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 cloudie weather when neither Sun nor Stars for many daies appear to be observed I thought it should not be impertinent to this place to set down the Theorick 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 Theorick to the end that such of our Sea-men as mean to be diligent observers hereof may make heedfull trial of that inclining propertie and compare the same with this Table in all parts of the world where they shall travell especially in those long Voyages to the East and West Indies and in their Northeast or Northwest discoveries The third part may be called Geometrical intreating of the Crosse-staffe and shewing how such errors may be avoided as have been commonly committed in the use thereof either by reason of the parallax or eccentricitie 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 quantitie of the angle that is to be abated out of the apparent altitude of the Sunne or starres observed by this staff for any height of the ey above the water it was needfull to know the quantitie of the earths semidiameter concerning which there is great varietie of opinions amongst learned authors I have therefore in this part of this treatise now shewed divers waies for the more certain finding thereof one of which waies I have also for my more assurance exemplified by observation as meanes and opertunitie served me neere Plimmouth 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 Sunne and fixed starres To which end there is first set down a table of the declination of every minute of the Ecliptick in degrees minutes and seconds calculated for the greatest obliquitie of the Zodiack as it is found by observation in this age 23 degrees 21 minutes and an half Whereto is adjoyned the use thereof for the readie finding of the place of the Sun by his declination given or contrariwise for finding the Suns declination his place being first known After this is shewed the way and means I used for exact observation of the Suns Meridian altitudes with a table of those observations for four yeeres together that so the more certaintie might be had of the declinations and places and consequently of the whole course and motion of the Sunne and that by comparing together so many observations the Sunnes Eccentricitie 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 Suns middle motions and Prosthaphaereses which were necessarie helps and means for calculating the Ephemerides of the Sun there set down without which the regiment or table of declination of the Sunne next following which I may commend as free from error observable at sea and seldome 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 capacitie I answer that it was not my purpose neither could I in all places apply my self to the most part of sea-mens capacitie 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 satisfie as I could for the present having seldome 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 farre differing in longitude from hence there followeth a Table of 32 principall fixed starres about the Aequinoctiall that have been most commonly known and observed by Seamen with their Declinations corrected and another Table of as many more of the notablest starrs 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 Suns Right Ascensions resolved into hours and minutes for every day of the year with the use thereof for finding at what houre any of those stars commeth 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 adjoyned the description and use of an Instrument which way not unfitly be called a Sea-quadrant whereby is shewed 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 Pole-star and Guard without making any abatement or allowance as the manner hath been in regard of the point of the compasse whereupon the Guard is situate But now for further satisfaction in every one of these particulars I refer the friendly Reader to the Treatise it self 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 shewing 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 adjoyn 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 alreadie 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 then 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 Pole-star which are many waies and much
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 commeth 6 hours sooner to your Meridian there then it doth to ours here at London and therefore because the Declination also is increasing and will be greater when the Sun commeth 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 commeth 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 then here Now imagine you sail in the year 1612 through the Streights of Magellan and having passed over the South Sea come the 12 of September to the Philippinas differing in Longitude from London VVestwards about 210 degrees In this example because the Sun is neer the Equinoctial point altering his Declination about 24 min. in 24 hours that is for every houre one minute therefore divide 210. the difference of Longitude by 15 the number of degrees conteined 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 then 10 min. 2 sec. the Declination found in the Table It would be at this time too tedious for me further to exemplifie every particularity specified in the former Rules which may cause some small diversitie in the use of the Suns 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 Suns motion and Declinations may most easily not onely 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 cleer if a Cloud cover the Sun but one quarter of an hour only about noon your Tables of the Suns 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 Pole-star and Guards but also in generall by the Meridian Altitude and Declination of any notable fixed star whatsoever So as not in the day time alone and that onely 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 cleer through the raking Clouds the Latitude of the place where you are may hereby bee more easily known then by Observation of the Suns Meridian Altitude For to omit the changing of the Suns 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 grosâ—y erred the Sun by reason of his swiftness of motion increaseth or diminisheth his Declination dayly yea hourly and that very sensibly many times whereof there must needs arise many severall considerations to be had of the right use and application of the Suns 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 Suns Declination were made and the place of Observation whether it be Easterly or VVesterly from thence besides many other particularities lately related and needlesse here to be repeated But the fixed stars mooving so exceeding slowly that in more then 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 especialy that are placed in the signs of Gemini Cancer Sagittarie or Capricorne neer the Solstitiall Colure which in an hundred years or two can alter their Declination scarce one minute whereas those stars that bee in Pisces Aries Virgo or Libra especialy if they be neer the Equinoctial colure 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 easie and generall use of the Declinations of the fixed stars then of the Sun I wish they were more generally known and observed by our sea-men then they are as whereby they might not onely 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 then otherwise they can because that in what latitude and how far soever they should come either Northwards or Southwards they might alwayes have their choice of divers fixed stars neer 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 errour then they are I mean especially the Tables published in Bourns regiment and Normans new Attractive which tables agreeing almost in
