Certain Errors in NAVIGATION.  
Detected and Corrected By Edw. Wright.  
With many Additions that were not in the former Editions  
London. Printed by joseph Moxon. and sold at his Shop at the Atlas on Cornhill. 1657.    

Additions To this Edition that were not in the former.  
THe Table for the true dividing of a Meridian of the Sea-Chart, here called the Table of Latitudes, made to every minute of the Quadrant, which in the former edition was to every tenth minute, from page. 14 to the 36.  
2 Divers additions concerning the true graduating and making both of a general and particular Sea-Chart, and touching the use of the Table of Latitudes, in the 4, 5, 6, and 7 Chapter.  
3 The angle of any Rumb or Helisphaerical line with the Equinoctial being given, to find presently the Latitude thereof for any Longitude given, page. 46.  
4 The Table of Rumbs more exactly calculated then before, and a Table of the eighth Rumb calculated to every tenth minute, and added to the former: from page. 25, to 54.  
5 The use and making of the Searings, from page. 75, to 79.  
6 A Table of the Magnetical inclination, calculated to every degree of the Quadrant, together with the Geometrical demonstration of the making thereof.  
7 To find the angle of the true Horizontal line, with the visual line touching the roundness of the Sea, at any height of the eye above the water, and to this end an Observation and demonstration for the finding of the quantity of the Earth's Semidiameter: from page 87, to 96.  
8 A Table of Refractions of the Sun and fixed Stars, pag. 97.  
9 The Table of Declination of every minute of the Ecliptic, 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 eccentricity 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 Theoric of the Sun, and the manner of making the Table of the Suns Prosthaphaereses thereby, from pag. 154.158.  
13 New Ephemerideses 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 Sun's 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 Sun's Declination made, and to be used according to the ordinary manner wherewith English Mariners have been most acquainted from pag. ●7 to 80.  
18 A most easy and exact way to find the true height of the Pole in any North Latitude, by knowledge of the height of the Polestar, when the Guard is in any of those 8 ordinary positions commonly noted amongst Seamen: from pag. 81 to 90.  
19 A Table of Observations of the variation of the Compass, 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.   

To the Worshipful Captain Thomas Whetstone Esquire.  
Much honoured Sir,  
THe loving respects which your pains expressed to me-wards, when some occasions urged me to make application to your Worship, hath so far obliged me, that I should not acquit myself of ingratitude if I should let slip the opportunity I have to render your Worship Thanks:  
And with all Sir, knowing your good affection to and perfection in Sciences Mathematical, and especially that most necessary, most profitable, and Honourable branch thereof, Navigation; I further make bold to Dedicate this the third Edition of Mr Edward wright's Correction of errors in the Art of Navigation, to the acceptance and Patronage of you most honoured Sir.  
The Author in his Time thought it a Present for a Prince, nay a splendent and illustrious Prince, and therefore Dedicated it to the eldest Son of James King of great Britain; viz. Henry, than Prince of Wales; whose budding virtues grow in you, whose Heroic spirit acts in you, and whose hopeful valour and Courage powerfully and effectually manifests its self in you.  
But Sir, Its Patron is Dead, and so is the Elementary part of its Author; and a shame it were so worthy a work should again enter on the stage of the world without either Author to own it, or Patron to Protect it: And therefore Sir, as this motive moved me (who am now become the Disposer of the Book) to Dedicate it to your Worship, so let the same argument persuade you to accept it; that so as the former Impressions have found a current vent, this the latter Edition may by your good Countenancing thereof, receive the quicker sail, to the Profit of the Printer, the benefit of the Buyer, and the general profit and benefit of the whole Art of Navigation.  
I desire the Almighty to bless your Worship with health and prosperity, and to carry you along in all your Worthy adventures: I wish your increase of Honour, and honourable actions; and that you may shine at Sea as a Star of the first Magnitude fixed in the Zenith; that so your Name may affright your Enemies, your deserts engage your friends, and your Example be as a Whetstone for all truly honourable, to set the edge of their virtues on.  
I subscribe myself, Your Worship's most affectionate and humble servant. Joseph Moxon.   

THE PUBLISHER TO THE READER.  
WHen I considered the elaborate pains of that able Mathematician Mr Edward Wright, I thought it very uncommendable to our English Nation that his so useful a book should (as it were) sleep itself to death; and therefore for the benefit of Seamen have I printed a third Impression.  
I shall not need to enconiumize upon the skill of the Author, nor excellency of the work; many learned and famous men having already eased me of that Task: Nay the book itself though others were silent (being the most Authentic Testimony) can speak for the abilities of the one, and accomplishment of the other.  
Some perhaps may think that because the Tables of the Sun's Epemerides and Declination were Calculated to the year 1608 etc. that they are for these present years useless, because of the length of time that is since then already past; and therefore that they ought to be new Calculated to this present time but herein they are over Curious; for our Author himself (than whom, I never heard of any man more precise) in an Example for finding the place and Declination of the Sun by those Tables, mentions a year yet to come, Pag. 171. and tells us that they will serve for many following years without any sensible error; which insencible error if the over nice will avoid, our Author hath not left him unfurnished with Rules sufficient for his purpose. Besides if in the New Calculation there had been any Difference (though never so small) the Tables would not have agreed with the Observations that he made at that Time, nor the operations that were wrought upon those Observations.  
I have added the Treatise called The Haven finding Art, to the end of this book; the subject being both suitable and serviceable to every Seaman, and the more Notable because of the great probability there is thereby to find the Longitude; which doubtless, if there be two such Magnetical Poles as our Countryman Mr Anthony Linton in his small Treatise entitled News of the Compliment of the Art of Navigation, and divers other learned men have affirmed, (though our Author herein Dissent from them) then may it not be very Difficult by the Latitude and Variation of the Compass observed to find the Longitude. I confess it may be thought that that opinion may be refuted by the Variation of Variation; But Time who hath lately revealed the Variation of Variation, hath also discovered the Regularity of the Motion of this Variation: by which, the Variation of any Place being already known, may be Calculated what the Variation shall be for any year to come. But it were to be wished that this knowledge had been revealed to our Author Mr Wright, or some other so public spirited as he was.  
Another way of finding Longitude there is, and that is by Celestial Observations, lately set forth by Andrea's Berlicome of Rotterdam, which indeed I have translated into English, and intended to have annexed to this Book; but two Considerations Diverted my purpose, the one was, because the way Berlicome shows, was long since set forth by a Countryman of our own; viz. Mr Anthony Linton aforesaid, and therefore I was unwilling to applaud a Stranger for the Credit an English man had Deserved. The other Consideration was because those Observations cannot well be made at Sea, in regard of the Ships continual Tossing; and therefore not useful for Seamen.  
Thus Courteous Reader wishing you to mend such literal faults with your pen as may have escaped the Press, I commend the book to your acceptance, and desire, that as formerly the name of Mr Wright hath been famous all the world over, where Navigation doth flourish, so still his memory may be remembered, and every leaf of this book may be as so many Heralds to proclaim the worth and Deserts of so excellent a Man.  
Farewell, Joseph Moxon.   

The Preface to the Reader.  
THe Art of Navigation (as it is called) though it hath now been in use some thousands of years, yet how far it is at this day from the perfection which is and were to be desired, we would scarce believe (as a wonder that a thing of so great commodity, should no more be sought into, in so many ages:) but that both the books of the learned are extant, to testify, and reason (approved by often trial) doth plainly show that the principal means, and Instruments this Art useth, have been thus long so far from this perfection, that chose they have been and are much stained with many blots and blemishes of error and imperfection.  
1 The Sea-Chart (the best mean the Mariner hath to know the course from place to place) as it hath been hitherto generally made, is so faulty in the very foundation and groundwork thereof (that is, in the Geometrical lineaments of the Meridian's, Parallels, and Rumbs described therein) that hereof there may arise so gross error, as may cause the Mariner to miss one, two, yea three whole points of the Compass (and more sometimes in a far Northerly or Southerly Navigation) in finding the course from place to place. Whereof it may also be necessarily inferred, that following the direction of his Chart, in such sort as hath been used for finding the distances of places, he may err twice, yea thrice so much as the whole distance cometh to, and more sometimes in those Northern parts, in taking the distance to be twice, thrice, yea four times greater than indeed it is.  
2. The Compass, the chiefest Instrument for keeping the course● showed by the Chart, by the Variation neglected (as by some it hath been) may cause you err 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 showed by the points of the Compass, without abatement or allowance, 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 Newfound land: where some also seeking to avoid this inconvenience, have fallen into another as ill or worse than the former, in making a double scale of Latitude. And thus one error as a fruitful mother breeding another, and one absurdity admitted drawing many with it: it will manifestly appear 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 Compass) that it cannot otherwise be, but that the ordinary 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 unwind himself.  
Hereto accord the often experiments and usual practice of many well experienced and judicial Mariners and Seamen of our time, who confess that in sailing from the West Indies to the Azores, they have often fallen with those Lands, 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 Island, when by account of the ordinary Chart we should have been fifty 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 showed 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, always heedfully keeping themselves under that Parallel till they come to the place desired. Then which way of sailing there is none more certain and infallible, for the sure finding of the place assigned: but it hath this inconvenience, that it maketh the way longer than otherwise in should be, if the strait course where kept.  
But to return to that from whence we have a little digressed: by these experiments and practice of the skilfullest Mariners, it is manifest that they themselves do often find the imperfections of their Charts, in showing the courses and distances of many places each from other, whereto we may adjoin the experience of the best Hydrographers of our time, who daily making their Charts after the accustomed manner with strait 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 err, by making too general a conclusion, in holding that to be simply impossible, which cannot be done by such a way and means as they know and use.  
3 The cross-staff, the principal Instrument, that hath at Sea been most generally used, for observing the Altitudes of the Sun or Stars, thereby to know more assuredly the Latitude, and so to examine and rectify the account of the course kept by direction of the Compass upon the Chart, if there be not abatement made answerable to the eccentricity of the eye (that is, to the distance wherewith the centre or point wherein the sight beams concur within the eye is further backward than the end of the staff) may through neglect of this abatement cause error in taking the height observed to be greater than indeed it is by 10, 20, 30 minutes, yea an whole degree, and more sometimes, if the height be much, the staff small, and the eccentricity of the eye great.  
4 But both this staff 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 Sun and Stars which we observe be not also known. To this end therefore there have been made tables of the Declinations, both of the Sun and fixed Stars: yet such as even that which hath been publicly 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 Stars, scarce one of them hath his declination truly set down, and agreeable to observation. Yea even the Polestar itself, though it be better known and more observed by the most part of Seamen than all the rest; and indeed as it might be used (being to be observed at any time of the night all the year long) might stand them in as much stead for finding the Latitude as all of the rest almost: yet in the books 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 than it should be. No marvel therefore if the Mariners complain (as I have heard them sometimes) that they cannot make their observations of the Latitude, by the Sun and this Star to agree.  
Neither is there more truth to be looked for in the declination of many other principal fixed Star●s, published in those books, divers of them erring from truth one, two, yea (some of them) three whole degrees and more, as in the treatise following shall be showed. And these errors in the declination of the Sun and fixed Stars, not only I, but also the right worshipful Sir Christopher Heydon Knight, and the noble Lord of Knudstrupp, Tycho Brahe founder of Vraniburg▪ with the gracious 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 half minutes might be easily discerned. Notwithstanding, if any stand in doubt hereof, I wish that he himself also would bestow no less cost, time and diligence to make often heedful and exact observations then either the Prince of Hassia, or Tycho Brahe, or at least as I myself have done; and then, let him believe that which he shall see to be true with his own eyes.  
These errors therefore in the Chart, Compass, cross-staff, and declinations of the Sun and Stars, I have in the treatise following laboured to reform to the utmost (yea rather beyond the utmost) of my poor ability▪ neglecting in the mean time other studies, and courses that might have been more beneficial 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 already 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 busy piece of work: yet as were most worthy, and necessary to be laboured in, as without which the Charts, Maps, and Globes, or any other Hydrographical or Geographical descriptions, cannot be freed from many intricate absurdities, wherewith now they must needs in many parts be pestered: because the courses and positions of places are in them set down as they were observed by the varying Compass, 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 pass (the motions of the Sun and Moon, and places of the fixed Stars 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 Moon and fixed Stars appear, he might be able hereby to know what Longitude he is in (yea even at Sea) more truly than many have done by their dead reckonings in sailing out of the bay of Mexico to the Azores, or from Newfoundland to England, or almost from the Azores to England. But on land the Longitude might by this means be found exactly as the Latitude hath been by many observers at Sea. And so opportunities of observation with meet Instruments on shore, not being neglected, (especially in long Voyages, far Eastward or Westward) many most notorious errors in the Longitudes of places would in short time be corrected, wherewith the most excellent arts of Geography, and Navigation are very much blemished. For who that loveth truth, can patiently endure to hear 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 intolerable and monstrous) of 600 leagues difference in the distance between Cape Mendosino and Cape California, some making that distance to be twelve or thirteen hundred leagues, where others will have it (and that more probably) to be no more than six or seven hundred.  
But for as much as the charge, though not great, (to speak of) of providing meet means for supply of these wants in the courses and Longitudes, (but chiefly in the latter) exceeds the mean ability of the most part of them that are most addicted to these ungainful studies (I must not say ungrateful, although in these days 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 certain kind of hope (whether vain or no I know not) of some Maecenas 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 remain 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 Liberal as Mechanical Arts do yield their aid and service unto this of Navigation) that can deny the excellency thereof, or the profitableness 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 been performed in this our age, even to the furthest parts of all the earth, and round about the whole compass 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 than can be thought, or now spoken of, performed chiefly (next under God's 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 less ought any notorious error to be tolerated therein, and so much the more ought all whom it may concern (yea but in good will only where it may do good) to endeavour 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 busy a fault-finder myself. 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 myself, and labouring much more, as for a thing much better, and far more needful, and profitable, to be a fault-mender, than a fault-finder. Or else I may so much the more be misliked, because in seeking to amend, some will think 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 go about is more than needs. For they without all this ado have ever performed their charge with good success, and are now too old to give ear to these innovations and new school tricks. But other Seafaring men who acknowledge the need hereof, are ashamed peradventure to receive (as it were) either correction from the schools, or direction from the land: and therefore stick not to condemn Universities, 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 men's fountains: All which (because we are now about a work of amendment) must also (if they will hear 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 years 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 sheepskinnes, they could keep a better account upon a board: and them that observed the Sun or stars for finding the Latitude, they would call Sun-shooters, and Star-shooters, and ask if they had hit it. But mark what cometh 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 michael's, (the Eastermost of the Azores) and after long seeking, not able to find it, for shame and sorrow cast himself over board. Wherefore these men, if they consider it well, have no cause to boast of success without skill; but to thank God for both, that is, for their great and often good hap and safety, and for their skill also were it smaller than it is. For I will do them no wrong, but do 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 sail truly enough from hence to Russie, or Island, or any other place. But if by the way they should cross over from the one to the other, following the direction that their Chart showeth them, they cannot but err a great deal, either in course or distance, or both; especially in those Northerly Navigations. Why then should they, where there is danger of wand'ring, refuse help of any that is willing to show a better course.  
But to come to those that may perhaps object I do but actum agere, in doing no more than hath been done already by Gerardus Mercator in his universal Map of the World many years since: and in publishing something already set forth by jodocus Hondius, in his greater Map of the World and of Europe, now of late: I must answer, that indeed by occasion of that Map of Mercator, I first thought of correcting so many, and gross errors, and absurdities, as I have already touched, and are hereafter at large showed 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 myself. For so perhaps it might have been more beneficial to me: neither should any man have had cause to think 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 Maps of jodocus Hondius. But were I brought before a judge, I should for my absolution, and jodocus his condemnation, make the contrary to appear, and that by his own confession in his letters to me, and to a friend of mine, which I have to show; written in Latin with his own hand: To me his writing englished is thus much in effect:  
I hear 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 Latin.  
And in a letter to M Briggs, now Professor of Geometry in Gresham College, he writeth thus:  
I have written to M. Wright in excuse of myself; I am very sorry that he is angry 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 faithful 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, etc.  
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 flattery, persuading 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 unthankful he hath been to me for that which hath been so gainful to himself, (as may appear by so common sale of his Maps 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 book) I myself know too well. But let him go as he is.  
Now if any shall think it to be beyond a Land-mans' skill, to find faults in matters belonging to the Seaman's 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 than most Seamen, know the nature and properties of the spherical form of the Earth and Sea, with all consequents and dependences 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 cross-staff, and Compass, and of the Regiments or Tables of Declination of the Sun and fixed stars, and of all other the principal 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 Captain discourse of Warlike affairs, be it never so slightly and out of reason or season, yet all (forsooth) must needs be greatly esteemed and admired, because he so great a Captain hath spoken it. But let Phormio a Philosopher speak of the same matter, especially in the hearing of Hannibal, be his speech furnished with never so much learning and Judgement, yet must he (there is no remedy) be either a fool or a madman for his hire. So by all likelihood, the case may stand with this poor Treatise of mine; which if it had come forth to public view, from out of the bosom (as once it was like) of a Master at Sea, of great reputed excellency, it had no doubt then found the favour, which now like enough it shall want: all winds than would have sweetly blown it into the pleasantest haven of every man's (at least of every Seaman's) 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 appear. 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 extremity of sickness, 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 news by a Captain that was familiarly acquainted and conversant with him in all that Voyage, and during the whole time of his sickness, in whose arms 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 he) 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 yourself then do: (quoth that Captain) Whereupon this great Navigator drew forth a book out of his bosom, and delivered it to this Captain a little before his death. This book was showed 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 Honourable the Earl of Cumberland hearing of it, was desirous also to have a sight thereof, and remembered 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 herewithal 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 remembered it did in my book. Being therefore yet more earnestly stirred up hereat, and wondering what the reason might be, that we should thus agree, I betook myself 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 copy 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 he 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 unadvisedness, who out of no better ground than so gross 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 believe 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 easy, so it is not inferior in truth to any way that he hath or can devise: his account, according to his own ways, yielding always more than truth, and mine something less; 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 whilst I labour to satisfy all, I shall offend some, as making too long a Preface to so small a volume: I will therefore hasten to an end: Only showing 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 itself, then to include it, as I was purposed, within this Preface, which is beyond his bounds already.  

The sum of the Treatise following.  
THe Treatise following containeth four principal parts; whereof the first may be called Hydrographical; wherein are set down the errors of the common Sea-Chart, with right lined Rumbs, and degrees of Latitudes every where equal: then the way to avoid these errors is Geometrically demonstrated, and out of this demonstration a Table is calculated and the use thereof showed, for the true and easy dividing of the Meridian's in the Chart, both general and particular, in to single minutes of Latitude, increasing in due proportion towards the Poles, whereto is adjoined, as arising from thence, the Table of the seven first Rumbs, showing by what points of Longitude and Latitude each of those Rumbs is to be drawn, from the Equinoctial till you come within a minute of the Pole: with help of which Tables, the Rumbs may in any Chart, Map, or Globe, much more truly be described, then by those maechanicall ways, long since published by Petrus Nonius, or lately practised by some Globe-makers in England. To which is annexed a Table of the eighth Rumb, showing the quantity of one degree of Longitude at any Latitude, in minutes seconds and thirds of one degree of the Equinoctial. Which degree of Longitude being divided by 3 at any Latitude, giveth you the number of leagues contained in one degree of the Parallel at that Latitude. By means of this Table, the Table of Rumbs may (according to Stevins way) be more truly and easily made or examined, then by that which he hath lately set forth, 4 libr. Geogr. de Histiodromia. After this followeth a most plain and sensible demonstration of the disagreement of the common Sea-Chart, and of the agreement of the Globe with the Chart before described, the use of which Chart is showed in the Chapter next following: where also (the Longitudes and Latitudes of any two places being given) the way is set down how to find their distance, measured either in the segment of the Rumb, or in the arch of the great circle that is drawn between them, both mechanically with Ruler and Compass, and Mathematically by the doctrine of Triangles; whereby it may without much difficulty be conceived how Navigation may by Arithmetical calculation only be performed without Chart or Globe, the Longitudes only and Latitudes of the places from whence you come and whither you go, being first known.  
The second principal part of this Treatise may be called Magnetical; because it intreateth of the Variation of the Compass, showing how the same may be found at Sea (the Latitude being given) by one observation of the Sun's height, and point of the Compass whereupon he is at the same instant, before or after noon, with help of the Globe or Astrolabe: which way of finding the Variation is also exemplified, with a Table of such observations as I took both at Sea and on shore, in the Voyage of the Right Honourable the Earl of Cumberland, in the year 1589. But this way of finding the Variation, being something tedious, I have now therefore hereto newly adjoined the making and use of the Seaman's Rings; an Instrument which long since I devised for the present finding both of the Variation and time of the day, at one instant, even together with the observation, without any further trouble of using any other Instrument, or working, either Mechanical or Arithmetical, after you have observed. Yet because these Rings, and the Globe and Astrolabe also are such Instruments as every one cannot easily have and use at Sea; I have further showed how by the Sun's point of the Compass (or Magnetical Azimuth) and altitude given by observation the Variation may be found, either mechanically, with Ruler and Compass, or Mathematically by the doctrine of Triangles, and Arithmetical calculation. And seeing moreover that of late years, divers industrious Seamen of our Nation have begun to make some observation of that new found property of the magnetical needle's inclination, or dipping under the Horizon, after it is touched with the Loadstone; by means whereof, it seemeth something probable, that Seamen may have some help to know their height or Latitude in dark and cloudy weather, when neither Sun, nor Stars for many days appear, to be observed: I thought it should not be impertinent to this place to set down the Theoric that hath been devised of this magnetical inclination, together with a demonstration for the making of a Table thereof, to every degree of Latitude, according to that Theoric▪ to the end that such of our Seamen as mean to be diligent observers hereof, may make heedful trial of that inclining property: and compare the same with this Table, in all parts of the world where they shall travel; especially in those long Voyages to the East and West Indies, and in their North-east or Northwest discoveries.  
The third part may be called Geometrical entreating of the cross-staff, and showing how such errors may be avoided, as have been commonly committed in the use thereof, either by reason of the parallax, or eccentricity of the eye, or by the height of the eye above the water, or by the parallax or refraction of the Sun. And because for finding the quantity of the angle that is to be abated out of the apparent altitude of the Sun or stars, observed by this staff, for any height of the eye above the water it was needful to know the quantity of the earth's semidiameter, concerning which there is great variety of opinions amongst learned authors: I have therefore in this part of this treatise now showed divers ways for the more certain finding thereof; one of which ways I have also for my more assurance exemplified by observation, as means and opportunity served me, near Plymouth sound anno 1589.  
The fourth and last part may be called Astronomical, wherein my chief intent was to correct the errors that are in the ordinary Tables of declination of the Sun, and fixed stars. To which end there is first set down a table of the declination of every minute of the Ecliptic, in degrees, minutes and seconds, calculated for the greatest obliquity of the Zodiac as it is found by observation in this age, 23 degrees, 21 minutes and an half. Whereto is adjoined the use thereof for the ready finding of the place of the Sun by his declination given: or chose for finding the Sun's declination, his place being first known. After this is showed the way and means I used for exact observation of the Sun's Meridian altitudes, with a table of those observations, for four years together, that so the more certainty might be had of the declinations and places, and consequently of the whole course and motion of the Sun: and that by comparing together so many observations, the Sun's eccentricity and Apogaeum might the more assuredly be known. By knowledge whereof, the way was laid open for the correcting, and true making, of the Tables of the Sun's middle motions and Prosthaphaereses, which were necessary helps and means for calculating the Ephemerideses of the Sun there set down, without which the regiment or table of declination of the Sun next following (which I may commend as free from error observable at sea, and seldom differing one minute from observation on land, and for which principally all the former pains were undertaken) could not so easily have been made. Now if any shall think that most of this fourth part going before this regiment, might have been omitted as being impertinent to the use of Mariners, and exceeding their capacity: I answer, that it was not my purpose, neither could I in all places apply myself to the most part of sea-mens' capacity, knowing many that would not be content with this regiment alone, but that desired more to know the ground and root from whence this fruit grew: whose desire I was also willing to satisfy as I could for the present, having seldom had a more inconvenient season for such a purpose. Then after some caution given, concerning the use of this table of Declination, and the Equation thereof in places far differing in longitude from hence, there followeth a Table of 32 principal fixed stars about the Equinoctial, that have been most commonly known and observed by Seamen with their Declinations corrected: and another Table of as many more of the notablest stars about the North Pole is thereto annexed, with their distances from the Pole, corrected also and verified by diligent Observation on land. To these is added a Table of the Sun's Right Ascensions (resolved into hours and minutes) for every day of the year with the use thereof, for finding at what hour any of those stars cometh to the Meridian at any time of the year: that hereby the Mariner might find at all times when they come to the Meridian, and so the easilier learn to know and observe them. Hereunto I have newly adjoined the description and use of an Instrument, which way not unfitly be called a Sea-quadrant; whereby is showed, how the height of the Sun at sea, may by two observers, be much more exctly observed then by any other means before published: and how the height of the Pole may readily be found at any time of the night, by observation of the Polestar and Guard, without making any abatement or allowance (as the manner hath been) in regard of the point of the compass whereupon the Guard is situate. But now for further satisfaction in every one of these particulars, I refer the friendly Reader to the Treatise itself here following, which Simon Stevins inconsiderate desire of finding fault with my Tables of Rumbs, hath caused me to conclude with an Answer to him plainly showing himself and not me, to be in the same fault that he would find with me.  
To this Treatise (for the benefit of the younger and unskilfuller sort of Seamen) it was thought not unmeet to adjoin the short Treatise following containing the sum of the whole Art of Navigation, first set forth in Spanish by Roderigo Samorano and since translated into English, by a friend of mine, for the benefit of our Nation: which Treatise I would wish all them that are but New beginners in that Art, first to peruse, and understand well, before they come to the reading of the former, which (for the reading thereof with the greater profit) requireth such a one as is already reasonably well acquainted with the rules and principles of that Art: which I have not hitherto known to be more briefly and plainly, nor yet more fully set down and published in any other book, than they are in that little Treatise. This notwithstanding I must admonish the Reader, that in stead of the Sea-Chart therein described, according to the common error, with equal degrees of Latitude, he follow that manner of making the same, which I have in the former Treatise set down, Chap. 3, 4, 5, and 6. And that in stead of the rules and allowances for finding the Latitude by the height of the Polestar (which are many ways, and much erroneous) he must follow the Tables adjoined to the end of that Treatise; which for any of those eight positions of the Guards, at which Seamen use to take the height of the Polestar, do in any Latitude truly show the height of the Pole by the height of the Polestar truly observed. Which Tables, together with some others in the former Treatise; as namely, that of the Declination of every minute of the Ecliptic in the 17 Chapter, together with those of the Suns Prosthaphaereses and Ephemerideses in the 22 and 25 Chapters, as also that of the Sun's Declination Chapter the 27: I could not by reason of my many distractions intent to make myself: but was enforced to procure my kind friend M. Henry Brigs to undertake that labour for me: which notwithstanding (I persuade myself) many will think might well have been spared; being all undertaken upon no greater occasion than the error of one minute and a half in the Sun's greatest Declination, which (by following the example of Copernicus and others, the chiefest Arts masters in Astronomy, in not regarding the Sun's Parallax, when by his Solstitial altitude, and the height of the Pole, I sought the obliquity of the Zodiac, and distance of the Tropics) was committed in those Tables in the former edition of my book of Errors in Navigation.  
But howsoever I may perhaps for this cause be censured by some, of too much curiosity; yet this I am sure of, that all Mariners and Seamen, and whosoever else shall have occasion to make use of this book, have just cause to think well of my carefulness herein; who would have so much labour undertaken, as to have all those Tables with great diligence newly calculated throughout: rather than so small a fault as that should in this edition also pass on uncorrected. This labour therefore together with the rest, I commend to thy friendly acceptance. Farewell.    

Certain Errors IN NAVIGATION CORRECTED.  

CHAP. I. Faults in the common Sea-Chart, with Rumbes expressed by right lines, and degrees of Latitude, every where equal.  
AS the Sea-Chart is one of the most principal Instruments that Mariners have for their direction in sailing, so there is not any, wherein there are so great and dangerous errors.  
1. For first, what places so ever are described therein, 
Error in the proportion of the length and breadth of places in the common Sea-chart  the length of them (from East to west) hath a greater proportion to the breadth (from North to South) then indeed it ought to have (except it be at the Aequinoctial.) And so much the more this error increaseth, by how much the further distant those places are from the Aequinoctial: even as the proportion of the Meridian to the Parallel, increaseth the more, the nearer you come to either Pole; so that at the Parallel of 60 degr. of latitude, the proportion of the length to the breadth is twice greater than indeed it should be; and that because the Meridian is double to that Parallel, and so in all the rest, the proportion of the length to the breadth shall be greater than the truth▪ in the same proportion, wherewith the Meridian exceedeth the Parallel.  
As for example: In the common Sea-Chart, the proportion of the length of Friesland, to the breadth thereof, is twofold greater than in the Globe, (which showeth the true proportion of the length to the breadth) because the Meridian is double to the parallel of that Island. In the Lands of Groenland and Grocland, the length to the breadth hath a fourfold greater proportion in the common Mariner's Chart, than it hath in the Globe; because the meridian is fourfold greater than the Parallel of those places.  
2. The way to find out the difference of longitude, by the common Sea-Chart, 
Error in finding out the difference of longitude by the common sea Chart.  is true at the Aequinoctial only, and near about the same may be used without sensible error: because there only the Meridian and parallel are equal But on this side or beyond the Aequinoctial, there is error committed proportionally to the difference of the Meridian and Parallel; that is, the difference of longitude found out by the Chart▪ hath the same proportion to the true difference of longitude, that the Parallel hath to the Meridian.  
As for example: At the Parallel of 60 degrees in the common Mariner's Chart (wherein the degrees of the Meridian's and Parallels are equal) admit BD be two places, bearing each from other South-west and North-east, differing in latitude so much as is the Ark of the Meridian BC, which for example sake we will suppose to be one degree, therefore by the ordinary Charts, the difference of Longitude CD, shall be likewise one degree: but yet in truth, because the Meridian is double to that Parallel, (and consequently, a degree of the Meridian double to a degree of that Parallel,) therefore B differing a degree in latitude from D should be placed twice so far from C, that is at A, so as ABC may all be counted but for one degree of the Meridian, and so be equal to two degrees of the Parallel; whereof should follow, that EC should be the difference of longitude: that is, two degrees, (as the truth is in the Globe) whereas the common Mariner's Chart shows the difference of longitude to be but half so much. And yet notwithstanding if you go nearer to the Poles, you shall err by their Chart a great deal more, even as the proportion of the Meridian to the Parallel increaseth more and more.  
In the Mariner's Chart, the distance betwixt Lisbon and Tercaera, is set down to be 262 Spanish leagues, (whereof 17 and one half make a degree of the Aequinoctial, or of any of the greatest Circles) for so much the Mariners do find that distance to be, not only by estimation of the way that the ship maketh, when they sail from East to West to that Island, but by another account which is more certain; and that is this In sailing from Lisbon to Madera, they keep their course South-west, and from this Island to Tercaera, they sail Northwest. Now because Lisbon and Tercaera have both almost the same latitude of 39 Degrees: and in sailing from North-east to South-west▪ and likewise from Southeast to Northwest, you alter the longitude as much as the latitude (because that in both those courses the angle that the way of the ship maketh with the Meridian, is equal to half a right angle: and the Island of Madera hath almost 31 degrees and an half of latitude towards the North, so that the difference of the latitudes of Lisbon and Madera, as also of Madera and Tercaera is about 7 degrees and ½.) Therefore the difference of the longitudes of Lisbon and Madera, and likewise of Madera and Teraeera shall be 7 and ½. of the same degrees of the Meridian, both which added together make the whole difference of longitude betwixt Lisbon and Tercaera, to be 15 degrees of the Meridian, which are equal to 262, and one half Spanish leagues. But in the Parallel that passeth by the 39 degree of latitude, wherein (almost) Lisbon and Tercaera are placed, there are more degrees in the same space, according to that proportion wherewith the Meridian is greater than that Parallel. Therefore the true difference of longitude betwixt Lisbon and Tercaera, (that is the ar● of the Parallel or Aeqinoctial contained betwixt the Meridian's of those places) shall thus be found out:  
It is a rule in Geometry, that the Diameters and Peripheries, and consequently the semidiameters, and like arks of Circles have the same proportion.  
Also it is manifest, that the Sine of the compliment of the distance of any Parallel from the Aequinoctial, is the Semediameter of the same Parallel.  
Now the distance of the Parallel of Lisbon and Tercaera from the Aequinoctial is about 39 degrees, the compliment whereof is 51 degrees: whose sine is 777, which is the Semidiameter of the foresaid Parallel, in such parts whereof the whole sine containeth 1000 which is the Semidiameter of the Meridan. Therefore by the rule of proportion inversed, if 262 Spanish leagues make 15 degrees in the Meridian, whose Semidiamiter is 1000 parts: then in the Parallel whose Semidiameter is 777 of the same parts, they shall make 19 degrees, and 237/777 parts of one degree, that is, 18 min. and little more: which (if it be true that the course from Lisbon to Madera is South-west, and from Madera to Tercaera Northwest: and that the Latitude of Madera is 31 degrees 30 min. and the Latitude of Lisbon and Tercaera 39 deg.) shall be the difference of Longitude betwixt Lisbon and Tercaera. Whereas Ortelius and Mercator following (as it seemeth) the Mariners Charts without correction in their universal Maps, make them to differ in Longitude scarce 15 degrees of their Parallel, as if it were equal to the Aequinoctial line.  
3. Moreover, they are deceived not only in the situation of many places, 
Error in the lying and bearing of places one from another in the common Sea-Chart.  which the Marine Chart showeth to be under the same Meridian: but also in the lying▪ or bearing of other places each from other. For the Meridian is a certain rule of the positions of places. If therefore error shall be committed in the situation of the Meridian, there must needs be error in the Inclinations of the other Rumbs, points, or lines of the Compass. And therefore not every Inclination, or respective position of place to place, which is set down in the Marine Chart, is to be taken for true: but that position or inclination only, by which some have sailed from the one place to the other. This may be seen in sailing to India. For the Marine Chart placeth that promontory of Africa, called the promontory of 3 points, being in Latitude towards the North, 4 degrees and one half, and the Lands of Tristan Acugna (which have 36 degrees of Southern Latitude) under the self same Meridian: Also the Marine Chart showeth the distance between these Lands and the promontory of Good Hope, to be almost 400 leagues: both which notwithstanding cannot stand together. For if all the shore from the promontory of 3 points unto the promontory of Good Hope be rightly described, and the promontory of 3 points also lie under the same Meridian with those Lands; the foresaid distance must needs be much less: but if it be not less it cannot be that they should have the same Meridian with the promontory of 3 points, but must needs be more to the Westward. Hereof it cometh, that the Mariners are very oft deceived, when they go from one place to another, following that direction which the Sea-Chart showeth them. Which place, when they find not by that course, they think that the cause of that error is either some swift current of the Sea, that carrieth them another way: or else the declination of the Poles of the Loadstone, from the true Poles of the World: although (perchance) they erred only because they knew not how those places did bear one from another. 
Error in setting of places out of the common Sea-Chart into the Globe.   
4. Neither are they only deceived in that▪ because they think that the Sea-Chart can show the situations of all places: but also because that when they will translate the Sea coasts out of the Chart into the Globe, they do it, having respect only to the numbers of the degrees of Longitude, and Latitude found therein; and no otherwise then when they set the fixed stars into a Celestial Globe. So it cometh to pass, that not only those errors are committed, which do necessarily arise out of the common Sea-Chart: but other errors also which might be avoided, if they first turned into degrees those distances of Longitude which they have truly known, and then followed the Longitudes and Latitudes of places. 
Error in showing the distances of places in the common Sea-Chart.   
5. In showing the distance of places, there is as great error committed, as in any of the former. For example: If you imagine 2 ships to be under the Aequinoctial 100 leagues asunder, and that each of them should sail from thence due North or South under his Meridian, until they come to the Parallel of 60 degrees Latitude: they should be there but only 50 leagues distant, because at that Parallel the Meridian's are distant but half so much one from another, as they were at the Aequinoctial; as it may most manifestly appear by the Globe: and yet the Chart will show that those two ships have the self same distance of 100 leagues, being under the parallel of 60 degrees▪ which they had before, when they were under the Aequinoctial line.  

Error in keeping always the same point of the Compass.  6 There is yet another error remaining (though all the former were avoided) which ariseth hereof, because that by the direction of the Compass, they bend and turn the ship, in such sort, that they constrain it always to make the same angles with the Meridian. As when they sail from Vshent to Cape Raso, both lying under the same Parallel, they guide the ship in such sort, that it maketh always right angles with the Meridian, and so holding on their course due West, they keep themselves always under the same Parallel; whereas notwithstanding, there is a more certain course, whereby they may go from one place to another without that loss of way, which they must needs make that keep themselves always under the same Parallel.  
There is moreover another commodity in this kind of sailing, that we may find every day by a more certain account what way we have made, and know in what place we are.  
But this way is not to be defined by any of the lesser Circles, but by a great Circle, which is to be drawn by those two places: and the ark of that great Circle contained betwixt the same places is less than the ark of the Parallel which lieth between them, as may be concluded by an evident and necessary reason out of the principles of Geometry: much like as a strait line is shorter than a crooked, both being extended between, the same pricks. Therefore this commodity is also hereunto adjoined, that in sailing by a great Circle, the way is more short, and compendious. But he that entereth into this course of sailing, must know, that he must often change the point of the Compass whereupon he guideth the ship, because of the variable, and inconstant inequality of the angles, which that great Circle maketh with every new Meridian. Of which angel's the Invention indeed (by the Chart especially) is very subtle, and consisteth herein, to wit, in knowing how much such kind of angles do decrease or increase, as the ship goeth forwards. And he that so shapeth his course, goeth the strait and nearest way. Otherwise it cannot be that a man should keep a strait course, if he shall continually follow one and the same point, or line of the Compass, (except he sail under a Meridian, or under the Aequinoctial line:) but he must change the point of the Compass so often as that strait course shall sensibly require.  
And therefore it cannot be by any means, that the Mariners when they go perpetualy towards the same part of the world, keeping the same angle of position in respect of the Meridian, or the same point of the Compass, should go the shortest and nearest way.  
This kind of sailing under a great Circle, is of special use in our Northern Navigations, for the discovery of the North-east or North west passage: which as it may most easily be performed by help of an Hydrographical Globe, with the Helisphaericall lines drawn thereupon: so for them that list not to be troubled with the cumbersome carriage and charge of the Globe, it may be done (in a manner) with no less facility by a nautical Planisphere, made after the projection of Gemma Erisius his Astrolabe, whereof more hereafter, when God shall give leisure.  
There be some also that hold it for erroneous, that the Rumbs in the Mariner's Chart should be expressed by right lines, 
The expressing of the Rumbs by right lines defended: which some hold for erroneous.  and consequently that the Meridian's should be Parallels, or equidistant every where; which because it is but barely affirmed, and the contrary may be proved, as well as that each Rumb, except the rumb of North and South maketh equal angles with every Meridian: we hold it not only as true, but also as most meet and commodious for the Mariners common use, that the Meridian's in the Sea-Chart should be every where equidistant each from other and consequently; that the Rumbs should be strait lines for these two causes.  
First, because the rumbs or points of the Compass may so most easily be drawn in the Nautical Planisphaere, only by a strait ruler. For seeing that any one and the same rumb (saving only the rumb of North and South, which is all one with the Meridian) maketh always equal angles with every Meridian, without either sensible, numerable, or measurable, though not without intelligible error (for indeed those angles are less and less as they come nearer to the Pole, much like as the angle of a little semicircle is less than the angle of a greater semicircle) all the rumbs must needs be strait lines, if the Meridian's be equidistant and right lines, by the 27 and 28 prop. 1. Euclid.  
Secondly, the respective situation of any place to other in the Chart (which they commonly call the lying or bearing of one place from another, according to the points of the Compass) may most easily be known by the Nautical Planisphaere with right lined rumbs and equidistant Meridian's. For that rumb from which both places are equidistant showeth how those two places lie one from another.  
And for these two causes of so great facility, both in the making, and using of the Mariner's Chart, with equidistant Meridian's, and straight-lined rumbs, it ought to be preferred before any other Instrument heretofore published to that end, for the common use of the Mariner, at Sea especially. And though the Globe be commended by some as most absolute and perfect for all courses and Climates whatsoever: yet for the chargeableness thereof, troublesome carriage, stowage and tedious usage for the most part in Navigation, following any other course, save East or West, North or South: it will for the most part be found unmeet and cumbersome, and nothing so fit and ready for the Mariners common use at sea, as the Nautical Planisphaere truly made.   

CHAP. II. How the former Errors may be avoided.  
THese Errors notwithstanding they have been much complained of by divers, as namely by Martin Cortese in his third book, and second chapter of the Art of Navigation, but specially by Petrus Nonius in his second book of Geometrical Observations, Rules, and Instruments: And although Gerardus Mercator in his universal Map of the World seemeth to correct them, by making the distances of the parallels greater and greater towards the Poles: yet none of them teacheth any certain way how to amend such gross faults, whereby the Mariner may be deceived many times an whole point of the Compass, yea sometimes two or three points and more, in judging by his ordinary Chart how one place beareth from another: especially if he sail far Northwards, or Southwards, whereby we may easily guess, how indirect a course he shall make to come to the desired haven, that shall follow so false and erroneous direction with great danger (at the least) many times to lose ship, goods, lives, and all.  
The fountain of all the errors aforesaid (the last only excepted) is in the very foundation and groundwork of the Mariner's Chart, that is, in the first Geometrical lineaments thereof: namely, because the Meridian's are not rightly divided, (the divisions being every where equal:) nor the Parallels rightly drawn (having in all places the same distances each from other that the Meridian's have at the Aequinoctial:) Whereas the spaces betwixt the Parallels should increase more and more as you go from the Aequinoctial towards either of the Poles, which Martin Cortese also noteth is his 3 book and 2 chapter of the Art of Navigation. But he omitteth that wherein all the difficulty lieth: that is, how much, or in what proportion those spaces should increase. Which, that it may the better be perceived, I think it not unmeet first to show by what kind of projection (or extension rather) the nautical planisphaere may not unfitly be conceived to be geometrically made, after this manner.  
Suppose a spherical superficies with Meridian's, Parallels, Rumbes, and the whole hydrographical description drawn thereupon, to be inscribed into a concave cylinder, their axes agreeing in one.  
Let this Spherical superficies swell like a bladder, (whiles it is in blowing) equally always in every part thereof (that is, as much in longitude as in latitude) till it apply, and join itself (round about, and all alongst also towards either pole) unto the concave superficies of the cylinder: each parallel upon this spherical superficies increasing successively from the Aequinoctial towards either pole, until it come to be of equal diameter with the cylinder, and consequently the Meridian's still widening themselves, till they come to be so far distant every where each from other as they are at the Aequinoctial. Thus it may most easily be understood, how a spherical superficies may (by extension) be made a cylindrical, and consequently a plain Parallelogram superficies; because the superficies of a cylinder is nothing else but a plain parallelogram wound about two equal equidistant circles that have one common axtree perpendicular upon the centres of them both, and the peripheries of each of them equal to the length of the parallelogram as the distance betwixt those circles, or height of the cylinder is equal to the breadth thereof. So as the nautical planisphaere may be defined to be nothing else but a parallellogram made of the spherical superficies of an Hydrographical Globe inscribed into a concave cylinder, both their axes concurring in one; 
The definition of the Nautical Planisphaere.  and the spherical superficies swelling in every part equally in longitude and latitude, till every one of the Parallels thereupon be inscribed into the cylinder (each parallel growing as great as the Aequinoctial:) or till the whole spherical superficies, touch and apply itself every where to the concavity of the cylinder.  
In this nautical planisphaere thus conceived to be made, all places must needs be situate in the same longitudes, latitudes, and directions or courses, and upon the same Meridian's, Parallels, and Rumbes, that they were in the Globe, because that at every point between the Aequinoctial and the Pole, we understand the Spherical superficies whereof this Plani-sphere is conceived to be made, to swell equally as much in longitude as in latitude (till it join itself unto the concavity of the cylinder, so as hereby no part thereof is any way distorted or displaced out of his true and natural situation upon his Meridian, Parallel, or Rumbe, but only dilated and enlarged: the Meridian's also, Parallels, and Rumbes dilating and enlarging themselves likewise, at every point of latitude in the same proportion.  
Now then let us diligently consider of the Geometrical lineaments, that is, the Meridian's, Rumbs, and Parallels of this imaginary nautical Planisphere, that we may in like manner express the same in the Mariners Chart. For so undoubtedly we shall have therein a true hydrographical description of all places, in their longitudes, latitudes, and directions, or respective situations each from other according to the points of the Compass in all things correspondent to the Globe, without either sensible, or explicable error.  
First therefore in this planisphaer, because the Parallels are every where equal each to other (for every one of them is equal to the Aequinoctial or circumference of the circumscribing cylinder) the Meridian's also must needs be Parallel and straight lines: 
27 Prop. 1. Euclid 17.  and consequently the rumbs (making equal angles with every Meridian) must likewise be straight lines.  
Secondly, because the Spherical superficies whereof this Planisphaere is conceived to be made, swelleth in every part thereof equally, that is, as much in latitude, as in longitude till it apply itself round about, to the concavity of the cylinder: therefore at every point of latitude in this planisphaere, a part of the Meridian keepeth the same proportion to the like part of the parallel, that the like parts of the Meridian, and Parallel have each to other in the Globe, without any explicable error.  
Now because like parts of wholes keep the same proportion that their wholes have, therefore the like parts of any Parallel and Meridian of the Globe, have the same proportion that the same Parallel and Meridian have.  
For example sake, as the Meridian is double to the Parallel of 60 degrees, so a degree of the Meridian is double to a degree of that Parallel▪ or a minute to a minute, etc. and what proportion the Parallel hath to the Meridian, the same proportion have their diameters and semidiameters each to other, 26.18. c. 2, c. 15. Ram.  
But the sine of the compliment of the Parallels latitude, or distance from the Aequinoct. is the Semidiameter of the Parallel;  
As here you see, ae the sine of ah the compliment of of the latitude or distance of the Parallel abcd, from the Aequinoctial, is the Semidiameter of the same Parallel abcd.  
And as the Semidiameter of the Meridian (or the whole sine) is to the Semidiameter of the Parallel, so is the Secans, or Hypotenusa of the Parallels latitude (or of the Parallels distance from the Aequinoctial) to the Semidiameter of the Meridian, or to the whole sine; as fk, (that is) ak, to ae (that is) gk; so is ik, to kf.  
Therefore in this nautical planisphaere, the Semidiameter of each Parallel being equal to the Semidiameter of the Aequinoctial (that is) to the whole sine; the parts of the Meridian at every point of latitude must needs increase with the same proportion wherewith the Secants of the ark, contained between those points of latitude and the Aequinoctial do increase.  
Now than we have an easy way laid open for the making of a table (by help of the Canon of Triangles) whereby the Meridian's of the Mariner's Chart may most easily and truly be divided into parts, in due proportion from the Aequinoctial towards either Pole.  
For (supposing each distance of each point of latitude, or of each Parallel from other, to contain so many parts as the Secans of the latitude of each point or Parallel containeth) by perpetual addition of the Secantes answerable to the latitudes of each point or Parallel unto the sum compounded of all the former secantes, beginning with the secans of the first Parallels latitude, and thereto adding the secans of the second Parallels latitude, and to the sum of both these adjoining the secans of the third Parallels latitude, and so forth in all the rest, we may make a table which shall truly show the sections and points of latitude in the Meridian's of the nautical planisphaere: by which sections, the Parallels are to be drawn.  
As in the table following, we make the distance of each Parallel from other, to be one minute: and we suppose the space between any two Parallels each next to other in the planisphaere to contain so many parts as the secans answerable to the distance of the furthest of those two Parallels from the Aequinoctial, and so by perpetual addition of the secans of each minute to the sum compounded of all the former secants, I make the whole table. As for example, the secans of one minute is 10,000,000. which also showeth the section of one minute of the Meridian from the Aequinoctial in the nautical planisphaere. Whereunto add the secans of 2. minutes that is 10,000,002, the sum is 20,000,002. which showeth the section of the second minute of the Meridian from the Aequinoctial, in the planisphaere: to this sum add the secans of 3. minutes, which is 10,000,004, the sum will be 30,000,006, which showeth the section of the third minute of the Meridian from the Aequinoctial: and so forth in all the rest: saving that in this table we have of purpose omitted in every secans the 3 first cyphers next the right hand: not only for the easier, but also for the truer making of the table, because that indeed, at every point of latitude, a minute of the Meridian in this nautical planisphaere, hath somewhat less proportion to a minute of the Parallel adjoining towards the Aequinoctial, than the secans of that Parallels latitude hath to the whole sine. But in this table it was thought sufficient to use such exactness as that thereby (in drawing the lineaments of the nautical planisphaere) sensible error might be avoided. He that listeth to be more precise may make the like table to decades or ten of seconds. out of joachimus Rhaeticus his Canon magnus triangulorum. Notwithstanding the Geometrician that desireth exact truth, cannot be so satisfied neither: for whose sake and further satisfaction, I thought good to adjoin also this Geometrical conceit of dividing a Meridian of the nautical planisphaere.  
Let the Aequinoctial and a Meridian be drawn upon a Globe: Let the Meridian (divided into degrees, minutes, seconds, etc.) roll upon a straight line beginning at the Aequinoctial, the Globe swelling in the mean time in such sort that the Semidiameter thereof may be always equal to the secans of the angle, or arch contained between the Aequinoctial and Semediameter insisting at right angles upon the foresaid straight line: The degrees, minutes, seconds, etc. of the Meridian, noted in the straight line, as they come to touch the same, are the divisions of the Meridian in the nautical planisphaere. And this conceit of dividing the Meridian of the nautical planisphaere may satisfy the curious exactness of the Geometritian: but for mechanical use, the table before mentioned (which here now followeth) may suffice.  
This Table (serving principally for the true dividing of the Meridian's of the Sea Chartley, in such sort that in any part thereof, a minute of the Meridian shall have the same proportion to a minute of the Parallel thereto adjoining that it hath in the Globe) may not unfitly be called, A Table of Latitudes.  
For as in Geographie, the latitude of a place is nothing else but the shortest distance thereof from the Aequinoctial line, measured upon the convexity of the earth or sea in degrees and minutes; and therefore Tables containing such distances are ordinarily called Tables of Latitudes: So this Table, showing the distance of every minute of a Meridian in the Sea Chartley from the Aequinoctial line thereof towards the North or South, in such equal parts whereof one minute of the Aequinoctial is supposed to contain 10,000, may with like reason, by a certain analogy and resemblance it holdeth with the foresaid tables, be very well called. A Table of Latitudes of every minute of a Meridian of the Sea Chartley, in such parts whereof each minute of the Aequinoctial containeth 10,000.  
This Table is divided into three columns; whereof the first containeth, in the head thereof the degrees, and in the rest of that column, minutes of a Meridian of the nautical planisphaer, beginning at the Aequinoctial line. In the second column are placed equal parts of the same Meridian, beginning likewise to be numbered from the Aequinoctial (of which parts each minute of the Aequinoctial is supposed to contain 10,000) and showeth how many of these parts each minute of latitude in the Sea Chartley must be distant from the Aequinoctial. The third column showeth the differences of the numbers set down in the second column.  
The use hereof followeth after this Table.  

