Certain errors in navigation detected and corrected by Edw. Wright ; with many additions that were not in the former editions.

THE DIVISION OF THE WHOLE ART OF NAVIGATION.

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

CHAP. I. The Definition of the Sphere.

A Sphere is a solid or 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 high∣est 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 corru∣ptible 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 Pri∣mum 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 Na∣vigation.

[illustration]

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 obser∣ved 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, a∣bout 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 round∣nesse 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 prin∣cipal 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 ma∣nifest 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 wheresoe∣ver 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 per∣ceive, that they are alwayes equally distant from our sight: and whereas they move round about it, it followeth, that we are up∣on 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 great∣est 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 ac∣counted. 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 Equino∣ctial Circle; because that when the Sun passeth under it, upon the 11 of March, and the 13 of September, it maketh the day e∣qual 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 pas∣seth 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 al∣wayes 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 call∣ed the South part.

CHAP, XI. Of the Eclipticke line

THe Equinoctial circle is divided into equal parts by an∣other 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 Equi∣noctial, 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 cir∣cle in all parts is equally distant from the Poles of the second mo∣tion, 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 dai∣ly swarving or Declining of the Sun from the Equi∣noctial line. And this Declination when the Sun is un∣der 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 grea∣test. And albeit this greatest Declination be now in our time a∣bout 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 de∣grees, 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, be∣cause 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 divi∣deth the Spring from the Summer, and hath his greatest Declina∣tion towards the North: and being in the other part, the Sun maketh the longest night, and shortest day, and divideth Win∣ter from Autumne, and is in his greatest Southerly Declination. These two Colures are noted in the Table of the Suns Declinati∣on 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 mo∣tion 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 no∣ted, that when the Sun is in that Circle, it hath the greatest alti∣tude 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 to∣wards 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 repre∣sented 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 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 pro∣ceed 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 di∣visions.

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 divi∣ded 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 exam∣ple, that half winde which is between the North, and the North-east▪ is called North-north-east, and that which bloweth be∣tween 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, to∣gether with an addition of the word (By) and the name of ano∣ther 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.

[illustration]

The Figure of the Sea-Compasse, and of the Horizon, divided into 32 Winds, by 16 Rumbs.

But here is to be noted,* 1.1 that there is difference between the Rumb and the Wind, because a Rumb is one direct line conti∣nued 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 Pri∣mum 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-stand∣ing; 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 de∣parteth from the Equinoctial one day more then another: but from thence forward he goeth back, diminishing his Declinati∣on, 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 ano∣ther 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 Equino∣ctial, nor goeth further from our Zenith one day more then o∣ther; but from thence forwards he commeth back again, dimi∣nishing 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 a∣bove our Horizon. But they which are without the said two Cir∣cles or lines, shall never have the Sun in their Zenith, because it cannot come to the height of 90 degr. above their Horizon.

CHAP. XVIII. Of the Parallels

THe parallel Circles are those which are in all parts equally distant from the Equinoctial. And these Circles may be in∣finite between the Equinoctial, and the North and South Poles; and in the Sea-chart some of them are represented by the lines which are drawn from East to West. And two of these Circles are the two Tropicks of Cancer and Capricorn, which are the bounds of the Suns greatest Declinations. Likewise all those Cir∣cles which the Sun and the stars in Heaven do by the motion of the first or highest moveable heaven describe from East to West, are parallels, and serve in the Sphere to shew the Latitude. And when a ship saileth in the same height of the pole, then she saileth in a parallel and runneth alwayes East or West. Which manner of sailing we use at all such times, when we find our ship in the height of that land, to which we are going.

CHAP. XIX. Of the Degrees.

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

such divisions as it is capable of, according to the largenesse of the Chart, beginning to make account from the Equinoctial.

CHAP. XX. What is meant by Longitude and Latitude.

THe Longitude of any place is a part of the Equinoctial, or of some other parallel contained between two Meri∣dians, whereof one passeth by the Canary Islands, and the other by the place given; but if neither of the said Meridians passe by the foresaid Islands, it is called respective Longitude. And this respective Longitude is called in the Art of Navigation the distance or length of the right line; which is de∣termined or bounded by two other right lines running North and South; of which two, the one passeth by the Port or Haven from whence we set sail, and the other by the place where our ship is. And so shall the distance of the right line be the part of any right line whatsoever running East and West, comprehended between the two foresaid right lines extended North and South.

The Latitude of a place is a part of any Meridian whatsoever contained between two parallels, whereof one is the Equinocti∣al, and the other the parallel of the place given. This Latitude the Mariners do call the Distance from the Line;* 1.2 understanding by the Line, the most principal of all others, which are drawn in the Chart, that is, the Equinoctial Line. They use also to call it the heighth, which is as much to say, as the heighth of the Pole above the Horizon. And so the Distance from the Equino∣ctial shall be a part of any North and South Line contained be∣tween the Equinoctial and any line running from East to West, which passeth in the graduation of the Chart, by the same degree of Latitude in which we find our selves to be.

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.

TO know the Latitude or distance from the Equinoctial line there are required five things; whereof any one be∣ing wanting, we cannot possibly finde out how far we are distant from the said Line. And these are, the Astrolabe or Quadrant, the height of the Sun, the Shadows, the Declination, the Regiment or Rules of the Sun.

The Astrolabe is to be made after this manner: In the midst of a round plate or table of mettal or wood, being smooth and plain every where, and about a finger thick, you shall take the center A, wherein having placed one foot of your compasses, you shall with the other draw as great a circle as conveniently you can in the said Table. And within this Circle must be drawn two other Circles, the one distant from the other about the breadth of a grain of wheat, and the third must be distant from the second twice so much as the second is from the first.

[illustration]

And your Ruler being laid just to the center A, you shall draw the line BAC, which divideth every one of the three cir∣cles into two equal parts. And putting one point of your com∣passes (standing open according to the length of the line BC) up∣on the point C, where the greatest Circle is divided by the line BC; with the other point, you shall draw above the point D a part of a Circle, and another under E. And then putting one foot of the compasses thus opened upon the point B, you shall draw other two parts of a Circle, which will crosse the first in F and G. And your Ruler being laid to F and G, you shall draw the line DE, which must passe by the center A. Then let the Quadrant DB be divided into 3 equal parts, and every one of

those into three other parts, and each of those nine into two, and every one of those 18 into 5; and so the said Quadrant shall be divided into 90 equal parts or degrees. Unto which de∣grees shall be placed the numbers belonging to them from 5 to 5, between the second and the third circle, beginning from B and ending with 90 at the point D. Then let there be made at the point D a little hole upon the line DE, through which may be put a little ring, or some strong riband or string, and you shall make a knot thereon, whereby your finger may take hold: and the Astrolabe hanging by that hole, you shall put through a slender threed with a plummet of lead, which may hang quite under the Astrolabe; which threed, if (while the Astrolabe hangeth immoveable) it fall just upon the line DE, then is the Astrolabe well rectified: If not▪ you must continue cutting off some thing, and lightning that side towards which the thred doth fall, until it hang even with the foresaid line. Then must you draw upon a Ruler of the same matter, (being about a fin∣ger and an half broad, the right line HI along through the very midst of the breadth thereof: which Ruler shall be made after the same fashion that here is set down, cutting away from one half of the length half of the breadth, alwayes saving whole the line HI. And so likewise shall you cut off along the half of the length on the contrary part, half of the breadth; so that the line HI may remain whole on that side also. And neer to the ends of the said Ruler▪ you shall set two little square Vanes of the breadth of the Ruler in the midst standing upright, the very midst of both Vanes being placed upon the line HI. Through the centers of which two Vanes shall be made two little holes, both which must stand directly over the line HI, and in equal distance from the upper face of the Ruler. This Ruler by a hole bored thorow the midst thereof, shall be fastened upon the said Astrolabe through another hole of the bignesse of that in the Ruler, at the very center A with a nail, which may be made fast with a little pin, as is to be seen in the figure.

CHAP. II. Of the heighth of the Sun.

TO take the heighth of the Sun, you must hold the Astro∣labe by the ring or knot D, in your left hand: and turn∣ing your right side to the Sun, lift up the Ruler with your

right hand, till the beam of the Sun entring by the hole of the uppermost Vane, doth also pierce thorow the hole of the ne∣thermost Vane. And then note the degree and part of the de∣gree which the line HI doth touch, for that is the heighth of the Sun above the Horizon; which if it be the greatest heighth that the Sun hath that day, it will teach us how far we are di∣stant from the Equinoctial. This greatest heighth is to be taken at mid-day, lifting up the uppermost Vane, till we be assured that the Sun ceaseth to rise any higher, but beginneth to fall again. Then note that greatest heighth, and keep it for the making of your account of the Latitude by the Sun.

CHAP. III. Of the Shadows.

THe shadowes being compared with the Sun, may be of three sorts, for at high noon the shadow falleth either to∣wards that part of the World ••o which the Sun declineth. or towards the contrary part, or else we make no shadow at all, The first and second sort are, when the heighth of the Sun is lesse then 90 degrees, and the third is, when it is just 90 degrees high. The first is, when the Sun keepeth his course on the North side of the Equinoctial, which is from the 1•• of March to the 13 of September; and likewise when the shadows fall towards the North of the Compasse: or when the Sun runneth on the South side of the Equinoctial (which is from the 14 of September to the 10 of March) and the shadows likewise fall towards the South of the Compasse: and this is when the Sun and the shadows go both one way. The second is, when the Sun coming towards the North, the shadows are cast towards the South of the Compasse; or when the Sun is on the South side of the Equinoctial, the shadows fall towards the North; and this is, when the Sun and the shadows are differing.

The rule of the shadowes is, that we look well to the lower Vane of the Astrolabe, when we are taking the height of the Sun at noon: For if the line HI fall directly upon the line of the Astrolabe DE, then we have no shadow, because the Sun is in our Zenith 90 degrees high. But if the line HI fall not upon the line DE▪ you must mark towards what part of the World the lower part of the Ruler doth decline from the point E; which if it decline towards the North of the Compasse, then the sha∣dowes

fall Northwards. But if it decline towards the South of the Compasse, then the shadows fall Southwards.

CHAP. IIII. Of the Regiment and Rules of the Sun.

WHen you know the part or parts of the Sun and sha∣dows and desire by the Sun to know how far you are distant from the Equinoctial, you have five rules: The first whereof sheweth in what part of the Heavens the Sun is, that is, whether he be North or South from the Equinoctial at the time of your observation. The second teacheth what account we are to take of the Sun, when he casteth no shadow, because he is in our Zenith and is found in the Astrolabe to be just 90 deg. high. The third is of the account to be made by the Sun, when taking the heighth thereof in lesse then 90 degr. it maketh a shadow at high noon, and hath no Declination, because it is un∣der the Equinoct••al. The fourth is, of the account that is to be made▪ when the Sun and the shadows are both one way from the line. The fifth is when the Sun and the shadows are diffe∣rent on•• being towards the North, and the other towards the South.

The first Rule of the Sun.

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

The second Rule of the Sun.

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

The third Rule of the Sun.

When the Sun is less then 90 degrees high, if there be no De∣clination the same day, then so much as it wanteth in heigth of 90 degrees, so much are we distant from the Equinoctial, towards that part of the world towards which the shadow falleth.

The fourth Rule of the Sun·

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

The fifth Rule of the Sun.

When the Declination of the Sun and the shadowes be diffe∣rent, we must add the height of the Sun unto the Declination which it hath the same day: And if the Sun amount to 90 degr. just, then are we under the Equinoctial line: but if it exceed 90 degrees, we are so much distant from the Equinoctial towards that part of the world wherein the Sun is▪ as that excesse or overpluss commeth to. And if the heigth and Declination added together come to lesse then 90, look how many degrees and minutes you want of 90, so many are you distant from the Equi∣noctial towards that part to which the shadowes fall.

And here is to be noted that we must likewise make account of the minutes, because they may be both in Declination, and in heigth, and so alwaies in that Declination where we shall find 60 minutes, we must make of them one degree And if in taking the heighth we find half a degree besides all the whole degrees▪ it is as much as 30 minutes, and one third part of a degree is 20 minutes, one fourth 15 minutes, one fifth part 12 minutes, and one sixth part 10 minutes.

CHAP. V. Of the Declination of the Sun, and of his Tables.

