THE NAVIGATORS SVPPLY.

Conteining many things of principall importance belonging to Nauigation, with the de­scription and vse of diuerse Instruments framed chiefly for that purpose; but seruing also for sun­dry other of Cosmography in generall: the particular Instruments are spe­cified on the next Page.

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They that goe downe to the Sea in Ships, and employ their labour in the great waters, They see the workes of the Lord, and his wonders in the deepe. Psal. 107.

Imprinted at London by G. Bishop, R. Newbery, and R. Barker. 1597.

The Contents.
  • 1. Of the Compasse in generall.
  • 2. Of the Compasse of Variation.
  • 3. Of the Trauailors Iewell.
  • 4. Of the Pantometer.
  • 5. Of the Hemisphere.
  • 6. Of the Trauerse-boorde.
  • 7. A friendly Aduertisement to the Nauigators of England.

To the Right Honorable, for all partes of true Christian Nobilitie worthily renowmed, and my singular good Lord, Rob. Earle of Essex, and Ewe, Vicount Here­ford and Bourgcher, Lord Ferrers of Chartley, Bourgcher and Louayn, Master of her Matesties Ordinance & Horse, Knight of the Hono­rable Order of the Garter, & of her Highnesse priuie Councell: Long life with encrease of Honor.

PLutarch in a Treatise, wherein he sheweth how a man may winne profite by the malice of his ene­mies, doeth manifest his drift and purpose with this conuenient simili­tude: That men of olde, in their encounters with saluage and wilde beasts, thought to haue made a great hand, if they coulde but saue and defende themselues from their iniuries and violence: But the succeeding ages proceeded further, conuerting the flesh of them vnto foode, their haire to the vse of garments, and their very gall, and other partes of them, to sundry most wholesome medicines: Yea the whole outward proportion of their fearefull [Page] shape, I meane their skinnes, which before had threat­ned man nothing but death, he afterward addressed to be conuenient Armour to saue him from harmes, and defend him from destruction. So that the life of man which to the foregoing Ages seemed to be miserable by hauing wilde beastes, to their Posteritie following should haue appeared in part miserable, if they had wanted wilde beastes. And Plutarch alleageth Xeno­phon to haue beene of this iudgement; That although some man can content him to escape the iniuries of his enemies; yet is it the part of the wise and valiant min­ded to make profite of their malice, by vsing such in­dustrie in attending his owne wayes, and marking his aduersaries, that the whole course of his life shoulde seeme nothing so happy and commendable, were it so in deede that vtterly he had none enemies at all.

Much in like sort, (my very honorable good Lord) fareth it with our Nauigators; who at the first aduen­tured to forsake the maine land, betaking themselues to the wide Ocean Sea, vpon the credit and fidelitie which they reposed on the Sailing Compasse; constant­ly beleeuing that it had euery where shewed the true North and South, and semblably all the other windes. But dangerous and dolefull experience within short time made it plaine and manifest, that where they re­posed greatest trust, there was some treacherie: For the vpholder of their life and safetie, did sometimes mis­leade [Page] them into destruction, and caried them in the proceeding of their course farre distant (they knew not whither) from that he in the beginning pretended. This vncertaintie therefore being so dangerous an ene­mie of their new practised arte, with might and maine they encountered: And hauing at length found out some tolerable meanes to auoide it, they thought them selues to haue done ynough, and rested therewith con­tented. But in this pregnant Age wherein we liue, the expert and skilfull Nauigators haue proceeded yet further, and made of that (as it were) venimous qua­litie of misleading an Antidote against it selfe; yea they vse it in steade of an armour and defence against error and perils. So that though in the rude beginnings of former times, men were drawen by it into many per­plexities: yet in the setled experience of these our dayes they reioyce therein (being vsed and ordered accor­dingly) as in a thing greatly concerning their good and welfare. But this is a principall secret, onely kno­wen vnto those that are of greatest skill among them.

A memorable example hereof fell out Anno 1586. when Sir Frances Drake, a Gentleman of famous me­morie, in his VVest Indian victorious voyage, depar­ting from the harbour of Cartagena, arriued some small time after at the VVestermost point of Cuba, called Cape S. Antony, and hauing stayed there some fewe dayes, put to Sea for Virginia, for the re­liefe [Page] of our Countreymen that were there in great dan­ger and distresse: Hauing continued at the Sea six­teene dayes tossed with variable windes, they came at last within sight of land: but by no meanes could they discerne, or giue any probable ghesse what lande it should be. So it was, that one of Southhampton, being an expert and skilfull Nauigator (though of other conditions not so good, but better might haue bin wi­shed) for his frowardnesse, hauing receaued disgrace before, was notwithstanding vpon this necessitie cal­led vnto conference: where, after Sir Francis had be­stowed on him some part of his eloquent perswasions and faire promises, at length he vndertaketh to doe his best. And hauing made his obseruations according vn­to Arte, he pronounced in laughing and disdainefull maner (because his aduise was not taken in the setting of their course) that looke what land they had bin at sixteene dayes before, the very same precisely was the land that now they were at againe. VVhich assertion of his being reiected, as a thing impossible, by all those of skill in the company, and especially by Sir Francis himselfe not without reprochfull wordes; he still per­seuered therein, and assured them, that vpon his life they should finde it so: like as in the ende they did.

This coulde he neuer haue done without his know­ledge of the Variation of the Compasse; as the partie himselfe more then once with great earnestnesse hath [Page] protested vnto me in conference that I haue had with him concerning those matters. Yea besides the particu­lar knowledge of Places, the expert Nauigator stan­deth in great hope hereby to attaine vnto good helpes for the finding of Longitudes, and according vnto the Poet, ‘Non fumum ex fulgore, sed ex fumo dare lucem Cogitat: vt speciosa dehinc miracula promat.’

But this is a matter somewhat daintie among the chiefest of them: As for the rest, in all their conclusi­ons about the Variation, they may as yet (for all their faire shewes) be well likened vnto Chapmen, that are merchandizing for the skinne of a wilde beast, before the beast be taken.

The great necessitie hereof, and the singular loue that for many yeres I haue borne to that laudable fa­cultie, and to the industrious practisers thereof, hath at length perswaded me, not onely to contriue certaine Instruments fitted for sundry their purposes, and espe­cially for taking the Variation of the Compasse; but also to set foorth diuers other principall vses of them, together with the Descriptions of the Instruments themselues. All which I doe the rather Dedicate to your Honorable Lordship, both in regard of my pri­uate duetie, as also of an earnest desire to doe them the more good: who by that meanes (I am right sure) will the sooner be induced to peruse these short Treatises [Page] with the more willingnesse, and to consider of them with the lesse preiudice. So that my good hope is, fewe of them will be founde, in whom reason shall haue so weake ankerhold, as to thinke that a man of my pro­fession would seeme to intrude himselfe into the my­steries of their Arte; and especially belonging to your Lordship, durst offer to the viewe of the world vnder your Lordships name, any thing that he knewe not as­suredly to stand grounded vpon infallible certainetie of trueth.

Touching experience in these matters, of my selfe I haue none: For, (besides the diuersitie of my calling,) by naturall constitution of body, euen when I was yong and strongest, I altogether abhorred the Sea: howbeit, that antipathie of my body against (as the Italian ter­med it) so barbarous an Element, could neuer hinder the sympathie of my minde, and heartie affection tow­ards so worthie an Arte as Nauigation is; tied, I con­fesse, to that Element, if you respect the outward toile of the hand, but clearely freed therefrom, if you regard the apprehension of the mind: And in the minde onely, pure and true Arte, refined from the drosse of sensible or experimentall knowledge, is to be found. VVhich when I perceaued must needes so be, and that the great skill of our Seamen was not performed either by rash­nesse of chaunce, or strangenesse of miracle, but ac­cording to certaine vniuersall precepts or documents, [Page] deriued from the fountaines Mathematicall, being the substance of that Arte; so farre as the studies of my profession, and other my necessary affaires would per­mit, I endeuoured by little and little to vnderstande somewhat thereof: And that which I thus learned by speculation, I haue conferred off with some of the skilfullest Nauigators of our Land; with such as haue bin principall Actors in our furthest Northeast and Northwest discoueries; with such as haue bin in the South Sea, and at the Cape of Bona Speransa; and also with Naturalists of the East Indies. I haue ente­red into the consideration of the making of all their Instruments, together with the maner of their obser­uation by them both on Land and Sea: And as I haue by conferring with them from time to time learned what they most desired and stoode in greatest neede off so framed I mine instruments accordingly; answe­rable for all purpose of practise vnto theirs, but for commodiousnes thereof, somewhat better, I doubt not, (if sincere triall be made) and for certaine points of chiefe importance, perfourming that, which all theirs hitherto in any common vse neuer could doe. VVhere­in I haue already the allowance of some among them, whom I haue esteemed to be of the greatest skill and practise: And very willing am I to stand to the iudge­ment of the rest of like skill.

A true prouerbe it is; he which buildeth in the [Page] market-place, shall be sure of many controwlers of his worke. And that made me stand long in suspence, whether I should suppresse, or set foorth these conclu­sions of mine. Of their trueth, their commodious vse, yea and of the good acceptance of them among those of the better sort, I nothing doubted: But how strange it would seeme vnto some, that a man of my calling should deale in this Argument; that in deede did a lit­tle trouble me; easily coniecturing that many woulde thinke I haue forgotten my selfe, and walked herein beyond the bounds of my profession.

As for my profession, I thanke God, I haue exerci­sed the preaching of the Gospell nowe these twentie yeeres, in a Countrey where both Preachers and Go­spell haue some store of aduersaries: And I trust that my trauaile therein hath not bin such, that I greatly neede be ashamed thereof, or can iustly be chalenged, that I euer, as a man carelesse, neglected my calling. But recording with my selfe, that the dispersion of Nations came by the confusion of Languages: vpon which occasion, they spread themselues ouer the face of the whole earth; yea and planted themselues (a thing most strange vnto our Capacitie) in many ex­ceeding remote Ilands in the Ocean Sea: and conside­ring that the knowledge of languages groweth by en­tercourse and mutuall accesse; I perceaued that God nowe towardes the ende of the worlde, had ordeyned [Page] the sayling Compasse to be the notable meanes and Instrument of this entercourse; euen thereby to ioyne dispersed Nations, not onely into the Ciuill or rather Cosmopoliticall vnion of humane societie; but also (as Christian hope bindeth vs to thinke) through the knowledge and faith of the Gospel, into the spirituall and mysticall fellowship of that Heauenly Ierusalem: And so by meanes hereof to make mutuall amitie be­tweene people and people, though neuer so farre sepa­rated; and to giue this as a leading guide, to carrie the sound of the Gospell, as the band of loue, into all di­spersed Islands and out-Angles of the world. (For God (as the Apostle speaketh) hath made all mankind of one blood, to dwell vpon all the face of the Earth; and hath assigned the times which were ordeined before, and the boundes of their habitation, that they might seeke the Lord:) weighing (I say) this with my selfe, that God of his infinite wisedome and vnspeakeable loue toward mankind, had appointed this simple In­strument in shewe, to performe matters of such ad­mirable importance; that the wisedome of man wan­ting this one, with all the other Instruments of the world coulde not possibly haue done, I did therefore iudge it a matter not vnfit for a Preacher of the Go­spel, to set to his helping hand for aduaūcing a Faculty that so much tendeth to Gods glorie in the spreading of the Gospell. Nowe if this be not against Diuinitie, [Page] doubtlesse to preserue men from danger, and to direct the wanderer, cannot be against humanitie: Against the duetie of a Subiect it cannot be, to further that knowledge, by which her Maiesties power is augmen­ted, and her Royall name continually caried to all the quarters of the world. Finally against my duetie in ge­nerall towards my natiue Countrey it is not, to ende­uour what in me lieth, the good encreasing of that skill, whereon dependeth a great part of the prosperi­tie of this Realme.

And if this were a worke that in the highest degree performed all these, my part it were, (though I were a mere stranger,) of very right to present and appro­priate it, rather vnto your Lordship, then to any o­ther: Because your sincere loue towardes our Coun­trey, your duetifull and loyall affection towardes her gracious Maiestie, your humanitie so full of honour towards all men, proceeding from the vnfained feare of God, (which continually encreasing, encreaseth like­wise the rest,) doeth in such plentifull measure a­abounde, that I dare appeale vnto him who is the su­preme Iudge of consciences, & the tryer of all trueths, I doe herein affirme such a trueth without flatterie, as your enemies themselues cannot denie, but being ouer­pestered with enuie.

Vouchsafe therefore mine Honourable good Lord, of your noble disposition, fauourably to accept this [Page] small Treatise, (such as it is) which of duetie and good will is offered vnto you; protecting it so farre foorth, and no further, then the trueth of demonstra­tion and commodiousnesse of the conclusions shall de­serue. And thus beseeching the Almightie to blesse your Lordship, to encrease his good giftes in you, and to prosper all your Honourable affaires: I commend your Lordship, and al yours in my humble and heartie prayers, vnto the protection of him, from whom all good giftes doe descend, and with whom there is no variablenesse, nor any sha­dowe of change; but yesterday, to day, and is the same for euer.

Your Honorable Lord­ships in all duetie to be commanded, VVilliam Barlowe.

Lectori S.

PRaesulis eximij gnatus, multis (que) verendis
Patribus affinis, pastor & ipse pius,
Hunc foetum peperit: quem si tu (candide lector)
Excipias gremio suauis, amans (que) tuo;
Dentibus haud metuet Criticorum rodier atris:
Quos tamen, vt tener est, non metuisse nequit.
Perlege, pertenta, bis ter (que) quater (que) licebit:
Quô mage creber eris, crescet & ille magis.
At simul hoc vsu matura adoleuerit aetas,
Iam benè tutus erit viribus ipse suis.

To the Reader.

THis booke was written by a Bishops sonne,
And by affinitie to many Bishops kinne:
Himselfe a godly Pastour, prayse hath wonne,
In being diligent to conquer sinne.
If to thee (Reader) it may welcome bee,
The Critickes censure it will feare the lesse:
For being young from feare it is not free,
Which otherwise more courage might professe.
Reade, way, and try, but reade, and often trye
The rules of skill whereto it doth direct:
Triall may bring as much authoritie,
As newnesse hinder it of due respect.
But yet when time shall to it ripenesse giue,
It will haue credite of it selfe to liue.

Uotum Authoris.

SVmme Deus, Coeli terrae (que) maris (que) tremende
Conditor, at (que) idem rector tersancte, patenti
Aure fauens, facilis mea percipe vota precantis.
Ex vno veluti gens est humana Noacho
Orta, vná (que) habitans linguâ celebrauit eâdem
Te solum verum (que) Deum, Babylonica turris
Quum nondum aethereas caput attollebat in auras;
Sic iterum, ô vtinam, miseros miseratus in vnum
Mortales redigas, laceros vt corporis artus,
Quosfuror ille tuus dispersit ad vltima mundi,
Coniuncti (que) ineant sancta vt commercia rursus,
Veliuolis iungas ratibus ceu pontibus ipsos
Mobilibus quamuis disiunctos aequore vasto:
Foelici celeres vento impellente carinas:
Miranda (que) agiles moderanti Pyxide clauos:
Inprimis tuus ille tuus, qui cuncta gubernat,
Spiritus, aspiret placidus: Sic, lampade diâ,
Verbo Euangelij, toto noscaris in orbe.

F. N.

O God, whose power heauen, earth & sea declare,
Which being by thy word, thy word obey:
And in their workes, which Natures called are,
Worke but that will of thine which all doth sway,
Hearken, O hearken for thy Christ his sake,
Vnto the prayer which in heart I make.
[Page]Looke downe with mercie from thy mercie-seate,
Vpon man-kinde dispersed here and there,
From Noahs familie, which grewe so greate:
For at the first all but one people were,
Which but one law, which but one language knew,
One God alone to serue, God onely true.
As yet mans heart did seeke no name of prayse
In stately towers, which threaten might the skie:
When pride began great Babel for to rayse,
Speach was confounded with varietie.
Since then deuided tongues deuided heartes,
By sea and land into a thousand partes.
Yet since thy Spirit of true vnitie,
In clouen tongues did on Apostles sitte:
That so thy cursing might a blessing be,
And clouen tongues deuided people knitte,
Let that thy Spirit breathe in euery place,
That all may know the Gospel of thy grace.
And since the Sea doth some so farre deuide,
That they may seeme an other world to bee:
Teach vs our Ships like horses so to ride,
That we may meete in one, and all in thee:
And as the Needle doth the North repect,
So all in Christ may onely thee affect.

A briefe discourse of the Sayling Compasse in generall.

