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
24 47 69 17 77 86 48 18 34 0 48 70 9 78 87 8 19 35 36 49 70 59 79 87 26 20 37 9 50 71 48 â—0 87 44 21 38 41 51 72 36 81 88 1 22 40 11 52 73 23 82 88 17 23 41 39 53 74 8 83 88 33 24 43 6 54 74 52 84 88 47 25 44 30 55 75 35 85 89 1 26 45 54 56 76 17 86 89 14 27 47 15 57 76 57 87 89 27 28 48 36 58 77 37 88 89 39 29 49 54 59 78 15 89 89 50 30 51 11 60 78 53 90 90 0 whose complement to a quadrant is the angle sought for ARZ According to this Diagram and demonstration was calculated the Table here following the first column whereof containeth the height of the Pole for every whole degree the second column sheweth the Inclination or Dipping of the Magnetical Needle answerable thereto in degrees and minutes CHAP. XV. Error in using the Crosse-staffe and how they may be avoided AFter the Chart and Compasse the Crosse-staffe may with good reason succeed as in the use whereof more error is committed then in any other Instrument of Navigation the two former excepted and that four severall waies First in neglecting the Paralax or Eccentricitie of the eye Secondly in not considering the height of the eye above the Water Thirdly and Fourthly in not regarding the Paralax and Refraction of the Sun For the first they count the height of the Sun and Stars in such sort as if the center of the eye or vertex of the visual cone in using the Staffe were even with the end thereof that is set to the eye Therefore how much the center of the sight is distant from the end of the Staffe so much are they deceived But how much the Eccentricitie or Paralax of the eye is it may be known after this manner Make two Transversaries the one twice so long as the other The longest of these two set fast at the further end of the Index the other of them move up or down upon the Index untill such time that your eye placed at the end of the Index in such sort as you use to place it when you observe you may see both ends of both Transversaries lie even together For then look how much the segment of the Index betwixt the two Transversaries exceedeth the segment from the shorter Transversarie unto the eye so much is the Parallax or Eccentricitie of your sight or the point wherein your eye wherein the visual beams concur is so much distant from the end of the Index As for example in this figure let the Transversarie HEI placed at E the end of the Index be double to the Transversarie FDG which is placed in such sort upon the Index that the visual lines AFH AGI of the eye placed at the end of the Index do passe straight on by FH and GI the ends of the Transversaries For in this figure A is the center of the sight or eye wherein the visual lines AFH AGI doe concurre B representeth the end of the Index placed at the corner of the eye and then AB is the Eccentricitie C signifieth the end of the Index set against the bone underneath the eye for observing of distances and then AC is the Eccentricitie which is thus demonstrated Secondly they increase the former error by not regarding the height of the eye above the Water Which although it be not so great a fault as the other yet it may deceive them by increasing the former error five or six minutes or more in a tall Ship For the higher the eye is above the water the greater is the angle contained betwixt the two visual lines whereof one toucheth the convex superficies of the Sea the other passeth on to the Sun or Stars And the lower the eye is the lesse is the foresaid angle and then onely it sheweth the true Altitude when the center of the sight is in the same line of levell with the superficies of the Water But if the eye be higher then the Water that angle is greater then the true Altitude and therefore subtraction must be made accordingly that you may have the true Altitude Now to find how much it is that should be subtracted at any height of the eye above the Water there be two waies the one without knowledge of the Earths semidiameter the other with knowledge of the same For the first you must have some such convenient place at the Water side where you may have a free and cleere prospect unto the Sea without impediment and where you may also have such provision made that you may place both your self and also an exact and large Water Levell in convenient manner to make exact observation at what height soever you desire above the superficies of the Sea till you come to the height of the tallest Ships that go upon the Seas that levell having the sight that you must look through at the end thereof next the eye so fitted that you may both easily and steadily set it higher then the fore sight that is the sight that is at the fore-end of the Levell so much as shall be needfull to lay the fore-sight precisely to the touching of the Sea and that you may also perfectly know how much the back-sight or sight at your eye is higher then the fore-sight above the line of Levell For by the difference of the heights of those sights above the line of Levell and the distance between them it may easily be found how much the visual line touching the roundnes of the Sea Dippeth under the line of levell or true Horizon from whence the height of the Sun and Stars is to be accounted thus As the distance betwixt the sights is to the difference of their heights above the line of levell so is the whole sine to the Tangent of the angle of Dipping which we desired to know This angle may otherwise be found the quantitie of the Earth semidiameter being first known which is to be done divers waies but they may be all reduced to two heads or kinds whereof the first requireth the certain measure of some arch of the Meridian to be first given which is also divers waies to be performed But the best and perfectest way of all others is to observe so axactly as is possible the Summer solstitiall Altitude of the Sun at two places so farr distant asunder and lying so neer North and South each from other with so direct and faire a way betweene them as conveniently may be chosen Suppose for example Portsmouth and Barwick or some other place in the furthest parts of Scotland for the further these places are each from other the more perfectly may this businesse be performed Then measure and plat down so truly as is possible all the way betweene those two places with all the turnings and windings ascents and descents that are therein out of which the arch of the great circle
