THE NAVIGATORS SUPPLY.  
Containing many things of principal importance belonging to Navigation, with the description and use of diverse Instruments framed chief for that purpose; but serving also for sundry other of Cosmography in general: the particular Instruments are specified on the next Page.  They that go down to the Sea in Ships, and employ their labour in the great waters, They see the works of the Lord, and his wonders in the deep. Psal. 107. 
Imprinted at London by G. Bishop, R. Newberry, and R. Barker. 1597.   


The Contents.  
1. Of the Compass in general.  
2. Of the Compass of Variation.  
3. Of the Travailors jewel.  
4. Of the Pantometer.  
5. Of the Hemisphere.  
6. Of the Traverse-boorde.  
7. A friendly Advertisement to the Navigators of England.    

To the Right Honourable, for all parts of true Christian Nobility worthily renowned, and my singular good Lord, Rob. Earl of Essex, and Ewe, Viscount Hereford and Bourgcher, Lord Ferrer of Chartley, Bourgcher and Lovayn, Master of her Matesties' Ordinance & Horse, Knight of the Honourable Order of the Garter, & of her highness privy Council: Long life with increase of honour.  
PLutarch in a Treatise, wherein he showeth how a man may win profit by the malice of his enemies, doth manifest his drift and purpose with this convenient similitude: That men of old, in their encounters with salvage and wild beasts, thought to have made a great hand, if they could but save and defend themselves from their injuries and violence: But the succeeding ages proceeded further, converting the flesh of them unto food, their hair to the use of garments, and their very gall, and other parts of them, to sundry most wholesome medicines: Yea the whole outward proportion of their fearful shape, I mean their skins, which before had threatened man nothing but death, he afterward addressed to be convenient Armour to save him from harms, and defend him from destruction. So that the life of man which to the foregoing Ages seemed to be miserable by having wild beasts, to their Posterity following should have appeared in part miserable, if they had wanted wild beasts. And Plutarch allegeth Xenophon to have been of this judgement; That although some man can content him to escape the injuries of his enemies; yet is it the part of the wise and valiant minded to make profit of their malice, by using such industry in attending his own ways, and marking his adversaries, that the whole course of his life should seem nothing so happy and commendable, were it so in deed that utterly he had none enemies at all.  
Much in like sort, (my very honourable good Lord) fareth it with our Navigators; who at the first adventured to forsake the main land, betaking themselves to the wide Ocean Sea, upon the credit and fidelity which they reposed on the Sailing Compass; constantly believing that it had every where showed the true North and South, and semblably all the other winds. But dangerous and doleful experience within short time made it plain and manifest, that where they reposed greatest trust, there was some treachery: For the upholder of their life and safety, did sometimes mislead them into destruction, and carried them in the proceeding of their course far distant (they knew not whither) from that he in the beginning pretended. This uncertainty therefore being so dangerous an enemy of their new practised art, with might and main they encountered: And having at length found out some tolerable means to avoid it, they thought themselves to have done enough, and rested therewith contented. But in this pregnant Age wherein we live, the expert and skilful Navigators have proceeded yet further, and made of that (as it were) venomous quality of misleading an Antidote against itself; yea they use it in stead of an armour and defence against error and perils. So that though in the rude beginnings of former times, men were drawn by it into many perplexities: yet in the settled experience of these our days they rejoice therein (being used and ordered accordingly) as in a thing greatly concerning their good and welfare. But this is a principal secret, only known unto those that are of greatest skill among them.  
A memorable example hereof fell out Anno 1586. when Sir Frances Drake, a Gentleman of famous memory, in his West Indian victorious voyage, departing from the harbour of Cartagena, arrived some small time after at the Westermost point of Cuba, called Cape S. Antony, and having stayed there some few days, put to Sea for Virginia, for the relief of our Countrymen that were there in great danger and distress: Having continued at the Sea sixteen days tossed with variable winds, they came at last within sight of land: but by no means could they discern, or give any probable guess what land it should be. So it was, that one of Southampton, being an expert and skilful Navigator (though of other conditions not so good, but better might have been wished) for his frowardness, having received disgrace before, was notwithstanding upon this necessity called unto conference: where, after Sir Francis had bestowed on him some part of his eloquent persuasions and fair promises, at length he undertaketh to do his best. And having made his observations according unto Art, he pronounced in laughing and disdainful manner (because his advise was not taken in the setting of their course) that look what land they had been at sixteen days before, the very same precisely was the land that now they were at again. Which assertion of his being rejected, as a thing impossible, by all those of skill in the company, and especially by Sir Francis himself not without reproachful words; he still persevered therein, and assured them, that upon his life they should find it so: like as in the end they did.  
This could he never have done without his knowledge of the Variation of the Compass; as the party himself more than once with great earnestness hath protested unto me in conference that I have had with him concerning those matters. Yea besides the particular knowledge of Places, the expert Navigator standeth in great hope hereby to attain unto good helps for the finding of Longitudes, and according unto the Poet, Non fumum ex fulgore, sed ex fumo dare lucem Cogitat: ut speciosa dehinc miracula promat.  
But this is a matter somewhat dainty among the chiefest of them: As for the rest, in all their conclusions about the Variation, they may as yet (for all their fair shows) be well likened unto Chapmen, that are merchandizing for the skin of a wild beast, before the beast be taken.  
The great necessity hereof, and the singular love that for many years I have borne to that laudable faculty, and to the industrious practisers thereof, hath at length persuaded me, not only to contrive certain Instruments fitted for sundry their purposes, and especially for taking the Variation of the Compass; but also to set forth divers other principal uses of them, together with the Descriptions of the Instruments themselves. All which I do the rather Dedicate to your Honourable Lordship, both in regard of my private duty, as also of an earnest desire to do them the more good: who by that means (I am right sure) will the sooner be induced to peruse these short Treatises with the more willingness, and to consider of them with the less prejudice. So that my good hope is, few of them will be found, in whom reason shall have so weak ankerhold, as to think that a man of my profession would seem to intrude himself into the mysteries of their Art; and especially belonging to your Lordship, durst offer to the view of the world under your Lordship's name, any thing that he knew not assuredly to stand grounded upon infallible certainty of truth.  
Touching experience in these matters, of myself I have none: For, (besides the diversity of my calling,) by natural constitution of body, even when I was young and strongest, I altogether abhorred the Sea: howbeit, that antipathy of my body against (as the Italian termed it) so barbarous an Element, could never hinder the sympathy of my mind, and hearty affection towards so worthy an Art as Navigation is; tied, I confess, to that Element, if you respect the outward toil of the hand, but clearly freed therefrom, if you regard the apprehension of the mind: And in the mind only, pure and true Art, refined from the dross of sensible or experimental knowledge, is to be found. Which when I perceived must needs so be, and that the great skill of our Seamen was not performed either by rashness of chance, or strangeness of miracle, but according to certain universal precepts or documents, derived from the fountains Mathematical, being the substance of that Art; so far as the studies of my profession, and other my necessary affairs would permit, I endeavoured by little and little to understand somewhat thereof: And that which I thus learned by speculation, I have conferred off with some of the skilfullest Navigators of our Land; with such as have been principal Actors in our furthest North-east and Northwest discoveries; with such as have been in the South Sea, and at the Cape of Bona Speransa; and also with Naturalists of the East Indies. I have entered into the consideration of the making of all their Instruments, together with the manner of their observation by them both on Land and Sea: And as I have by conferring with them from time to time learned what they most desired and stood in greatest need off so framed I mine instruments accordingly; answerable for all purpose of practice unto theirs, but for commodiousness thereof, somewhat better, I doubt not, (if sincere trial be made) and for certain points of chief importance, performing that, which all theirs hitherto in any common use never could do. Wherein I have already the allowance of some among them, whom I have esteemed to be of the greatest skill and practise: And very willing am I to stand to the judgement of the rest of like skill.  
A true proverb it is; he which buildeth in the marketplace, shall be sure of many controwlers of his work. And that made me stand long in suspense, whether I should suppress, or set forth these conclusions of mine. Of their truth, their commodious use, yea and of the good acceptance of them among those of the better sort, I nothing doubted: But how strange it would seem unto some, that a man of my calling should deal in this Argument; that in deed did a little trouble me; easily conjecturing that many would think I have forgotten myself, and walked herein beyond the bounds of my profession.  
As for my profession, I thank God, I have exercised the preaching of the Gospel now these twenty years, in a Country where both Preachers and Gospel have some store of adversaries: And I trust that my travail therein hath not been such, that I greatly need be ashamed thereof, or can justly be challenged, that I ever, as a man careless, neglected my calling. But recording with myself, that the dispersion of Nations came by the confusion of Languages: upon which occasion, they spread themselves over the face of the whole earth; yea and planted themselves (a thing most strange unto our Capacity) in many exceeding remote islands in the Ocean Sea: and considering that the knowledge of languages groweth by intercourse and mutual access; I perceived that God now towards the end of the world, had ordained the sailing Compass to be the notable means and Instrument of this intercourse; even thereby to join dispersed Nations, not only into the Civil or rather Cosmopoliticall union of human society; but also (as Christian hope bindeth us to think) through the knowledge and faith of the Gospel, into the spiritual and mystical fellowship of that Heavenly jerusalem: And so by means hereof to make mutual amity between people and people, though never so far separated; and to give this as a leading guide, to carry the sound of the Gospel, as the band of love, 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 upon all the face of the Earth; and hath assigned the times which were ordained before, and the bounds of their habitation, that they might seek the Lord:) weighing (I say) this with myself, that God of his infinite wisdom and unspeakable love toward mankind, had appointed this simple Instrument in show, to perform matters of such admirable importance; that the wisdom of man wanting this one, with all the other Instruments of the world could not possibly have done, I did therefore judge it a matter not unfit for a Preacher of the Gospel, to set to his helping hand for advancing a Faculty that so much tendeth to God's glory in the spreading of the Gospel. Now if this be not against Divinity, doubtless to preserve men from danger, and to direct the wanderer, cannot be against humanity: Against the duty of a Subject it cannot be, to further that knowledge, by which her majesties power is augmented, and her Royal name continually carried to all the quarters of the world. Finally against my duty in general towards my native Country it is not, to endeavour what in me lieth, the good increasing of that skill, whereon dependeth a great part of the prosperity of this Realm.  
And if this were a work 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 unto your Lordship, then to any other: Because your sincere love towards our Country, your dutiful and loyal affection towards her gracious Majesty, your humanity so full of honour towards all men, proceeding from the unfeigned fear of God, (which continually increasing, increaseth likewise the rest,) doth in such plentiful measure aabounde, that I dare appeal unto him who is the supreme judge of consciences, & the trier of all truths, I do herein affirm such a truth without flattery, as your enemies themselves cannot deny, but being overpestered with envy.  
Vouchsafe therefore mine Honourable good Lord, of your noble disposition, favourably to accept this small Treatise, (such as it is) which of duty and good will is offered unto you; protecting it so far forth, and no further, than the truth of demonstration and commodiousness of the conclusions shall deserve. And thus beseeching the Almighty to bless your Lordship, to increase his good gifts in you, and to prosper all your Honourable affairs: I commend your Lordship, and all yours in my humble and hearty prayers, unto the protection of him, from whom all good gifts do descend, and with whom there is no variableness, nor any shadow of change; but yesterday, to day, and is the same for ever.  
Your Honourable Lordships in all duty to be commanded, William Barlowe.   

Lectori S.  

PRaesulis eximij gnatus, multisque verendis  
Patribus affinis, pastor & ipse pius,  
Hunc foetum peperit: quem si tu (candide lector)  
Excipias gremio suavis, amansque tuo;  
Dentibus haud metuet Criticorum rodier atris:  
Quos tamen, ut tener est, non metuisse nequit.  
Perlege, pertenta, bis terque quaterque licebit:  
Quô mage creber eris, crescet & ille magis.  
At simul hoc usu matura adoleverit aetas,  
jam benè tutus erit viribus ipse suis.    

To the Reader.  

THis book was written by a Bishop's son,  
And by affinity to many Bishop's kin:  
Himself a godly Pastor, praise hath won,  
In being diligent to conquer sin.   

If to thee (Reader) it may welcome be,  
The Critics censure it will fear the less:  
For being young from fear it is not free,  
Which otherwise more courage might profess.   

Read, way, and try, but read, and often try  
The rules of skill whereto it doth direct:  
Trial may bring as much authority,  
As newness hinder it of due respect.   

But yet when time shall to it ripeness give,  
It will have credit of itself to live.    

Uotum Authoris.  

sum Deus, Coeli terraeque marisque tremende  
Conditor, atque idem rector tersancte, patenti  
Aure favens, facilis mea percipe vota precantis.  
Ex uno veluti gens est humana Noacho  
Orta, unáque habitans linguâ celebravit eâdem  
Te solum verumque Deum, Babylonica turris  
Quum nondum aethereas caput attollebat in auras;  
Sic iterum, ô utinam, miseros miseratus in unum  
Mortales redigas, laceros ut corporis artus,  
Quosfuror ille tuus dispersit ad ultima mundi,  
Coniunctique ineant sancta ut commercia rursus,  
Velivolis iungas ratibus ceu pontibus ipsos  
Mobilibus quamuis disiunctos aequore vasto:  
Foelici celeres vento impellente carinas:  
Mirandaque agiles moderanti Pyxide clavos:  
Inprimis tuus ille tuus, qui cuncta gubernat,  
Spiritus, aspiret placidus: Sic, lampade diâ,  
Verbo evangelii, toto noscaris in orb.    

F. N.  

O God, whose power heaven, earth & sea declare,  
Which being by thy word, thy word obey:  
And in their works, which Natures called are,  
Work but that will of thine which all doth sway,  
Hearken, O hearken for thy Christ his sake,  
Unto the prayer which in heart I make.   

Look down with mercy from thy mercyseat,  
Upon mankind dispersed here and there,  
From Noah's family, which grew so great:  
For at the first all but one people were,  
Which but one law, which but one language knew,  
One God alone to serve, God only true.   

As yet man's heart did seek no name of praise  
In stately towers, which threaten might the sky:  
When pride began great Babel for to raise,  
Speech was confounded with variety.  
Since than divided tongues divided hearts,  
By sea and land into a thousand parts.   

Yet since thy Spirit of true unity,  
In cloven tongues did on Apostles sit:  
That so thy cursing might a blessing be,  
And cloven tongues divided people knit,  
Let that thy Spirit breath in every place,  
That all may know the Gospel of thy grace.   