THat wee may know what use to make of the five fore∣said Rules of the Declination of the Sun, we are to note, that the year (which is the time of the Suns mo∣tion 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 (where∣of 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 al∣most which the Sun wanteth to come unto the point, from which it departed at the begining of the year: and also of the Declina∣tion 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 af∣ter 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 remain∣der and even number, then that year is leap year: and if the re∣mainder 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 Declina∣tion 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 lit∣tle 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 o•• the greater) and the difference, or remainder shall be multiplied by the leagues which our ship hath sailed from the Meridian of London; and the product of the multiplication must be divided by * 1.3 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 East∣ward 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 Sa∣morano, 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 there∣fore I took from 1608. the number of 1600. and their re∣main

8 whic•• 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 Equinocti∣al 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 North∣wards 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 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 mi∣nutes: 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 to∣ward 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 de∣grees and 55 minutes (which upon that day is the Suns Declina∣tion) 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 sha∣dowes, 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 be∣ing added to 12 degrees and 55 minutes of Declination▪ amount∣eth 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 de∣grees 34 minutes, which exceed 90 by 20 degrees and 34 mi∣nutes. I say therefore that this man is 20 degrees 34 minutes di∣stant from the Equinoctial, towards the part of the Sun, which is to the North, because the Sun and the shadowes being diffe••rent,

the heigth of the Sun, and the Declination being added to¦gether 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 De∣clination 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 sha∣dowes.

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 Equi∣noctial, if your distance from the line be equal to the Suns decli∣nation, 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 De∣clination 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 E∣quinoctial 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 know∣ledge 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 mani∣fest: for having 90 deg. of the Meridian from our Zenith by the Pole of the World to the Horizon; and other 90 deg of the Meridian from the Pole of the World, by our Zenith to the Equinoctial; because they are two quadrants of one and the same Circle, they must needs be of equal quantity: from both which that part being taken away, which is common to both (that is, the whole distance from the Pole of the world to our

Zenith) that which remaineth on both parts shall be equal. And so that space from our Zenith to the Equinoctial (which is called the distance from the line) is equal ••o the distance that is between the Pole of the World and the Horizon, which is cal∣led 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, because they are equal.

This heighth of the Pole is known by the help of four things, which are the Ball••stilla, or Crosse-staffe, the position of the North-star, the heighth of the said star, and certain Rules.

CHAP. XI. The making of the Cross-staff.

THe Mariners Crosse-staff is that which by the Astronomers is called Radius Astronomicus: and the manner how to make it is as followeth: First, upon a very plain and broad ta∣ble you may draw a semicircle, which from the center to the circumference must contain at the least four hand breadths. And having drawn thorow the center thereof the line ABC, divide the circumference into two equal parts, in the point E, as like∣wise you must divide the quadrant EC in the very midst by the point F. Then must you divide the arch EF into 90 equal parts, dividing it first into three, and every of these three into o∣ther three, and every of those nine into two, and each of those two into five, which you must do with much precisenesse and care. Then laying your Ruler to the point B (which is the cen∣ter) through every one those 90 divisions of the half quadrant, you must draw 90 lines: And keeping this quadrant so divi∣ded, it will serve you for a pattern to make us many Crosse-staves as you think good, of what bignesse soever you will. But to make the Crosse-staff, you must take a piece of wood of some three foot in length, and a finger thick, four square, and very e∣ven: and fitting a transversary thereto, which may with facility slide up and down upon the staff, alwayes right acrosse; take with your compasses half the length of the transversary, and placing one foot of the compasses upon the point B, make with the other a mark in the line BC, which may serve for the point G, and draw thorow the point G the line GI, which may run

equally distant from the line EB. Finally, laying one end of the staff upon the point G, let it lie all along just upon the line GI, and make your marks upon the edges of the staff, by which you may draw 90 lines, putting the number of every line upon the said edge, begining to place 90 where the line BE doth crosse the staff, and from thence descending unto one or two, which may be put down according to the length of the staffe, and the largenesse of the transversary.

[illustration]

CHAP. XII. Of the position of the North-star, and the Guards.

AMongst the 48 Constellations, which the Astronomers place in the Heavens, the neerest unto the pole of the World is

that which they call the lesser Bear, and the Mariners Bozina, or the horn, in regard of the fashion thereof: which Constellation consisteth of 7 stars, which are placed after this manner: And of these stars, the three greatest, mar∣ked

[illustration]

with the letters ABC do serve especially for our purpose. And so A is called the North-star, B the the formost guard, C the other guard behind. And they are so called, be∣cause that by force of the motion of the first moveable Heaven, the star B goeth alwayes before, and the star C behind. Every of these three stars as well as all others in the Hea∣vens besides, describe th•••• circles round about the pole with the mo∣tion of the first or highest moveable Heaven: 〈◊〉〈◊〉 which motion some∣times the 〈◊〉〈◊〉 stars AB are just of 〈…〉〈…〉 above the Horizon: 〈…〉〈…〉 they are said to be East and West one from another. Some∣times they are in a perpendicular line to the Horizon, according to our sight; and then they are said to be North and South: and sometimes also the two guards BC are East and West one from another▪ and then the former guard beareth from the North-star, North-east and South-west. And when these two guards be in a perpendicular line one above another, the former guard beareth from the North star North-east and South-west. Insomuch that from these four positions do arise eight rules for the eight Rumbs, wherein the former guard may stand, being considered in respect of the North star. And so presupposing that the North star is distant from the Pole three degrees and an half: (according to the opinion of some Mariners, who love numbers that have not any fractions) sometime the North star shall be as high as the Pole it self, sometime three degrees and an half lower or higher then the Pole, and sometime three de∣grees, and sometimes one and an half, and sometimes half a degree.

CHAP. XIII. Of the heighth of the Star taken with the Crosse-staffe.

TO know how much the North Star is elevated above the Horizon, you must take the heighth thereof onely at such times when as in respect of the former guard it is in some one of these four Rumbs, that is to say, North and South, East and West, North-east and South-west, and North-west and South-east. Wherefore seeing it placed in any of the foresaid Rumbs, you shall put that end of the Crosse-staffe which is next 90 degrees upon your cheek-bone, at the utter corner of your eye: and holding it there stedfast, you must move the trans∣versarie till you see the Horizon joyned with the lower end there∣of; and the North Star with the higher end. Then mark the degree, and part of the degree which the transuersarie sheweth upon the staffe; for that is the heighth of the Star.

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

The first Rules.

WHEN the guards are in the East, the former guard beareth with the North Star East and West, and then the North Star is a degree and half under the Pole: let us add this degree and half to the height which we Observed with the Crosse-staffe; and the whole product sheweth the number of degrees which the Pole is eleva∣ted above our Horizon. And so much are we distant from the Equinoctial toward the North.

The second Rule.

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

The third Rule.

When the guards be at the highest, then the former guard beareth from the North Star North and South; the North Star being then three degrees under the Pole: which three degrees be∣ing added to the height of the Star, do shew the true height of the Pole.

The fourth Rule.

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

The fifth Rule.

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

The sixth Rule.

When the guards are in the South-west, one beareth from an∣other East and West, and the former lieth from the North Star North-east and South-west, and then the North Star is above the Pole three degrees and an half: which three degrees and an half being deducted out of the heighth of the Star, that which re∣maineth shall be the heighth of the Pole.

The seventh Rule.

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

The eight Rule.

When the guards are in the South-east, one beareth from a∣nother North and South, and the former beareth from the North

Star North-west and South-east, and the North Star is above the Pole half a degree: which half degree being deducted from the heighth of the Star, the remainder is the heighth of the Pole above our Horizon, and just so much are we distant from the Equinoctial towards the North.

This is the account which alwaies hath bin made of the North Star from the time that it hath had three degrees and an half distance from the Pole unto this present. But because at this time by reason of the compound motion of the 8 and 9 heavens, the fixed Stars have notably varied from their places the Pole Star hath also approched neerer the Pole, being now distant therefrom not above three degrees and eight minutes, And so I think it convenient to set down the account which ought now to be made thereof,* 1.4 according to the foresaid distance: to the end that from henceforth the heighth of the Pole taken by the Star may agree justly with the distance from the Equinoctial taken by the Sun. Which two things have hitherto disagreed and caused no small confusion unto the Pilots, and some error in Navigation.

The guards being in the	East,	you shall adde unto the heighth taken by the Crosse-staffe,	1 degree 20 minutes
North-east,	3 degrees 8 minutes
North,	2 degrees 41 minutes
Northwest,	0 degree 27 minutes

In the contrary Rumbs to these you must deduct these degrees from the heighth of the Star, which you take with your Crosse-staffe, and then you shall have the heighth of the Pole above the Horizon.

CHAP. XV. Other things to be noted in Observing the heighth of the Pole.

NEXT unto the constellation of the Horn, here is a Star which is called by the Spaniards el Guion signified be∣fore by the letter D, which standing East and West from the North-star, giveth you to understand, that it and the North Star, and the very Pole are East and West. And so taking the heighth of the North Star, when it is thus situate in regard of the Guion, with out making any other account, you have the just heighth of the Pole, and the distance from the Equinoctial.

Sometimes also it falleth out, that being very neer unto the line, or for some other cause, the guards cannot be seen how they lie from the North star. For remedy whereof there are three stars, by which (seeing any of them and the North star, al∣beit you cannot see the guards) you may know the heighth of the pole, and these are stars which the Mariners call the third, sixth, and the ninth. The third is the head of that constellati∣on which the Astronomers call the Dragon, and it maketh with two other stars that follow it, this figure: The

[illustration]

sixth is the right foot of Cepheus: and the ninth is the left foot. The third was so called, because it commeth unto every third rumb three hours after the former guard; and the sixth is so cal∣led, because it cometh six hours after the former guard; and the ninth, because it cometh nine hours after the former guard. Whereof it followeth, that when the third star is directly above the North star, the former guard is in the Northwest, the sixth star in the Northeast, and the ninth in the East. And to know this is the other rumbs, you may peruse the Table following; wherein is manifestly set down where the guards are, and how they are situate, in what rumb soever any of these three stars is found. So that it will be an easie matter to know the place of the guards, and the heighth of the pole, the heighth of the Pole star being found, and the place of the third, sixth, or ninth star.

Here followeth the Table.

The guards being in the	East	The third star is in the	Southeast	The sixt star in the	South	The 9th star in the	Southwest
Northeast	East	Southeast	South
North	Northeast	East	Southeast
Northwest	North	Northeast	East
West	Northwest	North	Northeast
Southwest	West	Northwest	North
South	Southwest	West	Northwest
Southeast	South	Southwest	West

In this Table, the first column serveth for the guards; the se∣cond for the third star; the third column for the sixth star; and the fourth for the ninth star. Insomuch as if you seek the rumb, seeing any of these four stars in this Table, right against the same do answer those rumbs where the other three are, although we cannot see them in the Heavens.

CHAP. XVI. Of the Crosiers.

WHen the Mariners pass the Equinoctial line towards the South, so that they cannot see the North-star, they make use of another sta•• which is in the Constellation, called by the Astronomers the Centaur, which star, with other three no∣table stars, which are in the same Constellation, maketh the fi∣gure of a Crosse; for which cause they call it the Crosier. And it is holden for certain, that when the star A (which of all four commeth neerest to the South Pole) is North and South with the star B, that then it is rightly situate to take the heighth by. And because this star A (which

[illustration]

they call the Cocks foot) is thirty degrees from the South Pole, it co∣meth to passe, that if being situate, as is aforesaid, we take the heighth thereof (which is then the greatest that it can have) this heighth will truly shew how far we are distant from the Equinoctial. For if the said heighth be thirty degrees, then we are in the very Equinoctial: and if it be more then thirty degrees, then are we by so much past the Equinoctial towards the South. And if it be lesse then 30 degrees, so much as it wanteth are we to the North of the Equinoctial.

And here it is to be noted, that when the guards are in the North-east, then are the stars in the Crosier fitly situate for ob∣servation, because then they are in the Meridian.

CHAP. XVII. Of the Sea-Compass.

