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
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
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
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
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-Sea-Compass THe sea-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
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
sines of their Latitudes if one be Northerly another Southerly are equal to the square of the line subtending the distance of the places 5. e 12. Ram. 47. pr. 1. Eucl. With no lesse facilitie also by help of the former Tables and the Canon of Triangles any two places being given there may Arithmetically and most exactly be found out first by their Longitudes and Latitudes the Rumb and distance measured in the Rumb secondly by their distance and Latitudes the Rumb and difference of Longitude thirdly by their Rumb and Latitudes the distance and difference of Longitude fourthly by their Longiâ—udes Rumb and one Latitude the other Latitude and Distance fiftly by the Rumb distance and one Latitude the other Latitude and the difference of Longitude or any other Nauticall or Geographicall probleme that by the Chart may mechanically be performed and the whole Art of Navigation Arithmetical as some call it may as easily be practised So as having only the Longitudes and Latitudes of the places by which and to which you are to Sail set down in a Table you may by Arithmetical Calculation only if you list take the pains without any Chart Map or Globe shew the Course and Distance from any place to other and so give most exact direction for the performance of an whole Voyage to any known place assigned how oft soever you have traversed or been tossed this way and that way by reason of scant violent or contrarie winds or any other occasion But seeing the first grounds of this Art that is the observations of the Latitudes but especially of the Courses at Sea can not but be far from such exquisite truth as is to be found in those Arithmetical operations how exact soever you be in the rest of the means you can look for no more truth in conclusion then such as is answerable to the first grounds and principles out of which the conclusion is gathered So as the Mariner shall not need to trouble himself any further herewith but only to cast up his accounts upon the Chart truly made as before is shewed which of all other is most fit and ready for his ordinary use Now therefore it may be sufficient only to shew how the former Problems may mechanically be performed upon the Nauticall Planisphaere before described First by the Longitudes and Latitudes of both places given the Rumb and Distance may thus be found Draw parallels by both Latitudes take the distance of those parallels according to which distance draw a parallel to the Equinoctial Then from the end of the difference of Longitude reckoned from the concurse of the Rumbs in the Equinoctial erect a perpendicular crossing the said Parallel A line drawn by this crossing from the concurse of the Rumbs is the Rumb of the two places Now to find out the Distance take so many degrees of the Equinoctial as the difference of Latitude conteineth and guiding one foot of the Compasses in the Equinoctial with the other foot carried parallel-wise at equall distance from the Equinoctial crosse the Rumb newly found out take the distance of this crossing from the concurse of the Rumbs and set both feet of the Compasses in the Equinoctiall for the degrees contained between them shew you the distance desired Secondly by the distance and latitudes knowing which place is more Eastwards or Westwards the Rumb and difference of Longitude is thus found Take with the compasses so many degrees and minutes of the Equinoctial as the difference of Latitude conteineth According to that distance draw a parallel to the Equinoctial take so many degrees of the Equinoctial with your Compasses as the distance given commeth to then one foot being set in the concurse of the Rumbs in the Equinoctial with the other crosse the parallel aforesaid A line drawn by that crossing from the concurse of the Rumbs in the Equinoctiall giveth you the Rumb desired Then both Laititudes being noted in the graduated Meridian therein take their difference with the Compasses and guiding one foot in the Equinoctiall with the other carried at that distance parallel-wise from the Equinoctial crosse the Rumb of the two places the distance of that crossing from the Meridian that commeth from the common meeting of the Rumbs in the Equinoctial taken with the Compasses and brought to the Equinoctial shall there shew you the difference of Longitude Or a perpendicular to the Equinoctial from that crossing shall point you out therein the difference of longitude Thirdly by the Rumb and Latitudes being both Northerly or both Southerly the distance and difference of longitude is thus found Take the difference of Latitudes in the Equinoctial according to that distance draw a parallel to the Equinoctial as before crossing the Rumb of the two places given take the distance of this crossing from the concurse of the Rumbs Then both feet of the compasses set in the Equinoctial will shew the distance of the places The difference of Longitude is found as before Fourthly by the longitudes Rumb and one Latitude knowing whether it be the lesser or greater to find the other Latitude and the distance doe thus From the point of concurse of the Rumbs in the Equinoctial count the difference of longitude from hence erect a perpendicular crossing the Rumb the