any land This Horizon is of two sorts namely right and oblique The right Horizon is that which they have that live under the Equinoctial which passeth by their Zenith and therefore the Equinoctial line or circle falleth perpendicularly and right acrosse with their Horizon and both the South and the North Poles are in their Horizon The oblique Horizon is that which they have that live not directly under the Equinoctial for unto them the Equinoctial divideth the Horizon obliquely and not right acrosse and one Pole is alwayes above their Horizon and the other is beneath their Horizon and cannot be seen This Horizon is represented in the Sea-Chart by a certain imagined circle whose center is the point where our ship is From which center are imagined to proceed unto the said circle 32 lines which represent the 32 winds or rumbs which alwayes are drawn in our Sea-Compasse which likewise in a little peece of paper doth continually represent unto us both by day and night the whole Horizon with his 32 divisions CHAP. XVI Of the 32 Winds THis right or oblique Horizon is divided into 32 equal parts by 16 lines which they call Rumbs and they cut themselves in the point where we stand of which rumbs that which passeth by the points where the Equinoctial beginneth and endeth which are where the Sun riseth and setteth the 11 of March and the 13 of September is called East and West and that which cutteth it right acrosse is named North and South And the four extreams or ends of these two lines are distant upon the Horizon one fourth part of a circle and they make four quarters Every one of which quarters being divided in the midst do make four other points and that which falleth between the North and the East is called north-North-east and that between the North and the West North-west that between the South and the East South-east and that between the South and the West South-west And so the Horizon is divided by four lines or numbs into eight principal winds noted in the Sea-Chart with black lines And if you divide every one of those eight parts in the midst you shall have other eight lines and other four rumbs which in all are 16 winds And each one of these hath his name compounded of the names of those principal winds which are on either side thereof As for example that half winde which is between the North and the North-east is called North-north-east and that which bloweth between the East and the North-east is called East-north-east and that between the East and the South-east East-south-east and that between the South and the South-east South-south-east and that between the South-west and the VVest VVest-south-west and that between the VVest and North-west West-north-west and that between the North-west and the North North-north-west And these are noted in the Chart with green lines Finally if you divide every one of these sixteen winds in the midst they will yield you other 16 winds and will amount to 32 winds in all Which 16 last mentioned are drawn in the Sea-Chart with red lines and are by the Spaniards called quarters of the eighth first and principal winds and every one of these is called by the name of that principal wind which is next it together with an addition of the word By and the name of another principal wind which is next unto it As for example of the two quarter-winds which fall next the rumb of the North that which lieth towards the North-east is called North and by East and that which falleth towards the North-west is called North by West So likewise of those two winds which blow next the North-east that towards the North is called North-east and by North and that towards the East North-east and by East And after the same manner you may name all the rest The Figure of the Sea-Compasse and of the Horizon divided into 32 Winds by 16 Rumbs But here is to be noted that there is difference between the Rumb and the Wind because a Rumb is one direct line continued with two contrary winds as the Rumb of North South and the Rumb of East and West And so when we will name the lying of any Coast we will say that it lieth North and South or North and by East and South and by West But the wind is one line of those 32 into which the Horizon is divided and it is one part of those two which together are called the Rumb And so we say that Land lieth from us towards the South and towards the South and by West or towards the South-south-west c. CHAP. XVII Of the two Tropicks BEsides the six Circles above-mentioned which are drawn upon the superficies of the Sphere of the World there are other two which the Sun describeth with the motion of the Primum Mobile about the 12 day of June and of December of which two Circles that which the Sun describeth the 12 of June from the time of his rising till the time that he riseth the day following is called the Tropick of the Summer Sun-standing or the Tropick of Cancer for the Sun having departed from the Equinoctial and increasing his Declination towards the North when he cometh to describe that Circle for two or three dayes it semeth that he cometh no neerer to our Zenith nor departeth from the Equinoctial one day more then another but from thence forward he goeth back diminishing his Declination till he come to the Equinoctial and crossing the same he goeth on the other side increasing his Declination until the 12 of December upon which day from the time of his rising till he be come about to rise again the next morning he describeth another Circle called the Tropick of the Winter Sun-standing or the Tropick of Capricorn for the Sun being departed from the Equinoctial and increasing his Declination towards the South when he cometh to describe that Circle it seemeth for two or three dayes that he returneth not one whit towards the Equinoctial nor goeth further