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 fore-foot 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 Dragons 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 Dragons 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 Dragons tail 23 40 13 53 3 The formost guard 14 11 14 54 2 In the turning of the Dragons tail 29 37 15 14 3 The hindmost guard 16 42 15 26 2 Next after the turning of the Dragons tail 30 20 15 54 3 The Dragons eye 37 18 17 22 3 The Dragons 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 onely 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 shew at what hour and minute every star in the first of these two former tables commeth to the meridian for the beginning and midst of every moneth in the year agreeing likewise in every errour one with another but because these errours 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 then otherwise he needed this inconvenience onely 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 generall way I have also made the table following of the Suns right ascensions reduced into hours and minutes for every day of this present year 1599 according to the Ephemerides 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 onely 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 Finde out in the table following the moneth and day wherein you observe the moneth in the upper margine of the table the day in the first column thereof next the left hand the common meeting of the column descending from the moneth and of the line proceeding from that day towards the right hand shall give you the Suns right ascension in hours and minutes for the same day This right ascension of the Sun subtract alwayes out of the right ascension of the star adding 24 hours to the stars right ascension if it be lesse then the right ascension of the Sun the remainder sheweth how many hours and minutes after noon the star cometh to the upper part of the meridian which if they be more then 12 hours subtract 12 from them and the remainder shall shew 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 onely by adding 12 hours to the time of their coming to the upper part of the meridian if it be lesse then 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 finde 23 hours 10 min. the Suns right ascension that day at noon Then in the first table of fixed stars I finde the great dogs right ascension to be 6 degr 27 min. to which because it is lesse then the Suns right ascension I adde 24 hours and the sum of both cometh to 30 hours 27 min. out of this I subtract the Suns 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 formost Guard cometh to the Meridian beneath the Pole First therefore you shall finde as before the Suns 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 lesse then the Suns right ascension adde 24 hours and from the sum 38 hours 24 min. subtract the Suns right ascension 18 hours 36 min so there shall remain 20 hours 18 min. the time of the formost 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 Suns 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
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 shew the meanes how by observation of the pole-star and guards to finde presently the height of the pole not onely when the fore-guard is in some one of those eight principal positions before-mentioned as the manner hath been hitherto but in any other position also and at any time of the night when the pole-star 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 then 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 lesse principal The principal parts of this Quadrant are the Semidiameter thereof and the Arch. The Semidiameter I call the streight square Ruler The arch I call that part of the Quadrant that is made crooked like a bow The lesse principal parts are the double box or â—ocket and the sights or Vanes The double box or socket hath two square holes made crosse-wise thorow it in such sort that the arch and semidiameter of the Quadrant may be fitly put thorow them the flat side of the one passing close by the flat side of the other By means of this double crosse socket the arch and semidiameter of the Quadrant are so to be joyned 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 moveable 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 thorow it even with the end of the Arch. The moveable 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 center is which center is shewed by the little round hole bored overthwart thorow the midst of the thicknesse of the square Ruler neer 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 center of that hole which is also the center 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 straight or plain sides and the hollow side thereof are divided into 90 degrees and every degree into 6 parts each part conteining 10 min. and upon the straight 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 pole-star 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 dayes because it conteineth the dayes of all the moneths of the year which dayes are signified by the smal divisions round about at the circumference of this circle Every fifth day hath his stroke drawn a little longer then the rest that so any day you desire may the easilier be found The smal divisions contein but one day apiece The lines shewing the beginnings and endings of the moneths are drawn overthwart the whole breadth of this circle The beginning of January is known by the two lines drawn neer together overthwart this circle whereof one sheweth the end of the moneth of December and the other sheweth the beginning of the moneth of January which is marked with two pricks February is easily known in this circle because it hath but onely 28 dayes March is by the little pole-star circle and so all the rest of the moneths may easily be known by their order Upon the center 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 smal hole that there is made in that circle The shorter Index reaching from the center of the day-circle unto the limb or circumference thereof that is divided into dayes may be called the Day-Index This smal circle placed between the center of the day-circle and the moneth of March may not unfitly be called the Pole-star circle because the distance of the center thereof from the center of the day-circle is answerable to the distance of the pole-star from the Pole which at this time I have often found by exact observation not to be more then 2 degrees and 48 minutes CHAP. XXXVII The use of the Sea-Quadrant and that first in observing the height of the Sun looking onely by the sight at the center to the Horizon at Sea TUrn the center of the Quadrant towards the Sun so as the shadow of the Vane or sight placed at the center may fall upon the hollow side of the arch of the Quadrant then looking thorow the little sight fastened in the end of the arch of the Quadrant lay the upper edge of the sight placed at the center even with the Horizon and at the same instant let one that standeth by mark deligently upon what degree and minute of the Quadrant the edge of the shadow