A Table of Latitudes etc.  Min. 0 Degr.  1 Degr.  2 Degr.  3 Degr.  Equal parts of a Merid. Difference of equ▪ par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 00.000 10.000 600.012 10.001 1.200.196 10.006 1.800.749 10.013 1 10.000 10.000 610.013 10.001 1.210.202 10.006 1.810.762 10.014 2 20▪ 000 10.000 620.014 10.001 1.220.208 10.006 1.820.776 10.014 3 30.000 10.000 630.015 10.001 1.230.214 10.006 1.830.790 10.014 4 40.000 10.000 640 016 10.001 1.240.220 10.006 1.840.804 10.014 5 50.000 10.000 650.017 10.001 1.250.226 10.006 1.850.818 10.014 6 60 000 10.000 660.018 10.001 1.260.232 10.006 1.860.832 10.014 7 70 000 10.000 670.019 10.001 1.270.238 10.006 1.870.846 10.014 8 80.000 10.000 680.020 10.002 1.280.244 10.007 1.888.860 10.015 9 90.000 10.000 690.022 10.002 1.290.251 10.007 1.890.875 10.015 10 100 000 10.000 700.024 10.002 1.300.258 10.007 1.900.890 10.015 11 110 000 10.000 710.026 10.002 1.130.265 10.007 1.910.905 10.015 12 120.000 10.000 720.028 10.002 1.320.272 10.007 1.920.920 10.015 13 130.000 10.000 730.030 10.002 1.330.279 10.007 1.931.935 10.015 14 140·000 10.000 740.032 10.002 1.340.286 10.007 1.940.950 10.016 15 150.000 10.000 750.034 10.002 1.350.293 10.007 1.950.966 10.016 16 160.000 10.000 760.036 10.002 1.360.300 10.007 1.960.982 10.016 17 170.000 10.000 770.038 10.002 1.370.307 10.008 1.970.998 10.016 18 180.000 10.000 780.040 10.002 1.380.315 10.008 1.981.014 10.016 19 190.000 10.000 790.042 10.002 1.390.323 10.008 1.991.030 10.016 20 200.000 10.000 800.044 10.002 1.400.331 10.008 2.001.046 10.017 21 210.000 10.000 810.046 10.002 1.410.339 10.008 2.011.063 10.017 22 220.000 10.000 820.048 10.002 1.420.347 10.008 2.021.080 10.017 23 230.000 10.000 830.050 10.002 1.430.355 10.008 2.031.097 10.017 24 240.000 10.000 840·052 10.003 1.440.363 10.008 2.041.114 10.017 25 250.000 10.000 850.055 10.003 1.450.371 10.009 2.051.131 10.017 26 260.000 10.000 860.058 10.003 1.460.380 10.009 2·061S. 148 10.018 27 270.000 10.000 870.061 10.003 1.470.389 10.009 2·071S. 166 10.018 28 280.000 10.000 880.064 10.003 1.480.398 10.009 2·081S. 184 10.018 29 290.000 10.000 8●0 067 10. 00● 1.490.407 10.009 2·091S. 201 10.018 30 300.000 10.000 900.070 10.003 1.500.416 10.009 2.101.220 10.018 31 310.000 10.000 910.073 10.003 1.510.425 10.009 2.111.238 10.019 32 320.000 10.000 920.076 10.003 1.520.434 10.009 2.121.257 10.019 33 330.000 10.000 930.079 10.003 1.530.443 10.010 2.131.276 10.019 34 340.000 10.000 940.082 10.003 1.540.453 10.010 2.141.295 10 019 35 350.000 10.000 950.085 10.003 1.550.463 10.010 2.151.314 10.019 36 360. 00● 10 000 960.088 10.003 1.560.473 10.010 2.161.333 10.019 37 370. 00● 10.000 970.091 10.004 1.570.483 10.010 2.171.352 10.020 38 380.000 10.000 980.095 10. 0●4 1.580.493 10.010 2.181.372 10.020 39 390.000 10.000 990·099 10.004 1.590.503 10.010 2 191▪ 392 10.020 40 400.000 10. 0●0 1.000.103 10.004 1.600.513 10.010 2.201.412 10.020 41 410.000 10.000 1.010.107 10.004 1.610.523 10.011 2.211.432 10.021 42 420.000 10.000 1.020.111 10.004 1.620.534 10.011 2. 221.4●2 10.021 43 430.000 10.000 1.030.115 10.004 1.630.545 10.011 2.231.473 10.021 44 440.000 10▪ 000 1.040.119 10.004 1.640.556 10.011 2.241.494 10.001 45 450.000 10.000 1.050.123 10.004 1.650.567 10.011 2.251.515 12.021 46 460.000 10.000 1.060.127 10.004 1.660.578 10.011 2.261 536 12.021 47 470.000 10.000 1.070.131 10.004 1.670.589 10.011 2.271.557 11.002 48 480.000 10.001 1.080.135 10.005 1.680.600 10.012 2.281.570 10.022 49 490.000 10.001 1.090.140 10.005 1.690.612 10.012 2.291.601 10.022 50 500. 00● 10.001 1.100.145 10.005 1.709.624 10.012 2. 301.62● 10.022 51 510.000 10.001 1.110.150 10.005 1.710.636 10.012 2.311.645 10.022 52 520.000 10.001 1.120.155 10.005 1.720.648 10.012 2.321.667 10.023 53 530.000 10 001 1.130.160 10.005 1.730.660 10.012 2.331.690 10.023 54 540.000 10.001 1·140. 165 10.005 1.740.672 10.012 2.341.713 10.023 55 550.000 10.001 1.150.170 10.005 1.750.684 10.013 2.351.736 10.023 56 560.000 10.001 1.160.175 10.005 1.760.697 10.013 2.361.759 10.023 57 570.000 10.001 16170.180 10.005 1.770.710 10.013 2.371.782 10.024 58 580.000 10.001 1.180.185 10.005 1.780.723 10.013 2.381.806 10.024 59 590.000 10 001 1.190.190 10.006 1.790.736 10.013 2.391.830 10.024 Min. 4 Degr.  5 Degr.  6 Degr.  7 Degr.  Equal parts of a Merid. Difference of equ par. Equal parts of a Merid Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 2.401.854 10.024 3.003.694 10.038 3.606.455 10.055 4.210.328 10.075 1 2.411.878 10.024 3.013.732 10.038 3.616.510 10 055 4.220.403 10.075 2 2.421.902 10.025 3.023.770 10.038 3.626.565 10.056 4.230.478 10 076 3 2.431.927 10.025 3.033.808 10.039 3.636.621 10 056 4.240 554 10.076 4 2.441.952 10.025 3.043.847 10 039 3 646.677 10.056 4.250.630 10.076 5 2.451.977 10.025 3.053.886 10 039 3.656.733 10.056 4.260.706 10.077 6 2.462.002 10.025 3.063.925 10.040 3.666.789 10.057 4.270.783 10.077 7 2.472.027 10.026 3.073.965 10 040 3.676.846 10.057 4 280.860 10.078 8 2.482.053 10.026 3.084.005 10 040 3·686. 903 10.057 4.290.938 10.078 9 2.492.079 10.026 3.094.045 10.040 3.696.960 10.058 4.301.016 10.078 10 2.502.105 10.026 3.104.085 10.041 3.707.018 10 058 4.311.094 10 079 11 2.512.131 10.026 3.114.126 10.041 3.717.076 10.058 4.321.173 10 079 12 2.522.157 10.027 3 124.167 10 041 3.727.134 10 059 4.331.252 10.079 13 2.532.184 10.027 3.134 208 10.041 3.737.193 10.059 4.341.331 10.080 14 2.542.211 10.027 3.144 249 10.042 3.747.252 10.059 4 351.411 10.080 15 2.552.238 10.027 3.154.291 10.042 3.757.311 10.060 4.361.491 10.080 16 2.562.265 10.028 3.164 333 10.052 3.767.371 10.060 4.371.571 10.081 1● 2.572.293 10.028 3.174.375 10 042 3 777.431 10.060 4.381.652 10.081 18 ●. 582.321 10.028 3.184 417 10.043 3.787.491 10.061 4.391.733 10.082 19 2.592.349 10.028 3.194.460 10.043 3 797.552 10 061 4.401.815 10.082 20 2. ●02. 377 10.028 3·204 503 10.043 3.807.613 10.061 4·411S. 897 10.082 21 ●. ●22. 405 10.029 3.214.546 10 044 3.817.674 10.062 4 421.979 10.083 22 2.622.434 10.029 3·224 590 10.044 3.827 736 10.062 4.432.062 10.083 2● 2. 63●.463 10.029 3·234·634 10.044 3.837.798 10.062 4. 442·145 10.083 2● 2.642.492 10.029 3 244.678 10 044 3.847.860 10.063 4.452.228 10.084 25 2.652.521 10.039 3.254.722 10.045 3.857 923 10.063 4.462.312 10.084 26 2.662.551 10.030 3.264.767 10.045 3.867.986 10.063 4.472.396 10.085 27 2.672.581 10.030 3. 274·812 10 045 3.878.049 10.064 4.482.481 10.085 28 2.682.611 10.030 3. 284·857 10.045 3.888.113 10.064 4.492.566 10.085 29 2.692.641 10.030 3.294.902 10.046 3.898.177 10.064 4.502.651 10.086 30 2.702.671 10.031 3.304.948 10 046 3.908.241 10.065 4.512.737 10.086 31 2.712.702 10.031 3.314.994 10 046 3.918.306 10.065 4.522.823 10 087 32 2.722.733 10.031 3 325.040 10.047 3.928.371 10 065 4.532.910 10.087 33 2.732.764 10.031 3.335.087 10.047 3.938.436 10.066 4.542.997 10.087 34 2.742.795 10.032 3.345.134 10.047 3.948.502 10.066 4.553.084 10.088 35 2.752.827 10.032 3.355 181 10.047 3.958.568 10.066 4.563.172 10.088 36 2.762.859 10.032 3.365 228 10.048 3.968.934 10.067 4.573.260 10.889 37 2.772.891 10.032 3 375.276 10.048 3.978.701 10 067 4.583.349 10 089 38 2.782.923 10.033 3.385.324 10.048 3 988.768 10.067 4.543.438 10 099 39 2.792.956 10.033 3 395 372 10 049 3.998.835 10.068 4.603.527 10.090 40 2.802.989 10.033 3.405.421 10.049 4.008.903 10.068 4.613.617 10 090 41 2.813.022 10.033 3.415.470 10 049 4.018.971 10.068 4.623.707 10.090 42 2.823.055 10.033 3.425.519 10.049 4.029 039 10.069 4.633 797 10 091 43 2.833.088 10.034 3.435.568 10.050 4.039.108 10.069 4.643.888 10.091 44 2.843.122 10.034 3·445 618 10.050 4.049.177 10.069 4 653·979 10 092 45 2.853.156 10.034 3.455.668 10 050 4 059.246 10 070 4 664.071 10 092 46 2.863.190 10.034 3.465.718 10.051 4.069.316 10.070 4.674.136 10.092 47 2.873.224 10.035 3.475.769 10 051 4.079.386 10 070 4 684 228 10 093 48 2.883.259 10.035 3.485 820 10.051 4.089 456 10.071 4 694.321 10.093 49 2.893.294 10.035 3 495.871 10 052 4.099.527 10.071 4.704 414 10.094 50 2.903.329 10.035 3.505.923 10.052 4.109.598 10.071 4.714.508 10 094 51 2.913.364 10.036 3.515 975 10.052 4.119.669 10 072 4.724 602 10 095 52 2.923.300 10.036 3.526 027 10.052 4.129.741 10 072 4 734.697 10.095 53 2.933.436 10.036 3.536.079 10.053 4.139.813 10.072 4.744.792 10 095 54 2.943. ●72 10.036 3.546.132 10.053 4.149.885 10 073 4.754.887 10 096 55 2.953.508 10.037 3.556.185 10 053 4.159 958 10.073 4.764.983 10.096 56 2.963.545 10.037 3.566.238 10.054 4 170.031 10 074 4.775▪ 070 10.097 57 2.973.582 10.037 3.576.292 10.054 4.180.105 10.074 4. 785.17● 10 097 58 2.983.619 10.037 3.586.346 10.054 4 190.179 10.074 4.795.273 10 097 59 2.993.656 10.038 3.596.400 10 055 4.200.253 10.075 4.805 370 10.098 Min▪ 8 Degr.  9 Degr.  10 Degr.  11 Degr.  Equal parts of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 4.815.468 10.098 5.422.133 10.125 6 030.475 10 154 6.640.679 10.187 1 4.825 566 10.099 5.432.258 10 125 6.040.629 10 155 6.650.866 10.188 2 4.835.665 10.099 5.442.383 10.126 6.050.784 10 155 6.661.054 10.188 3 4.845.764 10.099 5.452 509 10.126 6 060 939 10.156 6.671 242 10 189 4 4.855.863 10.100 5.462.635 10.126 6 071 098 10 156 6.681.431 10.190 5 4.865.963 10.100 5.472.761 10.127 6 081.251 10.157 6.691.621 10.190 6 4.876 063 10.101 5.482.888 10.127 6.091.408 10 157 6.701.811 10 191 7 4.886.164 10.101 5.493.015 10.128 6.101.565 10.158 6.712.002 10.191 8 4.896.265 10.102 5.503.143 10.128 6.111.723 10 158 6.722.219 10.192 9 4.906.367 10.102 5.513 271 10.129 6.121.881 10 159 6.732.385 10.192 10 4.916.469 10.102 5.523.400 10.129 6.132.040 10 160 6 742.577 10 193 11 4.926.571 10.103 5.533.529 10.130 6 142.200 10.160 6.752.770 10.194 12 4 936 674 10.103 5.543.659 10.130 6.152.360 10 161 6 762.964 10.194 13 4.946.777 10.104 5.553.789 10.131 6.162.521 10.161 6 773.158 10.195 14 4.956.881 10.104 5 563 920 10 131 6.172.682 10.162 6 783.353 10.195 15 4.966.985 10.104 5.574.051 10.132 6.182.844 10.162 6.793.548 10.196 16 4.977.089 10.105 5.584.183 10.132 6.193 006 30.163 6.803 744 10.197 17 4.987 194 10.105 5.594▪ 315 10.133 6.203.169 10.163 6.813.941 10.197 18 4.997.299 10.106 5.604.448 10.133 6.213.332 10.164 6.824.138 10.198 19 5.007.405 10.106 5.614.581 10 134 6 223.496 10 165 6.834 336 10.198 20 5.017.511 10.107 5.624.715 10 134 6.233.661 10 165 6 844.534 10.199 21 5.027.618 10.107 5.634.849 10.135 6.243.826 10 165 6.854.733 10.200 22 5.037.725 10 108 5.644.984 10.135 6.253 991 10.166 6.864 933 10 200 23 5.047.833 10.108 5 655.119 10.136 6▪ 264.157 10.167 6.875.133 10.201 24 5▪ 057.941 10 108 5.665.255 10.136 6.274 324 10 167 6.885.334 10 201 25 5.068.049 10.109 5.675.391 10.137 6.284▪ 491 10.168 6.895.535 10.202 26 5.078.158 10.109 5 685.528 10.137 6 294.659 10.168 6.905.737 10.203 27 5.088.267 10.110 5.695.665 10.138 6.304 827 10.169 6.915 940 10 203 28 5.098 377 10.110 5.705.803 10.138 6.314.996 10 169 6.926.143 10.204 29 5.108.487 10.111 5 715 941 10.139 6. 325·165 10.170 6 936.347 10.204 30 5.118.598 10.111 5.726.080 10.139 6.335.335 10.170 6.946.551 10.205 31 5.128.709 10.111 5 736.219 10.140 6 345.505 10 171 6 956.756 10.206 32 5 138.820 10 112 5.746.359 10.140 6.355 676 10.171 6 966.962 10 206 33 5.148.932 10.112 5.756.499 10.141 6.365.847 10 172 6.977.168 10.207 34 5.159.044 10.113 5.766.640 10.141 6.379 019 10. 17● 6.987.375 10.207 35 5.169 157 10.113 5.776.781 10.142 6.386.192 10 173 6.997.582 10.208 36 5.179 270 10.114 5 786.923 10.142 6.396.365 10.174 7 007 790 10 209 37 5.189.384 10.114 5.797 065 10.143 6.406.539 10 174 7.017.999 10.209 38 5.199.498 10.115 5.807.208 10.143 6.416.713 10▪ 175 7.028 208 10 210 39 5.209.613 10 115 5.817.351 10.144 6.426.888 10 175 7.038 418 10.210 40 5.219.728 10 115 5.827 495 10.144 6.437.063 10 176 7.048 628 10 211 41 5. 229·843 10.116 5.837.639 10 145 6.447.239 10 176 7.058.839 10 212 42 5.239.959 10.116 5.847.784 10.145 6.457.415 10.177 7. 06●.051 10.212 43 5.250.075 10.117 5.857.929 10.146 6.467.592 10 178 7. 07●.263 10 213 44 5.260.193 10.117 5.868.075 10.146 6 477 770 10▪ 178 7. 08● 476 10 214 45 5.270 309 10.118 5.878.221 10.147 6.487.948 10.179 7.099.690 10.214 46 5.280 427 10.118 5.888.368 10.147 6.498.127 10.179 7.109 904 10.215 47 5.290.545 10.119 5.898.515 10.148 6.508.306 10 180 7.120 119 10 215 48 5.300.664 10.119 5.908.663 10.148 6 518.486 10.180 7 130 334 10.216 49 5.310.783 10 120 5. ●18. 811 10 149 6.528 666 10.181 7.140 550 10.217 50 5.320.903 10.120 5 928.960 10.149 6.538.847 10.182 7 150 767 10 217 51 5.331.023 10.120 5 939.109 10.150 6.549.029 10.182 7.160 984 10 218 52 5.341 143 10.121 5.949 259 10.150 6.559.211 10.183 7.171.202 10 219 53 5.351.264 10.121 5 959.409 10.151 6.569.394 10 183 7 181 421 10 219 5● 5. 361·385 10.122 5 969▪ 560 10.151 6.579.577 10.184 7 191.640 10.220 55 5 371.507 10.122 5 979.711 10.152 6 589.761 10 184 7.201.860 10.220 56 5.381.629 10.123 5.989 863 10 152 6.599.945 10.185 7.212.080 10 221 57 5 391.752 10.123 6 000.015 10 153 6.610 130 10.186 7.222.301 10 222 58 5.401.875 10.124 6.010.168 10.153 6.620.316 10 186 7.232.323 10.222 59 5.411 999 10.124 6.020.321 10.154 6.630 502 10 187 7.242.745 10.223 Mni 12 Degr.  13 Degr.  14 Degr.  15 Degr  Equal parts of a Merid Difference of equ par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 7.252.968 10.224 7 867.534 10.263 8.484 584 10.306 9·104. 325 10.353 1 7 263.192 10 224 7.877.797 10.264 8.494.890 10.307 9 114.678 10.354 2 7.273.416 10.225 7.888 061 10.265 8 505.197 10.308 9.125.032 10.355 3 7.283.641 10.225 7 898.326 10 265 8.515.505 10.309 9.135.387 10 355 4 7 293.866 10.226 7.908.591 10.266 8 525.814 10.309 9.145.742 10.356 5 7 304.092 10.227 7.918.857 10.267 8.536.123 10▪ 310 9.156.098 10 357 6 7.314.319 10.227 7.929.124 10.267 8.546.433 10.311 9.166.455 10 358 7 7.324.546 10 228 7.939.391 10.268 8.556.744 10.312 9.176.813 10.359 8 7.334 774 10.229 7.949.659 10.269 8.567.056 10.312 9.187.172 10 360 9 7.345 003 10.229 7.959.928 10.269 8.577.368 10 313 9.197.532 10.360 10 7.355 232 10 230 7 970.197 10.270 8.587.681 10.314 9.207.892 10.361 11 7.365.462 10.231 7.980.467 10.271 8.597.995 10.315 9.218.253 10.362 12 7.375.693 10.231 7.990.738 10.272 8.608.310 10.315 9.228.615 10.363 13 7.385.924 10.232 8.001.010 10.272 8.618.625 10 316 9.238.978 10 364 14 7.396.156 10.232 8.011.282 10.273 8.628.941 10.317 9.249.342 10.364 15 7.406.388 10.233 8.021.555 10.274 8.639.258 10.318 9.259.706 10 365 16 7.416.621 10.234 8.031.829 10.274 8 649.576 10. ●18 9.270 071 10.366 17 7.426.855 10.234 8.042.103 10.275 8.659.894 10. 31● 9.280.437 10.367 18 7.437.089 10.235 8.052.378 10.276 8 670.213 10.320 9.290.804 10.368 19 7.447.324 10.236 8.062.654 10.277 8.680.533 10.321 9.301.172 10.369 20 7.457.560 10.236 8.072.931 10.277 8.690.854 10.322 9.311.541 10.369 21 7.467.796 10.237 8.083.208 10.278 8.701.176 10.322 9.321.910 10.370 22 7.478.033 10.238 8.093.486 10.279 8.711.498 10.323 9.332.280 10.371 23 7.488.271 10.238 8.103.765 10.279 8.721 821 10.324 9.342.651 10.372 24 7.498.509 10.239 8.114.044 10.280 8.732.145 10.325 9.353.023 10.373 25 7.508.748 10.240 8.124.324 10.281 8 742.470 10.325 9.363.396 10.374 26 7.518.988 10.240 8.134.605 10.282 8.752.795 10.326 9.373.770 10 374 27 7.529.228 10.241 8.144.887 10.282 8.763.121 10.327 9.384.144 10.375 28 7.539.469 10.242 8.155.169 10.283 8. 773.44● 10.328 9.394.519 10.376 29 7.549 711 10.242 8.165.452 10.284 8.783.776 10.329 9.404.895 10.377 30 7. 559·953 10.243 8.175.736 10.284 8.794.105 10.329 9.415.272 10.378 31 7.570.196 10.244 8.186.020 10.285 8.804.434 10.330 9.425.650 10 379 32 7.580.440 10.244 8.196 305 10.286 8.814.764 10.331 9.436 029 10.379 33 7.590.684 10.245 8.206.591 10.287 8.825.095 10.332 9.446.408 10.380 34 7.600.929 10.246 8.216.878 10.287 8.835.427 10.332 9.456.788 10.381 35 7.611.175 10.246 8.227.169 10.288 8.845.759 10.333 9.467 169 10.382 36 7.621.421 10.247 8. 237·453 10.289 8.856.092 10 334 9.477.551 10 383 37 7.631.668 10.248 8.247.742 10.289 8.866.426 10.335 9.487.934 10.384 38 7.641.916 10.248 8 258.031 10.290 8.876.761 10.336 9.498.318 10.384 39 7.652 164 10.249 8.268.321 10.291 8.887.097 10.336 9.508.702 10 385 40 7.662.413 10.250 8.278.612 10.292 8 897.433 10.337 9.519.087 10.386 41 7.672.663 10.250 8.288.904 10.292 8.907.770 10.338 9.529.473 10.387 42 7.682.913 10.251 8.299.196 10.293 8.918.108 10 339 9.539 860 10.388 43 7.693.164 10.252 8.309.489 10.294 8.928.447 10.339 9.550.248 10.389 44 7.703.416 10.252 8.319.783 10.295 8 938.786 10.340 9 560.637 10.390 45 7.713.668 10.253 8.330.078 10.295 8.949.126 10.341 9.571.027 10.390 46 7.723.921 10.254 8.340.373 10.296 8.959.467 10.342 9.581.417 10.391 47 7.734.175 10.254 8.350.669 10.297 8.969.809 10.343 9.591.808 10.392 48 7.744.429 10.255 8.360.966 10.297 8.980.152 10.343 9.602 200 10.393 49 7.754.684 10.256 8 371.263 10.298 8.990.495 10.344 9.612.593 10.394 50 7.764.940 10.256 8.381.561 10.299 9 000.839 10.345 9.622.987 10.395 51 7.775.196 10.257 8.391.860 10.300 9.011.184 10.346 9.633.382 10.396 52 7.785.453 10.258 8.402.160 10 300 9 021.530 10.347 9 643.778 10.396 53 7.795.711 10.258 8.412.460 10.301 9.031.877 10.347 9.654.174 10.397 54 7 805.969 10.259 8.422.761 10.302 9.042.224 10.348 9.664 571 10.398 55 7.816.228 10.260 8.433.063 10.303 9 052.572 10.349 9.674.969 10 399 56 7.826.488 10.260 8.443.366 10.303 9.062.921 10.350 9.685.368 10.400 57 7.836.748 10.261 8.453.669 10.304 9.073.271 10.351 9.695.768 10.401 58 7.847.009 10.262 8.463.973 10.305 9.083.622 10.351 9.706.169 10.402 59 7.857.271 10.263 8.474.278 10.306 9.093.973 10.352 9.716.571 10.402 Min 16 Degr.  17 Degr.  18 Degr.  19 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a merid. Difference of equ. par. 0 9 726.973 10.403 10.352.748 10.457 10.981.870 10.515 11.614.570 10.577 1 9.737.376 10.404 10.363.205 10.458 10.992.383 10.516 11.625.147 10.578 2 9.747.780 10.405 10.373 663 10 459 11.002.899 10.517 11.635.725 10.579 3 9. 758.1●5 10 406 10.384.122 10.460 11.013.416 10.518 11.646.304 10.580 4 9.768.591 10 407 10.394.582 10.461 11.023.934 10.519 21.656.884 10.581 5 9. 778.9●● 10 408 10.405 043 10.462 11.034.453 10.520 11.667.465 10.582 6 9 789. 40● 10 409 10.415 505 10.463 11.044.973 10 521 11.678.047 10.583 7 9 799 815 10.409 10.425.968 10.464 11.055.494 10.522 11.688.630 10.584 8 9 810.224 10.410 10.436.432 10 465 11.066.016 10.523 11.699.214 10.585 9 9.820.634 10 411 10.446.897 10.466 11.076.539 10.524 11.709.799 10.586 10 9.831.045 10.412 10.457.363 10 467 11.087.063 10.525 11.720.385 10 587 11 9.841.457 10.413 10.467.830 10 468 11.097.588 10.526 11 730.972 10.588 12 9.851.870 10.414 10.478.298 10.469 11.108.114 10.527 11.741.560 10.590 13 9.862.284 10.415 10.488.767 10.470 11.118.641 10.528 11.752.150 10.591 14 9.872.699 10.416 10 499.237 10.470 11.129.169 10.529 11.762.741 10.592 15 9.883.115 10.417 10.509.707 10.471 11.139.698 10.530 11.773.333 10.593 16 9.893.532 10.417 10 520.178 10.472 11.150.228 10.531 11.783.926 10.594 17 9.903.949 10.418 10.530.650 10.473 11.160.759 10.532 11.794.520 10.595 18 9.914.367 10.419 10.541.123 10.474 11.171.291 10.533 11.805.115 10.596 19 9.924.786 10.420 10 551.597 10.475 11.181.824 10.534 11.815.711 10.597 20 9.935 206 10.421 10.562 072 10.476 11.192.358 10.535 11.826.308 10.598 21 9.945.627 10.422 10.572 548 10.477 11.202.893 10.536 11.836.906 10.599 22 9.956.049 10.423 10.583.025 10.478 11.213.429 10.537 11.847.505 10.600 23 9 966 472 10.424 10.593.503 10.479 11.223.966 10.538 11.858.105 10.601 24 9.976 896 10.425 10.603.982 10.480 11.234.504 10.539 11.868.706 10.603 25 9.987.321 10.425 10.614.462 10.481 11.245.043 10.540 11.879.309 10.604 26 9.997.746 10.426 10.624.943 10.482 11.255.583 10.541 11.889.913 10.605 27 10.008.172 10.427 10.635.425 10 483 11.266.124 10.542 11.900.518 10.606 28 10.018.599 10.428 10.645.908 10.484 11.276.666 10.543 11.911.124 10 607 29 10.029.027 10.429 10.656.392 10.485 11.287.209 10.544 11.921.731 10.608 30 10.039.456 10.430 10.666.877 10.486 11.297.753 10.545 11.932.339 10.609 31 10 049 886 10.431 10.677.363 10.487 11.308.298 10.546 11.912.948 10.610 32 10.060.317 10.432 10.687.850 10.488 11.318.844 10.548 11.953.558 10 611 33 10.070.749 10.433 10 698.338 10.489 11.329.392 10.549 11.964.169 10.612 34 10.081.182 10.433 10 708.827 10.490 11.339.941 10.550 11.974.781 10.613 35 10 091.615 10.434 10.719.317 10.491 11.350.491 10 551 11.985.394 10.615 36 10 102. 0●9 10.435 10.729 808 10.492 11.361.042 10.552 11.996.009 10.616 37 10.112.484 10 436 10▪ 740. 30● 10.493 11.371.594 10.553 12.006.625 10.617 38 10.122 920 10.437 10.750.793 10.493 11.382.147 10.554 12.017. ●42 10 618 39 10.133.357 10.438 10 761.286 10.494 11.392.701 10.555 12.027.860 10.619 40 10.143.795 10.439 10.771.780 10.495 11.403.256 10.556 12.038.479 10.620 41 10.154.234 10.440 10 782.275 10.496 11.413.812 10.557 12.049.099 10 621 42 10.164.674 10.441 10.792.771 10.497 11.424.369 10.558 12.059.720 10 622 43 10.175.115 10.442 10 803.268 10.498 11.434.927 10.559 12.070.342 10.623 44 10.185.557 10.443 10 813.766 10.499 11.445.486 10.560 12.080.965 10.625 45 10.196.000 10.443 10 824.265 10.500 11.456.046 10.561 12.091.590 10.626 46 10.206.443 10.444 10.834.765 10.501 11.466.607 10 562 12.102.216 10.627 47 10.216 887 10.445 10.845.266 10.502 11.477.169 10.563 12.112.843 10 628 48 10.227.332 10.446 10.855 768 10.503 11.487.732 10.564 12.123.471 10 629 49 10.237 778 10.447 10.866.271 10.504 11 498.296 10.565 12.134.100 10 630 50 10 248.225 10.448 10.876.775 10.505 11.508.861 10.566 12.144.730 10.631 51 10 258.673 10.449 10.887.280 10.506 11.519.427 10.567 12.155.361 10.632 52 10.269.122 10.450 10.897.786 10.507 11.529.994 10.568 12.165.993 10.633 53 10 279.572 10▪ 451 10.908.293 10.508 11.540.562 10.569 12.176.636 10.635 54 10.290.023 10.452 10.918.801 10.509 11.551.131 10.570 12.187.261 10.636 55 10.300 475 10 453 10.929.310 10.510 11.561.701 10.571 12.197.897 10.637 56 10.310.928 10 454 10.939.820 10.511 11.572.272 10.573 12.208.534 10.638 57 10.321 382 10.455 10.950 331 10.512 11.582.845 10.574 12.219.172 10.639 58 10.331 837 10.455 10.960 843 10.513 11.593.419 10.575 12.229.811 10.640 59 10.342 292 10.456 10.971.356 10.514 11.603.994 10.576 12.240.451 10.641 Min. 20 Degr.  21 Degr,  22 Degr.  23 Degr.  Equal parts of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. par. Equal parts of a Me●id. Difference of equ. par. Equal part of a Merid. Difference of equ par. 0 12.251 292 10.642 12 891.873 10 712 13.536 762 10 786 14 186.216 10 864 1 12.261.934 10.644 12.902.585 10 713 13.547.548 10.787 14.197.080 10.866 2 12 272.578 10.645 12. 913.29● 10.715 13.558.335 10.789 14.207.946 10. 8●7 3 12▪ 283 223 10.646 12.924.013 10.716 13.569 124 10.790 14.218.813 10 868 4 12.293 869 10.647 12 934 729 10.717 13.579.914 10.791 14.229.681 10.870 5 12.304.516 10.648 12.945.446 10.718 13.590.705 10.792 14.240.551 10.871 6 12.315 164 10.649 12.956.164 10 719 13.601.497 10 794 14.251.422 10 873 7 12.325.813 10.650 12.966 883 10.721 13.612 291 10.795 14.262.275 10.874 8 12.336.463 10.651 12.977.604 10 722 13.623.086 10.796 14.273.149 10.875 9 12 347 114 10.653 12.988.326 10.723 13 633.882 10.798 14.284.024 10.877 10 12.357.767 10.654 12.999.049 10.724 13 644.680 10.799 14.294.901 10.878 11 12.368 421 10.655 13.009 773 10.725 13.655 479 10.800 14.305.779 10.879 12 12.379.076 10.656 13.020.498 10.727 13.666 279 10.801 14.316.658 10.881 13 12. 389.7●2 10.657 13.031.225 10.728 13.677.070 10.803 14.327 539 10 882 14 12.400.389 10.658 13.041.953 10.729 13.687.873 10 804 14 338.421 10.883 15 12.411.047 10.659 13 052 682 10.730 13.698.677 10.805 14.349.304 10.885 16 12.421.706 10.661 13.063.412 10.731 13.709.492 10.807 14.360.189 10.886 17 12.432.367 10.662 13.074 143 10.733 13.720.299 10.808 14.371.075 10.887 18 12.443.029 10.663 13.084.876 10.734 13.731.107 10▪ 809 14 381.962 10.889 19 12.453.692 10.664 13.095.610 10.735 13.741.916 10 810 14 392.851 10.890 20 12.464.356 10.665 13.106.345 10.736 13.752 726 10.812 14.403.741 10.892 21 12.475.021 10.666 13.117 081 10.738 13.763.538 10.813 14.414.633 10.893 22 12.485 687 10.667 13.127.819 10.739 13.774.351 10 814 14.425.526 10.894 23 12 496.354 10.669 13.138.558 10 740 13.785.165 10.816 14.436 420 10.896 24 12 507.023 10.670 13.149.298 10.741 13.795.981 10.817 14.447.316 10.897 25 12 517.693 10.671 13.160 039 10.742 13.806.798 10.818 14.458.213 10.898 26 12.528.364 10.672 13.170.781 10.744 13.817.616 10.820 14.499.111 10.900 27 12.539.036 10 673 13.181.525 10.745 13 828.436 10.821 14.480 011 10.901 28 12.549.709 10.674 13.192.270 10.746 13.839.257 10 822 14.490 912 10.903 29 12.560.383 10.676 13.203.016 10.747 13.850.079 10 823 14.501.815 10.904 30 12.571.059 10.677 13.213.763 10.749 13.860.902 10.825 14.512.719 10.905 31 12.581.736 10.678 13.224.512 10.750 13.871.727 10.826 14.523.624 10.907 32 12.592.414 10.679 13.235.262 10.751 13.882.553 10.827 14.534.531 10.908 33 12.603.093 10.680 13.246.013 10.752 13.893.380 10.829 14 545 439 10.909 34 12.613.773 10.681 13.256.765 10.754 13.904.209 10.830 14. 5●6 348 10.911 35 12.624.454 10.683 13.267.519 10.755 13.915.039 10 831 14 567.259 10 912 36 12.635.137 10.684 13.278.274 10.756 13.925.870 10.833 14.578 171 10.914 37 12.645.821 10.685 13.289.030 10 757 13 936.703 10.834 14.589.085 10.915 38 12.656.506 10.686 13.299.787 10. 7●8 13 947 537 10.835 14.600.000 10.916 39 12.667.192 10.687 13.310.545 10.760 13.958 372 10.837 14.610.916 10.918 40 12.677.879 10.688 13.321.305 10.761 13.969.209 10.838 14 621.834 10.919 41 12.688.567 10.690 13.332.066 10.762 13.980.047 10.839 14.632.753 10.921 42 12.699.257 10 691 13.342.828 10.763 13.990.886 10.840 14 643.674 10.922 43 12 709.948 10.692 13.353.591 10·765 14.001.726 10 842 14.654.596 10.923 44 12.720.640 10.693 13.364.356 10 766 14.012.568 10.843 14.665.519 10 925 45 12 731.333 10.694 13.375.122 10.767 14.023.411 100844 14.676.444 10.926 46 12.742.027 10.696 13 385.889 10 768 14.034.255 10.846 14.687.370 10.928 47 12.752.723 10.697 12.396.657 10.770 14.045 101 10 847 14.698 298 10.929 48 12.763.420 10.698 13.407.427 10.771 14.055.948 10.848 14 709.227 10 930 49 12 774.118 10.699 13.418.198 10.772 14.066.796 10.850 14.720 157 10.932 50 12.784.817 10.700 13.428 970 10.773 14. ●77. 646 10.851 14.731 089 10.933 51 12 795.517 10.701 13.439.743 10.775 14.088.497 10.852 14.742.022 10.935 52 12.806.218 10.703 13.450.518 10.776 14.099.349 10.854 14.752.957 10 936 53 12.816.921 10.704 13.461.294 10.777 14.110.203 10 855 14.763 893 10 937 54 12.827.625 10.705 13 472.071 10.779 1●. 121.058 10.856 14.774.830 10.939 55 12 838.330 10.706 13.482.850 10.780 14.131.914 10.858 14.785.769 10.940 56 12.849.036 10.707 13.493.630 10.781 14.142.772 10.859 14.796.709 10.942 57 12.859.743 10.709 13.504.411 10.782 14.153.631 10.860 14.807.651 10.943 58 12.870.452 10.710 13.515.193 10 784 14.164 491 10.862 14 818 594 10.944 59 12.881.162 10.711 13.525.977 10.785 14.175.353 10.863 14.829.538 10.946 Min 24 Degr.  25 Degr.  26 Degr.  27 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a merid. Difference of equ. par. 0 14.840 484 10.947 15.499.878 11.035 16.164 663 11.127 16.835.136 11.224 1 14.851.431 10.949 15.510.913 11.036 16.175.790 .129 16.846.360 11 226 2 14.862.380 10.950 15.521.949 .038 16.186.919 .130 16.857.586 11.228 3 14.873.330 10 952 15.532.987 039 16.198.049 .132 16.868.814 11.229 4 14.884.282 10.953 15.544.026 .041 16.209.181 .133 16.880.043 11.231 5 14.895.235 10 954 15.555.067 .042 16.220.314 .135 16.891.274 11.233 6 14.906 189 10 950 15.566.109 .044 16.231.449 .137 16.902.507 11.234 7 14.917.145 10.957 15.577.153 .045 16.242.586 .138 16.913.741 11.236 8 14.928.102 10.959 15.588.198 .047 16.253.724 .140 16.924.977 11.238 9 14.939.061 10 960 15.599.245 .048 16.264.864 .141 16.936.215 11.239 10 14.950.021 10.962 15.610 293 11.050 16.276.005 11.143 16.947.454 11.241 11 14 960.983 .963 15.621.343 .051 16.287.148 .145 16.958.695 11.243 12 14.971.946 .964 15.632.394 .053 16.298.293 .146 16.969.938 11.245 13 14.982 910 .966 15.643.447 .054 16.309.439 .148 16.981.183 11.246 14 14.993.876 .967 15.654.501 .056 16.320.587 .149 16.992.429 11.248 15 15.094.843 .969 15.665.557 .057 16.331.736 .151 17.003.677 11.250 16 15 015.812 .970 15.676.614 .059 16.342.887 153 17.014.927 11.251 17 15.026.782 .972 15.687.673 .060 16.354.040 .154 17.026.178 11.253 18 15.037.854 .973 15.698 733 .062 16.365.194 .156 17.037.431 11.255 19 15.048.727 .974 15.709 805 .063 16.376.350 .157 17.048.686 11.256 20 15.059.701 10.976 15.720.858 11.065 16.387.507 11.159 17.059.942 11.258 21 15.070.677 .977 15.731.923 .067 16.398.666 .161 17.071.200 11.260 22 15.081.654 .979 15.742.990 .068 16.409.827 .162 17.082 460 11.261 23 15 092.633 .980 15.754.058 .070 16.420.989 .164 17.093.721 11.263 24 15.103.613 .982 15.765.128 .071 16.432.153 .165 17.104 964 11.265 25 15.114.595 .983 15.776.199 .073 16.443.318 .167 17.116.229 11 267 26 15.125.578 .985 15.787.272 .074 16.454.485 .169 17.127.496 11.268 27 15.136.563 .986 15.798.346 .076 16.465.654 .170 17.138.764 11.270 28 15.147.549 .988 15.809.432 .077 16.476.824 .172 17.150.034 11.272 29 15 158. 53● .989 15.820.499 .079 16.487.996 .174 17.161.306 11.273 30 15.169.526 10.990 15.831.578 11.080 16.499 170 11.175 17.172 579 11.275 31 15.180.516 .992 15.842.658 .082 16.510.345 .177 17.183.854 11.277 32 15.191.508 .993 15.853.740 .083 16.521.522 .178 17.195 131 11.278 33 15.202 501 .995 15.864.823 .085 16.532.700 .180 17.206.409 11.280 34 15.213.496 .996 15 875.908 .086 16.543.880 .182 17.217.689 11.282 35 15.224.492 .998 15.886 994 .088 16.555.062 .183 17.228.971 11.284 36 15.235.490 .999 15.898.082 .090 16.566.245 .185 17.240.255 11.285 37 15.246.489 11.001 15.909.172 .091 16.577.430 .187 17.251.540 11.287 38 15.257.490 11.002 15.920.263 .093 16.588.617 .188 17.262.827 11.289 39 15.268.492 11.004 15.931.356 .094 16.599.805 .190 17.274.116 11.290 40 15.279.496 11.005 15.942.450 11.096 16.610.995 11.191 17.285 406 11.292 41 15.290 501 .007 15.953.546 .097 16.622.186 .193 17. 296.69● 11.294 42 15.301 508 .008 15.964.643 .099 16.633.379 .195 17.307.992 11.296 43 15.312.516 .010 15.975.742 .100 16.644.574 .196 17.319 288 11.297 44 15.323.526 .011 15.986.842 .102 16.655.770 .198 17.330.585 11.299 45 15.334.537 .012 15.997.944 .104 16.666.968 .200 17.341.884 11.301 46 15.345.549 014 16.009.048 .105 16.678.168 .201 17.353.185 11.303 47 15.356.563 .015 16.020.153 .107 16.689.369 .203 17.364.488 11.304 48 15.367.578 .017 16 031.260 .108 16 700.572 .205 17.375.792 11.306 49 15.378.595 .018 16.042.368 .110 16.711.777 .206 17.387.098 11.308 50 15.389.613 11.020 16.053.478 11.111 16.722.983 11.208 17.398.406 11.309 51 15.400.633 .021 16.064.589 .113 16.734.191 .210 17.409.715 11.311 52 15 411.654 .023 16 075.702 .115 16.745.401 .211 17.421.026 11.313 53 15.422.677 .024 16 086.817 .116 16.756.612 .213 17.432.339 11.315 54 15. 433.7●1 .026 16.097 933 .118 16 767.825 .214 17.443.654 11.316 55 15.444 727 .027 16 109 051 .119 16.779.039 .216 17.454.970 11.318 56 15.455.754 .029 16.120.170 .121 16.790.255 .218 17.466.288 11.320 57 15.466 783 .030 16.131.291 .122 16.801.473 .219 17.477.608 11.322 58 15.477.813 .032 16.142.413 11.124 16.812.692 .221 17.488.930 11.323 59 15.488 845 11.033 16.153 537 11.126 16.823.913 11.223 17.500.253 11 325 Min. 28 Degr.  29 Degr.  30 Degr.  31 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par 0 17.511.578 11.327 18.194 351 11.435 18 883.768 11.548 19.580 154 11.668 1 17.522.905 11.329 18 205 786 11.437 18.895.316 11.550 19 591.822 11.670 2 17.534.234 11.330 18.217 223 11.439 18.906 866 11.552 19.603.492 11.672 3 17.545.564 11.332 18.228.662 11.440 18.918.418 11.554 19 615.164 11.674 4 17.556.896 11.334 18.240.102 11.442 18.929.972 11.556 19.626.838 11.676 5 17.568 230 11.336 18.251.544 11.448 18 941.528 11.558 19.638.514 11.678 6 17.579.566 11.337 18 262.988 11.446 18.953.066 11.560 19.650.192 11.680 7 17.590.903 11.339 18.274.434 11.448 18.964.646 11▪ 562 19.661.872 11.682 8 17.602 242 11.341 18.285.882 11 450 18 976.208 11.564 19 673.554 11.684 9 17.613.583 11.343 18.297.332 11.452 18.987.772 11.566 19 685.238 11.686 10 17.624.926 11.345 18.308.784 11.453 18.999.338 11.568 19.696.924 11.688 11 17.636.271 11.346 18.320.237 11.455 19.010.906 11.570 19.708 612 11.690 12 17.647.617 11.348 18.331.692 11.457 19.022 476 11.572 19.720.302 11.692 13 17.658.965 11.350 18.343.149 11.459 19.034.048 11.574 19.731 994 11.695 14 17.670.315 11.352 18.354 608 11.461 19.045.622 11 576 19.743.699 11 697 15 17.681.667 11.353 18.366.069 11.463 19.057.198 11 578 19.755.396 11 699 16 17.693.020 11.355 18.377.532 11.465 19.068.776 11.580 19.767.085 11.701 17 17.704.375 11 357 18.388▪ 997 11.466 19 080.356 11 582 19 778 786 11.703 18 17.715.732 11.359 18.400.403 11.468 19.091.938 11.584 19 790.489 11.705 19 17.727.091 11.361 18.411 931 11.470 19.103 522 11.586 19.802.194 11.707 20 17.738.452 11.362 18 423.401 11.472 19.115.108 11.588 19.813 901 11.709 21 17.749.814 11.364 18.434.873 11.474 19 126.696 11.590 19.825 610 11.711 22 17.761.178 11.366 18.446.347 11 476 19.138.286 11.592 19.837.321 11.713 23 17.772.544 11.368 18.457.823 11.478 19.149.878 11.594 19.849 034 11.715 24 17.783.912 11.369 18.409.301 11.480 19.161.472 11 595 19.860.749 11 717 25 17.795.281 11.371 18.480.781 11.482 19.173 067 11.597 19.872 466 11.719 26 17.806.652 11.373 18.492.263 11.483 19.184.664 11.599 19 884.185 11.722 27 17.818.025 11.375 18 503.746 11.485 19 196 263 11 601 19.895 907 11.724 28 17.829.400 11.377 18.515.231 11·487 19.207 864 11.603 19 907 631 11.726 29 17.840.777 11.378 18.526 718 11 489 19.219.467 11.605 19 919 357 11.728 30 17 852.155 11.380 18.538.207 11 491 19.231.072 11.607 19.931.085 11.730 31 17.863.535 11.382 18.549.698 11 493 19.242.679 11.609 19 942.815 11.732 32 17.874 917 11.384 18 561.191 11 495 19 254.288 11.611 19 954.547 11.734 33 17.886.301 11.386 18.572.686 11.497 19.265.899 11 613 19 966 281 11.736 34 17 897 687 11.387 18.584.183 11.499 19 277.512 11 615 19.678 017 11 738 35 17.909.074 11.389 18.595.682 11.500 19.289.127 11.617 19.989 755 11.740 36 17 920.463 11.391 18 607.182 11.502 19 300.734 11.619 20 001 495 11.742 37 17.931.854 11.393 18.618.684 11. 50● 19 312.353 11 621 20.013 237 11.745 38 17.943.247 11.395 18.630.188 11.506 19.323 974 11.623 20.024.982 11 747 39 17 954.642 11.396 18.641.694 11. 50● 19 335 597 11.425 20.036.729 11.749 40 17.966.038 11.398 18.653.202 11.510 19.347.222 11.627 20 048.478 11.751 41 17.977.436 11.400 18.664.712 11.512 19.358.849 11 629 20.060.229 11 753 42 17.988.836 11.402 18.676.224 11.514 19.370.478 11.631 20.071 982 11.755 43 18 000.238 11.404 18 687.738 11.516 19.382.109 11.633 20.083.737 11.757 44 18.011.642 11.406 18.699.254 11.518 19.393.742 11.635 20. 095.4●4 11 759 45 18.023.048 11.407 18.710 772 11 520 19. 4●5 377 11. SIXPENCES 20 107 253 11.761 46 18.034.455 11.409 18.722▪ 292 11.521 19.417.014 11. 63● 20.119.014 11.764 47 18 045.864 11.411 18.733.813 11.523 19.428.653 11 641 20 130.778 11 766 48 18 057.275 11.413 18.745.336 11.525 19.440.294 11.644 20.142.544 11 768 49 18.068 688 11 415 18.756.861 11.527 19.451 938 11.646 20 154.312 11.770 50 18.080 103 11.417 18 768.388 11.529 19.463.584 11.648 20.166 082 11.772 51 18.091.520 11.418 18.779.917 11 531 19 475.232 11 650 20.177.854 11.774 52 18.102 938 11.420 18. 7●1.448 11.533 19.486.882 11.652 20.189.628 11.776 53 18.114 358 11.422 18.802.911 11.535 19. 4●8.534 11.654 20.201.404 11.778 54 18.125.780 11.424 18 814 516 11.537 19.510.188 11 6●6 20. 213.1●2 11.781 55 18.137 204 11.426 18.826 053 11.539 19.521. ●4● 11.658 20.224.963 11 783 56 18.148.630 11.428 18.837.592 11.541 19 ●33. 502 11. 6●0 ●0 2●6 746 11.785 57 18.160.058 11.429 18.849.133 11. 54● 19 ●45. 162 11. ●●● 20 ●18. A 1 12. 7●7 58 18.171.487 11.431 18.860.676 11.545 19 556 8●● 11 66● 2●. 260.318 11.789 59 18 182 918 11.433 18 872.221 11.547 1●. 568.48● 11 ●66 20 272. 1●7 11.791 Min 32 Degr.  33 Degr.  34 Degr.  35 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ par. Equal parts of a Merid. Difference of equ. par. 0 20.283.898 11.793 20.995.367 11 925 21.714.945 12.064 22.443 047 12 210 1 20 295.691 11. 79● 21 007 292 11 928 21.727.009 12 066 22.455.257 12 212 2 20.307.487 11.798 21 019.220 11.930 21.739.075 12.069 22.467.469 12 215 3 20 319.285 11.800 21.031 150 11.932 21.751.144 12 071 22.479.684 12 217 4 20.331.085 11 802 21.043 0●2 11 934 21.763.215 12.074 22.491.901 12 220 5 20.342 ●87 11.804 21.055.016 11 937 21. 775.2●9 12.076 22.504.221 12 222 6 20 354 691 11. 80● 21 066.953 11.939 21.787.365 12 078 22.516.443 12 225 7 20.366.497 11.808 21.078.892 11.941 21.799.443 12.081 22.528.668 12.227 8 20. 37● 305 11.811 21.090.833 11.943 21.811.524 12.083 22.540.895 12.230 9 20 390.116 11.813 21.102 776 11.946 21 823 607 12 085 22.553.125 12.232 10 20.401.929 11 815 21.114.722 11.948 21.835.692 12 0●8 22 565 357 12 235 11 20.413 744 11 817 21 126.670 11.950 21.847.780 12.090 22.577.592 12.237 12 20.425 561 11.819 21.138.620 11 953 21.859.870 12 093 22.589.829 12.240 13 20.437.380 11.821 21.150 573 11.955 21.871 963 12.095 22 602 069 12 242 14 20.449.201 11.824 21 162.528 11.957 21.884.058 12.097 22.614.311 12.245 15 20. ●61. 025 11.826 21.174.485 11.959 21.896.155 12.100 22 626.556 12.247 16 20.472.851 11.828 21.186.444 11.962 21.908.255 12.102 22.638.803 12 250 17 20 484.679 11.830 21.198.406 11.964 21.920.357 12.105 22.651.053 12 252 18 20.496 509 11 832 21 210.370 11.966 21 932.462 12 107 22.663.305 12.255 19 20.508.311 11.835 21.222 336 11.969 21.944.569 12.109 22.675 560 12.257 20 20.520.176 11.837 21.234.305 11.971 21 956 678 12.112 22 687.817 12.260 21 20.532 013 11.839 21 246.276 11.973 21.968 790 12 114 22.700.077 12.262 22 20.543 852 11.841 21 258.249 11.975 21.980.904 12.117 22.712.339 12.265 23 20 555 693 11.843 21.270.224 11 978 21.993 021 12.119 22.724.604 12.268 24 20 567.536 11.845 21.282.202 11.980 22.005 140 12.121 22 736.872 12.270 25 20 579.381 11.848 21.294.182 11.982 22.017.261 12.124 22.749.142 12.273 26 20 591 229 11.850 21.306 164 11.985 22.029.385 12.126 22.761.415 12.275 27 20 603.079 11.852 21.318.149 11.987 22.041 511 12 129 22.773 690 12.278 28 20 614.031 11.854 21 330.136 11.989 22.053.640 12.131 22.785.968 12.280 29 20 626.785 11 856 21 342.125 11.992 22 065.771 12.134 22.798.248 12.283 30 20.638.641 11.859 21.354 117 11.994 22 077.905 12.136 22.810.531 12.285 31 20.650 500 11.861 21 366 111 11.996 22.090.041 12.138 22.822.816 12.288 32 20 662 361 11.863 21.378 107 11.998 22.102.179 12 141 22.835.104 12.290 33 20 674.224 11.865 21.390.105 12.001 22.114 320 12 143 22.847.394 12.293 34 20.686.089 11.867 21.402.106 12.003 22 126.463 12.146 22.859.687 12.296 35 20 697.956 11.870 21.414.109 12.005 22.138 609 12.148 22.871.983 12.298 36 20.709.826 11.872 21.426.114 12.008 22.150 757 12.150 22 884.281 12.301 37 20.721 702 11.874 21.438 122 12.010 22 162.907 12.153 22.896.582 12 303 38 20 733.576 11.876 21.450.132 12 012 22.175.060 12 155 22.908.885 12 306 39 20 745.452 11.878 21.462.144 12.015 22.187 215 12.158 22.921.191 12.308 40 20.757.330 11 881 21.474.159 12 017 22.199 373 12 160 22.933.499 12.311 41 20.769 211 11.883 21.486.176 12.019 22.211.533 12 163 22.945.810 12.314 42 20.781 094 11.885 21.498.195 12.022 22.223.696 12 165 22 958.124 12.316 43 20 792.979 11.887 21.510.217 12.024 22.235.861 12.168 22.970.440 12 319 44 20.801.866 11.890 21.522.241 12.026 22.248.029 12.170 22.982.759 12.321 45 20.816.756 11.892 21.534.267 12.029 22.260.199 12.173 22.995.080 12.324 46 20.828.648 11.894 21.546.296 12.031 22 272.372 12.175 23 007.404 12 326 47 20 840.542 11.896 21.558.327 12.033 22 284.547 12.178 23.019.730 12.329 48 20.852 438 11.898 21.570.360 12.036 22.296.725 12 180 23.032 059 12.332 49 20.864.336 11.901 21.582.396 12.038 22.308.905 12.182 23 044.391 12 334 50 20.876.237 11.903 21 594.434 12.040 22.321.087 12.185 23.056.725 12.337 51 20.888.140 11.905 21.606.474 12.043 22.333.272 12 187 23.069.062 12.339 52 20.900.045 11.907 21.618 517 12 045 22.345.459 12.190 23.081.401 12.342 53 20.911.952 11.910 21.630.562 12.048 22.357.649 12.192 23.093.743 12.345 54 20.923 862 11.912 21.642 610 12.050 22.369.841 12.195 23.106.088 12.347 55 20.935.774 11.914 21.654.660 12.052 22.382.036 12.197 23.118.435 12.350 56 20.947.688 11.916 21.666.712 12.055 22.394.233 12.200 23.130 785 12.352 57 20.959.604 11.919 21.687.767 12.057 22.406.433 12.202 23.143.137 12.355 58 20.971.523 11 921 21.690.824 12 059 22.418.635 12.205 23.155.492 12.358 59 20.983 444 11.923 21.720.883 12.062 22.430.840 12.207 23.167.850 12. 36● Min. 36 Degr.  37 Degr.  38 Degr.  39 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 23.180.210 12 363 23.926.786 12.524 24 683.145 12.693 25.449.892 12.870 1 23.192.573 12.365 23 939 310 12.526 24.695.838 12.695 25.462.762 12.873 2 23.204.938 12.368 23.951.836 12.529 24.708.533 12 698 25.475.635 12.876 3 23 217.306 12.371 23 964.365 12.532 24.721 231 12 701 25.488.511 12.879 4 23.229.677 12.373 23 976.897 12 5●5 24.733.932 12.704 25.501.390 12.882 5 23.242 050 12.376 23.989 432 12.537 24.746.636 12.707 25.514.272 12.885 6 23.254.426 12.379 24 001.969 12.540 24.659.343 12.710 25.527.157 12.888 7 23 266.805 12.381 24.014.509 12.543 24 772.053 12 713 25.540.045 12 891 8 23.279 186 12 384 24 027.052 12.546 24 784.766 12.716 25 552. 93● 12.894 9 23.291.570 12.386 24.039.598 12.548 24 797.482 12.719 25.565 830 12 898 10 23.303 956 12.389 24 052 146 12.551 24.810.201 12.722 25.578.738 12 901 11 23 316.345 12 392 24 064.697 12.554 24 822 923 12.724 25.591.639 12.904 12 23.328 737 12.394 24.077.251 12 557 24.835 647 12 727 25 604.533 12.907 13 23.341.133 12.397 24.089.808 12.560 24 848.374 12 730 25 617.440 12.910 14 23.353.530 12.400 24.102.368 12.562 24.861.104 12.733 25.630.350 12.913 15 23.365.930 12 402 24 114 930 12.565 24.873.837 12.736 25.643 263 12.916 16 23.378 332 12 405 24 127 495 12 568 24.886.573 12.739 25 65●. 179 12.919 17 23.390 837 12.408 24.140.063 12.571 24.899.312 12 742 25.669.098 12 922 18 23.403.245 12.410 24 152.634 12 573 24.912.054 12.745 25. 6●2 020 12.925 19 23.415.655 12.413 24.165.207 12.576 24.924.799 12 748 25.694.945 12.928 20 23.428.068 12 416 24 177.783 12.579 24.937.547 12.751 25.707.873 12.931 21 23.440.484 12.418 24 190 362 12.582 24.950.298 12.754 25.720.804 12.934 22 23.452 902 12.521 24.202.944 12 585 24.963.052 12.757 25.733 738 12.937 23 23.465.323 12 423 24.215.520 12.587 24.975.809 12.760 25.746.675 12 941 24 23.477.746 12.426 24.228.116 12.590 24.988.569 12.763 25.759.616 12.944 25 23.490.172 12.429 24 240.706 12.593 25.001 332 12.765 25.772 560 12.947 26 23.502.601 12.432 24. 253·299 12.596 25 014.097 12.768 25.785.507 12 950 27 23.515.033 12.434 24.265.895 12.599 25.026.865 12 771 25.798.457 12.953 28 23.527.467 12.437 24.278.494 12 601 25 039 636 12 774 25 811.410 12.956 29 22 539.904 12 440 24 291.095 12.604 25.052 410 12.777 25.824.366 12.959 30 23 552.344 12.442 24.303.699 12 607 25.065.187 12 780 25.837 325 12.962 31 23.564.786 12.445 24.316 306 12 610 25.077 967 12.783 25 850.287 12.965 32 23.577.231 12.448 24 328.916 12 613 25 090.750 12 786 25.863.252 12.969 33 23.589.679 12.450 24.341 529 12.615 25.103 536 12.789 25.876.221 12.972 34 23 602.129 12.453 24.354.144 12 618 25 116 325 12.792 25.889 193 12 975 35 23.614.582 12.456 24.366.762 12.621 25.129 117 12.795 25 902 168 12.978 36 23.627.038 12.458 24.379.383 12.624 25.141.912 12.798 25 915.146 12.981 37 23.639.496 12 461 24 392 007 12.627 25.154 710 12.801 25.928 127 12.984 38 23 651.957 12 464 24 404.634 12.630 25.167.511 12.804 25.941.111 12.987 39 23.664.421 12.466 24.417.264 12.632 25.180.315 12 807 25 954.098 12.990 40 23.676.887 12.469 24.429.896 12.635 25.193.122 12.810 25.967.088 12.994 41 23.689.356 12.472 24.442.531 12.638 25.205.932 12.813 25.980 082 12 997 42 23.701 828 12.475 24.455.169 12.641 25.218.745 12 816 25.993 079 13 000 43 23.714.303 12 477 24.467.810 12 644 25 231.561 12.819 26.006.079 13 003 44 23.726.780 12.480 24 480.454 12.647 25.244.380 12 822 26.019.072 13 006 45 23.739.260 12.483 24.493.101 12.650 25.257.202 12 825 26.032 078 13.009 46 23.751.743 12.485 24.505.751 12.652 25 270.027 12.828 26.045 097 13.012 47 23.764.228 12 488 24.518.403 12 655 25.282 855 12.831 26.058.109 13 016 48 23.776.716 12.491 24 531.058 12.648 25.295.686 12.834 26.071.125 13.019 49 23.789.207 12.494 24.543.716 12.661 25.308.520 12.837 26.084 144 13.022 50 23.801.701 12.496 24.556 377 12.664 25.321.357 12.840 26.097 166 13.025 51 23.814.197 12.499 24.569.041 12.667 25.334 197 12. 84● 26.110.191 13.028 52 23.226.696 12 502 24.581.708 12.670 25.347 040 12.846 26.123 219 13.031 53 23 839.198 12.504 24.594.378 12.672 25. 3●● 886 12. 84● 26 1●6 250 13.035 54 23.851.702 12.507 24.607.050 12 675 25 ●72. 7●5 12.852 26 149 285 13.038 55 23.864.209 12.510 24.619.725 12.678 25.385.587 12 855 26. 162.32● 13.041 56 23.876.719 12. 51● 24.632.403 12.681 25.398 442 12. 85● 26. 175.3●4 13.044 57 23.889.232 12.515 24.645.084 12.684 25.411.300 12. ●61 26.188 40● 13.047 58 23.901.747 12.518 24.657.768 12.687 25.424 161 12.864 26. 201.45● 13.050 59 23.914.265 12.521 24.670.455 12.690 25.437.025 12 867 26 214.505 13.054 Min. 40 Degr.  41 Degr.  42 Degr.  43 Degr.  Equal parts of a Merid. Difference of equ par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 26 227.559 13.057 27.016 632 13.253 27.817.839 13.459 28.631.657 13.676 1 26.240 616 13.060 27.029.885 13.256 27.831.295 13.463 28 645.333 13.680 2 26.253 676 13.063 27 043.141 13.260 27.844.758 13.466 28 659.013 13 684 3 26.266.739 13. 06● 27.056.401 13.263 27.858.224 13 470 28 672.697 13 688 4 26.279.805 13.070 27 069.664 13.266 27.871 694 13 473 28.686.385 13 691 5 26.292.875 13.073 27.082.930 13.270 27.885 167 13.477 28 700 076 13.695 6 26.305 948 13.076 27.096.200 13.273 27.898 644 13.481 28 713 771 13.699 7 26 319.024 13 079 27.109.473 13.277 27.912.125 13.484 28 727.470 13.703 8 26.332.103 13.082 27.122 750 13.280 27.925 609 13.488 28.741.173 13.706 9 26. 345.18● 13.086 27.136.030 13 283 27.939.097 13.491 28.754 879 13.710 10 26.358.271 13 089 27.149.313 13.287 27 952.588 13.495 28 768.589 13.714 11 26 371.36 13.092 27.162.600 13.290 27.966.083 13.498 28.782.303 13.718 12 26.384.452 13.095 27.175.890 13 293 27.979.581 13.502 28.796.021 13.721 13 26.397.547 13.098 27.189.183 13.297 27 993.083 13.505 28.809.742 13.725 14 26.410 645 13 102 27.202 480 13.300 28.006.588 13.509 28 823.467 13.729 15 26.423.747 13.105 27.215.780 13.304 28.020.097 13.513 28 837.196 13.733 16 26.436.852 13. 10● 27.229.084 13.307 28.033.610 13.516 28.850.929 13.736 17 26 449 960 13.111 27 242 391 13.310 28.047.126 13.520 28.864.665 13.740 18 26.463 071 13.115 27 255.701 13 314 28.060 646 13.523 28.878▪ 405 13.744 19 26.476.186 13. 11● 27.269.015 13.317 28.074 169 13.527 28.892.149 13 748 20 26.489.304 13.121 27.282.332 13.321 28.087 696 13.531 28.905.897 13.751 21 26.502.425 13.124 27.295.653 13.324 28.101.227 13.534 28.919.648 13.755 22 26 515.549 13.128 27.308.977 13.327 28.114.761 13.538 28 933.403 13.759 23 26.528 677 13.131 27.322.304 13.331 28.128.299 13.541 28.947.162 13.763 24 26.541 808 13. 13● 27.335.635 13.334 28.141.840 13 545 28.960.925 13.766 25 26.554.942 13.137 27 348.969 13.338 28.155.385 13.548 28.974 691 13.770 26 26.568.079 13.141 27.362.307 13 341 28.168.933 13.552 28.988.461 13.774 27 26.581.220 13.144 27 375.648 13 345 28.182.485 13.556 29.002.235 13.778 28 26.594.364 13.147 27.388.993 13.348 28.196.041 13.559 29.016.013 13.782 29 26.607.511 13.150 27.402.341 13 351 28.209 600 13.563 29.029.795 13.785 30 26.620 661 13 154 27.415.692 13.355 28.223.163 13.567 29.043.580 13.789 31 26.633 842 13.157 27.429.047 13.358 28.236.730 13 570 29.057.369 13.793 32 26.646.999 13.160 27.442.405 13.362 28.250.300 13 574 29.071 162 13.797 33 26.660 159 13 163 27.455.767 13 365 28.263.874 13 577 29.084 969 13.801 34 26.673.322 13.167 27.469.132 13.369 28. 277.4●1 13.581 29.098.760 13.805 35 26.686.489 13.170 27.482.501 13.372 28.291.032 13.585 29.112.565 13.808 36 26.699.659 13 173 27 495 873 13.376 28 304.617 13.588 29.126.373 13.812 37 26.712.832 13.177 27.509.249 13.379 28.318.205 13.592 29.140.185 13.816 38 26.729 009 13.180 27.522.628 13.382 28.331.807 13.596 29 154.001 13.820 39 26.739.189 13.183 27.536.010 13.386 28.345.403 13.599 29.167 821 13.824 40 26.752.372 13 186 27 549.396 13.389 28.358.902 13.603 29.181.645 13.828 41 26.765.558 13.190 27.562.785 13.393 28.372 505 13.607 29.195.473 13.831 42 26.778.648 13.193 27.576.178 13.396 28.386 112 13.610 29.209.304 13.839 43 26.791.841 13.196 27.589.574 13.400 28.399 722 13.614 29.223.139 13.835 44 26.805.037 13.200 27.602.974 13.403 28.413.336 13 617 29.236.978 13.843 45 26.818.237 13. 20● 27▪ 616 377 13.407 28.426.953 13.621 29.250.821 13.847 46 26.831.440 13. 20● 27.629.784 13.410 28.440.574 13 625 29.264 668 13.851 47 26.844.646 13.210 27.643.194 13.141 28.454.199 13 628 29.278.519 13.855 48 26.857.856 13. 21● 27.656.608 13.417 28.467.827 13.632 29.292.374 13.858 49 26.871.069 13. 21● 27.670.025 13.421 28.481.459 13.636 29.306 232 13.862 50 26.884.285 13.220 27.683.446 13.424 28.495.095 13.640 29.320 094 13.866 51 26.897.505 13 223 27.696.870 13.428 28.508.735 13.643 29.333.960 13.870 52 26 910.728 13.226 27.710.298 13.431 28.522.378 13 646 29.347.830 13.874 53 26.923.954 13 230 27.723.729 13.435 28.536.025 13.651 29.361 704 13.878 54 26.937 184 13.233 27.737.164 13.438 28.549.676 13.654 29.375.582 13.882 55 26.950 417 13. 23● 27.750 602 13.442 28.563.330 13.658 29.389.464 13.886 56 26.963.653 13.240 27.764.044 13.445 28.576.988 13.662 29 403.350 13.889 57 26.976.893 13 243 27.777.489 13.449 28.590.650 13.665 29.417.239 13 893 58 26.990.136 13.246 27.790.938 13 452 28.604.315 13 669 29.431.132 13.897 59 27.003.382 13.250 27.804.380 13 456 28.617.984 13.673 29.445.029 13.901 Min. 44 Degr.  45 Degr.  46 Degr.  47 Degr.  Equal parts of a Merid. Difference of equ. par. Equal part of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. par. Equal parts of a merid. Difference of equ. par. 0 29.458.930 13.905 30.301 271 14 146 31.156.423 14.399 32.028.087 14.667 1 29 472 835 13.909 30 314.417 14 150 31.170 822 14.404 32.042.754 14.671 2 29.486.744 13.913 30 328.567 14.154 31.185 226 14.408 32.057.425 14 676 3 29.500.657 13.917 30.342 721 14.158 31 199.634 14.412 32.072.101 14.681 4 29.514.574 13 921 30 356.879 14 162 31.214 046 14.417 32.086.782 14.685 5 29.528.495 13.925 30.371.041 14.166 31.228 463 14 421 32.101.467 14.690 6 29.542.420 13.929 30.385.207 14.171 31.242.884 14.426 32.116 157 14.694 7 29.556.349 13 932 30.399.378 14.175 31.257 310 14.430 32.130.851 14.699 8 29.570.281 13.936 30 413.553 14.179 31.271.740 14.434 32 145.550 14.704 9 29.584.217 13.940 30.427.732 14.183 31.286.174 14 439 32.160.254 14 708 10 29.598 157 13.944 30 441.915 14 187 31.300 613 14.443 32.174.962 14.713 11 29 612.101 13 948 30 456.102 14.191 31.315.056 14.447 32.189 675 14.717 12 29 626.049 13.952 30 470.293 14.195 31.329.503 14.452 32.204 392 14.722 13 29 640.001 13.956 30.484 488 14.200 31.343.955 14.456 32.219 114 14 727 14 29.653.957 13.960 30.498 688 14.204 31.358.411 14.461 32.233 841 14.731 15 29 667 917 13.964 30.512.892 14.208 31.372.872 14.465 32.248.572 14.736 16 29 681.881 13.968 30.527 100 14.212 31.387.337 14.469 32.263.308 14.741 17 29 695 849 13.972 30.541.312 14.216 31.401.806 14 474 32 278.049 14.745 18 29.709.821 13 976 30.555.528 14.220 31.416.280 14.478 32 292.794 14.750 19 29 723.797 13 980 30 569.748 14.225 31.430.758 14.483 32.307.544 14.755 20 29 737 777 13.984 30.583.973 14.229 31.445.241 14.487 32.322.299 14 759 21 29.751.761 13.988 30 598.202 14.233 31.459 728 14.491 32.337.058 14.764 22 29.765.749 13.992 30.612.435 14.237 31.474 219 14.496 32.351.822 14.769 23 29.779 741 13.996 30.626.672 14.241 31.488.715 14.500 32.366.591 14.773 24 29 793.737 14.000 30.640.913 14.246 31.503 215 14 505 32.381.364 14.778 25 29.807 737 14.004 30.655.159 14.250 31.517.720 14.509 32.396.142 14.783 26 29 821.741 14.008 30.669.409 14.254 31 532.229 14.514 32.410 925 14.787 27 29 83●. 749 14.012 30.683.663 14.258 31.546.743 14.518 32.425.712 14.792 28 29.849.761 14 016 30.697 921 14.262 31.561.261 14.522 32 440.504 14.797 29 29 863.777 14 0●0 30.712.183 14.267 31.575.783 14.527 32.455.301 14.801 30 29.877.797 14.024 30 726.450 14.271 31.590.310 14.531 32.470.102 14.806 31 29 891 821 14.028 30.740.721 14.275 31.604.841 14 536 32 484.908 14.811 32 29 905.849 14.032 30.754 996 14.279 31.619 377 14 540 32 499.719 14.815 33 29.919.881 14.036 30 769.275 14 284 31.633 917 14.545 32.514.534 14.820 34 29.933.917 14.040 30 783.559 14.288 31.648.462 14.549 32.529.354 14.825 35 29.947 957 14.044 30 7●7 847 14 292 31.663.011 14.554 32.544.179 14.830 36 29.962 001 14.048 30.812.139 14.296 31.677.545 14.558 32.559.009 14.834 37 29 976.049 14.052 30.826.435 14.301 31.692.103 14.563 32 573.843 14.839 38 29.990.101 14.056 30. 840.73● 14.305 31.706 666 14.567 32.588.682 14.844 39 30 004.157 14.060 30.855.041 14.309 31·721 133 14.572 32.603.526 14.849 40 30▪ 018.217 14.064 30.869.350 14.313 31.735▪ 705 14 576 32.618.375 14.853 41 30.032.281 14.068 30 883 663 14.318 31.750.281 14.581 32.633.228 14.858 42 30 046 349 14.072 30 897 981 14.322 31.764.862 14.585 32.648.086 14.863 43 30.060.421 14.076 30.912.303 14 326 31.779 447 14.590 32 662 949 14.868 44 30.074.497 14.080 30.926 629 14.330 31.794.037 14.594 32.677.817 14.872 45 30.088.577 14 084 30 940.959 14.335 31.808.631 14.599 32 692.689 14.877 46 30.102.661 14 088 30 955.294 14.339 31·823. 230 14 603 32.707.566 14.882 47 30.116.749 14 093 30.969.633 14 343 31·837 833 14 608 32.722.448 14.887 48 30.130 842 14.097 30 983. 97● 14.348 31·852. 441 14.612 32 737.335 14.891 49 30.144.939 14.100 30. 99●.324 14.352 31·867. 053 14.617 32. 752.22● 14 896 50 30 159.039 14.105 31.012 676 14.356 31.881.670 14.621 32 767 122 14.901 51 30.173.144 14 109 31.027.032 14.360 31.896.291 14.626 32. 782.02● 14.906 52 30 187.253 14.113 31.041.392 14.365 31.910 917 14. 6●0 32 796.929 14.911 53 30 201 366 14.117 31.055.757 14.369 31.925.547 14.635 32.811.840 14.915 54 30▪ 215.483 14.121 31.070.126 14 373 31.940.182 14. 6●0 32.826 755 14.920 55 30.229. ●04 14.125 31.084 499 14.378 31.954.821 14. 64● 32.841.675 14.925 56 30.243.729 14.129 31.098.877 14.382 31.969 465 14. 64● 32.856 595 14 930 57 30.257.858 14.133 31 113.250 14.386 31.984.114 14.653 32.871 525 14.935 58 30.271.991 14.138 31.127.635 14.391 31 998.767 14 65● 32. 8●6.460 14 939 59 30.286.129 14.142 31 142.026 14 20● 32 01●. 425 14.662 32 901 399 14. 9●4 Min. 48 Degr.  49 Degr.  50 Degr·  51 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 32.916.343 14.949 33 822.018 15.247 34 746.045 15.562 35 689 522 15.895 1 32 931 292 14.954 33.837.265 15.252 34.761 607 15.568 35 705.417 15.901 2 32▪ 946 246 14.959 33.852 517 15.257 34.777.175 15.573 35.721.318 15 907 3 32.961.205 14.964 33.867.774 15.262 34.792.748 15.578 35 737 225 15.913 4 32.976.169 14.968 33.883 036 15.268 34.808 326 15.584 35 753.138 15 918 5 32 991.137 14.973 33.898.304 15.273 34.823.910 15.589 35.769 056 15.924 6 33▪ 006.110 14. 97● 33.913.577 15 27● 34.839 499 15.595 35.784 980 15 930 7 33.021.088 14.983 33.928.855 15 283 34.855.094 15 600 35.800.910 15 936 8 33.036.071 14.988 33.944.138 15.288 34.870 694 15 605 35.816.846 15 941 9 33.051.059 14 993 33.959.426 15 293 34 886.299 15.611 35.832 787 15 947 10 33.066.052 14 998 33.974 719 15.298 34.901.910 15.616 35.848.734 15.953 11 33 081 050 15 003 33.990.017 15.304 34.917.526 15.622 35.864.687 15.959 12 33·096 053 15.007 34 005.321 15 309 34.933.148 15.627 35.880.646 15.964 13 33.111.060 15.012 34.020.630 15.314 34.948.775 15.633 35 896.610 15.970 14 33.126.072 15.017 34.035.944 15.319 34.964.408 15 638 35.912 580 15.976 15 33.141 089 15.022 34.051.263 15.324 34.980.046 15.644 35 928 556 15.982 16 33 156.111 15.027 34.066.587 15.329 34.995.690 15.649 35 944.538 15 987 17 33 171.138 15.032 34 081.916 15.335 35 011.339 15.655 35.960.525 15.993 18 33.186.170 15.037 34 097.251 15.340 35.026.994 15.660 35.976.518 15.999 19 33.201.227 15.042 34.112.591 15 345 35.042.654 15 666 35 992 517 16.005 20 33.216.269 15.047 34.127.936 15.350 35 058.320 15 671 36 008 522 16.011 21 33.231 316 15.052 34.143.286 15.355 35.073.991 15.677 36 024 533 16.017 22 33.246 368 15.056 34.158 641 15.361 35 089.668 15 682 36.040 550 16.022 23 33.261.424 15.061 34.173.102 15.366 35.105 350 15 688 36.056.572 16.028 24 33.276.485 15.066 34.189.368 15.371 35 121 038 15.693 36 072.600 16 034 25 33.291.551 15.071 34.204.739 15 376 35.136 731 15.699 36.088.634 16.040 26 33.306 622 15.076 34 220.115 15 381 35.152.430 15.704 36.104 674 16.046 27 33.321.698 15.081 34.235.496 15.387 35.168.134 15.710 36.120 720 16 052 28 33.336.779 15.086 34.250.883 15 392 35.183 844 15 715 36.136 772 16.058 29 33.351.865 15 091 34.266.275 15.397 35.199.559 15.721 36.152.830 16.063 30 33 366.956 15 096 34.281.672 15.402 35.215.280 15.726 36.168 893 16.069 31 33 382.052 15.101 34.297 074 15.408 35.231 006 15.732 36.184.962 16.075 32 33.397.153 15.106 34.312.482 15.413 35.246.738 15.738 36.201.037 16.081 33 33.412.259 15 111 34.327.895 15 418 35 262.476 15.743 36.217.118 16.087 34 33.427.370 15.116 34.343.313 15.423 35.278.219 15.749 36 233.205 16.093 35 33.442.486 15.121 34.358.733 15.429 35.293.968 15.754 36 249 298 16.099 36 33.457.607 15 126 34 374.162 15.434 35.309 722 15.760 36 265.397 16.105 37 33.472.733 15.131 34.389.596 15 439 35 325.482 15 765 36.281 502 16.111 38 33 487.864 15.136 34.405.035 15.445 35.341 247 15.771 36.297.613 16.116 39 33.503.000 15.141 34.420.480 15.450 35.357.028 15.777 36.313 729 16.122 40 33.518.141 15 146 34 435 930 15.455 35.372.805 15.782 36.329.851 16.128 41 33.533.287 15 151 34.451.385 15.460 35.388.587 15. 78● 36.345.979 16.134 42 33.548 438 15.156 34.466.845 15.466 35.404.375 15 793 36.362.113 16 140 43 33.563.594 15.161 34.482.311 15 471 35.420.168 15 799 36.378.253 16.146 44 33.578.755 15.166 34.487.782 15.476 35 435.967 15.805 36.394.399 16.152 45 33.593.921 15.171 34.513.258 15.482 35.451.772 15.810 36.410 551 16 158 46 33.609.092 15.176 34.528.740 15 487 35 467.582 15.816 36.426 709 16.164 47 33.624.268 15.181 34 544 227 15 402 35.483.398 15 822 36.442.873 16.170 48 33.639.449 15.186 34.559.719 15 498 35.499.220 15.827 36.459.043 16.176 49 33.654.635 15.191 34.575 217 15.503 35 515 047 15 833 36. 475·219 16 182 50 33 669.826 15.196 34 590.720 15.508 35.530.880 15.839 36 491.401 16 188 51 33 685.022 15.201 34.606.228 15.514 35.546.719 15.844 36.507 589 16.194 52 33.700.223 15.206 34.621.742 15.519 35.562.563 15 850 36.523.783 16.200 53 33.715.429 15.212 34.637.261 15.524 35.578 413 15.856 36.539.983 16.206 54 33 730.641 15.217 34.652.785 15.530 35.594 269 15 861 36.556.189 16.212 55 33 745.858 15.222 34 668 315 15.535 35.610.130 15.867 36 572 401 16.218 56 33.761.080 15.227 34.683 850 15.541 35.625.997 15.873 36.588.619 16.224 57 33.776.307 15 232 34 699.391 15 546 35 641 870 15.878 36.604 843 16.230 58 33.791.539 15 237 34.714.937 15 551 35.657.748 15.884 36.621.073 16.236 59 33.806.776 15.242 34 730.488 15.557 35 673.632 15.890 36 637 309 16.242 Min 52 Degr.  53 Degr.  54 Degr.  55 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 36.653.551 16.248 37.639.370 16 622 38.648.311 17.019 39.681.879 17.441 1 36.669.799 16.254 37 655.992 16.629 38.665 330 17.026 39.699 320 17.448 2 36.686.053 16.260 37.672.621 16.635 38 682.356 17.033 39.716.768 17.456 3 36.702.313 16.266 37.689.256 16.642 38.699 389 17.040 39.734.224 17.463 4 36 718.579 16.273 37.705.898 16.648 38 716.429 17 047 39.751.687 17 470 5 36.734.852 16.279 37.721.546 16.655 38 733.476 17.054 39.769.157 17.478 6 36 751.131 16 285 37.739.201 16 661 38.750.530 17.060 39.786.635 17 485 7 36.767 416 16.291 37.755.862 16.667 38.767.590 17.067 39.804.120 17.492 8 36.783.707 16.297 37.772 529 16.674 38.784 657 17.074 39.821.612 17.499 9 36.800.004 16.303 37 789.203 16 680 38.801 731 17.081 39.839.111 17.507 10 36.816 307 16 309 37 805.883 16 687 38.818.812 17.088 39 856.618 17.514 11 36 83●. 616 16.315 37.822.570 16.693 38 835.900 17.095 39.874.122 17.521 12 36.848.931 16.321 37.839.263 16.700 38.852 99● 17 102 39.891.643 17 529 13 6.865.252 16.327 37.855.963 16.706 38.870.097 17 109 34.909.172 17.536 1● 36.881.579 16.334 37.72.669 16.713 38.887.206 17.115 39.926.708 17. 5●3 15 36 897.913 16.340 37 889.382 16.719 38.904 321 17.122 39.944.251 17.551 16 36.914.253 16 346 37.906.101 16 726 38 921.443 17.129 39 961.802 17.558 17 36 930.599 16.352 37.922 8●7 16.732 38 938.572 17.136 39 979 360 17.566 18 36 946.951 16 358 37 939.559 16. 73● 38.955 708 17.143 39 996.926 17.573 19 36 963 30● 16 364 37.959.298 16.745 38.972 851 17.150 40.014 499 17.580 20 36.979 672 16 370 37 973.043 16.752 38.990.001 17 157 40. 032.07● 17.588 21 36 9●6. 043 16. ●77 37.989.795 16. 75● 38.007.158 17 164 40.049.667 17.595 22 ●7. ●12 ●20 16.383 38.006.554 16. 76● ●9. 024.324 17.171 40 067.262 17.603 23 ●7 ●●●. ●0● 16. 38● 38 023.319 16 77● 39.041.495 17 178 40.084.865 17.610 24 ●7. ●45. 19● 16 395 38 040 091 16. 77● 39.058 073 17.185 40.102.465 17.617 25 37. 0●1 5●● 16.401 38.056 869 16. 7●● 39 075 858 17.192 40.120.092 17.625 26 37.077.958 16.408 38.073 654 16.791 39. 0●3 050 17 199 40.137.717 17 632 27 37. 094.39● 16 414 38 090.445 16 798 39 110 24● 17.206 40.155.349 17.640 28 37.110 810 16.420 38.107 243 16 805 39.127.455 17. 21● 40.172.989 17 647 29 37.127.230 16.426 38.124.048 16 811 39.144 668 17 220 40 190.636 17.655 30 37.143.656 16 433 38.140 859 16.818 39. 161.88● 17 227 40 208.291 17.662 31 37.160.089 16.439 38.157 677 16. 8●4 39 179.115 17 234 40.225 953 17 670 32 37.176.528 16.445 38.174.501 16.831 39 196.349 17.241 40 243 623 17.677 33 37.192 ●73 16.451 38 191 332 16. 83● 39 213 590 17 248 40.261.300 17.685 34 37.200.424 16 458 38.208.170 16 84● 39.230.838 17.255 40.278 985 17.692 35 37 225.882 16.464 38.225.014 16 85● 39.248 093 17.262 40.296.677 17 700 36 37.242.346 16.470 38 241.865 16. 8●● 39 265.356 17.269 40.314 377 17.707 37 37 258.816 16.476 38 258.723 16 864 39.282.625 17.276 40.332.084 17.715 38 37 275.292 16.483 38.275.587 16.871 39.299 901 17.284 40.349.799 17.722 39 37.291 775 16.489 38.292.458 16 878 39.317 185 17.291 40.367 521 17 730 40 37.308.264 16.495 38.309.336 16 884 39.334.476 17. 29● 40.385 251 17.737 41 37.324.759 16 501 38·326 220 16.891 39.351.774 17 305 40 402.988 17 745 42 37 341.260 16.508 38.343.111 16.898 39.369.179 17.302 40.420.733 17.752 43 37.357.768 16.514 38.360.009 16.904 39 386 4●1 17. 3●● 40.438.485 17.760 44 37.374.282 16 420 38.376.913 16.911 39 403 800 17. 32● 40.456.245 17.768 45 37 390.802 16.527 38.393 824 16 918 39.421.126 17. 33● 40.474.013 17.775 46 37.407.329 16.533 38 410.742 16.925 39.438.459 17 340 40 491 788 17.783 47 37.423.862 16.539 38 427.667 16 931 39.455.799 17.348 40 509.571 17.790 48 37.440.401 16.546 38.444.598 16.948 39.473.147 17 35● 40.527.361 17.798 49 57 456.947 16. 55● 38. 4●1 546 16.945 39 490.502 17.362 40.545.159 17.806 50 37. 473.49● 16.558 38 478 491 16.501 39.507.864 17 369 40.562.965 17 813 51 37.490.057 16. 56● 38.495.442 16.958 39.525.233 17.376 40.580.778 17 821 52 37.506.622 16 571 38. 512.4● 0 16.965 39.542.609 17.383 40 598.599 17.829 53 37.523 193 16.578 38.529 365 16 972 39 559.992 17. ●9● 40.616.428 17.836 54 37 529.771 16.584 38.546 337 16.979 39. 57●.383 17 398 40.634.264 17.844 55 37 556.355 16.590 38.563.316 16.985 39 594 781 17.405 40.652 108 17. ●52 56 37 572 945 16 597 38.580.301 16 992 39.612.186 17.412 40 669 960 17 859 57 37.589 542 16.603 38.597 293 16 999 39.629.598 17.420 40 687 819 17.867 58 37.606.145 16.609 38.614.292 17 006 39.647.018 17.427 40. 705.6●6 17 875 59 37.622.754 16.616 38.631 268 17.013 39.664.445 17.434 40.723. ●61 17.832 Min 56 Degr.  57 Degr.  58 Degr.  59 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 40 741.423 17.890 41.828.810 18 369 42.945.909 18.879 44.094.550 19.425 1 40 759.313 17.898 41.847 179 18.377 42.964.788 18.888 .113.975 19 434 2 40.777.211 17.906 41.865 556 18.385 42.983.076 18.897 .133.409 19. 4●4 3 40 795.117 17 913 41.883.941 18 393 43 002.573 18. 90● .152.853 19 453 4 40.813 030 17.921 41.902.334 18.402 43.021.479 18 914 .172 30● 19.463 5 40.830.951 17 929 41.920.736 18 410 43.040.393 18.923 44.191.769 19.472 6 40.848 880 17.937 41.939.146 18.418 .059.316 18.932 .211.241 19.482 7 40 866.817 17.944 41.957.564 18.426 .078 248 18.941 .230.723 19.491 8 40.884.761 17.952 41.975 990 18.435 .097.189 18.950 .250 214 19.501 9 40.902.713 17.960 41.994▪ 425 18.443 .116.139 18 959 .269.715 19.510 10 40 920.673 17. 96● 42.012 868 18 451 43.135.098 18. 96● 44 289 225 19.520 11 40.938 641 17.976 42.031.319 18.460 .154.006 18.976 .308.745 19 529 12 40.956.617 17.983 42.049.779 18 468 .173.042 18 985 . 328.27● 19·539 13 40.974.601 17.991 42.068.247 18.470 .192 027 18.994 .347. ●13 19.548 14 40.992 592 17 999 42.086.723 18.485 .211.021 19.003 . 3●7.3●1 19.558 15 41.010 591 18 007 42 105.208 18.493 43.230.024 19.012 44.386. ●19 19.567 16 41.028.598 18 015 42.123.701 18.501 .249 03● 19.021 406 486 19.577 17 41.046 613 18.023 42.142.202 18.510 . 268.05● 19.030 .420.063 19 586 18 41.064 63● 18 030 42 160.712 18.518 .287 0●7 19. 03● .445 049 19 596 19 41.082 666 18 038 42.179.230 18 527 .306.126 19 04● .465.245 19 606 20 41. 100.70● 18.046 42. 197·757 18.535 43.325.174 19 057 44.484.851 19.615 21 41.118 750 18.054 42.216 392 18.543 .344.231 19. 06● .504 466 19.625 22 41.136.804 18.062 42.234 935 18 552 .363 297 19 075 .524.091 19.635 23 41·154 866 18.070 42.253.487 18 560 .382.372 19 084 .543 726 19.644 24 41 172.936 18.078 42.272.047 18. 56● .401.458 19.093 .563.370 19.654 25 41.191.014 18 086 42.290 608 18.577 43 420.551 19.102 44.583 024 19 664 26 41.209.100 18 094 42.309.185 18. 58● 439.653 19 111 602 688 19.673 27 41.227.194 18.102 42.327.771 18.594 .458 794 19.120 622.361 19.683 28 41.245.296 18.110 42 346.365 18.603 .477 880 19 129 .642.044 19 693 29 41.263.406 18.118 42.364 968 18.611 497 009 19.138 .661 737 19.702 30 41.281.524 18 125 42.383.579 18.620 43.516.147 19.147 44.681.439 19 712 31 41.299.649 18 133 42 402.199 18 62● 535.294 19.156 .701.151 19.722 32 41.317.782 18.141 42.420.827 18.637 .554 450 19.166 .720 873 19.732 33 41 335.923 18.149 42.439.464 18.645 .573.616 19.175 .740.605 19.741 34 41.354.072 18 157 42.458.109 18.654 .592.791 19 184 .760.346 19.751 35 41.372.229 18.165 42 476.763 18.662 43.611.975 19.193 44.780 097 19.761 36 41 390 394 18.173 42 495.425 18▪ 671 .631 168 19.202 .799 857 19.771 37 41.408 567 18.181 42.514.096 18.679 .650.370 19 211 .819 628 19 781 38 41.426.748 18.190 42.532.775 18.688 .669.581 19 220 .839.409 19.790 39 41 444.938 18 198 42.551.463 18.697 .688.801 19 230 .859.199 19.800 40 41.463.136 18 206 42.570.160 18.705 43.708 031 19 239 44 878.999 19.810 41 41.481.342 18 214 42.588.865 18.714 .727.270 19.248 .898.809 19.820 42 41.499.556 18.222 42.607.579 18.722 .746.518 19.257 .918.629 19.830 43 41.517.778 18.230 42.626.301 18.731 .765.775 19.267 .938.459 19.840 44 41.536.008 18.238 42.645.032 18.740 .785.042 19.276 .958.299 19.850 45 41.554.246 18.246 42.663.772 18.748 43.804.318 19.285 44. 978.14● 19 ●60 46 41.572.492 18.254 42.682.520 18.757 .823.603 19.294 44 998.009 19.869 47 41.590.746 18 262 42 701.277 18.766 .842 897 19 304 45.017.878 19.879 48 41 609 008 18.270 42.720.043 18.774 .862 201 19.313 45.037.757 19.889 49 41.627.278 18.278 42.738.817 18.783 .881.514 19 322 45 057.646 19.899 50 41.645.556 18.287 42.757.600 18.792 43.900.836 19.331 45.077 545 19.909 51 41.663.843 18.295 42.776.392 18.800 .920.167 19.341 .097.454 19 919 52 41 682.138 18.303 42.795.192 18.809 .939 508 19.350 .117.373 19.929 53 41.700.441 18.311 42 814.001 18.818 .958.858 19.359 .137.302 19.939 54 41.718.752 18.319 42.832.819 18 826 .978 217 19 369 .157.241 19.949 55 41.737.071 18.327 42.851.645 18.835 43.997.586 19 378 45.177.199 19.959 56 41.755.398 18 336 42.870.480 18 844 44.016.964 19.387 .197.149 19 969 57 41.773.734 18.344 42.889 324 18 853 44.936.351 19 397 .217.118 19.979 58 41.792.078 18 352 42 908.177 18.862 44 055.748 19 406 .237.097 19.989 59 41.810.430 18 360 42.927 039 18 87● 44.075.154 19.416 .257 086 20 000 Min. 60 Degr.  61 Degr.  62 Degr.  63 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ par. Equal parts of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. par. 0 45.277.106 20.010 46.495.960 20.637 47.753 829 21.312 49.053.607 22.039 1 45.297.116 20 020 46.516.597 20.648 47.775.141 21 323 49.075 646 22.052 2 45.317.136 20.030 46 537 245 20.659 47 796.464 21.335 49 097.698 22.064 3 45.337.166 20.040 46 557. 9●4 20.670 47.817.799 21.347 49 119.762 22.077 4 45.357 206 20.050 46.576.574 20.680 47.839.146 21.358 49 141.839 22.089 5 45. 377.25● 20.060 46.599.250 20.691 47 860.504 21.370 49.163.928 22.102 6 45.397 31● 20.070 46 619.941 20. 70● 47 881 874 21 382 . 1●●.030 22.115 7 45. 417.38● 20.080 46.640.643 20.713 47. 903.25● 21.394 .208.145 22.128 8 45.437.466 20.091 46.661.356 20.724 47.924.650 21 406 .230 273 22.140 9 45.457.557 20.101 46.682▪ 080 20.735 47.946.056 21.417 .252.413 22.153 10 45.477.658 20.111 46.702.815 20.746 47. 9●7.473 21.429 49.274.566 22▪ 166 11 45.497.769 20.121 46▪ 723.561 20.757 47.988.902 21.441 .296 732 22.178 12 45.517 890 20.132 46.744.318 20.768 48.010.343 21.453 .318.910 22 191 13 45.538.022 20.142 46.765.086 20.779 48 031.796 21.465 .341.101 22.204 14 45.558.164 20.152 46.785.865 20.790 48.053 261 21.476 .363.305 22.217 15 45.578.316 20.162 46.806 655 20.801 48.074.737 21.488 49.385.522 22.230 16 45.598.478 20.173 46 827.456 20.812 48.096 225 21.500 .407.752 22 243 17 45.618.651 20.163 46.848.268 20.823 48.117.725 21.512 .429 995 22.255 18 45.638 834 20.193 46.809.091 20.834 48.139.237 21.524 .452 250 22.268 19 45.659.027 20.203 46.889.925 20.845 48.160.761 21.536 .474.518 22.281 20 45.679.230 20.214 46.910.770 20. 85● 48.182.297 21 548 49 496.799 22 294 21 45.699.444 20.224 46.931.626 20.868 48.203.845 21.560 .519.093 22.307 22 45.719 668 20.234 46.952.494 20.879 48.225.405 21.572 .541.400 22.320 23 45.739 902 20.245 46.973.373 20.890 48.246.977 21.584 .563 720 22.333 24 45·760. 147 20.255 46.994 263 20.901 48.268.561 21.596 .586.053 22.346 25 45.780.402 20 266 47.015.164 20.912 48.290.157 21.608 49.608.399 22.359 26 45.800.668 20.276 47.036 076 20.923 48.311.765 21.620 .630 758 22.372 27 45.820.944 20.286 47.056.999 20.934 48.333.385 21.632 .653.130 22.385 28 45.841.230 20.297 47.077.923 20. 94● 48.355.017 21.644 .675.515 22.398 29 45.801 527 20.307 47.098.879 20.957 48.376.661 21.656 .697.913 22.411 30 45.881.827 20.318 47.119.836 20.968 48.398 317 21.668 49.720.324 22.424 31 45 902 145 20.320 47.140.804 20.979 48.419.985 21.681 .742.748 22.437 32 45.922 473 20 339 47.161.783 20.991 48.441.666 21.693 .765.185 22.450 33 45.942 812 20.349 47 182 774 21.002 48.463.359 21.705 .787 635 22.464 34 45.963.161 20.360 47. 203.77● 21.013 48.485.064 21.717 .810.099 22.477 35 45.983.521 20 370 47.224 709 21.025 48.506.781 21 729 49.832.576 22.490 36 46.003.891 20.381 47.245▪ 814 21. 03● 48.528 510 21.741 855.066 22.503 37 46.024 272 20.391 47.266.850 21·047 48.550.251 21.754 877.568 22 516 38 46.044.663 20.402 47.287.897 21·058 48.572.005 21.766 .900.084 22.529 39 46.065.065 20.412 47.308.955 21·070 48.593.771 21.778 .922.613 22 543 40 46.085.477 20.423 47.330.025 21.081 48 615 549 21.790 49 945.156 22 556 41 46.105.900 20.433 47 351.106 21.093 48.637.339 21.803 49.967.712 22 569 42 46.126.333 20.444 47.372.199 21.104 48.659.142 21.815 49.990.281 22.583 43 46.146.777 20.455 47.393.383 21.115 48.680.957 2●. 827 50 012.864 22.596 44 46.167.232 20.465 47.414.418 21.127 48.702▪ 784 21 840 50.035.460 22.609 45 46.187.697 20.476 47.435.545 21.138 48.724.624 21.852 50.058.069 22.623 46 46.208.173 20.487 47.456.683 21.150 48.746.476 21.864 50.080.692 22.636 47 46.228.660 20.497 47.477.833 21.161 48.768.340 21.877 50.103 328 22 649 48 46.249.157 20.508 47.498.984 21.173 48.790.217 21 889 50.125.977 22.663 49 46.269.665 20 519 47.520.167 21.184 48.812.106 21.901 50.148.640 22.676 50 46.290 184 20.529 47.541.351 21.196 48 834.017 21.914 50.171.316 22.690 51 46.310.713 20.540 47.562.547 21.207 48.855 821 21.926 50.194.006 22.703 52 46.331.253 20 551 47.583.754 21.219 48.877.747 21.939 50.216.709 22.716 53 46.351.814 20.561 47.604 973 21.230 48.899.686 21 951 50.239.425 22.730 54 46.372.365 20.572 47.626.203 21.242 48.921.637 21.964 50 262.155 22.743 55 46.382.937 20.583 47.647.445 21.254 48.943.601 21.976 50.284.898 22.757 56 46.413.520 20.594 47.668.699 21.265 48.965.557 21.989 50 307.655 22.770 57 46.434.114 20 605 47.689.964 21.277 48.987.566 22.001 50 330.425 22.784 58 46.454.719 20.615 47.711 241 21.288 49.009.567 22 014 50.353.209 22.798 59 46.475.334 20.626 47.732.529 21.300 49.031.581 22.026 50.376 007 22.811 Min 64 Degr.  65 Degr.  66 Degr.  67 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a merid. Difference▪ of equ. par 0 50.398 818 22 825 51.793.079 23.676 53.240.555 24.602 54.745.956 25.610 1 50.421.643 22.838 51.816.755 23.691 53.265.157 24 618 54.771.566 25.628 2 50.444.461 22.852 51.840.446 23 706 53.289.775 24.634 54.797.194 25.645 3 50.467.313 22 866 51.864.152 23.721 53.314.409 24.650 54.822.839 25.663 4 50.490.179 22.879 51.887.873 23.736 53.339.059 24.666 54.848.502 25.681 5 50.513.058 22.893 51.911.609 23 750 53.363.725 24.682 54.874.183 25 698 6 50 535.951 22.907 51.935.359 23.765 53.388.407 24.698 54.899.881 25.716 7 50.558.858 22.921 51.959.124 23.780 53.413.105 24.715 54.925.597 25.734 8 50.581.779 22.934 51.982.904 23.795 53.437.820 24.731 54.951.331 25.751 9 50 604.713 22.948 52.006.699 23.810 53.462.551 24 747 54.977.082 25.769 10 50.627.661 22.962 52.030.509 23.825 53.487.298 24.764 55.002.851 25.787 11 50 650.623 22.676 52 054.334 23.840 53.512.062 24 780 55.028.638 25.805 12 50.673.599 22.990 52.078.174 23 855 53.536.842 24.796 55.054.443 25.823 13 50.696.589 23.003 52.102.029 23 870 53.561.638 24.813 55.080.266 25.841 14 50.719.592 23.017 52.125.899 23.885 53.586 451 24.829 55. 10●.107 25.859 15 50.742.609 23.031 52.149 784 23 900 53.611.280 24.845 55.131.966 25.877 16 50.765.660 23.045 52.173.684 23.915 53.636.125 24.862 55.157.843 25.895 17 50.788.705 23.059 52.197.599 23.931 53. ●60. 9●7 24.878 55. 1●3.738 25.913 18 50.811.764 23.073 52.221.530 23 946 53▪ 685.865 24.895 55.209.651 25 931 1● 50.834 837 23.087 52.245.476 23.961 53.710.760 24.911 55. 235.5●2 25 949 20 50. ●57 924 23.101 52.269.437 23.976 53.735.671 24.928 55 261.531 25.967 21 50.881.025 23.115 52 293.413 23.991 53.760.599 24.944 55 287 498 25 985 22 50.904.140 23.129 52.317.404 24.006 53.785.543 24.961 55 313.483 26.003 23 50.927.269 23.143 52 341.410 24.022 53.810.514 24.978 55.339.486 26.021 24 50.950.412 23 157 52.365.432 24.037 53.835 482 24.994 55 365.507 26 039 25 50.973.569 23.171 52.389 469 24 052 53.860.476 25.011 55 391.546 26.058 26 50 996.740 23.185 52 413.521 24.068 53.885.487 25.028 55 417.604 26.076 27 51. 0●9.925 23.199 52 437 589 24.083 53.910.515 25.044 55 443.680 26.094 28 51 043.124 23.214 52.461.672 24.098 53.935.559 25.061 55.469.774 26.112 29 51 066.338 23.228 52.485.770 24.114 53.960.620 25.078 55.495.886 26.131 30 51. 089.56● 23.242 52.509.884 24.129 53.985.698 25.095 55.522.017 26.149 31 51.112.808 23.256 52.534 013 24.145 54.010.793 25.112 55.548.166 26.168 32 51.136.064 23.270 52.558.158 24.160 54.035.905 25.128 55.574.334 26.186 33 51.159.334 23.285 52.582 318 24.175 54.061.033 25.145 55.600.520 26.204 34 51.182.619 23.299 52.606.493 24.191 54.086.178 25.162 55.626.724 26.223 35 51 205.918 23.313 52.630.684 24.206 54.111.340 25.179 55.652.947 26.241 36 51.229.233 23.327 52 654.890 24.222 54.136.519 25.196 55.679.188 26.260 37 51.252.560 23.342 52.679.112 24.238 54.161.715 25.213 55.705.448 26.278 38 51.275.902 23.356 52▪ 703 350 24.253 54.186.928 25.230 55.731.726 26.297 39 51.299 258 23.270 52.727.603 24.269 54 212.158 25.247 55.758.023 26.316 40 51.322.628 23.385 52 751.872 24.284 54.237.405 25.264 55.784.339 26.334 41 51.346 013 23 399 52.776.156 24.300 54.262.669 25.281 55.810.670 26.353 42 51.369 41● 23 414 52 800.456 24.316 54.287.950 25.298 55.837.026 26 372 43 51.392.826 23. 42● 52.824.772 24.331 54.313 248 25.315 55.863.398 26.390 44 51 416. ●54 23.442 52.849.103 24.347 54.338.563 25.332 55.889.788 26.409 45 51.439.696 23 457 52.873.450 24.363 54.363.895 25 350 55.916.197 26.428 46 51.463.153 23.471 52.897.813 24.379 54.389.245 25.367 55.942.625 26.447 47 51.486 624 23.486 52 922.192 24.394 54.414.612 25.384 55.969 072 26.466 48 51 510.110 23.500 52.946.586 24.410 54.439.996 25.401 55.995.538 26.485 49 51.533 610 23 515 52.970.996 24.426 54.465.397 25. 41● 56 022.023 26.503 50 51.557.125 23.529 52.995.422 24.442 54.490.815 25.436 56 048.526 26.522 51 51.580.654 23.544 53.019.864 24.458 54.516.251 25.453 56.075.048 26.541 52 51 604.198 23 559 53.044.322 24.474 54.541.704 25.470 56.101 589 26.560 53 51.627.757 23.573 53.068.796 24.489 54.567.174 25.488 56.128.149 26.579 54 51.651.330 23.588 53 093 285 24.505 54 592.662 25.505 56.154.728 26.598 55 51.674.918 23 603 53.117.790 24.521 54.618.167 25.523 56.181 326 26 618 56 51.698.521 23 617 53.142.311 24.537 54.643.690 25.540 56.207 944 26.637 57 51.722.138 23.632 53.166.848 24.553 54.669.230 25.558 56.234 581 26.656 58 51.745.770 23 647 53.191.401 24 569 54.694.788 25.575 56.261.237 26.675 59 51.769.417 23.662 53.215.970 24 585 54 720.363 25 593 56.287.912 26 694 Min. 68 Degr  69 Degr.  70 Degr.  71 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 56.314.606 26.713 57.952.571 27.925 59.666.811 29.261 61.465.263 30 741 1 56 341.319 26 733 57 980 496 27.946 59.696.072 29.284 61.496.004 30.767 2 56.368.052 26.752 58.008.442 27.967 59.725 356 29.308 61.526.771 30.793 3 56.394.804 29.771 58.036.409 27 989 59.754.664 29 331 61.557.564 30.819 4 56.421.575 26.791 58.064.398 28.010 59 783.995 29 355 61. 58●.383 30845 5 56. 448.36● 26.810 58.092.408 28.031 59. 81● 350 29.378 61.619.228 30 872 6 56. 475.17● 26.829 58.120.439 28 053 59.842.728 29 402 61 650.100 30.898 7 56.502 00● 26.849 58.148.492 28.074 59.872.130 29.426 61.680 998 30.924 8 56.528 854 26.868 58 176.566 28.095 59.901.556 29.449 61.711.922 30.950 9 56 555 722 26.888 58.204.661 28.117 59.931.015 29.473 61.742.872 30 977 10 56.582.610 26.907 58 232.778 28.138 59.960.488 29.497 61.773.849 31.003 11 50.609.517 26.927 58 260 916 28.160 59 989.985 29 521 61.804 852 31.030 12 56.636.444 26.947 58.289 076 28.182 60.019.596 29 545 61.835.882 31.056 13 56.663 391 26 966 58.317.258 28 203 60 049.051 29.569 61.866.938 31 083 14 56.690.357 26.986 58.345.461 28.225 60.078.620 29.593 61 898.021 31.110 15 56.717 343 27.006 58.373.686 28.247 60.108.213 29.617 61.929.131 31.136 16 56.744.349 27.025 58.401.933 28. 26● 60.137.830 29 641 61.960.267 31.163 17 56.771.374 27.045 58.430.201 28.290 60.167.471 29 665 61.991.430 31.190 18 56 7●8 419 27.065 58. 45●.491 28.312 60.197.136 29.689 62.022 620 31.217 19 56.825.484 27 085 58.486 803 28.334 60.220.825 29 713 62.053.837 31.243 20 56.852 569 27.104 58.515.137 28.356 60.256.538 29 737 62.085.080 31.270 21 56.879 673 27.124 58.543.493 28.377 60.286.275 29.761 62 116.350 31.297 22 56.906.797 27.144 58.571 870 28. 39● 60.316.036 29.786 62 147.647 31.324 23 56.933 941 27.164 58 600.269 28.421 60.345.822 29.810 62.178.971 31.351 24 56.961 105 27. 1●4 58 628.690 28.443 60.375.632 29.834 62.210.322 31.379 25 56. 988.2●9 27.204 58.657.133 28.465 60.405 466 29.859 62.241.701 31 406 26 57.015 493 27.224 58 685 598 28.488 60.435.325 29.883 62.273.097 31.433 27 57.042.717 27 244 58.714 086 28.510 60.465.208 29 908 62.304 540 31.460 28 57.069.961 27.264 58.742.596 28.532 60 495.116 29 932 62.336.000 31.488 29 57.097.225 27.285 58.771.128 28 554 60.525.048 29.957 62 367.488 31.515 30 57.124.510 27.305 58 799.682 28.576 60.555.005 29.982 62.399.003 31.542 31 57.151.815 27.325 58. ●28. 258 28.599 60 584.987 30.006 62.430.545 31.570 32 37.179.140 27 345 58.856 857 28 621 60.614.993 30.031 62.462.115 31.597 33 57.206.485 27.365 58.885 478 28.643 60.645.024 30 056 62.493.712 31.625 34 57.233 850 27.386 58 914.121 28.666 60.675.080 30.081 62.525.337 31.653 35 57.261.236 27.406 58.942.787 28.688 60.705.161 30 105 62.556.990 31.680 36 57.288.642 27.426 58.971.475 28.710 60.735.266 30.130 62.588.670 31.708 37 57.316 068 27.447 59.000.185 28.733 60.765.396 30.155 62.620.378 31·736 38 57.343.515 27.467 59 028.918 28.755 60.795.551 30 180 62.652.114 31.764 39 57.370.982 27.488 59.057.673 28.778 60.825.731 30.205 62.683 878 31 791 40 57.398.470 27.508 59.086.451 28.801 60.855.936 30.230 62 715 669 31 819 41 57.425.978 27. 52● 59.115.252 28.823 60.886.166 30.255 62.747 478 31.847 42 57.453.507 27.549 59.144.075 28.846 60.916 421 30.281 62 779.335 31 875 43 57.481.056 27.570 59.172 921 28.869 60.946.702 30 306 62.811.210 31.904 44 57.508.626 27.590 59.201 790 28.891 60.977.008 30.331 62.843.114 31.932 45 57.536.216 27.611 59.230.681 28.914 61.007.339 30.356 62.875.046 31.960 46 57.563.827 27.632 59.259.595 28.937 61.037 695 30.382 62 907.006 31.988 47 57 591.459 27.652 59.288.532 28.960 61.068.077 30 407 62.938.994 32.016 48 57. 619.11● 27.673 59.317.492 28.983 61.098.484 30▪ 432 62.971.010 32.045 49 57. 646.7●4 27.694 59 346.475 29 006 61.128.916 30.458 63 003 055 32.073 50 57.674.478 27.715 59.375.481 29.029 61.159.374 30.483 63.035.128 32.102 51 57.702.193 27.736 59.404.510 29.052 61.189.857 30 509 63.067.230 32.130 52 57.720.929 27 757 59.433.562 29.075 61.220.366 30 535 63.099.360 32.159 53 57.757.686 27.778 59.462.637 29.098 61.250.901 30.560 63.131.519 32.187 54 57.785 464 27.798 59.491.735 29 121 61.281.461 30.586 63.163.706 32.216 55 57.813.262 27.819 59.520.856 29.144 61.311.947 30.612 63.195.922 32.245 56 57.841.081 27.841 59 550.000 29.168 61.342.559 30.637 63 228.167 32.274 57 57 868.922 27.862 59.579.168 29.191 61.373.196 30. 6●3 63.260 441 32 302 58 57.896 784 27.883 59.608.359 29.214 61. 403.85● 30.689 63.292.743 32.331 59 57 924 667 27.904 59.637.573 29.238 61.434.548 30.715 63.325.074 32.360 Min. 72 Degr.  73 Degr.  74 Degr.  75 Degr  Equal parts of a Merid. Difference of equ par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 63.357.434 32.389 65.354.167 34.235 67.468.378 36.316 69·715. 485 38.679 1 63 389 823 32. 41● 65.388.402 34.268 67.504.694 36 353 69.754 164 38.721 2 63 422 241 32.447 65.422.670 34.300 67.541.047 36.390 69.792 885 38.763 3 63.454.688 32.477 65.456 970 34.333 67.577.437 36 427 69.831.648 38.805 4 63.487.165 32.506 65.491.303 34.366 67.613 864 36.464 69.870 453 38.847 5 63.519.671 32.535 65.525.669 34.399 67.650 328 36.501 69.909.300 38.890 6 63.552 206 32.564 65.560.068 34.432 67.686 829 36 539 69.948 190 38.932 7 63.584.770 32.594 65 594·500 34.465 67.723.368 36 576 69.987.142 38 975 8 63.617.364 32.623 65 628.965 34.498 67 759.944 36 613 70.026.117 39.018 9 63 649.987 32 653 65.663.463 34.531 67.796.557 36 651 70.065 135 39.061 10 63.682.640 32 682 65. 697·994 34.564 67 833.208 36.689 70 104·196 39.104 11 63.715.322 32.712 65.732.558 34.598 67.869.897 36.726 70.143.300 39.147 12 63.748.034 32.741 65.767.150 34.631 67 906 623 36.764 70.182.447 39 190 13 63.780.775 32.771 65.801 7●7 34.665 67.943 387 36.802 70.221.637 39 233 14 63.813.546 32.801 65.836.452 34 698 67. 9●0.189 36.840 70.260 870 39.277 15 63.846.347 32.831 65 871.150 34 732 68 017.029 36.878 70.300.147 39.320 16 63 879.178 32.861 65.905.882 34 765 68.053.907 36.916 70.339.467 39.363 17 63▪ 912.039 32.891 65.940 647 34 799 68 090.823 36.954 70 378.830 39 407 18 63 944.930 32.921 65 975.446 34 833 68 127 777 36.993 70.418 237 39.451 19 63.977.851 32.951 66 010 279 34.867 68 164.770 37 031 70.457.688 39 495 20 64 010.802 32 981 66.045 146 34 901 68 201.801 37.069 70.497.183 39.539 21 64.043 783 33.011 66.080.047 34 935 68.238 870 37.108 70.536.722 39.583 22 .076 794 33 041 66.114 9●2 34 969 68 275.978 37 147 70.576.305 39 627 23 .109.835 33 072 66.149.951 35 003 68.313.125 37. 1●5 70.615.932 39.671 24 .142.907 33 102 66.184.954 35.037 68 350 310 37.224 70.655 ●03 39 715 25 64.176 009 33.132 66.219.991 35.071 68 387 534 37.263 70.695.318 39. 7●0 26 .209.141 33.163 66. 255·062 35.105 68 424.797 37.302 70.735 078 39.804 27 .242.304 33 193 66.290.107 35.140 68 462 099 37.341 70.774 882 39.849 28 .275.497 33.224 66.325.307 35.174 68.499.440 37 380 70 814.731 39.894 29 .308.721 33. 2●5 66 3●0. 481 35.209 68.536.820 37.419 70 854. ●25 39.939 30 64.341.976 33.285 66.395.690 35 243 68 574.239 37.459 70 894.564 39.984 31 375.261 33.316 66 430 933 35.278 68.611.698 37 49● 70 934.548 40.029 32 .408 577 33.347 66.406.211 35.313 68 649.196 37 537 70 974.577 40.074 33 .441.924 33.378 66.501.524 35.348 68.686.733 37.577 71 014.651 40.119 34 .475 302 33. 40● 66.536.872 35.383 68.714.310 37 617 71 054.770 40.165 35 64.508.711 33.440 66.572 255 35.418 68.761.927 37.656 71.094.935 40.210 36 .542.171 33 471 66.607 673 35 453 68 799. 5●3 37.696 71.135.145 40.256 37 .575.622 33.502 66 643.126 35.488 68.837.279 37·736 71.175.401 40 302 38 .609 124 33. 53● 66 678 614 35 523 68.874.915 37.776 71.215.703 40 347 39 .642.657 33 564 66.714.137 35.558 68.912 791 37.816 71.256 051 40 393 40 64.676.221 33. 5●● ●6. 748.695 35.594 68.950 607 37 856 71.296.444 40.439 41 .709 817 33 627 ●6. 785 289 35 629 68.988 463 37.897 71.336.883 40 485 42 743.444 33 65● 66.820.918 35 664 69 026.360 37 937 71·377. 358 40 532 43 .777.102 33.690 66.856.582 35.700 69.064.297 37.977 71 417.900 40.578 44 .810 792 33.722 66 892.282 35.736 69.102 274 38. ●18 71 458 478 40 625 45 64 844.514 33.753 66.928.018 35.771 69 140.292 38 058 71.499.103 40.671 46 878.267 33 785 66.963 789 35.807 69 178.350 38.099 71 53●. 774 40.718 47 .912.052 33. ●17 66 999.596 35 843 69.216 449 38. 1●0 71. 580.4●2 40.765 48 .945.869 33.848 67 035.439 35.879 69.254 589 38 181 71.621 257 40.812 49 64.979 717 33.880 67.071 318 35.915 69.292 770 38.222 71. 662.06● 40.859 50 65.013.597 33. 91● 67.107.233 35.951 69.330.992 38.263 71 702 92● 40.906 51 65.047 509 33.944 67 143.184 35.987 69 369.255 38.304 71 743.834 40.953 52 65. 0●1.453 33 97● 67 179.171 36.023 69.407 559 38.345 71. 7●4 787 41.000 53 65.115.429 34. 00● 67 215.194 36.060 69.445 904 38.387 71 825.787 41 048 54 65.149.437 34 041 67.251 254 36 096 69 484 291 38.428 71.866 835 41.095 55 65 183.478 34 073 67.287.350 36.132 69.522 719 38.470 71 907 930 41.143 56 65.217 551 34 105 67.323 482 36. 1●9 69.561.189 38.511 71.949.073 41.191 57 65 251 656 34. 13● 67 359 651 36.206 69 599 700 38.553 71.990.264 41▪ 239 58 65.285 794 34.170 67.395.857 36.242 69. 63●.253 38.595 72 031 503 41.287 59 65 ●19. 964 34 2●● 67 432.099 36.279 ●9. 676.848 38 637 72 072 790 41 33● Min 76 Degr.  77 Degr.  78 Degr.  79 Degr.  Equal parts of a Merid. Difference of equ. par Equal parts of a Merid. Difference of equ. pa● Equal parts of a Merid. Difference of equ. par Equal parts of a Merid Difference of equ. par. 0 72 114 125 41 383 74 687.014 44.510 77.462.411 48.163 80.475.935 52.486 1 72 155.508 41 432 74.731.524 44.566 77.510.574 48.229 80. 52●.421 52.563 2 72.196 940 41.480 74 776.090 44.622 77.558.803 48.295 80.580.986 52. ●44 3 72.238.420 41 529 74.820 712 44.679 77.607.098 48.362 80. 633.63● 52.724 4 72.279.949 41.578 74.865.391 44. 7●5 77. 655.4●0 48.428 80.686. ●54 52. ●●● 5 72.321.527 41.627 74 910.126 44.792 77. 703.8●8 48.405 80. 739.1●7 52. ●●● 6 72.363.154 41.676 74.954.918 44.849 77.752.383 48. 5●● 80. 7●2.04● 52. 9TH 7 72.404.830 41 725 74.999.767 44.906 77.800.945 48. 62● 80.845. ●03 5● 043 8 72 446 555 41.774 75.044.673 44 964 77.849 574 48. 69● 80.898.046 53. 12● 9 72.488.329 41▪ 823 75.089.637 45.021 77.898 2●● 48. 7●● 8●. 951.170 53.204 10 72.530.152 41.873 75.134.658 45.079 77.947.035 48.832 81.004.374 53 285 11 72.572.025 41.922 75 179 737 45.136 77.995.867 48.900 81.057.659 53.367 12 72.613.947 41.972 75.224.873 45.194 78.044.767 48. 96● 81.111.026 53.448 13 72 655 919 4●. 022 75.270 067 45 252 78.093.735 49.037 81.164.474 53.530 14 72.697.941 42.072 75.315.319 45.310 78.142.772 49.105 81. 218.0●4 53 612 15 72 740 013 42.122 75.360.629 45.369 78 191.877 49.174 81.271.616 53 694 16 72.782.135 42.172 75.405.998 45.427 78.241.051 49.243 81.325.310 53.777 17 72.824.307 42.222 75 451.425 45 486 78.290.294 49.312 81.379.087 53.859 18 72.866.529 42.273 75 496 911 45.545 78.339. ●06 49.382 81.432.946 53.943 19 72.908.802 42.323 75 542.456 45 604 78.388.988 49 451 81.486.889 54.026 20 72.951.125 42 374 75.588.060 45.663 78.438.439 49.521 81. 5●0. ●15 54.109 21 72.993.499 42.425 75.633.723 45.722 78 487. 9●0 49.591 81. 5●5.024 5● 1●3 22 73 035.924 42.476 75.679.445 45.781 78.537.551 49.661 81.649.217 54 277 23 73.078.400 42.527 75.725 226 45.841 78.587.212 49.731 81.703.494 54 362 24 73.120 927 42.578 75.771.067 45.901 78.636.943 49.802 81.757.856 54.446 25 73 163.505 42.629 75 816.968 45 961 78.686.745 49.873 81.812. ●02 54 531 26 73.206.134 42.681 75.862 929 46 021 78. 736.6●8 49. 94● 81. 8●●.833 54.616 27 73.248.815 42.732 75 90●. 950 46.081 78. ●76 592 50.015 81.921.449 54.702 28 73.291.547 42 784 75 955.031 46.141 78.836.577 50.086 81. 9TH 151 54. 7●8 29 73.334 331 42. 83● 76.001 1●2 46.202 78.886.663 50.158 82. ●30. 939 54.874 30 73.377 107 42 888 76.047.374 46.262 78.936.821 50.230 82.085.813 54.960 31 73.420.055 42 940 76.093.636 46 323 78.987.051 50.302 ●2. 140 773 55▪ 046 32 73.462.995 42.992 76 139.959 46.384 79.037.353 50.374 82.195 819 55.133 33 73 505.987 43.045 76 18●. 343 46.446 79.087.727 50.447 82. 2●0.952 55. 22● 34 73.549.032 43 097 76.232.789 46 507 79.138.174 50.519 82. 30● 172 55 30● 35 73.592 129 43.150 76. 279.29● 46. 56● 79.188.693 50.592 82.361 480 55 397 36 73 635.279 43 203 76.325.864 46.630 79.239.285 50.665 82.416.875 55 483 37 73.678 482 43 255 76 372 394 46.692 79.289.950 50.739 82.472.358 55 571 38 73.721 737 43 309 76.419 186 46.754 79.340.689 50.812 82.527 929 55 660 39 73.765.046 43.362 76. 465.94● 46.816 79. 391·501 50. ●86 82.583.589 55 749 40 73 808.408 43 415 76. 512.75● 46.879 79.442.387 50.960 82 639.338 55.838 41 73.851 823 43.468 76.559.635 46 941 79.493.347 51.034 82.695 17● 55. ●2● 42 73.895.291 43.522 76.606.576 47.004 79.544.381 51.108 82.751.103 56. 01● 43 73.938 813 43 576 76.653.580 47.067 79. 5●5.489 51.183 82 807 122 56. 1ST 44 73.982.389 43 629 76.700.647 47 130 79.646.672 51.258 82.863.227 56. 1ST 45 74.026.018 43.683 76.747.777 47.193 79.697.930 51.333 82.919.424 56 2●● 46 74.069 701 43.738 76.794.970 47.256 79.749.263 51.408 82 975.712 56 ●7● 47 74.113.439 43 792 76.842.226 47.320 79 8●0. 671 51.484 83.032.090 56 ●●● 48 74.157 231 43.846 76.889.546 47.384 79.852.155 51.559 83. 088.5●0 56. 5●● 49 74 201.077 43.901 76 936.930 47 448 79.903.714 51.635 83 149 121 56. ●●● 50 74.244.978 43.955 76.984.378 47.512 79.955.349 51.712 83.201 774 5●. 7●● 51 74.288 933 44 010 77 031.890 47.576 ●0. 007.061 51.788 83 258 519 5●●3● 52 74.332.943 44 065 77.079.466 47 641 80.058.849 51.865 83 315.356 56. 9TH 53 74 377.008 44.120 77.127 107 47 705 80.110.714 51. ●42 83. 3●2.286 57 ●●● 54 74.421 128 44.175 77.174 812 47. 77● 80.162.656 52.019 83. 4●9 30● 5●. 1ST 55 74 465.303 44.231 77.222.582 47 835 80.214.675 52. ●●● 83 ●●6 425 57. 2●● 56 74.509.534 44.286 77 270.417 47.900 80.266.771 52.174 83. ●43. 6●5 〈…〉 57 74. 553.82● 44.342 77.318.317 47.966 80.318.945 52. 25● 83 600. 9●9 〈…〉 58 74.598.162 44 398 77.366.283 48.031 80.371.197 52. ●●● 83 698.337 〈…〉 59 74.642.560 44 454 77.414.314 〈…〉 ●0. 423.527 52. ●●● ●3 71●. ●29 〈…〉 Min 80 Degr.  81 Degr.  82 Degr.  83 Degr  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ par. Equal parts of a Meid▪ Difference of equ. par. 0 83.773.416 57 682 87.415.219 64 042 91.483.111 72.001 96 091.773 82.249 1 83.831.098 57.778 87.479 261 64.160 91.555.113 72.151 96.174.022 82.445 2 83.888.876 57.874 87 543.421 64.278 91 627.264 72.301 96.256 467 82.642 3 83.946.750 57.970 87.607.699 64.397 91.699.565 72 452 96.339 00● 82.840 4 84 004 720 58.066 87.672.096 64.517 91.772 017 72.604 96.421.949 83 038 5 84.062.786 58.163 87.736 613 64.636 91.844.621 72.756 96.504.987 83 238 6 84.120.949 58.260 87 801.249 64.757 91.917 377 72 909 96.588.225 83.439 7 84.179 209 58 358 87.566.006 64.877 91.990.286 73.062 96.671.664 83 640 8 84.237.567 58 455 87 930.883 64.999 92.063.348 73.217 96.755.304 83.843 ● 84.296.022 58 553 87.995.882 65.120 92.136.565 73.371 96.839.147 84.046 1● 84.354.575 58.652 88.061.002 65.242 62.209 936 73.527 96.923.193 84.251 11 84.413.227 58.751 88.126 244 65.365 92.283 463 73.683 97.007 444 84.456 12 84.471.978 58 850 88.191.609 65.488 92 357.146 73.840 97.091.900 84.663 13 84.530 828 58 949 88.257.097 65.612 92.430.986 73.997 97.176.563 84.870 14 84 589.777 59 049 88.322.709 65.736 92.504 983 74.155 97.261.433 85.079 15 84.648.826 59.149 88.388.445 65 860 92.579.138 74.314 97.346.512 85.288 16 84.707 975 59.250 88.454.305 65.985 92.653.452 74.474 97.431.800 85.499 17 84.767.225 59 350 88.520 290 66 110 92 727.926 74.634 97.517.299 85.711 18 84.826.575 59.452 88.586 400 66.236 92 802.560 74.795 97.603.010 85.924 19 84.886 027 59.553 88.652.636 66 363 92.877.355 74.957 97.688.934 86 137 20 84.945 580 59.655 88.718.999 66.490 92.952.312 75.119 97.775.071 86.352 21 85.005.235 59 757 88 785.489 66.617 93.027.431 75.282 97.861.423 86.568 22 85.064.992 59.860 88.852.106 66 745 93.102.713 75.446 97.947.991 86.785 23 85.124 852 59.963 88 918.851 66.873 93.178.159 75.610 98.034.776 87.004 24 85.184.815 60 066 88.985.724 67 0●2 93.253.769 75 775 98.121 780 87.223 25 85.244.881 60.170 89.052.726 67.132 93.329.544 75.941 98 209.003 87.443 26 85.305.051 60.274 89 119.858 67.261 93.405.485 76 108 98.296.446 87.665 27 85.365 325 60.378 89.187.119 67.392 93.481.593 76.275 98.384.111 87.887 28 85.425 703 60 483 89.254.511 67.523 93.557.868 76.444 98 471.998 88.111 29 85.486.186 60 588 89.322.034 67.654 93.634.312 76.612 98.560.109 88.336 30 85.546.774 60.694 89.389 688 67.786 93.710.914 76.782 98.648.445 88.562 31 85.607.468 60 799 89.457.474 67.919 93.787.706 76.953 98.737.007 88.790 32 85.668.267 60.906 89.525.393 68.052 93.864.659 77.124 98.825.797 89.018 33 85.729.173 61.012 89.593.445 68.185 93.941.783 77.296 98.914.815 89.248 34 85.790.185 61.119 89.661 630 68.319 94.019.079 77.468 94.004.063 89.479 35 85.851.304 61.227 89.729 749 68.454 94 096.547 77.642 99.093.542 89.711 36 85.912.531 61.335 89.798.403 68.589 94.174.189 77.816 99 183.253 89 944 37 85.973.866 61.443 89.866.992 68.724 94.252.005 77.991 99.273.197 90.178 38 86 035.209 61.551 89.935.716 68.861 94.329.996 78.167 99.363.375 90.414 39 86.096.860 61.660 90.004.577 68 997 94.408.163 78.344 99.453.789 90.651 40 86.158 520 61.770 90.073.574 69.135 94.486.507 78.521 99.544.440 90 889 41 86.220.290 61.879 90 142.709 69.273 94.565.028 78.700 99.635.329 91.129 42 86.282.169 61 989 90.211 982 69.411 94.643.728 78.879 99.726 458 91.369 43 86.344 158 62.100 90.281.393 69.550 94.722 607 79.059 99.817 827 91.611 44 86.406.258 62.211 90.350 943 69.689 94.801.666 79 239 99.909.438 91 855 45 86.468.469 62.322 90.420.632 69.830 94.880.905 79.421 100.001.293 92.099 46 86.530 791 62.434 90 490.462 69 970 94.960.326 79.603 100.093.392 92.345 47 86.593.225 62.546 90.560.432 70.111 95.039 929 79.787 100 185.737 92.593 48 86 655.771 62.658 90.630.543 70.253 95.119.716 79.971 100.278.330 92.841 49 86.718.429 62 771 90.700.796 70.396 95.199.687 80 156 100.371.171 93.091 50 86.781 200 62.885 90.771.192 70.539 95.279.843 80.342 100.464.262 93.342 51 86 844 085 62.999 90.841 731 70.682 95.360.185 80 529 100.557.604 93.595 52 86.907.084 63.113 90 912.413 70.826 95.440.714 80.716 100.651.199 93.849 53 86.970.197 63.227 90.983.239 70.971 95 521.430 80.905 100.745 048 94 105 54 87.033.424 63.342 91.054 210 71.117 95.602.335 81.094 100 839.153 94.361 55 87.096.766 63.458 91.125.327 71.263 95.683 429 81 284 100 933.514 94 620 56 87.160.224 63.574 91.196 590 71 409 95.764.713 81.476 101.028 134 94.879 57 87.223.798 63.690 91.267.999 71.556 95.846.189 81.668 101.123 013 95.141 5● 87 287.488 63.807 91.339.555 71.704 95.927.857 81.861 101.218 154 95.403 59 87.351.295 63.924 91 411.159 71.852 96.009.718 82 055 101.313.557 95.667 Min. 84 Degr.  85 Degr.  86 Degr.  87 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 101.409.224 95.933 107.696.200 115 119 115.389.469 143.954 125 209.226 192.139 1 101.505.157 96.200 107.811 319 115.505 115 533.423 144.558 125.401.365 193.218 2 101.601.357 96 468 107.926.824 115.893 115. 677.9●1 145.167 125.594.583 194.308 3 101 697.825 96.738 108.042.717 116.283 115.823.148 145.781 125 788. ●91 195.411 4 101.794.563 97.010 108.159.002 116.676 115.968.929 146.401 125.984.102 196.527 5 101.891.573 97.283 108 275.678 117.072 116.115.330 147.025 126.180 829 197.656 6 101.988.856 97.557 108.392 750 117 471 116.262.355 147.655 126.378.485 198.797 7 102.086.413 97.834 108.510.221 117.872 116.410.010 148.291 126.577.282 199.952 8 102.184.247 98.111 108.628.093 118 276 116.558 001 148.932 126.777.234 201.120 9 102.282.358 98.391 108.746.369 118 683 116.707.233 149.578 126.978 354 202.302 10 102.380.749 98.672 108.865.052 119.093 116.856 811 150.230 127.180 656 203.498 11 102.479.421 98.954 108.984.145 119.506 117.007.041 150.888 127.384 154 204.709 12 102.578.375 99.238 109.103.651 119 921 117. 157.92● 151.552 127.588 863 205.934 13 102.677.613 99 524 109 223.572 120 339 117 309 481 152.222 127.794 797 207.173 14 102.777.137 99.812 109.343.911 120.760 117.461.703 152.897 128.001.970 208.428 15 102 876 949 100 101 109.464.671 121.185 117. 614.60● 153.579 128.210.398 209.698 16 102.977.050 100.392 109.585.856 121.612 117 768. 17● 154.267 128 420 096 210 983 17 103.077.442 100.684 109.707.468 122.042 ●17 622.441 154.961 128 631.079 212 285 18 103.178.126 100 979 109 829.510 122.476 118.077 407 1●5. 661 128.843.364 213.602 19 103.279.105 101.275 109.951.986 122 912 118.233.068 156.367 129.056 966 214.936 20 103.380.380 101.572 110.074.898 123 352 118.389.435 157.080 129.271.902 216.287 21 103.481.952 101 672 110.198.250 123.794 118 546.515 157.800 129.488 189 217.655 22 103.583 824 102.173 110 322.044 124.240 118.704 315 158 526 129 705 844 219.040 23 103.685.997 102.476 110.445.628 124 989 118.862 841 159.259 129.924.884 220.444 24 103.788 473 102.781 110.570.973 125 142 119.022 100 15●. 999 130.145 328 221.865 25 103.891.254 103.088 110 696.115 125.598 119.182 099 160.746 130.367.193 223.304 26 103.994.342 103.397 110.821.713 126.057 119.342 845 161.499 130 590.497 224.763 27 104.097 739 103 707 110.947.770 126.519 119.504.344 162.260 130 815.260 226 241 28 104. ●01. 446 104 019 111 074 289 126.985 119 666.604 163. 02● 131.041.501 227.738 29 104.305.465 104 334 111 201.274 127.454 119.829.632 163.804 131 269 239 229.255 30 104.409.799 104.650 111.328.728 127.927 119.993.436 164.586 131.498.494 230.793 31 104.514 449 104.968 111.456.655 128 404 120.158 022 165.377 131.729.287 232 351 32 104 619 417 105.288 111 585.059 128 884 120.323.399 166.175 131.961 638 233.936 33 104.724 705 105.610 111 713.943 129.367 120.489.574 166. 98● 132 195 574 235 532 34 104.830.315 105.934 111.843 310 129.854 120 656.554 167 794 132 431.106 237.156 35 104.936.249 106.260 111.973.164 130.345 120 824 348 168.615 132.668.262 238.802 36 105.042.509 106.588 112 103.509 130.840 120.992.963 169 445 132.907.064 240.470 37 105.149.097 106 918 112.234.349 131.338 121.162 40● 170.283 133 147 534 242.163 38 105.256.015 107.250 112.365 887 131 841 121.332.691 171.129 133.389 697 243.880 39 105.363.265 107.584 112.497 528 132.347 121.503.820 171. 98● 133.633.577 2●5. 621 40 105.470.849 107.921 112.029.875 132 857 121.675 ●04 172.847 133 879 19● 247. 3●7 41 105.578 770 108.259 112.762 732 133.371 121.848.651 173.719 134.126.585 249.178 42 105 687.029 108.600 112.895.803 133.889 122 022.370 174.600 134. 375.7●3 250.996 43 105.795.629 108 942 113.029 992 134.411 122.196 ●7● 175. 4●0 134 626.759 252.841 44 105.904 571 109 287 113.164.403 134 937 122 372.460 176.389 134.879.600 254 713 45 106.013.858 109.634 113.299 340 135.467 122 548.849 177 297 135.134.313 256.613 46 106 123 492 109.984 113.434 807 136.002 122. 726.14● 178.215 135.390 926 258 541 47 106.233.476 110.335 113.570.809 136.540 122.904.361 179.142 135.649.467 260.499 48 106.343.811 110.689 113 707.349 137.083 123.083.503 180 078 135.909.966 262.486 49 106 454.500 111.045 113.844.432 137 631 123.263.581 181.025 136.172.452 264.505 50 106 565 545 111.403 113.982 063 138.183 123.444.608 181 983 136.436.957 266.554 51 106.676.948 111.764 114.120 246 138.739 123 626.589 182 95● 136.703.511 268.636 52 106.788 712 112.127 114.258.685 139 299 123 809.539 183 927 136 972.147 270.750 53 106.900.839 112.493 114 398.284 139.865 123.993.466 184.915 137.242.897 272 898 54 107.013.332 112.861 114.538.149 140 435 124 078.381 185.913 137.515.795 275 080 55 107.126.193 113.231 114 678.584 141.009 124.264.294 186.923 137 790 87● 277.297 56 107.239.424 113.604 114 819.593 141.588 124.451.217 187.943 138 068.172 279.551 57 107.353 128 113.979 114.961.181 142.172 124 639 160 188.975 138.347.723 281. 8●1 58 107.467.107 114.356 115.103.353 142.761 124.828.135 190 018 13● 629.564 284.169 59 107 581.463 114.737 115.246.114 143.355 125.018.153 191 073 138 913 73● 286 537 Min. 88 Degr.  89 Degr.  Equal parts of a Merid. Difference of equ. par. Equal parts of a Merid. Difference of equ. par. 0 139.200.270 288.943 163.175.324 582.696 1 139.489 213 291.391 163.758.020 592.743 2 139.780.604 293.881 164.350 763 603.141 3 140.074.485 296.413 164.953.904 613.910 4 140 370 898 298.990 165.567.814 625 071 5 140 669.888 301.612 166.192.885 636.645 6 140.971.500 304.281 166.829.530 648.657 7 141.275.781 306.995 167.478 187 661.130 8 141 582.776 309.760 168.139.317 674 092 9 141.892.536 312.575 168.813.409 687 573 10 142.205 111 315.442 169.500.982 701.604 11 142.520.553 318.361 170.202.586 716.220 12 142.838.914 321.336 170.918 806 731.458 13 143 160.250 324.367 171.650.264 747 358 14 143.484.617 327.455 172.397.622 763.965 15 143 812.072 330.602 173.161.587 781.327 16 144 142 674 333.811 173.942.914 799.496 17 144.476 485 337.083 174·742. 410 818.531 18 144.813.568 340.419 175.560.941 838.494 19 145.153.987 343.823 176.399.435 859.456 20 145.497.810 347.295 177.285.891 881.492 21 145.845.105 350.838 178.140.383 904.688 22 146 195.943 354.453 179.045.071 929 138 23 146.550 396 358.145 179.974.209 954.947 24 146.908.541 361.914 180 929.156 982.230 25 147.270.455 365.763 181.911.386 1.011.118 26 147.636.218 369.695 182.922.504 1 041.757 27 148 005.913 373.712 183.964.261 1.074.311 28 148 379.625 377.818 185.038.572 1.108.965 29 148.757.443 382.015 186 147.537 1.145.930 30 149.139 458 386.306 187.293 467 1.185.443 31 149.525.764 390.695 188.478.910 1.227.780 32 149.916.459 395.185 189.706.690 1.273.252 33 150 311.944 399 779 190.979.942 1.322.222 34 150.711.423 404.482 192.302.164 1.375.110 35 151.115.905 409.296 193.677.274 1.432.406 36 151.525.201 414 226 195.109.680 1.494.683 37 151 939.427 419.277 196.604.363 1.562.622 38 152 358.704 424.452 198.166.985 1.637 032 39 152.783.156 429.752 199.804.017 1.718.883 40 153 212.913 435 196 201 522.900 1.809.349 41 153.648.109 440 774 203.332.249 1.909.868 42 154.088.883 446.497 205.242.117 2 022.212 43 154.535.380 452.371 207.264.329 2 148.599 44 154 987.751 458.402 209.412 928 2.291.838 45 155 446.153 464.596 211.704.766 2.455.540 46 155.910.749 470.959 214.160 306 2.644 426 47 156.381.708 477 499 216.804.732 2.864.794 48 156.859.207 484.224 219.669.526 3.125 229 49 157 343.431 491.140 222.794.755 3 437.751 50 157.834.571 498 257 226.232.506 3.819.723 51 158.332.828 505.583 230.052.229 4.297.187 52 158.838 411 513.129 234 349.416 4.911.090 53 159 351.540 520.902 239.260.506 5.729.580 54 159 872 442 528.915 244.990.086 6.875.496 55 160 401.357 537.178 251.865.582  56 160 938.535 545.704 260.459.920 8.594.338 57 161 484.239 554.505 271 919.077 11.459.157 58 162 038 744 563.594 289 107.811 17.188.734 59 162.602.338 572.986 323.485.279 34.377.468   

CHAP. III. The use of the two first columns of the Table of Latitudes, for graduating a Meridian in the general Sea-Chart.  
BEfore you can make use of this Table, for the true graduating, or dividing of a Meridian of this Chart into his degrees, or other parts of Latitude, increasing from the Aequinoctial towards the North and South, in such proportion, as before hath been showed, there must be first some preparation made to that end; which may be done after this manner: Overthwart the midst of the plain superficies, whereupon you will draw the lineaments of the Chart, describe a right line, (representing the Aequinoctial circle) which you shall divide into 360 parts or degrees, and cross the same squirewise with right lines, by every fifth or tenth degree. Then take with your compasses the length of half the Aequinoctial, (that is, 180 degrees) and setting one foot of your compasses in the mutual intersection of the Aequinoctial, with the perpendicular or Meridian that passeth by either end of the Aequinoctial, with the other foot make a prick in the same perpendicular or Meridian: the space contained betwixt this prick and the Aequinoctial, divide first into three equal parts, and every one of these into other three, so have you nine in all: and again every one of these into three, so have you 27 parts, and every one of these parts divide into four, so have you 108 parts: And again (if there be space enough) divide every one of these into 10 or 100 So shall you have 1080, or 10800 parts, which will bring you to the Latitude of 85 degrees and something more. But if you would make your Chart to any greater Latitude, you shall continue forth the foresaid perpendicular, and divide it into so many more of the same parts as you shall find needful to attain to the Latitude you desire. Then note every fifth and tenth part with black lead, and set figures at them, beginning at the Aequinoctial▪ 
The use of the two first Columns of the Table of Latitudes.  and from thence proceeding Northwards and Southwards. Then look what numbers in the second column are answerable to each degree, or minute in the first column of this Table of Latitudes (omitting always four or five of the first figures towards the right hand) and at the same numbers of parts in the perpendiculars, make pricks on either side the Aequinoctial: by which (pricks) draw right lines equidistant from the Aequinoctial, for they shall be the Parallels of the true Nautical Planisphere, or Sea-Chart.  
Notwithstanding these Parallels are all o●●hem a little further distant from the Aequinoctial then in truth they should be: and so much the more, the further they are from the Aequinoctial. Which error might be something the less, if the former Table had been first made to smaller parts than minutes. But that were a matter more curious than necessary, the Table here before set down being so near the truth, that it is not possible by any rules or Instruments of Navigation, to discover any sensible error in the Sea-Chart, so far forth as it shall be made according thereto.  
The figure following containeth only one part of the Nautical Planisphaere, from the Aequinoctial Northwards, because the other part from the Aequinoctial Southwards must be altogether like and equal to this. Herein first I drew the Aequinoctial line AC, and divided it into 36 equal parts, whereof every one is understood to contain ten degrees, and I raised perpendiculars from every one of those parts; which are the Meridian's of the Nautical Planisphaere, every where aequidistant each from other. Then I took half the length of the Aequinoctial with the compasses, and setting one foot in the end of the Aequinoctial at C, with the other foot I made a prick at D in the perpendicular or Meridian CD. The space contained betwixt C and D, I divided into 1080 parts, (understanding every one of the smaller parts, or segments of the line CD to contain ten lesser parts) in such sort as before hath been showed, and set figures to them, as here you see, for the readier numbering and finding out of any of those parts. Then I looked in the former Table what number of equal parts of the Meridian answered to every tenth degree▪ and casting away five of the first figures next the right hand (because I conceive the space betwixt C and D to be divided only into 1080 parts) I found out the parts answerable to the numbers remaining in the line CD: and at those parts I made pricks, by which I drew the Parallels.  
As for example: in the Table, the number answerable to ten degrees, is 60, casting away the five first figures towards the right hand: therefore I look 60 in the line CD, and by that part I draw the Parallel of ten degrees distance from the Aequinoctial. Likewise the number answering to twenty degrees (omitting the five first figures) is 122: therefore by that number of equal parts I draw the parallel of twenty degrees Latitude from the Equinoctial, etc. And after this manner I drew all the rest, as you may see in the former draught.  
The Draught of the Meridian's, Parallels and Rumbs, of the Nautical Planisphear, truly made.   

CHAP. FOUR 〈◊〉 way for graduating the Meridian of a general Sea-Chart.  
OTherwise for the dividing of the Meridian of a general Sea-Chart into his degrees, and other smaller parts of Latitude, when the Chart hath not so great Latitude or breadth from the Equinoctial towards the North or South, as hath the figure before set down; you may go thus to work: First find out what proportion the whole Longitude (or length of the Chart from West to East) must have to the whole breadth thereof betwixt the Parallels of the most Northerly and Southerly places, that are to be set down therein: which may be done after this manner: Out of the second Column of the table of Latitudes, take the numbers of equal parts of the Meridian answerable to the greatest North and South Latitudes that are to be set down in the Chart: divide those numbers by 600,000 (that is the number of equal parts of the Meridian answerable to one degree of the Equinoctial) the Quotients will show how many degrees of the Equinoctial the breadth of the Chart must be on either side the Equinoctial toward the North and South. As for example, in the general Sea-●hart to be adjoined to this book, the Latitude of the North 〈◊〉 of the New land, found by the Hollanders about the year ●596, and by them called Gebrooken land (lying Northwards ●rom Norway) is about 80 degrees. And the Latitude of Queen Elizabeth's Island (first found by Sir Francis Drake, lying to the southwards of Magellanes straits) is about 53 degrees. The ●umbers of equal parts of the Meridian answerable to these La●●tudes, found out in the foresaid Table of Latitudes, are 83, ●● 73, 416, and 37, 639, 370; which being divided by 600, ●●00, the Quotients are 140 and 63 almost, showing the breadth 〈◊〉 the Chart from the Equinoctial Northwards and Southwards, in such parts whereof the Equinoctial containeth 360; ●hich added together shall show that the whole breadth of 〈◊〉 Chart from North to South must be about 203 such parts. ●aving therefore divided the length of the Equinoctial or any ●ther parallel of the Chart (because they are all equal) into ●60 parts, take with a pair of compasses 210 of the same parts because that is the next greater number apt for division) and so keeping them unaltered, set both feet in the Meridian at one of the ends, or in the midst of the Chart, and divide the space contained between them first into seven parts, and every one of them into three, so have you 21 in all: then divide each of these into two, and these again into five; so shall you have in all 210, the number of the parts required. Now beginning at the Southermost of these parts, tell on Northwards, till you come to 66, and thereby draw the Equinoctial, overthwart the Meridian, at right Angles. After this you may divide the said parts of the Meridian every one into six, drawing forth every fifth or tenth, a little further than the rest, and setting figures to every hundreth part, for the readier finding out of any number of those parts that shall be required. This being done, the Meridian may be divided into his degrees of Latitude, and the parallels drawn after the same manner that we have already showed for the drawing of the former figure of a general Sea-Chart, in the Chapter next going before.   

CHAP. V. The use of the table of Latitudes for the true graduating of a particular Sea-Chart.  
TO make a particular Sea-Chart: first, consider at wha● Latitudes your Chart must begin and end: Ther● look in the former table of Latitudes what numbers of equal parts are answerable to both those Latitudes and subtract the equal parts answering to the lesser Latitude, ou● of the equal parts answerable to the greater Latitude; and drawing a line overthwart the breadth of the Chart from North to South (at one of the ends, or in some other vacant place thereof divide the same line into so many equal parts, as the differenc● remaining shall amount unto: if that difference be a compound number that may be divided into his unities by small diviso●● But if it fall out that the number of equal parts remining 〈◊〉 either a prime number, or else such a number as cannot otherwise be divided into his unities, but by some great divisors 〈◊〉 may then take the next compound number that is greater 〈◊〉 the said difference which may be divided into his unities 〈◊〉 small divisors. Thus having divided the line drawn 〈◊〉 thwart the breadth of the Chart, into so many equal parts, as 〈◊〉 compound number containeth unities, and beginning at 〈◊〉 end thereof which is supposed to be Southwards, or next the Equinoctial, set thereto the next number of whole hundreds, or thousands, less than the number of equal parts answerable to the lesser Latitude, and drawing forth every fifth, or tenth part, a little further than the rest, set figures to every tenth, hundred, or thousandth part, that you may readily number and find out any of them.  
Then look in the table of Latitudes which of these equal parts answer to each degree or half degree, or each tenth minute of Latitude (if your Chart be of a very large prick) and with the point of your pen or compasses make marks there, and so finish the graduation of the Meridian of your Chart after the accustomed manner before showed in the former Chapter.  
As for example: In the Particular Chart for the Azores hereunto adjoined, the least Latitude is 36 degrees 10 minutes; the greatest 52 degrees 20 minutes; the equal parts answerable to these in the table of Latitudes, (casting away the four first figures towards the right hand) are 2330 for the first, and 3698 for the second Latitude. The difference of these is 1368. Then at the West end of the Chart I draw the line AB something longer than the breadth of the Chart which I purpose to make, and divide it into 1400 parts, supposing every one of those smallest parts to stand for two. And this I do by dividing the whole line first into two parts, and each of these again into seven; so have you 14 parts in all, whereof every one must be understood to be divided into 100 equal parts after the ordinary manner, first dividing each of them into two parts, than every one of those into five, and these again every one into five parts, etc.  
Now because the least Latitude in this Chart beginneth at 2330 equal parts, I do therefore account the beginning of the line AB at A to be at 2300, and so proceed setting down numbers at every 100 part, as in that Chart you may see.  
Now for graduating the Meridian that is adjoining, or rather all one with the line AB, you may proceed in like sort, as before was showed, for the making of a general Sea-Chart in the thid chapter: looking what number of equal parts answer to each degree in the table of Latitudes; and at the same number of equal parts in the Chart, making marks signifying those degrees, etc. As for example: In the table I find answerable to 37 dgrees 0 minutes 2393, (casting away the four first figures next the right hand) therefore at the same number of equal parts in the line AB in the Chart, I draw forth the line of 37 degrees Latitude. In like manner, at 2468 equal parts in the Chart I set down 38 degrees, because in the table of Latitudes I find that number answerable to 38 degrees: And at 2545 I set 39 degrees. And so forth for all the rest.  
In like sort you may out of the table of Latitudes set down every tenth or fifth minute into this Chart; or else (which is also something easier, and not altogether so tedious) you may with a pair of compasses divide each degree in the Chart into 12 equal parts. In which division, although indeed there will be some error; yet in this particular Chart, or others not much exceeding this in the greatness either of the Latitude, or of the degrees thereof, that error will be so small, as that by sense it can either not at all, or very hardly be discerned.   

CHAP. VI The breadth of a particular Chart being given, to divide the same into the degrees and minutes contained in the difference of the least and greatest Latitudes therein to be expressed.  
But if you would make your Chart to a certain breadth limited, which you also desire to divide unequally in due proportion (as hath been showed) into the number of degrees and min, contained between the least and greatest latitudes which you would have therein set down: you may then go thus to work: Draw a line equal to the breadth of the Chart (as for example, the line CD at the East end of the particular Chart for the Azores) from the South end hereof draw another line something longer, making an angle therewith of some 20 or 30 degrees, or thereabouts, as the line CE: And having found out (as before in the former chapter) the number of equal parts answerable to the difference of the least and greatest Latitudes, (as the number of 1368) divide this line CE into some compound number of parts that may be divided by small divisors; (that compound number exceeding the number of those equal parts so little as conveniently may be) as into 1400. In this line, beginning from the angle at C, tell out the said number of equal parts 1368, from thence draw the base of that angle to the end of the first line (as the line F D:) for Parallels to this base, drawn by the divisions of the second line CE, shall divide the first line CD (that measureth the breadth of the Chart) into the number of equal parts answerable to the difference of the least and greatest Latitude in the Chart. But because the drawing of so many Parallels would not only be troublesome and tedious, but may also something deface the Chart; it will be better to draw Parallels by some few principal compound numbers of parts in the second line, as by every 100 or 1000 etc. to sub-divide with the compasses the segments of the first line contained between those Parallels, as in this particular Chart you may see. Thus having divided the breadth of the Chart into the number of parts required, and beginning at C the South end thereof to tell 2330, (which is the number of equal parts answerable to the least Latitude purposed to be set down in the Chart) tell on Northwards till you come to make up an even hundred (as till you come to 2400) and there begin to set figures, showing the number of the parts; and so proceed, setting figures to every hundred part, and finishing the graduation of the Meridian or division thereof into his unequal parts in due proportion, as before you were directed in the former chapter.   

CHAP. VII. The use of the third column of the table of Latitudes.  
THe third Column being nothing else but the table of Secants, in such parts whereof the whole sine or semidiameter of the circle is supposed to contain 10,000, may serve for all such purposes for which the table of Secans may be used. Moreover, as it served for the making of the second column of the table of Latitudes, as before is showed in the second chapter, page 11 and 12, so may it be of needful use for the more easy examination and correction thereof, if any error hath been committed therein.  
Hereby also may be known very exactly the proportion of any parallel to the Equinoctial. For what proportion the difference answerable to any degree and minute in this table hath to 10000, the same proportion hath the Equinoctial to the parallel answering to that degree and minute: (The difference answerable to any degree and minute is that which is placed next above the line of the same minute:) And consequently, because the like parts of circles are proportional to their wholes, you may hereby very easily and truly find out how many leagues any arch of any Parallel containeth: for as the difference answerable to the Latitude of the Parallel is to 10,000, so are the minutes contained in that arch to the miles thereof; which divided by 3, give the leagues.  
As for example, if you would know how many leagues make a degree in the Parallel of London, whose Latitude is 51 degrees 32 minutes: as 16,075 the difference answering to that Latitude page 26 is to 10,000, so is 20 (the number of leagues contained in one degree of the Equinoctial) to 12 294/●43 the number of leagues making one degree in the Parallel of London. Thus the difference of Longitude in any Parallel being given in degrees, may easily be reduced into leagues, multiplying the same by the leagues contained in one degree. But it may be done easier by multiplying the difference of Longitude (reduced into minutes) by 10,000, and dividing the product by the difference of equal parts (in the table of Latitudes) answerable to the Latitude of the Parallel wherein that difference of Longitude is taken; for then the quotient showeth the miles in the difference of Longitude, which being divided by 3, you have the leagues.  
As for example: admit the difference of Longitude between the Lizard and Fayal be 22 degrees 52 minutes, that is 1372 minutes, which multiplied by 10,000, make 13,720,000: and this divided by 12,898 (which is the difference of the equal parts answerable to 39 degrees 10 minutes, the latitude of the North-east corner of Fayal Island) shall give you 1064 miles almost, that is 354 ⅔ leagues, the difference of their Longitudes counted in the Parallel of Fayal.  
Moreover, by the differences set down in the third column may easily be found the sine of any arch of the quadrant: For as the difference answerable to any arch, or number of degrees and minutes in this table is to 10,000; so is 10,000 to the sine of the same arch.  
The demonstration hereof may easily be conceived out of the Diagramme set down in the second chapter, page. 11, wherein ik to fk. and ak to gk, that is ae, have all one and the same proportion; and therefore it shall here be needless any further to insist hereupon▪   

CHAP. VIII. How to describe the Rumbes mechanically in any Sea-chart, Globe, or Map of what form soever.  
NOw because the nautical planisphaere (as before hath been showed) is nothing else but a plain Parallellogramme superficies, made by extension of a spherical superficies inscribed into a concave cylinder, wherein the tumbes make equal angles with very Meridian: therefore in this nautical planisphaere, if a circle be drawn and divided into 32 equal parts, beginning at the Meridian passing by the centre, of that circle: right lines drawn from the centre by those divisions shall be the rumbes or lines which the ship describeth in sailing upon those points, because they make equal angles with every Meridian of the nautical planisphaere, those Meridian's being every where equidistant one from another, Example hereof you have in the former figure, and in the charts' adjoined hereunto.  
By help of this planisphaere with the Meridian's, rumbes, and Parallels thus described therein, the rumbes may much more easily and truly be drawn in the Globe, then by those mechanical ways which Petrus Nonius teacheth, cap. 26. lib, 2. the obser▪ Reg. & Instr. Geom. Hereby also they may with no less facility be inscribed into any other Chart or Map of what form or projection soever, if it be first divided by Meridian's and Parallels into degrees of Longitude and Latitude: For by what points of Longitude and Latitude in this Planisphaere the rumbes are described, by the same points must they be drawn in the Globe, or in any other Chart or Map whatsoever. Notwithstanding this may much more exactly be performed by the table of Rumbes following which I have made for that purpose, showing for every degree of Longitude, by what degree, and minute of Latitude every rumbe is to be drawn till you come within a minute of the Pole.   

CHAP. IX. The use of the table of Latitudes for making the table of Rumbs.  
THis table of Rumbes is most easily made by addition only with help of the former table of Lati●udes after this manner: Multiply the Tangent of the angle that the rumbe maketh with the Equinoctial by 60 (because every degree of the Equinoctial in that table is understood to contain 60 times 10000 parts, each minute containing (by supposition) 10000 parts:) the product shall be the first number at the beginning of the table of each rumbe, to be set over against one degree of Longitude, and all the rest are found by perpetual addition of this number, first to itself (for the sum is the number answerable to two degrees of Longitude) then to this sum; (the product is the number that answereth to three degrees of Longitude) and so forth in all the rest. These numbers being found out in the table of Latitudes, did show at what point of Latitude each rumbe should cross the Meridian for every degree of Longitude, till you come within a minute of the Pole. But these numbers were not thought needful to be set down in the table following, because they serve only for finding out the Latitudes, by which the rumbes must be drawn at every degree of Longitude; which Latitudes being once found, these numbers serve to no further use.  
Take for example the first rumbe from the Equinoctial, making an angle therewith of 11 degrees 15 minutes the tangent whereof 1,989,122 (the whole sine being 10000000) multiplied by 60, maketh 119,347,320: but cutting off the three first figures, and seeking out the rest in the table of Latitudes, you shall find answerable thereto 12 minutes the Latitude of that rumbe at one degree of Longitude. Also the same number doubled (that is 238,694) and found out in the same table, shall give you 24 minutes almost, the Latitude of the same rumbe for two degrees of Longitude: and so forth in the rest.  
Hereby it may appear that the Latitude of any rumbe, whatsoever angle it make with the Equinoctial, may presently be found for any Longitude you shall desire, if you do but multiply the number answering to one degree of Longitude (found as before) by the Longitude given, and find out the product in the second column of the foresaid table of Latitudes: for the number the degrees, minutes, etc. answering thereto in the first column of that table shall be the Latitude desired.  
As for example, suppose a rumbe that maketh an angle of 5 degrees with the Equinoctial, I would know what Latitude this rumbe must have at 360 degrees of Longitude: the tangent of five degrees is 874,887, which multiplied by 60, make 52, 493▪ 220, and this again by 360 maketh 18▪ 897▪ 559.200; but cutting off the three first figures, the rest found in the foresaid table sh●ll give us ●0 degrees, 1 minute, the Latitude of that Rumb at 360 degrees of Longitude.  

The Table of Rumbs.  