1 19 59 10 5 7 5 1 29 69 10 3 33 24 1 38 79 10 1 52 46 1 43 49 20 6 31 0 1 19 59 20 5 6 2 1 30 69 20 3 31 46 1 38 79 20 1 51 3 1 43 49 30 6 29 40 1 20 59 30 5 4 31 1 31 69 30 3 30 8 1 38 79 30 1 49 21 1 42 49 40 6 28 20 1 20 59 40 5 3 1 1 30 69 40 3 28 9 1 39 79 40 1 47 38 1 43 49 50 6 27 1 1 19 59 50 5 1 31 1 30 69 50 3 26 51 1 38 79 50 1 45 55 1 43 50 0 6 25 40 1 21 60 0 5 0 0 1 31 70 0 3 25 13 1 38 80 0 1 44 11 1 44 Lati. 10 in lon diffe gr mi m. sc. th sec th 80 10 1 42 28 1 43 80 20 1 40 45 1 43 80 30 1 39 0 1 43 80 40 1 37 18 1 44 80 50 1 35 35 1 44 81 0 1 33 52 1 43 81 10 1 32 8 1 44 81 20 1 30 25 1 43 81 30 1 28 41 1 44 81 40 1 26 58 1 43 81 50 1 25 14 1 44 82 0 1 23 40 1 44 82 10 1 21 57 1 43 82 20 1 20 3 1 44 82 30 1 18 19 1 44 82 40 1 16 35 1 44 82 50 1 14 51 1 44 83 0 1 13 7 1 44 83 10 1 11 23 1 44 83 20 1 9 39 1 44 83 30 1 7 55 1 44 83 40 1 6 11 1 44 83 50 1 4 27 1 44 84 0 1 2 43 1 44 84 10 1 0 59 1 44 84 20 0 59 15 1 44 84 30 0 57 31 1 44 84 40 0 55 46 1 44 84 50 0 54 2 1 44 85 0 0 52 18 1 44 85 10 0 50 33 1 45 85 20 0 48 49 1 44 85 30 0 47 5 1 45 85 40 0 45 20 1 45 85 50 0 43 36 1 44 86 0 0 41 51 1 45 86 10 0 40 7 1 44 86 20 0 38 22 1 45 86 30 0 36 38 1 44 86 40 0 34 53 1 45 86 50 0 33 9 1 44 87 0 0 31 24 1 45 87 10 0 29 40 1 44 87 20 0 27 55 1 45 87 30 0 26 10 1 45 87 40 0 24 26 1 44 87 50 0 22 41 1 45 88 0 0 20 56 1 45 88 10 0 19 12 1 44 88 20 0 17 27 1 45 88 30 0 15 42 1 45 88 40 0 13 58 1 44 88 50 0 12 13 1 45 89 0 0 10 28 1 45 89 10 0 9 44 1 44 89 20 0 6 59 1 45 89 30 0 5 14 1 45 89 40 0 3 29 1 45 89 50 0 1 45 1 44 90 0 0 0 0 Â Â This Table of the eight Rumb shewing the quantity of 10 minutes of Longitude at every 10 minutes of Latitude in minutes seconds and thirds of one degree of the Equinoctial I thought good here to adjoyn for their sakes that may peradventure be desirous by themselves to make triall of that I have before written concerning the grosse and rude manner of examination which Simon Stevin useth to make the world beleeve that my Table of Rumbs is so much erroneous as he saith and after his fashion would seeme to demonstrate And lest any should suspect that this Table also may be as faulty as Stevin would perswade us the other is I have thought good here to shew the way how I made the same that if any list take so much pains he may either examine and correct this if need shall be or make a new one if he will which may be done after this manner and by this rule What proportion the whole sine hath to the sine of the Latitudes complement the same proportion hath one sixth part of a degree of the Equinoctial that is 10 minutes which make 36000 thirds to the number of the same thirds of a degree of the Equinoctial contained in 10 minutes of Longitude at the same Latitude which being divided by 60 the remainder shall be the thirds remaining besides minutes and seconds and this first quotient being again divided by 60 the second quotient shall be the minutes and the remainder thereof the seconds For example suppose you would find the quantity of 10 minutes of a degree in the Parallel whose Latitude is 10 degrees now the complement of this Latitude is 80 degrees the sine whereof is 9848,078 the whole sine being 10,000,000 and as this whole sine is to the sine aforesaid so is 36,000 that is the number of thirds that are in ten minutes of the Equinoctial to 35,453 that is the number of the same thirds contained in ten min. of a degree of the said Parallel And these thirds divided by 60 give in the quotient 590 sec. and 53 thirds remaining and 590 divided again by 90 the quotient is 9 m and the remainder 50 sec So then the quantity of ten min. of Longitude at ten degr of Latitude shall be 9 min. 50 sec. 53 thirds of one degree of the Equinoctial And thus was made the whole Table The making of the Table of Rumbs Now by help of this Table of the eight Rumb the prâ—ceding Table of the first Rumb next the Meridian and all the rest may thus be made As the whole sine is to the Tangent of the Rumbs angle with the Equinoctial so is one minute of the Equinoctial to the Latitude of the same Rumb for one minute of Longitude And so is a minute of Longitude found out by this Table of the eighth Rumb at that Latitude to the difference of Latitude which added to the former Latitude giveth the Latitude of the same Rumb for two minutes of Longitude and again at this Latitude a minute of Longitude found by the same Table shall have the same proportion to the difference of Latitude which added to the Latitude of the same Rumb for two minutes of Longitude sheweth the Latitude of that Rumb for three minutes of Longitude And after this manner proceeding in all the rest you may make up the whole Table of Rumbs FINIS THE DIVISION OF THE WHOLE ART OF NAVIGATION THE whole Art of Navigation which teacheth us to sail by courses and by heights is divided into two principal parts the 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