And since the Sea doth some so far divide,  
That they may seem an other world to be:  
Teach us our Ships like horses so to ride,  
That we may meet in one, and all in thee:  
And as the Needle doth the North respect,  
So all in Christ may only thee affect.    

A brief discourse of the Sailing Compass in general.  
THE marvelous and divine Instrument, called the Sailing Compass, (being one of the greatest wonders that this World hath) is a Circle divided commonly into 32. parts, termed by our Seamen Winds, Rumbes, or Points of Compass: which Circle by the touch of the loadstone showeth the aforesaid divisions in all Orisons between the Poles, according to one and the self same perpetual position in respect of the true points of North and South in every Horizon. This Circle is commonly described upon Pasteboard of 5. 6. 7. or 8. inches diameter: And hath sometimes subdivisions, with the relation to the 32. and sometimes hath the ordinary division of Circles, namely 360. In the Centre of this Circle is fastened a little Diamond as it were, or a Capital, as some call it, of Latin, being cinquebored, the point thereof appearing a convenient space above the Circle, and the hollowed part downward, to be placed upon the pin. In the bottom of this Circle are glued two wyars about ¼ longer than the Diameter, bended proportionally the one toward the other in the form of a loop, so that the ends join close and even together in the circumference: and the Circle in this manner finished, is named the Fly of the Compass. The box wherein this Fly is placed, must be covered with clear glass, made close round about with wax mingled with Rosen, or some other kind of Simmond. The bottom of this box is to be taken off and on, as occasion shall serve: in the Centre whereof standeth the pin of Latin of a reasonable height, for the Fly to have sufficient scope. This box is to be hanged in two Circles of Latin within an other greater Box, that the Fly, which way soever the Ship swayeth, may always stand upon his pin parallel to the Horizon: to which end they fasten a piece of Lead to the bottom of the lesser box.  
As for the touching of the wyars of the Fly with the Loadstone, I would wish it to be performed after this sort. First of all, have a great care of the goodness, the quantity and the form of the Stone: for if he be never so good, and very small therewith, he can give but small force unto the Compass: And again, though he be never so great, yet if he be of base quality, his touch can be but faint. An oval form, or somewhat longer, retaining a like proportion from the middle to each end, is very good. Always provided, that the length of the Stone lie according to his own line of North and South: for a stone of this form giveth forth his virtue in the touch a great deal more forcibly than it can, if by reason of the evil shape thereof, his force in himself be confusedly dispersed, and not jointly directed to his due points. The wires before they be touched, aught to be polished and made very clean, and fitted unto the Fly, and then touched after this manner. With the North end of the Stone, press each wire, beginning at the middle, and so along unto that end, that you would have turn Southerly: And with the South end of the Stone do the like from the middle of each wire, unto the end that you would have turn Northerly. Then glue them in such sort, that the Fly may stand equally upon his pin, having both the North and South ends of the wires uncovered, that their touch may be refreshed, as occasion shall require.  
After all this is accomplished, that the Instrument thus furnished may truly perform his office, there must just regard be had of the Variation, as also of the diverse Set of the Compass: And likewise that it be not placed near any Loadstone, iron, or steel. By the Variation is understood the difference in the Horizon between the true and the magnetical Meridian. By the Set, is meant the setting or placing of the wires in the bottom of the Fly, which sometimes you shall find standing right under the Flower de luce, representing the North point, sometimes ½, ⅓ etc. toward the East of the Flower de luce.  
The Compass being artificially made and fitted as he ought to be, with all his just regards: we must conceive every line drawn from the Centre unto each division, to represent always the semidiameter of an Azimuth, bearing the same name with the division of the instrument. The line of North & South is every where the intersection of the Meridian with the Horizon: and the line that crosseth him at right angles, is every where the intersection of the East & West Azimuth with the Horizon. The like is to be understood of every one of the other, according to their natures: so that every point of the Compass, when the line thereof is by imagination produced in the Horizon unto the Heavens, is understood to be the base of a Quadrant of some one Azimuth or other: and the line falling from the Zenith, to the Centre of the Compass, is as the Perpendicular common to them all. Wherefore which way soever in any situation a ship doth sail upon any point of the Compass, it must needs be that she saileth within the plain of one Azimuth or other, in as much as every point is the Base of an Azimuth: and so performeth always her course upon the Conuexe of the Sea, in a portion or portions of one great Circle or other, because all Azimuthes are great Circles. Albeit therefore a voyage were to be made from any place in any Latitude, more or less (it skilleth not) unto any other of the same Latitude, and that according to the common trade (which should not be, if great Circle-sayling were known & brought to perfection) keeping as near as may be under one Parallel, from the beginning to the end of the voyage: yet because in all this Ships motion, the Compass is considered as equidistant always unto the Horizon, it must needs follow, that all the points of the Compass (his Variation remembered) continue their mutual respect to those of every 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 always at right angles: so that the situation of the ship continually altering, doth never alter the properties of the Compass: whose nature is to derive those his divisions unto every new Horizon that he approacheth unto; all the lines of his points ever remaining Semidiameters of Azimuthes and Bases of their quadrants: the line falling from the Zenith through his Centre, being still the perpendicular common to them all. Whereby it is manifest, that in as much as the direction of the sailing Compass is always some one Semidiameter of an Azimuth; and the ship (being the body moved) ever stemmeth in the plain of the self same Azimuth: also the wind, being the efficient that moveth, of his mutable property driveth foreright diametrally upon the plain of the Horizon: which cannot be but according to the intersection of the foresaid Azimuth: it is therefore impossible, if the ship be moved, that is, transferred or changed from place to place, that the line or tracing of her course comprehended between those places, should be any other, but only such as is composed of great Circular portions: of which, the length of the ship itself is always a segment. And so describeth she by that means in her course before mentioned, not a Parallel properly so called (as common opinion doth wrongfully imagine) consisting of one continual lesser Circular line; or otherwise, a spiral line truly so named, consisting of a continual uniform winding, answerable to the nature of the said line; but a course (quibusdam diverticulis, as learned Nonius termeth it) with certain turnings in and out, consisting of small segments of great Circles; keeping always as near the precise parallel, or spiral line, as art can aid them. Wherefore it is confessed, that those several courses have some show or resemblance of the two sorts of lines aforesaid: but by no means are they the very lines themselves in deed.  
Who was the first inventor of this Instrument miraculous, and endued, as it were with life, can hardly▪ be found. The lame tale of one Flavius at Amelphis, in the kingdom of Naples, for to have devised it, is of very slender probability. Pandulphus Collenutius writing the Neapolitan history telleth us, 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 Inventors of things, could never hear of this opinion (yet himself being an Italian) and as he confesseth in the later end of his third book de inventoribus rerum, could never understand any thing concerning the first invention of this instrument. Most men suppose the finding thereof to be very new, and hardly to be proved that it hath been in any use in these parts of the World full 200. years agone. But whether this property of the Loadstone was first known in the West or East parts of the world, it is very doubtful. The East Indian histories are pestered with such monstrous reports and Legendary tales, that as yet they are but of very small credit. Their fabulous genealogies and friarly discourses, do breed a linger expectation of some halting Post, that making not so much haste as good speed, may with more sincerity inform us of the state of those Countries and matters unto them belonging. Some few years since it so fell out, that I had several 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 japan. I questioned with them concerning their shipping, and manner of sailing. They described all things far different from ours, and showed, that in stead of our Compass, they use a Magnetical Needle of six inches long, and longer, upon a pin in a dish of white China earth filled with water: In the bottom whereof they have two cross lines, for the four principal winds: the rest of the divisions being reserved to the skill of their Pilots. Upon which report of theirs, I made present trial how a Magnetical Needle would stand in water, and found it to prove excellently well; not doubting but that many conclusions of importance in Marine affairs will thereby more readily be performed.  
I find that as the Portugals travailed in their very first discoveries for the East Indies, they got a Pilot of Melinde, that brought them from thence in 33. days, within the sight of Calecute, and had even then in use the Compass, the Card, and the sounding line. Ludovicus Vartomannus testifieth, that in his voyage from Bornco unto Giava, the Pilots of those countries had the use of both Compass and Card, and had skill to take direction from the South Pole, as ours do from the North, even in those days, when it was a very dainty matter for any of our Pilots to have performed the like: being as then possessed with an opinion, that the Compass would turn round, assoon as ever they came under the Equator: as some do yet surmise it would do under the Pole, or near the fantastical Rock of the purest Magnes. Philander in his annotations upon vitrvuius, showeth that some men deemed it not a new, but an old invention, and took it to be that Nautical instrument which is called by Plautus in Trinummo and Mercatore, by the name of Vorsoria. But this Adrianus Turnebus in no case will allow, affirming it rather to be a kind of tackle, wherewith they turned their Sail.  
If of old time they had not this Instrument, it seemeth impossible that ever they could have performed such voyages as they did: And if ever they had it, than were it as strange, that all memory thereof should be utterly suppressed, and that Ptolomey had not found some mention thereof made in Marinus Tyrius, or other Cosmographers, whose works were extant in his time. Experience testifieth, that this began to be in common use about the time that Printing was invented, and the making of Guns. Both which, although they are of very excellent use and great wonderments to the world, yet doth this far excel and exceed. For all things performed by them, are marshaled within the limits and bounds of human reason; and therefore their causes being known, their wonder ceaseth. But this being incomprehensible unto human reason, carrieth it away captive unto the astonishment thereof, and leadeth it to the admiration of him, whose wisdom comprehendeth all things, and distributeth knowledge and understanding among men, according to such measure, times, and means, as seemeth best unto himself; opening the eyes of the blind, and giving understanding to the simple, destroying the wisdom of the wise, and making the understanding of the prudent for to hide itself.  
Considering the fowl abuses and errors that daily are committed in the making and framing of this worthy Instrument, I have thought good here briefly to note the faults, and therewithal to show the way how they may be amended. Let no man mistake me: I speak not save only of ordinary Compasses (being the most that ever I saw) such as are in common use, and are sale-ware for Masters and Pilots. What some discreet skilful men carefully do provide for themselves, I speak not of. First therefore for the most part, the Card of the Fly is negligently divided, not only in the Compass which they ordinarily sail by, having the 32. common parts: but as great negligence may be found in the double Fly, for their Compass of Variation: where the uttermost Ring which they make movable about the ordinary Fly, is divided into degrees: and there a degree or two odds breaketh no square with them. The wires of the Fly are as rudely set together, having their ends not fitted even and close (as were meet) but starting a side each from other, not somuch as filled smooth, but rough even as they were broken: whereby they are also disabled from taking so strong a touch, as they would, if they were made smooth. For remedy hereof it were good, to draw the ovale lines upon the Card of the Fly, in such sort, that the ends being even with the circumference of the Fly, both the middles and the ends may have an equal distance from the Centre: Then according to those lines bow and cut the wires, fitting their ends smooth, and so closely joining them, that they may both seem to be but one. After that, holding them together, dip the ends in a little molten Tin, or if at the first they be wielded together, it is the better: and with the edge of a dull knife, scrape off the Tin again as much as you can come by, which will be all in a manner, saving only a very little that keepeth the ends together: and that will hold them so fast, that you may conveniently handle them at your pleasure, and fasten them on their place, according to your desire. (But before they be set on, let them be touched as abovesaid, and being set on their touchings at the ends must be refreshed.) Thus shall your Fly stand and turn equally upon his pin: if not, in stead of the ordinary dawhing with wax, two or three drops at the most will counterpoise any swerving: and many times you shall not need any at all; which is most commendable. 
*   
The Capital is commonly wide from the Centre of the Fly; and likewise the pin whereon the Fly standeth, from the Centre in the bottom of the Box: both gross and absurd faults, and yet easy to be avoided. 
*   
The glass that covereth the Box is commonly crackeled and snarled by the sides; and diverse times also too little. These faults they cover with their thick border of Rosen: but better were it to amend them with a little heed taking. The Glass ought therefore to be somewhat thin, smooth, and of even thickness; having the edges smoothed on a grinding stone, or by some other means, and made very fit to the Box. So shall you need but little quantity of Simmond, only to keep out the air: which is the better, both for the clearer view of the Fly, and that your Box may hang the steaddier: and that will it not do, if your Glass be much thicker on the one side, then on the other, or else being too little, be thrust nearer the one side, than the other, and the void place filled up with Rosen, according to ordinary custom.  
The Box is hanged in two Circles, the one within the other, having the pings that they turn on, a quarter of a Circle in the one distant from the other. But these Circles are commonly so unhandsomely made, and ill favouredly hanged upon their pings, that you should offer a Tinker discredit to compare his work with this. Add hereunto the rivetting of the Circles with iron, and hanging the bigger of them upon iron nails: which although they be but little, yet you must esteem a little in this case to be a great deal too much. And if they had any care of that they have in hand, they would not commit such a needless gross absurdity, only as it were in despite of Art, to make expense of wit without gain or profit. 
*   
The piece of Lead that is fastened to the bottom, aught to be round and of equal thickness, the pin passing through the Centre thereof. If you have it otherwise, then mark the Box and the bottom when it hangeth aright: and whensoever, having taken off the bottom, you will set it on again, see that you make your marks in the Box and bottom agree, or else it can never with any certainty hang as it should. Although it be exceeding loathsome unto me to deal in these mechanical base practices, yet the necessity is such, that one must needs deal therein. For of all the Instruments that the Navigator useth, this is far the most excellent: and yet of all others this is most negligently and unartificially made. Their staves and Sea Cards made in England are neat and fine. Their Astrolabes are tolerable: but these are even such, as I have showed unto you, which I could not so well have showed, but by this anatomizing of them: that the blame may be apparent, either in those that make them, or in such as buy them, that will not go to the price of better: wherein folly would show itself very eminent, if when a ship with her lading may be worth many thousands of pounds (besides the inestimable value of the men's lives that are in her) half a pound should be thought much to be bestowed on a perfect Compass; upon the goodness whereof many times, both ship, and goods, and lives of men do take their trial: yea all these do they jeopard (as it were) upon a wager that their Compass is true and perfect. To conclude, I would wish in any wise, that Artificers of these Instruments should make even great conscience of that they have in hand; and not slightly to pass them over 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 use them, do well examine their goodness, before they buy them.  
Moreover, it many times falleth out, that the hollow side of the Capital is made too narrow in the bottom: and then will the Fly never play well, except the pin be exceeding small & sharp: which assoon as by use it is a little dulled, the Fly will never show his points truly, though he were touched with the best stone in the world. And very oftentimes the oversight herein, is imputed wrongfully to the weakness of the Touch.  
And therefore take care, that the greater Box being square, be not set together with iron nails. But if it be round, then see that it be handsomely turned. And in any wise that the lesser Box, wherein the Fly standeth, be well & exactly turned, of seasoned wood, and having the inside coloured with some white glistering colour: and not according to the common custom rubbed about with a piece of Chalk, or a little white lime.  
Furthermore because it is very necessary, that whosoever saileth by any Card, ought diligently to foresee that the Set of his Compass be answerable to his Card, of the like Set (I mean) unto that his Card was made by; And for that the wires being once glued on, may not well be altered, or removed; And the double Fly by reason of his unwieldy corpulency is nothing nimble, I have framed one after this sort; a brief description whereof I thought not impertinent here to insert. The ends of the wires must be wielded together. The wires themselves are half round, with the otherside flat to be placed upon the bottom of the Flie. The capitle hath two thin narrow Stays of Latin reaching to the wires on each side and fast soldered unto them. The top of the capitle must be skrewed on the outside, and a little square piece of Latin with a small hollow bent fitted for to screw upon him; unto this end, that the capitle being put through the bottom of the Fly in the Centre, and the screw on the upper side, being turned on the top of the capitle, the Fly and wires both, may by this means be closely combined together without any paste or glue, and be left bare throughout, to the most advantage at any time for receiving the touch of the Stone, and more easily be kept from rust, being the greatest enemy that the touch of the Stone can have: unto which, all your pasted or glued wires are necessarily subject: insomuch as you shall very seldom and (as I think) never, in the whole many of your usual Flies see any one, that is not infected herewith: being far more noisome than Garlic, or Oil, and all the rest of those fond surmised conceits. If the screw come not close enough upon the Fly, a little piece of pastboorde put on before the screw, will be a remedy sufficient therein. When the wires are thus fastened unto the Fly, you may at all times remove them to any point or part of a point at your pleasure, without annoyance unto any thing. In such as I have caused to be made for this purpose, I have used a narrow form of a loop, the distance between the wires in the middle, being little more than the fifth part of their length: and have abated also the metal of the wyars about the middle of them, and allowed somewhat the more towards their ends.   