The first Rumb from the Meridian; viz. North and by East, North and by West. South and by East, South and by West.  long Latit long Latitude gr. gr. m gr. gr. mi. sec 1 5 1 61 89 27 2 2 10 0 62 89 29 46 3 14 55 63 89 32 15 4 19 43 64 89 34 33 5 24 22 65 89 36 39 6 28 52 66 89 38 33 7 33 10 67 89 40 19 8 37 16 68 89 41 56 9 41 10 69 89 43 24 10 44 50 70 89 44 45 11 48 18 71 89 46 0 12 51 32 72 89 47 8 13 54 33 73 89 48 10 14 57 22 74 89 49 7 15 59 5● 75 89 49 57 16 62 24 76 89 50 47 17 64 38 77 89 51 31 18 66 42 78 89 52 11 19 68 37 79 89 52 38 20 70 22 80 89 53 5 21 72 0 81 89 53 43 22 73 29 82 89 54 20 23 74 51 83 89 54 46 24 76 7 84 89 55 11 25 77 16 85 89 55 30 26 78 20 86 89 55 53 27 79 18 87 89 56 11 28 80 12 88 89 56 28 29 81 1 89 89 56 44 30 81 46 90 89 56 58 31 82 27 91 89 57 10 32 83 5 92 89 57 22 33 83 40 93 89 57 33 34 84 12 94 89 57 43 35 84 40 95 89 57 53 36 85 8 96 86 58 2 37 85 32 97 89 58 9 38 85 55 98 89 58 15 39 86 15 99 89 58 21 40 86 34 100 89 58 27 41 86 51 101 89 58 33 42 87 8 102 89 58 38 43 87 22 103 89 58 43 44 87 35 104 89 58 47 45 87 47 105 89 58 51 46 87 58 106 89 58 55 47 88 ● 107 89 58 59 48 88 18 108 89 59 3 49 88 26 109 89 59 6 50 88 34 110 89 59 9 51 88 41 111 89 59 12 52 88 48 112 89 59 15 53 88 54 113 89 59 18 54 88 59 114 89 59 20 55 ●9 5 115 89 59 22 56 89 9 116 89 59 24 57 89 13 117 89 59 26 58 89 17 118 89 59 28 59 89 21 119 89 59 30 60 89 24 120 89 59 32 
The second Rumb from the Meridian, viz. North North-east. North Northwest: South Southeast, South South-west.  long Latit long Latit gr. gr. m gr. gr. mi 1 2 25 61 81 15 2 4 49 62 81 36 3 7 14 63 81 57 4 9 37 64 82 17 5 11 59 65 82 36 6 14 20 66 82 54 7 16 40 67 83 12 8 18 58 68 83 28 9 21 14 69 83 44 10 23 27 70 84 0 11 25 39 71 84 15 12 27 49 72 84 29 13 29 55 73 84 42 14 32 0 74 84 56 15 34 1 75 85 8 16 36 0 76 85 20 17 37 55 77 85 32 18 39 48 78 85 43 19 41 38 79 ●5 53 20 43 25 80 86 3 21 45 8 81 86 13 22 46 49 82 86 22 23 48 27 83 86 31 24 50 1 84 86 40 25 51 33 85 86 48 26 53 1 86 86 57 27 54 27 87 87 4 28 55 50 88 87 11 29 57 10 89 87 18 30 58 27 90 87 25 31 59 41 92 87 37 32 60 53 94 87 49 33 62 2 96 87 59 34 63 9 98 88 9 35 64 13 100 88 13 36 65 15 102 88 26 37 66 14 104 88 34 38 67 12 106 88 41 39 68 7 108 88 47 40 69 0 110 88 53 41 69 50 112 88 58 42 70 39 114 89 3 43 71 26 116 89 8 44 72 12 118 89 12 45 72 55 120 89 16 46 73 37 122 89 19 47 74 17 124 89 23 48 74 55 126 89 26 49 75 32 128 89 28 50 76 8 130 89 31 51 76 42 134 89 35 52 77 14 138 89 39 53 77 46 142 89 42 54 78 16 146 89 45 55 78 44 150 89 47 56 79 12 158 89 51 57 79 39 166 89 53 58 80 4 178 89 56 59 80 29 201 89 58 60 80 52 225 89 59 
The third Rumb from the Meridian, viz▪ North-east by North, Northwest by North: Southeast by South, South west by South.  long Latit long Latit long Latit long Lati● gr. gr. m gr. gr. m gr. gr. m gr gr. m 1 1 30 61 67 1 121 85 8 181 88 59 2 3 0 62 67 36 122 85 16 182 89 0 3 4 29 63 68 10 123 85 23 183 89 2 4 5 59 64 68 43 124 85 30 184 89 3 5 7 28 65 69 15 125 85 37 185 89 5 6 8 57 66 69 46 126 85 43 186 89 6 7 10 25 67 70 17 127 85 50 187 89 8 8 11 53 68 70 47 128 85 57 188 89 9 9 13 21 69 71 16 129 86 3 189 89 10 10 14 48 70 71 44 130 86 9 190 89 12 11 16 14 71 72 12 131 86 15 191 89 13 12 17 40 72 72 39 132 86 21 192 89 14 13 19 6 73 73 6 133 86 27 192 89 15 14 20 30 74 73 32 134 86 32 194 89 16 15 21 54 75 73 57 135 86 37 195 89 17 16 23 17 76 74 21 136 86 43 196 89 19 17 24 39 77 74 45 137 86 48 197 89 20 18 26 0 78 75 8 13● 86 52 198 89 21 19 27 20 79 75 31 139 86 58 199 89 22 20 28 39 80 75 53 140 87 3 200 89 23 21 29 58 81 76 15 141 87 7 201 89 24 22 31 15 82 76 36 142 87 12 202 89 24 23 32 31 83 76 56 143 87 16 203 89 25 24 33 46 84 77 16 144 87 20 204 89 26 25 35 0 85 77 36 145 87 24 205 89 27 26 36 13 86 77 55 146 87 28 206 89 28 27 37 25 87 78 14 147 87 32 207 89 29 28 38 36 88 78 32 148 87 36 20● 89 30 29 39 46 89 78 49 149 87 40 209 89 30 30 40 54 90 79 6 150 87 43 210 89 31 31 42 1 91 79 23 151 87 47 212 89 33 32 43 8 92 79 40 152 87 50 214 89 34 33 44 12 93 79 55 153 87 54 216 89 35 34 45 16 94 80 11 154 87 57 218 89 36 35 46 19 95 80 26 155 88 0 220 89 38 36 47 20 96 80 41 156 88 3 222 89 39 37 48 21 97 80 55 157 88 6 224 89 40 38 49 20 98 81 9 158 88 9 226 89 41 39 50 18 99 81 23 159 88 12 228 89 42 40 51 14 100 81 36 160 88 15 230 89 43 41 52 10 101 81 49 161 88 17 234 89 44 42 53 5 102 82 2 162 88 20 23● 89 46 43 53 58 103 82 14 163 88 22 24● 89 47 44 54 50 104 82 26 164 88 25 24● 89 48 45 55 41 105 82 37 165 88 27 250 89 49 46 56 31 106 82 49 166 88 30 25● 89 50 47 57 20 107 83 0 167 88 32 258 89 51 48 58 8 108 83 11 168 88 34 262 89 52 49 5● 55 109 83 21 169 88 37 266 89 53 50 59 41 110 83 31 170 88 3● 270 89 54 51 60 26 111 83 41 171 88 41 27● 89 54 52 61 10 112 83 51 172 88 43 2●2 89 55 53 61 52 113 84 1 173 88 45 288 89 56 54 62 34 114 84 1● 174 88 47 294 89 56 55 63 15 115 84 19 175 88 49 300 89 57 56 63 55 116 84 28 176 88 50 312 89 58 57 64 34 117 84 36 177 88 52 324 89 58 58 65 12 118 84 44 178 88 54 33● 89 58 59 65 49 119 84 5● 179 88 5● 348 89 59 60 66 26 120 85 1 180 88 57 3●0 89 59 
The fourth Rumb from the Meridian, viz. North-east, Northwest. Southeast, South-west.  long Latit long Latit long Latit long Latit long Latit long Latit gr. gr m gr. gr. m gr gr. m gr. gr. m gr. gr. m gr. gr. m 1 1 0 61 51 57 121 76 12 181 85 8 241 88 17 302 89 24 2 2 0 62 52 33 122 76 26 182 85 13 242 88 19 304 89 25 3 3 0 63 53 10 123 76 40 183 85 18 243 88 21 306 89 27 4 4 0 64 53 45 124 76 54 184 85 23 244 88 23 308 89 28 5 5 0 65 54 21 125 77 7 185 85 27 245 88 24 310 89 29 6 5 59 66 54 55 126 77 20 186 85 32 246 88 2● 312 89 30 7 6 59 67 55 30 127 77 33 187 85 37 247 88 28 314 89 31 8 7 58 68 56 3 128 77 46 188 85 41 248 88 2● 316 89 32 9 8 58 69 56 37 129 77 59 189 85 46 249 88 31 318 89 33 10 9 57 70 57 9 130 78 11 190 85 50 250 88 32 320 89 34 11 10 56 71 57 42 131 78 23 191 85 54 251 88 34 322 89 35 12 11 55 72 58 13 132 78 35 192 85 59 252 88 35 324 89 36 13 12 53 73 58 45 133 78 47 193 86 3 253 88 37 326 89 36 14 13 52 74 59 16 134 78 59 194 86 7 254 88 38 328 89 37 15 14 50 75 59 46 135 79 10 195 86 11 255 88 39 330 89 38 16 15 48 76 60 16 136 79 21 196 86 15 ●56 88 41 332 89 39 17 16 45 77 60 46 137 79 32 197 86 1● 257 88 42 334 89 39 18 17 43 78 61 15 138 79 43 198 86 2● 258 ●8 44 336 89 40 19 18 40 79 61 43 139 79 53 199 86 2● 259 88 45 338 89 41 20 19 36 80 62 12 140 80 4 200 86 30 260 88 46 340 89 41 21 20 33 81 62 39 141 80 14 201 86 3● 261 88 47 342 89 42 22 21 20 82 63 7 142 80 24 202 86 37 262 88 49 344 89 43 23 22 24 83 63 34 143 80 34 203 86 41 263 ●8 50 346 89 43 24 23 20 84 64 0 144 80 44 204 86 44 264 88 51 34● 89 44 25 24 15 85 64 26 145 80 53 205 86 48 265 88 52 350 89 44 26 25 9 86 64 52 146 81 3 206 86 51 266 88 53 352 89 45 27 26 3 87 65 17 147 81 12 207 86 55 267 88 55 354 89 45 28 26 57 88 65 42 148 81 21 208 86 58 268 88 56 356 89 46 29 27 51 89 66 6 149 81 30 209 87 1 269 88 57 358 89 46 30 28 43 90 66 31 150 81 39 210 87 4 270 88 58 360 89 47 31 29 35 91 66 54 151 81 48 211 87 7 271 88 59 6 89 48 32 30 28 92 67 18 152 81 56 212 87 10 272 89 0 12 89 49 33 31 19 93 67 41 153 82 4 213 87 13 273 89 1 18 89 50 34 32 10 94 68 3 154 82 13 214 87 16 274 89 2 24 89 51 35 33 0 95 68 25 155 82 21 215 87 19 275 89 3 30 89 52 36 33 50 96 68 47 156 82 29 216 87 22 276 89 4 36 89 53 37 34 40 97 69 9 157 82 36 217 87 2● 277 89 5 42 89 53 38 35 29 98 69 30 158 82 44 218 87 27 278 89 6 48 89 54 39 36 18 99 69 51 159 82 51 219 87 30 279 89 7 54 89 55 40 37 6 100 70 11 160 82 59 220 87 32 280 89 8 60 89 55 41 37 53 101 70 31 161 83 6 221 87 35 281 89 9 66 89 55 42 38 41 102 70 51 162 83 13 222 87 37 282 89 10 72 89 56 43 39 27 103 71 11 163 83 20 223 87 4● 283 89 10 78 89 56 44 40 13 104 71 30 164 83 27 224 87 42 284 89 11 84 89 57 45 40 59 105 71 49 165 83 34 225 87 44 285 89 12 90 89 57 46 41 44 106 72 7 166 83 41 226 87 47 286 89 13 96 89 57 47 42 28 107 72 26 167 83 47 227 87 49 287 89 14 102 89 57 48 43 12 108 72 44 168 83 54 228 87 51 288 89 15 108 89 58 49 43 56 109 73 1 169 84 0 229 87 54 289 89 15 114 89 58 50 44 39 110 73 19 170 84 6 230 87 56 290 89 16 120 89 58 51 45 21 111 73 36 171 84 12 231 87 58 291 89 17 126 89 58 52 46 3 112 73 53 172 84 18 232 88 0 292 89 18 132 49 58 53 46 44 113 24 9 173 84 24 233 88 2 293 89 18 138 89 58 54 47 25 114 74 25 174 84 30 234 88 4 294 89 19 144 89 58 55 48 6 115 74 41 175 84 36 235 88 6 295 89 20 150 89 59 56 48 45 116 74 57 176 84 41 236 88 8 296 89 2● 156 89 59 57 49 25 117 75 12 177 84 47 237 88 10 297 89 21 162 89 59 58 50 3 118 75 28 178 84 52 238 88 12 298 89 22 168 89 59 59 50 42 119 75 43 179 84 57 239 88 14 299 89 2● 174 89 59 60 51 19 120 75 57 180 85 2 240 88 16 300 80 ●● 180 8● 59 
The fifth Rumb from the Meridian, viz. North-east & by East, Southeast & by East: Northwest & by West, South west & by West.  long Latit long Latit gr. gr. m gr. gr. m 1 0 40 61 37 42 2 1 20 62 38 14 3 2 0 63 38 45 4 2 40 64 39 16 5 3 20 65 36 47 6 4 0 66 40 18 7 4 40 67 40 48 8 5 20 68 41 18 9 6 0 69 41 48 10 6 40 70 42 18 11 7 20 71 42 48 12 8 0 72 43 17 13 8 39 73 43 46 14 9 19 74 44 14 15 9 58 75 44 44 16 10 38 76 45 12 17 11 17 77 45 40 18 11 56 78 46 8 19 12 36 79 46 36 20 13 15 80 47 3 21 13 54 81 47 30 22 14 32 82 47 57 23 15 11 83 48 24 24 15 50 84 48 50 25 16 28 85 49 17 26 17 7 86 49 43 27 17 45 87 50 9 28 18 33 88 50 34 29 19 1 89 50 59 30 19 39 90 51 25 31 20 17 91 51 49 32 20 54 92 52 14 33 21 31 93 52 39 34 22 9 94 53 3 35 22 46 95 53 27 36 23 23 96 53 50 37 23 59 97 54 14 38 24 36 98 54 37 39 25 12 99 55 0 40 25 48 100 55 23 41 26 24 101 55 46 42 27 0 102 56 8 43 27 36 103 56 31 44 28 11 104 56 53 45 28 47 105 57 14 46 29 22 106 57 36 47 29 56 107 57 57 48 30 31 108 58 19 49 31 5 109 58 40 50 31 40 110 59 0 51 32 14 111 59 20 52 32 48 112 59 41 53 33 21 113 60 1 54 33 55 114 60 21 55 34 28 115 60 41 56 35 1 116 61 0 57 35 33 117 61 20 58 36 5 118 61 3● 59 36 38 119 61 58 60 37 10 120 62 17 long Latit long Latit long Latit long Latit long Latit long Latit gr. gr. m gr. gr. m gr gr. m gr. gr. m gr, gr. m gr. gr. m 121 62 35 181 76 11 241 83 6 301 86 34 1 88 18 92 89 24 122 62 53 182 76 20 242 83 11 302 86 36 2 88 19 94 89 25 123 63 12 183 76 30 243 83 16 303 86 39 3 88 20 96 89 26 124 63 30 184 76 39 244 83 21 304 86 41 4 88 21 98 89 27 125 63 47 185 76 48 245 83 25 305 86 43 5 88 22 100 89 27 126 64 6 186 76 57 246 83 30 306 86 46 6 88 23 102 89 28 127 64 22 187 77 6 247 83 34 307 86 48 7 88 25 104 89 29 128 64 40 188 77 15 248 83 39 308 86 50 8 88 26 106 89 30 129 64 57 189 77 24 249 83 43 309 86 57 9 88 27 108 89 30 130 65 14 190 77 33 250 83 47 310 86 55 10 88 28 110 89 31 131 65 30 191 77 41 251 83 52 311 86 57 11 88 29 112 89 32 132 65 47 192 77 50 252 84 56 312 86 59 12 88 30 114 89 32 133 66 3 193 77 58 253 84 0 313 87 1 13 88 31 116 89 33 134 66 19 194 78 6 254 84 4 314 87 3 14 88 32 118 89 33 135 66 35 195 78 15 255 84 8 315 87 6 15 88 33 120 89 34 136 66 51 196 78 23 256 84 13 316 87 8 16 88 34 122 89 35 137 67 7 197 78 31 257 84 17 317 87 10 17 88 35 124 89 35 138 67 22 198 78 39 258 84 21 318 87 12 18 88 36 126 89 36 139 67 38 199 78 47 259 84 24 319 87 13 19 88 37 128 89 36 140 67 53 200 78 54 260 84 28 320 87 15 20 88 38 130 89 37 141 68 8 201 79 2 261 84 32 321 87 17 21 88 39 132 89 37 142 68 2● 202 79 10 262 84 36 322 87 19 22 88 40 134 89 38 143 68 37 203 79 17 263 84 40 323 87 21 23 88 41 136 89 38 144 68 52 204 79 24 264 84 43 324 87 23 24 88 42 138 89 39 145 69 6 205 79 32 265 84 47 325 87 25 25 88 43 140 89 39 146 69 21 20● 79 39 266 84 51 326 87 26 26 88 43 142 89 40 14● 69 35 207 79 46 267 84 54 327 87 28 27 88 44 144 89 40 148 69 49 208 79 53 268 84 58 328 87 30 28 88 45 146 89 41 149 70 2 209 80 0 269 85 1 32● 87 32 29 88 46 148 89 41 150 70 16 210 80 7 270 85 5 330 87 33 30 88 47 150 89 42 151 70 29 211 80 14 271 85 8 331 87 35 32 88 49 155 89 43 152 70 43 212 80 21 272 85 12 33● 87 37 34 88 50 160 89 44 153 70 50 213 80 27 273 85 15 333 87 38 36 88 52 165 89 44 154 7● 9 214 80 34 274 85 18 334 87 40 38 88 53 170 89 45 155 71 22 215 80 41 275 85 21 335 87 42 40 88 55 175 89 46 156 71 35 216 80 47 276 85 25 336 87 43 42 8● 56 180 89 47 157 71 47 217 80 53 277 85 2● 337 87 45 44 88 58 185 89 48 158 72 0 218 81 0 278 85 31 338 87 47 46 88 59 190 89 48 159 72 12 219 81 6 279 85 34 339 87 48 48 89 1 195 89 49 160 72 24 220 81 12 280 85 37 340 87 5● 50 89 2 200 89 49 161 72 36 221 81 1● 281 85 40 341 87 51 52 89 3 210 89 51 162 72 48 222 81 24 282 85 43 342 87 53 54 89 5 220 89 52 163 73 0 223 81 30 283 85 46 343 87 54 56 89 6 230 89 52 164 73 11 224 81 36 284 85 49 344 87 55 58 89 7 240 89 53 165 73 23 225 81 42 285 85 52 345 87 57 60 89 8 250 89 54 166 73 3● 226 81 4● 286 85 55 346 87 58 62 89 10 260 89 55 16● 73 4● 227 81 53 287 85 58 347 88 0 64 89 11 270 89 55 16● 73 57 22● 81 5● 288 86 0 348 88 1 66 89 12 280 89 56 16● 74 8 229 82 ● 289 86 3 349 88 2 68 89 13 290 89 56 170 74 19 230 82 10 290 86 6 550 88 4 70 89 14 300 89 56 171 74 29 231 82 15 291 86 8 351 88 5 72 89 15 310 89 57 172 74 40 232 82 21 292 86 11 352 88 6 74 89 16 320 89 57 17● 74 51 233 82 26 293 86 14 353 88 8 76 89 17 330 89 57 174 75 1 234 82 31 294 86 17 354 88 9 78 89 18 340 89 58 175 75 11 235 82 36 295 86 1● ●55 88 10 80 89 19 350 89 58 176 75 22 236 82 42 296 86 22 356 88 12 82 89 20 360 89 58 177 75 32 237 82 47 297 86 24 357 88 13 84 89 2● 30 89 58 178 75 42 238 82 52 298 86 27 358 88 14 86 89 22 60 89 59 179 75 51 239 ●2 57 299 86 29 359 88 15 88 89 23 90 89 59 180 76 1 240 83 2 300 86 32 ●60 88 17 90 89 23 120 89 59 
The sixth Rumb from the Meridian East Northeast, East Southeast: West Northwest, West Southwest.  long Latit long Latit long Latit gr. gr. m gr. gr. m gr. gr. m 1 0 25 61 24 29 121 44 43 2 0 50 62 24 52 122 45 1 3 1 15 63 25 14 123 45 18 4 1 39 64 25 37 124 45 36 5 2 4 65 25 59 125 45 53 6 2 29 66 26 21 126 46 10 7 2 54 67 26 44 127 46 28 8 3 19 68 27 6 128 46 45 9 3 44 69 27 28 129 47 2 10 4 8 70 27 50 130 47 19 11 4 33 71 28 12 131 47 35 12 4 58 72 28 34 132 47 53 13 5 23 73 28 55 133 48 9 14 5 47 74 29 17 134 48 25 15 0 12 75 29 39 135 48 42 16 6 37 76 30 0 136 48 59 17 7 1 77 30 22 137 49 14 18 7 2● 78 30 43 138 49 31 19 7 51 7● 31 5 139 49 47 20 8 15 80 31 20 140 50 3 21 8 40 81 31 46 141 50 1● 22 9 4 82 32 8 142 50 34 23 9 2 83 32 29 143 50 51 24 9 54 84 32 50 144 51 6 25 10 17 85 33 10 145 51 21 26 10 42 86 33 32 146 51 37 27 11 7 87 33 52 147 51 53 28 11 31 88 34 12 148 52 7 29 11 56 89 34 33 149 52 23 30 12 20 90 34 54 150 52 38 31 12 44 91 35 14 151 52 53 32 13 8 92 35 34 152 53 8 33 13 32 93 35 55 153 53 23 34 13 57 94 36 15 154 53 37 35 14 21 95 36 35 155 53 53 36 14 45 96 36 55 156 54 7 37 15 9 97 37 14 157 54 21 38 15 33 98 37 34 15● 54 36 39 15 57 99 37 54 159 54 50 40 16 21 100 38 13 1●0 55 4 41 16 44 101 38 32 161 55 18 42 17 8 102 38 52 162 55 33 43 17 31 103 39 12 163 55 47 44 17 55 104 39 31 164 56 0 45 18 20 105 39 49 165 56 14 46 18 42 106 40 8 166 56 2● 47 19 6 107 40 27 167 56 42 48 19 29 108 40 47 168 57 55 49 19 53 109 41 6 169 57 9 50 20 1● 110 41 24 170 57 22 51 20 40 111 41 42 171 57 36 52 21 2 112 42 1 172 57 50 53 21 26 113 42 20 173 58 2 54 21 49 114 42 38 174 58 15 55 22 12 115 42 56 175 58 28 56 22 35 116 43 14 176 58 41 57 22 5● 117 43 32 177 5● 54 58 23 20 118 43 50 178 59 7 59 23 44 119 44 8 179 59 20 60 24 6 120 44 26 180 59 3● long Latit long Latit long Latit long Latit long Latit long Latit long Latit gr. gr. m gr. gr. m gr. gr. m gr. gr. m gr. gr· m gr. gr. m gr. gr. m ●81 59 45 241 70 8 301 77 3 1 81 35 61 84 32 122 86 29 244 88 32 182 59 58 242 70 16 302 77 8 2 81 38 62 84 34 124 86 32 248 88 35 183 60 10 243 70 25 303 77 14 3 81 42 63 84 37 126 86 35 252 88 37 184 60 22 244 70 33 304 77 19 4 81 46 64 84 39 128 86 38 256 88 40 185 60 35 245 70 41 305 77 25 5 81 49 65 84 41 130 86 41 260 88 42 186 60 47 246 70 49 306 77 30 6 81 53 66 84 44 132 86 43 264 88 44 187 60 59 247 70 57 307 77 35 7 81 56 67 84 46 134 86 46 268 88 46 188 61 11 ●48 71 6 308 77 41 8 82 0 68 84 48 136 86 49 272 88 48 189 61 23 249 71 14 309 77 46 9 82 3 69 84 50 138 86 52 276 88 50 190 61 35 250 71 22 310 77 51 10 82 7 70 84 53 140 86 55 280 88 52 191 61 47 251 71 29 311 77 56 11 82 9 71 84 55 142 86 58 284 88 54 192 61 58 252 71 37 312 78 2 12 82 13 72 84 57 144 87 0 288 88 56 193 62 10 253 71 45 313 78 7 13 82 17 73 84 59 146 87 3 292 88 58 194 62 21 254 71 53 314 78 12 14 82 20 74 85 1 148 87 5 296 89 0 195 62 33 255 72 1 315 78 17 15 82 23 75 85 4 150 87 8 300 89 1 196 62 44 256 72 8 316 78 22 16 82 27 76 85 6 152 87 10 304 89 3 197 62 56 257 72 16 317 78 27 17 82 30 77 85 8 154 87 13 308 89 5 198 63 7 258 72 23 318 78 32 18 82 33 78 85 10 156 87 15 312 89 6 199 63 18 259 72 31 319 78 37 19 82 36 79 85 12 158 87 17 316 89 8 200 63 29 260 72 38 320 78 42 20 82 39 80 85 14 160 87 20 320 89 9 201 63 40 261 72 46 321 78 47 21 82 43 81 85 16 162 87 22 324 89 11 202 63 51 262 72 53 322 78 51 22 82 46 82 85 18 164 87 24 328 89 12 203 64 2 263 73 0 323 78 56 23 82 49 83 85 20 166 87 27 332 89 13 204 64 13 264 73 7 324 79 1 24 82 52 84 85 22 168 87 29 336 89 15 205 64 24 265 73 15 325 79 6 25 82 55 85 85 24 170 87 31 3●0 89 16 206 64 36 266 73 22 326 79 10 26 82 58 86 85 26 172 87 33 344 89 17 207 64 45 267 73 29 327 79 15 27 83 1 87 85 28 174 87 35 348 89 18 208 64 56 268 73 36 328 79 20 28 83 4 88 85 30 176 87 37 352 89 20 209 65 6 269 73 43 329 79 24 29 83 7 89 85 32 178 87 39 356 89 21 210 65 17 270 73 50 330 79 29 30 83 10 90 85 34 180 87 41 360 89 22 211 65 27 271 73 57 331 79 33 31 83 13 91 85 36 182 87 43 8 89 24 212 65 37 272 74 4 332 79 38 32 83 16 92 85 38 184 87 4● 16 89 26 213 65 48 273 74 10 333 79 42 33 83 19 93 85 40 186 87 47 24 89 28 214 65 58 274 74 17 334 79 47 34 83 22 94 85 42 188 87 49 32 89 30 215 66 8 275 74 24 335 79 51 35 83 25 95 85 43 190 87 51 40 89 31 216 66 18 276 74 31 336 79 55 36 83 27 96 85 45 192 87 53 48 89 33 217 66 28 277 74 37 337 80 0 37 83 30 97 85 47 194 87 55 56 89 34 218 66 38 278 74 44 338 80 4 38 83 33 98 85 49 19● 37 56 64 89 36 219 66 48 279 74 50 339 80 8 39 83 36 99 85 51 198 87 58 72 89 37 220 66 57 2●0 74 57 340 80 12 40 83 39 100 85 52 20● 88 0 80 89 38 221 67 7 281 75 3 341 80 17 41 83 41 101 85 54 202 88 2 88 89 40 222 67 17 282 75 9 342 80 21 42 83 44 102 85 56 204 88 3 96 89 41 223 67 26 283 75 16 343 80 25 43 83 47 103 85 57 2●● 88 5 104 89 42 224 67 36 284 75 22 344 80 29 44 83 49 104 85 59 20● 88 7 112 89 43 225 67 45 285 75 28 345 80 33 45 83 52 105 86 1 210 88 8 120 89 44 226 67 54 286 75 35 346 80 37 46 83 55 106 86 3 212 88 10 136 89 45 227 68 4 287 75 41 347 80 41 47 83 57 107 86 5 214 88 11 152 89 47 228 68 13 288 75 47 348 80 45 48 84 0 108 86 6 216 88 13 168 89 48 229 68 22 289 75 53 349 80 49 49 84 2 109 86 8 218 88 14 184 89 50 230 ●8 31 290 75 59 350 80 53 50 84 5 110 86 10 220 88 16 200 89 51 231 68 40 291 76 5 351 80 57 51 84 8 111 86 11 222 88 17 216 89 52 232 68 49 292 76 11 352 81 1 52 84 10 112 86 13 224 88 19 240 89 53 233 68 58 293 76 17 353 81 5 53 84 13 113 86 15 226 88 20 264 89 54 234 69 7 294 76 22 354 81 9 54 84 15 114 86 16 228 88 22 288 89 55 235 69 16 295 76 29 355 81 13 55 84 18 115 86 17 230 88 23 312 89 56 236 69 2● 296 76 34 356 81 16 56 84 20 116 86 19 232 88 25 336 89 56 237 69 34 297 76 40 357 81 20 57 84 22 117 86 21 234 88 2● ●60 89 57 238 69 42 298 76 46 358 81 24 58 84 25 118 86 2● 236 88 27 90 89 58 239 69 51 299 76 51 359 81 28 59 84 27 119 86 24 238 88 2● ●80 ●9 59 240 69 59 300 76 57 360 81 31 60 84 30 120 86 26 240 88 30 270 89 59  

The seventh Rumb from the Meridian. East and by North, East and by South, West and by North, West and by South.  long Latit long Latit gr. gr. m gr. gr▪ m 1 0 12 61 12 3 2 0 24 62 12 14 3 0 36 63 12 25 4 0 48 64 12 38 5 1 0 65 12 49 6 1 12 66 13 1 7 1 24 67 13 13 8 1 35 68 13 24 9 1 47 69 13 36 10 1 59 70 13 47 11 2 11 71 13 59 12 2 23 72 14 11 13 2 35 73 14. 22 14 2 47 74 14 34 15 2 59 75 14 45 16 3 11 76 14 57 17 3 23 77 15 8 18 3 35 78 15 20 19 3 47 79 15 31 20 3 59 80 15 43 21 4 10 81 15 54 22 4 22 82 16 6 23 4 34 83 16 17 24 4 46 84 16 29 25 4 58 85 16 40 26 5 10 86 16 51 27 5 22 87 17 3 28 5 34 88 17 14 29 5 45 89 17 26 30 5 57 90 17 37 31 6 9 91 17 48 32 6 21 92 18 0 33 6 33 93 18 11 34 6 45 94 18 22 35 6 57 95 18 34 36 7 9 96 18 44 37 7 20 97 18 56 38 7 32 98 19 8 39 7 44 99 19 20 40 7 56 100 19 30 41 8 8 101 19 41 42 8 19 102 19 53 43 8 32 103 20 4 44 8 43 104 20 15 45 8 5● 105 20 26 46 9 7 106 20 37 47 9 18 107 20 49 48 9 30 108 21 0 49 9 42 109 21 11 50 9 53 110 21 22 51 10 6 111 21 33 52 10 17 112 21 44 53 10 29 113 21 55 54 10 40 114 22 6 55 10 53 115 22 17 56 11 4 116 22 28 57 11 16 117 22 39 58 11 28 118 22 50 59 11 39 119 23 1 60 11 51 120 23 12 long Latit long Latit long Latit long Latit long Latit long Latit long Latit long Latit gr. gr. m gr. gr. m gr. gr. m gr. gr. m gr. gr m gr. gr. m gr. gr. m gr. gr. m 121 23 23 181 33 51 241 43 10 301 51 15 1 58 7 61 63 53 121 68 40 181 72 37 122 23 34 182 34 1 242 43 18 302 51 22 2 58 14 62 63 58 122 68 45 182 72 40 123 23 45 183 34 10 ●43 43 27 303 51 30 3 58 20 63 64 4 123 68 49 183 72 44 124 23 56 184 34 20 244 43 36 304 51 37 4 58 26 64 64 9 124 68 53 184 72 47 125 24 7 185 34 30 245 43 44 305 51 44 5 58 32 65 64 14 125 68 58 185 7 251 126 24 18 186 34 40 246 43 53 306 51 52 6 58 39 66 64 19 126 69 2 186 72 54 127 24 29 187 34 50 247 44 1 307 51 59 7 58 45 67 64 24 127 69 6 187 72 58 128 24 40 188 35 0 248 44 10 308 52 6 8 58 51 68 64 30 128 69 10 188 73 1 129 24 51 189 35 9 249 44 19 309 52 14 9 58 57 69 64 35 129 69 15 189 73 5 130 25 1 190 35 19 250 44 27 310 52 21 10 59 3 70 64 40 130 69 19 190 73 8 131 25 12 191 35 29 251 44 36 311 52 28 11 59 9 71 64 45 131 69 23 191 73 12 132 25 23 192 35 38 252 44 44 312 52 36 12 59 16 72 64 50 132 69 27 192 75 15 133 25 34 193 35 48 253 44 53 313 52 43 13 59 22 73 64 55 133 69 31 193 73 18 134 25 45 194 35 58 254 45 1 314 52 50 14 59 28 74 65 0 134 69 36 194 73 22 1●5 25 ●5 195 3● 7 255 45 9 315 52 57 15 59 34 75 65 5 135 69 40 195 73 25 1●6 2● ● 196 36 17 256 45 18 316 53 4 16 59 40 76 65 10 136 69 44 196 73 29 137 26 ●7 197 36 26 257 45 26 317 53 12 17 59 46 77 65 15 137 69 48 197 73 32 138 26 27 1●8 36 36 258 45 35 318 53 19 18 59 52 78 65 20 138 69 52 198 73 36 139 2● ●8 199 36 46 259 45 43 319 53 26 19 59 58 79 65 25 139 69 56 199 73 39 140 2● 49 200 36 55 260 45 51 320 53 33 20 60 4 80 65 30 140 70 0 200 73 42 141 26 59 201 37 5 261 46 0 321 53 40 21 60 10 81 65 35 141 70 4 201 73 46 1●2 27 10 202 37 14 262 46 8 322 53 47 22 60 16 82 65 40 142 70 8 202 73 49 143 27 21 203 37 24 263 46 16 323 53 54 23 60 22 83 65 45 143 70 12 203 73 52 144 27 31 204 37 33 264 46 24 324 54 1 24 60 27 84 65 50 14● 70 16 204 73 56 145 27 42 205 37 43 265 46 33 325 54 8 25 60 33 85 65 55 145 70 20 205 73 59 146 27 ●2 20● 37 52 266 46 41 326 54 15 26 60 39 86 66 0 146 70 24 206 74 2 147 28 3 207 38 2 267 46 49 327 54 22 27 60 45 87 66 4 147 70 28 207 74 6 148 28 13 208 38 11 268 46 57 328 54 29 28 60 51 88 66 9 148 70 32 208 74 9 149 28 24 209 38 20 269 47 5 329 54 36 29 60 57 89 66 14 149 70 36 209 74 12 150 28 34 210 38 30 270 47 13 330 54 43 30 61 2 90 66 19 150 70 40 210 74 15 151 28 45 211 58 39 271 47 21 331 54 50 31 61 8 91 66 24 151 70 44 211 74 19 152 28 55 212 38 48 272 47 29 332 54 57 32 61 14 92 66 28 152 70 48 212 74 22 153 29 6 213 38 58 273 47 38 333 55 ●3 33 61 20 93 66 33 153 79 52 213 74 25 154 29 16 214 39 7 274 47 46 334 55 10 34 61 25 94 66 38 154 70 56 214 74 28 155 29 27 215 39 16 275 47 54 335 55 17 35 61 31 95 66 43 155 71 0 215 74 31 156 29 37 216 39 25 276 48 2 336 55 24 36 61 37 96 66 47 156 71 4 216 74 35 157 29 47 217 39 35 277 48 10 337 55 31 37 61 42 97 66 52 157 71 8 217 74 38 158 29 58 218 39 44 278 48 17 338 55 37 38 61 48 98 66 57 158 71 12 218 74 41 159 30 8 219 39 53 279 48 25 339 55 44 39 61 54 99 67 1 159 71 15 219 74 44 160 30 18 220 40 2 280 48 33 340 55 51 40 61 59 100 67 6 160 71 19 220 74 47 161 30 29 221 40 11 281 48 41 341 55 58 41 62 5 101 67 11 161 71 23 221 74 50 162 30 39 222 40 20 282 48 49 342 56 4 42 62 10 102 67 15 162 71 27 222 74 53 163 30 49 223 40 30 283 48 57 343 56 11 43 62 16 103 67 20 163 71 31 223 74 56 164 30 59 224 40 39 284 49 5 344 56 17 44 62 22 104 67 24 164 71 34 224 75 0 165 31 10 225 40 48 285 49 13 345 56 24 45 62 27 105 67 29 165 71 38 225 75 3 166 31 20 226 40 57 286 49 20 346 56 31 46 62 33 106 67 34 166 71 42 226 75 6 167 31 30 227 41 6 287 49 28 347 56 37 47 62 38 107 67 38 167 71 46 227 75 9 168 31 40 228 41 15 288 49 36 348 56 44 48 62 44 108 67 43 168 71 49 228 75 12 169 31 50 229 41 24 289 49 44 349 56 50 49 62 49 109 67 47 169 71 53 229 75 15 170 32 0 230 41 33 290 49 51 350 56 57 50 62 54 110 67 52 170 71 57 230 75 18 171 32 10 231 41 41 291 49 59 351 57 3 51 63 0 111 67 56 171 72 0 231 75 21 172 32 20 232 41 50 292 50 7 352 57 10 52 63 5 112 68 1 172 72 4 232 75 24 173 32 31 233 41 59 293 50 14 353 57 16 53 63 11 113 68 5 173 72 8 233 75 27 174 32 41 234 42 8 294 50 22 354 57 23 54 63 16 114 68 10 174 72 11 234 75 30 175 32 51 235 42 17 295 50 29 355 57 29 55 63 21 115 68 14 175 72 15 235 75 33 176 33 1 236 42 26 296 50 37 356 57 36 56 63 27 116 68 18 176 72 19 236 75 36 177 33 11 237 42 35 297 50 45 337 57 42 57 63 32 117 68 23 177 72 22 237 75 39 178 33 21 238 42 43 298 50 52 358 57 48 58 63 37 118 68 27 178 72 26 238 75 42 179 33 31 239 42 52 299 51 0 359 57 55 59 63 43 119 68 32 179 72 30 239 75 45 180 33 41 240 43 1 300 51 7 360 58 1 60 63 48 120 68 36 180 72 33 240 75 48 long Latit long Latit long Latit long Latit long Latit long Latit gr. gr. m gr. gr. m gr. gr. m gr. gr· m gr. gr. m gr. gr. m 241 75 51 301 78 29 2 80 40 122 83 50 273 86 21 126 88 15 242 75 54 302 78 31 4 80 44 124 83 53 276 86 23 132 88 17 243 75 56 303 78 34 6 80 48 126 83 55 279 86 25 13● 88 20 244 75 59 304 78 36 8 80 52 128 83 5● 282 86 28 144 88 22 245 76 2 305 78 38 10 80 55 130 84 0 285 86 30 150 88 24 246 76 5 306 78 41 12 80 59 132 84 3 288 86 32 156 88 26 247 76 8 307 78 43 14 81 3 134 84 5 291 86 34 162 88 28 248 76 11 308 78 46 16 81 7 136 84 8 294 86 36 168 88 29 24● 76 14 309 78 48 18 81 10 138 84 10 297 86 38 174 88 31 250 76 16 310 78 50 20 81 14 140 84 13 300 86 40 180 88 33 251 76 19 311 78 52 22 81 18 142 84 15 303 86 42 189 88 36 252 76 22 312 78 55 24 81 21 144 84 17 30● 86 44 198 88 38 253 76 25 313 78 57 26 81 25 146 84 20 309 86 46 207 88 41 25● 76 2● 314 78 59 28 81 28 148 84 22 312 86 48 216 88 43 255 76 30 315 79 2 30 81 32 150 84 24 315 86 50 225 88 46 256 76 33 31● 79 4 32 81 35 152 84 26 318 86 52 234 88 48 257 76 36 317 79 6 34 81 39 154 84 29 321 86 55 243 88 50 258 76 39 318 79 8 36 81 42 156 84 31 324 86 57 252 88 52 259 76 42 319 79 11 38 81 46 158 84 34 327 86 59 261 88 54 260 76 44 320 79 13 40 81 49 160 84 36 330 87 1 270 88 56 261 76 47 321 79 15 42 81 52 162 84 38 333 87 2 279 88 5● 262 76 50 322 79 17 44 81 56 164 84 40 336 87 4 288 89 0 263 76 52 323 79 19 46 81 59 166 84 42 339 87 6 297 89 2 264 76 55 324 79 22 48 82 2 168 84 45 342 87 8 306 89 4 265 76 58 325 79 24 50 82 6 170 84 47 345 87 10 315 89 5 266 77 1 326 79 26 52 82 9 172 84 49 348 87 11 324 89 7 267 77 3 327 79 28 54 82 12 174 84 51 351 87 13 333 89 9 268 77 6 328 79 30 56 82 15 176 84 53 354 87 15 342 89 10 269 77 9 329 79 33 58 82 19 178 84 55 357 87 17 351 89 12 270 77 11 330 79 35 60 82 22 180 84 58 360 87 18 360 89 13 271 77 14 331 79 37 62 82 25 183 85 1 3 87 20 12 89 15 272 77 16 332 79 39 64 82 28 186 85 4 6 87 22 24 89 17 273 77 19 333 79 41 66 82 31 189 85 7 9 87 23 36 89 19 274 77 22 334 79 43 68 82 34 192 85 10 12 87 25 48 89 20 275 77 24 335 79 45 70 82 37 195 85 13 15 87 26 60 89 22 276 77 27 336 79 48 72 82 40 198 85 16 18 87 28 72 89 24 277 77 29 337 79 50 74 82 43 201 85 19 21 87 30 84 89 25 278 77 32 338 79 52 76 82 47 204 85 20 24 87 31 98 89 27 279 77 35 339 79 54 78 82 49 207 85 24 27 87 33 114 89 28 280 77 37 340 79 56 80 82 52 210 85 27 30 87 34 130 89 30 281 77 40 341 79 58 82 82 55 213 85 30 33 87 36 146 89 32 282 77 42 342 80 0 84 82 58 216 85 33 36 87 37 162 89 33 283 77 45 343 80 2 86 83 1 219 85 36 39 37 39 178 89 35 284 77 47 344 80 4 88 83 4 222 85 38 42 87 40 194 89 36 285 77 50 345 80 6 90 83 7 225 85 41 45 87 42 210 89 37 286 77 52 346 80 8 92 83 10 228 85 44 48 87 43 240 89 39 287 77 55 347 80 10 94 83 13 231 85 46 51 87 44 270 89 41 288 77 57 348 80 12 96 83 15 234 85 49 54 87 46 300 89 43 289 78 0 349 80 14 98 83 18 237 85 52 57 87 47 330 89 4● 29● 78 2 350 80 16 100 83 21 240 85 54 60 87 49 360 89 46 291 78 5 351 80 18 102 83 24 243 85 57 66 87 51 36 ●9 48 292 78 7 352 80 20 104 83 27 24● 85 59 72 87 54 72 89 49 2●● 78 10 353 80 22 10● 83 29 249 86 2 7● 87 56 10● 89 50 2●● 78 12 354 80 24 108 83 32 252 86 4 84 87 59 144 89 51 2●● 78 15 355 80 26 110 83 35 255 86 7 90 88 1 180 89 52 ●96 78 17 356 80 28 112 83 37 25● 86 9 9● 88 4 240 ●9 5● 297 78 19 ●57 80 30 114 ●3 40 261 86 11 102 88 6 36● 8● ●● 298 78 22 3●8 80 32 116 83 43 264 86 14 10● 88 9 1ST 89 57 299 78 24 359 80 34 118 83 45 267 86 16 ●14 88 11 360 89 58 ●●● ●● 27 360 80 36 110 82 4● 270 86 1● 120 88 13 180 89 5● 
The eighth Rumb from the Meridian. East: West.  Latit 1. gr. of lon diff. gr. m m. s thy s. thy 0 10 59 59 59 0 1 0 20 59 59 56 0 3 0 30 59 59 52 0 4 0 40 59 59 45 0 7 0 50 59 59 37 0 8 1 0 59 59 27 0 10 1 10 59 59 15 0 12 1 20 59 59 2 0 13 1 30 59 58 46 0 16 1 40 59 58 29 0 17 1 50 59 58 9 0 20 2 0 59 57 48 0 21 2 10 59 57 26 0 22 2 20 59 57 1 0 25 2 30 59 56 34 0 27 2 40 59 56 6 0 28 2 50 59 55 36 0 30 3 0 59 55 4 0 32 3 10 59 54 30 0 34 3 20 59 53 55 0 35 3 30 59 53 17 0 38 3 40 9 52 38 0 39 3 50 ●9 51 57 0 41 4 0 59 51 14 0 43 4 10 59 50 29 0 45 4 20 59 49 43 0 46 4 30 59 48 54 0 49 4 40 59 48 4 0 50 4 50 59 47 12 0 52 5 0 59 46 18 0 54 5 10 59 45 22 0 56 5 20 59 44 25 0 57 5 30 59 43 26 0 59 5 40 59 42 24 1 2 5 50 59 41 21 1 3 6 0 59 40 17 1 4 6 10 59 39 10 1 7 6 20 59 38 2 1 8 6 30 59 36 52 1 10 6 40 59 35 39 1 13 6 50 59 34 26 1 13 7 0 59 33 10 1 16 7 10 59 31 52 1 18 7 20 59 30 33 1 19 7 30 59 29 12 1 21 7 40 59 27 49 1 23 7 50 59 26 24 1 25 8 0 59 24 58 1 26 8 10 59 23 30 1 28 8 20 59 21 59 1 31 8 30 59 20 27 1 32 8 40 59 18 54 1 33 8 50 59 17 18 1 36 9 ●0 59 15 41 1 37 9 10 59 14 1 1 40 9 20 59 12 20 1 41 9 30 59 10 38 1 42 9 40 59 8 53 1 45 9 50 59 7 7 1 46 10 ●0 59 5 18 1 49 Latti 1. g. of lon diff. Latit 1. g of lon diff. Latit 1 g. of lon diffe Latit 1. g. of lon diffe gr. m m. s. th' s. thy gr. m m. s. thy s. th' gr. m m. s thy s. th' gr▪ m m. s. thy s. th' 10 10 59 3 28 1 50 20 10 56 19 18 3 36 30 10 51 52 26 5 15 40 10 45 51 1 6 45 10 20 59 1 37 1 51 20 20 56 15 40 3 38 30 20 51 47 10 5 16 40 20 45 45 15 6 46 10 30 58 59 43 1 54 20 30 56 12 1 3 39 30 30 51 41 52 5 18 40 30 45 37 28 6 47 10 40 58 57 49 1 54 20 40 56 8 20 3 41 30 40 51 36 32 5 20 40 40 45 30 39 6 49 10 50 58 55 50 1 59 20 50 56 4 38 3 42 30 50 51 31 11 5 21 40 50 45 23 49 6 50 11 0 58 53 51 1 59 21 0 56 0 53 3 45 31 0 51 25 48 5 23 41 0 45 16 57 6 50 11 10 58 51 51 2 0 21 10 55 57 7 3 46 31 10 51 20 24 5 24 41 10 45 10 4 6 53 11 20 58 49 48 2 3 21 20 55 53 20 3 47 31 20 51 14 58 5 26 41 20 45 3 10 6 54 11 30 58 47 44 2 4 21 30 55 49 30 3 50 31 30 51 9 30 5 28 41 30 44 56 14 6 56 11 40 58 45 38 2 6 21 40 55 45 39 3 51 31 40 41 4 1 5 29 41 40 44 49 17 6 57 11 50 58 43 30 2 8 21 50 55 41 48 3 51 31 50 50 58 31 5 30 41 50 44 42 19 6 58 12 0 58 41 20 2 10 22 0 55 37 52 3 56 32 0 50 52 58 5 33 42 0 44 35 19 7 0 12 10 58 39 8 2 12 22 10 55 33 55 3 57 32 10 50 47 25 5 33 42 10 44 28 18 7 1 12 20 58 36 55 2 13 22 20 55 29 58 3 57 32 20 50 41 47 5 36 42 20 44 21 16 7 2 12 30 58 34 40 2 15 22 30 55 25 58 4 0 32 30 50 36 13 5 36 42 30 44 14 12 7 4 12 40 58 32 23 2 17 22 40 55 21 57 4 1 32 40 50 30 34 5 39 42 40 44 7 7 7 5 12 50 58 30 4 2 19 22 50 55 17 54 4 3 32 50 50 24 54 5 40 42 50 43 0 0 7 7 13 0 58 27 44 2 20 23 0 55 13 49 4 5 33 0 50 19 13 5 41 43 0 43 52 52 7 8 13 10 58 25 22 2 22 23 10 55 9 43 4 6 33 10 50 13 30 5 43 43 10 43 45 43 7 9 13 20 58 22 58 2 24 23 20 55 5 35 4 8 33 20 50 7 45 5 45 43 20 43 38 33 7 10 13 30 58 20 32 2 26 23 30 55 1 25 4 10 33 30 50 1 59 5 46 43 30 43 31 21 7 12 13 40 58 18 4 2 28 23 40 54 57 14 4 11 33 40 49 56 12 5 47 43 40 43 24 8 7 13 13 50 58 15 35 2 29 23 50 54 53 1 4 13 33 50 49 50 23 5 49 43 50 43 16 53 7 15 14 0 58 13 4 2 31 24 0 54 48 46 4 15 34 0 49 44 32 5 51 44 0 43 9 37 7 16 14 10 58 10 31 2 33 24 10 54 44 29 4 17 34 10 49 38 40 5 52 44 10 43 2 20 7 17 14 20 58 7 56 2 35 24 20 54 40 11 4 18 34 20 49 32 46 5 54 44 20 42 55 2 7 18 14 30 58 5 20 2 36 24 30 54 35 52 4 19 34 30 49 26 51 5 55 44 30 42 47 42 7 20 14 40 58 2 42 2 38 24 40 54 31 30 4 22 34 40 49 20 55 5 56 44 40 42 40 21 7 21 14 50 58 0 2 2 40 24 50 54 27 07 4 23 34 50 48 14 56 5 59 44 50 42 52 59 7 22 15 0 57 57 20 2 42 25 0 54 22 42 4 25 35 0 49 8 57 5 59 45 0 42 25 35 7 24 15 10 57 54 36 2 44 25 10 54 18 16 4 26 35 10 49 2 56 6 1 45 10 42 18 10 7 25 15 20 57 51 51 2 45 25 20 54 13 48 4 28 35 20 48 56 53 6 3 45 2● 42 10 44 7 26 15 30 57 49 4 2 47 25 30 54 9 18 4 30 35 30 48 50 49 6 4 45 30 42 3 16 7 28 15 40 57 46 15 2 49 25 40 54 4 47 4 31 35 40 48 44 43 6 6 45 40 41 55 48 7 28 15 50 57 43 25 2 50 25 50 54 0 14 4 33 35 50 48 38 36 6 7 45 50 41 48 18 7 30 16 0 57 40 33 2 52 26 0 53 55 40 4 34 36 0 48 32 28 6 8 46 0 41 40 46 7 32 16 10 57 37 38 2 55 26 10 53 51 3 4 37 36 10 48 26 18 6 10 46 10 41 33 14 7 32 16 20 57 34 43 2 55 26 20 53 46 25 4 38 36 20 48 20 6 6 12 46 20 41 25 40 7 34 16 30 57 31 45 2 58 26 30 53 41 46 4 39 36 30 48 13 53 6 13 46 30 41 18 ● 7 34 16 40 57 28 46 2 59 26 40 53 37 5 4 41 36 40 48 7 39 6 14 46 40 41 10 28 7 38 16 50 57 25 45 3 1 26 50 53 32 22 4 43 36 50 48 1 23 6 16 46 50 41 2 51 7 37 17 0 57 22 42 3 3 27 0 53 27 37 4 45 37 0 47 55 5 6 18 47 0 40 55 12 7 39 17 10 57 19 37 3 5 27 10 53 22 51 4 46 37 10 47 48 46 6 19 47 10 40 47 32 7 40 17 20 57 16 31 3 6 27 20 53 18 4 4 47 37 20 47 42 26 6 20 47 20 40 39 50 7 42 17 30 57 13 23 3 8 27 30 53 13 14 4 50 37 30 47 36 4 6 22 47 30 40 32 7 7 43 17 40 57 10 13 3 10 27 40 53 8 23 4 51 37 40 47 929 41 6 23 47 40 40 24 24 7 43 17 50 57 7 2 3 11 27 50 53 3 31 4 52 37 50 47 23 16 6 25 47 50 40 16 39 7 45 18 0 57 3 48 3 14 28 0 52 58 37 4 54 38 0 47 16 50 6 26 48 0 40 8 52 7 47 18 10 57 0 33 3 15 28 10 52 53 41 4 56 38 10 47 10 23 6 27 48 10 40 1 5 7 47 18 20 56 57 16 3 17 28 20 52 48 44 4 57 38 20 47 3 54 6 29 48 20 39 53 16 7 49 18 30 56 53 58 3 18 28 30 52 43 44 5 0 38 30 46 57 23 6 31 48 30 39 45 26 7 50 18 40 56 50 38 3 22 2● 40 52 38 44 5 0 38 40 46 50 52 6 31 48 40 39 37 35 7 51 18 50 56 47 16 3 22 28 50 52 33 42 5 2 38 50 46 44 18 6 34 48 50 39 29 42 7 53 19 0 56 43 52 3 24 29 0 52 28 38 5 4 39 0 46 37 44 6 34 49 0 39 21 49 7 53 19 10 56 40 27 3 25 29 10 52 23 32 5 6 39 10 46 31 7 6 37 49 10 39 13 54 7 53 19 20 56 36 59 3 28 29 20 52 18 25 5 7 39 20 46 24 30 6 37 49 20 39 5 58 7 55 19 30 59 33 31 3 2 29 30 52 13 17 5 8 39 30 46 17 51 6 39 49 30 38 58 1 ● 57 19 40 56 30 0 3 31 29 40 52 8 7 5 10 39 4● 46 11 11 6 40 49 40 38 50 2 7 59 19 50 56 26 28 3 32 29 50 52 2 55 5 12 39 50 46 4 29 6 42 49 50 38 42 3 ● 59 20 0 56 22 54 3 34 30 0 51 57 41 5 14 40 0 ●5 ●● 46 6 4● ●● ●● ●● ●● ● 8 1 Latit 1. g. of lon diff. Latit 1. g of lon diff. Latit 1 g. of lon diffe Latit 1. g. of lon diffe. gr. m m. s. th' s. thy▪ gr. m m. s. thy s. th' gr. m m. s thy s. thy gr. m m. s. thy▪ s. thy 50 10 38 26 0 8 2 60 10 29 50 55 9 5 70 10 20 21 26 9 50 80 10 10 14 49 10 19 50 20 38 17 57 8 3 60 20 29 41 50 9 5 70 20 20 11 34 9 52 80 20 10 4 30 10 19 50 30 38 9 53 8 4 60 30 29 32 43 9 7 70 30 20 1 42 9 52 80 30 9 54 10 10 20 50 40 38 1 47 8 6 60 40 29 23 36 9 7 70 40 19 51 50 9 52 80 40 9 43 50 10 20 50 50 37 53 41 8 6 60 50 29 14 28 9 8 70 50 19 41 56 9 54 80 50 9 33 30 10 20 51 0 37 45 33 8 8 61 0 29 5 19 9 9 71 0 19 32 3 9 54 81 0 9 23 10 10 20 51 10 37 37 24 8 9 61 10 28 56 09 9 10 71 10 19 22 8 9 55 81 10 9 12 49 10 21 51 20 37 29 14 8 10 61 20 28 46 58 9 11 71 20 19 12 13 9 55 81 20 9 2 28 10 21 51 30 37 21 3 8 11 61 30 28 37 46 9 12 71 30 19 2 17 9 56 81 30 8 52 7 10 21 51 40 37 12 52 8 12 61 40 28 28 34 9 12 71 40 18 52 22 9 55 81 40 8 41 45 10 22 51 50 37 4 37 8 14 61 50 28 19 20 9 14 71 50 18 42 25 9 57 81 50 8 31 23 10 22 52 0 36 56 23 8 14 62 0 28 10 06 9 14 72 0 18 32 28 9 57 82 0 8 21 1 10 22 52 10 36 48 7 8 16 62 10 28 0 51 9 15 72 10 18 22 30 9 58 82 10 8 10 39 10 22 52 20 36 39 50 8 17 62 20 27 51 35 9 16 72 20 18 12 31 9 59 82 20 8 0 16 10 23 52 30 36 31 32 8 18 62 30 27 42 18 9 17 72 30 18 2 23 9 59 82 30 7 49 54 10 22 52 40 36 23 13 8 19 62 40 27 33 00 9 18 72 40 17 52 33 9 59 82 40 7 39 31 10 23 52 50 36 14 53 8 20 62 50 27 23 41 9 19 72 50 17 42 33 10 0 82 50 7 29 7 10 24 53 0 36 6 32 8 21 63 0 27 14 22 9 19 73 0 17 32 32 10 1 83 0 7 18 ●4 10 23 53 10 35 58 10 8 22 63 10 27 5 02 9 20 73 10 17 22 31 10 1 83 10 7 8 20 10 24 53 20 35 49 46 8 24 63 20 26 55 41 9 21 73 20 17 12 29 10 2 83 20 6 57 56 10 24 53 30 35 41 22 8 24 63 30 26 46 19 9 22 73 30 17 2 27 10 2 83 30 6 47 32 10 24 53 40 35 32 56 8 26 63 40 26 36 56 9 23 73 40 16 52 24 10 3 83 40 6 37 8 10 24 53 50 35 24 2● 8 27 63 50 26 27 33 9 23 73 50 16 42 21 10 3 83 50 6 26 43 10 25 54 0 35 16 2 8 27 64 0 26 18 08 9 25 74 0 16 32 18 10 3 84 0 6 16 18 10 25 54 10 35 7 33 8 29 64 10 26 8 43 9 25 74 10 16 22 13 10 3 84 10 6 5 53 10 25 54 20 34 59 3 8 30 64 20 25 59 17 9 26 74 20 16 12 9 10 4 84 20 5 55 28 10 25 54 30 34 50 32 8 31 64 30 25 49 50 9 27 74 30 16 2 3 10 6 84 30 5 45 3 10 25 54 40 34 42 0 8 32 64 40 25 40 23 9 27 74 40 15 51 58 10 5 84 40 5 34 37 10 26 54 50 34 33 27 8 33 64 50 25 30 55 9 28 74 50 15 41 5● 10 6 84 50 5 24 10 10 27 55 0 34 24 53 8 34 65 0 25 21 26 9 29 75 0 15 31 45 10 7 85 0 5 13 46 10 27 55 10 34 16 17 8 36 65 10 25 11 56 9 30 75 10 15 21 38 10 7 85 10 5 3 20 10 26 55 20 34 7 41 8 36 65 20 25 2 25 9 31 75 20 15 11 30 10 8 85 20 4 52 53 10 27 55 30 33 59 4 8 37 65 30 24 52 54 9 31 75 30 15 1 22 10 8 85 30 4 42 27 10 26 55 40 33 50 25 8 39 65 40 24 43 22 9 32 75 40 14 51 14 10 8 85 40 4 32 1 10 26 55 50 33 41 46 8 39 65 50 24 33 49 9 33 75 50 14 41 5 10 9 85 50 4 31 34 10 27 56 0 33 33 6 8 40 66 0 24 24 15 9 34 76 0 14 30 55 10 10 86 0 4 11 7 10 27 56 10 33 24 24 8 42 66 10 24 14 41 9 34 76 10 14 20 45 10 10 86 10 4 0 41 10 26 56 20 33 15 42 8 42 66 20 24 5 6 9 35 76 20 14 10 35 10 10 86 20 3 50 14 10 27 56 30 33 6 58 8 44 66 30 23 55 30 9 36 76 30 14 0 24 10 11 86 30 3 39 46 10 28 56 40 32 58 14 8 44 66 40 23 45 53 9 37 76 40 13 50 13 10 11 86 40 3 29 19 10 27 56 50 32 49 28 8 46 66 50 23 36 16 9 37 76 50 13 40 1 10 12 86 50 3 18 52 10 27 57 0 32 40 42 8 46 67 0 23 26 38 9 38 77 0 13 29 49 10 12 87 0 3 8 25 10 27 57 10 32 31 55 8 47 67 10 23 16 59 9 39 77 10 13 19 37 10 12 87 10 2 57 57 10 28 57 20 32 23 6 8 49 67 20 23 7 20 9 39 77 20 13 9 24 10 13 87 20 2 47 29 10 28 57 30 32 14 17 8 49 67 30 22 57 40 9 40 77 30 12 59 11 10 13 87 30 2 37 2 10 27 57 40 32 5 26 8 51 67 40 22 47 59 9 41 77 40 12 48 57 10 14 87 40 2 26 34 10 28 57 50 31 56 35 8 51 67 50 22 38 17 9 42 77 50 12 38 43 10 14 87 50 2 16 6 10 28 58 0 31 47 43 8 52 68 0 22 28 35 9 42 78 0 12 28 29 10 14 88 0 2 5 38 10 28 58 10 31 38 49 8 54 68 10 22 18 52 9 43 78 10 12 18 14 10 15 88 10 1 55 10 10 28 58 20 31 29 55 8 54 68 20 22 9 9 9 43 78 20 12 7 59 10 15 88 20 1 44 42 10 28 58 30 31 21 0 8 55 68 30 21 59 24 9 45 78 30 11 57 43 10 16 88 30 1 34 14 10 28 58 40 31 12 3 8 57 63 40 21 49 39 9 45 78 40 11 47 27 10 16 88 40 1 23 46 10 28 58 50 31 3 6 8 57 68 50 21 39 54 9 45 78 50 11 37 11 10 16 88 50 1 13 18 10 28 59 0 30 54 8 8 58 69 0 21 30 7 9 47 79 0 11 26 55 10 16 89 0 1 2 50 10 28 59 10 30 45 9 8 59 69 10 21 20 21 9 47 79 10 11 16 37 10 18 89 10 0 52 21 10 29 59 20 30 36 9 9 0 69 20 21 10 33 9 48 79 20 11 6 20 10 17 89 20 0 41 53 10 28 59 30 30 27 8 9 1 69 30 21 0 45 9 48 79 30 10 56 3 10 17 89 30 0 31 25 10 28 59 40 30 18 6 9 2 69 40 20 50 56 9 49 79 40 10 45 45 10 18 89 40 0 20 56 10 29 59 50 30 9 4 9 2 69 50 20 41 6 9 50 79 50 10 35 27 10 18 89 50 0 1 28 10 28 60 0 30 0 0 9 4 70 0 80 31 16 9 50 80 0 10 25 08 10 19 90 0 0 0 0 0 0    

CHAP. X. The use of this Table of Rumbs.  
THe especial use of this Table is for the true drawing of the Rumbs in the Globe and in the Chart, which some (with a name astonishing with an empty sound) call Paradoxal: but to speak plain English, it is nothing else but a Chart, whose centre is the Pole, and may best be made after the kind of projection used by Gemma Frisius in his general Astrolabe: wherein the Meridian's will be right lines passing by the centre, and the Parallels peripheries of a circle: supposing one half of the Spherical superficies of the Terrestrial Globe to be projected into the plain of the Equinoctial, Whose principal use may be in our Northerly Navigations and discoveries, wherein the Rumbs may most easily and truly be drawn by help of this Table, thus: Having an Index hanged upon the centre, and garduated with degrees of Latitude, with figures set to every fifth or tenth degree, beginning at the Equinoctial: having also divided the Equinoctial into degrees of Longitude, beginning at the first Meridian, lay the Index to every degr. of Longitude in order one after another; looking always withal in this Table, the Latitudes of the Rumb you desire to describe, and at the same Latitudes found in the fiducial line of the Index, make pricks in the Chart, for by th●se pricks, the Haelisphaerical line or Rumb desired must be drawn.  
After the same manner must you work with the Globe, having first truly hanged it upon his Poles within his Meridian divided into degrees, and subdivided also into smaller parts (if room will serve) with numbers set to every fifth, or tenth degree from the Equinoctial to the Pole, and then proceeding in all points, as before you did, with the Chart, only using the Meridian in stead of the Index.  
Hereby also the Rumbs may most exactly be described in those distorted heart-formed maps of Orontius and Vopelius, or in any other amongst Ptolemies or Ortelius his Geographical Tables, or any else whatsoever, so it be first distinguished by Meridian's and Parallels, whereby the Longitude and Latitude of any point assigned therein may be readily found; seeing it may easily be known out of this Table by what points of Longitude and Latitude each rumbe must be drawn from the Equinoctial to the Pole almost. But those two kinds of projection before mentioned, I mean of the Nautical Planisphaere, and Gemma Frisius his Astrolabe, are such as of all others do best represent in a plain, the true forms of all places that are upon the Spherical face of the earth.  
The Table of eighth Rumb serveth to show how many minutes, seconds and thirds of one degree of the Equinoctial, are contained in one degree of Longitude for every tenth minute of Latitude: whereby the whole Table of Rumbs may be made and examined more truly, and easily, then by that of Appian, lately set forth by Simon Stevin in his Hypomnemat, Mathemat.   

CHAP. XI. A most plain and sensible demonstration of the agreement of the Nautical Planisphaere, before described, with the Globe and of the disagreement of the common Sea-chart from them both.  
HAving thus showed the manifold uses of the Table of Latitudes, aswell for the true graduating of Sea-charts both general and particular, with degrees of Latitude increasing in their due proportion, as also for the making of the table of Rumbes, together with the use thereof; I will now come again to the matter, and mark principally intended and aimed at in this first book, and show how greatly the common Sea-chart (with Parallel Meridian's and degrees of Latitude every where equal) doth differ from the truth, as also how well the Chart, before described, agreeth with the same; which may most manifestly appear by comparing together these three figures following, whereof the first is in all points answerable to a part of a Spherical superficies, contained betwixt two Meridian's, differing in Longitude ten degrees, and extended from the Equinoctial to the Pole. The second containeth ten degrees in Longitude, and 90 degrees from the Equinoctial in Latitude, of the common Sea-chart with equidistant Meridian's and degrees of Latitude every where equal. The third containeth 10 degrees in Longitude, and 80 in Latitude of the Nautical Planisphaere, truly described with Meridian's in all places aequidistant, and degrees of Latitude increasing proportionally towards the Pole, as before we have showed.  
Past this upon the Margin of Letter M. fol. 52  
If there be two places differing in Longitude and Latitude 10 degrees (that which hath the greater Latitude being more to the Eastwards) the second figure (as you see) maketh them lie each from other North-east and Southwest, in what Latitude soever they be situate, either nearer or further from the Equinoctial, as in 50 and 60, or in 60 and 70; or in 70 and 80 degrees of Latitude. But in the first and third figure, these places shall bear almost North-east and Southwest each from other, at the Equinoctial only. And one place being situate in 50, and the other in 60 degrees of Latitude, they shall lie one from another North-east and by North, and almost half a point Northerly. In 60 and 70 degrees of Latitude they lie almost North Northeast: in 70 and 80 they bear each from other scarce so much as North and by East. Therefore the common Sea-Chart, in showing how one of those places beareth from another, erreth in the first one point of the Compass and almost an half; in the second, two whole points almost; but in the third, more than three whole points. Neither is it possible to avoid these so gross and intolerable errors (if the Rumbs be right lines, and the degrees of Longitude and Latitude every where equal) but we must needs fall into other errors as gross as these, either in the difference of Longitudes, or in the difference of Latitudes, or in the respective situation, which they commonly call, the lying or bearing of them one from another as may most plainly appear by comparing the common Sea-Chart and the Globe together. But in this Nautical planisphaere heretofore described, all these errors are avoided, aswell in the Longitudes and Latitudes▪ as also in the directional distances and respective situations of all places, each from other according to the points of the Compass, as by like comparison of it with the Globe, will be most manifest.   

CHAP. XII. The use of this Planisphaere.  
OF the use of this Planisphaere much more might be written then now I have leisure or cause to set down, a great part hereof being in such sort to be performed, as hath been heretofore accustomed in the ordinary Sea-Chart, saving that this Nautical planisphaere generally bringeth you to more certain truth in conclusion, than the ordinary Chart hitherto hath done, or possibly can do. Something notwithstanding (for the better satisfaction of the Reader) I thought meet at this time to add to the former treatise, especially in those points which may be most serviceable for Sea men, and wherein the use of this Nautical Planisphaere differeth from the use of the common Sea-Chart, heretofore ordinarily practised.  
To know upon what point of the Compass one place in this Chart lieth from another, try with your Compasses from what Rumb both places have equal distance, which may be found truly enough, for the Mariners use, for the most part, by estimation only. But if you would be precise, do thus: Draw a strait line by both places, for a line Parallel to it from the centre of the next Rose or Fly (as it is called) is the Rumb of those two places, showing upon what point of the Compass you must go from the one to the other.  
Or thus, (if you list not draw any lines upon your Chart) lay the edge of a long ruler (reaching overthwart the Chart) to both places: take with your Compasses the distance of the centre of the next Fly from the edge of the ruler, then guiding and carrying one foot along by the edge of the ruler, lead the other foot Parallel-wise (that is, keeping it always equally at that distance from the ruler) for so it showeth you how those places lie one from another.  
The distance of two places (as the Mariners commonly take it, and measure it in their Charts) is the segment or part of the Rumbe contained between them; which how much it is in the ordinary measure of leagues, shall truly be found out by this Planisphaere, thus.  
If both places have the same Latitude, take with your Compasses the length of a degree of the Meridian at that Latitude (take half the degree above, and half beneath that Latitude) for so oft as you shall find that length between the two places, so many score leagues are there betwixt them. If the distance be great, for the more expedition, you may take five times the length of that degree, and counting it for an hundred leagues, proceed as before.  
If both places have not the same Latitude, the Equinoctial also not coming between them, subtract the lesser Latitude out of greater; but if the Equinoctial come betwixt them, add both Latitudes together, so have you the difference of Latitude between both places.  
Now if both places have the same Longitude, so many degrees as there is in the difference of Latitude, so many score leagues is the distance.  
But if they differ also in Longitude as well as in Latitude, look how many degrees the difference of Latitude containeth, so many degrees of the Equinoctial take with your Compasses, and leading one foot in the Equinoctial, move forwards the other also Parallel-wise, keeping always that distance, till it cross the Rumb of those two places, in such sort, that one foot resting in that crossing, the other carried about, may but only touch the Equinoctial. Then having taken with your Compasses the segment or part of that Rumb between that crossing and the Equinoctial, set both feet in the Equinoctial, and see how many degrees are contained betwixt them, for so many score leagues is the distance of those two places.  
Or if that segment of the said Rumb be greater than well can be taken with the Compasses, take the length of five degrees of the Equinoctial, between the feet of your compasses, and look how oft you can find that length in the segment aforesaid of the Rumb' for so many hundred leagues is the distance of those two places.  
The demonstration hereof cannot be obscure to him that well considereth the Geometrical reason of the projection, and making of this Nautical planisphaere, before set down in the second Chapter, from whence it followeth, that because the spherical superficies (whereof this planisphaere is conceived to be Geometrically made) extendeth itself every way equally, at every point of Latitude betwixt the Equinoctial and Pole, till it apply and join itself round about to the concavity of the circumscribed Cylinder, therefore the segments of the Meridian, and of any other Rumb contained betwixt any the same two Parallels, must needs increase in one and the same proportion.  
And consequently, as often as the segment of a Meridian between any two Parallels, is contained in the segment of any Rumb intercepted betwixt the same Parallels in the Globe, so often is the like segment of a Meridian contained in the segment of the same Rumb intercepted between the Parallels correspondent in this planisphaere. Therefore (supposing the said segment of the Meridian in this planisphaere, to be divided into so many equal parts as it containeth degrees) it followeth that so often as one of these parts is contained in the segment of the Rumb aforesaid in this planisphaere, so many score leagues is the distance of the two places set at the ends of that segment.  
Now it is manifest, that by these three segments, that is the segment of the Rumb between the two places the segment of the Meridian betwixt one of the places, and the Parallel of the other (that is, the difference of Latitude) and the segment of the Parallel contained betwixt one of these places, and the Meridian of the other (which is the difference of Longitude) I say it is manifest, that by these three segments a right angled Triangle is made, because the segments of the Meridian and Parallel (which are two sides of this Triangle) include a right angle.  
Again it is plain, that taking with your Compasses so many degrees of the Equinoctial as are contained in the difference of Latitude, then guiding one foot in the Equinoctial, and carrying forwards the other Parallel wise, till it cross the Rumb of those two places in such sort that one foot of the Compasses being set in that crossing▪ the other moved about, may but only touch the Equinoctial: and lastly, drawing from that crossing a line perpendicular to the Equinoctial: It is plain, I say, that by this perpendicular and the two segments (one of the Equinoctial▪ between this perpendicular and the Rumb; the other of the Rumb, between the perpendicular and the Equinoctial:) by these segments, I say, and the said perpendicular, there is comprehended another right angled Triangle: which by the 14. e 4. & c▪ 3. e. 7 Ram. Is like to the former right angled Triangle, because two angles, of them both are equal, that is, the right angles▪ and the angles of the same Rumb. In the last of these Triangles▪ the side perpendicular to the Equinoctial, is proportional to the difference of Latitude, and the segment of the Rumb between the end of this perpendicular and the Equinoctial, is proportional to the segment of the same Rumb contained betwixt the two places. Therefore by the 2 p 6. & 17 p. 11 Eulc. Because the line perpendicular to the Equinoctial, containeth so many equal degrees of the Equinoctial, as there are equal parts in the difference of Latitude (that is) so many as there are degrees in the difference of Latitude these equal parts also of the perpendicular and difference of Latitude are proportional. Whereof it followeth, that so oft as one of these equal parts of the difference of Latitude is contained in the segment of the Rumb betwixt the two places (which before we showed to be so oft as a degree of the Meridian in the Globe is contained in the segment of the Rumb betwixt the same places in the Globe) so oft is one of the said equal parts of the perpendicular aforesaid (that is a degree of the Aequinoctial) contained in the segment of the same Rumb between the foresaid crossing or end of the perpendicular, and the Aequinoctial. Therefore look how many degrees of the Aequinoctial there are found in the segment of the Rumb of the two places, so many score leagues is the distance of those two places which was to be demonstrated.  
Thus have you a way infallible to find out the distance between any two places measured in their Rumb: which because it is then only their true distance (that is the shortest space betwixt them upon the superficies of the Terrestrial Globe) when both places lie North and South each from other, or East and West, having no Latitude, as under the Aequinoctial, whereas otherwise the segment of the Rumb between the two places is always greater than the true distance (yea sometime by half and more, in places far Northward, or Southward) I tho●ght good also here to set down the way to find out the true distance of any two places, according to the arch of a great circle drawn between them, wherein I have been, and yet am publicly charged with my promise, and mean at this time to discharge myself thereof.  
The true distance between two places is the arch of a great circle contained betwixt them, which is thus to be found out.  
If both places have no Latitude (as when they are both under the Aequinoctial) and one of them also no Longitude, the Longitude of the other being less, or not more than 180 degrees▪ the Longitude is the distance;  
But if the Longitude be greater than 180 degrees subtract it out of 360; the remainder is the distance.  
If both places have either none, or the same Longitude (as when they are in the same semicircle of the Meridian between the Poles) and one of them only have Latitude; that Latitude is the distance. But if both places agreeing in Longitude have Latitudes also of like denomination (as both Northerly, or both Southerly) subtract the lesser Latitude out of the greater, the distance remaineth: If one place have Northerly Latitude, and the other Southerly, add them together; for the sum is the distance.  
If one or both places have atitude, Land differ also in Longitude: in a great circle divided exactly into degrees (with figures set to every fifth or tenth degree) note the Longitudes of both places.  
Now if one place only have Latitude, draw a diameter from the Longitude thereof, noted in the circle, and with your Compasses take so many degrees and minutes in the same circle, as that Latitude containeth: then setting one foot of the Compasses in the Longitude of that place, with the other make a prick in the circle, which may be called the point of Latitude. From this point draw a line perpendicular, crossing the diameter drawn from the Longitude of that place. Take with your Compasses the distance of this crossing, from the point of the other places Longitude, noted in the circle, and leaving one foot in the said crossing, with the other make a prick, in the foresaid diameter: take the distance of this prick from the point of Latitude noted in the circle. Then setting one foot of the Compasses in that point of the circle where the degrees begin to be numbered, the other foot extended that way, which the numbers proceed, shall show you in the circle the distance of the places.  
Take for example the City of London, and Saint Thomas Island, which lieth right under the Aequinoctial line, in 32 degrees of Longitude. The Longitude of London admit to be 22 degrees, the Latitude 51 degrees, 32 minutes. Mark the Longitudes of Saint Thomas Island and of London with A and B. From the Longitude of London (because London hath also Latitude) draw the diameter BC. Having taken with the compasses the Latitude of London in the circle, set one foot in B, and with the other make the prick E in the circle, and draw the perpendicular OF, crossing the diameter BC at F. Make FG equal to FAVORINA, which is the distance of Saint Thomas Island from the sine of London's Latitude. Then GE shall be the line subtending the distance of those two places. Taking therefore the length of GE with the Compasses, and setting one foot in H (where the degrees begin) the other stretched forwards in the circle, will point you out the distance of Saint Thomas Island and London, 52 degrees of a great circle, and about one half, that is, 1050 leagues, or 3150 English miles.  
If both places have Latitude, do the like for both places as before you did for the one place having Latitude, till you have crossed both diameters with perpendiculars: then take with your Compasses the distance of those cross. Now if both their Latitudes be of one denomination (that is, both Northerly or both Southerly) and equal, set one foot of the Compasses where the degrees begin to be numbered in the circle, and the other foot extended therein that way which the numbers succeed, will show you the distance.  
As for example, London and Cape Blanco (near the coast of Newfound land) have both Northerly and almost equal Latitudes of 51 degrees, 32 minutes. Having therefore drawn as well the diameters BC and DL from B, determining the Longitude of London (viz. 22 degrees) and from the point of the Longitude of Cape Blanco (which admit to be 331 degrees, as also the perpendiculars or sins of both their Latitudes, OF, and KL, (as before was showed) crossing the diameters in F and L: the distance FL taken with the Compasses, and translated into the circle (as in the former example) will show you the distance of Cape Blanco from London, to be almost 31 degrees, of a great circle that is 620 leagues, or 1860 miles.  
If the Latitudes be not both equal, and also of one denomination, leaving one foot of the Compasses in the crossing of the sine or perpendicular descending from the point of the greater Latitude, with the other foot make a prick in the same diameter, wherein that crossing is: then if the Latitudes be both of one denomination, ●ake with the Compasses the length of the perpendicular or sine drawn from the point of the lesser Latitude: and setting one foot in the point of the greater Latitude, with the other make a prick in the perpendicular descending from it, that is, in the sine thereof: Take the distance of this prick from the former, made in the diameter: This distance transferred into the circle (as in the first example) will give you the distance of the places given.  
As London and Jerusalem have both Northerly and unequal Latitudes, Hierusalems' Latitude being only 32 degrees. First therefore note in the circle both their Longitudes: the Longitude of London (viz. 22 degrees) as before with B: The Longitude of Jerusalem (68 degrees) note with M: Let the perpendicular or the sins of the Latitudes of London and Jerusalem, OF, and NO be drawn as in the former examples Make FP equal to OF, and PQ equal to NO: The space betwixt P and Q taken with the Compasses, and then both feet set in the circle (in such sort as in the first example was showed) shall contain between them the desired distance of Jerusalem from London, 38 degrees, and about ¾, that is 775 leagues, which are 2325 miles.  
But if the Latitudes be of divers denominations; (that is, one Northerly, and the other Southerly) continue forth the perpendicular (that crosseth the diameter, wherein the foresaid prick was made) till it be equal to both perpendiculars, that is to the sins of both Latitudes. The distance of the end of this continued perpendicular from the prick aforesaid in the diameter, taken with the Compasses, and translated into the graduated periphery of the circle (as before) will show you how many degrees of a great circle are contained between both places.  
To shut up this matter with one example, suppose you would know how far Cusco in Peru is from London. Let the Longitude of Cusco be 295 degrees, the Latitude 11 degrees Southerly: The Longitude of London, as before, 22 degrees the Latitude 51 degrees, 32 minutes From both these Longitudes noted in the circle with B and R, draw the diameters, as before, BC, and RV: as also the perpendiculars or sins of their Latitudes OF, and 'tis: Make FX equal to FS, the distance of those sins▪ and AY equal to ST the sine of Cuscoes' Latitude. Take the distance XY between the feet of the Compasses, and set them both in the circumference of the circle, as in the first example, so shall you find that there are betwixt London and Cusco almost 97 degrees, of a great circle that is 1940 leagues, or 5820 miles.  
If you had rather keep within the compass of the circle, make the perpendicular XZ equal to ST, and proceed with EZ as you did before with XY.  
Paste this upon the Margin of Letter N. fol. 65. so as it may lie open all the while the foregoing matter of the same Chap. is reading.  
Also, because all the sins of Latitude (being perpendicular to the same plain of the Aequinoctial) are Parallels, by the 5. e 21. Ram. 6. pr. 11. Eucl. Therefore by the 11. e 2. Ram. or 35. d. 1. Eucl. FL is the line subtending the distance of London and Cape ●●anco.  
Again because FP whereto OF is perpendicular is made equal to FOE, (the distance of the sins of London and Jerusalem, to which (distance) OF is also perpendicular in the Globe) and EQ also equal to NO: Therefore FQ being the difference 〈◊〉 the sins of London's and Hierusalems' Latitudes▪ there must needs be the same distance betwixt P and Q that there is between the tops of the sins of Hierusalems' and London's Latitudes in the Globe.  
Lastly, FX being equal to FS (the distance of the sins of Latitude of London and Cusco in Peru) and XZ perpendicular to FX, and equal to ST the sine of Cuscoes' Latitude: as OF is the sine of London's Latitude and perpendicular to the same line XF: EZ (to which XY is equal by the 6. c. 12. e 5 Ram. 33. pr. 1. Eucl. YE being equal and Parallel to XZ) must needs be equal to a straight line extended within the Globe between the points of Latitude of Cusco and London.  
Now out of this demonstration it were an easy matter (if any list take the pains to be so curious) to find out the distance of any two places Arithmetically by the doctrine of Triangles, having always two sides given, which are the sins of the compliments of the Latitudes of the two places, as OPEN▪ FP: LP, FP: RP, FP: AP, FP: together with the angle contained between them, that is the difference of their Longitudes: whereby FAVORINA: FOYES: FL: FS, the distances of the sins of Latitude being found by 〈◊〉 2, 3, 4, 5, Copernic. de Triang. planis, the lines also subtending the distances of the places may most easily be found by the 3. Copernic. de Triang. plan. For the squares of the distance of the sins and of the difference of the sins of their Latitudes (if both be Northerly or both Southerly) or of the sum of the sins of their Latitudes (if one be Northerly▪ another Southerly) are equal to the square of the line subtending the distance of the places 5. e 12. Ram. 47. pr. 1. Eucl.  
With no less facility also by help of the former Tables, and the Canon of Triangles, any two places being given, there may Arithmetically and most exactly be found out, first, by their Longitudes and Latitudes, the Rumb, and distance measured in the Rumb: secondly, by their distance, and Latitudes, the Rumb and difference of Longitude: thirdly, by their Rumb, and Latitudes▪ the distance and difference of Longitude: fourthly, by their Longi●udes, Rumb, and one Latitude, the other Latitude and Distance: five, by the Rumb distance and one Latitude, the other Latitude, and the difference of Longitude; or any other Nautical or Geographical problem that by the Chart may mechanically be performed: and the whole Art of Navigation Arithmetical (as some call it) may as easily be practised: So as having only the Longitudes and Latitudes of the places (by which, and to which you are to Sail) set down in a Table, you may by Arithmetical Calculation only (if you list take the pains without any Chart, Map or Globe▪ show the Course and Distance from any place to other▪ and so give most exact direction for the performance of an whole Voyage to any known place assigned, how oft soever you have traversed or been tossed this way, and that way, by reason of scant, violent, or contrary winds, or any other occasion.  
But seeing the first grounds of this Art, that is, the observations of the Latitudes, but especially of the Courses at Sea, can not but be far from such exquisite truth as is to be found in those Arithmetical operations: how exact soever you be in the rest of the means, you can look for no more truth in conclusion then such as is answerable to the first grounds and principles, out of which the conclusion is gathered. So as the Mariner shall not need to trouble himself any further herewith, but only to cast up his accounts upon the Chart truly made (as before is showed) which of all other is most fit and ready for his ordinary use. Now therefore it may be sufficient, only to show how the former Problems may mechanically be performed upon the Nautical Planisphaere before described.  
First, by the Longitudes and Latitudes of both places given, the Rumb and Distance may thus be found: 
1. By the longitudes and latitudes of two places, to find the rumb and distance.  Draw parallels by both Latitudes: take the distance of those parallels: according to which distance draw a parallel to the Equinoctial. Then from the end of the difference of Longitude, reckoned from the concourse of the Rumbs in the Equinoctial erect a perpendicular crossing the said Parallel: A line drawn by this crossing from the concourse of the Rumbs is the Rumb of the two places. Now to find out the Distance, take so many degrees of the Equinoctial as the difference of Latitude containeth: and guiding one foot of the Compasses in the Equinoctial, with the other foot carried parallel-wise at equal distance from the Equinoctial, cross the Rumb newly found out: take the distance of this crossing from the concourse of the Rumbs, and set both feet of the Compasses in the Equinoctial, for the degrees contained between them show you the distance desired.  

2. By the distance and latitudes, to find the rumbe and difference of longitude.  Secondly, by the distance and latitudes (knowing which place is more Eastwards, or Westwards) the Rumb and difference of Longitude is thus found: Take with the compasses so many degrees and minutes of the Equinoctial as the difference of Latitude containeth: According to that distance draw a parallel to the Equinoctial; take so many degrees of the Equinoctial with your Compasses as the distance given cometh to: then one foot being set in the concourse of the Rumbs in the Equinoctial, with the other cross the parallel aforesaid: A line drawn by that crossing from the concourse of the Rumbs in the Equinoctial giveth you the Rumb desired. Then both Laititudes being noted in the graduated Meridian, therein take their difference with the Compasses, and guiding one foot in the Equinoctial▪ with the other carried at that distance parallel-wise from the Equinoctial cross the Rumb of the two places, the distance of that crossing from the Meridian (that cometh from the common meeting of the Rumbs in the Equinoctial) taken with the Compasses, and brought to the Equinoctial, shall there show you the difference of Longitude. Or a perpendicular to the Equinoctial from that crossing shall point you out therein, the difference of longitude.  
Thirdly, 
3. By the Rumb and latitudes to find the distance and difference of longitude.  by the Rumb and Latitudes (being both Northerly or both Southerly) the distance and difference of longitude is thus found: Take the difference of Latitudes in the Equinoctial: according to that distance draw a parallel to the Equinoctial (as before crossing the Rumb of the two places given: take the distance of this crossing from the concourse of the Rumbs: Then both feet of the compasses set in the Equinoctial will show the distance of the places. The difference of Longitude is found as before.  
Fourthly, 
4. By the longitudes, rumb, and one latitude, to find the other latitude and the distance.  by the longitudes, Rumb and one Latitude (knowing whether it be the lesser or greater) to find the other Latitude, and the distance, do thus: From the point of concourse of the Rumbs in the Equinoctial count the difference of longitude: from hence erect a perpendicular crossing the Rumb: the distance of this crossing from the Equinoctial translated into the graduated Meridian (setting one foot in the known Latitude, and extending the other Northwards or Southwards according as the unknown Latitude is greater or lesser) shall show you the Latitude desired. Now to find the distance, work as before in the first Problem.  
Fiftly, by the Rumb, distance and one Latitude, you may find the other Latitude and the difference of Longitude after this manner: 
5 By the Rumb, the distance, and one Latitude, to find the other Latitude and the difference of Longitude  Take the distance given with the Compasses in the Equinoctial: set one foot in the concourse of the Rumbs, and with the other cross the Rumb given: from this crossing draw a perpendicular to the Equinoctial: the length of that perpendicular taken with the compasses and brought into the Equinoctial, shall show you the difference of Latitude. Thus having both Latitudes given, the difference of longitude may also be found as before. Prob. 2.  
Now in every one of these Problems there may be some particular cases whereof some diversity of working may arise, yet such as can breed but small trouble to him that well doth conceive the reason of that is already set down in these five former Problems: which are especially to be applied to such places as are both on the same side of the Equinoctial, and differ also both in Longitude and Latitude: of which sort is the greatest number, and in which the greatest use, and most difficulty of working consisteth. To prosecute every particularity at large (whereof some perhaps less acquainted with the reason of these Mathematical practices may be desirous) would be now for me too long and tedious. For some taste therefore of the use of this Nautical Planisphere, let thus much for this time briefly suffice.   

CHAP. XIII Error in the use of the Compass, by the Variation neglected, and how to observe and avoid the same.  
NExt the Sea-chart there is not any instrument of Navigation whereby greater error may ensue then by the Compass, if the Variation be neglected▪ By which neglect alone we may often times miss an whole Point and more, in directing the Course from place to place. Notwithstanding, M. Peter of Medina laboureth greatly to prove that there is no Variation of the Compass, and that many inconveniences and absurdities must needs follow out of that opinion (as he esteemeth it) thinking it to have no better ground than the gross and erroneous observations of unskilful Mariners, as by the third Chapter of his sixth book of the Art of Navigation, may appear more at large. But daily experience (by many and diligent observations, with exact instruments, heedfully used by skilful Observers, not only at sea, the unconstancy whereof (which causeth the ship to be always unsteady) might give some colour to M. Peter's conceit of no Variation: but also on firm land, where most steady and certain observation may easily be made:) I say daily experience hath so often, so constantly, so manifestly proved this varying property to be in the Compass, that it cannot by any means with reason be denied.  
Now then for the better finding of this Variation there must be conceived two Meridian's; a true Meridian, and a Magnetical Meridian: also a true Azimuth, and a Magnetical Azimuth of the Sun.  
The true Meridian is an Azimuth passing by the Poles of the world▪  
The Magnetical Meridian is an Azimuth that passeth by the points of the wires in the Compass, or of the Needle touched with the Loadstone.  
The true Azimuth of the Sun is showed by the arch of the Horizon contained betwixt the Azmiuth of the Sun, and the true Meridian.  
The Magnetical Azimuth of the Sun is showed by the arch of the Horizon contained between the Magnetical Meridian and the Azimuth of the Sun.  
The difference of these two arks of the Horizon is always equal to the Variation of the Compass.  
To find out the Magnetical Azimuth of the Sun, we must first know upon what point of the Compass the Sun is: which although it may be done by aim very near the truth by him that is experienced, especially when the Sun is low, or at the Horizon, rising or setting: yet it may better be done with help of such a ruler and sights, as land-measurers use with their Plain Tables, wherewith you may thus find upon what point of the Compass the Sun is: Lay the edge of the ruler right over the centre of the Compass: then holding the ruler so fixed, and the Compass level so near as you can aim, turn it about until the midst of the Sunbeams passing through one of the sights▪ fall alongst upon the edge of the ruler, or midst of the opposite sight. Then holding your eye in such sort over the Compass, that the ruler's edge may lie right upon the centre of the Fly, look also upon what point of the Compass the edge of the ruler lieth to the Sun-wards for that is the point whereupon the Sun is at that time: which for brevity's sake may be called the Sun's point. This point you shall look in the instrument following, and it shall show you amongst the degrees the Magnetical Azimuth of the Sun, As for example, when the Sun is due East by the Compass, I would know in what Magnetical Azimuth he is: Therefore I look the East point in this Instrument, which directeth me to 84 degrees. which is the Magnetical Azimuth desired, And the difference betwixt this and the true Azimuth of the Sun is the Variation of the Compass, which we seek for. This difference therefore shall thus be found out: At the same time when you observe the Sun's point, let the height of the Sun be also observed. It is best to take both these observations about the midst of the forenoon, or afternoon, for then the height of the Sun altereth quickly, and the Refraction and Parallax cannot much deceive you; therefore at that time the true Azimuth of the Sun shall easily be known thus: First find-out the Declination of the Sun, remembering always to give allowance, or take away (according as the Declination increaseth or decreaseth) for the place and time of your Observation: Then set your Astrolabe to the Latitude of the place where you observe, and follow the Parallel of the Sun's Declination, until you come to the Almicantarath or height of the Sun known by observation: for the Azimuth that passeth by their mutual intersection is the true Azimuth of the Sun that was sought for: which if you follow down to the Horizon, you shall have that Azimuth given. Now of these two given Azimuths (that is the true and Magnetical Azimuth of the Sun) subtract the lesser from the greater, for the difference remaining is the Variation of the Compass: the denomination whereof (that is, whether it be Easterly or Westerly) shall easily be discerned thus: if the true Azimuth of the Sun counted from the South point in the forenoon, be less than the Magnetical Azimuth, the Variation is Easterly: otherwise it is Westerly. chose, in the afternoon: if the true Azimuth of the Sun be greater than the Magnetical Azimuth, the Variation of the Compass from the point of true North is Eastwards, otherwise it is Westwards. And for the better understanding of these rules, I have in the Table following exemplified them by such Observations as I took both at Sea and Land, in the year 1589.  
The instrument following is then to be used when Observation is made, as before hath been showed, by a Compass, wherein the North points of the wires are set half a point to the Eastwards from the North point of the Compass (of which sort are the Compasses that are commonly used by English Mariners) whereas if the points of the w●res were set just under the points of North and South: and the circumference of the Compass divided into degrees both Eastwards and Westwards, beginning at the North and South points▪ and ending with 90 at East and West: we might at the first have the Magnetical Azimuth of the Sun by Observation, and so there should be no need of this Instrument.  
In the Table here following the letters N, W, S, E, b, in the first and second columns, signify North, West, South, East, by. The fractions in the second column are parts of the point whereto they are annexed. In the column entitled▪ The time of Observation. the letters BN, and AN signify, before noon and After noon.  
An Instrument for the ready finding of the Sun's Magnetical Azimuth by the ordinary Compass.  
The place of Observation. The Sun's point of the Compass. The height of the sun The Sun's Magnetic. Azimuth.   Deg Min Deg Min About twenty leag. from Spain. W WNW ⅓ N 0 0 69 30 30 or 40 leagues from Spain. W EVEN ½ E 0 0 56 15 About midway betwixt Lisbon and Saint Mic●●●ls. EVEN 0 0 61 40 WNWS 0 0 73 7 Betwixt S. Michael's & Tercaera. E by N ⅕ N 2 0 70 52 About 3. leag. from Tercaera SSW E by N ¼ N 2 30 70 53 At Saint Cruz in Flores.  29 25 83 30 These Observations made in the town of Fayal and the former also at S. Cruz in Flores were taken by M. William Borowes Instrument of Variation (published in his book of the Variation of the Compass) and by a Quadrant, whose semidiameter was almost three foot.  18 0 73 0  16 36 74 40  20 30 62 20  20 0 62 54  19 20 63 35  18 16 64 45  30 41 57 15  46 13 17 53  46 18 16 36  40 42 32 45 or 4 leagues from Tercaera SE EASE ¼ E 0 0 75 50 From S. Mary's W by S 6 leagues WSW 13 0 61 50 From S. Mary's W by S 6 leagues W by S ½ 0 0 67 25 From S. Mary's South 5. leagues EASE ½ S 0 0 69 30 From Saint Mary's 16 leagues EASE ¼ E 0 0 75 50 NWS by W Northerly. EASE 2 30 73 7 ½ From S. George's SE by E 3 leag EASE ¼ E 0 0 75 50 From the East part of S. Michael WSW ¼ S 0 0 59 0 NE by N, about 15 or 20 leag. EASE ¼ E 0 0 70 23 From the rock W about 66 leag. SE by S ⅙ S 26  37 30 From C. Finisterre N Easterly EASE ½ S 0  67 30 EASE ⅔ S 2  65 37 sweet 11  39 22 The Time of Observation. The Latitude of the place of observation The Declination of the Sun. The true Azimuth of The Sun. The Variation of the Compass The middle Variation. The part of Variation   De. Mi De. Mi De. Mi De. Mi De. Min.  jul. 9 AN 39 50 20 53 62 0 7 30   Eastward 12 BN 39 0 20 25 63 20 6 45   Eastward 23 BN 38 0 17 55 67 0 5 20 5 38 Eastward 23 AN 38 0 17 46 67 10 5 57 Eastward Aug 8 B N 38 20 13 13 74 10 3 18   Eastward 9 BN 38 20 12 54 75 0 4 7   Eastward 14 AN 39 50 11 5 79 30 4 0   westward Se. 13 AN 38 54 0 8 74 35 1 35 3 5 Eastward 13 AN 38 54 0 9 76 0 1 20 Eastward 22 AN 38 54 3 39 67 10 4 50 Eastward 22 AN 38 54 3 39 67 30 4 36 Eastward 22 AN 38 54 3 30 68 15 4 40 Eastward 22 AN 38 54 3 40 69 20 4 35 Eastward 23 BN 38 54 3 53 54 20 2 55 Eastward 23 BN 38 54 3 54 14 0 3 53 Eastward 23 BN 38 54 3 54 13 30 3 6 Eastward 23 AN 38 54 4 0 35 15 2 30 Eastward Oc. 18 BN 38 20 13 5 73 0 2 5   Eastward 23 AN 37 0 14 50 60 0 1 50 0 55 Westward 23 AN 37 0 14 51 71 5 3 40 Eastward 24 BN 37 0 15 2 70 50 3 20 Westward 26 BN 37 30 15 38 69 50 6 0 5 34 Eastward 26 BN 37 30 15 39 68 0 5 7 Eastward 28 BN 38 40 16 16 68 45 7 5   Eastward No. 1 AN 38 40 17 30 67 10 8 10   Eastward 2 BN 38 40 17 41 66 50 3 33   Eastward 6 BN 38 35 18 43 31 0 6 30   Eastward 12 BN 44 25 20 5 61 0 6 30 7 4 Eastward 12 BN 44 25 20 5 58 0 7 37 Eastward 12 AN 44 30 20 11 46 15 6 52 Eastward  
Notwithstanding there be much difference betwixt some of these Variations taken at the same place with the same Instruments, yet we used with what diligence we could such Instruments as then we had prepared for that purpose: which I speak, that others that shall go about hereafter to observe the Variation (at Sea especially) may be the more circumspect to foresee and prevent all causes of error herein. Exact truth amongst the unconstant waves of the Sea is not to be looked for, though good Instruments be never so well applied to their use. Yet with heedful diligence we may come so near the truth, as the nature of the Sea and of our sight and Instruments will give us leave. Neither if there be some disagreement betwixt Observations, are they all by and by to be rejected. But as when many arrows are shot at a mark, and the mark afterwards taken away, he may be thought to work according to reason, who to find the place where the mark stood, shall seek out the middle place amongst all the arrows: so amongst many different Observations, the middlemost is likest to come nearest the Truth.  
Causes of error herein: Some cannot be avoided, as the unsteadiness of the Ship, the imperfection of the sense and Instruments, the weak respective force of the needle or wires, be they never so well touched. Others may be eschewed, as that there be no iron near the Compass in the time of Observation, that the wires be kept clean from rust, and that they be not kept too long untouched from the stone, that such Instruments be used for Observation as need least working afterwards for finding out the Variation: wherein the Instruments heretofore published for this purpose, are faulty; being such as serve for Observation only o● Land: as also requiring many workings afterwards, unfit for Mariners before the matter can come to issue, wherein are as many lurking holes of error, without great diligence. I have therefore here set down the making and use of a certain Instrument, whereby the Variation of the Compass and time of the day is presently given, together with the Observation (the Latitude of the place being known) and that universally throughout the World, both at Sea and Land. As also the Variation being given, the height of the Pole, and hour of the day may thereby be known, without those inconveniences, wherewith Martin Curtis his instrument, Chap. 11. part 3. of the Art of Navigation, and Michael Coignet his Nautical Hemisphere, are much encumbered: to omit the Observation of the height of the Sun, which (as I have oft made trial at Sea) may thereby be more exactly performed, then hath been hitherto by Staff, Ring, or Astrolabe, as they are commonly used.  

The making of the Searings.  
The figure of the Searings.  
Upon the concave side of the innermost Ring let be described the degrees of the Sun's declination, for the right placing of the little bead upon the thread according to the time of the year. Which may easiliest be done after this manner.  
The bead being thus rightly placed, put aside the Equinoctial Ring from the brass pointer (representing the Pole Actick) that it may cross the meridian at right angles, which it shall precisely do, if you bring the prick or little hole, upon the outside of the innermost circle to the end of the foresaid brass pointer, so as the end thereof may enter thereinto. Then set the line that is drawn from the end of the brass pointer, to the elevation of the Pole at the place of your Observation, and so have you all parts of your Instrument rightly placed for Observation.  
Now when you will make Observation with this Instrument, 
The use of this Instrument.  hang the same by this Ring upon your finger, as you do when you Observe the height of the Sun with the Astrolabe, turning the foresaid brass pointer Northwards, till you find the midst of the shadow of the bead to fall upon the periphery, drawn round about through the midst of the concavity of the Equinoctial ring, which periphery we called the parallel of the Sun: and so keep the whole Instrument and Compass as steady as you can, till the fly of the Compass remain quiet and still; keeping in the mean time the midst of the shadow of the bead always upon the foresaid parallel of the Sun; and withal looking close by the graduated side of the Meridian, directly down upon the midst of the Compass; and mark what degree and minute you see close thereby in the North part of the Fly: for so much as the North point of the needle or wires is from thence towards the East or West, so much is the Variation Eastwards or Westwards. And the shadow of the bead lighting upon the Parallel of the Sun showeth the hour and time of the day.  
The best time for the taking of these Observations is about the midst of the forenoon or afternoon, because that about those times the height of the Sun altereth quickly, and his Refraction also can breed no sensible error. But because there be many that want both this Instrument, and also the Globe and Astrolabe beforementioned, I have for their sakes thought it good to set down a way whereby (the Declination and height of the Sun being given, together with the Latitude of the place) the Sun's true Azimuth may be found with Ruler and Compasses only, after this manner: Draw the circle ABCDEFGH, representing the Meridian, by the centre hereof draw the diameter, of the Horizon AF. From A the end of this diameter, reckon the elevation of the Equinoctial AC; from whence draw a line by the centre (which may be called the diameter of the Equinoctial) AC; from C the end of this diameter count the declination of the Sun CD; thereby draw a Parallel to the diameter of the Equinoctial, which may be called the diameter of the Sun's Parallel DG: Likewise from the diameter of the Horizon count the height of the Sun AB, known by Observation, and thereby also draw BE a Parallel to the diameter of the Horizon, which may be called the diameter of the Suns Almicantar. From I, the intersection of these two Parallels, draw IK, a line perpendicular to the diameter of the Horizon. Then setting one foot of the Compasses in L, the midst of BE the diameter of the Suns Almicantar, and stretching out the other foot to B the end of this diameter: from thence draw therewith the arch BK till you come to the said perpendicular: This arch resolved into degrees shall give you the true Azimuth of the Sun.    

CHAP. XIIII. To find the Inclination or dipping of the Magnetical needle under the Horizon.  
First the angle OAR is given because of the arch OBR, measuring the same 150 degrees and consequently the angle at R 15 degrees being equal to the equal sided angle at O; both which together are 30 degrees because they are the compliment of the angle OAR (150 degrees) to a semicircle or 180 degrees.  
Secondly, in the Triangle ARS all the sides are given, ARE the Radius or semidiameter 10,000,000: RS equal to RO the subtense of 150 degrees 19,318,516: and AS equal to AD triple in power to AB, because it is equal in power to AB and BD, that is BOY; which is double in power to AB. Or else thus: The arch OB being 90 degrees, the subtense thereof OB, that is, the Tangent BD is 14,142,126, which sought in the Table of Tangents, shall give you the angle BADE 54 degrees 44 minutes 8 seconds: the Secant whereof is the line AD that is AS 17,320,508. Now then by 4 Axiom of the 2 book of Ptisc. As the base or greatest side SIR 19,318,516 is to the sum of the other two sides SA and ARE 27,320,508; so is the difference of them SX 7,320,508 to the segment of the greatest side SY 10,352,762; which being taken out of SIR 19,318,516, there remaineth YOUR 8,965,754, the half whereof RZ 4,482,877, is the sine of the angle RAZ 26 degrees 38 minutes 2 seconds, the compliment whereof 63 degrees 21 minutes 58 seconds is the angle ARZ, which added to the angle ARO 15 degrees maketh the whole angle ORSEOLO, 78 degrees ●1 minutes 58 seconds; whereof 60/90 make 52 degrees 14 minutes 38 seconds which taken out of ARZ 63 degrees 21 minutes 58 seconds there remaineth the angle TRA 11 degrees 7 minutes 20 seconds the compliment whereof is the Inclination sought for, 78 degrees, 52 minutes, 40 seconds.  
The sum and difference of the sides SA and ARE being always the same, viz. 27,320,508 and 7,320,508, 
A shorter way to calculate the Table of Magnetical Inclination▪  the product of them shall likewise be always the same, viz. 199,999,997,378.064 to be divided by the side SIR that is RO the subtense of RBO. Therefore there may be some labour saved in making the Table of Magnetical Inclination, if in stead of the said product you take continually but the half thereof that is 99,999,998,689,032, and so divide it by half the subtense RO, that is, by the sine of half the arch OBR. Or rather thus: As half the base RS (that is, as the sine of half the arch OBR) is to half the sum of the other two sides SA and ARE 13,660,254, so is half the difference of them 3,660,254 to half of the segment SY, which taken out of half the base, there remaineth RZ the sine of RAZ, 
The Table of Magnetical Inclination.  First col. Second col. First col· Second col First col▪ Second col. Height of the Pole Magnetical Inclination. Height of the Pole. Magnetical Inclination. Height of the Pole. Magnetical Inclination· Degrees Degr. Min. Degrees Degr. Min Degrees Degr. Min. 1 2 11 31 52 27 61 79 29 2 4 20 32 53 41 62 80 4 3 6 27 33 54 53 63 80 38 4 8 31 34 56 4 64 81 11 5 10 34 35 57 13 65 81 43 6 12 34 36 58 21 66 82 13 7 14 32 37 59 28 67 82 43 8 16 28 38 60 33 68 83 12 9 18 22 39 61 37 69 83 40 10 20 14 40 62 39 70 84 7 11 22 4 41 63 40 71 84 32 12 24 52 42 64 39 72 84 57 13 25 38 43 65 38 73 85 21 14 27 22 44 66 35 74 85 44 15 29 4 45 67 30 75 86 7 16 30 45 46 68 24 76 86 28 17 32 24 47 69 17 77 86 48 18 34 0 48 70 9 78 87 8 19 35 36 49 70 59 79 87 26 20 37 9 50 71 48 ●0 87 44 21 38 41 51 72 36 81 88 1 22 40 11 52 73 23 82 88 17 23 41 39 53 74 8 83 88 33 24 43 6 54 74 52 84 88 47 25 44 30 55 75 35 85 89 1 26 45 54 56 76 17 86 89 14 27 47 15 57 76 57 87 89 27 28 48 36 58 77 37 88 89 39 29 49 54 59 78 15 89 89 50 30 51 11 60 78 53 90 90 0 whose compliment to a quadrant is the angle sought for ARZ.  
According to this Diagram and demonstration, was calculated the Table here following; the first column whereof containeth the height of the Pole for every whole degree; the second column showeth the Inclination or Dipping of the Magnetical Needle answerable thereto in degrees and minutes.   