miles from Cape das Aguillas as it appeareth by the Table of variations which place is in the Longitude of 60 degrees and in the middest betwixt both at 30 degr as in the North part again there is the greatest Northeasting of which place there was this mention made in the Table or view of variations towards the Northwest Norâ—herly from the Ilands of Tristan de Cuncha where the variation is 19 degrees Out of these we may conclude that the Magneticall needle doth point due North in every place situate in two Meridiaâ— half Circles drawn from the one pole to the other by Corvo and Helmshudâ— And that the greatest Northeasting is in all places situate in the Meridian Semicircle drawn by that place which we said was distant one mile from Plimouth towards the East So as that part of the Earth which is conteyned between two Meridian Semicircles distant each from other 60 degrees in Longitude is the space wherein the Magneticall needle alwayes declineth from the North towards the East And the half of that part that is that portion of the Earth which is included between two Meridian Semicircles the first of which is drawn by the beginning the other by the 30 degr of Longitude is every where the place of the Northeasting increasing but the other half is the place of the Northeasting decreasing to wit when one goeth from the west Eastward following the order of the degrees of Longitude By this that hath been spoken of the first Segment with the Northeasting and his parts in one of which parts the Northeasting is increasing in the other decreasing it may easily be understood what the manner of the second Segment is with the Northwesting and what is the manner of the parts thereof whereof one is the part of the Northwesting increasing the other is the part of the Northwesting decreasing for in the mouth of the River Cantan in China at the Longitude of 160 degrees distant from Corvo the needle pointeth due North the third time there therefore drawing the third Meridian Semicircle the portion of the earth between the foresaid second Meridian Semicircle and this third distant each from other 100 degrees in Longitude shall be the space wherein the Magneticall needle declineth from the North towards the West and in the middle of both in the Meridian Semicircle 50 degrees distant from the second and as much from the third or otherwise 110 degrees removed from the first Meridian drawn by Corvo shall be the greatest variation of the Magneticall needle as it appeareth out of the Table of variations in two places whereof one is in Williams Iland at Nova Zembla where the greatest Northwesting is found to be 33 degrees The other is distant 34 Dutch miles to the Southeast from Brandaon where the greatest variation is found to be 22 degrees and the Longitude of each of those places is 110 degrees So as in the half of the second space which portion of the earth is conteyned between the Meridian Semicircles of 60 degrees Longitude and of 110 degr the Northwesting is every where increasing in the other half decreasing Of these 160 degrees of Longitude which arch wanteth but 20 degrees of half the compasse of the earth Plancius hath attained to the knowledg of the variation in such sort as now we have shewed As concerning the other parts of the World distant either towards the West from Corvo or towards the East from Cantan the experiments which hitherto the hath gotten from the Spaniards the Englishmen and our countrymen the Netherlanders doe not well agree Neither is it any marvell seeing they had neither perfect knowledge nor needfull Instruments for that purpose yet he expecteth other experiments from the ships which have now been abroad 14 moneths and more In the mean time we will bring forth that to publique view which a man may without absurditie imagine If so be that the propertie of pointing due North take place not onely in the three foresaid Semicircles which we conjecture to be Meridian Semicircles drawn from the one Pole to the other but in the whole Circles also there should then be six such Semicircles upon the earth conteyning also between them six parts or spaces of the upper face of the earth The first with the Northeasting 60 degrees long The second with the Northwesting 100 degr long The third with the Northeasting 20 degr long The fourth with the Northwesting 60 degr long The fifth with the Northeasting 100 degr long The sixth with the Northwesting 20 degr long That those things which have been spoken may by certain Geometricall figures be more clearly conceived let ABCDEFGHIKLM be the Equinoctiall of the earth let N be the Poâ—e then let NA be the half of the first Meridian Semicircle drawn by Corvo NC half of the second Semicircle NE of the third NG of the fourth NI of the fifth NL of the sixth So as the arch AC may make 60 degrees CE. 100 degr and so AE 160 degr EG 20 degr and so AG 180 degr GI 60. degr· and so AI 240. IL 100 degrees and so AL 340 degr LA 20 degr and so the whole Circle 360 degrees Then let the six points BDFHKM be the middles between AC CE EG GI IL LA. Which being supposed ANC shall signifie the first space with the Northeasting ANB the Northeasting of the first space increasing BNC the Northeasting of the first space decreasing CNE the second space with the Northwesting CND the Northwesting of the second space increasing DNE the Northwesting of the second space decreasing ENG the third space with the Northeasting ENF the Northeasting of the third space increasing FNG the Northeasting of the third space decreasing GNI the fourth space with the Northwesting GNH the Northwesting of the 4 space increasing HNI the Northwesting of the 4 space decreasing INL the fift space with