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
and inconstant inequality of the angles which that great Circle maketh with every new Meridian Of which angles the Invention indeed by the Chart especialy is very subtile and consisteth herein to wit in knowing how much such kind of angles do decrease or increase as the ship goeth forwards And he that so shapeth his course goeth the straight and neerest way Otherwise it cannot be that a man should keep a straight course if he shall continually follow one and the same point or line of the Compasse except he sail under a Meridian or under the Aequinoctial line but he must change the point of the Compasse so often as that straight course shall sensibly require And therefore it cannot be by any means that the Mariners when they go perpetualy towards the same part of the world keeping the same angle of position in respect of the Meridian or the same point of the Compasse should go the shortest and nearest way This kind of sayling under a great Circle is of special use in our Northern Navigations for the discovery of the North-east or North west passage which as it may most easily be performed by help of an Hydrographical Globe with the Helisphaericall lines drawn thereupon so for them that list not to be troubled with the cumbersome carriage and charge of the Globe it may be done in a manner with no lesse facility by a nautical Planisphere made after the projection of Gemma Erisius his Astrolabe whereof more hereafter when God shall give leasure There be some also that hold it for erroneous that the Rumbs in the Mariners Chart should be expressed by right lines and consequently that the Meridians should be Parallels or equidistant every where which because it is but barely affirmed and the contrary may be proved as well as that each Rumb except the rumb of North and South maketh equal angles with every Meridian we hold it not only as true but also as most meet and commodious for the Mariners common use that the Meridians in the Sea-Chart should be every where equidistant each from other and consequently that the Rumbs should be straight lines for these two causes First because the rumbs or points of the Compasse may so most easily be drawn in the Nautical Planisphaere onely by a straight ruler For seeing that any one and the same rumb saving onely the rumb of North and South which is all one with the Meridian maketh alwaies equal angles with every Meridian without either sensible numerable or measurable though not without intelligible error for indeed those angles are lesse and lesse as they come neerer to the Pole much like as the angle of a little semi-circle is lesse then the angle of a greater semi-circle all the rumbs must needes be straight lines if the Meridians be equidistant and right lines by the 27 and 28 prop. 1. Euclid Secondly the respective situation of any place to other in the Chart which they commonly call the lying or bearing of one place from another according to the points of the Compasse may most easily be known by the Nautical Planisphaere with right lined rumbs and equidistant Meridians For that rumb from which both places are equidistant sheweth how those two places lye one from another And for these two causes of so great facility both in the making and using of the Mariners Chart with equidistant Meridians and straight-lined rumbs it ought to be preferred before any other Instrument heretofore published to that end for the common use of the Mariner at Sea especially And though the Globe be commended by some as most absolute and perfect for all courses and Climates whatsoever yet for the chargeableness thereof troublesome carriage stowage and tedious usage for the most part in Navigation following any other course save East or West North or South it will for the most part be found unmeet and cumbersome and nothing so fit and ready for the Mariners common use at sea as the Nauticall Planisphaere truly made CHAP. II. How the former Errors may be avoyded THese Errors notwithstanding they have been much complained of by divers as namely by Martine Cortese in his third book and second chapter of the Art of Navigation but specially by Petrus Nonius in his second book of Geometrical Observations Rules and Instruments And although Gerardus Mercator in his universal Mappe of the World seemeth to correct them by making the distances of the parallels greater and greater towards the Poles yet none of them teacheth any certain way how to amend such grosse faults whereby the Mariner may be deceived many times an whole point of the Compasse yea sometimes two or three points and more in judging by his ordinarie Chart how one place beareth from another especially if he sail far Northwards or Southwards whereby we may easily guesse how indirect a course he shall make to come to the desired haven that shall follow so false and erroneous direction with great danger at the least many times to lose ship goods lives and all The fountain of all the errors aforesaid the last only excepted is in the very foundation and ground-work of the Mariners Chart that is in the first Geometricall lineaments thereof namely because the Meridians are not rightly divided the divisions being every where equall nor the