridian of latitude according as you were taught before in taking the distance from place to place , and apply your Compasses afterward vnto the equinoctiall line , the degrees thereof intercepted betweene the feete of your compasses being conuerted into miles or leagues , will giue the distance .

You said , that if I bring the place knowen vnto the meridian I shall finde the longitude , whereupon as I thinke I may contrariwise inferre this , that if the lon-longitude of any place knowen be brought vnto the meridian I shall be sure to finde the place vnder the meridian if it be expressed in the globe .

You say true , and hereby also you may learne thus much , that many places may haue one and the same longitude because many places of the terrestria● globe many be contained vnder one & the same meridian

But haue they all one longitude that are vnder the same meridian ?

Not so , for as you see by the Globe , each circle of longitude maketh 2. seuerall intersections with the equator the one on the one side , the other on the other side right opposite : whereupon it commeth to passe , that those places which are vnder one and the same meridian may differ 180. degrees in longitude . Those places therefore are sayd to be in one longitude which are vnder that halfe of the meridian , which is contained betweene the 2. poles from whom there cannot be imagined a right line to be drawen paralel vnto the diameter of the Equator . But if the one place lie vpon the one side of the meridian and the other place beyond the pole on the other side of the meridian , then cannot they haue the same longitude .

They that haue the same meridian , haue they any thing common , and what haue they differing one from another in respect of the thinges appearing in the reuolution of the heauen ?

I cannot conueniently answere vnto this question , vntill such time as I haue instructed you in the latitude , let it rest therefore vntill then , and note this in the meane time , that as two or more places may haue one longitude , so many may differ in longitude .

Is it expedient for me to obserue the difference of longitude betweene place and place , then tel me how I may finde it by the Globe ?

The longitude of the two places being seuerally sought out , as you were taught before , bring that place which hath the lesser longitude , vnto the South side of the meridian : if the other place be ether iust vnder the North side of the Meridian , or on the East side thereof , subduct the lesser longitude from the greater , the remainder giueth his difference of longitude : But the place which hath the lesser longitude beeing brought to the South side of the meridian , if the place which hath the greater longitude be on the West side thereof , subduct the greater longitude from 360. degrees , adde the remainder to the lesser longitude , the totall summe giueth the difference of longitude : otherwise if you be not skilful in Arithmetick , the place which hath the lesser longitude being as I told you brought vnto the meridian , the degrees of the equator contained between it &c the longitude of the other place , afford the difference of longitude .

The difference of longitude being knowen , what may I inferre thereon ?

First you may infer your course from the one place to the other can neuer be north & south : but vpon some other point of the compas . Secondly they neuer haue the same hours of the day or night : for if it be noon or midnight to the one , it is past , or before noone or midnight vnto the other : yet in the opposit houres they may agree as if it be 6. in the morning it may be 6. at night to the other , if it be noone to the one , it may be midnight to the other , the difference of longitude being iust 180. degrees .

If they that differ in longitude do thus differ in their houres , how shall I know by the globe ( comparing two places together ) which of them preuenteth one the other .

Bring ether of the two places vnto the meridian , if the other be to the Eastwaad thereof . I say that that place which is vnder the meridian is preuented in the time . As if the question were betweene London and Rome . London being brought to the meridian , Rome is found on the East side thereof , therefore I say that London is preuented in the time , and that at Rome it will be 6. 7. or 8. a clocke in the morning &c. before it be the same houres at London . Contrariwise if one of the 2. places being brought to the meridian , the other be found on the West side thereof , then doth the place vnder the meridian preuent the other , as for example . London & Mexico being compared together , London being placed vnder the meridian , Mexico is on the West side thereof , therefore London preuenteth Mexico : whereby I may conclude , that it is 6. a clocke in the morning at London before it be 6. a clocke at Mexico . &c.

You haue taught me to know which place preuenteth the other , tell mee now how long the time is wherein the one place preuenteth the other ?

If you conuert the difference of longitude into houres & partes of houres as is conuenient , you shal easily find out what the time is , wherein the one place preuenteth the other . Otherwise you may do it thus : bring the westermost of the two places assigned vnto the meridian , set the index of the houre circle vpon 12. a clocke , turne the globe Westward vntill the other citie come to the meridian , the Index expresseth how long the time is wherein the westermost of the two places is preuented . As for example , if the index light vpon the third houre , then doth it signify that it is but 9. a clocke at the westermost place when it is 12. a clocke at the other &c. and what eclipse or other celestiall appearance the Westermost place seeth at 12. a clock , the other seeth it at 3. a clocke after noone &c.

What haue you else to say of the equinoctiall circle ?

It is the beginning of latitude .

Let me throughly conferre with you about this matter : how do you define latitude in resspect of the terrestriall Globe ?

It is the distance of any point assigned in the terrestriall Globe from the equator , limited by the degrees of a great circle drawen from the poles of the World through the point assigned .

Then by your wordes I gather this , that for so much as the beginning of latitude is in the equinoctiall , what so euer is vnder that circle , can haue no latitude . Also the latitude may be counted toward ether of the poles , so that it is ether Northerne or Southerne according as the pole is , toward which the place bendeth from the equator . But when you say that the latitude must be accounted from the equinoctiall to the place , doe you not meane the Zenith ?

Yes , you must alwaies so vnderstand it : for albeit the word latitude be applyed to the terrestriall Globe , yet is it sought out by the circles of heauen , and commonly being demaunded what the latitude is , wee answere that it is the distance of our Zenith from the equator , notwithstanding it is sufficient speaking of the terrestriall Globe , to say that the latitude is to be accounted from the equator to the place assigned .

What great circle is it in which the latitude must be accounted ?

It is that great circle of longitude which is drawen from the poles of the world through the place assigned , but because it were an infinite worke to drawe a great circle through euery place , therefore in seeking out the latitude wee make the meridian of the Globe to serue our turnes in this manner . Bring the place assigned to the meridian of the Globe , the degrees of the meridian intercepted betweene the equator & the place assigned , expresse the latitude of it : so I say , that the latitude of London is 51. degrees , 30. min. because London being brought vnto the meridian falleth vnderneath that degree and minute , and is so farre distant from the equator .

Is the latitude of London 51. degrees . 30. min ? I tooke that to be the eleuation of the pole at London .

So it is also , for the eleuation of the pole and latitude are all one in number : for this is vsually to bee seene vpon the Globe , that so far as any place is distant from the equator , so high is the pole from the horizon : Therefore when you desire to raise the pole of your globe vnto his due height , seeke out the latitude of the place assigned , according to that raise the pole aboue the horizon .

The greatest longitude is 360. degrees what may be the greatest latitude ?

Nothing can be further distant from any circle then the pole , which is but 90. degrees , so that the greatest latitude is no more .

Be the circles of latitude expressed on the globe ?

Yea as many circles as are parallell to the equator , may rightly be called circles of latitude , albeit some of them admit particular names .

Thereupon I thinke it commeth to passe that wee confound those phrases of speech to haue the same la●itude , and to be in the same parallell .

You say right : for a place to be in the same parallell with London , is nothing els but to be in the same latitude , & to be of equal distance with it from the equator .

You said before , that if I see any place what soeuer vpon the Globe , bringing it vnto the meridian I shall find the latitude thereof . Contrariwise therefore if I know the latitude of a place and seeke it out in the meridian ether toward the North or South pole , according as the situation of the place requireth , I shall be sure to finde out the place in the reuolution of the globe , if it be inscribed in the globe .