from our Zenith one day more then other but from thence forwards he commeth back again diminishing his Declination till he be returned to the Equinoctial and from thence towards our Zenith These two Circles in Sea-Charts are marked with two great red lines drawn from East to West which lie on either side of the Equinoctial being distant from thence about 23 deg and an half And wheresoever our ship be in any place between these two Circles or lines we may in some time of the year take the Sun in our Zenith at which time it maketh no shadow at all being then just 90 degr high above our Horizon But they which are without the said two Circles or lines shall never have the Sun in their Zenith because it cannot come to the height of 90 degr above their Horizon CHAP. XVIII Of the Parallels THe parallel Circles are those which are in all parts equally distant from the
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 another East and West and the former lieth from the North Star North-east and South-west and then the North Star is above the Pole three degrees and an half which three degrees and an half being deducted out of the heighth of the Star that which remaineth 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 another 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 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 before by the letter D which standing East and West from the North-star giveth you to understand that it and the North Star and the very Pole are East and West And so taking the 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 Here followeth the Table The guards being in the East The third star is in the Southeast The sixt star in the South The 9 th 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 second for the third star the third column for the sixth star and the fourth for the ninth star Insomuch as if you seek the rumb seeing any of these four stars in this Table right against the same do answer those rumbs where the other three are although we cannot see them in the Heavens CHAP. XVI Of the Crosiers WHen the Mariners pass the Equinoctial line towards the South so that they cannot see the North-star they make use of another staâ— which is in the Constellation called by the Astronomers the Centaur which star with other three notable stars which are in the same Constellation maketh the figure of a 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 they call the Cocks foot is thirty degrees from the South Pole it cometh 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 observation 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 pastboard you draw a circle so big as you will have your Compasse to be which being divided into 32 equal parts as we have already 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 towards the north-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-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 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 circle a Capitel which must be very well bored in from off a round pyramis to the end
after it is touched with the Loadstone by means whereof it seemeth something probable that Seamen may have some help to know their height or Latitude in dark and cloudie weather when neither Sun nor Stars for many daies appear to be observed I thought it should not be impertinent to this place to set down the Theorick that hath been devised of this magnetical inclination together with a demonstration for the making of a Table thereof to every degree of Latitude according to that Theorick to the end that such of our Sea-men as mean to be diligent observers hereof may make heedfull trial of that inclining propertie and compare the same with this Table in all parts of the world where they shall travell especially in those long Voyages to the East and West Indies and in their Northeast or Northwest discoveries The third part may be called Geometrical intreating of the Crosse-staffe and shewing how such errors may be avoided as have been commonly committed in the use thereof either by reason of the parallax or eccentricitie of the eye or by the height of the eye above the water or by the parallax or refraction of the Sun And because for finding the quantitie of the angle that is to be abated out of the apparent altitude of the Sunne or starres observed by this staff for any height of the ey above the water it was needfull to know the quantitie of the earths semidiameter concerning which there is great varietie of opinions amongst learned authors I have therefore in this part of this treatise now shewed divers waies for the more certain finding thereof one of which waies I have also for my more assurance exemplified by observation as meanes and opertunitie served me neere Plimmouth sound anno 1589. The fourth and last part may be called Astronomical wherein my chief intent was to correct the errors that are in the ordinary Tables of declination of the Sunne and fixed starres To which end there is first set down a table of the declination of every minute of the Ecliptick in degrees minutes and seconds calculated for the greatest obliquitie of the Zodiack as it is found by observation in this age 23 degrees 21 minutes and an half Whereto is adjoyned the use thereof for the readie finding of the place of the Sun by his declination given or contrariwise for finding the Suns declination his place being first known After this is shewed the way and means I used for exact observation of the Suns Meridian altitudes with a table of those observations for four yeeres together that so the more certaintie might be had of the declinations and places and consequently of the whole course and motion of the Sunne and that by comparing together so many observations the Sunnes Eccentricitie and