55 160 401.357 537.178 251.865.582  56 160 938.535 545.704 260.459.920 8.594.338 57 161 484.239 554.505 271 919.077 11.459.157 58 162 038 744 563.594 289 107.811 17.188.734 59 162.602.338 572.986 323.485.279 34.377.468 CHAP. III. The use of the two first columnes of the Table of Latitudes for graduating a Meridian in the general Sea-Chart BEfore you can make use of this Table for the true graduating or dividing of a Meridian of this Chart into his degrees or other parts of Latitude increasing from the Aequinoctial towards the North and South in such proportion as before hath been shewed there must be first some preparation made to that end which may be done after this manner Overthwart the midst of the plain superficies whereupon you will draw the lineaments of the Chart describe a right line representing the Aequinoctial circle which you shall divide into 360 parts or degrees and crosse the same squirewise with right lines by every fift or tenth degree Then take with your compasses the length of half the Aequinoctial that is 180 degrees and setting one foote of your compasses in the mutuall intersection of the Aequinoctial with the perpendicular or Meridian that passeth by either end of the Aequinoctial with the other foote make a prick in the same perpendicular or Meridian the space contained betwixt this prick and the Aequinoctial divide first into three equal parts and every one of these into other three so have you nine in all and againe every one of these into three so have you 27 parts and every one of these parts divide into four so have you 108 parts And againe if there be space enough divide every one of these into 10 or 100. So shall you have 1080 or 10800 parts which will bring you to the Latitude of 85 degrees and something more But if you would make your Chart to any greater Latitude you shall continue forth the foresaid perpendicular and divide it into so many more of the same parts as you shall find needful to attain to the Latitude you desire Then note every fift and tenth part with black lead and set figures at them beginning at the Aequinoctial and from thence proceeding Northwards and Southwards Then look what numbers in the second column are answerable to each degree or minute in the first column of this Table of Latitudes omitting alwaies four or five of the first figures towards the right hand and at the same numbers of parts in the perpendiculars make pricks on either side the Aequinoctial by which pricks draw right lines equidistant from the Aequinoctial for they shall be the Parallels of the true Nautical Planisphere or Sea-Chart Notwithstanding these Parallels are all oâ—â—hem a little further distant from the Aequinoctial then in truth they should be and so much the more the further they are from the Aequinoctial Which error might be something the lesse if the former Table had been first made to smaller parts then minutes But that were a matter more curious then necessarie the Table here before set down being so neere the truth that it is not possible by any rules or Instruments of Navigation to discover any sensible error in the Sea-Chart so farre forth as it shall be made according thereto The figure following containeth onely one part of the Nauticall Planisphaere from the Aequinoctial Northwards because the other part from the Aequinoctial Southwards must be altogether like and equal to this Herein first I drew the Aequinoctial line AC and divided it into 36 equal parts whereof every one is understood to contain ten degrees and I raised perpendiculars from every one of those parts which are the Meridians of the Nauticall Planisphaere every where aequidistant each from other Then I took half the length of the Aequinoctial with the compasses and setting one foot in the end of the Aequinoctial at C with the other foot I made a prick at D in the perpendicular or Meridian CD The space contained betwixt C and D I divided into 1080 parts understanding every one of the smaller parts or segments of the line CD to contain ten lesser parts in such sort as before hath been shewed and set figures to them as here you see for the readier numbring and finding out of any of those parts Then I looked in the former Table what number of equal parts of the Meridian answered to every tenth degree and casting away five of the first figures next the right hand because I conceive the space betwixt C and D to be divided only into 1080 parts I found out the parts answerable to the numbers remaining in the line CD and at those parts I made prickes by which I drew the Parallels As for example in the Table the number answerable to ten degrees is 60 casting away the five first figures towards the right hand therefore I look 60 in the line CD and by that part I draw the Parallel of ten degrees distance from the Aequinoctial Likewise the number answering to twentie degrees omitting the five first figures is 122 therefore by that number of equal parts I draw the parallel of twentie degrees Latitude from the Equinoctial c. And after this manner I drew all the rest as you may see in the former draught The Draught of the Meridians Parallels and Rumbs of the Nautical Planisphear truly made CHAP. IIII. 〈◊〉 way for graduating the Meridian of a general Sea-Chart OTherwise for the dividing of the Meridian of a general Sea-Chart into his degrees and other smaller parts of Latitude when the Chart hath not so great Latitude or breadth from the Equinoctial towards the North or South as hath the figure before set down you may go thus to work First find out what proportion the whole Longitude or lenght of the Chart from West to East must have to the whole breadth thereof betwixt the Parallels of the most Northerly and Southerly places that are to be set down therin which may be done after this manner Out of the second Column of the table of Latitudes take the numbers of equal parts of the Meridian answerable to the greatest North and South Latitudes that are to be set down in the Chart divide those numbers by 600,000 that is the number of equal parts of the Meridian answerable to one degree of the Equinoctial the Quotients will shew how many degrees of the Equinoctial the breadth of the Chart must be on either side the Equinoctial toward the North and South As for example in the generall Sea-â—hart to be adjoyned to this book the Latitude of the North 〈◊〉 of the New land found by the Hollanders about the yeer â—596 and by them called Gebrooken land lying Northwards â—rom Norway is about 80 degrees And the Latitude of Queen Elizabeths Iland first found by Sir Francis Drake lying to the â—outhwards of Magellanes streights is about 53 degrees The â—umbers of equal parts of the Meridian answerable to these Laâ—â—tudes found out in the foresaid Table of
innermost circle to the end of the foresaid brasse pointer so as the end thereof may enter thereinto Then set the line that is drawn from the end of the brasse pointer to the elevation of the Pole at the place of your Observation and so have you all parts of your Instrument rightly placed for Observation Now when you will make Observation with this Instrument hang the same by this Ring upon your finger as you do when you Observe the height of the Sun with the Astrolabe turning the foresaid brasse pointer Northwards till you find the midst of the shadow of the bead to fall upon the peripherie drawn round about through the midst of the concavitie of the Equinoctial ring which peripherie we called the parallel of the Sun and so keep the whole Instrument and Compasse as steady as you can till the flie of the Compasse remain quiet and still keeping in the mean time the midst of the shadow of the bead alwaies upon the foresaid parallel of the Sun and withall looking close by the graduated side of the Meridian directly down upon the midst of the Compasse and mark what degree and minute you see close thereby in the North part of the Flie for so much as the North point of the needle or wiers is from thence towards the East or West so much is the Variation Eastwards or Westwards And the shadow of the bead lighting upon the Parallel of the Sun sheweth the hour and time of the day The best time for the taking of these Observations is about the midst of the forenoon or afternoon because that about those times the height of the Sun altereth quickly and his Refraction also can breed no sensible error But because there be many that want both this Instrument and also the Globe and Astrolabe before-mentioned I have for their sakes thought it good to set down a way whereby the Declination and height of the Sun being given together with the Latitude of the place the Suns true Azimuth may be found with Ruler and Compasses onely after this manner Draw the circle ABCDEFGH representing the Meridian by the center hereof draw the diameter of the Horizon AF. From A the end of this diameter reckon the elevation of the Equinoctial AC from whence draw a line by the center which may be called the diameter of the Equinoctial AC from C the end of this diameter count the declination of the Sun CD thereby draw a Parallel to the diameter of the Equinoctial which may be called the diameter of the Suns Parallel DG Likewise from the diameter of the Horizon count the height of the Sun AB known by Observation and thereby also draw BE a Parallel to the diameter of the Horizon which may be called the diameter of the Suns Almicantar From I the intersection of these two Parallels draw IK a line perpendicular to the diameter of the Horizon Then setting one foot of the Compasses in L the midst of BE the diameter of the Suns Almicantar and stretching out the other foot to B the end of this diameter from thence draw therewith the arch BK till you come to the said perpendicular This arch resolved into degrees shall give you the true Azimuth of the Sun CHAP. XIIII To find the Inclination or dipping of the Magnetical needle under the Horizon First the angle OAR is given because of the arch OBR measuring the same 150 degrees and consequently the angle at R 15 degrees being equal to the equal sided angle at O both which together are 30 degrees because they are the complement of the angle OAR 150 degrees to a semicircle or 180 degrees Secondly in the Triangle ARS all the sides are given AR the Radius or semidiameter 10,000,000 RS equal to RO the subtense of 150 degrees 19,318,516 and AS equal to AD triple in power to AB because it is equal in power to AB and BD that is BO which is double in power to AB Or else thus The