THe Sea-Compass is one of the most necessary Instruments, which are used in Navigation; for day and night, in clear and dark weather it sheweth always the right way through the Sea. And therefore it is meet that this Instrument be made with much care; to the end, that it may be most certain and

true. And the manner of making it is, that upon a piece of past∣board, you draw a circle so big as you will have your Compasse to be, which being divided into 32 equal parts (as we have al∣ready shewed in the Chapter of the winds) with sixteen lines crossing one another in the center, then you shall adorn the eight principal winds, as is to be seen in the figure following, ending in the North with a Flower deluis: and you shall paint the North and South, and East and West with blew, and the North-east and South-west, and the North-west and South-east with red. And then taking two steel wires, which are to be placed like the head of a launce, you must fasten them on the back side of the said circle, in such sort, that one meeting of the points of those steel wires be right under the North, allowing half a point to∣wards the North-east, in regard of the North-easting of the needle at Sevil: and the other meeting at the opposite point, which is South, and half a point towards the South-west: and touching or rubbing those two points of the wires with the ends of the Load-stone, which look to the North and to the South, to wit, the North points of the wires, with the South of the

[illustration]

stone: & the South point of the wires with the North of the stone This being done, you must place upon the center of the said cir∣cle a Capitel, which must be very well bored in, from off a round pyramis; to the end, that the rose or fly may play more nimbly upon the pin. This pin must be made of lattin, with a very sharp point, and is to be fastned upright in a round box of wood, which must be of the fashion of a great cup-dish, containing the rose within it, being covered above with a clear round glasse, and the joynts thereof must be stopped with wax, to the end, that no wind may enter into the rose to disturb it. There must be great care had, that this rose, with the wires placed upon the pin, may go nimbly, and may not swerve more to the one side then to the other, but may stand even and level. And when it inclineth towards either part, you must put on the contrary part a little wax, or a thin plate of lead fastened under the pastboard, which covereth the wires. This box wherein the rose plaieth up and down hangeth within two hoops of lattin, which are two round circles inclosed one within another, and distant asun∣der by the space of half a fingers breadth, with two nails of lattin, which are diametrally opposite. And the box being fitly placed within these hoops, you must make in the outward hoop two holes, which must be distant from the foresaid two nails a quarter of a Circle both wayes: And by these two holes must the outward hoop or circle be fastened within a square box, or a round, so as although that uttermost box be tossed up and down every way with the motion of the ship, yet alwayes the superficies and glasse of the inner box may lie level with the Horizon. And this being done with care, the instrument, which they call the Sea-Compasse is fully finished. The manner of u∣sing the same is, when being placed with the box in the midst of the poop of the ship where the bittacle standeth in a right line, which passeth from the bolt-sprit by the midst of the main mast to the poop, it serveth continually to govern the ship by mo∣ving of the Rudder, till the winde or the line of your Compass, towards which we desire to shape our course, stand directly to∣wards the prow or bolt-sprit of the ship. They use also for the night to mark a point within the inner part of the inner box, which in respect of the capitel of the Compasse, may stand di∣rectly towards the prow of the ship. And alwayes in guiding the ship▪ you must take heed that the said point be continually joyned with the winde of the rose towards which you intend your course.

CHAP. XVIII. How the Variation of the Compasse may be found.

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

The finding of the Meridian-line.

In a superficies, which is plain and level every where, and in a place where the Sun shineth at his rising and setting, you must draw certain circles upon one center: and having pitched a stile upright in the same center (the head whereof must be approved with a pair of compasses to be equally distant from all parts of one of those circles) observe you in the morning two or three hours before noon, when the point of the shadow of the stile toucheth the circumference of any of those circles: and having made a mark in the touches, take diligent heed in the afternoon also, when the same point of the shadow turneth about to touch in the same circle, and making another mark in that se∣cond touch, divide in the midst that part of the circle which is between those two marks. Then laying your Ruler upon the point of the division, and upon the center of those circles draw a line, which shall be your Meridian, and the true North and South Rumb; upon which setting your compasse▪ and laying your Ruler over the glasse, that it may passe along over the

Meridian, and over the center or capitel of the rose or flie: ei∣the said Ruler lieth over the North and South of the Compasse (and then is the Compasse without variation) or the Ruler de∣clineth toward the North-east or South-west; and how much it declineth that way, so much the Compasse North-westeth, or else it declineth towards the North-west, and then it North-easteth so much as the Ruler declineth that way. But to know the variation of the Compasse both at land and sea, we will de∣liver another far more easie and certain way▪ when we come to intreat of the universal Dial.

CHAP. XIX Of the Sea-chart.

THe Sea-chart is nothing else but a lively picture of the earth and water. And it containeth five notable things, which do concern as well the true making of the Chart, as also the inabling of the Mariner to know the way which he maketh, the place where he is, and the end of his journey.

The first is the laying out of the Coasts of the Land, which that it may be truly done, it is meet that every thing be set down in the Chart in the same course, distance, and heighth that shall be found in Navigation.

The second is, that it containeth not onely the coast of the firm land, but also all other particularities which do occur in sailing, as namely, Islands, Iselets, Banks, or Bars, Shoalds, Rocks, and Flats.

The third is the lines which signifie the 32 winds, by the help whereof we may see whether the parts of the land be well laid out, and in their true courses one from another. And of these winds the black are the eight principal, which are called whole winds. The green be half winds, or half parted winds: and the red be the quarters of the winds. You may know in your Chart whether these winds be well drawn, if you trie with your compasses that all points of them be equally distant one from another: and that all winds representing the same Rumb be parallels: As namely, that one Northeast and Southwest Rumb be parallel to another Northeast and Southwest Rumb. The fourth is the graduation, in all parts, whereof it is meet that the degrees † 1.5 be equal one to another: and that the parts of the land do directly lie East and West from those degrees under

which they are situate. The fifth is the scale of leagues, which you may see whether it be true, by taking betwixt the points of your compasses just 4 degr. out of the line of graduation which being applied to the scale of leagues must there agree exactly with 70 Spanish leagues or 80 English.

By the Sea-Chart are known five things: The first is the ly∣ing or trending of the Coast. The second is the distance or number of leagues from one coast to another. The third is, the latitude or distance from the Equinoctial, wherein all Lands both Continents and Islands, as also every Port, River, Isle, Shoald or Bank is situate. The fourth is the rumb or rumbs, by which we are to sail from one place to another. The fifth is the point or place where we are with our ship when we are sai∣ling. The first is known with a pair of compasses, putting one foot thereof upon the beginning of the coast, whose trending we desire to know, and the other foot upon the rumb, which to our thinking is every where equally distant from the said coast. For if one foot of the compasses running along the Coast, the other foot keepeth by the said Rumb, then we say the coast lieth even with that rumb. And if our compasse runneth with out swer∣ving one foot from the rumb, and the other from the Coast, till the point which runneth along the coast leaveth it, then from that very place where it leaveth the same, we may say, that un∣to the other place where it began, the coast runneth by such a rumb, as if a man should say East and West, Northeast and Southwest, or any other rumb whatsoever.

The second thing (which is the distance) may be found by taking between the points of your compasses out of your scale of leagues (if the distance be very great) an hundred leagues, and measuring with your compasse so opened from one place to another: now if in so doing it falleth not just, then remembring how many hundreds of leagues there are, you must for the mea∣suring of the rest pitch one foot of your compasse upon the point where the last hundred ended, and the other foot upon the land whose distance you desire to know: then bringing the compasse so opened to the scale of leagues, you shall see manifestly how many leagues the said distance surmounteth above the hundreds. But if the distance be lesse then an hundred leagues, then setting the points of your compasses upon those two places whose di∣stance you desire to know, and removing the compasse so opened to the scale of leagues, you shall easily know the distance of one of those places from the other.

The third (which is the heighth or latitude, wherein every Port, River, or Island standeth) is to be found by pitching one foot of your compasses upon the Land, Haven, or Cape, whose heighth you desire to know, and the other foot upon the next East and West parallel, and the compasse remaining in that sort, move the point thereof along the said parallel or rumb, to the line of graduation, and there the other foot which lay upon the land will shew you the heighth thereof.

The fourth (which is the rumb or rumbs, by which you must sail from one place to another) is known after this manner: If you be to sail by one rumb only, you may know it, by pitch∣ing one foot of your compasses upon the place from which you are to depart; and the other foot upon the very next rumb, which to your thinking goeth most directly to the place whi∣ther you would go; and running by that rumb with one foot of your compasse so opened, the other foot will touch the place whither you are going. But if it toucheth not the place whi∣ther you are going, then pitch one foot of your compasses upon the same place, and the other foot upon the second rumb, which you suppose may lead you thither. And placing one foot of a∣nother pair of compasses upon the place from whence we de∣part, and the other upon the most direct rumb toward the place desired; these two compasses running along the rumbs one to∣ward another; you must mark where those two points joyn to∣gether, one whereof came from the place of your departure, and the other from the place whither you are to go▪ & the point where they both concur is that to which we are to change our course.

As for example, if I sail from the bar of S. Lucan, to fall with Punta de Naga upon the Isle Teneriffe in time of winter; it is evident, that I must sail Southwest and by South, till I bring my self East and West with Cape Cantin in 32 degrees and an half: and from thence I must go Southwest and by west, but not all the way, because putting one point of the compasse upon Cape Cantin, and the other point upon the South west and by west rumb next unto it, my compasse thus running open alongst the said rumb, the point which departed from Cape Cantin, will run on the out-side of Punta de Naga. But in such a case as this I place one point of one pair of compasses at Punta de Naga, and the other point upon the Southwest rumb: Likewise I place one point of another pair of compasses at Cape Cantin, and the other upon the next Southwest and by west rumb. Then let these two compasses so opened run by their said rumbs one a∣gainst

another, and then you must look in what place & heighth the very point is, where those two points of the compasses which departed from Punta de Naga and Cape Cantin do meet: and I say, that when I am come to the said heighth and place, ha∣ving sailed from Cape Cantin Southwest and by west, then I must change my course, and run South-west.

CHAP. XX. Of the point of Imagination.

THe fifth thing to be known by the Sea-chart is the point of the ships place, and this they term to cast a point, or to set a prick upon the chart: which is no other thing but to finde a point therein, which is proportionally distant in the Chart from all the Lands and Islands there described so many leagues of the scale, as there are leagues of distance upon the sea from the place where you are to the Lands and Islands round about you, re∣presented by these that are in the Chart. This point is to be found two wayes; either by imagination, or by traversing, which may properly be called geometrical. The point of ima∣gination is usually found by the first of these two wayes, when we sail directly by a parallel circle; which is when we sail due East and West, keeping alwayes in one heighth and distance from the Equinoctial: or when we sail by any other rumb in close weather, when neither the Sun at noon, nor the North star in the night can be seen.

This point doth pre-suppose the knowledge of two things; to wit, the rumb, by which we have sailed, and that is known by the Compasse, and the leagues which we have run; and this hath no certainty, but is a little more or less then a good Mari∣ner, according to his imagination supposeth that he hath sailed: whereof the said point tooke his name.

This point is found in the Chart, by taking out of the scale of leagues so many leagues as a man can well estimate that the ship hath gone: and pitching one foot of the compasse in the place from which you departed, you shall set the other point in such sort, that both may be equally distant from the Rumb or wind where∣by you have sailed; and where that second point of your Com∣passe shall fall, there is your ship according to your imagination.

CHAP. XXI. Of the Traverse or Geometrical point.

THe point found by imagination is not so certain as is convenient, because it oft commeth to passe, either be∣cause the Mariner hath not made true account of the way that his ship hath made, or for some other causes therewith concurring, that if he taketh the heighth by the Sun, or by the North star, after he hath cast his point, he commeth not to find himself in that distance from the Equinoctial, which his point of imagination doth shew him, but in some other distance. And to avoid this error there is another way of casting your point in the Chart, which is called punto de esquadria (the Tra∣verse point) which point presupposeth the assured knowledge of two things; one is the Rumb by which you have sailed, the other is your distance from the Equinoctial.

For all this art of Navigation is grounded upon the course, and height, which is in quantity all one with the distance from the Equinoctial. The Rumb or course is alwaies known by the Compasse, the height by the star, and the distance from the Equi∣noctial by the Sun.

This being known, set the foot of one Compasse at the port or place from whence you departed, and the other foot in the next Rumb where upon you have sailed: and placing one point of an other paire of Compasses upon the line of graduation, in the degree of your distance from the Equinoctial, and the other point upon the next East and West Rumb, let these two pair of Com∣passes standing thus open, run along the Rumbs, one towards ano∣ther, till the point which came from the place of your departure, and that other which came from the height of your graduation meet: and where they meet, there is the place of your ship. And this point so found out, is most certain, when the height is carefully taken, and the Rumb known.

CHAP. XXII. Of the amending of the point of imagination.