distance of this crossing from the Equinoctial translated into the graduated Meridian setting one foot in the known Latitude and extending the other Northwards or Southwards according as the unknown Latitude is greater or lesser shall shew you the Latitude desired Now to find the distance work as before in the first Probleme Fiftly by the Rumb distance and one Latitude you may find the other Latitude and the difference of Longitude after this manner Take the distance given with the Compasses in the Equinoctial set one foot in the concurse of the Rumbs and with the other crosse the Rumb given from this crossing draw a perpendicular to the Equinoctial the length of that perpendicular taken with the compasses and brought into the Equinoctial shall shew you the difference of Latitude Thus having both Latitudes given the difference of longitude may also be found as before Prob. 2. Now in every one of these Problemes there may be some particular cases whereof some diversitie of working may arise yet such as can breed but small trouble to him that well doth conceive the reason of that is already set down in these five former Problems which are especialy to be applied to such places as are both on the same side of the Equinoctial and differ also both in Longitude and Latitude of which sort is the greatest number and in which the greatest use and most difficultie of working consisteth To prosecute every particularitie at large whereof some perhaps lesse acquainted with the reason of these Mathematical practises may be desirous would be now for me too long and tedious For some taste therefore of the use of this Nauticall Planisphere let thus much
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
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
themselves doe often find the imperfections of their Charts in shewing the courses and distances of many places each from other wherto we may adjoyne the experience of the best Hydrographers of our time who daily making their Charts after the accustomed manner with straight lined rumbes and degrees of Latitude every where equal have found such difficulties in labouring to bring their Marine descriptions to some due correspondence of truth in the courses heights and distances that tired herewith in the end they have holden it impossible to make the Chart agree in all these with the Globe Wherein notwithstanding they erre by making too generall a conclusion in holding that to be simplie impossible which cannot be done by such a way and meanes as they know and use 3 The Crosse-staffe the principall Instrument that hath at Sea been most generally used for observing the Altitudes of the Sunne or Starres thereby to know more assuredly the Latitude and so to examine and rectifie the account of the course kept by direction of the Compasse upon the Chart if there be not abatement made answerable to the eccentricitie of the eye that is to the distance wherewith the center or point wherein the sight beams concurre within the eye is further backward then the end of the staffe may through neglect of this abatement cause error in taking the height observed to be greater then indeed it is by 10 20 30 minutes yea an whole degree and more sometimes if the height be much the staffe small and the eccentricitie of the eye great 4 But both this staffe and all other Instruments though never so well made and used can do us but small pleasure for finding the Latitude at Sea if the declination of the Sunne and Starres which wee observe be not also known To this end therefore there have been made tables of the Declinations both of the Sun and fixed Starres yet such as even that which hath been publikely commended as not differing from truth in any place above one minute I mean the Regiment of the Sun set forth by R. N. doth notwithstanding differ from truth in many places eleven twelve or thirteen minutes And as for the fixed Starres scarce one of them hath his declination truly set down and agreeable to observation Yea even the Pole-starre it selfe though it be better known and more observed by the most part of Seamen then all the rest and indeed as it might be used being to be observed at any time of the night all the yeere long might stand them in as much stead for finding the Latitude as all of the rest almost yet in the bookes of Navigation that are most common amongst English Mariners the distance thereof from the Pole is made to be in our time above 40 minutes more then it should be No marvell therefore if the Mariners complain as I have heard them sometimes that they cannot make their observations of the Latitude by the Sunne and this Starre to agree Neither is there more truth to be looked for in the declination of many other principall fixed Starâ—s published in those bookes divers of them erring from truth one two yea some of them three whole degrees and more as in the treatise following shall be shewed And these errors in the declination of the Sunne and fixed Starres not only I but also the right worshipfull Sir Christopher Heydon Knight and the noble Lord of Knudstrupp Tycho Brahe founder of Vraniburg with the gratious Prince William Landtgrave of Hassia father of him that now is have often found by many and most diligent observations with large and exact Instruments wherein both minutes and halfe minutes might be easily discerned Notwithstanding if any stand in doubt hereof I wish that he himselfe also would bestow no lesse cost time and diligence to make often heedfull and exact observations then either the Prince of Hassia or Tycho Brahe or at least as I my