That also is true : but if both the longitude , & the latitude of a place be giuen , you cannot but find it out presently in this manner . Bring the degree of longitude vnto the meridian , set the Globe fast , and in the meridian seeking out the latitude you shall be sure to finde the place , or at leastwise where it should be , if it be not expressed in the globe . Thus much concerning the longitude and latitude .

Then must I trouble you with a question propounded before , which was this , what thing they haue common , and wherein they may differ that haue on● longitude : the which question you promised to satish me in , when you had discoursed of the latitude .

I will doe what I can , especially becuse I know it is most pleasant . You see by the Globe that of the seuerall inhabitants of the Earth dwelling ether on th● North or South side of the equator . Some may haue diuers longitudes , but the same latitude , as the German● the Muscouites , the Tartarians &c. differing in longitud% haue notwithstanding the same latitude with the Englis● men , These inhabitants generally considered are calle● Perieci : they haue their Zenith in the same parallell : the starres rise and set vnto them all vpon the same point of the compasse , and at the same houre , and haue the same height aboue the horizon . They haue the day and night increasing and decreasing alike vnto them all : & the seasons of the yeare changing after one manner and at one time , yet they that dwell to the Eastward of the other preuent the other dwelling to the westward in the time : as thus , they in Germanie may see the Sunne rise at sixe a clocke , so may we in England , yet their 6. a clocke preuenteth ours by an houre more or lesse , according as they are more or lesse vnto the Eastward , so that when the sunne riseth vnto them at sixe a clocke , it is then but fiue a clocke to vs that dwell fifteene degrees more vnto the Westwarde , and the Sunne will haue beene vp vnto them an houre , when hee beginneth but newly to rise vnto vs . And if wee happen to see the moone eclipsed at nine a clocke they that dwell forty fiue degrees from vs Eastward , shall fee her eclipsed at twelue a clocke , yet shall it be but sixe a clocke to them that dwel as many degrees from vs to the westward . Here you are to vnderstand this , that albeit the word Perieci according to the signification thereof , may bee generally applyed to all them that haue the same latitude , yet properly in Geographie , it is attributed vnto them that haue the same meridian , but dwel on the contrary sides thereof , and haue their difference of longitude 180. degrees and one of the poles of the world alwaies in the middest betweene their verticall pointes , such are they that dwell in Arabia , Felix on the one side , and in Hispania noua on the other side of the meridian .

These men differ one from another in this , that when it is high noone to the one , it is midnight to the other , and contrariwise : item when the Sunne setteth to the one , he riseth to the other , and contrariwise : item the South side of our meridian is their North side : all these communities and differences may be easily found out vppon the Globe ether by ayplying a thredde vnto the Globe in stead of another Horizon , or else by comparing the two globes together : The thredde must crosse the meridian so many degrees distant from the pole as the pole is distant from the horizon : as if the pole of the place assigned be 50. degrees , the thredde must crosse the meridian in the 50. degree on this side the pole . From the meridian , it must bee directed to the East point of the Horizon , and from thence crossing the nether side of the meridian in the 50. degree from the pole , it must be directed to the West side of the horizon vntil it come to the vpper side of the meridian againe . So shal you most easily perceaue all those communities , and differeces of the Perieci to be true , whereof I spake before : as that their dayes and nightes being seuerally compared are of an equall length : that the starres and the Sunne rise and set at the same houres &c.

If I were desirous to trye this by two seueral globes how shall I goe to worke ?

You may goe to worke diuers wayes , as yo● thinke best for your owne capacity : hauing raised th● poles of each globe according to one and the same eleuation : set the Globes so one by the other , that the Ea●point of the one may ioyne with the West point of th● other , or that the South pointes of their horizon ma● close and ioyne directlie all together , or which 〈◊〉 take to be better their Northren pointes , Set also the Zeniths in their places according as the eleuation of the pole doth direct you . Here must you conceaue this , that the greater arcke of the meridian is the noonesteed line and the lesser arcke from the pole downeward to the Horizon , and vnder it is the line of midnight : then seeke out the place of the Sunne for any day propounded , and bring it to the East side of the one globe , and ●o the West side of the other ( for of them that are pecu●atly called Perieci , the one seeth the sunne and starres ●etting , when the other seeth them rising ) afterwardes ●urne the Globes so about , the one from you , the o●her toward you in such sort ; that the place of the Sun ●rysing to the one may fall vnder the horizon of the o●her , for by that meanes you shall finde out the commu●ities and differences spoken of before .

I doe partly perceaue the matter I hope by practise 〈◊〉 vnderstand it the better . Proceede now I pray you in ●hat , which I requested at your handes .

As some of those which inhabit ether the North ●r South part of the earth may haue the same latitude , ●ut diuers longitudes : so agayne some may haue the ●●me longitude but diuers latitudes , as they here in Eng●●nd haue the same longitude , and are vnder the same meridian which the Spaniardes , and those that dwell to ●he West side of Africa , yet do they al differ in longitude : ●hese men haue the selfe same houres of the day and night , with the foure seasons of the yeare . But in many ●ther thinges they differ as they dwell nearer or further ●om the pole , or nearer or further from the equator . ●hey that dwell nearer the equator haue the Sunne al●aies higher aboue their Horizon than the other that well further of : also they which dwell nearer to the equator haue a longer day in Winter , but a shorter night , than they which dwel toward the pole : but in Somme● they which dwell toward the pole haue a longer day , & a shorter night than they that dwel toward the equator as for example , in Winter the Spaniardes day is longer than ours , namely whilest the Sunne is in the Southerne signes from the 13. of September to the 11. of March : but from the eleuenth of March to the 13 of September our day is alwaies longer than theirs . Againe from the 13. of September to the eleuenth of March their night is shorter than ours , but from the 11. of March to the 13. of September our night is shorter than theirs . Moreouer the Sunne neuer riseth vnto these men at one houre , ercept he bee in the equator : as for example to vs and the Spaniards . Whilest the Sunne is in the North signes he riseth more early and shineth longer to vs , than to them , but the Sunne being in the South signes , he riseth more early and shineth longer to them than to vs : Last of al● the Sunne neuer riseth or setteth to them and vs on the same point of the compasse . &c. all which thinges you may easily perceaue to be true by those rules which you haue heard before in the celestiall globe , if you do bu● find out by the terrestriall globe their , feuerall latitudes that dwell vnder the same meridian , and then raise the pole seuerally , working the conclusions aforesaid according as you haue bin taught .

Haue not these people any peculier name which dwell vnder one meridian , but differ in latitude ?