HE that knoweth how to find out the point by traversing, shall easily amend the point of imagination, when having

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

The amendment of the point of imagination by the traverse point.

When you will amend your point of imagination by traver∣sing, you must set one foot of one pair of your compasses in the point found by imagination, and the other foot upon the next rumb by which you have sailed: and setting the foot of ano∣ther pair of compasses in the line of graduation upon the num∣ber of degrees, which you finde your self distant from the Equi∣noctial, and the other foot upon the next East and West line; run with your compasses so opened by the foresaid rumbs, till the point proceeding from the graduation, and the other which proceedeth from the point of imagination do meet just together, and then you may say, that your point of imagination is mend∣ed by traversing.

The amendment of the point of imagination by North, South, East, and West.

The amendment by North, South, East, West, is after this manner: Set the foot of one compasse upon the point found by imagination, and the other foot upon the next North and South rumb: then place one foot of another compass in the line of graduation upon the degree wherein you find your self, and the other upon the next East and West rumb, and so let these two

compasses run thus open by their rumbs, till the point which 〈◊〉〈◊〉 from the point of imagination, and the other which co∣meth from the graduation do meet; for then is your point of i∣magination amended by the amendment of East, West, North, South.

Of these two amendments the first serveth when you sail in a large gulf, because you may run at liberty with the compass: the second serveth neer unto any coast.

CHAP. XXIII. The point by imagination, and the heighth.

WHen you sail by the sixth or seventh rumb, that is, by the East and by North, or East and by South, or by the West and by North, or West and by South: or else by the East Northeast, or VVest Southwest; or by the East Southeast, or West Northwest, there is a certain diffi∣culty which may breed great errour in finding the traverse point, notwithstanding the latitude be taken; by reason of the Rudder that guideth the ship, which giveth certain yawes out of the course that the Pilot pretendeth, or by reason of the winde which bloweth not right in the poop, but maketh the ship fall to the leeward, from the direct and true course which it ought to keep. Wherefore because in such a case, if you find your point by traversing, suppose by East and by North, the way which I think is made, and hath been failed may be by the East North∣east: which point so found, must stand more forward then the true point, by so much difference as there is between 42 and 88 Spanish leagues, which is 46 leagues, that is, the difference of distance from the Meridian, or North and South line in those two points. In such a case as this, it is not meet to find your point by traversing, to avoid the errour which hereupon may in∣sue, which errour ariseth of such a cause, as that a mans judge∣ment, be it never so good, cannot easily determine thereupon, and so consequently he cannot judge precisely. But to avoid con∣fusion and cause of errour, he must cast his point in manner fol∣lowing, and he shall errer as little as is possible.

Let him examine according to the ordinary running of his ship, how much way she might make every day that he hath sailed; and the leagues that shall amount in all the dayes, let him take between the points of one compass: and let him place

one point thereof upon the place from whence he departed: and taking another compass, let him set one point thereof upon the graduation, according to the heighth which he hath taken and the other point upon the next East and West Rumb. Now let this compass run by his East and West rumb, till the point com∣ing from the graduation meet with the second point of the o∣ther Compass which he holdeth not upon the Chart: and in the place where they meet, he may say that there is his point and his ship.

And because in this case all Pilots do not use this point of i∣magination and heighth, there grow great diversities among them concerning their distance from land, when as in long voy∣ages they confer and communicate their opinions one with ano∣ther; insomuch that one according to his conjecture judgeth himself to be 50 leagues from land, another 100, another 200, and another thinketh he is hard by the land. The reason is, be∣cause some of them cast their point by traversing, others by ima∣gination onely, and others by imagination and heighth, who are alwayes more certain then the rest.

CHAP. XXIV. What it is to increase or diminish in heighth.

THe Mariners call it increasing in heighth, when they go further and further from the Equinoctial; and diminish∣ing in height when they approach neerer to the Equi∣noctial. So that in our Navigation we either sail from a greater to a less altitude of the pole, and then we go towards the Equinoctial, and then the height is said to be diminished: or we sail from a less to a greater height of the pole, and then we go from the Equinoctial, and are said to increase our heighth. And hence it is, that casting our point by imagination, and af∣terwards (having taken the heigth) amending it by traversing, ei∣ther the heighth, wherein we find our selves being taken by the Sun or star is greater, or else it is less then that which we made account of by imagination. And hence do arise four rules: The first is, that when in sailing we do increase the heighth, if the point amended by traversing be of greater heighth then the point of imagination, the ship hath gone more then the point of imagination shewed us.

The second, when we increase our heighth, if the point a∣mended

by traversing be in lesse height then the point found by imagination, then hath the ship gone less way then we ima∣gined.

The third is, when we diminish our height in sailing, if the point amended by traversing be in a greater heighth then the point found by imagination, then hath the ship made less way then we ghessed by our imagination.

The fourth is, when we diminish our heighth, if the point a∣mended by traverse be in less heighth then the point found by imagination, then hath the ship made more way then we ima∣gined.

CHAP. XXV. How you may cast a traverse point without Compasses.

IF a Mariner chance to lose his Compasses, he may cast his point of traverse after this manner: Let him take two slen∣der threds, and putting the end of one of them upon the place from whence he departed, let him stretch it in equal distance from the Rumb by which he hath sailed, and putting another thred in equall distance from the next East and West rumb, let him make it to pass by the degrees of heighth, in which he findeth himself; and where the two threds cross one another, there is the point of the ship: and alwayes the first thred (if it hath not changed the course) sheweth the way which the ship hath gone, and the second the parallel wherein the ship is.

CHAP. XXVI. Of another kind of casting a point by traverse.

EXamine the difference of the degrees of distance from the Equinoctial, which are between the place from whence the ship set forth, and the place where the ship is: Then taking the heighths of both places very precisely, and subtracting the lesser out of the greater, that which remaineth is the difference: which difference you must multiply by the leagues, which answer to one degree in the rumb by which you have sailed, and those leagues, which the degrees and minutes of difference shall make, you shall take between the points of a pair of compasses out of your scale of leagues: and holding the said compass so o∣pen, set one foot thereof upon the point from whence the ship

departed, and the other foot stretching towards the place whithre the ship hath sailed, you must hold up a little from the Chart: and you must set one foot of the other Compasse at the degree of the distance wherein your ship is from the Equinoctial, when the said point is sought for, and the other point you must place upon the next East and West Parallel. And let this second Com∣passe run by his next East and West Rumb, untill the point of the first Compasse lifted up, being set downe, that point of the se∣cond Compasse which came from the said degree doth meete therewithal: and where those two points shall meet, there is the true point of the ship.

CHAP. XXVII. Of the leagues which in Navigation answer to each degree of Latitude in every Rumb.

IF we suppose (as we have before said in the chap. (of the quantity of the earth) that the greatest circle thereof conain∣eth in compasse 6300 common Spanish leagues; then unto every degree of the Meridian (which is the greatest circle) doe answer 17 Spanish leagus and an half: so that sailing North and South, if your heighth of the Pole, or your distance from the Equinoctial be varied one degree, you may say that you have gone seventeen leagues and an half: but if you varie one degree, and hold your course upon the first point, then have you sailed 17 leagues and ⅙: And you have declined from the Meridian or right line which passeth by the place from which you departed, three leagus and an half. And if you sail upon the second point from the North or South till your heighth of the Pole be chang∣ed one degree, you have then gone 19 leagues and ⅜, and are di∣stant from your right line 7 leagues and ¼: And varying a degree upon the third point of the Compasse from North or South, you have gone 21 leagues, and are departed from your right line 11 leagues and ⅔.

Sailing upon the fourth point of the Compasse, there doe an∣swer unto every degree 24 leagues and three fourths, and you are distant from the right line or Meridian 17 leagues and an half. Upon the fifth point you must allow for one degree 31 leagues and an half, and then are you distant from your right line 26 leagues and ⅕. Upon the sixth point doe answer unto one degree of Latitude 45 leagues and ¾, and you are then parted

from your right line 42 leagues and ¼. Upon the seventh point doe answer unto one degree of Latitude 89 leagues and ¾, and you are departed from your right line 88 leagues, as it appear∣eth out of the Table following,

The Table of the Author which is more precise.

Leagues of the course or Rumb.	Distance from the right line
1	17 ••/6	3 ½
2	19 ⅜	7 ¼
3	21	11 ⅔
4	24 ¾	17 ½
5	31 ½	26 ⅕
6	45 ¾	42 ¼
7	89 ¾	88

The old Table which is less certaine.

Leagus of the course or Rumb.	Distance from the right line or Meridian.
18	3 ½
18 ½	7 ½	21 ½	11 ⅔
25	17 ½
31 ½	26 ½
46 ½	42 ½
88	85

CHAP. XXVIII. How you may come to know the Longitude or the course from East to West.

THat which the Cosmographers call Longitude, is called by the Mariners the distance from the right line, and the course of East and West, and the heighth of East and West, and it is a part of an East and west Rumb contained between two Meridians, one of which runneth by the point or place from whence we departed, and the other by the point where the ship is. This distance from the right line is known by the mean of two things, namely of the course and of the difference of Latitude, or of the course and distance.

The course and the difference of the heighth being given, you may know the said distance by traverse or by numbers. By Geo∣metry, or traverse it is known in manner following: the heighth, or the distance of your ship from the Equinoctial being known, and the Rumb also upon which you have sailed, you must cast upon your chart a point by traverse, and placing upon that point one of the points of your Compasses, and the other upon the next Rumb of East and West; you must place one point of ano∣ther paire of Compasses at the haven or point from whence the

ship departed, and the other point upon the North and South Rumb which is next. These two Compasses thus opened, run∣ning by their Rumbs one towards another, you must mark where the two points meet; namely, that which came out of the part from whence you departed, and that which you removed from the point where the ship presently is, being found by traverse: and where those two points doe meet, there make another point or prick. Then looke how many leagues there are from the said third point to the point of traverse where the ship is, (both which doe alwaies beare East and West one from another) so many leagues is your distance from the right line. And if in stead of the leagues set down in the scale wee measure with de∣grees taken out of the graduation,* 1.6 we shall have the degrees of Longitude which are between the point of our departure, and the point of the place where presently we are.

And it is to be noted, that alwayes when we sail, we either alter our latitude onely, and that is, when we sail North and South, or we alter the longitude onely, that is, when we sail by the self-same latitude, going alwayes East and West by the same parrallel: or we alter both latitude and longitude, when we sail by any of the other 28 winds. When we alter the latitude on∣ly we swerve not one jot from the right line or Meridian; when we alter both longitude and latitude, then must we find the lon∣gitude or distance from the right line in manner above-said.

But when your longitude onely is altered, because then you must find out the point where the ship is by imagination onely, there is no certain manner to know the longitude or distance from the right line, but onely little more or lesse, setting down a point by imagination, and measuring by leagues, or by degrees, what distance there is between that and the point from which the ship departed. By numbers you may find out the longitude in manner following: The difference of your distance from the Equinoctial being known, which is so many degrees more or less, as you have increased or diminished in the heighth of the Pole, look in the Table annexed to the chapter next before this, for the leagues of distance from the right line, which an∣swer unto one degree by the rumb or point of the compass upon which you have sailed; and multiplying those leagues by the number of degrees which you have increased or diminished in the heighth of the pole in your Navigation, you shall then see how many leagues you are distant from the right line, which pas∣seth by the place from whence you came, which leagues if you

divide by 17 and an half, then will appear unto you the degrees of longitude between the place from whence you departed, and the point where you are.

CHAP. XXIX. How you may set down in your Chart a new Land, never before discovered.

IT may sometimes fall out in new Discoveries, or when your ship by means of a tempest is driven out of her right course, that you shall come to the sight of some Isle, Shoald, or new Land, whereof the Mariner is utterly ignorant. And to make some relation of the same, or to go unto it some other time, if you desire to set it down in your Sea-chart, in the true place, you may do it after this manner: So soon as you have sight thereof, mark it well first with your compass, observing diligently upon which point thereof it lieth. And secondly, you must there take the heighth of the Sun, or of the Pole-star, that you may know in what point your ship is, and that point you must call the first point; which being so done, your ship may sail on her course all that day, till the day following, without losing her way: and the next day mark the land again, and see upon what point it li∣eth, and then take your heighth, and with it cast your point of traverse once again; and that you may call your second point. Then take a pair of compasses, and placing one foot upon the first point, and the other upon the rumb towards which the land did bear, when you cast your first point: set also one foot of another pair of compasses in the second point, and the other foot upon the rumb upon which the land lay when you cast your second point; and these two compasses thus opened, you must move by their rumbs, till those two feet of both compasses do meet together, which were moved from the foresaid two points: and where they do so meet together, there may you say is the land which you discovered; which land you may point out with the in-lets and out-lets, or capes and other signes, which you saw thereupon. And by the graduation you may see the la∣titude thereof, that thereby you may finde it, if at any time af∣ter you go to seek for it.