The Compass of Variation.  
THe Compass of Variation is made in all respects like unto the ordinary sailing Compass, & is the very same in deed, excepting these two Additions. The one is, that on the inside of the lesser Box round about, just with the height of the Fly, either upon the Box itself, or else upon Paper or Pastboorde, fastened to the side thereof, there be a Circle divided into 360. parts. And at every 90. let a line be produced both upward to the top, and by the space of half an inch downward. 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, unto 90. do the like also from the opposite part, betokening the South. The other is, that athwart the upper face of the Glass, there be placed a Ruler of Latin in length answerable to the Diameter of the Box, bearing in breadth the third part of an inch or half an inch, if you think good, for a very great Compass. In the middle of which Ruler there must a line be drawn according to the length of the Ruler▪ And toward each end of equal distance therefrom, fit two Sights of three inches or longer (as your Compasis) and about a quarter of an inch broad at the top, waxing broader toward the foot; where they are to be jointed in such sort, that they may for handsomeness sake be folded the one close upon the other, and stand erected at right angles. In the one of these along the middle thereof cut out the metal, beginning a little beneath the top, down to the foot, of convenient breadth; that a Lute string having a small pearl or bugle on it to slide up and down, may be fastened precisely in the middle throughout from the top to the foot. The other Sight being made after the same proportion and form that the former was, hath only a fine small slit pierced from within very little off the top down to the foot, and must in his thickness be abated, that he weigh no more than the other. The Ruler thus furnished with his Sights, in the space between the sights and the brim of the Box, aught to have two loops cut out in decent manner to look down through them upon the Flie. And this Ruler must be divided into many equal small parts; as 20, to an inch, or such like; the numbers beginning from the Lute string sight unto the other; and from the foot of that other to the top. When the Ruler is finished, as before I have specified, it must a little be let into the brim of the Box, that it may stand fast having the middle of it right over the line of North and South in the Box; and the Sight with the Lute string, over the South. But let it in such sort be fastened, that you may conveniently either take it off, or set it on as occasion shall serve. So that the Ruler being taken off, it is a Sailing Compass, being set on, it serveth for the Variation in manner following.  
The Fly of the Compass having at opposite parts directly over the points of the wires some marks on the upper side easy to be discerned (if it be a Meridional Fly, it needeth not, in as much as the Flower de luce and the South point serve the purpose) turn the Box toward the East in the foorenoone with the Ruler on it, till the Lute string do cast his shadow right upon the middle line of the Ruler, or on the slit of the other Sight. Then mark immediately where the shadow of the pearl doth light, upon what division, if the lines be divided, otherwise mark it with a pen; And also what part the Southend of the wires, or, (which is all one) the Northend doth point unto in the side of the Box. In the afternoon do the like toward the West, with the pearl still unremooved, turning the Box, till the shadow of the pearl falleth full upon the place that it did in the forenoon: And note then also what part the ends of the wires do point unto. Then if the number of parts observed in the forenoon, be alone with those in the afternoon, there is no Variation at all: for the ends of the wires do show the true Meridian. But if the one exceed the other, subtrahe the lesser from the greater; And half the remainder is the Variation of the Compass toward that side, which had the greater number in his observation.  
This Compass serveth far better to set the land withal, and to describe any Harbour, Coast, Haven, Town, or Country, than any before in common use; by looking through the slit, and bringing the thing that you would note, and the Lute string both in one; withal marking what parts the wires do show at that instant. Likewise for taking of distances.  
All this may also be performed with a Circle of Latin about one quarter of an inch broad, having a stay going athwart pierced through with loop holes (that it be no hindrance to view the Fly) and a Ruler moving upon it in form like to the former. Which Circle must be divided, as that within the Box was, from the Flower de luce, which is to be placed a quarter of a Circle distant from the line passing along the middle of the stay, & have his numbers reckoned towards the ends of the same line. And so must the other half of the Circle be divided from the South point. Being thus divided it must be placed even fast and very fit, close above the Glass. And when you will use it, turn the Box about, till the flower de luce of the Circle stand right over the Northerly ends of the wires: And the Box so standing, set the Ruler according to the forenoon and afternoons observation, doing all things else, as before. And you shall find the self same effect.  
I have tried at land the Crosse-needle in stead of the Fly, and do like it exceeding well. Whether is the better at Sea, I do refer it unto their judgements that shall make due trial of both. The Crosse-needle I call two needles, the one of Steel, and the other of Latin, joined together in the capitle, where they cross each other at right angles; and so made, that they be of one length, very strait, and equally standing upon the pin, no end overweyghing the other. This Needle well made and fitted as it ought to be, will beside his proper use, supply the use also of a Perpendicle, (a matter of great importance) to show the upright standing of your Instrument, which the single Needle cannot do; neither yet the Fly any whit comparable unto this. But you are diligently to note, that in continuance of time as the force of the Touch of the Stone doth decay, so will the North end of either Needle or Fly rise somewhat higher, and the South end sink lower. For this is one of the wonderful properties that the touch of the magnet hath, that a needle as yet not touched standing equally upon his pin, being once touched with whether end of the Stone you list, the one end thereof shallbe reared higher, and the other fall lower: The difference whereof, as the goodness of the Stone is greater, will accordingly the more appear. And in process of time as his force still decayeth, so returneth he more and more to his even standing again. By reason of which property the Artificer is constrained, that he may make the Needle lie even, to abate somewhat of the falling end, that the other by virtue of the touch raised up, may through this abatement, be brought down to an equality of situation with his fellow. When therefore you perceive the rising of the North end (as aforesaid) assure yourself the Fly or Needle is weakened in strength, and hath need to be refreshed with the Stone. Otherwise, if it were at the first well touched, be not too busy with it, but let it alone; except you be well assured of the goodness of the Stone, and of the right manner of touching. If the Northend riseth not any thing at all, and yet the Fly playeth not, then is it to be remedied with sharpening of the pin. The commodity of the use of this Needle for a Perpendicle is, that because it is within the Box, the wind cannot hinder it, as it will any other Perpendicle (especially being small) that is in the open air.   

The Traveylors' jewel.  
THIS Instrument is a Circle about a quarter of an inch broad, having his diametral stay, Ruler, Sights, and all things else, as is last before described; saving these additaments. The Compass Box of this Instrument must be of Latin, of what depth or shallowness you please. Only so prepare it, that the Needle or Fly want not in any wise space enough at liberty to play in. Let the Circle have a Quadrant firmly sowdered to his uttermost 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. Divide the Quadrant into 90. degrees: and the numbers of those parts, placed in two several borders, must be reckoned contrary ways, the one beginning, where the other endeth. Upon the edge of the utter Circumference of the Circle, where it and the Quadrant meet, there must be a strong and firm joint fastening the Circle and Quadrant in that place unto the Box in such sort, that as the Circle continually riseth, so the Quadrant may still sink in the joint. For this joint must issue from the Box with a neck somewhat longer than the semidiameter of the Quadrant, standing at right angles upon the Box and Circle both: having in the middle a slit of capacity sufficient to receive the Quadrant, moved therein up and down according to the motion of the Circle itself, with a little screw pin on the one side to stay the Quadrant therewith, and so consequently the Circle, wheresoever you will have it. And on the other side an Inlet must be handsomely filled, that the lower part thereof, (being of a convenient quantity to contain within it both the borders of the Quadrant) may precisely make one right line with the middle of the Axis of the joint, and the neither semidiameter of the Quadrant erected. So shall it always supply the use of a fiducial line, and distinctly show the numbers that are cut in the borders aforesaid. Thus much concerning the description. The use is briefly this. When the Circle is not elevated, it is the above mentioned Compass of Variation: The middle line of the diametral Stay, representing East and West, and the Base of the Quadrant produced, serving for North and South, etc. But when it is elevated according to the height of the Equator (whose angle by the fiducial line of the Inlet, the Quadrant showeth in one number, and the height of the Pole in the other) it performeth the use of an Equinoctial Dial generally throughout the whole world. For, supposing the Circle raised as appertaineth, let the Needle (and a Crosse-needle seemeth the best) keep his due place agreeable to the Variation: Then turn the Ruler with his Sights about, till the shadow of the Lute string being toward the Sun, do fall upon the middle line or slit of the opposite Sight, being perpendicularly erected on the Ruler like unto the other. So shall the uppermost end of the Ruler directed toward the Sun, declare the true hour, either in the upper superficies of the Circle, to be reckoned by 15. degrees continually from East to South in the Forenoon, and from thence to West in the Afternoon: or else for more expedition in a peculiar Border of hours drawn according to every of those 15. degrees in the void superficies underneath.  
I had once purposed to have written somewhat of an Instrument devised by Robert Norman: who although he was not learned, yet was he a very expert Mechanician, of an honest and good mind, and found that by his own industrious practice, concerning a strange property of the Magnetical Needle, which no man (I think) before him did ever find, and which (the more is the shameful sloth of men) very few Navigators have practised ever sithence: Although the Instrument be very easy to be made, and the property no doubt in Navigation of great consequence. But understanding by conference with a man of rare learning both in Physic, his own profession, and in divers other laudable knowledges, besides that, he many years hath laboured in the consideration of the properties of that Stone, and mindeth now out of hand for the common benefit to publish those his labours, I surceased altogether from that purpose of mine, assuring me that he (if any other) will be able most exactly to handle that Argument: For I found him excellently skilled, far beyond any thing that I either knew or imagined in that matter. Albeit I had read all that I could hear to have written thereof, and had practised as many of their Conclusions, as I made any reckoning of. But I found mine Authors, even of the best account, in many things very frivolous and vain, and ignorant of the chiefest properties of importance. He that seemeth to have written most learnedly is a Neapolitan, whose footsteps I followed, and found his Assertions erroneous in six several Conclusions.   

The Pantometer.  

The Author's purpose in this Treatise.  
THis Instrument, that in respect of the 
Cap. 1.  manifold and general uses thereof, I call the Pantometer, I have framed chief for the Variation: And that principally to serve at land: yet some parts of it shallbe employed on practice 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 itself. And although the universality of the Pantometer would have ministered matter of very large discourse: yet for as much as my main purpose is, as in the rest, so in this Treatise likewise, to be aiding and assisting the Navigator by all good means possible: To his principal and most necessary uses I have therefore directed, and as it were, contracted the diffused nature of this Instrument. Notwithstanding, whatsoever Master Thomas Digges hath written of Measuring with his topographical Instrument, may be done aswell, and better with this. How convenient it is for observations Astronomical, the expert will soon perceive. All which, and many other Mathematical Conclusions easy by this Instrument to be performed, I must leave to the diligent trial of the studious delighted with those noble Sciences.   