Clavius his grosse demonstration hereof 90 A more exact demonst with the practise thereof 92 The angle of dipping for any heighth 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 Suns declination commonly called the Regiment of the Sun 97 Chap. 17. Of the Table of Declination of every minute of the Ecliptick in degrees min. and sec. made according to the greatest obliquity of the Zodiack 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 Ecliptick 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 Suns Meridian Altitudes taken by the foresaid Quadrant in the years 1594 1595 1596 1597 at London  Chap. 20. The finding of the Suns Apogeum and eccentricity out of the former observation 142 To know the time of the Suns comming to any point of the Ecliptick 142 Chap. 21. The middle motion of the Sun corrected out of the former Observations 150 A Table of the Suns middle motions 152 Chap. 22. A new theorick 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 Ephemerides 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 Ephemerides to make them serve for many years 163 Ephemerides of the Sun 164 Chap. 26. The use of these Ephemerides 169 Chap. 27. The making of the Table of the Suns Declination 170 Prosthaphaereses of the Suns Declination 172 A Table of the Suns 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 Suns right Ascensions in hours and minutes for every day of the year 204 Chap. 33. By the former Tables of fixed Stars and the Suns right Ascensions to know the houre 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 Diall 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 â—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 Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star the Guard and Horizon may be seen 213 To know the houre of the night by the Nocturnal 213 An answer to Simon Stevin shewing 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 Sphaere 2 2. That the whole World is a Sphaere 2 3. Of the division of the Sphaere 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 center of the world 5 8. The whole quantitie of the earth 5 9. Of the Equinoctial circle 6 10. Of the Poles of the world 6 11. Of the Ecliptick line 7 12. Of the Declination of the Sun 7 13. Of the Colures 8 14. Of the Meridian circle 8 15. Of the Horizon 9 16. Of the 32 Windes 10 17. Of the two Tropicks 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 Practick part shewing 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 heighth of the Sun pag. 17 3. Of the Shadowes 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 Suns Declination 22 7. Foure examples for the plainer declaration of that which is said before 22 8. Another manner of accounting by the Sun as they use in Portugall 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 Crosse-staffe 27 12. Of the position of the North-star and the Guards 28 13. Of the height of the Star taken with the Crosse-staffe 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 Compasse 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
0 0 56 15 About midway betwixt Lisbone and Saint Micâ—â—â—ls ENE 0 0 61 40 WNW 0 0 73 7 Betwixt S. Michaels Tercaera E by N â…• 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 booke of the Variation of the Compasse 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 ESE ¼ E 0 0 75 50 From S. Maries W by S 6 leagues WSW 13 0 61 50 From S. Maries W by S 6 leagues W by S ½ 0 0 67 25 From S. Maries South 5. leagues ESE ½ S 0 0 69 30 From Saint Maries 16 leagues ESE ¼ E 0 0 75 50 NW by W Northerly ESE 2 30 73 7 ½ From S. Georges SE by E 3 leag ESE 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 ESE ¼ E 0 0 70 23 From the rock W about 66 leag SE by S â…™ S 26  37 30 From C. Finisterre N Easterly ESE ½ S 0  67 30 ESE â…” S 2  65 37 SW 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 Compasse The middle Variation The part of Variation   De. Mi De. Mi De. Mi De. Mi De. Min.  Iul. 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 heedfull diligence we may come so neer 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 neerest the Truth Causes of error herein Some cannot be avoided as the unsteadinesse of the Ship the imperfection of the sence and Instruments the weak respective force of the needle or wires be they never so well touched Others may be eschued as that there be no iron neer the Compasse 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 faultie being such as serve for Observation onely oâ— 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 Compasse and time of the day is presently given together with the Observation the Latitude of the place being known and that universally throughouâ— 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 incumbred to omit the Observation of the height of the Sun which as I have oft made tryal at Sea may thereby be more exactly performed then hath been hitherto by Staffe Ring or Astrolabe as they are commonly used The making of the Sea-Rings The figure of the Sea-rings Vpon the concave side of the innermost Ring let be described the degrees of the Suns declination for the right placing of the little bead upon the thred according to the time of the yeer Which may easiliest be done after this manner The bead being thus rightly placed put aside the Equinoctial Ring from the brasse pointer representing the Pole Actick that it may crosse the meridian at right angles which it shall precisely do if you bring the prick or little hole upon the out-side of the
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 Suns Apogeum and Eccentricitie 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 bin 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 dayes wherein certain Observation was made so for finding out the Declinations of the middle dayes between the Observations I thought it the best way first to make the Ephemerides 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 Ephemerides it is needful to know the time of the Suns entrance into certain principal points of the Zodiack as also the time of the Suns continuance in the arches of the Zodiack contained between those points whereby the proportion of the Suns motion may Geometrically be found out his Eccentricitie and place of his Apogeum being hereby known To know the time of the Suns commnig 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 dayes 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 dayes 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 dayes wherein you Observed you shall easily know also the true place of the Sun in every each one of the same dayes with help of the former Table of the Declination of every minute of the Ecliptick in such sort as before was declared when I shewed the use of that Table Now if it fall out so happily that both the day be clear when the Sun entreth into the desired point of the Ecliptick 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 entreth 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 shew 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 Suns entrance into the point desired Example of the first I desired to know the time of the Suns 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 Iuly 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 Suns entrance into the midst of Taurus Having therfore to this end Observed the apparent Meridian Altitudes of the Sun the 24 25 and 26. Dayes of April in that year within the space of which dayes 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 dayes 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. Dayes 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 houres to 21 houres 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 Suns entrance into the midst of Taurus by the Observations of the 24 and 26 dayes 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 dayes between the 24 and 26 dayes 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 comming to the point desired as suppose I could not have Observed the 24 day but only the 25 and 26 dayes in both which dayes 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 dayes 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 smal 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 Zodiack cannot alter so much as â…“ of a minute which is so smal 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 recentiorâ—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 comming 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 shewed we found the time of the Suns entrance into the beginning of ♈ and ♎ and into the midst of ♉ ♌ â™ and â™’ as into places serving most fitly for finding out of the Suns Eccentricitie 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 Suns entrance into the Solsâ—itial points where the Meridian Altitudes and Declinations of the Sun continue almost the same without any sensible difference for two or three dayes together chose rather the parts of the Zodiack 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 then 17 min. The times therefore of the Suns comming 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. Ian.    24 17 35 25 0 7 24 5 54 â™’ 15 Mar.    10 13 26 9 18 43 10 0 37 ♈ 0 April    25 16 50 24 21 47 25 3 54 ♉ 15 Iuly 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 â™ 15 Hereby the times of the Suns continuance in the arks of the Zodiack betwixt those points as also the arks of the Eccentrick answerable to those times were more easily found then that it should now be needfull 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 then one minute in one Observation or little more then 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 practise 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 difficultie 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 Zodiack which Refraction admitteth some alteration according to the diversitie