CHAP. XXX. Seeing two known points or Capes of land as you sail along, how you may know the distance of your ship from them.

IT is the custome of passengers, when they first descrie that land which they would arrive at, to ask the Pilot, how far they are from land▪ Unto which question he may well an∣swer, if he know two capes, or points, or notable places there∣upon: which places the further they be asunder one from ano∣ther, the more certainly may he answer to that question.

Let him pitch therefore one foot of one pair of compasses up∣on one of the two foresaid capes, and the other foot upon the rumb which in his compasse pointeth towards that cape. And in like manner shall he do with another pair of compasses, pla∣cing one foot thereof upon the other known cape, and the other foot upon the rumb, which stretcheth towards the said second cape; and moving the two Compasses so opened by their two Rumbs off from the land, the very same point where the two feet which came from the two capes do meet, you may affirm to be the very point where your ship is. And then taking measure by the scale of leagues, you may see what distance there is from the said point to either of the foresaid capes, or to any other place, which you think good, for it is a very easie matter if you know the point where your ship is.

CHAP. XXXI. Of the account of the Moone.

THe account of the Moone and of the tides is most necessa∣rie to be known of Mariners, to enter and depart from any Havens, Rivers, or Barres, and to pass by some banks, and shoalds.

A tide is a regular motion of the Sea whereby at some times it seemeth more increased then at other. And these tides are of two sorts: for some are such as we call spring-tides and neap-tides, and the course of this motion hapneth from one half moneth to another half moneth. Others be those which we call more

properly by the names of tides; to wit, a full sea, and a low sea, a swelling and a falling sea; and these are from the one half lunar day, to the other half. Which tides, as well the first as the se∣cond, have their course and moving from the motion of the Moone: which is of two sorts; one proper from West to East, by means whereof in thirty days almost, it is in conjunction with the Sun, which we call the new Moone; and in opposition, which wee call the full of the Moone; and those wee name the quarters, when it shineth half unto us. The other motion is from East to West by the force of the Primum mobile, or the first moveable heaven, whereby in one lunar day the Moone passeth over all the two and thirty points of the compasse, or to speak more plainly, it riseth and setteth, and returneth again to arise, which two motions of the Moone being known, we may easily discerne the manner of both kinds of the foresaid tides. And because that to the knowledge hereof it is requisite that we know the middle motion of the Moone; I will first set down how it may be known, and then how thereby wee may discerne the seasons of the tides.

For which purpose, we are to note that the golden number, as it is commonly called, is a certain number of years wherein the Moone hath all the diversities of aspects with the Sun that can happen between them, which is done in every nineteen years almost.

As for example, if in the year 1588 there be a conjunction of the Sun and Moone upon the 26 of April, or an opposition upon the 11 of April, I say that there shall not happen a conjunction of the Sun and Moone upon the 26 of April, nor an opposition upon the 11 of April, till 19 years be expired, which will be in the year of our Lord 1607. And so are wee to conceive like∣wise of the quarters and other aspects.

The second thing to be noted, is, that from this golden num∣ber springeth another, which is called the concurrent, being the days of the Moone at the beginning of the year: which year, according to that account, beginneth from the last of February, about twelve a clock at night, which is the beginning of March. And the days of the Moone which then remain, besides all the whole lunare moneths of the year past, are called by Calculators The concurrents; because they serve to know the account of the Moone, throughout the whole year that is to come; and they concur with other numbers to know the age of the Moone. Now by these two numbers, to be able to discern the days of the

Moone, or the distance thereof from the Sun, you are to note the Rules following.

The first Rule of the Golden number.

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

The second Rule of the concurrent.

Divide the golden number by three, and if there remaine one, the concurrent is equall with the golden number; and if there remaine two, the concurrent is greater then the golden number by ten: but if nothing remaine, the concurrent exceedeth the golden number by twenty, And if this concurrent exceed the number of thirty, then the remainder or surplussage shall be the concurent.

The third Rule of the Conjunction.

The number of the concurent being known, you must add it unto the number of moneths, which have passed from the be∣ginning of March last past, till the end of that moneth wherein you would know the same: and if the whole product amounteth not to thirty, mark how much it wanteth of thirty: and if it ex∣ceedeth thirty, see what it lacketh of sixty, and that which it wanteth either of thirty or sixty is the number of the days of such a moneth wherein the Conjunction hapneth.

The fourth Rule of the full and quarters of the Moone.

If the day of the Conjunction be before the 15 day of the moneth, add 15 unto the day of the Conjunction, and you shall find the day of the full Moone; and if the Conjunction happen after the 15 day, take away 15 from the number of the day of the Conjunction, and you shall have the full Moone of that moneth.

The first quarter is seven daies after the Conjunction, and the last quarter seven days after the full Moone.

The fifth Rule of the Spring-tides and Neap-tides.

Upon the day of the Conjunction, and of the full Moone, are the Spring-tides▪ and upon the two quarter days are the Neap-tides: and so much the more doe the waters increase, as the Conjunction or full Moon are nerer: and so much the more they decrease also the neerer they come unto the quarters.

An example whereby the foresaid Rules are made more plain.

Suppose a fleet of Ships lie within the heaven of San Lucar de barrameda, expecting a fit time to 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 re∣maineth and because there is no remainder, I will take two more of the concurrent th••n of the golden number, and there shall be two of the concurrent, casting away thirty; by the second Rule. Adding these two to the four moneths which are from the be∣ginning of March past till this present moneth of Iune,* 1.7 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 hap∣pen every day, which depend upon another swift mo∣tion 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 be∣ing 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 where∣in 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 ⅘ of fifteene degrees contained in each hour. Insomuch that the Moon by her mid∣dle motion is every day distant from the Sun about twelve de∣grees; which being reduced into time, do make ⅘ 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 ⅘ 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 com∣meth 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 con∣current, 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 con∣taineth 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 ma∣keth 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 ⅕ after the first full Sea, commeth the second Tide: and other six hours and ⅕ 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 form••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 ⅘ of an hour, according to the fourth Rule, and they may make 24/5 I divide these 24 by 5, and I find the quotient to be four, and the remainder four. And so I say that the Moon 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 com∣meth the second ebb or low Sea.

CHAP. XXXIII. Of a certain Instrument, whereby you may in gene∣rall 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 In∣strument, 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 pro∣ceed 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 num∣bers that you did at the first.

These 32 lines so drawn, doe represent the 32 winds, where∣by 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 to∣wards 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.

[illustration]

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 un∣derneath, 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 se∣cond 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 di∣vided, 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 to∣wards 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 morn∣ing▪ and five of the clock at evening. And counting other fif∣teen degrees on both sides, more towards the point B, and pla∣cing

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 after∣noon. And if you will have the half hours also, you must ac∣count 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.

[illustration]

Then placing your compasses upon the center E, and upon eve∣ry division of the line EB you shall draw the same divisions like∣wise upon the line ED which being done, draw certain obscure lines from the point A to the divisions of the line EB: and draw∣ing 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 Equi∣noctiall 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 Hori∣zon, and let every one of these parts be divided into five other parts or degrees. Then accounting from the Center E in the Hori∣zon 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 ma∣king 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 distin∣guished 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 Astro∣labe, 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 end∣eth; 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 ei∣ther 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 vari∣ation 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 Instru∣ment, 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 set∣eth more to the North then the Instrument sheweth, all the dif∣ference 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 Equinocti∣al 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 for∣mer 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 No∣vember, 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 menti∣oned, 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 follow∣ing, bearing in a manner the same form and shape, and therefore also to be used altogether almost in the same sort that those Ta∣bles have been, which for these many years have been most used by English Mariners.

This Table of the Suns Declination containeth twelve particu∣lar 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 follow∣ing after the leap year: the next rank containeth the second years after the leap year: in the third rank are set down the years that follow three years after the leap year: and in the fourth and last rank are the fourth years after the precedent leap years, which are also leap years themselves.

Under every one of these ranks of years there are two columns; the first whereof containeth the degrees and min. of the Suns De∣clination, answerable to every day of the moneth, superscribed in each of those years, without sensible error. In the second column are set down the minutes of the differences of the Suns Declinations for every one of those dayes, for the readier finding of the part proportional of this difference, answering to any difference of Longitude from London, whereof you may read more pag. 181, &c. In the first column of each of these Tables next the left hand are placed the numbers of the days of the moneth that is set down in the head thereof. The use of this Table for knowing the Declination of the Sun at any time is thus:* 1.8 look the moneth and year wherein you would know the same in the head of the Table, and the day of the moneth in the first column next the left hand; then proceeding from that day directly in the same line towards the right hand till you come right under the same year, you shall there find the Declination you sought for.

〈1 page duplicate〉〈1 page duplicate〉

〈1 page duplicate〉〈1 page duplicate〉

Take for example the 24 day of February in the year 1610. Finding therefore that moneth and year in the head of the Table, and the 24 day in the first column; in the same line pro∣ceeding towards the right hand, till you come right under that year, you have there the Suns Declination for that time 5 degrees 34 minutes towards the South.

January

	1	2	3	4
Day	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
deg.	mi.	di.	deg.	mi.	di.	deg.	mi.	di.	deg.	mi.	di
1	21	47		21	50		21	52		21	54
2	21	37	10	21	40	10	21	42	10	21	45	9
3	21	27	10	21	30	10	21	32	10	21	35	10
4	21	17	10	21	19	11	21	22	10	21	24	11
5	21	6	11	21	8	11	21	11	11	21	13	11
6	20	54	12	20	57	11	21	0	11	21	2	11
7	20	42	12	20	45	12	20	48	12	20	51	11
8	20	30	12	20	33	12	20	36	12	20	39	12
9	20	17	13	20	20	13	20	23	13	20	26	13
10	20	4	13	20	7	13	20	10	13	20	13	13
11	19	50	14	19	54	13	19	57	13	20	0	13
12	19	36	14	19	40	14	19	43	14	19	47	13
13	19	22	14	19	26	14	19	29	14	19	33	14
14	19	8	14	19	11	15	19	15	14	19	18	15
15	18	53	15	18	56	15	19	0	15	19	4	14
16	18	38	15	18	41	15	18	45	15	18	49	15
17	18	22	16	18	26	15	18	30	15	18	33	16
18	18	6	16	18	10	16	18	14	16	18	18	15
19	17	50	16	17	54	16	17	58	16	18	2	16
20	17	33	17	17	37	17	17	41	17	17	45	17
21	17	16	17	17	21	16	17	25	16	17	29	16
22	16	59	17	17	4	17	17	8	17	17	12	17
23	16	42	17	16	46	18	16	50	18	16	55	17
24	16	24	18	16	29	17	16	33	17	16	37	18
25	16	6	18	16	11	18	16	15	18	16	19	18
26	15	48	18	15	52	19	15	57	18	16	1	18
27	15	29	19	15	34	18	15	38	19	15	43	18
28	15	10	19	15	15	19	15	20	18	15	24	19
29	14	51	19	14	56	19	15	1	19	15	5	19
30	14	32	19	14	37	19	14	41	20	14	46	19
31	14	13	19	14	17	20	14	22	19	14	27	19