Parallels rightly drawne having in all places the same distances each from other that the Meridians have at the Aequinoctial Whereas the spaces betwixt the Parallels should increase more and more as you go from the Aequinoctial towards either of the Poles which Martin Cortese also noteth is his 3 book and 2 chapter of the Art of Navigation But he omitteth that wherein all the difficultie lieth that is how much or in what proportion those spaces should increase Which that it may the better be perceived I think it not unmeet first to shew by what kind of projection or extension rather the nauticall planisphaere may not unfitly be conceived to be geometrically made after this manner Suppose a sphaerical superficies with Meridians Parallels Rumbes and the whole hydrographicall description drawn thereupon to be inscribed into a concave cylinder their axes agreeing in one Let this Sphaerical superficies swel like a bladder whiles it is in blowing aequally alwayes in every part thereof that is as much in longitude as in latitude till it apply and joyn it self round about and all alongst also towards either pole unto the concave superficies of the cylinder each parallel upon this sphaerical superficies increasing successively from the Aequinoctial towards either pole until it come to be of aequal diameter with the cylinder and consequently the Meridians still widening themselves till they come to be so far distant every where each from other as they are at the Aequinoctial Thus it may most easily bee understood how a sphaerical superficies may by extension be made a cylindrical and consequently a plain Parallelogram superficies because the superficies of a cylinder is nothing else but
the Sun and the shadow are both one way Then I look for the height which is 85 degrees and three quarters so that it lacketh of 90 degrees four degrees and one quarter which is fifteen minutes These four degrees and fifteen minutes being added to the Declination which is twenty degrees and 41 minutes amount in all to 24 degrees and 56 minutes And so much am I distant from the Equinoctial towards the North which is the part of the Sun and of the shadowes An example of the fifth Rule Upon the 17 of October 1609 which is the first year after the leap year the Sun now going his course towards the South suppose I took his Altitude in 50 degrees and one third And when I took it the lower vain of mine Astrolabe Declined toward the North of my Compasse wherefore I say that the Sun and the shadowes are different And so adding 05 degrees and 20 minutes which is one third part of a degree with 12 degrees and 55 minutes which upon that day is the Suns Declination they amount in all to 63 degrees and 15 minutes which are lesse then 90 degrees by 26 degrees and 45 minutes and so far I am distant from the Equinoctial to the part of the shadowes that is to the North for the Sun and shadowes being different the heigth and Declination came not to 90 degr A second example of the fifth Rule The same day and year suppose that some man found the Sun in 77 degrees and five minutes of heighth the Sun it self declining to the South and the shadowes falling to the North which being added to 12 degrees and 55 minutes of Declination amounteth in all to 90 degrees just whereby I know that the ship wherein this Altitude is taken is under the Equinoctial because the Sun and shadowes being different the heigth and Declination make just 90 degrees The third example of the fifth Rule Upon the 20 of May 1608 suppose a certain man found the Suns heighth to be 88 degrees and two third parts the Sun and shadowes being different which being added to 21 degr 54 minutes the Suns Declination that day amounteth to 110 degrees 34 minutes which exceed 90 by 20 degrees and 34 minutes I say therefore that this man is 20 degrees 34 minutes distant from the Equinoctial towards the part of the Sun which is to the North because the Sun and the shadowes being diffeâ—rent the heigth of the Sun and the Declination being added together exceed 90 degrees CHAP. VIII Another manner of accounting by the Sun as they use in Portugall SOme Astrolabes there bee whose account beginneth not from the Horizon but from the Zenith and endeth with 90 degr in the Horizon and the heigth taken by them is nothing else but the distance of the Sun from our Zenith And to make an account of the Sun according to the Altitude taken with such Astrolabes there are these Rules following to be Observed 1. When the Sun and the shadows are both one way add the heighth unto the Declination and the product will shew how far you are distant from the line towards the part of the Sun and shadows 2. If the Sun and the shadow be differing subduct the Declination from the height or the height from the Declination the lesser from the greater and the remainder will shew how far you are from the line towards the part of that which is greater and if the height be greater then are you on the part of the shadowes 3. When the Sun is in the line and hath no Declination so much altitude as you shall find so far are you distant from the Equinoctial towards the part of the shadowes 4. When you shall take the Sun in your Zenith having then no altitude his Declination will shew you how far you