No , but there are another kinde of people hauing one longitude which haue a peculier name , and are called Anteci . They are such inhabitants of the earth as dwell vnder one meridian , and haue the same longitude & also the same latitude , but toward diuers poles : so that as farre the one dwelleth from the equator northward , the others haue the same distance from it Southward , and as high as the North pole is raised to the one , so high is the South Pole raised to the other . Such are they that dwell in the West side of Arabia twentie degrees Northward , and they that dwel in Madagascar in the same longitude twentie degrees to the South warde . These men haue the day and night of equall length , the Sunne rising and setting at the same houres on the same point of the compasse , but at diuers times and the seasons of the yeare are opposite : as when it is Sommer to them which dwell in A●abia , it is Winter to them in Madagascar . And con●rariwise , when the day is longest to them in Arabia , it ●s shortest to them in Madagascar . Furthermore , if the Sunne rise 25 degrees from the East to them in Arabia , hee riseth so many degrees from the East to them in Madagascar , but to the one in Sommer , to the other in winter if the day be fourteene houres long to them in A●abia it is so long also to them in Madagascar , but hee possesseth contrary signes . These thinges may seuerally be tried by the globe , or by comparing your 2. Globes ●ogether , and raising the North pole of the one , and he South pole of the other aboue the Horizon , so ●hall you see that that degree of the Eclipticke which ●ontinueth longest aboue the horizon to them that dwel Northward , continueth the shortest aboue their Ho●izon that dwel Southward . Moreouer also you may per●eaue this , that they which dwell Northward see the Sunne rising , and the Heauens moouing from the left and to the right , but they which are to the Southward see the Sunne arysing , and the heauens moouing fro● the right hand to the left . Besides these inhabitant before named there are other to be noted , which because they goe foot to foote right opposite one to the other , they are therefore called of the Grecians Ant●podes , and Antichthones , because they dwell in opposite places of the earth .

Mee thinketh it is impossible that you speake o● how can they that are vnder vs walke vpon the ea●● without falling . Can two men walke the one on the to of a wheele , the other on the nether side thereof with out tumbling downe ?

Your reason is not alike in the wheele and 〈◊〉 the earth . All they that dwell vpon the earth haue o● common centre in the Globe of th● earth , vnto whi●● they doe naturally tend in respect of their grauity , an● therefore where soeuer they stand they cannot fall from the earth , but bend naturally vnto the centre thereo● But they which stand vpon a wheele , or any such roun● thinge els haue not any one point in the wheele , or 〈◊〉 the round bodie , vnto the which they doe natural bend , and therefore whensoeuer he commeth vnto an● such place of the wheele , wherin his legs cannot keep th● weightines of his bodie perpendicular and imminent the centre of the Wheele , he must needes fall from th● wheele toward that centre , vnto which naturally he i● clineth , which is the centre of the earth . This is certai● both by reason and experience of our owne countrie●● that there are Antipodes , and therefore let the tru● preuaile with vs more than the opinions either of A●gustine or Lactantius , who haue stoutly denied t●● Antipodes , yea Lactantius ( as I remember ) held it heresie , and counted them accursed that sayd there were ●ntipodes .

How doe you define the Antipodes ?

They are certaine inhabitants of the earth right opposite one to another in the extremities of the diame●er of the Globe . Therefore the antipodes haue the same meridian , yet they differ in longitude one from the other 80 degrees . They haue the same horizon indeede , but ●iffering in reason , namely thus , that the Zenith or ver●icall point of the one is the nadir to the horizon of the other : and contrariwise , they haue also the same latitude , but bending toward contrarie poles .

How shall I readily by the globe finde out who ●e antipodes one to another ?

Bring any point or place assigned in the globe into the meridian , and note what latitude it hath , the ●oint or places hauing the selfe same latitude in the me●dian vnder the Horizon is the habitation of them , that ●●e antipodes to the former . Such are the inhabitants of Trinideda and Iaua maior , also the inhabitantes of old , and new Guinea , with infinit other places of the earth , whose antipodes are not yet discouereed . The Antipo●es haue all thinges contrary ( excepting those that dwel ●nder the equinoctiall ) if the heauen moue to the one ●●om the left hand to the right it moueth contrary waies into the other , if it be day to the one it is night to the ●ther , if the Sunne rise to the one he setteth to the other , 〈◊〉 the day or night increase to the one , it decreaseth to ●he other , if it be Sommer to the one , it is Winter to he other &c.

Why do you make exception of those that dwel ●nder the equator .

Because they being aswell Perieci , as antipodes , haue all the seasons of the yeare agreeable , and the same length of day & night , & the Sun rising & setting at the same houre , yet when he riseth to the one , he setteth to the other , & the houres of day and night are opposite , for when it is high noone to the one , it is midnights to the other : when it is 11. a clocke in the morning to the one , it is 11. a clocke at night to the other &c. Thus briefly concerning the communities & differences incident to sundry inhabitautes of the earth in regard of their difference and agreement ether in longitude or latitude . Let vs now speake of the meridian .

Me thinketh that it hath the same vse in diuiding the terrestriall , which it hath in diuiding the celestiall Globe into two seuerall partes , whereof the one is the East , the other the West : So that what people or countries soeuer are toward the East side from the meridian of any place may be called the Easterne people , and the other toward the setting of the Sunne may be called the Westerne people .

It is true that they may bee so called , but it is respectiuely , onely in regard of the place wherein you dwell , otherwise the true East and west parts of the terrestriall Globe are limited by the first meridian , or circle of longitude : what countries soeuer lie from that meridian Eastward an hundred and eightie degrees are called the East countries , and the other are called the West : yea the names of these places by meanes o● the first inuentors of Geographie are knowen so authenticall , that they are not chaunged as the other be , which only are spoken respectiuely , for albeit it so fall out ( a● many times it doth in trauailing farre ) that Hispaniola or Cuba , Brasill , and all that cost of America do lie from vs to the Eastwarde , yet doe wee commonly call them the West India . Agayne thongh that Sumatra , Borneo , the Moluccas , and diuers other places also thereaboutes bee from vs towardes the setting of the Sun , yet doe wee tearme and call them by the name of East India .

What are the partitions in the meridian ?

Those which are next vnto the Globe are the legrees , which haue no other vse than hath bin spoken of , ●ther in the celestial globe , or heretofore in the terrestri●ll , when I spake of finding the latitude of any place . But ●esides the degrees , there are other partitions seruing ●articularly vnto the terrestriall Globe . Those partitions which are next aboue the degrees expresse the quantitie ●f the longest day , so that when you shall heare the day 〈◊〉 be 13.15.24 . houres long , or 1.2.3 . moneths long &c. You may by these partitions finde out what people ●●ey are which haue the day of such a length . The vpper ●ost partitions are the climates .

What is that which you call a climate ?

It is nothing but a certaine space of the earth ●ntained betweene two imaginarie circles parallell ●●to the Equator : From the beginning of which space ●●to the ende the longest Daye admitteth the diffe●●nce of halfe an houre . As for example , the space of the trestriall globe betweene the 12. d. 45. min. of latitude ●here the longest day is 12. houres and three quarters , to the latitude of 20. d. 30. m. where the longest day is th oures ¼ is called a climate .

How many climates are there ?

The number of the climats are diuers . The ancient Cosmographers made but 7. beginning at the 12. d. 45. m. of latitude , and ending at the 50. d. 30. m. But they which succeded , added two other , and made 9. climates the which number is expressed vpon the meridian of the Globe . Others made 19. neglecting the ordinarie increase of halfe an houre in the longest day , and the place also where the ancient Cosmographers began their climates . Others made 23. others 47.

Why did the ancient Cosmographers begin 〈◊〉 the 12. degree 45. minutes of latitude , & end at the 50. d. 30. m.

They thought that that part of the earth betweene those two paralleles to bee habitable , & therefore had onely respect to them . But the latter Cosmographers knowing the earth to be more habitable , extended their climates ouer the whole surface thereof from the equator to the pole .

Me thinketh the Climates on the meridian , a● extended but toward one pole , are they not also to be considered toward the other pole .

Yes , in the selfe same distance from the equ●tor , but with contrarie names .

Hath each climate , a seuerall name ?