the Northeasting INK the Northeasting of the fift space increasing KNL the Northeasting of the fift space decreasing LNA the sixt space with the Northwesting LNM the Northwesting of the 6 space increasing MNA the Northwesting of the 6 space decreasing The second Definition The Northeasting or Northwesting increasing is that whereby the variation increaseth the Magneticall needle being caried from the West Eastwards and the Northeasting or the Northwesting decreasing is that whereby it decreaseth The third Definition The Semicircles of the Meridian in which the needle pointeth due North wee call the first and second Meridian Semicircles and so forwards according to the order of the degrees of Longitude how many soever such Semicircles there shal be beginning at the Semicircle drawn by Corvo The fourth Definition The portion of the Sphaericall superficies or round upper face of the earth conteyned by the first and second Meridian Semicircles is called the first part or space and the rest in order the second the third and so forth unto the end Having thus set down the manner of the variation it remaineth that we shew by examples that which
truly as I could to the very touching of the Sphaericall superficies of the Sea and then the Plumbline fell 22 minutes from the same right angle forwards towards the Sea Out of these observations the semidiameter of the earth was found thus Let O be the center of the earth SVCE the circumference of the Sea B the place of observation BVFO a perpendicular line drawn from thence to the center of the earth BD the line of Level or true Horizon BC the distance from the place of observation to the mark in the Sea 17,825 foot the angle CBD found by observation 1. degree 14 minutes BRE a visuall line from the place of observation touching the Sea E the point of touching EBD the angle betwixt that visuall line and the line of Level or true Horizon 22 minutes RCFS a Parallel to BD or line of Level drawn by the mark C OFV and OP semidiameters of the Seas circumference at the time of observation ED the continuation of the semidiameter OE to the line of Level or true Horizon BD. Now in the Triangle BCF right-angled at F the side BC being 17,825 foot and the angle at B 88 degrees 46 minutes because it is the complement of the angle CBD 1 degree 14 minutes the side FC shall be 17,821 foot which doubled maketh CFS 35,642 foot and the angle at C being the complement of the angle at B is 1 degr 14 minutes Then in the Triangle BCR the angle at C being the Complement of the angle BCF to a semi-circle is 178 degrees 46 minutes and the angle at B being the difference of the angles DBR 22 min. and DBC 1 degr 14 minutes shall be 52 min. and consequently the angle at R the complement of the two former to two right angles 22 min. Now because in all plain Triangles the sides and Sines of the opposite angles are proportional therefore as 63,995 the sine of BRC 22 minutes in such parts whereof the whole Sine conteineth 10,000,000 is to BC 17,825 foot so is 151,256 the Sine of CBR 52 min. to CR 42,130 foot which added to CFS 35,642 foot giveth you the whole line RCFS 77,772 foot Also in the same Triangle as 63 995 the Sine of BRC 22 min. is to BC 17,825 foot so is 215,241 the Sine of BCR 178 degrees 46 minutes to BR 59,95â— foot Moreover by the 36 prop. 3 Eucl. because the oblong of the Secant RS and the utter Segment thereof RC is equal to the square of the Tangent RE therefore multiplying SR 77,772 foot by RC 42,130 foot the product will be 3,276,534,360 the square root or side whereof is the line RE 57,241 foot which added to BR 59,953 foot maketh the whole line BRE 117,194 foot Lastly in the Triangle BOD right-angled at B because the Tangent BE is perpendicular to OD by the 16 pr. 3. Eucl. therefore by the 8 pr. 6. Eucl. EBD and EOB are like Triangles and consequently the angle EOB equal to the angle EBD 22 minutes Therefore BE and EO having the same proportion each to other that 6,399,628 the Tangent of BOE 22 min. hath to the whole Sine 100,000,0000 the Tangent BRE being already found to be 117,194 foot the Semidiameter of the Earth OE shall be 18,312,621 foot And as the same Tangent 6,399,628 is to 20477 the excesse of the secant of 22 min. above the whole Sine so is BRE 117,194 foot to VB 375 foot the height of the place of observation above the convexitie of the Seas superficies at the same time Hereby it may be easily found how much the visible or apparent Horizon is lower then the true Horizon at any other height of the eye above the water thus As 375 is to 20477 so is any other height of the eye above the water to a number which added to the whole Sine maketh the Secant of the angle that sheweth how much the apparent Horizon dippeth under the true Horizon at that height As for example if the height of your eye above the water be 20 foot you shall find by the former rule the fourth proportional number to be 1092 which added to the whole Sine 1,000,000,000 maketh 1,000,001,092 which is the secant of 5 min. 5 sec. the angle of dipping answerable to that height After this manner was made this table here adjoyned in the first columne wherof is set down the height of the eye above the water from one foot to 50. The second column sheweth how much the visual line touching the sea dippeth under the true Horizon at any height of the eye above the water not exceeding 50 foot The use of which table is this When you observe the height of the Sun or Stars at Sea with the Crosse-staffe you shall also find out how many foot high your eye is above the water with a plumb-line or otherwise seek that height in the first column of this Table and in the second colume intituled