arch OB being 90 degrees the subtense therof OB that is the Tangent BD is 14,142,126 which sought in the Table of Tangents shall give you the angle BAD 54 degrees 44 minutes 8 seconds the Secant whereof is the line AD that is AS 17,320,508 Now then by 4 Axiom of the 2 book of Ptisc As the base or greatest side SR 19,318,516 is to the sum of the other two sides SA and AR 27,320,508 so is the difference of them SX 7,320,508 to the segment of the greatest side SY 10,352,762 which being taken out of SR 19,318,516 there remaineth YR 8,965,754 the half whereof RZ 4,482,877 is the sine of the angle RAZ 26 degrees 38 minutes 2 seconds the complement whereof 63 degrees 21 minutes 58 seconds is the angle ARZ which added to the angle ARO 15 degrees maketh the whole angle ORS 78 degrees â—1 minutes 58 seconds whereof 60 90 make 52 degrees 14 minutes 38 seconds which taken out of ARZ 63 degrees 21 minutes 58 seconds there remaineth the angle TRA 11 degrees 7 minutes 20 seconds the complement whereof is the Inclination sought for 78 degrees 52 minutes 40 seconds The sum and difference of the sides SA and AR being alwaies the same viz. 27,320,508 and 7,320,508 the product of them shall likewise be alwaies the same viz. 199,999,997,378.064 to be divided by the side SR that is RO the subtense of RBO. Therefore there may be some labour saved in making the Table of Magnetical Inclination if in stead of the said product you take continually but the half thereof that is 99,999,998,689,032 and so divide it by half the subtense RO that is by the sine of half the arch OBR Or rather thus As half the base RS that is as the sine of half the arch OBR is to half the sum of the other two sides SA and AR 13,660,254 so is half the difference of them 3,660,254 to half of the segment SY which taken out of half the base there remaineth RZ the sine of RAZ The Table of Magnetical Inclination First col Second col First col· Second col First col Second col Height of the Pole Magnetical Inclination Height of the Pole Magnetical Inclination Height of the Pole Magnetical Inclination· Degrees Degr. Min. Degrees Degr. Min Degrees Degr. Min. 1 2 11 31 52 27 61 79 29 2 4 20 32 53 41 62 80 4 3 6 27 33 54 53 63 80 38 4 8 31 34 56 4 64 81 11 5 10 34 35 57 13 65 81 43 6 12 34 36 58 21 66 82 13 7 14 32 37 59 28 67 82 43 8 16 28 38 60 33 68 83 12 9 18 22 39 61 37 69 83 40 10 20 14 40 62 39 70 84 7 11 22 4 41 63 40 71 84 32 12 24 52 42 64 39 72 84 57 13 25 38 43 65 38 73 85 21 14 27 22 44 66 35 74 85 44 15 29 4 45 67 30 75 86 7 16 30 45 46 68 24 76 86 28 17 32
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
only 12 seconds hereof that is the Part Proportional answerable to the excesse of 9. sec. above 4 sec. Where Maginus after the Prutenick account maketh it to be in 0 degr 25 min. of Aries that is 33 minutes wanting of the truth found by Observation The like difference I have often found by many and diligent Observations especially for the space of the four years before mentioned the whole Catalogue of which Observations I thought good for thy further satisfaction herein to set down in a Table after I have first shewed with what Instrument and after what manner I Observed the same that if any error herein hath been committed it may the more easily appeare and be amended CHAP. XIX The description and use of a great Quadrant for Observation of the Sun on Land THe Instrument therefore wherewith I took those Observations was a Quadrant of more then six foot and a quarter semidiameter for the room wherein I was to use it could not well admit a greater quantity which by reason of his largeness was so exactly made and divided that both minutes and half minutes might therein be easily discerned The Limb and sides of the Quadrant were about two inches and a quarter in thickness the breadth of the Limb about four inches the breadth of the Sides about two inches and an half In the midst of the ends of one side of this Quadrant were two round holes made in either end one whereby the Quadrant was hanged like a gate on his hinges upon two round pins fitted to those holes and fixed in the ends of a copple of sockets put close upon a strong square post Perpendicularly erected and the upper end thereof fastned to the side of a principal rafter in an upper chamber where a window according to the Reclination of the Roof of the house was made between it and the next rafter in such sort that carrying your eye along by the circumference of the Quadrant you might by the Center thereof placed at the window see any part of the Heavens neer the Meridian from the Zenith to the Horizon The nether end of this post resting on the floor was put into the midst of a socket nailed to the floor which was so wide that on every side the post wedges might be put in to coyn it at pleasure this way or that way till the side of the Quadrant were found to stand exactly Perpendicular by the hanging of the plum-line all alongst most precisely upon a line Parallel to the Zenith line of the Quadrant To the Center of the Quadrant was fastned a strong Ruler of one inch in thickness two inches in breadth and almost six foot and an half in length carrying two Sights upon it viz. at either end one of equal breadth and length the end of the middle line of each Sight falling Perpendicularly upon the middle or fiducial line and plain Superficies of the Ruler Through the upper Sight placed at the Center was made a square hole as great as it could well be Through the midst of this Sight and hole was put a straight wyre erected Perpendicularly from the Fiducial line and plain of the Ruler and so much of it made flat and thin as was between the top and base of that square hole This wyer served for Observing the Stars the flat side whereof was to be turned towards the eye in Observing of great Stars and the narrow side or edge of it was turned to the eye-ward when smal Stars were to be Observed Through the midst of the nether Sight from the top of it to the Base thereof was made a narrow slit Perpendicularly erected likewise from the Fiducial line and plain of the Ruler and Quadrant When I Observed the Stars I looked through this slit Elevating and Depressing the Ruler till the wyer being first fitted to bigness of the Star did even cover the Star from my sight in such sort that I might see both edges of the Star alike on either side above and beneath the wyre The square hole in the Sight had a cover fitted to it like the cover of a box wherewith it was wholly covered when the Sun was to be Observed The nether end of the Ruler carrying the Sights was to be fastned with a screw-pin at any part of the Circumference of the Quadrant as need required With this Quadrant alwaies rectified by the Plumb line in time of Observation as before is shewed the height of the Sun was most easily and exactly Observed by turning the Quadrant this way or that away and Elevating or depressing the Ruler carrying the Sights till the top and sides of the shadow of the Upper Sight placed at the center fell upon the nether Sight placed at the center fell upon the nether Sight placed at the Circumference equidistantly from the top and sides thereof For then the upper edge of the Ruler sheweth precisely the height of the Sun desired in degrees and minutes upon the limb of the Quadrant saving that one whole degree was alwaies to be added thereto because the breadth of that part of the Ruler that lay upon the Limb of the Quadrant was made to be just equal to two degrees that is on either side one degree from the fiducial line Now for finding out the Meridian Altitudes of the Sun and Stars I first found the Meridian line thus with the quadrant rectified and used as before is shewed I Observed the height of the Sun in the forenoon and so warily letting the Quadrant stand immoveable and laying the side of a straight Ruler that was about seven foot in length close along to the perpendicular side of the Quadrant close by the end of that side of the Ruler touching the floor of the chamber I made a prick upon the floor Also laying the side of the Ruler to the perpendicular side and limb of the Quadrant I made in like manner another prick so far as conveniently I could from the former upon the floor close by the corner of that side of the Ruler By these two pricks I drew a right line which represented the intersection of the Suns Azimuth or of the continued plain of the Quadrant and of the plain of the floor in the time of Observation Likewise in the afternoon the Ruler of the Quadrant carrying the Sights being fixed in the same place where it was in time of Observation in the forenoon I Observed diligently till the Sun came to the same height that he had when I Observed in the forenoon which I did by following the motion of the Suns shadow with the Quadrant till the edges of the top and sides of the shadow of the upper Sight fell upon the nether Sight equidistantly from the top and Sides thereof Then carefully letting the quadrant stand immovable and drawing the line of intersection of the floor and Suns Azimuth in time of the afternoon Observation in like manner as I did in the forenoon setting one foot of the Compasses in the