February

	1	2	3	4
Day	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
deg.	mi.	di.	deg	mi.	di.	deg.	mi.	di.	deg.	mi.	di.
1	13	53		13	58		14	2		14	7
2	13	33	20	13	38	20	13	42	20	13	47	20
3	13	12	21	13	17	21	13	22	20	13	27	20
4	12	52	20	12	57	20	13	2	20	13	6	21
5	12	31	21	12	36	21	12	41	21	12	46	20
6	12	10	21	12	16	20	12	21	20	12	26	20
7	11	49	21	11	55	21	12	0	21	12	5	21
8	11	28	21	11	33	22	11	38	22	11	44	21
9	11	7	21	11	12	21	11	17	21	11	22	22
10	10	45	22	10	50	22	10	56	21	11	1	21
11	10	23	22	10	28	22	10	34	22	10	39	22
12	10	1	22	10	7	21	10	12	22	10	17	22
13	9	39	22	9	45	22	9	50	22	9	55	22
14	9	17	22	9	23	22	9	28	22	9	33	22
15	8	55	22	9	0	23	9	6	22	9	11	22
16	8	32	23	8	38	22	8	43	23	8	49	22
17	8	10	22	8	15	23	8	21	22	8	26	23
18	7	47	23	7	53	22	7	58	23	8	4	22
19	7	24	23	7	30	23	7	35	23	7	41	23
20	7	1	23	7	7	23	7	12	23	7	18	23
21	6	38	23	6	44	23	6	49	23	6	55	23
22	6	15	23	6	21	23	6	26	23	6	32	23
23	5	52	23	5	58	23	6	3	23	6	9	23
24	5	29	23	5	34	24	5	40	23	5	46	23
25	5	5	24	5	11	23	5	17	23	5	22	24
26	4	42	23	4	48	23	4	53	24	4	59	23
27	4	18	24	4	24	24	4	30	23	4	36	23
28	3	55	23	4	1	23	4	6	24	4	12	24
29										3	49	23

March

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di	Deg.	M	di.	De.	mi.	di.	Deg.	M	di
1	3	31		3	37		3	43		3	23
2	3	8	23	3	13	24	3	19	24	3	1	24
3	2	44	24	2	50	23	2	56	23	2	37	24
4	2	20	24	2	26	24	2	32	24	2	14	23
5	1	57	23	2	3	23	2	8	24	1	50	24
6	1	33	24	1	39	24	1	45	23	1	27	23
7	1	9	24	1	15	24	1	21	24	1	3	24
8	0	46	23	0	51	24	0	57	24	0	39	24
9	0	22	24	0	28	23	0	33	24	0	15	24
			24	0	4	24	0	10	23			23* 1.9
10	0	2	23			24			24	0	8	24
11	0	25	24	0	20	23	0	14	24	0	32	24
12	0	49	24	0	43	24	0	38	23	0	56	23
13	1	13	23	1	7	24	1	1	24	1	19	24
14	1	36	24	1	31	23	1	25	24	1	43	23
15	2	0	24	1	54	24	1	49	23	2	6	24
16	2	24	23	2	18	23	2	12	24	2	30	23
17	2	47	23	2	41	24	2	36	23	2	53	24
18	3	10	24	3	5	23	2	59	23	3	17	23
19	3	34	23	3	28	23	3	22	24	3	40	23
20	3	57	23	3	51	24	3	46	23	4	3	24
21	4	20	23	4	15	23	4	9	23	4	27	23
22	4	43	23	4	38	23	4	32	23	4	50	23
23	5	6	23	5	1	23	4	55	23	5	13	23
24	5	29	23	5	24	23	5	18	23	5	36	23
25	5	52	23	5	47	23	5	41	23	5	59	22
26	6	15	23	6	10	22	6	4	23	6	21	23
27	6	38	22	6	32	23	6	27	22	6	44	22
28	7	0	23	6	55	22	6	49	23	7	6	23
29	7	23	22	7	17	23	7	12	22	7	29	22
30	7	45	22	7	40	22	7	34	22	7	51	22
31	8	7		8	2		7	56		8	13

April.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di	deg.	mi.	d.	deg.	mi.	di	deg.	mi.	di
1	8	29		8	24		8	18		8	35
2	8	51	22	8	46	22	8	40	22	8	57	22
3	9	13	22	9	8	22	9	2	22	9	19	22
4	9	34	21	9	29	21	9	24	22	9	40	21
5	9	56	22	9	51	22	9	46	22	10	2	22
6	10	17	21	10	12	21	10	7	21	10	23	21
7	10	38	21	10	33	21	10	28	21	10	44	21
8	10	59	21	10	54	21	10	49	21	11	5	21
9	11	20	21	11	15	21	11	10	21	11	26	21
10	11	41	21	11	36	21	11	31	21	11	46	20
11	12	1	20	11	56	20	11	51	20	12	6	20
12	12	21	20	12	16	20	12	11	20	12	26	20
13	12	41	20	12	36	20	12	31	20	12	46	20
14	13	1	20	12	56	20	12	51	20	13	6	20
15	13	20	19	13	16	20	13	10	19	13	26	20
16	13	40	20	13	35	19	13	30	20	13	45	19
17	13	59	19	13	54	19	13	50	20	14	4	19
18	14	18	19	14	13	19	14	9	19	14	23	19
19	14	36	18	14	32	19	14	27	18	14	41	18
20	14	55	19	14	50	18	14	46	19	15	0	19
21	15	13	18	15	9	19	15	4	18	15	18	18
22	15	31	18	15	27	18	15	22	18	15	36	18
23	15	49	18	15	44	17	15	40	18	15	53	17
24	16	6	17	16	2	18	15	58	18	16	11	18
25	16	23	17	16	19	17	16	15	17	16	28	17
26	16	40	17	16	36	17	16	32	17	16	45	17
27	16	57	17	16	53	17	16	49	17	17	1	16
28	17	13	16	17	9	16	17	5	16	17	17	16
29	17	29	16	17	25	16	17	21	16	17	33	16
30	17	45	16	17	41	16	17	37	16	17	49	16

May.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di	degr.	mi	di▪	degr.	mi	di	degr.	mi	di.
1	18	0		17	57		17	53		18	4
2	18	15	15	18	12	15	18	8	15	18	19	15
3	18	30	15	18	27	15	18	23	15	18	34	15
4	18	45	15	18	41	14	18	38	15	18	49	15
5	18	59	14	18	56	15	18	52	14	19	3	14
6	19	13	14	19	10	14	19	6	14	19	17	14
7	19	27	14	19	23	13	19	20	14	19	30	13
8	19	40	13	19	37	14	19	34	14	19	43	13
9	19	53	13	19	50	13	19	47	13	19	56	13
10	20	5	12	20	2	12	19	59	12	20	9	13
11	20	18	13	20	15	13	20	12	13	20	21	12
12	20	30	12	20	27	12	20	24	12	20	33	12
13	20	41	11	20	38	11	20	36	12	20	44	11
14	20	52	11	20	50	12	20	47	11	20	55	11
15	21	3	11	21	1	11	20	58	11	21	6	11
16	21	14	11	21	11	10	21	9	11	21	17	11
17	21	24	10	21	22	11	21	19	10	21	27	10
18	21	34	10	21	32	10	21	29	10	21	36	9
19	21	43	9	21	41	9	21	39	10	21	46	10
20	21	52	9	21	50	9	21	48	9	21	55	9
21	22	1	9	21	59	9	21	57	9	22	3	8
22	22	9	8	22	7	8	22	5	8	22	11	8
23	22	17	8	22	15	8	22	13	8	22	19	8
24	22	25	8	22	23	8	22	21	8	22	27	8
25	22	32	7	22	30	7	22	28	7	22	34	7
26	22	38	6	22	37	7	22	35	7	22	40	6
27	22	45	7	22	43	6	22	42	7	22	46	6
28	22	51	6	22	49	6	22	48	6	22	52	6
29	22	56	5	22	55	6	22	54	6	22	58	6
30	23	1	5	23	0	5	22	59	5	23	3	5
31	23	6	5	23	5	5	23	4	5	23	8	5

June.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di.	degr.	mi	di	degr.	mi	di.	degr.	mi	di.
1	23	10		23	10		23	8		23	12
2	23	14	4	23	14	4	23	12	4	23	16	4
3	23	18	4	23	17	3	23	16	4	23	19	3
4	23	21	3	23	20	3	23	20	4	23	22	3
5	23	24	3	23	23	3	23	23	3	23	25	3
6	23	26	2	23	26	3	23	25	2	23	27	2
7	23	28	2	23	28	2	23	27	2	23	29	2
••	23	30	2	23	29	1	23	29	2	23	30	1
9	23	31	1	23	30	1	23	30	1	23	31	1
10	23	31	0	23	31	1	23	31	1	23	31	0
11	23	31	0	23	31	0	23	31	0	23	31	0
12	23	31	0	23	31	0	23	31	0	23	31	0
13	23	31	0	23	31	0	23	31	0	23	30	1
14	23	30	1	23	30	1	23	30	1	23	29	1
15	23	28	2	23	29	1	23	29	1	23	28	••
16	23	26	2	23	27	2	23	27	2	23	26	2
••••	23	24		23	25	2	23	25	2	23	24	2
••8	23	21	3	23	22	3	23	23	2	23	21	3
19	23	18	3	23	19	3	23	20	3	23	18	3
20	23	15	3	23	16	3	23	17	3	23	••4	4
21	23	11	4	23	12	4	23	13	4	23	10	4
22	23	7	4	23	8	4	23	9	4	23	6	4
23	23	2	5	23	4	4	23	5	4	23	1	5
2••	22	57	5	22	59	5	23	0	5	22	56	5
25	22	52	5	22	53	6	22	55	5	22	50	6
26	22	46	6	22	48	5	22	49	6	22	44	6
27	22	40	6	22	41	7	22	43	6	22	38	6
••8	22	33	7	22	35	6	22	36	7	22	31	7
••9	22	26		22	28	7	22	29	7	22	24	7
••0	22	19		22	21	7	22	22	7	22	1••	7

July.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr	mi	di	degr.	mi	di	degr,	m.	di	degr.	mi	di.
1	22	11		22	13		22	15		22	9
2	22	3	8	22	5	8	22	7	8	22	0	9
3	21	54	9	21	56	9	21	58	9	21	52	8
4	21	45	9	21	47	9	21	50	8	21	43	9
5	21	36	9	21	38	9	21	41	9	21	33	10
6	21	26	10	21	29	9	21	31	10	21	24	9
7	21	16	10	21	19	10	21	21	10	21	13	11
8	21	6	10	21	8	11	21	11	10	21	3	10
9	20	55	11	20	58	10	21	0	11	20	52	11
10	20	44	11	20	47	11	20	49	11	20	41	11
11	20	33	11	20	35	12	20	38	11	20	29	12
12	20	21	12	20	24	11	20	27	11	20	17	12
13	20	9	12	20	12	12	20	15	12	20	5	12
14	19	56	13	19	59	13	20	2	13	19	53	12
15	19	43	13	19	46	13	19	50	12	19	40	13
16	19	30	13	19	33	13	19	37	13	19	27	13
17	19	17	13	19	20	13	19	23	14	19	13	14
18	19	3	14	19	6	14	19	10	13	18	59	14
19	18	49	14	18	52	14	18	56	14	18	45	14
20	18	34	15	18	38	14	18	41	15	18	30	15
21	18	20	14	18	23	15	18	27	14	18	16	14
22	18	5	15	18	8	15	18	12	15	18	1	15
23	17	49	16	17	53	15	17	57	15	17	45	16
24	17	34	15	17	38	15	17	41	16	17	30	15
25	17	18	16	17	22	16	17	26	15	17	14	16
26	17	2	16	17	6	16	17	10	16	16	57	17
27	16	45	17	16	49	17	16	53	17	16	41	16
28	16	29	16	16	33	16	16	37	16	16	24	17
29	16	12	17	16	16	17	16	20	17	16	7	17
30	15	54	18	15	59	17	16	3	17	15	50	17
31	15	37	17	15	41	18	15	4••	18	15	3••	18

August.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di.	degr.	mi	di	degr.	mi	di▪	degr.	mi	di.
1	15	19		15	24		15	28		15	14
2	15	1	18	15	6	18	15	10	18	14	56	18
3	14	43	18	14	47	19	14	52	18	14	38	18
4	14	24	19	14	29	18	14	33	19	14	19	19
5	14	6	18	14	10	19	14	15	18	14	1	18
6	13	47	19	13	51	19	13	56	19	13	42	19
7	13	28	19	13	32	19	13	37	19	13	22	20
8	13	8	20	13	13	19	13	18	19	13	••	19
9	12	49	19	12	54	19	12	58	20	12	43	20
10	12	29	20	12	34	20	12	39	21	12	24	19
11	12	9	20	12	14	20	12	19	20	12	4	20
12	11	48	21	11	54	20	11	59	20	11	43	21
13	11	28	20	11	33	21	11	38	21	11	23	20
14	11	8	20	11	13	20	11	18	20	11	2	21
15	10	47	21	10	52	21	10	57	21	10	41	21
16	10	26	21	10	31	21	10	36	21	10	20	21
17	10	5	21	10	10	21	10	15	21	9	59	21
18	9	44	21	9	49	21	9	54	21	9	38	21
19	9	23	21	9	28	21	9	33	21	9	17	21
20	9	1	22	9	6	22	9	12	21	8	55	22
21	8	39	22	8	45	21	8	50	22	8	33	22
22	8	18	21	8	23	22	8	28	22	8	11	22
23	7	56	22	8	1	22	8	6	22	7	49	22
24	7	34	22	7	39	22	7	44	22	7	27	22
25	7	11	23	7	17	22	7	22	22	7	5	22
26	6	49	22	6	54	23	7	0	22	6	43	22
27	6	26	23	6	32	22	6	37	23	6	20	23
28	6	4	22	6	9	23	6	15	22	5	58	22
29	5	41	23	5	47	22	5	52	23	5	35	23
30	5	19	22	5	24	23	5	30	22	5	12	23
31	4	56	23	5	1	23	5	7	23	4	49	23