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 center E and upon every division of the line EB 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 EB 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 Tropicks also shall be divided Then by every three points answerable in the Equinoctial and the two Tropicks you shall draw certain parts of Circles seeking the center 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 Equinoctiall from one to another and those shall be the Parallels of the Suns 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 EB 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 EB And so the line EB must be divided from five to five degrees which divisions shall be removed into the said Horizon fastning it to the Center and laying it to the line BD and dividing it both ways as the line EB 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 Center 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 Compasse 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 doe 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 Tropicks of Cancer and Capricorn And the other lines between those are the Parallels of the Suns Declination which have their numbers agreeable to them And those that are between the Equinoctial and the Tropick of Cancer doe 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 heighth of the Sun with your Astrolabe and seeking the Table of the Suns 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 thred overthwart which shall be equally distant from the Horizon Then reckon the Suns 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 thred for that hour is the hour of the day But note this that if the crossing of the thred and Parallel doe 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 c. Now although every hour line hath two numbers one of the morning and another of the afternoon yet it is an easie 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 Compasse by this Instrument IF you would know by this Instrument the Variation of the Compasse you must doe thus When the Sun riseth or goeth down at the Horizon Observe him with your Compasse noting very diligently upon what Rumb and part of the Rumb he riseth or falleth And if the compasse 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 then you shall see
the very degree of the Compasse upon which the Sun riseth or setteth Then the Horizon being set fast as we have shewed in the former chapter mark in the Instrument by which part or degree of those upon the Horizon the Parallel of the Suns Declination that day doth cross the same counting in the numbers of the Horizon from the center 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 Compasse or at his going down was distant from the West thereof for then you may say that the Compasse 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 Compasse which the Instrument doth shew the Compasse hath no variation at all 2 When the Sun riseth more to the North of the Compasse or goeth down more to the South then is shewed by the Instrument all the difference between the Instrument and the Compasse is the North-easting or variation thereof to the East-ward 3 If the Sun riseth more to the South of the Compasse or seteth more to the North then the Instrument sheweth all the difference between the Instrument and the Compasse 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 heighth of the Pole in that part where you desire to know this being known place the Horizon in such sort as was shewed in the 36 chapter And finding by the Table of the Suns 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 shew 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 mid-night 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 mid-night the Rule following is to be Observed The Rule The number of the whole moneths 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 moneths fall not out just add for every fifteen days above the whole moneths 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 moneths 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 North-west 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 passe 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 mid-night 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 compasse 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 mid-night if it have gone beyond As for example I see the former Guard in the Northwest upon the 15 of Iuly because that upon the 15 of Iuly 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 Suns Declination that have bin most in use amongst English Sea-men doe both in fashion and manner of using something differ from those before set down pag. 173 174 c. Least any therefore of the meanner sort might be mistaken or should not rightly conceive the manner of using these Tables I thought good to adjoyn 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 Suns Declination containeth twelve particular Tables shewing the Declinations of the Sun for every day of the twelve moneths 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 moneth 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 Arithmeticall 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
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 Spring-tides 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 certaine Instrument whereby you may in generall judge of the tides 58 The use of this Instrument 59 34. Of the making of an uniuersal Diall 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 Compasse 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 Diall by the North stars 65 The use of the Table of the Suns declnation 67 A Table of the Suns declination 69 By the height of the Pole-star 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 Pole-star 83 2 When the two Guards are of equall height betwixt the East and the highest 84 3 When the greatest or formost Guard is right above the Pole-star 85 4 When the two Guards are directly one over another betwixt the highest and the West 86 5 When the greater or formost Guard is in the West of the same height with the Pole-star 87 6 When the two Guards are of equall height betwixt the West and the lowest 88 7 When the greater or former Guard is directly under the Pole-star 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 Cornhil at the signe of Atlas GLobes Coelestial 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 Gunters Quadrant and Nocturnal Stirrups Universal Quadrat These with divers other Mathematical Instruments are printed on Papers and exactly pasted on Boards c. with Indexes and other appurtenances proper to each Instrument very commodious for any mans use Also Books for the use of every of the foresaid Instruments Sea-plats printed on paper or parchment and pasted on Boards Vignola or the compleat 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 then 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 shewing 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 appoynted 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 sayled 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 goe unto and so come to any Haven or place appointed at Sea But I know not how it hath come to passe that there could not hitherto any