coming from the said edge of the sight falleth for that edge of the shadow upon the hollow side of the arch of the Quadrant sheweth the height of the upper edge of the Sun From this therefore subtract 16 minutes and so much also as is answerable to the height of your eye above the water in such sort as I have shewed in the use of the Crosse-staff in the 15 Chapter of this Book and so you shall have the apparent height of the Sun above the true Horizon CHAP. XXXVIII How with this Quadrant to observe the height of the Sun with your back turned towards the Sun SEt the edge of one of the broad moveable sights or vanes even with that end of the Quadrant where the little sight is fixed Then looking thorow the slit which is made thorow the midst of the middle sight that is fastened to the double box or socket turn your back toward the Sun and laying the edge of the vane at the center even with the Horizon lift up or put down the arch of the Quadrant till the upper edge of the shadow of the broad moveable sight placed even with the upper end of the arch of the Quadrant agree justly with the edge of the sight or vane placed at the center Then reckoning from the upper end of the arch of the Quadrant downwards see what number of degrees and minutes you finde at the upper edge or end of the socket through which the Quadrant moveth adding alwayes thereto two degrees for so shall you have the height of the Sun if you abate from hence 16 min for the Suns semidiameter and the surplussage answerable to the height of the eye above the water as before is shewed in the former Chapter CHAP. XXXIX How to observe with this Quadrant the height of the Sun or Star looking both to the Sun or Star and to the Horizon SEt the upper edge of the uppermost moveable sight of the Quadrant at some even number of degrees as at 10 20 or 30 c. And setting the end of the semidiameter of the Quadrant where the center is to the corner of the eye as you do when you observe with the Crosse-staffe lay that edge of the sight even with the upper edge of the Sun and move the nether moveable sight up or down till the upper edge thereof lie even with the Horizon Then see how many degrees and minutes are conteined between the upper edges of both sights from which abate as before 16 minutes for the Suns semidiameter and the surplus answerable to the height of your eye above the water so shall you have the apparent height of the Sun above the true Horizon But when you observe the height of any star lay the upper edge of the upper sight even with the midsâ— of the star and from the number of degrees and minutes conteined between the upper edges of both sights abate onely the surplus answerable to the height of your eye above the water and so you shall have the true height of the star But here iâ— must be remembred that before you observe the Sun or star after this manner you must finde out the eccentricity of your eye in such sort as I have shewed in the 15 Chapter of this book which eccentricity you must adde to the distance of the center oâ— the Quadrant from the end of the Semidiameter where you seâ— your eye for so much as the sum of this distance and eccentriâ—city amounteth unto so much must you thrust forward the foreâ—end of the semidiameter of the Quadrant beyond the further end of the square socket thorow which it is put that so the center oâ— your eye may be brought to the center of the Quadrant CHAP. XL. How to find the height of the Pole by Observation of the Pole-star and Guard without giving or taking any allowance or abatement at any time when the Pole-star the Guard and Horizon may be seen THe long Index of the Nocturnal which I called the Guard Index being fixed upon the place of the middle Guard in the day-circle and the Nocturnal being put upon the end of the arch of the Quadrant placing also the end of the Semidiamter to your eye as before and holding the Quadrant upright with the Nocturnal towards the Pole-star till the Diameter of the Semicircular hole of the Pole-star circle lie by estimation aequidistant from the Horizon both ends of the Diameter being level or of like height one with another and so keeping the Pole-star so neer as you can guesse upon the midst of that Diameter and the fiducial line of the Guard-Index upon the Guard move one of the moveable sights of the Quadrant up or down till the edge thereof lie even with the Horizon Thus therefore the Pole-star lying upon the midst of the Diameter that is upon the center of the Pole-star circle and the fiducial line of the Guard Index upon the Guard and the edge of the sight even with the Horizon the number of degrees and minutes from the end of the Quadrant where the Nocturnal is placed to the edge of the sight adding thereto five degrees that is the distance of the center of the Nocturnal from the end of the Quadrant shall be the height of the Pole saving that you must abate as before so much as is answerable to the height of your eye above the water To know the Hour of the Night by the Nocturnall ANd the point of the short Index which we called the Day-Index being first set to the day of the moneth sheweth in the Hour-circle the Hour of the night at the time of your Observation SIMON STEVIN his Errors in blaming me of error in my Tables of Rumbs Wherein also I am the more confirmed by the like triall I have made of the first Rumb counted from the Meridian though Simon Stevin in his solemne demonstration continued almost in three whole pages in folio wherein he professeth that the scope or mark he aimeth at is to demonstrate that my Table of Rumbs is erroneous would make the world beleeve that my Table erreth above two minutes in the Latitude of that Rumb before I come to so little as two degrees of Longitude But the truth is he much mistaketh the matter the error being indeed in his own grosse manner of triall much more then in my Table for working after his own way by whole degrees as he doth it falleth out even so as he saith that the Latitude of that Rumb for two degrees of Longitude will be above 2 minutes greater then my Table hath But if he worke the very same way by sixth parts of degrees or tens of minutes he shall find but little above half a minute more then is in my Table of Rumbs Nay moreover if it shall please him at his leisure to take the pains to make triall hereof to every single minute he shall not find so much as one second more then my account giveth For
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-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
5 I divide these 24 by 5 and I find the quotient to be four and the remainder four And so I say that the Moon commeth to the North-east four hours and ⅘ later then the Sun And because the Sun commeth to the North-east at three a clock in the morning I add those 4 hours and ⅘ unto the 3 hours last mentioned and they make seven hours and ⅘ which is the hour of the morning wherein the Tide or full Sea happeneth And adding unto these seven hours and ⅘ other six hours and ⅕ they make in all fourteene hours which falleth out at two a clock in the afternoon which is the hour of the first low water or ebb And adding unto the said hour of the full Sea twelve hours and ⅖ it will amount unto eight of the clock and ⅕ part of an hour which is the hour of the night wherein the second Tide or high water was And add unto this second Tide other six hours and ⅕ and they make two of the clock in the morning and ⅕ at which time there commeth the second ebb or low Sea CHAP. XXXIII Of a certain Instrument whereby you may in generall judge of the Tides BEcause the Tides it being supposed that in all places they proceed from the motion of the Moon run not in every part of the world by one and the same Rumb as it is manifest in the channell of Flanders and in all the coasts of the Northern Sea which is a matter of great confusion and difficulty to Mariners I thought good here to set down an Instrument whereby the daies of the Moon and the Rumb whereupon the Moon causeth the Tide in every part being known they may judge of the ebb and flood with great facility Draw upon a sheet of paper or upon a plate of tinn or any other matter a circle as bigg as the palm of a mans hand and half a fingers bredth within that circle draw another circle and having divided them both into 32 equall parts with lines drawn from the center to the circumference of the greater circle upon the upper end of one of those lines place a flower-deluis and the number of 12 and in the next line thereunto toward the left hand set down 12 and ¾ and in the third line 1 ½ and so proceed forwards putting down upon every line following ¾ of an hour more untill you come again to the number of 12 in the lowest line And from thence forwards set down the same numbers that you did at the first These 32 lines so drawn doe represent the 32 winds whereby the Sun and Moon pass every day And so you may set down the names of the principal Winds to the end that you may know them and those that are next them And then in like manner make another round and slender Table as bigg as the innermost circle of those two which you drew in the first Table and dividing it into thirty equal parts first into two by a line dividing it in the midst and then either of those two into three and every of those three into five these divisions will represent the days of the Moon And leaving upon 1 of those parts an Index or small point which may reach without the circle set down the numbers thereof beginning with 30 in that part where that point endeth and the number of 1 in the line following towards the left hand and then 2 c. till you end at the same point with 30 This being done fasten with a thred or nail the second Table or Circle upon the center of the first so that it may freely without impediment turne round about The use of this Instrument The use of this Instrument is that knowing in every Port or part of any coast the Rumb or quarter on which the Moon maketh full Sea or high water you must note upon the outward Circle of the Winds that quarter or Rumb and placing the tooth or point of the inner Circle were the number of 30 is upon that quarter or Rumb make it there fast puting a litle wax underneath that it may not move Then account the days of the Moons age in the inner Circle and over against the end of your account you shall see in the uttermost Circle the hour of the full Sea of that day together with the Rumb where the Sun is at that hour And at the same hour when it is in the contrary part it will make a full Sea The place of the moon at the hour of the tide is alwaies either where the point is or at the point right over against it and hence you may easily find both ebbes also This little Instrument although it be but of small Invention is of great use and profit for the Navigations of Flanders France England Ireland and all the Northern regions where you have much variety in the tides CHAP. XXXIIII Of the making of an universall Diall which may serve Generally all the World over DRaw upon a Table or pastboord the Circle ABCD upon the center E and half a fingers breadth within that Circle upon the same center draw another Circle and about the breadth of a wheat corn within the second Circle draw a third and placing your Ruler upon the center E by the right line AC divide the two inner Circles in the midst ABC and CDA in the points BD upon which and upon the center E the Ruler being placed you may draw the line BD whereby every one of the foresaid Circles shall be divided into four equal parts And dividing every one of those four Quadrants of the inner Circle to wit AB BC CD DA into 90 parts as the manner is in the making of an Astrolabe set numbers thereto from 5 to 5. begining your account from the two points AC and so proceding both ways till you end your account in 90 at the points BD and this inner Circle thus divided representeth the Meridian And the point C is the North A the South and the points B D are those where the Equinoctial cutteth the Meridian Then count 23 degres and an half from the point B to F and to G on both sides And so much account also from the point D to H and to I. And then drawing two right lines FH and GI the line FH shall represent the Tropick of Cancer and GI the Tropick of Capricorn And those two lines shall cut the line CA which is the Axtree of the World and the Circle of six of the clock in the morning and evening upon the points LM Then count fifteene degrees from C towards B and other fifteeen from A towards B and placing your Ruler on either side upon the end of your account you shall cut the Equinoctial BD upon a certain point which shall represent unto you seven a clock in the morning and five of the clock at evening And counting other fifteen degrees on both sides more towards the point B and placing