September.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di.	degr.	mi	di	degr.	mi	di.	degr.	mi	di
1	4	33		4	38		4	44		4	26
2	4	10	23	4	15	23	4	21	23	4	3	23
3	3	47	23	3	52	23	3	58	23	3	40	23
4	3	24	23	3	29	23	3	35	23	3	17	23
5	3	0	24	3	6	23	3	12	23	2	54	23
6	2	37	23	2	43	23	2	48	24	2	31	23
7	2	14	23	2	19	24	2	25	23	2	7	24
8	1	50	24	1	56	23	2	2	23	1	44	23
9	1	27	23	1	33	23	1	38	24	1	20	24
10	1	3	24	1	9	24	1	15	23	0	57	23
11	0	40	23	0	46	23	0	51	24	0	34	23
12	0	16	24	0	22	24	0	28	23	0	10	24
—	—	—	23	—	—	23	0	4	24	—	—	24
13	0	7	24	0	1	24	—	—	23	0	14	23* 1.10
14	0	31	23	0	25	23	0	19	24	0	37	24
15	0	54	24	0	48	24	0	43	23	1	1	23
16	1	18	23	1	12	24	1	6	24	1	24	24
17	1	41	24	1	36	23	1	30	23	1	48	23
18	2	5	23	1	59	24	1	53	24	2	11	24
19	2	28	24	2	23	23	2	17	23	2	35	23
20	2	52	23	2	46	24	2	40	24	2	58	24
21	3	15	24	3	10	23	3	4	23	3	22	23
22	3	39	23	3	33	23	3	27	24	3	45	23
23	4	2	23	3	56	24	3	51	23	4	8	24
24	4	25	24	4	20	23	4	14	23	4	32	23
25	4	49	23	4	43	23	4	37	24	4	55	23
26	5	12	23	5	6	24	5	1	23	5	18	23
27	5	35	23	5	30	23	5	24	23	5	41	24
28	5	58	23	5	53	23	5	47	23	6	5	23
29	6	21	23	6	16	23	6	10	23	6	28	23
30	6	44		6	39		6	33		6	51

October.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di.	degr.	mi	di.	degr.	mi	di.	degr.	mi	di
1	7	7		7	1		6	56		7	13
2	7	30	23	7	24	23	7	19	23	7	36	23
3	7	52	22	7	47	23	7	41	22	7	59	23
4	8	15	23	8	9	22	8	4	23	8	21	22
5	8	37	22	8	32	23	8	27	23	8	43	22
6	9	0	23	8	54	22	8	49	22	9	6	23
7	9	22	22	9	16	22	9	11	22	9	28	22
8	9	44	22	9	38	22	9	33	22	9	50	22
9	10	6	22	10	0	22	9	55	22	10	12	22
10	10	27	21	10	22	22	10	17	22	10	33	21
11	10	49	22	10	44	22	10	39	22	10	55	22
12	11	11	22	11	5	21	11	0	21	11	16	21
13	11	32	21	11	27	22	11	21	21	11	38	22
14	11	53	21	11	48	21	11	43	22	11	59	21
15	12	14	21	12	9	21	12	4	21	12	19	20
16	12	34	20	12	29	20	12	24	20	12	40	21
17	12	55	21	12	50	21	12	45	21	13	1	21
18	13	15	20	13	10	20	13	5	20	13	21	20
19	13	35	20	13	30	20	13	26	21	13	41	20
20	13	55	20	13	50	20	13	46	20	14	1	20
21	14	15	20	14	10	20	14	5	19	14	20	19
22	14	34	19	14	30	20	14	25	20	14	40	20
23	14	54	20	14	49	19	14	44	19	14	59	19
24	15	13	19	15	8	19	15	3	19	15	18	19
25	15	31	18	15	27	19	15	22	19	15	36	18
26	15	50	19	15	45	18	15	41	19	15	55	19
27	16	8	18	16	3	18	15	59	18	16	13	18
28	16	26	18	16	21	18	16	17	18	16	31	18
29	16	43	17	16	39	18	16	35	18	16	48	17
30	17	1	18	16	57	18	16	52	17	17	5	17
31	17	18	17	17	14	17	17	10	18	17	22	17

November.

	1	2	3	4
Day.	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
degr.	mi	di.	degr.	mi	di.	degr.	mi	di.	degr.	mi	di.
1	17	35		17	31		17	26		17	39
2	17	51	16	17	47	16	17	43	17	17	55	16
3	18	7	16	18	3	16	17	59	16	18	11	16
4	18	23	16	18	19	16	18	15	16	18	27	16
5	18	39	16	18	35	16	18	31	16	18	43	16
6	18	54	15	18	50	15	18	46	15	18	58	15
7	19	9	15	19	5	15	19	1	15	19	13	15
8	19	23	14	19	19	14	19	16	15	19	27	14
9	19	37	14	19	34	15	19	30	14	19	41	14
10	19	51	14	19	47	13	19	44	14	19	55	14
11	20	4	13	20	1	14	19	58	14	20	8	13
12	20	17	13	20	14	13	20	11	••3	20	21	13
13	20	30	13	20	27	13	20	24	••3	20	34	13
14	20	42	12	20	39	12	20	36	12	20	45	12
15	20	54	12	20	51	12	20	48	12	20	57	12
16	21	6	12	21	3	12	21	0	12	21	8	11
17	21	17	11	21	14	11	21	11	11	21	19
18	21	27	10	21	25	11	21	22	11	21	30	1••
19	21	38	11	21	35	10	21	33	11	21	40	10
20	21	47	9	21	45	10	21	43	0	21	50	10
21	21	57	10	21	55	10	21	53	10	21	59	9
22	22	6	9	22	4	9	22	2	9	22	8	9
23	22	14	8	22	12	8	22	11	9	22	17	9
24	22	23	9	22	21	9	22	19	8	22	25	8
25	22	30	7	22	29	8	22	27	8	22	33	8
26	22	38	8	22	36	7	22	34	7	22	40	7
27	22	44	6	22	43	7	22	41	7	22	47	7
28	22	51	7	22	49	6	22	48	7	22	5	6
29	22	56	5	22	55	6	22	54	6	22	59
30	23	2	6	23	1	6	23	0	6	23	4	5

December.

	1	2	3	4
Day	1609	1610	1611	1612
1613	1614	1615	1616
1617	1618	1619	1620
deg.	mi.	di.	deg.	mi.	di.	deg.	mi.	di.	degr.	mi	di
1	23	7		23	6		23	5		23	8
2	23	12	5	23	11	5	23	10	5	23	13	5
3	23	16	4	23	15	4	23	14	4	23	17	4
4	23	20	4	23	19	4	23	18	4	23	20	3
5	23	23	3	23	22	3	23	21	3	23	23	3
6	23	25	2	23	25	3	23	24	3	23	26	3
7	23	27	2	23	27	2	23	26	2	23	28	2
8	23	29	2	23	29	2	23	28	2	23	30	2
9	23	30	1	23	30	1	23	30	2	23	31	1
10	23	31	1	23	31	1	23	31	1	23	31	0
11	23	31	0	23	31	0	23	31	0	23	31	0
12	23	31	0	23	31	0	23	31	0	23	31	0
13	23	31	0	23	31	0	23	31	0	23	30	1
14	23	30	1	23	30	1	23	30	1	23	29	1
15	23	28	2	23	28	2	23	29	1	23	27	2
16	23	26	2	23	26	2	23	27	2	23	25	2
17	23	23	3	23	24	2	23	25	2	23	22	3
18	23	20	3	23	21	3	23	22	3	23	19	3
19	23	17	3	23	18	3	23	19	3	23	16	3
20	23	13	4	23	14	4	23	15	4	23	12	4
21	23	8	5	23	10	4	23	11	4	23	7	5
22	23	3	5	23	5	5	23	6	5	23	2	5
23	22	58	5	23	0	5	23	1	5	22	57	5
24	22	52	6	22	54	6	22	55	6	22	51	6
25	22	46	6	22	48	6	22	49	6	22	44	7
26	22	39	7	22	41	7	22	43	6	22	37	7
27	22	32	7	22	34	7	22	36	7	22	30	7
28	22	25	7	22	26	8	22	29	7	22	22	8
29	22	17	8	22	18	8	22	21	8	22	14	8
30	22	8	9	22	10	8	22	13	8	22	6	8
31	21	59	9	22	1	9	22	4	9	21	57	9

By the height of the Pole-star to know the height of the Pole.

THe Tables following are calculated for the end of the year 1610. serving without sensible error for many years to come; they shew the height of the Pole for convenient Latitudes, by the height of the Pole star and the help of the Guards, in eight severall positions: so that you may by help of them, in any place on the North side of the Equator, to the Latiude of 74 degrees, or further, once in three hours every cleer night, make a good Observation of the Latitude. In the three last positions, if the height of the Pole be but little, the Guards will be hid under the Horizon: notwithstanding if by the hour of the night, or the height of any known star, by the help of a Globe, or Astrolabe, wee know when the stars doe come to their due position, we may Observe the Pole star, and find the height of the Pole near as well, as if they were above the Hori∣zon. The Positions are carefully to be Observed, that the two stars mentioned in the head of the Table be either in the same Azimuth one directly over another (which is known, if looking with the one eye onely, a perpendicular cord will hide or cover them both) or else of the same Altitude above the Horizon, which is discerned by the Crosse-staffe. At that instant that any such Position shall happen, take the height of the Pole star; and the Table answerable to that Position shall give you the height of the Pole.

For example; when the greater Guard is directly under the Pole star, I find the height of the Pole star to be 47 degrees and twenty minutes: I looke in the seventh Table and find the height of the Pole for 47, to be 44 degrees, 36 minutes: to this I add 20 minutes, because the height of the star is 20 minutes above 47. then is the height of the Pole 44 degrees 56 min. the se∣conds may safely be neglected, though they be inserted in the Table, rather for satisfaction of the reader, in the certainty of the Calculation, then for any necessary use.

If when the greater Guard is in the East, of equal height with the Pole star, I find the height of that star to be 75 degrees, 40 minutes. In the first Table I find the height of the Pole answer∣ing to 75 deg. to be 77 deg. 26 min. and the difference one de∣gree, three minutes: the part proportionall whereof for 40 mi∣nutes,

is 42 min. which added to 77 degrees, 26 min. maketh the true Elevation of the Pole 78 degres. 8 minutes.

Where the height of the Pole star is but little, there you must subduct the refraction from the height observed: otherwise we shall alwayes find the height more then in truth it is, this Refra∣ction causeth the Observations of the Sun at the South, and at the North, (when the Sun never setteth in Northern climates) to give severall Latitudes in the same place, the Observation at the North alwaies making the latitude too great. Concerning this Refraction, see page 97.