Yea , for they are denominated according to th● name of certaine notable places , which are in the midde● of them , as appeareth in the Table following : the C●●mates to the Southward are called by the same name the word anti ( which signifieth against ) being put there vnto : as for example , that which is the next beyond thre equator to the Southward is called anti dia Meroes , because it is as farre beyonde the Equator as that Clima●● which passeth through Meroe is on this side therof , &c.

Loe here is the Table of the ancient Cosmographers , wherein is expressed the number of the Climates with their limites , &c. as you see it set downe in the front thereof .

( g ) By this Table , as also by the Globe you may gather ( Philomathes ) the whole difference of time from the beginning of the first climate to the last to be 4. houres and an halfe : but the diuersitie of the height of the pole is 42. d. 49. m the breadth of them according to Ptolemee is 2359. miles ⅜ : but according to our account , that ascribe to euery degree of a great circle 60 miles , it amounteth vnto 2569. miles . The other thinges which may be sayd concerning the Climates , as that the beginning of the one climate is the end of the other , and that the climates next vnto the equator are greater than those which are further of &c. I leaue them to your owne contemplacion because you may gather them not onely out of this table , but also out of ehe globe it selfe . Yet this I must tell you that the Cosmographers haue diuided each climate into two partes , whereof each part is called a parallell . So that in this sence a parallell may be defined briefly to be the limite of halfe a Climate or otherwise , it is a portion of the terrestriall Globe contayned betweene two circles from the beginning whereof vnto the end the longest day admitteth the difference of a quarter of an houre . But of this matter let this suffice . Let vs now speake of the eclipticke .

With a good will , to what ende serueth that circle , mee thinketh it should be needles in this globe .

No , for hereby the terrestriall Globe is not only made fit to serue for all those propositions , which in the Celestiall globe are performed by knowing the place of the Sunne , but hereby also wee learne whether the Sun passeth by the Zenith of any people yea or no , & what people they be by whose Zenith he passeth not , and how many times hee passeth by them , and how far he is distant from their Zenith , with other conclusions more , whereof I will speake hereafter , as they come to my memory .

How shall I know whether the Sunne passeth by the Zenith of any place yea or no ?

You know , that the Eclipticke expresseth the high way of the Sunne : therefore as many as dwel within the obliquitie thereof betweene tropicke and tropicke must needes see the Sunne in their Zenith , the rest from ether tropick to each pole neuer haue the Sunne in their Zenith .

How often may the Sunne bee in the Zenith .

Not aboue twise to any nation , and to some but once . As many as haue their latitude equall to the greatest declination of the Sunne , they neuer see the Sun in their Zenith but once , such are all they that dwell iust vnder the tropickes . But as many as dwell within the two tropickes haue the Sunne perpendicular ouer their heads twise in the yeare , namely at that time , when the declination of the Sunne , and the latitude of the place are equall one to the other , for then the Sunne declining from the equator commeth to their Zennith , and passeth beyonde it to the tropicke , and descendinge from the tropicke hee crosseth their verticall points againe .

Then in seeking out the declination of the Sun , & the latitude of any place , I shall not only know whether the Sunne commeth to the Zenith of the said place , but also at what time he commeth thether .

You say well , for if the declination of the sunne , & the latitude of the place ether are , or may be equall , then wil the Sun passe by the Zenith , but if the latitude be greater than the declination of the Sunne may be , the Sunne neuer commeth to the Zenith . Againe when the Sunne possesseth any degree of the eclipticke hauing a declination equall vnto the latitude of the place assigned , that day will he crosse the verticall point of the said place .

If the Sun be not in the Zenith , how shall I know his distance from it by the Globe ?

Seeke out in the meridian the declination of the Sunne , and there make a marke , seke out also the latitude of the place assigned , there also make a marke , the degrees of the meridian intercepted betweene the two markes expresse the distance of the Sunne from the Zenith : So shall you finde the Sunne in Cancer to be distant from our Zenith here at London 28. degrees , but being in Capricorne , hee is distant from it 75. degrees . If you desire to know this by rule , the rule is : the place assigned being without the Tropickes , and the Sunne declining toward the pole eleuated , the declination of the Sunne taken from the latitude geueth his distance from the Zenith , as the Sunne declining northward twenty degrees , twelue minutes , is distant from our Zenith at London thirtie degrees , eighteene minutes . If the Sun decline from the pole eleuated , his declination added to the latitude , giueth his elongation from the Zenith . Item , if his place assigned bee within the two Tropicks , his declination toward the pole cleuated , compared with his latitude , and the lesser : being subducted from the greater , the remainder geueth his distance from the Zenith : Otherwise if the Sunne decline from the pole eleuated , the totall summe made of the declination , and the latitude affordeth the foresayd distance . If the place assigned be vnder the equator the declination of the Sun is equal to his distance from the Zenith according as you may perceaue by the Globe .

What other vse hath the eclipticke in the terrestriall Globe .

We are hereby certifyed of the seuerall seasons of the yeare in each seuerall place . Summer is caused by the accesse of the Sun vnto our Zenith : Winter , by his recesse from the same . Hereby therefore wee may gather what people haue two winters and two Summers : also who haue but one winter and one Summer : as many as dwell vnder the tropicks , and from thence toward the poles haue but one , because the Sunne falleth from their Zenith , & commeth toward them but once in a yeare , they which dwell within the tropicke haue two , because the Sunne crosseth their Zenith twise , and falleth twise also from it , once to the North , and agayne to the Southward . But betweene their Summers and Winters there is not an equall distance vnto any of them , those onely excepted which liue vnder the equator : who being iust in the middest of the Sunnes proper motion haue the seuerall seasons of their yeare distinguished equally in common sence . The other haue their seasons diuided vnequally , as they that dwell in the 20. d. 12. m. to the Northward haue from their first Summer to the second two moneths , but from the second to the first Summer following in the next yeare , they haue ten moneths , namely all that time , wherein the Sunne is going from Leo to Gemini : Furthermore this is generally to bee noted by the eclipticke , that they which dwell on seuerall sides of the equator haue neuer the same seasons falling out at the same time : for if it be Winter to them that dwell to the Northward of the line , it is Summer to them that dwell to the Southward , and contrariwise .

But they that dwell on one and the same side of the Equator haue their Summer and Winter at one time .

Not so , as many as are vnder or without the tropick toward the pole haue their Winter and Summer at one time , namely , when the Sunne entreth the hed of Cancer , but they that dwel from the equator to the tropicke haue their Winter and Summer onely then , when the Sunne is furthest from their Zenith , or els crosseth it . As they that doe dwell vnder the equator haue their Summers when the Sunne entreth into Aries and Libra , and then crosseth their Zenith But their Winters fall out when he commeth to the tropicall points , and is furthest distant from their Zenith : they that dwell 11. d. 30. m. to the Northward of the line , haue their Summers when the Sunne entreth into Taurus & Virgo , but their Winters are in his entrance into the tropickes , for that is generall to them that dwel within the tropickes , that howsoeuer their Summers alter their times , their Winters alwaies keepe their appointed dayes , which are those , wherein the Sunne entreth the tropicall pointes .

Shall wee now proeceede vnto the other circles of the Globe .

Not yet , there is one rhing remaining to be noted in the terrestriall globe concerning the shadowes , that are made vpon earth at noone wherevpon the inhabitantes reccaue diuers names , for some of them are called Ascij , others Amphiscij , others Heteroscij , & others Periscij . They are called Ascij who hauing the Sun in their vertical point do want the shadow of any thing that standeth vpright vpon the ground , for the Sun beame falling perpendicular vpon the earth doth illuminate the thing , which standeth vpright round about , so that the shadow thereof cannot be seene vntill the Sun declineth from the Zenith . Such are all they that dwel ether under or within the tropickes , as by experience you may proue vpon the terrestriall Globe by the sphericall gnomon .