The Declaration of the parts of the Pantometer.  
THe chief parts of this Instrument are two: 
Cap. ●  The horizontal, to be placed always equidistant to the plain of the Horizon, which it representeth: And the Vertical, perpendicularly erected upon the former, and therefore in power any Azimuth or Vertical, whereof also it is named. In the horizontal there are two Semicircles; The one hath the ordinary Points of the Compass: the other the common degrees of a Circle, both of them meeting in one Diameter. The round void space in the middle of the horizontal, must be filled up with the Centre-pinne thereof, in such sort, that being from underneath fastened thereinto, the one half and more of the said Pin, somewhat beyond the Diameter of his thickness, shallbe cut away, and be made even with the upper side of the horizontal: But the other part remaining, shall stand directly upright of a convenient length above the horizontal: And this I term the Axis of the Vertical: because by means of it the Vertical is turned round about upon the horizontal, and made to take any manner of position.  
The Vertical hath in it a Quadrant as big as it may receive, to be drawn not after the common fashion, but according to the description invented by that famous Mathematician Petrus Nonius in his Treatise of Instruments and Rules for Navigation, and of the Twilight: which Quadrant, in respect of the kind of working thereby, I call the Proportional Quadrant. And on that side it hath nothing else, saving the Alhidada, or Sight Ruler (as the manner is) fastened in the Centre, and carrying in his margin above the Fiducial or Levell-line all the several numbers of the inner Quadrants underneath, for more readiness and certainty sake. For the speedier dividing of the inner Quadrants, do thus▪ Part the Fiducial line of the Sight Ruler into halves, from the innermost circumference of the Limb unto the Centre. The medietie next unto the Limb, divide into 45. equal parts: setting down their several denominations by five or tens, upon the Ruler rightover the divisions: their numbers decreasing from the Limb towards the medietie after this sort. The division next unto the Limb is accounted for to be 89. the next 88 then 87. 86. etc. until you come unto 46. next unto the medietie itself. According unto these divisions precisely answering unto them, draw so many inner Quadrants upon the Centre of the great Quadrant of 90. Then must you with a pair of dividing Compasses very exactly take the quantity of a degree in the Quadrant of 90. and that will perfectly divide every one of the inner Quadrants into their assigned numbers. Only you are carefully to foresee, that when the Vertical on the back part thereof through the hole of his Border is firmly fixed upon the Axis of the Center-pinne, the nethermost edge on the forepart of it (being equally distant from the lower side or Base of the proportional Quadrant) do in any case precisely light upon the Centre of the horizontal: to the end that it may always serve it in stead of a movable Diameter.  
The back of the Vertical hath these three necessary Implements. The first is a Compass, with his line of North and South parallel, to the Vertical: And the same must be handsomely and fitly let in to the border of the Vertical beneath, that the Axis of the Centre pin, passing through both the handle of the Compass and the said Border, may clasp it exactly close unto both the back of the Vertical, and the plain of the horizontal, in such sort, that as the Vertical is moved round about, so jointly together with it and in it shall the Compass likewise.  
The second is the Directory, so named, because it guideth the eye-beame directly forth unto the Horizon. And this consisteth of two parts: The Ruler and his Sights. Whereof the Ruler being of a reasonable length, straight, and even, shall be drawn to and fro athwart the back of the Vertical in two loops standing parallel to the horizontal, or (which is all one) to the Border of the Vertical. The two Sights, which ought to be 2. or 3. inches long, are movable likewise but upon the Ruler: the one beyond the Vertical, the other behether it towards your eye.  
The third is the Perpendicle or thread, with a little plummet hanging thereat, requisite for the due placing of the horizontal: which turn the Cross-needle also will serve. Last of all, when you are to use the Vertical alone by itself (as hereafter shall be showed you) there is a handle belonging thereunto, having the lower end of what form you will, (the best is which may best fill the hand) but the upper end must be of the same fashion and bigness that the Axis of the Centre-pinne is of: for it hath (as you shall perceive) the same use, and must be fastened likewise in the same place.   

The Mechanical Description 
Cap. 3.  of those Parts.  

The horizontal.  
The Compass.  
The Back of the Vertical with his Border, Inlets, Loops, and Perpendicle.  
The Centre-pinne.  
The Vertical and his Sight-Ruler.  
The Directory.  
The handle of the Vertical.    

The exact finding of Altitudes or Heights.  
FOr as much as the usual Quadrant of 
Cap. 4.  90. degrees only doth very seldom yield the precise elevation sought for in a known and certain denomination, because most commonly the Sight Ruler, or Alhidada (as they call it) cutteth not exactly at a full degree, but upon the space between the beginning and ending of a degree (which is infinitely divisible) the proportional Quadrant of Nonius, by drawing and dividing many inner Quadrants (as before you have seen) shows that easily within a narrow circuit; which otherwise a very large, yea a huge Instrument with no small encumbrance would hardly do in a mighty circumference. For the parts being so many, in a continual train following one an other, and the Ruler every where in a manner crossing them, it must needs cut some one of the inner Quadrants upon a full degree. And so by this means, that part of the uttermost or great Quadrant, which before was but confusedly conjectured, without any determinate denomination, is now distinctly made known under a certain name, by the ready help of the Golden Rule, after this manner. When the Ruler showeth some portion of a degree in the uttermost Quadrant, whose certain value in minutes, seconds, etc. you would gladly learn, observe at the same instant what whole degree in one of the inner Quadrants it precisely cutteth: And market therewithal in the side of the Ruler the entire sum of all the parts whereinto that Quadrant is divided. So have you of four proportional numbers, three given: namely, the whole inner Quadrant, his part cut, and the whole uttermost Quadrant of 90. Wherefore to find out the fourth, multiply 90. into the parts of the inner Quadrant that the Ruler cut, and the Product divide by the whole inner Quadrant, the Quotient shall tell you the degrees of the uttermost Quadrant together with the portion sought for, in a fraction distinctly known: which to reduce unto the usual denomination of Minutes, Seconds, etc. do thus. Multiply the Numerator of your Fraction by 60, and divide the product by the Denominator: the Quotient shows your Minutes. And if any remainder be, again multiply that by 60. and divide in like sort as before, this second Operation brings forth Seconds. And in the same manner still working, as often as any thing is left of the former Operation, you may proceed on to Thirds, fourths, Fifthes etc. till you have obtained a most sufficient preciseness.   

The Observing of the Variation at Land by the Sun.  
SEt the Instrument upon a Staff prepared 
Cap. 5.  for this purpose, his horizontal being parallel to the Horizon of the World: And placing the Vertical upon the line of North and South in the horizontal, turn the horizontal about, till the Needle stand equidistant to the Vertical: Then fasten the horizontal to the staff with the screw pin of his Socket: which in that sort remaining steaddy and immovable, turn the Vertical in the Forenoon towards the East, moving the Sight Ruler up and down, till the Sun beam doth pierce both Sights: and immediately note what parts the edge of the Vertical doth cut in the horizontal: Also what part the Sight-Ruler falleth on in the Vertical: where if it light not on a just part in the utter Quadrant; mark where it doth upon one in any of the inner Quadrants. Again, in the Afternoon, the horizontal continuing still in his former place, and the Ruler likewise abiding upon the foresaid part unchangeable, turn the Vertical towards the West, till the Sun entereth in at both the sights: And note therewithal what part the edge of the Vertical cutteth in the horizontal. If then the parts cut by the edge of the Vertical in the Forenoon, and those other in the Afternoon, be equally distant from the South point of the horizontal; then is there no Variation at all. For the line of North and South in the horizontal, is one and the self same with the true Meridian. But if the parts of the Forenoon's observation be fewer than those of the Afternoon, subtrahe the smaller number from the greater: and half the remainder discovereth the Variation from the South Westwards to be 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 horizontal, doth not possess the true Meridian: but swerveth therefrom, as the parts observed do show. Lastly, if the parts of the Forenoon's observation be more than those of the Afternoon, subtrahe (as before) the smaller number from the greater, and half the remainder showeth the Variation of the South end of the Needle to be so many degrees Eastward, and the Northerly end thereof to vary so many parts Westward. Now for the more certainty in your working, you must ever be mindful to make 3. or 4. several observations in the Forenoon: that although a Cloud should hinder you of your first in the Afternoon, yet some one at the least of the other may be clearly observed: where otherwise, if you miss of one, all your labour for that whole day is lost.   

The observing of the Variation at Land by the Stars.  
THe Variation of the Compass, (and so 
Cap. 6.  likewise the Latitude) may be taken as well by the Stars in the night, as by the Sun in the day. And sith the Almighty hath ordained but one Sun, and a great multitude of Stars, Navigators should offer themselves much wrong, if they would not make their benefit of these, as they do of that: And so much the rather, because the Sun is South but once in four and twenty hours: The Stars come to the Meridian continually one after another all the night long. The ordinary instrument for the Variation, is not of any use at all in respect of the Stars, no not though he have his Astrolabe to help him: whereas this instrument by itself, without the aid of any other, performeth all things exquisitely by the Stars: And by the Sun so exactly with all advantage, that when many Instruments can do nothing without a clear Sunshine; this in a misty or foggy weather through a Cloud, if that you may but only discern the body of the Sun, craveth no more to accomplish your desire.  
The manner of observing a Star is this. First prepare a little Notche or slit of equal depth in the two sights of the sight-Ruler, parallel to the leavell line thereof: And the Instrument being placed (as before is specified) turn the Vertical towards the Star, being on the Eastside of the Meridian, moving the sight-Ruler up or down, till you may perceive the Star even with those two Notches. Then note the parts that the sight Ruler doth cut in the Quadrant: And those also that the edge of the Quadrant or Vertical cutteth in the horizontal. Afterward do the like again when the same star is on the West side of the Meridian. And for the rest, following the same manner of Operation that above I delivered, you shall here obtain the self same truth of Variation by any star that there you found only by the Sun.  
Touching the Latitude, the like kind of working is to be used for the taking thereof by a star, as is by the sun: I mean the observing of his Meridian height, and subtrahing, or adding, as the nature thereof requireth.  
And for this cause is the Vertical so placed, that about an inch of it (more or less, according to the proportion of the Instrument) at that corner, where the Ruler is fastened to the Centre, may always in the turning about reach over the horizontal: that you may conveniently apply your eye, by the sights to discern any star, or espy the top of any body erected, whose height you would measure: which otherwise you could not do, if the Vertical were but even with the horizontal. As for the other end of the Base of the Vertical, it is no matter how far it be extended, but only according as the quantity and comeliness of the Instrument shall require; so that the Border, wherewith the Base of the Vertical is lengthened, do reach precisely straight, and even unto the edge of the horizontal, for the cutting of the parts thereof.  
Moreover, if the half Circle of the horizontal, which is parted into degrees, were divided also into a pair of Proportional Quadrants: then both for the former uses, and infinite others, would this Instrument prove most exact and perfect. But those that are willing to bestow so much cost, I wish they should do it in metal, 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 receiving any work very easily and fairly. The imperfection of brickleness, a little the more care must amend and strengthen. And thus much for the use of the Pantometer complete.   

The manner of observing the Variation at Sea.  
WHen the Vertical of the Pantometer together 
Cap. 7.  with his Compass is fitted to the handle, hold it directly toward the Sun in the Forenoon, in such sort, that the Perpendicle keeping his due place, the Sun may pierce both the sights: And noting the height of the sun, mark also at that instant, what Point or Degree the Needle doth show. Again when the Sun cometh to the same height in the Afternoon, observe likewise what Point or Degree the Needle is at: And then working in all respects (as before I declared) the Variation is made known unto you.  
If you have a Crosse-needle well made, it will serve in stead of the Perpendicle, better than the Perpendicle itself: In as much as it is not subject to the whirling of the wind, but is quiet therefrom, being defended by the Glass close symmond round about.   

The taking of the height of the Sun at Sea.  
PLace the Vertical upon his handle, the 
Cap. 8.  limb towards you, and his perpendicular side over against you, and turning your back towards the Sun, keep the two sights of the Directory, even with the parting of the water, and the Element over right against you. Move also the sight Ruler of the Vertical up or down, till at one instant you may see, both the Sunbeam through the upper sight to fall upon his due place in the neither, and jointly therewithal the parting of the water and Element: Then have you the degrees & minutes of the suns height, by means of the Proportional Quadrant, as heretofore is specified.  
This may in like manner be performed by looking toward the Horizon directly under the Sun, placing the Perpendicular side towards you, and the limb from you, and thrusting the Directory with his long sights from you, or else drawing it towards you, as you may most conveniently discern the sunbeam of the upper sight to be upon his just place in the neither. For the better effecting whereof, it is requisite to have a third square sight, forked on the neither 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 Centre of the sight Ruler, ready to be taken off or on; and having a little mark with two Crosse-lines of equal distance to the holes of the other two sights, and the Fiducial line: To the end that this third sight, being fastened right over the Centre of the sight Ruler, (with his lower edge somewhat aslope, and not at right angles with the Fiducial line) you may the more easily discern, by means of the said mark, when the sunbeam hath pierced the other two sights above: And then have you all things as before. Wherefore if two observations be made together, the one from the Sun, and the other towards it, and both these agree in one; The whole Operation must needs be exact and without any doubt of error.  
The ordinary staves (so that they be well made, and good regard had to the eccentricity of the eye) be very commodious for so much as they can perform: which cannot be much above 45. degrees: because the eye at one view is scarce capable of a larger Angle. And therefore in great Altitudes of the Sun, they are unserviceable, the Astrolabe or searing, (as some term it) coming in place of them: And yet the use of this also in a high Sea is very uncertain. But with the Instrument that now is described unto you, you may take the height of the Sun at what angle so ever, yea although he be vertical. Herein, this and the staff agree, that both of them have a special respect to the Horizon: but they differ in the danger of the eccentricity of the eye; whereunto the staff is subject, but this is not so, and never requireth any Angle in the eye of the Observer, that shall exceed the capacity of 20. degrees. Somewhat also might here have been added of the diverse placing of the sights upon the Directory: but for brevity sake, I refer it to the consideration and choice of the Practiser, upon diligent trial thereof.    

The Hemisphere.  

The Scope of this Treatise.  
TWo things there are in every Instrument 
Cap. 1.  of special and most necessary consideration; the one the body (as it were) and substance of it: the other, the end or purpose whereunto it serves. The body or substance of every Instrument, and namely of this (whereof now we treat) I call the Material parts of which it consists, together with their peculiar forms, such, as whereby that end may be best attained: best, I mean, with the greatest both certainty and facility possible. The purpose or end, I term the manifold commodities to be reaped thereby, and especially in this Instrument, the singular most pleasant and profitable uses whereunto it is and may be applied. All which fully to discourse of, would require far more leisure, then either my vocation, or other many affairs of importance, may permit me. I shall therefore sufficiently content myself in this behalf, if first I deliver to the skilfuller and more industrious sort, a brief and perfect view of the Instrument by a particular and evident description to the eye of all the Members thereof: which once conceived, the thing of itself without any further words of mine, will most easily and readily unto them, declare his own use from point to point in Astronomy, Geographie, Navigation, and such like excellent faculties. But because that the Navigatour is the man, for whose sake chiefly I have taken these pains: And among those of that trade, the most part are, though commendably perhaps furnished with experience, yet but weakly assisted with fit Instruments: and of themselves, for want of some contemplative knowledge Mathematical, not able either to invent fit, or to reform and better those that presently they use: I thought it requisite for them, together with the description and frame of the Instrument, to add in the second place some few principal admonitions, concerning the several most necessary uses thereof upon sea or land. And in so doing, I will leave many things to the Readers own ingenious practice: Many also will I omit, or rather presuppose as already known, namely what a Pole is, an Equinoctial, a Meridian, etc. being such as are the first Principles of this Art, wherewith every man is commonly acquainted, and by diverse in our own vulgar speech have in the largest manner oftentimes be handled.   