THE merueilous and diuine In­strument, called the Sayling Com­passe, (being one of the greatest wonders that this World hath) is a Circle diuided commonly into 32. partes, tearmed by our Seamen Windes, Rumbes, or Points of Compasse: which Cir­cle by the touch of the Loadestone sheweth the afore­said diuisions in all Horisons betweene the Poles, accor­ding to one and the selfe same perpetuall position in respect of the true points of North and South in euery Horison. This Circle is commonly described vpon Pastbord of 5. 6. 7. or 8. inches diameter: And hath sometimes subdiuisions, with the relation to the 32. and sometimes hath the ordinarie diuision of Circles, namely 360. In the Center of this Circle is faste­ned a little Diamond as it were, or a Capitall, as some call it, of Latten, being cinquebored, the point thereof appearing a conuenient space aboue the Circle, and the hollowed part downeward, to be placed vpon the pinne. In the bottome of this Circle are glewed two wyars about ¼ longer then the Diameter, bended proportionally the one toward the other in the forme [Page] of a loope, so that the endes ioyne close and euen toge­ther in the circumference: and the Circle in this ma­ner finished, is named the Flie of the Compasse. The boxe wherein this Flie is placed, must bee couered with cleare glasse, made close round about with waxe mingled with Rosen, or some other kind of Simmond. The bottome of this boxe is to be taken off and on, as occasion shall serue: in the Center whereof standeth the pinne of Latten of a reasonable height, for the Flie to haue sufficient scope. This boxe is to be hanged in two Circles of Latten within an other greater Boxe, that the Flie, which way soeuer the Ship swayeth, may alwayes stand vpon his pinne parallele to the Horizon: to which end they fasten a piece of Lead to the bot­tome of the lesser boxe.

As for the touching of the wyars of the Flie with the Loade-stone, I would wish it to be perfourmed af­ter this sort. First of all, haue a great care of the good­nesse, the quantitie and the forme of the Stone: for if he be neuer so good, and very small therewith, he can giue but small force vnto the Compasse: And againe, though he be neuer so great, yet if he be of base quali­tie, his Touche can be but faint. An ouall forme, or somewhat longer, reteining a like proportion from the middle to each end, is very good. Alwayes prouided, that the length of the Stone lie according to his owne line of North and South: for a stone of this forme gi­ueth foorth his vertue in the Touche a great deale more forcibly then it can, if by reason of the euil shape thereof, his force in himselfe be confusedly dispersed, and not ioyntly directed to his due points. The wyers before they bee touched, ought to bee polished and made very cleane, and fitted vnto the Flie, and then [Page] touched after this maner. With the North end of the Stone, presse each wyer, beginning at the middle, and so along vnto that ende, that you would haue turne Southerly: And with the South end of the Stone doe the like from the middle of eache wyer, vnto the ende that you would haue turne Northerly. Then glewe them in such sort, that the Flie may stand equally vp­on his pinne, hauing both the North and South endes of the wyers vncouered, that their Touche may be re­freshed, as occasion shall require.

After all this is accomplished, that the Instrument thus furnished may truely performe his office, there must iust regard be had of the Variation, as also of the diuerse Set of the Compasse: And likewise that it be not placed neare any Loade-stone, yron, or steele. By the Variation is vnderstood the difference in the Hori­zon betweene the true and the magneticall Meridian. By the Set, is meant the setting or placing of the wyers in the bottome of the Flie, which sometimes you shal finde standing right vnder the Flower de luce, repre­senting the North point, sometimes ½, ⅓ &c. toward the East of the Flower de luce.

The Compasse being artificially made and fitted as he ought to be, with al his iust regards: we must cō ­ceaue euery line drawen from the Center vnto each diuision, to represent alwayes the semidiameter of an Azimuth, bearing the same name with the diuision of the instrument. The line of North & South is eue­ry where the intersection of the Meridian with the Ho­rizon: and the line that crosseth him at right angles, is euery where the intersectiō of the East & West Azi­muth with the Horizon. The like is to be vnderstood of euery one of the other, according to their natures: [Page] so that euery point of the Cōpas, when the line there­of is by imagination produced in the Horizon vnto the Heauens, is vnderstood to be the base of a Quadrant of some one Azimuth or other: and the line falling from the Zenith, to the Center of the Compas, is as the Perpendicular cōmon to them all. Wherefore which way soeuer in any situation a ship doth saile vpon any point of the Compas, it must needes be that shee say­leth within the plaine of one Azimuth or other, in as much as euery point is the Base of an Azimuth: and so performeth alwayes her course vpon the Conuexe of the Sea, in a portion or portions of one great Circle or other, because all Azimuthes are great Circles. Albeit therfore a voyage were to be made from any place in any Latitude, more or lesse (it skilleth not) vnto any o­ther of the same Latitude, and that according to the common trade (which should not be, if great Circle­sayling were knowen & brought to perfectiō) keeping as neere as may be vnder one Parallele, from the be­ginning to the ende of the voyage: yet because in all this Ships motion, the Compas is considered as equi­distant alwayes vnto the Horizon, it must needes fol­lowe, that all the points of the Compasse (his Variation remembred) continue their mutuall respect to those of euery Horizon: the line of South and North, being still the Intersection of the Meridian with the Horizon: the line of East and West being still the Intersecti­on of the East and West Azimuth with the Horizon, crossing one an other alwayes at right angles: so that the situation of the shippe continually altering, doeth neuer alter the properties of the Compas: whose na­ture is to deriue those his diuisions vnto euery newe Horizon that hee approcheth vnto; all the lines of his [Page] points euer remaining Semidiameters of Azimuthes and Bases of their quadrants: the line falling from the Zenith through his Center, being still the perpendi­cular common to them all. Whereby it is manifest, that in as much as the direction of the sayling Com­passe is alwayes some one Semidiameter of an Azi­muth; and the shippe (being the body mooued) euer stemmeth in the plaine of the selfe same Azimuth: also the winde, being the efficient that moueth, of his mu­table propertie driueth foreright diametrally vpon the plaine of the Horizon: which cannot be but accor­ding to the intersection of the foresaid Azimuth: it is therefore impossible, if the shippe be moued, that is, transferred or changed from place to place, that the line or tracing of her course comprehended betweene those places, should be any other, but onely such as is composed of great Circular portions: of which, the length of the shippe it selfe is alwayes a segment. And so describeth she by that meanes in her course before mentioned, not a Parallele properly so called (as com­mon opinion doth wrongfully imagine) consisting of one continual lesser Circular line; or otherwise, a Spi­rall line truely so named, consisting of a continuall vniforme winding, answerable to the nature of the said line; but a course (quibusdam diuerticulis, as learned Nonius termeth it) with certaine turnings in and out, consisting of small segments of great Circles; keeping alwayes as neere the precise parallele, or Spirall line, as arte can ayde them. Wherefore it is confessed, that those seuerall courses haue some shew or resemblance of the two sorts of lines aforesaide: but by no meanes are they the very lines themselues in deede.

Who was the first inuenter of this Instrument mi­raculous, [Page] and endued, as it were with life, can hardly▪ be found. The lame tale of one Flauius at Amelphis, in the kingdome of Naples, for to haue deuised it, is of ve­ry slender probabilitie. Pandulphus Collenutius writing the Neapolitane historie telleth vs, that they of Amel­phis say, it is a common opinion there, that it was first found out among them. But Polidore Virgil, who sear­ched most diligently for the Inuentors of things, could neuer heare of this opinion (yet himselfe being an Ita­lian) and as he confesseth in the later ende of his third booke de inuentoribus rerum, could neuer vnderstand any thing concerning the first inuention of this instru­ment. Most men suppose the finding thereof to bee very newe, and hardly to be proued that it hath beene in any vse in these partes of the Worlde full 200. yeeres agone. But whether this propertie of the Load­stone was first knowen in the West or East partes of the world, it is very doubtfull. The East Indian histo­ries are pestered with such monstrous reports and Le­gendarie tales, that as yet they are but of very small credite. Their fabulous genealogies and Frierly dis­courses, doe breede a lingering expectation of some halting Poste, that making not so much haste as good speede, may with more sinceritie enforme vs of the state of those Countreis and matters vnto them be­longing. Some fewe yeeres since it so fell out, that I had seuerall conference with two East Indians which were brought into England by master Candish, and had learned our language: The one of them was of Mamillia, in the Isle of Luzon, the other of Miaco in Ia­pan. I questioned with them concerning their ship­ping, and maner of sayling. They described all things farre different from ours, and shewed, that in steade [Page] of our Compas, they vse a Magneticall Needle of sixe ynches long, and longer, vpon a pinne in a dish of white China earth filled with water: In the bottome whereof they haue two crosse lines, for the foure prin­cipall windes: the rest of the diuisions being reserued to the skill of their Pilots. Vpon which report of theirs, I made present triall howe a Magneticall Nee­dle would stand in water, and found it to proue excel­lently well; not doubting but that many conclusions of importance in Marine affaires will thereby more readily be performed.

I finde that as the Portugals traueiled in their very first discoueries for the East Indies, they got a Pilote of Melinde, that brought them from thence in 33. dayes, within the sight of Calecute, and had euen then in vse the Compas, the Carde, and the sownding line. Lu­douicus Vartomannus testifieth, that in his voyage from Bornco vnto Giaua, the Pilots of those Countreys had the vse of both Compas and Carde, and had skill to take direction from the South Pole, as ours doe from the North, euen in those dayes, when it was a very daintie matter for any of our Pilots to haue performed the like: being as then possessed with an opinion, that the Compas would turne round, assoone as euer they came vnder the Equator: as some doe yet surmise it would doe vnder the Pole, or neere the fantasticall Rocke of the purest Magnes. Philander in his annota­tions vpon Vitruuius, sheweth that some men deemed it not a newe, but an olde inuention, and tooke it to be that Nauticall instrument which is called by Plautus in Trinummo and Mercatore, by the name of Vorsoria. But this Adrianus Turnebus in no case will allowe, af­firming it rather to bee a kinde of tackle, wherewith [Page] they turned their Sayle.

If of olde time they had not this Instrument, it see­meth impossible that euer they could haue performed such voyages as they did: And if euer they had it, then were it as strange, that all memorie thereof should be vtterly suppressed, and that Ptolomey had not found some mention thereof made in Marinus Tyrius, or o­ther Cosmographers, whose workes were extant in his time. Experience testifieth, that this began to be in common vse about the time that Printing was in­uented, and the making of Gunnes. Both which, al­though they are of very excellent vse and great won­derments to the world, yet doeth this farre excell and exceede. For all things performed by them, are mar­shalled within the limittes and bounds of humane rea­son; and therefore their causes being knowen, their wonder ceaseth. But this being incomprehensible vn­to humane reason, carieth it away captiue vnto the a­stonishment thereof, and leadeth it to the admiration of him, whose wisedome comprehendeth all things, and distributeth knowledge and vnderstanding among men, according to such measure, times, and meanes, as seemeth best vnto himselfe; opening the eyes of the blind, and giuing vnderstanding to the simple, destroy­ing the wisedome of the wise, and making the vnder­standing of the prudent for to hide it selfe.

Considering the fowle abuses and errors that dayly are committed in the making and framing of this wor­thie Instrument, I haue thought good heere briefely to note the faults, and therewithall to shew the way how they may bee amended. Let no man mistake me: I speake not saue onely of ordinarie Compasses (being the most that euer I sawe) such as are in common vse, [Page] and are sale-ware for Masters and Pilots. What some discreete skilfull men carefully doe prouide for them­selues, I speake not of. First therefore for the most part, the Carde of the Flie is negligently diuided, not only in the Compas which they ordinarily saile by, hauing the 32. common partes: but as great negligence may be found in the double Flie, for their Compasse of Variation: where the vttermost Ring which they make moueable about the ordinary Flie, is diuided into de­grees: and there a degree or two oddes breaketh no square with them. The wyers of the Flie are as rudely set together, hauing their ends not sitted euen and close (as were meete) but starting a side eache from other, not somuch as filed smoothe, but rough euen as they were broken: whereby they are also disabled from taking so strong a touch, as they would, if they were made smoothe. For remedie hereof it were good, to drawe the ouale lines vpon the Carde of the Flie, in such sort, that the endes being euen with the circumference of the Flie, both the middles and the endes may haue an equall distance from the Center: Then according to those lines bow and cut the wyers, fitting their endes smoothe, and so closely ioyning them, that they may both seeme to be but one. After that, holding them together, dippe the endes in a little moulten Tinne, or if at the first they be welded toge­ther, it is the better: and with the edge of a dull knife, scrape off the Tinne againe asmuch as you can come by, which will be all in a maner, sauing onely a very lit­tle that keepeth the endes together: and that will hold them so fast, that you may conueniently handle them at your pleasure, and fasten them on their place, accor­ding to your desire. (But before they be set on, let them [Page] be touched as abouesaid, and being set on their tou­chings at the ends must be refreshed.) Thus shall your Flie stand and turne equally vpon his pinne: if not, in stead of the ordinary dawhing with waxe, two or three drops at the most will counterpoyse any swaruing: and many times you shall not neede any at all; which is most commendable. [...]

The Capitall is commonly wide from the Center of the Flie; and likewise the pinne whereon the Flie stan­deth, from the Center in the bottome of the Boxe: both grosse and absurd faultes, and yet easie to bee auoyded. [...]

The glasse that couereth the Boxe is commonly crackeled and snarled by the sides; and diuerse times also too little. These faults they couer with their thicke border of Rosen: but better were it to amend them with a little heede taking. The Glasse ought therefore to be somewhat thinne, smoothe, and of euen thicke­nesse; hauing the edges smoothed on a grinding stone, or by some other meanes, and made very fitte to the Boxe. So shall you neede but little quantitie of Sim­mond, onely to keepe out the ayre: which is the bet­ter, both for the clearer view of the Flie, and that your Boxe may hang the steaddier: and that will it not doe, if your Glasse be much thicker on the one side, then on the other, or els being too little, bee thrust neerer the one side, then the other, and the voide place filled vp with Rosen, according to ordinary custome.

The Boxe is hanged in two Circles, the one within the other, hauing the pinnes that they turne on, a quar­ter of a Circle in the one distant from the other. But these Circles are commonly so vnhandsomely made, and ill fauouredly hanged vpon their pinnes, that you [Page] should offer a Tincker discredit to compare his worke with this. Adde hereunto the riuetting of the Circles with yron, and hanging the bigger of them vpon yron nayles: which although they be but little, yet you must esteeme a litle in this case to bee a great deale too much. And if they had any care of that they haue in hand, they would not commit such a needelesse grosse absurditie, onely as it were in despite of Arte, to make expense of wit without gaine or profite. [...]

The piece of Lead that is fastened to the bottome, ought to be round and of equall thicknesse, the pinne passing through the Center thereof. If you haue it otherwise, then marke the Boxe and the bottome when it hangeth aright: and whensoeuer, hauing taken off the bottome, you will set it on againe, see that you make your markes in the Boxe and bottome agree, or else it can neuer with any certeintie hang as it should. Although it be exceeding lothsome vnto me to deale in these mechanicall base practises, yet the necessitie is such, that one must needes deale therein. For of all the Instruments that the Nauigator vseth, this is farre the most excellent: and yet of all others this is most negli­gently and vnartificially made. Their Staues and Sea Cardes made in England are neate and fine. Their A­strolabes are tolerable: but these are euen such, as I haue shewed vnto you, which I could not so well haue shewed, but by this anatomizing of them: that the blame may bee apparant, either in those that make them, or in such as buy them, that will not goe to the price of better: wherein folly would shewe it selfe ve­ry eminent, if when a shippe with her lading may bee woorth many thousands of poundes (besides the ine­stimable value of the mens liues that are in her) halfe a [Page] pound should be thought much to be bestowed on a perfect Compasse; vpon the goodnesse whereof many times, both shippe, and goods, and liues of men doe take their triall: yea all these doe they ieopard (as it were) vpon a wager that their Compasse is true and perfect. To conclude, I would wish in any wise, that Artificers of these Instruments shoulde make euen great conscience of that they haue in hand; and not sleightly to passe them ouer after the order of dozen ware. Also that such as exactly make them, should be rewarded and esteemed accordingly. And finally that they which are to vse them, doe well examine their goodnesse, before they buy them.

Moreouer, it many times falleth out, that the hol­lowe side of the Capitall is made too narrowe in the bottome: and then will the Flie neuer play well, except the pinne be exceeding small & sharpe: which assoone as by vse it is a little dulled, the Flie will neuer shewe his pointes truely, though hee were touched with the best stone in the world. And very oftentimes the ouer­sight herein, is imputed wrongfully to the weaknesse of the Touch.

And therefore take care, that the greater Boxe be­ing square, be not set together with yron nayles. But if it be round, then see that it be handsomely turned. And in any wise that the lesser Boxe, wherein the Flie standeth, be well & exactly turned, of seasoned wood, and hauing the inside coloured with some white gli­stering colour: and not according to the common cu­stome rubbed about with a piece of Chalke, or a little white lime.

