9 The Table of Declination of every minute of the Ecliptick , newly and exactly calculated in degr. min. and seconds , to the greatest obliquity of 23 degrees , 31 min. 30 seconds , from pag. 100 , to 115.

10 The Table of Observations of the Sun , corrected by his Parallax , from pag. 124 , to 141.

11 The eccentricitie of the Sun , the place of his Apogaeum , and Tables of his middle motions , found out and corrected according to the said observations in Chap. 20 , 21.

12 A new Theorick of the Sun , and the manner of making the Table of the Suns Prosthaphaereses thereby , from pag. 154.158 .

13 New Ephemerides of the Sun for five years , and how to make them and continue them for many years past or to come , from pag. 159 , to 168.

14 A new Table of the Suns Declination for the Mariners use , and how by certain Prosthaphaereses to continue the same for many years , from pa. 170 , to 181.

15 The errors of Simon Stevin in finding fault with my Table of Rumbs , from the 214 pag. to the 224.

16 A short Treatise of the whole Art of Navigation .

17 A ●ew and exact Table of the Suns Declination made , and to be used according to the ordinarie manner wherewith English Mariners have been most acquainted from pag. ●7 to 80.

18 A most easie and exact way to find the true height of the Pole in any North Latitude , by knowledge of the heighth of the Pole-star , when the Guard is in any of those 8 ordinarie positions commonly noted amongst Sea-men : from pag. 81 to 90.

19 A Table of Observations of the variation of the Compasse , taken in all parts of the world almost whither any Navigation hath been made in our age ▪ from pag. 91 , to 101 ▪

20 The Haven finding Art or the way to find any Haven or place at Sea , by the Latitude and Variation .

2. The Compass , the chiefest Instrument for keeping the course● shewed by the Chart , by the Variation neglected ( as by some it hath been ) may cause you erre an whole point or two in the courses of divers places : and not rightly used , hath bred much confusion in many parts of the Chart , in laying out many places in false courses : which must needs follow when the Chart is made according to the direction shewed by the points of the Compasse , without abatement or alowance , answerable to the variation in every place . This may especially be seen in those places where the variation is greatest ; as upon the coast of Florida , Nova Francia , and New-found land : where some also seeking to avoid this inconvenience , have fallen into another as ill or worse then the former , in making a double scale of Latitude . And thus one error as a fruitfull mother breeding another , and one absurditie admitted drawing many with it : it will manifestly appeare by exact discourse out of these grounds ( that partly through the false projection of the Chart , and partly through neglecting , or not rightly using the variation of the Compasse ) that it cannot otherwise be , but that the ordinarie Charts are in many places much like an inextricable labyrinth of error , out of which it will be very hard for a man easily to unwinde himselfe .

Hereto accord the often experiments and usuall practise of many well experienced and judicial Mariners and Seamen of our time , who confesse that in sailing from the West Indies to the Azores , they have often fallen with those Ilands , when by their account , according to the Chart , they should have been 150 , or two hundred leagues to the Westwards of them . The like hath been found in sailing from the Azores for Vshent , as I have also partly seen in the little experience I have had at Sea ; where we were come within sight of that Iland , when by account of the ordinarie Chart we should have been fiftie leagues short of it

And as concerning the Courses from place to place , I have observed that some of our Masters take a wise course , in not trusting to those courses which are shewed by their Charts . But first getting themselves into the height or Parallel of the place to which they are going , and withal knowing assuredly whether they be more Eastward or Westward then that place ; they then proceed , alwaies heedfully keeping themselves under that Parallel till they come to the place desired . Then which way of sailing there is none more certaine and infallible , for the sure finding of the place assigned : but it hath this inconvenience , that it maketh the way longer then otherwise in should be , if the straight course where kept .

But to returne to that from whence wee have a little digressed : by these experiments and practise of the skilfullest Mariners , it is manifest that they themselves doe often find the imperfections of their Charts , in shewing the courses and distances of many places each from other , wherto we may adjoyne the experience of the best Hydrographers of our time , who daily making their Charts after the accustomed manner with straight lined rumbes and degrees of Latitude every where equal have found such difficulties in labouring to bring their Marine descriptions to some due correspondence of truth in the courses , heights , and distances ; that tired herewith in the end , they have holden it impossible , to make the Chart agree in all these with the Globe . Wherein notwithstanding they erre , by making too generall a conclusion , in holding that to be simplie impossible , which cannot be done by such a way and meanes as they know and use .