selfe have done and then let him beleeve that which he shall see to be true with his own eyes These errors therefore in the Chart Compasse Crosse-staffe and declinations of the Sun and Starrs I have in the treatise following laboured to reforme to the utmost yea rather beyond the utmost of my poore abilitie neglecting in the meane time other studies and courses that might have been more beneficiall to me which may argue my good will to have proceeded further to the amendment of such other faults and imperfections as yet remain besides those that are alreadie specified and that especially in two points that is in the courses and Longitudes of places The reforming of the Chart in reducing all places from those varying courses wherein now they are set down to the true positions they have each from other by separating the variation wherewith they are in the ordinary Charts for the most part intermingled were a busie peece of work yet as were most worthie and necessarie to be laboured in as without which the Charts Maps and Globes or any other Hydrographicall or Geographical descriptions cannot be freed from many intricate absurdities wherewith now they must needes in many parts be pestered because the courses and positions of places are in them set down as they were observed by the varying Compasse without separating the variation afterwards that so the true courses and positions of places might be known The Longitude also would well deserve both labour and cost to be both skilfully and liberally bestowed for the finding thereof whereby it were possible to bring it to that passe the motions of the Sunne and Moone and places of the fixed Starres being verified whereof that noble Tycho Brahe hath afforded great hope that the industrious and willing minded Mariner might be capable thereof in such sort that for the most part when the Moone and fixed Starres appeare he might be able hereby to know what Longitude he is in yea even at Sea more truly then many have done by their dead reckonings in sailing out of the bay of Mexico to the Azores or from New-found-land to England or almost from the Azores to England But on land the Longitude might by this meanes be found exactly as the Latitude hath been by many observers at Sea And so opportunities of observation with meet Instruments on shoar not being neglected especially in long Voyages farr Eastward or Westward many most notorious errors in the Longitudes of places would in short time be corrected wherewith the most excellent arts of Geographie and Navigation are very much blemished For who that loveth truth can patiently endure to heare the Mariners common and constant complaint of 150 or 200 leagues error in the distance between the bay of Mexico and the Azores or that which is yet most intollerable and monstrous of 600 leagues difference in the distance between Cape Mendosino and Cape California some making that distance to be twelve or thirteene hundred leagues where others will have it and that more probably to be no more then six or
it followeth that so often as one of these parts is contained in the segment of the Rumb aforesaid in this planisphaere so many score leagues is the distance of the two places set at the ends of that segment Now it is manifest that by these three segments that is the segment of the Rumb betweene the two places the segment of the Meridian betwixt one of the places and the Parallel of the other that is the difference of Latitude and the segment of the Parallel contained betwixt one of these places and the Meridian of the other which is the difference of Longitude I say it is manifest that by these three segments a right angled Triangle is made because the segments of the Meridian and Parallel which are two sides of this Triangle include a right angle Againe it is plaine that taking with your Compasses so many degrees of the Equinoctial as are contained in the difference of Latitude then guiding one foote in the Equinoctial and carrying forwards the other Parallel wise till it crosse the Rumb of those two places in such sort that one foote of the Compasses being set in that crossing the other moved about may but only touch the Equinoctial and lastly drawing from that crossing a line perpendicular to the Equinoctial It is plaine I say that by this perpendicular and the two segments one of the Equinoctial betweene this perpendicular and the Rumb the other of the Rumb betweene the perpendicular and the Equinoctial by these segments I say and the said perpendicular there is comprehended another right angled Triangle which by the 14. e 4. c 3. e. 7 Ram. Is like to the former right angled Triangle because two angles of them both are equal that is the right angles and the angles of the same Rumb In the last of these Triangles the side perpendicular to the Equinoctial is proportional to the difference of Latitude and the segment of the Rumb betweene the end of this perpendicular and the Equinoctial is proportional to the segment of the same Rumb contained betwixt the two places Therefore by the 2 p 6. 