Angle of dipping you shall find the number of minutes and seconds that are to be subtracted from the apparent height of the Sun or Stars above the superficies of the Sea observed with the Staffe that you may have the apparent height above the true Horizon The third error hath place in taking the height of the Sun or Moon with the Staffe Ring Quadrant or Astrolabe or any other Instrument whether by Sea or Land but in taking the height of the fixed Stars this error is not to be regarded being altogether in sensible by reason of their exceeding great distance from the Earth which is so much that in comparison thereof the semidiameter of the whole Earth hath not any sensible proportion and therefore the fixed Stars cannot have any sensible Paralax But the Sun by reason of his lesser distance from the Earth hath a sensible Paralax in so much that in taking his height we may for this cause onely be deceived sometimes about three minutes by counting it lesse then indeed it is and that especially in Winter Time when the Sun draweth neer the Horizon which although it be no great error yet it is not altogether to be neglected in the rules and grounds of Art which so much as is possible ought to be without error For this cause I have adjoyned this Table following of the Suns Paralax the use whereof is this in the first column intituled Suns height look the Suns apparent height and in the same line in the Second column you shall have the Paralax of the Sun which alwaies is to be added to the apparent height that so you may have the true height of the Sun above the Horizon As for example admit I find the apparent height of the Sun to be 25 degrees therefore I seek that number in the first column and in the Second column I find the Paralax answerable thereto to be two minutes 44 seconds which added to 25 degrees make the true height of the Sun to be 25 degrees two minutes 44
Rules of the Declination of the Sun we are to note that the year which is the time of the Suns motion from any point of the Ecliptick till he return again to the same point consisteth not alwaies of an equal number of days For besides 365 days it containeth almost one quarter of a day but the year which we commonly account containeth 365 days in common years and in leap years 366. It was therefore needfull to make foure Tables of twelve moneths apeece whereof the three first contain 365 days and the fourth 366 and in such sort to distribute the Declination of the Sun among them that you may make account of the Declination which is wanting to the Sun at the end of 365 days for lack of those six hours almost which the Sun wanteth to come unto the point from which it departed at the begining of the year and also of the Declination which resulteth in the fourth year because it consisteth of 366 days at what time it cometh to recover that which in the three former years it had lost Therfore to know at all times which of the foure Tables we ought to make use of I will set down a Rule whereby you may know whether the present year be leap year or whether it be the first second or third year after the leap year And the Rule is this that taking from the years of our Lord which run in our common account the number of 1600 if the remainder thereof be an even number and half of the remainder and even number then that year is leap year and if the remainder be even and the half thereof odd then that year is the second year after the leap year But if the remainder of the years numbred be odd we must try the year next going before to see whether the remainder thereof and half the remainder be even numbers for then the present year is the first after the leap year And if the remainder of the year going before be even and the half thereof odd then the present year is the third year after the leap year How the Declination of the Sun may be found out Now to know the Suns Declination every day we must look in that Table which answereth to the present year and seeking the moneth in the upper part of the page and the day of the moneth wherein we would know the Declination in the column which defendeth towards the left hand right over against the said day and under the title of our moneth we shall find two numbers one of degrees and the other of minutes which are the Declination of the Sun that day towards that part of the world which the first Rule of the Sun doth teach CHAP. VI. The Equation of the Suns Declination THey which sail in the moneth of Iune and December need not much to make any Equation in the Table of the Suns Declination because that in those moneths the Declination of one day differeth very little from the Declination of another But at all other times of the year we ought to make some kind of Equation to know precisely our height or our distance from the Equinoctial This Equation is to be made after this manner You must subtract the Declination of the Sun for the present day from the Declination of the day following or contrariwise subtract alwaies the lesse out oâ— the greater and the difference or remainder shall be multiplied by the leagues which our ship hath sailed from the Meridian of London and the product of the multiplication must be divided by 7200 leagues which are contained in the compasse of the whole earth then if you have sailed Westward the Quotient must be added to the Declination of the Sun that day if it be from the 11 of March to the 12 of Iune or from the 13 of September to the 12 of December or it must if the shippe also hath sailed Westward be subtracted if you find it in any other time of the year except in the daies of the Equinoctium for then this difference is known by taking the Declination