Apogaeum might the more assuredly be known By knowledge whereof the way was laid open for the correcting and true making of the Tables of the Suns middle motions and Prosthaphaereses which were necessarie helps and means for calculating the Ephemerides of the Sun there set down without which the regiment or table of declination of the Sunne next following which I may commend as free from error observable at sea and seldome differing one minute from observation on land and for which principally all the former pains were undertaken could not so easily have been made Now if any shall think that most of this fourth part going before this regiment might have been omitted as being impertinent to the use of Mariners and exceeding their capacitie I answer that it was not my purpose neither could I in all places apply my self to the most part of sea-mens capacitie knowing many that would not be content with this regiment alone but that desired more to know the ground and root from whence this fruit grew whose desire I was also willing to satisfie as I could for the present having seldome had a more inconvenient season for such a purpose Then after some caution given concerning the use of this table of Declination and the Equation thereof in places farre differing in longitude from hence there followeth a Table of 32 principall fixed starres about the Aequinoctiall that have been most commonly known and observed by Seamen with their Declinations corrected and another Table of as many more of the notablest starrs about the North Pole is thereto annexed with their distances from the Pole corrected also and verified by diligent Observation on land To these is added a Table of the Suns Right Ascensions resolved into hours and minutes for every day of the year with the use thereof for finding at what houre any of those stars commeth to the Meridian at any time of the year that hereby the Mariner might find at all times when they come to the Meridian and so the easilier learn to know and observe them Hereunto I have newly adjoyned the description and use of an Instrument which way not unfitly be called a Sea-quadrant whereby is shewed how the height of the Sun at sea may by two observers be much more exctly observed then by any other means before published and how the height of the Pole may readily be found at any time of the night by observation of the Pole-star and Guard without making any abatement or allowance as the manner hath been in regard of the point of the compasse whereupon the Guard is situate But now for further satisfaction in every one of these particulars I refer the friendly Reader to the Treatise it self here following which Simon Stevins inconsiderate desire of finding fault with my Tables of Rumbs hath caused me to conclude with an Answer to him plainly shewing himself and not me to be in the same fault that he would find with me To this Treatise for the benefit of the younger and unskilfuller sort of Seamen it was thought not unmeet to adjoyn the short Treatise following containing the sum of the whole Art of Navigation first set forth in Spanish by Roderigo Samorano and since translated into English by a friend of mine for the benefit of our Nation which Treatise I would wish all them that are but New beginners in that Art first to peruse and understand well before they come to the reading of the former which for the reading thereof with the greater profit requireth such a one as is alreadie reasonably well acquainted with the rules and principles of that Art which I have not hitherto known to be more briefly and plainly nor yet more fully set down and published in any other book then they are in that little Treatise This notwithstanding I must admonish the Reader that in stead of the Sea-Chart therein described according to the common error with equal degrees of Latitude he follow that manner of making the same which I have in the former Treatise set down Chap. 3 4 5 and 6. And that in stead of the rules and allowances for finding the Latitude by the height of the Pole-star which are many waies and much
Draw a line equal to the breadth of the Chart as for example the line CD at the East end of the particular Chart for the Azores from the South end hereof draw another line something longer making an angle therewith of some 20 or 30 degrees or thereabouts as the line CE And having found out as before in the former chapter the number of equal parts answerable to the difference of the least and greatest Latitudes as the number of 1368 divide this line CE into some compound number of parts that may be divided by small divisors that compound number exceeding the number of those equal parts so little as conveniently may be as into 1400. In this line beginning from the angle at C tell out the said number of equal parts 1368 from thence draw the base of that angle to the end of the first line as the line F D for Parallels to this base drawne by the divisions of the second line CE shall divide the first line CD that measureth the breadth of the Chart into the number of equal parts answerable to the difference of the least and greatest Latitude in the Chart. But because the drawing of so many Parallels would not onely be troublesome and tedious but may also something deface the Chart it will be better to draw Parallels by some few principall compound numbers of parts in the second line as by every 100 or 1000 c. to sub-divide with the compasses the segments of the first line contained between those Parallels as in this particular Chart you may see Thus having divided the breadth of the Chart into the number of parts required and beginning at C the South end thereof to tell 2330 which is the number of equal parts answerable to the least Latitude purposed to be set downe in the Chart tell on