the Ruler as before you shall cut the line BD in another point which shall represent eight of the clock in the morning and four in the afternoon And accounting higher fifteen degrees more one both sides and placing your Ruler upon the end of your account it will divide the line BD at another point which shall be nine a clock in the morning and three in the afternoon and so you shall proceed from fifteen to fifteen degrees till you come to eleven of the clock in the morning and one in the afternoon And if you will have the half hours also you must account from seven degrees and an half to seven and an half and doing as you did with the fifteenth degrees you shall have the half hours also Then placing your compasses upon the center E and upon every division of the line EB you shall draw the same divisions likewise upon the line ED which being done draw certain obscure lines from the point A to the divisions of the line EB and drawing the right line GF see where GF is cut at the highest of the obscure lines which must be at the point N from whence the line NO is to be drawn equally distant from the line BE. And this line NO shall be divided proportionally by the obscure lines even as the line BE. Then let the divisions of the line NO be transferred into the lines MG MI LF LH and then the Tropicks also shall be divided Then by every three points answerable in the Equinoctial and the two Tropicks you shall draw certain parts of Circles seeking the center of those three points in the Equinoctial line extended forth on either side and these parts of Circles represent the hours then make an account of the degr of Declination from the point B and from D on both sides by every 2 degr and draw lines Parallel to the Equinoctiall from one to another and those shall be the Parallels of the Suns Declination Moreover you shall make an Horizon as large as the Diameter of the inner Circle which shall be divided after this manner Count from the points AC towards B five degrees and putting your Ruler upon the end of the account of both parts see where it cutteth the line EB and there make a mark and then counting on both sides other five degrees and putting the Ruler once again at the end of your account make another mark where it cutteth the line EB And so the line EB must be divided from five to five degrees which divisions shall be removed into the said Horizon fastning it to the Center and laying it to the line BD and dividing it both ways as the line EB is divided and set numbers thereinto from 5 to 5 which may begin in the midst and end with 90 at the ends of the Horizon and let every one of these parts be divided into five other parts or degrees Then accounting from the Center E in the Horizon eleven degrees and ¼ you shall set there a mark which shall be the seventh point from North and South that is it shall represent the points which are next to the East and West in the Compasse And accounting another eleven degrees and a quarter and making there a mark it shall represent the sixth point from North and South And so you must doe with the other points and then your Instrument is finished CHAP. XXXV Of the parts of this Instrument IN this Instrument the first thing is a Circle divided into 360 degrees which is the Meridian and the line of twelve a clock The second are the right lines of which that in the midst is the Equinoctial and the two others are the Tropicks of Cancer and Capricorn And the other lines between those are the Parallels of the Suns Declination which have their numbers agreeable to them And those that are between the Equinoctial and the Tropick of Cancer doe serve from the 11 of March to the 13 of September and the others for the residue of the year The crooked lines which cross those Parallels are the hour lines And the point of the Meridian which in 90 degrees distant from the Equinoctial towards the left hand is the North Pole and the point opposite to that is the South Pole In the Horizon there are first the degrees and then the points of the Compass distinguished by the small pricked lines CHAP. XXXVI How you may know what a clock it is by this Instrument AT any time of the day when you would know what a clock it is take the heighth of the Sun with your Astrolabe and seeking the Table of the Suns Declination what Declination it hath the same day and the height of the Pole which a good Mariner knoweth at all times because he must direct his course thereby This being known place the Horizon Instrument on the one side under the North and on the other side above the South so many degrees as his distance from the Equinoctial is the same day and fasten it there with a little wax that it may not move Then count in the Meridian on either side from the Horizon which now standeth firm the height of the Sun above the Horizon take with your Astrolabe and by the end of the account draw a line or thred overthwart which shall be equally distant from the Horizon Then reckon the Suns Declination in the parallels beginning from the Equinoctial of the Instrument that way which the Sun Declineth and mark the line or Parallel at which the account of the Declination endeth where and at what hour it is crossed by the thred for that hour is the hour of the day But note this that if the crossing of the thred and Parallel doe fall upon the division of the Parallel and of the hour it is a just hour but if it fall beside the common meeting of the Parallel and of the hour-line upon that side where it falleth see how much more there is then an hour whether ¼ or 1 ◠or ½ c. Now although every hour line hath two numbers one of the morning and another of the afternoon yet it is an easie matter to distinguish which of them will serve your turn if you know whether your Observation be before high noon or after which is to be known by your Astrolabe for if the Sun ascend it is before noon but if it descend it is afternoon CHAP. XXXVII Of the Variation of the Compasse by this Instrument IF you would know by this Instrument the Variation of the Compasse you must doe thus When the Sun riseth or goeth down at the Horizon Observe him with your Compasse noting very diligently upon what Rumb and part of the Rumb he riseth or falleth And if the compasse be divided into 360 parts beginning to reckon them from the East and from the West on either side and ending in the North and South with 90 degrees it shall be the fitter for this purpose because then you shall see
Certain Errors in NAVIGATION Detected and Corrected By Edw. Wright With many Additions that were not in the former Editions London Printed by joseph Moxon and sold at his Shop at the Atlas on Cornhill 1657. Additions To this Edition that were not in the former THe Table for the true dividing of a Meridian of the Sea-Chart heer called the Table of Latitudes made to every minute of the Quadrant which in the former edition was to every tenth minute from page 14 to the 36. 2 Divers additions concerning the true graduating and making both of a general and particular Sea-Chart and touching the use of the Table of Latitudes in the 4 5 6 and 7 Chapter 3 The angle of any Rumb or Helisphaerical line with the Equinoctial being given to find presently the Latitude thereof for any Longitude given page 46. 4 The Table of Rumbs more exactly calculated then before and a Table of the eighth Rumb calculated to every tenth minute and added to the former from page 25 to 54. 5 The use and making of the Sea-rings from page 75 to 79. 6 A Table of the Magnetical inclination calculated to every degree of the Quadrant together with the Geometrical demonstration of the making thereof 7 To find the angle of the true Horizontal line with the visuall line touching the roundness of the Sea at any heighth of the eye above the water and to this end an Observation and demonstration for the finding of the quantitie of the Earths Semidiameter from page 87 to 96. 8 A Table of Refractions of the Sun and fixed Stars pag. 97. 9 The Table of Declination of every minute of the Ecliptick newly and exactly calculated in degr min. and seconds to the greatest obliquity of 23 degrees 31 min. 30 seconds from pag. 100 to 115. 10 The Table of Observations of the Sun corrected by his Parallax from pag. 124 to 141. 11 The eccentricitie of the Sun the place of his Apogaeum and Tables of his middle motions found out and corrected according to the said observations in Chap. 20 21. 12 A new Theorick of the Sun and the manner of making the Table of the Suns Prosthaphaereses thereby from pag. 154.158 13 New Ephemerides of the Sun for five years and how to make them and continue them for many years past or to come from pag. 159 to 168. 14 A new Table of the Suns Declination for the Mariners use and how by certain Prosthaphaereses to continue the same for many years from pa. 170 to 181. 15 The errors of Simon Stevin in finding fault with my Table of Rumbs from the 214 pag. to the 224. 16 A short Treatise of the whole Art of Navigation 17 A â—ew and exact Table of the Suns Declination made and to be used according to the ordinarie manner wherewith English Mariners have been most acquainted from pag. â—7 to 80. 18 A most easie and exact way to find the true height of the Pole in any North Latitude by knowledge of the heighth of the Pole-star when the Guard is in any of those 8 ordinarie positions commonly noted amongst Sea-men from pag. 81 to 90. 