CHAP. XV. Error in using the cross-staff, and how they may be avoided.  
AFter the Chart and Compass, the cross-staff may with good reason succeed, as in the use whereof more error is committed, then in any other Instrument of Navigation, the two former excepted; and that four several ways: First in neglecting the Paralax or eccentricity of the eye: Secondly, in not considering the height of the eye above the Water: Thirdly and Fourthly, in not regarding the Paralax and Refraction of the Sun.  
For the first, they count the height of the Sun and Stars in such sort as if the centre of the eye, or vertex of the visual cone in using the Staff, were even with the end thereof, that is set to the eye. Therefore how much the centre of the sight is distant from the end of the Staff, so much are they deceived. But how much the eccentricity or Paralax of the eye is, it may be known after this manner: Make two Transversaries, the one twice so long as the other. The longest of these two set fast at the further end of the Index, the other of them move up or down upon the Index, until such time that your eye placed at the end of the Index (in such sort as you use to place it when you observe) you may see both ends of both Transversaries lie even together. For then look how much the segment of the Index betwixt the two Transversaries exceedeth the segment from the shorter transversary unto the eye, so much is the Parallax or eccentricity of your sight, or the point wherein your eye, wherein the visual beams concur, is so much distant from the end of the Index.  
As for example, in this figure let the transversary HEI placed at E the end of the Index be double to the transversary FDG, which is placed in such sort upon the Index, that the visual lines (AFH, AGI) of the eye placed at the end of the Index, do pass strait on by FH and GI'▪ the ends of the Transversaries. For in this figure, A is the centre of the sight or eye, wherein the visual lines (AFH, AGI) do concur: B representeth the end of the Index, placed at the corner of the eye, and then AB is the eccentricity: C signifieth the end of the Index set against the bone underneath the eye, for observing of distances, and then AC is the eccentricity, which is thus demonstrated:  
Secondly, they increase the former error by not regarding the height of the eye above the Water. Which although it be not so great a fault as the other, yet it may deceive them by increasing the former error, five or six minutes or more in a tall Ship. For the higher the eye is above the water, the greater is the angle contained betwixt the two visual lines, whereof one toucheth the convex superficies of the Sea, the other passeth on to the Sun or Stars: And the lower the eye is, the less is the foresaid angle: and then only it showeth the true Altitude, when the centre of the sight is in the same line of level with the superficies of the Water. But if the eye be higher than the Water, that angle is greater than the true Altitude, and therefore subtraction must be made accordingly, that you may have the true Altitude.  
Now to find how much it is that should be subtracted at any height of the eye above the Water there be two ways; the one without knowledge of the Earth's semidiameter, the other with knowledge of the same. For the first, you must have some such convenient place at the Water side where you may have a free and clear prospect unto the Sea without impediment, and where you may also have such provision made, that you may place both yourself, and also an exact and large Water Level in convenient manner to make exact observation at what height soever you desire above the superficies of the Sea, till you come to the height of the tallest Ships that go upon the Seas: that level having the sight that you must look through at the end thereof next the eye so fitted, that you may both easily and steadily set it higher than the fore sight (that is the sight that is at the fore-end of the Level) so much as shall be needful to lay the foresight precisely to the touching of the Sea; and that you may also perfectly know how much the back-sight, or sight at your eye, is higher than the foresight above the line of Level: For by the difference of the heights of those sights above the line of Level, and the distance between them, it may easily be found how much the visual line touching the roundness of the Sea, Dippeth under the line of level, or true Horizon, from whence the height of the Sun and Stars is to be accounted, thus: As the distance betwixt the sights is to the difference of their heights above the line of level; so is the whole sine to the Tangent of the angle of Dipping, which we desired to know.  
This angle may otherwise be found, the quantity of the Earth; semidiameter being first known, which is to be done divers ways; but they may be all reduced to two heads or kinds, whereof the first requireth the certain measure of some arch of the Meridian to be first given, which is also divers ways to be performed. But the best and perfectest way of all others is to observe so axactly as is possible the Summer solstitial Altitude of the Sun at two places, 
A most exact way to find the quantity of the Earth's semidiameter  so far distant asunder, and lying so near North and South each from other with so direct and fair a way between them as conveniently may be chosen. Suppose for example Portsmouth and Barwick, or some other place in the furthest parts of Scotland; for the further these places are each from other, the more perfectly may this business be performed. Then measure, and plate down so truly as is possible all the way between those two places, with all the turnings and windings, ascents and descents that are therein; out of which the arch of the great circle, or shortest distance betwixt them. together with the angle of declination thereof from the true Meridian line truly found by observation at either of those places, may most exactly be known: whereby (with help of the doctrine of right angled spherical triangles) the difference of the latitudes of those two places in miles and forlongs etc. may easily appear; which compared with the difference of the latitudes of the same places, found by observation of the Sun in degrees and minutes, etc. will show how many miles and furlongs answer to one, or more degrees of the meridian: and so the whole circumference, diameter, and semidiameter of the earth will easily, and more truly be found, than any other way yet used for this purpose. But means convenient for the trial hereof have hitherto been wanting, and so I must omit it, till some better opportunity, if any shall befall hereafter, by the bounty of any such as are of more ability to bear the charge hereof. Yet besides our purpose now in hand, this would be the best ground that can be both for the making and continuing of a Standard, and all other measures thereon depending, at a certainty for ever; insomuch that although all the Standards, weights and measures in the world were lost, they might notwithstanding upon record of such Observation and means as here we have mentioned, be again restored much more perfectly then by the ordinary way of beginning all our measures from a barley grain taken out of the midst of the Ear, whereof there is no such certain determinate bigness that can be set down, but that they may be something greater in one Ear then another; neither can there be any certain rule or reason given how to know which Ear to choose rather than other▪ for this purpose. And if any error be committed herein, though insensible (which cannot be avoided) yet in going about to make other greater measures by often taking this least▪ and so proceeding à minimis ad maxima, so often as you take your first or least measure, so often do you increase and multiply your error: which though at the first it seem very small and scarcely perceivable, yet cometh at the last to be very notorious and intolerable. But the other way I here speak of taking the length of all England, or of the whole Island, for our first measure, and out of it by subdivision dividing all the rest, although we may err something in taking the length hereof (which notwithstanding, I dare undertake▪ may be so handled, that it shall not be so much as the thousand part of the whole distance between the two places, before mentioned) yet because we proceed à maximis ad minima, so still dividing, and the more diminishing this error, the further we proceed; it will in the end▪ when we come to our ordinary measures most in use, become very insensible and not worth the regarding  
But to return to our purpose from whence we have a little digressed: The Earth's semidiameter may in like manner be found by Observation of the Meridian Altitudes of any notable fixed Star at the two places before mentioned: but because the heights of Stars cannot by any means be so exactly observed as the height of the Sun may be; the difference of the Latitudes of the two●places and consequently the Perimeter (that is the Circuit or Compass and the diameter of the Earth cannot be so perfectly found by this way as by the former.  
As for that way which findeth the height of the Sun and so the Latitudes. by the length of the shadow of a 〈◊〉 o● Gnomon perpendicularly erected, it is like to be more uncertain then either of the former. by reason of the scattering and uncertain determining of the end of the shadow; beside the knowledge of the Sun's semidiameter hereunto required, which inconveniences may in the former ways be avoided.  
The quantity of the Earth's diameter is also to be found more easily, though not so exactly (without observing any height of Sun or Star, or measuring any arch of the Meridian) by means of some great height given near the Sea side; as namely the height of some high mountain, from whose top you may have a free prospect so far as you can see upon the Sea. Which Maurolycus endeavoureth to do after this manner. 
Clau Comm. in 1 Cap joan. de Sacrobosc.   
But having not hitherto had means requisite to make trial of any of these ways already mentioned, I have thought of another way, whereby the height of the mountain, and consequently the quantity of the Earth's semidiameter may be known; wherein because there is great variety of Opinions amongst the Ancient and later Writers, some making it to be almost 8000 miles; some little more than 5500, some others not much exceeding 5000; others making it less than 3600; and others not much more than 3200, as Alphraganus▪ though Fernelius, according to his Observation, finds it to be 3900 miles, whereas others of late will have it little more than 3000: therefore in so great diversity and uncertainty of opinions, I took it to be the best course, both for mine own and others satisfaction, to rest myself upon such grounds as I could find by mine own experience and observation, and that after this manner:  
First, I made for this purpose an Instrument in form of a right angled Triangle, whose sides containing the right angle were about six foot long; one of which sides was divided into 10,000 equal parts, whereby the degrees and minutes answerable to them were easily to be found out of the Table of Tangents. This Instrument thus prepared and placed flatlings upon his Bases, about three foot above ground, on a hill near Plymouth sound I directed one side thereof about the right angle, as exactly as I could, to the midst of a small Rock, appearing a little above the Sea water, near the great Rock called the Meustone, lying at the entrance of Plymouth sound: Then, as the other side of the Instrument about the right angle directed me, I took my second standing 664 foot by just measure from the first▪ which distance was so much as the ground would well give me leave to take, for otherwise I would have gone further. At this second station I found the angle contained between the visual lines directed to the first station and that small Rock to be 87 degrees. 52 minutes; the Tangent whereof is 26,845 such parts whereof the distance of the standing or whole sine containeth 1000: whereby the distance from the first station to the said small Rock was found to be 17,825 foot: for as 1000 to 26,845; so are 664 foot to 17,825 foot.  
Then coming again to the first station, and setting the Instrument steady up on edge I first directed one of the sides about the right angle (lying near the ground) to the said little Rock, and then a Plumbline hanging at the upper corner of this Triangular Instrument did fall 1 degree 14 minutes from the right angle forwards. After this I directed the same side, as truly as I could, to the very touching of the Spherical superficies of the Sea; and then the Plumbline fell 22 minutes from the same right angle forwards towards the Sea.  
Out of these observations the semidiameter of the earth was found thus: Let O be the centre of the earth. SUCE the circumference of the Sea: B the place of observation. BUFO a perpendicular line drawn from thence to the centre of the earth: BD, the line of Level or true Horizon: BC, the distance from the place of observation to the mark in the Sea 17,825 foot: the angle CBD found by observation 1. degree 14 minutes: BRE a visual line from the place of observation, touching the Sea: E, the point of touching: EBBED, the angle betwixt that visual line and the line of Level or true Horizon, 22 minutes: RCFS, a Parallel to BD, or line of Level drawn by the mark C: OFV, and OPEN, semidiameters of the Seas circumference at the time of observation: ED, the continuation of the semidiameter OE to the line of Level or true Horizon BD.  
Now in the Triangle BCF, rightangled at F, the side BC being 17,825 foot, and the angle at B, 88 degrees 46 minutes, (because it is the compliment of the angle CBD 1 degree 14 minutes) the side FC shall be 17,821 foot; which doubled maketh CFS 35,642 foot, and the angle at C (being the compliment of the angle at B) is 1 degr. 14 minutes.  
Then in the Triangle BCR, the angle at C (being the Compliment of the angle BCF to a semicircle) is 178 degrees 46 minutes, and the angle at B (being the difference of the angel's DBR 22 min. and DBC, 1 degr. 14 minutes) shall be 52 min. and consequently the angle at R (the compliment of the two former, to two right angles) 22 min. Now because in all plain Triangles the sides and Sins of the opposite angles are proportional; therefore as 63,995 (the sine of BRC 22 minutes, in such parts whereof the whole Sine containeth 10,000,000) is to BC 17,825 foot; so is 151,256 the Sine of CBR 52 min. to CR 42,130 foot: which added to CFS 35,642 foot, giveth you the whole line RCFS. 77,772 foot.  
Also in the same Triangle as 63▪ 995 the Sine of BRC 22 min. is to BC 17,825 foot; so is 215,241 the Sine of BCR 178 degrees 46 minutes, to BR 59,95● foot.  
Moreover (by the 36 prop. 3 Eucl.) because the oblong of the Secant RS, and the utter Segment thereof RC is equal to the square of the Tangent RE; therefore multiplying SIR 77,772 foot by RC 42,130 foot, the product will be 3,276,534,360, the square root or side whereof is the line RE 57,241 foot: which added to BR 59,953 foot, maketh the whole line BRE 117,194 foot.  
Lastly, in the Triangle BOD, rightangled at B, because the Tangent BE is perpendicular to ODD by the 16 pr. 3. Eucl. therefore by the 8 pr. 6. Eucl. EBBED and EOB are like Triangles▪ and consequently▪ the angle EOB equal to the angle EBBED 22 minutes. Therefore BE and EO having the same proportion each to other that 6,399,628 the Tangent of BOE 22 min. hath to the whole Sine 100,000,0000, the Tangent BRE being already found to be 117,194 foot, the Semidiameter of the Earth OE shall be 18,312,621 foot.  
And as the same Tangent 6,399,628 is to 20477 the excess of the secant of 22 min. above the whole Sine; so is BRE (117,194 foot) to VB (375 foot) the height of the place of observation above the convexity of the Seas superficies at the same time.  
Hereby it may be easily found, how much the visible or apparent Horizon is lower than the true Horizon, at any other height of the eye above the water, thus: As 375 is to 20477, so is any other height of the eye above the water to a number, which added to the whole Sine, maketh the Secant of the angle that showeth how much the apparent Horizon dippeth under the true Horizon at that height.  
As for example: if the height of your eye above the water be 20 foot, you shall find by the former rule the fourth proportional number to be 1092, which added to the whole Sine 1,000,000,000, maketh 1,000,001,092; which is the secant of 5 min. 5 sec. the angle of dipping answerable to that height.  
After this manner was made this table here adjoined; in the first column whereof is set down the height of the eye above the water, from one foot to 50. The second column showeth how much the visual line touching the sea, dippeth under the true Horizon, at any height of the eye above the water, not exceeding 50 foot. The use of which table is this: When you observe the height of the Sun or Stars at Sea with the cross-staff, you shall also find out how many foot high your eye is above the water with a plumbline or otherwise: 
Height of the eye Angle of dipping Foot min. se 1 1 8 2 1 36 3 1 58 4 2 16 5 2 33 6 2 47 7 3 0 8 3 13 9 3 24 10 3 35 12 3 56 14 4 15 16 4 33 18 4 40 20 5 5 22 5 20 24 5 3● 26 5 40 28 6 1 30 6 13 32 6 25 34 6 38 36 6 49 38 7 0 40 7 11 42 7 21 44 7 32 46 7 42 48 7 52 50 8 2  seek that height in the first column of this Table; and in the second column entitled Angle of dipping, you shall find the number of minutes and seconds that are to be subtracted from the apparent height of the Sun or Stars above the superficies of the Sea, observed with the Staff▪ that you may have the apparent height above the true Horizon.  
The third error hath place in taking the height of the Sun or Moon with the Staff Ring Quadrant, or Astrolabe, or any other Instrument, whether by Sea or Land: but in taking the height of the fixed Stars▪ this error is not to be regarded, being altogether in sensible, by reason of their exceeding great distance from the Earth, which is so much that in comparison thereof the semidiameter of the whole Earth hath not any sensible proportion▪ and therefore the fixed Stars cannot have any sensible Paralax. But the Sun by reason of his lesser distance from the Earth, hath a sensible Paralax, in so much that in taking his height we may for this cause only be deceived sometimes about three minutes▪ by counting it less than indeed it is, and that especially in Winter Time, when the Sun draweth near the Horizon: which although it be no great error, yet it is not altogether to be neglected in the rules and grounds of Art, which so much as is possible, aught to be without error. 
Sun's height Sun's Paralax gr. M Sec 0 3 0 5 2 59 10 2 57 15 2 54 20 2 50 25 2 44 30 2 36 35 2 27 40 2 18 45 2 7 50 1 56 55 1 43 60 1 30 65 1 16 70 1 2 75 0 46 80 0 31 85 0 15   
For this cause I have adjoined this Table following of the Sun's Paralax: the use whereof is this, in the first column entitled Sun's height, look the Sun's apparent height, and in the same line in the Second column, you shall have the Paralax of the Sun, which always is to be added to the apparent height, that so you may have the true height of the Sun above the Horizon. As for example, admit I find the apparent height of the Sun to be 25 degrees therefore I seek that number in the first column, and in the Second column I find the Paralax answerable thereto to be two minutes, 44 seconds, which added to 25 degrees, make the true height of the Sun to be 25 degrees, two minutes, 44 seconds. 
The Suns The Suns The fix St. Altitude. Refraction. Altitude. Refraction. Altitude. Refraction. De. Mi. se De. Mi. se De. Mi. se 0 34 0 23 3 10 0 30 0 1 26 0 24 2 50 1 21 30 2 20 0 25 2 30 2 15 30 3 17 0 26 2 15 3 12 30 4 15 30 27 2 0 4 11 0 5 14 30 28 1 45 5 10 0 6 13 30 29 1 35 6 9 0 7 12 45 30 1 25 7 8 15 8 11 15 31 1 15 8 6 45 9 10 30 32 1 5 9 6 0 10 10 0 33  55 10 5 30 11 9 30 34  45 11 5 0 12 9 0 35  35 12 4 30 13 8 30 36  30 13 4 0 14 8 0 37  25 14 3 30 15 7 30 38  20 15 3 0 16 7 0 39  15 16 2 30 17 6 30 40  10 17 2 0 18 5 45 41  9 18 1 30 19 5 0 42  8 19 1 0 20 4 30 43  7 20 0 30 21 4 0 44  6 21 0 0 22 3 30 45  5      
A fourth cause of error is the refraction of the Beams of the Sun or Stars, which we observe, by reason of the Vaporous thickness of the air that is betwixt us and them, especially when they are near the Horizon. For the finding whereof; not having hitherto had sufficient means by mine own observation for my full satisfaction herein: I have therefore thought good to adjoin these Tables of the Suns and fixed Stars refractions out of Tycho Brahe, which differ little from such observations as I have made for trial hereof: the use whereof is this▪ In the first column seek the Altitude or height of the Sun or fixed Star, and in the second you shall have the refraction answering thereto, which being subtracted out of the observed height, you shall have the height of the Sun or Star remaining, without refraction.   

CHAP. XVI. Faults amended in the Table of the Sun's Declination: commonly called the Regiment of the Sun.  
NOtwithstanding the Sun and Stars are at Sea the most certain marks and guides the Navigator hath, whereby he may direct himself to rectify his course, and know where he is after many turnings, and traversings this way and that way, especially in long Voyages, wherein he may be forced many times by contrary Winds and Calms, to sing with the Poet for many Weeks and Months together.  
Coelum undique & undique Pontus: and  
Nihil est nisi Pontus & aether:  
Yet the Tables of Declinations of the Sun and fixed Stars hitherto published, which I have compared together and examined by observation, are oft times very faulty: the declination of the Sun in them set down, being many times less than truth, by 10, 11, or 12 minutes, especially in the months of February and March: and some of the principal fixed Stars that are of most use in Navigation, differing in declination from that is set down in the Tables more than one whole degree, as I have found by many observations.  
For the easier mending of these faults in the Tables of the Sun's declination, I thought it meet, first, to set down the Table following▪ which showeth the declination of every minute of the Ecliptik in degrees, minutes, and seconds, whereby the place of the Sun is presently known, his declination being first given by observation, and consequently, his Eccentricity and Apogeum were easily found, and the Theoric of the Sun corrected: out of which the Ephemerideses hereafter following, were calculated, showing the true place of the Sun for every day of five years, agreeable, (without notable error) to the truth of the Heavens: and out of these with help of this Table of declination, a new Regiment (or Table of the Sun's declination, for every day of five years) was most easily made: free from such errors wherewith the Tables hitherto published and commonly used, have been too much pestered: as by comparison of this, and those Tables with the observations hereafter following may evidently appear.   

CHAP. XVII Of the Table of declination of every minute of the Ecliptic in degrees, minutes and seconds: Made according to the greatest obliquity of the Zodiac this present age: which by exact observation, is found to bo 23 degrees 31 minutes and an halfe·  
BEcause the table of declination here following, doth differ something from the Table heretofore published by others, whereof some make the greatest declination of the Sun to be 23 degr. and 28 minutes only, as Copernicus and his followers (according to which the Tables of declination and regiments of the Sun, that have been used for the most part by our English Mariners are made): whereas others of late, as that noble Astronomer Thyco Brahe in his second book De recentioribus aetherei mundi phoenomenis, findeth the same to be by his observations 23 degr. 27 mi. pag. 38. 23 degr. 31 mi. pag. 386. 23 degr. 31 mi. 30 sec. pag. 217. (according to which there is a Table of Declination already published by Maginus) and that excellent Geometrician Regiomontanus (whom Petrus Nonius compared by Ramus to Archimedes and Clavius, chose rather to follow) maketh it to be but 23 degr. 30 min. I thought it therefore needful to show what reasons moved me to make choice of the greatest of all the Declinations before recited, being thereunto induced, not only by the authority of that famous Astronomer of our time Tycho Brahe: but resting also upon many and diligent observations of mine own, (taken by a quadrant of more than six foot semidiameter, so exactly made and divided into minutes and half minutes, as I could, and as heedfully used and truly rectified by Plumbline (every time I observed as my sight could discern:) All which observations do prove with one consent, that the greatest declination of the Sun in this our age. is 23 degrees, 31 minutes and an half; as thus it may appear.  
In the year 1594 the 11 and 12 days of june, the apparent Meridian altitude of the Sun was observed to be 61 degr. 58 min. whereto the observations of the 8, 9, 10, 13, 14 and 15 days of the same month do well agree, wherein the apparent Meridian altitudes of the Sun, were 61 degr. 55 ½ mi. 61 degr. 56 ½ mi. 61 degr. 57 mi. 61 degr. 57 ½ mi. 61 degr. 57 mi. 61 degr. 56 mi. almost, as also the observations of the 9, 11, 12 and 13 days of june, in the year 1597 in which days the apparent Meridian altitudes of the Sun, were 61 degr. 57 mi. 61 degr. 58 ½ mi. almost, 61 degr. 58 mi. 61 degr. 57 ½. mi. By all which observations it may be certainly concluded. that the greatest apparent height of the Sun here at London, is 61 degr. and 58 minutes.  
Moreover by many, and heedful observations of the Polestar, taken about the year 1593. and 1594 I found the greatest height thereof at that time here in London, to be 54 degrees, 24 minutes and an half, and the least height 48 degr. 39 ½ minutes the difference of which heights is 5 degrees 45 minutes: the half whereof is 2 degrees 52 ½ min. that is, (the distance of the Polestar from the Pole) at that time added to the lowest height of the Polestar, showeth the height of the Pole at London, to be 51 degrees, 32 minutes: the compliment whereof (38 degrees, 28 minutes) is the height of the Equinoctial, which substracted out of the greatest apparent height of the Sun, 61 degrees 58 minutes: there remaineth the greatest apparent declination of the Sun, 23 degrees 30 minutes: whereto if we add 1 minute 22, seconds, that is the parallax of the Sun answerable to that height, we shall have the greatest true height of the Sun, 61 degrees, 59 minutes, 22 seconds: and consequently the greatest true declination of the Sun for our time, 23 degrees, 31 minutes, 22 seconds, differing but half a quarter of one minute from the greatest declination finally determined and resolvedly set down by Tycho Brahe for this our age 23 degrees, 31 minutes and one half.  

Aries. Libra.   Degr. 0 di Degr. 1 di Degr. 2 di 3 di 4 di 5 di  m gr. mi. se· se gr. m. sec se. gr. mi sec se gr. mi. se se. gr. mi. se. se. gr. mi se se. m. 0 0 0 0 24 0 23 57 24 0 47 53 24 1 11 49 24 1 35 44 24 1 59 37 24 59 1 0 0 24 24 0 24 21 24 0 48 17 24 1 12 13 24 1 36 8 24 2 0 1 24 58 2 0 0 48 24 0 24 45 24 0 48 41 24 1 12 37 24 1 36 32 24 2 0 25 24 57 3 0 1 12 24 0 25 9 24 0 49 5 24 1 13 1 24 1 36 56 23 2 0 49 24 56 4 0 1 36 24 0 25 33 24 0 49 29 24 1 13 25 24 1 37 19 24 2 1 13 23 55 5 0 2 0 24 0 25 57 24 0 49 53 24 1 13 29 24 1 37 43 24 2 1 36 24 54 6 0 2 24 24 0 26 21 23 0 50 17 24 1 14 13 24 1 38 7 24 2 2 0 24 53 7 0 2 48 24 0 26 44 24 0 50 41 24 1 14 37 24 1 38 31 24 2 2 24 2● 52 8 0 3 12 24 0 27 8 24 0 51 5 24 1 15 1 23 1 38 55 24 2 2 48 24 51 9 0 3 36 24 0 27 32 24 0 51 29 24 1 15 24 ●4 1 39 19 24 2 3 12 24 50 10 0 4 0 23 0 27 56 24 0 51 53 24 1 15 48 24 1 39 43 24 2 3 36 24 49 11 0 4 23 24 0 28 20 24 0 52 17 24 1 16 12 24 1 40 7 24 2 4 0 24 48 12 0 4 47 24 0 28 44 24 0 52 41 24 1 16 36 24 1 40 31 23 2 4 23 24 47 13 0 5 11 24 0 29 8 24 0 53 5 23 1 17 0 24 1 40 54 24 2 4 47 24 46 14 0 5 35 24 0 29 32 24 0 53 28 24 1 17 24 24 1 41 18 24 2 5 11 24 45 15 0 5 59 24 0 29 56 24 0 53 52 24 1 17 48 24 1 41 42 24 2 5 35 24 44 16 0 6 23 24 0 30 20 24 0 54 16 24 1 18 12 24 1 42 6 24 2 5 59 24 43 17 0 6 47 24 0 30 44 24 0 54 40 24 1 18 36 24 1 42 30 24 2 6 23 24 42 18 0 7 11 24 0 31 8 24 0 55 4 24 1 19 0 24 1 42 54 24 2 6 47 24 41 19 0 7 35 24 0 31 32 24 0 55 28 24 1 19 24 24 1 43 18 24 2 7 11 23 40 20 0 7 59 24 0 31 56 24 0 55 52 24 1 19 48 23 1 43 42 24 2 7 34 24 39 21 0 8 23 24 0 32 20 24 0 56 16 24 1 20 11 24 1 44 6 24 2 7 58 24 38 22 0 8 47 24 0 32 44 24 0 56 40 24 1 20 35 24 1 44 30 23 2 8 22 24 37 23 0 9 11 24 0 33 8 24 0 57 4 24 1 20 59 24 1 44 53 24 2 8 46 24 36 24 0 9 35 24 0 33 32 23 0 57 28 24 1 21 23 24 1 45 17 24 2 9 10 24 35 25 0 9 59 24 0 33 55 24 0 57 52 24 1 21 47 24 1 45 41 24 2 9 34 24 34 26 0 10 23 24 0 34 19 24 0 58 16 24 1 22 11 24 1 46 5 24 2 9 58 23 33 27 0 10 47 24 0 34 43 24 0 58 40 24 1 22 35 24 1 46 29 24 2 10 21 24 32 28 0 11 11 24 0 35 7 24 0 59 4 23 1 22 59 24 1 46 53 24 2 10 45 24 31 29 0 11 35 23 0 35 31 24 0 59 27 24 1 23 23 24 1 47 17 24 2 11 9 24 30 30 0 11 58 24 0 35 55 24 0 59 51 24 1 23 47 24 1 47 41 24 2 11 33 24 29 31 0 12 22 24 0 36 19 24 1 0 15 24 1 24 11 23 1 48 5 23 2 11 57 24 28 32 0 12 46 24 0 36 43 24 1 0 39 24 1 24 34 24 1 48 28 24 2 12 21 24 27 33 0 13 10 24 0 37 7 24 1 1 3 24 1 24 58 24 1 48 52 24 2 12 45 23 26 34 0 13 34 24 0 37 31 24 1 1 27 24 1 25 22 24 1 49 16 24 2 13 8 24 25 35 0 13 58 24 0 37 55 24 1 1 51 24 1 25 46 24 1 49 40 24 2 13 32 24 24 36 0 14 22 24 0 38 19 24 1 2 15 24 1 26 10 24 1 50 4 24 2 13 56 24 23 37 0 14 46 24 0 38 43 24 1 2 39 24 1 26 34 24 1 50 28 24 2 14 20 24 22 38 0 15 10 24 0 39 7 24 1 3 3 24 1 26 58 24 1 50 52 24 2 14 44 24 21 39 0 15 34 24 0 39 37 24 1 3 27 24 1 27 22 24 1 51 16 23 2 15 8 23 20 40 0 15 58 24 0 39 55 24 1 3 51 24 1 27 46 24 1 51 39 24 2 15 31 24 19 41 0 16 22 24 0 40 19 24 1 4 15 24 1 28 10 24 1 52 3 24 2 15 55 24 18 42 0 16 46 24 0 40 42 24 1 4 39 23 1 28 34 23 1 52 27 24 2 16 19 24 17 43 0 17 10 24 0 41 6 24 1 5 2 24 1 28 57 24 1 52 51 24 2 16 43 24 16 44 0 17 34 24 0 41 30 24 1 5 26 24 1 29 21 24 1 53 15 24 2 17 7 24 15 45 0 17 58 24 0 41 54 24 1 5 50 24 1 29 45 24 1 53 39 24 2 17 31 24 14 46 0 18 22 24 0 42 18 24 1 6 14 24 1 30 9 24 1 54 3 24 2 17 55 23 13 47 0 18 46 24 0 42 42 24 1 6 38 24 1 30 33 24 1 54 27 24 2 18 18 24 12 48 0 19 10 23 0 43 6 24 1 7 2 24 1 30 57 24 1 54 51 23 2 18 42 24 11 49 0 19 33 24 0 43 30 24 1 7 26 24 1 31 21 24 1 55 14 24 2 19 6 24 10 50 0 19 57 24 0 43 54 24 1 7 50 24 1 31 45 24 1 55 38 24 2 19 30 24 9 51 0 20 21 24 0 44 18 24 1 8 14 24 1 32 9 24 1 56 2 24 2 19 54 24 8 52 0 20 45 24 0 44 42 24 1 8 38 24 1 32 33 24 1 56 26 24 2 20 18 23 7 53 0 21 9 24 0 45 6 24 1 9 2 24 1 32 57 23 1 56 50 24 2 20 41 24 6 54 0 21 33 24 0 45 30 24 1 9 26 24 1 33 20 24 1 57 14 24 2 21 5 24 5 55 0 21 57 24 0 45 54 24 1 9 50 23 1 33 44 24 1 57 38 24 2 21 29 24 4 56 0 22 21 24 0 46 18 24 1 10 13 24 1 34 8 24 1 58 2 23 2 21 53 24 3 57 0 22 45 24 0 46 42 24 1 10 37 24 1 34 32 24 1 58 25 24 2 22 17 24 2 58 0 23 9 24 0 47 6 23 1 11 1 24 1 34 56 24 1 58 49 24 2 22 41 24 1 59 0 23 33 24 0 47 29 24 1 11 25 24 1 35 20 24 1 59 13 24 2 23 5 23 0  29  28  27  26  25  24    6 di 7 di 8 di 9 di 10 di 11 di  m gr▪ mi. se s. gr. mi s se. gr. mi se s. gr. mi. se. se gr. mi. se se. gr. mi sec se. m 0 2 23 28 24 2 47 18 23 3 11 4 24 3 34 48 23 3 58 28 24 4 22 5 23 59 1 2 23 52 24 2 47 41 24 3 11 28 24 3 35 11 24 3 58 52 23 4 22 28 24 58 2 2 24 16 24 2 48 5 24 3 11 52 23 3 35 35 24 3 59 15 24 4 22 52 23 57 3 2 24 40 24 2 48 29 24 3 12 15 24 3 35 59 23 3 59 39 24 4 23 15 24 56 4 2 25 4 24 2 48 53 24 3 12 39 24 3 36 22 24 4 0 3 23 4 23 39 23 55 5 2 25 28 23 2 49 17 23 3 13 3 24 3 36 46 24 4 0 26 24 4 24 2 24 54 6 2 25 51 24 2 49 40 24 3 13 27 23 3 37 10 24 4 0 50 23 4 24 26 24 53 7 2 26 15 24 2 50 4 24 3 13 50 24 3 37 34 23 4 1 13 24 4 24 50 23 52 8 2 26 39 24 2 50 28 24 3 14 14 24 3 37 57 24 4 1 37 24 4 25 13 24 51 9 2 27 3 24 2 50 52 23 3 14 38 24 3 38 21 24 4 2 1 23 4 25 37 23 50 10 2 27 27 24 2 51 15 24 3 15 2 23 3 38 45 23 4 2 24 24 4 26 0 24 49 11 2 27 51 23 2 51 39 24 3 15 25 24 3 39 8 24 4 2 48 24 4 26 24 23 48 12 2 28 14 2● 2 52 3 24 3 15 49 24 3 39 32 24 4 3 12 23 4 26 47 24 47 13 2 28 38 24 2 52 27 24 3 16 13 24 3 39 56 23 4 3 35 24 4 27 11 24 46 14 2 29 2 24 2 52 51 25 3 16 37 23 3 40 19 24 4 3 59 24 4 27 35 23 45 15 2 29 26 24 2 53 14 24 3 17 0 24 3 40 43 24 4 4 23 23 4 27 58 24 44 16 2 29 50 24 2 53 38 24 3 17 24 24 3 41 7 23 4 4 46 24 4 28 22 23 43 17 2 30 14 23 2 54 2 24 3 17 48 24 3 41 30 24 4 5 10 23 4 28 45 24 42 18 2 30 37 24 2 54 26 24 3 18 12 23 3 41 54 24 4 5 33 24 4 29 9 23 41 19 2 31 1 24 2 54 50 23 3 18 35 24 3 42 18 24 4 5 57 24 4 29 32 24 40 20 2 31 25 24 2 55 13 24 3 18 59 24 3 42 42 23 4 6 21 23 4 29 56 23 39 21 2 31 4● 24 2 55 37 24 3 19 23 23 3 43 5 24 4 6 44 24 4 30 19 24 38 22 2 32 13 23 2 56 1 24 3 19 46 24 3 43 29 24 4 7 8 23 4 30 43 24 37 23 2 32 36 24 2 56 25 2● 3 20 10 24 3 43 53 23 4 7 31 24 4 31 7 23 36 24 2 33 0 24 2 56 48 24 3 20 34 24 3 44 16 24 4 7 55 24 4 31 30 24 35 25 2 33 24 24 2 57 12 24 3 20 58 23 3 44 40 24 4 8 19 23 4 31 54 23 34 26 2 33 48 24 2 57 36 24 3 21 21 24 3 45 4 23 4 8 42 24 4 32 17 24 33 27 2 34 12 24 2 58 0 24 3 21 45 24 3 45 17 24 4 9 6 24 4 32 41 23 32 28 2 34 36 23 2 58 24 2● 3 22 9 24 3 45 51 24 4 9 30 23 4 33 4 24 31 29 2 34 59 24 2 58 47 24 3 22 33 23 3 46 15 23 4 9 53 24 4 33 28 23 30 30 2 35 23 24 2 59 11 24 3 22 56 24 3 46 38 24 4 10 17 23 4 33 51 24 29 31 2 35 47 24 2 59 35 24 3 23 20 24 3 47 2 24 4 10 40 24 4 34 15 24 28 32 2 36 11 24 2 59 59 23 3 23 44 23 3 47 26 23 4 11 4 24 4 34 39 23 27 33 2 36 35 24 3 0 22 24 3 24 7 24 3 47 49 24 4 11 28 23 4 35 2 24 26 34 2 36 59 23 3 0 46 24 3 24 31 24 3 48 13 24 4 11 51 24 4 35 26 23 25 35 2 37 22 24 3 1 10 24 3 24 55 24 3 48 37 23 4 12 15 23 4 35 49 24 24 36 2 37 46 24 3 1 34 24 3 25 19 23 3 49 0 24 4 12 38 24 4 36 13 23 23 37 2 38 10 24 3 1 58 23 3 25 42 24 3 49 24 24 4 13 2 24 4 36 30 24 22 38 2 38 34 24 3 2 21 24 3 26 6 24 3 49 48 23 4 13 26 23 4 37 0 23 21 39 2 38 58 23 3 2 45 24 3 26 30 24 3 50 11 24 4 13 49 24 4 37 23 24 20 40 2 39 21 24 3 3 9 24 3 26 54 23 3 59 35 24 4 14 13 23 4 37 47 23 19 41 2 39 45 24 3 3 33 23 3 27 17 24 3 50 59 23 4 14 36 24 4 38 10 24 18 42 2 40 9 24 3 3 56 24 3 27 41 24 3 51 22 24 4 15 0 24 4 38 34 23 17 43 2 ●0 33 24 3 4 20 24 3 28 5 23 3 51 46 24 4 15 24 23 4 38 57 24 16 44 2 ●● 57 23 3 4 44 24 3 28 28 24 3 52 10 23 4 16 47 24 4 39 21 23 15 45 2 4● 20 24 3 5 8 23 3 28 52 24 3 52 33 24 4 16 11 23 4 39 44 24 14 46 2 41 44 24 3 5 31 24 3 29 16 24 3 52 57 24 4 16 34 24 4 40 8 23 13 47 2 42 8 24 3 5 55 24 3 29 40 23 3 53 21 23 4 16 58 24 4 40 31 24 12 48 2 42 32 24 3 6 19 24 3 30 3 24 3 53 44 24 4 17 22 23 4 40 55 24 11 49 2 42 56 24 3 6 43 24 3 30 27 24 3 54 8 24 4 17 45 24 4 41 19 23 10 50 2 43 20 23 3 7 7 23 3 30 51 23 3 54 32 23 4 18 9 23 4 41 42 24 9 51 2 43 43 24 3 7 30 24 3 31 14 24 3 54 55 24 4 18 32 24 4 42 6 23 8 52 2 44 7 24 3 7 54 24 3 31 38 24 3 55 19 23 4 18 56 24 4 42 29 24 7 53 2 44 31 24 3 8 18 24 3 32 2 23 3 55 42 24 4 19 20 23 4 42 53 23 6 54 2 44 55 24 3 8 42 23 3 32 25 24 3 56 6 24 4 19 43 24 4 43 16 24 5 55 2 45 19 23 3 9 5 24 3 32 49 24 3 56 30 23 4 20 7 23 4 43 40 23 4 56 2 45 42 24 3 9 29 24 3 33 13 24 3 56 53 24 4 20 30 24 4 44 3 24 3 57 2 46 6 24 3 9 53 24 3 33 37 23 3 57 17 24 4 20 54 23 4 44 27 23 2 58 2 46 30 24 3 10 17 23 3 34 0 24 3 57 41 23 4 21 17 24 4 44 50 24 1 59 2 46 54 24 3 10 40 24 3 34 24 24 3 58 4 24 4 21 41 24 4 45 14 23 0  23  22  21  20  19  18    12 di 13 di 14 di 15 di 16 di 17 di m gr. mi. se▪ se gr. mi. se se gr. mi. se se gr. mi· s. s. gr. mi. s. s. gr. mi. s. s. m 0 4 45 37 23 5 9 5 24 5 32 29 23 5 55 47 23 6 18 59 24 6 42 6 23 59 1 4 46 0 24 5 9 29 23 5 32 52 23 5 56 10 23 6 19 23 23 6 42 29 23 58 2 4 46 24 24 5 9 52 24 5 33. 15 24 5 56 33 23 6 19 46 23 6 42 52 23 57 3 4 46 48 23 5 10 16 23 5 33 39 23 5 56 56 24 6 20 9 23 6 43 15 23 56 4 4 47 11 24 5 10 39 23 5 34 2 23 5 57 20 23 6 20 32 23 6 43 38 23 55 5 4 47 35 23 5 11 2 24 5 34 25 24 5 57 43 23 6 20 55 23 6 44 1 23 54 6 4 47 58 24 5 11 26 23 5 34 49 23 5 58 ● 24 6 21 18 23 6 44 24 23 53 7 4 48 22 23 5 11 49 24 5 35 12 23 5 58 30 23 6 21 41 24 6 44 47 23 52 8 4 48 45 24 5 12 13 23 5 35 35 24 5 58 53 23 6 22 5 23 6 45 10 24 51 9 4 49 9 23 5 12 36 24 5 35 59 23 5 59 16 23 6 22 28 23 6 45 34 23 50 10 4 49 32 24 5 13 0 23 5 36 22 23 5 59 39 24 6 22 51 23 6 45 57 23 49 11 4 49 56 23 5 13 23 23 5 36 45 24 6 0 3 23 6 23 14 23 6 46 20 23 48 12 4 50 19 24 5 13 40 24 5 37 9 23 6 0 26 23 6 23 37 23 6 46 43 23 47 13 4 50 43 23 5 14 10 23 5 37 32 23 6 0 49 23 6 24 0 23 6 47 0 23 46 14 4 51 6 24 5 14 33 23 5 37 55 24 6 1 12 23 6 24 23 24 6 47 29 23 45 15 4 51 30 23 5 14 56 24 5 38 19 23 6 1 35 24 6 24 47 23 6 47 52 23 44 16 4 51 53 24 5 15 20 23 5 38 42 23 6 1 59 23 6 25 10 23 6 48 15 23 43 17 4 52 17 23 5 15 43 24 5 39 5 24 6 2 22 23 6 25 33 23 6 48 38 23 42 18 4 52 40 24 5 16 7 23 5 39 29 23 6 2 45 23 6 25 5● 23 6 49 1 23 41 19 4 53 4 23 5 16 30 23 5 39 52 23 6 3 8 24 6 26 19 23 6 49 24 23 40 20 4 53 27 24 5 16 53 24 5 40 15 24 6 3 32 23 6 26 42 23 6 49 47 23 39 21 4 53 51 23 5 17 17 23 5 40 39 23 6 3 55 23 6 27 5 24 6 50 10 23 38 22 4 54 14 24 5 17 40 24 5 41 2 23 6 4 18 23 6 27 29 23 6 50 33 23 37 23 4 54 38 23 5 18 4 23 5 41 25 24 6 4 41 23 6 27 52 23 6 50 56 23 36 24 4 55 1 23 5 18 27 2● 5 41 49 23 6 5 5 23 6 28 15 23 6 51 19 23 35 25 4 55 24 24 5 18 50 24 5 42 12 23 6 5 28 23 6 28 38 23 6 51 42 23 34 26 4 55 48 23 5 19 14 23 5 42 35 23 6 5 51 23 6 29 1 23 6 52 5 23 33 27 4 56 11 24 5 19 37 24 5 42 58 24 6 6 14 23 6 29 24 23 6 52 2● 23 32 28 4 56 35 23 5 20 1 23 5 43 22 23 6 6 37 24 6 29 47 23 6 52 51 23 31 29 4 56 58 24 5 20 24 24 5 43 45 23 6 7 1 23 6 30 10 23 6 53 14 23 30 30 4 57 22 23 5 20 48 23 5 44 8 24 6 7 24 23 6 30 33 24 6 53 37 23 29 31 4 57 45 24 5 21 11 23 5 44 32 23 6 7 47 23 6 30 57 23 6 54 0 23 28 32 4 58 9 23 5 21 34 24 5 44 55 23 6 8 10 23 6 31 20 23 6 54 23 23 27 33 4 58 32 24 5 21 58 23 5 45 18 24 6 8 33 24 6 31 43 23 6 54 46 23 2● 34 4 58 56 23 5 22 21 24 5 45 42 23 6 8 57 23 6 32 ● 23 6 55 9 23 25 35 4 59 19 24 5 22 45 23 5 46 5 23 6 9 20 23 6 32 29 23 6 55 32 23 24 36 4 59 43 23 5 23 8 23 5 46 28 23 6 9 43 23 6 32 52 23 6 55 55 23 23 37 5 0 6 24 5 23 31 24 5 46 51 24 6 10 6 23 6 33 15 23 6 56 18 23 22 38 5 0 30 23 5 23 55 23 5 47 15 23 6 10 29 24 6 33 38 23 6 56 41 23 21 39 5 0 53 23 5 24 18 23 5 47 38 23 6 10 53 23 6 34 1 24 6 57 4 23 20 40 5 1 16 24 5 24 41 24 5 48 1 24 6 11 16 23 6 34 25 23 6 57 27 23 19 41 5 1 40 23 5 25 5 23 5 48 25 23 6 11 39 23 6 34 48 23 6 57 50 23 18 42 5 2 3 24 5 25 28 23 5 48 48 23 6 12 2 23 6 35 11 23 6 58 13 23 17 43 5 2 27 23 5 25 51 24 5 49 11 23 6 12 25 24 6 35 34 23 6 58 36 23 16 44 5 2 50 24 5 26 15 23 5 49 34 24 6 12 49 23 6 35 57 23 6 58 59 23 15 45 5 3 14 23 5 26 38 24 5 49 58 23 6 13 15 23 6 36 20 23 6 59 22 23 14 46 5 3 37 24 5 27 2 23 5 50 21 23 6 13 35 23 6 36 43 23 6 59 45 23 13 47 5 4 1 23 5 27 25 23 5 50 44 24 6 13 58 23 6 37 6 23 7 0 8 23 12 48 5 4 24 23 5 27 48 24 5 51 8 23 6 14 21 24 6 37 29 23 7 0 31 23 11 49 5 4 47 24 5 28 12 23 5 51 31 23 6 14 45 23 6 37 52 23 7 0 54 23 10 50 5 5 11 23 5 28 35 23 5 51 54 23 6 15 8 23 6 38 15 23 7 1 17 23 9 51 5 5 34 24 5 28 58 24 5 52 17 24 6 15 31. 23 6 38 38 24 7 1 40 23 8 52 5 5 58 23 5 29 22 23 5 52 41 23 6 15 54 23 6 39 2 23 7 2 3 23 7 53 5 6 21 24 5 29 45 24 5 53 4 23 6 16 17 23 6 39 25 23 7 2 20 23 6 54 5 6 45 23 5 30 9 23 5 53 27 23 6 16 40 24 6 39 40 23 7 2 49 23 5 55 5 7 8 24 5 30 32 23 5 53 50 24 6 17 4 23 6 40 11 23 7 3 12 23 4 56 5 7 32 23 5 30 55 24 5 54 14 23 6 17 27 23 6 40 3 23 7 3 35 23 3 ●7 5 7 55 23 5 31 19 23 5 54 37 23 6 17 50 23 6 40 57 23 7 3 ●8 23 2 58 5 8 18 2● 5 31 42 23 5 55 0 24 6 1● 13 23 6 41 20 23 7 4 21 23 1 59 5 8 42 2● 5 32 5 2● 5 55 24 23 6 18 30 23 6 41 43 23 7 4 44 22 0  17  16  15  14  13  12    18 di 19 di 20 di 21 di 22 di 23 di  m. gr. mi. se se gr. mi. s se gr. mi. s. s. gr. mi. s. s. gr. mi· se se. gr. mi. se se m 0 7 5 6 23 7 28 0 23 7 50 47 23 8 13 26 23 8 35 58 22 8 58 21 22 59 1 7 5 29 23 7 28 23 23 7 51 10 22 8 13 49 22 8 36 20 23 8 58 43 23 58 2 7 5 52 23 7 28 46 23 7 51 32 23 8 14 11 23 8 36 43 22 8 59 6 22 57 3 7 6 15 23 7 29 9 23 7 51 55 23 8 14 34 22 8 37 5 22 8 59 28 22 56 4 7 6 38 23 7 29 32 22 7 52 1● 22 8 14 56 23 8 37 27 23 8 59 50 22 55 5 7 7 1 23 7 29 54 23 7 52 40 23 8 15 19 23 8 37 50 22 9 0 12 23 54 6 7 7 24 23 7 30 17 23 7 53 3 23 8 15 42 22 8 38 12 23 9 0 35 22 53 7 7 8 47 23 7 30 40 23 7 53 26 23 8 16 4 23 8 38 35 22 9 0 57 22 52 8 7 8 10 23 7 31 3 23 7 53 49 22 8 16 27 22 8 38 57 23 9 1 16 23 51 9 7 8 33 23 7 31 26 22 7 54 11 23 8 16 49 23 8 39 20 22 9 1 42 22 5● 10 7 8 56 23 7 31 48 23 7 54 34 23 8 17 12 23 8 39 42 23 9 2 4 22 49 11 7 9 19 23 7 32 11 23 7 54 57 22 8 17 35 22 8 40 5 22 9 2 26 23 48 12 7 9 42 23 7 32 34 23 7 55 19 23 8 17 57 23 8 40 27 22 9 2 49 22 47 13 7 10 5 23 7 32 57 23 7 55 42 23 8 18 20 22 8 40 49 23 9 3 11 22 46 14 7 10 28 22 7 33 20 23 7 56 5 22 8 18 42 23 8 41 12 22 9 3 33 22 45 15 7 10 51 23 7 33 43 22 7 56 27 23 8 19 5 22 8 41 34 23 9 3 55 23 44 16 7 11 13 23 7 34 5 23 7 56 50 23 8 19 27 23 8 41 57 22 9 4 18 22 43 17 7 11 36 23 7 34 28 23 7 57 13 22 8 19 50 22 8 42 19 22 9 4 40 22 4● 18 7 11 59 23 7 34 51 23 7 57 35 23 8 20 12 23 8 42 41 23 9 5 2 23 41 19 7 12 22 23 7 35 14 23 7 57 58 23 8 20 35 23 8 43 4 22 9 5 25 22 40 20 7 12 45 23 7 35 37 22 7 58 21 22 8 20 58 22 8 43 26 23 9 5 47 22 39 21 7 13 8 23 7 35 59 23 7 58 43 23 8 21 20 23 8 43 49 22 9 6 9 22 38 22 7 13 31 23 7 36 22 23 7 59 6 23 8 21 43 22 8 44 11 23 9 6 31 23 37 23 7 13 54 23 7 36 4● 23 7 59 29 22 8 22 5 23 8 44 34 22 9 6 54 22 36 24 7 14 17 23 7 37 8 23 7 59 51 23 8 22 28 22 8 44 56 22 9 7 16 22 35 25 7 14 40 23 7 37 31 22 8 0 14 23 8 22 50 23 8 45 18 23 9 7 38 22 34 26 7 15 3 22 7 37 5● 23 8 0 37 22 8 23 13 22 8 45 41 22 9 8 0 23 33 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8 6 17 22 8 28 51 22 8 51 16 23 9 13 34 22 18 42 7 21 9 23 7 43 58 22 8 6 39 23 8 28 13 23 8 51 39 22 9 13 56 22 17 43 7 21 32 23 7 44 20 23 8 7 2 22 8 29 36 22 8 52 1 23 9 14 18 23 16 44 7 21 55 22 7 44 43 23 8 7 24 23 8 29 58 23 8 52 24 22 9 14 41 22 15 45 7 22 17 23 7 45 6 23 8 7 47 23 8 30 21 22 8 52 46 22 9 15 3 22 14 46 7 22 40 23 7 45 29 22 8 8 10 22 8 30 43 22 8 53 8 23 9 15 25 22 13 47 7 23 3 23 7 45 51 23 8 8 32 23 8 31 5 23 8 53 31 22 9 15 47 22 12 48 7 23 26 23 7 46 14 23 8 8 55 23 8 31 28 22 8 53 53 22 9 16 9 23 11 49 7 23 49 23 7 46 37 23 8 9 18 22 8 31 50 23 8 54 15 23 9 16 32 22 10 50 7 24 12 23 7 47 0 22 8 9 40 23 8 32 13 22 8 54 38 22 9 16 54 22 9 51 7 24 35 22 7 47 22 23 8 10 3 22 8 32 35 23 8 55 0 22 9 17 16 22 8 52 7 24 57 23 7 47 45 23 8 10 25 23 8 32 58 22 8 55 22 23 9 17 38 22 7 53 7 25 20 23 7 48 8 23 8 10 48 23 8 33 20 23 8 55 45 22 9 18 0 23 6 54 7 25 43 23 7 48 31 22 8 11 11 22 8 33 43 22 8 56 7 22 9 18 23 22 5 55 7 26 6 23 7 48 53 23 8 11 33 23 8 34 5 23 8 56 29 22 9 18 45 22 4 56 7 26 29 23 7 49 16 23 8 11 56 22 8 34 28 22 8 56 51 23 9 19 7 22 3 57 7 26 52 23 7 49 39 22 8 12 18 23 8 34 50 23 8 57 14 22 9 19 29 22 2 58 7 27 15 22 7 50 1 23 8 12 41 23 8 35 13 22 8 57 36 23 9 19 51 23 1 59 7 27 37 23 7 50 24 23 8 13 4 22 8 35 35 23 8 57 59 22 9 20 14 22 0  11  10  9  8  7  6    24 di 25 di 26 di 27 di 28 di 29 di  m. gr. mi. se. se. gr. mi. sec se. gr. mi. se. se. gr. mi. se. s. gr. mi. se s. gr. mi. se. s. M 0 9 20 36 22 9 42 42 22 10 4 38 22 10 26 25 22 10 48 2 21 11 9 28 21 59 1 9 20 58 22 9 43 4 22 10 5 0 22 10 26 47 21 10 48 23 22 11 9 49 22 58 2 9 21 20 22 9 43 26 22 10 5 22 22 10 27 8 22 10 48 45 21 11 10 11 21 57 3 9 21 42 22 9 43 48 22 10 5 44 21 10 27 30 22 10 49 6 22 11 10 32 21 56 4 9 22 4 23 9 44 10 22 10 6 5 22 10 27 52 21 10 49 28 21 11 10 53 22 55 5 9 22 27 22 9 44 32 22 10 6 27 22 10 28 13 22 10 49 49 22 11 11 15 21 54 6 9 22 49 22 9 44 54 22 10 6 49 22 10 28 35 22 10 50 11 21 11 11 36 21 53 7 9 23 11 22 9 45 16 22 10 7 11 22 10 28 57 21 10 50 32 22 11 11 57 22 52 8 9 23 33 22 9 45 38 22 10 7 33 22 10 29 18 22 10 50 54 21 11 12 19 21 51 9 9 23 55 22 9 46 0 22 10 7 55 22 10 29 40 22 10 51 15 22 11 12 40 21 50 10 9 24 17 22 9 46 22 22 10 8 17 21 10 30 2 21 10 51 37 21 11 13 1 22 49 11 9 24 39 23 9 46 44 22 10 8 38 22 10 30 23 22 10 51 58 22 11 13 23 21 48 12 9 25 2 22 9 47 6 22 10 9 0 22 10 30 45 22 10 52 20 21 11 13 44 21 47 13 9 25 24 22 9 47 28 22 10 9 22 22 10 31 7 21 10 52 41 22 11 14 5 22 46 14 9 25 46 22 9 47 50 22 10 9 44 22 10 31 28 2 10 53 3 21 11 14 27 21 45 15 9 26 8 22 9 48 12 22 10 10 6 21 10 31 50 22 10 53 24 22 11 14 48 21 44 16 9 26 30 22 9 48 34 22 10 10 27 22 10 32 12 21 10 53 46 21 11 15 9 22 43 17 9 26 52 22 9 48 56 21 10 10 49 22 10 32 33 22 10 54 7 22 11 15 31 21 42 18 9 27 14 23 9 49 17 22 10 11 11 22 10 32 55 22 10 54 29 21 11 15 52 21 41 19 9 27 37 22 9 49 39 22 10 11 33 22 10 33 17 21 10 54 50 22 11 16 13 21 40 20 9 27 59 22 9 50 1 22 10 11 55 22 10 33 38 22 10 55 12 21 11 16 34 22 39 21 9 28 21 22 9 50 23 22 10 12 17 21 10 34 0 22 10 55 33 22 11 16 56 21 38 22 9 28 43 22 9 50 45 22 10 12 38 22 10 34 22 21 10 55 55 21 11 17 17 21 37 23 9 29 5 23 9 51 7 22 10 13 0 22 10 34 43 22 10 56 16 21 11 17 38 22 36 24 9 29 27 22 9 51 29 22 10 13 22 22 10 35 5 21 10 56 37 22 11 18 0 21 35 25 9 29 49 22 9 51 51 22 10 13 44 22 10 35 26 22 10 56 59 21 11 18 21 21 34 26 9 30 11 22 9 52 13 22 10 14 6 21 10 35 48 22 10 57 20 22 11 18 42 21 33 27 9 30 33 23 9 52 35 22 10 14 27 22 10 36 10 21 10 57 42 21 11 19 3 22 32 28 9 30 56 22 9 52 57 22 10 14 49 22 10 36 31 22 10 58 3 22 11 19 25 21 31 29 9 31 18 22 9 53 19 22 10 15 11 22 10 36 53 22 10 58 25 21 11 19 46 21 30 30 9 31 40 22 9 53 41 22 10 15 33 21 10 37 15 21 10 58 46 22 11 20 7 21 29 31 9 32 2 22 9 54 3 22 10 15 54 22 10 37 36 22 10 59 8 21 11 20 28 22 28 32 9 32 24 22 9 54 25 22 10 16 16 22 10 37 58 21 10 59 29 21 11 20 50 21 27 33 9 32 46 22 9 54 47 22 10 16 38 22 10 38 19 22 10 59 50 22 11 21 11 21 26 34 9 33 8 22 9 55 9 22 10 17 0 22 10 38 41 22 11 0 12 21 11 21 32 21 25 35 9 33 30 22 9 55 31 22 10 17 22 21 10 39 3 21 11 0 33 22 11 21 53 22 24 36 9 33 52 22 9 55 53 22 10 17 43 22 10 39 24 22 11 0 55 21 11 22 15 21 23 37 9 34 14 22 9 56 15 21 10 18 5 22 10 39 46 21 11 1 16 22 11 22 36 21 22 38 9 34 36 23 9 56 36 22 10 18 27 22 10 40 7 22 11 1 38 21 11 22 57 21 21 39 9 34 59 22 9 56 58 22 10 18 49 21 10 40 39 22 11 1 59 21 11 23 18 22 20 40 9 35 21 22 9 57 20 22 10 19 10 22 10 40 51 21 11 2 20 22 11 23 40 21 19 41 9 35 43 22 9 57 42 22 10 19 32 22 10 41 12 22 11 2 42 21 11 24 1 21 18 42 9 36 5 22 9 58 4 22 10 19 54 22 10 41 34 21 11 3 3 22 11 24 22 21 17 43 9 36 27 22 9 58 26 22 10 20 16 21 10 41 55 22 11 3 25 21 11 24 43 21 16 44 9 36 49 22 9 58 48 22 10 20 37 22 10 42 17 21 11 3 46 21 11 25 4 22 15 45 9 37 11 22 9 59 10 22 10 20 59 22 10 42 38 22 11 4 7 22 11 25 26 21 14 46 9 37 33 22 9 59 32 22 10 21 21 22 10 43 0 22 11 4 29 21 11 25 47 21 13 47 9 37 55 22 9 50 54 22 10 21 43 21 10 43 22 21 11 4 50 21 11 26 8 21 12 48 9 38 17 22 10 0 16 21 10 22 4 22 10 43 43 22 11 5 11 22 11 26 29 21 11 49 9 38 39 22 10 0 37 22 10 22 26 22 10 44 5 21 11 5 33 21 11 26 50 22 10 50 9 39 1 22 10 0 59 22 10 22 48 21 10 44 26 22 11 5 54 22 11 27 12 21 9 51 9 39 23 22 10 1 21 22 10 23 9 22 10 44 48 21 11 6 16 21 11 27 33 21 8 52 9 39 45 22 10 1 43 22 10 23 31 22 10 45 9 22 11 6 37 21 11 27 54 21 7 53 9 40 7 22 10 2 5 22 10 23 53 22 10 45 31 21 11 6 58 22 11 28 15 21 6 54 9 40 29 22 10 2 27 22 10 24 15 21 10 45 52 22 11 7 20 21 11 28 36 22 5 55 9 40 41 22 10 2 49 22 10 24 36 22 10 46 14 22 11 7 41 22 11 28 58 21 4 56 9 41 13 22 10 3 11 21 10 24 58 22 10 46 36 21 11 8 3 21 11 29 19 21 3 57 9 41 35 22 10 3 32 22 10 25 20 21 10 46 57 22 11 8 24 21 11 29 40 21 2 58 9 41 57 22 10 3 54 22 10 25 41 22 10 47 19 21 11 8 45 22 11 30 1 21 1 59 9 42 19 23 10 4 16 22 10 26 3 22 10 47 40 22 11 9 7 21 11 30 22 22 0  5  4  3  2  1  0   
Taurus. Scorpio.   0 di 1 di 2 di 3 di 4 di 5 di  M gr. mi. se. s. gr. mi. se s. gr. m. se. s. gr. mi. se s. gr. mi. se. s. gr. mi sec s M 0 11 30 44 21 11 51 48 21 12 12 41 20 12 33 21 21 12 53 50 20 13 14 5 21 59 1 11 31 5 21 11 52 9 21 12 13 1 21 12 33 42 20 12 54 10 20 13 14 26 20 58 2 11 31 26 21 11 52 30 21 12 13 22 21  34 2 21  54 30 21  14 46 20 57 3 11 31 47 21 11 52 51 21 12 13 43 21  34 23 21  54 51 20  15 6 20 56 4 11 32 8 21 11 53 12 21 12 14 4 20  34 44 20  55 11 20  15 26 20 55 5 11 32 29 21 11 53 33 21 12 14 24 21  35 4 21  55 31 21  15 46 20 54 6 11 32 50 22 11 53 54 21 12 14 45 21  35 25 20  55 52 20  16 6 20 53 7 11 33 12 21 11 54 15 21 12 15 6 21  35 45 21  56 12 21  16 26 20 52 8 11 33 33 21 11 54 36 20 12 15 27 20  36 6 20  56 33 20  16 46 21 51 9 11 33 54 21 11 54 56 21 12 15 47 21  36 26 21  56 53 20  17 7 20 50 10 11 34 15 21 11 55 17 21 12 16 8 21  36 47 20  57 13 21  17 27 20 49 11 11 34 36 21 11 55 38 21 12 16 29 21  37 7 21  57 34 20  17 47 20 48 12 11 34 57 21 11 55 59 21 12 16 50 20  37 28 20  57 54 20  18 7 20 47 13 11 35 18 22 11 56 20 21 12 17 10 21  37 48 21  58 14 20  18 27 20 46 14 11 35 40 21 11 56 41 21 12 17 31 21  38 9 21  58 34 21  13 47 20 45 15 11 36 1 21 11 57 2 21 12 17 52 21  38 30 20  58 55 20  19 7 20 44 16 11 36 22 21 11 57 23 21 12 18 13 20  38 50 21  59 15 20  19 27 20 43 17 11 36 43 21 11 57 44 21 12 18 33 21  39 11 20  59 35 21  19 47 21 42 18 11 37 4 21 11 58 5 21 12 18 54 21  39 31 21  59 56 20  20 8 20 41 19 11 37 25 21 11 58 26 21 12 19 15 20  39 52 20 13 0 16 20  20 28 20 40 20 11 37 46 21 11 58 47 21 12 19 35 21  40 12 21 13 0 30 21  20 48 20 39 21 11 38 7 21 11 59 8 21 12 19 56 21  40 33 20  0 57 20  21 8 20 38 22 11 38 28 21 11 59 29 20 12 20 17 21  40 53 21  1 17 20  21 28 20 37 23 11 38 49 22 11 59 49 21 12 20 38 20  41 14 20  1 37 21  21 48 20 36 24 11 39 11 21 12 0 10 21 12 20 58 21  41 34 21  1 58 ●0  22 8 20 35 25 11 39 32 21 12 0 31 21 12 21 19 21  41 55 20  2 18 20  22 28 20 34 26 11 39 53 21 12 0 52 21 12 21 40 20  42 15 21  2 38 20  22 48 20 33 27 11 40 14 21 12 1 13 21 12 22 0 21  42 36 20  2 58 21  23 8 20 32 28 11 40 35 21 12 1 34 21 12 22 21 21  42 56 21  3 19 20  23 28 20 31 29 11 40 56 21 12 1 55 21 12 22 42 20  43 17 20  3 39 20  23 4● 20 30 30 11 41 17 21 12 2 16 21  23 2 21  43 37 21  3 59 20  24 8 20 29 31 11 41 38 21 12 2 37 20  23 23 21  43 58 20  4 19 21  24 28 20 28 32 11 41 59 21 12 2 57 21  23 44 20  44 18 20  4 40 20  24 48 20 27 33 11 42 2● 21 12 3 18 21  24 4 21  44 38 21  5 0 20  25 8 20 26 34 11 42 41 21 12 3 39 21  24 25 21  44 59 20  5 20 20  25 28 20 25 35 11 43 2 21 12 4 0 21  24 46 20  45 19 21  5 40 21  25 48 21 24 36 11 43 23 22 12 4 21 21  25 6 21  45 40 20  6 1 20  26 9 20 23 37 11 43 45 21 12 4 42 21  25 27 21  46 0 21  6 21 20  26 29 20 22 38 11 44 6 21 12 5 3 20  25 48 20  46 21 20  6 41 20  26 49 20 21 39 11 44 27 21 12 5 23 21  26 8 21  46 41 21  7 1 21  27 9 20 20 40 11 44 48 21 12 5 44 21  26 29 21  47 2 20  7 22 20  27 29 20 19 41 11 45 9 21 12 6 5 21  26 50 20  47 22 20  7 42 20  27 49 20 18 42 11 45 30 21 12 6 26 21  27 10 21  47 42 21  8 2 20  28 9 20 17 43 11 45 51 21 12 6 47 21  27 31 21  48 3 20  8 22 20  28 29 20 16 4● 11 46 12 21 12 7 8 20  27 52 20  48 23 21  8 42 21  28 49 20 15 45 11 46 33 21 12 7 28 21  28 12 21  48 44 20  9 3 20  29 9 20 14 46 11 46 54 21 12 7 49 21  28 33 20  49 4 21  9 23 20  29 29 20 13 47 11 47 15 21 12 8 10 21  28 53 21  49 25 20  9 43 20  29 49 1● 12 48 11 47 36 21 12 8 31 21  29 14 21  49 45 20  10 3 20  30 8 20 11 49 11 47 57 21 12 8 52 21  29 35 20  50 5 21  10 23 21  30 28 22 10 50 11 48 18 21 12 9 13 20  29 55 21  50 26 20  10 44 20  30 48 20 9 51 11 48 39 21 12 9 33 21  30 16 21  50 46 21  11 4 20  31 8 20 8 52 11 49 0 21 12 9 54 21  30 37 20  51 7 20  11 24 20  31 28 20 7 53 11 49 21 21 12 10 15 21  30 57 21  51 27 20  11 44 20  31 48 20 6 54 11 49 42 21 12 10 36 21  31 18 20  51 47 21  12 4 21  32 8 20 5 55 11 50 3 21 12 10 57 20  31 38 21  52 8 20  12 25 20  32 28 20 4 56 11 50 24 21 12 11 17 21  31 59 21  52 28 21  12 45 20  32 48 20 3 57 11 50 45 21 12 11 38 21  32 20 20  52 49 20  13 5 20  33 8 20 2 58 11 51 6 21 12 11 59 21  32 40 21  53 9 20  13 25 20  33 28 20 1 59 11 51 27 21 12 12 20 21  33 1 20  53 29 21  13 45 20  33 48 20 0  29  28  27  26  52  24    6 di 7 di 8 di 9 di 10 di 11 di  m. gr. mi. se. s. gr. mi. sec se. gr. mi. se. se. gr. mi. se. se. gr. mi se s. gr. mi. se. s. M 0 13 34 8 20 13 53 57 20 14 13 32 20 14 32 53 19 14 51 59 19 15 10 51 19 59 1 13 34 28 20 13 54 17 19 14 13 52 19 14 33 12 20 14 52 10 19 15 11 10 18 58 2  34 48 20  54 36 20  14 11 20 14 33 32 19 14 52 37 19 15 11 28 19 57 3  35 8 20  54 56 20  14 31 19 14 33 51 19 14 52 56 19 15 11 47 19 56 4  35 28 20  55 16 19  14 50 20 14 34 10 19 14 53 15 19 15 12 6 18 55 5  35 48 09  55 35 20  15 10 19 14 34 29 19 14 53 34 19 15 12 24 19 54 6  36 7 20  55 55 20  15 29 19 14 34 48 20 14 53 53 19 15 12 43 19 53 7  36 27 20  56 15 19  15 48 20 14 35 8 19 14 54 12 19 15 13 2 19 52 8  36 47 20  56 35 20  16 8 19 14 35 27 19 14 54 31 19 15 13 21 18 51 9  37 7 20  56 54 20  16 27 20 14 35 46 19 14 54 50 19 15 13 39 19 50 10  37 27 20  57 14 20  16 47 19 14 36 5 19 14 55 9 19 15 13 58 19 49 11  37 47 20  57 34 10  17 6 20 14 36 24 20 14 55 2● 19 15 14 17 18 48 12  38 7 20  57 53 20  17 26 19 14 36 44 19 14 55 47 19 15 14 35 19 47 13  38 27 20  58 13 19  17 45 19 14 37 3 19 14 56 ● 19 15 14 54 19 46 14  38 47 19  58 32 20  18 4 20 14 37 22 19 14 56 25 19 15 15 13 19 45 15  39 6 20  58 52 20  18 24 19 14 37 41 19 14 56 44 19 15 15 31 19 44 16  39 26 20  59 12 19  18 43 20 14 38 0 19 14 57 3 19 15 15 50 19 43 17  39 46 20  59 31 2●  19 3 19 14 38 19 20 14 57 22 18 15 16 9 18 42 18  40 6 20  59 51 2●  19 22 19 14 38 39 19 14 57 40 19 15 16 27 19 41 19  40 26 20 14 0 11 19  19 41 20 14 38 58 19 14 57 59 ●9 15 16 4● ●9 40 20  40 46 20  0 30 20  20 1 19 14 39 17 19 14 58 18 19 15 17 5 1● 39 21  41 6 20  0 50 20  20 20 20 14 39 36 19 14 58 37 19 15 17 23 19 38 22  41 26 20  1 10 19  20 4 19 14 39 55 19 14 58 5● 19 15 17 42 18 37 23  41 46 19  1 29 20  20 59 19 14 40 14 19 14 59 15 19 15 18 0 19 36 24  42 5 20  1 49 19  21 18 20 14 40 33 20 14 59 34 1● 15 18 19 19 35 25  42 25 20  2 8 20  21 38 19 14 40 53 19 14 59 53 19 15 18 38 18 34 26  42 45 20  2 2● 20  21 57 19 14 41 12 19 15 0 12 18 15 18 56 1● 33 27  43 5 20  2 48 19  22 16 20 14 41 31 19 15 0 30 19 15 19 15 19 32 28  43 25 19  3 7 20  22 36 19 14 41 50 19 15 0 ●9 19 15 19 34 1● 31 29  43 44 20  3 2● 19  22 55 20 14 42 9 19 15 1 8 19 15 19 ●● 19 30 30  44 4 20  3 46 20  23 15 19 14 42 28 19 15 1 27 19 15 20 11 1● 29 31  44 24 20  4 6 19  23 34 19 14 42 47 19 15 1 4● 19 15 20 29 19 28 32  44 44 20  4 29 20  23 53 20 14 43 6 19 15 2 5 19 15 20 48 19 27 33  45 4 19  4 45 19  24 13 19 14 43 25 20 15 2 24 18 15 21 7 18 26 34  45 23 20  5 5 19  24 32 19 14 43 45 19 15 2 44 19 15 21 25 19 25 35  45 43 20  5 24 20  24 51 20 14 44 4 19 15 3 1 19 15 21 44 18 24 36  46 3 20  5 44 19  25 11 19 14 44 23 19 15 3 20 19 15 22 2 19 23 37  46 23 20  6 3 20  25 30 19 14 44 42 19 15 3 39 19 15 22 21 18 22 38  46 43 19  6 23 20  25 49 19 14 45 1 19 15 3 5● 19 15 22 39 19 21 39  47 2 20  6 43 19  26 8 20 14 45 20 19 15 4 17 18 15 22 58 19 20 40  47 22 20  7 2 20  26 28 19 14 45 39 19 15 4 35 19 15 23 17 18 19 41  47 42 20  7 22 19  26 47 19 14 45 58 19 15 4 54 19 15 23 35 19 18 42  48 2 19  7 41 20  27 6 20 14 40 17 19 15 5 13 19 15 23 54 18 17 43  48 21 20  8 1 19  27 26 19 14 46 30 19 15 5 32 19 5 24 12 19 16 44  48 41 20  8 20 20  27 45 19 14 46 55 19 15 5 51 18 15 24 31 18 15 45  49 1 20  8 40 19  28 4 20 14 47 14 19 15 6 9 19 15 24 49 19 14 46  49 21 20  8 59 20  28 24 19 14 47 33 19 15 6 28 19 15 25 8 18 13 47  49 41 19  9 19 19  28 43 19 14 47 52 19 15 6 47 19 15 25 26 19 12 48  50 0 20  9 38 20  29 2 19 14 48 11 19 15 7 0 19 15 25 45 18 11 49  50 20 20  9 58 19  29 21 20 14 48 30 19 15 7 25 18 15 26 3 19 10 50  50 40 20  10 17 20  29 41 19 14 48 49 19 15 7 43 19 15 26 22 18 9 51  51 0 19  10 37 19  30 0 19 14 49 8 20 15 8 2 19 15 26 40 19 8 52  51 19 20  10 56 20  30 19 19 14 49 28 19 15 8 21 19 15 26 59 18 7 53  51 39 20  11 16 19  30 38 20 14 49 47 19 15 8 40 18 15 27 17 19 6 54  51 59 19  11 35 20  30 58 19 14 50 6 19 15 8 58 19 15 27 36 18 5 55  52 18 20  11 55 19  31 17 19 14 50 25 19 15 9 17 19 15 27 54 19 4 56  52 38 20  12 14 20  31 36 19 14 50 44 19 15 9 36 19 15 28 13 18 3 57  52 58 20  12 34 19  31 55 20 14 51 3 19 15 9 55 18 15 28 31 19 2 58  53 18 19  12 53 20  32 15 19 14 51 22 19 15 10 13 19 15 28 50 18 1 59  53 37 20  13 13 19  32 34 19 14 51 41 18 15 10 32 19 15 29 8 19 0  23  22  21  20  19  18    12 di 13 di 14 di 15 di 16 di 17 di  M gr. mi. se. s. gr. mi. se s. gr. mi sec s. gr. m. sec s. gr. mi. se. s. gr. mi. s. s. 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M 0 17 15 18 17 17 31 56 16 17 48 15 16 18 4 16 16 18 19 58 15 18 35 20 15 59 1 17 15 35 17 17 32 12 17 17 48 31 17 18 4 32 16 18 20 13 16  35 35 15 58 2  15 52 16  32 29 16  48 48 16  4 48 16  20 29 15  35 50 15 57 3  16 8 17  32 45 17  49 4 16  5 4 15  20 44 16  36 5 10 56 4  16 25 17  33 2 16  49 20 16  5 19 16  21 0 15  36 21 15 55 5  16 42 17  33 18 17  49 36 16  5 35 16  21 15 16  36 36 15 54 6  16 59 16  33 35 16  49 52 16  5 51 16  21 31 15  39 51 15 53 7  17 15 17  33 51 17  50 8 16  6 7 16  21 46 16  37 6 15 52 8  17 32 17  34 8 16  50 24 17  6 23 15  22 2 15  37 21 15 51 9  17 49 17  34 24 16  50 41 16  6 38 16  22 17 16  37 36 16 50 10  18 6 16  34 40 17  50 57 16  6 54 16  22 33 15  37 52 15 49 11  18 22 17  34 57 16  51 13 16  7 10 16  22 48 16  38 7 15 48 12  18 39 17  35 13 17  51 29 16  7 26 16  23 4 15  38 22 15 47 13  18 56 16  35 30 16  51 45 16  7 42 15  23 19 16  38 37 15 46 14  19 12 17  35 46 17  52 1 16  7 57 16  23 35 15  38 52 15 45 15  19 29 17  36 3 16  52 17 16  8 13 16  23 50 15  39 7 15 44 16  19 46 17  36 19 16  52 33 16  8 29 26  24 5 16  39 22 16 43 17  20 3 16  36 35 17  52 49 17  8 45 15  24 21 15  39 38 15 42 18  20 19 17  36 52 16  53 6 16  9 0 16  24 36 16  39 53 15 41 19  20 36 17  37 8 16  53 22 16  9 16 16  24 52 15  40 8 15 40 20  20 53 16  37 24 17  53 38 16  9 32 16  25 7 16  40 23 15 39 21  21 9 17  37 41 16  53 54 16  9 48 15  25 23 15  40 38 15 38 22  21 26 17  37 57 17  54 10 16  10 3 16  25 38 15  40 53 15 37 23  21 43 16  38 14 16  54 26 16  10 19 16  25 53 16  41 8 15 36 24  21 59 17  38 30 16  54 42 16  10 35 16  26 9 15  41 25 15 35 25  22 16 17  38 46 17  54 58 16  10 51 15  26 24 16  41 38 15 34 26  22 33 16  39 3 16  55 14 16  11 6 16  26 50 15  41 53 15 33 27  22 49 17  39 39 16  55 30 16  11 22 16  26 55 15  42 8 15 32 28  23 ● 17  39 35 17  56 46 16  11 38 16  27 10 16  42 23 15 31 29  23 3 16  39 52 16  56 2 16  11 54 15  27 21 15  42 38 10 30 30  23 39 17  40 8 16  56 18 16  12 9 16  27 41 16  42 54 15 29 31  23 56 17  40 24 17  56 34 16  12 25 16  27 57 15  43 9 15 28 32  24 13 16  40 41 16  56 50 16  12 41 15  28 12 15  43 24 15 27 33  24 29 17  40 57 16  57 6 16  12 56 16  28 27 16  43 39 15 26 34  24 46 16  41 13 16  57 22 16  13 12 16  28 43 15  43 54 15 25 35  25 2 17  41 29 17  57 38 16  13 28 15  28 58 15  44 9 15 24 36  25 19 17  41 46 16  57 54 16  13 43 16  29 13 16  44 24 15 23 37  25 36 16  42 2 16  58 10 16  13 59 16  29 29 15  44 39 15 22 38  25 52 17  42 18 17  58 26 16  14 15 15  29 44 15  44 54 15 ●1 39  26 9 16  42 35 16  58 42 16  14 30 16  29 59 16  45 9 15 20 40  26 25 17  42 51 16  58 58 16  14 46 16  30 15 15  45 24 15 19 41  26 42 17  43 7 16  59 14 16  15 2 15  30 30 15  45 39 15 18 42  26 59 16  43 23 17  59 30 16  15 17 16  30 45 16  45 54 15 17 43  27 15 17  43 40 16  59 46 16  15 33 15  31 1 15  46 9 15 16 44  27 32 16  43 56 16 18 0 2 16  15 48 10  31 16 15  46 24 14 15 45  27 48 17  44 12 16 18 0 18 16  16 4 16  31 31 15  46 38 15 14 46  28 5 16  44 28 17  0 34 16  16 20 15  31 46 16  46 53 15 13 47  28 21 17  44 45 16  0 50 15  16 35 16  32 2 15  47 8 15 12 48  28 38 16  45 1 16  1 5 16  16 51 15  32 17 15  47 23 15 11 49  28 54 17  45 17 16  1 21 16  17 9 16  32 32 15  47 38 15 10 50  29 11 16  45 33 17  1 37 16  17 22 16  32 47 16  47 53 15 9 51  29 27 17  45 50 16  1 53 16  17 38 15  33 3 15  48 8 15 8 52  29 44 16  46 6 16  2 9 16  17 53 16  33 1● 15  48 23 15 7 53  30 0 17  46 22 16  2 25 16  18 9 15  33 33 15  48 38 15 6 54  30 17 16  46 38 16  2 41 16  18 24 16  33 48 16  48 53 15 5 55  30 33 17  46 54 17  2 57 16  18 40 15  34 4 15  49 8 15 4 56  30 50 16  47 11 16  3 13 15  18 55 16  34 19 15  49 23 15 ● 57  31 6 17  47 27 16  3 28 16  19 11 1●  34 34 15  49 38 14 2 58  31 23 16  47 43 16  3 44 16  19 27 15  34 49 1●  49 52 15 1 59  31 39 17  47 59 16  4 0 16  19 42 16  35 5 14  50 7 15 0  11  10  9  8  7  6    24 di 25 di 26 di 27 di 28 di 29 di  M gr, mi. sec s. gr. mi. s. s. gr. mi. se. s. gr. mi. sec s. gr. m. se s. gr. mi. se s. 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28 10  51 0 9 22 0 7 9  8 49 9  17 7 8 10 50  31 42 11  41 38 10  51 9 10 22 0 16 9  8 58 8  17 15 8 9 51  31 53 10  41 48 10  51 19 9  0 25 9  9 6 9  17 23 8 8 52  32 3 10  41 58 9  51 28 9  0 34 9  9 15 8  17 31 8 7 53  32 13 10  42 7 10  51 37 10  0 43 9  9 23 9  17 39 8 6 54  32 23 10  42 17 10  51 47 9  0 52 9  9 32 8  17 47 8 5 55  32 33 10  42 27 9  51 56 9  1 1 8  9 40 9  17 55 8 4 56  32 43 10  42 36 10  52 5 9  1 9 9  9 49 8  18 3 8 3 57  32 53 10  42 46 10  52 14 10  1 18 9  9 57 9  18 11 8 2 58  33 3 10  42 56 9  52 24 9  1 27 9  10 6 8  18 19 8 1 59 21 33 ●3 10 21 43 5 10 21 52 33 9  1 36 9  10 14 8  18 27 8 0  23  22  21  20  19  18    12 di 13 di 14 di 15 di 16 di 17 di  m. gr. m. sec. se gr. mi. s. se gr. mi. se se. gr. mi. se se gr. mi· se s. gr. mi. s. se. m 0 22 18 35 8 22 26 22 8 22 33 44 7 22 40 40 7 22 47 10 6 22 53 14 6 59 1 22 18 43 8 22 26 30 7 22 33 51 7 22 40 47 6 22 47 16 7 22 53 20 6 58 2 22 18 51 8 22 26 37 8 22 33 58 7 22 40 53 7 22 47 23 6 22 53 26 6 57 3 22 18 59 8 22 26 45 8 22 34 5 8 22 41 0 7 22 47 29 6 22 53 32 5 56 4 22 19 7 8 22 26 53 7 22 34 13 7 22 41 7 7 22 47 35 6 22 53 37 6 55 5 22 19 15 8 22 27 0 8 22 34 20 7 22 41 14 6 22 47 41 7 22 53 43 6 54 6 22 19 23 8 22 27 8 7 22 34 27 7 22 41 20 7 22 47 4● 6 22 53 49 6 53 7 22 19 31 8 22 27 15 8 22 34 34 7 22 41 27 7 22 47 54 6 22 53 55 6 52 8 22 19 39 8 22 27 23 7 22 34 41 7 22 41 34 6 22 48 0 6 22 54 1 5 51 9 22 19 47 8 22 27 30 8 22 34 48 7 22 41 40 7 22 48 6 7 22 54 6 6 50 10 22 19 55 8 22 27 38 7 22 34 55 7 22 41 47 7 22 48 13 6 22 54 12 6 49 11 22 20 3 8 22 27 45 8 22 35 2 7 22 41 54 6 22 48 19 6 22 54 18 6 48 12 22 20 11 7 22 27 53 7 22 35 9 7 22 42 0 7 22 48 25 6 22 54 24 5 47 13 22 20 18 8 22 28 0 8 22 35 16 7 22 42 7 6 22 48 31 6 22 54 29 6 46 14 22 20 26 8 22 28 8 7 22 35 23 7 22 42 13 7 22 48 37 7 22 54 35 6 45 15 22 20 34 8 22 28 15 8 22 35 30 8 22 42 20 7 22 48 44 6 22 54 41 6 44 16 2● 20 4● 8 22 28 23 7 22 35 38 7 22 42 27 6 22 48 50 6 22 54 47 5 43 17 22 20 5● 8 22 28 30 8 22 35 45 7 22 42 33 7 22 48 56 6 22 54 52 6 42 18 22 20 5● 8 22 28 38 7 22 35 52 7 22 42 40 6 22 49 2 6 22 54 58 6 41 19 22 21 6 8 22 2● 45 7 22 35 59 7 22 42 46 7 22 49 8 6 22 55 4 6 40 20 22 21 14 7 22 28 52 8 22 36 6 7 22 42 53 7 22 49 14 6 22 55 10 5 39 21 22 21 21 8 22 29 0 7 22 36 13 7 22 43 0 6 22 49 20 7 22 55 15 6 38 22 22 21 29 8 22 29 7 8 22 36 20 7 22 43 6 7 22 49 27 6 22 55 21 6 37 23 22 21 37 8 2● 29 15 7 22 36 27 7 22 43 13 6 22 49 33 6 22 55 27 5 36 2● 22 21 45 8 22 29 22 7 22 36 34 7 22 43 19 7 22 49 39 6 22 55 32 6 35 25 22 21 53 8 22 29 29 8 22 36 41 6 22 43 26 6 22 49 45 6 22 55 38 6 34 26 22 22 1 7 22 29 37 7 22 36 47 7 22 43 32 7 22 49 51 6 22 55 44 5 33 27 22 22 8 8 22 29 44 8 22 36 54 7 22 43 39 6 22 49 57 6 22 55 49 6 32 28 22 22 16 8 22 29 52 7 22 37 1 7 22 43 45 7 22 50 3 6 22 55 55 6 31 29 22 22 24 8 22 29 59 7 22 37 8 7 22 43 52 6 22 50 9 6 22 56 1 5 30 30 22 22 32 8 22 30 6 8 22 37 15 7 22 43 58 7 22 50 15 6 22 56 6 6 29 31 22 22 40 7 22 30 14 7 22 37 22 7 22 44 5 6 22 50 21 6 22 56 12 5 28 32 22 22 47 8 22 30 21 7 22 37 29 7 22 44 11 7 22 50 27 7 22 56 17 6 27 33 22 22 55 8 22 30 28 8 22 37 36 7 22 44 18 6 22 50 34 6 22 56 23 6 26 34 22 23 3 8 22 30 36 7 22 37 43 7 22 44 24 7 22 50 40 6 22 56 29 5 25 35 22 23 11 7 22 30 43 7 22 37 50 7 22 44 31 6 22 50 46 6 22 56 34 6 24 36 22 23 18 8 22 30 50 8 22 37 57 7 22 44 37 7 22 50 52 6  56 40 5 23 37 22 23 26 8 22 30 58 7 22 38 4 7 22 44 44 6 22 50 58 6  56 45 6 22 38 22 23 34 8 22 31 5 7 22 38 11 6 22 44 50 7 22 51 4 6  56 51 6 21 39 22 23 42 7 22 31 12 8 22 38 17 7 22 44 57 6 22 51 10 6  56 57 5 20 40 22 23 49 8 22 31 20 7 22 38 24 7 22 45 3 6 22 51 16 6 22 57 2 6 19 41 22 23 57 8 22 31 27 7 22 38 31 7 22 45 9 7 22 51 22 6  57 8 5 18 42 22 24 5 7 22 31 34 7 22 38 38 7 22 45 16 6 22 51 28 6  57 13 6 17 43 22 24 12 8 22 31 41 8 22 38 45 7 22 45 22 7 22 51 34 6  57 19 5 16 44 22 24 20 8 22 31 49 7 22 38 52 6 22 45 29 6 22 51 40 6  57 24 6 15 45 22 24 28 8 22 31 56 7 22 38 58 7 22 45 35 6 22 51 46 6 22 57 30 5 14 46 22 24 36 7 22 32 3 8 22 39 5 7 22 45 41 7 22 51 52 5  57 35 6 13 47 22 24 43 8 22 32 11 7 22 39 12 7 22 45 48 6 22 51 57 6  57 41 5 12 48 22 24 51 8 22 32 18 7 22 39 19 7 22 45 54 7 22 52 3 6  57 46 6 11 49 22 24 59 7 22 32 25 7 22 39 26 7 22 46 1 6 22 52 9 6  57 52 5 10 50 22 25 6 8 22 32 32 7 22 39 33 6 22 46 7 6 22 52 15 6 22 57 57 6 9 51 22 25 14 7 22 32 39 8 22 39 39 7 22 46 13 7 22 52 21 6  58 3 5 8 52 22 25 21 8 22 32 47 7 22 39 46 7 22 46 20 6 22 52 27 6  58 8 6 7 53 22 25 29 8 22 32 54 7 22 39 53 7 22 46 26 6 22 52 33 6  58 14 5 6 54 22 25 37 7 22 33 1 7 22 40 0 6 22 46 32 7 22 52 39 6  58 9 6 5 55 22 25 44 8 22 33 8 7 22 40 6 7 22 46 39 6 22 52 45 6 22 58 25 5 4 56 22 25 52 8 22 33 15 8 22 40 13 7 22 46 45 6 22 52 51 6  58 30 6 3 57 22 26 0 7 22 33 23 7 22 40 20 7 22 46 51 7 22 52 57 5  58 36 5 2 58 22 26 7 8 22 33 30 7 22 40 27 6 22 46 58 6 22 53 2 6  58 41 5 1 59 22 26 15 7 22 33 37 7 22 40 33 7 22 47 4 6 22 53 8 6  58 46 6 0  17  16  15  14  13  12    18 di 19 di 20 di 21 di 22 di 23 di  m gr. mi s se. gr. mi. se s. gr. mi se. s gr. mi. se. se gr. mi. se s. gr. mi. se se. m 0 22 58 52 5 23 4 3 5 23 8 48 4 23 13 6 4 23 16 57 4 23 20 21 3 59 1 22 58 58 6 23 4 8 5 23 8 52 5 23 13 10 4 23 17 1 3 23 20 24 3 58 2 22 59 3 5 23 4 13 5 23 8 57 4 23 13 14 4 23 17 4 4 23 20 27 4 57 3 22 59 8 5 23 4 18 5 23 9 1 5 23 13 18 4 23 17 8 3 23 20 31 3 56 4 22 59 13 6 23 4 23 5 23 9 6 4 23 13 22 4 23 17 11 4 23 20 34 3 55 5 22 59 19 5 23 4 28 5 23 9 10 5 23 13 26 4 23 17 15 4 23 20 37 3 54 6 22 59 24 5 23 4 33 5 23 9 15 4 23 13 30 4 23 17 19 3 23 20 40 3 53 7 22 59 29 6 23 4 38 5 23 9 19 5 23 13 34 4 23 17 22 4 23 20 43 3 52 8 22 59 35 5 23 4 43 4 23 9 24 4 23 13 38 4 23 17 26 3 23 20 46 3 51 9 22 59 40 5 23 4 47 5 23 9 28 5 23 13 42 4 23 17 29 4 23 20 4● 4 50 10 22 59 45 6 23 4 52 5 23 9 33 4 23 13 46 4 23 17 33 3 23 20 53 3 49 11 22 59 51 5 23 4 5● 5 23 9 37 5 23 13 50 4 23 17 36 4 23 20 56 3 48 12 22 59 56 5 23 5 2 5 23 9 42 4 23 13 54 4 23 17 40 3 23 20 59 3 47 13 23 0 1 6 23 5 7 5 23 9 46 4 ●3 13 58 4 23 17 43 4 23 21 2 3 46 14 23 0 7 5 23 5 12 5 23 9 50 5 23 14 2 4 23 17 47 4 23 21 5 3 45 15 23 0 12 5 23 5 17 5 23 9 55 4 23 14 6 4 23 17 51 3 23 21 8 3 44 16 23 0 17 6 23 5 22 4 23 9 59 5 23 14 10 4 23 17 54 4  21 11 3 43 17 23 0 23 5 23 5 26 5 23 10 4 4 23 14 14 4 23 17 58 3  21 14 3 42 18 23 0 28 5 23 5 31 5 23 10 8 4 23 14 18 4 23 18 1 4  21 17 3 41 19 23 0 33 5 23 5 36 5 23 10 12 5 23 14 22 4 23 18 5 3  21 20 3 40 20 23 0 38 6 23 5 41 5 23 10 17 4 23 14 26 4 23 18 8 3 23 21 23 3 39 21 23 0 44 5 23 5 46 5 23 10 21 4 23 14 30 4 23 18 11 4  21 26 3 38 22 23 0 49 5 23 5 51 4 23 10 25 5 23 14 34 4 23 18 15 3  21 29 3 37 23 23 0 54 5 23 5 55 5 23 10 30 4 23 14 38 3 23 18 18 4  21 32 3 36 24 23 0 59 6 23 6 0 5 23 10 34 5 23 14 41 4 23 18 22 3  21 35 3 35 25 23 1 5 5 23 6 5 5 23 10 39 4 23 14 45 4 23 18 25 4 23 21 38 3 34 26 23 1 10 5 23 6 10 4 23 10 43 4 23 14 49 4 23 18 29 3  21 41 3 33 27 23 1 15 5 23 6 14 5 23 10 47 5 23 14 53 4 23 18 32 4  21 44 3 32 28 23 1 20 5 23 6 19 5 23 10 52 4 23 14 57 4 23 18 36 3  21 47 3 31 29 23 1 25 6 23 6 24 5 23 10 56 4 23 15 1 4 23 18 39 3  21 50 3 30 30 23 1 31 5 23 6 29 4 23 11 0 4 23 15 5 4 23 18 42 4 23 21 53 3 29 31 23 1 36 5 23 6 33 5 23 11 4 5 23 15 9 3 23 18 46 3  21 56 3 28 32 23 1 41 5 23 6 38 5 23 11 9 4 23 15 12 4 23 18 49 4  21 59 3 27 33 23 1 46 5 23 6 43 5 23 11 13 4 23 15 16 4 23 18 53 3  22 2 3 26 34 23 1 51 6 23 6 48 4 23 11 17 5 23 15 20 4 23 18 56 3  22 5 3 25 35 23 1 57 5 23 6 52 5 23 11 22 4 23 15 24 4 23 18 59 4 23 22 8 3 24 36 23 2 2 5 23 6 57 5 23 11 26 4 23 15 28 4 23 19 3 3  22 11 3 23 37 23 2 7 5 23 7 2 4 23 11 30 4 23 15 32 3 23 19 6 3  22 14 3 22 38 23 2 12 5 23 7 6 5 23 11 34 5 23 15 35 4 23 19 9 4  22 17 2 21 39 23 2 17 5 23 7 11 5 23 11 39 4 23 15 39 4 23 19 13 3  22 19 3 20 40 23 2 22 5 23 7 16 5 23 11 43 4 23 15 43 4 23 19 16 3 23 22 22 3 19 41 23 2 27 5 23 7 21 4 23 11 47 4 23 15 47 3 23 19 19 4  22 25 3 18 42 23 2 32 6 23 7 25 5 23 11 51 4 23 15 50 4 23 19 23 3  22 28 3 17 43 23 2 38 5 23 7 30 4 23 11 55 5 23 15 54 4 23 19 26 3  22 31 3 16 44 23 2 43 5 23 7 34 5 23 12 0 4 23 15 58 4 23 19 29 4  22 34 3 15 45 23 2 48 5 23 7 39 5 23 12 4 4 23 16 2 3 23 19 33 3 23 22 37 2 14 46 23 2 53 5 23 7 44 4 23 12 8 4 23 16 5 4 23 19 36 3  22 39 3 13 47 23 2 58 5 23 7 48 5 23 12 12 4 23 16 9 4 23 19 39 3  22 42 3 12 48 23 3 3 5 23 7 53 5 23 12 16 4 23 16 13 4 23 19 42 4  22 45 3 11 49 23 3 8 5 23 7 58 4 23 12 20 5 23 16 17 3 23 19 46 3  22 4● 3 10 50 23 3 13 5 23 8 2 5 23 12 25 4 23 16 20 4 23 19 49 3 23 22 51 2 9 51 23 3 18 5 23 8 7 4 23 12 29 4 23 16 24 4 23 19 52 4  22 53 3 8 52 23 3 23 5 23 8 11 5 23 12 33 4 23 16 28 3 23 19 56 3  22 56 3 7 53 23 3 28 5 23 8 16 4 23 12 37 4 23 16 31 4 23 19 59 3  22 59 3 6 54 23 3 33 5 23 8 20 5 23 12 41 4 23 16 35 4 23 20 2 3  23 2 3 5 55 23 3 38 5 23 8 25 5 23 12 45 4 23 16 39 3 23 20 5 3 23 23 5 2 4 56 23 3 43 5 23 8 30 4 23 12 49 5 23 16 42 4 23 20 8 4  23 7 3 3 57 23 3 48 5 23 8 34 5 23 12 54 4 23 16 46 4 23 20 12 3  23 10 3 2 58 23 3 53 5 23 8 39 4 23 12 58 4 23 16 50 3 23 20 15 3  23 13 3 1 59 23 3 58 5 23 8 43 5 23 13 2 4 23 16 53 4 23 20 18 3  23 16 2 0  11  10  9  8  7  6    24 di 25 di 26 di 27 di 28 di 29 di  m gr. mi sec se. gr. mi. s. s. gr. mi. s. s. gr. mi s. se gr. mi. se▪ th'. th' gr. mi. se. th' t● m 0 23 23 18 3 23 25 48 3 23 27 51 2 23 29 27 1 23 30 35 16 53 23 31 16 17 27 59 1  23 21 3  25 51 2  27 53 2  29 28 1  30 36 9 54 23 31 16 44 27 5● 2  23 24 3  25 53 2  27 55 2  29 29 2  30 37 3 54 23 31 17 11 26 5● 3  23 27 2  25 55 2  27 57 2  29 31 1  30 37 57 54 23 31 17 37 26 5● 4  23 29 3  25 57 3  27 59 1  29 32 1  30 38 51 51 23 31 18 3 25 5● 5 23 23 32 3 23 26 0 2 23 28 0 2 23 29 33 1 23 30 39 42 52 23 31 18 28 25 5● 6  23 35 2  26 2 2  28 2 2  29 34 2  30 40 34 52 23 31 18 53 24 5● 7  23 37 3  26 4 2  28 4 2  29 36 1  30 41 26 52 23 31 19 17 24 5● 8  23 40 2  26 6 3  28 6 1  29 37 1  30 42 18 50 23 31 19 41 24 51 9  23 42 3  26 9 2  28 7 2  29 38 2  30 43 8 50 23 31 20 5 23 5● 10 23 23 45 3 23 26 11 2 23 28 9 2 23 29 40 1 23 30 43 58 50 23 31 20 28 22 4● 11  23 48 3  26 13 2  28 11 2  29 41 1  30 44 48 51 23 31 20 50 22 4● 12  23 51 2  26 15 2  28 13 1  29 42 2  30 45 39 49 23 31 21 12 22 4● 13  23 53 3  26 17 3  28 14 2  29 44 1  30 46 28 48 23 31 21 34 21 4● 14  23 56 2  26 20 2  28 16 2  29 45 1  30 47 16 48 23 31 21 55 21 4● 15 23 23 58 3 23 26 22 2 23 28 18 2 23 29 46 1 23 30 48 4 48 23 31 22 16 21 44 16  24 1 3  ●6 24 2  28 20 1  29 47 2  30 48 52 47 23 31 22 37 19 4● 17  24 4 2  ●6 26 2  28 21 2  29 49 1  30 49 39 47 23 31 22 56 20 4● 18  24 6 3  26 28 2  28 23 2  29 50 1  30 50 26 46 23 31 23 16 19 41 19  24 9 2  26 30 2  28 25 1  29 51 1  30 51 12 46 23 31 23 35 18 4● 20 2● 2● 11 3 23 26 32 3 23 28 26 2 23 29 52 1 23 30 51 58 44 23 31 23 53 18 3● 21  24 14 3  26 35 2  28 28 2  29 53 2  30 52 42 45 23 31 24 11 18 3● 22  24 17 2  26 37 2  28 30 1  29 55 1  30 53 27 45 23 31 24 29 17 37 23  24 19 3  26 39 2  28 31 2  29 56 1  30 54 12 45 23 31 24 46 17 3● 24  24 22 2  26 41 2  28 33 1  29 57 1  30 54 57 42 23 31 25 3 16 35 25 23 24 24 3 23 26 43 2 23 28 34 2 23 29 58 1 23 30 55 39 43 23 31 25 19 16 34 26  24 27 2  26 45 2  28 36 2  29 59 2  30 56 22 43 23 31 25 35 15 33 27  24 29 3  26 47 2  28 38 1  30 1 1  30 57 5 43 23 31 25 50 15 32 28  24 32 2  26 49 2  28 39 2  30 2 1  30 57 48 41 23 31 26 5 14 31 29  24 34 3  26 51 2  28 41 2  30 3 1  30 58 29 41 23 31 26 19 14 30 30 23 24 37 2 23 26 53 2 23 28 43 1 23 30 4 1 23 30 59 10 41 23 31 26 33 14 29 31  24 39 3  26 55 2  28 44 2  30 5 1  30 59 51 41 23 31 26 47 13 28 32  24 42 2  26 57 2  28 46 1  30 6 1  31 0 32 40 23 31 27 0 12 27 33  24 44 3  26 59 2  28 47 2  30 7 2  31 1 12 40 23 31 27 12 12 26 34  24 47 2  27 1 2  28 49 1  30 9 1  31 1 52 38 23 31 27 24 12 25 35 23 24 49 3 23 27 3 2 23 28 50 2 23 30 10 1 22 31 2 30 39 23 31 27 36 11 24 36  24 52 2  27 5 2  28 52 1  30 11 1  31 3 9 37 23 31 27 47 11 23 37  24 54 3  27 7 2  28 53 2  30 12 1  31 3 46 38 23 31 27 58 10 22 38  24 57 2  27 9 2  28 55 2  30 13 1  31 4 24 37 23 31 28 8 10 21 39  24 59 2  27 11 2  28 57 1  30 14 1  31 5 1 37 23 31 28 18 10 20 40 23 25 1 3 23 27 13 2 23 28 58 2 23 30 15 1 23 31 5 38 35 23 31 28 28 9 19 41  25 4 2  27 15 2  29 0 1  30 16 1  31 6 13 35  31 28 37 8 18 42  25 6 3  27 17 2  29 1 2  30 17 1  31 6 48 36  31 28 45 8 17 43  25 9 2  27 19 2  29 3 1  30 18 1  31 7 24 37  31 28 53 8 16 44  25 11 2  27 21 2  29 4 2  30 19 1  31 8 1 33  31 29 1 7 15 45 23 25 13 3 23 27 23 2 23 29 6 1 23 30 20 1 23 31 8 34 34 23 31 29 8 6 14 46  25 16 2  27 25 2  29 7 2  30 21 1  31 9 8 34  31 29 14 7 13 47  25 18 3  27 27 2  29 9 1  30 22 1  31 9 42 34  31 29 21 5 12 48  25 21 2  27 29 2  29 10 1  30 23 1  31 10 16 33  31 29 26 6 11 49  25 23 2  27 31 2  29 11 2  30 24 1  31 10 49 32  31 29 32 5 10 50 23 25 25 3 23 27 33 2 23 29 13 1 23 30 25 1 23 31 11 21 31 23 31 29 37 4 9 51  25 28 2  27 35 1  29 14 2  30 26 1  31 11 52 31  31 29 41 4 8 52  25 30 2  27 36 2  29 16 1  30 27 1  31 12 23 31  31 29 45 3 7 53  25 32 3  27 38 2  29 17 2  30 28 1  31 12 54 30  31 29 48 3 6 54  25 35 2  27 40 2  29 19 1  30 29 1  31 13 24 30  31 29 51 3 5 55 23 25 37 2 23 27 42 2 23 29 20 1 23 30 30 1 23 31 13 54 30 23 31 29 54 2 4 56  25 39 3  27 44 2  29 21 2  30 31 1  31 14 24 29  31 29 56 2 3 57  25 42 2  27 46 2  29 23 1  30 32 1  31 14 53 28  31 29 58 1 2 58  25 44 2  27 48 1  29 24 2  30 33 1  31 15 21 28  31 29 59 1 1 59  25 46 2  27 49 2  29 26 1  30 34 1  31 15 49 28  31 30 0 0 0  5  4  3  2  1  0     

CHAP. XVIII. The use of the Table of Declination  
THis Table of Declination is made so particularly to every min. of the Ecliptic, to avoid tediousness, in seeking the part proportional, when you would find out thereby either the Declination of the Sun, his place being first given in degrees and minutes: or else the place of the Sun in the Zodiac; his Declination being first known by Observation, for which cause especially this labour was undertaken, that hereby it might presently appear how well the Ephemerideses and Astronomical Tables hitherto published, agree with the truth of the heavens. Wherein many times no small difference is found, even in the Prutenick Tables themselves, (which have been hitherto accounted the most perfect in that kind) disagreeing half a degree and more from the truth, and that in the place of the Sun, whose motion of all others is accounted most simple and regular, and most easy to be found out.  
To find out the Declination of the Sun by his place first given, by help of this table do thus: If the Sun be in Aries, Taurus, Gemini, Libra, Scorpio, Sagittarie, seek the Sign and degree of the Sun in the upper margin or head of the Table, and the odd minutes (if there be any) in the first column towards the left hand: then look where the line proceeding towards the right hand from the minute of the Sun crosseth the column coming downwards from the degree of the Sun, for there you have the Declination of the Sun. But if the Sun be in Cancer, Leo Virgo, Capricorn, aquary, or Pisces, do chose, that is, seek the sign and degrees of the Sun in the nether margin or foot of the Table, and the minutes (if there be any) in the last column next the right hand: and following the line of the minute of the Sun towards the left hand: and the column of the degree of the Sun upwards, in the common meeting of that line and column you shall find the declination of the Sun.  
Example of the first: the first of May 1609, the place of the Sun is in 20 degrees 45 minutes of Taurus according to the Ephemerideses of the Sun hereafter following, made agreeable to many exact Observations, taken by a Quadrant of six foot and a quarter semidiameter in the years 1594. 1595. 1596. 1597. Finding therefore Taurus and the 20 degree in the upper part of this Table, and 45 minutes in the first column, I have in the common meeting (of the column descending from 20. and of the line proceeding from 45. minutes towards the right hand) 18. degrees, 0▪ minute's 18. seconds, the Declination of the Sun the same day at noon here at London.  
Example of the second: The 15. of August the same year by the same Ephemerideses, the Sun is in 2, degr. 2. minutes of Virgo, Therefore I seek Virgo, and 2. in the nether part of this Table and 50. minutes in the last column towards the right hand ascending upwards. Then following the line of 2 minutes leftwards and the column of 2. degrees upwards in the common meeting of the line and column, I find ten degrees, 47. minutes, 19 sec. the declination of the Sun the same day at noon, for the Meridian of London.  
But the Declination of the Sun being first known (by Observation or otherwise) the place of the Sun shall most easily be found out by this Table, after this manner: Seek the Sun's Declination in the Area of the Table: then if the sign wherein the Sun is (which you may for the most part easily know by estimation) be in the head of the Table, ascend upwards to the top of the same column in which you found the Declination given, for there you shall have the degree of the Sun: follow also the line wherein you find the given Declination towards the left hand till you come to the first column leftwards, and there you shall have the minute also.  
But if the name of the sign wherein the Sun is, be in the nether part of the Table, you must do all things chose; descending from the Declination found in the Area of this Table in the same column, till you come to the lowest part thereof, where you shall find the degree of the Sun: and proceeding from the Declination towards the right hand in the same line till you come to the last column, where you shall find the minutes to be adjoined, that you may have the true place of the Sun.  
This way of finding out the place of the Sun by his Declination, first known by Observation, is then of especial use and truth, when the Sun is near the Equinoctial points; for there, his Declination altereth quickest, increasing or decreasing about 24 min. in 24. hours. But when the Sun is near either of the Tropics, the missing of one minute, yea or half a minute in observing the Declination, may cause you err an whole degree and more, in the place of the Sun. He therefore that listeth try how well the Ephemerideses and Astronomical Tables hitherto published agree with the truth of the heavens, had best make Observation when the Sun is in Pisceses, Aries, Virgo, and Libra, where mising one whole minute in Observing the declination, will cause you miss not past two minutes and an half in the true place of the Sun.  
When the Sun is near either of the Equinoctial points, there may sometimes be some small difficulty in finding out what sign the Sun is in, which may easily be avoided thus: The Meridian Altitude of the Sun increasing (as in Winter and Spring time) if the height of the Sun be less than the compliment of the Poles elevation, the Sun is in Pisces: otherwise in Aries. But if the Meridian Altitudes of the Sun be every day less than other, (as in Summer and Autumn, and the height of the Sun at noon greater than the height of the Equinoctial, the Sun is in Virgo, otherwise in Libra.  
There may likewise be some doubt in what sign the Sun is, being near either of the Tropics, which may be resolved thus: the Sun having South Declination increasing, is in sagittary: but if the Declination of the Sun be Southerly and decreasing, he is in Capricorn. chose the Declination of the Sun being Northerly and increasing, he is in Gemini, if decreasing he is Cancer.  
Now whether the Declination of the Sun increase or decrease, you may know by comparing the Declinations of two days together. For if the Declination answerable to the second day be greater, the Declination increaseth: otherwise it decreaseth. If both days have equal Declination, the first day the Sun is in Gemini, the second in Cancer, if his Declination be Northerly; if Southerly, the first day he is in sagittary, the second in Capricorn.  
An example or two will make all plain: The eighth day of April 1597. the Declination of the Sun was found by Observation to be 10. degrees, 55. minutes, 27. seconds, which I seek out in the Area of this Table: and in the head of the same column, in which I find the Declination that cometh nearest unto this, that is 10 degr. 55. min. 33. sec. I see 28. degrees of Aries, (for in April, the Sun cannot be in Libra,) and in the same line wherein I found this Declination, in the furthest column towards the left hand I find 21. minutes, out of which abate 17. seconds, that is the part proportional answerable to 6. sec. which is the excess of 10, degr, 55. minutes, 33. sec. (the Declination found in the Table) above. 10. degr. 55. min 27. sec. (the Declination found by Observation) and there shall remain the true place of the Sun the same year and day 28. degr. 20. min. 43. sec. of Aries. Which Maginus following Copernicus and the Prutenical Tables (as he professeth) maketh to be the 27. degr. 57 minutes of Aries almost: that is, 24. minutes, less than truth, that equation also being abated, which is answerable to the difference of Longitude betwixt London and Venice.  
The 11. of March the same year at London (whereby many and diligent Observations by large and several Instruments, the height of the Pole is found to be 51 degrees, 32 minutes) the apparent Meridian Altitude of the Sun was exactly Observed to be 38 degrees, 49 minutes: but being corrected by the Parallax and Refraction of the Sun, answerable to that height, his true height shallbe 38 degr. 51 min. 4 sec. Whereby it appeareth that his true Declination the same day at Noon was 0 degr. 23 min, 4 sec. And that Northerly, because the height of the Sun was greater than the height of the Equinoctial. It is plain therefore that at that time the Sun was entered into Aries. But now to know how far he was entered; seek out 0 degr. 23 min. 4 sec. Or the number next to it, which is 0 degr. 23 min. 9 sec. In the Area of this Table: wherewith you shall also find in the same line in the column next the left hand 58 minutes, and in the top of the column right over this Declination you shall have 0 degr. Therefore it is manifest that at that time the Sun was in 0 degr. 58 min. of Aries almost, for there wanteth only 12 seconds hereof, that is the Part Proportional answerable to the excess of 9 sec. above 4 sec. Where Maginus, after the Prutenick account, maketh it to be in 0 degr. 25 min. of Aries; that is, 33 minutes wanting of the truth found by Observation.  
The like difference I have often found by many and diligent Observations, especially for the space of the four years before mentioned: the whole Catalogue of which Observations I thought good (for thy further satisfaction herein) to set down in a Table. (after I have first showed with what Instrument, and after what manner I Observed the same) that if any error herein hath been committed, it may the more easily appear, and be amended.   

CHAP. XIX. The description and use of a great Quadrant, for Observation of the Sun on Land.  
THe Instrument therefore wherewith I took those Observations was a Quadrant of more than six foot and a quarter semidiameter, (for the room wherein I was to use it, could not well admit a greater quantity) which by reason of his largeness was so exactly made and divided, that both minutes and half minutes might therein be easily discerned. The Limb and sides of the Quadrant were about two inches and a quarter in thickness; the breadth of the Limb about four inches: the breadth of the Sides about two inches and an half.  
In the midst of the ends of one side of this Quadrant were two round holes made, in either end one: whereby the Quadrant was hanged (like a gate on his hinges, upon two round pins, fitted to those holes, and fixed in the ends of a copple of sockets, put close upon a strong square post, Perpendicularly erected, and the upper end thereof fastened to the side of a principal rafter in an upper chamber, where a window (according to the Reclination of the Roof of the house) was made between it and the next rafter, in such sort, that carrying your eye along by the circumference of the Quadrant, you might by the Centre thereof placed at the window; see any part of the Heavens near the Meridian, from the Zenith to the Horizon. The nether end of this post resting on the floor was put into the midst of a socket nailed to the floor, which was so wide, that on every side the post, wedges might be put in to coin it at pleasure this way or that way, till the side of the Quadrant were found to stand exactly Perpendicular, by the hanging of the plumline all alongst most precisely upon a line Parallel to the Zenith line of the Quadrant. To the Centre of the Quadrant was fastened a strong Ruler of one inch in thickness, two inches in breadth, and almost six foot and an half in length, carrying two Sights upon it (viz. at either end one) of equal breadth and length, the end of the middle line of each Sight falling Perpendicularly upon the middle or fiducial line and plain Superficies of the Ruler. Through the upper Sight placed at the Centre, was made a square hole as great as it could well be. Through the midst of this Sight and hole was put a strait wire, erected Perpendicularly from the Fiducial line and plain of the Ruler, and so much of it made flat and thin, as was between the top and base of that square hole. This wire served for Observing the Stars, the flat side whereof was to be turned towards the eye in Observing of great Stars, and the narrow side or edge of it was turned to the eye-ward when small Stars were to be Observed. Through the midst of the nether Sight (from the top of it to the Base thereof) was made a narrow slit Perpendicularly erected likewise from the Fiducial line and plain of the Ruler and Quadrant. When I Observed the Stars▪ I looked through this slit, Elevating and Depressing the Ruler, till the wire (being first fitted to bigness of the Star) did even cover the Star from my sight: in such sort, that I might see both edges of the Star alike on either side above and beneath the wire. The square hole in the Sight had a cover fitted to it like the cover of a box; wherewith it was wholly covered when the Sun was to be Observed. The nether end of the Ruler carrying the Sights, was to be fastened with a screw-pin, at any part of the Circumference of the Quadrant as need required,  
With this Quadrant (always rectified by the Plumb line in time of Observation, as before is showed) the height of the Sun was most easily and exactly Observed, by turning the Quadrant this way or that away, and Elevating or depressing the Ruler carrying the Sights, till the top and sides of the shadow of the Upper Sight, placed at the centre fell upon the nether Sight placed at the centre fell upon the nether Sight placed at the Circumference, equidistantly from the top and sides thereof; For then the upper edge of the Ruler showeth precisely the height of the Sun desired in degrees and minutes upon the limb of the Quadrant: saving that one whole degree was always to be added thereto, because the breadth of that part of the Ruler that lay upon the Limb of the Quadrant was made to be just equal to two degrees: that is on either side one degree from the fiducial line.  
Now for finding out the Meridian Altitudes of the Sun and Stars, I first found the Meridian line thus: with the quadrant rectified and used, as before is showed, I Observed the height of the Sun in the forenoon; and so warily letting the Quadrant stand immovable, and laying the side of a strait Ruler (that was about seven foot in length) close along to the perpendicular side of the Quadrant: close by the end of that side of the Ruler (touching the floor of the chamber, I made a prick upon the floor: Also laying the side of the Ruler to the perpendicular side, and limb of the Quadrant, I made in like manner another prick (so far as conveniently I could from the former) upon the floor, close by the corner of that side of the Ruler.  
By these two pricks, I drew a right line which represented the intersection of the Sun's Azimuth, or of the continued plain of the Quadrant, and of the plain of the floor, in the time of Observation. Likewise in the afternoon (the Ruler of the Quadrant carrying the Sights, being fixed in the same place, where it was in time of Observation in the forenoon) I Observed diligently till the Sun came to the same height that he had when I Observed in the forenoon, which I did by following the motion of the Sun's shadow with the Quadrant, till the edges of the top and sides of the shadow of the upper Sight fell upon the nether Sight, equidistantly from the top and Sides thereof.  
Then carefully letting the quadrant stand immovable, and drawing the line of intersection of the floor, and Sun's Azimuth, in time of the afternoon Observation, in like manner as I did in the forenoon, setting one foot of the Compasses in the intersection of those two lines, with the other, drawing an arch, so great as I could between the same lines and finding out the midst of this arch, a line from the Centre drawn by this midst, was the Meridian line: over which, with help of a long Ruler laid to the upright Side, and Limb of the Quadrant, and extended to the floor, (as before) I always placed and fastened the plain of the Quadrant (understood to be continued to the floor) so oft as I Observed the Meridian Altitudes of the Sun or Stars.  
Notwithstanding there is some little error in finding the Meridian after this manner, except it be when the Sun is in, or so near one of the Tropical points, that there can be no sensible alteration of his Declination between the times of the forenoon and afternoon Observations. But the consequents of this error in Observing Meridian Altitudes, may for their smallness justly be neglected and easily avoided if you attend your Observation, but a little before and after the Sun or Stars to be Observed, come upon the Meridian thus found. And for the more certainty, I took three Observations in the forenoon, and as many in the afternoon, and so found out three Meridian lines, all Parallels each to other, without notable difference; which if it should have chanced to be any, the middlemost Meridian should be like to be the truest.  