are distant from the line towards the part of the Sun These Rules because they are so easie and plain need no examples CHAP. IX How the height of the Sun may be known in any place whatsoever without an Astrolabe first knowing your distance from the Equinoctial SOme Pilots for their curiosities sake desire to know the height of the Sun for any day without an Astrolabe For the performance whereof it is expedient that they know three things that is to say the Declination of the Sun the distance of the place from the Equinoctial and the part whereunto the shadows do incline at mid-day These three things being known you shall come to the knowledge of the Suns heighth by four Rules 1 When you and the Sun be both on one side of the Equinoctial if your distance from the line be equal to the Suns declination you shall finde the Sun in your Zenith in 90 degr and shall have no shadow 2 When the Sun hath no declination look how much your distance from the Equinoctial wanteth of 90 deg for so much is heighth of the Sun 3 When the Sun and the shadows are both towards one part subtract out of your distance from the Equinoctial the Declination of the Sun that day and that which the remainder shall want of 90 deg shall be the heighth of the Sun 4 VVhen the Sun and the shadows are different if the Equinoctial be between you and the Sun adde the Declination of the Sun to your distance from the Equinoctial and that which these two numbers added together shall want of 90 deg shall be the heighth of the Sun But if you be between the Sun and the line you must subduct your distance from the line out of the Suns Declination and then that which the remainder shall want of 90 deg shall be the heighth of the Sun CHAP. X. The Rule or Regiment of the North-star for the knowledge of the heighth of the Pole THe Zenith is the Pole of the Horizon because it is every where distant from it just 90 deg And hence it is that the Pole of the World is so much elevated above our Horizon as our Zenith is distant from the Equinoctial which is very manifest for having 90 deg of the Meridian from our Zenith by the Pole of the World to the Horizon and other 90 deg of the Meridian from the Pole of the World by our Zenith to the Equinoctial because they are two quadrants of one and the same Circle they must needs be of equal quantity from both which that part being taken away which is common to both that is the whole distance from the Pole of the world to our Zenith that which remaineth on both parts shall be equal And so that space from our Zenith to the Equinoctial which is called the distance from the line is equal â—o the distance that is between the Pole of the World and the Horizon which is called the heighth of the Pole VVhereby it is manifest that the heighth of the Pole is so much as our distance from the line is And although they are two different things yet the one is taken for the other
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
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
any land This Horizon is of two sorts namely right and oblique The right Horizon is that which they have that live under the Equinoctial which passeth by their Zenith and therefore the Equinoctial line or circle falleth perpendicularly and right acrosse with their Horizon and both the South and the North Poles are in their Horizon The oblique Horizon is that which they have that live not directly under the Equinoctial for unto them the Equinoctial divideth the Horizon obliquely and not right acrosse and one Pole is alwayes above their Horizon and the other is beneath their Horizon and cannot be seen This Horizon is represented in the Sea-Chart by a certain imagined circle whose center is the point where our ship is From which center are imagined to proceed unto the said circle 32 lines which represent the 32 winds or rumbs which alwayes are drawn in our Sea-Compasse which likewise in a little peece of paper doth continually represent unto us both by day and night the whole Horizon with his 32 divisions CHAP. XVI Of the 32 Winds THis right or oblique Horizon is divided into 32 equal parts by 16 lines which they call Rumbs and they cut themselves in the point where we stand of which rumbs that which passeth by the points where the Equinoctial beginneth and endeth which are where the Sun riseth and setteth the 11 of March and the 13 of September is called East and West and that which cutteth it right acrosse is named North and South And the four extreams or ends of these two lines are distant upon the Horizon one fourth part of a circle and they make four quarters Every one of which quarters being divided in the midst do make four other points and that which falleth between the North and the East is called North-east and that between the North and the West North-west that between the South and the East South-east and that between the South and the West South-west And so the Horizon is divided by four lines or numbs into eight principal winds noted in the Sea-Chart with black lines And if you divide every one of those eight parts in the midst you shall have other eight lines and other four rumbs which in all are 16 winds And each one of these hath his name compounded of the names of those principal winds