3 The Crosse-staffe , the principall Instrument , that hath at Sea been most generally used , for observing the Altitudes of the Sunne or Starres , thereby to know more assuredly the Latitude , and so to examine and rectifie the account of the course kept by direction of the Compasse upon the Chart , if there be not abatement made answerable to the eccentricitie of the eye ( that is , to the distance wherewith the center or point wherein the sight beams concurre within the eye is further backward then the end of the staffe ) may through neglect of this abatement cause error in taking the height observed to be greater then indeed it is by 10 , 20 , 30 minutes , yea an whole degree , and more sometimes , if the height be much , the staffe small , and the eccentricitie of the eye great .

4 But both this staffe and all other Instruments ( though never so well made and used ) can do us but small pleasure , for finding the Latitude at Sea , if the declination of the Sunne and Starres which wee observe be not also known . To this end therefore there have been made tables of the Declinations , both of the Sun and fixed Starres : yet such as even that which hath been publikely commended , as not differing from truth in any place above one minute ( I mean the Regiment of the Sun , set forth by R. N. ) doth notwithstanding differ from truth in many places eleven , twelve , or thirteen minutes . And as for the fixed Starres , scarce one of them hath his declination truly set down , and agreeable to observation . Yea even the Pole-starre it selfe , though it be better known and more observed by the most part of Seamen then all the rest ; and indeed as it might be used ( being to be observed at any time of the night all the yeere long ) might stand them in as much stead for finding the Latitude as all of the rest almost : yet in the bookes of Navigation that are most common amongst English Mariners , the distance thereof from the Pole is made to be in our time above 40 minutes more then it should be . No marvell therefore if the Mariners complain ( as I have heard them sometimes ) that they cannot make their observations of the Latitude , by the Sunne and this Starre to agree .

Neither is there more truth to be looked for in the declination of many other principall fixed Star●s , published in those bookes , divers of them erring from truth one , two , yea ( some of them ) three whole degrees and more , as in the treatise following shall be shewed . And these errors in the declination of the Sunne and fixed Starres , not only I , but also the right worshipfull Sir Christopher Heydon Knight , and the noble Lord of Knudstrupp , Tycho Brahe founder of Vraniburg ▪ with the gratious Prince William Landtgrave of Hassia , father of him that now is , have often found by many and most diligent observations , with large and exact Instruments , wherein both minutes and halfe minutes might be easily discerned . Notwithstanding , if any stand in doubt hereof , I wish that he himselfe also would bestow no lesse cost , time and diligence to make often heedfull and exact observations then either the Prince of Hassia , or Tycho Brahe , or at least as I my selfe have done ; and then , let him beleeve that which he shall see to be true with his own eyes .

These errors therefore in the Chart , Compasse , Crosse-staffe , and declinations of the Sun and Starrs , I have in the treatise following laboured to reforme to the utmost ( yea rather beyond the utmost ) of my poore abilitie ▪ neglecting in the meane time other studies , and courses that might have been more beneficiall to me : which may argue my good will to have proceeded further , to the amendment of such other faults and imperfections as yet remain , besides those that are alreadie specified , and that especially in two points , that is , in the courses , and Longitudes of places .

The reforming of the Chart in reducing all places from those varying courses , wherein now they are set down , to the true positions they have each from other , by separating the variation ( wherewith they are in the ordinary Charts for the most part intermingled were a busie peece of work : yet as were most worthie , and necessarie to be laboured in , as without which the Charts , Maps , and Globes , or any other Hydrographicall or Geographical descriptions , cannot be freed from many intricate absurdities , wherewith now they must needes in many parts be pestered : because the courses and positions of places are in them set down as they were observed by the varying Compasse , without separating the variation afterwards , that so the true courses and positions of places might be known .

The Longitude also would well deserve both labour and cost to be both skilfully and liberally bestowed , for the finding thereof , whereby it were possible to bring it to that passe ( the motions of the Sunne and Moone , and places of the fixed Starres being verified , whereof that noble Tycho Brahe hath afforded great hope ) that the industrious and willing minded Mariner might be capable thereof , in such sort that for the most part , when the Moone and fixed Starres appeare , he might be able hereby to know what Longitude he is in ( yea even at Sea ) more truly then many have done by their dead reckonings in sailing out of the bay of Mexico to the Azores , or from New-found-land to England , or almost from the Azores to England . But on land the Longitude might by this meanes be found exactly as the Latitude hath been by many observers at Sea . And so opportunities of observation with meet Instruments on shoar , not being neglected , ( especially in long Voyages , farr Eastward or Westward ) many most notorious errors in the Longitudes of places would in short time be corrected , wherewith the most excellent arts of Geographie , and Navigation are very much blemished . For who that loveth truth , can patiently endure to heare the Mariners common and constant complaint of 150 , or 200 leagues error in the distance between the bay of Mexico and the Azores ; or ( that which is yet most intollerable and monstrous ) of 600 leagues difference in the distance between Cape Mendosino and Cape California , some making that distance to be twelve or thirteene hundred leagues , where others will have it ( and that more probably ) to be no more then six or seven hundred .