Northwards till you come to make up an even hundred as till you come to 2400 and there begin to set figures shewing the number of the parts and so proceed setting figures to every hundred part and finishing the graduation of the Meridian or division thereof into his unequal parts in due proportion as before you were directed in the former chapter CHAP. VII The use of the third columne of the table of Latitudes THe third Columne being nothing else but the table of Secants in such parts whereof the whole sine or semidiameter of the circle is supposed to containe 10,000 may serve for all such purposes for which the table of Secans may be used Moreover as it served for the making of the second columne of the table of Latitudes as before is shewed in the second chapter page 11 and 12 so may it be of needfull use for the more easie examination and correction thereof if any error hath been committed therein Hereby also may bee knowne very exactly the proportion of any parallel to the Equinoctiall For what proportion the difference answerable to any degree and minute in this table hath to 10000 the same proportion hath the Equinoctiall to the parallel answering to that degree and minute The difference answerable to any degree and minute is that which is placed next above the line of the same minute And consequently because the like parts of circles are proportional to their wholes you may hereby very easily and truly finde out how many leagues any arch of any Parallel containeth for as the difference answerable to the Latitude of the Parallel is to 10,000 so are the minutes contained in that arch to the miles thereof which divided by 3 give the leagues As for example if you would know how many leagues make a degree in the Parallel of London whose Latitude is 51 degrees 32 minutes as 16,075 the difference answering to that Latitude page 26 is to 10,000 so is 20 the number of leagues contained in one degree of the Equinoctiall to 12 294 â—43 the number of leagues making one degree in the Parallel of London Thus the difference of Longitude in any Parallel being given in degrees may easily be reduced into leagues multiplying the same by the leagues contained in one degree But it may be done easier by multiplying the difference of Longitude reduced into minutes by 10,000 and dividing the product by the difference of equal parts in the table of Latitudes answerable to the Latitude of the Parallel wherein that difference of Longitude is taken for then the quotient sheweth the miles in the difference of Longitude which being divided by 3 you have the leagues As for example admit the difference of Longitude betweene the Lizard and Fayal be 22 degrees 52 minutes that is 1372 minutes which multiplied by 10,000 make 13,720,000 and this divided by 12,898 which is the difference of the equal parts answerable to 39 degrees 10 minutes the latitude of the Northeast corner of Fayal Iland shall give you 1064 miles almost that is 354 â…” leagues the difference of their Longitudes counted in the Parallel of Fayal Moreover by the differences set downe in the third columne may easily be found the sine of any arch of the quadrant For as the difference answerable to any arch or number of degrees and minutes in this table is to 10,000 so is 10,000 to the sine of the same arch The demonstration hereof may easily be conceived out of the Diagramme set down in the second chapter page 11 wherein ik to fk and ak to gk that is ae have all one and the same proportion and therefore it shall here be needlesse any further to insist hereupon CHAP. VIII How to describe the Rumbes mechanically in any Sea-chart Globe or Mappe of what forme soever NOw because the nauticall planisphaere as before hath been shewed is nothing else but a plaine Parallellogramme superficies made by extension of a sphaerical superficies inscribed into a concave cylinder wherein the tumbes make equal angles with very Meridian therefore in this nauticall planisphaere if a circle be drawne and divided into 32 equal parts beginning at the Meridian passing by the center of that circle right lines drawne from the center by those divisions shall be the rumbes or lines which the ship describeth in sailing upon those points because they make equal angles with every Meridian of the nautical planisphaere those Meridians being every where equidistant one from another Example hereof you have in the former figure and in the charts adjoyned hereunto By helpe of this planisphaere with the Meridians rumbes and Parallels thus described therein the rumbes may much more easily and truly be drawne in the Globe then by those mechanical waies which Petrus Nonius teacheth cap. 26. lib 2. de obser Reg. Instr. Geom. Hereby also they may with no lesse facilitie be inscribed into any other Chart or Mappe of what forme or projection soever if it be first divided by Meridians and Parallels into degrees of Longitude and Latitude For by what points of Longitude and Latitude in this Planisphaere the rumbes are described by the same points must