The names of all the parts of the Hemisphere.  
Now if any desire to know what this 
Cap. 2.  Hemisphere is by itself, (and so must he first, if he will orderly proceed to the getting of perfect knowledge in the use: for no man can well handle an Instrument that he knoweth not) a general declaration of the parts accompanied with their Mechanical description, and a brief comparing of them with the Globe, may so thoroughly suffice, as more herein is not to be required. There are therefore in this Instrument two sides to be considered, the one more principal, which I term the Face; the other less, which I call the Back. The Face consisteth of whole Circles and half Circles. The whole Circles are two in number: whereof the one being the Base (as it were) of all the Instrument and immovable, is the fixed Meridian, because that turn most commonly it serveth: the other, movable, I call the Deferent; for that it carrieth up & down upon and in itself, according to any greater or lesser Elevation or Latitude, the Equator and Axis of the World, with the two extreme points thereof being the Poles. The half Circles being four in number, are all belonging to the former two entire Circles: For either are they placed upon the great Meridian aforesaid; and then, if fixed or movable thereupon, it is the half Horizon; if movable, it is the Semicircle of Altitudes, to be turned to and fro upon his own Poles, equidistant on all sides from the Horizon: or else they are situated upon the Deferent; and those two likewise in number having the self same differences between them that the former had: For one of them is fixed or fastened upon the Deferent, and that is the Semiequator: the other is voluble, which I call the Movable Meridian.  
The Back of this Instrument needeth not any thing, but the usual Mariner's Compass to be artificially annexed thereunto with the line of North and South parallel to the Back.   

The Mechanical Description 
Cap. 3.  of all those several Parts.  

1 The fixed Meridian.  
2 The Deferent with the Axis and Poles.  
3 The half Horizon.  
4 The Semicircle of Altitudes.  
5 The Semiequator.  
6 The movable Meridian with the two Sight-Rulers.  
7 The Back, with the Mariner's Compass.    

The agreeing of the Hemisphere with the Globe.  
BY that which hath hitherto been spoken touching the Structure of this Instrument, 
Cap. 4.  may soon be discerned the original descent thereof to be from the Globe. For the better conceiving whereof, vouchsafe I pray you a little to remember with me the chief 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 adjoined only as the former; but continual therewith, being described in the superficies or outface of the Globe itself, the Equator, I mean, and the Zodiac, with their appendants, the two Colours, one Equinoctial, & the other Solstitial. All these to make and use together in this sort with the Globe, when experience had taught to be a matter of great difficulty, the learned of former times, & of these our days, have laboured how without the Globe by sundry rare inventions to represent the Globe, in separating those necessary Circles from the massines of the Instrument: wherein the Astronomers Ring (commonly so called) doth justly deserve right worthy commendation. And I now the rather make mention of it, for that it first gave occasion of devising, and ministered good help 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 either speak for itself, and let the skilful Reader judge. Touching the Hemisphere, if you imagine the Meridian of the Globe to be a Plain, it shall pass through the Centre thereof, and cut it together with all the great Circles thereunto belonging in two equal parts: The self same doth the Meridian likewise in the Hemisphere: And therefore have you here the Equator, Horizon, Movable Meridian, and that of Altitudes, all these half in stead of whole Circles. As for the Zodiac, it is not here wanting: for sith all great Circles, and so their medieties are equal the one unto the other, the half Horizon here, may well be used for the half Zodiac, when the Equator is placed according to the greatest declination: or contrariwise the Horizon to be the Equinoctial, the Semiequator shall be the half Zodiac. Thus have you the Zodiac both ways: that I say nothing of the little one in the limb of the Movable Meridian. For the two Colours there, serves the two Meridian's here: the fixed for the Sostitiall, the Movable for the Equinoctial. The little Circle for the hours there, is here the Equator itself, and so it is also in effect in the Globe. The Index there, is the Movable Meridian here, and so must you likewise understand it in the Globe. Of the Axis and Poles you have heard enough before. To conclude, here is presented to your view a Halfe-sphere in name and show, but a whole or entire Sphere in deed & practice. For proof whereof (omitting many other) I refer you to these few Propositions ensuing. Only by the way, in the behalf 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 truly divided, that they be exactly placed upon their right Centre, that the hanging of the instrument be exquisite, having the Horizon thereof parallel to the great Horizon of the world. Finally that all things be accomplished accordingly, as above by the Pattern is signified, before he proceed to any experimental handling of it: lest otherwise the work be unjustly blamed for the errors and imperfections of the workman: let (as reason would) the fault there lie, where the fault is.   

To find the place of the Sun.  
THe day being given, the Place, that is, 
Cap. 5.  the sign and degree of the Zodiac, wherein the Sun is, may thus be found. Seek in the uttermost Circle described upon the Deferent the month and day given; whereupon if you place the linea fiduciae, or level line of the Ruler, the same shall in the lower or inner Circle thereof being the Zodiac, show you the thing sought for: And the opposite point thereof shallbe the Suns Nadyr for that day. But if the year be leap, wherein the place of the Sun is demanded; then must you from the 24. of February, till the end of that year, add always one more to the number of that day which you seek 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 forth.   

The place of the Sun, being given to find his Declination.  
FOr as much as all the Declinations of 
Cap. 6.  the whole Zodiac may exactly be considered in one only Quadrant thereof, thus briefly shall you work by the Hemisphere. Let the Horizon be in stead of the Zodiac: Then number in the fixed Meridian (which now must be taken for the Solstitial Colour) the suns greatest Declination, & thereat fasten the Equinoctial: So shall the pin, whereupon the two Semicircles cut one an other, be the beginnings of Aries and Libra, and the point of the Orisons meeting with the fixed Meridian, the beginnings of Cancer and Capricorn: Between which two extremes, the space of every 30. degrees in the Horizon of the Instrument shall be as a whole sign in the Zodiac, to be reckoned in order thus. From the pin to 60. is Aries, from thence to 30. Taurus, from thence to the fixed Meridian Gemini: Then back again from the Meridian to 30. Cancer, from thence to 60. Leo, from thence to 90. being in the Intersection, Virgo. The self same order must be used in the other half of the Zodiac: For the reason is like in both. Having therefore found the true place of the Sun in the Horizon of the Instrument (now the Zodiac) turn the Movable Meridian, till it exactly agree therewith: so shall the degrees thereof intercepted between the Equinoctial and the Horizon, (now the Zodiac) show the declination demanded. Or supposing the Equator of the Instrument to be as the Zodiac, and the Horizon as the Equator, you may after the same manner also find the same declination in the Semicircle of Altitudes. Or finally, if you set the Ruler on the place of the Sun found in the little Zodiac of the Movable Meridian, his end in the uttermost limb or border of that Semicircle shall point out unto you the true declination.   

The Longitude and Latitude of any Star being given to find his Declination.  
LEt the Horizon of the Hemisphere be as 
Cap. 7.  the Equator of the World; and the Equator of the Hemisphere as the Zodiac, by separating the one from the other, according to the Angle of the suns greatest declination: so shall the Zenith of the Instrument be as the Pole of the World, and the Semicircle of Altitudes, fit to express any declination. Again, the Pole of the Instrument shallbe in stead of the Pole of the Zodiac; and the movable Meridian shall truly represent any Semicircle of Longitude. Wherefore supposing in the Instrument the one Quadrant of the Equator (now the Zodiac) from the pin to the fixed Meridian or Solstitial Colour upward, and so down again, to be the Northern half of the Zodiac, containing ♈· ♉· ♊· ♋· ♌· ♍· And the other Quadrant thereof from the pin to the same Meridian or Colour downward, and so up again, to be the Southern half comprehending ♎· ♏· ♐· ♑· ♒· ♓· in this sort have you by the continual addition of 30. according to the number of the Signs, the whole Zodiac given withal his degrees of Longitude. So that first seek the degree of Longitude supposed: After bring the Semicircle of Longitudes, or the Movable Meridian to that degree, and in it number the Latitude of the Star given: Lastly apply the Semicircle of Altitudes in such sort, that it may exactly agree with the same Latitude: then shall the Ark thereof comprehended between that point of Latitude and the Horizon of the Instrument (now the Equator) precisely show the degrees of declination of the Star in that point.   

The Declination of Sun or Star, being given to find the height of the Pole or Latitude.  
THe Latitude by Sun or Star to be 
Cap. 8.  found, is either when they are in the Horizon of the World, or above: And if above, either in the Meridian, or without. When the Sun or Star is in the Meridian, take by some Instrument the precise height of them: After, place the Movable Meridian in the Hemisphere parallel with the fixed Meridian, toward either the South or North there, according as the height observed was in the Meridian of the World: And close unto the Movable Meridian join the Semicircle of Altitudes: Then seek the point of Declination given, in the Movable Meridian, and raise the same so many degrees in the Semicircle of Altitudes above the Horizon of the Hemisphere, as the height observed was above the Horizon of the World. So shall the Pole of the Hemisphere have one and the same Elevation with the Pole of the world in the place supposed. But when either Sun or Star is in the Horizon rising or setting, in stead of observing the height before, now only take the distance thereof from the true point of East or West: This done, remembering that the pin whereupon the Equator cutteth the Horizon in the Hemisphere, standeth for those points of East and West, turn the Movable Meridian to or fro, and the Deferent with the Pole therein up or down, till the Declination of Sun or Star noted in the Movable Meridian, do exactly agree with the Horizon, at such a distance from the Pin aforesaid, as by your observation the Sun or Star did differ from the true East or West. Then shall the Pole of the Hemisphere show you the Latitude. Lastly if the Sun or star be elevated between the Meridian and the Horizon, then shall you need both the former observations, the one of height, the other of distance from East or West, that is, in what Azimuth the sun or star is, or as the seaman termeth it, upon what point or part of the Compass: which with a fit Instrument is easy to be performed. And for that the Semicircle of Altitudes expresseth any Azimuth, set that in respect of the Pin before mentioned, according to the distance observed from East or West; And in the self-same semicircle also mark the height observed: whereunto having brought the Declination in the Movable Meridian, you shall ever find the Pole in the Hemisphere of equal Elevation with that of the World.   

The Latitude being given, and the Declination, to find very readily by the Sun beam without any help of the Magnetical Needle, the hour of the day, the height of the Sun, and the true point of the Compass whereon the Sun than is.  
FOr the performing of this Problem, 
Cap. 9  raise the Pole of the Hemisphere agreeable to the Latitude or Elevation given: and place the Ruler in the little zodiac, upon the degree of the suns Declination: Then move the Movable Meridian higher or lower, that is, nearer or farther from the fixed Meridian, till the Sun beam pierceth through both the sights of the Ruler: So shall the middle edge of the Movable Meridian show you in the Semiequator the the just hour Antemeridian above, or Pomeridian underneath it. And if beyond the full hour, it falleth upon any of the 15. degrees between, multiply those odd degrees by 4. and the product thereof shall be horary minutes. Afterwards the parts of the Instrument standing still without any alteration, apply the Semicircle of Altitudes to the point of Declination, then shall the portion thereof contained between that Point and the Horizon, discover the true height of the Sun for that time. And withal the self same Semicircle of Altitudes in the Horizon, shall exactly declare upon what point of the Compass the Sun than is: And in the Equator it shall further show upon what point of the Compass the Sun truly is in respect of the Parallel of his daily Revolution.   

The Latitude and Declination being given, and the Height taken by any other Instrument, to find the residue before specified any time of the Day.  
SVpposing the Pole at his due Elevation 
Cap. 10.  in the Hemisphere, and the Sun upon his point of Declination there, turn the movable Meridian and the Semicircle of Altitudes to and fro, till the height observed in this, do precisely agree with the point of Declination in that: Forthwith in the Semiequator the Movable Meridian telleth you the hour, and the Semicircle of Altitudes in the Horizon, makes manifest the true Point of the Compass.   

The Latitude being given together with the Height of any fixed Star of known Declination, to perform all the former any time of the Night.  
Observe first the height of the Star above 
Cap. 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 given: And having marked in the Movable Meridian the Declination of the star, whose height you found, move that Semicircle with the point of the stars Declination, till in a correspondent Quarter of the Hemisphere, to that which it possesseth in the Heavens, the star obtain his precise equal height from the Horizon: which is soon measured (as before we declared) by turning the Movable Meridian and the Semicircle of Altitudes to and fro, till both cut each other in the point of Declination. That portion of the Semicircle of Altitudes, comprehended between their Intersection and the Horizon is the stars height: And immediately therewithal appears upon what point of the Compass the star is: Also in the Semiequator the movable Meridian shows you the stars hour. Howbeit, because all distinction of time proceedeth originally from the Sun, that is not the true hour of the Night sought for; but an other must be found by the distance of the star from the Sun: And for this purpose serveth the Zodiac or Circle of right Ascensions described in the Deferent. Seek therefore therein the place of your star (if it be of the number of those that are there set down) otherwise the degree of your stars Coeli-mediation; which by the help of the Ruler, make perfectly to agree with the hour of the star, now to be reckoned in the Circle of hours in the fixed Meridian: Finally, keeping the said Circle of right Ascensions in this sort immovable, look therein for the place or degree of the Sun for that Day, and thither move the Ruler till it lie directly thereon: Then shall the end of the Ruler in the Circle of hours upon the fixed Meridian, show you the true hour of the Night required.   

The Latitude being given, and the Declination of either Sun or Star, to find how long they appear above the Horizon, and at what Point they rise or set: also the Amplitude Oriental.  
SEt the Equator of the Hemisphere according 
Cap. 12.  to the Latitude given, and apply the degree of Declination to the Horizon: Afterwards, the Instrument thus standing, note upon what hour, or part of time the Movable Meridian falleth in the Equinoctial: For that shallbe the precise time of rising, to be numbered in the hours above; or of setting, in those underneath: And the Ark of the Equator, contained between the Movable and fixed Meridian, being doubled, declareth how long either sun or star continueth above the Horizon. Now touching the Point of the Compass, it doth presently offer itself, to be seen in the utter margin of the Horizon, over-right against the point of Rising or setting aforesaid. From which point to the Pin (being in stead of the true East or West) the degrees contained in the Horizon, represent unto you the Amplitude Oriental or Occidental.   

By the Sunbeam to draw readily the Meridian line, and to find the Variation of the Compass.  
FOr more speedy and certain operation 
Cap. 13.  herein, if the Sun be in the East half of the world, turn the face of the Hemisphere Eastward; if in the West half, then Westward; altering a little the situation of the Pole, and consequently of the Equinoctial, that the Pole and semicircles of the Instrument, may agree and be equidistant unto those of like denomination in the Heavens. Then hold it perpendicularly upon or over any flat and smooth superficies, lying parallel or even with the Horizon of the world: and that directly toward the Sun, that the beam thereof passing through both the sights, may show the exact minute of time. Now sith the fixed Meridian of the Hemisphere is in the Meridian of the world, the foot of the Hemispheres said Meridian must needs be so likewise. Draw therefore either by direction of the foot itself, or of the shadow of it, a strait line, and produce it in length as you think expedient. This shall be the Meridian line required, with his two extremes pointing out the true South and North: whereunto if you draw a perpendicular crossing it, that shall be the Line of the true East and West. The variation is thus known: when the hour is found (as immediately before you have heard) at that instant turn your eye aside toward the Back of the Instrument, and mark what Angle the Needle of the Compass maketh with the line of North & South underneath it: For this Line being by the structure of the Instrument equidistant to the fixed Meridian of it, is understood to be in the great Meridian of the world▪ as the fixed Meridian is▪ And therefore look how much the Needle swerveth from the same Line, so much it declineth from the true Meridian. The quantity of which declining (being nothing else but the Variation) is forthwith made manifest by the degrees of the Circles circumference underneath, contained between that Line, and the end of the Needle.   