19 A Table of Observations of the variation of the Compasse taken in all parts of the world almost whither any Navigation hath been made in our age from pag. 91 to 101 20 The Haven finding Art or the way to find any Haven or place at Sea by the Latitude and Variation To the Worshipfull Captain Thomas Whetstone Esquire Much honored Sir THe loving respects which your pains expressed to me-wards when some occasions urged me to make application to your Worship hath so far obliged me that I should not acquit my self of ingratitude if I should let slip the opportunity I have to render your Worship Thanks And with all Sir knowing your good affection to and perfection in Sciences Mathematical and especially that most necessary most profitable and Honourable branch thereof Navigation I further make bold to Dedicate this the third Edition of Mr Edward Wrights Correction of errors in the Art of Navigation to the acceptance and Patronage of you most honoured Sir The Author in his Time thought it a Present for a Prince nay a splendent and illustrious Prince and therefore Dedicated it to the eldest Son of James King of great Brittain viz. Henry then Prince of Wales whose budding vertues grow in you whose Heroick spirit acts in you and whose hopefull vallor and Corage powerfully and effectually manifests its self in you But Sir Its Patron is Dead and so is the Elementary part of its Author and a shame it were so worthy a work should again enter on the stage of the world without either Author to own it or Patron to Protect it And therefore Sir as this motive moved me who am now become the Disposer of the Book to Dedicate it to your Worship so let the same argument perswade you to accept it that so as the former Impressions have found a current vent this the latter Edition may by your good Countenancing thereof receive the quicker sail to the Profit of the Printer the benefit of the Buyer and the general profit and benefit of the whole Art of Navigation I desire the Almighty to bless your Worship with health and prosperity and to carry you along in all your Worthy adventures I wish your encrease of Honor and honourable actions and that you may shine at Sea as a Star of the first Magnitude fixed in the Zenith that so your Name may afright your Enemies your deserts engage your friends and your Example be as a Whetstone for all truly honourable to set the edge of their vertues on I subscribe my self Your Worships most affectionate and humble servant Joseph Moxon THE PUBLISHER TO THE READER WHen I considered the elaborate pains of that able Mathematician Mr Edward Wright I thought it very uncommendable to our English Nation that his so usefull a book should as it were sleep it self to death and therefore for the benefit of Sea-men have I printed a third Impression I shall not need to enconiumize upon the skil of the Author nor excellency of the work many learned and famous men having already eased me of that Task Nay the book it self tho others were silent being the most Authentique Testimony can speak for the abilities of the one and accomplishment of the other Some perhaps may think that because the Tables of the Suns Epemerides and Declination were Calculated to the year 1608 c. that they are for these present years useless because of the lenghth of time that is since then already past and therefore that they ought to be new Calculated to this present time but herein they are over Curious for our Author himself then whom I never heard of any man more precise in an Example for finding the place and Declination of the Sun by those Tables mentions a year yet to come Pag. 171. and tells us that they will serve for many following years without any
Latitudes are 83 â—â— 73 416 and 37 639 370 which being divided by 600 â—â—00 the Quotients are 140 and 63 almost shewing the breadth 〈◊〉 the Chart from the Equinoctial Northwards and Southâ—ards in such parts whereof the Equinoctial containeth 360 â—hich added together shall shew that the whole breadth of 〈◊〉 Chart from North to South must be about 203 such parts â—aving therefore divided the length of the Equinoctial or any â—ther parallel of the Chart because they are all equal into â—60 parts take with a pair of compasses 210 of the same parts because that is the next greater number apt for division and so keeping them unaltered set both feet in the Meridian at one of the ends or in the midst of the Chart and divide the space conteined betweene them first into seven parts and every one of them into three so have you 21 in all then divide each of these into two and these againe into five so shall you have in all 210 the number of the parts required Now beginning at the Southermost of these parts tell on Northwards till you come to 66 and thereby draw the Equinoctial overthwart the Meridian at right Angles After this you may divide the said parts of the Meridian every one into six drawing forth everie fifth or tenth a little further then the rest and setting figures to every hundreth part for the readier finding out of any number of those parts that shall be required This being done the Meridian may be divided into his degrees of Latitude and the parallels drawne after the same manner that we have alreadie shewed for the drawing of the former figure of a generall Sea-Chart in the Chapter next going before CHAP. V. The use of the table of Latitudes for the true graduating of a particular Sea-Chart TO make a particular Sea-Chart first consider at whaâ— Latitudes your Chart must begin and end Therâ— looke in the former table of Latitudes what numbers of equal parts are answerable to both those Latitudes and subtract the equal parts answering to the lesser Latitude ouâ— of the equal parts answerable to the greater Latitude and drawing a line overthwart the breadth of the Chart from North to South at one of the ends or in some other vacant place therof divide the same line into so many equal parts as the differencâ— remaining shall amount unto if that difference bee a compounâ— number that may be divided into his unities by small divisoâ—â— But if it fall out that the number of equal parts remining 〈◊〉 either a prime number or else such a number as cannot otheâ—â—wise be divided into his unities but by some great divisors 〈◊〉 may then take the next compound number that is greater 〈◊〉 the said difference which may bee divided into his unities 〈◊〉 small divisors Thus having divided the line drawne 〈◊〉 thwart the breadth of the Chart into so many equal parts as 〈◊〉 compound number containeth unities and beginning at 〈◊〉 end thereof which is supposed to bee Southwards or next the Equinoctial set thereto the next number of whole hundreds or thousands lesse then the number of equal parts answerable to the lesser Latitude and drawing forth every fifth or tenth part a little further then the rest set figures to every tenth hundred or thousandth part that you may readily number and find out any of them Then looke in the table of Latitudes which of these equal parts answer to each degree or half degree or each tenth minute of Latitude if your Chart be of a very large prick and with the point of your penne or compasses make marks there and so finish the graduation of the Meridian of your Chart after the accustomed manner before shewed in the former Chapter As for example In the Particular Chart for the Azores hereunto adjoyned the least Latitude is 36 degrees 10 minutes the greatest 52 degrees 20 minutes the equal parts answerable to these in the table of Latitudes casting away the four first figures towards the right hand are 2330 for the first and 3698 for the second Latitude The difference of these is 1368. Then at the West end of the Chart I draw the line AB something longer then the breadth of the Chart which I purpose to make and divide it into 1400 parts supposing every one of those smallest parts to stand for two And this I doe by dividing the whole line first into two parts and each of these againe into seven so have you 14 parts in all whereof every one must bee understood to be divided into 100 equal parts after the ordinarie manner first dividing each of them into two parts then every one of those into five and these againe every one into five parts c. Now because the least Latitude in this Chart beginneth at 2330 equal parts I do therefore account the beginning of the line AB at A to be at 2300 and so proceed setting down numbers at every 100 part as in that Chart you may see Now for graduating the Meridian that is adjoyning or rather all one with the line AB you may proceed in like sort as before was shewed for the making of a generall Sea-Chart in the thid chapter looking what number of equal parts answer to each degree in the table of Latitudes and at the same number of equal parts in the Chart making marks signifying those degrees c. As for example In the table I finde answerable to 37 dgrees 0 minutes 2393 casting away the foure first figures next the right hand therefore at the same number of equal parts in the line AB in the Chart I draw forth the line of 37 degrees Latitude In like manner at 2468 equal parts in the Chart I set downe 38 degrees because in the table of Latitudes I finde that number answerable to 38 degrees And at 2545 I set 39 degrees And so forth for all the rest In like sort you may out of the table of Latitudes set downe every tenth or fifth minute into this Chart or else which is also something easier and not altogether so tedious you may with a paire of compasses divide each degree in the Chart into 12 equal parts In which division although indeede there will be some error yet in this particular Chart or others not much exceeding this in the greatnesse either of the Latitude or of the degrees thereof that error will bee so small as that by sense it can either not at all or very hardly be discerned CHAP. VI. The breadth of a particular Chart being given to divide the same into the degrees and minutes contained in the difference of the least and greatest Latitudes therein to be expressed BVt if you would make your Chart to a certaine breadth limitted which you also desire to divide unequally in due proportion as hath been shewed into the number of degrees and min conteined between the least and greatest latitudes which you would have therein set downe you may then goe thus to worke
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