In what manner I pray you ?

Rectify your globe perfectly in the open aire , where the Sunne doth shine , and set your sphericall gnomon ether vpon the degree of the eclipticke , which the Sun doth possesse , or vpon any place of the globe hauing a latitude answerable to the declination of that degree which the Sun doth possesse , then turn the globe toward the Sun , & the gnomon being right against him will cast no shadow , or otherwise bring the gnomon close to the meridian , and there set it fast vntill noone , for then the Sun will fall so iust vpon the point of the gnomon that it will yeeld no shadow .

What are they whom you call Amphiscij .

They are such as haue a shadow falling two seuerall wayes , one while to the Northward , and another while to the Southward . These dwell within the two tropickes , as you may perceaue by the terrestriall globe This you know standeth with reason , & common sence proueth it true , that the shadow bendeth to the opposite place from the Sunne , as if the Sunne be South ware the shadow runneth Northward , whereuppon this must needs follow , that for so much as they which dwel within the tropicks haue the Sunne sometimes to the northward of their Zenith ( as those in the Iland of S. Thomas ) & sometimes to the Southward , they must of necessity haue the shadow bending to the same places , as when the sun is in the north signes , the shadow of any thing standing vpright vpon the horizon must at noone run Southward , when he is in the south signes the shadow will bend northward . You may trie , if you wil abide the trial of it , by the spherical gnomon : rectify your globe , place the gnomon vpon the Iland of S. Thomas , or vpon any degree of the equator , or any other degree of the ecliptick , bring the guomō to the meridian when the sun approcheth neer vnto that degree , & mark which way the shadow falleth & after the sun is past that degree ether ascending or descending do the like againe , and you shall finde the shadow of the gnomon to fall toward a contrary place to that , toward which it fel before : the Hetroscij are those whose noonstid shadow falleth but one way onely : such are all they that dwel between the tropickes & the circle arctick or antarcticke : they that dwel betweene the tropick of cancer , & the circle arctick neuer see their noonstid shadow bending but to the northward because the sunne is alwaies south vnto them : contrariwise they which dwel to the south between the tropick of capricorn , & the circle , antarctick neuer see the noonstid shadow , but bending southward . You may trye this also by the globe , for the globe being rectified , & the gnomon applied to any place betweene the foresayd circles , and then brought vnto the meridian , & there set fast , you shall not at any time finde the Sunne to cast the shadow any way but one .

The last of these are the Periscii whose shadow runneth round about them to euery point of their Horizon in one and the same day , wherein they differ from the Amphiscii : For albeit their shadow being also vnto all partes of their Horizon , yet vpon one and the same day it tendeth but toward one halfe of the Horizon that is ether to the Northward or to the Southward . But the Periscii haue their shadowe going round about in one day . Such are they that dwell within or vnder the circles Arcticke or Antarcticke : The reason wherof is the long continuance of the Sunne aboue the horizon , who neuer setteth sometimes vntill he haue compassed the horizon round about . Now let vs come vnto the Horizon .

Is there nothing then to bee sayd of the two colures ?

No , for they haue no vse but this , that the degrees of longitude beginne at that place where theequinoctiall colure and the hed of Aries concurre in the Equator , so that it may in that respect bee counted the first meridian or first circle of Longitude .

Well then , let vs discourse of the horizon : what vse hath it in the terrestrial globe ?

It seuereth the antipodes one from another , how soeuer the globe is situated , and is common to them both . And whereas in the Celestiall Globe you were taught to finde the length of the artificiall day , with the time of the Sunnes rising and setting : vppon the terrestriall Globe you may readily see who they be that haue the day of such a length , and the Sunne rising and setting at such a time .

Howe is that to bee found out , I pray you rub my memorie but with one example .

The length of any day being propounded seek which degree of the eclipticke the Sunne possesseth , that present day , as for example , the day being 16. houres long , I suppose the Sunne to bee in the head of Cancer : then in the first meridian or circle of longitude which is distinguished into degrees count his declination , and at the end thereof make a pricke , which in this example selleth out to be in the very intersection of the tropicke , and the foresayd circle of longitude : thirdly diuide the length of the day into two equall partes , and conuert the houres into degrees of the Equator , which as this example requireth are 120. from the head of Aries toward your right hand count so many degrees in the equator : applye the end of that number close to the meridan , raise or let fal the pole of the Globe vntil the mark of the declination made in the circle of longitude , doe touch the Horizon : the cities or other places of the terrestriall globe which are then 90. degrees distant from the Horizon in the reuolution● of the globe are those , which haue the day of such a length : or otherwise , as many as haue their latitude correspondent to the eleuaon of the pole are those , whose day is so long as it was propounded to be .

I remember now very well , that you taught mee the like of this in that proposition of the celestiall globe , wherein I learned the length of the day being giuen to finde the height of the pole .

You say true : this is the onely difference , that here wee must haue an eie to the latitude , because the true place of any citie or towne vppon the terrestriall Globe is found rather by it than by the cleuation of the pole , albeit in number they be all one . By that which I taught you euen now , this also may be gathered , that if the Sunne being in any certayne signe assigned do rise an houre two or three ether sooner or later vnto others , than vnto mee , I say I may know what people they are as for example , if the sunne in Cancer rise vnto me at 4. a clocke , and to another at 3. or 2. a clocke in the morning or to another at 5. clocke : how farre do they differ in latitude from me ether to the northward or to the southwarde .

I pray you tell mee , how this may bee dispatched readily .

The chiefest consideration , which is to bee had in this matter is in what halfe of the Zodiacke the sunne is . If the sunne be in the northren signes , they which haue the longer day haue the pole higher eleuated , than they which haue a shorter , but the sun possessing the southern signes , they which haue the longest day haue a lesser latitude , if you remember this you cannot erre , so that the situation of the places be both toward one pole , or one of them vnder the equator .

Let me try if I my selfe can hammer out this question : the Sunne in Cancer riseth to me at London at 4. a clocke and 45. minutes in the morning how far do they dwell from me ether Northward or Southward , that is to say otherwise , how do they differ in latitude from me , to whom being in the same signe he riseth at 3. a clocke 45. minutes . First I conclude this , that they dwell to the Northward , because their day is longer , the Sunne possessing the Northren signes : then doe I raise the pole according as the fatitude of London doth require , and afterwardes bring the intersection of the first circle of ongitude , and the tropicke vnto the Horizon , setting fast the Globe that it sturre not , and notinge what degree of the Equator is vnder the meridian . 〈◊〉 doe consider moreouer how much their day is longer than ours : in this example it is longer by an houre conuert that time into degrees , and count from that degree of the Equator , which is vnder the me●idian to the Westwarde ( where as otherwise if their ●ay had begun after ours I should haue counted them 〈◊〉 the Eastwarde , that is , I should haue subducted them ) I turne that degree to the Meridian , and afterwardes raise the pole of the Globe vntill the foresaid ●●tersection of the tropicke and the circle of longitude , ●oe touch the Horizon , for then is the pole at his due eight , from whence if I subduct the latitude of Lon●on , I shall finde them to be the Northward of vs 5. derees .