A Table of OBSERVATIONS Of the Meridian Altitudes of the Sun, taken by a large Quadrant, of more than six foot Semidiameter, in the years 1594, 1595, 1596, 1597, at London, where the Elevation of the Pole was by the same Quadrant, and otherwise also exactly observed and found to be 51 degr. 32 min.  1594 May. The Sun's apparent height. The Sun's true height. The Sun's apparent declination. Day. Degr. Min. Sec. Degr. Min. Sec Degr. Min. Sec. 9 Thursd. 58 14  58 15 36 19 46 0 11 Satur. 58 41  58 42 33 20 13 0 13 Mund. 59 4  59 5 33 20 36 0 14 Tuesd. 59 15  59 16 33 20 47 0 17 Frid. 59 45  59 46 30 21 17 0 26 Sund. 61 1 30 61 2 58 22 33 30 27 Mund. 61 8  61 9 28 22 40 0 28 Tuesd. 61 14  61 15 28 22 46 0 29 Wednes. 61 20 30 61 21 58 22 52 30 31 Frid. 61 31  61 32 25 23 3 0 june          1 Saturd. 61 35  61 36 25 23 7 0 2 Sund. 61 40  61 41 25 23 12 0 4 Tuesd. 61 46 30 61 47 55 23 18 30 6 Thurs. 61 52 30 61 53 55 23 24 30 7 Frid. 61 54  61 55 25 23 26 0 8 Saturd. 61 55 30 61 56 55 23 27 30 9 Sund. 61 56 30 61 57 55 23 28 30 10 Mund 61 57  61 58 25 23 29 0 11 Tuesd. 61 58  61 59 25 23 30 0 12 Wednes 61 58  61 59 25 23 30 0 13 Thursd 61 57 30 61 58 55 23 29 30 14 Frid. 61 57  61 58 25 23 29 0 15 Saturd. 61 56  61 57 25 23 28 0 22 Saturd. 61 35  61 36 25 23 7 0 23 Sund. 61 32  61 33 25 23 4 0 24 Mund. 61 26 30 61 27 58 22 58 30 july          6 Saturd. 59 56 00 59 57 30 21 28 0 8 Mund. 59 36 30 59 38 00 21 8 30 9 Tuesd. 59 26 0 59 27 33 20 58 0 15 Mond. 58 14 0 58 15 34 19 46 0 16 Tuesd. 58 1 0 58 2 36 19 33 0 The Suns true declination. The Sun's place by observation. The Sun's place by Prutenick Tables. The difference. Degr. Min. Sec Degr. Min. Sec. Degr. Min. Sec. Min. Sec. 19 47 36 28 2 0 27 ♉ 43 0 19 0 20 14 33 ♊ 5 30 29 39 0 26 30 20 37 33 1 57 0 1 ♊ 34 0 23 0 20 48 33 2 52 40 2 32 0 20 40 21 18 30 5 33 40 5 25 0 8 40 22 34 58 14 10 30 14 2 0 8 30 22 41 28 15 7 0 15 0 0 7 0 22 47 28 16 3 0 15 57 0 6 0 22 53 58 17 7 30 16 55 0 12 30 23 4 25 19 4 30 18 50 0 14 30            23 8 25 19 55 0 19 47 0 8 0 23 13 25 21 5 0 20 44 0 21 0 23 49 55 22 52 0 22 39 0 13 0 23 25 55 25 3 0 24 34 0 29 0 23 27 25 25 46 0 25 31 0 15 0 23 28 25 26 19 0 26 29 0 10 0 23 29 55 27 22 0 27 26 0 4 0 23 30 25 27 50 0 28 23 0 33 0 23 31 25 29 24 0 29 21 0 3 0 23 31 25 0 ♋ 35 0 0 ♋ 18 0 17 0 23 30 55 1 36 0 1 15 0 21 0 23 30 25 2 10 0 2 12 0 2 0 23 29 25 3 1 30 3 10 0 8 30 23 8 25 10 5 0 9 51 0 46 0 23 5 25 10 43 0 10 48 0 5 0 22 59 58 11 47 30 11 45 0 2 0            21 29 30 23 23 0 23 13 0 10 0 21 10 0 25 13 40 25 8 0 5 40 20 59 33 26 10 0 26 5 0 5 0 19 47 34 1 ♌ 58 0 1 ♌ 50 0 8 0 19 34 36 2 55 0 2 47 0 11 0 1594 Iul●. The Sun's Apparent height. The Sun's True height The Sun's apparent Declination. Day. Deg. Min. Sec. Deg. Min. Sec. Degr. Min. Sec. 19 Frid. 57 20 0 57 21 39 18 52 0 25 Thursd. 55 50 0 55 51 41 17 22 0 31 Wednes. 54 9 30 54 11 11 15 41 30 August.          3 Saturd. 53 15 30 53 17 18 14 47 30 6 Tuesd. 52 19 30 52 21 21 13 51 30 7 Wednes. 52 0 0 52 1 51 13 32 0 8 Thurs. 51 40 30 51 42 21 13 12 30 9 Frid. 51 21 30 51 23 24 12 53 30 12 Mond. 50 23 0 50 24 54 11 55 0 15 Thursd. 49 21 0 49 22 58 10 53 0 19 Mond. 47 57 0 47 47 59 9 29 0 23 Frid. 46 30 0 46 32 2 8 2 0 24 Satur. 46 7 30 46 9 35 7 39 30 26 Mond. 45 23 30 45 25 32 6 55 30 29 Thursd. 44 16 0 44 18 4 5 48 0 September.          16 Mond. 37 18 0 37 19 58 1 10 0 17 Tuesd. 36 54 0 36 55 58 1 34 0 19 Thursd. 36 7 0 36 8 55 2 21 0 20 Frid. 35 44 0 35 45 55 2 44 0 October.          1 Tuesday. 31 28 0 31 29 19 7 0 0 3 Thursd. 30 43 30 30 44 49 7 44 30 4 Friday. 30 21 0 30 22 11 8 7 0 5 Saturd. 29 58 30 29 59 41 8 29 30 16 Wednes. 26 0 30 26 0 58 12 27 30 18 Friday. 25 20 30 25 20 44 13 7 30 19 Saturd. 25 0 0 25 0 14 13 28 0 21 Mond. 24 20 0 24 19 45 14 8 0 25 Friday. 23 5 0 23 4 16 15 23 0 29 Tuesd. 21 52 0 21 50 48 16 36 0 The Suns true declination. The Sun's place by Observation. The Sun's place by Prutenick Tables The difference. Degr. Min. Sec. Degr. Min. Sec Degr. Min. Sec. Min. Sec. 18 53 39 5 ♌ 47 45 5 ♌ 39 0 8 45 17 23 41 11 29 52 11 25 0 4 52 15 43 11 17 15 6 17 10 0 5 6            14 49 18 20 8 30 20 3 0 5 30 13 53 21 23 2 0 22 57 0 5 0 13 33 51 24 1 0 23 54 0 7 0 13 14 21 24 59 0 24 52 0 7 0 12 55 24 25 55 20 25 50 0 5 20 11 56 54 28 45 24 28 44 0 1 24 10 54 58 1 ♍ 40 36 1 ♍ 38 0 2 36 9 19 59 6 1 40 5 30 0 31 40 8 4 2 9 25 0 9 22 0 3 0 7 41 35 10 24 15 10 21 0 3 15 6 57 32 12 19 45 12 17 0 2 45 5 50 4 15 14 45 15 12 0 2 45            1 8 2 2 ♎ 50 30 2 ♎ 48 0 2 0 1 32 2 3 50 42 3 47 0 2 42 2 19 5 5 49 0 5 45 0 2 0 2 42 5 6 46 52 6 44 0 2 52            6 58 41 17 43 13 17 35 0 6 13 7 43 11 19 40 0 19 34 0 6 0 8 5 4● 20 39 48 20 33 0 6 48 8 28 19 21 39 36 21 33 0 6 36 12 27 2 2 ♏ 40 36 2 ♏ 30 0 10 0 13 7 16 4 42 42 4 30 0 12 42 13 27 46 5 40 51 5 30 0 10 51 14 8 15 7 43 45 7 30 0 13 45 15 23 44 11 41 30 11 30 0 11 30 16 37 12 15 46 20 15 31 0 14 20 1594 November. The Sun's Apparent height. The suns True height The ●uns apparent Declination. Day. Degr· Min. Sec. Degr. Min. Sec. Degr. Min. Sec. 1 Friday 21 0 0 20 58 19 17 28 0 3 Sund. 20 27 0 20 24 50 18 1 0 4 Mund. 20 12 0 20 9 50 18 16 0 7 Thursd. 19 27 0 19 24 20 19 1 0 10 Sund. 18 43 0 18 40 20 19 45 0 19 Tuesd. 16 55 0 16 51 22 21 33 0 20 Wednes·s 16 45 0 16 41 22 21 43 0 22 Friday. 16 27 0 16 22 53 22 1 0 23 Saturd. 16 18 0 16 13 53 22 10 0 27 Wednes. 15 48 0 15 43 53 22 40 0 28 Thursd. 15 41 0 15 36 53 22 47 0 29 Friday. 15 35 0 15 30 53 22 53 0 December.          17 Tuesd. 15 6 0 15 1 24 23 22 0 18 Wednes. 15 9 0 15 4 24 23 19 0 20 Friday. 15 16 0 15 11 24 23 12 0 22 Sunday. 15 25 0 15 20 24 23 3 0 29 Sunday. 16 10 30 16 6 23 22 17 30 January.          9 Thursd. 18 4 30 18 1 21 20 23 30 18 Saturd. 30 13 0 20 10 50 18 15 0 23 Thursd. 21 35 0 21 33 48 16 53 0 26 Sunday. 22 28 30 22 27 18 15 59 30 31 Friday. 24 3 0 24 2 45 14 25 0 February.          1 Saturd. 24 22 0 24 21 45 14 6 0 5 Wednes. 25 43 0 25 43 28 12 45 0 8 Satur. 26 46 0 26 46 41 11 42 0 13 Thursd. 28 33 0 28 34 2 9 55 0 15 Saturd. 29 19 0 29 20 2 9 9 0 16 Sund. 29 40 30 29 41 41 8 47 30 17 Mond. 30 3 0 30 4 11 8 25 0 20 Thursd 31 11 30 31 12 49 7 16 30 The Suns true declination. The Sun's place by Observation. The Sun's place by Prutenick Tables The difference. Degr. Min. Sec. Degr. Min. Sec. Degr. Min. Sec. Min. Sec. 17 29 41 18 51 48 18 32 0 19 48 18 3 10 20 55 48 20 33 0 22 48 18 18 10 21 53 4 21 33 0 20 4 19 3 40 24 54 12 24 35 0 19 12 19 47 40 28 2 25 27 36 0 26 25 21 36 38 7 ♐ 19 30 6 ♐ 43 0 36 30 21 46 38 8 21 12 7 43 0 38 12 22 5 7 10 23 6 9 45 0 38 6 ●2 14 7 11 27 0 10 46 0 41 0 22 44 7 15 31 20 14 49 0 42 20 22 51 7 16 38 30 15 50 0 48 30 22 57 7 17 40 50 16 48 0 52 50            23 26 36 4 ♑ 38 30 5 ♑ 10 0 31 30 23 23 3● 5 53 30 6 11 0 18 30 23 16 36 8 5 45 8 13 0 7 15 23 7 36 10 15 36 10 16 0 0 24 22 21 37 17 37 0 17 23 0 14 0            20 26 39 28 56 40 28 35 0 21 4 18 17 10 8 ♒ 10 45 7 ♒ 43 0 27 45 16 54 12 13 14 38 12 47 0 27 38 16 0 42 16 17 10 15 50 0 27 10 14 25 15 21 23 48 20 53 0 30 48            14 6 15 22 22 24 21 53 0 29 24 12 44 32 26 27 18 25 56 0 31 18 11 41 19 29 29 54 28 57 0 32 54 9 53 58 4 ♓ 29 14 3 ♓ 59 0 30 14 9 71 58 6 34 6 5 59 0 35 6 8 46 19 7 32 18 6 59 0 33 18 8 23 49 8 32 23 7 59 0 33 23 7 15 11 11 33 36 11 0 0 33 36 1595. February. The Sun's apparent height. The Sun's True height The Sun's apparent Declination. Day. Degr. Min. Sec. Degr. Min. Sec. Degr. Min· Sec. 21 Friday. 31 34 0 31 35 27 6 54 0 27 Thursd. 33 54 0 33 55 44 4 34 0 March.          1 Saturd. 34 40 0 34 41 52 3 48 0 3 Mond. 35 27 0 35 28 52 3 1 0 12 Wednes. 39 0 0 39 2 4 0 32 0 15 Saturd. 40 10 0 40 12 8 1 42 0 17 Mond. 40 58 0 41 0 7 2 30 0 18 Tuesd. 41 22 0 41 24 7 2 54 0 19 Wednes. 41 45 0 41 47 6 3 17 0 20 Thurs. 42 9 0 42 11 6 3 41 0 21 Friday. 42 31 0 42 33 5 4 3 0 25 Tuesd. 44 4 0 44 6 4 5 36 0 26 Wednes. 44 26 30 44 28 34 5 58 30 27 Thursd. 44 49 0 44 51 2 6 21 0 31 Monday. 46 19 0 46 21 5 7 51 0 April.          3 Thursd. 47 25 0 47 27 3 8 57 0 7 Monday. 48 51 0 48 52 58 20 23 0 8 Tuesd●y 49 12 0 49 13 58 10 44 0 14 Mond●y. 51 14 0 51 15 54 12 46 0 May.          3 Satur●. 56 47 0 56 48 39 18 19 0 6 Tuesday▪ 57 29 30 57 31 9 19 1 31 14 Wednes. 59 10 0 59 11 33 20 42 0 17 Tuesday. 59 43 30 59 45 0 21 25 30 21 Wednes. 60 21 30 60 23 0 21 53 30 23 Friday. 60 38 0 60 39 28 22 10 0 24 Saturd. 60 46 0 60 47 28 22 18 0 29 Thursd. 61 19 0 61 20 28 22 51 0 june.          7 Saturd. 61 54 0 21 55 25 23 26 0 9 Monday 61 56 30 61 57 55 23 28 30 The Suns true declination. The Sun's Place by observation. The Sun's place by Prutenick Tables. The difference· Degr. Min. Sec. Degr. Min. Sec Degr. Min. ●ec. Min. Sec. 6 52 33 12 32 45 12 0 0 32 45 4 32 16 18 34 3 17 59 0 35 3            3 46 8 20 31 17 19 59 0 32 17 2 59 8 22 30 8 21 58 0 32 8 0 34 4 1 ♈ 25 22 0 ♈ 55 0 30 22 1 44 8 4 21 5 3● 53 0 28 5 2 32 7 6 21 45 5 51 0 30 45 2 56 7 7 22 15 6 50 0 32 15 3 19 6 8 20 18 7 50 0 30 18 3 43 6 9 21 3 8 49 0 32 3 4 5 5 10 16 48 9 48 0 28 48 5 38 4 14 14 23 13 44 0 30 23 6 0 34 15 12 20 14 43 0 29 20 6 23 2 16 10 30 15 42 0 28 30 7 53 5 20 6 5 19 38 0 28 5            8 59 3 23 1 52 22 34 0 27 52 10 24 58 26 56 0 26 28 0 28 0 10 45 58 17 54 16 27 27 0 27 16 12 47 54 3 ♉ 42 33 3 ♉ 18 0 24 33            18 20 39 22 2 40 21 42 0 20 40 19 3 9 24 52 4 24 36 0 16 4 20 43 33 2 ♊ 27 10 2 ♊ 17 0 10 10 21 17 0 5 25 12 5 10 0 15 12 21 55 0 9 15 0 9 1 0 14 0 22 11 28 11 7 45 10 56 0 11 45 22 19 28 12 6 38 11 53 0 13 38 22 52 28 16 52 10 16 40 0 12 10            23 27 25 25 46 0 25 17 0 29 0 32 29 55 27 22 0 27 12 0 10 0 1595 june. The Sun's apparent height The Sun's true height. The Sun's apparent Declination. Day. Degr. Min Sec. Degr Min. Sec. Degr. Min. Sec. 21 Saturd. 61 40 30 61 41 55 33 21 30 23 Mond. 61 32 0 61 33 25 23 4 0 26 Thursd. 61 16 0 61 17 28 22 48 0 july.          30 Wednes. 54 30 0 54 31 45 16 2 0 31 Thursd. 54 14 0 54 15 46 15 46 0 August.          1 Frid. 53 56 0 53 57 46 15 28 0 2 Saturd. 53 37 0 53 38 46 15 9 0 8 Frid. 51 45 0 51 46 51 13 17 0 9 Saturd. 51 26 0 51 27 54 12 58 0 10 Sund. 51 6 0 51 7 54 12 38 0 19 Tusd. 48 2 0 48 4 0 9 34 0 21 Thursd. 47 20 0 47 22 3 8 52 0 23 Friday 46 57 30 46 59 33 8 29 30 26 Tuesd. 45 30 0 45 32 4 7 2 0 29 Friday. 44 22 0 44 24 4 5 54 0 September.          7 Sund. 40 54 0 40 56 7 2 26 0 8 Mond. 40 30 0 40 32 7 2 2 0 9 Tuesd. 40 7 0 40 9 8 1 39 0 10 Wed. 39 44 0 39 46 8 1 16 0 11 Thursd. 39 20 0 39 22 5 0 52 0 16 Tuesd. 37 23 30 37 25 29 1 4 30 17 Wed. 37 0 0 37 1 58 1 28 0 18 Thursd. 36 36 0 36 37 58 1 52 0 19 Friday. 36 12 0 36 13 55 2 16 0 20 Saturd. 35 48 30 35 50 25 2 39 30 23 Tuesd. 34 38 0 34 39 52 3 50 0 26 Friday 33 29 0 33 30 39 4 59 0 October.          2 Thursd. 31 11 30 31 12 49 7 16 30 3 Friday. 30 48 0 30 49 19 7 40 0 The Suns true declination The Sun's place by Observation. The Sun's place by Prutenick Tables. The difference. Degree. Min. Sec Degr. Min. Sec. Degr. Min. Sec. Min. Sec. 28 13 55 8 ♋ 47 45 8 39 0 8 45 23 5 25 10 43 15 10 34 0 9 15 22 49 28 13 37 50 13 26 0 11 50            16 3 45 16 ♌ 7 0 15 ♌ 58 0 9 0 15 47 46 17 0 3 16 0 2 4 3            15 29 46 17 58 57 17 54 0 4 57 15 10 46 19 0 16 18 51 0 9 16 13 18 51 24 45 48 24 38 0 7 48 12 59 54 25 42 6 25 36 0 6 6 12 39 34 26 40 54 26 34 0 6 54 9 36 0 5 ♍ 18 14 5 ♍ 15 0 3 14 8 54 3 7 11 32 7 12 0 0 28 8 31 33 8 11 46 8 10 0 1 46 7 4 4 12 2 44 12 3 0 0 16 5 56 4 14 59 16 14 58 0 1 16            2 28 7 23 48 18 23 44 0 4 18 2 4 7 24 48 42 24 43 0 5 42 1 41 8 25 46 25 25 41 0 5 25 1 18 8 26 44 10 26 40 0 4 10 0 54 5 27 44 27 27 39 0 5 27 1 2 31 2 ♎ 36 40 2 ♎ 33 0 3 40 1 26 2 3 35 40 3 32 0 3 40 1 50 2 4 35 35 4 31 0 4 55 2 14 5 5 36 22 5 30 0 6 22 2 37 35 6 35 32 6 29 0 6 32 3 48 8 9 33 52 9 26 0 7 52 4 57 21 12 29 57 12 24 0 5 57            7 15 11 18 26 22 18 20 0 6 22 7 38 41 19 28 5 19 19 0 9 5 1595 October. The Sun's Apparent height. The Sun's True height▪ The Suns apparent Declination. Day. Deg. Min. Sec. Degr. Min. Sec. Deg. Min. Sec. 9 Thursd. 28 35 0 28 35 55 9 53 0 11 Saturd. 27 12 0 27 52 54 10 36 0 12 Sund. 27 30 0 27 30 47 10 58 0 15 Wednes. 26 26 30 26 27 3 12 1 30 17 Friday. 25 45 0 25 45 25 12 43 0 30 Thursd. 21 37 30 21 36 8 16 50 30 Novemb.          18 Tuesd. 17 8 0 17 4 26 21 20 0 19 Wed. 16 58 0 16 54 21 21 30 0 20 Thursd. 16 48 0 16 44 16 21 40 0 24 Mond. 16 13 30 16 9 30 22 14 30 December.          2 Tusd. 15 20 30 15 15 34 23 7 30 10 Wednes. 15 0 0 14 55 30 23 28 0 12 Friday. 14 58 0 14 53 23 23 30 0 18 Thursd. 15 8 0 15 3 28 23 20 0 20 Saturd. 15 14 0 15 9 31 23 14 0 21 Sund. 15 18 0 15 13 33 23 10 0 24 Wed. 1 34 0 15 29 40 22 54 0 30 Tuesd 16 16 0 16 12 0 22 12 0 January.          1 Thursd. 16 34 0 16 30 7 21 54 0 3 Saturd. 16 53 0 16 44 18 21 35 0 10 Saturd. 18 14 0 28 18 58 20 14 0 12 Mond. 18 39 30 18 36 40 19 48 30 14 Wednes. 19 8 0 19 5 24 19 20 0 22 Thursd. 21 14 0 21 12 26 17 14 0 24 Wednes. 21 48 0 21 16 42 16 40 0 February.          13 Friday. 28 29 0 28 29 58 9 59 0 17 Tuesd. 29 57 0 29 58 10 8 31 0 18 Wed. 30 10 0 30 11 12 8 18 0 24 Tuesd. 32 37 30 32 39 2 5 50 30 The Suns true declination. The Sun's place by observation. The Sun's place by Prutenick Tables. The difference. Degr. Min. Sec· Degr. Min. Sec. Degr. Min. Sec Min. Sec. 9 52 1 25 25 27 25 17 0 8 27 10 35 6 27 24 3 27 16 0 8 2 10 57 13 28 25 40 28 16 0 9 40 12 0 57 1 ♏ 26 14 1 ♏ 15 0 11 14 12 42 35 3 26 57 3 15 0 11 57 16 51 52 16 37 14 16 16 0 21 14            21 23 34 6 ♐ 2 30 5 ♐ 27 0 35 30 21 33 39 7 1 33 6 28 0 33 33 21 43 44 8 3 0 7 28 0 35 0 22 18 30 11 59 22 11 32 0 27 22            23 12 26 20 50 15 16 39 0   23 32 30    27 47 0   23 34 37    29 50 0   23 24 32 5 ♑ 32 0 5 ♑ 56 0 24 0 23 18 29 7 34 0 7 58 0 24 0 23 14 27 8 39 45 8 59 0 19 15 22 58 20 12 5 50 12 3 0 2 50 22 16 0 18 19 15 18 9 0 10 15            21 57 53 20 26 0 20 11 0 15 0 21 38 42 22 28 0 22 24 0 14 0 20 17 2 29 42 45 29 22 0 20 45 19 51 20 1 ♒ 41 13 1 ♒ 23 0 18 13 19 22 36 3 46 34 3 25 0 21 34 17 15 34 11 59 4 11 32 0 27 4 16 41 18 13 59 30 13 30 0 29 30            9 58 2 4 ♓ 18 6 3 ♓ 40 0 38 6 8 29 50 8 16 22 7 44 30 31 52 8 16 48 8 51 3 8 45 0 6 3 5 48 57 15 18 10 14 45 0 33 10 1595 February. The Sun's Apparent height. The Sun's True height The Sun's apparent Declination. Day. Degr. Min. Sec. Degr. Min. Sec. Dege. Min. Sec. 25 Wed. 33 1 0 33 2 35 5 27 0 26 Thursd. 33 24 0 33 25 39 5 3 0 29 Sund. 34 34 30 34 36 19 3 53 30 March.          13 Saturd. 39 42 0 39 44 7 1 14 0 14 Sund. 40 6 0 40 8 8 1 38 0 16 Tuesd. 40 52 0 4 54 7 2 24 0 April.          20 Tuesd. 53 23 0 53 24 48 14 55 0 24 Saturd. 54 35 0 54 36 44 16 7 0 25 Sund. 54 51 30 54 53 13 16 23 30 26 Mond 55 8 30 55 10 13 16 40 0 28 Wed. 55 41 0 55 42 41 17 13 0 19 Thursd 55 57 0 55 58 36 17 29 0 May.          4 Tuesd 57 13 0 57 14 39 18 45 0 11 Tuesd. 58 45 30 58 47 5 20 17 30 jund.          15 Tuesd. 61 54 0 61 55 25 23 26 0 18 Friday. 61 47 0 61 48 25 23 19 0 july.          24 Saturd. 55 56 0 55 57 41 16 28 30 27 Tuesd. 55 8 0 55 9 43 16 40 0 29 Thursd. 54 34 0 54 35 44 16 6 0 30 Friday 54 17 0 54 18 46 15 49 0 31 Saturd. 54 0 0 54 1 46 15 32 0 August          10 Tuesd. 50 51 0 50 52 54 12 23 0 13 Friday 49 50 30 49 52 26 11 22 30 16 Mond. 48 48 0 48 49 58 10 20 0 21 Saturd. 47 1 30 47 3 33 8 33 30 30 Mond. 43 41 0 43 43 4 5 13 0 The Suns true declination The Sun's place by Observation. The Sun's place by Prutenick Tables. The difference Degree. Min. Sec Degr. Min. Sec. Degr. Min. Sec. Min. Sec. 5 25 25 16 18 8 15 45 0 33 8 5 2 21 17 17 15 16 45 0 32 15 3 51 41 20 17 12 19 45 0 32 12            1 16 7 3 ♈ 10 48 2 ♈ 39 0 31 48 1 40 8 4 11 2 3 38 0 33 2 2 26 7 6 6 40 5 37 0 29 40            14 56 48 10 ♉ 15 13 9 ♉ 51 0 24 13 16 8 44 14 9 40 13 44 0 25 40 16 25 13 15 5 20 14 42 0 23 20 16 42 13 16 3 42 15 40 0 23 42 17 14 41 17 57 45 17 36 0 21 45 17 30 36 18 55 10 18 34 0 21 10            18 46 39 23 45 4 23 24 0 21 4 20 19 5 0 ♊ 27 0 0 ♊ 8 0 19 0            23 27 25 4 ♋ 14 0 3 ♋ 39 0 35 0 23 20 25 6 58 40 6 31 0 27 40            17 29 41 11 ♌ 8 11 10 ♌ 56 0 12 11 16 41 43 13 58 3 13 49 0 9 3 16 7 44 15 53 40 15 44 0 9 40 15 50 46 16 50 10 16 42 0 8 10 15 33 46 17 45 3 17 39 0 6 3            12 24 54 27 24 24 27 17 0 7 24 11 24 26 0 ♍ 17 48 0 ♍ 11 0 6 48 10 21 58 3 12 17 3 5 0 7 17 8 35 33 8 1 5 7 55 0 6 5 5 15 4 16 44 40 16 40 0 4 40 1596 August. The Sun's apparent height The Sun's true height. The Sun's apparent Declination. Day. Degr. Min. Sec. Degr. Min. Sec Degr. Min. Sec. 31 Tuesd. 43 17 30 43 19 35 4 46 30 September.          5 Sund. 41 22 30 41 24 37 2 54 30 6 Mond. 40 59 0 41 1 7 2 31 0 7 Tuesd. 40 36 0 40 38 7 2 8 0 8 Wed. 40 12 30 40 14 38 1 44 30 13 Mond. 38 16 0 38 18 1 0 12 0 14 Tuesd. 37 52 0 37 54 1 0 36 0 25 Saturd. 33 34 30 33 36 10 4 53 30 27 Mond. 32 48 0 32 49 34 5 40 0 October.          4 Mond. 30 9 0 30 10 12 8 19 0 November.          2 Tuesd. 20 35 0 20 33 7 17 53 0 5 Friday. 19 47 30 19 45 14 18 40 30 January.          
1597  25 Tuesday▪ 22 19 0 22 17 57 16 9 0 29 Saturd. 23 34 0 23 33 32 14 54 0 March.          11 Friday. 38 49 0 38 51 4 0 21 0 12 Saturd· 39 13 0 39 15 4 0 45 0 13 Sund. 39 36 30 39 38 36 1 8 30 14 Monday 40 0 0 40 2 8 1 32 0 15 Tuesd. 40 23 0 40 25 8 1 55 0 16 Wednes. 40 46 30 40 48 37 2 18 30 20 Sund. 42 21 30 42 23 36 3 53 30 21 Mond. 42 44 0 42 46 5 4 16 0 April·s          8 Friday. 49 21 30 49 23 27 10 53 30 30 Saturd. 56 9 0 56 10 41 17 41 0 May.          2 Mond. 56 40 0 56 41 40 18 12 0 The Suns true declination The Sun's place by Observation. The Sun's place by Prutenick Tables. The difference. Degr. Min. Sec. Degr. Min. Sec. Degr. Min. Sec. Min. Sec▪ 4 51 35 17 44 47 17 38 30 6 17            2 56 37 22 36 26 22 31 0 5 26 2 33 7 23 35 43 23 30 0 5 43 2 10 7 24 33 40 24 28 0 5 40 1 46 38 25 32 38 25 27 0 5 38 0 9 59 0 ♎ 25 0 0 ♎ 21 0 4 0 0 33 59 1 25 10 1 19 30 5 40 4 51 50 12 15 52 12 9 0 6 52 5 38 26 14 15 18 14 8 0 7 18            8 17 48 21 11 35 21 3 0 8 35            17 54 53 20 ♏ 24 41 20 ♏ 3 0 21 41 18 42 46 23 29 30 23 4 0 25 30            16 10 3 15 ♒ 45 53 17 ♒ 20 0 25 53 14 54 28 19 52 9 19 22 0 30 9            0 23 4 0 ♈ 57 48 0 ♈ 25 0 32 48 0 47 4 1 57 55 1 25 0 32 55 1 10 36 2 56 58 2 24 0 32 58 1 34 8 3 56 0 3 23 0 33 0 1 57 8 4 53 45 4 23 0 30 45 2 20 37 5 52 50 5 22 0 30 50 3 55 36 9 52 45 9 19 0 33 45 4 18 5 10 49 50 10 18 0 31 50            10 55 27 28 20 43 27 57 0 23 43 17 42 41 19 ♉ 39 22 19 ♉ 18 0 21 22            18 13 40 21 35 48 21 14 0 21 48 1597 June. The Sun's Apparent height. The Sun's True height The Sun's apparent Declination. Day Degr. Min. Sec Degr. Min Sec. Degr. Min. Sec. 9 Thursd 61 57 0 61 58 25 23 29 0 11 Saturd. 61 58 0 61 59 25 23 30 0 12 Sund. 61 58 0 61 59 25 23 30 0 13 Mond. 61 57 30 61 58 55 23 29 30 16 Sund. 61 46 0 61 47 25 23 18 0 july.          4 Mond. 60 12 30 60 14 0 21 44 30 5 Tuesd. 60 3 30 60 5 0 21 35 30 6 Wed. 59 54 0 59 55 30 21 26 0 8 Friday 59 34 0 59 35 31 21 6 0 24 Sund. 56 1 30 56 3 11 17 33 30 26 Tuesd. 55 30 0 55 31 42 17 2 0 August          3 Wed. 53 11 0 53 12 48 14 43 0 9 Tuesd. 51 16 0 51 17 53 12 48 0 September.          22 Thursd. 34 50 0 34 51 51 3 38 0 30 Friday 31 44 30 31 45 55 6 43 30 October.          6 Thursd 29 29 0 29 30 6 8 59 0 12 Wed. 27 19 0 27 19 45 11 9 0 14 Friday. 26 36 30 26 37 5 11 51 30 24 Mond. 23 16 0 23 15 23 15 12 0 27 Thursd. 22 22 0 22 20 50 16 6 30 29 Saturd. 21 46 0 21 44 41 16 42 0 November.          3 Thursd. 20 24 0 20 22 2 18 4 0 7 Mond. 19 21 30 19 19 0 19 6 30 22 Tuesd 16 24 0 16 20 5 22 4 0 The Suns true declination. The Sun's place by Observation. The Sun's place by Prutenick Tables The difference. Degr. Min. Sec. Degr. Min. Sec. Degr. Min. Sec. Min. Sec. 23 30 25 27 ♊ 50 0 27 ♊ 41 0 9 0 23 31 25 29 24 0 29 35 0 11 0 23 31 25 0 ♋ 36 0 0 ♋ 33 0 3 0 23 30 55 1 35 0 1 30 0 5 0 23 19 25 7 17 20 7 14 0 3 20            21 46 0 21 43 0 21 33 0 10 0 21 37 0 22 38 18 22 31 0 7 18 21 27 30 23 34 42 23 28 0 6 42 21 7 31 25 27 11 25 23 0 4 11 17 35 11 10 ♌ 48 8 10 ♌ 42 0 6 8 17 3 42 12 41 14 12 37 0 4 14            14 44 48 20 22 41 20 18 0 4 41 12 49 53 26 11 36 26 5 0 6 36            3 36 9 9 ♎ 3 26 8 ♎ 57 0 6 26 6 42 5 16 59 57 16 51 0 8 57            8 57 54 22 58 13 22 48 0 10 13 11 8 15 28 56 34 28 46 0 10 34 11 50 55 0 ♏ 57 28 0 ♏ 45 0 12 28 15 12 37 11 5 41 10 46 0 19 41 16 17 10 14 4 23 13 46 0 18 23 16 43 19 16 7 30 15 47 0 20 30            8 5 58 21 6 26 20 48 0 18 26 16 9 0 25 16 16 24 50 0 26 16 22 7 55 10 ♐ 42 36 10 ♐ 1 0 41 36   

CHAP. XX. The finding of the Sun's Apogeum and eccentricity, out of the former Observations.  
NOw by the whole course of these Observations, it manifestly appeareth, that the Declinations set down in the Regiments of the Sun, that are, and have been hitherto ordinarily used by our Seamen, do for the most part notably err from the truth of the Heavens. Which errors as they may most truly be corrected by Observation only in those days wherein certain Observation was made: so for finding out the Declinations of the middle days between the Observations, I thought it the best way, first to make the Ephemerideses of the Sun hereafter following, agreeable to the former Observations, and then to find out the Declinations answerable to the places of the Sun for every day of four years together, because that after that number of years the same places of the Sun, and the same Declinations return again without sensible error, which also by a certain Equation may be corrected: and for the easier finding out of this Equation, I have continued these Tables for one year more, making them for five years, and so including two Leap years, by the difference of which years we may easily find the said Equation, by means whereof these Tables may be made serviceable for many years.  
First therefore for making these Ephemerideses, it is needful to know the time of the Sun's entrance into certain principal points of the Zodiac: as also the time of the Sun's continuance in the arches of the Zodiac contained between those points, whereby the proportion of the Sun's motion may Geometrically be found out, his eccentricity and place of his Apogeum being hereby known.  
To know the time of the Suns commnig to any point of the Ecliptic, 
To know the time of the Suns coming to any point of the Ecliptick·  it is best to Observe exactly the Meridian Altitude of the Sun, not only the same day wherein he is like to enter into the point desired, but every day also, for two or three days together, both before and after that day, that both by the testimony of so many Observations compared together, you may have the more assured truth: as also, that if the day you most desire fall not out to be so clear as you would wish, you may notwithstanding, by the Observations of the days going before, and following after, or either of them, obtain your desire.  
Having thus Observed the Meridian Altitudes of the Sun, and thereby also found his Declinations for every one of those days wherein you Observed, you shall easily know also the true place of the Sun in every each one of the same days, with help of the former Table of the Declination of every minute of the Ecliptic, in such sort as before was declared, when I showed the use of that Table.  
Now if it fall out so happily, that both the day be clear, when the Sun entereth into the desired point of the Ecliptic, and that the place of the Sun answerable to the Declination of that day, be all one with the point desired, you have already that you sought for, without any more ado, viz. That the Sun entereth that day at Noon into the point desired. Otherwise subtract the Observed place of the Sun, next before the point desired out of the Observed place of the Sun, next following that point, and the remainder shall show you the true motion of the Sun, answerable to the time between those Observations. Subtract also the former place of the Sun, from his place in the point desired, and note the difference: for as the former remainder (that is the apparent motion of the Sun between the Observations) is to the time between those Observations: so is this difference to the time between the first Observation, and the Sun's entrance into the point desired.  
Example of the first: I desired to know the time of the Sun's entrance into 17 degrees, 0 min. of ♌ in the year 1595. I Observed therefore (at London) the apparent height of the Sun at Noon, the 31 of july the same year, and found it to be 54 degrees, 14 minutes, out of which his true height (corrected by his Parallax) was found to be 54 degr. 15 min. 46 sec. Whereby his Declination was gathered to be 15. degrees, 47 minutes, 46 sec. And consequently his place in 17 degrees, 0 minutes of ♌ that day at Noon.  
Example of the second: admit the year following 1596, You would know the time of the Sun's entrance into the midst of Taurus. Having therefore to this end Observed the apparent Meridian Altitudes of the Sun, the 24, 25, and 26. Days of April, in that year (within the space of which days I am sure the Sun must needs be in that point) to be 54 degrees, 35 minutes, 54 degrees, 51 min. ½, 55 degrees, 8 min. ½, and consequently the true heights 54 degr. 36 min. 44 sec. 54 degr. 53 min. 13 sec. 55 degrees, 10 min. 13 sec And out of these the true Declinations 16 degr. 8 min. 44 sec. 16 degr. 25 min. 13 sec. 16. degr. 52 min. 13. sec. Hereby I found the true places of the Sun the same days to be 14 degr. 9 min. 40 sec. Of Taurus, 15 degr. 5 min. 20 sec. of Taurus, 16 degr. 3 min. 42 sec. Of Taurus. Subtracting therefore 14 degr. 9 min 40 sec. Of Taurus, (that is, the place of the Sun the 24 day) out of 15 degr. 5 min. 20 sec. of Taurus, the place of the Sun the 25 day) the remainder shall be 55 min. 40 sec. Which is the true motion of the Sun, between the 24, and 25. Days at Noon, that is, the Diurn motion of the Sun at that time. Subtracting also 14 degr. 9 min. 40 sec. Of Taurus, out of 15 degr 0 min. of Taurus, the difference is 50 min. 20 sec. Now as 55 min. 40 sec is to 50 min. 20 sec. so are 24 hours, to 21 hours, 42 min. and 2 sec▪ It appeareth therefore by subtracting 21 hours, 42 min. 2 sec. Out of 24 hours, that the Sun should enter into the midst of Taurus, the 25 day about two hours and almost 18 min. before Noon, that is, at nine a clock and 42 minutes.  
Now supposing I had not, or could not have Observed the 25 day, I may notwithstanding find the time of the Sun's entrance into the midst of Taurus, by the Observations of the 24 and 26 days after this manner: Subtract 14 degr. 9 min. 40 sec. Of Taurus, out of 16 degr. 3 min. 42 sec. of Taurus, the remainder will be one degr. 54 min. 2 sec. that is the motion of the Sun for two days, between the 24 and 26 days at Noon. Therefore as 1 degr. 54 min. is to 48 hours: so are 50 min. 20 sec. (That is the Difference of the place of the Sun the 24 day from the midst of Taurus, found out as before) to 21 hours and 12. min. almost. So as hereby it seemeth the Sun should enter into the midst of Taurus the 25 day about two hours and 48 minutes before Noon, that is, at nine of the clock and 12 minutes.  
But if it so fall out that you do not or cannot Observe, both before and after the time of the Suns coming to the point desired, (as suppose I could not have Observed the 24 day, but only the 25 and 26 days, in both which days the Sun is gone past the point desired) notwithstanding you may Obtain your desire thus: Subtract 15 degr. 5 min. 20 sec, Taurus, (the place of the Sun the 25 day) out of 16 degr, 3 min. 42 sec. Taurus (the place of the Sun the 26 day) there will remain 58 min. 22 sec. the Diurn motion of the Sun between the Noon-tides of the 25 and 26 days. Now because that on the 25 day at Noon the Sun was gone 5 min. 20 sec. past the point desired: therefore as 58. min. 20 sec. Are to 24 hours, so are 5 min. 20 sec. to 2 hours 12 min. almost. By this account then the Sun should enter into the midst of Taurus the 25 day, 2 hours and about 12 min. before Noon: that is, at nine of the clock and 48 minutes. Neither ought that small difference that appeareth between these accounts to be greatly regarded, which amounts not to so much as half an hour, in which time the motion of the Sun is little above a minute, and the Declination of the Sun in that part of the Zodiac cannot alter so much as ⅓ of a minute, which is so small, as can by sense very hardly be Observed or discerned. Neither yet ought that little difference of a minute or two that appeareth between the Diurn motions of the Sun; found by Observation, greatly move any man (in that by the first and second Observations the Diurn motion should be almost 56 min. by the first and third 57 min. by the second and third 58 min. and more) the greatest of which differences may almost arise by erring but one half minute only, in taking the height of the Sun; which error is in a manner altogether insensible, and will be easily pardoned by them that have or shall accustom themselves to make the like Observations, when besides their own experience they shall find that they which have most excelled in this Art, as Tycho Brahe de recentior●b. Aetherei mundi phaenom. lib 2 cap. 10. part 1. Copern. Revol. Libr. 4. cap. 21. and Ptoleme himself in all his Catalogue of the fixed Stars, Almagest. lib. 7. cap. 5. When they shall find (I say) that even these Princes in Astronomy, so greatly exercised in Observations, have accounted an whole minute or two, hardly sensible: Ptoleme also in his Almagest. Contenting himself, for the most part, to have set down the places of the fixed Stars to sixth parts of degrees, and very seldom coming to twelfth parts, thinking it sufficient (as it may seem by the perpetual course of that Catalogue) to come within five or ten minutes of the truth.  
But to return again to that from whence we have a little digressed. After this manner now showed, we found the time of the Sun's entrance into the beginning of ♈ and ♎, and into the midst of ♉, ♌, ♏, and ♒, as into places serving most fitly for finding out of the Sun's eccentricity and Apogeum: following also herein the example of Copernicus, lib. 3. cap. 16. Revol. Who well perceiving how hard, yea rather impossible a thing it is, to find by Observation the time of the Sun's entrance into the Solstitial points (where the Meridian Altitudes, and Declinations of the Sun continue almost the same, without any sensible difference, for two or three days together) chose rather the parts of the Zodiac already mentioned, where the place of the Sun may more truly be known by reason of the quicker altering of his Declination, the difference thereof in the space of 24 hours amounting to more than 17 min. The times therefore of the Suns coming to the foresaid points in the years 1594, 1595, 1596, 1597. We found to be such as are set down in the Table following.  
 1594 1595 1596 1597    Da. Ho. Mi. Da. Ho. Mi. Da. Ho. Mi. Da. Ho. Mi. Sig. De. jan.    24 17 35 25 0 7 24 5 54 ♒ 15 Mar.    10 13 26 9 18 43 10 0 37 ♈ 0 April.    25 16 50 24 21 47 25 3 54 ♉ 15 july. 28 15 35 28 20 4 28 1 43 28 9 56 ♌ 15 Sept. 13 2 45 13 7 39 12 13 48 12 19 15 ♎ 0 Octob. 28 5 46 28 9 36 27 15 23 272 1 50 ♏ 15  
Hereby the times of the Sun's continuance in the arks of the Zodiac betwixt those points, as also the arks of the Eccentrick answerable to those times, were more easily found then that it should now be needful for me to be further tedious, in setting down the manner of finding the same, wherein notwithstanding there may some difference of an hour or two sometimes appear, by comparing together those times in several years: yet this error being such as may arise by missing little more than one minute in (one Observation: or little more than half a minute in two Observations of the Meridian Altitudes of the Sun, one Observation being made when the Sun is about the beginning of the ark, the other when he is about the ending thereof) I make no doubt, but that it will at the least be favourably censured by them that have acquainted themselves with some practice of Observing: wherein he shall (in my opinion) quit himself meetly well who neither through imperfection of sense, either in making or dividing, or in rectifying, or in using his Instrument, and every part thereof: nor through the difficulty of noting precisely the edges of the shadow of the upper sight falling upon the nether: (the limits or bounds of which shadow are but a confused mixture (as it were) of light and darkness▪ or else a mean equally compounded of them both, which can no better be discerned then by guessing:) nor yet by Rrefraction of the Sun beams through the thickness of the air; especially when the Sun is in the Southerly Semicircle of the Zodiac, which Refraction admitteth some alteration, according to the diversity of the rarity or density of the Vapours in the air interposed betwixt our sight and the Sun; he shall (I say) quit himself well that neither by one, nor some, nor all these, shall miss a minute, and more sometimes, in Observing the meridian Altitude of the Sun: whereby if error be committed both at the beginning and ending of the aforesaid arks (especially of those arks that are contained between the midst of Taurus, and Leo, of Leo, and Scorpio, of Scorpio, and Aquarius, of Aquarius, and Taurus,) the place of the Sun found by such Observation, may be more or less than truth by three or four minutes, and both errors together may amount to six or eight min. error in the motion of the Sun, whereof may follow two or three hours' error in the time of the Suns abiding in one of those arks.  
Out of the former Table I found (by the Observations of the two last years especially) that the time of the Sun's Revolution through the Zodiac in our time, is 365. days 5. hours, and about 48. min. Also the Sun's continuance in the Northerly Semicircle of the Ecliptic, from the beginning of Aries to the beginning of Libra, to be 186. days, 18. hours, and about one half, and consequently in the Southerly Semicircle from Libra to Aries 178. days 11. hours 18. minutes: whereby the arks of the Sun's Eccentrick, answerable to those Semicircles, appeared to be 184 degrees, 5, min. 25. sec. from Aries to Libra, and 175 degrees, 54. min. 35. sec. from Libra to Aries.  
Therefore because the place of the Sun being at, or near the Equinoctial points, is most certainly known (his Meridian Altitude and Declination altering there most swiftly) and consequently the ark of the Eccentrick contained betwixt those points are most certainly found: it appeareth to be most certain that the eccentricity of the Sun at this time must needs be at the least 3.569. such parts whereof the Semidiameter of the Eccentrick containeth 100,000. though the Sun's Apogeum were but in the beginning of Cancer: whereas if it be in 9 degr. 22. min. of Cancer (as Copernicus would have it) the eccentricity cannot be less than 3616. of the same parts; notwithstanding he maketh it to be little more than 3220. such parts in this Age.  
But finding by the Observations I took in the year 1596. that the Sun is also in going from the beginning of Aries to the midst of Taurus 46. days, and about three hours and four minutes, and consequently the arch of the Sun's Eccentrick, answerable to that time and arch of the Ecliptic 45. degr. 27 min. 56. sec. I found hereby, the Sun's eccentricity and place of his Apogeum, as followeth.  
Past this upon the Margin of Letter Z. fol. 148 so as it may lie open all the while the following matter of the 20 and 21 chap, are reading.  
Which may yet also be more easily found by the Tetragonical Table, or Table of Roots and Squares, for taking AO and OB to be 2290, and 2757, their Squares will be 5,244,100. And 7,601,049. Which added together make 12,845,149. The Square Root or side whereof is 3584. The Sun's eccentricity, in such parts whereof the Semidiameter of the Eccentrick Be containeth 100,000. Agreeing exactly with the Sun's eccentricity, found by Tycho Brahe Progymnasmat. Pag. 26.  
The same may also be further confirmed thus: We have found the arch of the Sun's Eccentrick from the beginning of Aries to the beginning of Libra, to be 184 5 26, the excess whereof above a Semicircle is 4 5 26, the half of this is the arch IK 2 2 43 the Sine whereof IX (equal to AD) is 356,892 (whereof the semidiameter of the Eccentrick is 10,000,000) which should be the Sun's eccentricity, if his Apogeum were in the beginning of Cancer. But having found that the Sun's Apogeum is about 5 degrees 17 minutes of Cancer; therefore as the whole Sine 10,000,000 is to the Secant of 5 degr. 17 min. 10,042,667 so is AD in the Right Angled Triangle ADB 356,892 to AB the eccentricity of the Sun 358,414, which hath not any sensible difference from that we found before.  
But the place of the Sun's Apogeum, found by the foresaid Observations, differeth from Tycho twenty minutes (if we add ●o his place of the Apogeum of the Sun 7 minutes, for the Mo●●on of the Sun's Apogeum in the ten years' space betwixt his Observation and mine.) All which difference notwithstanding may arise by erring little more than half a quarter of a minute in Observing the the Sun's height about the midst of Tarus. Which error although it be so small that it may worthily be neglected, for whether of them soever you follow either his (Apogeum) or mine, for the making of the Ephemerideses and Tables ensuing, there cannot hereof arise any such disagreement as can by sight be diserned: yet in that small difference that is (though insensible) I shall not unwillingly yield unto him, considering with how great Preparation, cost, skill, diligence, and circumspection every way he went about this business, as all they that have any judgement and use of Observation will easily grant. I say therefore not building only upon his authority (though in this kind it be greater than any others, yet known to the world) that following the ordinary received Hypothesis of an Eccentrick for salving the Sun's apparent inequality of motion) the Sun's eccentricity and place of his Apogeum, set down by Tycho, as before we have showed, are in this our Age very agreeable to truth and without all such error as can by sense be discerned. And as for the difference that seemeth to be betwixt us, being so small and insensible; so far ought it to be from breeding doubtfulness in any, that it may rather make not a little for the confirmation of the truth both of his and my Observations; so as none shall need to make scruple of the certainty and infallibility of those Tables of the Sun's Declination, which for the Navigators use shall out of these grounds be gathered and deduced.   

CHAP. XXI. The middle motion of the Sun, Corrected out of the former Observations.  
THE eccentricity therefore and Apogeum of the Sun being thus known, together with his true place (which by so exact Observation as we could in the year 1597. the 11. of March at noon, we found to be 0 degr. 57 min. 48. sec. of Aries:) his middle motion from the beginning of Aries was also easily found after this manner.  
Let a be the place of the Sun in his Eccentrick; b the Sun's true place in the Zodiac.  
B a a line drawn from the centre of the Eccentrick to the centre of the Sun.  
A d a line drawn from the centre of the Ecliptic Parallel to B a, showing the middle place of the Sun in the Zodiac.  
AB, a line drawn from the centre of the Ecliptic, by the centre of the Sun to the Zodiac, showing the true place of the Sun.  
Therefore the Angle BADE being 5. degr. 37. min. and consequently the Angle BAJAZET 95. degr. 37, min. because DAI is a right Angle: the Angle aAI, found by Observation to be 0 degrees 57 min. 48. seconds, being subtracted from the Angle BAJAZET, there shall remain the angle BASILIUS a in the Triangle BASILIUS a 94. degr. 39 min. 12 sec. and two sides also of the same Triangle being given aB 100.000 parts, and BA 3584 of the same parts, therefore by the doctrine of Triangles, the Angle B aA equal to aA d (because B a and AD are Parallels) shall likewise be found to be 2. degrees 2. min. 52. sec. (the Prostapheraeresis or equation of the Sun at that time; which subtracted from E b the true motion of the Sun, that is 57 min. 58. sec (adding thereto an whole circle) there shall remain the middle motion of the sun from the beginning of Aries, EFGH d, 358. degr. 54. min 56. sec. According to Tycho his Tables Progymnasmat, part. 1. page. 59 (if we account the difference of Longitude between London and Vraniburg to be about 11. deg. 15. min. as by our best Sea-Charts it seemeth it should be) it is then 358. degr. 55. min. 45. sec. differing from the former only 49. sec- Which difference may arise almost of one third part of a minute error in Observing the Meridian Altitude of the Sun: Notwithstanding the account of the Prutenick Tables maketh it to be 358, degrees, 35. min. 15. sec. differing from both the former about 20 minutes.  
Thus having found, that neither in the place the Sun's Apogeum, nor in his eccentricity or middle motion, there is any sensible difference betwixt the accounts arising out of Tycho Brahe his Observations and mine own; I have therefore here set down the Tables of the Sun's middle motions altogether agreeable to those of his; Progymnasmat. part. 1. pag. 57.58.59. allowing only to his Epochaes so much more as is answerable to the difference of Longitude between the place of his Observation and mine, that is, to the Epochaes of the Sun's middle motion of Longitude, 1. min. 52. sec. answerable to 45. min. of an hour almost, or 11 degr. and ¼, that is, so much as the City of London seemeth to be more Westerly than Vraniburg.  

EPOCHAES OF THE MIDDLE MOTIONS OF THE SUN.   Apogeum. Longitude.  Apogeum. Longitude. Years Si. P. Mi. Se· Si. P. Mi. Se. Years Si. P. Mi. Se. Si. P. Mi. Se. 1500 3 4 24 45 9 20 10 52 1625 3 5 58 30 9 20 53 50 1520 3 4 39 45 9 20 20 6 1626. 3 5 59 15 9 20 39 30 1540 3 4 54 45 9 20 29 20 1627. 3 6 0 0 9 20 25 11 1560 3 5 9 45 9 20 38 35 1628. 3 6 0 45 9 21 10 0 1580 3 5 24 45 9 20 47 49 1629 3 6 1 30 9 20 55 40 1600 3 5 39 45 9 20 57 4 1630 3 6 2 15 9 20 41 21 1601 3 5 40 30 9 20 42 44 1631 3 6 3 0 9 20 27 2 1602 3 5 41 15 9 20 28 25 1632 3 6 3 45 9 21 11 51 1603 3 5 42 0 9 20 14 6 Middle motions in single years until 20. 1604 3 5 42 45 9 20 58 54 1605 3 5 43 30 9 20 44 35 1 0 0 0 45 11 29 45 41 1606 3 5 44 15 9 20 30 16 2 0 0 1 30 11 29 31 21 1607 3 5 45 0 9 20 15 56 3 0 0 2 15 11 29 17 2 1608 3 5 45 45 9 21 0 45 4 0 0 3 0 0 0 1 51 1609 3 5 46 30 9 20 46 26 5 0 0 3 45 11 29 47 32 1610 3 5 47 15 9 20 32 7 6 0 0 4 30 11 29 33 12 1611 3 5 48 0 9 20 17 47 7 0 0 5 15 11 29 18 53 1612 3 5 48 45 9 21 2 36 8 0 0 6 0 0 0 3 42 1613 3 5 49 30 9 20 48 17 9 0 0 6 45 11 29 49 22 1611 3 5 50 15 9 20 33 58 10 0 0 7 30 11 29 35 3 1615 3 5 51 0 9 20 19 38 11 0 0 8 15 11 29 20 44 1616 3 5 51 45 9 21 4 7 12 0 0 9 0 0 0 5 33 1617. 3 5 52 30 9 20 50 8 13 0 0 9 45 11 29 51 13 1618. 3 5 53 15 9 20 35 48 14 0 0 10 30 11 29 36 54 1619 3 5 54 0 9 20 21 29 15 0 0 11 15 11 29 22 35 1620 3 5 54 45 9 21 6 18 16 0 0 12 0 0 0 7 24 1621. 3 5 55 37 9 20 52 1 17 0 0 12 45 11 29 53 4 1622 3 5 56 15 9 20 37 39 18 0 0 13 30 11 29 38 45 1623. 3 5 57 0 9 20 23 20 19 0 0 14 15 11 29 24 26 1624. 3 5 57 45 9 21 8 9 20 0 0 15 0 0 0 9 14 
THE SUNS EQVAL MOTION OF LONGITUDE.  In months of the common year- In days: In hours In minutes:  S. D. M. Se. Da De. M. See H Mi. S. M M. S. M M. S. Ianu. 1 0 33 18 1 0 59 8 1 2 28 0 0 0 30 1 14 Febr. 1 28 9 11 2 1 58 17 2 4 56 1 0 2 31 1 16 Mar. 2 28 42 30 3 2 50 25 3 7 24 2 0 5 32 1 19 April. 3 28 16 39 4 3 56 33 4 9 51 3 0 7 33 1 21 May. 4 28 49 58 5 4 55 42 5 12 19 4 0 10 34 1 24 june. 5 28 24 7 6 5 54 50 6 14 47 5 0 12 35 1 26 july. 6 23 57 26 7 6 53 58 7 17 15 6 0 15 36 1 29 Aug. 7 29 30 44 8 7 53 7 8 19 34 7 0 17 37 1 31 Sept. 8 29 4 54 9 8 52 15 9 22 11 8 0 20 38 1 34 Octob. 9 29 38 12 10 9 51 23 10 24 38 9 0 22 39 1 36 Nou. 10 29 12 22 11 10 50 32 11 27 6 10 0 25 40 1 39 Dec. 11 29 45 40 12 11 49 40 12 29 34 11 0 27 41 1 41 In months of the leap year. 13 12 48 48 13 32 2 12 0 30 42 1 43 14 13 47 57 14 34 30 13 0 32 43 1 46 15 14 47 5 15 36 58 14 0 34 44 1 48      16 15 46 13 16 39 26 15 0 37 45 1 51  S. D. M. Se· 17 16 45 21 17 41 53 16 0 39 46 1 53 18 10 44 30 18 44 21 17 0 42 40 1 56 Ianu. 1 0 33 18 19 18 43 38 19 46 49 18 0 44 48 1 58 Febr. 1 29 8 20 20 19 42 47 20 49 17 19 0 47 49 2 1 Mar. 2 29 41 38 21 20 41 55 21 51 45 20 0 49 50 2 3 April. 3 29 15 48 22 21 41 3 22 54 13 21 0 52 51 2 6 May. 4 29 49 6 23 22 40 12 23 56 40 22 0 54 52 2 8 june. 5 29 23 16 24 23 39 20 24 59 8 23 0 57 53 2 11 july. 6 29 56 34 25 24 38 28 In hours 24 0 59 54 2 13 Aug: 8 0 29 53 26 25 37 37 25 1 2 55 2 15 Sept: 9 0 4 3 27 26 36 45    26 1 4 56 2 18 Octob. 10 0 37 21 28 27 35 53    27 1 7 57 2 20 Nov: 11 0 11 31 29 28 35 1    28 1 9 58 2 23 Dec: 0 0 44 49 30 29 34 10    29 1 11 59 2 25 In Months. 31 30 33 18    30 1 14 60 2 28   

CHAP. XXII. A new Theoric of the Sun for the making of the Table of the Suns Prosthaphaereses following.  
But for the making of the table of the Suns Prosthaphaereses, because it may be gathered not only out of the observations of Mars, that both myself, together with that honourable and learned Knight Sir. Christopher Heyden, have taken for many years; but also by the observations of that famous Tycho (as appeareth in the Appendix annexed to his Progymnasmata, pag. 821) that the Sun's eccentricity should be but half so much, as out of the former Hypothesis we have found, the place of his Apogaeum notwithstanding and greatest Prosthapaereses remaining as before: we have therefore in stead of the former Hypothesis of an Eccentrick devised another Theoric for the Sun, of an Homocentrick with a double Epicycle answerable to those Observations after this manner: Let BCD be an homocentrical circle equal to the Eccentrick aforesaid, (whose Semediameter AB admi: to be 100,000 parts) in the circumference whereof, taking the centre B, describe the greater Epicycle EGLANTINE, whole Semidiameter EBB let be 2688. of the same parts, that is, three quarters of the fore said eccentricity 3584. Also upon the centre E, taken in the greater Epicycle, describe the little Epicycle FH, and let the Radius or Semediameter thereof EH be 896 such parts, that is one quarter of the former eccentricity of the Eccentrick. Let all these circles be moved about their own centres equally; the Homocentrick carrying about the centre of the greater Epicycle from the West Eastwards in the time that the Sun returneth again to his Apogaeum; the greater Epicycle moving about from East Westward in the same time also, and the lesser Epicycle carrying about the centre of the Sun chose from West Eastwards in half that time.  
Moreover, let them be moved with this condition, that whensoever the centre of the great Epicycle B cometh to the place of the Suns Apogaeum, the centre of the little Epicycle shall be in the Apogeum of the greater, and the Sun in F next to B the great Epicycles centre, and consequently BE and F (that is, the centres of both the Epicycles and of the Sun coming all together into the same right line of the Suns Apogaeum AGBFEH. Hereof it will follow that the Diameter of the greater Epicycle shall always be Parallel to the line of the Suns Apogaeum BAD, and whiles the centre of the greater Epicycle from B to ay, and the centre of the lesser Epicycle from O to E moveth half a Quadrant, the centre of the Sun from R to L shall move an whole Quadrant. Also the greater Epicycle having moved a whole Quadrant from B to C, and the lesser likewise a whole Quadrant from P to E, the Sun shall move an whole Semicircle from F to M. Therefore by this compound motion of the Homocentrick and both Epicycles, the Sun shall seem to describe as it were an Eccentrical circle FLMNO, according to the eccentricity AS, which is but half so much as before, and yet the greatest Prostaphaeresis MAC, shall be the same almost as before, according to the Hypothesis of a simple Eccentrick, whose Eccetricitie were AT.  
According to this Hypothesis was made the Table of Prostaphaeresis here following, to every degree of the Sun's Anomaly, and that after this manner.  
Thus we may find the Suns Prosthaphaereses for every degree of his Anomaly, and so make this Table following.  
 0 Subt. Diff. ad. 1 Subtr. Di. ad 2 Subtr. Di. ad  De Dig. Mi. Se Mi. Sec. Deg. M. S. Mi. Se. De. Mi. Se. Mi. Se· De 0  0 0   1 0 38   1 45 41   30 1 0 2 7 2 7 1 2 28 1 50 1 46 46 1 5 29 2 0 4 13 2 6 1 4 17 1 49 1 47 48 1 2 28 3 0 6 20 2 7 1 6 5 1 48 1 48 49 1 1 27 4 0 8 26 2 6 1 7 51 1 46 1 49 48 0 59 26 5 0 10 33 2 7 1 9 37 1 46 1 50 45 0 57 25 6 0 12 39 2 6 1 11 21 1 44 1 51 40 0 55 24 7 0 14 45 2 6 1 13 4 1 43 1 52 33 0 53 23 8 0 16 51 2 6 1 14 46 1 42 1 53 24 0 51 22 9 0 18 56 2 5 1 16 26 1 40 1 54 11 0 48 21 10 0 21 1 2 5 1 18 5 1 39 1 54 59 0 47 20 11 0 23 6 2 5 1 19 43 1 38 1 55 44 0 45 19 12 0 25 10 2 4 1 21 19 1 36 1 56 27 0 43 18 13 0 27 14 2 4 1 22 54 1 35 1 57 7 0 40 17 14 0 29 17 2 3 1 24 27 1 33 1 57 46 0 39 16 15 0 31 20 2 3 1 25 59 1 32 1 58 22 0 36 15 16 0 33 22 2 2 1 27 29 1 30 1 58 57 0 35 14 17 0 35 24 2 2 1 28 58 1 29 1 59 29 0 32 13 18 0 37 25 2 1 1 30 25 1 27 1 59 59 0 30 12 19 0 39 26 2 1 1 31 51 1 26 2 0 26 0 27 11 20 0 41 26 2 0 1 33 15 1 24 2 0 52 0 26 10 21 0 43 25 1 59 1 34 37 1 22 2 1 15 0 23 9 22 0 45 23 1 58 1 35 58 1 21 2 1 37 0 22 8 23 0 47 20 1 57 1 37 17 1 19 2 1 56 0 19 7 24 0 49 17 1 57 1 38 34 1 17 2 2 12 0 16 6 25 0 51 13 1 56 1 39 50 1 16 2 2 27 0 15 5 2● 0 53 8 1 55 1 41 4 1 14 2 2 39 0 12 4 ●● 0 55 2 1 54 1 42 16 1 12 2 2 50 0 11 3 28 0 56 55 1 53 1 43 26 1 10 2 2 58 0 8 2 19 0 58 47 1 52 1 44 34 1 8 2 3 3 0 5 1 30 1 ●0 38 1 51 1 45 41 1 7 2 3 7 0 4 0 D. 11 Add. Dif. S. 10 Add· Dif. S. 9 Add. Dif. S· D.  3 Subtr. Dif. S. 4 Subtr. Dif. S. 5. Subtr. Dif. S.  D. Deg. Mi. Se. M. Sec. Deg. M. S. Mi. Se. De. Mi. Se. Mi. Se. D. 0 2 3 7   1 47 35   1 2 33   30 1 2 3 8 0 1 1 46 31 1 4 1 0 39 1 54 29 2 2 3 7 0 1 1 45 25 1 6 0 48 45 1 54 28 3 2 3 3 0 4 1 44 17 1 8 0 56 49 1 56 27 4 2 2 58 0 5 1 43 7 1 10 0 94 52 1 57 26 5 2 2 50 0 8 1 41 54 1 13 0 52 55 1 57 25 6 2 2 40 0 10 1 40 40 1 14 0 50 56 1 59 24 7 2 2 28 0 12 1 39 24 1 16 0 48 56 2 0 23 8 2 2 13 0 15 1 38 7 1 17 0 46 55 2 1 22 9 2 1 56 0 17 1 36 47 1 20 0 44 53 2 2 21 10 2 1 37 0 19 1 35 25 1 22 0 42 51 2 2 20 11 2 1 16 0 21 1 34 2 1 23 0 40 47 2 4 19 12 2 0 52 0 24 1 32 37 1 25 0 38 43 2 4 18 13 2 0 27 0 25 1 31 10 1 27 0 36 38 2 5 17 14 1 59 59 0 28 1 29 42 1 28 0 34 33 2 5 16 15 1 59 28 0 31 1 28 11 1 31 0 32 26 2 7 15 16 1 58 56 0 32 1 26 39 1 32 0 30 19 2 7 14 17 1 58 21 0 35 1 25 6 1 33 0 28 12 2 7 13 18 1 57 44 0 37 1 23 30 1 36 0 26 4 2 8 12 19 1 57 5 0 39 1 21 54 1 36 0 23 55 2 9 11 20 1 56 24 0 41 1 20 15 1 39 0 21 46 2 9 10 21 1 55 41 0 43 1 18 43 1 40 0 19 37 2 9 9 22 1 54 55 0 46 1 16 54 1 41 0 17 27 2 10 8 23 1 54 8 0 47 1 15 11 1 43 0 15 17 2 10 7 24 1 53 18 0 50 1 13 27 1 44 0 13 6 2 11 6 25 1 52 26 0 52 1 11 41 1 46 0 10 56 2 10 5 26 1 51 32 0 54 1 9 54 1 47 0 8 45 2 11 4 27 1 50 36 0 56 1 8 6 1 48 0 6 34 2 11 3 28 1 49 38 0 58 1 6 16 1 50 0 4 23 2 11 2 29 1 48 38 1 0 1 4 25 1 51 0 2 11 2 12 1 30 1 47 35 1 3 1 2 33 1 52 0 0 0 2 11 0  8 Add. Dif. ad 7 Add. Dif. ad 6. Add. Dif. ad    

CHAP. XXIII. The making of the Ephemerideses of the Sun here following.  
WIth help of the two former Tables of the Sun's middle motions and of his prosthaphaerese, the Sun's true place may be readily found, and so the Ephemerideses following easily made, after this manner: Reduce the apparent time given to the equal time answering thereto, with help of Tycho Brahe his table of Equation of natural days; and for that time so reduced add together the Sun's middle motions of longitude in years, months, days, hours, and minutes: out of the sum subtract the place of the Suns Apogaeum; the remainder shall be the Sun's motion of Anomaly, or his distance from his Apogaeum.  
Now if this Anomaly be less than a semicircle, look the sign thereof in the head of the table of the Sun's prostaphaerese, and the degree in the first column towards the left hand descending, and proceed in the same line towards the right hand, till you come under the foresaid sign of the Sun's Anomaly, for there shall you have the Suns prostaphaeresis for that t●me; remembering this withal, that if there be any minutes adhering to those degrees of Anomaly, that prostaphaeresis must be corrected by the part of the adjacent difference proportional to those minutes, adding or subtracting the same hereto: according as you are directed in the head of the column, wherein that difference is set down.  
But if the Sun's Anomaly be more than a semicircle, you must find the signs thereof in the foot of the table, and the degrees in the last column next the right hand ascending, and in the common meeting of the line wherein you find this degree, and of the column of the said sign of the Sun's Anomaly, you shall find the Suns Prostaphaeresis, as before; which if there be any minutes adherent to the Sun's Anomaly, must be corrected by the part proportional of the disterence adjoining, as before; adding or subtracting the same, according as you find your direction in the foot of the column containing that difference.  
As for example: Suppose you would know the Sun's true place the 6 of May at noon (that is, the 5 of May complete according to Astronomical account) in the year 1608, which time reduced to equality by the foresaid Table, shall be the 4 of May complete 23 hours, 48 minutes; for the Sun being at that time about the 26 degree of Taurus, that Table showeth you that 12 minutes are to be subtracted from the apparent time to make it equal. For this time therefore let the middle motions of the Sun be gathered together in this manner: 
The Sun's middle motion of Longitude for   Si. D. M. Se. the year of Christ 1607 complete, 9 20 15 56 Four months of the leap year, 3 29 15 48 Four days,  3 56 33 23 hours,   56 40 48 minutes.   1 58  Si. D. M S. The sum of all these is the Sun's middle motion of Longitude for the time aforesaid. 1 24 26 55 The place of the Suns Apogaeum for the year of Christ 1607 complete, is 3 5 45 0 The motion thereof in the months, days, hours, etc. remaining, is    15 which put together, make the place of the Suns Apogaeum for the time aforesaid 3 5 45 15 This being subducted out of the Sun's middle motion, 1 24 26 55 There shall remain the Sun's motion of Anomaly 10 18 41 40 The Prosthaphaeresis answerable to 10 signs, 18 degr. you shall find in the Table of Prosthaphaeresis  1 21 19 with the difference answering thereto   1 36 the part proportional whereof answering to 41 min. 40 seconds, you shall find to be   1 7 which subtracted out of the Prosthaphaeresis answering to 10 sig. 18 de.  1 21 19 there remaineth the Prosthaphaeresis corrected  1 20 12 which being added to the Sun's middle motion of Longitude for the time aforesaid 1 24 26 25 you shall have the Sun's true place for that time 1 25 47 7 agreeing justly with the Ephemerideses following, where you shall find the Sun at that time to be in 25 degr. 47 min, 7 sec. of Taurus.  
Admit also I would know the true place of the Sun the 27. of October 1609. at noon, as we commonly account, (that is) for the 26. of October complete, by the foresaid account Astronomical, which reduced to the equal time, will make 25. days, 23. hours, 36. min. The Sun's middle motion therefore, together with the rest of the account, for finding the Sun's true place for that time, may be shortly gathered after this manner: 
The Sun's middle motion of Longitude for   Si. D. M See the year of Christ 1608 complete, 9 21 0 45 September of the common year, complete 8 29 4 54 Five and twenty days  24 38 28 Twenty three hours   56 40 Thirty six minutes   1 29 The sum of these is the Sun's middle motion of Longitude for that time: 7 15 42 14 From whence subtract the place of the Suns Apogaeum, 3 5 46 18 there remaineth the Sun's Anomaly; 4 9 55 56 whereby is found the Suns Prosthaphaeresis:  1 35 31 and by subtraction hereof, his true Longitude, 7 14 6 45 agreeing likewise justly with the Emphemerides following: after which manner also they may be wholly made. Notwithstanding it is sufficient to make some convenient part of them in this manner, and (for sparing time and labour) to supply the rest by convenient parts proportional, whereof there may sometimes arise some small difference of a few seconds, which may worthily be neglected, seeing they can breed no sensible error in this business.   

CHAP. XXIV. How to reduce the apparent time to the equal time answering thereto.  
NOtwithstanding the greatest difference between the apparent and equal time to be small, that by neglect thereof there can scarce at any time arise thereof so much as one minute error in the place of the Sun; and consequently not so much as half a minute error in his declination: yet because the rules and grounds of Arts ought so much as may be to be free from all error, I have therefore thought it better here to set down the foresaid Table of Equation of natural days, rather than to leave the Reader to seek any further for so small a matter, if any perhaps shall be desirous to exercise himself in calculating the Sun's true place, according to the manner here before set down, either for the examining of the Suns Ephemerideses hear following, or any other; or for making some other like to these, when the date of them shall be expired; wherein, if perhaps you find some little difference of a few seconds from your calculation, you need not therewith to be any thing troubled, seeing it cannot produce any sensible error, neither in the Sun's declination, nor yet in his place.  

A Table of Equation of natural days.   ♈ ♉ ♊ ♋ ♌ ♍ ♎ ♏ ♐ ♑ ♒ ♓  S S S S S S S S S S A A D. M There Mi. M M Mi. Mi. Mi. Mi. Mi. M M 2 0 9 12 6 2 6 16 ½ 24 21 7 5 7 4 1 9 ½ 11 6 2 7 17 24 20 6 6 7 6 1 10 11 5 ½ 2 7 18 24 19 ½ 5 6 7 8 2 10 11 5 2 8 18 24 ½ 19 4 6 ½ 6 ½ 10 3 11 11 5 2 9 19 24 18 3 ½ 7 6 12 3 11 10 4 2 9 20 24 17 2 ½ 7 6 14 4 11 10 4 3 10 20 24 16 2 7 ½ 5 16 5 11 10 3 ½ 3 11 21 24 15 1 8 5 18 5 11 ½ 9 3 3 11 ½ 21 24 14 0 8 4 20 6 12 9 3 3 12 22 23 ½ 13 ½ A 1 8 4 22 6 12 8 ½ 3 4 13 22 23 12 1/● 2 8 3 24 7 12 8 2 ½ 4 13 ½ 23 23 11 ½ 3 8 2 ½ 26 7 ½ 12 8 2 5 14 23 22 10 ½ 3 8 2 28 8 12 7 2 5 15 23 22 9 ½ 4 8 1 30 8 ½ 12 7 2 6 16 24 21 8 ½ 5 7 ½ 0 ½  
This Table must be thus used: With the sign and degree of the Sun's true place take out in the common meeting the minutes of time; which according to the letters A▪ S, in the head of the Table, must be added to or subtracted from the apparent time to make it equal: remembering to do chose if the equal time must be changed into the apparent.   

CHAP. XXV. A Table of Equations of the Suns Ephemerideses.  
 january Febr. March. April. May. june. Day. Mi. Se Mi. Se Mi. Se Mi. Se Mi. Se Mi. Se 3 1 53 1 51 1 49 1 47 1 46 1 45 6 1 52 1 50 1 49 1 47 1 46 1 45 9 1 52 1 50 1 49 1 47 1 45 1 45 12 1 52 1 51 1 48 1 46 1 46 1 44 15 1 52 1 50 1 49 1 47 1 45 1 45 18 1 52 1 50 1 48 1 46 1 45 1 45 21 1 51 1 50 1 48 1 46 1 45 1 45 24 1 52 1 50 1 48 1 46 1 45 1 44 27 1 51 1 50 1 48 1 46 1 45 1 45 30 1 52   1 47 1 46 1 45 1 45  july. August Sept. Octob Novem Decem. Day. Mi. Se▪ Mi. Se. Mi. Se. Mi. Se. Mi. Se. Mi. Se. 3 1 45 1 45 1 48 1 49 1 51 1 52 6 1 45 1 46 1 48 1 50 1 52 1 52 9 1 45 1 46 1 48 1 50 1 52 1 52 12 1 45 1 46 1 48 1 50 1 52 1 53 15 1 45 1 47 1 49 1 50 1 52 1 52 18 1 45 1 47 1 48 1 51 1 52 1 52 21 1 45 1 47 1 49 1 50 1 52 1 52 24 1 46 1 47 1 49 1 51 1 52 1 53 27 1 46 1 47 1 49 1 51 1 52 1 52 30 1 45 1 47 1 49 1 52 1 53 1 52  
By means of this Table, and these Ephemerideses, the true place of the Sun may most easily be found, for many years, either past, or to come; as shall hereafter be showed in the next Chapter.  

Ephemerideses the Sun 1608. Leap year.   January.  Februar.  March.  April.  May.  June. D gr. mi. sec D gr. mi. se. D gr. mi. se. D gr. mi se D gr. mi. sec D gr. mi. sec 1 20 47 21 1 22 17 51 1 21 23 9 1 21 56 7 1 20 59 3 1 20 37 23 2 21 48 38 2 23 18 28 2 22 22 49 2 22 54 41 2 21 56 43 2 21 34 31 3 22 49 52 3 24 19 3 3 23 22 27 3 23 53 13 3 22 54 21 3 22 31 38 4 23 51 6 4 25 19 37 4 24 22 2 4 24 51 42 4 23 51 58 4 23 28 46 5 24 52 18 5 26 20 8 5 25 21 36 5 25 50 10 5 24 49 33 5 24 25 52 6 25 53 30 6 27 20 39 6 26 21 7 6 26 48 35 6 25 47 7 6 25 22 58 7 26 54 40 7 28 21 7 7 27 20 37 7 27 46 58 7 26 44 40 7 26 20 4 8 27 55 49 8 29 21 34 8 28 20 4 8 28 45 19 8 27 42 11 8 27 17 10 9 28 56 57 9 ♓ 21 59 9 29 19 28 9 29 43 37 9 28 39 41 9 28 14 15 10 29 58 5 10 1 22 22 10 ♈ 18 51 10 ♉ 41 55 10 29 37 9 10 29 11 20 11 ♒ 59 11 11 2 22 43 11 1 18 12 11 1 40 10 11 ♊ 34 36 11 ♋ 8 24 12 2 0 16 12 3 23 2 12 2 17 31 12 2 38 24 12 1 32 2 12 1 5 29 13 3 1 21 13 4 23 19 13 3 16 47 13 3 36 35 13 2 29 27 13 2 2 33 14 4 2 25 14 5 23 35 14 4 16 2 14 4 34 45 14 3 26 51 14 2 59 37 15 5 3 27 15 6 23 49 15 5 15 14 15 5 32 53 15 4 24 14 15 3 56 41 16 6 4 28 16 7 24 0 16 6 14 24 16 6 30 59 16 5 21 36 16 4 53 45 17 7 5 29 17 8 24 10 17 7 13 32 17 7 29 4 17 6 18 56 17 5 50 49 18 8 6 28 18 9 24 18 18 8 12 37 18 8 27 6 18 7 16 16 18 6 47 53 19 9 7 26 19 10 24 23 19 9 11 40 19 9 25 6 19 8 13 35 19 7 44 57 20 10 8 22 20 11 24 27 20 10 10 41 20 10 23 5 20 9 10 53 20 8 42 1 21 11 9 18 21 12 24 29 21 11 9 40 21 11 21 3 21 10 8 10 21 9 39 5 22 12 10 11 22 13 24 28 22 12 8 37 22 12 18 58 22 11 5 26 22 10 36 9 23 13 11 4 23 14 24 25 23 13 7 32 23 13 16 52 23 12 2 41 23 11 33 14 24 14 11 55 24 15 24 21 24 14 6 25 24 14 14 44 24 12 59 55 24 12 30 19 25 15 12 45 25 16 24 14 25 15 5 15 25 15 12 34 25 13 57 9 25 13 27 24 26 16 13 33 26 17 24 5 26 16 4 4 26 16 10 23 26 14 54 22 26 14 24 29 27 17 14 20 27 18 23 54 27 17 2 50 27 17 8 10 27 15 51 33 27 15 21 24 28 18 15 5 28 19 23 41 28 18 1 34 28 18 5 56 28 16 48 45 28 16 18 40 29 19 15 49 29 20 23 26 29 19 0 15 29 19 3 40 29 17 45 55 29 17 15 47 30 20 16 31     30 19 58 54 30 20 1 22 30 18 43 5 30 18 12 53 31 21 17 12     31 20 57 32     31 19 40 14      July.  August  Septemb  October.  Novem.  Decemb. D gr. mi. se. D gr. mi. se. D gr. mi. se D gr. mi. se. D gr. mi. se. D gr. mi. se 1 19 10 0 1 18 47 12 1 18 46 59 1 18 19 25 1 19 24 15 1 19 53 44 2 20 7 7 2 19 44 50 2 19 45 33 2 19 19 3 2 20 24 55 2 20 54 58 3 21 4 15 3 20 42 30 3 20 44 8 3 20 18 44 3 21 25 36 3 21 56 13 4 22 1 24 4 21 40 10 4 21 42 46 4 21 18 26 4 22 26 19 4 22 57 29 5 22 58 33 5 22 37 53 5 22 41 26 5 22 18 11 5 23 27 3 5 23 58 45 6 23 55 43 6 23 35 37 6 23 40 7 6 23 17 58 6 24 27 49 6 25 0 2 7 24 52 53 7 24 33 23 7 24 38 51 7 24 17 47 7 25 28 37 7 26 1 19 8 25 50 4 8 25 31 10 8 25 37 37 8 25 17 38 8 26 29 25 8 27 2 37 9 26 47 16 9 26 28 59 9 26 36 26 9 26 17 32 9 27 30 15 9 28 3 55 10 27 44 28 10 27 26 49 10 27 35 17 10 27 17 28 10 28 31 7 10 29 5 13 11 28 41 41 11 28 24 41 11 28 34 10 11 28 17 26 11 29 32 0 11 ♑ 6 32 12 29 38 55 12 29 22 35 12 29 33 5 12 29 17 27 12 ♐ 32 55 12 1 7 50 13 ♌ 36 10 13 ♍ 20 31 13 ♎ 32 2 13 ♏ 17 29 13 1 33 51 13 2 9 9 14 1 33 26 14 1 18 28 14 1 31 1 14 1 17 33 14 2 34 49 14 3 10 29 15 2 30 42 15 2 16 27 15 2 30 2 15 2 17 39 15 3 35 47 15 4 11 48 16 3 28 0 16 3 14 28 16 3 29 6 16 3 17 47 16 4 36 47 16 5 13 7 17 4 25 19 17 4 12 31 17 4 28 12 17 4 17 57 17 5 37 48 17 6 14 26 18 5 22 3● 18 5 10 35 18 5 27 20 18 5 18 9 18 6 38 50 18 7 15 45 19 6 19 5● 19 6 8 42 19 6 26 30 19 6 18 23 19 7 39 53 19 8 17 3 20 7 17 2● 20 7 6 50 20 7 25 43 20 7 18 40 20 8 40 58 20 9 18 22 21 8 14 43 21 8 5 0 21 8 24 5● 21 8 18 58 21 9 42 3 21 10 19 40 22 9 12 6 22 9 3 12 22 9 24 15 22 9 19 18 22 10 43 9 22 11 20 58 23 10 9 31 23 10 1 26 23 10 23 34 23 10 19 39 23 11 44 17 23 12 22 16 24 11 6 57 24 10 59 42 24 11 22 55 24 11 20 3 24 12 45 25 24 13 23 34 25 12 4 25 25 11 57 59 25 12 22 18 25 12 20 29 25 13 46 34 25 14 24 52 26 13 1 53 26 12 56 18 26 13 21 43 26 13 20 56 26 14 47 ●4 26 15 26 9 27 13 59 23 27 13 54 40 27 14 21 11 27 14 21 25 27 15 48 55 27 16 27 26 28 14 56 54 28 14 53 0 28 15 20 41 28 15 21 55 28 16 50 6 28 17 28 43 29 15 54 27 29 15 51 29 29 16 20 13 29 16 22 28 29 17 51 18 29 18 ●9 59 30 16 52 1 30 16 49 57 30 17 19 48 30 17 23 1 30 18 52 30 30 19 31 15 31 17 49 36 31 17 48 82     31 18 23 38     31 20 32 ●0 
Ephemerideses of the Sun 1609. First year.   January.  Februar  March.  April.  May  June. D gr. mi. s. D gr. mi. s. D gr. mi se. D gr. mi. se. D gr. mi. se. D gr. m. se 1 21 33 47 1 23 3 46 1 21 8 40 1 21 41 55 1 20 45 5 1 20 23 32 2 22 35 2 2 24 4 22 2 22 8 21 2 22 40 29 2 21 42 44 2 21 20 40 3 23 36 16 3 25 4 56 3 23 8 0 3 23 39 2 3 22 40 23 3 22 17 48 4 24 37 29 4 26 5 28 4 24 7 36 4 24 37 32 4 23 38 0 4 23 14 55 5 25 38 40 5 27 5 59 5 25 7 10 5 25 36 0 5 24 35 36 5 24 12 2 6 26 39 51 6 28 6 2● 6 26 6 42 6 26 34 25 6 25 33 10 6 25 9 8 7 27 41 0 7 29 6 55 7 27 6 12 7 27 32 49 7 26 30 43 7 26 6 14 8 28 42 9 8 ♓ 7 20 8 28 5 39 8 28 31 10 8 27 28 14 8 27 3 19 9 29 43 16 9 1 7 43 9 29 5 4 9 29 29 29 9 28 25 44 9 28 0 25 10 ♒ 44 22 10 2 8 5 10 ♈ 4 28 10 ♉ 27 47 10 29 23 13 10 28 57 30 11 1 45 28 11 3 8 25 11 1 3 49 11 1 26 3 11 ♊ 20 41 11 29 54 34 12 2 46 33 12 4 8 43 12 1 3 8 12 2 24 17 12 1 18 7 12 ♋ 51 39 13 3 47 37 13 5 8 59 13 3 2 25 13 3 22 29 13 2 15 32 13 1 48 43 14 4 48 39 14 6 9 13 14 4 1 41 14 4 20 40 14 3 12 56 14 2 45 47 15 5 49 41 15 7 9 25 15 5 0 53 15 5 18 48 15 4 10 19 15 3 42 51 16 6 50 42 16 8 9 35 16 6 0 4 1● 6 16 55 16 5 7 41 16 4 39 55 17 7 51 41 17 9 9 43 17 6 59 12 1● 7 14 59 17 6 5 3 17 5 36 59 18 8 52 39 18 10 9 50 18 7 58 18 18 8 13 2 18 7 2 23 18 6 34 3 19 9 53 36 19 11 9 54 19 8 57 21 19 9 11 3 19 7 59 42 19 7 31 7 20 10 54 32 20 12 9 56 20 9 56 23 20 10 9 2 20 8 57 0 20 8 28 11 21 11 55 26 21 13 9 56 21 10 55 22 21 11 7 0 21 9 54 17 21 9 25 15 22 12 56 19 22 14 9 54 22 11 54 20 22 12 4 56 22 10 51 33 22 10 22 20 23 13 57 10 23 15 9 49 23 12 53 15 23 13 2 50 23 11 48 49 23 11 19 24 24 14 5● 0 24 16 9 43 24 13 52 8 24 14 0 42 24 12 46 3 24 12 16 29 25 15 58 49 25 17 9 35 25 14 51 0 25 14 58 33 25 13 43 17 25 13 13 34 26 16 59 36 26 18 9 24 26 15 49 49 26 15 56 22 26 14 40 30 26 14 10 39 27 18 0 22 27 19 9 12 27 16 48 35 27 16 54 10 27 15 37 42 27 15 7 34 28 19 1 6 28 20 8 57 28 17 47 20 28 17 51 56 28 16 34 53 28 16 4 50 29 20 1 49     29 18 46 0 29 18 49 40 29 17 32 4 29 17 1 56 30 21 2 30     30 19 44 41 30 19 47 23 30 18 29 14 30 17 59 3 31 22 3 9     31 20 43 19     31 19 26 23      July.  August.  Septemb  October.  Novomb  Decembe D gr. mi. se. D gr mi. se. D gr. mi. se. D gr· mi. se. D gr. mi. sec D gr. m. sec. 1 18 56 9 1 18 33 14 1 18 32 48 1 18 4 58 1 19 9 34 1 19 38 53 2 19 53 17 2 19 30 52 2 19 31 21 2 19 4 36 2 20 10 13 2 20 40 7 3 20 50 24 3 20 28 31 3 20 29 56 3 20 4 16 3 21 10 54 3 21 41 22 4 21 47 33 4 21 26 12 4 21 28 33 4 21 3 58 4 22 11 36 4 22 42 38 5 22 44 42 5 22 23 54 5 22 27 12 5 22 3 42 5 23 12 20 5 23 43 54 6 23 41 51 6 23 21 37 6 23 25 54 6 23 3 29 6 24 13 6 6 24 45 11 7 24 39 2 7 24 19 23 7 24 24 38 7 24 3 17 7 25 13 53 7 25 46 2● 8 25 36 13 8 25 17 10 8 25 23 23 8 25 3 8 8 26 14 41 8 26 47 45 9 26 33 24 9 26 14 58 9 26 22 11 9 26 3 1 9 27 15 31 9 27 49 3 10 27 30 36 10 27 12 48 10 27 21 1 10 27 2 57 10 28 16 22 10 28 50 22 11 28 27 49 11 28 10 40 11 28 19 53 11 28 2 54 11 29 17 15 11 29 51 40 12 29 25 3 12 2● 8 33 12 29 18 48 12 29 2 54 12 ♐ 18 9 12 ♑ 52 5● 13 ♌ 22 18 13 ♍ 6 28 13 ♎ 17 45 13 ♏ 2 56 13 1 19 5 13 1 54 18 14 1 19 33 14 1 4 25 14 1 16 43 14 1 2 59 14 2 20 2 14 2 55 37 15 2 16 49 15 2 2 24 15 2 15 44 15 2 3 5 15 3 21 1 15 3 56 56 16 3 14 7 16 ● 0 2● 16 3 14 47 16 3 3 13 16 4 22 0 16 4 58 15 17 4 11 25 17 3 58 27 17 4 13 52 17 4 3 22 17 5 23 1 17 5 59 34 18 5 8 44 ●● 4 56 31 18 5 13 0 18 5 3 34 18 6 24 3 18 7 0 53 19 6 6 ● 19 5 5● ●7 19 6 12 10 19 6 3 48 19 7 25 6 19 8 2 11 20 7 3 2● ●0 6 5● ●● 20 7 11 22 20 7 4 3 20 8 26 10 20 9 3 30 21 8 0 ●● 21 7 ●● ●● 21 8 10 36 21 8 4 21 21 9 27 15 21 10 4 49 22 8 58 1● ●2 8 49 6 22 9 9 5● 22 9 4 40 22 10 28 21 22 11 6 7 23 9 55 3● 23 9 47 2● 23 10 9 11 23 10 5 2 23 11 29 28 23 12 7 25 24 10 53 2 2● 10 45 3● 24 11 8 32 24 11 5 25 24 12 30 3● 24 13 8 43 25 11 50 20 ●5 11 43 52 25 12 7 54 25 12 5 50 25 13 31 45 25 14 10 1 26 12 47 5● ●● 12 4● 10 26 13 7 19 26 13 6 17 26 14 32 55 26 15 11 18 27 13 45 27 ●● 13 40 3● 27 14 6 4● 27 14 6 45 27 15 34 5 27 16 12 35 28 14 42 5● 28 14 ●8 54 2● 15 6 16 28 15 7 15 28 16 35 16 28 17 13 52 29 15 40 30 29 15 37 19 29 16 5 47 29 16 7 47 29 17 36 2● 29 18 15 8 30 16 38 ● 30 16 35 47 30 17 5 22 30 17 8 21 30 18 37 40 30 14 16 24 31 17 35 3● 31 17 34 16     31 18 8 57     31 20 17 39 
Ephemerideses of the Sun 1610. Second year   january.  Februar.  March.  April.  May  june. D gr. mi. se. D gr. mi. se. D gr. mi. se. D gr. mi. se. D gr. mi. se▪ D gr. mi. se. 1 21 18 56 1 22 49 5 1 20 54 12 1 21 27 43 1 20 31 6 1 20 9 41 2 22 20 11 2 23 49 41 2 21 53 53 2 22 26 18 2 21 28 46 2 21 6 49 3 23 21 25 3 24 50 15 3 22 53 32 3 23 24 50 3 22 26 25 3 22 3 57 4 24 22 38 4 25 50 48 4 23 53 9 4 24 23 21 4 23 24 2 4 23 1 4 5 25 23 50 5 20 51 19 5 24 52 44 5 25 21 50 5 24 21 38 5 23 58 11 6 26 25 1 6 ●7 51 48 6 25 52 16 6 26 20 16 6 25 19 13 6 24 55 18 7 27 26 51 7 28 52 16 7 26 51 46 7 27 18 40 7 26 16 40 7 25 52 24 8 28 27 19 8 29 52 41 8 27 51 15 8 28 17 2 8 27 14 18 8 26 49 29 9 29 28 27 9 ♓ 53 5 9 28 50 40 9 29 15 21 9 28 11 48 9 27 46 35 10 ♒ 29 34 10 1 53 27 10 29 50 4 10 ♉ 13 39 10 29 9 17 10 28 43 40 11 1 30 40 11 2 53 48 11 ♈ 49 26 11 1 11 56 11 ♊ 6 45 11 29 40 44 12 2 31 45 12 3 54 6 12 1 48 46 12 2 10 10 12 1 4 12 12 ♋ 37 49 13 3 32 49 13 4 54 22 13 2 48 3 13 3 8 23 13 2 1 37 13 1 34 53 14 4 33 52 14 5 54 37 14 3 47 19 14 4 6 34 14 2 59 2 14 2 31 57 15 5 34 54 15 6 54 50 15 4 46 32 15 5 4 43 15 3 56 25 15 3 29 2 16 6 35 54 16 7 55 0 16 5 45 44 16 6 2 50 16 4 53 47 16 4 26 6 17 7 36 54 17 8 55 9 17 6 44 52 17 7 0 55 17 5 51 9 17 5 23 9 18 8 37 53 18 9 55 16 18 7 43 59 18 7 58 58 18 6 48 29 18 0 20 13 19 9 38 50 19 10 55 20 19 8 43 3 19 8 56 59 19 7 45 48 19 7 17 17 20 10 39 46 20 11 55 23 20 9 42 5 20 9 54 59 20 8 42 7 20 8 14 21 21 11 40 40 21 12 55 23 21 10 41 5 21 10 52 57 21 9 40 24 21 9 11 25 22 12 41 34 22 13 55 22 22 11 40 2 22 11 50 53 22 10 37 41 22 10 8 30 23 13 42 25 23 14 55 18 23 12 38 58 23 12 48 48 23 11 34 56 23 11 5 34 24 14 43 16 24 15 55 12 24 13 37 52 24 13 46 41 24 12 32 11 24 12 2 39 25 15 44 5 25 16 55 4 25 14 36 44 25 14 44 32 25 13 29 25 25 12 59 43 26 16 44 52 26 17 54 54 26 15 35 33 26 15 42 22 26 14 26 38 26 13 56 49 27 17 45 38 27 18 54 43 27 16 34 20 27 16 40 10 27 15 23 50 27 14 53 44 28 18 46 23 28 19 54 28 28 17 33 5 28 17 37 56 28 16 21 1 28 15 51 0 29 19 47 6     29 18 31 48 29 18 35 41 29 17 18 12 29 16 48 6 30 20 47 47     30 19 30 28 30 19 33 24 30 18 15 22 30 7 45 12 31 21 48 27     31 20 29 7     31 19 12 32      july  August.  Sete●be  October.  Novemb.  Decemb. D gr. mi. se D gr. mi. se D gr. mi. sec D gr. mi se. D gr, mi. sec D gr. mi. sec 1 18 42 19 1 18 19 17 1 18 18 37 1 17 50 31 1 18 54 52 1 19 24 3 2 19 39 26 2 19 16 54 2 19 17 10 2 18 50 9 2 19 55 31 2 20 25 17 3 20 36 34 3 20 14 33 3 20 15 44 3 19 49 48 3 20 56 11 3 21 26 32 4 21 33 42 4 21 12 13 4 21 14 21 4 20 49 30 4 21 56 53 4 22 27 47 5 22 30 51 5 22 9 55 5 22 12 59 5 21 49 13 5 22 57 37 5 23 29 3 6 23 28 0 6 23 7 38 6 23 11 40 6 22 48 59 6 23 58 22 6 24 30 20 7 24 25 10 7 24 5 23 7 24 10 23 7 23 48 47 7 24 59 3 7 25 31 37 8 25 22 21 8 25 3 9 8 25 9 8 8 24 48 37 8 25 59 57 8 26 32 54 9 26 19 32 9 26 0 57 9 26 7 56 9 25 48 30 9 27 0 46 9 27 34 12 10 27 16 45 10 26 58 47 10 27 6 45 10 26 48 25 10 28 1 37 10 28 35 30 11 28 13 57 11 27 56 38 11 28 5 37 11 27 48 22 11 29 2 30 11 29 36 49 12 29 11 11 12 28 54 31 12 29 4 31 12 28 48 22 12 ♐ 3 23 12 ♑ 38 7 13 ♌ 8 25 13 29 52 26 13 ♎ 3 27 13 29 48 23 13 1 4 19 13 1 39 26 14 1 5 40 14 ♏ 50 23 14 1 2 25 14 ♏ 48 26 14 2 5 16 14 2 40 45 15 2 2 57 15 1 48 21 15 2 1 26 15 1 48 31 15 3 6 14 15 3 42 4 16 3 0 14 16 2 46 21 16 3 0 28 16 2 48 38 16 4 7 13 16 4 43 24 17 3 57 32 17 3 44 23 17 3 59 33 17 3 48 47 17 5 8 14 17 5 44 43 18 4 54 51 18 4 42 26 18 4 58 40 18 4 48 58 18 6 9 15 18 6 46 1 19 5 52 11 19 5 40 32 19 5 57 49 19 5 49 12 19 7 10 18 19 7 47 20 20 6 49 32 20 6 38 39 20 6 57 1 20 6 49 27 20 8 11 22 20 8 48 39 21 7 46 54 21 7 36 49 21 7 56 15 21 7 49 44 21 9 12 26 21 9 49 57 22 8 44 17 22 8 35 0 22 8 55 31 22 8 50 3 22 10 13 32 22 10 51 16 23 9 41 42 23 9 33 13 23 9 54 49 23 9 50 24 23 11 14 39 23 11 52 34 24 10 39 7 24 10 31 27 24 10 54 9 24 10 50 47 24 12 15 47 24 12 53 52 25 11 36 34 25 11 29 44 25 11 53 31 25 11 51 11 25 13 16 56 25 13 55 9 26 12 34 2 26 12 28 0 26 12 52 55 26 12 51 38 26 14 18 5 26 14 56 27 27 13 31 31 27 13 26 22 27 13 52 21 27 13 52 6 27 15 19 15 27 15 57 44 28 14 29 2 28 14 24 45 28 14 51 50 28 14 52 36 28 16 20 2● 2● 16 59 1 29 15 26 33 29 15 23 10 29 15 51 22 29 15 53 7 29 17 21 38 29 18 0 17 30 1● 24 7 30 16 21 36 30 16 50 55 30 16 53 40 30 18 22 50 30 19 1 33 ●1 17 21 41 ●1 17 20 5     31 17 54 15     31 20 2 48 
Ephemerideses of the Sun 1611. Third year.   January.  Februar.  March.  April.  May.  June. D gr. mi. sec D gr mi. se. D gr. mi. se. D gr. mi se D gr. mi. sec D gr. mi. sec 1 21 4 5 1 22 34 23 1 20 39 44 1 21 13 31 1 20 17 7 1 19 55 50 2 22 5 21 2 23 35 0 2 21 39 26 2 22 12 6 2 21 14 48 2 20 52 58 3 23 6 35 3 24 35 35 3 22 39 5 3 23 10 39 3 22 12 27 3 21 50 6 4 24 7 48 4 25 36 8 4 23 38 43 4 24 9 10 4 23 10 4 4 22 47 14 5 25 9 0 5 26 36 39 5 24 38 18 5 25 7 39 5 24 7 41 5 23 44 21 6 26 10 11 6 27 37 9 6 25 37 51 6 26 6 6 6 25 5 16 6 24 41 27 7 27 11 21 7 28 37 37 7 26 37 21 7 27 4 31 7 26 2 49 7 25 38 33 8 28 12 30 8 29 38 3 8 27 36 50 8 28 2 53 8 27 0 21 8 26 35 39 9 29 13 38 9 ♓ 38 27 9 28 36 17 9 29 1 13 9 27 57 52 9 27 32 44 10 ♒ 14 45 10 1 38 50 10 29 35 41 10 29 53 32 10 28 55 22 10 28 29 50 11 1 15 51 11 2 39 10 11 ♈ 35 3 11 ♉ 57 49 11 29 52 50 11 29 26 54 12 2 16 56 12 3 39 29 12 1 34 23 12 1 56 4 12 ♊ 50 17 12 ♋ 24 0 13 3 18 1 13 4 39 46 13 2 33 41 13 2 54 17 13 1 47 43 13 1 21 3 14 4 19 4 14 5 40 1 14 3 32 58 14 3 52 28 14 2 45 7 14 2 18 8 15 5 20 6 15 6 40 14 15 4 32 12 15 4 50 37 15 3 42 31 15 3 15 12 16 6 21 7 16 7 40 25 16 5 31 23 16 5 48 45 16 4 39 53 16 4 12 16 17 7 22 7 17 8 40 35 17 6 30 33 17 6 46 50 17 5 37 15 17 5 9 20 18 8 23 6 18 9 40 42 18 7 29 40 18 7 44 54 18 6 34 35 18 6 6 24 19 9 24 4 19 10 40 47 19 8 28 44 19 8 42 56 19 7 31 55 19 7 3 28 20 10 25 0 20 11 40 50 20 9 27 47 20 9 40 56 20 8 28 14 20 8 0 32 21 11 25 55 21 12 40 51 21 10 26 47 21 10 38 54 21 9 26 31 21 8 57 36 22 12 26 48 22 13 40 50 22 11 25 45 22 11 36 51 22 10 23 48 22 9 54 40 23 13 27 40 23 14 40 47 23 12 24 42 23 12 34 46 23 11 21 4 23 10 51 44 24 14 28 31 24 15 40 41 24 13 23 36 24 13 32 39 24 12 18 18 24 11 48 49 25 15 29 21 25 16 40 34 25 14 22 28 25 14 30 31 25 13 15 33 25 12 45 53 26 16 30 8 26 17 40 25 26 15 21 18 26 15 28 21 26 14 12 46 26 13 42 58 27 17 30 55 27 18 40 13 27 16 20 6 27 16 26 9 27 15 9 54 27 14 39 54 28 18 31 40 28 19 40 0 28 17 18 51 28 17 23 56 28 16 7 10 28 15 37 9 29 19 32 23     29 18 17 35 29 18 21 41 29 17 4 21 29 16 34 15 30 20 33 5     30 19 16 15 30 19 19 25 30 18 1 31 30 17 31 22 31 21 33 45     31 20 14 54     31 18 58 41      July.  August.  Septemb  October.  Novem.  Decemb. D gr. mi. se. D gr. mi. se. D gr. mi. se D gr. mi. se. D gr. mi. se. D gr. mi. se 1 18 28 28 1 18 5 19 1 18 4 25 1 17 36 4 1 18 40 11 1 19 9 13 2 19 25 35 2 19 2 56 2 19 2 48 2 18 35 41 2 19 40 49 2 20 10 26 3 20 22 43 3 20 0 34 3 20 1 32 3 19 35 21 3 20 41 29 3 21 11 41 4 21 19 51 4 20 58 14 4 21 0 8 4 20 35 2 4 21 42 10 4 22 12 56 5 22 17 0 5 21 55 55 5 21 58 46 5 21 34 45 5 22 42 54 5 23 14 12 6 23 14 9 6 22 53 38 6 22 57 26 6 22 34 30 6 23 43 38 6 24 15 29 7 24 11 19 7 23 51 23 7 23 56 9 7 23 34 17 7 24 44 19 7 25 16 45 8 25 8 29 8 24 49 9 8 24 54 53 8 24 34 7 8 25 45 12 8 26 18 3 9 26 5 41 9 25 46 56 9 25 53 40 9 25 33 59 9 26 46 2 9 27 19 20 10 17 2 53 10 26 44 56 10 26 52 30 10 26 33 54 10 27 47 52 10 28 20 39 11 28 0 5 11 27 42 37 11 27 51 20 11 27 33 50 11 28 47 44 11 29 21 57 12 28 57 19 12 28 40 29 12 28 50 14 12 28 33 49 12 29 48 38 12 ♑ 23 16 13 29 54 33 13 29 38 24 13 29 49 10 13 29 33 50 13 ♐ 49 33 13 1 24 34 14 ♌ 51 48 14 ♍ 36 20 14 ♎ 48 8 14 ♏ 33 52 14 1 50 29 14 2 25 54 15 1 49 4 15 1 34 18 15 1 47 7 15 1 33 57 15 2 51 27 15 3 27 13 16 2 46 21 16 2 32 17 16 2 46 9 16 2 34 4 16 3 52 26 16 4 28 32 17 3 43 39 17 3 30 19 17 3 45 13 17 3 34 12 17 4 53 26 17 5 29 51 18 4 40 57 18 4 28 22 18 4 44 20 18 4 34 23 18 5 54 28 18 6 31 10 19 5 38 17 19 5 26 27 19 5 43 29 19 5 34 36 19 6 55 30 19 7 32 29 20 6 35 38 20 6 24 34 20 6 42 40 20 6 34 50 20 7 56 33 20 8 33 47 21 7 33 0 21 7 22 43 21 7 41 53 21 7 35 7 21 8 57 38 21 9 35 6 22 8 30 23 22 8 20 53 22 8 41 9 22 8 35 26 22 9 58 44 22 10 36 24 23 9 27 47 23 9 19 6 23 9 40 26 23 9 35 46 23 10 59 50 23 11 37 42 24 10 25 12 24 10 17 20 24 10 39 46 24 10 36 8 24 12 0 58 24 12 39 0 25 11 22 38 25 11 15 36 25 11 39 7 25 11 36 32 25 13 2 6 25 13 40 18 26 12 20 6 26 12 13 54 26 12 38 31 26 12 36 58 26 14 3 16 26 14 41 35 27 13 17 35 27 13 12 14 27 13 37 57 27 13 37 26 27 15 4 26 27 15 42 53 28 14 15 5 28 14 10 36 28 14 37 25 28 14 37 56 28 16 5 36 28 16 44 9 29 15 12 37 29 15 9 0 29 15 36 56 29 15 38 27 29 17 6 48 29 17 45 26 30 16 10 9 30 16 7 26 30 16 36 29 30 16 38 59 30 18 8 0 ●0 18 4● 42 31 17 7 44 31 17 5 55     31 17 39 34     31 1● 47 58 
Ephemerideses of the Sun 1612. Fourth year.   january.  Februar  March.  April.  May.  june. D gr m●. se. D gr mi. se. D gr. mi. se. D gr. mi se D gr mi. se. D gr. mi. se 1 20 49 14 1 22 19 42 1 21 24 58 1 21 57 55 1 21 0 49 1 20 39 8 2 21 50 30 2 23 20 19 2 22 24 38 2 22 56 28 2 21 58 29 2 21 36 16 3 22 51 45 3 24 20 54 3 23 24 16 3 23 55 0 3 22 56 7 3 22 33 23 4 23 52 58 4 25 21 28 4 24 23 52 4 24 53 29 4 23 53 43 4 23 30 30 5 24 54 11 5 26 21 59 5 25 23 25 5 25 51 57 5 24 51 19 5 24 27 37 6 25 55 22 6 27 22 29 6 26 22 56 6 26 50 22 6 25 48 53 6 25 24 23 7 26 56 32 7 28 22 58 7 27 22 26 7 27 48 45 7 26 46 25 7 26 21 49 8 27 57 41 8 29 23 24 8 28 21 53 8 28 47 5 8 27 43 56 8 27 18 54 9 28 58 49 9 ♓ 23 49 9 29 21 17 9 29 45 24 9 28 41 26 9 28 16 0 10 29 59 57 10 1 24 12 10 ♈ 20 40 10 ♉ 43 41 10 29 38 54 10 29 13 4 11 1 ♒ 1 3 11 2 24 33 11 1 20 1 11 1 41 57 11 ♊ 36 22 11 ♋ 10 10 12 2 2 8 12 3 24 53 12 2 19 19 12 2 40 10 12 1 33 48 12 1 7 13 13 3 3 13 13 4 25 10 13 3 18 36 13 3 38 22 13 2 31 12 13 2 4 18 14 4 4 16 14 5 25 25 14 4 17 51 14 4 36 32 14 3 28 36 14 3 1 22 15 5 5 10 15 6 25 39 15 5 17 3 15 5 34 40 15 4 25 59 15 3 58 26 16 6 6 20 16 7 25 51 16 6 16 13 16 6 32 46 16 5 23 21 16 4 55 30 17 7 7 20 17 8 26 0 17 7 15 20 17 7 30 50 17 6 20 42 17 5 52 34 18 8 8 20 18 9 26 8 18 8 14 25 18 8 28 52 18 7 18 1 18 6 49 38 19 9 9 17 19 10 26 14 19 9 13 28 19 9 26 53 19 8 14 20 19 7 46 42 20 10 10 14 20 11 26 17 20 10 12 29 20 10 24 52 20 9 12 38 20 8 43 46 21 11 11 9 21 12 26 19 21 11 11 28 21 11 22 49 21 10 9 55 21 9 40 50 22 12 12 3 22 13 28 18 22 12 10 25 22 12 20 44 22 11 7 11 22 10 37 54 23 13 12 56 23 14 26 15 23 13 9 20 23 13 18 38 23 12 4 26 23 11 34 59 24 14 13 47 24 15 26 11 24 14 8 13 24 14 16 30 24 13 1 40 24 12 32 3 25 15 14 36 25 16 26 4 25 15 7 3 25 15 14 20 25 13 58 54 25 13 29 8 26 16 15 24 26 17 25 55 26 16 5 51 26 16 12 9 26 14 56 6 26 14 26 4 27 17 16 11 27 18 25 44 27 17 4 37 27 17 9 56 27 15 53 18 27 15 23 19 28 18 16 57 28 19 25 31 28 18 3 21 28 18 7 42 28 16 50 29 28 16 20 25 29 19 17 41 29 20 25 16 29 19 2 2 29 19 5 25 29 17 47 40 29 17 17 31 30 20 18 23     30 20 0 42 30 20 3 8 30 18 44 50 30 18 14 38 31 21 19 3     31 20 59 19     31 19 41 59      july.  August.  Septemb.  October.  Novemb  Decemb D gr. mi. se. D gr. mi se. D gr. mi. se D gr. mi. sec D gr. mi. se. D gr. mi se. 1 19 11 45 1 18 48 58 1 18 48 46 1 18 21 14 1 19 26 7 1 19 55 36 2 20 8 52 2 19 46 36 2 19 47 20 2 19 20 53 2 20 26 46 2 20 56 50 3 21 6 0 3 20 44 15 3 20 45 56 3 20 20 33 3 21 27 27 3 21 58 5 4 22 3 9 4 21 41 56 4 21 44 33 4 21 20 16 4 22 28 10 4 22 59 21 5 23 0 18 5 22 39 39 5 22 43 13 5 22 20 0 5 23 28 55 5 24 0 37 6 23 57 28 6 23 37 23 6 23 41 55 6 23 19 48 6 24 29 41 6 25 1 54 7 24 54 38 7 24 35 8 7 24 40 39 7 24 19 37 7 25 30 28 7 26 3 11 8 25 51 49 8 25 32 56 8 25 39 25 8 25 19 28 8 26 31 17 8 27 4 29 9 26 49 1 9 26 30 45 9 26 38 14 9 26 19 22 9 27 32 7 9 28 5 47 10 27 46 13 10 27 28 35 10 27 37 5 10 27 19 18 10 28 32 59 10 29 7 5 11 28 43 26 11 28 26 27 11 28 35 58 11 28 19 17 11 29 33 52 11 ♑ 8 24 12 29 40 40 12 29 24 21 12 29 34 53 12 29 19 17 12 ♐ 34 47 12 1 9 43 13 ♌ 37 55 13 ♍ 22 17 13 ♎ 33 50 13 ♏ 19 19 13 1 35 43 13 2 11 2 14 1 35 11 14 1 20 14 14 1 32 49 14 1 19 23 14 2 36 40 14 3 12 21 15 2 32 27 15 2 18 14 15 2 31 51 15 2 19 29 15 3 37 39 15 4 13 40 16 3 29 45 16 3 16 15 16 3 30 54 16 3 19 37 16 4 38 39 16 5 14 59 17 4 27 4 17 4 14 7 17 4 30 0 17 4 19 47 17 5 39 40 17 6 16 18 18 5 24 23 18 5 12 2● 18 5 29 8 18 5 20 0 18 6 40 4● 18 7 17 37 19 6 21 44 19 6 10 2● 19 6 28 19 19 6 20 14 19 7 41 45 19 8 18 56 20 7 19 5 20 7 8 37 20 7 27 32 20 7 20 30 20 8 42 50 20 9 20 14 21 8 16 28 21 8 6 47 21 8 26 47 21 8 20 48 21 9 43 55 21 10 21 33 22 9 13 52 22 9 4 59 22 9 26 4 22 9 21 8 22 10 45 1 22 11 22 51 23 10 11 17 23 10 3 13 23 10 25 23 23 10 21 30 23 11 46 9 23 12 24 9 24 11 8 43 24 11 1 29 24 11 24 44 24 11 21 54 24 12 47 17 24 13 25 27 25 12 6 10 25 11 59 46 25 12 24 7 25 12 22 19 25 13 48 26 25 14 26 44 26 13 3 39 26 12 58 5 26 13 23 32 26 13 22 47 26 14 49 36 26 15 28 1 27 14 1 9 27 13 56 27 27 14 23 0 27 14 23 16 27 15 50 47 27 16 29 18 28 14 58 40 28 14 54 50 28 15 22 30 28 15 23 46 28 16 51 58 28 17 30 35 29 15 56 12 29 15 53 16 29 16 22 3 29 16 24 19 29 17 53 10 29 18 31 51 30 16 53 46 30 16 51 44 30 17 21 37 30 17 24 53 30 18 54 23 30 19 33 7 31 17 51 21 31 17 50 14     31 18 25 29     31 20 34 22   

CHAP. XXVI. The use of these Ephemerideses.  
OF the use of these Ephemerideses, because they be altogether of the same form, that others generally are, and have been heretofore: and to be used also in all points after the same manner, for finding out by them the true place of the Sun at any time desired, for so many years as they serve: I think it needless for me in this place to make any further mention: it being my purpose in this book, rather to make supply of that is wanting in others, then to meddle with that which is by them sufficiently handled and already published. This notwithstanding I thought good to advertise the Reader, that these Ephemerideses, though th●y be made for five years only▪ yet may profitably serve for many years to come after this manner: Subtract 1612 out of the year of Christ given, divide that remaineth by four; if any thing remain after division made, it showeth which of the three common years in these Ephemerideses answereth to the year given: if nothing remain, the fourth year is answerable to the year given. Then seek out the month and day of the time given both in these Ephemerideses for that year, and in the Table of their Equations; and out of them take both the place of the Sun, and the Equation answerable to that month and day: for the product of this Equation by the quotient▪ added to the said place of the Sun, if the number of the year given be more than 1612; or subtracted, if it be less, shall give you the true place of the Sun for the time given.  
As for example, the 1 of July 1620▪ suppose you would know the place of the Sun: Subtracting therefore 1612 out of 1620, the remainder is 8, which being divided by 4, the quotient is 2, and nothing remaining; which showeth that the fourth year (viz. 1612) answereth to the year given. Also the said month and day sought out in these Ephemerideses, and in the Table of their Equations, give you the place of the Sun 19 degr. 11 min. 45 sec. of Cancer; and the Equation 1 min. 45 seconds which multiplied by the quotient 2, make 3 min. 30 sec. And this added to the said place of the Sun the 1 of July 1612, showeth you the true place of the Sun, for the time given, to be 19 degr. 15 min. and 15 sec. of Cancer.   