When the greater guard is in the same heighth with the Pole Star.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.
Deg.	deg.	mi.	se.	Deg.	degr.	mi.	sec	Degr	degr.	mi.	sec
1	2	26	49	28	29	35	46	55	56	50	52
2	3	27	8	29	30	36	9	56	57	51	46
3	4	27	26	30	31	36	33	57	58	52	42
4	5	27	44	31	32	36	57	58	59	53	41
5	6	28	2	32	33	37	22	59	60	54	44
6	7	28	21	33	34	37	47	60	61	55	50
7	8	28	40	34	35	38	13	61	62	57	0
8	9	28	58	35	36	38	39	62	63	58	14
9	10	29	17	36	37	39	6	63	64	59	33
10	11	29	36	37	38	39	34	64	66	0	58
11	12	29	55	38	39	40	3	65	67	2	28
12	13	30	14	39	40	40	31	66	68	4	3
13	14	30	33	40	41	41	1	67	69	5	46
14	15	30	53	41	42	41	32	68	70	7	38
15	16	31	12	42	43	42	3	69	71	9	40
16	17	31	32	43	44	42	36	70	72	11	13
17	18	31	52	44	45	43	9	71	73	14	20
18	19	32	11	45	46	43	44	72	74	17	0
19	20	32	32	46	47	44	20	73	75	19	54
20	21	32	52	47	48	44	57	74	76	23	0
21	22	33	13	48	49	45	36	75	77	26	19
22	23	33	34	49	50	46	15	76	78	29	51
23	24	33	55	50	51	46	57	77	79	33	36
24	25	34	17	51	52	47	40	78	80	37	36
25	26	34	38	52	53	48	25	79	81	41	49
26	27	35	1	53	54	49	12	80	82	46	17
27	28	35	23	54	55	50	1

When the two guards are of equal heighth betwixt the East and the highest.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.
Degr	degr.	mi.	sec.	Degr	degr.	mi.	sec	Deg.	degr.	mi.	sec
1	3	46	20	28	30	46	37	55	57	42	26
2	4	46	23	29	31	46	36	56	58	41	57
3	5	46	25	30	32	46	33	57	59	41	26
4	6	46	27	31	33	46	31	58	60	40	51
5	7	46	29	32	34	46	29	59	61	40	11
6	8	46	31	33	35	46	26	60	62	39	26
7	9	46	32	34	36	46	22	61	63	38	36
8	10	46	34	35	37	46	19	62	64	37	39
9	11	46	36	36	38	46	15	63	65	36	34
10	12	46	37	37	39	46	10	64	66	35	19
11	13	46	38	38	40	46	5	65	67	33	53
12	14	46	39	39	41	46	0	66	68	32	14
13	15	46	40	40	42	45	54	67	69	30	19
14	16	46	41	41	43	45	47	68	70	28	3
15	17	46	42	42	44	45	40	69	71	25	21
16	18	46	43	43	45	45	32	70	72	22	7
17	19	46	43	44	46	45	23	71	73	18	13
18	20	46	43	45	47	45	14	72	74	13	30
19	21	46	43	46	48	45	3	73	75	7	36
20	22	46	43	47	49	44	52	74	76	0	4
21	23	46	44	48	50	44	39	75	76	50	17
22	24	46	43	49	51	44	25	76	77	36	46
23	25	46	43	50	52	44	10	77	78	17	2
24	26	46	42	51	53	43	53	78	78	47	20
25	27	46	41	52	54	43	35	79
26	28	46	40	53	55	43	14	80
27	29	46	39	54	56	42	51	81

When the greatest guard is directly above the Pole Star.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.
Degr	degr.	mi.	sec	Deg.	degr.	mi.	sec	Deg.	degr.	mi.	sec
1	3	22	29	28	30	21	55	55	57	20	51
2	4	22	28	29	31	21	53	56	58	20	47
3	5	22	27	30	32	21	52	57	59	20	43
4	6	22	26	31	33	21	50	58	60	20	38
5	7	22	25	32	34	21	48	59	61	20	34
6	8	22	23	33	35	21	47	60	62	20	28
7	9	22	22	34	36	21	45	61	63	20	23
8	10	22	21	35	37	21	43	62	64	20	17
9	11	22	20	36	38	21	41	63	65	20	11
10	12	22	19	37	39	21	39	64	66	20	4
11	13	22	17	38	40	21	38	65	67	19	57
12	14	22	16	39	41	21	36	66	68	19	48
13	15	22	15	40	42	21	33	67	69	19	40
14	16	22	14	41	43	21	31	68	70	19	30
15	17	22	13	42	44	21	29	69	71	19	20
16	18	22	11	43	45	21	27	70	72	19	8
17	19	22	10	44	46	21	25	71	73	18	55
18	20	22	9	45	47	21	22	72	74	18	40
19	21	22	7	46	48	21	20	73	75	18	23
20	22	22	6	47	49	21	17	74	76	18	4
21	23	22	5	48	50	21	14	75	77	17	42
22	24	22	3	49	51	21	11
23	25	22	2	50	52	21	8
24	26	22	1	51	53	21	5
25	27	21	59	52	54	21	2
26	28	21	58	53	55	20	59
27	29	21	56	54	56	20	55

When the two guards are directly one over another betwixt the highest and the West,

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole,
Degr	degr.	mi.	sec	Deg.	degr.	mi.	sec	Deg.	degr.	mi.	sec.
1	1	20	22	28	28	38	3	55	56	8	51
2	2	20	58	29	29	38	50	56	57	10	44
3	3	21	34	30	30	39	37	57	58	12	43
4	4	22	11	31	31	40	25	58	59	14	49
5	5	22	47	32	32	41	15	59	60	17	2
6	6	23	23	33	33	42	5	60	61	19	23
7	7	24	0	34	34	42	57	61	62	21	53
8	8	24	37	35	35	43	50	62	63	24	34
9	9	25	13	36	36	44	44	63	64	27	25
10	10	25	50	37	37	45	40	64	65	30	30
11	11	26	28	38	38	46	37	65	66	33	48
12	12	27	5	39	39	47	35	66	67	37	23
13	13	27	43	40	40	48	36	67	68	41	16
14	14	28	21	41	41	49	38	68	69	45	30
15	15	29	0	42	42	50	42	69	70	50	7
16	16	29	38	43	43	51	48	70	71	55	13
17	17	30	18	44	44	52	56	71	73	0	52
18	18	30	57	45	45	54	7	72	74	7	9
19	19	31	37	46	46	55	20	73	75	14	8
20	20	32	18	47	47	56	36	74	76	21	52
21	21	32	59	48	48	57	55
22	22	33	40	49	49	59	17
23	23	34	22	50	51	0	43
24	24	35	5	51	52	2	12
25	25	35	48	52	53	3	45
26	26	36	33	53	54	5	22
27	27	37	17	54	55	7	4

When the greater guard is in the West, of the same heighth with the Pole Star.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.
Deg.	degr.	mi.	sec.	Degr	degr.	mi.	sec	Deg.	degr.	mi.	sec
2	0	34	7	29	27	43	27	56	55	0	53
3	1	34	26	30	28	43	52	57	56	2	1
4	2	34	44	31	29	44	18	58	57	3	12
5	3	35	3	32	30	44	44	59	58	4	26
6	4	35	22	33	31	45	11	60	59	5	43
7	5	35	41	34	32	45	39	61	60	7	8
8	6	36	0	35	33	46	7	62	61	8	39
9	7	36	19	36	34	46	36	63	62	10	18
10	8	36	38	37	35	47	6	64	63	12	5
11	9	36	57	38	36	47	37	65	64	13	59
12	10	37	17	39	37	48	8	66	65	16	4
13	11	37	36	40	38	48	40	67	66	18	21
14	12	37	56	41	39	49	15	68	67	20	53
15	13	38	16	42	40	49	49	69	68	23	37
16	14	38	37	43	41	50	25	70	69	26	38
17	15	38	57	44	42	51	2	71	70	29	40
18	16	39	18	45	43	51	40	72	71	33	13
19	17	39	39	46	44	52	21	73	72	37	28
20	18	40	0	47	45	53	3	74	73	42	42
21	19	40	21	48	46	53	46	75	74	49	8
22	20	40	43	49	47	54	31	76	75	56	59
23	21	41	5	50	48	55	17	77	77	6	26
24	22	41	28	51	49	56	7	78	78	17	40
25	23	41	51	52	50	56	59	79	79	30	54
26	24	42	14	53	51	57	53	80	80	46	22
27	25	42	33	54	52	58	49
28	26	43	2	55	53	59	48

When the two guards are of equal height betwixt the West and the lowest.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star:	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Poe.
Deg,	degr.	mi	sec.	Deg.	degr.	mi.	sec.	Deg.	degr.	mi.	sec
3	0	13	50	30	27	16	9	57	54	24	47
4	1	13	53	31	28	16	17	58	55	25	31
5	2	13	56	32	29	16	26	59	56	26	19
6	3	14	0	33	30	16	36	60	57	27	12
7	4	14	3	34	31	16	46	61	58	28	10
8	5	14	6	35	32	16	56	62	59	29	14
9	6	14	10	36	33	17	7	63	60	30	26
10	7	14	14	37	34	17	18	64	61	31	45
11	8	14	18	38	35	17	30	65	62	33	14
12	9	14	22	39	36	17	43	66	63	34	54
13	10	14	26	40	37	17	56	67	64	36	47
14	11	14	30	41	38	18	10	68	65	38	57
15	12	14	35	42	39	18	25	69	66	41	26
16	13	14	39	43	40	18	40	70	67	44	22
17	14	14	44	44	41	18	57	71	68	47	48
18	15	14	49	45	42	19	14	72	69	51	48
19	16	14	55	46	43	19	33	73	70	56	40
20	17	15	0	47	44	19	53	74	72	2	46
21	18	15	6	48	45	20	14	75	73	10	39
22	19	15	12	49	46	20	36	76	74	21	29
23	20	15	18	50	47	21	0	77	75	37	16
24	21	15	24	51	48	21	26	78	77	1	13
25	22	15	31	52	49	21	53
26	23	15	38	53	50	22	23
27	24	15	45	54	51	22	55
28	25	15	53	55	52	23	29
29	26	16	1	56	53	24	7

When the greater guard is directly under the Pole star.

Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.	Heighth of the Pole Star.	Heighth of the Pole.
Deg.	degr,	mi.	se.	Deg.	degr.	mi.	sec.	Deg.	degr.	mi.	sec.
3	0	37	26	31	28	36	51	59	56	35	48
4	1	37	25	32	29	36	50	60	57	35	44
5	2	37	24	33	30	36	48	61	58	35	40
6	3	37	23	34	31	36	47	62	59	35	36
7	4	37	22	35	32	36	45	63	60	35	31
8	5	37	21	36	33	36	44	64	61	35	26
9	6	37	19	37	34	36	42	65	62	35	21
10	7	37	18	38	35	36	40	66	63	35	15
11	8	37	17	39	36	36	38	67	64	35	10
12	9	37	16	40	37	36	37	68	65	35	3
13	10	37	15	41	38	36	35	69	66	34	56
14	11	37	14	42	39	36	33	70	67	34	49
15	12	37	12	43	40	36	31	71	68	34	40
16	13	37	11	44	41	36	29	72	69	34	31
17	14	37	10	45	42	36	27	73	70	34	22
18	15	37	9	46	43	36	25	74	71	34	11
19	16	37	7	47	44	36	23	75	72	33	59
20	17	37	6	48	45	36	20	76	73	33	45
21	18	37	5	49	46	36	18	77	74	33	30
22	19	37	4	50	47	36	15	78	75	33	13
23	20	37	2	51	48	36	13	79	76	32	54
24	21	37	1	52	49	36	10	80	77	32	30
25	22	37	0	53	50	36	7	81	78	32	4
26	23	36	58	54	51	36	5	82	79	31	34
27	24	36	57	55	52	36	2	83	80	30	54
28	25	36	56	56	53	35	58	84	81	30	7
29	26	36	54	57	54	35	55	85	82	29	7
30	27	36	53	58	55	35	52	86	83	27	50

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When the 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 th•• Pole Star.	Heighth of ••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

Notes

• * 1.1

  Difference between the Rumb and the Wind▪
• * 1.2

  The Equinoc∣tial is called the line, be∣cause it is the principal of all others which are drawn in the Chart.
• * 1.3

  These leagues must be coun∣ted in the E∣quinoctial be∣tween the me∣ridians of the two places. But it were better to find the difference of Longitude: for then as 360 degrees are to that difference so is the diffe∣rence of Decli∣nation to the Equation desi∣red,
• * 1.4

  In stead of all these Rules of the North Star (which are er∣roneous) use the Tables of Equations of the Pole Stars heighth, set down in the latter end of this book.
• † 1.5

  Or rather in∣creased pro∣portionally from the Equi∣noctial line to∣ward the North & South.
• * 1.6

  This for the most part is not true in the ordinary Sea-chart.
• * 1.7

  These days mentioned in this example, are to be un∣derstood ac∣cording to the new Roman Gregorian Kalender, which goeth always ten days before ours used in England.
• * 1.8

  The use of this Table.
• * 1.9

  Equi∣noct∣al
• * 1.10

  Equi∣nocti∣al.