You haue concluded well : and in like man●●r may you finde , how farre another is to the Southward , and which of the two poles is raysed aboue the round : but I leaue these thinges to your hammering , ●eing you can hammer them out so well . Let vs now ●ll in hand with those thinges which are inscribed in the ●orizon .

I had thought that you had sufficiently discoursed 〈◊〉 them in the celestiall globe .

Yet there is in regard of the terrestriall globe peculiar vse of the pointes of the compasse , or windes we commonly terme them . For by them may wee now how one coast or countrey beareth from another , which way it lieth , ether East , West , North or South , 〈◊〉 otherwise .

I imagined that thing to be knowen by the crooked lines described vpon the terrestriall Globe , which you called the Rhombes .

Not so , indeede they teach vs how to direct our course to any place : but they teach vs not how one place lyeth from another : and therefore the Latines in this case vse 2. seuerall words , whereof the one is Plaga a coast , the other directio , a direction . Whereof the one greatly and alwayes differeth from the other , except the two places assigned , whose coast or direction I seeke for lie vnder the same meridian , or neare the equator .

This seemeth to be a Paradox vnto me , must not direct my course vnto a place according as it lyeth from me ?

No , except the places lie North , and South : fo● a place may be East or West from you , as the Ilandes 〈◊〉 Maldinar , which lie Easte from London , yet if you d●●rect your course by the East , or West point of the compasse , you shall neuer come there .

What doe you call a coast ?

A coast is an Arke of the horizon contained betweene two verticall circles , whereof the one is alwaie● the meridian , and the other is the circle , which passe●●● from our Zenith through the place whose position from vs wee seeke for . This arcke and position of the place vsually is denominated according to the point of the compasse , vpon which the verticall circle lighteth in th● Horizon : as for example , if the verticall circle light vppon the Northeast point of the Horizon , I pronoun● the place to lie Northeast from me .

By what meanes shall I finde vpon the terrestria● globe , how any Citie doth lie from mee , and toward what coast .

First rectify your globe according as the latitude of your place doth require wherein you are , then fasten ●he quadrant of altitude to the Zenith , and bring the ●nowen place vnto the meridian , turne the quadrant of ●ltitude to the citie , or towne assigned , whose coasting ●om you , you desire to know , and marke vpon what soint of the compasse it lighteth in the Horizon : for ac●●ding thereunto you must pronounce the place to lie ●●om you , northeast or Southeast , or otherwise as it fal●th out .

Is there any other vse of these points of the com●●sse described vpon the Horizon of the globe .

Yea , for being at Sea the latitude being giuen , & ●e point of the compasse whereupon anie knowen land ●escried doth beare from you , you shall know how farre ●●u are from it : In this manner : rayse the pole of your ●●be according to the latitude , bring the quadrant of ●itude to the Zenith , and then turne it to the point of ●e compasse vpon which the land descried doth beare ●●m you , bring the said point of the land close vnto ●e quadrant , and see how manie degrees of the quadrant ●e contained betweene it , and your Zenith , those de●ees conuerted into miles or leagues ( as you were ●●ght before ) do yeld the distance . Here also note this ●at as you do in one so you may do in two or more hed ●●des if you descrie them being at sea . Thus much con●ning the vse of the greater circles of the terrestriall ●●be , it remaineth now to speake of the lesser : but for much as this matter whereof I haue now last of all in●ated hath great affinitie with the Rhombes , if it please 〈◊〉 I wil instruct you in them , and their vse before I fall in hand with the lesser circles .

I pray you doe so , and for so much as I cold neuer see any Author which did write of them , giue me leaue to require what I doubt of them and their vse ?

With a good will , I will doe what I can to ●a●tissy you .

What is the reason of this name , & why are they called Rhombes ?

We in our speach all them the points of the c●passe : but the name of Rhombe is receaued from th●● Spaniard the reason of the name is this , as I gather it . Among the geometricians as you know this kind of sigu●● ◊ is called a Rhombe : for so much therefore as the pointes of the compasse described vpon th● globes , but especially in the plaine sea card , do represent such a like forme , hereupon the Spaniard hath giuen this name vnto these lines , translating the name from the plaine Sea card to the Globe . And here I m●● craue leaue of you to vse this name , because I find it is teaching to be most conuenient , for there is such affinity in your English tong betweene the point of the compa● vsed in failing , and the point of the compasses vsed i● making of Circles , and other Geometrical descriptions that many times it breedeth an error : so that when soeuer I shall haue occasion to speake of any line of direction , I thinke it best to call it a Rhombe .

What vse haue they in the terrestriall globe ?

Their vse is manifold , as I will teach you by seueral propositions whereof this shal be the first , because is most generall , and chiefly respecteth these lines : any 〈◊〉 places , or points being assigned in the terrestrial globe , ●●find their rhombe , that is , vpon what point of the compasse I am to direct my course from the one vnto the other

Then as it should seeme by your words , these spiral & winding lines , which you call the rhombes , do imitate the winding nature of the Mariners compasse .

They doe so , for if you marke them , they make alwayes one & the same angle with the meridian of any place , & doe run on by little & little as the very nature of the compasse would direct you , if you should follow any one point thereof . In these rhombes you may note this , that the rhombe of north or south is alwaies some meridian or other , but the line of East , & west is parallell alwaies to the equator , whereby you may perceiue that to be true , which I told you before , that it is one thing for a place to lie or coast East & west from you , but it is another thing to direct your course East & west , for hee ●hat directeth his course according to the Rhombe of East & west neuer altereth his latitude , but keepeth alwayes in one distance from the equator , whereas hee which runneth continually vpon a greate circle must of necessity at length make an intersection with the equa●or . The other Rhombes trauerse the globe more or lesse according as they come nearer vnto , or are further off from the meridian . Let vs return to the proposition propounded .

Goe too then , two places being propounded , how shall I finde vppon what Rhombe I am to direct my ●ourse ?

Take your Quadrant of Altitude , or some ●ther Brasen ruler bowed according to the circumfe●ence of the Globe , lay it precisely vpon the two places ●ssigned , & marke where it cutteth any 2. circles of lati●●de on the globe , set one foot of your compasses in the on ●terfectiō , extend the other foot vnto the other interfection then come downe vnto the equator , and wheresoeuer you see these rhombes to meet together ( we cal it commonly the center of the slye or rose ) there set the foot of your compasse & extend the other compasse to the next circle of latitude to the equator , the Rhombe , vpon which the foot of your compasse doth light , will giue you you● direction .

I must needes trouble you with certaine questions , because this matter is very strange vnto me . Where I set the onefoot of my compasse in the centre of the flie , is it not materiall , which way I turne the other foot , ether vpward , or downward to the right hand , or to the left .

As for turning your compasses vpward to th● parallell next aboue , or downward to the parallell next beneath the equator , it is not greatly materiall , yet you must consider this , that if you turne your compasses vpward to the parallell the centre of the flie doth represe●● the nethermost place of the two , if you turne it dow●ward it representeth the vppermost . As for turning you compasse to the right or to the left hand you must take a● especial care of that : this rule you must obserue that you compasses must alwaies imitate the situation of your 〈◊〉 ler that if the vpper end of your ruler bende to the right hand or to the left , the vpper foot of your compasse● must doe the like , and this must be your continuall pro●●uiso , that the feet of your compasses touch the two parallelles exactly .

But I perceaue this , that albeit the compasse● light vpon the parallell , yet it will not alwayes light vpon a Rhombe .