with the Regiment of the Sun and of the star the rules of the Moon and of the Tides the declaration of the Sea-chart and other things appertaining hereunto CHAP. I. The Definition of the Sphere A Sphere is a solid or massie body without hollownesse and perfectly round in the midst whereof there is a prick called the center by which there passeth a right line named the Axtree and the points where this line endeth upon the superficies of the whole body are called Poles because upon them the Sphere is moved CHAP. II. That the whole World is a Sphere AND so it is evident that the whole frame of the World wherein we live is a Sphere being as it is solid so that in the whole World there is no empty place also it is perfectly round upon the upper Superficies of the highest heaven and it hath in the very midst a certain point to wit the center of the earth by which we do imagine a right line or Axtree to passe from one pole to another upon which the World is moved about from East to West CHAP. III. Of the division of the Sphere THE whole Sphere of the World is divided into two parts or Regions the Elementary and Celestial The Elementary part or Region hath four parts the first whereof is the earth which together with the element of water which is the second maketh one perfect Globe and round about both these are two other elements namely the Air and above that the fire which filleth the space between the Air and the Sphere of the Moon of which Elements by vertue of the heat of the Heavens are made and compounded all corruptible things in the world The celestial Region consisteth of other ten parts the first whereof is the Sphere of the Moon the second the Sphere of Mercury the third of Venus the fourth is the Sphere of the Sun the fifth of Mars the sixth of Jupiter the seventh of Saturn the eighth is the Sphere of the fixed stars which is called the Firmament the ninth is the Crystalline heaven and lastly the tenth and highest is the Sphere called the Primum mobile that is the first or highest moveable heaven That which remaineth called the Empyreal heaven because it hath no motion cometh not to be considered on in the Art of Navigation A Figure wherein may be seen the Composition of the whole Sphere of the World CHAP. IV. Of the motion of the Heavens THe number of the Heavens is known by the motions observed in them which are ten distinct one from another For the Moon moveth her proper and peculiar motion in 27 dayes and 8 hours which is one Revolution Mercury Venus and the Sun finish their motion in one year which conteineth 365 dayes and almost a quarter of a day Mars runneth his course in two years Jupiter in twelve years Saturn in thirty years the eight Sphere according to the opinion of some in seven thousand years the ninth in five and twenty thousand and eight hundred years and the tenth in four and twenty hours almost Which ten motions are reduced unto three principal the first is that of the first moveable upon the two ends of the Axletree which are called the Poles of the World from East to West turning about again unto the East in 24 hours and this Sphere by the force of his motion carrieth about with it all the other lower Spheres in the space of 24 hours Howbeit they move also the contrary way with a second motion which is from West to East upon two other poles distant from the first about three and twenty and an half such parts whereof the whole compasse of heaven conteineth three hundred and sixty And this second motion is accomplished in each of the lower Heavens in divers spaces of time as is before said The third motion is proper to the eighth Heaven wherein the fixed stars are placed which motion is the cause that the distance of the poles of the first motion from them of the second motion doth vary being sometimes greater and sometimes lesse CHAP. V. Of the Figure of the Heavens THat the Heavens are round it is proved because roundnesse is the most perfect Figure of all others being whole and intire having no need of any joynts being also of the greatest capacity of all figures that have the same compasse and in that respect most fit to contain all other things Also the principal bodies of the World as the Sun the Moon and the stars are of this Figure and we see the same likewise in those things which are bounded by themselves as it is manifest in drops of water and all other liquid things CHAP. VI. That the Earth and Water make one perfect Globe THere is nothing that sheweth more cleerly that the earth and water make one round Globe then the shadow which they make in the Eclipses of the Moon which shadow we alwayes see to be a part of a circle For if the body which is the cause of the same shadow were three-square or four-square the shadow it self also would appear in the same fashion Wherefore the shadow of these two bodies together being round it is manifest that they are round also CHAP. VII That the Earth is in the center of the World ONe sign we have to be assured that the Earth is in the midst and center of the World namely that wheresoever we are upon the face of the earth we alwayes see one half of the Heavens the other half being hidden out of our sight Moreover the stars in what part of the Heavens soever they be either in the East West or South we see that they are alwayes of the very same bignesse Whereby we may easily perceive that they are alwayes equally distant from our sight and whereas they move round about it it followeth that we are upon the center of that body on whose superficies the said stars describe their circles CHAP. VIII The whole quantity of the Earth ANd albeit the Globe of the Earth and Water compared with the Spheres of the Stars is as it were a center or prick yet being considered by it self it conteineth in the greatest circle thereof 6300 common Spanish leagues Which a man may easily perceive by taking two such points or head-lands of the earth as are under the same Meridian and which differ in distance one from another so much as one of those parts is whereof the compasse of the whole world conteineth 360 and it is found both by Navigation at Sea and also by travel on land that the two foresaid points are distant each from other 17 leagues and an half of which leagues each one conteineth 4000 paces every pace 5 foot every foot 16 fingers and every finger 4 grains of barley CHAP. IX Of the Equinoctial Circle BEing to treat of the Circles of the Sphere of the World the first which offereth it self to be spoken of is the Equinoctial Circle by means whereof we do know in