To find when the Twilight begin beginneth, and how long it continueth.  
THE suns depression under the Horizon, 
Cap. 14.  may soon be known by the manner of finding the height thereof above: And thereunto belongeth this observation of the Twilight: The beginning whereof in the Morning, and end in the Evening, is commonly supposed to be, when the Sun in a Vertical Circle is by the space of 〈◊〉 under our Horizon. Move therefore the Movable Meridian, and the Semicircle of Altitudes both together toward the North part of the Horizon (the Pole before being raised accordingly) till the point of the suns declination and the end of 18. degrees, being reckoned from the Horizon downward in the Semicircle of Altitudes, do meet jointly in one: And straightway note what hour the Movable Meridian lighteth on in the Equator: for that is the time when the Twilight beginneth in the Morning, if you look on the upper side of the Equator, and endeth at night, if on the neither side: Again turn the Movable Meridian with the declination or place of the Sun in it, till it be just in the Horizon, and forthwith see what hour it showeth in the Equator: That segment of the Equator which is comprehended between this point of time and the former, declares the quantity or continuance of the Twilight.   

The true measuring of any distance upon the Globe of the Earth.  
THe Geographical measuring of mighty 
Cap. 15.  Distances upon the Globe of the Earth, is a thing not only of marvelous pleasure for knowledge, but of singular commodity for practice, serving to many excellent purposes both bysea and land. And although the Computation Arithmetical, used herein by the learned, & grounded upon the doctrine of Spherical Triangles, is absolute and exquisite, yet is the deducing thereof (especially when Places differ in Longitude and Latitude) not void of great obscurity; and the operation, both by reason of so many multiplications, divisions, yea and extractions of roots, exceeding tedious; and for the slippery mistaking or omitting now and then of but one poor little figure (which may soon fall out) somewhat doubtful and hazardous. In regardwherof the Globe hath ever, not without due desert, been admired as a principal necessary Instrument for the readiness, certainty, and eminent perspicuity of demonstration. In which very respects, present trial shall prove this Instrument, the Hemisphere, to be nothing inferior to the Globe itself. But to come to the purpose, because that upon the Globe of the Earth, the true distance of one place from an other must be measured by the shortest line that may be drawn from this unto that; and the shortest of all other that there possibly can be described, is always the portion of a great Circle; Therefore by it, and by none other, all exact Geographical mensuration ought to be made. Again, sith the Hemisphere consisteth of nothing else but great Circles, being divided all of them into their degrees, and movable in such sort, that any manner situation may precisely by them be represented, no doubt can remain of the sufficiency of this Instrument for the perfect performing of this Proposition.  
The diversities of situation of one place in respect of an other, are three in general: For either have they one and the same Meridian, though not one Parallel; and these are from the West and East of equal distance, but unequal from the Equator, and differ therefore only in Latitude: or else have one Parallel, and a diverse Meridian, and these are of unequal distance from West and East, but equal from the Equator, differing only in Longitude: or finally have a diverse both Meridian & Parallel, 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 several Latitudes of either being given, whereof always the one must needs be greater, the other less; subtrahe this from that, and the remainder shall be the distance between both places in the degrees of a great Circle: which, according to the common supposition of 60. miles English answerable to one degree, may soon be converted into miles.  
Distances of the second sort, such I mean as are under any Parallel 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 ways, but most easy and ready with help 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 seek: Likewise the Zenith of the Instrument to be the Zenith of the same place, or rather that very place in deed. Then bring the Equator of the Instrument, and set it at such a distance from the Zenith aforesaid, as doth exactly agree with the Latitude of your first place: So shall the Pole have his true situation in respect of the sa de former place; And the Movable Meridian issuing from it, shallbe in power any Meridian, that can be drawn 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 Semiequator, (remaining, as before it was placed immovable) the difference of Longitude between both places, and at the end thereof fasten the Movable Meridian: This than shall be the Meridian of the second place: In which reckoning from the Equator toward the Pole the Latitude known, you shall take the extreme point thereof for the true Zenith of the second place. Last of all move the semicircle of Altitudes (now it may be called of Mensurations, being in power any great Circle that may be drawn from Zenith to Zenith) till in the Movable Meridian it precisely lighteth upon the Zenith of the second place. The degrees of this portion of that semicircle contained between the two Zenithes, is the exact distance sought for. Here it is to be observed, that if the places be separated one from an other, not by the segment of a Parallel, but by the one half thereof, then are both their Zenithes in one Meridian, and the Pole in the middle: so that the space between both zenithes, and the Pole being doubled, shall yield the distance demanded. And this is the greatest direct distance that can be of places under one Parallel.  
It remaineth, that we speak 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 commonly occurring: which if by the Hemisphere, with all demonstrative certainty, it shallbe no more hard to find, nor less ready to follow, than the wide beaten high way, my good hope is, that the better opinion willbe conceived of so faithful a guide. To be plain therefore and short: He that knoweth the former kind of operation, cannot be ignorant of this, being both one in effect. For setting the Semiequator so far from the zenith of the Instrument upon the fixed Meridian, as is the Latitude of one of the places; And fastening the Movable Meridian, so far likewise from the fixed upon the Equator, as is the Difference of Longitude between both places (which is soon known by abating the less Longitude out of the greater:) Afterward, when in the Movable Meridian, above, beneath, or just in the Equator (if it so happen) the zenith of the other place is truly noted according to the Latitude thereof, apply thereunto the Semicircle of Altitudes, or Mensurations: And his portion comprehended between both zenithes, shall in the parts of a great Circle, make manifest the exact distance required.  
Moreover, if you desire to know how the one of those places beareth from the other: The Semicircle of Mensurations still remaining, as before it was situated for finding the distance, observe in the Horizon upon what point of the Compass it falleth: for that showeth the true bearing of the places proposed the one from the other.   

The Longitude and Latitude of any two Stars being known without any other Observation to find the Distance of the one from the other in the Heavens.  
THat which hitherto hath been spoken 
Cap. 16.  for the finding of Distances between place & place upon the outface of the Globe of the Earth beneath, may serve aswell for observing of them between Star and Star in the Sphere of the Heavens above; with the Longitude and Latitude here to be given in respect of the zodiac, like as there it was and is always to be considered in regard of the Equator. And albeit I know it would have been more agreeable with the suit of our discourse to have handled this matter before, yet considering the near affinity, or rather identity and selfesamenes of these two operations, I thought it best to join them close together. Suppose therefore the Equator of the Hemisphere to be the zodiac, then shall the Pole thereof be the Pole of the zodiac: The fixed Meridian shall be one Circle of Longitudes, and the Movable Meridian any other of the same sort: And every degree of the Movable Meridian, shallbe the Intersection of any Parallel defining the Latitude either Septentrional or Austrine, and therefore the place of one of the Stars proposed: The other star shall be in the zenith of the Instrument: And finally (as before) the Semicircle of Altitudes shall serve for Mensurations. Now then according to the Latitude of one of the stars (which for distinctions sake I call the first) remove the Equator (now the zodiac) from the zenith of the Instrument (now that first star) And the zodiac thus standing immovable, number therein from the fixed Meridian, the degrees of the difference of Longitude, and at the end thereof fasten the Movable Meridian: In which Semicircle beginning from the Zodiac, reckon the Latitude of the second star either upward or downward, as it is either Septentrional or Austrine: And unto the end thereof, being the true place of that second star, fit the Semicircle of Mensurations aforesaid: So shall that portion of it, which is intercepted between both points, be the precise distance in the heavens between the two stars demanded.  
And of the Hemisphere thus much. Hereunto might 
Cap. 17.  I have added the doctrine of right and obliqne Ascensions, together with Dialling and other matters gnomonical: But because the fruit and use of the doctrine of Ascensions consists in the measuring of the true quantity of time, whereof you have before sufficiently heard; I thought it not expedient any further to enlarge this Treatise therewith: The rather, considering my principal purpose, namely the Seaman's Commodity; who little needeth that doctrine: and Dialling less than that. Yet whoso desireth to be doing in both of them, shall by that which hitherto hath been delivered & diligent practice withal, find the Hemisphere very able to satisfy his desire. And not only so, but to minister unto him many rare and goodly conclusions of further invention. Among which I earnestly wish that chief secret of Navigation, the sailing, I mean, by a great Circle, to be always principally remembered: Not doubting, but this Instrument (if any other) will prove a most apt and serviceable one for that purpose: which knowledge, because it requireth long, learned, and very painful experience, joined with singular dexterity, I willingly leave unto those that make special profession of that Art.    

The description and use of a Traverse Board, serving readily to set down the Ships way, according to the usual account, and at all times to prick in the Card accordingly, the true place that she cometh unto.  
LEt there be a Table prepared after the 
Cap. 1.  form of a long square, of 16. inches in length, and 12. in breadth, or else 20. long, and 16. broad, (as you think good, more or less) plain and smooth, with Angles precisely right; and having a square border enclosing it to keep down a sheet of Paper, like as Surveying tables have. Divide the four sides of the border into equal divisions of 8. unto an inch, or any other, (as may be most convenient) reaching all a long the inner side of the square, and number them by five, the figures of every side being twice set down to be reckoned both ways (as occasion shall serve.) Again, subdivide every of those divisions by two pricks into 3. parts, not adding any numbers. If these divisions be wrought upon Latin plates being laid on & riveted to the Border, it willbe a great deal the fairer. Your Table thus finished, you must provide a Ruler and a Quadrant, as necessary furniture belonging thereunto. Let the Ruler be as long as the Diagoniall line of your square, that is, reaching athwart from corner to corner, having the oneside handsomely abated, and both sides perfectly divided from within half an inch of one end throughout, into the very same divisions wherewith the Border was parted, with his numbers also redoubled and (as that) both ways to be accounted in such sort, that the divisions be drawn down to the lowermost edge of the sides of the Ruler, that lieth close on the Table.  
The Quadrant is best of Latin, with his semidiameter of 3. or 4. inches (more or less) somewhat thin, having all the middle of his substance cut away, save about a quarter of an inch breadth reserved for his Circular limb, & there about also for the breadth of his two right sides. Divide the limb into ordinary points of the Compass, expressing them in siphers 1. 2. 3. etc. Let those numbers be twice set down to be reckoned forward & backward, and between every Point let there be halves and quarters. All which parts (as before in the Ruler) must be produced to the nethermost edge of the limb. Divide also the two outsides of the Quadrant into such divisions as the Ruler hath, so far as they will reach, placing the numbers along from the Center-corner, to the meeting of the sides with the limb, and drawing those divisions likewise to the lowermost edge of the sides.  
Now must you consider, that the Navigator hath three helps to find out the place of his Ship, that he may set down the prick thereof upon his Card, viz.  

1. The Angle, on which the Ship maketh her way: which is given by the Compass.  
2. The quantity of the Ships way, to wit, how many leagues she saileth in an hour, or a watch: which they term the dead reckoning, and is learned by often experience.  
3. The Latitude, taken by observation with Mathematical Instruments.   
Any two of these being given, this Instrument maketh the third manifest, and giveth the prick in the Card very readily. Except it so be, that the Ship doth run upon 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 Radical place: And so is every place in the proceeding of the voyage named, whereof the Navigator either by his own, or by other men's practice, hath learned the true situation. And now to approach unto the use, spread a sheet of large paperupon the Table, fastening it with the Border placed thereon, to keep it even and smooth: 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 show to be most convenient) about the middle thereof. That one mark is sufficient to determine all the other sides, towards which of the 4. principal winds they do bear: for his opposite must needs be South, and the other two East and West. So that the divisions in the sides of East and West, do all of them in power represent so many Parallels: and those of North and South in like manner so many Meridian's.  

The use of the Traverse Board.  
FIrst of all mark by the view of your 
Cap. 2  Notes of the Ships way & course, whether it be Northerly or Southerly from the Radical place, and likewise whether Eastwards or Westwards: and according to discretion set your Flower de luce, as may best fit the way of your course. And therefore if it be most South or North, let the longer sides of your Table stand in stead of those parts: if it be East or West, then name the sides accordingly. For example, if it be Eastwards Northerly, set down a prick betokening your Radical place upon the West end of the South side: if it be any other way, set down your prick as may be answerable thereunto: and placing your Ruler square upon equal divisions in the sides East & West, with the edge thereof touching the said Prick, draw a line representing the Parallel of the Ships Radical place, and hard by the point or prick of your Radical place, note the Latitude there of in degrees and minutes: Then set the Centre corner of your Quadrant unto the Radical point, elevating the limb of the Quadrant above the Parallel, according to the quantity 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 end thereof make a prick as close unto the edge as may be. Lastly fastening your Ruler directly upon the prick, and square with the sides of East and West, draw a line, which shall serve for the Parallel that the Ship at that instant is in. And this order of working must from time to time be iterated, till at length opportunity be offered by your Instruments Mathematical to make an observation of Latitude. But if it so fall out, that the Ships way do contain more leagues, than there are divisions in the side of the Quadrant, then applying either side of the Ruler close unto the edge of the Quadrant, by that means you may prick down the number. Having upon shift of winds (as it happeneth) made diverse Traverses, if you desire to know how the place your Ship is in beareth from your Radical 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 have made as yet no observation) do after this sort. Set the one end of your Ruler where the numbers do begin to the Radical point, and directing the other end towards the prick of your Ships last place, cause the edge to lie just & even upon it: Then reckon how many divisions you do find between the two points, and so many leagues distance there is. If it fall not full upon a division, but upon one of those pricks between, they signify English miles. Look how many divisions are contained between the two Parallels, the one of the ships Radical place, and the other of her last place, every twenty of those do make a degree; every several division, 3. minutes; and every prick one minute. Moreover as occasion serveth, you may account 4. or 5. divisions for a league, or more, or less: yea every prick for a league, if you find it requisite, as experience in divers shifts of winds will show you to be most convenient.   