That is true , if it light vpon a rhombe , then our direction from place to place precisely according 〈◊〉 the denomination of the Rhombe : As for example , if light ( being turned vpward ) vpon the the third Rhombe , ●om the meridian to the right hand , then must your diction be from the nethermost place vpward North●st , and by North. But from the vppermost place downward it is South west & by South .

Doth one and the same line geue me alwaies two rections .

Yea , according as you mooue from one place another , if you bend your course vnder the meridian ●om the North pole to the South , then is your directi●● southward , but from the South pole vpward it is forth , though the line of direction , that is , the Rhombe ●●e all one , so likewise descending , one and the same ●ombe is Southwest , which in ascending is North●●t .

If the foote of my compasse lighting vpon the pallell doth not exactly touch any Rhombe , what shall I 〈◊〉 then ?

Marke vnto which Rhombe the compasses come ●arest , let that giue the denomination to your directi●● , adding these wordes , and a litle more , or a quarter a point more , to the Eastward or to the Northward ●c . as falleth out .

Yet there ariseth another doubt : in searching the ●ombe betweene Trinidada , and Cape verde and lay●●g my ruler vpon them as you willed me , I perceaue the ●ersections of it , and the parallells to fall out so far a●●der , that my compasses cannot conueniently reach ●m . In this case , what shall I doe for to fynde the ●ombe ?

You must vnderstand , that so longe as you canne reach the intersections of the Parallelles , with your Compasses , that rule which I haue set downe is most ready for vse , otherwise let this serue your turne which doth insue . When the landes assigned bears near vnto the East & West , or vpon any other Rhombe , with a blacke leade applyed close vnto the meridian , from the places assigned describe two obscure parallells of a sufficient length , then with your compasses take the distance of the one land from the other , and guiding your compasses continually vpon the two parallells , see which 〈◊〉 the Rhombes contained betweene them will best agree or come nearest vnto the extention of their feete , th●● is the Rhombe of your direction . As for example , bei●●● desirous to know the Rhombe , which is to direct me from Cape D'al Cuer on the Coast of Maroco , to th● Southermost side of the Ilande of Coruo , from th● sayd places I describe parallelles , then taking the cances of those places , I guide the feete of my compases vppon the parallells , to the westward : but I find that they will not exactly agree with any of the Rhombes , but that which commeth nearest vnto the is the Rhombe of North West and by West , which must bee my direction , sauing that I must bear somewhat lesse than halfe a pointe vnto the West ward .

I must confesse this to bee an exact way , but feareth me with the hurt of my globe by making so m●ny paralles on it .

Then take this rule , whereby you shall ne●● hurt your globe . Suppose alwayes that one of the t●● places assigned , wheresoeuer they bee were the cen●● of the Flie described vppon the Equinoctiall line , then with our payre of Compasses take the distaunce of the two places as they lie on the Globe , and with another payre take the difference of their Latitude . Sette the one Compasse in the Centre of the Flye , and guide the other as you see occasion ether Eastward or Westward , Vppon the Equator from the said Centre vntill the two compasses doe coneurre , the Rhombe next vnto the Feete of the Compasses meeting togeather , is the direction which you seeke for . Thus much concerning the finding of the Rhombe , whereby you are to direct your course from place to place : Nowe learne another Proposition , which is ●his , the Rhombe being giuen , and the latitude to finde the place wherewith you fall , or wherein you are : ●he which proportion is performed in this maner . Seeke ●he rhombe vpon the globe , vppon which you directed your course , in it ( by the helpe of the meridian ) mark the atitude of the place from whence you come : and the la●tude also of the place with which you fell : take the di●ance of those two markes made in the Rhombe : then ●etting one foote of your compasses in the place from whence you came , turne the globe to & froetoward the neridian , vntil the other foote light vnder the meridian ●pon that degree of latitude with which you fell , that is ●e place wherein you are . As for example , put case I put ●ff from the Lizarde Southwest , and came vnto the ●ortie degree of latitude , in the Rhombe of South●est I note the latitude of the Lizarde , and the for●e degree also of Latitude , I take the distaunce of ●ose two markes , & setting the one foot of my com●asses in the Lizarde I turne the other foot to the fortie degree of latitude , whereby I perceaue I am wide o●● the Coast of Portingall vnto the Westward thirti● leagues .

I vnderstand you well : now tell me , how shall finde how many leagues I haue runne vppon that Rhombe ?

The second marke being made in the rhombe assigned as you were taught euen now , take with you compasse one degreeof the equator or of the meridian which according to our account is 20. leagues , and according to the Spanish account 17. ½ . measure there with the portionof the Rhombe contained betweene th●● two markes , so shall you finde the distance which you haue runne .

Before you taught mee to take the distance of th● two places assigned otherwise .

You say true , for then you sought not the d●●stance according to the course which you did runne , b●● according to the great circle imagined to be drawe betweene them : which kinde of measuring , if it should be obserued in your cour5e you should greatly decea● your selfe , as you may perceaue in this example , put ca●● you runne vnder the 60. parallell ether East or West , vntill you passed halfe thereof , taking your distance as you were taught at the first in a great circle the two place can be but 1200 leagues asunder : but your distance being taken according to your course as I taught you euer now amounteth vnto 1800. leagues . Therefore the be way is this , especially if your course made vppon a●● rhombe fall out to be great .

Let this be the fourth proposition concerning th● Rhombes , the Rhombe being giuen , and the distan●● knowen to finde the latitude , with which I fall , how shal 〈◊〉 doe this ?

In the Rhombe geuen , make a pricke according ●o the latitude of the place from whence you departed , from that pricke , counte the distance , which you haue ●unne , at the end thereof make a note bring that note ●o the meridian , the degree of the meridian expresseth ●he latitude , which you seeke for .

May I not also make this conclusion vpon the ●lobe , the rhombe being giuen , and the distance to finde ●ow far I am parted from my meridian .

Yes most readily : in the Rhombe giuen the la●●tude of the place being noted from whence you depar●ed , and the course also which you haue runne , bring ●he first marke vnto the meridian of the globe , fixe the ●obe that it may not stirre , then setting the one foote of our compasses in the second marke , take the shortest actention betweene it , and the meridian , the degrees of ●●e equator contained betweene the feete of your com●asses being conuerted into leagues , or miles wil giue you ●●e distance from the meridian , from whence you de●●rted .

Me thinketh this rule may leade me to the longi●●de .

So it will , for the Rhombe being geuen , and the ●●stance or els the latitude wherewith you fal , it is an easie ●atter to finde the longitude according to your globe : ●he markes being made in the rhombe as you were ●ught euen now , bring the marke which representeth ●●e place from whence you departed vnto the meridian , ●●d note in what place it cutteth the equator , bring also ●●e ●econd marke vnto the meridian , and note in what place the equator is cutte , the degrees of the Equator intercepted betweene those markes expresse the longitude betweene the two places .

There is yet another question to be answered . If I runne vpon any Rhombe may I not know how many leagues I haue runne hauing raised , or let the pole fall a degree ?