CHAP, XXVII▪ The making of the Table of the Sun's Declination.  
THE place of the Sun being thus easily known by these Ephemerideses for every day of five years, the Declinations of the Sun for every day of the same years were easily found out of the former Table of the Declination of every minute of the Ecliptic, in such sort as was showed in the use of that Table before set down, chap. 18. pag. 116. and 117: And so was made with no less facility the Table following of the Sun's Declination for every day of five years together, commonly called by Seamen, A Regiment of the Sun. For although it hath been thought sufficient in books of Navigation hitherto published, to make the Regiment of the Sun, or the Table of the Sun's Declination for every day of 4 years, beginning with the first year after the leap year, and ending with the next Leap year, because the Declinations of the Sun for the 4 years following have been supposed to be the same, in a manner that they were the 4 years before; and so to continue alike, without any notable difference for many years: yet to bring this matter to some more certainty▪ I have to this Table of Declination prefixed the fifth year also viz. the leap year going before the first of the said common years; that by comparing the Declinations of both leap years together it might the better appear what difference of Declination there is in every 4 years: by addition or subtraction of which difference, to the Declinations set down in this Table, this Table may be made to serve for a great many years yet to come, as truly as if it were made of purpose for them.  
And for the more easy and readier use of all Seamen, I have to this end gathered into this little Table, the differences of the Sun's Declinations for every day of the first and last years, set down in this Table of the Sun's Declinations here following; which differences may be called the Prosthaphaereses, or Equations of the Sun's Declination; because that by adding them to, or subtracting them from the Declinations contained in this Table, the true Declination of the Sun for any day (though many years hence) may easily be found; and that after this manner.  
Out of the number of the year of Christ given, subtract 1612; divide the remainder by four, and set aside the quotient; if any thing remain, that remainder showeth in which of the 3 common years you are to seek the Sun's Declination: if nothing remain, you must look the Sun's Declination in the fourth and last year, which is leap year. Then seek the month and day of the time given, both in that year so found in the Table of the Sun's Declination, and also in this little Table of Prosthaphaereses of the Sun's Declination, here immediately following; taking out of that the Sun's Declination, and out of this little Table the Equation of that Declination for four years; which Equation you shall multiply by the said quotient, and add the product to the Declination found in the Table, in the Spring and Autumn; that is, if the Sun be in Aries, Taurus, Gemini, Libra, Scorpio, or sagittary; or subtract it in Summer and winter, viz. the Sun being in Cancer, Leo, Virgo, Capricorn, aquary, or Pisces▪ for so shall you have the Sun's true Declination for the time given.  
Take for example the 15 of March in the year of Christ 1630: out of this subtract 1612, the remainder is 18; which being divided by 4, the quotient is also 4, and 2, remain; which showeth that you must seek the Sun's Declination in the second year after the leap year for the month and day aforesaid. Therefore I find the Sun's Declination in that year (viz. 1610) to be 1 degr. 54 min. 16 sec. and in this little Table of Prosthaphaereses his difference of Declination for 4 years, 44 sec. which multiplied by the foresaid quotient 4, make 2 min. 56 sec. to be added to the said Declination 1 degr. 54 min 16 sec. that so you may have the true Declination of the Sun for that time, viz. 1 degr. 57 min. 12 sec.  
Take also the 30 of August, in the year of our Lord 1659.; out of which, if you subtract 1612, there shall remain 47; which being divided by 4, the quotient will be 11, and 3 remaining. I find therefore in the Table of the Sun's Declination in the third year, for the month and day aforesaid, the Sun's Declination 5 degr 29 min. ●5 sec. Also in this little Table of Prosthaphaereses of the Sun's Declination, I find for the same month and day, the difference of the Declination of the Sun for 4 years, to be 42 sec. which multiplied by the quotient 11, make the product 7 min. 42 sec. which subtracted out of the Declination aforesaid 5 degr. 29 min. 35 seconds, shall leave you the Sun's true Declination for the 30 of August 1659., 5 degr. 21 min. 53 sec.  

Prosthaphereses of the Sun's Declination.   ja Fe. M A. M Ju Ju A. Se. O. N D. Day. Se. Se. Se. Se. Se. Se. Se Se. Se. Se. Se. Se. 1 17 36 42 40 28 8 15 33 42 41 30 9 2 18 37 43 39 28 7 15 34 43 42 29 8 3 19 37 43 40 27 6 16 35 43 42 29 7 4 20 38 44 40 27 5 17 35 43 42 28 6 5 20 37 44 39 26 4 18 34 43 41 28 5 6 21 37 43 39 25 4 19 35 43 41 28 4 7 21 38 43 38 25 3 19 35 44 41 27 3 8 22 39 43 38 24 2 19 35 43 40 26 2 9 24 38 44 38 23 2 20 36 44 40 25 1 10 24 39 45 37 23 1 21 36 43 40 24 1 11 25 39 44 37 22 0 21 37 43 40 24 0 12 25 40 44 37 22 1 22 38 43 39 23 0 13 26 41 43 37 21 1 22 38 43 39 22 1 14 26 40 44 37 20 2 23 38 44 38 21 2 15 27 41 44 35 20 3 23 38 43 38 21 3 16 28 42 43 35 19 4 24 39 44 37 20 4 17 28 41 42 35 19 4 25 39 43 38 20 5 18 29 41 43 35 18 5 26 39 43 37 19 6 19 30 41 43 34 17 6 26 39 43 37 18 7 20 31 42 42 34 17 7 27 40 43 36 17 8 21 31 42 43 33 16 8 27 40 43 36 16 9 22 32 42 43 33 15 8 28 41 44 35 16 10 23 32 43 43 32 14 9 29 40 43 35 15 11 24 32 43 42 32 14 10 29 41 42 34 14 12 25 33 44 42 31 12 11 30 41 43 34 13 12 26 33 44 41 31 12 12 30 41 42 33 13 13 27 34 43 41 30 11 13 30 41 42 34 12 14 28 35 43 41 29 11 13 31 42 42 33 11 15 29 35 43 41 29 9 14 31 41 43 32 11 16 30 35  41 29 9 14 32 42 42 32 10 16 31 36  41  8  33 42  31  17 
A Table of the Sun's Declination, 1608. Leap year.   Jan. decls differ  Feb. decls differ  Mar. decls differ  Apr. decls differ D gr. mi. s. mi. se D gr. mi. s mi. se D gr. mi se. mi. se D gr mi. se. mi. se 1 21 54 39 9 35 1 14 7 44 20 11 1 3 25 38 23 36 1 8 34 21 21 52 2 21 45 4 9 59 2 13 47 33 19 45 2 3 2 2 23 38 2 8 56 23 21 42 3 21 35 5 10 24 3 13 27 48 21 18 3 2 38 24 23 41 3 9 18 5 21 33 4 21 24 41 10 54 4 13 6 30 20 52 4 2 14 43 23 41 4 9 39 38 21 25 5 21 13 45 11 7 5 12 46 38 20 23 5 1 51 2 23 43 5 10 1 3 21 14 6 21 2 38 11 37 6 12 26 15 20 54 6 1 27 19 23 43 6 10 22 17 21 4 7 20 51 1 12 2 7 12 5 21 21 6 7 1 3 36 23 43 7 10 43 21 20 53 8 20 38 59 12 24 8 11 44 15 21 18 8 0 39 53 23 42 8 11 4 14 20 36 9 20 26 35 12 48 9 11 22 57 21 27 9 0 16 11 23 42 9 11 24 50 20 38 10 20 13 47 13 10 10 11 1 30 21 39 10 0 7 31 23 42 10 11 45 28 20 20 11 20 0 37 13 34 11 10 39 51 21 47 11 0 31 13 23 39 11 12 5 48 20 8 12 19 47 3 13 54 12 10 18 4 21 56 12 0 54 52 23 39 12 12 25 56 19 56 13 19 33 9 14 17 13 9 56 8 22 7 13 1 18 31 23 36 13 12 45 52 18 43 14 19 18 52 14 24 14 9 34 1 22 14 14 1 42 7 23 34 14 13 4 35 20 31 15 19 4 28 15 12 15 9 11 47 22 22 15 2 5 41 23 31 15 13 25 6 19 18 16 18 49 16 15 33 61 8 49 25 22 31 16 2 29 12 23 28 16 13 44 24 19 4 17 18 33 43 15 26 17 8 26 54 22 37 17 2 52 40 23 24 17 14 3 2● 18 50 18 18 18 17 15 59 18 8 4 17 22 45 18 3 16 4 23 20 18 14 22 18 18 37 19 18 2 18 16 18 19 7 41 32 22 50 19 3 39 24 23 16 19 14 40 55 18 22 20 17 46 0 16 38 20 7 18 42 22 58 20 4 2 40 23 12 20 14 59 17 18 9 21 17 29 22 16 55 21 6 55 44 23 3 21 4 25 52 23 7 21 15 17 26 17 50 22 17 12 27 17 14 22 6 32 41 23 8 22 4 48 59 23 2 22 15 35 16 17 38 23 16 55 13 17 31 23 6 9 33 23 13 23 5 12 1 22 58 23 15 52 54 17 20 24 16 37 42 17 49 24 5 46 20 23 17 24 5 34 59 22 50 24 16 10 14 17 6 25 16 19 53 18 6 25 5 23 3 23 22 25 5 57 49 22 45 25 16 27 20 16 49 26 16 1 47 18 21 26 4 59 41 23 27 26 6 20 34 22 37 26 16 44 9 16 33 27 15 43 26 18 38 27 4 36 14 23 28 27 6 43 11 22 31 27 17 0 42 16 16 28 15 24 48 18 54 28 4 12 46 23 32 28 7 5 42 22 24 28 17 16 58 15 58 29 15 5 54 19 9 29 3 49 14 23 36 29 7 28 6 22 16 29 17 32 56 15 41 30 14 46 45 19 23       30 7 50 22 22 8 30 17 48 37 15 24 31 14 27 22 19 38       31 8 12 30 22 1        Ma. decls differ.  Ju decls. Diff.  Ju decls Diff.  Au decls Diff. D gr. mi. se. mi se D gr. m. se mi. se D gr. mi. se mi. se D gr. mi se. mi. s▪ 1 18 4 1 15 5 1 23 11 32 3 50 1 22 8 57 8 16 1 15 14 50 18 3 2 18 19 6 14 48 2 23 15 22 3 26 2 22 0 42 8 39 2 14 56 47 18 17 3 18 33 54 14 28 3 23 18 48 3 1 3 21 52 3 9 2 3 14 38 30 18 32 4 18 48 22 14 10 4 23 21 49 2 38 4 21 43 1 9 23 4 14 19 58 18 47 5 19 2 32 13 51 5 23 24 27 1 12 5 21 33 38 9 45 5 14 1 11 18 58 6 19 16 23 13 21 6 23 25 39 2 47 6 21 23 53 10 8 6 13 42 13 19 13 7 19 29 54 13 12 7 23 28 26 1 23 7 21 13 45 10 29 7 13 23 0 19 24 8 19 43 6 12 52 8 23 29 49 0 58 8 21 3 16 10 50 8 13 3 36 19 38 9 19 55 58 12 35 9 23 30 47 0 34 9 20 52 26 11 10 9 12 43 58 19 50 10 20 8 33 12 8 10 23 31 21 0 9 10 20 41 16 11 33 10 12 24 8 20 ● 11 20 20 41 11 49 11 23 31 30 0 16 11 20 29 43 11 53 11 12 4 7 20 13 12 20 32 30 11 30 12 23 31 14 0 42 12 20 17 50 12 13 12 11 43 54 20 25 13 20 44 0 11 9 13 23 30 32 1 5 13 20 5 37 12 34 13 11 23 29 20 36 14 20 55 9 10 8 14 23 29 27 1 29 14 19 53 3 12 53 14 11 2 53 20 46 15 21 6 7 10 14 15 23 27 58 1 56 15 19 40 10 13 12 15 10 42 7 20 56 16 21 16 21 10 3 16 23 26 2 2 19 16 19 26 58 13 33 16 10 21 11 21 6 17 21 26 24 10 42 17 23 23 43 2 44 17 19 13 25 13 51 17 10 0 5 21 17 18 21 36 6 9 19 18 23 20 59 3 2 18 18 59 34 14 10 18 9 38 48 21 25 19 21 45 25 8 57 19 23 17 57 3 39 19 18 45 24 14 28 19 9 17 23 21 34 20 21 54 22 8 34 20 23 14 18 3 57 20 18 30 56 14 47 20 8 55 59 21 44 21 22 2 56 8 12 21 23 10 21 3 22 21 18 16 9 15 6 21 8 34 5 21 5● 22 22 11 8 7 48 22 23 4 59 3 45 22 18 1 3 15 22 22 8 12 14 22 0 23 22 18 56 7 25 23 23 1 14 5 10 23 17 45 41 15 40 23 7 50 14 22 7 24 22 26 21 7 3 24 22 56 4 5 33 24 17 30 1 15 57 24 7 28 7 22 15 25 22 33 24 9 48 25 22 50 31 5 57 25 17 14 4 16 14 25 7 5 52 22 21 26 22 40 2 6 15 26 22 44 34 6 19 26 16 57 50 16 31 26 6 43 31 22 28 27 22 46 17 5 50 27 22 38 15 6 45 27 16 41 19 16 46 27 6 21 3 22 33 28 22 52 7 5 28 28 22 31 30 7 8 28 16 24 33 17 3 28 5 58 30 22 43 29 22 57 35 5 3 29 22 24 22 7 3 29 16 7 30 17 18 29 5 35 47 22 40 30 23 2 38 4 39 30 22 16 51 7 53 30 15 50 12 17 33 30 5 13 1 22 52 31 23 7 17 4 15       31 15 32 39 17 49 31 4 50 9 22 58  Sep. decls diff.  Oct. Decl Diff.  No. decls, Diff.  Dec. decls dffe, D gr. mi. se. mi. s. D gr. mi. sec mi. s. D gr· mi. se. mi. s. D gr. m. sec mi. s▪ 1 4 27 11 23 1 1 7 12 32 22 43 1 17 38 34 16 23 1 23 8 20 4 25 2 4 4 10  6 2 7 35 15 22 37 2 17 54 57 16 3 2 23 12 45 3 58 3 3 41 4  10 3 7 57 52 22 30 3 18 11 0 15 55 3 23 16 43 3 30 4 3 17 54  14 4 8 20 22 22 23 4 18 26 55 15 14 4 23 20 13 3 2 5 2 54 40  18 5 8 42 45 22 16 5 18 42 9 15 5 5 23 23 15 2 33 6 2 31 22  20 6 9 5 1 22 8 6 18 57 14 14 44 6 23 25 48 2 6 7 2 8 2 23 23 7 9 27 9 22 0 7 19 11 58 14 23 7 23 27 54 1 36 8 1 44 39  26 8 9 49 9 21 52 8 19 26 21 14 3 8 23 29 30 1 9 9 1 21 13  28 9 10 11 1 21 42 9 19 40 24 13 41 9 23 30 49 0 39 10 0 57 45  30 10 10 32 43 21 33 10 19 54 5 13 18 10 23 31 18 0 12 11 0 34 15  30 11 10 54 16 21 24 11 20 7 23 12 56 11 23 31 30 0 18 12 0 10 45  32 12 11 15 40 21 13 12 20 20 19 12 24 12 23 31 12 0 46 13 0 12 47  32 13 11 36 53 21 3 13 20 32 43 12 21 13 23 30 26 1 14 14 0 36 19  33 14 11 57 56 20 51 14 20 45 4 11 47 14 23 29 12 1 43 15 0 59 52  33 15 12 18 47 20 40 15 20 56 51 11 24 15 23 27 29 2 11 16 1 23 25  33 16 12 39 27 20 27 16 21 8 15 10 59 16 23 25 18 2 40 17 1 46 58  31 17 12 59 54 20 17 17 21 19 14 10 35 17 23 22 38 3 8 18 2 10 29  31 18 13 20 11 20 3 18 21 29 49 10 12 18 23 19 30 3 36 19 2 34 0  29 19 13 40 14 19 50 19 21 40 1 9 44 19 23 15 54 4 4 20 2 57 29  28 20 14 0 4 19 37 20 21 49 45 9 21 20 23 11 50 4 32 21 3 20 57  25 21 14 19 41 19 23 21 21 59 6 8 53 21 23 7 18 5 1 22 3 44 22  23 22 14 39 4 19 7 22 22 7 59 8 29 22 23 2 17 5 28 23 4 7 55  20 23 14 58 11 18 55 23 22 16 28 8 3 23 22 56 49 5 54 24 4 31 5  16 24 15 17 6 18 38 24 22 24 31 7 29 24 22 50 55 6 23 25 4 54 21  13 25 15 35 44 18 23 25 22 32 0 7 17 25 22 44 32 6 50 26 5 17 34  9 26 15 54 7 18 6 26 22 39 17 6 43 26 22 37 42 7 17 27 5 40 43  5 27 16 12 13 17 51 27 22 46 0 6 16 27 22 30 25 7 43 28 6 3 48 22 59 28 16 30 4 17 34 28 22 52 16 5 48 28 22 22 42 8 10 29 6 26 47  55 29 16 47 38 17 16 29 22 58 4 5 21 29 22 14 32 8 36 30 6 49 42  50 30 17 4 54 16 59 30 23 3 25 4 55 30 22 5 56 9 2       31 17 21 53 16 41       31 21 56 54 9 27 
First year. 1609.   jan. decls. diff.  Feb. decls Diff.  Mar. dec diffe.  Apr. decls diffe. D gr. m. se. mi se D gr mi. se. mi. se D gr. mi. se mi se D gr. mi. se. mi. se 1 21 47 27 9 54 1 13 52 43 20 2 1 3 31 22 23 36 1 8 29 11 21 54 2 21 37 33 10 19 2 13 32 41 20 15 2 3 7 46 23 39 2 8 51 5 21 46 3 21 27 14 10 43 3 13 12 26 20 28 3 2 44 7 23 40 3 9 12 51 21 35 4 21 16 31 11 7 4 12 51 58 20 40 4 2 20 27 23 41 4 9 34 26 21 27 5 21 5 24 11 33 5 12 31 18 20 52 5 1 56 46 23 43 5 9 55 53 21 16 6 20 53 51 11 55 6 12 10 26 21 3 6 1 33 3 23 42 6 10 17 9 21 7 7 20 41 56 12 19 7 11 49 23 21 15 7 1 9 21 23 43 7 10 38 16 20 46 8 20 29 37 12 41 8 11 28 8 21 26 8 0 45 38 23 43 8 10 59 12 20 44 9 20 16 56 13 6 9 11 6 42 21 35 9 0 21 55 23 42 9 11 19 56 20 34 10 20 3 50 13 27 10 10 45 7 21 45 10 0 1 47 23 42 10 11 40 30 20 23 11 19 50 23 13 49 11 10 23 22 21 55 11 0 25 29 23 39 11 12 0 53 20 11 12 19 36 34 14 13 12 10 1 27 22 4 12 0 49 8 23 39 12 12 21 4 19 59 13 19 22 21 14 31 13 9 39 23 22 12 13 1 12 47 23 37 13 12 41 3 19 47 14 19 7 50 14 54 14 9 17 11 22 20 14 1 36 24 23 34 14 13 0 50 19 34 15 18 52 56 15 15 15 8 54 51 22 29 15 1 59 58 23 32 15 13 20 24 19 20 16 18 37 41 15 35 16 8 32 22 22 35 16 2 23 30 23 29 16 13 39 44 19 8 17 18 22 6 15 53 17 8 9 47 22 43 17 2 46 59 23 25 17 13 58 52 18 54 18 18 6 13 16 15 18 7 47 4 22 50 18 3 10 24 23 21 18 14 17 46 18 39 19 17 49 58 16 31 19 7 24 14 22 55 19 3 33 45 23 17 19 14 36 25 18 26 20 17 33 27 16 52 20 7 1 19 23 25 20 3 57 2 23 14 20 14 54 51 18 11 21 17 16 35 17 9 21 6 37 54 22 44 21 4 20 16 23 8 21 15 13 2 17 51 22 16 59 26 17 28 22 6 15 10 23 12 22 4 43 24 23 3 22 15 30 53 17 47 23 16 41 58 17 44 23 5 51 58 23 16 23 5 6 27 22 58 23 15 48 38 17 26 24 16 24 14 18 2 24 5 28 42 23 21 24 5 29 25 22 52 24 16 6 4 17 9 25 16 6 12 18 18 25 5 5 21 23 25 25 5 52 17 22 47 25 16 23 13 16 53 26 15 47 54 18 34 26 4 41 56 23 29 26 6 15 4 22 38 26 16 40 6 16 37 27 15 29 20 18 50 27 4 18 27 23 31 27 6 37 42 22 34 27 16 56 43 16 20 28 15 10 30 19 5 28 3 54 56 23 34 28 7 0 16 22 24 28 17 13 3 16 2 29 14 51 25 19 19       29 7 22 40 22 19 29 17 29 5 15 46 30 14 32 6 19 35       30 7 44 59 22 10 30 17 44 51 14 32 31 14 12 31 19 48       31 8 7 9 22 2        Ma. decls diff.  Iu. decli. diff.  Jul decls diff.  Au. decls diff. D gr▪ mi. se. mi. s. D gr. mi. se mi. se D gr. mi se. mi. se D gr. mi. sec mi. s. 1 18 0 23 15 6 1 23 10 32 3 57 1 22 10 55 8 11 1 15 19 11 18 1 2 18 15 29 14 52 2 23 14 39 3 31 2 22 2 44 8 34 2 15 1 10 18 14 3 18 30 21 14 33 3 23 18 0 3 8 3 21 54 10 8 56 3 14 42 56 18 28 4 18 44 54 14 16 4 23 21 8 2 43 4 21 45 14 9 17 4 14 24 28 18 42 5 18 59 10 13 53 5 23 23 51 2 18 5 21 35 57 9 40 5 14 5 46 18 56 6 19 13 3 13 37 6 23 25 9 2 53 6 21 26 17 10 2 6 13 46 50 19 9 7 19 26 40 13 16 7 23 28 2 1 29 7 21 16 15 10 24 7 13 27 41 20 22 8 19 39 56 12 57 8 23 29 31 1 4 8 21 5 51 10 45 8 13 7 19 18 34 9 19 52 53 12 36 9 23 30 35 0 40 9 20 55 6 11 6 9 12 48 45 19 48 10 20 5 29 12 16 10 23 31 15 0 15 10 20 44 0 11 29 10 12 28 57 19 58 11 20 17 45 11 55 11 23 31 30 0 10 11 20 32 31 11 47 11 12 8 59 20 11 12 20 29 40 11 35 12 23 31 20 0 35 12 2● 20 44 12 6 12 11 48 48 20 22 13 20 41 15 11 13 13 23 30 45 1 0 13 20 8 38 12 30 13 11 28 26 20 32 14 20 52 28 10 52 14 23 29 45 1 24 14 19 56 8 12 48 14 11 7 54 20 43 15 21 3 20 10 32 15 23 28 21 2 49 15 19 43 20 13 9 15 10 47 11 20 55 16 21 13 52 10 9 16 23 25 32 1 13 16 19 30 11 13 27 16 10 26 16 21 4 17 21 24 1 9 47 17 23 24 19 2 38 17 19 16 44 13 47 17 10 5 12 21 13 18 21 33 48 9 24 18 23 21 41 3 2 18 19 2 57 14 5 18 9 43 59 21 23 19 21 43 12 9 2 19 23 18 39 3 28 19 18 48 52 14 24 19 9 22 36 21 33 20 21 52 14 8 41 20 23 15 11 3 50 20 18 34 28 14 42 20 9 1 3 21 41 21 22 0 55 8 16 21 23 11 21 4 12 21 18 19 46 15 1 21 8 39 22 21 49 22 22 9 11 7 55 22 23 7 9 5 44 22 18 4 45 15 19 22 8 17 33 21 59 23 22 17 6 7 30 23 23 2 25 5 3 23 17 49 2● 15 36 23 7 55 34 22 4 24 22 24 36 7 7 24 22 57 22 5 28 24 17 33 50 15 52 24 7 33 30 22 19 25 22 31 43 6 45 25 22 51 54 5 53 25 17 17 58 16 19 25 7 11 16  14 26 22 38 28 6 20 26 22 46 3 6 14 26 17 1 48 16 36 26 6 48 57  17 27 22 44 48 5 57 27 22 39 49 6 40 27 16 45 21 16 52 27 6 26 30  33 28 22 50 45 5 32 28 22 33 9 7 1 28 16 28 38 16 58 28 6 3 57  39 29 22 56 17 5 9 29 22 26 8 7 25 29 16 11 40 17 15 29 5 41 18 22 46 30 23 1 26 4 46 30 22 18 43 7 48 30 15 54 25 17 29 30 5 18 32  50 31 23 6 12 4 20       31 15 36 56 17 45 31 4 55 42  56  Sep decls▪ Diff.  Oct. decls Diff  Nou. dec diff.  Dec. decls diff. D gr. mi. se mi. se D gr. mi. se▪ mi. se D gr. mi. se. mi. se D gr. mi. se. mi. se 1 4 32 46 23 1 1 7 7 0 22 45 1 17 34 33 16 28 1 23 7 10 4 33 2 4 9 45  5 2 7 29 45 22 39 2 17 51 1 16 7 2  11 43 4 5 3 3 46 40  9 3 7 52 24  31 3 18 7 8 15 50 3  15 48 3 37 4 3 23 31  14 4 8 14 55  25 4 18 22 58 15 29 4  19 25 3 9 5 3 0 17  16 5 8 37 20  19 5 18 38 27 15 10 5  22 34 2 40 6 2 37 1  20 6 8 59 39  9 6 18 53 37 14 4● 6  25 14 2 12 7 2 13 41  22 7 9 21 48  2 7 19 8 25 14 29 7  27 26 1 44 8 1 50 19  25 8 9 43 51 21 53 8 9 22 54 14 7 8  29 10 1 14 9 1 26 54  27 9 10 5 44 21 45 9 19 37 1 13 46 9  30 24 0 48 10 1 3 27  29 10 10 27 29 21 35 10 19 50 47 13 24 10 23 31 12 0 18 11 0 39 58 23 31 11 10 49 4 21 26 11 20 4 11 13 2 11  31 30 0 11 12 0 16 27  32 12 11 10 30 21 16 12 20 17 13 12 39 12  31 19 0 39 13 0 7 5  32 13 11 31 46 21 5 13 20 29 52 12 10 13  30 40 1 7 14 0 30 37  33 14 11 52 51 20 54 14 20 42 8 11 53 14  29 33 1 36 15 0 54 10  33 15 12 13 45 20 43 15 20 54 1 11 30 15  27 57 2 4 16 1 17 43  31 16 12 34 28 20 30 16 21 5 31 11 5 16  25 53 2 34 17 1 41 14  33 17 12 54 58 2● 19 17 21 16 36 10 42 17  23 19 3 1 18 2 4 47  31 18 13 15 17 20 7 18 21 27 1● 10 16 18 23 20 18 3 29 19 2 28 18 23 30 19 13 35 24 19 53 19 21 37 34 9 52 19  16 49 3 57 20 2 51 48  28 20 13 55 17 19 40 20 21 47 26 9 2● 20  12 52 4 26 21 3 15 16  26 21 14 14 57 19 2● 21 21 56 51 9 1 21  8 26 4 54 22 3 38 42  23 22 14 34 23 19 12 22 22 5 52 8 3● 22  3 32 5 20 23 4 2 5  21 23 14 53 35 18 57 23 22 14 2● 8 8 23 22 58 12 5 49 24 4 25 26  17 24 15 12 32 18 42 24 22 22 36 7 43 24 22 52 23 6 16 25 4 48 43  14 25 15 31 14 18 27 25 22 30 19 7 16 25  46 7 6 43 26 5 11 57  10 26 15 49 41 18 10 26 22 37 35 6 50 26  39 24 7 10 27 5 35 7  5 27 16 7 51 17 55 27 22 44 25 6 23 27  32 14 7 37 28 5 58 12 23 1 28 16 25 46 17 38 28 22 50 48 5 54 28  24 37 8 4 29 6 21 13  56 29 16 43 24 17 21 29 22 56 42 5 26 29 22 16 33 8 2● 30 6 44 9 22 1 30 17 0 45 17 3 30 23 2 8 5 2 30  8 4 8 5●       31 17 17 48 16 45       31 21 59 8 9 2● 
A Table of the Sun's Declination, 1610. Second year.   Jan. decls diff.  Feb. decls diff.  Mar. dec diff.  Apr. decls diff. D gr. mi. se. mi se D gr. mi. sec mi. se D gr. mi. se. mi s D gr. mi. se. mi. s. 1 21 49 46 9 48 1 13 57 32 19 59 1 3 37 5 23 36 1 8 23 52 21 56 2 21 39 58 10 11 2 13 37 33 20 11 2 3 13 29 23 38 2 8 45 48 21 46 3 21 29 47 10 38 3 13 17 22 20 25 3 2 49 51 23 40 3 9 7 34 21 39 4 21 19 9 11 1 4 12 56 57 20 37 4 2 26 11  41 4 9 29 13 21 28 5 21 8 8 11 26 5 12 36 20 20 49 5 2 2 30  41 5 9 50 41 21 20 6 20 56 42 11 50 6 12 15 31 21 1 6 1 38 49  43 6 10 12 1 21 9 7 20 44 52 12 14 7 11 54 30 21 11 7 1 15 6  43 7 10 33 10 20 58 8 20 32 38 12 36 8 11 33 19 21 24 8 0 51 23  43 8 10 54 8 20 47 9 20 20 2 12 59 9 11 11 55 21 32 9 0 27 30  42 9 11 14 55 20 37 10 20 7 3 13 23 10 10 50 23 21 54 10 0 3 58  41 10 11 35 32 20 26 11 19 53 40 13 44 11 10 28 29 21 42 11 0 19 43  41 11 11 55 58 20 14 12 19 39 56 14 6 12 10 6 47 22 1 12 0 43 24  39 12 12 16 12 20 2 13 19 25 50 14 29 13 9 44 46 22 11 13 1 7 3  38 13 12 36 14 19 49 14 19 11 21 14 47 14 9 22 35 22 19 14 1 30 41  35 14 12 56 3 19 38 15 18 56 34 15 9 15 9 0 16 22 26 15 1 54 16 23 32 15 13 15 41 19 24 16 18 41 25 15 29 16 8 37 50 22 35 16 2 17 48  29 16 13 35 5 19 10 17 18 25 56 15 51 17 8 15 15 22 41 17 2 41 17  27 17 13 54 15 18 57 18 18 10 5 16 8 18 7 52 34 22 48 18 3 4 44  22 18 14 13 12 18 43 19 17 53 57 16 29 19 7 29 46 22 54 19 3 28 6  18 19 14 31 55 18 30 20 17 37 28 16 4● 20 7 6 52 23 0 20 3 51 24  26 20 14 50 25 18 14 21 17 20 42 17 ● 21 6 43 52 23 5 21 4 14 50 23 58 21 15 8 39 17 59 22 17 3 36 17 22 22 6 20 47 23 11 22 4 37 48  4 22 15 26 38 17 44 23 16 46 14 17 41 23 5 57 36 23 16 23 5 0 52  0 23 15 44 22 17 29 24 16 28 33 17 58 24 5 34 20 23 20 24 5 23 52 22 53 24 16 1 51 17 14 25 16 10 35 18 13 25 5 11 0 23 4 25 5 46 45 22 48 25 16 19 5 16 57 26 15 52 22 18 31 26 4 47 56 23 47 26 6 9 33 22 41 26 16 36 2 16 41 27 15 33 51 18 45 27 4 24 9 23 30 27 6 32 14  34 27 16 52 43 16 24 28 15 15 6 19 2 28 4 0 39 23 34 28 6 54 48  27 28 17 9 7 16 7 29 14 56 4 19 16       29 7 17 15  20 29 17 25 14 16 49 30 14 36 48 19 31       30 7 39 35  13 30 17 41 3 15 33 31 14 17 17 19 4●       31 8 1 48  44        May. dec diffe.  Jun. decls Diff.  jul. decli Diffe  Aug. dec Diff. D gr. mi. se mi. s▪ D gr. mi. s. mi. se D gr. mi. se mi. s. D gr. mi. se. mi. s· 1 17 56 36 15 14 1 23 9 31 4 2 1 22 12 50 8 5 1 15 23 30 17 56 2 18 11 50 15 6 2 23 13 33 3 38 2 22 4 45 8 28 2 15 5 34 18 1● 3 18 26 56 14 30 3  17 11 3 13 3 21 56 17 8 51 3 14 47 22 18 24 4 18 41 26 14 17 4  20 24 2 50 4 21 47 26 9 13 4 14 28 58 18 39 5 18 55 43 14 0 5  23 14 2 24 5 21 38 13 9 34 5 14 10 19 18 5● 6 19 9 43 13 41 6  25 38 1 59 6 21 28 39 9 57 6 13 51 26 19 6 7 19 23 24 13 21 7  27 37 1 35 7 21 18 42 10 18 7 13 32 20 19 18 8 19 36 45 13 1 8  29 12 1 10 8 21 8 24 10 40 8 13 13 2 19 32 9 19 49 46 12 41 9  30 22 0 46 9 20 57 44 11 1 9 12 53 30 19 44 10 20 2 27 12 22 10  31 8 0 21 10 20 46 43 11 22 10 12 33 46 20 16 11 20 14 49 12 1 11  31 29 0 4 11 20 35 21 10 52 11 12 13 30 19 49 12 20 26 50 11 38 12 23 31 25 0 29 12 20 24 29 12 54 12 11 53 41 20 17 13 20 38 28 11 19 13  30 56 0 54 13 20 11 35 12 24 13 11 33 2● 20 31 14 20 49 47 10 57 14  30 2 1 18 14 19 59 11 12 44 14 11 12 53 20 40 15 21 0 44 10 37 15  28 44 1 43 15 19 46 27 13 7 15 10 52 13 20 52 16 21 11 21 10 14 1●  27 1 2 7 16 19 33 20 13 18 16 10 31 21 21 2 17 21 21 35 10 2 17  24 54 2 33 17 19 20 2 13 43 17 10 10 19 21 11 18 21 31 37 9 20 18  22 21 2 56 18 19 6 19 14 1 18 9 49 8 21 21 19 21 40 57 8 59 19  19 25 3 21 19 18 52 18 14 19 19 9 27 47 21 30 20 21 49 56 8 55 20  16 4 3 46 20 18 37 59 14 38 20 9 6 17 21 39 21 21 58 51 8 22 21  12 18 4 9 21 18 23 21 14 57 21 8 44 38 21 48 22 22 7 13 8 0 22 23 8 9 4 34 22 18 8 24 15 13 22 8 22 50 21 56 23 22 15 13 7 35 23 23 3 35 4 57 23 17 53 11 15 32 23 8 0 54 22 2 24 22 22 48 7 14 24 22 58 38 5 22 24 17 37 39 15 49 24 7 38 52 22 12 25 22 30 2 6 49 25  53 16 5 45 25 17 21 50 16 6 25 7 16 40 22 17 26 22 36 51 6 27 26  47 31 6 9 26 17 5 44 16 22 26 6 54 23 22 26 27 22 43 18 6 2 27  41 22 6 34 27 16 49 22 16 40 27 6 31 57 22 31 28 22 49 20 5 39 28  34 48 6 56 28 16 32 42 16 54 28 6 9 36 22 39 29 22 54 59 5 15 29  27 52 7 20 29 16 15 48 17 11 29 5 46 47 22 43 30 23 0 14 4 51 30  20 32 7 42 30 15 58 37 17 26 30 5 24 4 22 50 31 32 5 5 4 26       31 15 41 11 17 41 31 5 1 14 22 55  Sep. decls diff.  Oct. Decl Diff.  Nou. dec. diffe,  Dec. decls diff. D gr. mi. se. mi. s. D gr. mi. sec mi▪ s. D gr, mi. sec mi. s. D gr. m. se▪ mi. se 1 4 38 19 22 59 1 7 1 29 22 47 1 17 30 31 16 32 1 23 5 0 5 40 2 4 15 20 23 4 2 7 24 16 22 39 2 17 47 3 16 13 2 23 10 40 4 11 3 3 52 16  8 3 7 46 55 22 34 3 18 3 16 15 53 3 23 14 51 3 44 4 3 29 8  12 4 8 9 29 22 26 4 18 19 9 15 34 4 23 18 35 3 15 5 3 5 56  16 5 8 31 55 22 20 5 18 34 43 15 15 5 23 21 50 2 48 6 2 42 40  19 6 8 54 15 22 12 6 18 49 58 14 55 6 23 24 38 2 18 7 2 19 21 23 22 7 9 16 27 22 3 7 19 4 53 14 32 7 23 26 56 1 51 8 1 55 59  24 8 9 38 30 21 57 8 19 19 25 14 13 8 23 28 47 1 22 9 1 32 35  27 9 10 0 27 21 46 9 19 33 38 13 51 9 23 30 9 0 54 10 1 9 ●  29 10 10 22 13 21 38 10 19 47 29 13 30 10 23 31 3 0 25 11 0 45 39  30 11 10 43 51 21 28 11 20 0 59 13 7 11 23 31 28 0 4 12 0 22 9  32 12 11 5 19 21 18 12 20 14 6 12 45 12 23 31 24 0 32 13 0 1 23  32 13 11 26 37 21 8 13 20 26 51 12 21 13 23 30 52 1 1 14 0 24 55  32 14 11 47 45 20 57 14 20 39 12 12 10 14 23 29 51 1 28 15 0 48 27  33 15 12 8 42 20 45 15 20 51 22 11 24 15 23 28 23 2 58 16 1 1● 0  33 16 12 29 27 20 34 16 21 2 46 11 12 16 23 25 25 1 23 17 1 35 33  32 17 12 50 1 20 21 17 21 13 58 10 46 17 23 24 2 2 7 18 1 59 5  32 18 13 9 22 20 10 18 21 24 44 10 23 18 23 21 5 3 23 19 2 22 37  29 19 13 30 32 19 57 19 21 35 7 9 57 19 23 17 42 3 50 20 2 46 6  29 20 13 50 29 19 43 20 21 45 4 9 33 20 23 13 52 4 19 21 3 9 35  26 21 14 10 12 19 30 21 21 54 37 9 7 21 23 9 33 4 47 22 3 33 1  25 22 14 29 42 19 15 22 22 3 44 8 41 22 23 4 46 5 14 23 3 56 26  21 23 14 48 57 19 1 23 22 12 25 8 15 23 22 59 32 5 42 24 4 19 47  18 24 15 7 58 18 56 24 22 20 40 7 50 24 22 53 50 6 10 25 4 43 5  14 25 15 26 44 18 30 25 22 28 30 7 23 25 22 47 40 6 36 26 5 6 19  11 26 15 45 14 18 15 26 22 35 53 6 55 26 22 41 4 7 4 27 5 29 30  7 27 16 3 29 17 59 27 22 42 48 6 29 27 22 34 0 7 30 28 5 52 37  3 28 16 21 28 17 41 28 22 49 17 6 2 28 22 26 30 7 57 29 6 15 40 22 56 29 16 39 9 17 25 29 22 55 19 5 34 29 22 18 33 8 23 30 6 38 36  53 30 16 56 34 17 7 30 23 0 53 4 7 30 22 10 10 8 50       31 17 13 41 16 50       31 22 1 20 9 16 
Third year. 1611.   jan. decls. diff.  Feb. decls diff.  Mar. dec diffe.  Apr. decls diffe▪ D gr. mi. se mi. se D gr mi. e. mi se D gr. mi. se mi se D gr. mi▪ se. mi. se 1 21 52 4 9 41 1 14 2 20 19 55 1 3 42 48 23 35 1 8 18 31 21 58 2 21 42 23 10 6 2 13 42 25 20 9 2 3 19 13 23 38 2 8 40 29 21 49 3 21 32 17 10 31 3 13 22 16 20 21 3 2 55 35 23 39 3 9 2 18 21 41 4 21 21 46 10 56 4 13 1 55 20 35 4 2 31 56  41 4 9 23 59 21 31 5 21 10 50 11 20 5 12 41 20 20 45 5 2 8 15  42 5 9 45 30 21 21 6 20 59 30 11 44 6 12 20 35 20 58 6 1 44 33  42 6 10 6 51 21 12 7 20 47 46 12 8 7 11 59 37 21 10 7 1 20 51  43 7 10 28 3 21 1 8 20 35 38 12 31 8 11 38 27 21 27 8 0 57 8  43 8 10 49 4 20 50 9 20 23 7 12 54 9 11 17 0 21 23 9 0 33 25  42 9 11 9 54 20 40 10 20 10 13 13 16 10 10 55 37 21 41 10 0 9 43 23 42 10 11 30 34 20 28 11 19 56 57 13 39 11 10 33 5● 21 50 11 0 13 59  41 11 11 51 2 20 16 12 19 43 18 14 1 12 10 12 6 22 0 12 0 37 40  39 12 12 11 18 20 6 13 19 29 17 14 22 13 9 50 6 22 7 13 1 1 19  38 13 12 31 24 19 52 14 19 14 55 14 44 14 9 27 59 22 17 14 1 24 57  36 14 12 51 16 19 40 15 19 0 11 15 4 15 9 5 42 22 25 15 1 48 33  33 15 13 9 56 19 27 16 18 45 7 15 25 16 8 43 17 22 32 16 2 12 6  30 16 13 30 23 19 15 17 18 29 42 15 45 17 8 20 45 22 40 17 2 35 36 23 27 17 13 49 38 19 0 18 18 13 57 16 4 18 7 58 5 22 46 18 2 59 3  24 18 14 8 38 18 47 19 17 57 53 16 24 19 7 35 19 22 53 19 3 22 27  19 19 14 27 25 18 32 20 17 41 29 16 42 20 7 12 26 22 59 20 3 45 46  15 20 14 45 57 18 18 21 17 24 47 17 1 21 6 49 2● 23 4 21 4 9 1  10 21 15 4 15 18 3 22 17 7 46 17 17 22 6 26 23  10 22 4 32 11  6 22 15 22 18 17 48 23 16 50 29 17 37 23 6 3 13  14 23 4 55 17  1 23 15 40 6 17 33 24 16 32 52 17 53 24 5 39 59  19 24 5 18 18 22 55 24 15 57 59 17 17 25 16 14 59 18 10 25 5 16 40  23 25 5 41 13 22 49 25 16 14 56 17 1 26 15 56 49 18 27 26 4 53 17  26 26 6 4 2  42 26 16 31 57 16 45 27 15 38 22 18 42 27 4 29 51  30 27 6 26 44  37 27 16 48 42 16 28 28 15 19 40 18 58 28 4 6 21  33 28 6 49 21  28 28 17 5 10 16 11 29 15 0 42 19 13 29      29 7 11 49  22 29 17 21 21 15 5● 30 14 41 29 19 27 30      30 7 34 11  14 30 17 37 15 15 3● 31 14 22 2 19 42 31      31 7 56 25  6        Ma. decls diff.  Iu. decl●▪ diff.  Jul. dec. diff.  Au. decls diff. D gr▪ mi. se. mi. s. D gr. mi. se▪ mi▪ se D gr. mi. se. mi. se D gr. mi. sec mi. s. 1 17 52 51 15 19 1 23 8 29 4 8 1 22 14 44 7 59 1 15 27 48 17 52 2 18 8 10 15 1 2 23 12 37 3 43 2 22 6 45 8 2● 2 15 9 56 18 7 3 18 23 11 14 42 3 23 16 20 3 20 3 21 58 23 8 46 3 14 51 49 18 22 4 18 37 53 14 23 4 23 19 40 2 55 4 21 49 37 9 7 4 14 33 27 18 35 5 18 52 16 14 5 5 23 22 35 2 30 5 21 40 30 9 30 5 14 14 52 18 50 6 19 6 21 13 45 6 23 25 5 2 5 6 21 31 0 9 51 6 13 56 2 19 3 7 19 20 6 13 26 7 23 27 10 1 41 7 21 21 9 10 13 7 13 36 59 19 15 8 19 33 32 13 6 8 23 28 51 1 16 8 21 10 56 10 35 8 13 17 44 19 29 9 19 46 38 12 47 9 23 30 7 0 52 9 21 0 21 10 56 9 12 58 15 19 40 10 19 59 25 12 26 10 23 30 59 0 27 10 20 49 25 11 17 10 12 38 35 19 54 11 20 11 51 12 5 11 23 31 26 0 2 11 20 38 8 11 38 11 12 18 41 20 4 12 20 23 56 11 45 12 23 31 28 0 23 12 20 26 30 11 58 12 11 58 37 20 17 13 20 35 41 11 23 13 23 31 5 0 48 13 20 14 32 12 18 13 11 38 20 20 27 14 20 47 4 11 4 14 23 30 17 1 11 14 20 2 14 12 40 14 11 17 53 20 39 15 20 58 8 10 41 15 23 29 6 1 40 15 19 49 34 12 58 15 10 57 14 20 49 16 21 8 49 10 19 16 23 27 26 1 59 16 19 36 36 13 18 16 10 36 25 20 59 17 21 19 8 9 58 17 23 25 27 2 26 17 19 23 18 13 37 17 10 15 26 21 9 18 21 29 6 9 35 18 23 23 1 2 51 18 19 9 41 13 57 18 9 54 17 21 19 19 21 38 41 9 4 19 23 20 10 3 15 19 18 55 44 14 15 19 9 32 58 21 29 20 21 47 4● 9 0 20 23 16 55 3 39 20 18 41 29 14 34 20 9 11 31 21 38 21 21 56 45 8 28 21 23 13 16 4 4 21 18 26 55 14 52 21 8 49 53 21 45 22 22 5 13 8 6 22 23 9 12 4 29 22 18 12 3 15 9 22 8 2● 8 21 53 23 22 13 1● 7 41 23 23 4 ●3 4 51 23 17 56 54 15 29 23 8 6 17 2● 2 24 22 21 0 7 19 24 22 59 52 5 16 24 17 41 25 15 43 24 7 44 13 22 9 25 22 18 19 6 55 25 22 54 36 5 40 2● 17 25 42 16 2 25 7 22 4  17 26 22 35 14 6 33 26 22 48 56 6 2 26 17 9 40 16 19 2● 6 59 47  23 27 22 41 47 6 8 27 22 42 54 6 1● 27 16 53 21 16 34 27 6 37 ●●  30 28 22 47 55 5 44 28 22 36 2● 6 51 28 16 36 47 16 51 28 6 14 54  ●2 29 22 53 39 5 21 29 22 29 35 7 14 29 16 19 ●● 17 8 29 ● 52 17 22 47 30 22 59 0 4 56 30 22 22 21 7 37 30 16 2 48 17 22 30 5 ●● ●●  48 31 23 3 56 4 33       31 15 45 26 17 38 31 5 ● ●●  ●4  Sep decls▪ Diff.  Oct. decls Diff  Nou. dec deaf▪  Dec dec diff. D gr. mi se mi. se D gr. mi. se. mi. se D gr. mi se. mi. se D gr. mi se mi se 1 4 43 53 22 58 1 6 55 57 22 48 1 17 26 28 16 36 1 23 4 48 4 47 2 4 20 55 23 3 2 7 18 45 22 41 2 17 43 4 16 1● 2 23 9 35 4 18 3 3 57 52  7 3 7 41 26  37 3 17 59 22 15 58 3  13 ●3 3 50 4 3 34 45  11 4 8 4 3  27 4 18 15 20 15 37 4  17 4● 3 23 5 3 11 34  15 5 8 26 30  21 5 18 30 57 15 22 5  21 6 2 53 6 2 48 19  19 6 8 48 51  51 6 18 46 19 14 57 6  23 59 1 26 7 2 25 0  21 7 9 10 42  29 7 19 1 16 14 40 7  25 25 2 58 8 2 1 39  24 8 9 33 11 21 58 8 19 15 56 14 18 8  28 23 1 28 9 1 38 15  26 9 9 55 9 21 49 9 19 30 14 13 56 9  29 51 1 1 10 1 14 49  28 10 10 16 58 21 39 10 19 44 10 13 35 10  30 52 0 32 11 0 51 21 23 31 11 10 38 37 21 31 11 19 57 45 13 12 11  31 2● 0 4 12 0 27 50  31 12 11 0 8 21 20 12 20 10 57 13 50 12  31 28 0 25 13 0 4 19  32 13 11 21 28 21 10 13 20 24 47 11 28 13  31 3 0 54 14 0 19 13  32 14 11 42 38 21 0 14 20 36 15 12 4 14 23 30 9 1 22 15 0 42 45  33 15 12 3 38 20 48 15 20 48 19 11 41 15  28 47 1 51 16 1 6 18  32 1● 12 24 26 20 37 16 21 0 0 11 17 ●  26 56 2 19 17 1 29 50  33 17 12 45 3 20 25 17 21 11 17 10 53 17  24 37 2 47 18 1 53 23  32 18 13 5 28 20 12 18 21 22 10 10 28 18  21 50 3 16 19 2 16 55 23 30 19 13 25 40 20 0 19 21 32 38 10 4 19  18 34 3 44 20 2 40 25  28 20 13 45 40 19 46 20 21 42 42 9 38 20 23 14 50 4 11 21 3 3 53  20 21 14 5 26 19 34 21 21 52 20 9 14 21  10 39 4 41 22 3 27 13  32 22 14 25 0 19 19 22 22 1 34 8 47 22  5 58 5 1 23 3 50 45  22 23 14 44 19 19 4 23 22 10 21 8 22 23  0 57 5 42 24 4 14 7  19 24 15 3 23 18 49 24 22 18 43 7 55 24 22 55 15 6 3 25 4 37 26  16 25 15 22 12 18 34 25 22 26 38 7 29 2● 22 49 12 6 30 26 5 0 42  12 26 15 40 46 18 19 26 22 34 7 7 3 2●  42 42 6 56 27 5 23 54  7 27 15 59 5 18 3 27 22 41 10 6 35 27  35 46 7 24 28 5 47 1 23 3 28 16 17 8 17 46 28 22 47 45 6 9 28  28 22 7 52 29 6 10 4 22 59 29 16 34 54 17 29 29 22 53 54 5 41 29  20 30 8 16 30 6 33 3 22 54 30 16 52 23 17 12 30 22 59 35 5 13 30  12 14 8 44       31 17 9 35 16 53       31  3 30 ● 8  Jan. decls differ  Feb. decls differ  Mar. decls differ  Apr decls differ D gr. mi s. mi. se D gr. mi. s mi. se D gr. mi se. mi. se D gr mi. se. mi. se 1 21 54 22 9 36 1 14 7 8 19 52 1 3 24 56 23 37 1 8 35 11 21 51 2 21 44 46 9 59 2 13 47 16 20 5 2 3 1 19 24 3 2 8 57 2 21 43 3 21 34 47 10 26 3 13 27 11 21 1● 3 2 37 16 23 17 3 9 18 45 21 33 4 21 24 21 10 50 4 13 5 52 19 31 4 2 13 59 23 41 4 9 40 18 21 24 5 21 13 31 11 14 5 12 40 21 20 43 5 1 50 18 23 42 5 10 1 42 21 14 6 21 2 17 11 3 6 12 25 38 20 55 6 1 26 36 23 43 6 10 22 56 21 3 7 20 51 14 12 37 7 12 4 43 21 7 7 1 2 53 23 43 7 10 43 5● 20 53 8 20 38 37 12 26 8 11 43 36 21 17 8 0 39 10 23 43 8 11 4 52 20 42 9 20 26 11 12 48 9 11 22 19 21 28 9 0 15 27 23 44 9 11 25 34 20 31 10 20 13 23 13 11 10 11 0 51 21 39 10 0 8 17 23 39 10 11 46 5 20 20 11 20 0 12 13 34 11 ●0 39 12 21 4● 11 0 31 56 23 40 11 12 6 25 20 8 12 19 46 38 13 55 12 10 17 24 21 57 12 0 55 36 23 38 12 12 26 33 19 56 13 19 32 43 14 17 13 9 55 27 22 8 13 1 19 14 23 27 13 12 46 29 19 43 14 19 18 20 14 39 14 9 33 21 22 15 14 1 42 41 23 43 14 13 6 12 19 29 15 19 3 47 14 59 15 9 11 6 22 23 15 2 6 24 23 31 15 13 25 41 19 18 16 18 48 48 15 20 61 8 48 43 22 30 16 2 29 55 23 27 1● 13 44 59 19 4 17 18 33 2● 15 40 17 8 26 13 22 37 17 2 53 22 23 25 17 14 4 3 18 50 18 18 17 48 16 0 18 8 3 36 22 45 18 3 16 47 23 20 18 14 22 53 18 36 19 18 1 48 16 19 19 7 40 51 22 52 19 3 40 7 23 15 19 14 41 29 18 22 20 17 45 29 16 37 20 7 17 59 22 57 20 4 3 22 23 13 20 14 59 51 18 6 21 17 28 5● 16 57 21 6 55 2 23 49 21 4 2● 35 23 7 21 15 17 57 17 52 22 17 11 55 17 14 22 6 31 13 22 22 22 4 49 42 23 2 22 15 35 49 17 36 23 16 54 41 17 31 23 6 8 51 23 13 23 5 12 44 22 50 23 15 53 25 17 21 24 16 37 10 17 5● 24 5 45 38 23 19 24 5 35 40 22 51 24 16 10 4● 17 5 25 16 19 20 18 6 25 5 22 19 23 22 25 5 58 31 22 44 25 16 27 51 16 49 26 16 1 14 18 22 26 4 58 57 23 25 26 6 21 15 22 37 26 16 44 4● 16 32 27 15 42 52 18 39 27 4 35 42 23 29 27 6 43 52 22 31 27 17 1 12 16 15 28 15 24 13 18 54 28 4 12 3 23 32 28 7 6 23 22 24 28 17 17 27 15 58 29 15 5 19 19 9 29 3 48 31 23 35 29 7 28 47 22 16 29 17 33 25 15 41 30 14 46 10 19 24       30 7 51 3 22 8 30 17 49 6 15 23 31 14 26 46 19 38       31 8 13 11 ●● 0        Ma decls differ  Ju decls. Diff  Ju decls. Diff.  Au decls. Diff▪ D gr. mi. se. mi se D gr. m. se mi. se D gr. mi. se mi. se D gr. mi▪ se. mi s▪ 1 18 4 29 15 5 1 23 11 40 3 49 1 22 8 43 8 17 1 15 14 18 18 5 2 18 19 34 14 47 2 23 15 2● 3 25 2 22 0 26 8 39 2 14 56 13 18 18 3 18 34 21 14 2● 3 23 18 54 3 0 3 21 51 47 9 3 3 14 37 55 18 32 4 18 48 49 13 9 4 23 21 54 2 37 4 21 42 44 9 24 ● 14 19 23 18 46 5 19 2 58 13 50 5 23 24 31 2 11 5 21 33 20 9 46 5 14 0 37 18 59 6 19 16 48 13 31 6 23 26 42 1 48 6 21 23 34 10 8 6 13 41 38 19 13 7 19 30 19 13 11 7 23 28 30 1 21 7 21 13 26 10 29 7 13 22 25 19 26 8 19 43 30 12 51 8 23 29 51 0 58 ● 21 2 57 10 51 8 13 2 59 19 57 9 19 56 21 12 31 9 23 30 49 0 33 9 20 52 6 11 11 9 12 43 22 19 50 10 20 8 52 12 10 10 23 31 22 0 8 10 20 40 55 11 33 10 12 23 32 20 2 11 20 21 2 11 50 11 23 31 30 0 17 11 20 29 22 11 55 11 12 3 30 20 14 12 20 32 52 11 29 12 23 31 13 0 42 12 20 17 27 12 13 12 11 43 1● 20 25 13 20 41 21 11 8 13 23 30 31 1 6 13 20 5 14 12 34 13 11 22 51 20 36 14 20 55 29 10 46 14 23 29 25 1 31 14 19 52 40 12 53 14 11 2 15 20 46 15 21 6 15 10 22 15 23 27 54 1 55 15 19 39 47 13 13 15 10 41 29 20 57 16 21 16 37 10 6 16 23 25 59 2 20 16 19 26 34 13 34 16 10 20 32 21 3 17 21 26 43 9 40 17 23 23 39 2 45 17 19 13 0 13 52 17 9 59 29 21 20 18 21 36 23 9 10 18 23 20 54 3 10 18 18 59 8 14 10 18 9 38 19 21 25 19 21 45 33 9 6 19 23 17 44 3 33 19 18 44 58 14 29 19 9 16 44 21 35 20 21 54 39 8 33 20 23 14 11 3 57 20 18 30 20 14 40 20 8 55 9 21 44 21 22 3 12 8 11 21 23 10 13 4 22 21 18 15 41 15 5 21 8 33 25 21 52 22 22 11 23 7 47 22 23 5 51 4 46 22 18 0 3● 15 24 22 8 11 33 21 59 23 22 19 10 7 25 2● 23 1 5 5 10 23 17 45 12 15 40 23 7 49 34 22 8 24 22 26 35 7 1● 24 22 55 55 5 35 24 17 29 32 15 58 24 7 27 26 22 15 25 22 33 36 6 38 25 22 50 20 5 55 25 17 13 34 16 14 25 7 5 11 22 21 26 22 40 14 6 14 26 22 44 24 6 22 26 16 57 20 16 31 26 6 42 50 22 28 27 22 46 28 5 50 27 22 38 2 6 45 27 16 40 49 16 47 27 6 20 22 22 35 28 22 52 18 5 26 28 22 31 17 7 9 28 16 24 2 17 3 28 5 57 47 22 41 29 22 57 44 5 3 29 22 24 8 7 31 29 16 6 59 17 19 29 5 35 6 22 47 30 23 2 47 4 38 30 22 16 37 7 54 30 15 49 40 17 34 30 5 12 19 22 52 31 23 7 25 4 15       31 15 32 6 17 48 31 4 49 27 22 58  Sep, decls diffe.  Oct. decls, Diff.  No. decls, diff.  Dec. decls Diff. D gr. mi. sec mi▪ s. D gr. mi. se mi. s. D gr. mi. se. mi. se D gr. m. sec mi. se 1 4 26 29 23 2 1 7 13 13 22 44 1 17 39 5 16 21 1 23 8 28 4 25 2 4 3 27  6 2 7 35 57  34 2 17 55 26 16 3 2  12 53 3 57 3 3 40 21  10 3 7 58 34  30 3 18 11 29 15 44 3  16 50 3 29 4 3 17 11  14 4 8 21 4  22 4 18 27 13 15 24 4  20 19 3 1 5 2 53 57  18 5 8 43 26  17 5 18 42 37 15 3 5  23 20 2 33 6 2 30 39  21 6 9 5 43  8 6 18 57 40 14 45 6  25 53 2 4 7 2 7 18  22 7 9 27 51 21 58 7 19 12 25 14 23 7  27 57 1 45 8 1 43 56  27 8 9 49 49  52 8 19 26 48 14 1 8  29 32 1 8 9 1 20 29  27 9 10 11 41  42 9 19 40 49 13 40 9  30 40 0 39 10 0 57 2  29 10 10 33 23  33 10 19 54 29 13 18 10  31 19 0 11 11 0 33 33  31 11 10 54 56 21 23 11 20 7 47 12 55 11  31 30 0 18 12 0 10 2  32 12 11 16 19  13 12 20 20 42 12 34 12  31 12 0 48 13 0 13 30  33 13 11 37 32  2 13 20 33 16 12 9 13  30 24 1 14 14 0 37 3  32 14 11 58 34 20 51 14 20 45 25 11 48 14  29 10 1 44 15 1 0 35 23 34 15 12 19 25  39 15 20 57 12 11 23 15  27 26 2 13 16 1 24 9  32 16 12 40 4  28 16 21 8 35 10 59 16  25 13 2 40 17 1 47 41  31 17 13 0 32  16 17 21 19 34 10 34 17  22 33 3 9 18 2 11 12  31 18 13 20 48 20 3 18 21 30 8 10 9 18  19 24 3 37 19 2 34 43  29 19 13 40 51 19 49 19 21 40 17 9 46 19  15 47 4 5 20 2 58 12  28 20 14 0 40 19 36 20 21 50 3 9 19 20  11 42 4 34 21 3 21 40  26 21 14 20 16 19 23 21 21 59 22 8 53 21  7 8 5 0 22 3 45 6  22 22 14 39 39 19 8 22 22 8 15 8 28 22  2 8 5 29 23 4 8 28  19 23 14 58 47 18 53 23 22 16 43 8 2 23 22 56 39 5 56 24 4 31 47  17 24 15 17 40 18 38 24  24 45 7 36 24  50 43 6 23 25 4 55 4  12 25 15 36 18 18 22 25  32 21 7 9 25  44 20 6 51 26 5 18 16  9 26 15 54 40 18 7 26  39 30 6 42 26  37 29 7 10 27 5 41 25 23 5 27 16 12 47 17 50 27  46 12 6 15 27  30 19 7 52 28 6 4 30  0 28 16 30 37 17 33 28  52 27 5 48 28  22 27 8 11 29 6 27 30 22 54 29 16 48 10 17 16 29  58 15 5 20 29  14 16 8 36 30 6 50 24 22 49 30 17 5 26 16 58 30 23 3 35 4 53 30  5 40 9 3       31 17 22 24 16 41       31 21 56 37 9 26   

CHAP. XXVIII. The use of the former Table, or regiment of the Sun.  
THis Table of the Sun's declinations, as it differeth nothing in form from others that have been published heretofore: so likewise the manner of using it, is altogether the same that hath been accustomed in former Tables of this kind, saving that I must give warning of one error that hath been committed herein; which is (as I have observed) that some of our Seamen do take the Sun's declination out of their regiments, without any aequation by addition or subtraction of the part proportional, agreeable to the difference of Longitude of the place where they are, as if they were always at the same place, or under the same meridian, for which their Regiments were made; for which cause alone, (though they avoid all other errors, it may so fall out, that they may be deceived sometimes 10, or 12. minutes (or more in a long voyage) in taking the Sun's declination. For there is not any Table of the Sun's declination, but that it must needs be made for some one meridian (as this former Table was made for the meridian of London) and therefore cannot be truly used in any other, without some Equation answerable to the distance of the meridians or difference of Longitude.  
To avoid this error therefore, first learn how much you differ in Longitude from the place for which your Table was made, (and though you miss half a dozen, or half a score degrees herein, it cannot in this point breed any sensible error.) Secondly, take out the difference of the Sun's declination, agreeable to the space of 24. hours, about the time of your observation. Thirdly, as 360. is to this difference of declination; so is the difference of Longitude to the part proportional, or Equation of the declination; which Equation is to be added to the declination of the day of observation, if the declination of the Sun be either increasing, and the place of observation westward; or else decreasing, and the place of observation eastwards from the place for which your Table of declination was made: otherwise this Equation is to be subtracted from the declination of your day of observation, that you may have the true declination of the Sun, for the time and place of your observation.  
But if the time of your observation be the noon-tide immediately before or after the Sun's entrance into either of the aequinoctial points, you must follow another rule, and that is this: divide the difference of Longitude by 15, mark how many unites the quotient containeth, and so many minutes add to the Declination found in the former Table, if you be either Eastward from the Meridian of London and observe the noontide before the Equinoctium: or if you be Westward from that Meridian and, observe the noontide after the Equinoctium; for the sum shall be the Declination desired. Otherwise, if you be either Westward from the Meridian of London, and observe the noontide next before the Equinoctium, or Eastward from that Meridian, and Observe the day immediately after the Equinoctium, compare the Declination found in the Table with the foresaid quotient, and subtract the lesser out of the greater, for that remaineth is the Declination desired: Which Declination hath the same denomination of North or South that the Table showeth, if the quotient be less than the Declination found in the Table: but if the quotient be greater the denomination must be altered from North to South, or from South to North, contrary to that the Table showeth. If the quotient be equal to the Declination found in the former Table, the Sun is in the very Equinoctial point, and hath no Declination at all.  
A few examples will make these rules more plain: suppose therefore the 30 of March 1610. you were sailing in the bay of Mexico, differing in Longitude to the Westwards from the Meridian of London, about 90 degrees by estimation: the Declination of the Sun for that day found in the former Table, is 7 degrees, 39 minutes, 35 seconds, the difference of the declination in 24 hours at that time 22 minutes, 13 seconds. Now as 360 is to 22 minutes, 13 seconds; so is 90 degrees, to 5 minutes, 33 seconds, (the part proportional or equation desired) which because the Declination increaseth, and the bay of Mexico is also Westward from the Meridian of London, must be added to the Declination before found in the Table, and so shall you have the true Declination of the Sun that day at noon for that place, 7 degr. 45 min. 8 sec. But admit you had sailed Eastwards▪ and were in the East Indian Ocean sea, differing likewise in Longitude from London about 90 deg. therefore the difference of Declination, and the part proportional thereof, or equation of the Declination shall be the same they were before. But because you are gone so much Eastwards, the Sun cometh 6 hours sooner to your Meridian there, than it doth to ours here at London: and therefore because the Declination also is increasing▪ and will be greater when the Sun cometh to our Meridian then it was, the Sun being under the Meridian of the East indies, that equation of Declination must there be subtracted out of the Declination found in the Table, which before was to be added when we supposed you to be in the bay of Mexico, because the Sun cometh later by six hours to the Meridian of that place, then to ours; and therefore the Declination of the Sun increasing in the mean time, will be greater there than here.  
Now imagine you sail in the year 1612 through the straits of Magellan, and having passed over the South Sea, come the 12 of September to the Philippinas, differing in Longitude from London Westwards about 210 degrees.  
In this example, because the Sun is near the Equinoctial point (altering his Declination about 24 min. in 24 hours, that is, for every hour one minute) therefore divide 210. (the difference of Longitude) by 15 (the number of degrees contained in one hour) the Quotient will be 14 minutes (the difference of Declination answerable to that difference of Longitude) The Declination found in the Table for that day is 10 minutes, 2 seconds Northerly: which (Declination) because it decreaseth (the Sun not being yet come to the Equinoctial) must be subtracted out of 14. and there shall remain 3 min. 58 sec. the Declination of the Sun that day at noon, for that place. But this Declination is Southerly, because the Quotient 14 min. is greater than 10 min. 2 sec. the Declination found in the Table. It would be at this time too tedious for me further to exemplify every particularity specified in the former Rules▪ which may cause some small diversity in the use of the Sun's Declination, having already given examples of the hardest cases that may befall herein, which if they be well considered, and especially compared with the Globe or Sphere, (wherein the whole manner of the Sun's motion and Declinations may most easily, not only be seen, but also felt as it were with the fingers ends) the reason and Demonstration of all those Rules, and of all the diversities of working therein specified, may most plainly appear to him that is but of a mean capacity.   

CHAP. XXIX. The Declinations of the principal fixed stars about the Equinoctial, corrected by Observation.  
BUt because the Declination of the Sun is then only of good use for knowing the Latitude at Sea when his Meridian Altitude may be Observed: so as although all the rest of the day and night be fair and clear, if a Cloud cover the Sun but one quarter of an hour only, about noon, your Tables of the Sun's Declination will stand you in no stead: there have been therefore other means divised for attaining to the knowledge of the height of the Pole, not only in particular, by Observation of the Polestar and Guards, but also in general by the Meridian Altitude and Declination of any notable fixed star whatsoever. So as not in the day time alone, and that only at noon, but almost at any time of the night, if any small portion of the heavens towards the North or South, appear but a small time clear through the raking Clouds, the Latitude of the place where you are, may hereby be more easily known, then by Observation of the Sun's Meridian Altitude. For to omit the changing of the Sun's Declination from North to South; and from South to North twice in every year, which notwithstanding breedeth some diversity of working (by neglect whereof some have gros●y erred) the Sun by reason of his swiftness of motion, increaseth or diminisheth his Declination daily, yea hourly, and that very sensibly many times, whereof there must needs arise many several considerations to be had of the right use and application of the Sun's Declination found in the Table, as well in respect of the part of Declination, (whether it be North or South) as also in regard of the difference of Longitude between the place, for which the Tables of the Sun's Declination were made, and the place of Observation, whether it be Easterly or Westerly from thence, besides many other particularities lately related, and needless here to be repeated. But the fixed stars moving so exceeding slowly, that in more than 70 years, they go not so much as one degree in there proper motion from the west Eastwards, keep not only the same part of the North, or South, but almost the same point and minute of Declination for many years together, I mean those stars especially that are placed in the signs of Gemini, Cancer, Sagittarie, or Capricorn, near the Solstitial Colour, which in an hundred years or two, can alter their Declination scarce one minute: whereas those stars that be in Pisces, Aries, Virgo, or Libra, especially if they be near the Equinoctial colour, may differ in there Declinations about one minute in 3 years; which difference, though it be something, yet for a dozen or twenty years, will hardly be so much as can at Sea be Observed by any Instrument hitherto had in use there.  
For these two causes therefore (that is, for the more easy and general use of the Declinations of the fixed stars then of the Sun) I wish they were more generally known and observed by our seamen then they are, as whereby they might not only most easily know the elevation of the Pole at any time of the night, but also in any place of the world, much more commodiously than otherwise they can, because that in what latitude, and how far soever they should come either Northwards or Southwards, they might always have their choice of divers fixed stars near the meridian, both towards the North and South, of a convenient height to be observed. But herewith it were also to be wished, that the tables of the fixed stars declinations, which are most common amongst English Mariners had been more free from error than they are; I mean, especially the Tables published in bourn's regiment, and Normans new Attractive, which (tables agreeing almost in every tittle one with another) seem to be taken word for word one out of another, errors and all; so as you cannot find any error in the one, but you shall be sure also to have the same in the other: notwithstanding some of those errors are more than two or three whole degrees, (which because being neglected, or unknown to the Mariner that shall use those tables) they may bring him in greater danger than many a hidden rock under sea: I have therefore by diligent observation, with a quadrant of more than six foot semidiameter, detected and corrected those errors▪ showing not only the truth to be heedfully followed, but those errors also to be as carefully avoided, in such sort as is set down in the Table following, wherein the first column containeth the names of the stars; the second, the true declinations (as they were found by observation) in degrees and minutes, together with the part of declination, signified by the letters N and S, whereof N signifieth the declination to be North, and S South; the third column containeth the declinations published in bourn's and Normans tables; the fourth showeth the difference of these declinations from the truth; the fifth giveth the right ascensions of those stars, resolved into hours and minutes: in the sixth and last column are set down the magnitudes or bigness of the same stars.  

Fixed Stars about the Equinoctial.  The names of the Stars. Declinat. by observa. B. & N Declin. Difference. Right Ascens. Bigness  Deg. Min. D. M. D M H. M.  Whales back 12 20 S 12 11  09 0 50 3 Whales belly 12 22 S 12 20  02 1 32 3 Rams horn 17 17 N 17 19  02 1 32 3 Rams head 21 33 N 21 16  17 1 46 3 Bulls eye 15 38 N 15 42  04 4 13 1 Orion's left foot 08 43 S 09 14  29 4 55 1 Orion's left shoulder 05 56 N 04 37 1 19 5 04 2 First in Orion's girdle 00 38 S 01 19  41 5 12 2 Orion's right shoulder 06 17 N 06 18  01 5 34 1 Great Dog 16 12 S 15 30  42 6 27 1 Lesser Dog 06 13 N 06 04  09 7 18 1 Brightest in Hydra 06 53 S 04 47 2 06 9 08 2 Lions heart 13 55 N 21 59  17 9 57 1 Lions neck 21 52 N 14 03  08 9 46 2 Lions back 22 43 N 22 30  13 10 52 2 Lions tail 16 50 N 16 46  04 11 29 1 Ravens head 20 45 S 19 53  52 11 50 3 Ravens wing 15 16 S 17 08 1 52 11 56 3 Virgins spike 09 00 S 08 53  07 13 05 1 Betwixt Boötes' thighs 21 20 N 22 09  49 13 56 1 South Ballance 14 14 S 13 44  30 14 30 2 North Ballance 07 46 S 07 33  13 14 55 2 Scorpion's heart 25 25 S 24 47  38 16 06 1 Hercules head 14 57 N 15 20  23 16 56 3 Serpentaries head 12 57 N 14 07 1 10 17 16 3 Eagles heart 17 54 N 17 28  26 19 32 2 Dolphins tail 10 00 N 10 01  01 20 16 3 Goats tail 17 51 S 14 13 3 38 21 27 3 Water powrers leg 18 10 S 15 52 2 18 22 35 3 Pegasus shoulder 12 58 N 13 01  03 22 46 2 Pegasus leg 25 58 N 26 30  32 22 44 2 Whales tail 20 12 S 21 47 1 35 00 24 3   

CHAP, XXX. The use of the former Table.  
THe declinations of the fixed stars contained in this table, being to be used altogether after the same manner, as the declination of the Sun, for finding out the height of the Pole; it would be but needless for me in this place, to write any more of the use thereof, being a thing so easy and so commonly known amongst mariners, and already sufficiently delivered by others.   

CHAP. XXXI. The true distances of certain principal fixed Stars from the North Pole, found by late observation.  
BUt seeing this former table containeth almost no other stars▪ but such as are betwixt the Tropics, and near about the Equinoctial circle, which are not so fit to be observed by them that sail far Southwards, or under the burnt Zone (for there they will be too high above the Horizon) I thought good here to adjoin another table of as many more principal fixed stars (heedfully observed also with the same quadrant) that are placed near about the North Pole, which may stand you in as much stead, as twice so many taken out of other parts of the heavens, because they come twice to the meridian above our horizon, in every 24 hours; so as in wintertime many of them may be observed both evening and morning, twice in one night, both above and beneath the Pole. Notwithstanding▪ for them that sail Northwards, it shall be best to observe these stars when they come to the meridian under the Pole. chose, they that travel far Southwards, may best observe their meridian altitudes above the Pole. Herein also this table differeth from the former; that whereas in the former were set down the declinations of the stars, or their distances from the Equinoctial; in this chose are set down the compliments of their declinations, or their distances from the Pole; whereby the height of the Pole may more easily be found▪ then by their declinations, only by adding the height of the star observed beneath the Pole, to the distance thereof from the Pole: or by subtracting only the distance of the star from the Pole out of the Northerly meridian altitude, observed above the Pole.  
But if the meridian altitude of the star be southerly (the star observed being southwards from the Zenith) subtract the height of the star from 180, and out of the remainder subtract the distance of the star from the Pole, so shall you have the height of the Pole: thus also there would be a more easy way, then that is commonly used for knowing the latitude by the Sun or stars, having southerly declination. For if instead thereof, the compliment of declination were set down in the table; the height of the Sun or stars always subtracted out of this compliment, should leave you the height of the Pole, or latitude desired.  
But to return to the table of fixed stars here following, the first column therein containeth (as before) the names of the stars: the second, their compliments of declination, or distances from the Pole: the third column giveth you their right ascensions, reduced into hours and minutes of an hour: the fourth showeth their bigness or magnitudes.  
The names of the stars. Distance from the Pole: Right ascension. Bigness.  D. M. H. M.  In the breast of Cassiopeia 35 35 0 19 3 In her lip 31 26 0 32 3 The Polestar 02 52 0 50 3 At the knees of Cassiopeia 31 50 1 00 3 In her leg 28 18 1 25 3 Perseus right shoulder 38 05 2 35 3 Perseus right side 41 38 2 56 2 The goat, or wagoners left shoulder 44 30 4 49 1 The wagoners right shoulder 45 11 5 30 2 The first in the great bears forefoot 40 30 8 24 3 The second in the same foot 41 28 8 32 3 In her former left knee 36 37 8 58 3 The great bears side 31 26 10 58 2 The great bears back 26 05 10 40 2 The end of the Dragon's tail 18 26 11 08 3 The great bears thigh 34 03 11 32 2 The great bears rump 30 41 11 54 2 The next to the end of the Dragon's tail 17 57 12 14 3 The first in the great bears tail next her rump 31 49 12 32 2 The middlemost in her tail 32 55 13 06 2 In the end of her tail 38 37 13 32 2 The next before the turning of the Dragon's tail 23 40 13 53 3 The foremost guard 14 11 14 54 2 In the turning of the Dragon's tail 29 37 15 14 3 The hindmost guard 16 42 15 26 2 Next after the turning of the Dragon's tail 30 20 15 54 3 The Dragon's eye 37 18 17 22 3 The Dragon's head 38 22 17 44 3 In the Swans right wing 45 44 19 34 3 In her tail 46 06 20 30 2 Cepheus his right shoulder 29 00 21 10 3 The back of Cassiopeia's chair 33 02 23 48 3   

CHAP. XXXII. To know at what time any of the foresaid fixed stars come to the Meridian for any day of the year.  
NOw because the fixed stars are then only meet to be observed for finding the latitude, when they are in the meridian; it is therefore good for him that meaneth to observe them, to know at what time they come to the meridian. To this end there are tables published, and almost in every mariners hands, pretending to show at what hour and minute every star in the first of these two former tables cometh to the meridian, for the beginning and midst of every month in the year, agreeing likewise in every error one with another: but because these errors breed not (at any time) greater danger or damage to the Mariner that is ware of them, then to make him watch for their coming to the meridian, a quarter, or half an hour longer than otherwise he needed (this inconvenience only provided for) those tables may serve the turn well enough, for them that list not trouble themselves to learn a better way.  
But for them that are desirous of a more true and general way, I have also made the table following of the Sun's right ascensions, reduced into hours and minutes for every day of this present year 1599, according to the Ephemerideses of the Sun, before set down; with help of which table it may easily be known for any day of any year in our age, at what time not only any of the foresaid fixed stars about the Equinoctial▪ but those also about the Pole, or any other, (whose right ascensions are known in hours and minutes) come to the meridian, and that after this manner. Find out in the table following the month and day wherein you observe; the month in the upper margin of the table, the day in the first column thereof next the left hand, the common meeting of the column descending from the month, and of the line proceeding from that day towards the right hand, shall give you the Sun's right ascension in hours and minutes for the same day. This right ascension of the Sun, subtract always out of the right ascension of the star, adding 24 hours to the stars right ascension, if it be less than the right ascension of the Sun: the remainder showeth how many hours and minutes after noon the star cometh to the upper part of the meridian; which if they be more than 12 hours, subtract 12 from them, and the remainder shall show you how many hours and minutes after midnight the star cometh to the upper part of the meridian. The upper part of the meridian I call that which passeth from the Pole, by the Zenith to the Horizon southwards. But it shall be needful also many times when you would observe the stars about the Pole (which never set) to know the time of their coming to the nether part of the meridian, which may easily be done, only by adding 12 hours to the time of their coming to the upper part of the meridian, if it be less than 12 hours, or by subtracting as much, if it be more.  
Suppose for example, the 25 of February 1599, I would know the time of the great dogs coming to the meridian. First therefore (in the next table) following the column descending from February downwards, and the line proceeding from the 25 day towards the right hand, in the common meeting of them both, I find 23 hours, 10 min. the Sun's right ascension that day at noon. Then in the first table of fixed stars, I find the great dogs right ascension to be 6 degr. 27 min. to which (because it is less than the Sun's right ascension) I add 24 hours, and the sum of both cometh to 30 hours, 27 min. out of this I subtract the Sun's right ascension, 23 hours, 10. min. and there remais 7 hours, 17 min. the time of the great dogs coming to the upper part of the meridian in the afternoon.  
Take one example also of a star that never setteth: and admit the 20 of December the same year, you would know what time the foremost Guard cometh to the Meridian beneath the Pole: First therefore you shall find, as before, the Sun's right ascension that day to be 18 hours, 36 min. and the right ascension of that star (in the second table of fixed stars) 14 hours, 54 min. to which (being less than the Sun's right ascension) add 24 hours, and from the sum (38 hours, 24 min.) subtract the Sun's right ascension 18 hours 36 min so there shall remain 20 hours 18 min. the time of the foremost Guards coming to the upper part of the meridian, from which subtract 12, so you have the time when it cometh to the nether part of the meridian, 8 hours, 18 min. after noon.  

A Table of the Sun's Right Ascension in hours and minutes, for every day of the year.   January February March April May June D. H. M. H. M. H. M. H. M. H. M. H. M. 1 19 30 21 39 23 25 1 18 3 11 5 15 2 19 34 21 43 23 28 1 22 3 15 5 19 3 19 39 21 47 23 32 1 26 3 19 5 25 4 19 43 21 50 23 36 1 29 3 23 5 27 5 19 47 21 54 23 40 1 33 3 27 5 31 6 19 52 21 58 23 44 1 36 3 30 5 36 7 19 56 22 02 23 47 1 40 3 34 5 40 8 20 00 22 06 23 51 1 43 3 38 5 45 9 20 04 22 09 23 55 1 47 3 42 5 49 10 20 08 22 14 23 58 1 51 3 46 5 53 11 20 13 22 18 0 02 1 55 3 50 5 57 12 20 17 22 21 0 06 1 58 3 54 6 01 13 20 22 22 25 0 09 2 02 3 58 6 05 14 20 26 22 29 0 12 2 06 4 03 6 09 15 20 30 22 32 0 16 2 10 4 07 6 13 16 20 34 22 36 0 20 2 14 4 11 6 18 17 20 38 22 40 0 23 2 18 4 15 6 22 18 20 42 22 44 0 27 2 22 4 19 6 26 19 20 46 22 48 0 31 2 26 4 23 6 30 20 20 50 22 52 0 35 2 30 4 27 6 34 21 20 54 22 56 0 38 2 33 4 31 6 38 22 20 58 22 59 0 42 2 37 4 35 6 42 23 21 03 23 03 0 46 2 41 4 39 6 46 24 21 07 23 07 0 49 2 44 4 43 6 51 25 21 11 23 10 0 53 2 48 4 47 6 55 26 21 15 23 14 0 57 2 52 4 51 6 59 27 21 19 23 18 1 00 2 56 4 56 7 03 28 21 23 23 22 1 03 3 00 5 00 7 07 29 21 27   1 07 3 04 5 03 7 11 30 21 31   1 11 3 07 5 07 7 15 31 21 35   1 15   5 11    July August Septemb. October. Novemb. Decemb D. H. M. H. M. H. M. H. M. H. M. H. M. 1 7 19 9 22 11 16 13 05 15 05 17 12 2 7 23 9 26 11 20 13 08 15 09 17 17 3 7 27 9 30 11 23 13 12 15 13 17 21 4 7 31 9 33 11 27 13 16 15 17 17 25 5 7 35 9 36 11 30 13 19 15 21 17 30 6 7 40 9 40 11 33 13 23 15 25 17 34 7 7 44 9 44 11 37 13 27 15 29 17 39 8 7 48 9 48 11 41 13 31 15 33 17 43 9 7 52 9 52 11 44 13 34 15 37 17 47 10 7 56 9 56 11 48 13 38 15 42 17 52 11 8 00 9 59 11 52 13 42 15 46 17 56 12 8 04 10 03 11 55 13 45 15 50 18 00 13 8 08 10 07 11 59 13 49 15 54 18 05 14 8 12 10 11 12 03 13 53 15 58 18 10 15 8 16 10 15 12 07 13 57 16 03 18 14 16 8 20 10 18 12 11 14 01 16 07 18 18 17 8 24 10 22 12 14 14 05 16 11 18 23 18 8 28 10 26 12 18 14 09 16 16 18 27 19 8 31 10 29 12 22 14 13 16 20 18 32 20 8 35 10 33 12 25 14 17 16 24 18 36 21 8 39 10 36 12 29 14 20 16 28 18 41 22 8 43 10 40 12 32 14 24 16 33 18 45 23 8 47 10 44 12 36 14 28 16 37 18 50 24 8 52 10 47 12 40 14 32 16 41 18 55 25 8 55 10 51 12 43 14 36 16 46 18 59 26 8 59 10 54 12 47 14 40 16 50 19 03 27 9 03 10 58 12 51 14 44 16 55 19 07 28 9 07 11 02 12 54 14 48 16 59 19 12 29 9 11 11 06 12 58 14 53 17 03 19 16 30 9 15 11 09 13 02 14 57 17 08 19 21 31 9 19 11 13   15 01   19 25   

CHAP. XXXIII. By the former Tables of the fixed Stars, and the Sun's right ascensions, to know the hour of the night, at any time of the year.  
BY these tables of fixed stars, and right ascensions of the Sun, you may easily know also the hour of the night at any time of the year, after this manner: look which of those stars is at the meridian; which may easily be known by a Needle-Dial or Compass: or if you will observe the North stars, that never set, (which indeed are fittest for this purpose, especially when they come to the meridian under the Pole) you shall first find the place of the Pole in the heavens, so near as you can by estimation (for a little error herein breaks no square) which may be done thus; From the Polestar directly towards the first star next the rump in the great Bear's tail, imagine almost so much space as the Guards are distant asunder, for near thereabouts is the place of the Pole. Now betwixt your eye and this place of the Pole, hold a plumbline hanging as perpendicularly, and steadfastly as you may, and mark withal if that plumbline come betwixt your sight, and any of the stars noted in the table of fixed stars about the Pole; for that star is at the meridian. Then learn (as before was showed) at what time that star cometh to the meridian, and so you shall have the hour of the night.  
Suppose for example, the 10 of February you find after this manner the Swans tail at the meridian, under the Pole, desiring hereby to know the hour of the night at that time. The right ascension of the Sun for that day you shall find as before to be 22 hours, 14 minutes, whereto you may add a minute or two more (because that star will come to the meridian very late in the evening) so making the Sun's right ascension 22 hours, 16 minutes. The right ascension of that star in the second table of fixed stars, you shall find to be 20 hours, 30 minutes. From which (because now you desire to know the time of that stars coming to the nether part of the meridian) you may subtract 12 hours, and there shall remain 8 hours 30 minutes. To this remainder (because it is less than then the Sun's right ascension) add 24 hours, and from the sum (32 hours, 30 minutes) subtract the right ascension of the Sun 22 hours, 16 minutes, so there shall remain 10 hours, 14 minutes, the time of the night desired.   

CHAP. XXXIV. Of finding the elevation of the Pole, by observation of the Polestar and Guard.  
BEsides the ways already spoken of to find the elevation of the Pole by the meridian altitudes, and declinations of the Sun and fixed stars in general: there hath been also used another way more special, by the height of the polestar, when the fore-guard is situate from it, either towards the East, West, North or South, or else upon the middle points betwixt these principal, as upon the North-east, Northwest, Southeast, and Southwest points. Of which way, as it hath been hitherto published and used, I must for the present only give the Mariner warning that he trust not to it, being very erroneous, and grounded upon two false positions. The one is, that the distance of the polestar from the pole is 3 degrees 30 minutes, which by often and exact observation is found to be at this time not above 2 degrees, 48 minutes. The other is, that the equations or allowances to be added to, or subtracted from the height of the polestar, to find thereby the height of the pole, are made the same for all latitudes.  
But having already showed sufficiently how to know the latitude almost at any time of the night, by the fixed stars in the former tables, I hope to be the easilier excused for finding a fault herein, and not amending it at this time, and that so much the rather, because that (according to promise made in the first Edition of this Book) I will now show the means how by observation of the polestar and guards, to find presently the height of the pole; not only when the fore-guard is in some one of those eight principal positions beforementioned, as the manner hath been hitherto; but in any other position also, and at any time of the night, when the polestar and guards may be seen, and that without any allowance or abatement, giving or taking by addition or subtraction of any Equation, in regard of the pole-stars being higher or lower than the Pole. All which, besides divers other pleasant and profitable conclusions, may easily be performed by means of an Instrument by me divised, which may not unfitly be called the Sea-Quadrant, the description and use whereof here followeth.  
The figure of the Sea-quadrant.   

CHAP. XXXV. The description and parts of the Sea-Quadrant.  
THis Quadrant consisteth of many parts, whereof some may be called principal, and some less principal.  
The principal parts of this Quadrant are the Semidiameter thereof, and the Archippus  
The Semidiameter I call the straight square Ruler.  
The arch, I call that part of the Quadrant that is made crooked like a bow.  
The less principal parts are the double box or ●ocket, and the sights or Vanes.  
The double box or socket hath two square holes made crosse-wise thorough it, in such sort that the arch and semidiameter of the Quadrant may be fitly put thorough them, the flat side of the one passing close by the flat side of the other. By means of this double cross socket the arch and semidiameter of the Quadrant are so to be joined together, that the two angles made by the hollow side of the arch, with the semidiameter, may be equal each to other.  
The sights or vanes are either fixed or movable.  
There be two fixed sights; the one greater, the other lesser.  
The greater fixed sight is fastened upon the double socket, and hath a narrow slit cut through the midst thereof.  
The lesser fixed sight is fastened to the end of the arch of the Quadrant, and hath a small sight-hole bored thorough it, even with the end of the Archippus  
The movable sights are three in number; whereof two are to be moved up and down upon the arch of the Quadrant, as need shall require for observation. The third is to be put on, or taken off that end of the semidiameter of the Quadrant where the centre is, which centre is showed by the little round hole bored overthwart thorough the midst of the thickness of the square Ruler, near the end thereof; which Ruler we called the Semidiameter of the Quadrant.  
This sight (whensoever it is to be used) must so be put on upon the end of that Ruler, that the flat side thereof (which must be set towards the arch of the Quadrant) may divide the foresaid round hole even by the midst thereof, the sharp edge of that sight arising perpendicularly from the very midst or centre of that hole; which is also the centre of the Quadrant, when the other end of the square Ruler, or Semidiameter thereof being put into his socket, is thrust so far forwards, that the end thereof cometh to be even with the fore-end of the socket.  
Two sides of the arch of the Quadrant, that is to say, one of the strait or plain sides, and the hollow side thereof are divided into 90 degrees, and every degree into 6 parts, each part containing 10 min. and upon the strait side of the Quadrant there be figures set to every fifth degree, and that in two ranks or limbs; the one beginning from that end of the arch, where the small fixed sight is placed; the other beginning and proceeding from the other end of the arch, where the Nocturnal is to be fastened or put on, that so the number of the degrees and minutes might the easilier be reckoned from either end of the arch, as need shall require.   

CHAP. XXXVI. Of the Nocturnal or Night-dial.  
THe Nocturnal containeth three circles; that is, the hour circle, the day circle, and the polestar circle.  
The biggest of these circles (which is to be fastened to the end of the arch of the Quadrant) I call the Hour-circle, and it is divided into 24 hours, and half hours, with figures set to every hour, for the easier reckoning of them.  
Next within this is the Day-circle, or circle of days, because it containeth the days of all the months of the year; which days are signified by the small divisions round about, at the circumference of this circle. Every fifth day hath his stroke drawn a little longer than the rest, that so any day you desire may the easilier be found. The small divisions contain but one day apiece. The lines showing the beginnings and end of the months are drawn overthwart the whole breadth of this circle. The beginning of January is known by the two lines drawn near together overthwart this circle; whereof one showeth the end of the month of December, and the other showeth the beginning of the month of January, which is marked with two pricks. February is easily known in this circle, because it hath but only 28 days. March is by the little polestar circle: and so all the rest of the months may easily be known by their order. Upon the centre of this arch (which representeth the Pole of the World) there be two Indices fastened: the longer of them may be called the Guard-Index, whereto a short pin is fastened underneath, which serveth to set this Index right upon the place of the middle Guard in the day-circle, by putting it into the small hole that there is made in that circle. The shorter Index reaching from the centre of the day-circle, unto the limb or circumference thereof, that is divided into days, may be called the Day-Index.  
This small circle placed between the centre of the day-circle, and the month of March, may not unfitly be called the Polestar circle; because the distance of the centre thereof, from the centre of the day-circle, is answerable to the distance of the polestar from the Pole; which at this time I have often found by exact observation, not to be more than 2 degrees, and 48 minutes.   

CHAP. XXXVII. The use of the Sea-Quadrant: and that first in observing the height of the Sun, looking only by the sight at the centre, to the Horizon at Sea.  
TUrn the centre of the Quadrant towards the Sun, so as the shadow of the Vane or sight placed at the centre may fall upon the hollow side of the arch of the Quadrant: then looking thorough the little sight fastened in the end of the arch of the Quadrant, lay the upper edge of the sight placed at the centre even with the Horizon, and at the same instant let one that standeth by, mark diligently upon what degree and minute of the Quadrant, the edge of the shadow coming from the said edge of the sight, falleth: for that edge of the shadow, upon the hollow side of the arch of the Quadrant, showeth the height of the upper edge of the Sun. From this therefore subtract 16 minutes, and so much also as is answerable to the height of your eye above the water (in such sort, as I have showed in the use of the Crosse-staff, in the 15 Chapter of this Book) and so you shall have the apparent height of the Sun above the true Horizon.   

CHAP. XXXVIII. How with this Quadrant to observe the height of the Sun, with your back turned towards the Sun.  
SEt the edge of one of the broad movable sights or vanes even with that end of the Quadrant where the little sight is fixed. Then looking thorough the slit which is made thorough the midst of the middle sight that is fastened to the double box or socket, turn your back toward the Sun, and laying the edge of the vane at the centre even with the Horizon, lift up, or put down the arch of the Quadrant, till the upper edge of the shadow of the broad movable sight, placed even with the upper end of the arch of the Quadrant, agree justly with the edge of the sight or vane placed at the centre. Then reckoning from the upper end of the arch of the Quadrant downwards, see what number of degrees and minutes you find at the upper edge or end of the socket, through which the Quadrant moveth, adding always thereto two degrees; for so shall you have the height of the Sun (if you abate from hence 16 min▪ for the Sun's semidiameter) and the surplusage answerable to the height of the eye above the water, as before is showed in the former Chapter.   

CHAP. XXXIX. How to observe with this Quadrant, the height of the Sun, or Star, looking both to the Sun or Star, and to the Horizon.  
SEt the upper edge of the uppermost movable sight of the Quadrant at some even number of degrees, as at 10, 20, or 30, etc. And setting the end of the semidiameter of the Quadrant, where the centre is, to the corner of the eye (as you do when you observe with the cross-staff) lay that edge of the sight even with the upper edge of the Sun, and move the nether movable sight up or down, till the upper edge thereof lie even with the Horizon. Then see how many degrees and minutes are contained between the upper edges of both sights▪ from which abate as before 16 minutes for the Sun's semidiameter, and the surplus answerable to the height of your eye above the water: so shall you have the apparent height of the Sun above the true Horizon. But when you observe the height of any star, lay the upper edge of the upper sight, even with the midst of the star, and from the number of degrees and minutes contained between the upper edges of both sights, abate only the surplus answerable to the height of your eye above the water and so you shall have the true height of the star. But here i● must be remembered, that before you observe the Sun or star after this manner, you must find out the eccentricity of your eye in such sort as I have showed in the 15 Chapter of this book which eccentricity you must add to the distance of the centre o● the Quadrant, from the end of the Semidiameter where you se● your eye: for so much as the sum of this distance and eccentri●city amounteth unto, so much must you thrust forward the fore●end of the semidiameter of the Quadrant beyond the further end of the square socket thorough which it is put, that so the centre o● your eye may be brought to the centre of the Quadrant.   

CHAP. XL. How to find the height of the Pole, by Observation of the Polestar and Guard, without giving or taking any allowance or abatement, at any time when the Polestar, the Guard, and Horizon may be seen.  
THe long Index of the Nocturnal (which I called the Guard Index) being fixed upon the place of the middle Guard in the day-circle and the Nocturnal being put upon the end of the arch of the Quadrant, placing also the end of the Semidiamter to your eye, as before, and holding the Quadrant upright, with the Nocturnal towards the Polestar, till the Diameter of the Semicircular hole of the Polestar circled lie (by estimation) aequidistant from the Horizon, both ends of the Diameter being level or of like height one with another, and so keeping the Polestar so near as you can guess, upon the midst of that Diameter, and the fiducial line of the Guard-Index upon the Guard, move one of the movable sights of the Quadrant up or down, till the edge thereof lie even with the Horizon. Thus therefore the Polestar lying upon the midst of the Diameter, (that is, upon the centre of the Polestar circle) and the fiducial line of the Guard Index upon the Guard, and the edge of the sight even with the Horizon; the number of degrees and minutes from the end of the Quadrant (where the Nocturnal is placed) to the edge of the sight, adding thereto five degrees, that is, the distance of the centre of the Nocturnal from the end of the Quadrant, shall be the height of the Pole; saving that you must abate (as before) so much as is answerable to the height of your eye above the water.  

To know the Hour of the Night by the Nocturnal.  
ANd the point of the short Index (which we called the Day-Index) being first set to the day of the month, showeth in the Hour-circle the Hour of the night, at the time of your Observation.  