To know how much the Ships last place doth differ from his Radical place in Longitude: also the Angle of Position.  
SEt the Ruler square North and South, 
Cap. 3.  so that the Radical place may touch the side thereof, marking what divisions the Ruler doth cut in the North and Southsides. Again, set the Ruler in like manner square, touching the point of the Ships last place: the number of parts contained between 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 Radical be Easterly, the Longitude is so much increased: if Westerly, it is lessened. Always have you respect to the Meridian, from whence Longitudes do begin to be reckoned, that you may express the number answerable thereunto. Moreover place your Ruler where the numbers begin, at the Radical point, and the side thereof upon the point of the Ships last place: Then apply the Centre corner of the Quadrant unto the Radical point (the Ruler still keeping his place) in such sort, that the side of the Quadrant do lie even with the Ruler: Look how much of the elevated limb above the Parallel, the Parallel itself cutteth off, that is the Angle of Position upon which the last place of the Ship doth bear from the Radical places. But whenso ever you have opportunity to observe the Latitude, draw your Parallel upon the Traverse board according thereunto: and where the line of the Ships course doth cross the Parallel, you must conclude that to be the place which your ship was in at the time of your observation, correcting by that means the other Parallel and distance taken by the dead reckoning, so far forth as it doth differ from this. For of those three helps before specified, the Latitude is only certain: The Angle of the Ships way is reasonable good: but the dead reckoning is an uncertain guess; And if you please to call it a probable conjecture, you shall grace it with the uttermost: notwithstanding it is admitted into Art for want of better helps.  
In considering the Angle of the Ships way, by all means you must have careful regard both unto the Set, and the Variation of your Compass. Otherwise, assure yourself, you shall make but wide reckonings. I have known a very expert Navigator, that making his reckoning without regard of the Variation (which for all that he observed, though he did not reckon by it) overshot the way of his Ship 70. leagues, in a voyage not of so far distance as hence to Cape Verde. Whereas casting over his reckoning with due respect of his Variation, he made a perfect good account of of the very same voyage.   

Having found the place of your Ship in the Traverse-boorde, how to prick it in your Card.  
FOr the conclusions to be performed upon 
Cap. 4.  your Card, it is requisite, that you have a Ruler of some fine wood made very thin, of an inch & a half broad, and of sufficient length: also a Quadrant like unto the former, saving that his two sides must have their divisions agreeable to the Scale of leagues expressed in your Card: and finally 2. pair of Compasses. Being furnished with these, seek out your Radical place from whence you did proceed: Apply the Center-corner of your Quadrant unto it, his limb, respecting the way answerable to the Angle of position in your Traverse-boorde. Set one foot of your Compass upon any Parallel of convenient distance from it (on which side it skilleth not) reaching the other precisely unto it in the nearest distance. Then remove one foot upon that Parallel, the other keeping his scantling, until the division of the Angle of Position in the limb, & the point of the other foot do meet exactly together, the Center-corner still abiding in his place, but moving the limb to or fro, and likewise the Compass (as before I specified) till they meet. Last of all, reckon from the Center-corner your observed number of leagues upon the side of the Quadrant, & there set down a prick or note for the place of your Ship. So shall the Radical angle of Position be limited by the other foot of the Compass in the limb; & the quantity of the way that the Ship hath made, by that prick in the side of the Quadrant.   

Though you have not any Quadrant with his sides divided according to your Card, but only that which you used for the Traverse Board, and also the same Ruler: how to perform all this with the help of two pair of Compasses.  
Search in the Card your Radical place 
Cap. 5.  from whence you did proceed, and apply the Center-corner of your Quadrant unto it, the limb thereof respecting the way answerable to the Angle of Position in your Traverse-boord: After this, with the one pair of your Compasses take the shortest distance from your Radical place to some one Parallel or other, as you may conveniently: and with the other pair, take the distance in leagues, according to the Scale of the Card. Remove the limb (the Centre corner keeping his place) to & fro, and also the Compass (keeping still his scantling) with the one foot a long the Parallel, till the other foot, and the division agreeable to the foresaid Angle, do meet together. The Quadrant remaining in that place, let your other Compasses (being extended according to the number of leagues found out by your Traverse-boorde, but answerable to the quantities of them which are described in the Scale of your Card) have one foot set upon the Radical place, the other along the side of your Quadrant, marking it with a prick or some other note, for the place of your Ship. And after this manner may you find how any one place in your Card doth bear from any other, having regard unto that which hath been before declared.   

Being in a Ship at Sea, to know any places in your Card (that are within your kenning) how far they are from you.  
SEt any two of them by your Compass, 
Cap. 6.  (so that they be not in one right line) and observe according to what Angle of Position they do bear from you; thereby collecting how you also bear from them. Then place your Quadrant upon one of them, agreeable to his Angle (as before hath been taught) and lay a Ruler to the side of the Quadrant that pointeth out the Angle. That Ruler so remaining, remove the Quadrant unto the other place, giving it the quantity of that Angle: and placing a Ruler likewise close unto the side of the Quadrant which pointeth out the Angle, thrust this Ruler directly forward along that side of the Quadrant, till his corner doth touch the edge of the other Ruler: where the touch is, set down a mark, signifying the place of the Ship. And then measure by the Scale of your Card, how far that mark is from either of those places: so have you the distance desired.  
All these Conclusions of the Traverse▪ board may be performed (with a little more pains) by the help of the afore mentioned Quadrant and Ruler upon a fair sheet of large paper, having only a plain Square consisting of four strait lines meeting at right Angles, without any divisions at all: for all the divisions above 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 may easily passed on the Square of an other sheet of paper, and so join both squares together, that your line of the second become all one with that of the first. And thus may your work be continued for the tracing out of any whole voyage, not omitting any Traverse, and noting (if you think good) whatsoever accident you shall judge to be needful. It is convenient to have two of those Quadrants, the one of 5. or 6. inches semidiameter, and the other scarce half so large: The greater for the Traverse-boord will be the more commodious, and the other for the Card.   

How to describe the spiral line of a Ships course.  
WIth a quadrant of this fashion it is a very 
Cap. 7.  easy matter to describe the spiral line of a ships course, from any known Longitude and Latitude, after this sort. The Meridian's and Parallels first supposed to be drawn as the spiral Card requireth, set the Center-corner of your Quadrant upon that point where the Meridian and Parallel of the place, from whence you first departed, do cross one an other: And directing the side of your Quadrant along the Meridian, either Northward or Southward (as the case shall demand) note in the Meridian next adjoining, where the Angle of the Ships way cutteth it: And there making a small prick, trace a line from the former point unto this. Again place the Center-corner (as before) on that second prick, and mark the Intersection in the third Meridian, continually proceeding after this manner, from Meridian to Meridian, till you have finished the whole course. The thicker your Meridian's are drawn, the more perfect will your Card be: but this may be also supplied, with a thin Ruler movable upon the Pole or Centre of your Card. The manner of the draft of the spiral Card, I will show in the next Treatise.    

A friendly Advertisement to the Navigators of England.  
THe duties of a Friend, and the properties of a Flatterer do differ so greatly, that a man cannot perform the office of the one, but he must renounce the practice of the other. And a very fountain it is, from whence many mischiefs do spring, and overflow the wretched life of mankind: That the true dealing of friends is most commonly unpleasant and hateful, but the soothing of Flatterers is become plausible and much set by. In resemblances they bear many times like show, but in purposes they do always differ. A true Friend will sometimes commend and praise divers things in his friend: And so also will the Flatterer in those whom he flattereth: The one commendeth that which in judgement he thinketh commendable, and unto that end that the party commended should still proceed in actions worthy of commendation: The other commendeth even those things many times, which in judgement he doth detest, and unto that end, that he may soothe up the humour of the party, and make his own profit thereby. Moreover, a Friend will dispraise in his friend those things which in judgement he doth disallow; and the greater the faults are, the more earnest will he be: to the end that the party may amend and give no advantage to his enemy. The Flatterer sometimes (though seldom) will also discommend, but evermore trifing matters, and therein will he be very vehement; but in great faults he is both blind and dumb: fearing to offend the party, if he should touch them; and in the other counterfeiting sincere love (the badge only oftrue friendship) And so leaveth he the party thus abused, to the scorn and reproach of the adversary, reaping the commodity which he looked for, as the only end of his travail.  
I do not think there is any man that either regardeth God's glory, or esteemeth of human society, but holdeth your Art worthy to be numbered 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 Art, wherein God showeth his divine power so manifestly, as in yours; permitting unto you certain Rules to work by, and increasing them from time to time, growing still onwards toward perfection, as the World doth toward his end; And yet reserveth still unto himself the managing of the whole: That when you have done what you can, according to the skill you already have, or shall do, by any that you may learn hereafter: yet always will he make it manifest, that he alone is the Lord of the Seas, that all storms and tempests do but fulfil his will and pleasure, and that all the waves of the Sea are continually at his commandment: finally that it is he, who oftentimes administereth many helps beyond all expectation, when the Art of man utterly faileth. All which in the CVII. Psalm is so lively expressed by the Prophet David, that in all writers, whether sacred or profane that ever I read, or by any reports that ever I heard, or in the liveliest pictures that at any time I beheld, it is in my judgement, pierlesse and unmatcheable: describing the whole in brief, and yet in the brevity omitting nothing that was necessary; and affirming nothing but that, which the continual experience of our days doth proclaim to be most true. O that Navigatours therefore would praise the Lord for his mercies, and show forth his wonders before the children of men. That they would once learn that, The fear of the Lord is the beginning of Wisdom. Most undoubtedly then would their Art flourish, their voyages prosper and have better success: yea themselves would be more esteemed & honoured of all men. Whereas now the profane lives and brutish behaviour of diverse of that trade, doth somewhat eclipse the glory of the profession itself: And, besides other manifold punishments, God striketh them with such blindness, as no men living of any trade whatsoever are to be found so ignorant, as many of them are of theirs; so senseless in their own defect, or so little desirous to amend them. Yea, and some of the greatest skill and practice are so loath to give God his due glory, that many times labouring to suppress it, they make shipwreck of their own credits and reputations, which otherwise of right might accrue unto them. When they have performed along voyage of great difficulty, wherein many a time and oft they have been at their wit's end, and knew not which way in the world they should turn themselves, God delivering them beyond their own expectations, as their consciences can witness: 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 credits, to give God the praise, and to yield him thanks, imagining that would derogate too much from the admiration, which they so greedily hunt after among men.  
I have heard a merry report: Ships of sundry Nations lying in a harbour in fair weather, the young mariners were climbing and showing feats of activity, one of one Nation to outbragge the other. At length a nimble yoncker getteth him to the very top of the Foremast, and raising himself bolt upright, turned round upon his foot without any stay, chalendging his Antagonist, or any of the Nation to do the like. His Antagonist presently undertaketh the challenge; but having turned scarce half about, fell down, and (as God would) in his tumbling by good hap caught hold of the shrouds: and assoon as ever he had a little recovered his spirits, being half dead for fear, yet set a bold countenance on the matter: and he also again with a loud voice dared his adversary or any other of that Nation to do the like; as though that which befell him by his error, he had done of very purpose. Even so diverse that have performed long voyages, God knoweth how, but not they themselves; yet will swear and stare, crack & boast, that they have done all things according unto Art: and tell us of such Gulfs and swift Currents, more by a great many then ever God made, and are but devised by themselves for shifts to shadow their ignorance, and to rob God of his praise: the thing being as strange a matter, and as much according unto Art that ever they came home again, as that was, which the fellow before specified wrought his feat by.  
Petrus Nonius maketh mention of one in his days, that had ten times passed from Portugal to the East Indies: And yet diverse times when he should have subtrahed his declination, did add it, and when he should have added, did subtrahe it.  
But for you the Navigatours of England, this I do verily think in my conscience, that divers of you do fear God unfeignedly, and do 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 few in our Nation, yet are they more than any Nation in Christendom can show beside. And albeit your skill is not such, but that amendment may become it well enough: yet do I not judge that either the Spaniards or Portugals, who are accounted the best, do better yours: and for their life and behaviour I take it to be worse than the worst among you, reserving still for them, that which Horace long since imputed unto them:  