certain knowledge of that matter be attayned unto For some when they indevoured to find this thing by the magnetical needle gave the Load-stone it self a Pole which of the Load-stone called also the Magnet they named the Magnetical Pole or Pole of the Load-stone But that this is otherwise the thing it self 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 shewed and that the circumstances hereof may more clearely 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 dayly experience that the Magnetical Needle touched with the Load-stone 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 wherof we made mention before sometimes indeed it sheweth 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 smal distance of places hath most manifestly appeared to them which have directed their course from the Easterne 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 dayly experience plentifully teacheth For that we may make this matter plain by examples especially if the Mariner know that the Latitude of the Citie of Amsterdam is 52 degr and 20 min. and that the variation of the Compasse 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 Citie have But some man may object that there are many places which have the same Latitude and variation that the Citie of Amsterdam hath whereto we may readily answer that indeed there be such places but yet very far distant from thence and
innermost circle to the end of the foresaid brasse pointer so as the end thereof may enter thereinto Then set the line that is drawn from the end of the brasse 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 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 brasse pointer Northwards till you find the midst of the shadow of the bead to fall upon the peripherie drawn round about through the midst of the concavitie of the Equinoctial ring which peripherie we called the parallel of the Sun and so keep the whole Instrument and Compasse as steady as you can till the flie of the Compasse remain quiet and still keeping in the mean time the midst of the shadow of the bead alwaies upon the foresaid parallel of the Sun and withall looking close by the graduated side of the Meridian directly down upon the midst of the Compasse and mark what degree and minute you see close thereby in the North part of the Flie for so much as the North point of the needle or wiers 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 sheweth 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 before-mentioned 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 Suns true Azimuth may be found with Ruler and Compasses onely after this manner Draw the circle ABCDEFGH representing the Meridian by the center 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 center 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 Suns 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 complement of the angle OAR 150 degrees to a semicircle or 180 degrees Secondly in the Triangle ARS all the sides are given AR 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 BO which is double in power to AB Or else thus The arch OB being 90 degrees the subtense therof OB that is the Tangent BD is 14,142,126 which sought in the Table of Tangents shall give you the angle BAD 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 SR 19,318,516 is to the sum of the other two sides SA and AR 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 SR 19,318,516 there remaineth YR 8,965,754 the half whereof RZ 4,482,877 is the sine of the angle RAZ 26 degrees 38 minutes 2 seconds the complement whereof 63 degrees 21 minutes 58 seconds is the angle ARZ which added to the angle ARO 15 degrees maketh the whole angle ORS 78 degrees â—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 complement whereof is the Inclination sought for 78 degrees 52 minutes 40 seconds The sum and difference of the sides SA and AR being alwaies the same viz. 27,320,508 and 7,320,508 the product of them shall likewise be alwaies the same viz. 199,999,997,378.064 to be divided by the side SR 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 AR 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
of the raritie or densitie 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 misse a minute and more somtimes 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 lesse then 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 Suns Revolution through the Zodiack in our time is 365. dayes 5. hours and about 48. min. Also the Suns continuance in the Northerly Semicircle of the Ecliptick from the beginning of Aries to the begining of Libra to be 186. dayes 18. hours and about one half and consequently in the Southerly Semicircle from Libra to Aries 178. dayes 11. houres 18. minutes whereby the arks of the Suns 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 neer 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 Eccentricitie 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 Suns 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 Eccentricitie cannot be lesse then 3616. of the same parts notwithstanding he maketh it to be little more then 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. daies and about three hours and foure minutes and consequently the arch of the Suns Eccentrick answerable to that time and arch of the Ecliptick 45. degr 27 min. 56. sec. I found hereby the Suns Eccentricitie and place of his Apogeum as followeth Past this upon the Margin of Letter Z. fol. 148 so as it may ly 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 Suns Eccentricitie in such parts whereof the Semidiameter of the Eccentrick Be containeth 100,000 Agreeing exactly with the Suns Eccentricitie found by Tycho Brahe Progymnasmat Pag. 26. The same may also be further confirmed thus We have found the arch of the Suns Eccentrick from the beginning of Aries to the beginning of Libra to be 184 5 26 the excesse wherof 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 Suns Eccentricitie if his Apogeum were in the beginning of Cancer But having found that the Suns Apogeum is about 5 degrees 17 minutes of Cancer therfore 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 Eccentricitie of the Sun 358,414 which hath not any sensible difference from that we found before But the place of the Suns Apogeum found by the foresaid Observations differeth from Tycho twenty minutes if we add â—o his place of the Apogeum of the Sun 7 minutes for the Moâ—â—on of the Suns Apogeum in the ten years space betwixt his Observation and mine All which difference notwithstanding may arise by erring little more then half a quarter of a minute in Observing the the Suns height about the midst of Tarus Which error although it be so smal that it may worthily be neglected for whether of them soever you follow either his Apogeum or mine for the making of the Ephemerides and Tables ensuing there cannot hereof arise any such disagreement as can by sight be diserned yet in that smal difference that is though insensible I shall not unwillingly yeeld 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 judgment and use of Observation will easily grant I say therefore not building only upon his authoritie though in this kind it be greater then any others yet known to the world that following the ordinary received Hypothesis of an Eccentrick for saâ—ving the Suns apparent inequalitie of motion the Suns Eccentricitie and place of his Apogeum set down by Tycho as before we have shewed 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 smal 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 certaintie and infallibilitie of those Tables of the Suns Declination which for the Navigators use shall out of these grounds be gathered and diduced CHAP. XXI The middle motion of the Sun Corrected out of the former Observations THE Eccentricitie 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 Suns true place in the Zodiack B a a line drawn from the center of the Eccentrick to the center of the Sun A d a line drawn from the center of the Ecliptick Parallel to B a shewing the middle place of the Sun in the Zodiack AB a line drawn from the center of the Ecliptick by the center of the Sun to the Zodiack shewing the true place of the Sun Therefore the Angle BAD being 5. degr 37. min. and consequently the Angle BAI 95. degr