41 12 49 53 26 11 36 26 5 0 6 36            3 36 9 9 ♎ 3 26 8 ♎ 57 0 6 26 6 42 5 16 59 57 16 51 0 8 57            8 57 54 22 58 13 22 48 0 10 13 11 8 15 28 56 34 28 46 0 10 34 11 50 55 0 ♠57 28 0 ♠45 0 12 28 15 12 37 11 5 41 10 46 0 19 41 16 17 10 14 4 23 13 46 0 18 23 16 43 19 16 7 30 15 47 0 20 30            8 5 58 21 6 26 20 48 0 18 26 16 9 0 25 16 16 24 50 0 26 16 22 7 55 10 ♠42 36 10 ♠1 0 41 36 CHAP. XX. The finding of the Suns Apogeum and Eccentricitie out of the former Observations NOw by the whole course of these Observations it manifestly appeareth that the Declinations set down in the Regiments of the Sun that are and have bin hitherto ordinarily used by our Seamen do for the most part notably err from the truth of the Heavens Which errors as they may most truly be corrected by Observation only in those dayes wherein certain Observation was made so for finding out the Declinations of the middle dayes between the Observations I thought it the best way first to make the Ephemerides of the Sun hereafter following agreeable to the former Observations and then to find out the Declinations answerable to the places of the Sun for every day of four years together because that after that number of years the same places of the Sun and the same Declinations return again without sensible error which also by a certain Equation may be corrected and for the easier finding out of this Equation I have continued these Tables for one year more making them for five years and so including two Leap years by the difference of which years we may easily find the said Equation by means whereof these Tables may be made serviceable for many years First therefore for making these Ephemerides it is needful to know the time of the Suns entrance into certain principal points of the Zodiack as also the time of the Suns continuance in the arches of the Zodiack contained between those points whereby the proportion of the Suns motion may Geometrically be found out his Eccentricitie and place of his Apogeum being hereby known To know the time of the Suns commnig to any point of the Ecliptick it is best to Observe exactly the Meridian Altitude of the Sun not only the same day wherein he is like to enter into the point desired but every day also for two or three dayes together both before and after that day that both by the testimony of so many Observations compared together you may have the more assured truth as also that if the day you most desire fall not out to be so clear as you would wish you may notwithstanding by the Observations of the dayes going before and following after or either of them obtain your desire Having thus Observed the Meridian Altitudes of the Sun and thereby also found his Declinations for every one of those dayes wherein you Observed you shall easily know also the true place of the Sun in every each one of the same dayes with help of the former Table of the Declination of every minute of the Ecliptick in such sort as before was declared when I shewed the use of that Table Now if it fall out so happily that both the day be clear when the Sun entreth into the desired point of the Ecliptick and that the place of the Sun answerable to the Declination of that day be all one with the point desired you have already that you sought for without any more ado viz. That the Sun entreth that day at Noon into the point desired Otherwise subtract the Observed place of the Sun next before the point desired out of the Observed place of the Sun next following that point and the remainder shall shew you the true motion of the Sun answerable to the time between those Observations Subtract also the former place of the Sun from his place in the point desired and note the difference for as the former remainder that is the apparent motion of the Sun between the Observations is to the time between those Observations so is this difference to the time between the first Observation and the Suns entrance into the point desired Example of the first I desired to know the time of the Suns entrance into 17 degrees 0 min. of ♌ in the year 1595. I Observed therefore at London the apparent height of the Sun at Noon the 31 of Iuly the same year and found it to be 54 degrees 14 minutes out of which his true height corrected by his Parallax was found to be 54 degr 15 min. 46 sec. Whereby his Declination was gathered to be 15. degrees 47 minutes 46 sec. And consequently his place in 17 degrees 0 minutes of ♌ that day at Noon Example of the second admit the year following 1596 You would know the time of the Suns entrance into the midst of Taurus Having therfore to this end Observed the apparent Meridian Altitudes of the Sun the 24 25 and 26. Dayes of April in that year within the space of which dayes I am sure the Sun must needs be in that point to be 54 degrees 35 minutes 54 degrees 51 min. ½ 55 degrees 8 min. ½ and consequently the true heights 54 degr 36 min. 44 sec. 54 degr 53 min. 13 sec. 55 degrees 10 min. 13 sec And out of these the true Declinations 16 degr 8 min. 44 sec. 16 degr 25 min. 13 sec. 16. degr 52 min. 13. sec. Hereby I found the true places of the Sun the same dayes to be 14 degr 9 min. 40 sec. Of Taurus 15 degr 5 min. 20 sec. of Taurus 16 degr 3 min. 42 sec. Of Taurus Subtracting therefore 14 degr 9 min 40 sec. Of Taurus that is the place of the Sun the 24 day out of 15 degr 5 min. 20 sec. of Taurus the place of the Sun the 25 day the remainder shall be 55 min. 40 sec. Which is the true motion of the Sun between the 24 and 25. Dayes at Noon that is the Diurn motion of the Sun at that time Subtracting also 14 degr 9 min. 40 sec. Of Taurus out of 15 degr 0 min. of Taurus the difference is 50 min. 20 sec. Now as 55 min. 40 sec is to 50 min. 20 sec. so are 24 houres to 21 houres 42 min. and 2 sec It appeareth therefore by subtracting 21 hours 42 min. 2 sec. Out of 24 hours that the Sun should enter into the midst of Taurus the 25 day about two hours and almost 18 min. before Noon that is at nine a clock and 42 minutes Now supposing I had not or could not have Observed the
excused for finding a fault herein and not amending it at this time and that so much the rather because that according to promise made in the first Edition of this Book I will now shew the meanes how by observation of the pole-star and guards to finde presently the height of the pole not onely when the fore-guard is in some one of those eight principal positions before-mentioned as the manner hath been hitherto but in any other position also and at any time of the night when the pole-star and guards may be seen and that without any allowance or abatement giving or taking by addition or subtraction of any Equation in regard of the pole-stars being higher or lower then the Pole All which besides divers other pleasant and profitable conclusions may easily be performed by means of an Instrument by me divised which may not unfitly be called the Sea-Quadrant the description and use whereof here followeth The figure of the Sea-quadrant CHAP. XXXV The description and parts of the Sea-Quadrant THis Quadrant consisteth of many parts whereof some may be called principal and some lesse principal The principal parts of this Quadrant are the Semidiameter thereof and the Arch. The Semidiameter I call the streight square Ruler The arch I call that part of the Quadrant that is made crooked like a bow The lesse principal parts are the double box or â—ocket and the sights or Vanes The double box or socket hath two square holes made crosse-wise thorow it in such sort that the arch and semidiameter of the Quadrant may be fitly put thorow them the flat side of the one passing close by the flat side of the other By means of this double crosse socket the arch and semidiameter of the Quadrant are so to be joyned together that the two angles made by the hollow side of the arch with the semidiameter may be equal each to other The sights or vanes are either fixed or moveable There be two fixed sights the one greater the other lesser The greater fixed sight is fastened upon the double socket and hath a narrow slit cut through the midst thereof The lesser fixed sight is fastened to the end of the arch of the Quadrant and hath a small sight-hole bored thorow it even with the end of the Arch. The moveable sights are three in number whereof two are to be moved up and down upon the arch of the Quadrant as need shall require for observation The third is to be put on or taken off that end of the semidiameter of the Quadrant where the center is which center is shewed by the little round hole bored overthwart thorow the midst of the thicknesse of the square Ruler neer the end thereof which Ruler we called the Semidiameter of the Quadrant This sight whensoever it is to be used must so be put on upon the end of that Ruler that the flat side thereof which must be set towards the arch of the Quadrant may divide the foresaid round hole even by the midst thereof the sharp edge of that sight arising perpendicularly from the very midst or center of that hole which is also the center of the Quadrant when the other end of the square Ruler or Semidiameter thereof being put into his socket is thrust so far forwards that the end thereof cometh to be even with the fore-end of the socket Two sides of the arch of the Quadrant that is to say one of the straight or plain sides and the hollow side thereof are divided into 90 degrees and every degree into 6 parts each part conteining 10 min. and upon the straight side of the Quadrant there be figures set to every fifth degree and that in two ranks or limbs the one beginning from that end of the arch where the small fixed sight is placed the other beginning and proceeding from the other end of the arch where the Nocturnal is to be fastened or put on that so the number of the degrees and minutes might the easilier be reckoned from either end of the arch as need shall require CHAP. XXXVI Of the Nocturnal or Night-dial THe Nocturnal containeth three circles that is the hour circle the day circle and the pole-star circle The biggest of these circles which is to be fastened to the end of the arch of the Quadrant I call the Hour-circle and it is divided into 24 hours and half hours with figures set to every hour for the easier reckoning of them Next within this is the Day-circle or circle of dayes because it conteineth the dayes of all the moneths of the year which dayes are signified by the smal divisions round about at the circumference of this circle Every fifth day hath his stroke drawn a little longer then the rest that so any day you desire may the easilier be found The smal divisions contein but one day apiece The lines shewing the beginnings and endings of the moneths are drawn overthwart the