which are on either side thereof As for example that half winde which is between the North and the North-east is called North-north-east and that which bloweth between the East and the North-east is called East-north-east and that between the East and the South-east East-south-east and that between the South and the South-east South-south-east and that between the South-west and the VVest VVest-south-west and that between the VVest and North-west West-north-west and that between the North-west and the North North-north-west And these are noted in the Chart with green lines Finally if you divide every one of these sixteen winds in the midst they will yield you other 16 winds and will amount to 32 winds in all Which 16 last mentioned are drawn in the Sea-Chart with red lines and are by the Spaniards called quarters of the eighth first and principal winds and every one of these is called by the name of that principal wind which is next it together with an addition of the word By and the name of another principal wind which is next unto it As for example of the two quarter-winds which fall next the rumb of the North that which lieth towards the North-east is called North and by East and that which falleth towards the North-west is called North by West So likewise of those two winds which blow next the North-east that towards the North is called North-east and by North and that towards the East North-east and by East And after the same manner you may name all the rest The Figure of the Sea-Compasse and of the Horizon divided into 32 Winds by 16 Rumbs But here is to be noted that there is difference between the Rumb and the Wind because a Rumb is one direct line continued with two contrary winds as the Rumb of North South and the Rumb of East and West And so when we will name the lying of any Coast we will say that it lieth North and South or North and by East and South and by West But the wind is one line of those 32 into which the Horizon is divided and it is one part of those two which together are called the Rumb And so we say that Land lieth from us towards the South and towards the South and by West or towards the South-south-west c. CHAP. XVII Of the two Tropicks BEsides the six Circles above-mentioned which are drawn upon the superficies of the Sphere of the World there are other two which the Sun describeth with the motion of the Primum Mobile about the 12 day of June and of December of which two Circles that which the Sun describeth the 12 of June from the time of his rising till the time that he riseth the day following is called the Tropick of the Summer Sun-standing or the Tropick of Cancer for the Sun having departed from the Equinoctial and increasing his Declination towards the North when he cometh to describe that Circle for two or three dayes it semeth that he cometh no neerer to our Zenith nor departeth from the Equinoctial one day more then another but from thence forward he goeth back diminishing his Declination till he come to the Equinoctial and crossing the same he goeth on the other side increasing his Declination until the 12 of December upon which day from the time of his rising till he be come about to rise again the next morning he describeth another Circle called the Tropick of the Winter Sun-standing or the Tropick of Capricorn for the Sun being departed from the Equinoctial and increasing his Declination towards the South when he cometh to describe that Circle it seemeth for two or three dayes that he returneth not one whit towards the Equinoctial nor goeth further from our Zenith one day more then other but from thence forwards he commeth back again diminishing his Declination till he be returned to the Equinoctial and from thence towards our Zenith These two Circles in Sea-Charts are marked with two great red lines drawn from East to West which lie on either side of the Equinoctial being distant from thence about 23 deg and an half And wheresoever our ship be in any place between these two Circles or lines we may in some time of the year take the Sun in our Zenith at which time it maketh no shadow at all being then just 90 degr high above our Horizon But they which are without the said two Circles or lines shall never have the Sun in their Zenith because it cannot come to the height of 90 degr above their Horizon CHAP. XVIII Of the Parallels THe parallel Circles are those which are in all parts equally distant from the
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