2 30 39 Â 21 6 9 5 43 Â 8 6 18 57 40 14 45 6 Â 25 53 2 4 7 2 7 18 Â 22 7 9 27 51 21 58 7 19 12 25 14 23 7 Â 27 57 1 45 8 1 43 56 Â 27 8 9 49 49 Â 52 8 19 26 48 14 1 8 Â 29 32 1 8 9 1 20 29 Â 27 9 10 11 41 Â 42 9 19 40 49 13 40 9 Â 30 40 0 39 10 0 57 2 Â 29 10 10 33 23 Â 33 10 19 54 29 13 18 10 Â 31 19 0 11 11 0 33 33 Â 31 11 10 54 56 21 23 11 20 7 47 12 55 11 Â 31 30 0 18 12 0 10 2 Â 32 12 11 16 19 Â 13 12 20 20 42 12 34 12 Â 31 12 0 48 13 0 13 30 Â 33 13 11 37 32 Â 2 13 20 33 16 12 9 13 Â 30 24 1 14 14 0 37 3 Â 32 14 11 58 34 20 51 14 20 45 25 11 48 14 Â 29 10 1 44 15 1 0 35 23 34 15 12 19 25 Â 39 15 20 57 12 11 23 15 Â 27 26 2 13 16 1 24 9 Â 32 16 12 40 4 Â 28 16 21 8 35 10 59 16 Â 25 13 2 40 17 1 47 41 Â 31 17 13 0 32 Â 16 17 21 19 34 10 34 17 Â 22 33 3 9 18 2 11 12 Â 31 18 13 20 48 20 3 18 21 30 8 10 9 18 Â 19 24 3 37 19 2 34 43 Â 29 19 13 40 51 19 49 19 21 40 17 9 46 19 Â 15 47 4 5 20 2 58 12 Â 28 20 14 0 40 19 36 20 21 50 3 9 19 20 Â 11 42 4 34 21 3 21 40 Â 26 21 14 20 16 19 23 21 21 59 22 8 53 21 Â 7 8 5 0 22 3 45 6 Â 22 22 14 39 39 19 8 22 22 8 15 8 28 22 Â 2 8 5 29 23 4 8 28 Â 19 23 14 58 47 18 53 23 22 16 43 8 2 23 22 56 39 5 56 24 4 31 47 Â 17 24 15 17 40 18 38 24 Â 24 45 7 36 24 Â 50 43 6 23 25 4 55 4 Â 12 25 15 36 18 18 22 25 Â 32 21 7 9 25 Â 44 20 6 51 26 5 18 16 Â 9 26 15 54 40 18 7 26 Â 39 30 6 42 26 Â 37 29 7 10 27 5 41 25 23 5 27 16 12 47 17 50 27 Â 46 12 6 15 27 Â 30 19 7 52 28 6 4 30 Â 0 28 16 30 37 17 33 28 Â 52 27 5 48 28 Â 22 27 8 11 29 6 27 30 22 54 29 16 48 10 17 16 29 Â 58 15 5 20 29 Â 14 16 8 36 30 6 50 24 22 49 30 17 5 26 16 58 30 23 3 35 4 53 30 Â 5 40 9 3 Â Â Â Â Â Â 31 17 22 24 16 41 Â Â Â Â Â Â 31 21 56 37 9 26 CHAP. XXVIII The use of the former Table or regiment of the Sun THis Table of the Suns 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 Sea-men do take the Suns 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 alwayes 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 somtimes 10 or 12. minutes or more in a long voyage in taking the Suns declination For there is not any Table of the Suns 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 truely 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 misse 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 Suns declination agreable 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 Suns 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 conteineth and so many minutes adde 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 immediatly 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 sheweth if the quotient be lesse then 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 sheweth 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
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 Â Â 1 07 3 04 5 03 7 11 30 21 31 Â Â 1 11 3 07 5 07 7 15 31 21 35 Â Â 1 15 Â Â 5 11 Â Â Â 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 Â Â 15 01 Â Â 19 25 CHAP. XXXIII By the former Tables of the fixed Stars and the Suns 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 starres is at the meridian which may easily be known by a Needle-Dial or Compasse 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 neer as you can by estimation for a little errour herein breaks no square which may be done thus From the Pole-star directly towards the first star next the rump in the great Bears tail imagine almost so much space as the Guards are distant asunder for neer thereabouts is the place of the Pole Now betwixt your eye and this place of the Pole hold a plumb-line hanging as perpendicularly and stedfastly as you may and mark withall if that plumb-line 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 shewed 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 finde 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 finde as before to be 22 hours 14 minutes whereto you may adde a minute or two more because that star will come to the meridian very late in the evening so making the Suns right ascension 22 hours 16 minutes The right ascension of that star in the second table of fixed stars you shall finde 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 remainer because it is lesse then then the Suns right ascension adde 24 hours and from the summe 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 Pole-star and Guard BEsides the wayes already spoken of to finde the elevation of the Pole by the meridian altitudes and declinations of the Sunne and fixed stars in general there hath been also used another way more special by the height of the pole-star 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 Northeast Northwest Southeast and Southwest points Of which way as it hath been hitherto published and used I must for the present onely 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 pole-star 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 pole-star to finde thereby the height of the pole are made the same for all latitudes But having already shewed 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
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 sheweth 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 shewed 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 moveable sights or vanes even with that end of the Quadrant where the little sight is fixed Then looking thorow the slit which is made thorow 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 center even with the Horizon lift up or put down the arch of the Quadrant till the upper edge of the shadow of the broad moveable 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 center Then reckoning from the upper end of the arch of the Quadrant downwards see what number of degrees and minutes you finde at the upper edge or end of the socket through which the Quadrant moveth adding alwayes thereto two degrees for so shall you have the height of the Sun if you abate from hence 16 min for the Suns semidiameter and the surplussage answerable to the height of the eye above the water as before is shewed 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 moveable sight of the Quadrant at some even number of degrees as at 10 20 or 30 c. And setting the end of the semidiameter of the Quadrant where the center is to the corner of the eye as you do when you observe with the Crosse-staffe lay that edge of the sight even with the upper edge of the Sun and move the nether moveable sight up or down till the upper edge thereof lie even with the Horizon Then see how many degrees and minutes are conteined between the upper edges of both sights from which abate as before 16 minutes for the Suns 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 midsâ— of the star and from the number of degrees and minutes conteined between the upper edges of both sights abate onely 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 iâ— must be remembred that before you observe the Sun or star after this manner you must finde out the eccentricity of your eye in such sort as I have shewed in the 15 Chapter of this book which eccentricity you must adde to the distance of the center oâ— the Quadrant from the end of the Semidiameter where you seâ— your eye for so much as the sum of this distance and eccentriâ—city amounteth unto so much must you thrust forward the foreâ—end of the semidiameter of the Quadrant beyond the further end of the square socket thorow which it is put that so the center oâ— your eye may be brought to the center of the Quadrant CHAP. XL. How to find the height of the Pole by Observation of the Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star 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 Pole-star till the Diameter of the Semicircular hole