whole breadth of this circle The beginning of January is known by the two lines drawn neer together overthwart this circle whereof one sheweth the end of the moneth of December and the other sheweth the beginning of the moneth of January which is marked with two pricks February is easily known in this circle because it hath but onely 28 dayes March is by the little pole-star circle and so all the rest of the moneths may easily be known by their order Upon the center of this arch which representeth the Pole of the World there be two Indices fastened the longer of them may be called the Guard-Index whereto a short pin is fastened underneath which serveth to set this Index right upon the place of the middle Guard in the day-circle by putting it into the smal hole that there is made in that circle The shorter Index reaching from the center of the day-circle unto the limb or circumference thereof that is divided into dayes may be called the Day-Index This smal circle placed between the center of the day-circle and the moneth of March may not unfitly be called the Pole-star circle because the distance of the center thereof from the center of the day-circle is answerable to the distance of the pole-star from the Pole which at this time I have often found by exact observation not to be more then 2 degrees and 48 minutes CHAP. XXXVII The use of the Sea-Quadrant and that first in observing the height of the Sun looking onely by the sight at the center to the Horizon at Sea TUrn the center of the Quadrant towards the Sun so as the shadow of the Vane or sight placed at the center may fall upon the hollow side of the arch of the Quadrant then looking thorow the little sight fastened in the end of the arch of the Quadrant lay the upper edge of the sight placed at the center even with the Horizon and at the same instant let one that standeth by mark deligently upon what degree and minute of the Quadrant the edge of the shadow
any land This Horizon is of two sorts namely right and oblique The right Horizon is that which they have that live under the Equinoctial which passeth by their Zenith and therefore the Equinoctial line or circle falleth perpendicularly and right acrosse with their Horizon and both the South and the North Poles are in their Horizon The oblique Horizon is that which they have that live not directly under the Equinoctial for unto them the Equinoctial divideth the Horizon obliquely and not right acrosse and one Pole is alwayes above their Horizon and the other is beneath their Horizon and cannot be seen This Horizon is represented in the Sea-Chart by a certain imagined circle whose center is the point where our ship is From which center are imagined to proceed unto the said circle 32 lines which represent the 32 winds or rumbs which alwayes are drawn in our Sea-Compasse which likewise in a little peece of paper doth continually represent unto us both by day and night the whole Horizon with his 32 divisions CHAP. XVI Of the 32 Winds THis right or oblique Horizon is divided into 32 equal parts by 16 lines which they call Rumbs and they cut themselves in the point where we stand of which rumbs that which passeth by the points where the Equinoctial beginneth and endeth which are where the Sun riseth and setteth the 11 of March and the 13 of September is called East and West and that which cutteth it right acrosse is named North and South And the four extreams or ends of these two lines are distant upon the Horizon one fourth part of a circle and they make four quarters Every one of which quarters being divided in the midst do make four other points and that which falleth between the North and the East is called North-east and that between the North and the West North-west that between the South and the East South-east and that between the South and the West South-west And so the Horizon is divided by four lines or numbs into eight principal winds noted in the Sea-Chart with black lines And if you divide every one of those eight parts in the midst you shall have other eight lines and other four rumbs which in all are 16 winds And each one of these hath his name compounded of the names of those principal winds which are on either side thereof As for example that half winde which is between the North and the North-east is called North-north-east and that which bloweth between the East and the North-east is called East-north-east and that between the East and the South-east East-south-east and that between the South and the South-east South-south-east and that between the South-west and the VVest VVest-south-west and that between the VVest and North-west West-north-west and that between the North-west and the North North-north-west And these are noted in the Chart with green lines Finally if you divide every one of these sixteen winds in the midst they will yield you other 16 winds and will amount to 32 winds in all Which 16 last mentioned are drawn in the Sea-Chart with red lines and are by the Spaniards called quarters of the eighth first and principal winds and every one of these is called by the name of that principal wind which is next it together with an addition of the word By and the name of another principal wind which is next unto it As for example of the two quarter-winds which fall next the rumb of the North that which lieth towards the North-east is called North and by East and that which falleth towards the North-west is called North by West So likewise of those two winds which blow next the North-east that towards the North is called North-east and by North and that towards the East North-east and by East And after the same manner you may name all the rest The Figure of the Sea-Compasse and of the Horizon divided into 32 Winds by 16 Rumbs But here is to be noted that there is difference between the Rumb and the Wind because a Rumb is one direct line continued with two contrary winds as the Rumb of North South and the Rumb of East and West And so when we will name the lying of any Coast we will say that it lieth North and South or North and by East and South and by West But the wind is one line of those 32 into which the Horizon is divided and it is one part of those two which together are called the Rumb And so we say that Land lieth from us towards the South and towards the South and by West or towards the South-south-west c. CHAP. XVII Of the two Tropicks BEsides the six Circles above-mentioned which are drawn upon the superficies of the Sphere of the World there are other two which the Sun describeth with the motion of the Primum Mobile about the 12 day of June and of December of which two Circles that which the Sun describeth the 12 of June from the time of his rising till the time that he riseth the day following is called the Tropick of the Summer Sun-standing or the Tropick of Cancer for the Sun having departed from the Equinoctial and increasing his Declination towards the North when he cometh to describe that Circle for two or three dayes it semeth that he cometh no neerer to our Zenith nor departeth from the Equinoctial one day more then another but from thence forward he goeth back diminishing his Declination till he come to the Equinoctial and crossing the same he goeth on the other side increasing his Declination until the 12 of December upon which day from the time of his rising till he be come about to rise again the next morning he describeth another Circle called the Tropick of the Winter Sun-standing or the Tropick of Capricorn for the Sun being departed from the Equinoctial and increasing his Declination towards the South when he cometh to describe that Circle it seemeth for two or three dayes that he returneth not one whit towards the Equinoctial nor goeth further from our Zenith one day more then other but from thence forwards he commeth back again diminishing his Declination till he be returned to the Equinoctial and from thence towards our Zenith These two Circles in Sea-Charts are marked with two great red lines drawn from East to West which lie on either side of the Equinoctial being distant from thence about 23 deg and an half And wheresoever our ship be in any place between these two Circles or lines we may in some time of the year take the Sun in our Zenith at which time it maketh no shadow at all being then just 90 degr high above our Horizon But they which are without the said two Circles or lines shall never have the Sun in their Zenith because it cannot come to the height of 90 degr above their Horizon CHAP. XVIII Of the Parallels THe parallel Circles are those which are in all parts equally distant from the
Equinoctial And these Circles may be infinite between the Equinoctial and the North and South Poles and in the Sea-chart some of them are represented by the lines which are drawn from East to West And two of these Circles are the two Tropicks of Cancer and Capricorn which are the bounds of the Suns greatest Declinations Likewise all those Circles which the Sun and the stars in Heaven do by the motion of the first or highest moveable heaven describe from East to West are parallels and serve in the Sphere to shew the Latitude And when a ship saileth in the same height of the pole then she saileth in a parallel and runneth alwayes East or West Which manner of sailing we use at all such times when we find our ship in the height of that land to which we are going CHAP. XIX Of the Degrees EVery one of these Circles is divided into 360 equal parts which they call degrees and every degree is divided into other 60 equal parts which are called minutes which degrees and minutes are the common measure that we use in Navigation when we make any account in the Heavens either in taking the the height of the Sun and stars above the Horizon or in measuring the distance from our Zenith to the Equinoctial These degrees are marked in a line drawn from North to South in the most vacant part of the Sea-Chart This line in general Sea-Charts is divided into 90 equal parts which are counted beginning at the Equinoctial line from one to 90 both Northwards and Southwards And in those Charts which are not general this line hath such divisions as it is capable of according to the largenesse of the Chart beginning to make account from the Equinoctial CHAP. XX. What is meant by Longitude and Latitude THe Longitude of any place is a part of the Equinoctial or of some other parallel contained between two Meridians whereof one passeth by the Canary Islands and the other by the place