of the present day with that of the day following but if you be to the Eastward from the Meridian of London you must doe contrariwise subtracting the said Squation where before you added it In stead of the Table of the Suns Declination here inserted by Roderigo Samorano use the Table before set down from the 174 page to the 180 page CHAP. VII Foure examples for the plainer declaration of that which is said before An example of the second Rule IN the year 1608 the 15 of April suppose I was sailing and took the height of the Sun with my Astrolabe at noone and found the height thereof to be iust 90 degrees First therefore I took from 1608. the number of 1600. and their remain 8 whicâ— remainder being an even number and foure the half thereof being even also I say the year 1608 is the Leape year And so I goe unto the fourth year in the Table of the Suns Declination which is leap year and under the moneth of April over against the 15 day I find 13 degrees and 25 minutes 41 seconds I say therefore that I am distant from the Equinoctial towards the North 13 degrees and 26 minutes almost because it is betwen the 11 of March and the 13 of September in which space falleth the 15 day of April The second example of the third Rule In the year 1602 upon the 13 day of September admit I tooke the height of the Sun and found it in my Astrolabe to be 70 degrees and an half and that in the Table of Declination belonging to the same year upon the foresaid day of September I found that the Sun had no declination but that it was under the very Equinoctial line Now because the degrees of the height which the Sun wanteth of 90 are 19 and an half I say that I am so much distant from the Equinoctial toward that part of the world unto which the shadow falleth Example of the fourth Rule Upon the 13 of May 1609 suppose I took the height of the Sun at noon in my Astrolabe and found it to be 85 degrees and three quarters Now because 1609 is an odde number I goe back to the former year of 1608. and I find according to the Rule of leap years that the year 1608 is leap year and hence I judge that the year 1609 is the year next following the leap year Then I go to the Tables of Declination belonging to the first year after the leap year and under the moneth of May against the 13 day the Suns Declination is found to be 20 degrees 41 minutes 15 seconds and because that from the 11 of March to the 13 of September the Sun keepeth his course to the Northwards of the Equinoctial having marked the shadow at midday I see that the lower vain of mine Astrolabe looketh to the North of the Compasse and so I say that
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 asunder 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 using the same is when being placed with the box in the midst of the poop of the ship where the bittacle standeth in a right line which passeth from the bolt-sprit by the midst of the main mast to the poop it serveth continually to govern the ship by moving of the Rudder till the winde or the line of your Compass towards which we desire to shape our course stand directly towards the prow or bolt-sprit of the ship They use also for the night to mark a point within the inner part of the inner box which in respect of the capitel of the Compasse may stand directly 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 variation 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 second touch divide in the midst that part of the circle which is between those two marks Then laying your Ruler upon the point of the division and upon the 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 eithe said Ruler lieth over the North and South of the Compasse and then is the Compasse without variation or the Ruler declineth 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 deliver 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 be equal one to another and that the parts of the land do directly lie East
Clavius his grosse demonstration hereof 90 A more exact demonst with the practise thereof 92 The angle of dipping for any heighth of the eye 96 3 Error by the Parallax of the Sun corrected 96 4 Error in Observing by the refraction of the Sun or Stars corrected 97 Chap. 16· Faults amended in the Table of the Suns declination commonly called the Regiment of the Sun 97 Chap. 17. Of the Table of Declination of every minute of the Ecliptick in degrees min. and sec. made according to the greatest obliquity of the Zodiack this present age which by exact Observation is found to be 23 degrees 31 min. and an half 98 A Table of the Declination of every minute of the Ecliptick in degrees min. and sec. 101 Chap. 18. The use of the former Table of Declination 116 Chap. 19. The description and use of a great Quadrant for observation of the Sun on Land 120 A Table of observations of the Suns Meridian Altitudes taken by the foresaid Quadrant in the years 1594 1595 1596 1597 at London  Chap. 20. The finding of the Suns Apogeum and eccentricity out of the former observation 142 To know the time of the Suns comming to any point of the Ecliptick 142 Chap. 21. The middle motion of the Sun corrected out of the former Observations 150 A Table of the Suns middle motions 152 Chap. 22. A new theorick of the Sun for the making of the Table of the Suns Prosthaphaereses 154 A Table of the Suns Prosthaphaereses 157 Chap. 23. The making of the Ephemerides of the Sun 159 Chap. 24. How to reduce the apparent time to the equal time answering thereto 162 A Table of the Aequation of natural days 162 Chap. 25. A Table of Aequations of the Suns Ephemerides to make them serve for many years 163 Ephemerides of the Sun 164 Chap. 