Furthermore because it is very necessarie, that who­soeuer sayleth by any Carde, ought diligently to fore­see [Page] that the Set of his Compasse be answerable to his Card, of the like Set (I meane) vnto that his Card was made by; And for that the wyers being once glewed on, may not well be altered, or remoued; And the dou­ble Flie by reasō of his vnwildie corpulēcie is nothing nimble, I haue framed one after this sort; a briefe de­scription whereof I thought not impertinent here to insert. The endes of the wyers must bee welded toge­ther. The wyers themselues are halfe round, with the otherside flatte to be placed vpon the bottome of the Flie. The Capitell hath two thinne narrowe Stayes of Latten reaching to the wyers on each side and fast sol­dered vnto them. The toppe of the Capitell must bee skrewed on the outside, and a little square piece of Latten with a small hollowe bent fitted for to skrewe vpon him; vnto this ende, that the Capitell being put through the bottome of the Flie in the Centre, and the skrewe on the vpper side, being turned on the top of the Capitell, the Flie and wyers both, may by this meanes bee closely combined together without any paste or glewe, and bee left bare throughout, to the most aduantage at any time for receauing the touche of the Stone, and more easily be kept from rust, being the greatest enemie that the touche of the Stone can haue: vnto which, all your pasted or glewed wyers are necessarily subiect: insomuch as you shall very sel­dome and (as I thinke) neuer, in the whole many of your vsuall Flies see any one, that is not infected here­with: being farre more noisome then Garlike, or Oile, and all the rest of those fondly surmised conceites. If the skrewe come not close ynough vpon the Flie, a little piece of pastboorde put on before the skrew, will be a remedie sufficient therein. When the wyers are [Page] thus fastened vnto the Flie, you may at al times remoue them to any point or part of a point at your pleasure, without anoyance vnto any thing. In such as I haue caused to be made for this purpose, I haue vsed a nar­rowe forme of a loope, the distance betweene the wy­ers in the middle, being little more then the fifth part of their length: and haue abated also the mettall of the wyars about the middle of them, and allowed some­what the more towards their ends.

The Compasse of Variation.

THe Compasse of Variation is made in all respects like vnto the ordinary sayling Compasse, & is the very same in deede, excepting these two Additions. The one is, that on the inside of the lesser Boxe round about, iust with the height of the Flie, either vp­on the Boxe it selfe, or else vpon Paper or Pastboorde, fastened to the side thereof, there be a Circle diuided into 360. partes. And at euery 90. let a line be produ­ced both vpward to the top, and by the space of halfe an ynche downeward. At any one of which lines make a Flower de luce representing the North; and there begin your numbers on both sides thereof from 1, vn­to 90. doe the like also from the opposite part, betoke­ning the South. The other is, that a thwart the vpper face of the Glasse, there be placed a Ruler of Latten in length answerable to the Diameter of the Boxe, bea­ring in breadth the third part of an ynche or halfe an ynche, if you thinke good, for a very great Compasse. In the middle of which Ruler there must a line bee drawen according to the length of the Ruler▪ And to­ward [Page] eache end of equall distance therefrom, fitte two Sights of three ynches or longer (as your Compasis) and about a quarter of an ynche broade at the toppe, waxing broader toward the foote; where they are to be ioynted in such sort, that they may for handsome­nesse sake be folded the one close vpon the other, and stand erected at right angles. In the one of these along the middle thereof cut out the mettall, beginning a lit­tle beneath the top, downe to the foote, of conuenient breadth; that a Lute string hauing a small pearle or bugle on it to slide vp and downe, may be fastened pre­cisely in the middle throughout from the toppe to the foote. The other Sight being made after the same pro­portion and forme that the former was, hath onely a fine small slit pearced from within very little off the toppe downe to the foote, and must in his thickenesse be abated, that he weigh no more then the other. The Ruler thus furnished with his Sights, in the space be­tweene the sights and the brimme of the Boxe, ought to haue two loopes cut out in decent maner to looke downe through them vpon the Flie. And this Ruler must be diuided into many equall small partes; as 20, to an ynche, or such like; the numbers beginning from the Lute string sight vnto the other; and from the foote of that other to the toppe. When the Ruler is finished, as before I haue specified, it must a little be let into the brimme of the Boxe, that it may stand fast ha­uing the middle of it right ouer the line of North and South in the Boxe; and the Sight with the Lute string, ouer the South. But let it in such sort be fastened, that you may conueniently either take it off, or set it on as occasion shall serue. So that the Ruler being taken off, it is a Sayling Compasse, being set on, it serueth for [Page] the Variation in maner following.

The Flie of the Compas hauing at opposite partes directly ouer the points of the wyers some markes on the vpper side easie to be discerned (if it be a Meridio­nall Flie, it needeth not, in as much as the Flower de luce and the South point serue the purpose) turne the Boxe toward the East in the foorenoone with the Ru­ler on it, till the Lute string doe cast his shadowe right vpon the middle line of the Ruler, or on the slit of the other Sight. Then marke immediatly where the sha­dowe of the pearle doth light, vpon what diuision, if the lines be diuided, otherwise marke it with a penne; And also what part the Southend of the wyers, or, (which is all one) the Northend doth point vnto in the side of the Boxe. In the afternoone doe the like to­ward the West, with the pearle still vnremooued, tur­ning the Boxe, till the shadowe of the pearle falleth full vpon the place that it did in the forenoone: And note then also what part the endes of the wyers doe point vnto. Then if the number of partes obserued in the forenoone, be alone with those in the afternoone, there is no Variation at all: for the ends of the wyers doe shewe the true Meridian. But if the one exceede the other, subtrahe the lesser from the greater; And halfe the remainder is the Variation of the Compasse toward that side, which had the greater number in his obseruation.

This Compasse serueth farre better to set the land withall, and to describe any Harbour, Coaste, Hauen, Towne, or Countrey, then any before in common vse; by looking through the slitte, and bringing the thing that you would note, and the Lute string both in one; withall marking what partes the wyers doe shewe at [Page] that instant. Likewise for taking of distances.

All this may also bee performed with a Circle of Latten about one quarter of an ynche broade, hauing a stay going athwart perced through with loope holes (that it be no hindrance to viewe the Flie) and a Ruler mouing vpon it in forme like to the former. Which Circle must be diuided, as that within the Boxe was, frō the Flower de luce, which is to be placed a quarter of a Circle distant frō the line passing along the mid­dle of the stay, & haue his numbers reckoned towards the endes of the same line. And so must the other halfe of the Circle be diuided from the South point. Being thus diuided it must be placed euen fast and very fitte, close aboue the Glasse. And when you will vse it, turne the Boxe about, till the flower de luce of the Cir­cle stand right ouer the Northerly endes of the wyers: And the Boxe so standing, set the Ruler according to the forenoone and afternoones obseruation, doing all things els, as before. And you shall finde the selfe same effect.

I haue tryed at land the Crosse-needle in steade of the Flie, and do like it exceeding well. Whether is the better at Sea, I doe referre it vnto their iudgements that shall make due triall of both. The Crosse-needle I call two needles, the one of Steele, and the other of Latten, ioyned together in the Capitell, where they crosse each other at right angles; and so made, that they be of one length, very straight, and equally stan­ding vpon the pinne, no end ouerweyghing the other. This Needle well made and fitted as it ought to bee, will besides his proper vse, supply the vse also of a Per­pendicle, (a matter of great importance) to shewe the vpright standing of your Instrument, which the single [Page] Needle cannot doe; neither yet the Flie any whit com­parable vnto this. But you are diligently to note, that in continuance of time as the force of the Touch of the Stone doeth decay, so will the North ende of either Needle or Flie rise somewhat higher, and the South end sincke lower. For this is one of the wonderful pro­perties that the touch of the Magnete hath, that a nee­dle as yet not touched standing equally vpō his pinne, being once touched with whether ende of the Stone you list, the one end thereof shalbe reared higher, and the other fall lower: The difference whereof, as the goodnes of the Stone is greater, will accordingly the more appeare. And in processe of time as his force stil decaieth, so returneth hee more and more to his euen standing againe. By reason of which propertie the Ar­tificer is constrained, that he may make the Needle lie euen, to abate somewhat of the falling end, that the o­ther by vertue of the touch raised vp, may through this abatement, be brought downe to an equalitie of situa­tion with his fellowe. When therefore you perceaue the rising of the North end (as aforesaid) assure your selfe the Flie or Needle is weakened in strength, and hath neede to be refreshed with the Stone. Otherwise, if it were at the first well touched, be not too busie with it, but let it alone; except you bee well assured of the goodnesse of the Stone, and of the right maner of tou­ching. If the Northend riseth not any thing at all, and yet the Flie playeth not, then is it to be remedied with sharpening of the pinne. The commoditie of the vse of this Needle for a Perpendicle is, that because it is within the Boxe, the winde cannot hinder it, as it will any other Perpendicle (especially being small) that is in the open ayre.

The Traueylors lewell.

THIS Instrument is a Circle about a quarter of an ynch broade, hauing his diametrall staye, Ruler, Sights, and all things else, as is last before described; sauing these additaments. The Com­passe Boxe of this Instrument must be of Latten, of what depth or shallownes you please. Only so prepare it, that the Needle or Flie want not in any wise space ynough at libertie to play in. Let the Circle haue a Quadrant firmely sowdered to his vttermost circum­ference, making right angles with the superficies of the Circle: whose semidiameter let be about the length of the semidiameter of the innermost circumference of the Circle, or somewhat shorter. Diuide the Quadrant into 90. degrees: and the numbers of those parts, pla­ced in two seueral borders, must be reckoned contrary wayes, the one beginning, where the other endeth. Vpon the edge of the vtter Circumference of the Cir­cle, where it and the Quadrant meete, there must be a strong and firme ioynt fastening the Circle and Qua­drant in that place vnto the Boxe in such sort, that as the Circle continually riseth, so the Quadrant may still sinke in the Ioynt. For this Ioynt must issue from the Boxe with a necke somewhat longer then the se­midiameter of the Quadrant, standing at right angles vpon the Boxe and Circle both: hauing in the middle a slit of capacitie sufficient to receaue the Quadrant, moued therein vp and downe according to the motion of the Circle itselfe, with a little screwe pinne on the one side to stay the Quadrant therewith, and so conse­quently the Circle, wheresoeuer you will haue it. And [Page] on the other side an Inlet must bee handsomely filed, that the lower part thereof, (being of a conuenient quantitie to conteine within it both the borders of the Quadrant) may precisely make one right line with the middle of the Axis of the Ioynt, and the neither se­midiameter of the Quadrant erected. So shall it al­wayes supply the vse of a fiduciall line, and distinctly shewe the numbers that are cut in the borders afore­said. Thus much concerning the description. The vse is briefely this. When the Circle is not eleuated, it is the aboue mentioned Compas of Variation: The mid­dle line of the diametrall Stay, representing East and West, and the Base of the Quadrant produced, ser­uing for North and South, &c. But when it is eleua­ted according to the height of the Equator (whose an­gle by the fiduciall line of the Inlet, the Quadrant sheweth in one number, and the height of the Pole in the other) it performeth the vse of an Equinoctiall Dyall generally throughout the whole world. For, supposing the Circle raysed as apperteyneth, let the Needle (and a Crosse-needle seemeth the best) keepe his due place agreeable to the Variation: Then turne the Ruler with his Sights about, till the shadowe of the Lute string being toward the Sunne, doe fall vpon the middle line or slit of the opposite Sight, being per­pendicularly erected on the Ruler like vnto the other. So shall the vppermost end of the Ruler directed to­ward the Sunne, declare the true houre, either in the vpper superficies of the Circle, to be reckoned by 15. degrees continually from East to South in the Fore­noone, and from thence to West in the Afternoone: or else for more expedition in a peculiar Border of houres drawen according to euery of those 15. degrees [Page] in the voide superficies vnderneath.

I had once purposed to haue written somewhat of an Instrument deuised by Robert Norman: who al­though he was not learned, yet was hee a very expert Mechanician, of an honest and good mind, and found that by his owne industrious practise, concerning a strange propertie of the Magneticall Needle, which no man (I thinke) before him did euer finde, and which (the more is the shamefull slouth of men) very fewe Nauigators haue practised euer sithence: Al­though the Instrument be very easie to be made, and the propertie no doubt in Nauigation of great conse­quence. But vnderstanding by conference with a man of rare learning both in Phisicke, his owne profession, and in diuers other laudable knowledges, besides that, he many yeeres hath laboured in the consideration of the properties of that Stone, and mindeth nowe out of hand for the common benefite to publish those his la­bours, I surceassed altogether from that purpose of mine, assuring me that hee (if any other) will be able most exactly to handle that Argument: For I found him excellently skilled, farre beyond any thing that I either knewe or imagined in that matter. Albeit I had read all that I could heare to haue written thereof, and had practised as many of their Conclusions, as I made any reckoning of. But I found mine Authours, euen of the best accompt, in many things very friuolous and vaine, and ignorant of the chiefest properties of im­portance. He that seemeth to haue written most lear­nedly is a Neapolitane, whose footesteps I followed, and found his Assertions erroneous in sixe seuerall Conclusions.

The Pantometer.

The Authors purpose in this Treatise.

THis Instrument, that in respect of theCap. 1. manifold and generall vses thereof, I call the Pantometer, I haue framed chiefly for the Variation: And that prin­cipally to serue at land: yet some partes of it shalbe employed on practise of good importance at Sea; both by helping the Hemisphere (wherewith hereafter you shall be further acquainted) in some things, & by performing other some for it self. And al­though the vniuersalitie of the Pantometer would haue ministred matter of very large discourse: yet for as much as my maine purpose is, as in the rest, so in this Treatise likewise, to be ayding and assisting the Naui­gator by al good meanes possible: To his principal and most necessarie vses I haue therefore directed, and as it were, contracted the diffused nature of this Instru­ment. Notwithstanding, whatsoeuer Master Thomas Digges hath written of Measurings with his Topogra­phicall Instrument, may bee done aswell, and better with this. Howe conuenient it is for obseruations A­stronomical, the expert wil soone perceaue. Al which, and many other Mathematicall Conclusions easie by this Instrument to be performed, I must leaue to the diligent tryall of the studious delighted with those noble Sciences.

The Declaration of the partes of the Pantometer.

THe chiefe partes of this Instrument are two:Cap. [...] The Horizontall, to be placed alwayes equi­distant to the plaine of the Horizon, which it representeth: And the Verticall, perpendicu­larly erected vpon the former, and therefore in power any Azimuth or Verticall, whereof also it is named. In the Horizontall there are two Semicircles; The one hath the ordinarie Points of the Compasse: the other the common degrees of a Circle, both of them mee­ting in one Diameter. The round voide space in the middle of the Horizontall, must be filled vp with the Centre-pinne thereof, in such sort, that being from vnderneath fastened thereinto, the one halfe and more of the said Pinne, somewhat beyond the Diameter of his thicknes, shalbe cut away, and be made euen with the vpper side of the Horizontall: But the other part re­maining, shall stand directly vpright of a conuenient length aboue the Horizontall: And this I terme the Axis of the Verticall: because by meanes of it the Verti­call is turned round about vpon the Horizontall, and made to take any maner of position.

The Verticall hath in it a Quadrant as bigge as it may receaue, to be drawen not after the common fa­shion, but according to the description inuented by that famous Mathematician Petrus Nonius in his Trea­tise of Instruments and Rules for Nauigation, and of the Twilight: which Quadrant, in respect of the kinde of working thereby, I call the Proportionall Quadrant. And on that side it hath nothing else, sauing the Al­hidada, [Page] or Sight Ruler (as the maner is) fastened in the Center, and carying in his margen aboue the Fiduci­all or Leuell-line all the seuerall numbers of the inner Quadrants vnderneath, for more readinesse and cer­taintie sake. For the speedier diuiding of the inner Quadrants, doe thus▪ Part the Fiduciall line of the Sight Ruler into halfes, from the innermost circumfe­rence of the Limbe vnto the Center. The medietie next vnto the Limbe, diuide into 45. equall partes: set­ting downe their seuerall denominations by fiues or tennes, vpon the Ruler rightouer the diuisions: their numbers decreasing from the Limbe towards the me­dietie after this sort. The diuision next vnto the Limbe is accounted for to be 89. the next 88. then 87. 86. &c. vntil you come vnto 46. next vnto the medietie it selfe. According vnto these diuisions precisely answering vnto them, drawe so many inner Quadrants vpon the Center of the great Quadrant of 90. Then must you with a payre of diuiding Compasses very exactly take the quantitie of a degree in the Quadrant of 90. and that will perfectly diuide euery one of the inner Qua­drants into their assigned numbers. Onely you are carefully to foresee, that when the Verticall on the backe part thereof through the hole of his Border is firmely fixed vpon the Axis of the Center-pinne, the neathermost edge on the forepart of it (being equally distant from the lower side or Base of the proportionall Quadrant) doe in any case precisely light vpon the Center of the Horizontall: to the ende that it may al­wayes serue it in steade of a moueable Diameter.