Yes that you may , and you may also finde this how farre you are distant from your meridian . Here note this , that in the performance of these conclusion● without any great errour you may reckon fiue or ten degrees of the meridian to be but as one , yet with this caueat , that if you count fiue degrees as one , euery degre● is twelue minutes or miles , if ten be taken for one , ther● is euery degree sixe minutes or miles , but it is best no● to exceede fiue or tenne . To answere therefore to th● first of these two questions : come to the Centre of th● Flye , which is in the equator , and counte the ten●● degrees of the meridian ether next aboue , or next be neath it to be but as one , and euery degree to be sin miles , or two Leagues : then if you measure fro●● the Centre of the Flie vnto the interiection , which any Rhombe maketh with the tenth circle of latitude you shall readily , and easily finde how many leagues 〈◊〉 miles you runne vppon any Rhombe , in raising or leting fall the pole a degree . Againe if from the said Intersections of the Rhombe , and the Parallell , you measure the distaunce vnto the Meridian , accounti●● as you did before each degree to be but sixe miles or leagues , you shall finde the distance from the maridian Is there any thing els which you desire concerning vse of the Rhombes .

Yea there is one thing , which hath trobled me most of all , & that is the trauersing vppon the globe : as thus , sometimes I runne South about 60. leagues , sometimes South Southwest as many leagues , then South and by East 100. leagues , then after that Southwest I know not how farre , but I finde my selfe to bee in four degrees of latitude South ward . How shall I obserue this course vpon the Globe ?

If you were perfect in that which I haue taught you , you would not make a doubt of this : but for so much as you are but yet a nouice herein , I will exempli●ie the matter vnto you , that by this one example you may gather what you haue to doe in the rest . The example shall be that which you haue propounded , supposing the place from whence wee set sayle to be the Southermost side of cape de verde , at that place where the tenth ●●eridian or circle of longitude toucheth the land . First Therefore in that meridian I count 60. leagues , which are degrees where I make a mark , whereby I find my selfe ●o be in 11. degrees of latitude , and vnder the same messdian : from thence you ranne according to your suppo●tion 60. leagues : from the marke which I made in the 〈◊〉 , circle of longitude I draw with a blacke leade an ob●ture parallell , which shall cut the Rhombe of South ●outh west , in that Rhombe I account 60. leagues ( which ●●e three degrees ) as I did before , and from thence pre●ntly toward the Cape I draw a parallell to the equator , ●●en taking with my compasses the 6o . leagues noted in ●e Rhombe of South Southwest , I set the one foote of ●y compasses in the marke made in the 10. circle of lon●tude , & stretch the other foote westward to the paral●● which was last drawen , and there make a marke . Here I finde my selfe to be almost in the eight degree of latitude , and from the place of my departure a little more than sixe score leagues , and from the meridian thirtie leagues Afterward you suppose your course to be South and by East an hundred leagues : continuing the last parallell vnto that Rhombe I count in it an hundred leagues : making a marke therein as I did before , and from it also drawing a parallell line toward the cape , then my compasse being extended to an hundred leagues I set the one foot in the marke made in the former parallell , and turne the other Eastwards according to my direction vntill I touch this last parallel which was described , there also I make a pricke : your last course was Southwest , you know not how farre , but you found your selfe to be in foure degrees of South latitude : I bring the meridian to the rhombe of Southwest , and there make a note vnder the fourth degree of latitude , and from thence I draw another parallell toward the Cape : then taking as much of the Rhombe of Southwest as was contained between these parallell lines , I set the one foote of my compasse in the marke which was last made , and extend the other foote to the last parallell , making a marke therein , which is the place of my being : and thereby I gather that I am fallen to the Southward of the line foure degrees , & am distant from cape verde 390. leagues , and from the meridian from whence I departed 140. Thus much concerning the vse of the rhombes described vpon the terrestrial globe . There remaine now Philoma a thes none of the circles of the Globe to be spoken of but the lesser circles onely , which are the limites of the siue Zones , whereof mention was made in the ende of the celestial Globe . The vse of the which circles in the terrestriall Globe is no more than this , to signify what inhabitants of the earth , doe dwell in euerie Zone , and who they bee which feele that distemperature , or temperature of heate and cold . Whereby you may perceaue how great●y they erred , which though the temperate Zones onely to be habitable , and the other by meanes of their extre●mitie of heate and cold to be vnhabited .

Concerning the qualities of the 5. Zones I would gladly be resolued in those questions , first whether each part of the burning Zone be of a like heate : and if they be not , which is the hottest . Secondly , whether the other Zones bee of a likely condition , or if they bee not , which exceedeth one another in their qualities .

I will willingly satisfy your desire , and that so much the rather because some of the argumentes vsed in deciding those questions may be expressed on the globe . You must here note what be the efficient causes effectes are counted 3. First the heat is caused by the perpendicu●tity . Secondly , the long abroad . Thirdly , the neerenes of the Sunne : The cold therefore must be effected by the obliquitie , by the ●mall abode and by the elongation of ●he sunne . This also standeth with reason , that where here are most causes there must be the greatest heate or old : Let vs therefore examin them in the Zones , begin●ing first with the burning Zone . For so much as the bur●ing Zone is contained within the Tropickes , so many ●herefore as inhabit that Zone must of necessity haue the ●unne perpendicular vnto them , so that in that respect , they are all equall , though in the other causes they disare●e . The abode of the Sunne is lesser vnder the Equa●●r than vnder the tropickes , for the day is but of 12. houres vnder the equator but vnder the tropickes it 〈◊〉 13. ½ . And somewhat more . Moreouer the Sunne comming toward the Equator , and depatting from it , declineth almost in one moneth so much as he doth in moneths , neere to the tropickes : Last of all , the Sunne comming toward the equator , keepeth on his course 〈◊〉 rectly , not comming that way agayne till halfe a yea● be past , but comming toward the tropickes as he h●teth the earth mightily by his slow ascending , so doth encrease the heart by his slow descending , and his so dait returne . The heate therefore neare vnto the tropickes greater than vnder the equator .

Then which is the hotter of the two tropickes

Then tropicke of Capricorne , for it hath not o●ly the Sunne perpndicular and continuing a long ti●● aboue the horizon , as the other tropicke hath . But 〈◊〉 hereafter you your selfe will confesse according as y●● goe one forwarde in these studies . Hereupon the cond question may bee resolued , that of the two ●●zones the antarcticke is the colder , and in the tem●rate zones the winter is colder to the Southward th● to the Northward : for albeit hee bee oblique to th● both , and continue a like time aboue ether of their 〈◊〉 rizons : yet for so much as in Winter hee is neer●● them that dwell in the Northren zones , than to th●● that dwell in the Southern zones : they therefore h●● the warmer Winter , and consequently the colder Su●mer . Hauing now answered your questions , it maineth Philomathes to aduise you to acquaint y●● selfe throughly with your globe , not onely that you 〈◊〉 be readie to perform those conclusions , which you 〈◊〉 learned , but also that you may know , and distinguish the seuerall partes of the world with the chiefe Kingdomes , Cities , Capes , neckes of land , Seas , Streightes , and Riuers throughout the whole world , for it wil be vnto you a great disgrace , especially in this our trauelling age , not ●o be cunning in these thinges : which cunning you may ●asily attaine vnto , if you doe but furnish your studie with the Globes , and now and then as your leasure ser●eth , looke vpon them .

I will doe mine indeuor , especially , because as I ●ue a good hope of the profite that may ensue , so I find ●●e pleasuce to be exceeding great . And to you sit for the ●ines which you haue taken in furthwering my study , I al thinke my selfe greatly beholding so longe as I liue .

That is my desire Philomathes , to make ●●ng students to be beholding vnto me , & if so be here●er you shall stand in need of my helpe , ether through getfulnes or hardnes of that , which I haue taught , you , if you will repaire to my poore lodging in Abchurch lane , you shall find me ready to doe you what pleasure I can . And so farewell .

FINIS .