of the Pole-star circle 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 Pole-star so neer as you can guesse upon the midst of that Diameter and the fiducial line of the Guard-Index upon the Guard move one of the moveable sights of the Quadrant up or down till the edge thereof lie even with the Horizon Thus therefore the Pole-star lying upon the midst of the Diameter that is upon the center of the Pole-star 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 center 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 Nocturnall ANd the point of the short Index which we called the Day-Index being first set to the day of the moneth sheweth 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 triall I have made of the first Rumb counted from the Meridian though Simon Stevin in his solemne demonstration continued almost in three whole pages in folio wherein he professeth that the scope or mark he aimeth at is to demonstrate that my Table of Rumbs is erroneous would make the world beleeve 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 grosse manner of triall much more then 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 then my Table hath But if he worke the very same way by sixth parts of degrees or tens of minutes he shall find but little above half a minute more then is in my Table of Rumbs Nay moreover if it shall please him at his leisure to take the pains to make triall hereof to every single minute he shall not find so much as one second more then my account giveth For
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 massie body without hollownesse and perfectly round in the midst whereof there is a prick called the center 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 center of the earth by which we do imagine a right line or Axtree to passe 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 vertue 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 moveable 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. IV. 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 dayes and 8 hours which is one Revolution Mercury Venus and the Sun finish their motion in one year which conteineth 365 dayes 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 moveable 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 compasse of heaven conteineth 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 lesse CHAP. V. Of the Figure of the Heavens THat the Heavens are round it is proved because roundnesse is the most perfect Figure of all others being whole and intire having no need of any joynts being also of the greatest capacity of all figures that have the same compasse 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 sheweth more cleerly that the earth and water make one round Globe then the shadow which they make in the Eclipses of the Moon which shadow we alwayes see to be a part of a circle For if the body which is the cause of the same shadow were three-square or four-square the shadow it self 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 center of the World ONe sign we have to be assured that the Earth is in the midst and center of the World namely that wheresoever we are upon the face of the earth we alwayes 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 alwayes of the very same bignesse Whereby we may easily perceive that they are alwayes equally distant from our sight and whereas they move round about it it followeth that we are upon the center 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 center or prick yet being considered by it self it conteineth in the greatest circle thereof 6300 common Spanish leagues Which a man may easily perceive by taking two such points or head-lands 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 compasse of the whole world conteineth 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 conteineth 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 it self 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 alwayes 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 alwayes 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 Eclipticke line THe Equinoctial circle is divided into equal parts by another circle called the Ecliptick 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 Ecliptick And through this circle the Sun is continually move by his propper 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 quantitie of his greatest distance is about 23 degrees and an half and so much is the distance of the Poles of the Ecliptick from the Poles of the Equinoctial And albeit this circle is not drawn in the Sea Chart yet is it in some sort represented in the Table of the Suns Declination which are gathered from the motion which the Sun maketh under the Ecliptick CHAP. XII Of the Declination of the Sun THe motion of the Sun under the Ecliptick 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 alwaies keepeth between 23 degrees 28 minutes and 23 degrees 53 minutes From hence therefore we doe infer that at divers times it is meet to make new and divers Tables of the Declination of the Sun CHAP. XIII Of the Colures There are two Circles of the Sphere either of which divideth in into two equal parts and they are called Colures because that in the revolution which they make by force of the Primum mobile they do not shew themselves wholly unto us so as we may see all parts of them One of them is called the Equinoctial Colure because it passeth by the Poles of the World and the points where the Ecliptick cutteth the Equinoctial and when the Sun by his own proper motion commeth 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 Autumne at which times the Sun hath no declination at all The other is called the Solstitial Colure because it passeth by the Poles of the World and of the Ecliptick and by the points where the Ecliptick is furthest distant from the Equinoctial And when the Sun by his proper motion commeth 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 Autumne and is in his greatest Southerly Declination These two Colures are noted in the Table of the Suns Declination because the Equinoctial Colure passeth by the two points where there is no Declination at all because the Sun is under the very Equinoctial circle and the Solstitial Colure 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 commeth unto this circle it maketh mid-day 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 onely 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 joyned with the water when we are at Sea without sight of
Rules of the Declination of the Sun we are to note that the year which is the time of the Suns motion from any point of the Ecliptick till he return again to the same point consisteth not alwaies 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 needfull to make foure Tables of twelve moneths apeece 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 begining 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 Therfore to know at all times which of the foure 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 then that year is leap year and if the remainder be even and the half thereof odd then that year is the second year after the leap year But if the remainder of the years numbred 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 then 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 Suns Declination every day we must look in that Table which answereth to the present year and seeking the moneth in the upper part of the page and the day of the moneth 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 moneth 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 Suns Declination THey which sail in the moneth of Iune and December need not much to make any Equation in the Table of the Suns Declination because that in those moneths 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 contrariwise subtract alwaies the lesse out oâ— 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 7200 leagues which are contained in the