But for as much as the charge , though not great , ( to speake of ) of providing meet meanes for supply of these wants in the courses and Longitudes , ( but chiefly in the latter ) exceeds the meane abilitie of the most part of them that are most addicted to these ungainfull studies ( I must not say ungratefull , although in these daies they prove most unprofitable to their greatest lovers ) therefore they are for my part like to rest ( as hitherto they have done ) untouched , and only commended unto a certaine kind of hope ( whether vaine or no I know not ) of some Mecaenas at length of manificent spirit to be stirred up , to have some due consideration both of these , and other such wants and imperfections , as yet remaine in so excellent an Art as this of Navigation is .

For surely there is no man ( considering how many other both ingenious and ingenuous , as well Liberall as M●chanicall Arts doe yeeld their aid and service unto this of Navigation ) that can denie the excellencie thereof , or the profitablenes either . But if he will , my purpose is not to stand upon it , nor to convince him by reasons , by records , or by the more wonderful discoveries that have bin performed in this our age , even to the furthest parts of all the earth , and round about the whole compasse of the same , whereby we have been made partakers of the most rare and richest commodities and treasures of the utmost Indies and Islands of the world , and they likewise have participated with us ( or else they have had the more wrong ) in the most precious treasures of heavenly truth . All which and much more then can be thought , or now spoken of , performed chiefly ( next under Gods providence ) by the rules and directions of this art , who seeth not that by how much the more excellent , and unto mankind abudantly profitable it is , so much the lesse ought any notorious error to be tolerated therein , and so much the more ought all whom it may concerne ( yea but in good will only where it may doe good ) to endevour themselves that it may be brought to the highest pitch of perfection . I know not then if any one be unto so excellent an enterprise drawn on to give the best furtherance he can , why he should for his labour fall into any danger of reprehension at all . Yet it may be , I shall be blamed by some , as being too busie a fault-finder my selfe . For when they shall see their Charts and other Instruments controlled , which so long time have gone for currant , some of them perhaps will scarcely with patience endure it . But they may be pacified , if not by reason of the good that ensueth hereupon , yet towards me at the least , because the errors I point at in the Chart , have been heretofore complained of by others ▪ especially by Martin Cortese . and Petrus Nonius , out of whom most part of the first Chapter of the Treatise following is almost word for word translated ; I for my part desiring rather that faults should be found by others then by my selfe , and labouring much more , as for a thing much better , and far more needfull , and profitable , to be a fault-mender , then a fault-finder . Or else I may so much the more be misliked , because in seeking to amend , some will thinke I take too much upon me : For some will say , and of those perhaps that have been employed in Sea affairs all their life long , that all this we goe about is more then needs . For they without all this ado have ever performed their charge with good successe , and are now too old to give eare to these innovations and new schoole tricks . But other Sea-faring men who acknowledge the need hereof , are ashamed peradventure to receive ( as it were ) either correction from the schooles , or direction from the land : and therefore stick not to condemne Vniversities , and all in comparison of their long and daily experience . Others also as more indifferent for the matter , will yet have a fling at the person , thinking this reformation , which is professed , to spring out of other mens fountaines : All which ( because wee are now about a work of amendment ) must also ( if they will heare reason ) amend their opinions . For the first , which seem most unreasonable , do not consider ( being addict to these unreformed Instruments ) how like they are to those old ship-masters , of whom Master Bourne maketh mention , who not many yeeres since , wedded likewise too much to their old accustomed usage , have mocked them that have used Charts , or Crosse-staves , saying , they cared not for their sheep-skinnes , they could keep a better account upon a boord : and them that observed the Sunne or starres for finding the Latitude , they would call Sun-shooters , and Star-shooters , and ask if they had hit it . But marke what commeth hereof : for one of these Masters was he , as I take it , of whom an ancient Seaman ( yet living , as I think ) once told me , who having undertaken the charge of conducting a ship from England to Saint Michaels , ( the Eastermost of the Azores ) and after long seeking , not able to find it , for shame and sorrow cast himself over boord . Wherefore these men , if they consider it well , have no cause to boast of successe without skill ; but to thank God for both , that is , for their great and often good hap and safetie , and for their skill also were it smaller then it is . For I will do them no wrong , but doe freely grant and acknowledge , that from any one place to other , the course , height and distance may be truly set down in the ordinary Chart , wherein the Rumbes are right lines , and the degrees of Latitude every where equal : and so by that Chart they may saile truly enough from hence to Russie , or Island , or any other place . But if by the way they should crosse over from the one to the other , following the direction that their Chart sheweth them , they cannot but erre a great deale , either in course or distance , or both ; especially in those Northerly Navigations . Why then should they , where there is danger of wandring , refuse helpe of any that is willing to shew a better course .