because they are equal This heighth of the Pole is known by the help of four things which are the Ballâ—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 table 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 likewise 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 other 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 center through every one those 90 divisions of the half quadrant you must draw 90 lines And keeping this quadrant so divided it will serve you for a pattern to make us many Crosse-staves as you think good of what 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 even 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 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 marked 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 because 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 Heavens besides describe thâ—â— circles round about the pole with the motion of the first or highest moveable Heaven 〈◊〉 which motion sometimes the 〈◊〉 stars AB are just of 〈…〉 above the Horizon 〈…〉 they are said to be East and West one from another Sometimes they are in a perpendicular line to the Horizon according to our sight and then they are said to be North and South and sometimes also the two guards BC are East and West one from another and then the former guard beareth from the North-star North-east and South-west And when these two guards be in a perpendicular line one above another the former guard beareth from the North star North-east and South-west Insomuch that from these four positions do arise eight rules for the eight Rumbs wherein the former guard may stand being considered in respect of the North star And so presupposing that the North star is distant from the Pole three degrees and an half according to the opinion of some Mariners who love numbers that have not any fractions sometime the North star shall be as high as the Pole it self sometime three degrees and an half lower or higher then the Pole and sometime three degrees 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-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 transversarie till you see the Horizon joyned with the lower end thereof and the North Star with the higher end Then mark the degree and part of the degree which the transuersarie 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 elevated above our Horizon And so much are we distant from the Equinoctial toward the North. The second Rule When the guards are in the North-east one guard beareth from another East and West and the former guard standeth from the North Star North-east and South-west and then the North Star is under the Pole three degrees and one half which being added to the height of the Star will 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 being 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 degree and an half above the Pole which degree and
cast his point in manner following and he shall errer as little as is possible Let him examine according to the ordinary running of his ship how much way she might make every day that he hath sailed and the leagues that shall amount in all the 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 coming from the graduation meet with the second point of the other Compass which he holdeth not upon the Chart and in the place where they meet he may say that there is his point and his ship And because in this case all Pilots do not use this point of imagination and heighth there grow great diversities among them concerning their distance from land when as in long voyages they confer and communicate their opinions one with another insomuch that one according to his conjecture judgeth himself to be 50 leagues from land another 100 another 200 and another thinketh he is hard by the land The reason is because some of them cast their point by traversing others by imagination 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 diminishing in height when they approach neerer to the Equinoctial So that in our Navigation we either sail from a greater to a less altitude of the pole and then we go towards the Equinoctial and then the height is said to be diminished or we sail from a less to a greater height of the pole and then we go from the Equinoctial and are said to increase our heighth And hence it is that casting our point by imagination and afterwards having taken the heigth amending it by traversing either 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 amended by traversing be in lesse height then the point found by imagination then hath the ship gone less way then we imagined 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 amended by traverse be in less heighth then the point found by imagination then hath the ship made more way then we imagined CHAP. XXV How you may cast a traverse point without Compasses IF a Mariner chance to lose his Compasses he may cast his point of traverse after this manner Let him take two slender 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 open set one foot thereof upon the point from whence the ship departed and the other foot stretching towards the place whithre the ship hath sailed you must hold up a little from the Chart and you must set one foot of the other 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 Compasse run by his next East and West Rumb untill the point of the first Compasse lifted up being set downe that point of the second 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 conaineth 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 changed one degree you have then gone 19 leagues and ⅜ and are distant from your right line 7 leagues and ¼ And varying a degree upon the third point of the 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 answer 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