compasse 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 Iune or from the 13 of September to the 12 of December or it must if the shippe also hath sailed Westward be subtracted if you find it in any other time of the year except in the daies 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 doe contrariwise subtracting the said Squation where before you added it In stead of the Table of the Suns Declination here inserted by Roderigo Samorano use the Table before set down from the 174 page to the 180 page CHAP. VII Foure 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 noone and found the height thereof to be iust 90 degrees First therefore I took from 1608. the number of 1600. and their remain 8 whicâ— remainder being an even number and foure the half thereof being even also I say the year 1608 is the Leape year And so I goe unto the fourth year in the Table of the Suns Declination which is leap year and under the moneth 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 betwen 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 tooke 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 odde number I goe 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 moneth of May against the 13 day the Suns 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 Compasse and so I say that
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 passe over the barre towards the Indies It is evident that if the Ships be great they have need of much water to pass the bank or the barre which quantity of water is only in the Spring-tides And because they are twice in one moneth namely in the Conjunction and in the full of the Moon I desire to know when the Spring-tides and Neap-tides of the moneth of Iune in the year 1588 were to be expected in which moneth 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 foure and nothing remaineth and because there is no remainder I will take two more of the concurrent thâ—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 moneths which are from the beginning of March past till this present moneth of Iune 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 Iune by the third Rule and adding seven unto the day of this Conjunction you have the first day of Iuly 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 moneth 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 Iune by the fourth Rule I say therefore that the Spring-tides or greatest waters of the moneth of Iune were in that year upon the ninth and four and twentieth days of Iune and the Neap-tides or less waters were upon the sixteenth-day of Iune and the first of Iuly by the fifth Rule CHAP. XXXII Of the daily Tides NOW that we know the Rules of the Spring-tides 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 Compasse and this dayly motion of the Sea falleth not every day at the same hour because the Moon doth not alwaies keep one and the same distance from the Sun For the Moon moveth almost thirteene degrees of her proper motion in one natural day whereas the Sun moveth scarce one and so one being taken from thirteene there remain 12. And because the Sun doth give and marke out unto us hours and the Moon Tides it commeth to pass that an hour being that space of time wherein fifteene degrees of the Equinoctial pass by every point of the Compasse the part by which the Moon is distant from the Sun shall be twelve degrees which twelve are â…˜ of fifteene 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 â…˜ parts of an hour whereby the Moon is every day slower then the Sun in comming 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 commeth to passe that so many days as the Moon is old so many times â…˜ parts of an hour it is slower then the Sun in passing by each Rumb untill the day of their conjunction when as they passe 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 daies of the Moon the full Sea falleth out at the same hour when the Moon commeth 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 daies old the Moon is you must add three numbers together to wit the concurrent and the moneths from the beginning of March to the moneth present and the daies of the moneth wherein you would know this and if the whole product exceedeth not thirtie it containeth just the daies of the Moon but if it doth exceed thirtie the surplussage sheweth the daies of the Moons age The fourth Rule Multiplie the daies of the Moons age by four and divide the product by five and the remainder after division containeth the hours whereby the Moon commeth more slowly then 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 commeth the first ebbe or low water and 12 hours and â…• after the first full Sea commeth the second Tide and other six hours and â…• after the second Tide commeth the second ebbe The fifth Rule When the daies of the Moons age are less then fifteene we may make by them our account for the Tides but if they exceed fifteene we must make our account by the surplussage 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 ebbe to make choice of that which might seem most expedient for my Voyage By the formâ—r 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 Gregorie the 13. Then I add this number of 2 to the number of 5 moneths which have passed from the beginning of March and the 29 days of the moneth of July all which 3 numbers make 36 then I cast away 30 and there remain six daies for the age of the Moon and because they exceed not fifteene I multiply them by â…˜ 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 commeth to the North-east four hours and ⅘ later then the Sun And because the Sun commeth 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 fourteene 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 commeth the second ebb or low Sea CHAP. XXXIII Of a certain Instrument whereby you may in generall 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 channell 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 daies 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 bigg as the palm of a mans hand and half a fingers bredth within that circle draw another circle and having divided them both into 32 equall parts with lines drawn from the center to the circumference of the greater circle upon the upper end of one of those lines place a flower-deluis 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 untill 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 doe 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 bigg 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 c. till you end at the same point with 30 This being done fasten with a thred or nail the second Table or Circle upon the center of the first so that it may freely without impediment turne 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 puting a litle wax underneath that it may not move Then account the days of the Moons 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 alwaies either where the point is or at the point right over against it and hence you may easily find both ebbes 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 universall Diall which may serve Generally all the World over DRaw upon a Table or pastboord the Circle ABCD upon the center E and half a fingers breadth within that Circle upon the same center draw another Circle and about the breadth of a wheat corn within the second Circle draw a third and placing your Ruler upon the center 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 center 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 DA into 90 parts as the manner is in the making of an Astrolabe set numbers thereto from 5 to 5. begining your account from the two points AC and so proceding 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 degres 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 Tropick of Cancer and GI the Tropick 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 fifteene degrees from C towards B and other fifteeen 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