two guards are in the same Azimuth or the one directly over the other betwixt the lowest and the East Heighth of the Pole Star Heighth of the Pole Heighth of thâ— Pole Star Heighth of â—he Pole Heighth of the Pole Star Heighth of the Pole Deg. degr mi. sec. Deg. degr mi. sec. Deg. degr mi. sec. 1 0 40 50 28 27 58 43 55 55 30 47 2 1 41 27 29 28 59 31 56 56 32 47 3 2 42 3 30 30 0 19 57 57 34 54 4 3 42 39 31 31 1 9 58 58 37 9 5 4 43 16 32 32 1 59 59 59 39 32 6 5 43 52 33 33 2 51 60 60 42 4 7 6 44 29 34 34 3 44 61 61 44 46 8 7 45 6 35 35 4 39 62 62 47 41 9 8 45 43 36 36 5 34 63 63 50 48 10 9 46 20 37 37 6 32 64 64 54 11 11 10 46 58 38 38 7 30 65 65 57 51 12 11 47 36 39 39 8 31 66 67 1 49 13 12 48 14 40 40 9 33 67 68 6 11 14 13 48 52 41 41 10 38 68 69 10 59 15 14 49 31 42 42 11 44 69 70 16 16 16 15 50 10 43 43 12 53 70 71 22 11 17 16 50 50 44 44 14 4 71 72 28 54 18 17 51 30 45 45 15 17 72 73 36 34 19 18 52 10 46 46 16 33 73 74 45 18 20 19 52 52 47 47 17 53 74 75 55 14 21 20 53 33 48 48 19 15     22 21 54 15 49 49 20 41     23 22 54 58 50 50 22 11     24 23 55 42 51 51 23 45     25 24 56 26 52 52 25 23     26 25 57 11 53 53 27 5     27 26 57 57 54 54 28 54     An Addition touching the Variation of the Compasse WHeras there have been some of opinion that there be two Magnetical Poles by knowledge whereof and of the Magnetical Variation Observed in any place they have imagined they could find the Longitude thereof to shew the great error and uncertainty of this their opinion I have here set down this Table of observations of the Variation of the Magnetical Needle which partly by my self but for the most part by others both English and strangers have bin taken in all parts of the World almost whither any Navigation hath bin made for these many years Which Observations I wish the Juditious Reader to compare together with so good advice and judgment as he can whereby I assure my self he will be enforced to acknowlege with me that there can be no such Magnetical Poles found as they imagine To prove these a few instances may be sufficâ—ent amongst many that may be gathered out of these Observations For if there be two such Magnetical Poles there can be but one common Magnetical Meridian passing by them and the poles of the World but by these Observations it is manifest that there be many Magnetical meridians passing by the Poles of the World as namely the Magnetical Meridian about Trinidado and Barbudas also the Meridian about the Westermost of the Azores also about P. das Agulhas lastly amongst the East Indian Ilands some what beyond Iava Maior the magnetical and true meridian must needs agree in one Now seeing that all these Magnetical Meridians passe by the Poles of the World there can be no reason given why the magnetical Poles should be said to be in one of them more then in another and if in any then in all whereof it must needs follow that as many Magnetical Meridians as you have that passe by the Poles of the World so many paire of Magnetical Poles must you have which is absurd and therefore no such Magnetical Poles Now if any shall think that the great difference that is found betwixt divers of these Observations taken at the same place by divers Observers doth make any thing against the intention of this Argument he is much deceived For although there be three or four degrees difference betwixt some Observations taken at the same place as namely at S. Helena some make the Variation to be almost three degrees some almost four others will have it to be about five degrees and an half and some others seven and an half And although there be some four or five score leagues difference in determining the place where the true and Magnetital Meridian should concur or where there should be no variation about Flores and Corvo and about P. das Agulhas some making to be about seventy or eighty leagues Westward from Flores and some about thirty leagues Eastward from thence where some others will have it hard by Flores or somewhat to the Eastwards thereof And at P. das Agulhas some say there is no variation at all but according to others we must goe 80 leagues further to the Eastward before we come to no variation All these differences notwithstanding how great soever they be can be of no validity to infringe the force of the foresaid argument for still these Observations will necessarily prove that either at Flores and at P. das Agulhas or at the most within three or four score leagues of those places there is a Magneticall Meridian passing by both the Poles of the World which two Meridians differing so much in Longitude each from other and having in all Latitudes great variations betwixt them it cannot be with any reason imagined how they may be reduced into one so to make two Magnetical Poles only But of all these so great differences either of the same or of divers mens Observations we may justly take occasion to admonish all Seamen especially such as are to take charge that they be very carefull both in providing themselves of the most convenient Instruments that can be gotten for this purpose and also in the circumspect and artificiall handling of them whensoever they goe about to make use of them in Observing to find the variation considering how great and excellent use there may be made hereof for finding out the place whereabouts you are betwixt East and West upon the huge and vast Ocean though you have seen no land for a long time  Variat West Latit North.  De. M De. M. In the Ice Haven at Nova Zembla 22 30 76 0 On the West side of Nova Zembla 26 0 76 0 From Nova Zembla Westward 20 leagues 31 0 73 0 At Crosse Iland near Nova Zembla 17 0   At the Hollanders Newland 16 0 81 0 In the Iland of Vaygats 7 0 71 0 Amongst the Iles of Vaygats 8 0 70 25 At S. James Ile 7 30 70 40 On Land near the bar of Pechora 3 30 69 10 At the North Cape 1 0 71 30 From Fowlay Iland half way almost to Friseland 11 15   From Friseland half way to Labrador now called Newfoundland 28 0 62 0  East
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