17 p. 11 Eulc Because the line perpendicular to the Equinoctial containeth so many equal degrees of the Equinoctial as there are equal parts in the difference of Latitude that is so many as there are degrees in the difference of Latitude these equal parts also of the perpendicular and difference of Latitude are proportional Whereof it followeth that so oft as one of these equal parts of the difference of Latitude is contained in the segment of the Rumb betwixt the two places which before we shewed to be so oft as a degree of the Meridian in the Globe is contained in the segment of the Rumb betwixt the same places in the Globe so oft is one of the said equal parts of the perpendicular aforesaid that is a degree of the Aequinoctial contained in the segment of the same Rumb betweene the foresaid crossing or end of the perpendicular and the Aequinoctial Therefore look how many degrees of the Aequinoctial there are found in the segment of the Rumb of the two places so many score leagues is the distance of those two places which was to be demonstrated Thus have you a way infallible to find out the distance between any two places measured in their Rumb which because it is then onely their true distance that is the shortest space betwixt them upon the superficies of the Terrestriall Globe when both places lie North and South each from other or East and West having no Latitude as under the Aequinoctial whereas otherwise the segment of the Rumb betweene the two places is alwaies greater then the true distance yea sometime by halfe and more in places far Northward or Southward I thoâ—ght good also here to set down the way to find out the true distance of any two places according to the arch of a great circle drawn betweene them wherein I have been and yet am publikely charged with my promise and meane at this time to discharge my selfe thereof The true distance betweene two places is the arch of a great circle contained betwixt them which is thus to be found out If both places have no Latitude as when they are both under the Aequinoctial and one of them also no Longitude the Longitude of the other being lesse or not more then 180 degrees the Longitude is the distance But if the Longitude be greater then 180 degrees subtract it out of 360 the remainder is the distance If both places have either none or the same Longitude as when they are in the same semicircle of the Meridian betweeene the Poles and one of them onely have Latitude that Latitude is the distance But if both places agreeing in Longitude have Latitudes also of like denomination as both Northerly or both Southerly subtract the lesser Latitude out of the greater the distance remaineth If one place have Northerly Latitude and the other Southerly adde them together for the summe is the distance If one or both places have atitude Land differ also in Longitude in a great circle divided exactly into degrees with figures set to every fifth or tenth degree note the Longitudes of both places Now if one place only have Latitude draw a diameter from the Longitude thereof noted in the circle and with your Compasses take so many degrees and minutes in the same circle as that Latitude containeth then setting one foote of the Compasses in the Longitude of that place with the other make a pricke in the circle which may be called the point of Latitude From this point draw a line perpendicular crossing the diameter drawn from the Longitude of that place Take with your Compasses the distance of this crossing from the point of the other places Longitude noted in the circle and leaving one foote in the said crossing with the other make a pricke in the foresaid diameter take the distance of this pricke from the point of Latitude noted in the circle Then setting one foote of the Compasses in that point of the circle where the degrees begin to be numbred the other foote extended that way which the numbers proceed shall shew you in the circle the distance of the places Take for example the Citie of London and Saint Thomas Iland which lieth right under the Aequinoctial line in 32 degrees of Longitude The Longitude of London admit to be 22 degrees the Latitude 51 degrees 32 minutes Marke the Longitudes of Saint Thomas Iland and of London with A and B. From the Longitude of London because London hath also Latitude draw the diameter BC. Having taken with the compasses the Latitude of London in the circle set one foote in B and with the other make the prick E in the circle and draw the perpendicular EF crossing the diameter BC at F. Make FG equal to FA which is the distance of Saint Thomas Iland from the sine of Londons Latitude Then GE shall be the line
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-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
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
cast his point in manner following and he shall errer as little as is possible Let him examine according to the ordinary running of his ship how much way she might make every day that he hath sailed and the leagues that shall amount in all the dayes let him take between the points of one compass and let him place one point thereof upon the place from whence he departed and taking another compass let him set one point thereof upon the graduation according to the heighth which he hath taken and the other point upon the next East and West Rumb Now let this compass run by his East and West rumb till the point coming from the graduation meet with the second point of the other Compass which he holdeth not upon the Chart and in the place where they meet he may say that there is his point and his ship And because in this case all Pilots do not use this point of imagination and heighth there grow great diversities among them concerning their distance from land when as in long voyages they confer and communicate their opinions one with another insomuch that one according to his conjecture judgeth himself to be 50 leagues from land another 100 another 200 and another thinketh he is hard by the land The reason is because some of them cast their point by traversing others by imagination onely and