SIMON STEVIN his Errors, in blaming me of error in my Tables of Rumbs.  
Wherein also I am the more confirmed by the like trial I have made of the first Rumb (counted from the Meridian) though Simon Stevin in his solemn demonstration continued almost in three whole pages in folio (wherein he professeth that the scope or mark he aimeth at, 
Pag. 153. Pag. 154. Pag. 155.  is to demonstrate that my Table of Rumbs is erroneous) would make the world believe that my Table erreth above two minutes in the Latitude of that Rumb, before I come to so little as two degrees of Longitude. But the truth is, he much mistaketh the matter, the error being indeed in his own gross manner of trial, much more than in my Table: for working after his own way by whole degrees, as he doth, it falleth out even so as he saith, that the Latitude of that Rumb for two degrees of Longitude will be above 2 minutes greater than my Table hath. But if he work the very same way by sixth parts of degrees, or ten of minutes, he shall find but little above half a minute more than is in my Table of Rumbs. Nay moreover, if it shall please him at his leisure to take the pains to make trial hereof to every single minute, he shall not find so much as one second more than my account giveth. For following the very same way that he prescribeth for the true making of the Table of Rumbs in his 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Appendice pag. 154.155. and so calculating the Latitude of the first Rumb for every single minute of Longitude, the Latitude of that Rumb for two degrrees of Longitude, shall be found to be not so much as 10 degrees 0 minutes 14 sec. 46 third. which Latitude according to my manner of making my Table of Rumbs, is not so little as 10 degr. 0 min. 13 sec. 47 third. differing not so much as one second from the former. But according to M Stevins account by whole degrees, it should be 10 degr. 2 min. 6 seconds, exceeding the truth of both the foresaid accounts almost two minutes in Latitude, before he be come to so little as two degrees in Longitude, and so grossly erring himself, whilst he too unadvisedly, and without just cause indevoureth to publish to the world my supposed errors. Which that it may the more manifestly appear, either to him, 


By whole degrees, the first Rumbes  Lon· Latitu. gr. m. gr. mi. se. 1 0 5 1 38 2 0 10 2 6 
By tins of min. the first Rumbs  Lon· Latitude. gr. m. gr. mi. se. th'. 0 10 0 50 16 23 0 20 1 40 32 26 0 30 2 30 47 33 0 40 3 21 1 5 0 50 4 11 12 16 1 0 5 1 20 46 1 10 5 51 25 35 1 20 6 41 26 18 1 30 7 31 22 14 1 40 8 21 12 38 1 50 9 10 57 0 2 0 10 0 34 40   or to any other that shall be disposed to make trial, as I have done, I have here set down the particular account hereof in the Tables following.  
The first table accounting by whole degrees, as Stevin doth, showeth the latit. of the first rumb for 2 gr. of long. to be 10 gr. 2 m. 6 sec. Whereas the second table accounting by ten of minutes, giveth it to be no more than 10 gr. 0 m. 34 s. 40 th'. And the third by single min. finds but 10 gr. 0 m. 14 s▪ 45 their. 21 fourth's.  
By single minutes, the first Rumbs. By single minutes, the first Rumbs. Longit. Latitude. Longit. Latitude. Deg. mi. gr. mi. sec. th'. four. Degr. mi. gr. mi. sec. th'. four. 0 1 0 5 1 38 25 0 31 2 35 47 48 29 0 2 0 10 3 16 50 0 32 2 40 49 8 18 0 3 0 15 4 55 10 0 33 2 45 50 26 56 0 4 0 20 6 33 25 0 34 2 50 51 44 14 0 5 0 25 8 11 30 0 35 2 55 53 0 17 0 6 0 30 9 49 25 0 36 3 0 54 14 59 0 7 0 35 11 27 10 0 37 3 5 55 28 21 0 8 0 40 13 4 40 0 38 3 10 56 40 17 0 9 0 45 14 41 50 0 39 3 15 57 50 48 0 10 0 50 16 18 40 0 40 3 20 58 59 48 0 11 0 55 17 55 10 0 41 3 26 0 7 18 0 12 1 0 19 31 15 0 42 3 31 1 14 3 0 13 1 5 21 6 55 0 43 3 36 2 18 22 0 14 1 10 22 42 4 0 44 3 41 3 21 6 0 15 1 15 24 16 43 0 45 3 46 4 22 9 0 16 1 20 25 50 47 0 46 3 51 5 21 26 0 17 1 25 27 24 15 0 47 3 56 6 19 3 0 18 1 30 28 57 4 0 48 4 1 7 14 49 0 19 1 35 30 29 12 0 49 4 6 8 8 45 0 20 1 40 32 0 40 0 50 4 11 9 0 50 0 21 1 45 33 31 22 0 51 4 16 9 51 0 0 22 1 50 35 1 14 0 52 4 21 10 39 14 0 23 1 55 36 30 16 0 53 4 26 11 25 27 0 24 2 0 37 58 28 0 54 4 31 12 9 39 0 25 2 5 39 25 53 0 55 4 36 12 51 51 0 26 2 10 40 52 14 0 56 4 41 13 31 57 0 27 2 15 42 17 45 0 57 4 46 14 9 53 0 28 2 20 43 42 5 0 58 4 51 14 45 37 0 29 2 25 45 5 20 0 59 4 56 15 19 11 0 30 2 30 46 27 30 1 0 5 1 15 50 29 By single minutes, the first Rumbs. By single minutes, the first Rumbs. Longitu. Latitude. Longitu. Latitude. Degr. mi. gr. mi. se. th'. four. gr. min. gr. mi. se th'. four 1 1 5 6 16 19 32 1 31 7 36 9 56 9 1 2 5 11 16 46 14 1 32 7 41 8 55 28 1 3 5 16 17 10 35 1 33 7 46 7 51 20 1 4 5 21 17 32 30 1 34 7 51 6 43 41 1 5 5 26 17 52 0 1 35 7 56 5 32 26 1 6 5 31 18 8 59 1 36 8 1 4 17 34 1 7 5 36 18 23 27 1 37 8 6 2 59 7 1 8 5 41 18 35 19 1 38 8 11 1 36 58 1 9 5 46 18 44 40 1 39 8 16 0 11 8 1 10 5 51 18 51 20 1 40 8 20 58 41 32 1 11 5 56 18 55 20 1 41 8 25 57 8 5 1 12 6 1 18 56 38 1 42 8 30 55 30 51 1 13 6 6 18 55 11 1 43 8 35 53 49 46 1 14 6 11 18 50 58 1 44 8 40 52 4 45 1 15 6 16 18 43 54 1 45 8 45 50 15 48 1 16 6 21 18 33 59 1 46 8 50 48 22 54 1 17 6 26 18 21 13 1 47 8 55 46 25 59 1 18 6 31 18 5 31 1 48 9 0 44 25 3 1 19 6 36 17 46 48 1 49 9 5 42 20 1 1 20 6 41 17 25 4 1 50 9 10 40 10 52 1 21 6 46 17 0 9 1 51 9 15 37 57 36 1 22 6 51 16 31 28 1 52 9 20 35 40 9 1 23 6 56 16 0 31 1 53 9 25 33 18 26 1 24 7 1 15 26 23 1 54 9 30 30 52 27 1 25 7 6 14 49 4 1 55 9 35 28 22 11 1 26 7 11 14 8 34 1 56 9 40 25 47 34 1 27 7 16 13 24 48 1 57 9 45 23 8 40 1 28 7 21 12 37 41 1 58 9 50 20 25 20 1 29 7 26 11 47 13 1 59 9 55 17 37 34 1 30 7 31 10 53 24 2 0 10 0 14 45 21 
A Table of the eight Rumb.  Lati. 10 m lon diffe▪ Lati· 10 m. lon diffe. Lati 10 m. lon diffe. Lati. 10 m. lon diffe· gr. m. m. sec th' se. th'. gr. m mi. se. th'. se. th' gr mi mi. se. th'. sec. th' gr. mi mi. se. th' se. th' 0 10 10 0 0 0 0 10 10 9 50 35 0 10 20 10 9 23 13 0 36 30 10 8 38 44 0 53 0 20 9 59 59 0 1 10 20 9 50 16 0 19 20 20 9 22 37 0 36 30 20 8 37 52 0 52 0 30 9 59 59 0 0 10 30 9 49 57 0 19 20 30 9 22 0 0 37 30 30 8 36 59 0 53 0 40 9 59 58 0 1 10 40 9 49 37 0 19 20 40 9 21 23 0 37 30 40 8 36 5 0 54 0 50 9 59 56 0 2 10 50 9 49 18 0 20 20 50 9 20 4● 0 37 30 50 8 35 12 0 53 1 0 9 59 54 0 2 11 0 9 48 59 0 19 21 0 9 20 9 0 37 31 0 8 34 18 0 54 1 10 9 59 52 0 2 11 10 9 48 39 0 20 21 10 9 19 31 0 38 31 10 8 33 24 0 54 1 20 9 59 50 0 2 11 20 9 48 18 0 21 21 20 9 18 53 0 38 31 20 8 32 30 0 54 1 30 9 59 48 0 2 11 30 9 47 57 0 21 21 30 9 18 15 0 38 31 30 8 31 35 0 55 1 40 9 59 45 0 3 11 40 9 47 36 0 22 21 40 9 17 37 0 38 31 40 8 30 40 0 55 1 50 9 59 41 0 4 11 50 9 47 15 0 21 21 50 9 16 58 0 39 31 50 8 29 45 0 55 2 0 9 59 38 0 3 12 0 9 46 53 0 22 22 0 9 16 19 0 39 32 0 8 28 50 0 55 2 10 9 59 34 0 4 12 10 9 46 31 0 22 22 10 9 15 39 0 40 32 10 8 27 54 0 56 2 20 9 59 30 0 4 12 20 9 46 9 0 22 22 2● 9 15 0 0 39 32 20 8 26 58 0 56 2 30 9 59 26 0 4 12 30 9 45 47 0 22 22 30 9 14 20 0 40 32 30 8 26 2 0 56 2 40 9 59 21 0 5 12 40 9 45 24 0 23 22 40 9 13 40 0 40 32 40 8 25 6 0 5● 2 50 9 59 16 0 5 12 50 9 45 1 0 23 22 50 9 12 59 0 41 32 50 8 24 9 0 57 3 0 9 59 11 0 5 13 0 9 44 37 0 24 23 0 9 12 18 0 41 33 0 8 23 12 0 57 3 10 9 59 5 0 6 13 10 9 44 14 0 23 23 10 9 11 37 0 41 33 10 8 22 15 0 57 3 20 9 58 5● 0 6 13 20 9 43 50 0 24 23 20 9 10 56 0 41 33 20 8 21 18 0 47 3 30 9 58 53 0 6 13 30 9 43 25 0 25 23 30 9 10 14 0 42 33 30 8 20 20 0 58 3 40 9 58 46 0 7 13 40 9 43 1 0 24 23 40 9 9 32 0 42 33 40 8 19 22 0 58 3 50 9 58 40 0 6 13 50 9 42 3● 0 25 23 50 9 8 50 0 42 33 50 8 18 24 0 58 4 0 9 58 32 0 8 14 0 9 42 11 0 25 24 0 9 8 8 0 42 34 0 8 17 25 0 59 4 10 9 58 26 0 6 14 10 9 41 45 0 26 24 10 9 7 25 0 43 34 10 8 16 27 0 58 4 20 9 58 17 0 9 14 20 9 41 19 0 26 24 20 9 6 42 0 43 34 20 8 15 28 0 59 4 30 9 58 9 0 8 14 30 9 40 53 0 26 24 30 9 5 59 0 43 34 30 8 14 29 0 59 4 40 9 58 1 0 8 14 40 9 40 27 0 26 24 40 9 5 15 0 44 34 40 8 13 29 1 0 4 50 9 57 52 0 9 14 50 9 40 0 0 27 24 50 9 4 31 0 44 34 50 8 12 29 1 0 5 0 9 57 43 0 9 15 0 9 39 33 0 27 25 0 9 3 47 0 44 35 0 8 11 30 0 59 5 10 9 57 34 0 9 15 10 9 39 6 0 27 25 10 9 3 3 0 44 35 10 8 10 29 1 1 5 20 9 57 24 0 10 15 20 9 38 39 0 27 25 20 9 2 18 0 45 35 20 8 9 29 1 0 5 30 9 57 14 0 10 15 30 9 38 11 0 28 25 30 9 1 33 0 45 35 30 8 8 28 1 1 5 40 9 57 4 0 10 15 40 9 37 43 0 28 25 40 9 0 48 0 45 35 40 8 7 27 1 1 5 50 9 56 54 0 10 15 50 9 37 14 0 29 25 50 9 0 2 0 46 35 50 8 6 26 1 1 6 0 9 56 43 0 11 16 0 9 36 46 0 28 26 0 8 59 17 0 45 36 0 8 5 25 1 1 6 10 9 56 32 0 11 16 10 6 36 16 0 30 26 10 8 58 31 0 46 36 10 8 4 23 1 2 6 20 9 56 20 0 12 16 20 9 35 47 0 29 26 20 8 57 44 0 47 36 20 8 3 21 1 2 6 30 9 56 9 0 11 16 30 9 35 18 0 29 26 30 8 56 5● 0 46 36 30 8 2 19 1 3 6 40 9 55 57 0 12 16 40 9 34 48 0 30 26 40 8 56 11 0 47 36 40 8 1 17 1 2 6 50 9 55 44 0 13 16 50 9 34 17 0 31 26 50 8 55 24 0 47 36 50 8 0 14 1 3 7 0 9 55 32 0 12 17 0 9 33 47 0 30 27 0 8 54 36 0 48 37 0 7 59 11 1 3 7 10 9 55 19 0 13 17 10 9 33 16 0 31 27 10 8 53 49 0 47 37 10 7 58 8 1 3 7 20 9 55 6 0 13 17 20 9 32 45 0 31 27 20 8 53 1 0 48 37 20 7 57 4 1 4 7 30 9 54 52 0 14 17 30 9 32 14 0 31 27 30 8 52 12 0 49 37 30 7 56 1 1 3 7 40 9 54 38 0 14 17 40 9 31 42 0 32 27 40 8 51 24 0 48 37 40 7 54 57 1 4 7 50 9 54 24 0 14 17 50 9 31 9 0 33 27 50 8 50 35 0 49 37 50 7 53 53 1 4 8 0 9 54 10 0 14 18 0 9 30 38 0 31 28 0 8 49 46 0 49 38 0 7 52 48 1 5 8 10 9 53 55 0 15 18 10 9 30 4 0 34 28 10 8 48 57 0 49 38 10 7 51 44 1 4 8 20 9 53 40 0 15 18 20 9 29 33 0 31 28 20 8 48 7 0 50 38 20 7 50 39 1 5 8 30 9 53 25 0 15 18 30 9 29 0 0 33 28 30 8 47 17 0 50 38 30 7 49 34 1 5 8 40 9 53 9 0 16 18 40 9 28 26 0 34 28 40 8 46 27 0 50 38 40 7 48 29 1 5 8 50 9 52 53 0 16 18 50 9 27 53 0 33 28 50 8 45 37 0 50 38 50 7 47 23 1 6 9 0 9 52 37 0 16 19 0 9 27 19 0 34 29 0 8 44 46 0 51 39 0 7 46 17 1 6 9 10 9 52 20 0 17 19 10 9 26 45 0 34 29 10 8 43 55 0 51 39 10 7 45 11 1 6 9 20 9 52 3 0 17 19 20 9 26 10 0 35 29 20 8 43 4 0 51 39 20 7 44 5 1 6 9 30 9 51 46 0 17 19 30 9 25 35 0 35 29 30 8 42 13 0 51 39 30 7 42 59 1 6 9 40 9 51 29 0 17 19 40 9 25 0 0 35 29 40 8 41 21 0 52 39 40 7 41 52 1 7 9 50 9 51 11 0 18 19 50 9 24 25 0 35 29 50 8 40 29 0 52 39 50 7 40 4● 1 7 0 0 9 50 53 0 18 20 0 9 23 49 0 36 30 0 8 39 37 0 52 40 0 7 39 38 1 7 Lati 10 mi. lon diffe. Lati. 10 m. lon diff. Lat. 10 m lon diff. Lat. 10 m. lon diffe. gr. mi. mi. se. th' se, th'. gr. m. mi▪ se. th'. se. th'. gr. m. mi sec. th' se. th'. gr. m. mi se th' se. th' 40 10 7 38 30 1 8 50 10 6 24 20 1 20 60 10 4 58 29 1 31 70 10 3 23 14 1 39 40 20 7 37 23 1 7 50 20 6 23 0 1 20 60 20 4 56 58 1 31 70 20 3 21 56 1 38 40 30 7 36 15 1 8 50 30 6 21 39 1 21 60 30 4 55 22 1 31 70 30 3 20 17 1 39 40 40 7 35 7 1 8 50 40 6 20 18 1 21 60 40 4 53 56 1 31 70 40 3 18 38 1 39 40 50 7 33 58 1 9 50 50 6 18 57 1 21 60 50 4 52 25 ● 31 70 50 3 16 59 1 39 41 0 7 32 48 1 10 51 0 6 17 36 1 21 61 0 4 50 53 1 32 71 0 3 15 21 1 38 41 10 7 31 41 1 7 51 10 6 16 14 1 22 61 10 4 49 22 1 31 71 10 3 13 41 1 40 41 20 7 30 32 1 9 51 20 6 14 52 1 22 61 20 4 47 50 1 32 71 20 3 12 0 1 38 41 30 7 29 22 1 10 51 30 6 13 31 1 21 61 30 4 46 18 1 32 71 30 3 10 23 1 40 41 40 7 28 13 1 9 51 40 6 12 9 1 22 61 40 4 44 46 1 32 71 40 3 8 44 1 39 41 50 7 27 3 1 10 51 50 6 10 46 1 23 61 50 4 43 13 1 33 71 50 3 7 4 1 40 42 0 7 25 53 1 10 52 0 6 9 24 1 22 62 0 4 41 41 1 32 72 0 3 5 25 1 39 42 10 7 24 43 1 10 52 10 6 8 1 1 23 62 10 4 40 9 1 32 72 10 3 3 45 1 40 42 20 7 23 33 1 10 52 20 6 6 38 1 23 62 20 4 38 36 1 33 72 20 3 2 5 1 40 42 30 7 22 22 1 11 52 30 6 5 15 1 23 62 30 4 37 3 1 33 72 30 3 0 25 1 40 42 40 7 21 11 1 11 52 40 6 3 52 1 23 62 40 4 35 30 1 33 72 40 2 58 46 1 39 42 50 7 20 0 1 11 52 50 6 2 29 1 23 62 50 4 33 57 1 33 72 50 2 57 6 1 40 43 0 7 18 49 1 11 53 0 6 1 5 1 24 63 0 4 32 42 1 33 73 0 2 55 25 1 41 43 10 7 17 37 1 12 53 10 5 59 42 1 23 63 10 4 30 50 1 34 73 10 2 53 45 1 40 43 20 7 16 26 1 11 53 20 5 58 18 1 24 63 20 4 29 17 1 33 73 20 2 52 5 1 40 43 30 7 15 14 1 12 53 30 5 56 54 1 24 63 30 4 27 43 1 34 73 30 2 50 25 1 4● 43 40 7 14 1 1 13 53 40 5 55 29 1 25 63 40 4 26 9 1 34 73 40 2 48 44 1 41 43 50 7 12 49 1 12 53 50 5 54 5 1 24 63 50 4 24 36 1 33 73 50 2 47 4 1 40 14 0 7 11 36 1 13 54 0 5 52 40 1 25 64 0 4 23 1 1 35 74 0 2 45 23 1 41 44 10 7 10 23 1 13 54 10 5 51 16 1 24 64 10 4 21 27 1 34 74 10 2 43 42 1 41 44 20 7 9 10 1 13 54 20 5 49 51 1 25 64 20 4 19 53 1 34 74 20 2 42 2 1 40 44 30 7 7 57 1 13 54 30 5 48 25 1 26 64 30 4 18 18 1 35 74 30 2 40 20 1 42 44 40 7 6 44 1 13 54 40 5 47 0 1 25 64 40 4 16 44 1 34 74 40 2 38 40 1 40 44 50 7 5 30 1 14 54 50 5 45 35 1 25 64 50 4 15 9 1 35 74 50 2 36 59 1 41 45 ●● 7 4 16 1 14 55 0 5 44 9 1 26 65 0 4 13 14 1 35 75 0 2 35 18 1 41 45 10 7 3 2 1 14 55 10 5 42 43 1 26 65 10 4 11 59 1 35 75 10 2 33 36 1 42 45 20 7 1 47 1 15 55 20 5 41 17 1 26 65 20 4 10 24 1 35 75 20 2 31 59 1 41 45 30 7 0 33 1 14 55 30 5 39 51 1 26 65 30 4 8 49 1 35 75 30 2 30 14 1 41 45 40 6 59 18 1 15 55 40 5 38 24 1 27 65 40 4 7 17 1 35 75 40 2 28 32 1 42 45 50 6 58 3 1 15 55 50 5 36 58 1 26 65 50 4 5 38 1 35 75 50 2 26 51 1 41 46 0 6 56 48 1 15 56 0 5 35 31 1 27 66 0 4 4 3 1 35 76 0 2 25 9 1 42 46 10 6 55 32 1 16 56 10 5 34 4 1 27 66 10 4 2 27 1 36 76 10 2 23 28 1 41 46 20 6 54 17 1 15 56 20 5 32 37 1 27 66 20 4 0 51 1 36 76 20 2 21 46 1 42 46 30 6 53 1 1 16 56 30 5 31 10 1 27 66 30 3 59 15 1 36 76 30 2 20 4 1 42 46 40 6 51 45 1 16 56 40 5 29 42 1 28 66 40 3 57 39 1 36 76 40 2 18 22 1 42 46 50 6 50 29 1 16 56 50 5 28 15 1 27 66 50 3 56 3 1 36 76 50 2 16 50 1 42 47 0 6 49 12 1 17 57 0 5 26 47 1 28 67 0 3 54 26 1 37 77 0 2 14 58 1 42 47 10 6 47 55 1 17 57 10 5 25 16 1 28 67 10 3 52 50 1 36 77 10 2 13 16 1 42 47 20 6 46 38 1 17 57 20 5 23 51 1 28 67 20 3 51 53 1 37 77 20 2 11 34 1 42 47 30 6 45 21 1 17 57 30 5 22 23 1 28 67 30 3 49 37 1 36 77 30 2 9 52 1 42 47 40 6 44 4 1 17 57 40 5 20 54 1 29 67 40 3 48 0 1 37 77 40 2 8 10 1 42 47 50 6 42 47 1 17 57 50 5 19 26 1 28 67 50 3 46 23 1 37 77 50 2 6 27 1 43 48 0 6 41 29 1 18 58 0 5 17 57 1 29 68 0 3 44 46 1 37 78 0 2 4 45 1 42 48 10 6 40 11 1 18 58 10 5 16 28 1 29 68 10 3 43 9 1 37 78 10 2 3 2 1 43 48 20 6 38 53 1 18 58 20 5 14 59 1 29 68 20 3 41 3● 1 37 78 20 2 1 20 1 42 48 30 6 37 34 1 19 58 30 5 13 30 1 29 68 30 3 39 4● 1 38 78 30 1 59 37 1 43 48 40 6 36 16 1 18 58 40 5 12 1 1 29 68 40 3 38 17 1 37 78 40 1 57 55 1 42 48 50 6 34 57 1 19 58 50 5 10 31 1 30 68 50 3 36 39 1 38 78 50 1 56 12 1 43 49 0 6 33 38 1 19 59 0 5 9 1 1 30 69 0 3 35 1 1 37 79 0 1 54 29 1 43 49 10 6 32 19 1 19 59 10 5 7 5 1 29 69 10 3 33 24 1 38 79 10 1 52 46 1 43 49 20 6 31 0 1 19 59 20 5 6 2 1 30 69 20 3 31 46 1 38 79 20 1 51 3 1 43 49 30 6 29 40 1 20 59 30 5 4 31 1 31 69 30 3 30 8 1 38 79 30 1 49 21 1 42 49 40 6 28 20 1 20 59 40 5 3 1 1 30 69 40 3 28 9 1 39 79 40 1 47 38 1 43 49 50 6 27 1 1 19 59 50 5 1 31 1 30 69 50 3 26 51 1 38 79 50 1 45 55 1 43 50 0 6 25 40 1 21 60 0 5 0 0 1 31 70 0 3 25 13 1 38 80 0 1 44 11 1 44 Lati. 10 in lon diffe. gr. mi m. sc. th'. sec th' 80 10 1 42 28 1 43 80 20 1 40 45 1 43 80 30 1 39 0 1 43 80 40 1 37 18 1 44 80 50 1 35 35 1 44 81 0 1 33 52 1 43 81 10 1 32 8 1 44 81 20 1 30 25 1 43 81 30 1 28 41 1 44 81 40 1 26 58 1 43 81 50 1 25 14 1 44 82 0 1 23 40 1 44 82 10 1 21 57 1 43 82 20 1 20 3 1 44 82 30 1 18 19 1 44 82 40 1 16 35 1 44 82 50 1 14 51 1 44 83 0 1 13 7 1 44 83 10 1 11 23 1 44 83 20 1 9 39 1 44 83 30 1 7 55 1 44 83 40 1 6 11 1 44 83 50 1 4 27 1 44 84 0 1 2 43 1 44 84 10 1 0 59 1 44 84 20 0 59 15 1 44 84 30 0 57 31 1 44 84 40 0 55 46 1 44 84 50 0 54 2 1 44 85 0 0 52 18 1 44 85 10 0 50 33 1 45 85 20 0 48 49 1 44 85 30 0 47 5 1 45 85 40 0 45 20 1 45 85 50 0 43 36 1 44 86 0 0 41 51 1 45 86 10 0 40 7 1 44 86 20 0 38 22 1 45 86 30 0 36 38 1 44 86 40 0 34 53 1 45 86 50 0 33 9 1 44 87 0 0 31 24 1 45 87 10 0 29 40 1 44 87 20 0 27 55 1 45 87 30 0 26 10 1 45 87 40 0 24 26 1 44 87 50 0 22 41 1 45 88 0 0 20 56 1 45 88 10 0 19 12 1 44 88 20 0 17 27 1 45 88 30 0 15 42 1 45 88 40 0 13 58 1 44 88 50 0 12 13 1 45 89 0 0 10 28 1 45 89 10 0 9 44 1 44 89 20 0 6 59 1 45 89 30 0 5 14 1 45 89 40 0 3 29 1 45 89 50 0 1 45 1 44 90 0 0 0 0    
This Table of the eight Rumb, showing the quantity of 10 minutes of Longitude at every 10 minutes of Latitude, in minutes seconds, and thirds of one degree of the Equinoctial, I thought good here to adjoin for their sakes that may peradventure be desirous by themselves to make trial of that I have before written, concerning the gross and rude manner of examination, which Simon Stevin useth, to make the world believe that my Table of Rumbs is so much erroneous as he saith, and after his fashion would seem to demonstrate. And lest any should suspect that this Table also may be as faulty as Stevin would persuade us the other is, I have thought good here to show the way how I made the same, that if any list take so much pains, he may either examine and correct this if need shall be, or make a new one if he will, which may be done after this manner, and by this rule: What proportion the whole sine hath to the sine of the Latitudes compliment; the same proportion hath one sixth part of a degree of the Equinoctial, that is, 10 minutes, which make 36000 thirds, to the number of the same thirds of a degree of the Equinoctial, contained in 10 minutes of Longitude at the same Latitude, which being divided by 60, the remainder shall be the thirds remaining besides minutes and seconds, and this first quotient being again divided by 60, the second quotient shall be the minutes, and the remainder thereof the seconds. For example, suppose you would find the quantity of 10 minutes of a degree in the Parallel, whose Latitude is 10 degrees; now the compliment of this Latitude is 80 degrees; the sine whereof is 9848,078, the whole sine being 10,000,000: and as this whole sine is to the sine aforesaid, so is 36,000 (that is, the number of thirds that are in ten minutes of the Equinoctial) to 35,453, that is, the number of the same thirds contained in ten min. of a degree of the said Parallel. And these thirds divided by 60, give in the quotient 590 sec. and 53 thirds remaining, and 590 divided again by 90, the quotient is 9 m, and the remainder 50 sec So then, the quantity of ten min. of Longitude at ten degr. of Latitude, shall be 9 min. 50 sec. 53 thirds of one degree of the Equinoctial. And thus was made the whole Table.  

The making of the Table of Rumbs.  
Now by help of this Table of the eight Rumb, the preceding Table of the first Rumb next the Meridian, and all the rest may thus be made: As the whole sine, is to the Tangent of the Rumbs angle with the Equinoctial; so is one minute of the Equinoctial to the Latitude of the same Rumb for one minute of Longitude. And so is a minute of Longitude (found out by this Table of the eighth Rumb) at that Latitude, to the difference of Latitude; which added to the former Latitude, giveth the Latitude of the same Rumb, for two minutes of Longitude: and again at this Latitude, a minute of Longitude (found by the same Table) shall have the same proportion to the difference of Latitude; which added to the Latitude of the same Rumb for two minutes of Longitude, showeth the Latitude of that Rumb for three minutes of Longitude. And after this manner proceeding in all the rest, you may make up the whole Table of Rumbs.      
FINIS.   


THE DIVISION OF THE WHOLE ART OF NAVIGATION.  
THE whole Art of Navigation, which teacheth us to sail by courses and by heights, is divided into two principal parts; the Theoric, and the Practic. The Theoric teacheth the composition of the Sphere of the World in general; and in particular informeth us of the number, figure, and motions of the Heavens, especially of the highest movable heaven, called Primum Mobile, and of the ninth, eighth, fourth, and first heaven: also it showeth us the quantity and situation of the elements, and principally of the earth and water; and the circles which are imagined to be in that Sphere; without the knowledge of which it is impossible to be a Navigator. The Practic part teacheth the making and use of those Instruments which are used in Navigation, as namely the Astrolabe, the cross-staff, the Sea-compasse, and the Dial, with the Regiment of the Sun, and of the star, the rules of the Moon, and of the Tides, the declaration of the Sea-chart, and other things appertaining hereunto.  

CHAP. I. The Definition of the Sphere.  
A Sphere is a solid or massy body, without hollowness, and perfectly round; in the midst whereof there is a prick called the centre, by which there passeth a right line, named the Axtree, and the points where this line endeth upon the superficies of the whole body are called Poles, because upon them the Sphere is moved.   

CHAP. II. That the whole World is a Sphere.  
AND so it is evident that the whole frame of the World wherein we live is a Sphere; being as it is solid, so that in the whole World there is no empty place: also it is perfectly round upon the upper Superficies of the highest heaven: and it hath in the very midst a certain point, to wit, the centre of the earth▪ by which we do imagine a right line or Axtree, to pass from one pole to another, upon which the World is moved about from East to West.   

CHAP. III. Of the division of the Sphere.  
THE whole Sphere of the World is divided into two parts or Regions; the Elementary and Celestial. The Elementary part or Region hath four parts: the first whereof is the earth, which together with the element of water (which is the second) maketh one perfect Globe: and round about both these are two other elements, namely, the Air, and above that the fire, which filleth the space between the Air, and the Sphere of the Moon: of which Elements (by virtue of the heat of the Heavens) are made and compounded all corruptible things in the world.  
The celestial Region consisteth of other ten parts: the first whereof is the Sphere of the Moon; the second the Sphere of Mercury; the third, of Venus; the fourth, is the Sphere of the Sun; the fifth, of Mars; the sixth, of Jupiter; the seventh, of Saturn; the eighth, is the Sphere of the fixed stars, which is called the Firmament; the ninth, is the Crystalline heaven; and lastly, the tenth and highest, is the Sphere, called the Primum mobile, that is, the first or highest movable heaven. That which remaineth, called the Empyreal heaven, because it hath no motion, cometh not to be considered on in the Art of Navigation.  
A Figure wherein may be seen the Composition of the whole Sphere of the World.   

CHAP. IU. Of the motion of the Heavens.  
THe number of the Heavens is known by the motions observed in them, which are ten, distinct one from another. For the Moon moveth her proper and peculiar motion in 27 days, and 8 hours, which is one Revolution: Mercury, Venus, and the Sun finish their motion in one year, which containeth 365 days, and almost a quarter of a day: Mars runneth his course in two years; Jupiter in twelve years; Saturn in thirty years; the eight Sphere (according to the opinion of some) in seven thousand years; the ninth, in five and twenty thousand, and eight hundred years: and the tenth, in four and twenty hours almost. Which ten motions are reduced unto three principal: the first is that of the first movable upon the two ends of the Axletree, which are called the Poles of the World from East to West, turning about again unto the East in 24 hours: and this Sphere, by the force of his motion, carrieth about with it all the other lower Spheres in the space of 24 hours. Howbeit, they move also the contrary way with a second motion, which is from West to East, upon two other poles distant from the first, about three and twenty, and an half such parts, whereof the whole compass of heaven containeth three hundred and sixty. And this second motion is accomplished in each of the lower Heavens, in divers spaces of time, as is before said. The third motion is proper to the eighth Heaven, wherein the fixed stars are placed; which motion is the cause that the distance of the poles of the first motion, from them of the second motion doth vary, being sometimes greater, and sometimes less.   

CHAP. V. Of the Figure of the Heavens.  
THat the Heavens are round, it is proved, because roundness is the most perfect Figure of all others, being whole and entire, having no need of any joints, being also of the greatest capacity of all figures that have the same compass, and in that respect most fit to contain all other things. Also the principal bodies of the World, as the Sun, the Moon, and the stars are of this Figure, and we see the same likewise in those things which are bounded by themselves; as it is manifest in drops of water, and all other liquid things.   

CHAP. VI That the Earth and Water make one perfect Globe.  
THere is nothing that showeth more clearly that the earth and water make one round Globe, than the shadow which they make in the Eclipses of the Moon; which shadow we always see to be a part of a circle. For if the body, which is the cause of the same shadow, were threesquare, or foursquare, the shadow itself also would appear in the same fashion. Wherefore the shadow of these two bodies together, being round, it is manifest that they are round also.   

CHAP. VII. That the Earth is in the centre of the World.  
ONe sign we have to be assured, that the Earth is in the midst and centre of the World; namely, that wheresoever we are upon the face of the earth, we always see one half of the Heavens, the other half being hidden out of our sight. Moreover, the stars (in what part of the Heavens soever they be) either in the East, West, or South, we see that they are always of the very same bigness. Whereby we may easily perceive, that they are always equally distant from our sight: and whereas they move round about it, it followeth, that we are upon the centre of that body, on whose superficies the said stars describe their circles.   

CHAP. VIII. The whole quantity of the Earth.  
ANd albeit the Globe of the Earth and Water, compared with the Spheres of the Stars, is as it were a centre or prick; yet being considered by itself, it containeth in the greatest circle thereof 6300 common Spanish leagues. Which a man may easily perceive, by taking two such points or headlands of the earth, as are under the same Meridian, and which differ in distance one from another so much as one of those parts is, whereof the compass of the whole world containeth 360; and it is found both by Navigation at Sea and also by travel on land, that the two foresaid points are distant each from other 17 leagues and an half: of which leagues, each one containeth 4000 paces, every pace 5 foot, every foot 16 fingers, and every finger 4 grains of barley.   

CHAP. IX. Of the Equinoctial Circle.  
BEing to treat of the Circles of the Sphere of the World, the first which offereth itself to be spoken of is the Equinoctial Circle; by means whereof we do know in what part of the World we are: and in it, in the Sea-Chart are placed all these points or degrees of Longitude and from it the Latitudes are accounted. So that the Equinoctial is a Circle which divideth the World into two equal portions, and is equally distant every where from either of the poles. And it is called the Equinoctial Circle; because that when the Sun passeth under it, upon the 11 of March, and the 13 of September, it maketh the day equal to the night. The knowledge of this Circle in the Art of Navigation, doth help us to find the Latitude or distance from the Line; and from this Circle are reckoned the declinations of the Sun in the regiment thereof. And always those Charts of Navigation which are either universal, or half universal, have this Equinoctial circle, drawn with a great red line, which passeth by the beginning of the account of the degrees of Latitude.   

CHAP. X. Of the Poles of the World.  
AND here it is to be noted, that one of those two Poles, (from which the Equinoctial is equally distant) which is always in our sight, (because it is continually above our Horizon) is called the Pole-artick, the Septentrional, or North Pole. But the other opposite pole (which we never see, because it is under our Horizon) is called the Pole-antartick, and the Meridional, or South Pole. And so that part of the world which is between the Equinoctial and the North pole, is called the North part and that which is from the Equinoctial to the South pole, is called the South part.   

CHAP, XI. Of the Ecliptic line  
THe Equinoctial circle is divided into equal parts by another circle called the Ecliptic, whereof one half is between the Equinoctial and the North pole, and the other half between the Equinoctial and the South pole. And that part thereof which is furthest distant from the Equinoctial, is distant from the same about 23 degrees and an half. And because the Sun moveth in this circle without departing from it, hereof proceed the Declinations thereof. And this circle in all parts is equally distant from the Poles of the second motion, which are called the Poles of the Ecliptic, And through this circle the Sun is continually move by his proper motion from East to West: by means of which motion sometimes he passeth under the Equinoctial, and at other times departeth from it, both towards the North and towards the South: and the quantity of his greatest distance is about 23 degrees and an half: and so much is the distance of the Poles of the Ecliptic, from the Poles of the Equinoctial. And albeit this circle is not drawn in the Sea Chartley, yet is it in some sort represented in the Table of the Sun's Declination, which are gathered from the motion which the Sun maketh under the Ecliptic.   

CHAP. XII. Of the Declination of the Sun.  
THe motion of the Sun under the Ecliptic, is the cause of his Declination: which is nothing else but the daily swarving or Declining of the Sun from the Equinoctial line. And this Declination when the Sun is under the Equinoctial, upon the eleventh of March, and thirteenth of September, is nothing at all: so likewise upon the twelfth of June, and twelfth of December, the Declination is at the greatest. And albeit this greatest Declination be now in our time about three and twenty degrees and an half; yet hath it at other times been found otherwise, by reason of a third motion proper to the eighth Heaven: but it always keepeth between 23 degrees, 28 minutes; and 23 degrees, 53 minutes. From hence therefore we do infer, that at divers times it is meet to make new and divers Tables of the Declination of the Sun.   

CHAP. XIII. Of the Colours.  
There are two Circles of the Sphere, either of which divideth in into two equal parts: and they are called Colours, because that in the revolution which they make, by force of the Primum mobile, they do not show themselves wholly unto us; so as we may see all parts of them. One of them is called the Equinoctial Colour, because it passeth by the Poles of the World, and the points where the Ecliptic cutteth the Equinoctial; and when the Sun by his own proper motion cometh unto it, he maketh the day and the night equal, and divideth the Winter from the Spring by the one part; and by the other, Summer from Autumn; at which times the Sun hath no declination at all. The other is called the Solstitial Colour, because it passeth by the Poles of the World and of the Ecliptic, and by the points where the Ecliptic is furthest distant from the Equinoctial. And when the Sun by his proper motion cometh unto it, in the one part it maketh the longest day, and the shortest night, and divideth the Spring from the Summer, and hath his greatest Declination towards the North: and being in the other part, the Sun maketh the longest night, and shortest day, and divideth Winter from Autumn, and is in his greatest Southerly Declination. These two Colours are noted in the Table of the Sun's Declination because the Equinoctial Colour passeth by the two points, where there is no Declination at all; because the Sun is under the very Equinoctial circle: and the Solstitial Colour passeth by that place where the Sun hath his greatest Declination, which is in 23 degrees and an half, or thereabouts.   

CHAP. XIV. Of the Meridian circle.  
THe Meridian is a circle drawn by the Poles of the World (which are all one with the Poles of the Equinoctial) and and by the point directly over our heads called the Zenith. And it is called the Meridian, because that when the Sun by the motion of the Primum mobile cometh unto this circle, it maketh midday, and then he hath been running his course from his rising till he come thither, just so long time as he shall be running from thence to the place of his setting. The Zenith is a point in the Firmament, placed directly over our heads. And it is to be noted, that when the Sun is in that Circle, it hath the greatest altitude above our Horizon, that it can possibly have the same day: by this and the Declination, we come to know how far we are distant from the Equinoctial, either towards the North, or towards the South. And hence it is, that the height of the Sun in Navigation is understood only for that height which the Sun hath, when he is in this Circle. And so the height of the Sun shall be that part of the Meridian, which is contained between the Sun and our Horizon. This Circle in the Sea-Chart is represented by all those lines which are drawn from North to South.   

CHAP. XV. Of the Horizon.  
THe Horizon is a Circle which divideth that part of the Heavens which we see from the residue which we do not see: and it is properly that Circle by which, according to our sight, the Heaven seemeth to be joined with the water, when we are at Sea, without sight of any land. This Horizon is of two sorts, namely, right and oblique. The right Horizon is that which they have that live under the Equinoctial, which passeth by their Zenith; and therefore the Equinoctial line or circle falleth perpendicularly and right across with their Horizon, and both the South and the North Poles are in their Horizon. The oblique Horizon is that which they have that live not directly under the Equinoctial; for unto them the Equinoctial divideth the Horizon obliquely, and not right across: and one Pole is always above their Horizon, and the other is beneath their Horizon, and cannot be seen. This Horizon is represented in the Sea-Chart by a certain imagined circle, whose centre is the point where our ship is From which centre are imagined to proceed unto the said circle 32 lines, which represent the 32 winds or rumbs; which always are drawn in our Sea-Compasse: which likewise in a little piece of paper doth continually represent unto us, both by day and night, the whole Horizon, with his 32 divisions.   

CHAP. XVI. Of the 32 Winds.  
THis right or oblique Horizon is divided into 32 equal parts by 16 lines, which they call Rumbs: and they cut themselves in the point where we stand: of which rumbs, that which passeth by the points where the Equinoctial beginneth and endeth (which are where the Sun riseth and setteth the 11 of March, and the 13 of September) is called East and West; and that which cutteth it right across, is named North and South. And the four extremes or ends of these two lines, are distant upon the Horizon one fourth part of a circle, and they make four quarters. Every one of which quarters being divided in the midst, do make four other points: and that which falleth between the North and the East, is called North-east; and that between the North and the West, Northwest; that between the South and the East, Southeast; and that between the South and the West, South-west. And so the Horizon is divided by four lines or numbs, into eight principal winds, noted in the Sea-Chart with black lines. And if you divide every one of those eight parts in the midst, you shall have other eight lines, and other four rumbs, which in all are 16 winds. And each one of these hath his name compounded of the names of those principal winds, which are on either side thereof. As for example, that half wind which is between the North, and the North-east▪ is called North-north-east, and that which bloweth between the East and the North-east, is called East-north-east; and that between the East and the Southeast, East-south-east; and that between the South and the Southeast, South-south-east; and that between the South-west and the West West-south-west; and that between the West and Northwest, West-north-west; and that between the Northwest and the North, North-north-west. And these are noted in the Chart with green lines.  
Finally, if you divide every one of these sixteen winds in the midst, they will yield you other 16 winds, and will amount to 32 winds in all. Which 16 last mentioned, are drawn in the Sea-Chart with red lines, and are by the Spaniards called quarters of the eighth first and principal winds: and every one of these is called by the name of that principal wind which is next it, together with an addition of the word (By) and the name of another principal wind which is next unto it. As for example, of the two quarter-winds which fall next the rumb of the North, that which lieth towards the North-east is called North and by East; and that which falleth towards the Northwest, is called North by West. So likewise of those two winds, which blow next the North-east, that towards the North is called North-east and by North and that towards the East, North-east and by East. And after the same manner you may name all the rest.  
The Figure of the Sea-Compasse, and of the Horizon, divided into 32 Winds, by 16 Rumbs.  
But here is to be noted, 
Difference between the Rumb and the Wind▪  that there is difference between the Rumb and the Wind, because a Rumb is one direct line continued with two contrary winds, as the Rumb of North & South, and the Rumb of East and West. And so when we will name the lying of any Coast, we will say, that it lieth North and South, or North and by East, and South and by West. But the wind is one line of those 32, into which the Horizon is divided; and it is one part of those two which together are called the Rumb. And so we say, that Land lieth from us towards the South, and towards the South and by West, or towards the South-south-west, etc.   

CHAP. XVII. Of the two Tropics.  
BEsides the six Circles abovementioned, which are drawn upon the superficies of the Sphere of the World; there are other two which the Sun describeth with the motion of the Primum Mobile, about the 12 day of June and of December; of which two Circles that which the Sun describeth the 12 of June, from the time of his rising, till the time that he riseth the day following, is called the Tropic of the Summer Sun-standing; or the Tropic of Cancer: for the Sun having departed from the Equinoctial, and increasing his Declination towards the North, when he cometh to describe that Circle, for two or three days it seemeth, that he cometh no nearer to our Zenith, nor departeth from the Equinoctial one day more than another: but from thence forward he goeth back, diminishing his Declination, till he come to the Equinoctial; and crossing the same, he goeth on the other side, increasing his Declination until the 12 of December, upon which day, from the time of his rising, till he be come about to rise again the next morning, he describeth another Circle, called the Tropic of the Winter Sun-standing, or the Tropic of Capricorn; for the Sun being departed from the Equinoctial, and increasing his Declination towards the South, when he cometh to describe that Circle, it seemeth for two or three days, that he returneth not one whit towards the Equinoctial, nor goeth further from our Zenith one day more than other; but from thence forwards he cometh back again, diminishing his Declination, till he be returned to the Equinoctial, and from thence towards our Zenith. These two Circles in Sea-Charts are marked with two great red lines drawn from East to West, which lie on either side of the Equinoctial, being distant from thence about 23 deg. and an half. And wheresoever our ship be in any place between these two Circles or lines, we may in some time of the year take the Sun in our Zenith, at which time it maketh no shadow at all, being then just 90 degr. high above our Horizon. But they which are without the said two Circles or lines, shall never have the Sun in their Zenith, because it cannot come to the height of 90 degr. above their Horizon.   

CHAP. XVIII. Of the Parallels  
THe parallel Circles are those which are in all parts equally distant from the Equinoctial. And these Circles may be infinite between the Equinoctial, and the North and South Poles; and in the Sea-chart some of them are represented by the lines which are drawn from East to West. And two of these Circles are the two Tropics of Cancer and Capricorn, which are the bounds of the Sun's greatest Declinations. Likewise all those Circles which the Sun and the stars in Heaven do by the motion of the first or highest movable heaven describe from East to West, are parallels, and serve in the Sphere to show the Latitude. And when a ship saileth in the same height of the pole, than she saileth in a parallel and runneth always East or West. Which manner of sailing we use at all such times, when we find our ship in the height of that land, to which we are going.   

CHAP. XIX. Of the Degrees.  
EVery one of these Circles is divided into 360 equal parts, which they call degrees, and every degree is divided into other 60 equal parts, which are called minutes: which degrees and minutes, are the common measure that we use in Navigation, when we make any account in the Heavens, either in taking the the height of the Sun and stars above the Horizon, or in measuring the distance from our Zenith to the Equinoctial. These degrees are marked in a line drawn from North to South in the most vacant part of the Sea-Chart. This line in general Sea-Charts is divided into 90 equal parts, which are counted (beginning at the Equinoctial line) from one to 90, both Northwards and Southwards. And in those Charts which are not general, this line hath such divisions as it is capable of, according to the largeness of the Chart, beginning to make account from the Equinoctial.   

CHAP. XX. What is meant by Longitude and Latitude.  
THe Longitude of any place is a part of the Equinoctial, or of some other parallel contained between two Meridian's, whereof one passeth by the Canary Islands, and the other by the place given; but if neither of the said Meridian's pass by the foresaid Islands, it is called respective Longitude. And this respective Longitude is called in the Art of Navigation the distance or length of the right line; which is determined or bounded by two other right lines running North and South; of which two, the one passeth by the Port or Haven from whence we set sail, and the other by the place where our ship is. And so shall the distance of the right line be the part of any right line whatsoever running East and West, comprehended between the two foresaid right lines extended North and South.  
The Latitude of a place is a part of any Meridian whatsoever contained between two parallels, whereof one is the Equinoctial, and the other the parallel of the place given. This Latitude the Mariners do call the Distance from the Line; 
The Equinoctial is called the line, because it is the principal of all others which are drawn in the Chart.  understanding by the Line, the most principal of all others, which are drawn in the Chart, that is, the Equinoctial Line. They use also to call it the height, which is as much to say, as the height of the Pole above the Horizon. And so the Distance from the Equinoctial shall be a part of any North and South Line contained between the Equinoctial and any line running from East to West, which passeth in the graduation of the Chart, by the same degree of Latitude in which we find ourselves to be.    

THE SECOND PART OF THE Art of Navigation.  
Wherein is handled the Practic Part, showing the making and use of the principal Instruments belonging to this ART.  

CHAP. 1. The making of the Astrolabe.  
TO know the Latitude or distance from the Equinoctial line there are required five things; whereof any one being wanting, we cannot possibly find out how far we are distant from the said Line. And these are, the Astrolabe or Quadrant, the height of the Sun, the Shadows, the Declination, the Regiment or Rules of the Sun.  
The Astrolabe is to be made after this manner: In the midst of a round plate or table of metal or wood, being smooth and plain every where, and about a finger thick, you shall take the centre A, wherein having placed one foot of your compasses, you shall with the other draw as great a circle as conveniently you can in the said Table. And within this Circle must be drawn two other Circles, the one distant from the other about the breadth of a grain of wheat, and the third must be distant from the second twice so much as the second is from the first.  
And your Ruler being laid just to the centre A, you shall draw the line BAC, which divideth every one of the three circles into two equal parts. And putting one point of your compasses (standing open according to the length of the line BC) upon the point C, where the greatest Circle is divided by the line BC; with the other point, you shall draw above the point D a part of a Circle, and another under E. And then putting one foot of the compasses thus opened upon the point B, you shall draw other two parts of a Circle, which will cross the first in F and G. And your Ruler being laid to F and G, you shall draw the line DE, which must pass by the centre A. Then let the Quadrant DB be divided into 3 equal parts, and every one of those into three other parts, and each of those nine into two, and every one of those 18 into 5; and so the said Quadrant shall be divided into 90 equal parts or degrees. Unto which degrees shall be placed the numbers belonging to them from 5 to 5, between the second and the third circle, beginning from B and ending with 90 at the point D. Then let there be made at the point D a little hole upon the line DE, through which may be put a little ring, or some strong ribbon or string, and you shall make a knot thereon, whereby your finger may take hold: and the Astrolabe hanging by that hole, you shall put through a slender thread with a plummet of lead, which may hang quite under the Astrolabe; which thread, if (while the Astrolabe hangeth immovable) it fall just upon the line DE, then is the Astrolabe well rectified: If not▪ you must continue cutting off some thing, and lightning that side towards which the thread doth fall, until it hang even with the foresaid line. Then must you draw upon a Ruler of the same matter, (being about a finger and an half broad, the right line HI along through the very midst of the breadth thereof: which Ruler shall be made after the same fashion that here is set down, cutting away from one half of the length half of the breadth, always saving whole the line HI. And so likewise shall you cut off along the half of the length on the contrary part, half of the breadth; so that the line HI may remain whole on that side also. And near to the ends of the said Ruler▪ you shall set two little square Vanes of the breadth of the Ruler in the midst standing upright, the very midst of both Vanes being placed upon the line HI. Through the centres of which two Vanes shall be made two little holes, both which must stand directly over the line HI, and in equal distance from the upper face of the Ruler. This Ruler by a hole bored thorough the midst thereof, shall be fastened upon the said Astrolabe through another hole of the bigness of that in the Ruler, at the very centre A with a nail, which may be made fast with a little pin, as is to be seen in the figure.   

CHAP. II. Of the height of the Sun.  
TO take the height of the Sun, you must hold the Astrolabe by the ring or knot D, in your left hand: and turning your right side to the Sun, lift up the Ruler with your right hand, till the beam of the Sun entering by the hole of the uppermost Vane, doth also pierce thorough the hole of the nethermost Vane. And then note the degree and part of the degree which the line HI doth touch, for that is the height of the Sun above the Horizon; which if it be the greatest height that the Sun hath that day, it will teach us how far we are distant from the Equinoctial. This greatest height is to be taken at midday, lifting up the uppermost Vane, till we be assured that the Sun ceaseth to rise any higher, but beginneth to fall again. Then note that greatest height, and keep it for the making of your account of the Latitude by the Sun.   

CHAP. III. Of the Shadows.  
THe shadows being compared with the Sun, may be of three sorts, for at high noon the shadow falleth either towards that part of the World ●o which the Sun declineth. or towards the contrary part, or else we make no shadow at all, The first and second sort are, when the height of the Sun is less than 90 degrees, and the third is, when it is just 90 degrees high. The first is, when the Sun keepeth his course on the North side of the Equinoctial, which is from the 1● of March to the 13 of September; and likewise when the shadows fall towards the North of the Compass: or when the Sun runneth on the South side of the Equinoctial (which is from the 14 of September to the 10 of March) and the shadows likewise fall towards the South of the Compass: and this is when the Sun and the shadows go both one way. The second is, when the Sun coming towards the North, the shadows are cast towards the South of the Compass; or when the Sun is on the South side of the Equinoctial, the shadows fall towards the North; and this is, when the Sun and the shadows are differing.  
The rule of the shadows is, that we look well to the lower Vane of the Astrolabe, when we are taking the height of the Sun at noon: For if the line HI fall directly upon the line of the Astrolabe DE, than we have no shadow, because the Sun is in our Zenith 90 degrees high. But if the line HI fall not upon the line DE▪ you must mark towards what part of the World the lower part of the Ruler doth decline from the point E; which if it decline towards the North of the Compass, than the shadows fall Northwards. But if it decline towards the South of the Compass, than the shadows fall Southwards.   

CHAP. FOUR Of the Regiment and Rules of the Sun.  
WHen you know the part or parts of the Sun and shadows and desire by the Sun to know how far you are distant from the Equinoctial, you have five rules: The first whereof showeth in what part of the Heavens the Sun is, that is, whether he be North or South from the Equinoctial at the time of your observation. The second teacheth what account we are to take of the Sun, when he casteth no shadow, because he is in our Zenith and is found in the Astrolabe to be just 90 deg. high. The third is of the account to be made by the Sun, when taking the height thereof in less than 90 degr. it maketh a shadow at high noon, and hath no Declination, because it is under the Equinoctial. The fourth is, of the account that is to be made▪ when the Sun and the shadows are both one way from the line. The fifth is when the Sun and the shadows are different on● being towards the North, and the other towards the South.  

The first Rule of the Sun.  
From the 11 of M●rch, to the 13 of September, the Sun runneth on the North side of the Equinoctial. And from the 14 of September to the 10 of March he goeth on the South side thereof.   

The second Rule of the Sun.  
When we observe the Sun in 00 degrees of height, we must see what degrees and minutes of Declination the Sun hath the same day: And then we may say that we are so much distant from the Equinoctial towards that part of the world to which the Sun declineth.   

The third Rule of the Sun.  
When the Sun is less than 90 degrees high, if there be no Declination the same day, than so much as it wanteth in height of 90 degrees, so much are we distant from the Equinoctial, towards that part of the world towards which the shadow falleth.   

The fourth Rule of the Sun·  
When the Sun and the shadows are both towards the same part of the world, we must note how much the Sun wanteth of 90 degrees in height; And that which it wanteth (being added to the Declination of the Sun the same day) is our just distance from the Equinoctial towards that part of the world to which the Sun and shadows decline.   

The fifth Rule of the Sun.  
When the Declination of the Sun and the shadows be different, we must add the height of the Sun unto the Declination which it hath the same day: And if the Sun amount to 90 degr. just, then are we under the Equinoctial line: but if it exceed 90 degrees, we are so much distant from the Equinoctial towards that part of the world wherein the Sun is▪ as that excess or overpluss cometh to. And if the height and Declination added together come to less than 90, look how many degrees and minutes you want of 90, so many are you distant from the Equinoctial towards that part to which the shadows fall.  
And here is to be noted that we must likewise make account of the minutes, because they may be both in Declination, and in height, and so always in that Declination where we shall find 60 minutes, we must make of them one degree And if in taking the height we find half a degree besides all the whole degrees▪ it is as much as 30 minutes, and one third part of a degree is 20 minutes, one fourth 15 minutes, one fifth part 12 minutes, and one sixth part 10 minutes.    

CHAP. V. Of the Declination of the Sun, and of his Tables.  
THat we may know what use to make of the five foresaid Rules of the Declination of the Sun, we are to note, that the year (which is the time of the Sun's motion from any point of the Ecliptic till he return again to the same point) consisteth not always of an equal number of days. For besides 365 days it containeth almost one quarter of a day: but the year which we commonly account containeth 365 days in common years, and in leap years 366. It was therefore needful to make four Tables of twelve months apiece (whereof the three first contain 365 days, and the fourth 366) and in such sort to distribute the Declination of the Sun among them, that you may make account of the Declination which is wanting to the Sun at the end of 365 days, for lack of those six hours almost which the Sun wanteth to come unto the point, from which it departed at the beginning of the year: and also of the Declination which resulteth in the fourth year, because it consisteth of 366 days, at what time it cometh to recover that which in the three former years it had lost▪ Therefore to know at all times which of the four Tables we ought to make use of. I will set down a Rule whereby you may know whether the present year be leap year, or whether it be the first, second or third year after the leap year.  
And the Rule is this, that taking from the years of our Lord (which run in our common account) the number of 1600, if the remainder thereof be an even number, and half of the remainder and even number, than that year is leap year: and if the remainder be even and the half thereof odd, than that year is the second year after the leap year. But if the remainder of the years numbered be odd, we must try the year next going before, to see whether the remainder thereof▪ and half the remainder be even numbers, for then the present year is the first after the leap year. And if the remainder of the year going before be even, and the half thereof odd, than the present year is the third year after the leap year.  

How the Declination of the Sun may be found out.  
Now to know the Sun's Declination every day, we must look in that Table which answereth to the present year, and seeking the month in the upper part of the page, and the day of the month wherein we would know the Declination, in the column which defendeth towards the left hand; right over against the said day, and under the title of our month, we shall find two numbers; one of degrees, and the other of minutes; which are the Declination of the Sun that day▪ towards that part of the world which the first Rule of the Sun doth teach.    

CHAP. VI The Equation of the Sun's Declination  
THey which sail in the month of june and December need not much to make any Equation, in the Table of the Sun's Declination, because that in those months the Declination of one day differeth very little from the Declination of another. But at all other times of the year we ought to make some kind of Equation to know precisely our height, or our distance from the Equinoctial. This Equation is to be made after this manner: You must subtract the Declination of the Sun for the present day from the Declination of the day following, or chose (subtract always the less out o● the greater) and the difference, or remainder shall be multiplied by the leagues which our ship hath sailed from the Meridian of London; and the product of the multiplication must be divided by 
These leagues must be counted in the Equinoctial between the meridians of the two places. But it were better to find the difference of Longitude: for then as 360 degrees are to that difference so is the difference of Declination to the Equation desired,  7200 leagues, which are contained in the compass of the whole earth: then (if you have sailed Westward) the Quotient must be added to the Declination of the Sun that day▪ if it be from the 11 of March to the 12 of june or from the 13 of September to the 12 of December: or it must (if the ship also hath sailed Westward) be subtracted if you find it in any other time of the year, except in the days of the Equinoctium, for then this difference is known by taking the Declination of the present day with that of the day following: but if you be to the Eastward from the Meridian of London, you must do chose, subtracting the said Squation where before you added it.  
In stead of the Table of the Sun's Declination here inserted by Roderigo Samorano, use the Table before set down from the 174 page, to the 180 page.   

CHAP. VII. Four examples for the plainer declaration of that which is said before.  

An example of the second Rule.  
IN the year 1608 the 15 of April, suppose I was sailing▪ and took the height of the Sun with my Astrolabe at noon, and found the height thereof to be just 90 degrees. First therefore I took from 1608. the number of 1600. and their remain 8 whic● remainder being an even number, and four the half thereof being even also, I say the year 1608 is the Leap year. And so I go unto the fourth year in the Table of the Sun's Declination, which is leap year, and under the month of April, over against the 15 day, I find 13 degrees and 25 minutes 41 seconds: I say therefore that I am distant from the Equinoctial towards the North 13 degrees and 26 minutes almost, because it is between the 11 of March and the 13 of September, in which space falleth the 15 day of April.   

The second example of the third Rule.  
In the year 1602 upon the 13 day of September, admit I took the height of the Sun, and found it in my Astrolabe to be 70 degrees and an half: and that in the Table of Declination belonging to the same year, upon the foresaid day of September, I found that the Sun had no declination, but that it was under the very Equinoctial line. Now because the degrees of the height which the Sun wanteth of 90 are 19 and an half, I say that I am so much distant from the Equinoctial toward that part of the world unto which the shadow falleth.   

Example of the fourth Rule.  
Upon the 13 of May 1609 suppose I took the height of the Sun at noon in my Astrolabe, and found it to be 85 degrees and three quarters. Now because 1609 is an odd number. I go back to the former year of 1608. and I find (according to the Rule of leap years) that the year 1608 is leap year; and hence I judge that the year 1609 is the year next following the leap year.  
Then I go to the Tables of Declination belonging to the first year after the leap year, and under the month of May against the 13 day, the Sun's Declination is found to be 20 degrees, 41 minutes, 15 seconds; and because that from the 11 of March to the 13 of September the Sun keepeth his course to the Northwards of the Equinoctial, having marked the shadow at midday, I see that the lower vain of mine Astrolabe, looketh to the North of the Compass, and so I say that the Sun and the shadow are both one way. Then I look for the height which is 85 degrees, and three quarters, so that it lacketh of 90 degrees four degrees and one quarter, which is fifteen minutes. These four degrees and fifteen minutes being added to the Declination, which is twenty degrees and 41 minutes, amount in all to 24 degrees and 56 minutes: And so much am I distant from the Equinoctial towards the North, which is the part of the Sun and of the shadows.   

An example of the fifth Rule.  
Upon the 17 of October 1609 which is the first year after the leap year) the Sun now going his course towards the South, suppose I took his Altitude in 50 degrees and one third. And when I took it, the lower vain of mine Astrolabe Declined toward the North of my Compass: wherefore I say that the Sun and the shadows are different. And so adding 05 degrees and 20 minutes (which is one third part of a degree) with 12 degrees and 55 minutes (which upon that day is the Sun's Declination) they amount in all to 63 degrees and 15 minutes: which are less than 90 degrees by 26 degrees and 45 minutes: and so far I am distant from the Equinoctial to the part of the shadows, that is, to the North: for the Sun and shadows being different, the height and Declination came not to 90 degr.   

A second example of the fifth Rule.  
The same day and year suppose that some man found the Sun in 77 degrees and five minutes of height, the Sun itself declining to the South, and the shadows falling to the North; which being added to 12 degrees and 55 minutes of Declination▪ amounteth in all to 90 degrees, just: whereby I know that the ship wherein this Altitude is taken, is under the Equinoctial: because the Sun and shadows being different, the height and Declination make just 90 degrees.   

The third example of the fifth Rule.  
Upon the 20 of May 1608, suppose a certain man found the Sun's height to be 88 degrees and two third parts, the Sun and shadows being different: which being added to 21 degr. 54 minutes, (the Sun's Declination that day) amounteth to 110 degrees 34 minutes, which exceed 90 by 20 degrees and 34 minutes. I say therefore that this man is 20 degrees 34 minutes distant from the Equinoctial, towards the part of the Sun, which is to the North, because the Sun and the shadows being diffe●rent, the height of the Sun, and the Declination being added together exceed 90 degrees.    

CHAP. VIII. Another manner of accounting by the Sun, as they use in Portugal.  
SOme Astrolabes there be, whose account beginneth not from the Horizon, but from the Zenith, and endeth with 90 degr. in the Horizon; and the height taken by them is nothing else but the distance of the Sun from our Zenith: And to make an account of the Sun, according to the Altitude, taken with such Astrolabes, there are these Rules following to be Observed,  
1. When the Sun and the shadows are both one way, add the height unto the Declination, and the product will show how far you are distant from the line, towards the part of the Sun and shadows.  
2. If the Sun and the shadow be differing, subduct the Declination from the height, or the height from the Declination (the lesser from the greater) and the remainder will show how far you are from the line, towards the part of that which is greater: and if the height be greater, then are you on the part of the shadows.  
3. When the Sun is in the line and hath no Declination, so much altitude as you shall find, so far are you distant from the Equinoctial towards the part of the shadows.  
4. When you shall take the Sun in your Zenith, having then no altitude, his Declination will show you how far you are distant from the line towards the part of the Sun.  
These Rules, because they are so easy and plain, need no examples.   

CHAP. IX. How the height of the Sun may be known in any place whatsoever without an Astrolabe; first knowing your distance from the Equinoctial.  
SOme Pilots for their curiosities sake desire to know the height of the Sun for any day without an Astrolabe. For the performance whereof, it is expedient, that they know three things: that is to say, the Declination of the Sun, the distance of the place from the Equinoctial, and the part whereunto the shadows do incline at midday. These three things being known, you shall come to the knowledge of the Sun's height by four Rules.  
1 When you and the Sun be both on one side of the Equinoctial, if your distance from the line be equal to the Sun's declination, you shall find the Sun in your Zenith in 90 degr, and shall have no shadow.  
2 When the Sun hath no declination, look how much your distance from the Equinoctial wanteth of 90 deg. for so much is height of the Sun.  
3 When the Sun and the shadows are both towards one part, subtract out of your distance from the Equinoctial the Declination of the Sun that day, and that which the remainder shall want of 90 deg. shall be the height of the Sun.  
4 When the Sun and the shadows are different, if the Equinoctial be between you and the Sun, add the Declination of the Sun to your distance from the Equinoctial, and that which these two numbers added together shall want of 90 deg. shall be the height of the Sun. But if you be between the Sun and the line, you must subduct your distance from the line out of the Sun's Declination, and then that which the remainder shall want of 90 deg. shall be the height of the Sun.   

CHAP. X. The Rule or Regiment of the North-star, for the knowledge of the height of the Pole.  
THe Zenith is the Pole of the Horizon, because it is every where distant from it just 90 deg. And hence it is, that the Pole of the World is so much elevated above our Horizon▪ as our Zenith is distant from the Equinoctial, which is very manifest: for having 90 deg. of the Meridian from our Zenith by the Pole of the World to the Horizon; and other 90 deg of the Meridian from the Pole of the World, by our Zenith to the Equinoctial; because they are two quadrants of one and the same Circle, they must needs be of equal quantity: from both which that part being taken away, which is common to both (that is, the whole distance from the Pole of the world to our Zenith) that which remaineth on both parts shall be equal. And so that space from our Zenith to the Equinoctial (which is called the distance from the line) is equal ●o the distance that is between the Pole of the World and the Horizon, which is called the height of the Pole.  
Whereby it is manifest, that the height of the Pole is so much as our distance from the line is. And although they are two different things yet the one is taken for the other, because they are equal.  
This height of the Pole is known by the help of four things, which are the Ball●stilla, or cross-staff, the position of the North-star, the height of the said star, and certain Rules.   

CHAP. XI. The making of the Crossstaff.  
THe Mariner's Crosse-staff is that which by the Astronomers is called Radius Astronomicus: and the manner how to make it is as followeth: First, upon a very plain and broad table you may draw a semicircle, which from the centre to the circumference must contain at the least four hand breadths. And having drawn thorough the centre thereof the line ABC, divide the circumference into two equal parts, in the point E, as likewise you must divide the quadrant EC in the very midst by the point F. Then must you divide the arch OF into 90 equal parts, dividing it first into three, and every of these three into other three, and every of those nine into two, and each of those two into five, which you must do with much preciseness and care. Then laying your Ruler to the point B (which is the centre) through every one those 90 divisions of the half quadrant, you must draw 90 lines: And keeping this quadrant so divided, it will serve you for a pattern to make us many Crosse-staves as you think good, of what bigness soever you will. But to make the Crosse-staff, you must take a piece of wood of some three foot in length, and a finger thick, four square, and very even: and fitting a transversary thereto, which may with facility slide up and down upon the staff, always right across; take with your compasses half the length of the transversary, and placing one foot of the compasses upon the point B, make with the other a mark in the line BC, which may serve for the point G, and draw thorough the point G the line GI', which may run equally distant from the line EBB. Finally, laying one end of the staff upon the point G, let it lie all along just upon the line GI', and make your marks upon the edges of the staff, by which you may draw 90 lines, putting the number of every line upon the said edge, beginning to place 90 where the line BE doth cross the staff, and from thence descending unto one or two, which may be put down according to the length of the staff, and the largeness of the transversary.  
  

CHAP. XII. Of the position of the North-star, and the Guards.  
AMongst the 48 Constellations, which the Astronomers place in the Heavens, the nearest unto the pole of the World is that which they call the lesser Bear, and the Mariners Bozina, or the horn, in regard of the fashion thereof: which Constellation consisteth of 7 stars, which are placed after this manner: And of these stars, the three greatest, marked with the letters ABC do serve especially for our purpose. And so A is called the North-star, B the the foremost guard, C the other guard behind. And they are so called, because that by force of the motion of the first movable Heaven, the star B goeth always before, and the star C behind. Every of these three stars as well as all others in the Heavens besides, describe th●● circles round about the pole with the motion of the first or highest movable Heaven: 〈◊〉 which motion sometimes the 〈◊〉 stars AB are just of 〈…〉 above the Horizon: 〈…〉 they are said to be East and West one from another. Sometimes they are in a perpendicular line to the Horizon, according to our sight; and then they are said to be North and South: and sometimes also the two guards BC are East and West one from another▪ and then the former guard beareth from the North-star, North-east and South-west. And when these two guards be in a perpendicular line one above another, the former guard beareth from the North star North-east and South-west. Insomuch that from these four positions do arise eight rules for the eight Rumbs, wherein the former guard may stand, being considered in respect of the North star. And so presupposing that the North star is distant from the Pole three degrees and an half: (according to the opinion of some Mariners, who love numbers that have not any fractions) sometime the North star shall be as high as the Pole itself, sometime three degrees and an half lower or higher than the Pole, and sometime three degrees, and sometimes one and an half, and sometimes half a degree.   

CHAP. XIII. Of the height of the Star taken with the cross-staff.  
TO know how much the North Star is elevated above the Horizon, you must take the height thereof only at such times when as in respect of the former guard it is in some one of these four Rumbs, that is to say, North and South, East and West, North-east and South-west, and Northwest and Southeast. Wherefore seeing it placed in any of the foresaid Rumbs, you shall put that end of the cross-staff which is next 90 degrees upon your cheekbone, at the utter corner of your eye: and holding it there steadfast, you must move the transversary till you see the Horizon joined with the lower end thereof; and the North Star with the higher end. Then mark the degree, and part of the degree which the transuersarie showeth upon the staff; for that is the height of the Star.   

CHAP. XIIII. The regiment or Rules of the North Star.  

The first Rules.  
WHEN the guards are in the East, the former guard beareth with the North Star East and West, and then the North Star is a degree and half under the Pole: let us add this degree and half to the height which we Observed with the cross-staff; and the whole product showeth the number of degrees which the Pole is elevated above our Horizon. And so much are we distant from the Equinoctial toward the North.   

The second Rule.  
When the guards are in the North-east, one guard beareth from another East and West: and the former guard standeth from the North Star North-east and South-west; and then the North Star is under the Pole three degrees and one half; which being added to the height of the Star, will show you the height of the Pole.   

The third Rule.  
When the guards be at the highest, than the former guard beareth from the North Star North and South; the North Star being then three degrees under the Pole: which three degrees being added to the height of the Star, do show the true height of the Pole.   

The fourth Rule.  
When the guards are in the Northwest, they bear one from another North and South, and the former guard lieth from the North Star North-east and South-west: and then the North Star is under the Pole half a degree: which half degree being added to the height of the Star, giveth you the height of the Pole.   

The fifth Rule.  
When the guards are in the East, the former guard lieth from the North Star East and West, and then the North Star is a degree and an half above the Pole; which degree and an half being deducted out of the height of the North Star, the remainder is the just height of the Pole.   

The sixth Rule.  
When the guards are in the South-west, one beareth from another East and West, and the former lieth from the North Star North-east and South-west, and then the North Star is above the Pole three degrees and an half: which three degrees and an half being deducted out of the height of the Star, that which remaineth shall be the height of the Pole.   

The seventh Rule.  
When the guards are at the lowest, the former guard beareth with the North Star North and South: and then the North Star is above the Pole three degrees; which being deducted, the remainder is the height of the Pole.   

The eight Rule.  
When the guards are in the Southeast, one beareth from another North and South, and the former beareth from the North Star Northwest and Southeast, and the North Star is above the Pole half a degree: which half degree being deducted from the height of the Star, the remainder is the height of the Pole above our Horizon, and just so much are we distant from the Equinoctial towards the North.  
This is the account which always hath been made of the North Star from the time that it hath had three degrees and an half distance from the Pole unto this present. But because at this time by reason of the compound motion of the 8 and 9 heavens, the fixed Stars have notably varied from their places the Pole Star hath also approached nearer the Pole, being now distant therefrom not above three degrees and eight minutes, And so I think it convenient to set down the account which ought now to be made thereof, 
In stead of all these Rules of the North Star (which are erroneous) use the Tables of Equations of the Pole Stars height, set down in the latter end of this book.  according to the foresaid distance: to the end that from henceforth the height of the Pole taken by the Star may agree justly with the distance from the Equinoctial taken by the Sun. Which two things have hitherto disagreed and caused no small confusion unto the Pilots, and some error in Navigation.  
The guards being in the East, you shall add unto the height taken by the cross-staff, 1 degree 20 minutes North-east, 3 degrees 8 minutes North, 2 degrees 41 minutes Northwest, 0 degree 27 minutes  
In the contrary Rumbs to these you must deduct these degrees from the height of the Star, which you take with your cross-staff, and then you shall have the height of the Pole above the Horizon.    

CHAP. XV. Other things to be noted in Observing the height of the Pole.  
NEXT unto the constellation of the Horn, here is a Star which is called by the Spaniards el Guion signified before by the letter D, which standing East and West from the North-star, giveth you to understand, that it and the North Star, and the very Pole are East and West. And so taking the height of the North Star, when it is thus situate in regard of the Guion, with out making any other account, you have the just height of the Pole, and the distance from the Equinoctial.  
Here followeth the Table.  
The guards being in the East The third star is in the Southeast The sixth star in the South The 9 th' star in the South-west Northeast East Southeast South North Northeast East Southeast Northwest North North-east East West Northwest North North-east Southwest West Northwest North South Southwest West Northwest Southeast South Southwest West  
In this Table, the first column serveth for the guards; the second for the third star; the third column for the sixth star; and the fourth for the ninth star. Insomuch as if you seek the rumb, seeing any of these four stars in this Table, right against the same do answer those rumbs where the other three are, although we cannot see them in the Heavens.   

CHAP. XVI. Of the Crosiers.  
WHen the Mariners pass the Equinoctial line towards the South, so that they cannot see the North-star, they make use of another sta● which is in the Constellation, called by the Astronomers the Centaur, which star, with other three notable stars, which are in the same Constellation, maketh the figure of a Cross; for which cause they call it the Crosier. And it is holden for certain, that when the star A (which of all four cometh nearest to the South Pole) is North and South with the star B, that than it is rightly situate to take the height by. And because this star A (which they call the Cock's foot) is thirty degrees from the South Pole, it cometh to pass, that if being situate, as is aforesaid, we take the height thereof (which is then the greatest that it can have) this height will truly show how far we are distant from the Equinoctial. For if the said height be thirty degrees, than we are in the very Equinoctial: and if it be more than thirty degrees, then are we by so much past the Equinoctial towards the South. And if it be less than 30 degrees, so much as it wanteth are we to the North of the Equinoctial.  
And here it is to be noted, that when the guards are in the North-east, then are the stars in the Crosier fitly situate for observation, because than they are in the Meridian.   

CHAP. XVII. Of the Sea-Compass.  
THe Sea-Compass is one of the most necessary Instruments, which are used in Navigation; for day and night, in clear and dark weather it showeth always the right way through the Sea. And therefore it is meet that this Instrument be made with much care; to the end, that it may be most certain and true. And the manner of making it is, that upon a piece of pasteboard, you draw a circle so big as you will have your Compass to be, which being divided into 32 equal parts (as we have already showed in the Chapter of the winds) with sixteen lines crossing one another in the centre, than you shall adorn the eight principal winds, as is to be seen in the figure following, ending in the North with a Flower deluis: and you shall paint the North and South, and East and West with blue, and the North-east and South-west, and the Northwest and Southeast with red. And then taking two steel wires, which are to be placed like the head of a lance, you must fasten them on the back side of the said circle, in such sort, that one meeting of the points of those steel wires be right under the North, allowing half a point towards the North-east, in regard of the North-easting of the needle at Sevil: and the other meeting at the opposite point, which is South, and half a point towards the South-west: and touching or rubbing those two points of the wires with the ends of the Loadstone, which look to the North and to the South, to wit, the North points of the wires, with the South of the stone: & the South point of the wires with the North of the stone This being done, you must place upon the centre of the said circle a Capitel, which must be very well bored in, from off a round pyramid; to the end, that the rose or fly may play more nimbly upon the pin. This pin must be made of latin, with a very sharp point, and is to be fastened upright in a round box of wood, which must be of the fashion of a great cup-dish, containing the rose within it, being covered above with a clear round glass, and the joints thereof must be stopped with wax, to the end, that no wind may enter into the rose to disturb it. There must be great care had, that this rose, with the wires placed upon the pin, may go nimbly, and may not swerve more to the one side then to the other, but may stand even and level. And when it inclineth towards either part, you must put on the contrary part a little wax, or a thin plate of lead fastened under the pasteboard, which covereth the wires. This box wherein the rose playeth up and down hangeth within two hoops of latin, which are two round circles enclosed one within another, and distant asunder by the space of half a finger's breadth, with two nails of latin, which are diametrally opposite. And the box being fitly placed within these hoops, you must make in the outward hoop two holes, which must be distant from the foresaid two nails a quarter of a Circle both ways: And by these two holes must the outward hoop or circle be fastened within a square box, or a round, so as although that uttermost box be tossed up and down every way with the motion of the ship, yet always the superficies and glass of the inner box may lie level with the Horizon. And this being done with care, the instrument, which they call the Sea-Compasse is fully finished. The manner of using the same is, when being placed with the box in the midst of the poop of the ship where the bittacle standeth in a right line, which passeth from the bolt-sprit by the midst of the main mast to the poop, it serveth continually to govern the ship by moving of the Rudder, till the wind or the line of your Compass, towards which we desire to shape our course, stand directly towards the prow or bolt-sprit of the ship. They use also for the night to mark a point within the inner part of the inner box, which in respect of the capitel of the Compass, may stand directly towards the prow of the ship. And always in guiding the ship▪ you must take heed that the said point be continually joined with the wind of the rose towards which you intent your course.   

CHAP. XVIII. How the Variation of the Compass may be found.  
THe Mariners use to examine whether their Compass North-easteth or South-westeth, watching for that purpose when the former guard beareth with the North star North-east and South-west, taking a little of the point of North and South. And placing their Compass in an open place, where the North star may be seen, if the flowerdeluis of the Rose looketh directly towards the star, their Compass varieth nothing at all: but if the star be to the North-east, so much as it varieth from the point of the flowerdeluis▪ so much the Compass North-westeth: and if it varieth to the Northwest of the Compass, how much the star swerveth from the point of the flowerdeluis, so much the Compass North-easteth. And in regard of this variation of the Compass there must always allowance be made in the course which is holden. This manner of finding out the variation I do account to be somewhat subject unto error: but at land there is another more certain way by the Meridian line, which is to be taken in manner following.  

The finding of the Meridian-line.  
In a superficies, which is plain and levelly every where, and in a place where the Sun shineth at his rising and setting, you must draw certain circles upon one centre: and having pitched a stile upright in the same centre (the head whereof must be approved with a pair of compasses to be equally distant from all parts of one of those circles) observe you in the morning two or three hours before noon, when the point of the shadow of the stile toucheth the circumference of any of those circles: and having made a mark in the touches, take diligent heed in the afternoon also, when the same point of the shadow turneth about to touch in the same circle, and making another mark in that second touch, divide in the midst that part of the circle which is between those two marks. Then laying your Ruler upon the point of the division, and upon the centre of those circles draw a line, which shall be your Meridian, and the true North and South Rumb; upon which setting your compass▪ and laying your Ruler over the glass, that it may pass along over the Meridian, and over the centre or capitel of the rose or fly: either said Ruler lieth over the North and South of the Compass (and then is the Compass without variation) or the Ruler declineth toward the North-east or South-west; and how much it declineth that way, so much the Compass North-westeth, or else it declineth towards the Northwest, and then it North-easteth so much as the Ruler declineth that way. But to know the variation of the Compass both at land and sea, we will deliver another far more easy and certain way▪ when we come to entreat of the universal Dial.    

CHAP. XIX Of the Sea-chart.  
THe Sea-chart is nothing else but a lively picture of the earth and water. And it containeth five notable things, which do concern as well the true making of the Chart, as also the enabling of the Mariner to know the way which he maketh, the place where he is, and the end of his journey.  
The first is the laying out of the Coasts of the Land, which that it may be truly done, it is meet that every thing be set down in the Chart in the same course, distance, and height that shall be found in Navigation.  
The second is, that it containeth not only the coast of the firm land, but also all other particularities which do occur in sailing, as namely, Islands, Iselets, Banks, or Bars, Shoalds, Rocks, and Flats.  
The third is the lines which signify the 32 winds, by the help whereof we may see whether the parts of the land be well laid out, and in their true courses one from another. And of these winds the black are the eight principal, which are called whole winds. The green be half winds, or half parted winds: and the red be the quarters of the winds. You may know in your Chart whether these winds be well drawn, if you try with your compasses that all points of them be equally distant one from another: and that all winds representing the same Rumb be parallels: As namely, that one North-east and Southwest Rumb be parallel to another North-east and Southwest Rumb. The fourth is the graduation, in all parts, whereof it is meet that the degrees 
† Or rather increased proportionally from the Equinoctial line toward the North & South.  be equal one to another: and that the parts of the land do directly lie East and West from those degrees under which they are situate. The fifth is the scale of leagues, which you may see whether it be true, by taking betwixt the points of your compasses just 4 degr. out of the line of graduation which being applied to the scale of leagues must there agree exactly with 70 Spanish leagues or 80 English.  
By the Sea-Chart are known five things: The first is the lying or trending of the Coast. The second is the distance or number of leagues from one coast to another. The third is, the latitude or distance from the Equinoctial, wherein all Lands both Continents and Islands, as also every Port, River, Isle, Should or Bank is situate. The fourth is the rumb or rumbs, by which we are to sail from one place to another. The fifth is the point or place where we are with our ship when we are sailing. The first is known with a pair of compasses, putting one foot thereof upon the beginning of the coast, whose trending we desire to know, and the other foot upon the rumb, which to our thinking is every where equally distant from the said coast. For if one foot of the compasses running along the Coast, the other foot keepeth by the said Rumb, than we say the coast lieth even with that rumb. And if our compass runneth with out swerving one foot from the rumb, and the other from the Coast, till the point which runneth along the coast leaveth it, then from that very place where it leaveth the same, we may say, that unto the other place where it began, the coast runneth by such a rumb, as if a man should say East and West, Northeast and Southwest, or any other rumb whatsoever.  
The second thing (which is the distance) may be found by taking between the points of your compasses out of your scale of leagues (if the distance be very great) an hundred leagues, and measuring with your compass so opened from one place to another: now if in so doing it falleth not just, then remembering how many hundreds of leagues there are, you must for the measuring of the rest pitch one foot of your compass upon the point where the last hundred ended, and the other foot upon the land whose distance you desire to know: then bringing the compass so opened to the scale of leagues, you shall see manifestly how many leagues the said distance surmounteth above the hundreds. But if the distance be less than an hundred leagues, then setting the points of your compasses upon those two places whose distance you desire to know, and removing the compass so opened to the scale of leagues, you shall easily know the distance of one of those places from the other.  
The third (which is the height or latitude, wherein every Port, River, or Island standeth) is to be found by pitching one foot of your compasses upon the Land, Haven, or Cape, whose height you desire to know, and the other foot upon the next East and West parallel, and the compass remaining in that sort, move the point thereof along the said parallel or rumb, to the line of graduation, and there the other foot which lay upon the land will show you the height thereof.  
The fourth (which is the rumb or rumbs, by which you must sail from one place to another) is known after this manner: If you be to sail by one rumb only, you may know it, by pitching one foot of your compasses upon the place from which you are to depart; and the other foot upon the very next rumb, which to your thinking goeth most directly to the place whither you would go; and running by that rumb with one foot of your compass so opened, the other foot will touch the place whither you are going. But if it toucheth not the place whither you are going, then pitch one foot of your compasses upon the same place, and the other foot upon the second rumb, which you suppose may lead you thither. And placing one foot of another pair of compasses upon the place from whence we depart, and the other upon the most direct rumb toward the place desired; these two compasses running along the rumbs one toward another; you must mark where those two points join together, one whereof came from the place of your departure, and the other from the place whither you are to go▪ & the point where they both concur is that to which we are to change our course.  
As for example, if I sail from the bar of S. Lucan, to fall with Punta de Naga upon the Isle Teneriffe in time of winter; it is evident, that I must sail Southwest and by South, till I bring myself East and West with Cape Cantin in 32 degrees and an half: and from thence I must go Southwest and by west, but not all the way, because putting one point of the compass upon Cape Cantin, and the other point upon the South west and by west rumb next unto it, my compass thus running open alongst the said rumb, the point which departed from Cape Cantin, will run on the outside of Punta de Naga. But in such a case as this I place one point of one pair of compasses at Punta de Naga, and the other point upon the South-west rumb: Likewise I place one point of another pair of compasses at Cape Cantin, and the other upon the next South-west and by west rumb. Then let these two compasses so opened run by their said rumbs one against another, and then you must look in what place & height the very point is, where those two points of the compasses which departed from Punta de Naga and Cape Cantin do meet: and I say, that when I am come to the said height and place, having sailed from Cape Cantin Southwest and by west, than I must change my course, and run South-west.   

CHAP. XX. Of the point of Imagination.  
THe fifth thing to be known by the Sea-chart is the point of the ships place, and this they term to cast a point, or to set a prick upon the chart: which is no other thing but to find a point therein, which is proportionally distant in the Chart from all the Lands and Islands there described so many leagues of the scale, as there are leagues of distance upon the sea from the place where you are to the Lands and Islands round about you, represented by these that are in the Chart. This point is to be found two ways; either by imagination, or by traversing, which may properly be called geometrical. The point of imagination is usually found by the first of these two ways, when we sail directly by a parallel circle; which is when we sail due East and West, keeping always in one height and distance from the Equinoctial: or when we sail by any other rumb in close weather, when neither the Sun at noon, nor the North star in the night can be seen.  
This point doth pre-suppose the knowledge of two things; to wit, the rumb, by which we have sailed, and that is known by the Compass, and the leagues which we have run; and this hath no certainty, but is a little more or less than a good Mariner, according to his imagination supposeth that he hath sailed: whereof the said point took his name.  
This point is found in the Chart, by taking out of the scale of leagues so many leagues as a man can well estimate that the ship hath gone: and pitching one foot of the compass in the place from which you departed, you shall set the other point in such sort, that both may be equally distant from the Rumb or wind whereby you have sailed; and where that second point of your Compass shall fall, there is your ship according to your imagination.   

CHAP. XXI. Of the Traverse or Geometrical point.  
THe point found by imagination is not so certain as is convenient, because it oft cometh to pass, either because the Mariner hath not made true account of the way that his ship hath made, or for some other causes therewith concurring, that if he taketh the height by the Sun, or by the North star, after he hath cast his point, he cometh not to find himself in that distance from the Equinoctial, which his point of imagination doth show him, but in some other distance. And to avoid this error there is another way of casting your point in the Chart, which is called punto de esquadria (the Traverse point) which point presupposeth the assured knowledge of two things; one is the Rumb by which you have sailed, the other is your distance from the Equinoctial.  
For all this art of Navigation is grounded upon the course, and height, which is in quantity all one with the distance from the Equinoctial. The Rumb or course is always known by the Compass, the height by the star, and the distance from the Equinoctial by the Sun.  
This being known, set the foot of one Compass at the port or place from whence you departed, and the other foot in the next Rumb where upon you have sailed: and placing one point of an other pair of Compasses upon the line of graduation, in the degree of your distance from the Equinoctial, and the other point upon the next East and West Rumb, let these two pair of Compasses standing thus open, run along the Rumbs, one towards another, till the point which came from the place of your departure, and that other which came from the height of your graduation meet: and where they meet, there is the place of your ship. And this point so found out, is most certain, when the height is carefully taken, and the Rumb known.   

CHAP. XXII. Of the amending of the point of imagination.  
HE that knoweth how to find out the point by traversing, shall easily amend the point of imagination, when having taken his height he findeth the said point not to be good and certain. And here is to be noted, that when you sail East and West and find the point by imagination, this point cannot be amended, but you must sail in doubt how many leagues you have gone until you fall with the land; because that sailing in that course neither the height of the pole, nor your distance from the Equinoctial, doth any whit alter. But when you sail by any other rumb, your point of imagination may be amended, and the amendment thereof shall be so much the more certain as the rumb of your Navigation cometh nearer to the North or South, and by so much the more uncertain as it cometh nearer to the East or West. This amendment is made two manner of ways, namely, either by traversing, or by the amendment of North and South and East and West; which second amendment, though it be a kind of traversing, yet it is called by another name, to distinguish it from the first.  

The amendment of the point of imagination by the traverse point.  
When you will amend your point of imagination by traversing, you must set one foot of one pair of your compasses in the point found by imagination, and the other foot upon the next rumb by which you have sailed: and setting the foot of another pair of compasses in the line of graduation upon the number of degrees, which you find yourself distant from the Equinoctial, and the other foot upon the next East and West line; run with your compasses so opened by the foresaid rumbs, till the point proceeding from the graduation, and the other which proceedeth from the point of imagination do meet just together, and then you may say, that your point of imagination is mended by traversing.   

The amendment of the point of imagination by North, South, East, and West.  
The amendment by North, South, East, West, is after this manner: Set the foot of one compass upon the point found by imagination, and the other foot upon the next North and South rumb: then place one foot of another compass in the line of graduation upon the degree wherein you find yourself, and the other upon the next East and West rumb, and so let these two compasses run thus open by their rumbs, till the point which 〈◊〉 from the point of imagination, and the other which cometh from the graduation do meet; for than is your point of imagination amended by the amendment of East, West, North, South.  
Of these two amendments the first serveth when you sail in a large gulf, because you may run at liberty with the compass: the second serveth near unto any coast.    

CHAP. XXIII. The point by imagination, and the height.  
WHen you sail by the sixth or seventh rumb, that is, by the East and by North, or East and by South, or by the West and by North, or West and by South: or else by the East Northeast, or West Southwest; or by the East Southeast, or West Northwest, there is a certain difficulty which may breed great error in finding the traverse point, notwithstanding the latitude be taken; by reason of the Rudder that guideth the ship, which giveth certain yawes out of the course that the Pilot pretendeth, or by reason of the wind which bloweth not right in the poop, but maketh the ship fall to the leeward, from the direct and true course which it ought to keep. Wherefore because in such a case, if you find your point by traversing, suppose by East and by North, the way which I think is made, and hath been failed may be by the East Northeast: which point so found, must stand more forward than the true point, by so much difference as there is between 42 and 88 Spanish leagues, which is 46 leagues, that is, the difference of distance from the Meridian, or North and South line in those two points. In such a case as this, it is not meet to find your point by traversing, to avoid the error which hereupon may ensue, which error ariseth of such a cause, as that a man's judgement, be it never so good, cannot easily determine thereupon, and so consequently he cannot judge precisely. But to avoid confusion and cause of error, he must cast his point in manner following, and he shall errer as little as is possible.  
Let him examine according to the ordinary running of his ship, how much way she might make every day that he hath sailed; and the leagues that shall amount in all the days, let him take between the points of one compass: and let him place one point thereof upon the place from whence he departed: and taking another compass, let him set one point thereof upon the graduation, according to the height which he hath taken and the other point upon the next East and West Rumb. Now let this compass run by his East and West rumb, till the point coming from the graduation meet with the second point of the other Compass which he holdeth not upon the Chart: and in the place where they meet, he may say that there is his point and his ship.  
And because in this case all Pilots do not use this point of imagination and height, there grow great diversities among them concerning their distance from land, when as in long voyages they confer and communicate their opinions one with another; insomuch that one according to his conjecture judgeth himself to be 50 leagues from land, another 100, another 200, and another thinketh he is hard by the land. The reason is, because some of them cast their point by traversing, others by imagination only, and others by imagination and height, who are always more certain than the rest.   

CHAP. XXIV. What it is to increase or diminish in height.  
THe Mariners call it increasing in height, when they go further and further from the Equinoctial; and diminishing in height when they approach nearer to the Equinoctial. So that in our Navigation we either sail from a greater to a less altitude of the pole, and then we go towards the Equinoctial, and then the height is said to be diminished: or we sail from a less to a greater height of the pole, and then we go from the Equinoctial, and are said to increase our height. And hence it is, that casting our point by imagination, and afterwards (having taken the height) amending it by traversing, either the height, wherein we find ourselves being taken by the Sun or star is greater, or else it is less than that which we made account of by imagination. And hence do arise four rules: The first is, that when in sailing we do increase the height, if the point amended by traversing be of greater height than the point of imagination, the ship hath gone more than the point of imagination showed us.  
The second, when we increase our height, if the point amended by traversing be in less height than the point found by imagination, then hath the ship gone less way than we imagined.  
The third is, when we diminish our height in sailing, if the point amended by traversing be in a greater height than the point found by imagination, then hath the ship made less way than we guessed by our imagination.  
The fourth is, when we diminish our height, if the point amended by traverse be in less height than the point found by imagination, then hath the ship made more way than we imagined.   

CHAP. XXV. How you may cast a traverse point without Compasses.  
IF a Mariner chance to lose his Compasses, he may cast his point of traverse after this manner: Let him take two slender threads, and putting the end of one of them upon the place from whence he departed, let him stretch it in equal distance from the Rumb by which he hath sailed, and putting another thread in equal distance from the next East and West rumb, let him make it to pass by the degrees of height, in which he findeth himself; and where the two threads cross one another, there is the point of the ship: and always the first thread (if it hath not changed the course) showeth the way which the ship hath gone, and the second the parallel wherein the ship is.   

CHAP. XXVI. Of another kind of casting a point by traverse.  
EXamine the difference of the degrees of distance from the Equinoctial, which are between the place from whence the ship set forth, and the place where the ship is: Then taking the heights of both places very precisely, and subtracting the lesser out of the greater, that which remaineth is the difference: which difference you must multiply by the leagues, which answer to one degree in the rumb by which you have sailed, and those leagues, which the degrees and minutes of difference shall make, you shall take between the points of a pair of compasses out of your scale of leagues: and holding the said compass so open, set one foot thereof upon the point from whence the ship departed, and the other foot stretching towards the place whithre the ship hath sailed, you must hold up a little from the Chart: and you must set one foot of the other Compass at the degree of the distance wherein your ship is from the Equinoctial, when the said point is sought for, and the other point you must place upon the next East and West Parallel. And let this second Compass run by his next East and West Rumb, until the point of the first Compass lifted up, being set down, that point of the second Compass which came from the said degree doth meet therewithal: and where those two points shall meet, there is the true point of the ship.   

CHAP. XXVII. Of the leagues which in Navigation answer to each degree of Latitude in every Rumb.  
IF we suppose (as we have before said in the chap. (of the quantity of the earth) that the greatest circle thereof conaineth in compass 6300 common Spanish leagues; then unto every degree of the Meridian (which is the greatest circle) do answer 17 Spanish leagus and an half: so that sailing North and South, if your height of the Pole, or your distance from the Equinoctial be varied one degree, you may say that you have gone seventeen leagues and an half: but if you vary one degree, and hold your course upon the first point, then have you sailed 17 leagues and ⅙: And you have declined from the Meridian or right line which passeth by the place from which you departed, three leagus and an half. And if you sail upon the second point from the North or South till your height of the Pole be changed one degree, you have then gone 19 leagues and ⅜, and are distant from your right line 7 leagues and ¼: And varying a degree upon the third point of the Compass from North or South, you have gone 21 leagues, and are departed from your right line 11 leagues and ⅔.  
Sailing upon the fourth point of the Compass, there do answer unto every degree 24 leagues and three fourth's, and you are distant from the right line or Meridian 17 leagues and an half. Upon the fifth point you must allow for one degree 31 leagues and an half, and then are you distant from your right line 26 leagues and ⅕. Upon the sixth point do answer unto one degree of Latitude 45 leagues and ¾, and you are then parted from your right line 42 leagues and ¼. Upon the seventh point do answer unto one degree of Latitude 89 leagues and ¾, and you are departed from your right line 88 leagues, as it appeareth out of the Table following, 
The Table of the Author which is more precise.  Leagues of the course or Rumb. Distance from the right line 1 17 ●/6 3 ½ 2 19 ⅜ 7 ¼ 3 21 11 ⅔ 4 24 ¾ 17 ½ 5 31 ½ 26 ⅕ 6 45 ¾ 42 ¼ 7 89 ¾ 88 
The old Table which is less certain.  Leagus of the course or Rumb. Distance from the right line or Meridian. 18 3 ½ 18 ½ 7 ½ 21 ½ 11 ⅔ 25 17 ½ 31 ½ 26 ½ 46 ½ 42 ½ 88 85   

CHAP. XXVIII. How you may come to know the Longitude or the course from East to West.  
THat which the Cosmographers call Longitude, is called by the Mariners the distance from the right line, and the course of East and West, and the height of East and West, and it is a part of an East and west Rumb contained between two Meridian's, one of which runneth by the point or place from whence we departed, and the other by the point where the ship is. This distance from the right line is known by the mean of two things, namely of the course and of the difference of Latitude, or of the course and distance.  
The course and the difference of the height being given, you may know the said distance by traverse or by numbers. By Geometry, or traverse it is known in manner following: the height, or the distance of your ship from the Equinoctial being known, and the Rumb also upon which you have sailed, you must cast upon your chart a point by traverse, and placing upon that point one of the points of your Compasses, and the other upon the next Rumb of East and West; you must place one point of another pair of Compasses at the haven or point from whence the ship departed, and the other point upon the North and South Rumb which is next. These two Compasses thus opened, running by their Rumbs one towards another, you must mark where the two points meet; namely, that which came out of the part from whence you departed, and that which you removed from the point where the ship presently is, being found by traverse: and where those two points do meet, there make another point or prick. Then look how many leagues there are from the said third point to the point of traverse where the ship is, (both which do always bear East and West one from another) so many leagues is your distance from the right line. And if in stead of the leagues set down in the scale we measure with degrees taken out of the graduation, 
This for the most part is not true in the ordinary Sea-chart.  we shall have the degrees of Longitude which are between the point of our departure, and the point of the place where presently we are.  
And it is to be noted, that always when we sail, we either alter our latitude only, and that is, when we sail North and South, or we alter the longitude only, that is, when we sail by the selfsame latitude, going always East and West by the same parallel: or we alter both latitude and longitude, when we sail by any of the other 28 winds. When we alter the latitude only we swerve not one jot from the right line or Meridian; when we alter both longitude and latitude, then must we find the longitude or distance from the right line in manner abovesaid.  
But when your longitude only is altered, because than you must find out the point where the ship is by imagination only, there is no certain manner to know the longitude or distance from the right line, but only little more or less, setting down a point by imagination, and measuring by leagues, or by degrees, what distance there is between that and the point from which the ship departed. By numbers you may find out the longitude in manner following: The difference of your distance from the Equinoctial being known, which is so many degrees more or less, as you have increased or diminished in the height of the Pole, look in the Table annexed to the chapter next before this, for the leagues of distance from the right line, which answer unto one degree by the rumb or point of the compass upon which you have sailed; and multiplying those leagues by the number of degrees which you have increased or diminished in the height of the pole in your Navigation, you shall then see how many leagues you are distant from the right line, which passeth by the place from whence you came, which leagues if you divide by 17 and an half, then will appear unto you the degrees of longitude between the place from whence you departed, and the point where you are.   

CHAP. XXIX. How you may set down in your Chart a new Land, never before discovered.  
IT may sometimes fall out in new Discoveries, or when your ship by means of a tempest is driven out of her right course, that you shall come to the sight of some Isle, Should, or new Land, whereof the Mariner is utterly ignorant. And to make some relation of the same, or to go unto it some other time, if you desire to set it down in your Sea-chart, in the true place, you may do it after this manner: So soon as you have sight thereof, mark it well first with your compass, observing diligently upon which point thereof it lieth. And secondly, you must there take the height of the Sun, or of the Polestar, that you may know in what point your ship is, and that point you must call the first point; which being so done, your ship may sail on her course all that day, till the day following, without losing her way: and the next day mark the land again, and see upon what point it lieth, and then take your height, and with it cast your point of traverse once again; and that you may call your second point. Then take a pair of compasses, and placing one foot upon the first point, and the other upon the rumb towards which the land did bear, when you cast your first point: set also one foot of another pair of compasses in the second point, and the other foot upon the rumb upon which the land lay when you cast your second point; and these two compasses thus opened, you must move by their rumbs, till those two feet of both compasses do meet together, which were moved from the foresaid two points: and where they do so meet together, there may you say is the land which you discovered; which land you may point out with the in-lets and outlets, or capes and other signs, which you saw thereupon. And by the graduation you may see the latitude thereof, that thereby you may find it, if at any time after you go to seek for it.   

CHAP. XXX. Seeing two known points or Capes of land as you sail along, how you may know the distance of your ship from them.  
IT is the custom of passengers, when they first descry that land which they would arrive at, to ask the Pilot, how far they are from land▪ Unto which question he may well answer, if he know two capes, or points, or notable places thereupon: which places the further they be asunder one from another, the more certainly may he answer to that question.  
Let him pitch therefore one foot of one pair of compasses upon one of the two foresaid capes, and the other foot upon the rumb which in his compass pointeth towards that cape. And in like manner shall he do with another pair of compasses, placing one foot thereof upon the other known cape, and the other foot upon the rumb, which stretcheth towards the said second cape; and moving the two Compasses so opened by their two Rumbs off from the land, the very same point where the two feet which came from the two capes do meet, you may affirm to be the very point where your ship is. And then taking measure by the scale of leagues, you may see what distance there is from the said point to either of the foresaid capes, or to any other place, which you think good, for it is a very easy matter if you know the point where your ship is.   

CHAP. XXXI. Of the account of the Moon.  
THe account of the Moon and of the tides is most necessary to be known of Mariners, to enter and depart from any Havens, Rivers, or Bars, and to pass by some banks, and shoalds.  
A tide is a regular motion of the Sea whereby at some times it seemeth more increased then at other. And these tides are of two sorts: for some are such as we call springtides and neap-tides, and the course of this motion happeneth from one half month to another half month. Others be those which we call more properly by the names of tides; to wit, a full sea, and a low sea, a swelling and a falling sea; and these are from the one half lunar day, to the other half. Which tides, as well the first as the second, have their course and moving from the motion of the Moon: which is of two sorts; one proper from West to East, by means whereof in thirty days almost, it is in conjunction with the Sun, which we call the new Moon; and in opposition, which we call the full of the Moon; and those we name the quarters, when it shineth half unto us. The other motion is from East to West by the force of the Primum mobile, or the first movable heaven, whereby in one lunar day the Moon passeth over all the two and thirty points of the compass, or to speak more plainly, it riseth and setteth, and returneth again to arise, which two motions of the Moon being known, we may easily discern the manner of both kinds of the foresaid tides. And because that to the knowledge hereof it is requisite that we know the middle motion of the Moon; I will first set down how it may be known, and then how thereby we may discern the seasons of the tides.  
For which purpose, we are to note that the golden number, as it is commonly called, is a certain number of years wherein the Moon hath all the diversities of aspects with the Sun that can happen between them, which is done in every nineteen years almost.  
As for example, if in the year 1588. there be a conjunction of the Sun and Moon upon the 26 of April, or an opposition upon the 11 of April, I say that there shall not happen a conjunction of the Sun and Moon upon the 26 of April, nor an opposition upon the 11 of April, till 19 years be expired, which will be in the year of our Lord 1607. And so are we to conceive likewise of the quarters and other aspects.  
The second thing to be noted, is, that from this golden number springeth another, which is called the concurrent, being the days of the Moon at the beginning of the year: which year, according to that account, beginneth from the last of February, about twelve a clock at night, which is the beginning of March. And the days of the Moon which then remain, besides all the whole lunare months of the year past, are called by Calculators The concurrents; because they serve to know the account of the Moon, throughout the whole year that is to come; and they concur with other numbers to know the age of the Moon. Now by these two numbers, to be able to discern the days of the Moon, or the distance thereof from the Sun, you are to note the Rules following.  

The first Rule of the Golden number.  
From the present year of our Lord you must deduct 1500. and out of the remainder, taking one in every twenty, we shall find the golden number, if they be just twenties. But if they be not just twenties; above the number of twenties we must add that which remaineth above the twenties: all which being added together, if it exceed not nineteen, shall be the golden number. But if it exceed nineteen, cast away nineteen, and the remainder is the golden number.   

The second Rule of the concurrent.  
Divide the golden number by three, and if there remain one, the concurrent is equal with the golden number; and if there remain two, the concurrent is greater than the golden number by ten: but if nothing remain, the concurrent exceedeth the golden number by twenty, And if this concurrent exceed the number of thirty, than the remainder or surplusage shall be the concurent.   

The third Rule of the Conjunction.  
The number of the concurent being known, you must add it unto the number of months, which have passed from the beginning of March last passed, till the end of that month wherein you would know the same: and if the whole product amounteth not to thirty, mark how much it wanteth of thirty: and if it exceedeth thirty, see what it lacketh of sixty, and that which it wanteth either of thirty or sixty is the number of the days of such a month wherein the Conjunction happeneth.   

The fourth Rule of the full and quarters of the Moon.  
If the day of the Conjunction be before the 15 day of the month, add 15 unto the day of the Conjunction, and you shall find the day of the full Moon; and if the Conjunction happen after the 15 day, take away 15 from the number of the day of the Conjunction, and you shall have the full Moon of that month.  
The first quarter is seven days after the Conjunction, and the last quarter seven days after the full Moon.   

The fifth Rule of the Springtides and Neap-tides.  
Upon the day of the Conjunction, and of the full Moon, are the Springtides▪ and upon the two quarter days are the Neap-tides: and so much the more do the waters increase, as the Conjunction or full Moon are nearer: and so much the more they decrease also the nearer they come unto the quarters.   

An example whereby the foresaid Rules are made more plain.  
Suppose a fleet of Ships lie within the heaven of San Lucar de barrameda, expecting a fit time to pass over the bar towards the Indies. It is evident that if the Ships be great, they have need of much water to pass the bank, or the bar: which quantity of water is only in the Springtides. And because they are twice in one month, namely in the Conjunction, and in the full of the Moon, I desire to know when the Springtides and Neap-tides of the month of june in the year 1588. were to be expected, in which month I presuppose the fleet was to depart. First therefore I cast away 1500▪ and cut of the 88 remaining I take from each 20. One, which make four in all; which being added to the 8 that surmount 80. they make the golden number to be 12▪ according to the first Rule. I divide these twelve by three, and the quotient is four, and nothing remaineth and because there is no remainder, I will take two more of the concurrent th●n of the golden number, and there shall be two of the concurrent, casting away thirty; by the second Rule. Adding these two to the four months which are from the beginning of March passed till this present month of june, 
These days mentioned in this example, are to be understood according to the new Roman Gregorian Calendar, which goeth always ten days before ours used in England.  I find that they make six. And because six want twenty four to make up thirty, I say that in the year 1588., we had a Conjunction of the Moon upon the 24 of june, by the third Rule, and adding seven unto the day of this Conjunction, you have the first day of july, which is the day of the first quarter. And taking away 15 from 24 being the number of the Conjunction day▪ there remain nine, and upon that day of the month you have the full Moon. And adding other seven unto the nine days of the full Moon, you have the last quarter upon the sixteenth of june by the fourth Rule. I say therefore that the Springtides or greatest waters of the month of june, were in that year upon the ninth, and four and twentieth days of june; and the Neap-tides, or less waters were upon the sixteenth-day of june, and the first of july by the fifth Rule.    

CHAP. XXXII. Of the daily Tides.  
NOW that we know the Rules of the Springtides and neap-tides, let us say somewhat of the Tides that happen every day, which depend upon another swift motion of the Moon, whereby turning round about the world from East to West, it passeth every day by the 32 points of the Compass: and this daily motion of the Sea, falleth not every day at the same hour, because the Moon doth not always keep one and the same distance from the Sun. For the Moon moveth almost thirteen degrees of her proper motion in one natural day, whereas the Sun moveth scarce one: and so one being taken from thirteen, there remain 12. And because the Sun doth give, and mark out unto us hours, and the Moon Tides, it cometh to pass that an hour being that space of time wherein fifteen degrees of the Equinoctial pass by every point of the Compass, the part by which the Moon is distant from the Sun shall be twelve degrees, which twelve are ⅘ of fifteen degrees contained in each hour. Insomuch that the Moon by her middle motion is every day distant from the Sun about twelve degrees; which being reduced into time, do make ⅘ parts of an hour, whereby the Moon is every day slower than the Sun, in coming to each point of the Heavens by the motion from East to West, in regard of that which she hath borrowed for her own proper motion from West to East. Whereof it cometh to pass, that so many days as the Moon is old▪ so many times ⅘ parts of an hour it is slower than the Sun in passing by each Rumb, until the day of their conjunction, when as they pass both by the same Rumb, in one and the same hour. And so accordingly, because we are to set down the certain hour of every day wherein the Tide happeneth, we must diligently Observe the Rules following.  

The first Rule.  
In divers parts of the Sea coast, the Moon maketh a full Sea every day, being in divers Rumbs, according to the disposition of the Land. But upon all the coast of Spain in the Ocean, it is full Sea when the Moon is in the North-east and South-west.   

The second Rule.  
Upon the day of the conjunction and full Moon, you have a full Sea at three a clock in the morning, and at three in the after noon; for at those hours the Moon goeth with the Sun at the North-East and at the South-west. But upon other days of the Moon, the full Sea falleth out at the same hour when the Moon cometh to those two points; which is known by counting the age of the Moon.   

The third Rule.  
That you may know at all times how many days old the Moon is, you must add three numbers together; to wit▪ the concurrent, and the months from the beginning of March to the month present, and the days of the month wherein you would know this: and if the whole product exceedeth not thirty, it containeth just the days of the Moon; but if it doth exceed thirty, the surplusage showeth the days of the Moon's age.   

The fourth Rule.  
Multiply the days of the Moon's age by four, and divide the product by five, and the remainder after division containeth the hours whereby the Moon cometh more slowly than the Sun, to the North-east or South-west, or to that Rumb wherein it maketh a full Sea; which hours shall be added to the three hours of the morning, and then you have the hours of the first Tide or of the full and swelling Sea; and six hours and almost a quarter after, cometh the first ebb, or low water, and 12 hours and ⅕ after the first full Sea, cometh the second Tide: and other six hours and ⅕ after the second Tide, cometh the second ebb.   

The fifth Rule.  
When the days of the Moon's age are less than fifteen, we may make by them our account for the Tides: but if they exceed fifteen, we must make our account by the surplusage.   

An example of the said Rules▪  
Upon the 29 of July 1588., I desired to know the hours of the full Sea and of the ebb; to make choice of that which might seem most expedient for my Voyage. By the former example I find that the golden number of this year is 12 and the concurrent 2, according to the correction of the year by Pope Gregory the 13. Then I add this number of 2 to the number of 5 months, which have passed from the beginning of March, and the 29 days of the month of July, all which 3 numbers make 36; then I cast away 30, and there remain six days for the age of the Moon: and because they exceed not fifteen, I multiply them by ⅘ of an hour, according to the fourth Rule, and they may make 24/5 I divide these 24 by 5, and I find the quotient to be four, and the remainder four. And so I say that the Moon cometh to the North-east four hours and ⅘ later than the Sun. And because the Sun cometh to the North-east at three a clock in the morning, I add those 4 hours and ⅘ unto the 3 hours last mentioned, and they make seven hours and ⅘, which is the hour of the morning wherein the Tide or full Sea happeneth. And adding unto these seven hours and ⅘ other six hours and ⅕, they make in all fourteen hours, which falleth out at two a clock in the afternoon, which is the hour of the first low water or ebb. And adding unto the said hour of the full Sea twelve hours and ⅖, it will amount unto eight of the clock and ⅕ part of an hour, which is the hour of the night wherein the second Tide or high water was. And add unto this second Tide other six hours and ⅕, and they make two of the clock in the morning and ⅕, at which time there cometh the second ebb or low Sea.    

CHAP. XXXIII. Of a certain Instrument, whereby you may in general judge of the Tides.  
BEcause the Tides (it being supposed that in all places they proceed from the motion of the Moon) run not in every part of the world by one and the same Rumb, as it is manifest in the channel of Flanders, and in all the coasts of the Northern Sea, which is a matter of great confusion and difficulty to Mariners; I thought good here to set down an Instrument, whereby (the days of the Moon and the Rumb, whereupon the Moon causeth the Tide in every part, being known) they may judge of the ebb and flood with great facility.  
Draw upon a sheet of paper, or upon a plate of tinn, or any other matter, a circle as big as the palm of a man's hand, and half a finger's breadth; within that circle draw another circle; and having divided them both into 32 equal parts, with lines drawn from the centre to the circumference of the greater circle, upon the upper end of one of those lines, place a flowerdeluis, and the number of 12, and in the next line thereunto toward the left hand, set down 12 and ¾, and in the third line 1 ½, and so proceed forwards, putting down upon every line following ¾ of an hour more, until you come again to the number of 12 in the lowest line. And from thence forwards set down the same numbers that you did at the first.  
These 32 lines so drawn, do represent the 32 winds, whereby the Sun and Moon pass every day. And so you may set down the names of the principal Winds, to the end that you may know them, and those that are next them. And then in like manner make another round and slender Table, as big as the innermost circle of those two which you drew in the first Table: and dividing it into thirty equal parts, first into two by a line, dividing it in the midst, and then either of those two into three, and every of those three into five: these divisions will represent the days of the Moon. And leaving upon 1 of those parts an Index or small point, which may reach without the circle, set down the numbers thereof, beginning with 30 in that part where that point endeth, and the number of 1 in the line following towards the left hand, and then 2, etc. till you end at the same point with 30, This being done, fasten with a thread or nail, the second Table or Circle upon the centre of the first, so that it may freely without impediment turn round about.  

The use of this Instrument.  
The use of this Instrument is, that knowing in every Port or part of any coast, the Rumb or quarter on which the Moon maketh full Sea, or high water, you must note upon the outward Circle of the Winds that quarter or Rumb: and placing the tooth or point of the inner Circle were the number of 30 is upon that quarter or Rumb; make it there fast, putting a little wax underneath, that it may not move. Then account the days of the Moon's age in the inner Circle, and over against the end of your account you shall see in the uttermost Circle the hour of the full Sea of that day, together with the Rumb where the Sun is at that hour. And at the same hour when it is in the contrary part, it will make a full Sea. The place of the moon at the hour of the tide, is always either where the point is, or at the point right over against it, and hence you may easily find both ebbs also. This little Instrument, although it be but of small Invention, is of great use and profit for the Navigations of Flanders, France, England, Ireland, and all the Northern regions, where you have much variety in the tides.    

CHAP. XXXIIII. Of the making of an universal Dial, which may serve Generally all the World over.  
DRaw upon a Table or pastboord the Circle ABCD upon the centre E: and half a finger's breadth within that Circle, upon the same centre draw another Circle: and about the breadth of a wheat corn within the second Circle, draw a third; and placing your Ruler upon the centre E, by the right line AC divide the two inner Circles in the midst ABC, and CDA in the points BD, upon which, and upon the centre E the Ruler being placed, you may draw the line BD, whereby every one of the foresaid Circles shall be divided into four equal parts. And dividing every one of those four Quadrants of the inner Circle, to wit, AB, BC, CD▪ DAMN into 90 parts (as the manner is in the making of an Astrolabe) set numbers thereto from 5 to 5. beginning your account from the two points AC, and so proceeding both ways till you end your account in 90, at the points BD; and this inner Circle thus divided, representeth the Meridian.  
And the point C is the North, A the South, and the points B D are those where the Equinoctial cutteth the Meridian. Then count 23 degrees and an half from the point B to F, and to G on both sides. And so much account also from the point D to H and to I. And then drawing two right lines FH and GI', the line FH shall represent the Tropic of Cancer, and GI' the Tropic of Capricorn. And those two lines shall cut the line CA, (which is the Axtree of the World, and the Circle of six of the clock in the morning and evening) upon the points LM. Then count fifteen degrees from C towards B, and other fifteen from A towards B▪ and placing your Ruler on either side upon the end of your account, you shall cut the Equinoctial BD upon a certain point which shall represent unto you seven a clock in the morning▪ and five of the clock at evening. And counting other fifteen degrees on both sides, more towards the point B, and placing the Ruler as before, you shall cut the line BD in another point, which shall represent eight of the clock in the morning, and four in the afternoon. And accounting higher fifteen degrees more one both sides, and placing your Ruler upon the end of your account, it will divide the line BD at another point, which shall be nine a clock in the morning, and three in the afternoon; and so you shall proceed from fifteen to fifteen degrees, till you come to eleven of the clock in the morning, and one in the afternoon. And if you will have the half hours also, you must account from seven degrees and an half, to seven and an half; and doing as you did with the fifteenth degrees, you shall have the half hours also.  
Then placing your compasses upon the centre E, and upon every division of the line EBB you shall draw the same divisions likewise upon the line ED which being done, draw certain obscure lines from the point A to the divisions of the line EBB: and drawing the right line GF, see where GF is cut at the highest of the obscure lines, which must be at the point N, from whence the line NO is to be drawn equally distant from the line BE. And this line NO shall be divided proportionally by the obscure lines, even as the line BE. Then let the divisions of the line NO be transferred into the lines MG, MI, LF, LH, and then the Tropics also shall be divided. Then by every three points answerable in the Equinoctial, and the two Tropics, you shall draw certain parts of Circles, seeking the centre of those three points in the Equinoctial line extended forth on either side; and these parts of Circles represent the hours: then make an account of the degr. of Declination from the point B, and from D on both sides by every 2 degr. and draw lines Parallel to the Equinoctial from one to another; and those shall be the Parallels of the Sun's Declination. Moreover you shall make an Horizon as large as the Diameter of the inner Circle, which shall be divided after this manner: Count from the points AC towards B five degrees; and putting your Ruler upon the end of the account of both parts, see where it cutteth the line EBB, and there make a mark: and then counting on both sides other five degrees, and putting the Ruler once again at the end of your account, make another mark where it cutteth the line EBB. And so the line EBB must be divided from five to five degrees; which divisions shall be removed into the said Horizon, fastening it to the Centre, and laying it to the line BD, and dividing it both ways as the line EBB is divided; and set numbers thereinto from 5 to 5, which may begin in the midst, and end with 90 at the ends of the Horizon, and let every one of these parts be divided into five other parts or degrees. Then accounting from the Centre E in the Horizon eleven degrees and ¼▪ you shall set there a mark, which shall be the seventh point from North and South, that is, it shall represent the points which are next to the East and West in the Compass. And accounting another eleven degrees and a quarter, and making there a mark, it shall represent the sixth point from North and South And so you must do with the other points, and then your Instrument is finished.   