The backe of the Verticall hath these three necessa­rie Implements. The first is a Compasse, with his line of North and South parallele, to the Verticall: And the [Page] same must be handsomely and fitly let in to the border of the Verticall beneath, that the Axis of the Center pinne, passing through both the handle of the Com­passe and the said Border, may claspe it exactly close vnto both the backe of the Verticall, and the plaine of the Horizontall, in such sort, that as the Verticall is mo­ued round about, so ioyntly together with it and in it shall the Compasse likewise.

The second is the Directory, so named, because it guideth the eye-beame directly foorth vnto the Hori­zon. And this consisteth of two partes: The Ruler and his Sights. Whereof the Ruler being of a reasonable length, streight, and euen, shall be drawen to and fro athwart the backe of the Verticall in two loopes stan­ding parallele to the Horizontall, or (which is all one) to the Border of the Verticall. The two Sights, which ought to be 2. or 3. inches long, are moueable likewise but vpon the Ruler: the one beyond the Verticall, the other behether it towards your eye.

The third is the Perpendicle or threed, with a little plummet hanging thereat, requisite for the due pla­cing of the Horizontall: which turne the Cross-nee­dle also will serue. Last of all, when you are to vse the Verticall alone by it selfe (as hereafter shall be shewed you) there is a handle belonging thereunto, hauing the lower ende of what forme you will, (the best is which may best fill the hand) but the vpper end must be of the same fashion and bignesse that the Axis of the Centre-pinne is of: for it hath (as you shall per­ceaue) the same vse, and must be fastened likewise in the same place.

The Mechanicall Description Cap. 3. of those Partes.

  • The Horizontall.
  • The Compasse.
  • The Backe of the Verticall with his Border, Inlets, Loopes, and Perpendicle.
  • The Centre-pinne.
  • The Verticall and his Sight-Ruler.
  • The Directory.
  • The handle of the Verticall.

The exact finding of Altitudes or Heights.

FOr as much as the vsuall Quadrant ofCap. 4. 90. degrees onely doeth very seldome yeeld the precise eleuation sought for in a knowen and certaine denomination, because most commonly the Sight Ru­ler, or Alhidada (as they call it) cutteth not exactly at a full degree, but vpon the space betweene the begin­ning and ending of a degree (which is infinitely diuisi­ble) the proportionall Quadrant of Nonius, by draw­ing and diuiding many inner Quadrants (as before you haue seene) shewes that easily within a narrowe circuite; which otherwise a very large, yea a huge In­strument with no small incumbrance would hardly doe in a mightie circumference. For the partes being so many, in a continuall traine following one an other, and the Ruler euery where in a maner crossing them, it must needes cut some one of the inner Quadrants vp­on a full degree. And so by this meanes, that part of the vttermost or great Quadrant, which before was [Page] but confusedly coniectured, without any determinate denomination, is now distinctly made knowen vnder a certaine name, by the ready helpe of the Golden Rule, after this maner. When the Ruler sheweth some portion of a degree in the vttermost Quadrant, whose certaine value in minutes, seconds, &c. you would gladly learne, obserue at the same instant what whole degree in one of the inner Quadrants it precisely cut­teth: And market therewithall in the side of the Ruler the entire summe of all the parts whereinto that Qua­drant is diuided. So haue you of foure proportionall numbers, three giuen: namely, the whole inner Qua­drant, his part cut, and the whole vttermost Quadrant of 90. Wherefore to finde out the fourth, multiplie 90. into the partes of the inner Quadrant that the Ruler cut, and the Product diuide by the whole inner Qua­drant, the Quotient shall tell you the degrees of the vttermost Quadrant together with the portion sought for, in a fraction distinctly knowen: which to reduce vnto the vsuall denomination of Minutes, Seconds, &c. doe thus. Multiplie the Numerator of your Fra­ction by 60, and diuide the product by the Denomi­nator: the Quotient shewes your Minutes. And if any remainder be, againe multiplie that by 60. and diuide in like sort as before, this second Operation brings foorth Seconds. And in the same maner still wor­king, as often as any thing is left of the former Ope­ration, you may proceede on to Thirds, Fourthes, Fifthes &c. till you haue obteyned a most sufficient precisenesse.

The Obseruing of the Variation at Land by the Sunne.

SEt the Instrument vpon a Staffe pre­paredCap. 5. for this purpose, his Horizontall being parallele to the Horizon of the World: And placing the Verticall vpon the line of North and South in the Ho­rizontall, turne the Horizontall about, till the Needle stand equidistant to the Verticall: Then fasten the Ho­rizontall to the staffe with the skrewe pinne of his Soc­ket: which in that sort remaining steaddy and im­moueable, turne the Verticall in the Forenoone tow­ards the East, mouing the Sight Ruler vp and downe, till the Sunne beame doth pearce both Sights: and im­mediatly note what partes the edge of the Verticall doth cut in the Horizontall: Also what part the Sight­Ruler falleth on in the Verticall: where if it light not on a iust part in the vtter Quadrant; marke where it doth vpon one in any of the inner Quadrants. Againe, in the Afternoone, the Horizontall continuing still in his former place, and the Ruler likewise abiding vpon the foresaid part vnchangeable, turne the Verticall towards the West, till the Sunne entreth in at both the sights: And note therewithall what part the edge of the Ver­ticall cutteth in the Horizontall. If then the partes cut by the edge of the Verticall in the Forenoone, and those other in the Afternoone, bee equally distant from the South point of the Horizontall; then is there no Variation at all. For the line of North and South in the Horizontall, is one and the selfe same with the true Meridian. But if the partes of the Forenoones [Page] obseruation be fewer then those of the Afternoone, subtrahe the smaller number from the greater: and halfe the remainder discouereth the Variation from the South Westwards to bee so many degrees: and the Northerly end of the Needle to decline so many parts from the true North towards the East. Wherefore the line of North and South in the Horizontall, doeth not possesse the true Meridian: but swarueth therefrom, as the partes obserued doe shewe. Lastly, if the partes of the Forenoones obseruation be moe then those of the Afternoone, subtrahe (as before) the smaller number from the greater, and halfe the remainder sheweth the Variation of the South end of the Needle to be so ma­ny degrees Eastward, and the Northerly end thereof to vary so many partes Westward. Nowe for the more certeinetie in your working, you must euer be mind­full to make 3. or 4. seuerall obseruations in the Fore­noone: that although a Cloude should hinder you of your first in the Afternoone, yet some one at the least of the other may be clearely obserued: where other­wise, if you misse of one, all your labour for that whole day is lost.

The obseruing of the Variation at Land by the Starres.

THe Variation of the Compasse, (and soCap. 6. likewise the Latitude) may bee taken as well by the Starres in the night, as by the Sunne in the day. And sithe the Al­mightie hath ordeyned but one Sunne, and a great multitude of Starres, Nauigators should offer themselues much wrong, if they would not make [Page] their benefite of these, as they do of that: And so much the rather, because the Sunne is South but once in foure and twentie houres: The Starres come to the Meridian continually one after another all the night long. The ordinarie instrument for the Variation, is not of any vse at all in respect of the Starres, no not though he haue his Astrolabe to helpe him: whereas this instrument by it selfe, without the ayde of any o­ther, performeth all things exquisitely by the Starres: And by the Sunne so exactly with all aduantage, that when many Instruments can doe nothing without a cleare Sunneshine; this in a mystie or foggie weather through a Cloude, if that you may but onely discerne the body of the Sunne, craueth no more to accom­plish your desire.

The maner of obseruing a Starre is this. First pre­pare a little Notche or slit of equall deapth in the two sights of the sight-Ruler, parallele to the leauell line thereof: And the Instrument being placed (as before is specified) turne the Verticall towards the Starre, be­ing on the Eastside of the Meridian, mouing the sight­Ruler vp or downe, till you may perceaue the Starre euen with those two Notches. Then note the partes that the sight Ruler doth cut in the Quadrant: And those also that the edge of the Quadrant or Verticall cutteth in the Horizontall. Afterward doe the like a­gaine when the same starre is on the West side of the Meridian. And for the rest, following the same maner of Operation that aboue I deliuered, you shall here obteine the selfe same trueth of Variation by any starre that there you found onely by the Sunne.

Touching the Latitude, the like kinde of working is to be vsed for the taking thereof by a starre, as is by the [Page] sunne: I meane the obseruing of his Meridian height, and subtrahing, or adding, as the nature thereof re­quireth.

And for this cause is the Verticall so placed, that a­bout an ynch of it (more or lesse, according to the pro­portion of the Instrument) at that corner, where the Ruler is fastened to the Center, may alwayes in the turning about reache ouer the Horizontall: that you may conueniently apply your eye, by the sights to dis­cerne any starre, or espie the top of any body erected, whose height you would measure: which otherwise you could not doe, if the Verticall were but euen with the Horizontall. As for the other end of the Base of the Verticall, it is no matter howe farre it be extended, but onely according as the quantitie and comelines of the Instrument shall require; so that the Border, where­with the Base of the Verticall is lengthened, doe reache precisely streight, and euen vnto the edge of the Hori­zontall, for the cutting of the partes therof.

Moreouer, if the halfe Circle of the Horizontall, which is parted into degrees, were diuided also into a payre of Proportionall Quadrants: then both for the for­mer vses, and infinite others, woulde this Instrument prooue most exact and persite. But those that are wil­ling to bestowe so much cost, I wish they should doe it in mettall, and not in wood. If in wood, then let the same especially be chosen, whereof Cypers chests are made: For that I take to be best, as being most free from warping, and receauing any worke very easily and fairely. The imperfection of bricklenesse, a little the more care must amend and strengthen. And thus much for the vse of the Pantometer complete.

The maner of obseruing the Variation at Sea.

WHen the Verticall of the Pantometer to­getherCap. 7. with his Compasse is fitted to the handle, holde it directly toward the Sunne in the Forenoone, in such sort, that the Perpendicle keeping his due place, the Sunne may pearce both the sights: And no­ting the height of the sunne, marke also at that instant, what Point or Degree the Needle doth shew. Againe when the Sunne commeth to the same height in the Afternoone, obserue likewise what Point or Degree the Needle is at: And then working in all respects (as before I declared) the Variation is made knowen vnto you.

If you haue a Crosse-needle well made, it will serue in steade of the Perpendicle, better then the Perpen­dicle it selfe: In as much as it is not subiect to the whir­ling of the winde, but is quiet therefrom, being defen­ded by the Glasse close symmond round about.

The taking of the height of the Sunne at Sea.

PLace the Verticall vpon his handle, theCap. 8. limbe towards you, and his perpendi­cular side ouer against you, and turning your backe towards the Sunne, keepe the two sights of the Directory, euen with the parting of the water, and the Element ouer right against you. Moue also the sight Ruler of the [Page] Verticall vp or downe, till at one instant you may see, both the Sunne-beame through the vpper sight to fall vpon his due place in the neather, and ioyntly there­withall the parting of the water and Element: Then haue you the degrees & minutes of the sunnes height, by meanes of the Proportionall Quadrant, as heretofore is specified.

This may in like maner be performed by looking toward the Horizon directly vnder the Sunne, placing the Perpendicular side towardes you, and the limbe from you, and thrusting the Directory with his long sights from you, or else drawing it towards you, as you may most conueniently discerne the sunne-beame of the vpper sight to be vpon his iust place in the nea­ther. For the better effecting whereof, it is requisite to haue a third square sight, forked on the neather side with a couple of small peakes to be placed, the one on the one side, and the other on the other side of the Center of the sight Ruler, ready to be taken off or on; and hauing a little marke with two Crosse-lines of e­quall distance to the holes of the other two sights, and the Fiduciall line: To the end that this third sight, be­ing fastened right ouer the Center of the sight Ruler, (with his lower edge somewhat aslope, and not at right angles with the Fiducial line) you may the more easily discerne, by meanes of the said marke, when the sunne-beame hath perced the other two sights aboue: And then haue you all things as before. Wherefore if two obseruations be made together, the one from the Sunne, and the other towards it, and both these agree in one; The whole Operation must needes bee exact and without any doubt of error.

The ordinary staues (so that they be well made, [Page] and good regard had to the Eccentricitie of the eye) be very commodious for so much as they can performe: which cannot be much aboue 45. degrees: because the eye at one viewe is scarce capable of a larger Angle. And therefore in great Altitudes of the Sunne, they are vnseruiceable, the Astrolabe or searing, (as some terme it) comming in place of them: And yet the vse of this also in a hie Sea is very vncertaine. But with the Instrument that nowe is described vnto you, you may take the height of the Sunne at what angle so euer, yea although he be verticall. Herein, this and the staffe a­gree, that both of them haue a speciall respect to the Horizon: but they differ in the danger of the Eccentri­citie of the eye; whereunto the staffe is subiect, but this is not so, and neuer requireth any Angle in the eye of the Obseruer, that shall exceede the capacitie of 20. degrees. Somewhat also might here haue beene ad­ded of the diuerse placing of the sights vpon the Di­rectorie: but for breuitie sake, I referre it to the consi­deration and choise of the Practiser, vpon diligent tri­all thereof.

The Hemisphere.

The Scope of this Treatise.

TWo things there are in euery Instru­mentCap. 1. of speciall and most necessarie consideration; the one the body (as it were) and substance of it: the other, the ende or purpose whereunto it serues. The body or substāce of euery [Page] Instrument, and namely of this (whereof nowe wee treate) I call the Materiall partes of which it consists, together with their peculiar formes, such, as whereby that end may be best atteyned: best, I meane, with the greatest both certeintie and facilitie possible. The pur­pose or end, I terme the manifold commodities to be reaped thereby, and especially in this Instrument, the singuler most pleasant and profitable vses whereunto it is and may be applied. All which fully to discourse of, would require farre more leysure, then either my vocation, or other many affaires of importance, may permit me. I shall therefore sufficiently content my selfe in this behalfe, if first I deliuer to the skilfuller and more industrious sort, a briefe and perfect viewe of the Instrument by a particular and euident description to the eye of all the Members thereof: which once con­ceaued, the thing of it selfe without any further words of mine, wil most easily and readily vnto them, declare his owne vse from point to point in Astronomie, Geogra­phie, Nauigation, and such like excellent faculties. But because that the Nauigatour is the man, for whose sake chiefely I haue taken these paines: And among those of that trade, the most part are, though commen­dably perhaps furnished with experience, yet but weakely assisted with fitte Instruments: and of them­selues, for want of some contemplatiue knowledge Mathematicall, not able either to inuent fitter, or to reforme and better those that presently they vse: I thought it requisite for them, together with the de­scription and frame of the Instrument, to adde in the second place some fewe principall admonitions, con­cerning the seuerall most necessarie vses thereof vpon sea or land. And in so doing, I wil leaue many things to [Page] the Readers owne ingenious practise: Many also will I omit, or rather presuppose as already knowen, name­ly what a Pole is, an Equinoctiall, a Meridian, &c. being such as are the first Principles of this Arte, wherewith euery man is commonly acquainted, and by diuerse in our owne vulgar speache haue in the largest maner of­tentimes be handled.

The names of all the partes of the Hemisphere.

NOwe if any desire to knowe what thisCap. 2. Hemisphere is by it selfe, (and so must he first, if hee will orderly proceede to the getting of perfect knowledge in the vse: for no man can well handle an In­strument that he knoweth not) a generall declaration of the partes accompanied with their Mechanicall de­scription, and a briefe comparing of them with the Globe, may so throughly suffice, as more herein is not to be required. There are therefore in this Instrument two sides to be considered, the one more principall, which I terme the Face; the other lesse, which I cal the Backe. The Face consisteth of whole Circles and halfe Circles. The whole Circles are two in nūber: where­of the one being the Base (as it were) of all the Instru­ment and immoueable, is the fixed Meridian, because that turne most commonly it serueth: the other, moue­able, I call the Deferent; for that it carieth vp & downe vpon and in it selfe, according to any greater or lesser Eleuation or Latitude, the Equator and Axis of the World, with the two extreame points thereof being the Poles. The halfe Circles being foure in number, are [Page] all belonging to the former two entire Circles: For either are they placed vpon the great Meridian afore­said; and then, if fixed or moueable thereupon, it is the halfe Horison; if moueable, it is the Semicircle of Al­titudes, to be turned to and fro vpon his owne Poles, equidistant on all sides from the Horizon: or else they are situated vpon the Deferent; and those two likewise in number hauing the selfe same differences betweene them that the former had: For one of them is fixed or fastened vpon the Deferent, and that is the Semi-equa­tor: the other is voluble, which I call the Moueable Me­ridian.