But to come to those that may perhaps object I doe but actum agere , in doing no more then hath bin done alreadie by Gerardus Mercator in his universall Mappe of the World many yeers since : and in publishing something already set forth by Iodocus Hondius , in his greater Mappe of the World and of Europe , now of late : I must answer , that indeed by occasion of that Mappe of Mercator , I first thought of correcting so many , and grosse errors , and absurdities , as I have alreadie touched , and are hereafter at large shewed in the common Sea-Chart , by increasing the distances of the Parallels from the Aequinoctial towards the Poles , in such sort , that at every point of Latitude in the Chart , a small part of the Meridian might have the same proportion almost to the like part of the Parallel , that it hath in the Globe . But the way how this should be done , I learned neither of Mercator , nor of any man else . And in that point I wish I had been as wise as he in keeping it more charily to my self . For so perhaps it might have been more beneficiall to me : neither should any man have had cause to thinke at the first sight of the fourth Chapter of this book ▪ that all I have there set down is stolen out of one of the foresaid Mappes of Iodocus Hondius . But were I brought before a Iudge , I should for my absolution , and Iodocus his condemnation , make the contrary to appeare , and that by his own confession in his letters to me , and to a friend of mine , which I have to shew ; written in Latin with his own hand : To me his writing englished is thus much in effect :

I heare that you are somewhat offended with me , because I have taken those few things out of your manuscript book , whereas I promised you that I would not publish it : which also I would in no wise do without your leave . For my conscience something grudged , even to publish this little , if the distance of places would have suffered me conveniently to send letters unto you . I was purposed to have set this forth under your name : but I feared that you would be displeased therewith , because I have but rudely translated it into Latine .

And in a letter to M Briggs , now Professor of Geometrie in Gresham Colledge , he writeth thus :

I have written to M. Wright in excuse of my self ; I am very sorry that he is angrie with me for that cause . I pray you learn of him how he is affected towards me , and write back unto me , and excuse me unto him as much as you can . I would have published his whole book for the common good , if I might have done it without breach of my faithfull promise . And surely my conscience grudged to publish even this little which I have taken out of his book : but the profit thereof moved me , &c.

The truth is , that at his own instant request , when he wrought as an Ingraver here at London , some of my friends also procured by his flatterie , perswading me thereto , he also assuring me upon his faith and credit that he would not publish it , or any part thereof without my knowledge and consent . But how well and honestly he hath performed that protestation grounded upon faith and credit , the World may now see : and how unthankfull he hath been to me for that which hath been so gainfull to himself , ( as may appeare by so common sale of his Mappes of the World , of Europe , Asia , Africa , and America , all which had yet been unhatched , had he not learned the right way to lay the ground work of them out of this booke ) I my self know too well . But let him goe as he is .