given but if neither of the said Meridians passe by the foresaid Islands it is called respective Longitude And this respective Longitude is called in the Art of Navigation the distance or length of the right line which is determined or bounded by two other right lines running North and South of which two the one passeth by the Port or Haven from whence we set sail and the other by the place where our ship is And so shall the distance of the right line be the part of any right line whatsoever running East and West comprehended between the two foresaid right lines extended North and South The Latitude of a place is a part of any Meridian whatsoever contained between two parallels whereof one is the Equinoctial and the other the parallel of the place given This Latitude the Mariners do call the Distance from the Line understanding by the Line the most principal of all others which are drawn in the Chart that is the Equinoctial Line They use also to call it the heighth which is as much to say as the heighth of the Pole above the Horizon And so the Distance from the Equinoctial shall be a part of any North and South Line contained between the Equinoctial and any line running from East to West which passeth in the graduation of the Chart by the same degree of Latitude in which we find our selves to be THE SECOND PART OF THE Art of Navigation Wherein is handled the Practick Part shewing the making and use of the principal Instruments belonging to this ART CHAP. 1. The making of the Astrolabe TO know the Latitude or distance from the Equinoctial line there are required five things whereof any one being wanting we cannot possibly finde out how far we are distant from the said Line And these are the Astrolabe or Quadrant the height of the Sun the Shadows the Declination the Regiment or Rules of the Sun The Astrolabe is to be made after this manner In the midst of a round plate or table of mettal or wood being smooth and plain every where and about a finger thick you shall take the center A wherein having placed one foot of your compasses you shall with the other draw as great a circle as conveniently you can in the said Table And within this Circle must be drawn two other Circles the one distant from the other about the breadth of a grain of wheat and the third must be distant from the second twice so much as the second is from the first And your Ruler being laid just to the center A you shall draw the line BAC which divideth every one of the three circles into two equal parts And putting one point of your compasses standing open according to the length of the line BC upon the point C where the greatest Circle is divided by the line BC with the other point you shall draw above the point D a part of a Circle and another under E. And then putting one foot of the compasses thus opened upon the point B you shall draw other two parts of a Circle which will crosse the first in F and G. And your Ruler being laid to F and G you shall draw the line DE which must passe by the center A. Then let the Quadrant DB be divided into 3 equal parts and every one of those into three other parts and each of those nine into two and every one of those 18 into 5 and so the said Quadrant shall be divided into 90 equal parts or degrees Unto which degrees shall be placed the numbers belonging to them from 5 to 5 between the second and the third circle beginning from B and ending with 90 at the point D. Then let there be made at the point D a little hole upon the line DE through which may be put a little ring or some strong riband or string and you shall make a knot thereon whereby your finger may take hold and the Astrolabe hanging by that hole you shall put through a slender threed with a plummet of lead which may hang quite under the Astrolabe which threed if while the Astrolabe hangeth immoveable it fall just upon the line DE then is the Astrolabe well rectified If not you must continue cutting off some thing and lightning that side towards which the thred doth fall until it hang even with the foresaid line Then must you draw upon a Ruler of the same matter being about a finger and an half broad the right line HI along through the very midst of the breadth thereof which Ruler shall be made after the same fashion that here is set down cutting away from one half of the length half of the breadth alwayes saving whole the line HI And so likewise shall you cut off along the half of the length on the contrary part half of the breadth so that the line HI may remain whole on that side also And neer to the ends of the said Ruler you shall set two little square Vanes of the breadth
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
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-east in regard of the North-easting of the needle at Sevil and the other meeting at the opposite point which is South and half a point towards the South-west and touching or rubbing those two points of the wires with the ends of the Load-stone which look to the North and to the South to wit the North points of the wires with the South of the 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
   Near England sayling from Yarmouth Northwards 12 40 55 14 In the way from London to Russia 13 0 55 20 West    3 30 69 0 7 0 70 40 8 0 70 30 East    4 0 65 40 5 10 64 30 3 0 66 30 At Antwerpe in Brabâ—â—t 9 0   Near London at Limehouse 11 0 51 30 11 15   About Portland 10 0   In S. Ives Churchyard in Cornwall 8 0 50 30 From Cape Lizard South by West 8 leagues 12 50 49 55 South Easterly from C. Clear comming from our Channel 7 36   At Youghall in Ireland 10 0   At Sylly 10 0    Variat East Latit North.  De. M. De. M. From Bell I le East-ward 350 leagues 1 0 52 10 From Syllie West Northwest 235 leagues 0 0 54 0  West    From Syllie West Northwest five hundred and thirtie leagues 10 0 60 0 From that place Northwest by North 16 0 63 30 From thence North and by West 22 0 66 0 From this last place North by West 28 0 73 0 From thence due West 40 leagues 33 0 73 0 At the Earle of Cumberlands Iles 30 0 64 0 At Hope Sanderson 28 0 72 12 At Cape Rase in Newfoundland 16 0 47 0 From Cape Rase South by West Southerly 2 52 34 35 5 35 35 30 From C. Rase South Southwest Southerly 6 30 39 40  East    At Cape Finister 8 30   From Cape Finister west by North 38 leagues 7 55 43 20 From the Rock Westward about 50 leagues 6 15 39 10 From the Rock West Northwest 7 leagues 7 0   About Lisbone 6 30   From Lisbone to Cape Verde almost 8 30   From C. Saker 3 or 4 leagues Eastward 5 38   From S. Maries one of the Azores 9 leagues East by South 2 20   At Fayal and from thence to Tercaera 3 45   From Tercaera to Lisbon 7 30   8 30   From Flores Eastward scarce 40 leagues and from C. Blanco 300 leagues 4 0   From Flores Eastward 70 or 80 leagues 0 0   Hard by Flores or betwixt it and Fayal 0 0   From Flores Westward 30 leagues 0 0    West    Crossing the Meridian of Flores and Corvo 1 0   From Flores 100 or 120 leagues Westward 2 0   1 0   Within sight of Flores Southeast from thence 5 37   From Flores West 230 leagues 3 30 39 19 Falling with the Pike 1 30   From the Canaries 300 leagues 1 0 19 0  East    At the Canaries 5 37   From the Grand Canarie Northward 4 37 32 0 Northeast from the I le Salvages 5 37 31 0 On the Southwest side of the Grand Canarie 5 20 28 0 From the Canaries 230 leagues 0 0 20 0 Sailing for the Canaries from the West Indies 0 0 33 0 0 0 31 0 Sailing further in 5 37 27 20 From Palma Sailing towards Cape Blanco 3 0 24 0 Near to C. Blanco not two leag from shore 2 40 21 0 Riding at anchor near C. Blanco 3 0 20 25 From C. Blanco West S. w. some 20 leagues 2 40   From C. Blanco Westward 63 leagues 5 37 19 20 From C. Blanco Westward 90 leagues 5 0 18 35 From C. Blanco Westward 100 leagues 6 0   From C. Blanco 436 leagues 7 30 17 42 From C. Blanco 470 leagues 7 30 11 57 From C. Blanco 476 leagues 7 36 16 35 From C. Blanco 535 leagues 7 30 10 59 From C. Blanco 595 leagues 5 0 10 15 From C. Blanco 640 leagues 4 36 10 0 From C. Blanco 700 leagues Westward 1 3 9 20 From C. Blanco going towards the West Indies in many distances 6 0   5 40 14 54 At Cape Verde 7 0   About the Ilands of C. Verde 4 0   From these Ilands 300 leagues Westward 5 38   At S Jago and S. Nicholas Iles of C. Verde 2 30   From C. Verde 100 or 120 leagues 3 45 14 0 From the Iles of Brava Fogo W.N. 12 leag 4 30   From Maio 46 leagues East by South 5 8 14 20 From Cape Verde in the way to the East Indies passing the Equinoctial 4 0   5 0   5 37   At the Iland of Trinidado 0 0 9 46 From Trinidado Iland Eastw 90 leagues 1 30   2 0    West    At Margarita 0 0   At S. Cruce near S. John de Porto Rico 0 0   At Cape Rosse of S. Johns Iland 1 52 17 44 In the Meridian of Porto Rico 2 52 21 30 At anker on the West side of S. John 1 52   At the West end of S. John de Porto Rico 2 30 17 44 From S. John de P. Rico North Northwest northerly half a point 8 0 23 0 Also in the same course 8 0 26 0 Again in the same course 8 0 26 20 From Dominica about some 140 leagues 0 0 14 0 In the Meridian of Barbados fiftie leagues from Martinico 0 0 14 20 At the Iland of Guardelupo 1 0 15 18 At Cursands an Iland of the West Indies 4 0 12 13 At the town of Rio de Hacha 7 36 11 20 At Cape la vela 7 0 11 50 Thwart Rio de Mayo 15 0 31 0 15 0 36 0 At Cape Codera 2 30 9 30 At Cape Corientes in Cuba 3 0   At Cape S. Anthonie in Cuba 13 0 22 0 At Cape Cameron 5 0 25 40 At Cape Florida 3 0 25 30 To the Northward of the Cape of Florida 13 0 28 0 Near the coast of America 11 0 35 30 From Barmudas Westward 140 leagues 10 0 30 35 From Barmudas Westward 100 leagues 10 3 34 0 Again from Barmudas 80 or 85 leagues 11 15 34 0 From Cape Raso S. Southwest Southerly 6 30 39 40  East    From Serraleona West by South and from the shoalds of Madrabombe or S. Anne West and by North 160 leagues 6 10 7 0  Varia West Latit South  De. M De. M In the harbour of Serraleona 1 50 8 30 From the shoar of Serraleona 17 leagues 2 2 3 54 From Serraleona 61 leagues VVest Southerly 2 56 7 58 From the Meridian of Sierraleona 76 leagues VVestward 3 29 7 25 From the Meridian of Sierraleona 97 leagues VVestward 3 45 6 0 From the Meridian of Sierraleona 153 leagues VVestward 4 20 4 50 From the Meridian of Sierraleona 137 leagues VVestward 4 12 4 40 From the Meridian of Sierraleona 127 leagues VVestward 3 56 4 30 From the Meridian of Sierraleona 142 leagues VVestward 4 20 4 18 From the Meridian of Sierraleona 160 leagues VVestward 4 58 4
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