The Backe of this Instrument needeth not any thing, but the vsuall Mariners Compasse to be artifici­ally annexed thereunto with the line of North and South parallele to the Backe.

The Mechanicall DescriptionCap. 3. of all those seuerall Partes.

  • 1 The fixed Meridian.
  • 2 The Deferent with the Axis and Poles.
  • 3 The halfe Horizon.
  • 4 The Semi-circle of Altitudes.
  • 5 The Semi-equator.
  • 6 The moueable Meridian with the two Sight-Rulers.
  • 7 The Backe, with the Mariners Com­passe.

The agreeing of the Hemisphere with the Globe.

BY that which hath hitherto beene spoken touching the Structure of this Instrumēt,Cap. 4. may soone be discerned the originall des­cent thereof to be from the Globe. For the better conceauing whereof, vouchsafe I pray you a litle to remēber with me the chiefe Circles belonging to the Globe; as the Horizon cutting it in two Hemispheres, the Meridian wherein it is hanged, the Quart of Altitudes whereby it is measured: And then those other two not adioyned only as the former; but continual therwith, being described in the superficies or outface of the Globe it selfe, the Equator, I meane, and the Zodiake, with their appendāts, the two Colures, one Equinoctiall, & the other Solstitiall. All these to make and vse together in this sort with the Globe, when experi­ence had taught to be a matter of great difficultie, the learned of former times, & of these our dayes, haue la­boured how without the Globe by sundry rare inuenti­ons to represēt the Globe, in seperating those necessa­rie Circles frō the massines of the Instrument: wherein the Astronomers Ring (commonly so called) doth iustly deserue right worthy cōmendation. And I now the ra­ther make mention of it, for that it first gaue occasion of deuising, and ministred good helpe toward the fra­ming and perfecting of this Instrument. Both of them are (as it were) Anatomeis of the Globe: But whether in all respects the more absolute let eyther speake for itselfe, and let the skilfull Reader iudge. Touching the Hemisphere, if you imagine the Meridian of the Globe to be a Plaine, it shall passe through the Center there­of, and cut it together with all the great Circles there­unto [Page] belonging in two equall partes: The selfe same doth the Meridian likewise in the Hemisphere: And therefore haue you here the Equator, Horizon, Moueable Meridian, and that of Altitudes, all these halfe in steade of whole Circles. As for the Zodiake, it is not heere wanting: for sith all great Circles, and so their medie­ties are equall the one vnto the other, the halfe Hori­zon here, may well be vsed for the halfe Zodiake, when the Equator is placed according to the greatest decli­nation: or contrariwise the Horizon to be the Equino­ctiall, the Semiequator shall be the halfe Zodiake. Thus haue you the Zodiake both wayes: that I say nothing of the little one in the limbe of the Moueable Meridian. For the two Colures there, serues the two Meridians here: the fixed for the Sostitiall, the Moueable for the Equinoctiall. The little Circle for the houres there, is here the Equator it selfe, and so it is also in effect in the Globe. The Index there, is the Moueable Meridian here, and so must you likewise vnderstand it in the Globe. Of the Axis and Poles you haue heard ynough before. To conclude, here is presented to your viewe a Halfe-sphere in name and shewe, but a whole or entire Sphere in deede & practise. For proofe whereof (omit­ting many other) I referre you to these fewe Proposi­tions ensuing. Onely by the way, in the behalfe of the Instrument I am to request the Reader, that he be cir­cumspect to foresee that the Circles and Semicircles be perfect in any case and truely diuided, that they be exactly placed vpon their right Centre, that the han­ging of the instrument be exquisite, hauing the Hori­zon thereof parallele to the great Horizon of the world. Finally that all things be accomplished accordingly, as aboue by the Patterne is signified, before hee pro­ceede [Page] to any experimentall handling of it: least other­wise the worke be vniustly blamed for the errors and imperfections of the workeman: let (as reason would) the fault there lie, where the fault is.

To finde the place of the Sunne.

THe day being giuen, the Place, that is,Cap. 5. the signe and degree of the Zodiake, wherein the Sunne is, may thus bee found. Seeke in the vttermost Circle described vpon the Deferent the Mo­neth and day giuen; whereupon if you place the linea fiduciae, or leuell line of the Ruler, the same shall in the lower or inner Circle thereof being the Zodiake, shew you the thing sought for: And the opposite point thereof shalbe the Sunnes Nadyr for that day. But if the yeere be leape, wherein the place of the Sunne is de­maunded; then must you from the 24. of Februarie, till the ende of that yeere, adde alwayes one moe to the number of that day which you seeke for: as if the day required be the 2. of March, set the Ruler at the 3. if the 3. then at the 4. and so foorth.

The place of the Sunne, being giuen to finde his Declination.

FOr as much as all the Declinations ofCap. 6. the whole Zodiak may exactly be con­sidered in one onely Quadrant thereof, thus briefly shall you worke by the He­misphere. Let the Horizon be in steade of the Zodiake: Then number in the fixed Meridian (which [Page] now must be taken for the Solstitiall Colure) the Sunnes greatest Declination, & thereat fasten the Equinoctial: So shal the pinne, whereupō the two Semicircles cut one an other, be the beginnings of Aries and Libra, and the point of the Horizons meeting with the fixed Meridian, the beginnings of Cancer and Capricorne: Betweene which two extreames, the space of euery 30. degrees in the Horizon of the Instrument shall be as a whole signe in the Zodiake, to bee reckoned in order thus. From the pinne to 60. is Aries, from thence to 30. Taurus, from thence to the fixed Meridian Gemini: Then backe againe from the Meridian to 30. Cancer, from thence to 60. Leo, from thence to 90. being in the Intersection, Virgo. The selfe same order must be vsed in the other halfe of the Zodiake: For the reason is like in both. Hauing therefore found the true place of the Sunne in the Horizon of the Instrument (nowe the Zodiake) turne the Moueable Meridian, till it ex­actly agree therewith: so shall the degrees thereof in­tercepted betweene the Equinoctiall and the Horizon, (nowe the Zodiake) shewe the declination demaun­ded. Or supposing the Equator of the Instrument to be as the Zodiake, and the Horizon as the Equator, you may after the same maner also finde the same declina­tion in the Semicircle of Altitudes. Or finally, if you set the Ruler on the place of the Sunne founde in the little Zodiake of the Moueable Meridian, his ende in the vttermost limbe or border of that Semicircle shall point out vnto you the true declination.

The Longitude and Latitude of any Starre being giuen to finde his Declination.

LEt the Horizon of the Hemisphere be asCap. 7. the Equator of the World; and the E­quator of the Hemisphere as the Zodiake, by seperating the one from the other, according to the Angle of the Sunnes greatest declination: so shall the Zenith of the Instru­ment be as the Pole of the World, and the Semicircle of Altitudes, fitte to expresse any declination. Againe, the Pole of the Instrument shalbe in stead of the Pole of the Zodiake; and the moueable Meridian shall truely represent any Semicircle of Longitude. Wherefore sup­posing in the Instrument the one Quadrant of the E­quator (nowe the Zodiake) from the pinne to the fixed Meridian or Solstitiall Colure vpward, and so downe a­gaine, to be the Northerne halfe of the Zodiake, con­teyning ♈·♉·♊·♋·♌·♍· And the other Quadrant there­of from the pinne to the same Meridian or Colure downeward, and so vp againe, to be the Southerne halfe comprehending ♎·♏·♐·♑·♒·♓· in this sort haue you by the continuall addition of 30. according to the number of the Signes, the whole Zodiake giuen withall his degrees of Longitude. So that first seeke the degree of Longitude supposed: After bring the Semicircle of Longitudes, or the Moueable Meridian to that degree, and in it number the Latitude of the Starre giuen: Lastly apply the Semicircle of Altitudes in such sort, that it may exactly agree with the same Latitude: then shall the Arke thereof comprehended betweene that [Page] point of Latitude and the Horizon of the Instrument (nowe the Equator) precisely shewe the degrees of de­clination of the Starre in that point.

The Declination of Sunne or Starre, being giuen to finde the height of the Pole or Latitude.

THe Latitude by Sunne or Starre to beCap. 8. found, is either when they are in the Ho­rizon of the World, or aboue: And if a­boue, either in the Meridian, or without. When the Sunne or Starre is in the Meridian, take by some Instrument the precise height of them: After, place the Moueable Meridian in the He­misphere parallele with the fixed Meridian, toward ei­ther the South or North there, according as the height obserued was in the Meridian of the Worlde: And close vnto the Moueable Meridian ioyne the Semi­circle of Altitudes: Then seeke the point of Declination giuen, in the Moueable Meridian, and rayse the same so many degrees in the Semicircle of Altitudes aboue the Horizon of the Hemisphere, as the height obserued was aboue the Horizon of the World. So shall the Pole of the Hemisphere haue one and the same Eleuation with the Pole of the world in the place supposed. But when either Sunne or Starre is in the Horizon rising or set­ting, in steade of obseruing the height before, nowe onely take the distance thereof from the true point of East or West: This done, remembring that the pinne whereupon the Equator cutteth the Horizon in the He­misphere, standeth for those points of East and West, [Page] turne the Moueable Meridian to or fro, and the Deferent with the Pole therein vp or downe, till the Declination of Sunne or Starre noted in the Moueable Meridian, doe exactly agree with the Horizon, at such a distance from the Pinne aforesaid, as by your obseruation the Sunne or Starre did differ from the true East or West. Then shall the Pole of the Hemisphere shewe you the Latitude. Lastly if the Sunne or starre be eleuated be­tweene the Meridian and the Horizon, then shall you neede both the former obseruatiōs, the one of height, the other of distance from East or West, that is, in what Azimuth the sunne or starre is, or as the seaman termeth it, vpon what point or part of the Compasse: which with a fit Instrument is easie to be perfourmed. And for that the Semicircle of Altitudes expresseth any Azimuth, set that in respect of the Pinne before men­tioned, according to the distance obserued from East or West; And in the selfesame semicircle also marke the height obserued: whereunto hauing brought the Declination in the Moueable Meridian, you shall euer finde the Pole in the Hemisphere of equall Eleuation with that of the World.

The Latitude being giuen, and the Declination, to finde very readily by the Sunne beame without any helpe of the Magneticall Needle, the houre of the day, the height of the Sunne, and the true point of the Compas whereon the Sunne then is.

FOr the perfourming of this Probleme,Cap. 9. rayse the Pole of the Hemisphere agree­able to the Latitude or Eleuation giuen: and place the Ruler in the litle zodiake, vpon the degree of the sunnes Decli­nation: [Page] Then moue the Moueable Meridian higher or lower, that is, neerer or farther from the fixed Meri­dian, till the Sunne beame pearceth through both the sights of the Ruler: So shall the middle edge of the Moueable Meridian shewe you in the Semi-equator the the iust houre Antemeridian aboue, or Pomeridian vn­derneath it. And if beyond the full houre, it falleth vp­on any of the 15. degrees betweene, multiplie those odde degrees by 4. and the product thereof shall be horary minutes. Afterwards the partes of the Instru­ment standing still without any alteration, apply the Semicircle of Altitudes to the point of Declination, then shall the portion thereof conteyned betweene that Point and the Horizon, discouer the true height of the Sunne for that time. And withall the selfe same Semi­circle of Altitudes in the Horizon, shall exactly declare vpon what point of the Compasse the Sunne then is: And in the Equator it shall further shewe vpon what point of the Compasse the Sunne truely is in respect of the Parallele of his dayly Reuolution.

The Latitude and Declination being giuen, and the Height taken by any other In­strument, to finde the residue before specified any time of the Day.

SVpposing the Pole at his due Eleuati­onCap. 10. in the Hemisphere, and the Sunne vp­on his point of Declination there, turne the moueable Meridian and the Semicir­cle of Altitudes to and fro, till the height obserued in this, doe precisely agree with the point of [Page] Declination in that: Foorthwith in the Semi-equator the Moueable Meridian telleth you the houre, and the Se­micircle of Altitudes in the Horizon, makes manifest the true Point of the Compasse.

The Latitude being giuen together with the Height of any fixed Starre of knowen Declination, to performe all the former any time of the Night.

OBserue first the height of the Starre a­boueCap. 11. the Horizon of the World, and on what side of the Meridian it is, whether East or West. Set then the Equator in the Hemisphere, according to the Lati­tude giuen: And hauing marked in the Moueable Meri­dian the Declination of the starre, whose height you found, moue that Semicircle with the point of the stars Declination, till in a correspondent Quarter of the Hemisphere, to that which it possesseth in the Heauens, the starre obteine his precise equall height from the Horizon: which is soone measured (as before we decla­red) by turning the Moueable Meridian and the Semi­circle of Altitudes to and fro, til both cut eache other in the point of Declination. That portion of the Semicir­cle of Altitudes, comprehended betweene their Inter­section and the Horizon is the starres height: And im­mediatly therewithal appeares vpon what point of the Compasse the starre is: Also in the Semi-equator the moueable Meridian shewes you the starres houre. How­beit, because all distinction of time proceedeth origi­nally from the Sunne, that is not the true houre of the [Page] Night sought for; but an other must be found by the distance of the starre from the Sunne: And for this purpose serueth the Zodiake or Circle of right Ascen­sions described in the Deferent. Seeke therefore there­in the place of your starre (if it be of the number of those that are there set downe) otherwise the degree of your starres Coeli-mediation; which by the helpe of the Ruler, make perfectly to agree with the houre of the starre, now to be reckoned in the Circle of houres in the fixed Meridian: Finally, keeping the said Circle of right Ascensions in this sort immoueable, looke therein for the place or degree of the Sunne for that Day, and thither mooue the Ruler till it lie directly thereon: Then shall the end of the Ruler in the Circle of houres vpon the fixed Meridian, shewe you the true houre of the Night required.

The Latitude being giuen, and the Declination of eyther Sunne or Starre, to finde howe long they appeare aboue the Horizon, and at what Point they rise or set: also the Amplitude Orientall.

SEt the Equator of the Hemisphere accor­dingCap. 12. to the Latitude giuen, and apply the degree of Declination to the Horizon: Afterwards, the Instrument thus stan­ding, note vpon what houre, or part of time the Moueable Meridian falleth in the Equinoctiall: For that shalbe the precise time of rising, to be nūbred in the houres aboue; or of setting, in those vnder­neath: And the Arke of the Equator, conteyned be­tweene [Page] the Moueable and fixed Meridian, being dou­bled, declareth howe long either sunne or starre conti­nueth aboue the Horizon. Now touching the Point of the Compasse, it doth presently offer it selfe, to be seene in the vtter margen of the Horizon, ouer-right against the point of Rising or setting aforesaid. From which point to the Pinne (being in steade of the true East or West) the degrees conteyned in the Horizon, repre­sent vnto you the Amplitude Orientall or Occidentall.

By the Sunne-beame to drawe redily the Meridian line, and to finde the Variation of the Compasse.

FOr more speedie and certaine operati­onCap. 13. herein, if the Sunne be in the East halfe of the world, turne the face of the Hemisphere Eastward; if in the West halfe, then Westward; altering a little the situation of the Pole, and consequently of the E­quinoctiall, that the Pole and semicircles of the Instru­ment, may agree and be equidistant vnto those of like denomination in the Heauens. Then hold it perpen­dicularly vpon or ouer any flatte and smooth superfi­cies, lying parallele or euen with the Horizon of the world: and that directly toward the Sunne, that the beame thereof passing through both the sights, may shewe the exact minute of time. Nowe sith the fixed Meridian of the Hemisphere is in the Meridian of the world, the foote of the Hemispheres said Meridian must needes be so likewise. Drawe therefore either by dire­ction of the foote it selfe, or of the shadowe of it, a [Page] straight line, and produce it in length as you thinke expedient. This shall be the Meridian line required, with his two extreames pointing out the true South and North: whereunto if you drawe a perpendicular crossing it, that shall be the Line of the true East and West. The variation is thus knowen: when the houre is found (as immediatly before you haue heard) at that instant turne your eye aside toward the Backe of the Instrument, and marke what Angle the Needle of the Compas maketh with the line of North & South vnderneath it: For this Line being by the structure of the Instrument equidistant to the fixed Meridian of it, is vnderstood to be in the great Meridian of the world▪ as the fixed Meridian is▪ And therefore looke howe much the Needle swarueth from the same Line, so much it declineth from the true Meridian. The quanti­tie of which declining (being nothing else but the Va­riation) is foorthwith made manifest by the degrees of the Circles circumference vnderneath, conteyned be­tweene that Line, and the end of the Needle.