Now if any shall think it to be beyond a Land-mans skill , to find faults in matters belonging to the Seamans profession ; they must know , if they be yet to learn , that one that is but reasonably well acquainted with Geometrical conceits , may as well , if not better then most Seamen , know the nature and properties of the sphaerical form of the Earth and Sea , with all consequents and dependances thereof . By consideration whereof , the true understanding and reason of the Nautical Planisphaere , or Sea-Chart , may by him that hath been but meanly conversant in Mathematical meditations , be better apprehended , then otherwise it can by the Seafaring man , though he spend his whole life in sailing over all the Seas in the World . The like may be said of the Crosse-staffe , and Compasse , and of the Regiments or Tables of Declination of the Sunne and fixed stars , and of all other the principall means and Instruments serving for the Art of Navigation . But it is strange to see the difference of things that in this World is made by the difference of hands from which they are received , howsoever the things themselves be . For let Hannibal a Captaine discourse of Warlike affaires , be it never so slightly and out of reason or season , yet all ( forsooth ) must needes be greatly esteemed and admired , because he so great a Captaine hath spoken it . But let Phormio a Philosopher speake of the same matter , especially in the hearing of Hannibal , be his speech furnished with never so much learning and Judgment , yet must he ( there is no remedie ) be either a foole or a madman for his hire . So by all likelihood , the case may stand with this poore Treatise of mine ; which if it had come forth to publike view , from out of the bosome ( as once it was like ) of a Master at Sea , of great reputed excellencie , it had no doubt then found the favour , which now like enough it shall want : all windes then would have sweetly blown it into the pleasantest haven of every mans ( at least of every Sea-mans ) favourable entertainment . I shall therefore with their patience set down the matter as it was , that none may mistake a truth , which is daughter , not only of time , but of occasion , as hereby may appeare . It is not unknown to some of good place and reckoning , that one of the skilfullest Navigators ( as he was by many accounted ) of our time and Nation , ( who died in Sir Francis Drakes last Voyage ) when he came to that extremitie of sicknes , that he saw there was no other way with him but one , was reported to have gathered and bound together into a bundle all his Nautical notes and observations , and to have cast them into the Sea . But soon after , notwithstanding that report , there came more comfortable newes by a Captain that was familiarly acquainted and conversant with him in all that Voyage , and during the whole time of his sicknes , in whose armes also he died : who moving some speech unto him touching something of Sir Francis Drakes , that might then after his death be expected to come to light concerning Navigation ; Tush ( saith hee ) for that matter there is not much to be looked for at his hands , he had but small skill in that Art . Why , and what will your self then do : ( quoth that Captain ) Whereupon this great Navigator drew forth a book out of his bosome , and delivered it to this Captain a little before his death . This book was shewed by the same Captain to the Right Honourable the Lord high Admiral of England in the Cales Voyage , as being made by that famous Navigator , which his Lordship also ( as it was reported ) thought good should be perused and published . These news moved some expectation of that book : so as the Right Honorable the Earl of Cumberland hearing of it , was desirous also to have a sight thereof , and remembred me unto that Captain , as one not insufficient to peruse and correct the same ▪ And hereupon the book was brought unto his Lordship , at the time and place appointed at Westminster , and was there also delivered unto me to be perused and corrected . Having therefore opened it , and beginning a little to turn over the leaves , to take some general view what matter might be contained therein : I first espied a Diagram , the like whereof I knew very well I had made in a book of min● . And herewithall I was the more moved to see if there were any more that I could know as well as the former : turning over therefore two or three leaves more , I presently espied another figure also , wherewith I was as well acquainted , as with the former for I found not only the very same figure , but ( that which made me the more to marvel for the present ) following also in the same order , as I well remembred it did in my book . Being therefore yet more earnestly stirred up hereat , and wondring what the reason might be , that we should thus agree , I betook my self to the reading of that book . And looking first upon the first leaf thereof , and afterwards in many other places , I found it every where to agree with mine , and to be a coppie of the same book , word for word , which I made , and presented unto his Lordship almost seven years before , as the next morning it plainly appeared , both to his Lordship and to the Captain himself that brought it , by comparing it in all points , with the original exemplar of the same book , which I then brought unto his Lordship .

One crime there yet remaineth which Simon Stevin of late hath charged me with , in the former edition of my Tables of Rumbs , namely , that I have erred about 12 minutes in the Latitude of the fourth Rumb at 78 degrees of Longitude , and above two minutes in the Latitude of the first Rumb from the Meridian , before I come to so little as two degrees of Longitude : whereby hee would prove that my way of making the Table of Rumbs should be erroneous . But the truth is , the error is not so much in my Tables , as in his own too rash unadvisednes , who out of no better ground then so grosse a manner of trial , as he useth in finding out the Latitudes of the Rumbs , working by whole degrees of Longitudes , would make the world beleeve I had committed so great errors in those Tables ; which Latitudes if he had sought by single minutes , he should not by his own way and manner of account have found so much as the sixtieth part of one minute difference from my way whereby I made those Tables ; which as it is of all other the most easie , so it is not inferiour in truth to any way that he hath or can devise : his account , according to his own waies , yeelding alwaies more then truth , and mine something lesse ; and yet not differing so much as one second one from another , if you work his way exactly by small differences of Longitude .

But I fear that whilest I labour to satisfie all , I shall offend some , as making too long a Preface to so smal a volumne : I will therefore hasten to an end : Only shewing the sum of this Treatise ; which I thought good to offer unto your view , as a short abridgement of all that followeth , and rather to set it apart by it self , then to include it , as I was purposed , within this Preface , which is beyond his bounds alreadie .