others by imagination and heighth who are alwayes more certain then the rest CHAP. XXIV What it is to increase or diminish in heighth THe Mariners call it increasing in heighth when they go further and further from the Equinoctial and diminishing in height when they approach neerer to the Equinoctial So that in our Navigation we either sail from a greater to a less altitude of the pole and then we go towards the Equinoctial and then the height is said to be diminished or we sail from a less to a greater height of the pole and then we go from the Equinoctial and are said to increase our heighth And hence it is that casting our point by imagination and afterwards having taken the heigth amending it by traversing either the heighth wherein we find our selves being taken by the Sun or star is greater or else it is less then that which we made account of by imagination And hence do arise four rules The first is that when in sailing we do increase the heighth if the point amended by traversing be of greater heighth then the point of imagination the ship hath gone more then the point of imagination shewed us The second when we increase our heighth if the point amended by traversing be in lesse height then the point found by imagination then hath the ship gone less way then we imagined The third is when we diminish our height in sailing if the point amended by traversing be in a greater heighth then the point found by imagination then hath the ship made less way then we ghessed by our imagination The fourth is when we diminish our heighth if the point amended by traverse be in less heighth then the point found by imagination then hath the ship made more way then we imagined CHAP. XXV How you may cast a traverse point without Compasses IF a Mariner chance to lose his Compasses he may cast his point of traverse after this manner Let him take two slender threds and putting the end of one of them upon the place from whence he departed let him stretch it in equal distance from the Rumb by which he hath sailed and putting another thred in equall distance from the next East and West rumb let him make it to pass by the degrees of heighth in which he findeth himself and where the two threds cross one another there is the point of the ship and alwayes the first thred if it hath not changed the course sheweth the way which the ship hath gone and the second the parallel wherein the ship is CHAP. XXVI Of another kind of casting a point by traverse EXamine the difference of the degrees of distance from the Equinoctial which are between the place from whence the ship set forth and the place where the ship is Then taking the heighths of both places very precisely and subtracting the lesser out of the greater that which remaineth is the difference which difference you must multiply by the leagues which answer to one degree in the rumb by which you have sailed and those leagues which the degrees and minutes of difference shall make you shall take between the points of a pair of compasses out of your scale of leagues and holding the said compass so open set one foot thereof upon the point from whence the ship departed and the other foot stretching towards the place whithre the ship hath sailed you must hold up a little from the Chart and you must set one foot of the other Compasse at the degree of the distance wherein your ship is from the Equinoctial when the said point is sought for and the other point you must place upon the next East and West Parallel And let this second Compasse run by his next East and West Rumb untill the point of the first Compasse lifted up being set downe that point of the second Compasse which came from the said degree doth meete therewithal and where those two points shall meet there is the true point of the ship CHAP. XXVII Of the leagues which in Navigation answer to each degree of Latitude in every Rumb IF we suppose as we have before said in the chap. of the quantity of the earth that the greatest circle thereof conaineth in compasse 6300 common Spanish leagues then unto every degree of the Meridian which is the greatest circle doe answer 17 Spanish leagus and an half so that sailing North and South if your heighth of the Pole or your distance from the Equinoctial be varied one degree you may say that you have gone seventeen leagues and an half but if you varie one degree and hold your course upon the first point then have you sailed 17 leagues and ⅙ And you have declined from the Meridian or right line which passeth by the place from which you departed three leagus and an half And if you sail upon the second point from the North or South till your heighth of the Pole be changed one degree you have then gone 19 leagues and ⅜ and are distant from your right line 7 leagues and ¼ And varying a degree upon the third point of the Compasse from North or South you have gone 21 leagues and are departed from your right line 11 leagues and ⅔ Sailing upon the fourth point of the Compasse there doe answer unto every degree 24 leagues and three fourths and you are distant from the right line or Meridian 17 leagues and an half Upon the fifth point you must allow for one degree 31 leagues and an half and then are you distant from your right line 26 leagues and ⅕ Upon the sixth point doe