To finde when the Twylight begin­ neth, and howe long it continueth.

THE Sunnes depression vnder the Hori­zon, Cap. 14. may soone be knowen by the man­ner of finding the height thereof aboue: And thereunto belongeth this obser­uation of the Twylight: The beginning whereof in the Morning, and ende in the Euening, is commonly supposed to be, when the Sunne in a Verti­call Circle is by the space of [...] vnder our Ho­rizon. Moue therefore the Moueable Meridian, and the [Page] Semicircle of Altitudes both together towarde the North part of the Horizon (the Pole before being ray­sed accordingly) till the point of the Sunnes declina­tion and the end of 18. degrees, being reckoned from the Horison downeward in the Semicircle of Altitudes, doe meete ioyntly in one: And straightway note what houre the Moueable Meridian lighteth on in the Equa­tor: for that is the time when the Twylight beginneth in the Morning, if you looke on the vpper side of the Equator, and endeth at night, if on the nether side: A­gaine turne the Moueable Meridian with the declinati­on or place of the Sunne in it, till it be iust in the Hori­zon, and foorthwith see what houre it sheweth in the Equator: That segment of the Equator which is com­prehended betweene this point of time and the for­mer, declares the quantitie or continuance of the Twylight.

The true measuring of any distance vpon the Globe of the Earth.

THe Geographicall measuring of migh­tieCap. 15. Distances vpon the Globe of the Earth, is a thing not onely of maruei­lous pleasure for knowledge, but of singuler commoditie for practise, ser­uing to many excellent purposes both bysea and land. And although the Computation Arithmeticall, vsed herein by the learned, & grounded vpon the doctrine of Sphericall Triangles, is absolute and exquisite, yet is the deducing thereof (especially when Places differ in Longitude and Latitude) not voide of great obscu­ritie; and the operation, both by reason of so many [Page] multiplications, diuisions, yea and extractions of rootes, exceeding tedious; and for the slipperie mista­king or omitting now and then of but one poore little figure (which may soone fall out) somewhat doubtfull and hazardous. In regardwherof the Globe hath euer, not without due desert, beene admired as a principall necessarie Instrument for the readinesse, certainetie, and eminent perspicuitie of demonstration. In which very respects, present triall shall prooue this Instru­ment, the Hemisphere, to be nothing inferiour to the Globe it selfe. But to come to the purpose, because that vpon the Globe of the Earth, the true distance of one place from an other must bee measured by the shortest line that may be drawen from this vnto that; and the shortest of all other that there possibly can be described, is alwayes the portion of a great Circle; Therefore by it, and by none other, all exact Geogra­phicall mensuration ought to be made. Againe, sithe the Hemisphere consisteth of nothing else but great Circles, being diuided all of them into their degrees, and moueable in such sort, that any maner situation may precisely by them be represented, no doubt can remaine of the sufficiencie of this Instrument for the perfect perfourming of this Proposition.

The diuersities of situation of one place in respect of an other, are three in generall: For either haue they one and the same Meridian, though not one Parallele; and these are from the West and East of equall di­stance, but vnequall from the Equator, and differ there­fore onely in Latitude: or els haue one Parallele, and a diuerse Meridian, and these are of vnequall distance from West and East, but equall from the Equator, dif­fering only in Longitude: or finally haue a diuerse both [Page] Meridian & Parallele, and therefore differ accordingly both in Longitude and Latitude. Places of the first situa­tion are most easily measured without any Instrument at all. For the two seuerall Latitudes of either being gi­uen, whereof alwayes the one must needes be greater, the other lesse; subtrahe this from that, and the remain­der shall be the distance betweene both places in the degrees of a great Circle: which, according to the common supposition of 60. miles English answerable to one degree, may soone be conuerted into myles.

Distances of the second sort, such I meane as are vnder any Parallele without the Equator (for there the operation is all one with the former, because it is a great Circle like the Meridian) are not altogether of the readiest to be found by other wayes, but most easie and ready with helpe of the Hemisphere. For the doing whereof, you are to suppose the fixed Meridian of the Instrument, to be the Meridian also of either of the two places, whose distance you seeke: Likewise the Zenith of the Instrument to be the Zenith of the same place, or rather that very place in deede. Then bring the E­quator of the Instrument, and set it at such a distance from the Zenith aforesaide, as doth exactly agree with the Latitude of your first place: So shall the Pole haue his true situation in respect of the sa de former place; And the Moueable Meridian issuing from it, shalbe in power any Meridian, that can be drawen from the one Pole of the world to the other, according to any Lon­gitude in the Equator assigned. Number therefore from the fixed Meridian in the Semi-equator, (remaining, as before it was placed immoueable) the difference of Longitude betweene both places, and at the end there­of fasten the Moueable Meridian: This then shall be the [Page] Meridian of the second place: In which reckoning from the Equator toward the Pole the Latitude knowē, you shall take the extreame point thereof for the true Zenith of the second place. Last of all moue the semi­circle of Altitudes (nowe it may be called of Mensura­tions, being in power any great Circle that may bee drawen from Zenith to Zenith) till in the Moueable Me­ridian it precisely lighteth vpon the Zenith of the se­cond place. The degrees of this portion of that semi­circle conteyned betweene the two Zenithes, is the ex­act distance sought for. Here it is to be obserued, that if the places be separated one frō an other, not by the segment of a Parallele, but by the one halfe thereof, then are both their Zenithes in one Meridian, and the Pole in the middle: so that the space betweene both zenithes, and the Pole being doubled, shall yeelde the distance demanded. And this is the greatest direct di­stance that can be of places vnder one Parallele.

It remaineth, that we speake of the third sort of pla­ces, differing both in Longitude & Latitude. The finding of whose distance is a matter intricate and laborious o­therwise, and yet often, yea most cōmonly occurring: which if by the Hemisphere, with all demōstratiue cer­taintie, it shalbe no more hard to finde, nor lesse ready to followe, then the wide beaten high way, my good hope is, that the better opinion wilbe conceaued of so faithfull a guide. To be plaine therefore and short: He that knoweth the former kind of operation, cannot be ignorant of this, being both one in effect. For setting the Semi-equator so farre frō the zenith of the Instrumēt vpon the fixed Meridian, as is the Latitude of one of the places; And fastening the Moueable Meridian, so farre likewise from the fixed vpon the Equator, as is the Diffe­rence [Page] of Longitude betweene both places (which is soone knowen by abating the lesse Longitude out of the greater:) Afterward, when in the Moueable Meri­dian, aboue, beneath, or iust in the Equator (if it so hap­pen) the zenith of the other place is truely noted ac­cording to the Latitude thereof, apply thereunto the Semi-circle of Altitudes, or Mensurations: And his por­tion comprehended betweene both zenithes, shall in the partes of a great Circle, make manifest the exact distance required.

Moreouer, if you desire to knowe howe the one of those places beareth from the other: The Semicircle of Mensurations still remaining, as before it was situated for finding the distance, obserue in the Horison vpon what point of the Compasse it falleth: for that sheweth the true bearing of the places proposed the one from the other.

The Longitude and Latitude of any two Starres being knowen without any other Obseruation to finde the Distance of the one from the other in the Heauens.

THat which hitherto hath beene spo­kenCap. 16. for the finding of Distances be­tweene place & place vpon the out­face of the Globe of the Earth be­neath, may serue aswell for obseruing of them betweene Starre and Starre in the Sphere of the Heauens aboue; with the Longi­tude and Latitude here to be giuen in respect of the zo­diake, like as there it was and is alwayes to be conside­red in regard of the Equator. And albeit I knowe it [Page] would haue beene more agreeable with the suite of our discourse to haue handled this matter before, yet considering the neere affinitie, or rather identitie and selfesamenes of these two operations, I thought it best to ioyne them close together. Suppose therefore the E­quator of the Hemisphere to be the zodiake, then shall the Pole thereof be the Pole of the zodiake: The fixed Meridian shall be one Circle of Longitudes, and the Moueable Meridian any other of the same sort: And euery degree of the Moueable Meridian, shalbe the In­tersection of any Parallele defining the Latitude either Septentrionall or Austrine, and therefore the place of one of the Starres proposed: The other starre shall be in the zenith of the Instrument: And finally (as before) the Semicircle of Altitudes shall serue for Mensurations. Nowe then according to the Latitude of one of the starres (which for distinctions sake I call the first) re­moue the Equator (now the zodiake) from the zenith of the Instrument (now that first starre) And the zodiake thus standing immoueable, number therein from the fixed Meridian, the degrees of the differēce of Lōgitude, and at the end thereof fasten the Moueable Meridian: In which Semicircle beginning frō the Zodiak, reckon the Latitude of the second starre either vpward or downe­ward, as it is either Septentrionall or Austrine: And vnto the ende thereof, being the true place of that second starre, fitte the Semicircle of Mensurations aforesaid: So shall that portion of it, which is intercepted be­tweene both points, be the precise distance in the hea­uens betweene the two starres demaunded.

And of the Hemisphere thus much. Hereunto mightCap. 17. I haue added the doctrine of right and oblique Ascen­sions, together with Dialling and other matters Gnomo­nicall: [Page] But because the fruite and vse of the doctrine of Ascensions cōsisteth in the measuring of the true quan­titie of time, whereof you haue before sufficiently heard; I thought it not expedient any further to en­large this Treatise therewith: The rather, considering my principal purpose, namely the Seamans Commo­ditie; who little needeth that doctrine: and Dialling lesse then that. Yet whoso desireth to be doing in both of them, shall by that which hitherto hath beene deli­uered & diligent practise withall, finde the Hemisphere very able to satisfie his desire. And not onely so, but to minister vnto him many rare and goodly conclusions of further inuention. Among which I earnestly wish that chiefe secret of Nauigation, the sayling, I meane, by a great Circle, to be alwayes principally remem­bred: Not doubting, but this Instrument (if any other) will proue a most apt and seruiceable one for that pur­pose: which knowledge, because it requireth long, learned, and very painefull experience, ioyned with singular dexteritie, I willingly leaue vnto those that make speciall profession of that Art.

The description and vse of a Trauerse Boord, seruing readily to set downe the Shippes way, according to the vsuall accompt, and at all times to pricke in the Card accordingly, the true place that she commeth vnto.

LEt there be a Table prepared after theCap. 1. forme of a long square, of 16. inches in length, and 12. in breadth, or else 20. long, and 16. broade, (as you thinke good, more or lesse) plaine and smooth, [Page] with Angles precisely right; and hauing a square bor­der inclosing it to keepe downe a sheete of Paper, like as Surueying tables haue. Diuide the foure sides of the border into equall diuisions of 8. vnto an ynche, or a­ny other, (as may be most conuenient) reaching all a long the inner side of the square, and number them by fiues, the figures of euery side being twise set downe to be reckoned both wayes (as occasion shall serue.) Againe, subdiuide euery of those diuisions by two prickes into 3. partes, not adding any numbers. If these diuisions be wrought vpon Latten plates being laide on & riuetted to the Border, it wilbe a great deale the fairer. Your Table thus finished, you must prouide a Ruler and a Quadrant, as necessarie furniture belon­ging thereunto. Let the Ruler be as long as the Diago­niall line of your square, that is, reaching athwart frō corner to corner, hauing the oneside handsomely a­bated, and both sides perfectly diuided from within halfe an ynch of one ende throughout, into the very same diuisiōs wherewith the Border was parted, with his numbers also redoubled and (as that) both wayes to bee accompted in such sort, that the diuisions bee drawen downe to the lowermost edge of the sides of the Ruler, that lieth close on the Table.

The Quadrant is best of Latten, with his semidia­meter of 3. or 4. ynches (more or lesse) somewhat thinne, hauing al the middle of his substance cut away, saue about a quarter of an ynch breadth reserued for his Circular limbe, & there about also for the breadth of his two right sides. Diuide the limbe into ordina­rie points of the Compasse, expressing them in siphers 1. 2. 3. &c. Let those numbers be twise set downe to be reckoned forward & backward, and betweene euery [Page] Point let there be halfes and quarters. All which parts (as before in the Ruler) must be produced to the nea­thermost edge of the limbe. Diuide also the two out­sides of the Quadrant into such diuisions as the Ruler hath, so farre as they will reach, placing the numbers along from the Center-corner, to the meeting of the sides with the limbe, and drawing those diuisions like­wise to the lowermost edge of the sides.

Nowe must you consider, that the Nauigator hath three helpes to finde out the place of his Ship, that he may set downe the pricke thereof vpon his Carde, viz.

  • 1. The Angle, on which the Ship maketh her way: which is giuen by the Compasse.
  • 2. The quantitie of the Ships way, to wit, howe many leagues she sayleth in an houre, or a watche: which they terme the dead recko­ning, and is learned by often experience.
  • 3. The Latitude, taken by obseruation with Mathematicall Instruments.

Any two of these being giuen, this Instrument ma­keth the third manifest, and giueth the pricke in the Carde very readily. Except it so be, that the Ship doth runne vpon the Points of East or West: for then all three are necessarily required.

You are further here to note, that the place from whence any course is begun, is called a Radicall place: And so is euery place in the proceeding of the voyage named, whereof the Nauigator either by his owne, or by other mens practise, hath learned the true situation. And nowe to approch vnto the vse, spread a sheete of large papervpō the Table, fastening it with the Border [Page] placed thereon, to keepe it euen and smoothe: And set a Flower de luce, or any other note, for the North, hard by the edge of any one of the sides (which your course shall shewe to be most conuenient) about the middle thereof. That one marke is sufficient to determine all the other sides, towards which of the 4. principall windes they doe beare: for his opposite must needes be South, and the other two East and West. So that the diuisions in the sides of East and West, doe al of them in power represent so many Paralleles: and those of North and South in like maner so many Meridians.

The vse of the Trauerse Boorde.

FIrst of all marke by the viewe of yourCap. 2 Notes of the Ships way & course, whe­ther it be Northerly or Southerly from the Radicall place, and likewise whether Eastwards or Westwards: and accor­ding to discretion set your Flower de luce, as may best fitte the way of your course. And therefore if it be most South or North, let the longer sides of your Table stand in steade of those partes: if it be East or West, then name the sides accordingly. For example, if it be Eastwards Northerly, set downe a pricke betokening your Radicall place vpon the West end of the South side: if it be any other way, set downe your pricke as may be answerable thereunto: and placing your Ruler square vpon equal diuisions in the sides East & West, with the edge thereof touching the said Pricke, drawe a line representing the Parallele of the Ships Radicall place, and hard by the point or pricke of your Radicall [Page] place, note the Latitude there of in degrees and mi­nutes: Then set the Center corner of your Quadrant vnto the Radicall point, eleuating the limbe of the Quadrant aboue the Parallele, according to the quan­titie of that Angle, whereon the Ship made her first way, and reckoning in the edge of the Quadrant the leagues of the Ships way, at the ende thereof make a pricke as close vnto the edge as may be. Lastly faste­ning your Ruler directly vpon the pricke, and square with the sides of East and West, drawe a line, which shal serue for the Parallele that the Ship at that instant is in. And this order of working must from time to time be iterated, till at length opportunitie be offered by your Instruments Mathematicall to make an ob­seruation of Latitude. But if it so fall out, that the Shippes way doe conteyne moe leagues, then there are diuisions in the side of the Quadrant, then apply­ing either side of the Ruler close vnto the edge of the Quadrant, by that meanes you may pricke downe the number. Hauing vpon shift of windes (as it happe­neth) made diuerse Trauerses, if you desire to knowe howe the place your Ship is in beareth from your Ra­dicall place (which is called the Angle of position) and likewise the distance from it, as also the Latitude, together with the Difference of Longitude (when you haue made as yet no obseruation) doe after this sort. Set the one end of your Ruler where the numbers doe beginne to the Radicall point, and directing the other end towards the pricke of your Ships last place, cause the edge to lie iust & euen vpon it: Then reckon howe many diuisions you do finde betweene the two points, and so many leagues distance there is. If it fall not full vpon a diuision, but vpō one of those pricks betweene, [Page] they signifie English miles. Looke howe many diuisi­ons are conteyned betweene the two Paralleles, the one of the ships Radicall place, and the other of her last place, euery twentie of those doe make a degree; euery seuerall diuision, 3. minutes; and euery pricke one minute. Moreouer as occasion serueth, you may accompt 4. or 5. diuisions for a league, or more, or lesse: yea euery pricke for a league, if you finde it requisite, as experience in diuers shiftes of windes will shewe you to be most conuenient.

To knowe howe much the Ships last place doeth differ from his Radicall place in Longitude: also the Angle of Position.