26. The use of these Ephemerides 169 Chap. 27. The making of the Table of the Suns Declination 170 Prosthaphaereses of the Suns Declination 172 A Table of the Suns Declination 173 Chap. 28· The use of the former Table of Declination or Regiment of the Sun 181 Chap. 29 The Declinations of the principal fixed stars about the Equinoctial corrected by Observation 183 A Table of fixed Stars about the Equinoctial 198 Chap. 30. The use of the former Table 199 Chap. 31. The true distances of certain principal fixed Stars from the North Pole found by late Observation 199 Chap. 32. To know at what time any of the foresaid fixed Stars come to the Meridian for any day of the year 202 A Table of the Suns right Ascensions in hours and minutes for every day of the year 204 Chap. 33. By the former Tables of fixed Stars and the Suns right Ascensions to know the houre of the night at any time of the year 206 Chap. 34. Of finding the Elevation of the Pole by Observation of the Pole Star and Guard 207 Chap. 35. The description and parts of the Sea Quadrant 208 Chap. 36. The description of the Nocturnal or night Diall 210 Chap. 37. The use of the Sea Quadrant first in Observing the height of the Sun looking only to the Horizon at Sea 211 Chap. 38. How with this Quadrant to Observe the height of the Sun with â—our back turned towards the Sun 211 Chap. 39. How to Observe with this Quadrant the height of the Sun or Star looking both to the Sun or Star and to the Horizon 212 Chap 40. How to find the height of the Pole by Observation of the Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star the Guard and Horizon may be seen 213 To know the houre of the night by the Nocturnal 213 An answer to Simon Stevin shewing his erorrs in blaming me of error in my table of Rumbs 214 The Contents of the TREATISE Of the ART of NAVIGATION The division of the whole Art of Navigation pag. 1 Chap. 1. The definition of the Sphaere 2 2. That the whole World is a Sphaere 2 3. Of the division of the Sphaere 2 4. Of the motion of the Heavens 4 5. Of the figure of the Heavens 4 6. That the earth and water make one perfect Globe 5 7. That the earth is in the center of the world 5 8. The whole quantitie of the earth 5 9. Of the Equinoctial circle 6 10. Of the Poles of the world 6 11. Of the Ecliptick line 7 12. Of the Declination of the Sun 7 13. Of the Colures 8 14. Of the Meridian circle 8 15. Of the Horizon 9 16. Of the 32 Windes 10 17. Of the two Tropicks 12 18. Of the Parallels 13 19. Of the degrees 13 20. What is meant by Longitude and Latitude 14 THE SECOND PART OF THE ART OF Navigation wherein is handled the Practick part shewing the making and use of the principal Instruments belonging to this ART Chap. 1. The making of the Astrolabe pag. 15 Chap. 2. Of the heighth of the Sun pag. 17 3. Of the Shadowes 18 4. Of the Regiment and Rules of the Sun 19 5. Of the Declination of the Sun and of the Tables thereof 20 How the Declination of the Sun may be found out 21 6. The Equation of the Suns Declination 22 7. Foure examples for the plainer declaration of that which is said before 22 8. Another manner of accounting by the Sun as they use in Portugall 25 9. How the height of the Sun may be known in any place whatsoever without an Astrolabe first knowing your distance from the Equinoctial 25 10. The Rule or Regiment of the North-star for the knowledge of the height of the Pole 26 11. The making of the Crosse-staffe 27 12. Of the position of the North-star and the Guards 28 13. Of the height of the Star taken with the Crosse-staffe 30 14. The Regiment or Rules of the North Star 30 15. Other things to be noted in observing the height of the Pole 32 16. Of the Crosiers 34 17. Of the Sea-Compasse 34 18. How the variation of the Compasse may be found 37 The finding of the Meridian line 37 19. Of the Sea-Chart 38 20. Of the point of Imagination 41 21. Of the Traverse or Geometrical point 42 22. Of the amending of the point of Imagination 42 The amending of the point of Imagination by the Traverse point 43 The amendment of the point of Imagination by North South East West 43 23. The point by Imagination and the height 44 24. What it is to increase or diminish in height 45 25. How you may cast a traverse point without Compasses 46 26. Of another kind of casting a point by traverse 46 27. Of the leagues which in Navigation answer to each degree of latitude in every Rumb 47 Chap. 28. How you may come to know the Longitude or the course from East to West pag 48 29. How you may set down in your Chart a new land never before discovered 50 30. Seeing two known points or Capes of land as you sail along
such as may easily be known by other circumstances whereof we shall speake hereafter And although the Mariners may find Amsterdam otherwise as by the places near adjoining by conjectures by the soundings by the sands and many other signes without any regard of the variation yet I thought good to propound a known place for example that the Universality of the same Rule might be known in long Navigations wherein no land appeareth As for example if the Master of a ship desire to sayle from hence to Cape S. Augustine in Brasile and know that the variation there as it is reported is 3 deg and 10 min. and the Latitude 8 deg 30 min. towards the South when in going thitherwards he shall come to that Latitude and variation he shall then know that he is come to the Cape of S. Augustine and although he think otherwise by his conjecture and reckoning yet not regarding that conjecture he shall confess himself either to have guessed ill or els to have been deceived with some Eastern or western currents For reason will not suffer us to think