CHAP. XXXV. Of the parts of this Instrument.  
IN this Instrument, the first thing is a Circle divided into 360 degrees, which is the Meridian and the line of twelve a clock. The second are the right lines, of which that in the midst is the Equinoctial, and the two others are the Tropics of Cancer and Capricorn. And the other lines between those are the Parallels of the Sun's Declination▪ which have their numbers agreeable to them. And those that are between the Equinoctial, and the Tropic of Cancer, do serve from the 11 of March to the 13 of September, and the others for the residue of the year. The crooked lines which cross those Parallels are the hour lines. And the point of the Meridian, which in 90 degrees distant from the Equinoctial, towards the left hand, is the North Pole: and the point opposite to that, is the South Pole. In the Horizon there are first the degrees, and then the points of the Compass distinguished by the small pricked lines.   

CHAP. XXXVI. How you may know what a clock it is by this Instrument.  
AT any time of the day, when you would know what a clock it is, take the height of the Sun with your Astrolabe, and seeking the Table of the Sun's Declination what Declination it hath the same day, and the height of the Pole; which a good Mariner knoweth at all times, because he must direct his course thereby. This being known, place the Horizon Instrument on the one side under the North, and on the other side above the South, so many degrees as his distance from the Equinoctial is the same day: and fasten it there with a little wax that it may not move. Then count in the Meridian on either side from the Horizon (which now standeth firm) the height of the Sun above the Horizon, take with your Astrolabe: and by the end of the account, draw a line or thread overthwart, which shall be equally distant from the Horizon. Then reckon the Sun's Declination in the parallels, beginning from the Equinoctial of the Instrument that way which the Sun Declineth, and mark the line or Parallel at which the account of the Declination endeth; where and at what hour it is crossed by the thread, for that hour is the hour of the day. But note this, that if the crossing of the thread and Parallel do fall upon the division of the Parallel and of the hour, it is a just hour; but if it fall beside the common meeting of the Parallel and of the hour-line upon that side where it falleth, see how much more there is then an hour, whether ¼, or 1/●, or ½, etc. Now although every hour line hath two numbers, one of the morning and another of the afternoon, yet it is an easy matter to distinguish which of them will serve your turn, if you know whether your Observation be before high noon or after; which is to be known by your Astrolabe: for if the Sun ascend, it is before noon; but if it descend, it is afternoon.   

CHAP. XXXVII. Of the Variation of the Compass, by this Instrument.  
IF you would know by this Instrument the Variation of the Compass, you must do thus: When the Sun riseth or goeth down at the Horizon, Observe him with your Compass, noting very diligently upon what Rumb and part of the Rumb he riseth or falleth. And if the compass be divided into 360 parts, beginning to reckon them from the East and from the West on either side, and ending in the North and South with 90 degrees, it shall be the fitter for this purpose, because than you shall see the very degree of the Compass upon which the Sun riseth or setteth. Then the Horizon being set fast (as we have showed in the former chapter) mark in the Instrument by which part or degree of those upon the Horizon, the Parallel of the Sun's Declination that day doth cross the same: counting in the numbers of the Horizon from the centre towards the North Pole, if it be from the 11 of March to the 13 of September; or towards the South Pole, the other half of the year▪ And mark also whether this crossing be so many deg. distant from the division of the Equinoctial of your Instrument, as the Sun in his rising was distant from the East of the Compass, or at his going down was distant from the West thereof; for than you may say that the Compass hath no variation at all. But if it be not so, mark the Rules following.  
1 When the Sun riseth by the same Rumb of the Compass which the Instrument doth show, the Compass hath no variation at all.  
2 When the Sun riseth more to the North of the Compass, or goeth down more to the South, then is showed by the Instrument, all the difference between the Instrument and the Compass is the North-easting, or variation thereof to the Eastward.  
3 If the Sun riseth more to the South of the Compass, or seateth more to the North than the Instrument showeth, all the difference between the Instrument and the Compass is the North-westing, or Westerly variation thereof.   

CHAP. XXXVIII. At what hour the Sun riseth and setteth every day, in all parts of the world.  
THE height of the Pole in that part where you desire to know this, being known; place the Horizon in such sort as was showed in the 36 chapter. And finding by the Table of the Sun's Declinations the Declination which the Sun hath that day, count the same from the Equinoctial of the Instrument towards that part whither the Sun declineth among the Parallels, and then mark the Parallel whereat your account endeth, in what hour, and in what part of the hour it cutteth the Horizon; noting that every hour hath two numbers, one afternoon which is the hour of the Suns setting; and another before noon, which is that wherein the Sun riseth.   

CHAP. XXXIX. Of the length of the Day and of the Night.  
THe hour of the Suns going down being known, double it▪ and the double number of hours will show you the length of the day. Also the hour of the Suns rising being known, and doubled, will manifest unto you the length of the Night, in that part of the year when you desire to know the same.   

CHAP. XL. Of a Night-diall by the North.  
THAT being known which is before declared of the situation of the North Star and of the guards, we may easily know in the night what a clock it is, wheresoever we can see the North Stars: presupposing that upon the 15 of April at the very point of midnight, the former guard goeth a-head in respect of the North Star. And because by this account of the hour of the night, we must take for a beginning, the very instant when the former guard maketh midnight; the Rule following is to be Observed.  

The Rule▪  
The number of the whole months which have passed since the 15 of April forward being double, you have the number of the hour wherein the former guard maketh midnight, being head-most: and if the months fall not out just, add for every fifteen days, above the whole months, one day, and for every day four minutes, and you shall know when it is midnight.   

As for example.  
If I would know upon the 15 of November, where the former Guard maketh midnight, I account the whole months from the 15 of April, and I find them to be seven: which being doubled, make fourteen. I say therefore, that upon the 15 of November, it shall be midnight, when the former Guard hath passed before the North or head fourteen hours. And so allowing three to the Northwest, three to the West, and six to the foot, it may be said that the former Guard going two hours before the foot towards the South-west, that it is midnight, which shall come to pass when the former Guard goeth an hour before from the South-west. This being thus presupposed, when I would know in the night what a clock it is, I must note two things: the one is, in what part the former Guard maketh midnight the same night. The second is, in what part the said Guard is at the same instant, when I would know the time of the night; which being understood, I will make mine account from that which the Guard wanteth of being come to the place where that day it maketh midnight; or from so much as it hath passed the same place, making mine account that one third part of four points of the compass is an hour, and that which it wanteth of being come, or which it hath passed forward, are the hours before midnight, if it be not come to the place; or after midnight, if it have gone beyond.   

As for example.  
I see the former Guard in the Northwest upon the 15 of july; because that upon the 15 of july, by the account before mentioned, the former Guard maketh midnight in the West: and from the North or head to the West, are six hours; and from the Northwest, where I saw the Guard, to the West, where it maketh midnight are three hours; I say therefore that it is three hours before midnight; that is to say, nine of the clock at night.  
FINIS   

BEcause the Tables of the Sun's Declination that have been most in use amongst English Seamen, do both in fashion and manner of using something differ from those before set down, pag. 173, 174, etc. Lest any therefore of the meanner sort might be mistaken, or should not rightly conceive the manner of using these Tables; I thought good to adjoin these also here following, bearing in a manner the same form and shape, and therefore also to be used altogether almost in the same sort that those Tables have been, which for these many years have been most used by English Mariners.  
This Table of the Sun's Declination containeth twelve particular Tables, showing the Declinations of the Sun for every day of the twelve months of the year for four years together, from leap year to leap year. In the head of every one of these Tables is first set down the month for which that Table is made. Under this are placed the years of our Lord, for which those Tables may serve: which years are divided into four ranks, signified by the four Arithmetical characters 1, 2, 3, 4, that are set over them. The first rank containeth the first years immediately following after the leap year: the next rank containeth the second years after the leap year: in the third rank are set down the years that follow three years after the leap year: and in the fourth and last rank are the fourth years after the precedent leap years, which are also leap years themselves.  
Under every one of these ranks of years there are two columns; the first whereof containeth the degrees and min. of the Sun's Declination, answerable to every day of the month, superscribed in each of those years, without sensible error. In the second column are set down the minutes of the differences of the Sun's Declinations for every one of those days, for the readier finding of the part proportional of this difference, answering to any difference of Longitude from London, whereof you may read more pag. 181, etc. In the first column of each of these Tables next the left hand are placed the numbers of the days of the month that is set down in the head thereof. The use of this Table for knowing the Declination of the Sun at any time is thus: 
The use of this Table.  look the month and year wherein you would know the same in the head of the Table, and the day of the month in the first column next the left hand; then proceeding from that day directly in the same line towards the right hand till you come right under the same year, you shall there find the Declination you sought for.  
Take for example the 24 day of February in the year 1610. Finding therefore that month and year in the head of the Table, and the 24 day in the first column; in the same line proceeding towards the right hand, till you come right under that year, you have there the Sun's Declination for that time 5 degrees 34 minutes towards the South.  

January   1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 deg. mi. di. deg. mi. di. deg. mi. di. deg. mi. di 1 21 47  21 50  21 52  21 54  2 21 37 10 21 40 10 21 42 10 21 45 9 3 21 27 10 21 30 10 21 32 10 21 35 10 4 21 17 10 21 19 11 21 22 10 21 24 11 5 21 6 11 21 8 11 21 11 11 21 13 11 6 20 54 12 20 57 11 21 0 11 21 2 11 7 20 42 12 20 45 12 20 48 12 20 51 11 8 20 30 12 20 33 12 20 36 12 20 39 12 9 20 17 13 20 20 13 20 23 13 20 26 13 10 20 4 13 20 7 13 20 10 13 20 13 13 11 19 50 14 19 54 13 19 57 13 20 0 13 12 19 36 14 19 40 14 19 43 14 19 47 13 13 19 22 14 19 26 14 19 29 14 19 33 14 14 19 8 14 19 11 15 19 15 14 19 18 15 15 18 53 15 18 56 15 19 0 15 19 4 14 16 18 38 15 18 41 15 18 45 15 18 49 15 17 18 22 16 18 26 15 18 30 15 18 33 16 18 18 6 16 18 10 16 18 14 16 18 18 15 19 17 50 16 17 54 16 17 58 16 18 2 16 20 17 33 17 17 37 17 17 41 17 17 45 17 21 17 16 17 17 21 16 17 25 16 17 29 16 22 16 59 17 17 4 17 17 8 17 17 12 17 23 16 42 17 16 46 18 16 50 18 16 55 17 24 16 24 18 16 29 17 16 33 17 16 37 18 25 16 6 18 16 11 18 16 15 18 16 19 18 26 15 48 18 15 52 19 15 57 18 16 1 18 27 15 29 19 15 34 18 15 38 19 15 43 18 28 15 10 19 15 15 19 15 20 18 15 24 19 29 14 51 19 14 56 19 15 1 19 15 5 19 30 14 32 19 14 37 19 14 41 20 14 46 19 31 14 13 19 14 17 20 14 22 19 14 27 19 
February   1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 deg. mi. di. deg mi. di. deg. mi. di. deg. mi. di. 1 13 53  13 58  14 2  14 7  2 13 33 20 13 38 20 13 42 20 13 47 20 3 13 12 21 13 17 21 13 22 20 13 27 20 4 12 52 20 12 57 20 13 2 20 13 6 21 5 12 31 21 12 36 21 12 41 21 12 46 20 6 12 10 21 12 16 20 12 21 20 12 26 20 7 11 49 21 11 55 21 12 0 21 12 5 21 8 11 28 21 11 33 22 11 38 22 11 44 21 9 11 7 21 11 12 21 11 17 21 11 22 22 10 10 45 22 10 50 22 10 56 21 11 1 21 11 10 23 22 10 28 22 10 34 22 10 39 22 12 10 1 22 10 7 21 10 12 22 10 17 22 13 9 39 22 9 45 22 9 50 22 9 55 22 14 9 17 22 9 23 22 9 28 22 9 33 22 15 8 55 22 9 0 23 9 6 22 9 11 22 16 8 32 23 8 38 22 8 43 23 8 49 22 17 8 10 22 8 15 23 8 21 22 8 26 23 18 7 47 23 7 53 22 7 58 23 8 4 22 19 7 24 23 7 30 23 7 35 23 7 41 23 20 7 1 23 7 7 23 7 12 23 7 18 23 21 6 38 23 6 44 23 6 49 23 6 55 23 22 6 15 23 6 21 23 6 26 23 6 32 23 23 5 52 23 5 58 23 6 3 23 6 9 23 24 5 29 23 5 34 24 5 40 23 5 46 23 25 5 5 24 5 11 23 5 17 23 5 22 24 26 4 42 23 4 48 23 4 53 24 4 59 23 27 4 18 24 4 24 24 4 30 23 4 36 23 28 3 55 23 4 1 23 4 6 24 4 12 24 29          3 49 23 
March   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di Deg. M di. De. mi. di. Deg. M di 1 3 31  3 37  3 43  3 23  2 3 8 23 3 13 24 3 19 24 3 1 24 3 2 44 24 2 50 23 2 56 23 2 37 24 4 2 20 24 2 26 24 2 32 24 2 14 23 5 1 57 23 2 3 23 2 8 24 1 50 24 6 1 33 24 1 39 24 1 45 23 1 27 23 7 1 9 24 1 15 24 1 21 24 1 3 24 8 0 46 23 0 51 24 0 57 24 0 39 24 9 0 22 24 0 28 23 0 33 24 0 15 24    24 0 4 24 0 10 23   23 
Equinoctal  10 0 2 23   24   24 0 8 24 11 0 25 24 0 20 23 0 14 24 0 32 24 12 0 49 24 0 43 24 0 38 23 0 56 23 13 1 13 23 1 7 24 1 1 24 1 19 24 14 1 36 24 1 31 23 1 25 24 1 43 23 15 2 0 24 1 54 24 1 49 23 2 6 24 16 2 24 23 2 18 23 2 12 24 2 30 23 17 2 47 23 2 41 24 2 36 23 2 53 24 18 3 10 24 3 5 23 2 59 23 3 17 23 19 3 34 23 3 28 23 3 22 24 3 40 23 20 3 57 23 3 51 24 3 46 23 4 3 24 21 4 20 23 4 15 23 4 9 23 4 27 23 22 4 43 23 4 38 23 4 32 23 4 50 23 23 5 6 23 5 1 23 4 55 23 5 13 23 24 5 29 23 5 24 23 5 18 23 5 36 23 25 5 52 23 5 47 23 5 41 23 5 59 22 26 6 15 23 6 10 22 6 4 23 6 21 23 27 6 38 22 6 32 23 6 27 22 6 44 22 28 7 0 23 6 55 22 6 49 23 7 6 23 29 7 23 22 7 17 23 7 12 22 7 29 22 30 7 45 22 7 40 22 7 34 22 7 51 22 31 8 7  8 2  7 56  8 13  
April.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di deg. mi. d. deg. mi. di deg. mi. di 1 8 29  8 24  8 18  8 35  2 8 51 22 8 46 22 8 40 22 8 57 22 3 9 13 22 9 8 22 9 2 22 9 19 22 4 9 34 21 9 29 21 9 24 22 9 40 21 5 9 56 22 9 51 22 9 46 22 10 2 22 6 10 17 21 10 12 21 10 7 21 10 23 21 7 10 38 21 10 33 21 10 28 21 10 44 21 8 10 59 21 10 54 21 10 49 21 11 5 21 9 11 20 21 11 15 21 11 10 21 11 26 21 10 11 41 21 11 36 21 11 31 21 11 46 20 11 12 1 20 11 56 20 11 51 20 12 6 20 12 12 21 20 12 16 20 12 11 20 12 26 20 13 12 41 20 12 36 20 12 31 20 12 46 20 14 13 1 20 12 56 20 12 51 20 13 6 20 15 13 20 19 13 16 20 13 10 19 13 26 20 16 13 40 20 13 35 19 13 30 20 13 45 19 17 13 59 19 13 54 19 13 50 20 14 4 19 18 14 18 19 14 13 19 14 9 19 14 23 19 19 14 36 18 14 32 19 14 27 18 14 41 18 20 14 55 19 14 50 18 14 46 19 15 0 19 21 15 13 18 15 9 19 15 4 18 15 18 18 22 15 31 18 15 27 18 15 22 18 15 36 18 23 15 49 18 15 44 17 15 40 18 15 53 17 24 16 6 17 16 2 18 15 58 18 16 11 18 25 16 23 17 16 19 17 16 15 17 16 28 17 26 16 40 17 16 36 17 16 32 17 16 45 17 27 16 57 17 16 53 17 16 49 17 17 1 16 28 17 13 16 17 9 16 17 5 16 17 17 16 29 17 29 16 17 25 16 17 21 16 17 33 16 30 17 45 16 17 41 16 17 37 16 17 49 16 
May.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di degr. mi di▪ degr. mi di degr. mi di. 1 18 0  17 57  17 53  18 4  2 18 15 15 18 12 15 18 8 15 18 19 15 3 18 30 15 18 27 15 18 23 15 18 34 15 4 18 45 15 18 41 14 18 38 15 18 49 15 5 18 59 14 18 56 15 18 52 14 19 3 14 6 19 13 14 19 10 14 19 6 14 19 17 14 7 19 27 14 19 23 13 19 20 14 19 30 13 8 19 40 13 19 37 14 19 34 14 19 43 13 9 19 53 13 19 50 13 19 47 13 19 56 13 10 20 5 12 20 2 12 19 59 12 20 9 13 11 20 18 13 20 15 13 20 12 13 20 21 12 12 20 30 12 20 27 12 20 24 12 20 33 12 13 20 41 11 20 38 11 20 36 12 20 44 11 14 20 52 11 20 50 12 20 47 11 20 55 11 15 21 3 11 21 1 11 20 58 11 21 6 11 16 21 14 11 21 11 10 21 9 11 21 17 11 17 21 24 10 21 22 11 21 19 10 21 27 10 18 21 34 10 21 32 10 21 29 10 21 36 9 19 21 43 9 21 41 9 21 39 10 21 46 10 20 21 52 9 21 50 9 21 48 9 21 55 9 21 22 1 9 21 59 9 21 57 9 22 3 8 22 22 9 8 22 7 8 22 5 8 22 11 8 23 22 17 8 22 15 8 22 13 8 22 19 8 24 22 25 8 22 23 8 22 21 8 22 27 8 25 22 32 7 22 30 7 22 28 7 22 34 7 26 22 38 6 22 37 7 22 35 7 22 40 6 27 22 45 7 22 43 6 22 42 7 22 46 6 28 22 51 6 22 49 6 22 48 6 22 52 6 29 22 56 5 22 55 6 22 54 6 22 58 6 30 23 1 5 23 0 5 22 59 5 23 3 5 31 23 6 5 23 5 5 23 4 5 23 8 5 
June.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di. degr. mi di degr. mi di. degr. mi di. 1 23 10  23 10  23 8  23 12  2 23 14 4 23 14 4 23 12 4 23 16 4 3 23 18 4 23 17 3 23 16 4 23 19 3 4 23 21 3 23 20 3 23 20 4 23 22 3 5 23 24 3 23 23 3 23 23 3 23 25 3 6 23 26 2 23 26 3 23 25 2 23 27 2 7 23 28 2 23 28 2 23 27 2 23 29 2 ● 23 30 2 23 29 1 23 29 2 23 30 1 9 23 31 1 23 30 1 23 30 1 23 31 1 10 23 31 0 23 31 1 23 31 1 23 31 0 11 23 31 0 23 31 0 23 31 0 23 31 0 12 23 31 0 23 31 0 23 31 0 23 31 0 13 23 31 0 23 31 0 23 31 0 23 30 1 14 23 30 1 23 30 1 23 30 1 23 29 1 15 23 28 2 23 29 1 23 29 1 23 28 ● 16 23 26 2 23 27 2 23 27 2 23 26 2 ●● 23 24  23 25 2 23 25 2 23 24 2 ●8 23 21 3 23 22 3 23 23 2 23 21 3 19 23 18 3 23 19 3 23 20 3 23 18 3 20 23 15 3 23 16 3 23 17 3 23 ●4 4 21 23 11 4 23 12 4 23 13 4 23 10 4 22 23 7 4 23 8 4 23 9 4 23 6 4 23 23 2 5 23 4 4 23 5 4 23 1 5 2● 22 57 5 22 59 5 23 0 5 22 56 5 25 22 52 5 22 53 6 22 55 5 22 50 6 26 22 46 6 22 48 5 22 49 6 22 44 6 27 22 40 6 22 41 7 22 43 6 22 38 6 ●8 22 33 7 22 35 6 22 36 7 22 31 7 ●9 22 26  22 28 7 22 29 7 22 24 7 ●0 22 19  22 21 7 22 22 7 22 1● 7 
July.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr mi di degr. mi di degr, m. di degr. mi di. 1 22 11  22 13  22 15  22 9  2 22 3 8 22 5 8 22 7 8 22 0 9 3 21 54 9 21 56 9 21 58 9 21 52 8 4 21 45 9 21 47 9 21 50 8 21 43 9 5 21 36 9 21 38 9 21 41 9 21 33 10 6 21 26 10 21 29 9 21 31 10 21 24 9 7 21 16 10 21 19 10 21 21 10 21 13 11 8 21 6 10 21 8 11 21 11 10 21 3 10 9 20 55 11 20 58 10 21 0 11 20 52 11 10 20 44 11 20 47 11 20 49 11 20 41 11 11 20 33 11 20 35 12 20 38 11 20 29 12 12 20 21 12 20 24 11 20 27 11 20 17 12 13 20 9 12 20 12 12 20 15 12 20 5 12 14 19 56 13 19 59 13 20 2 13 19 53 12 15 19 43 13 19 46 13 19 50 12 19 40 13 16 19 30 13 19 33 13 19 37 13 19 27 13 17 19 17 13 19 20 13 19 23 14 19 13 14 18 19 3 14 19 6 14 19 10 13 18 59 14 19 18 49 14 18 52 14 18 56 14 18 45 14 20 18 34 15 18 38 14 18 41 15 18 30 15 21 18 20 14 18 23 15 18 27 14 18 16 14 22 18 5 15 18 8 15 18 12 15 18 1 15 23 17 49 16 17 53 15 17 57 15 17 45 16 24 17 34 15 17 38 15 17 41 16 17 30 15 25 17 18 16 17 22 16 17 26 15 17 14 16 26 17 2 16 17 6 16 17 10 16 16 57 17 27 16 45 17 16 49 17 16 53 17 16 41 16 28 16 29 16 16 33 16 16 37 16 16 24 17 29 16 12 17 16 16 17 16 20 17 16 7 17 30 15 54 18 15 59 17 16 3 17 15 50 17 31 15 37 17 15 41 18 15 4● 18 15 3● 18 
August.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di. degr. mi di degr. mi di▪ degr. mi di. 1 15 19  15 24  15 28  15 14  2 15 1 18 15 6 18 15 10 18 14 56 18 3 14 43 18 14 47 19 14 52 18 14 38 18 4 14 24 19 14 29 18 14 33 19 14 19 19 5 14 6 18 14 10 19 14 15 18 14 1 18 6 13 47 19 13 51 19 13 56 19 13 42 19 7 13 28 19 13 32 19 13 37 19 13 22 20 8 13 8 20 13 13 19 13 18 19 13 ● 19 9 12 49 19 12 54 19 12 58 20 12 43 20 10 12 29 20 12 34 20 12 39 21 12 24 19 11 12 9 20 12 14 20 12 19 20 12 4 20 12 11 48 21 11 54 20 11 59 20 11 43 21 13 11 28 20 11 33 21 11 38 21 11 23 20 14 11 8 20 11 13 20 11 18 20 11 2 21 15 10 47 21 10 52 21 10 57 21 10 41 21 16 10 26 21 10 31 21 10 36 21 10 20 21 17 10 5 21 10 10 21 10 15 21 9 59 21 18 9 44 21 9 49 21 9 54 21 9 38 21 19 9 23 21 9 28 21 9 33 21 9 17 21 20 9 1 22 9 6 22 9 12 21 8 55 22 21 8 39 22 8 45 21 8 50 22 8 33 22 22 8 18 21 8 23 22 8 28 22 8 11 22 23 7 56 22 8 1 22 8 6 22 7 49 22 24 7 34 22 7 39 22 7 44 22 7 27 22 25 7 11 23 7 17 22 7 22 22 7 5 22 26 6 49 22 6 54 23 7 0 22 6 43 22 27 6 26 23 6 32 22 6 37 23 6 20 23 28 6 4 22 6 9 23 6 15 22 5 58 22 29 5 41 23 5 47 22 5 52 23 5 35 23 30 5 19 22 5 24 23 5 30 22 5 12 23 31 4 56 23 5 1 23 5 7 23 4 49 23 
September.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di. degr. mi di degr. mi di. degr. mi di 1 4 33  4 38  4 44  4 26  2 4 10 23 4 15 23 4 21 23 4 3 23 3 3 47 23 3 52 23 3 58 23 3 40 23 4 3 24 23 3 29 23 3 35 23 3 17 23 5 3 0 24 3 6 23 3 12 23 2 54 23 6 2 37 23 2 43 23 2 48 24 2 31 23 7 2 14 23 2 19 24 2 25 23 2 7 24 8 1 50 24 1 56 23 2 2 23 1 44 23 9 1 27 23 1 33 23 1 38 24 1 20 24 10 1 3 24 1 9 24 1 15 23 0 57 23 11 0 40 23 0 46 23 0 51 24 0 34 23 12 0 16 24 0 22 24 0 28 23 0 10 24 — — — 23 — — 23 0 4 24 — — 24 13 0 7 24 0 1 24 — — 23 0 14 23 
Equinoctial.  14 0 31 23 0 25 23 0 19 24 0 37 24 15 0 54 24 0 48 24 0 43 23 1 1 23 16 1 18 23 1 12 24 1 6 24 1 24 24 17 1 41 24 1 36 23 1 30 23 1 48 23 18 2 5 23 1 59 24 1 53 24 2 11 24 19 2 28 24 2 23 23 2 17 23 2 35 23 20 2 52 23 2 46 24 2 40 24 2 58 24 21 3 15 24 3 10 23 3 4 23 3 22 23 22 3 39 23 3 33 23 3 27 24 3 45 23 23 4 2 23 3 56 24 3 51 23 4 8 24 24 4 25 24 4 20 23 4 14 23 4 32 23 25 4 49 23 4 43 23 4 37 24 4 55 23 26 5 12 23 5 6 24 5 1 23 5 18 23 27 5 35 23 5 30 23 5 24 23 5 41 24 28 5 58 23 5 53 23 5 47 23 6 5 23 29 6 21 23 6 16 23 6 10 23 6 28 23 30 6 44  6 39  6 33  6 51  
October.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di. degr. mi di. degr. mi di. degr. mi di 1 7 7  7 1  6 56  7 13  2 7 30 23 7 24 23 7 19 23 7 36 23 3 7 52 22 7 47 23 7 41 22 7 59 23 4 8 15 23 8 9 22 8 4 23 8 21 22 5 8 37 22 8 32 23 8 27 23 8 43 22 6 9 0 23 8 54 22 8 49 22 9 6 23 7 9 22 22 9 16 22 9 11 22 9 28 22 8 9 44 22 9 38 22 9 33 22 9 50 22 9 10 6 22 10 0 22 9 55 22 10 12 22 10 10 27 21 10 22 22 10 17 22 10 33 21 11 10 49 22 10 44 22 10 39 22 10 55 22 12 11 11 22 11 5 21 11 0 21 11 16 21 13 11 32 21 11 27 22 11 21 21 11 38 22 14 11 53 21 11 48 21 11 43 22 11 59 21 15 12 14 21 12 9 21 12 4 21 12 19 20 16 12 34 20 12 29 20 12 24 20 12 40 21 17 12 55 21 12 50 21 12 45 21 13 1 21 18 13 15 20 13 10 20 13 5 20 13 21 20 19 13 35 20 13 30 20 13 26 21 13 41 20 20 13 55 20 13 50 20 13 46 20 14 1 20 21 14 15 20 14 10 20 14 5 19 14 20 19 22 14 34 19 14 30 20 14 25 20 14 40 20 23 14 54 20 14 49 19 14 44 19 14 59 19 24 15 13 19 15 8 19 15 3 19 15 18 19 25 15 31 18 15 27 19 15 22 19 15 36 18 26 15 50 19 15 45 18 15 41 19 15 55 19 27 16 8 18 16 3 18 15 59 18 16 13 18 28 16 26 18 16 21 18 16 17 18 16 31 18 29 16 43 17 16 39 18 16 35 18 16 48 17 30 17 1 18 16 57 18 16 52 17 17 5 17 31 17 18 17 17 14 17 17 10 18 17 22 17 
November.   1 2 3 4 Day. 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 degr. mi di. degr. mi di. degr. mi di. degr. mi di. 1 17 35  17 31  17 26  17 39  2 17 51 16 17 47 16 17 43 17 17 55 16 3 18 7 16 18 3 16 17 59 16 18 11 16 4 18 23 16 18 19 16 18 15 16 18 27 16 5 18 39 16 18 35 16 18 31 16 18 43 16 6 18 54 15 18 50 15 18 46 15 18 58 15 7 19 9 15 19 5 15 19 1 15 19 13 15 8 19 23 14 19 19 14 19 16 15 19 27 14 9 19 37 14 19 34 15 19 30 14 19 41 14 10 19 51 14 19 47 13 19 44 14 19 55 14 11 20 4 13 20 1 14 19 58 14 20 8 13 12 20 17 13 20 14 13 20 11 ●3 20 21 13 13 20 30 13 20 27 13 20 24 ●3 20 34 13 14 20 42 12 20 39 12 20 36 12 20 45 12 15 20 54 12 20 51 12 20 48 12 20 57 12 16 21 6 12 21 3 12 21 0 12 21 8 11 17 21 17 11 21 14 11 21 11 11 21 19  18 21 27 10 21 25 11 21 22 11 21 30 1● 19 21 38 11 21 35 10 21 33 11 21 40 10 20 21 47 9 21 45 10 21 43 0 21 50 10 21 21 57 10 21 55 10 21 53 10 21 59 9 22 22 6 9 22 4 9 22 2 9 22 8 9 23 22 14 8 22 12 8 22 11 9 22 17 9 24 22 23 9 22 21 9 22 19 8 22 25 8 25 22 30 7 22 29 8 22 27 8 22 33 8 26 22 38 8 22 36 7 22 34 7 22 40 7 27 22 44 6 22 43 7 22 41 7 22 47 7 28 22 51 7 22 49 6 22 48 7 22 5 6 29 22 56 5 22 55 6 22 54 6 22 59  30 23 2 6 23 1 6 23 0 6 23 4 5 
December.   1 2 3 4 Day 1609 1610 1611 1612 1613 1614 1615 1616 1617. 1618. 1619 1620 deg. mi. di. deg. mi. di. deg. mi. di. degr. mi di 1 23 7  23 6  23 5  23 8  2 23 12 5 23 11 5 23 10 5 23 13 5 3 23 16 4 23 15 4 23 14 4 23 17 4 4 23 20 4 23 19 4 23 18 4 23 20 3 5 23 23 3 23 22 3 23 21 3 23 23 3 6 23 25 2 23 25 3 23 24 3 23 26 3 7 23 27 2 23 27 2 23 26 2 23 28 2 8 23 29 2 23 29 2 23 28 2 23 30 2 9 23 30 1 23 30 1 23 30 2 23 31 1 10 23 31 1 23 31 1 23 31 1 23 31 0 11 23 31 0 23 31 0 23 31 0 23 31 0 12 23 31 0 23 31 0 23 31 0 23 31 0 13 23 31 0 23 31 0 23 31 0 23 30 1 14 23 30 1 23 30 1 23 30 1 23 29 1 15 23 28 2 23 28 2 23 29 1 23 27 2 16 23 26 2 23 26 2 23 27 2 23 25 2 17 23 23 3 23 24 2 23 25 2 23 22 3 18 23 20 3 23 21 3 23 22 3 23 19 3 19 23 17 3 23 18 3 23 19 3 23 16 3 20 23 13 4 23 14 4 23 15 4 23 12 4 21 23 8 5 23 10 4 23 11 4 23 7 5 22 23 3 5 23 5 5 23 6 5 23 2 5 23 22 58 5 23 0 5 23 1 5 22 57 5 24 22 52 6 22 54 6 22 55 6 22 51 6 25 22 46 6 22 48 6 22 49 6 22 44 7 26 22 39 7 22 41 7 22 43 6 22 37 7 27 22 32 7 22 34 7 22 36 7 22 30 7 28 22 25 7 22 26 8 22 29 7 22 22 8 29 22 17 8 22 18 8 22 21 8 22 14 8 30 22 8 9 22 10 8 22 13 8 22 6 8 31 21 59 9 22 1 9 22 4 9 21 57 9   

By the height of the Polestar to know the height of the Pole.  
THe Tables following are calculated for the end of the year 1610. serving without sensible error for many years to come; they show the height of the Pole for convenient Latitudes, by the height of the Pole star and the help of the Guards, in eight several positions: so that you may by help of them, in any place on the North side of the Equator, to the Latiude of 74 degrees, or further, once in three hours every clear night, make a good Observation of the Latitude. In the three last positions, if the height of the Pole be but little, the Guards will be hid under the Horizon: notwithstanding if by the hour of the night, or the height of any known star, by the help of a Globe, or Astrolabe, we know when the stars do come to their due position, we may Observe the Pole star, and find the height of the Pole near as well, as if they were above the Horizon. The Positions are carefully to be Observed, that the two stars mentioned in the head of the Table be either in the same Azimuth one directly over another (which is known, if looking with the one eye only, a perpendicular cord will hide or cover them both) or else of the same Altitude above the Horizon, which is discerned by the cross-staff. At that instant that any such Position shall happen, take the height of the Pole star; and the Table answerable to that Position shall give you the height of the Pole.  
For example; when the greater Guard is directly under the Pole star, I find the height of the Pole star to be 47 degrees and twenty minutes: I look in the seventh Table and find the height of the Pole for 47, to be 44 degrees, 36 minutes: to this I add 20 minutes, because the height of the star is 20 minutes above 47. then is the height of the Pole 44 degrees 56 min. the seconds may safely be neglected, though they be inserted in the Table, rather for satisfaction of the reader, in the certainty of the Calculation, then for any necessary use.  
If when the greater Guard is in the East, of equal height with the Pole star, I find the height of that star to be 75 degrees, 40 minutes. In the first Table I find the height of the Pole answering to 75 deg. to be 77 deg. 26 min. and the difference one degree, three minutes: the part proportional whereof for 40 minutes, is 42 min. which added to 77 degrees, 26 min. maketh the true Elevation of the Pole 78 degrees. 8 minutes.  
Where the height of the Pole star is but little, there you must subduct the refraction from the height observed: otherwise we shall always find the height more than in truth it is, this Refraction causeth the Observations of the Sun at the South, and at the North, (when the Sun never setteth in Northern climates) to give several Latitudes in the same place, the Observation at the North always making the latitude too great. Concerning this Refraction, see page 97.  

When the greater guard is in the same height with the Pole Star.  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Deg. deg. mi. se. Deg. degr. mi. sec Degr degr. mi. sec 1 2 26 49 28 29 35 46 55 56 50 52 2 3 27 8 29 30 36 9 56 57 51 46 3 4 27 26 30 31 36 33 57 58 52 42 4 5 27 44 31 32 36 57 58 59 53 41 5 6 28 2 32 33 37 22 59 60 54 44 6 7 28 21 33 34 37 47 60 61 55 50 7 8 28 40 34 35 38 13 61 62 57 0 8 9 28 58 35 36 38 39 62 63 58 14 9 10 29 17 36 37 39 6 63 64 59 33 10 11 29 36 37 38 39 34 64 66 0 58 11 12 29 55 38 39 40 3 65 67 2 28 12 13 30 14 39 40 40 31 66 68 4 3 13 14 30 33 40 41 41 1 67 69 5 46 14 15 30 53 41 42 41 32 68 70 7 38 15 16 31 12 42 43 42 3 69 71 9 40 16 17 31 32 43 44 42 36 70 72 11 13 17 18 31 52 44 45 43 9 71 73 14 20 18 19 32 11 45 46 43 44 72 74 17 0 19 20 32 32 46 47 44 20 73 75 19 54 20 21 32 52 47 48 44 57 74 76 23 0 21 22 33 13 48 49 45 36 75 77 26 19 22 23 33 34 49 50 46 15 76 78 29 51 23 24 33 55 50 51 46 57 77 79 33 36 24 25 34 17 51 52 47 40 78 80 37 36 25 26 34 38 52 53 48 25 79 81 41 49 26 27 35 1 53 54 49 12 80 82 46 17 27 28 35 23 54 55 50 1     
When the two guards are of equal height betwixt the East and the highest.  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Degr degr. mi. sec. Degr degr. mi. sec Deg. degr. mi. sec 1 3 46 20 28 30 46 37 55 57 42 26 2 4 46 23 29 31 46 36 56 58 41 57 3 5 46 25 30 32 46 33 57 59 41 26 4 6 46 27 31 33 46 31 58 60 40 51 5 7 46 29 32 34 46 29 59 61 40 11 6 8 46 31 33 35 46 26 60 62 39 26 7 9 46 32 34 36 46 22 61 63 38 36 8 10 46 34 35 37 46 19 62 64 37 39 9 11 46 36 36 38 46 15 63 65 36 34 10 12 46 37 37 39 46 10 64 66 35 19 11 13 46 38 38 40 46 5 65 67 33 53 12 14 46 39 39 41 46 0 66 68 32 14 13 15 46 40 40 42 45 54 67 69 30 19 14 16 46 41 41 43 45 47 68 70 28 3 15 17 46 42 42 44 45 40 69 71 25 21 16 18 46 43 43 45 45 32 70 72 22 7 17 19 46 43 44 46 45 23 71 73 18 13 18 20 46 43 45 47 45 14 72 74 13 30 19 21 46 43 46 48 45 3 73 75 7 36 20 22 46 43 47 49 44 52 74 76 0 4 21 23 46 44 48 50 44 39 75 76 50 17 22 24 46 43 49 51 44 25 76 77 36 46 23 25 46 43 50 52 44 10 77 78 17 2 24 26 46 42 51 53 43 53 78 78 47 20 25 27 46 41 52 54 43 35 79    26 28 46 40 53 55 43 14 80    27 29 46 39 54 56 42 51 81    
When the greatest guard is directly above the Pole Star.  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Degr degr. mi. sec Deg. degr. mi. sec Deg. degr. mi. sec 1 3 22 29 28 30 21 55 55 57 20 51 2 4 22 28 29 31 21 53 56 58 20 47 3 5 22 27 30 32 21 52 57 59 20 43 4 6 22 26 31 33 21 50 58 60 20 38 5 7 22 25 32 34 21 48 59 61 20 34 6 8 22 23 33 35 21 47 60 62 20 28 7 9 22 22 34 36 21 45 61 63 20 23 8 10 22 21 35 37 21 43 62 64 20 17 9 11 22 20 36 38 21 41 63 65 20 11 10 12 22 19 37 39 21 39 64 66 20 4 11 13 22 17 38 40 21 38 65 67 19 57 12 14 22 16 39 41 21 36 66 68 19 48 13 15 22 15 40 42 21 33 67 69 19 40 14 16 22 14 41 43 21 31 68 70 19 30 15 17 22 13 42 44 21 29 69 71 19 20 16 18 22 11 43 45 21 27 70 72 19 8 17 19 22 10 44 46 21 25 71 73 18 55 18 20 22 9 45 47 21 22 72 74 18 40 19 21 22 7 46 48 21 20 73 75 18 23 20 22 22 6 47 49 21 17 74 76 18 4 21 23 22 5 48 50 21 14 75 77 17 42 22 24 22 3 49 51 21 11     23 25 22 2 50 52 21 8     24 26 22 1 51 53 21 5     25 27 21 59 52 54 21 2     26 28 21 58 53 55 20 59     27 29 21 56 54 56 20 55     
When the two guards are directly one over another betwixt the highest and the West,  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole, Degr degr. mi. sec Deg. degr. mi. sec Deg. degr. mi. sec. 1 1 20 22 28 28 38 3 55 56 8 51 2 2 20 58 29 29 38 50 56 57 10 44 3 3 21 34 30 30 39 37 57 58 12 43 4 4 22 11 31 31 40 25 58 59 14 49 5 5 22 47 32 32 41 15 59 60 17 2 6 6 23 23 33 33 42 5 60 61 19 23 7 7 24 0 34 34 42 57 61 62 21 53 8 8 24 37 35 35 43 50 62 63 24 34 9 9 25 13 36 36 44 44 63 64 27 25 10 10 25 50 37 37 45 40 64 65 30 30 11 11 26 28 38 38 46 37 65 66 33 48 12 12 27 5 39 39 47 35 66 67 37 23 13 13 27 43 40 40 48 36 67 68 41 16 14 14 28 21 41 41 49 38 68 69 45 30 15 15 29 0 42 42 50 42 69 70 50 7 16 16 29 38 43 43 51 48 70 71 55 13 17 17 30 18 44 44 52 56 71 73 0 52 18 18 30 57 45 45 54 7 72 74 7 9 19 19 31 37 46 46 55 20 73 75 14 8 20 20 32 18 47 47 56 36 74 76 21 52 21 21 32 59 48 48 57 55     22 22 33 40 49 49 59 17     23 23 34 22 50 51 0 43     24 24 35 5 51 52 2 12     25 25 35 48 52 53 3 45     26 26 36 33 53 54 5 22     27 27 37 17 54 55 7 4     
When the greater guard is in the West, of the same height with the Pole Star.  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Deg. degr. mi. sec. Degr degr. mi. sec Deg. degr. mi. sec 2 0 34 7 29 27 43 27 56 55 0 53 3 1 34 26 30 28 43 52 57 56 2 1 4 2 34 44 31 29 44 18 58 57 3 12 5 3 35 3 32 30 44 44 59 58 4 26 6 4 35 22 33 31 45 11 60 59 5 43 7 5 35 41 34 32 45 39 61 60 7 8 8 6 36 0 35 33 46 7 62 61 8 39 9 7 36 19 36 34 46 36 63 62 10 18 10 8 36 38 37 35 47 6 64 63 12 5 11 9 36 57 38 36 47 37 65 64 13 59 12 10 37 17 39 37 48 8 66 65 16 4 13 11 37 36 40 38 48 40 67 66 18 21 14 12 37 56 41 39 49 15 68 67 20 53 15 13 38 16 42 40 49 49 69 68 23 37 16 14 38 37 43 41 50 25 70 69 26 38 17 15 38 57 44 42 51 2 71 70 29 40 18 16 39 18 45 43 51 40 72 71 33 13 19 17 39 39 46 44 52 21 73 72 37 28 20 18 40 0 47 45 53 3 74 73 42 42 21 19 40 21 48 46 53 46 75 74 49 8 22 20 40 43 49 47 54 31 76 75 56 59 23 21 41 5 50 48 55 17 77 77 6 26 24 22 41 28 51 49 56 7 78 78 17 40 25 23 41 51 52 50 56 59 79 79 30 54 26 24 42 14 53 51 57 53 80 80 46 22 27 25 42 33 54 52 58 49     28 26 43 2 55 53 59 48     
When the two guards are of equal height betwixt the West and the lowest.  Height of the Pole Star. Height of the Pole. Height of the Pole Star: Height of the Pole. Height of the Pole Star. Height of the Poe. Deg, degr. mi sec. Deg. degr. mi. sec. Deg. degr. mi. sec 3 0 13 50 30 27 16 9 57 54 24 47 4 1 13 53 31 28 16 17 58 55 25 31 5 2 13 56 32 29 16 26 59 56 26 19 6 3 14 0 33 30 16 36 60 57 27 12 7 4 14 3 34 31 16 46 61 58 28 10 8 5 14 6 35 32 16 56 62 59 29 14 9 6 14 10 36 33 17 7 63 60 30 26 10 7 14 14 37 34 17 18 64 61 31 45 11 8 14 18 38 35 17 30 65 62 33 14 12 9 14 22 39 36 17 43 66 63 34 54 13 10 14 26 40 37 17 56 67 64 36 47 14 11 14 30 41 38 18 10 68 65 38 57 15 12 14 35 42 39 18 25 69 66 41 26 16 13 14 39 43 40 18 40 70 67 44 22 17 14 14 44 44 41 18 57 71 68 47 48 18 15 14 49 45 42 19 14 72 69 51 48 19 16 14 55 46 43 19 33 73 70 56 40 20 17 15 0 47 44 19 53 74 72 2 46 21 18 15 6 48 45 20 14 75 73 10 39 22 19 15 12 49 46 20 36 76 74 21 29 23 20 15 18 50 47 21 0 77 75 37 16 24 21 15 24 51 48 21 26 78 77 1 13 25 22 15 31 52 49 21 53     26 23 15 38 53 50 22 23     27 24 15 45 54 51 22 55     28 25 15 53 55 52 23 29     29 26 16 1 56 53 24 7     
When the greater guard is directly under the Pole star.  Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Height of the Pole Star. Height of the Pole. Deg. degr, mi. se. Deg. degr. mi. sec. Deg. degr. mi. sec. 3 0 37 26 31 28 36 51 59 56 35 48 4 1 37 25 32 29 36 50 60 57 35 44 5 2 37 24 33 30 36 48 61 58 35 40 6 3 37 23 34 31 36 47 62 59 35 36 7 4 37 22 35 32 36 45 63 60 35 31 8 5 37 21 36 33 36 44 64 61 35 26 9 6 37 19 37 34 36 42 65 62 35 21 10 7 37 18 38 35 36 40 66 63 35 15 11 8 37 17 39 36 36 38 67 64 35 10 12 9 37 16 40 37 36 37 68 65 35 3 13 10 37 15 41 38 36 35 69 66 34 56 14 11 37 14 42 39 36 33 70 67 34 49 15 12 37 12 43 40 36 31 71 68 34 40 16 13 37 11 44 41 36 29 72 69 34 31 17 14 37 10 45 42 36 27 73 70 34 22 18 15 37 9 46 43 36 25 74 71 34 11 19 16 37 7 47 44 36 23 75 72 33 59 20 17 37 6 48 45 36 20 76 73 33 45 21 18 37 5 49 46 36 18 77 74 33 30 22 19 37 4 50 47 36 15 78 75 33 13 23 20 37 2 51 48 36 13 79 76 32 54 24 21 37 1 52 49 36 10 80 77 32 30 25 22 37 0 53 50 36 7 81 78 32 4 26 23 36 58 54 51 36 5 82 79 31 34 27 24 36 57 55 52 36 2 83 80 30 54 28 25 36 56 56 53 35 58 84 81 30 7 29 26 36 54 57 54 35 55 85 82 29 7 30 27 36 53 58 55 35 52 86 83 27 50 
When the two guards are in the same Azimuth, or the one directly over the other betwixt the lowest and the East.  Height of the Pole Star. Height of the Pole. Height of th● Pole Star. Height of ●he Pole. Height of the Pole Star. Height of the Pole. Deg. degr. mi. sec. Deg. degr. mi. sec. Deg. degr. mi. sec. 1 0 40 50 28 27 58 43 55 55 30 47 2 1 41 27 29 28 59 31 56 56 32 47 3 2 42 3 30 30 0 19 57 57 34 54 4 3 42 39 31 31 1 9 58 58 37 9 5 4 43 16 32 32 1 59 59 59 39 32 6 5 43 52 33 33 2 51 60 60 42 4 7 6 44 29 34 34 3 44 61 61 44 46 8 7 45 6 35 35 4 39 62 62 47 41 9 8 45 43 36 36 5 34 63 63 50 48 10 9 46 20 37 37 6 32 64 64 54 11 11 10 46 58 38 38 7 30 65 65 57 51 12 11 47 36 39 39 8 31 66 67 1 49 13 12 48 14 40 40 9 33 67 68 6 11 14 13 48 52 41 41 10 38 68 69 10 59 15 14 49 31 42 42 11 44 69 70 16 16 16 15 50 10 43 43 12 53 70 71 22 11 17 16 50 50 44 44 14 4 71 72 28 54 18 17 51 30 45 45 15 17 72 73 36 34 19 18 52 10 46 46 16 33 73 74 45 18 20 19 52 52 47 47 17 53 74 75 55 14 21 20 53 33 48 48 19 15     22 21 54 15 49 49 20 41     23 22 54 58 50 50 22 11     24 23 55 42 51 51 23 45     25 24 56 26 52 52 25 23     26 25 57 11 53 53 27 5     27 26 57 57 54 54 28 54          

An Addition touching the Variation of the Compass.  
Whereas there have been some of opinion that there be two Magnetical Poles, by knowledge whereof, and of the Magnetical Variation Observed in any place, they have imagined they could find the Longitude thereof: to show the great error and uncertainty of this their opinion, I have here set down this Table of observations of the Variation of the Magnetical Needle, which partly by myself, but for the most part by others, both English and strangers, have been taken in all parts of the World almost, whither any Navigation hath been made, for these many years. Which Observations I wish the Judicious Reader to compare together, with so good advice and judgement as he can▪ whereby I assure myself he will be enforced to acknowledge with me that there can be no such Magnetical Poles found; as they imagine. To prove these, a few instances may be sufficient amongst many that may be gathered out of these Observations. For if there be two such Magnetical Poles, there can be but one common Magnetical Meridian passing by them and the poles of the World: but by these Observations it is manifest that there be many Magnetical meridians passing by the Poles of the World: as namely the Magnetical Meridian about Trinidado and Barbudas: also the Meridian about the Westermost of the Azores also about P. das Agulhas: lastly amongst the East Indian Lands some what beyond java Maior, the magnetical and true meridian must needs agree in one. Now seeing that all these Magnetical Meridian's pass by the Poles of the World there can be no reason given why the magnetical Poles should be said to be in one of them more than in another: and if in any, then in all: whereof it must needs follow, that as many Magnetical Meridian's as you have that pass by the Poles of the World, so many pair of Magnetical Poles must you have, which is absurd; and therefore no such Magnetical Poles.  
Now if any shall think that the great difference that is found betwixt divers of these Observations, taken at the same place by divers Observers, doth make any thing against the intention of this Argument, he is much deceived. For although there be three or four degrees difference betwixt some Observations taken at the same place; as namely at S. Helena, some make the Variation to be almost three degrees, some almost four, others will have it to be about five degrees and an half, and some others seven and an half. And although there be some four or five score leagues difference in determining the place where the true and Magnetital Meridian should concur, or where there should be no variation about Flores and Corvo, and about P. das Agulhas, some making to be about seventy or eighty leagues Westward from Flores; and some about thirty leagues Eastward from thence; where some others will have it hard by Flores, or somewhat to the Eastwards thereof: And at P. das Agulhas some say there is no variation at all, but according to others we must go 80 leagues further to the Eastward before we come to no variation. All these differences notwithstanding how great soever they be, can be of no validity to infringe the force of the foresaid argument; for still these Observations will necessarily prove, that either at Flores and at P. das▪ Agulhas, or at the most, within three or four score leagues of those places, there is a Magnetical Meridian passing by both the Poles of the World; which two Meridian's differing so much in Longitude each from other, and having in all Latitudes great variations betwixt them, it cannot be with any reason imagined how they may be reduced into one, so to make two Magnetical Poles only. But of all these so great differences either of the same or of divers men's Observations, we may justly take occasion to admonish all Seamen, especially such as are to take charge, that they be very careful both in providing themselves of the most convenient Instruments that can be gotten for this purpose, and also in the circumspect and artificial handling of them whensoever they go about to make use of them in Observing to find the variation, considering how great and excellent use there may be made hereof, for finding out the place whereabouts you are betwixt East and West upon the huge and vast Ocean, though you have seen no land for a long time.  
 Variat. West. Latit. North.  De. M De. M. In the Ice Haven at Nova Zembla 22 30 76 0 On the West side of Nova Zembla 26 0 76 0 From Nova Zembla Westward 20 leagues 31 0 73 0 At Cross Island near Nova Zembla 17 0   At the Hollanders Newland 16 0 81 0 In the Island of Vaygats 7 0 71 0 Amongst the Isles of Vaygats 8 0 70 25 At S. James Ile 7 30 70 40 On Land near the bar of Pechora 3 30 69 10 At the North Cape 1 0 71 30 From Fowlay Island half way almost to Friesland 11 15   From Friesland half way to Labrador, now called Newfoundland 28 0 62 0  East.    Near England sailing from Yarmouth Northwards 12 40 55 14 In the way from London to Russia 13 0 55 20 West.    3 30 69 0 7 0 70 40 8 0 70 30 East.    4 0 65 40 5 10 64 30 3 0 66 30 At Antwerp in Brab●●t 9 0   Near London at Limehouse 11 0 51 30 11 15   About Portland 10 0   In S. Ives Churchyard in Cornwall 8 0 50 30 From Cape Lizard South by West 8 leagues 12 50 49 55 South Easterly from C. Clear coming from our Channel 7 36   At Youghall in Ireland 10 0   At Silly 10 0    Variat. East Latit. North.  De. M. De. M. From Bell I'll Eastward 350 leagues 1 0 52 10 From Silly West Northwest 235 leagues 0 0 54 0  West.    From Silly West Northwest five hundred and thirty leagues 10 0 60 0 From that place Northwest by North 16 0 63 30 From thence North and by West 22 0 66 0 From this last place North by West 28 0 73 0 From thence due West 40 leagues 33 0 73 0 At the Earl of Cumberlands Isles 30 0 64 0 At Hope Sanderson 28 0 72 12 At Cape Raze in Newfoundland 16 0 47 0 From Cape Raze South by West Southerly 2 52 34 35 5 35 35 30 From C. Raze South Southwest Southerly 6 30 39 40  East.    At Cape Finister 8 30   From Cape Finister west by North 38 leagues 7 55 43 20 From the Rock Westward about 50 leagues 6 15 39 10 From the Rock West Northwest 7 leagues 7 0   About Lisbon 6 30   From Lisbon to Cape Verde almost 8 30   From C. Saker 3 or 4 leagues Eastward 5 38   From S. mary's (one of the Azores) 9 leagues East by South 2 20   At Fayal, and from thence to Tercaera 3 45   From Tercaera to Lisbon 7 30   8 30   From Flores Eastward scarce 40 leagues, and from C. Blanco 300 leagues 4 0   From Flores Eastward 70 or 80 leagues 0 0   Hard by Flores or betwixt it and Fayal 0 0   From Flores Westward 30 leagues 0 0    West.    Crossing the Meridian of Flores and Corvo 1 0   From Flores 100 or 120 leagues Westward 2 0   1 0   Within sight of Flores Southeast from thence 5 37   From Flores West 230 leagues 3 30 39 19 Falling with the Pike 1 30   From the Canaries 300 leagues 1 0 19 0  East.    At the Canaries 5 37   From the Grand Canary Northward 4 37 32 0 North-east from the I'll Savages 5 37 31 0 On the South-west side of the Grand Canary 5 20 28 0 From the Canaries 230 leagues 0 0 20 0 Sailing for the Canaries from the West Indies 0 0 33 0 0 0 31 0 Sailing further in 5 37 27 20 From Palma Sailing towards Cape Blanco 3 0 24 0 Near to C. Blanco not two leag. from shore 2 40 21 0 Riding at anchor near C. Blanco 3 0 20 25 From C. Blanco West S. w. some 20 leagues 2 40   From C. Blanco Westward 63 leagues 5 37 19 20 From C. Blanco Westward 90 leagues 5 0 18 35 From C. Blanco Westward 100 leagues 6 0   From C. Blanco 436 leagues 7 30 17 42 From C. Blanco 470 leagues 7 30 11 57 From C. Blanco 476 leagues 7 36 16 35 From C. Blanco 535 leagues 7 30 10 59 From C. Blanco 595 leagues 5 0 10 15 From C. Blanco 640 leagues 4 36 10 0 From C. Blanco 700 leagues Westward 1 3 9 20 From C. Blanco going towards the West Indies in many distances 6 0   5 40 14 54 At Cape Verde 7 0   About the Lands of C. Verde 4 0   From these Lands 300 leagues Westward 5 38   At S Jago and S. Nicholas Iles of C. Verde 2 30   From C. Verde 100 or 120 leagues 3 45 14 0 From the Isles of Brava & Fogo W.N. 12 leag. 4 30   From Maio 46 leagues East by South 5 8 14 20 From Cape Verde in the way to the East Indies passing the Equinoctial 4 0   5 0   5 37   At the Island of Trinidado 0 0 9 46 From Trinidado Island Eastw. 90 leagues 1 30   2 0    West.    At Margarita 0 0   At S. Cruse near S. John de Porto Rico 0 0   At Cape Rosse of S. John's Island 1 52 17 44 In the Meridian of Porto Rico 2 52 21 30 At anchor on the West side of S. John 1 52   At the West end of S. John de Porto Rico 2 30 17 44 From S. John de P. Rico North Northwest northerly half a point 8 0 23 0 Also in the same course 8 0 26 0 Again in the same course 8 0 26 20 From Dominica about some 140 leagues 0 0 14 0 In the Meridian of Barbados fifty leagues from Martinico 0 0 14 20 At the Island of Guardelupo 1 0 15 18 At Cursands an Island of the West Indies 4 0 12 13 At the town of Rio de Hacha 7 36 11 20 At Cape la vela 7 0 11 50 Thwart Rio de Mayo 15 0 31 0 15 0 36 0 At Cape Codera 2 30 9 30 At Cape Corientes in Cuba 3 0   At Cape S. Anthony in Cuba 13 0 22 0 At Cape Cameron 5 0 25 40 At Cape Florida 3 0 25 30 To the Northward of the Cape of Florida 13 0 28 0 Near the coast of America 11 0 35 30 From Bermudas Westward 140 leagues 10 0 30 35 From Bermudas Westward 100 leagues 10 3 34 0 Again from Bermuda 80 or 85 leagues 11 15 34 0 From Cape Raso S. Southwest Southerly 6 30 39 40  East.    From Serraleona West by South, and from the shoalds of Madrabombe or S. Anne West and by North 160 leagues 6 10 7 0  Varia. West. Latit. South,  De. M De. M In the harbour of Serraleona 1 50 8 30 From the shore of Serraleona 17 leagues 2 2 3 54 From Serraleona 61 leagues West Southerly 2 56 7 58 From the Meridian of Sierraleona 76 leagues Westward 3 29 7 25 From the Meridian of Sierraleona 97 leagues Westward 3 45 6 0 From the Meridian of Sierraleona 153 leagues Westward 4 20 4 50 From the Meridian of Sierraleona 137 leagues Westward 4 12 4 40 From the Meridian of Sierraleona 127 leagues Westward 3 56 4 30 From the Meridian of Sierraleona 142 leagues Westward 4 20 4 18 From the Meridian of Sierraleona 160 leagues Westward 4 58 4 6 From the Meridian of Sierraleona 187 leagues Westward 4 50 3 0 From the Meridian of Sierraleona 187 leagues Westward 5 40 1 50 From the Meridian of Sierraleona 194 leagues Westward 5 45 0 45    South. From the Meridian of Sierraleona 195 leagues Westward 5 26 0 10 From the Meridian of Sierraleona 198 leagues Westward 5 30 0 35 From the Meridian of Sierraleona 206 leagues Westward 6 33 2 0 From the Meridian of Sierraleona 210 leagues Westward 6 55 2 35 From the Meridian of Sierraleona 220 leagues Westward 6 45 3 35 From C.S. Augustine North and by West 7 0 7 16 From C.S. Augustine North by East Easterly 6 40 1 4 From C.S. Augustine North Northeast 8 0 4 0 From Cape S. Augustine East Northerly 30 leagues 8 10 8 20 From C.S. Augustine 100 leagues 11 6 8 30 From C.S. Augustine not 120 leagues 5 37 11 30 At the I'll Fernando Laronho near Brasil 8 30 2 20 Close by the coast Brasil 3 45 7 0 8 0 10 0 A little West from the Meridian of Trinidad near Brasil 11 10 18 30 Among the Lands of Trinidad and Ascension 12 8 20 35 On the backside of the I'll of Ascension 12 10 20 30 At the I'll of Ascension 10 0 20 0 In the Meridian of Trinidad Easterly 14 53 27 0 Between the Isles of Trinidad and Tristan de Acunha 18 0   19 0    Varia. East. Latit. South.  De. M De. M From the shoalds of Brasil East Southerly about 14 leagues 12 30 19 30 From the same shoalds Southeast about 55 leagues 13 52 20 10 Also from the same shoalds Southeast by East 13 20 19 37 From the coast of Brasil 150 leagues 10 0 18 0 At Cape S. Vincent in Brasil 12 0   From the coast of Brasil 100 or 120 leagues 8 30 17 0 7 30 18 0 From Laronho Southwest 12 leagues 8 1 4 20 From Ascension Ile 20 or 30 leagues Eastward at the Cliff Penedo de S. Pedro 5 30   Betwixt Ascension Ile and S. Helen's 7 30   At S. Helena 2 48   3 46   5 37   7 30   From S. Helena a little Westward 9 0   From S. Helen's not 19 leagues 5 40 18 30 From S. Helena northwest by West 16 leagues 3 45   From S, Helena northwest 156 leagues 7 40 10 20 From S, Helena 230 leagues 5 38 8 20 From Ascension I'll north-east half a point northerly about 12 leagues 6 0   About the Lands of Martin Vaz 13 0 19 0 Alongst by those Isles 11 15   From those Lands northerly 30 leagues 18 30   From the shore of afric Westward some 130 leagues 4 8 27 0 Bearing from thence toward S. Helena 2 48 25 0 From the main of Africa 160 leagues 2 50 23 0 In the Longitude of 28 degrees 15 20 32 0 A little Westward from the Meridian of the Isles of Martin Vaz 14 58 28 35 Eastward from thence 15 37 28 53 From the former Observation 60 leagues 16 8 29 0 From the last Observation Eastward 27 leagues 16 52 29 33 Beyond Tristan da cunha 70 or 80 leagues coming from Martin Vaz 16 53 33 0 From Tristan da cunha Westward 17 52 34 35 14 0 At the Island of Tristan da cunha 19 0   From thence northward 16 8 33 34 Past the Island towards C. Bona Speranza 14 0   From Tristan da cunha W. n. W. 368 leagues 14 0 2● 25 At Cape Frio 13 0   Near Cape Frio 12 0 23 30 From Cape Frio Eastward towards Africa 17 0   18 0   From Cape Frio about 125 leagues Eastward 11 8   About 155 leagues from Cape Frio 14 8 25 0 At Port desire 5 0 47 40 At the East mouth or entrance into Magellans' straits 5 30   In the straits of Magellan 5 0   From Cape Bonae spei 900 leagues West by north half a point northerly 15 52 26 50 From Cape Bonae spei almost West by N. 180 leagues 8 50 34 0 At the bay of Soldania 0 20 33 55 1 30 33 20 At Cape Buona Esperanza 0 15   1 30   About Cape Buona Esperanza 2 0 35 0 From Cape Buona Esperanza Westwards 30 or 40 leagues 5 38   Betwixt C. Buona Esperanza and S. Helena 3 45   From C. Buona Esperanza South 3 45   From C. Bona Speranza Westward 40 or 50 leagues 3 0   From C. Buona Esperanza due northwest 5 37 20 0  West.   From C. Bonae spei S.w. by S. 36 leagues 4 10 35 25 From C. Bonae spei S.w. by S. 28 leagues 3 50 35 30 At Cape das Agulhas near C. Bonae Spei 0 0   From thence 80 leagues Eastward 0 0   At Cape Talhada 40 leagues East from Cape das Agulhas, being in sight of land lying from us north by East 3 47 34 20 At C. Corientes beyond C. Bonae spei 7 30   11 0 25 0 From C. Corientes Southwards 8 30 30 30 About the Land's Primeras towards Mozambique 15 0 18 0 In the I'll Mozambique 12 0 14 45    North. At the Isles of Nicobar 7 36 7 30 10 0   From thence till you come to the Line going towards the East Indies 11 0   At the Isle de Almirant near the line 13 0   Near to C. Guarda fui, or Porto Galeacea 8 15 13 15 At P. de estreito or the mouth of the Red sea 5 15 12 15 At Baxos de Cuaqem 1 15 19 15 At Port de Igidid 0 40 22 0 At Xuarit 0 15    East.   At Sidon in the bottom of the straigts 2 35 33 30  West. North. From the place that is 200 leagues Westward from Goa to Cape Comorin 15 0   At Goa 15 0 15 20 At the Isles Comoro 13 0   In the Bay of S. Augustine in Madagascar 15 0   At Cape Romano in Madagascar 17 40 26 0 Near Madagascar 8 30 26 0 20 0 From Cape Romano Southerly 14 4 27  30  From C. Romano West Southwest half a point Southerly 110 leagues 14 14 36 34  Variat. East. Latit. North.  De. M De. M. From C. Romano Southwest 50 leagues 15 25 28 20 In the height of C. Romano 8 leagues off 16 45 25 50 At the I'll of S. Mary entering the Bay of Antongil 17 0 17 0 In the bottom of the Bay of Antongil by many and exact Observations 20 0   At the Bay of Tanassarin 5 30   At the West side of the sands of Saya de Malha 15 0 11 30 At the Island Ragapez 22 11 10 0 From the Island of Gratia West S.w. 36 leagues 24 11 9 20 At the shoalds called Baixos de India 8 30 30 0 At Diego Roiz Island 21 0 20 0 From Los Romeros Iles South Westerly 68 leag. 24 15 31 0 From Los Romeros East by South 50 leagues 22 16   From Los Romeros East 110 leagues 21 20   At the shoalds of Adu and Candu 19 30 6 0 At the I'll Diego Gratiosa 24 0 9 0 From Diego Gratiosa Westward 20 leagues 22 0 7 30 At Diego Roderigo's Island 20 0   From Diego Rodericos Island South, and South and by East 23  35 0 24  25  At Maldiviae Island 17 0      North. At Cochin 13 0 9 40 From Cochin till you be passed Maldiviae Iles South and South-west till you be under 8 and 10 deg. of South Latitude 16 52   At Zeilan 15 30 9 0 At the Isle Pulobatum 4 0 4  At Achin in Sumatra 8 0   In the Road of Achin 6 30      South. In Priaman on the West side of Sumatra 5 40 0 22 At Bantam in Java 5 0 7 0 4 30   At Madura 2 30 6 50 At the North-east corner of Balij 3 0 8 30 At Banda 4 45 4 50  
FINIS.   

A Table Showing the Contents of this Treatise.  

Chap. 1. Fault's in the common Sea-Chart with Rumbs expressed by Right lines and degrees of Latitude every where equal. pag. 1 

1 Error in the proportion of the length and breadth of places in the common Sea-Chart. 1  
2 Error in finding out the difference of Longitude by the common Sea-Chart. 2  
3 Error in the lying or bearing of places one from another in the common ea-Chart. 4  
4 Error in setting of places out of the common Sea-Chart into the Globe. 5  
5 Error in showing the distances of places in the common Sea-Chart. 5  
6 Some Error in keeping always the same point of the Compass in sailing 6  
The expressing of the Rumbs by right lines defended, which some hold for erroneous. 7    
Chap. 2. How the former errors may be avoided. 8 

The definition of the Nautical Planisphaere. 9  
A Table of the Latitudes of every minute of a Meridian of the Nautical Planisphaere or Sea-Chart, in such parts whereof each minute of the Equinoctial containeth 10,000. pag. 14 etc. 14    
Chap. 3. The use of the two first columns of this Table of Latitudes, for graduating a Meridian in the general Sea-Chart. 37 

Example of the graduating of a Meridian in the general Sea-Chart 38    
Chap. 4. Another way for graduating the Meridian of a general Sea-Chart. 39  
Chap. 5. The use of the Table of Latitudes, for the true graduating of a Particular Sea-Chart. 40  
Chap. 6. The breadth of a particular Chart being given, to divide the same into the degrees and minutes, contained in the difference of the least and greatest Latitudes therein to be expressed. 42  
Chap. 7. The use of the third column of the Table of Latitudes 43 

An easy way to reduce the difference of Longitude into leagues 44    
Chap. 8. How to describe the Rumbs Mechanically in any Sea-Chart, Globe, or Map, of what form soever. 45  
Chap. 9: The use of the Table of Latitudes for making the Table of Rumbs. 46 

To find presently the Latitude of any Rumb for any Longitude 46  
A Table of the first Rumb from the Meridian, that is, the Rumb of North and by East, North and by West, South and by East, South and by West. 47  
The second Rumb from the Meridian, the Rumb of North North-east, North NorthWest, South Southeast, South SouthWest. 47  
The third Rumb from the Meridian Northeast and by North, Northwest and by North: Southeast and by South, SouthWest and by South. 47  
The fourth Rumb from the Meridian, North-east Northwest, Southeast Southwest. 48  
The fifth Rumb from the Meridian: Northeast and by East, Northwest and by West, Southeast and by East, Southwest and By West. 48  
The sixth Rumb from the Meridian, East Northeast, East Southeast, West Northwest, West Southwest. 49  
The seventh Rumb from the Meridian, East and by North, East and by South▪ West and by North, West and by South. 50    
Chap. 10. The use of this Table of Rumbs. 55 

The use of the Table of the eighth Rumb 56    
Chap. 11. A most plain and sensible demonstration of the agreement of the Nautical Planisphere, before descibed, with the Globe, and of the disagreement of the common Sea-Chart from them both. 56  
Chap. 12. The use of the Nautical Planisphere or Sea-Chart. 58 

To know how one place in the Chart lieth from another. 58  
To find the distance of places in their Rumb. 58  
If both places have one Latitude. 58  
If both places have the same Longitude. 59  
If both places differ both in Longitude and Latitude. 59  
The demonstration of the truth of the former rules. 59  
To find the distance of any two places in the arch of the great circle drawn by them. 61  
If both places have no Latitude. 61  
If both places have the same Longitude. 61  
If both places differ in Longitude, and but one of them have Latitude. 62  
If both places have Latitude of one denomination and equal. 63  
If the latitudes be of one denomination and unequal. 63  
If the Latitudes be of divers denominations. 64  
The demonstration of the former Rules. 64  
To find the distance of any two places Arithmetically 65  
The Art of Navigation Arithmetical. 66  
1 By the Longitudes and Latitudes of two places to find the Rumb and distance. 66  
2 By the distance and Latitudes to find the Rumb and difference of Longitude. 66  
3 By the Rumb and Latitudes to find the distance and difference of Longitude. 67  
4 By the Longitudes, Rumb, and one Latitude, to find the other Latitude and the distance. 67  
5 By the Rumb, the distance, and one Latitude, to find the other Latitude and the difference of long. 68    
Chap. 13. Error in the use of the Compass by the variation neglected, and how to Observe and avoid the same. 68 

The making of the the Sea Rings. 75  
The use of the Sea Rings. 79    
Chap. 14. To find the inclination or dipping of the magnetical Needle under the Horizon. 82 

A short way to calculate the Table of magnetical inclination. 83  
The Table of magnetical inclination. 84    
Chap. 15. Errors in using the cross-staff. 85 

1 Error by reason of the eccentricity of the eye. 85  
How it may be found and corrected. 86  
2 Error by the height of the eye above the water. 87  
To find how much this error is at any height of the eye. First without knowing the quantity of the earth's Semidiameter. 88  
Secondly, with knowledge thereof, found either by the highest Meridian Altitudes of the Sun. 88  
Or by the Meridian Altitudes of some principal fixed Stars. 89  
Or by the shadow of a Perpendicular stile. 89  
The finding of the earth's semidiameter by the height of some Mountain near the Sea. 90  
Maurolycus and Clavius his gross demonstration hereof. 90  
A more exact demonst. with the practice thereof. 92  
The angle of dipping for any height of the eye. 96  
3 Error by the Parallax of the Sun, corrected. 96  
4 Error in Observing by the refraction of the Sun or Stars, corrected. 97    
Chap. 16· Faults amended in the Table of the Sun's declination, commonly called the Regiment of the Sun. 97  
Chap. 17. Of the Table of Declination of every minute of the Ecliptic in degrees min. and sec. made according to the greatest obliquity of the Zodiac this present age; which by exact Observation is found to be 23 degrees, 31 min. and an half. 98 

A Table of the Declination of every minute of the Ecliptic, in degrees, min. and sec. 101    
Chap. 18. The use of the former Table of Declination. 116  
Chap. 19 The description and use of a great Quadrant, for observation of the Sun on Land. 120 

A Table of observations of the Sun's Meridian Altitudes, taken by the foresaid Quadrant, in the years 1594, 1595, 1596, 1597 at London.     
Chap. 20. The finding of the Sun's Apogeum and eccentricity out of the former observation. 142 

To know the time of the Suns coming to any point of the Ecliptic. 142    
Chap. 21. The middle motion of the Sun, corrected out of the former Observations. 150 

A Table of the Sun's middle motions. 152    
Chap. 22. A new theoric of the Sun, for the making of the Table of the Suns Prosthaphaereses 154 

A Table of the Suns Prosthaphaereses. 157    
Chap. 23. The making of the Ephemerideses of the Sun. 159  
Chap. 24. How to reduce the apparent time to the equal time answering thereto. 162 

A Table of the Aequation of natural days. 162    
Chap. 25. A Table of Aequations of the Suns Ephemerideses to make them serve for many years. 163 

Ephemerideses of the Sun. 164    
Chap. 26. The use of these Ephemerideses. 169  
Chap. 27. The making of the Table of the Sun's Declination. 170 

Prosthaphaereses of the Sun's Declination. 172  
A Table of the Sun's Declination. 173    
Chap. 28· The use of the former Table of Declination, or Regiment of the Sun. 181  
Chap. 29 The Declinations of the principal fixed stars about the Equinoctial, corrected by Observation. 183 

A Table of fixed Stars about the Equinoctial. 198    
Chap. 30. The use of the former Table. 199  
Chap. 31. The true distances of certain principal fixed Stars from the North Pole, found by late Observation. 199  
Chap. 32. To know at what time any of the foresaid fixed Stars come to the Meridian for any day of the year. 202 

A Table of the Sun's right Ascensions in hours and minutes, for every day of the year. 204    
Chap. 33. By the former Tables of fixed Stars, and the Sun's right Ascensions to know the hour of the night at any time of the year. 206  
Chap. 34. Of finding the Elevation of the Pole, by Observation of the Pole Star and Guard. 207  
Chap. 35. The description and parts of the Sea Quadrant 208  
Chap. 36. The description of the Nocturnal or night Dial. 210  
Chap. 37. The use of the Sea Quadrant: first in Observing the height of the Sun, looking only to the Horizon at Sea. 211  
Chap. 38. How with this Quadrant to Observe the height of the Sun, with ●our back turned towards the Sun. 211  
Chap. 39 How to Observe with this Quadrant the height of the Sun or Star, looking both to the Sun or Star, and to the Horizon. 212  
Chap 40. How to find the height of the Pole by Observation of the Polestar and Guard, without giving or taking any allowance or abatement, at any time when the Polestar the Guard and Horizon may be seen. 213 

To know the hour of the night by the Nocturnal. 213  
An answer to Simon Stevin, showing his erorrs in blaming me of error in my table of Rumbs. 214      

The Contents of the TREATISE Of the ART of NAVIGATION.  

The division of the whole Art of Navigation. pag. 1  
Chap. 1. The definition of the Sphere. 2  
2. That the whole World is a Sphere. 2  
3. Of the division of the Sphere▪ 2  
4. Of the motion of the Heavens. 4  
5. Of the figure of the Heavens. 4  
6. That the earth and water make one perfect Globe. 5  
7. That the earth is in the centre of the world. 5  
8. The whole quantity of the earth. 5  
9 Of the Equinoctial circle. 6  
10. Of the Poles of the world. 6  
11. Of the Ecliptic line. 7  
12. Of the Declination of the Sun. 7  
13. Of the Colours. 8  
14. Of the Meridian circle. 8  
15. Of the Horizon. 9  
16. Of the 32 Winds. 10  
17. Of the two Tropics. 12  
18. Of the Parallels. 13  
19 Of the degrees. 13  
20. What is meant by Longitude and Latitude. 14   

THE SECOND PART OF THE ART OF Navigation▪ wherein is handled the Practic part, showing the making and use of the principal Instruments belonging to this ART.  
Chap. 1. The making of the Astrolabe. pag. 15  
Chap. 2. Of the height of the Sun. pag. 17  
3. Of the Shadows. 18  
4. Of the Regiment and Rules of the Sun. 19  
5. Of the Declination of the Sun, and of the Tables thereof. 20 

How the Declination of the Sun may be found out. 21    
6. The Equation of the Sun's Declination. 22  
7. Four examples for the plainer declaration of that which is said before. 22  
8. Another manner of accounting by the Sun, as they use in Portugal. 25  
9 How the height of the Sun may be known in any place whatsoever, without an Astrolabe; first knowing your distance from the Equinoctial. 25  
10. The Rule or Regiment of the North-star for the knowledge of the height of the Pole. 26  
11. The making of the cross-staff. 27  
12. Of the position of the North-star, and the Guards, 28  
13. Of the height of the Star taken with the cross-staff. 30  
14. The Regiment or Rules of the North Star. 30  
15. Other things to be noted in observing the height of the Pole. 32  
16. Of the Crosiers. 34  
17. Of the Sea-Compasse. 34  
18. How the variation of the Compass may be found. 37 

The finding of the Meridian line. 37    
19 Of the Sea-Chart. 38  
20. Of the point of Imagination. 41  
21. Of the Traverse or Geometrical point. 42  
22. Of the amending of the point of Imagination. 42 

The amending of the point of Imagination by the Traverse point. 43  
The amendment of the point of Imagination by North, South East, West. 43    
23. The point by Imagination and the height. 44  
24. What it is to increase or diminish in height 45  
25. How you may cast a traverse point without Compasses. 46  
26. Of another kind of casting a point by traverse. 46  
27. Of the leagues which in Navigation answer to each degree of latitude in every Rumb. 47  
Chap. 28. How you may come to know the Longitude, or the course from East to West. pag▪ 48  
29. How you may set down in your Chart a new land never before discovered. 50  
30. Seeing two known points or Capes of land as you sail along, how you may know the distance of the Ship▪ from them. 51  
31. Of the account of the Moon. 51 

The first Rule of the golden number. 53  
The second Rule of the concurrent. 53  
The third Rule of the Conjunction. 53  
The fourth Rule, of the full, and quarters of the Moon. 53  
The first Rule of the Springtides and Neap-tides. 54  
An example whereby the foresaid Rules are made more plain. 54    
32. Of the daily tides. 55 

The first Rule. 56  
The second Rule. 56  
The third Rule. 56  
The fourth Rule. 56  
The fifth Rule. 57  
An example of the said Rules. 57    
33. Of a certain Instrument, whereby you may in general judge of the tides. 58 

The use of this Instrument. 59    
34. Of the making of an universal Dial, which may serve generally all the World over. 60  
35. Of the parts of this Instrument. 62  
36. How you may know what a clock it is by this Instrument. 36  
37. Of the variation of the Compass by this Instrument. 64  
38. At what hour the Sun riseth and setteth every day, in all parts of the World. 65  
39 Of the length of the day and of the night. 65  
40. Of a night Dial by the North stars. 65 

The use of the Table of the Sun's declnation. 67  
A Table of the Sun's declination. 69  
By the height of the Polestar to know the height of the Pole. 81  
1 When the greater or former Guard is in the East of the same height with the Polestar. 83  
2 When the two Guards are of equal height betwixt the East and the highest. 84  
3 When the greatest or foremost Guard is right above the Polestar. 85  
4 When the two Guards are directly one over another betwixt the highest and the West. 86  
5 When the greater or foremost Guard is in the West of the same height with the Polestar. 87  
6 When the two Guards are of equal height betwixt the West and the lowest. 88  
7 When the greater or former Guard is directly under the Polestar. 89  
8 When the two Guards are directly the one over the other, betwixt the lowest and the East. 90     
FINIS.   

Made and sold by Joseph Moxon, at his shop, on Cornhill, at the sign of Atlas.  

GLobes Celestial and Terrestrial, of all sizes; and Books for the use of them.  
Sphaers, great and small, according to the Ptolemean Systeme  
Sphaers, great and small, according to the Tychonean Systeme  
Sphaers, great and small, according to the Copernican Systeme  
With Books for the use of them.  
Blagraves' Mathematical Jewel.  
Oughtreds Circles of Proportion.  
The Spiral Line.  
Gunter's Quadrant and Nocturnal.  
Stirrups Universal Quadrat.  
These, with divers other Mathematical Instruments, are printed on Papers, and exactly pasted on Board's, &c. with Indices, and other appurtenances proper to each Instrument: very commodious for any man's use. Also Books for the use of every of the foresaid Instruments.  
Sea-plats, printed on paper or parchment, and pasted on Board's.  
Vignola, or the complete Architect, useful for all Carpenters, Masons, Painters, Carvers, or any Gentlemen or others that delight in rare Building.  
A new Invention to raise water higher than the Spring, with certain Engines to produce either motion or sound by the water: very useful, profitable and delightful for such as are addicted to rare curiosities: by Isaac de Caus.  
A Help to calculation By J. Newton.  
A Mathematical Manuel, showing the use of Napiers bones, by J. Dansie.  
A Tutor to Astrology, with an Ephemeris for the year 1657, intended to be annually continued, by W. E.  
Also all manner of Mathematical Books, or Instruments, and Maps whatsoever are sold by the foresaid Joseph Moxon.    

The Haven-finding Art, Or The way to find any Haven or place apppointed at Sea.  
THere is no man, I suppose, that knoweth not with how great diligence now of a long time (especially since men leaving no part of the world unattempted, have sailed into America, and to the utmost Indies) the searchers out of excellent things have sought some certain way, whereby they which take charge of Ships might know assuredly the situation and Longitude of what place soever they would go unto, and so come to any Haven or place appointed at Sea. But I know not how it hath come to pass, that there could not hitherto any certain knowledge of that matter be attained unto. For some when they endeavoured to find this thing by the magnetical needle gave the Loadstone itself a Pole, which of the Loadstone (called also the Magnet) they named the Magnetical Pole, or Pole of the Loadstone. But that this is otherwise, the thing itself hath taught us, because the variation of the needle is found not to follow the Rule of that Pole. Yet in the mean time this continual searching gave occasion of another mean whereby a Ship might certainly direct her course unto any Haven or place at Sea whereto you would desire to go, although the true Longitude both of the place wherein the Ship is, as also of the place where the Haven is, were both unknown. Which that it may in some sort be rudely showed, and that the circumstances hereof may more clearly be set forth before your eyes, whereby there may ensue a more certain and general use of the same, first of all it must be known that we are taught by daily experience, that the Magnetical Needle touched with the Loadstone or Magnet (which therefore we call the Magnetical needle) doth not always point out the same part of the world, but without any respect of that Magnetical Pole, (whereof we made mention before) sometimes indeed it showeth the true place of the North: but for the most part it declineth either towards the East or West: which variation, yea even in a small distance of places, hath most manifestly appeared to them which have directed their course from the Eastern parts towards the West: For examples sake at Amsterdam the variation is 9 degrees and 30 min. towards the East. In the Foreland of England 11 degr. At London 11 degr. 30 min· Near Tinmouth in the Sea 12 degr. 40 min. and so forth.  

How any Haven or place at Sea may be found, the Latitude and variation of the same place only being known.  
THe variation of the Magnetical Needle and the Latitude of the place being known the same place may be found although the Longitude be unknown, and that daily experience plentifully teacheth. For (that we may make this matter plain by examples especially) if the Mariner know that the Latitude of the City of Amsterdam is 52 degr. and 20 min. and that the variation of the Compass in the same place is 9 deg. and 30 min. he must needs not be ignorant, that when he hath brought himself to that Latitude and variation, he is not far from Amsterdam, what Longitude soever that City have▪ But some man may object that there are many places which have the same Latitude and variation that the City of Amsterdam hath: whereto we may readily answer that indeed there be such places: but yet very far distant from thence, and such as may easily be known by other circumstances, whereof we shall speak hereafter. And although the Mariners may find Amsterdam otherwise, as by the places near adjoining, by conjectures by the soundings, by the sands, and many other signs, without any regard of the variation: yet I thought good to propound a known place for example, that the Universality of the same Rule might be known in long Navigations, wherein no land appeareth. As for example if the Master of a ship desire to sail from hence to Cape S. Augustine in Brasile, and know that the variation there (as it is reported) is 3 deg. and 10 min. and the Latitude 8 deg. 30 min. towards the South, when in going thitherwards he shall come to that Latitude, and variation, he shall then know that he is come to the Cape of S. Augustine: and although he think otherwise by his conjecture, and reckoning yet not regarding that conjecture he shall confess himself either to have guessed ill, or else to have been deceived with some Eastern or western currents: For reason will not suffer us to think that that variation which before was found at the Cape of S. Augustine is changed, that he should need to yield himself to that opinion. So also who will not esteem it to be absurd, and altogether against reason, that he which knoweth very well that he findeth at sea another variation then that which is at Cape S. Augustine▪ of 3 degr. 10 min. should notwithstanding neglecting the experience of the variation, and resting upon conjecture only affirm that he is near the Cape S. Augustine? Because he speaketh contrary things, when he saith that the variation there is 3 degrees 10 minutes, and again avoucheth that it is not.  
Neither is this unworthy the marking which hath often happened, that he which should have sailed to the Isle of S. Helena when he was come to the Latitude of the same Island, and saw not there the Island, and was also ignorant whether he were to the Eastwards or Westward from the same, by conjectures sought that place towards the East, which indeed lay from him towards the West: and so the further he sailed the further always he went from that Island. Now I leave it to thy consideration if he, (whosoever he were that was Master of that ship, which diligently sought that Island for the space of certain weeks, tacking about also divers times before he could find any place to abide in) if he I say had not been ignorant what the variation of the Compass was at S. Helen's Island, and what the use of the variation is at sea, and how to find it out I leave it I say, to thy consideration, whether he would willingly have floated doubtfully to and fro following a greater variation, knowing assuredly that the variation there was lesser.  
Hereby it may easily be conceived how great use there is of the variation, when they especially which in sailing follow the lines showing the courses (which lines because now they have found this name among the Portugals we call Rumbs, the ignorance of which (lines) can hardly be permitted in them which attempt long voyages upon the huge Ocean) ought every where to know certainly the place of the true North, which is commonly found by the knowledge of the variation.  
If any man likewise consider the uncertain situation of those places which are set into Globes or Sea Charts by the mariners relation, which uncertainty taketh his beginning from hence, because every man thinketh that to be the true place of the North which is showed by the Flower deluce (as they call it) of the Compass which they brought with them from home, (which thing also bringeth no less doubtfulness to the Mariners themselves) he will think (and that not without cause) that the Observation of the variation is a very needful thing even for this cause also: Because it is an easy matter to place the flowerdeluce in such sort that it shall not miss any thing in showing the true North part of the World, to wit, if one move the Magnetical needle or points of the wires in the Compass from the flowerdeluce so much as need shall require.  
These things therefore have been Observed and granted, and this especially, that the variation altereth according to the variety of countries, (as by the common testimony of all men it is proved) it is in some sort manifest that they which deny this varying property to be of very great use for Navigation, are either wiser than the common sort, and have some hidden secrets which are not revealed to every man, or else are notable fools and mad men.  
Therefore when the most excellent Prince Maurice, having throughly considered hereof, thought that it might assuredly be brought to that pass that Mariners might receive great profit by this means, He (the high Admiral) gave commandment to all the companies of the Admiralty (adjoining also thereto a certain introduction) that they should do their best indevor, that all Masters of ships should provide themselves for this purpose: that is to say that to what place soever they should come, they should seek out the Declination of the Magnetical needle from the North, or the variation of the Compass, not lightly, running over the matter as it were by the way, and for fashion's sake only; but with great carefulness and diligence, taking with them meet and needful Instruments for that purpose: and that after their return into their own country they should truly and faithfully certify their companies or brotherhoods of the Admiralty of that matter: that the self same experiments being by them brought into good order, might be published for the common good.  
But that every man may more perfectly learn the circumstances of this matter, I thought it meet here to set down certain principles of this thing, which is yet notwithstanding to be further searched into by more experiments, in which shall be showed a general view or Table of those places, whose variations have already been Observed by the learned Geographer Petrus Plancius, with continual labour, and not without great charges, from divers corners of the earth near and far off: whom for honour's sake I therefore name, that as well they that shall hereafter find out places or havens after this manner, as also they that have already found, may know that they are bound to give thanks to Plancius alone, as to him that is the chief cause of this Observation. But that Table or general view of variations, whereof there shall hereafter follow a plainer declaration is this.  

A Table or View of variation.  The Northeasting, or the East variation of the first part or space towards the North. Increasing.  Northeasting. Latitude Longitude.  Deg. M Deg. Mi Deg. Mi. In the Flemish Island Corvo 0 0 N 37 0 0 0 In the Flemish Island Saint Mary 3 20 N 37 0 8 20 Near the Island Maio 4 55 N 15 0 11 20 At Palma one of the Canary Lands 6 10 N 28 30 16 20 At the Rock near Lisbon 10 0 N 38 55 24 30 In the Westermost part of Ireland 11 0 N 52 8 24 12 In the West part of England 12 40 N 50 21 28 0 Decreasing. About one mile Eastward from Plymouth 13 24 N ●0 18 30 0 By Tin mouth in the Sea 12 40 N 55 0 33 0 At London in England 11 30 N 51 24 34 6 In the Foreland of England 11 0 N 51 8 35 40 In Amsterdam 9 30 N 52 20 39 30    Northwesting     The Northwesting, or the West variation of the second part or space towards the North Increasing. At Helmshade to the westward from the North Cape of Finmarke 0 0   60 0 At the North Cape of Finmarke 0 55 N 71 25 61 30 At Norquinda 2 0 N 71 10 63 30 At S. Michael or Archangel in Russia 12 30 N 64 54 83 30 In the South straight of Vaigatz 24 30 N 69 30 103 0 At Langeness in Nova Zembla 25 0 N 73 20 100 30 Decreasing. In William's Island In Nova Zembla 33 0 N 75 35 110 0 At Yshouck In Nova Zembla 27 0 N 77 12 120 30 At Winter-house In Nova Zembla 26 0 N 76 0 120 30 The Northeasting of the first part or space towards the South. Increasing. 105 Spanish leagues Westwards from Cape S Augustine in Brasile 0 0 S  0 0 At Cape S. Augustine in Brasile 3 10 S 8 30 6 0 North and South with Cape das Almas in Guinea 12 15 S 0 0 29 0 Towards the Northwest Northerly from the Lands of Tristan da Cuneha 19 0 S 31 30 30 0 Decreasing Towards the Northwest, Westerly from the same Lands 15 0 S 31 30 36 0 North and South with the Cape of Good Hope 2 30 S 35 30 57 0    Northwesting     The Northwesting of the second part or space towards the South, except Go, Cochin, & Cantan. Increasing▪ 17 Germane miles from Cape das Aguillas Eastwards 0 0 S  60 0 5 miles in the Sea from Terra de Natal 4 30 S 33 0 66 0 At the shoalds of Indie 11 0 S 22 0 79 30 In M●sambique 11 0 S 14 50 81 40 In the Bay of S. Augustine in Mada●gascar 13 0 S 23 30 83 0 Southwards from Cape S Roman 16 0 S 28 0 86 20 In Anthony Gills Bay in Madagascar 15 0 S 16 20 91 0 Decreasing. 34 Germane miles Southeast from Brandaon 22 0 S 19 20 110 0 In Goa a famous Mart town in Indie 15 10 N 25 30 120 0 In Cochin 15 0 N 9 45 120 0 25 Germane miles West. a little Northerly from the South-west corner of Sumatra 6 0 S 5 28 147 0 In Bantam a Mart town of Java 4 45 S 6 0 150 0 In the Island Lubocqua 2 25 S 6 10 155 0 In the South-west corner from the I'll of Balij 1 30 S 8 40 157 0 In the mouth of the river Cantan in China 0 0 N 23 0 160 0 In Bu●●a● 46 Dutch miles Eastwards from the East part of Java 0 0 S  160 0   

A declaration of the form ●r Table or view of variations.  
BEfore we come to the Declaration of this Table, this first of all we would not have unknown, namely, that if perchance hereafter by more diligent and more exact experience, any other variation, Longitude, or Latitude of places can be found, then that which is set down in this Table, so as it should be needful to change the difinitions and expositions of some things and words here set down: yet we ought not therefore to be scared from this purpose; but much rather ought we to strive with all our strength to attain thereto, that by little and little we may come to a more certain knowledge of things; building upon these as upon foundations: we therefore following this opinion will prosecute that as true, which at this time is most like to be true; that if others also do the same when occasion is given, we may always come nearer to that which is most true in the nature of things.  
Which things being omitted, that we may come to the declaration of the former Table, first of all we say, that the first of the three columns which thou seest in the Table, showeth the variation of the place, the second, the Latitude to which the third is adjoined containing the Longitudes, as we could by conjecture attain unto them, that the places might so much the more easily be found in the Globe, and the manner of the variations might more plainly be showed in that which followeth hereafter. The mark of the letter N in the second column, signifieth North Latitude, and S South.  
Then, because in them mention is made of the variation of the Northeasting, or the Northwesting increasing or decreasing, all which (as proper words of art) have need of there several definitons: first of all we must know that the Magnetical needle in one and the same place, doth always show the same part of heaven, but not the same part in all places: for in some places it pointeth due North, in other places it declineth more or less to the East or West. Therefore in manner of a definition, we will say thus.  

The first definition.  
THE Declination of the Magnetical needle from the North towards the East, is called the Northeasting, towards the West, Northwesting; and with a general name it is called the variation: but the variation and the North pointing of the needle (that is the pointing of the needle due North) may by a general name be called the needle pointing, or pointing of the needle.  
As concerning those words of increasing and decreasing, as also of the first and second part or space, before we come to the definitions of them, they have need of some precedent declaration. It may be seen in the Table of variations, that in Corvo the Magnetical needle pointeth due North: but after that, the more a man shall go towards the East, so much the more also shall he see the needle vary towards the East, till he come one mile to the eastward from Plymouth, where the variation coming to the greatest is 13 degr. 24 min. From hence the Northeasting beginneth to decrease till you come to Helmshude (which place is Westwards from the North Cape of Finmark) where again the needle pointeth due North. Now the Longitude from Corvo to Helmshude is 60 Degr Which things being well weighed, it appeareth that the greatest variation 13 degr. 24 minutes at Plymouth (the Longitude whereof is 30 degr,) is in the midst between the places where the needle pointeth due North. For 30 degrees is the midst between the beginning and 60 degrees. And what is here said of the North part, experience teacheth that the same taketh place in the South part also, for 105 Spanish miles from Cape S Augustine at the beginning of Longitude again it pointeth due North, as it doth 17 German miles from Cape das Aguillas (as it appeareth by the Table of variations) which place is in the Longitude of 60 degrees, and in the midst betwixt both at 30 degr. (as in the North part) again, there is the greatest Northeasting; of which place there was this mention made in the Table or view of variations: towards the Northwest Northerly from the Lands of Tristan de Cuncha, where the variation is 19 degrees  
Out of these we may conclude that the Magnetical needle doth point due North in every place situate in two Meridian half Circles drawn from the one pole to the other by Corvo and Helmshud●. And that the greatest Northeasting is in all places situate in the Meridian Semicircle drawn by that place, which we said was distant one mile from Plymouth towards the East. So as that part of the Earth which is contained between two Meridian Semicircles, distant each from other 60 degrees in Longitude, is the space wherein the Magnetical needle always declineth from the North towards the East. And the half of that part, that is, that portion of the Earth which is included between two Meridian Semicircles, the first of which is drawn by the beginning, the other by the 30 degr. of Longitude, is every where the place of the Northeasting increasing: but the other half is the place of the Northeasting decreasing, to wit when one goeth from the west Eastward, following the order, of the degrees of Longitude.  
By this that hath been spoken of the first Segment, with the Northeasting and his parts (in one of which parts the Northeasting is increasing, in the other decreasing) it may easily be understood what the manner of the second Segment is with the Northwesting, and what is the manner of the parts thereof, whereof one is the part of the Northwesting increasing, the other is the part of the Northwesting decreasing: for in the mouth of the River Cantan in China, at the Longitude of 160 degrees distant from Corvo, the needle pointeth due North the third time: there therefore drawing the third Meridian Semicircle the portion of the earth between the foresaid second Meridian Semicircle, and this third (distant each from other 100 degrees in Longitude) shall be the space wherein the Magnetical needle declineth from the North towards the West: and in the middle of both in the Meridian Semicircle 50 degrees distant from the second, and as much from the third, (or otherwise 110 degrees removed from the first Meridian drawn by Corvo) shall be the greatest variation of the Magnetical needle as it appeareth out of the Table of variations in two places, whereof one is in William's Island at Nova Zembla, where the greatest Northwesting is found to be 33 degrees. The other is distant 34 Dutch miles to the Southeast from Brandaon, where the greatest variation is found to be 22 degrees, and the Longitude of each of those places is 110 degrees. So as in the half of the second space (which portion of the earth is contained between the Meridian Semicircles of 60 degrees Longitude, and of 110 degr.) the Northwesting is every where increasing in the other half decreasing.  
Of these 160 degrees of Longitude (which arch wanteth but 20 degrees of half the compass of the earth) Plancius hath attained to the knowledge of the variation, in such sort as now we have showed. As concerning the other parts of the World, distant either towards the West from Corvo, or towards the East from Cantan, the experiments which hitherto the hath gotten from the Spaniards, the Englishmen, and our countrymen (the Netherlanders) do not well agree. Neither is it any marvel, seeing they had neither perfect knowledge, nor needful Instruments for that purpose: yet he expecteth other experiments from the ships which have now been abroad 14 months and more. In the mean time we will bring forth that to public view, which a man may without absurdity imagine.  
If so be that the property of pointing due North, take place not only in the three foresaid Semicircles (which we conjecture to be Meridian Semicircles drawn from the one Pole to the other) but in the whole Circles also; there should then be six such Semicircles upon the earth, containing also between them six parts or spaces of the upper face of the earth.  
The first with the Northeasting 60 degrees long.  
The second with the Northwesting 100 degr. long.  
The third with the Northeasting 20 degr. long.  
The fourth with the Northwesting 60 degr. long.  
The fifth with the Northeasting 100 degr. long.  
The sixth with the Northwesting 20 degr. long.  
That those things which have been spoken may by certain Geometrical figures be more clearly conceived let ABCDEFGHIKLM, be the Equinoctial of the earth; let N be the Po●e: then let NA be the half of the first Meridian Semicircle drawn by Corvo: NC, half of the second Semicircle: NE of the third: NG, of the fourth: NI of the fifth: NL of the sixth So as the arch AC. may make 60 degrees: CE. 100 degr. and so A, 160 degr. EGLANTINE, 20 degr. and so AGNOSTUS, 180 degr. GI'▪ 60. degr· and so AI, 240. IL, 100 degrees, and so ALL, 340 degr. LA, 20 degr. and so the whole Circle 360 degrees. Then let the six points BDFHKM be the middles between AC▪ CE, EGLANTINE▪ GI', IL, LA. Which being supposed, ANC shall signify the first space with the Northeasting, ANB the Northeasting of the first space increasing. BNC the Northeasting of the first space decreasing. CNE the second space with the Northwesting: CND the Northwesting of the second space increasing. DNE the Northwesting of the second space decreasing ENG the third space with the Northeasting. ENF the Northeasting of the third space increasing. FNG the Northeasting of the third space decreasing GNI the fourth space with the Northwesting. GNH the Northwesting of the 4 space increasing, HNI the Northwesting of the 4 space decreasing, INL the fifth space with the Northeasting. INK the Northeasting of the fifth space increasing, KNL the Northeasting of the fifth space decreasing. LNA the sixth space with the Northwesting. LNM the Northwesting of the 6 space increasing. MNA the Northwesting of the 6 space decreasing.   

The second Definition.  
The Northeasting or Northwesting increasing is that whereby the variation increaseth, the Magnetical needle, being carried from the West Eastwards and the Northeasting or the Northwesting decreasing is that whereby it decreaseth.   

The third Definition.  
The Semicircles of the Meridian, in which the needle pointeth due North, we call the first and second Meridian Semicircles, and so forwards according to the order of the degrees of Longitude, how many soever such Semicircles there shallbe, beginning at the Semicircle drawn by Corvo.   

The fourth Definition.  
The portion of the Spherical superficies, or round upper face of the earth contained by the first and second Meridian Semicircles, is called the first part or space, and the rest in order, the second, the third, and so forth unto the end.  
Having thus set down the manner of the variation, it remaineth that we show by examples (that which before we promised) that although in divers places having the same Latitude there be the same variation also, yet nevertheless the master of the ship may know in what part of the world, and in what place he is. Let us therefore again suppose that a ship had appointed to go from Amsterdam to Cape S. Augustine, in Brasile, the Latitude whereof in the Table of variations is set down to be 8 degrees 30 minutes, and the variation Northeasting increasing of the first space 3 degr. 10 minutes. The same ship sailing along by the coast of England, the variation shall be found to North-east or vary towards the East daily more and more until you come to Plymouth, where it cometh to the greatest, and is 13 degr. 24 min. Therefore the Master of the ship shall know assuredly that hitherto he hath sailed in the Northeasting of the first space decreasing, and that after this he shall have the Northeasting increasing, which when he shall find to be 10 degrees in the Latitude of 38 deg. 55 min. than he may assure himself that he is come to the Rock near Lisbon. Going forwards again from thence as it were towards the South-west, he shall daily find the Latitude to be diminished, and the Magnetical needle declining towards the North. Or otherwise if the Magniticall needle recline not towards the North, but either stand still or else decline more towards the East, than he may assure himself that he is carried Eastwards by some secret current not perceived: which notwithstanding he may remedy, if he go so much the more towards the West, until the Magnetical needle recover his due variation. But if he should come to the Northeasting of 3 degr. 10 minutes, before he have his Southerly Latitude to be 8 deg. 30 min. he shall then endeavour as much as in him lieth to keep that variation▪ and so sail on towards the South part of the world, guiding the ship so much the more towards the West or East as occasion shall require. And although he may deem otherwise by conjecture▪ yet he shall not follow that conjecture, for the reasons before showed, for so coming to the Southerly Latitude of 8 deg. 30 min. with the Northeasting increasing 3 deg. 10 min. he may assuredly persuade himself that he is near Cape S. Augustine, whereas otherwise trusting to conjectures he may very easily miss an hundred leagues of the place to which he had appointed to go, not knowing in the mean time whether he be to the Eastwards or to the Westwards from thence; which experience itself hath also taught too much in such Navigations. And therefore the Latitude and variation in all places of the earth being observed, and the knowledge thereof published, there shall be a much more easy way of sailing about the World, than ever hath been heretofore.  
Hitherto we have described the kinds of the variation which are afterwards declared out of those things which were set down in the Table of variations. If the Mistress of things (experience) shall hereafter teach that any thing is otherwise, that thing may also out of the same experience be otherwise defined that the Masters of ships in their Navigations may follow that only which shall be best and most profitable.    

How the North point, and the variation may be found.  
But if in the same afternoon experiment, the shadow of the Perpendicular stile L had showed 30 degr. from F the ark FL (containing 30 deg.) must by imagination be divided at M, so as MF, ML may either of them contain 15 degrees; which being thus performed, M shall be the North point and A the point of variation sought for, Northeasting from M to A 25 degr. and so in the rest.  
But if the needle only were turned about and not fastened to the paper or pastboord (as before) and the degrees were marked in the margin or limb of the Box, or case of the Instrument as is sometimes used, there is the same manner of using it, that was before rehearsed: saving that in the beginning of the Observation▪ the Box must be turned about so far till the Magnetical needle show the beginning of the degrees.  
The fashion of this Instrument may be described after this manner: ABC signifieth a Quadrant of a Circle standing at right Angles upon the Circle BDCE divided into 360 degrees, whereby the plain of the Horizon is signified. The centre thereof is F, upon which the Quadrant may be turned about: and that it may always remain at right Angles upon the Circle BDCE it is under-propped on both sides from G to D and E and those props are fastened to the same quadrant, that they may be turned about together with it. Moreover in the Circle BDCE there is a glass and under the glass a Magnetical needle, which must be so long as the box may suffer it. And the box or case hath within it 360 degrees, which the magnetical needle may precisely point unto, which likewise do agree with as many other degrees inscribed into the horizontal plain.  
This Instrument was made according to the invention of Reginaldus Petraeus, hanging upon two Axtrees like the Sea-Compass that so the Circle BDCE notwithstanding the motion of the ship, may always be equally distant from the Horizon. And that this may be done with the greater security the weight marked with the letter H is adjoined underneath, containing 25 or 30 pounds, or so many as the greatness of the Instrument shall require. But this also is worthy to be noted, to wit, that the Quadrant Perpendicularly erect in his place is of the same weight on both sides of the centre, that is to say, the side from F to C counterpoyseth the side from F to B, which may be known if a man take up the Quadrant, hanging it with G downwards▪ the thread being fastened in the midst of BC at F, and then cut off so much of the heavier part, as may suffice, that the line BC may hang level. But because some man may object that the Ruler or Index which the barbarians call the A●hidada, may bring a great variety in the weight as it shall be turned higher or lower: we must know that any such thing need not to be greatly feared because of the great weight H, and the lightness of the Ruler.  
The use of this Instrument in finding the North point and variation is this: you must begin to Observe (as in the former kind) certain hours before noon, and the instrument must be turned until the Magnetical needle point to the beginning of the Circle: then the Quadrant must be turned this way or that way, and the sight Rule● of the Quadrant must be lifted up or put down till the Sun shine through the sight. All which being done, suppose it be found (for examples sake) that the utmost Margin or Index of the Quadrant show in the Horizontal plain 40. degr. and admit the height of the Sun be also found to be 25 degrees, which together with the 40. degrees he shall for memory's sake have need to note. And when he hath expected afternoon till the Sun descending by the same Instrument be found placed in the same 25. degr▪ of Altitude, than the Box itself must again be turned this way or that way, until (the Sun again shining through the sights) the Magnetical needle do point to the beginning of the Circle. Which things being thus dispatched, the middle point of the arch in the horizontal plain between the first and second experiment is the North point, and how much the needle declineth from that point, so much is the variation sought for, as before we have showed in the first example more at large.  
Whatsoever we have affirmed to be available in the day time, in these experiments of the Sun, the same may be understood and done in like manner in the night, by any of the fixed stars, whereof there is the same use in this matter that there is of the Sun. But there is not the same reason of the Moon, aswell because of the swiftness of her proper motion, as also because of the greatness of her Parallax (as they call it) which the overmuch neereness of the Moon to the Globe of the earth bringeth forth. But this also is to be noted that two, three, or four, yea and more Observations may be made in the foorenoon. As for example, let the first be when the Sun is 10 degrees above the Horizon, the second when it is 15. degr. the third when it is 20. degr. and if any man will make trial as often after noon, he shall see how every experiment agreeth with other, and when at every moment the same North point is found, that thing shall give the Master of the ship no small courage, and more certain confidence of his work.  
But notwithstanding, when the Mariner saileth from the East Westwards, or chose from the West Eastwards, it may be that in the space of 10 or 12 hours between the first and second experiment, there may be difference of one degree or more in the variation, whereof may follow that the North point found by the first forenoon Observation, and the last in the afternoon, shall not agree with that which was found by the first in the afternoon and the last in the forenoon: when notwithstanding the Mariner hath not erred in Observing.  
Which if it shall happen often, the skilful Mariner may judge thereby what difference of variation is answerable to any determinate time of sailing, and so find a way whereby the North point may be found with more certainty and security: which thing may thus also be done▪ if a man diligently compare the variation found in the former days with the variation which he presently seeth.   
FINIS