SEt the Ruler square North and South,Cap. 3. so that the Radicall place may touche the side thereof, marking what diuisi­ons the Ruler doeth cut in the North and Southsides. Againe, set the Ruler in like maner square, touching the point of the Ships last place: the number of partes conteyned betweene those two places of the Ruler in either of the two sides North or South, is the difference of Longitude. If the ships last place from the Radicall be Easterly, the Lon­gitude is so much encreased: if Westerly, it is lessened. Alwayes haue you respect to the Meridian, from whence Longitudes doe beginne to be reckoned, that you may expresse the number answerable thereunto. Moreouer place your Ruler where the numbers begin, at the Radicall point, and the side thereof vpon the point of the Ships last place: Then apply the Center [Page] corner of the Quadrant vnto the Radicall point (the Ruler still keeping his place) in such sort, that the side of the Quadrant doe lie euen with the Ruler: Looke howe much of the eleuated limbe aboue the Parallele, the Parallele it selfe cutteth off, that is the Angle of Position vpon which the last place of the Ship doeth beare from the Radicall places. But whenso euer you haue opportunitie to obserue the Latitude, drawe your Parallele vpon the Trauerse boorde according there­unto: and where the line of the Ships course doeth crosse the Parallele, you must conclude that to be the place which your ship was in at the time of your obser­uation, correcting by that meanes the other Parallele and distāce taken by the dead reckoning, so farre forth as it doth differ from this. For of those three helpes be­fore specified, the Latitude is only certaine: The Angle of the Ships way is reasonable good: but the dead rec­koning is an vncertaine ghesse; And if you please to call it a probable coniecture, you shal grace it with the vttermost: notwithstanding it is admitted into Art for want of better helpes.

In considering the Angle of the Ships way, by all meanes you must haue carefull regard both vnto the Set, and the Variation of your Compasse. Otherwise, assure your selfe, you shall make but wide reckonings. I haue knowen a very expert Nauigator, that making his reckoning without regard of the Variation (which for all that he obserued, though he did not reckon by it) ouershot the way of his Ship 70. leagues, in a voy­age not of so farre distance as hence to Cape Verde. Whereas casting ouer his reckoning with due respect of his Variation, he made a perfect good accompt of of the very same voyage.

Hauing found the place of your Ship in the Trauerse-boorde, howe to pricke it in your Carde.

FOr the conclusions to be performed vp­onCap. 4. your Carde, it is requisite, that you haue a Ruler of some fine wood made very thinne, of an inche & a halfe broad, and of sufficient length: also a Quadrant like vnto the former, sauing that his two sides must haue their diuisions agreeable to the Scale of leagues expressed in your Carde: and finally 2. paire of Com­passes. Being furnished with these, seeke out your Ra­dicall place from whence you did proceede: Apply the Cēter-corner of your Quadrant vnto it, his limbe, respecting the way answerable to the Angle of positi­on in your Trauerse-boorde. Set one foote of your Compasse vpon any Parallele of conuenient distance from it (on which side it skilleth not) reaching the o­ther precisely vnto it in the nearest distance. Then re­moue one foote vpon that Parallele, the other keeping his scantling, vntill the diuision of the Angle of Po­sition in the limbe, & the point of the other foote doe meete exactly together, the Center-corner stil abiding in his place, but mouing the limbe to or fro, and like­wise the Compas (as before I specified) til they meete. Last of all, reckon from the Center-corner your ob­serued number of leagues vpon the side of the Qua­drant, & there set downe a pricke or note for the place of your Ship. So shal the Radicall angle of Position be limitted by the other foote of the Compasse in the limbe; & the quantitie of the way that the Ship hath made, by that pricke in the side of the Quadrant.

Though you haue not any Quadrant with his sides diuided according to your Carde, but onely that which you vsed for the Trauerse Boorde, and also the same Ruler: howe to performe all this with the helpe of two paire of Compasses.

SEarche in the Carde your Radical placeCap. 5. from whence you did proceede, and ap­ply the Center-corner of your Qua­drant vnto it, the limbe thereof respe­cting the way answerable to the Angle of Position in your Trauerse-boord: After this, with the one paire of your Compasses take the shortest di­stance from your Radicall place to some one Parallele or other, as you may conueniently: and with the other paire, take the distance in leagues, according to the Scale of the Carde. Remooue the limbe (the Center corner keeping his place) to & fro, and also the Com­passe (keeping still his scantling) with the one foote a long the Parallele, till the other foote, and the diuision agreeable to the foresaid Angle, doe meete together. The Quadrant remaining in that place, let your other Compasses (being extended according to the number of leagues found out by your Trauerse-boorde, but answerable to the quantities of them which are de­scribed in the Scale of your Carde) haue one foote set vpon the Radicall place, the other along the side of your Quadrant, marking it with a pricke or some other note, for the place of your Ship. And after this maner may you finde howe any one place in your Carde doeth beare from any other, hauing regard vnto that which hath bin before declared.

Being in a Ship at Sea, to knowe any places in your Carde (that are within your kenning) how farre they are from you.

SEt any two of them by your Compasse,Cap. 6. (so that they be not in one right line) and obserue according to what Angle of Position they doe beare from you; thereby collecting howe you also beare from them. Then place your Quadrant vpon one of them, agreable to his Angle (as before hath beene taught) and lay a Ruler to the side of the Quadrant that pointeth out the Angle. That Ruler so remaining, remoue the Quadrant vnto the other place, giuing it the quantitie of that Angle: and placing a Ruler like­wise close vnto the side of the Quadrant which poin­teth out the Angle, thrust this Ruler directly forward along that side of the Quadrant, till his corner doeth touche the edge of the other Ruler: where the touche is, set downe a marke, signifying the place of the Ship. And then measure by the Scale of your Carde, howe farre that marke is from either of those places: so haue you the distance desired.

All these Conclusions of the Trauerse▪boord may be performed (with a little more paines) by the helpe of the afore mentioned Quadrant and Ruler vpon a faire sheete of large paper, hauing only a plaine Square consisting of foure straight lines meeting at right An­gles, without any diuisions at all: for all the diuisions aboue mentioned, the Ruler applied to those lines will presently supply. And when your operation groweth so large, that it surpasseth any side of the Square, you [Page] may easily paste on the Square of an other sheete of paper, and so ioyne both squares together, that your line of the second become all one with that of the first. And thus may your worke be continued for the tra­cing out of any whole voyage, not omitting any Tra­uerse, and noting (if you thinke good) whatsoeuer ac­cident you shall iudge to be needefull. It is conueni­ent to haue two of those Quadrants, the one of 5. or 6. ynches semidiameter, and the other scarce halfe so large: The greater for the Trauerse-boord will be the more commodious, and the other for the Carde.

Howe to describe the Spirall line of a Shippes course.

WIth a quadrant of this fashion it is a veryCap. 7. easie matter to describe the spirall line of a shippes course, from any knowen Longitude and Latitude, after this sort. The Meridians and Paralleles first suppo­sed to be drawen as the spirall Carde requireth, set the Center-corner of your Quadrant vpon that point where the Meridian and Parallele of the place, from whence you first departed, doe crosse one an other: And directing the side of your Quadrant along the Meridian, either Northward or Southward (as the case shall demaund) note in the Meridian next adioyning, where the Angle of the Shippes way cutteth it: And there making a small pricke, trace a line from the for­mer point vnto this. Againe place the Center-corner (as before) on that second pricke, and marke the In­tersection in the third Meridian, continually procee­ding [Page] after this maner, from Meridian to Meridian, till you haue finished the whole course. The thicker your Meridians are drawen, the more perfect will your Card be: but this may be also supplied, with a thinne Ruler moueable vpon the Pole or Center of your Carde. The maner of the draught of the Spirall Carde, I will shewe in the next Treatise.

A friendly Aduertisement to the Nauigators of England.

THe dueties of a Friend, and the pro­perties of a Flatterer doe differ so greatly, that a man cannot performe the office of the one, but he must re­nounce the practise of the other. And a very fountaine it is, from whence many mischiefes doe spring, and ouerflowe the wret­ched life of mankinde: That the true dealing of friends is most commonly vnpleasant and hatefull, but the soothing of Flatterers is become plausible and much set by. In resemblances they beare many times like shewe, but in purposes they doe alwayes differ. A true Friend will sometimes commend and prayse diuers things in his friend: And so also will the Flatterer in those whom he flattereth: The one commendeth that which in iudgement he thinketh commendable, and vnto that ende that the partie commended should still proceede in actions worthy of commendation: The other commendeth euen those things many times, which in iudgement he doth detest, and vnto that end, that hee may sooth vp the humour of the partie, and make his owne profite thereby. Moreouer, a Friend [Page] will dispraise in his friend those things which in iudge­ment he doth disallow; and the greater the faultes are, the more earnest will he be: to the end that the partie may amend and giue no aduantage to his enemie. The Flatterer sometimes (though seeldome) will also dis­commend, but euermore trifing matters, and therein will he be very vehement; but in great faults he is both blinde and dumbe: fearing to offend the partie, if he should touch them; and in the other counterfeiting sincere loue (the badge onely oftrue friendship) And so leaueth he the partie thus abused, to the scorne and reproch of the aduersarie, reaping the commoditie which he looked for, as the onely end of his trauaile.

I doe not thinke there is any man that either regar­deth Gods glory, or esteemeth of humane societie, but holdeth your Arte woorthy to be numbred with the most excellent, that are exercised among men: And therefore is it of very due right, that you the practisers of it, should be had in great reputation. Neither is there any other Arte, wherein God sheweth his diuine power so manifestly, as in yours; permitting vnto you certaine Rules to worke by, and increasing them from time to time, growing stil onwards toward perfection, as the World doth toward his end; And yet reserueth still vnto himselfe the managing of the whole: That when you haue done what you can, according to the skill you already haue, or shall doe, by any that you may learne hereafter: yet alwayes will he make it ma­nifest, that he alone is the Lord of the Seas, that all stormes and tempestes doe but fulfill his will and plea­sure, and that all the waues of the Sea are continually at his commaundement: finally that it is he, who often­times administreth many helpes beyond all expecta­tion, [Page] when the Arte of man vtterly faileth. All which in the CVII. Psalme is so liuely expressed by the Prophet Dauid, that in all writers, whether sacred or prophane that euer I read, or by any reports that euer I heard, or in the liueliest pictures that at any time I behelde, it is in my iudgement, pierlesse and vnmatcheable: descri­bing the whole in briefe, and yet in the breuitie omit­ting nothing that was necessarie; and affirming no­thing but that, which the continuall experience of our dayes doth proclaime to be most true. O that Nauiga­tours therefore would prayse the Lord for his mercies, and shewe foorth his wonders before the children of men. That they would once learne that, The feare of the Lord is the beginning of Wisedome. Most vndoubtedly then would their Arte flourish, their voyages prosper and haue better successe: yea themselues would be more estee­med & honoured of all men. Whereas nowe the pro­phane liues and brutish behauiour of diuerse of that trade, doth somewhat eclipse the glorie of the professi­on it selfe: And, besides other manifolde punishments, God striketh them with such blindnesse, as no men li­uing of any trade whatsoeuer are to be found so igno­rant, as many of them are of theirs; so senselesse in their owne defect, or so litle desirous to amend them. Yea, and some of the greatest skill and practise are so loathe to giue God his due glorie, that many times labouring to suppresse it, they make shipwracke of their owne credites and reputations, which otherwise of right might accrewe vnto them. Whē they haue performed along voyage of great difficultie, wherin many a time and oft they haue beene at their wits end, and knewe not which way in the world they should turne them selues, God deliuering them beyond their owne ex­pectations, [Page] as their consciences can witnes: yet when the danger is one past, and that home they be come, they take it as a blemish of their estimations, and great impeachment to their credites, to giue God the praise, and to yeeld him thankes, imagining that would de­rogate too much from the admiration, which they so greedily hunt after among men.

I haue heard a merie report: Shippes of sundry Nations lying in a harbour in faire weather, the yong mariners were climing and shewing feates of actiuitie, one of one Nation to outbragge the other. At length a nimble yoncker getteth him to the very toppe of the Foremast, and raysing himselfe boult vpright, turned round vpon his foote without any staye, chalendging his Antagonist, or any of the Nation to doe the like. His Antagonist presently vndertaketh the chalendge; but hauing turned scarse halfe about, fell downe, and (as God would) in his tumbling by good hap caught hold of the shrowdes: and assoone as euer he had a lit­tle recouered his spirits, being halfe dead for feare, yet set a bould countenance on the matter: and he also a­gaine with a loude voyce dared his aduersarie or any other of that Nation to doe the like; as though that which befell him by his errour, he had done of very purpose. Euen so diuerse that haue perfourmed long voyages, God knoweth how, but not they themselues; yet will sweare and stare, crake & boast, that they haue done all things according vnto Arte: and tell vs of such Gulfes and swift Currents, moe by a great many then euer God made, and are but deuised by themselues for shiftes to shadowe their ignorance, and to robbe God of his prayse: the thing being as strange a matter, and as much according vnto Arte [Page] that euer they came home againe, as that was, which the fellowe before specified wrought his feate by.

Petrus Nonius maketh mention of one in his dayes, that had tenne times passed from Portugall to the East Indies: And yet diuerse times when he shoulde haue subtrahed his declination, did adde it, and when he should haue added, did subtrahe it.

But for you the Nauigatours of England, this I doe verely thinke in my conscience, that diuers of you doe feare God vnfeinedly, and doe as much dislike the dis­solute course of the common sort, as any men can. And I do nothing doubt, although the number of such are too fewe in our Nation, yet are they moe then any Nation in Christendome can shewe besides. And al­beit your skill is not such, but that amendment may become it well ynough: yet doe I not iudge that either the Spaniards or Portugals, who are accompted the best, doe better yours: and for their life and behauiour I take it to be worse then the worst among you, reser­uing still for them, that which Horace long since impu­ted vnto them:

Nauis Hispanae magister,
Dedecorum preciosus emptor.

For notwithstanding their first Nauigatours were men of good skill, these now a dayes for the most part are grossely ignorant: And a great folly it is in diuerse of our Nation to haue such confidence in Portugall Pilottages for long voyages, hauing farre more skil­full of our owne Countreymen at home, both better to be trusted, and more valiant and present minded in any danger. And it is a thing very certaine, that ours doe encrease in skill, and better very much their Aun­cestours, [Page] whereas theirs for the most part are a great deale worse: And if they be once any thing out of their ordinary traded course, they are the seeliest fel­lowes that doe floate vpon the Seas. Their Cardes are decked with much Golde and little Arte, out of mea­sure false (as I haue heard by men of good experience) euen vpon their owne coastes, and are but transcripts newe furbished. Their other Instruments very simple, especially their Staues most contemptibly nought. I haue seene diuerse of them, euen as vnfit for the pur­pose they should serue, as an Oxe is to weare a saddle. But wee are very much addicted to admire strangers, and contemne our owne, according to the olde Pro­uerbe, For soothe it must needes be true; for I haue learned it of a Iewe. Two things therefore there are greatly wi­shed by all your well willers to encrease in you, The true feare of God, and a carefull diligence in things belonging to your Arte. Where the feare of God is not, no Arte can serue the turne: for that were to make of Arte an Idole. And yet all those that feare God, must take heede, that they doe not tempt God: And therefore ought they to vse Arte, as the meanes that God hath ordeyned for their benefite, and be thanke­full vnto him for it.