Navis Hispanae magister,  
Dedecorum preciosus emptor.   
For notwithstanding their first Navigatours were men of good skill, these now a days for the most part are grossly ignorant: And a great folly it is in diverse of our Nation to have such confidence in Portugal Pilottages for long voyages, having far more skilful of our own Countrymen at home, both better to be trusted, and more valiant and present minded in any danger. And it is a thing very certain, that ours do increase in skill, and better very much their Ancestors, whereas theirs for the most part are a great deal worse: And if they be once any thing out of their ordinary traded course, they are the seeliest fellows that do float upon the Seas. Their Cards are decked with much Gold and little Art, out of measure false (as I have heard by men of good experience) even upon their own coasts, and are but transcripts new furbished. Their other Instruments very simple, especially their staves most contemptibly nought. I have seen diverse of them, even as unfit for the purpose they should serve, as an Ox is to wear a saddle. But we are very much addicted to admire strangers, and contemn our own, according to the old Proverb, For sooth it must needs be true; for I have learned it of a jewe. Two things therefore there are greatly wished by all your well willers to increase in you, The true fear of God, and a careful diligence in things belonging to your Arte. Where the fear of God is not, no Art can serve the turn: for that were to make of Art an Idol. And yet all those that fear God, must take heed, that they do not tempt God: And therefore ought they to use Art, as the means that God hath ordained for their benefit, and be thankful unto him for it.  
These Instruments, that, for the assistance of your Art, it hath pleased God to give me a small portion of knowledge to compose, whether without pains and charges they have been finished and brought to this pass, I commit to your judgements. For mine own part, I am one that in any private respect hath as little to do with the Sea, as any other; and in particular have no cause for to hope that I shall reap any manner commodity thereby. And for these my travails and expenses, although it should be well accepted according to my desire among Navigatours; yet have I no reason to think me one jot to be benefited thereby, no not so much as in any credit (which notwithstanding, if it were one of an other profession, possible he might obtain.) Nay, if I may escape handsomely from mocks and scorns, usual with some Contemners of laudable Sciences, I must think that I have made a fair hand. But I thank God I have bestowed neither pains nor charges, more than I was willing and might well do. And if it may by God's grace prosper to the end that I have purposed, that is, to some of your good, little do I esteem what every Idiot doth think or judge of my labour. I know right well, that among the vulgar people, there are many thousands, which going unto market, do bring home with them a pennyworth or two of Cloaves or Mace now and then; and yet never asked the question where they grew, nor by which way they were transported from their Native country unto us, whether by the way of Ormus through Persia, or of Arabia by Caravan unto Aleppo, or by the Red Sea unto Alexandria, and thence out of the Levant unto us: or whether they came through the huge Ocean by the Cape of Bona Speransa. They take no knowledge of such matters: The consideration of any dangers in the straits of Cincapura, or of the Showldes of Maldivar never troubleth them: And yet it relisheth even as well and serveth their uses as commodiously, as if they had all the afore mentioned knowledge. Albeit I hope that men of understanding and wisdom will easiyly perceive, that God's providence in his works is only manifest unto those which do consider them, and of others is nothing at all discerned, & as little regarded. If it were only among the common sort, that cosmography should be so contemned, it were the less to be marveled at: but that any which profess learning of any faculty whatsoever, should altogether neglect it, and be utterly ignorant of it, it is to be more then pitied, and especially in Gentlemen and Noblemen is it no small defect: who diverse times in this our age have some occasion or other, at the least to talk and discourse thereof. Wherein I could wish they would have in remembrance a saying of Apelles unto Megabysus a Nobleman of Persia▪ who coming into his Shop, although his knowledge was but small, yet was he loath to have it appear that he was ignorant of any thing; And therefore began to question and dispute of lines, of shadows, and of such like matters belonging unto that Arte. But Apelles entreated him to make more spare of his speech: for saith he, my youths which grind my colours, hearing your idle discourses, do 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 cosmography, could be persuaded how easy a matter it were to attain unto some competent knowledge therein, I do verily think, that among those that are of wit and judgement, somewhat more than they of the very vulgar sort, you should not find one among a thousand, that would be ignorant of it, whereas now you have even scant one among a thousand, that hath any understanding therein. For I am well assured, and do speak it upon some experience, that one but of mean capacity, so that he be of a willing mind, and have a sufficient Instructor, with fit Instruments, may very easily in one months space attain unto great contentment of knowledge, yea such, as they commonly imagine, could not be learned in seven years. Now as it is seemly for all men to have at the least some taste in such knowledges, so unto Navigators it is necessary in the highest degree. And I do nothing doubt, but that any one of them, with a two months learning of a skilful Teacher, and three years practice in a few good voyages (God blessing his labours) shall get more perfection in that Art in so small a space, than he could otherwise with twenty years experience, according to the ordinary ignorant practice. Although such instructors are in number but few, yet I think there are more than are greatly employed; and would be many more, if they were in request, and better esteemed, especially about the City of London; whither there is so great repair and concourse of men addicted unto those affairs: where possible (though unknown unto me) there may be diverse, yet know I but one, whose name is john Goodwin, dwelling in Bucklersbury: A man unskilful in the Latin tongue, yet having proper knowledge in Arithmetic, and Land-measuring, in the use of the Globe, and sundry other Instruments: And hath obtained, partly by his own industry, and by reading of English Writers (whereof there are many very good) and partly with conference with learned men, (of which he is passing desirous) such ready knowledge and dexterity of teaching and practising the grounds of those Arts, as (giving him but his due) I have not been acquainted with his like. And great pity it is that in so populous a place, many such were not employed: But greater is the grief unto divers well willers of that noble City, and lovers of good Arts, that where as not many years since, there was a Mathematical Lecture publicly erected for those purposes, and furnished with a learned man of sufficiency answerable, of very honest and courteous behaviour, affable to resolve beginners of their doubts; the party was afterwards dismissed, and the thing (that began to be so great a commendation to the Founders, so principal an ornament to the City, and a commodity (both unto it and the whole Realm in general) was notwithstanding without all regard, basely suffered to sink and vanish in the end unto nothing. Surely in all equity and reason it were fit, that every City standing upon merchandise and marine trades, should be aiding unto those Faculties, whereby the greatest part of their well gotten goods doth accrue unto them: And especially that honourable City, which is not only made rich, but by the means of Navigation is grown famous also throughout the whole World. As therefore I unfeignedly acknowledge that in divers good respects no one City of the whole Earth is comparable unto it. so do I heartily 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 public benefit in that behalf, shall thereby highly commend his own true love towards his City and Country unto all Posterity, and become more renowned by such actions, then by any painted glorious Tomb, or the like kind of monuments.  
The only good method of teaching and learning Cosmography (after a few principles of Geometry and Arithmetic first known) is, to begin with the Celestial Globe, and to be perfect therein, before you deal with the Terrestrial: for this dependeth on that, and the former being once reasonably understood, the other is not two days work. After you have thus received a sufficient impression of the Globe (whereunto all true Maps and Cards have a necessary reference) then will the consideration of them become exceeding pleasant and easy unto you; but never before. This I mention, because I have heard ere now, of certain Teachers, that undertaking men of good ability to be instructed by them, have been a great while about a little; spending the time about diverse pretty particular toys, which full easily would have been known of themselves without any teaching, if they had taken the course that I speak off: But such imitate ill disposed Surgeons, which love to protract a cure, of purpose to suck the more gain therefrom.  
Maps and Cards of the Globe of the Earth are of three sorts most usual, distinguished by their several kinds of Meridian's and Parallels. The first hath his Meridian's and Parallels described by Circular lines: And among those I take that manner of Projection, which Rumoldus Mercator hath used (proposed long before by Orontius in his French Cosmography, as I have heard) to be of all other the very best, having the Meridian's and Parallels drawn according to the Mater of Gemma Frisius general Astrolabe. The reason that I so greatly like of this, is, for that the projection is very Regular, and therein the native Geographical description may nearest of all others obtain their due situation.  
another sort there is, wherein the Globe of the Earth is divided in two Hemispheres, the Centre in both of them being one of the Poles, and the Circumference the Equator. In this the Meridian's are straight lines drawn from the Poles unto the Equator; and the Parallels are Circles. These Parallels may be described after two ways: The one enlarging the lands described towards the Equator, the other, towards the Poles. The former is thus delineated. Set the one end of a Ruler upon the end of one of the Diameters or Meridian's aforesaid, and the other part of the Ruler 90. degrees from that: And keeping the former end fixed upon his place, remove the other to every one, or fifth, or tenth degree of the next Quadrant, till your Ruler passing through the Pole, becometh all one with the same Diameter, noting continually in the Semidiameter of 90. degrees distance, whence you first began to move your Ruler, where it cutteth the said Semidiameter: Then placing one foot of the Compass upon the Centre or Pole, the other upon any of those divisions of the Semidiameter, describe a Circle, which shall be a Parallel answerable to that division: And so may you draw as many, or few, as you think convenient. The other is thus described. Begin at the end of any Semidiameter where it toucheth the Equator, and numbering still equal degrees on each side thereof, mark what intersections your Ruler applied unto them maketh in that Semidiameter: Then may you draw the Parallels here also, even as before. The former of these two is represented unto you by the figure A. the later by the figure B. This kind of Projection serveth most aptly to express in a Card the spiral course of a Ship, which some term paradoxal. But whether of these names (being both as yet strangers) shall best deserve to be freedenized, I leave to other men's judgements: Only I say, (paradoxal) is beside the purpose, and astonisheth with an empty sound: but (spiral) appertaineth directly to the matter, and declareth the true essence of the thing signified.  
The third sort of Cards have both their Meridian's and Parallels of straight lines equidistant, and these only are in ordinary use with Sailors. Of these I need not write any thing, they are so commonly known, and their imperfections in long voyages so manifest, though in short they may well serve the turns. And yet I cannot here conceal one great secret concerning these Cards, namely, that there is a certain draft of them very Artificial and regular: which being well understood, redresseth the errors of the other; and (as far as I can discern) will so satisfy the Navigators expectation, as no Card hitherto invented was ever comparable unto it, neither (as I think) any that shallbe hereafter, will in all respects surpass it. Although for the Geographical descriptions, they may and must alter from time to time, as newer discoveries by light of truth shall make them better known unto us.  
This manner of Card hath been publicly extant in print these thirty years at least, but a cloud (as it were) and thick mist of ignorance doth keep it hitherto concealed: And so much the more, because some who were reckoned for men of good knowledge, have by glancing speeches, (but never by any one reason of moment) gone about what they could to disgrace it. The Card (which I mean) is the same, that was set forth by the excellent Cosmograpber Gerardus Mercator, in show resembling ordinary Sea Cards, save that the degrees of the Meridian's in it do proportionally increase from the Equator toward each Pole, upon good reason and firm Demonstration: thereby showing the true Position of any one place in respect of an other: which the usual Cards in a far distance cannot do, being yet the very principal point that the Navigator desireth.  
For the better understanding and making of Sea Cards of that sort, I have here immediately ensuring set down a Demonstration, which I obtained of a friend of mine of like profession unto myself, evidently showing the proportional increasing of those degrees, wherein consisteth the excellency of that Card.  
First determine the degree of the Equator, in respect whereof you would frame the Meridian of your Card: for example, the little line a. Next describe the Quadrant of a Circle, so large, that it may perfectly and distinctly receive every of the usual 90. degrees, into which it must be divided. Then from the Centre A. toward B. take in the Semidiameter A B. (from whence the degrees of the Quadrant begin) a line precisely equal unto a, namely D F. And from the points D and F. to the Semidiameter A C. raise two Parallels D E. and F G. Again from F. toward B. at a distance convenient, take the second line K H. equal unto a. And from the points H K. raise other Parallels, H I. and K L. equidistant to the former. Afterwards applying the one end of your Ruler to the Centre A. and the other to every the degrees of the Quadrant B C. draw lines athwart between the Parallels aforesaid: so shall all the lines thus drawn contained between the Parallels, 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 soever your Cards be, you must always remember, that the knowledge of the use of the Globe must be a moderator unto them: and that thereby you shall still become master over your Card, to espy and amend his faults; whereas otherwise you shall be mastered by your Cards, blindly embracing their errors. By means hereof it was, that the famous Navigators of the World performed their discoveries & renowned voyages, having no manner of Cards to sail by. And an easy matter it is, for a man that already hath ordinary skill and practise in sailing by usual Cards, to learn in one fortnight so much of the use of the Globe, that upon his observations he may either keep or change his Points for his best advantage; And of any places, whose Longitudes or Latitudes are known, may tell without any Card, upon what point they lie, and how far they are distant from you: Also upon what Point they lie each from other, & the distance between them, with diverse other things that are necessary, and held for rareties in that faculty. For in very many of them Envy doth so reign, that almost every one keepeth his own knowledge to himself, without imparting it unto others: whereas they should all profit a great deal more, if they would communicate their knowledges one with an other, for the public benefit: But in so much as each one affecteth to be singular, disdaining the knowledge of others, they have far less knowledge among them all, then otherwise they might have: for of necessity many men's practices must concur, to make experimental knowledge exact. It were greatly to be wished, that many of them might be found so well minded towards their own trade, as was that notable Pilot Steven Burrowes: who for his skill, industry, and performance, may justly be reckoned among the chief of our Nation, and of the world also; if we respect that only, in stead of all, which he worthily achieved in the first Moscovian discovery by the Scythian Sea: who if he had been employed one Summer more again towards the River of Obbe, I doubt not, but proceeding with his former success, he would have performed more in that Summer for trial of a Passage (any or none) that way unto Catthay, then for the space of these 40. years all Christendom hath done beside; not having (asitseemeth) added unto his, 40. leagues of good discovery, ever since. The good mind he bore towards his profession he testified herein, that by his very earnest means he procured that learned and easy Treatise of Martin Curteise, concerning the Art of Navigation, to be translated into our English tongue. The which doubtless hath given great light unto all of skill in that faculty, that ever were since of our Nation: And is more almost, than all our Navigators have helped the Art of Navigation withal beside. A great help also would it be for the furtherance of skill, if those that are practisers in that Art, and such as are Students of the Mathematics, might often confer together. For except there be a uniting of knowledge with practice, there can be nothing excellent: Idle knowledge without practice, & ignorant practice without knowledge, serve unto small purpose. But certain it is, that all the good parts which may be wished for, or aimed at, shall never absolutely concur in one man. And therefore if there be but some convenient mixture of them in any, that party is to be esteemed. For although many things appertaining to Navigation, may be learned & taught by rules of Art, yet some necessary points (without which all the rest is nothing) are beyond the compass of Art: As for a man to be of a ready and valiant mind; to handle and order those things, that are within the reach of his knowledge, with dexterity upon every present occasion: These and such like are justly termed the gifts of God: For although all things termed by Art are the gifts of God (sith even Art itself is given by God, who is the Author and fountain of all knowledge) yet these are termed his gifts more peculiarly: because the other are given by means, and these without means. Suppose that a man have all the knowledge that may be wished for, & be notwithstanding faint hearted, & his wits (as they say) to seek, when he hath most need of them, his knowledge will aid him very little. Again, if he be of never so bolda courage, & want discretion, knowledge, & judgement, he is very unfit for the government of a Ship: But if such a one be also (as most commonly they are) wilful, taking it for a glory to be foolhardy, this is as great a mischief, as all other dangers of the Sea, if they were all set together. Where therefore boldness of courage, directed & moderated by discretion & judgement; also a body enhabled to brook the Seas, are matched with a willing mind unto Marine affairs, & endued with the fear of God; wheresoever I say, these special gifts of God are to be found, there the ornaments of Art, as necessary additaments, will always most effectually take place, & are most easily attained unto. But where those former, at the least in some comperent measure, are not, all the rest is vanity. It is even a most irksome and woeful sight, to behold a company of courageous young Gentlemen to be led on blindfolded (as it were) in marine actions, by such as have no fear 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 accounted good, where the fear of God is not) but only can tell of their own experience, how they have dissimboched from Terra Stolida, making their voyage toward the Isle of Pickery: gracing themselves (as they suppose) with swearing and staring, and wishly looks. A few such monsters having the chief government in Ships, and voyages, are a great deal more dangerous, than all the monsters in the Sea: And for every one that is bereft of life by these, a hundred at the least are destroyed by the other.  
The serious consideration of these things have occasioned me of a friendly mind and entire good will, (wherein toward your profession, I will give place unto no man living) to admonish you of these points, which I have thought necessary; Beseeching Almighty God, (who is the Lord both of Sea & dry Land) by his holy Spirit of true wisdom to govern & direct you in all your actions, that employing your diligent endeavour in your Art in his fear, and calling upon him in the time of trouble, he may hear and deliver you from all your distresses; And that being delivered, you may accordingly glorify him, yielding praise and thanks for his mercies before the sons of men.  

Let Staff, Card, Compass, Ship, and Skill,  
Depend upon Gods blessed will.