that that variation which before was found at the Cape of S. Augustine is changed that he should need to yeeld himself to that opinion So also who will not esteem it to be absurd and altogether against reason that he which knoweth very well that he findeth at sea another variation then that which is at Cape S. Augustine of 3 degr 10 min. should notwithstanding neglecting the experience of the variation and resting upon conjecture onely affirme that he is neer the Cape S. Augustine Because he speaketh contrary things when he saith that the variation there is 3 degrees 10 minutes and again avovcheth that it is not Neither is this unworthy the marking which hath often hapned that he which should have sailed to the Isle of S. Helena when he was come to the Latitude of the same Iland and saw not there the Iland and was also ignorant whether he were to the Eastwards or Westward from the same by conjectures sought that place towards the East which indeed lay from him towards the West and so the further he sailed the further always he went from that Iland Now I leave it to thy consideration if he whosoever he were that was Master of that ship which diligently sought that Iland for the space of cerain weekes tacking about also divers times before he could find any place to abide in if he I say had not been ignorant what the variation of the Compasse was at S. Helens Iland and what the use of the variation is at sea and how to find it out I leave it I say to thy consideration whether he would willingly have floated doubtfully to and fro following a greater variation knowing assuredly that the variation there was lesser Hereby it may easily be conceived how great use there is of the variation when they especially which in sayling follow the lines shewing the courses which lines because now they have found this name among the Portugales we call Rumbs the ignorance of which lines can hardly be permitted in them which attempt long voyages upon the huge Ocean ought every where to know certainly the place of the true North which is commonly found by the knowledge of the variation If any man likewise consider the uncertain situation of those places which are set into Globes or Sea Charts by the mariners relation which uncertainty taketh his beginning from hence because every man thinketh that to be the true place of the North which is shewed by the Flower deluce as they call it of the Compass which they brought with them from home which thing also bringeth no less doubtfulness to the Mariners themselves he will think and that not without cause that the Observation of the variation is a very needfull thing even for this cause also Because it is an easie matter to place the flower-deluce in such sort that it shall not miss any thing in shewing the true North part of the World to wit if one move the Magneticall needle or points of the wires in the Compasse from the flower-deluce so much as need shall require These things therefore have been Observed and granted and this especially that the variation altereth according to the variety of countries as by the common testimonie of all men it is proved it is in some sort manifest that they which denie this varying property to be of very great use for Navigation are either wiser then the common sort and have some hidden secrets which are not revealed to every man or else are notable fooles and mad men Therefore when the most excellent Prince Maurice having throughly considered hereof thought that it might assuredly be brought to that pass that Mariners might receive great profit by this means He the high Admirall gave commandment to all the companies of the Admiralty adjoyning also thereto a certain introduction that they should doe their best indevor that all Masters of ships should provide themselves for this purpose that is to say that to what place soever they should come they should seek out the Declination of the Magneticall needle from the North or the variation of the Compasse not lightly running over the matter as it were by the way and for fashions sake onely but with great carefulness and diligence taking with them meet and needfull Instruments for that purpose and that after their return into their own countrey they should truly and faithfully certifie their companies or brotherhoods of the Admiralty of that matter that the selfe same experiments being by them brought into good order might be published for the common good But that every man may more perfectly learn the circumstances of this matter I thought it meet here to set down certain principles of this thing which is yet notwithstanding to be further searched into by more experiments in which shall be shewed a generall view or Table of those places whose variations have already been Observed by the learned Geographer Petrus Plancius with continual labour and not without great charges from divers corners of the earth neer and farr off whom for honours sake I therefore name that as well they that shall hereafter find out places or havens after this manner as also they that have already found may know that they are bound to give thanks to Plancius alone as to him that is the chief cause of this Observation But that Table or generall view of variations whereof there shall hereafter follow a plainer declaration is this A Table or View of variation The Northeasting or the East variation of the first part or space towards the North. Increasing  Northeasting Latitude Longitude  Deg. M Deg. Mi Deg. Mi. In the Flemish Iland Corvo 0 0 N 37 0 0 0 In the Flemish Iland Saint Mary 3 20 N 37 0 8 20 Near the Iland Maio 4 55 N 15 0 11 20 At Palma one of the Canary Ilands 6 10 N 28 30 16 20 At