These Instruments, that, for the assistance of your Arte, it hath pleased God to giue me a small portion of knowledge to compose, whether without paynes and chardges they haue beene finished and brought to this passe, I commit to your iudgements. For mine owne part, I am one that in any priuate respect hath as little to doe with the Sea, as any other; and in perti­culer haue no cause for to hope that I shall reape any maner cōmoditie thereby. And for these my trauailes [Page] and expences, although it should be well accepted ac­cording to my desire among Nauigatours; yet haue I no reason to thinke me one iot to be benefited there­by, no not so much as in any credite (which notwith­standing, if it were one of an other profession, possible he might obtaine.) Nay, if I may escape handsomely from mockes and scornes, vsuall with some Contem­ners of laudable Sciences, I must thinke that I haue made a faire hand. But I thanke God I haue bestowed neither paines nor charges, more then I was willing and might well doe. And if it may by Gods grace prosper to the ende that I haue purposed, that is, to some of your good, little doe I esteeme what euery Idiote doeth thinke or iudge of my labour. I knowe right well, that among the vulgar people, there are many thousands, which going vnto market, doe bring home with them a peniworth or two of Cloaues or Mace nowe and then; and yet neuer asked the questi­on where they grewe, nor by which way they were transported from their Natiue countrey vnto vs, whe­ther by the way of Ormus through Persia, or of Arabia by Carauan vnto Alepo, or by the Red Sea vnto A­lexandria, and thence out of the Leuant vnto vs: or whe­ther they came through the huge Ocean by the Cape of Bona Speransa. They take no knowledge of such mat­ters: The cōsideration of any dangers in the Streights of Cincapura, or of the Showldes of Maldiuar neuer troubleth them: And yet it relisheth euen as well and serueth their vses as commodiously, as if they had all the afore mentioned knowledge. Albeit I hope that men of vnderstanding and wisedome will easiyly per­ceaue, that Gods prouidence in his workes is onely manifest vnto those which doe consider them, and of [Page] others is nothing at all discerned, & as little regarded. If it were onely among the common sort, that Cosmo­graphie should be so contemned, it were the lesse to be meruailed at: but that any which professe learning of any facultie whatsoeuer, should altogether neglect it, and be vtterly ignorant of it, it is to be more then pi­tied, and especially in Gentlemen and Noblemen is it no small defect: who diuerse times in this our age haue some occasion or other, at the least to talke and dis­course thereof. Wherein I coulde wish they woulde haue in remembrance a saying of Apelles vnto Me­gabysus a Nobleman of Persia▪ who comming into his Shop, although his knowledge was but small, yet was he loath to haue it appeare that he was ignorant of a­ny thing; And therefore began to question and dis­pute of lines, of shaddowes, and of such like matters belonging vnto that Arte. But Apelles entreated him to make more spare of his speache: for saieth hee, my youthes which grinde my colours, hearing your idle discourses, doe deride them, which before had you in great admiration for your gallant and glittering attire. If it were a thing possible, that they which are altoge­ther ignorant of Cosmographie, coulde be perswaded howe easie a matter it were to attaine vnto some com­petent knowledge therein, I doe verely thinke, that a­mong those that are of witte and iudgement, some­what more then they of the very vulgar sort, you should not finde one among a thousand, that woulde be ignorant of it, whereas nowe you haue euen scant one among a thousand, that hath any vnderstanding therein. For I am well assured, and doe speake it vp­on some experience, that one but of meane capacitie, so that he be of a willing minde, and haue a sufficient [Page] Instructour, with fitte Instruments, may very easily in one moneths space attaine vnto great contentment of knowledge, yea such, as they commonly imagine, coulde not be learned in seuen yeeres. Nowe as it is seemely for all men to haue at the least some taste in such knowledges, so vnto Nauigators it is necessarie in the highest degree. And I doe nothing doubt, but that any one of them, with a two moneths learning of a skilfull Teacher, and three yeeres practise in a fewe good voyages (God blessing his labours) shall get more perfection in that Arte in so small a space, then he coulde otherwise with twentie yeeres experience, according to the ordinarie ignorant practise. Al­though such Instructours are in number but fewe, yet I thinke there are moe then are greatly employ­ed; and would be many moe, if they were in request, and better esteemed, especially about the Citie of London; whither there is so great repaire and con­course of men addicted vnto those affaires: where pos­sible (though vnknowen vnto me) there may be di­uerse, yet knowe I but one, whose name is Iohn Good­wyn, dwelling in Bucklers-burie: A man vnskilfull in the Lattin tongue, yet hauing proper knowledge in Arithmetike, and Land-measuring, in the vse of the Globe, and sundry other Instruments: And hath ob­teined, partly by his owne industrie, and by reading of English Writers (whereof there are many very good) and partly with conference with learned men, (of which hee is passing desirous) such ready know­ledge and dexteritie of teaching and practising the groundes of those Artes, as (giuing him but his due) I haue not beene acquainted with his like. And great pitie it is that in so populous a place, many such were [Page] not employed: But greater is the griefe vnto diuers well willers of that noble Citie, and louers of good Artes, that where as not many yeeres since, there was a Mathematicall Lecture publiquely erected for those purposes, and furnished with a learned man of suffici­encie answerable, of very honest and courteous beha­uiour, affable to resolue beginners of their doubts; the partie was afterwards dismissed, and the thing (that beganne to be so great a commendation to the Foun­ders, so principall an ornament to the Citie, and a commoditie (both vnto it and the whole Realme in generall) was notwithstanding without all regarde, basely suffered to sincke and vanish in the ende vnto nothing. Surely in all equitie and reason it were fitte, that euery Citie standing vpon merchandise and ma­rine trades, should be ayding vnto those Faculties, whereby the greatest part of their well gotten goodes doeth accrewe vnto them: And especially that hono­rable Citie, which is not onely made riche, but by the meanes of Nauigation is growē famous also through­out the whole World. As therefore I vnfainedly ac­knowledge that in diuers good respectes no one Citie of the whole Earth is comparable vnto it. so doe I heartely wish an increase in all commendable actions, (among which this was none of the least) and not a decrease: The rather sith the augmentour of the pub­lique benefite in that behalfe, shall thereby highly commend his owne true loue towards his Citie and Countrey vnto all Posteritie, and become more re­nowmed by such actions, then by any painted glorious Tombe, or the like kinde of monuments.

The onely good methode of teaching and learning Cosmography (after a fewe principles of Geometry and [Page] Arithmetike first knowen) is, to beginne with the Ce­lestiall Globe, and to be perfect therein, before you deale with the Terrestriall: for this dependeth on that, and the former being once reasonably vnderstoode, the other is not two dayes worke. After you haue thus receaued a sufficient impression of the Globe (where­vnto all true Mappes and Cardes haue a necessarie re­ference) then will the consideration of them become exceeding pleasant and easie vnto you; but neuer be­fore. This I mention, because I haue heard ere nowe, of certaine Teachers, that vndertaking men of good habilitie to be instructed by them, haue beene a great while about a little; spending the time about diuerse pretie particular toyes, which full easely would haue beene knowen of themselues without any teaching, if they had taken the course that I speake off: But such imitate ill disposed Surgeons, which loue to protract a cure, of purpose to sucke the more gaine there­from.

Mappes and Cardes of the Globe of the Earth are of three sortes most vsuall, distinguished by their seue­rall kindes of Meridians and Paralleles. The first hath his Meridians and Paralleles described by Circular lines: And among those I take that manner of Proie­ction, which Rumoldus Mercator hath vsed (proposed long before by Orontius in his Frenche Cosmography, as I haue heard) to be of all other the very best, hauing the Meridians and Paralleles drawen according to the Mater of Gemma Frisius generall Astrolabe. The rea­son that I so greatly like of this, is, for that the proie­ction is very Regular, and therein the natiue Geogra­phicall description may neerest of all others obteyne their due situation.

[Page]An other sort there is, wherein the Globe of the Earth is diuided in two Hemispheres, the Center in both of them being one of the Poles, and the Circum­ference the Equator. In this the Meridians are streight lines drawen from the Poles vnto the Equator; and the Paralleles are Circles. These Paralleles may be described after two wayes: The one enlarging the landes descri­bed towardes the Equator, the other, towardes the Poles. The former is thus delineated. Set the one end of a Ruler vpon the ende of one of the Diameters or Meridians aforesaide, and the other part of the Ruler 90. degrees from that: And keeping the former ende fixed vpon his place, remooue the other to euery one, or fifth, or tenth degree of the next Quadrant, till your Ruler passing through the Pole, becommeth all one with the same Diameter, noting continually in the Semidiameter of 90. degrees distance, whence you first beganne to moue your Ruler, where it cutteth the saide Semidiameter: Then placing one foote of the Compasse vpon the Center or Pole, the other vpon any of those diuisions of the Semidiameter, describe a Circle, which shall be a Parallele answerable to that diuision: And so may you drawe as many, or fewe, as you thinke conuenient. The other is thus described. Beginne at the ende of any Semidiameter where it toucheth the Equator, and numbring still equall de­grees on eache side thereof, marke what intersections your Ruler applyed vnto them maketh in that Semi­diameter: Then may you drawe the Paralleles here al­so, euen as before. The former of these two is repre­sented vnto you by the figure A. the later by the figure B. This kinde of Proiection serueth most aptly to ex­presse in a Carde the Spirall course of a Ship, which [Page] some terme Paradoxall. But whether of these names (being both as yet strangers) shall best deserue to bee freedenized, I leaue to other mens iudgements: One­ly I say, (Paradoxall) is beside the purpose, and asto­nisheth with an emptie sound: but (Spirall) appertei­neth directly to the matter, and declareth the true es­sence of the thing signified.

The third sort of Cardes haue both their Meridians and Paralleles of streight lines equidistant, and these onely are in ordinarie vse with Saylers. Of these I neede not write any thing, they are so commonly knowen, and their imperfections in long voyages so manifest, though in short they may well serue the turnes. And yet I cannot here conceale one great se­crete concerning these Cardes, namely, that there is a certaine draught of them very Artificiall and regular: which being well vnderstoode, redresseth the errours of the other; and (as farre as I canne discerne) will so satisfie the Nauigators expectation, as no Carde hi­therto inuented was euer comparable vnto it, neither (as I thinke) any that shalbe hereafter, wil in al respects surpasse it. Although for the Geographicall descrip­tions, they may and must alter from time to time, as newer discoueries by light of trueth shall make them better knowen vnto vs.

This manner of Carde hath beene publiquely ex­tant in print these thirtie yeeres at least, but a cloude (as it were) and thicke myste of ignorance doth keepe it hitherto concealed: And so much the more, because some who were reckoned for men of good know­ledge, haue by glauncing speaches, (but neuer by any one reason of moment) gone about what they coulde to disgrace it. The Carde (which I meane) is the same, [Page] that was set foorth by the excellent Cosmograpber Ge­rardus Mercator, in shewe resembling ordinarie Sea Cardes, saue that the degrees of the Meridians in it doe proportionally encrease from the Equator toward eache Pole, vpon good reason and firme Demon­stration: thereby shewing the true Position of any one place in respect of an other: which the vsuall Cardes in a farre distance cannot doe, being yet the very principall point that the Nauigator desireth.

For the better vnderstanding and making of Sea Cardes of that sort, I haue here immediatly ensewing set downe a Demonstration, which I obteined of a friende of mine of like profession vnto my selfe, eui­dently shewing the proportionall encreasing of those degrees, wherein consisteth the excellencie of that Carde.

First determine the degree of the Equator, in respect whereof you woulde frame the Meridian of your Carde: for example, the little line a. Next describe the Quadrant of a Circle, so large, that it may per­fectly and distinctly receaue euery of the vsuall 90. de­grees, into which it must be diuided. Then from the Centre A. towarde B. take in the Semidiameter A B. (from whence the degrees of the Quadrant be­ginne) a line precisely equall vnto a, namely D F. And from the points D and F. to the Semidiameter A C. raise two Paralleles D E. and F G. Againe from F. toward B. at a distance conuenient, take the second line K H. equall vnto a. And from the points H K. rayse other Paralleles, H I. and K L. equidistant to the former. Afterwards applying the one ende of your Ruler to the Center A. and the other to euery the de­grees of the Quadrant B C. drawe lines athwart be­tweene [Page] the Paralleles aforesaid: so shall all the lines thus drawen cōteyned betweene the Paralleles, be the degrees of the Meridian sought for, taking their several Denominations of their correspondent degrees in the Quadrant, as by the figure here ensuing is manifest. Of what sort soeuer your Cardes be, you must alwayes remember, that the knowledge of the vse of the Globe must be a moderator vnto them: and that thereby you shall still become master ouer your Card, to espie and amend his faults; whereas otherwise you shall be ma­stered by your Cards, blindly embracing their errors. By meanes hereof it was, that the famous Nauigators of the World performed their discoueries & renow­med voyages, hauing no maner of Cardes to sayle by. And an easie matter it is, for a man that already hath ordinary skill and practise in sayling by vsuall Cardes, to learne in one fourthnight so much of the vse of the Globe, that vpon his obseruations he may either keepe or change his Points for his best aduantage; And of a­ny places, whose Longitudes or Latitudes are knowen, may tell without any Carde, vpon what point they lie, and howe farre they are distant from you: Also vpon what Point they lie each from other, & the distance be­tweene them, with diuerse other things that are neces­sarie, and helde for rareties in that facultie. For in very many of them Enuie doth so reigne, that almost euery one keepeth his owne knowledge to himselfe, without imparting it vnto others: whereas they should all pro­fite a great deale more, if they would communicate their knowledges one with an other, for the publique benefite: But in so much as eache one affecteth to be singular, disdayning the knowledge of others, they haue farre lesse knowledge amōg them all, then other­wise [Page] they might haue: for of necessitie many mens pra­ctises must cōcurre, to make experimental knowledge exact. It were greatly to be wished, that many of them might be founde so well minded towardes their owne trade, as was that notable Pilot Steuen Burrowes: who for his skill, industrie, and performance, may iustly be reckoned among the chiefe of our Nation, and of the world also; if we respect that only, in stead of al, which he worthily atchieued in the first Moscouian discouerie by the Scythian Sea: who if he had bin employed one Sommer more againe towardes the Riuer of Obbe, I doubt not, but proceeding with his former successe, he would haue performed more in that Sommer for trial of a Passage (any or none) that way vnto Catthay, then for the space of these 40. yeeres all Christendome hath done besides; not hauing (asitseemeth) added vnto his, 40. leagues of good discouerie, euer since. The good mind he bare towards his profession he testified here­in, that by his very earnest meanes he procured that learned and easie Treatise of Martine Curteise, concer­ning the Arte of Nauigation, to be translated into our English tongue. The which doubtles hath giuen great light vnto all of skil in that faculty, that euer were since of our Nation: And is more almost, then all our Naui­gators haue holpen the Arte of Nauigation withall besides. A great helpe also would it be for the furthe­rance of skill, if those that are practisers in that Arte, and such as are Students of the Mathematikes, might often conferre together. For except there be a vniting of knowledge with practise, there can be nothing ex­cellent: Idle knowledge without practise, & ignorant practise without knowledge, serue vnto small purpose. But certaine it is, that all the good partes which may [Page] be wished for, or aymed at, shall neuer absolutely con­curre in one man. And therefore if there be but some conuenient mixture of them in any, that party is to be esteemed. For although many things appertayning to Nauigatiō, may be learned & taught by rules of Arte, yet some necessarie points (without which all the rest is nothing) are beyond the compasse of Arte: As for a man to be of a ready and valiant mind; to handle and order those things, that are within the reache of his knowledge, with dexteritie vpon euery present occa­sion: These and such like are iustly termed the giftes of God: For although all things tearmed by Arte are the giftes of God (sith euen Arte it selfe is giuen by God, who is the Authour and fountaine of all know­ledge) yet these are tearmed his giftes more peculi­arly: because the other are giuen by meanes, and these without meanes. Suppose that a man haue all the knowledge that may be wished for, & be notwithstan­ding faint hearted, & his wits (as they say) to seeke, whē he hath most neede of them, his knowledge will ayde him very little. Againe, if he be of neuer so bolda cou­rage, & want discretion, knowledge, & iudgement, he is very vnfit for the gouernement of a Ship: But if such a one be also (as most cōmonly they are) wilfull, taking it for a glorie to be foolehardie, this is as great a mis­chiefe, as all other dangers of the Sea, if they were all set together. Where therefore boldnes of courage, di­rected & moderated by discretion & iudgement; also a body enhabled to brooke the Seas, are matched with a willing mind vnto Marine affaires, & endued with the feare of God; wheresoeuer I say, these speciall giftes of God are to be found, there the ornaments of Arte, as necessary additaments, will alwayes most effectually [Page] take place, & are most easily attained vnto. But where those former, at the least in some comperent measure, are not, al the rest is vanitie. It is euen a most irkesome and wofull sight, to behold a company of courageous yong Gentlemen to be led on blindfolded (as it were) in marine actions, by such as haue no feare of God be­fore their eyes; and many times by those, that are very ignorant of almost any thing that good is if any thing might be accompted good, where the feare of God is not) but onely can tell of their owne experience, howe they haue dissimboched from Terra Stolida, making their voyage toward the Isle of Pickery: gracing them­selues (as they suppose) with swearing and staring, and wishly lookes. A few such monsters hauing the chiefe gouernement in Ships, and voyages, are a great deale more dangerous, then all the monsters in the Sea: And for euery one that is bereft of life by these, a hundred at the least are destroyed by the other.

The serious consideration of these things haue oc­casioned me of a friendly mind and entire good will, (wherein toward your profession, I wil giue place vnto no man liuing) to admonish you of these points, which I haue thought necessary; Beseeching Almighty God, (who is the Lord both of Sea & dry Land) by his holy Spirit of true wisedome to gouerne & direct you in all your actions, that employing your diligent endeuour in your Arte in his feare, and calling vpon him in the time of trouble, he may heare and deliuer you from all your distresses; And that being deliuered, you may accordingly glorifie him, yeelding praise and thankes for his mercies before the sonnes of men.

Let Staffe, Carde, Compasse, Ship, and Skill,
Depend vpon Gods blessed will.

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