sake have need to note And when he hath expected afternoon till the Sun descending by the same Instrument be found placed in the same 25. degr of Altitude then the Box it self must again be turned this way or that way untill the Sun again shining through the sights the Magneticall needle doe point to the beginning of the Circle Which things being thus dispatched the middle point of the arch in the Horizontall plain between the first and second experiment is the North point and how much the needle declineth from that point so much is the variation sought for as before wee have shewed in the first example more at large Whatsoever we have affirmed to be available in the day time in these experiments of the Sun the same may be understood and done in like manner in the night by any of the fixed stars whereof there is the same use in this matter that there is of the Sun But there is not the same reason of the Moon aswell because of the swiftnesse of her proper motion as also because of the greatness of her Parallax as they call it which the over-much neereness of the Moon to the Globe of the earth bringeth forth But this also is to be noted that two three or four yea and more Observations may be made in the foore-noon As for example let the first bee when the Sun is 10 degrees above the Horizon the second when it is 15. degr the third when it is 20. degr and if any man will make triall as often after noon hee shall see how every experiment agreeth with other and when at every moment the same North point is found that thing shall give the Master of the ship no small courage and more certain confidence of his work But notwithstanding when the Mariner sayleth from the East Westwards or contrariwise from the West Eastwards it may be that in the space of 10 or 12 hours between the first and second experiment there may be difference of one degree or more in the variation whereof may follow that the North point found by the first forenoon Observation and the last in the afternoon shall not agree with that which was found by the first in the afternoon and the last in the forenoon when notwithstanding the Mariner hath not erred in Observing Which if it shall happen often the skilfull Mariner may judge thereby what difference of variation is answerable to any determinate time of sayling and so find a way whereby the North poynt may be found with more certainty and security which thing may thus also be done if a man diligently compare the variation found in the former days with the variation which he presently seeth FINIS Error in the proportion of the length and breadth of places in the common Sea-chart Error in finding out the difference of longitude by the common sea Chart. Error in the lying and bearing of places one from another in the common Sea-Chart Error in setting of places out of the common Sea-Chart into the Globe Error in shewing the distances of places in the common Sea-Chart Error in keeping alwaies the same point of the Compasse The expressing of the Rumbs by right lines defended which some hold for erroneous The definition of the Nautical Planisphaere 27 Prop. 1. Euclid 17. The use of the two first Columns of the Table of Latitudes 1. By the longitudes and latitudes of two places to find the rumb and distance 2. By the distance and latitudes to find the rumbe and difference of longitude 3. By the Rumb and latitudes to find the distance and difference of longitude 4. By the longitudes rumb and one latitude to find the other latitude and the distance 5 By the Rumb the distance and one Latitude to find the other Latitude and the difference of Longitude The use of this Instrument A shorter way to calculate the Table of Magnetical Inclination A most exact way to find the quantitie of the Earths semidiameter Clau Comm. in 1 Cap Ioan. de Sacrobosc Height of the eye Angle of dipping Foot min. se 1 1 8 2 1 36 3 1 58 4 2 16 5 2 33 6 2 47 7 3 0 8 3 13 9 3 24 10 3 35 12 3 56 14 4 15 16 4 33 18 4 40 20 5 5 22 5 20 24 5 3◠26 5 40 28 6 1 30 6 13 32 6 25 34 6 38 36 6 49 38 7 0 40 7 11 42 7 21 44 7 32 46 7 42 48 7 52 50 8 2 Suns height Suns Paralax gr M Sec 0 3 0 5 2 59 10 2 57 15 2 54 20 2 50 25 2 44 30 2 36 35 2 27 40 2 18 45 2 7 50 1 56 55 1 43 60 1 30 65 1 16 70 1 2 75 0 46 80 0 31 85 0 15 The Suns The Suns The fix St. Altitude Refraction Altitude Refraction Altitude Refraction De. Mi. se De. Mi. se De. Mi. se 0 34 0 23 3 10 0 30 0 1 26 0 24 2 50 1 21 30 2 20 0 25 2 30 2 15 30 3 17 0 26 2 15 3 12 30 4 15 30 27 2 0 4 11 0 5 14 30 28 1 45 5 10 0 6 13 30 29 1 35 6 9 0 7 12 45 30 1 25 7 8 15 8 11 15 31 1 15 8 6 45 9 10 30 32 1 5 9 6 0 10 10 0 33  55 10 5 30 11 9 30 34  45 11 5 0 12 9 0 35  35 12 4 30 13 8 30 36  30 13 4 0 14 8 0 37  25 14 3 30 15 7 30 38  20 15 3 0 16 7 0 39  15 16 2 30 17 6 30 40  10 17 2 0 18 5 45 41  9 18 1 30 19 5 0 42  8 19 1 0 20 4 30 43  7 20 0 30 21 4 0 44  6 21 0 0 22 3 30 45  5    1597 To know the time of the Suns comming to any point of the Ecliptick· Pag. 153. Pag. 154. Pag. 155. By whole degrees the first Rumbes Lon· Latitu gr m. gr mi. se. 1 0 5 1 38 2 0 10 2 6 By tins of min. the first Rumbs Lon· Latitude gr m. gr mi. se. th 0 10 0 50 16 23 0 20 1 40 32 26 0 30 2 30 47 33 0 40 3 21 1 5 0 50 4 11 12 16 1 0 5 1 20 46 1 10 5 51 25 35 1 20 6 41 26 18 1 30 7 31 22 14 1 40 8 21 12 38 1 50 9 10 57 0 2 0 10 0 34 40 Difference between the Rumb and the Wind The Equinoctial is called the line because it is the principal of all others which are drawn in the Chart. These leagues must be counted in the Equinoctial between the meridians of the two places But it were better to find the difference of Longitude for then as 360 degrees are to that difference so is the difference of Declination to the Equation desired In stead of all these Rules of the North Star which are erroneous use the Tables of Equations of the Pole Stars heighth set down in the latter end of this book †Or rather increased proportionally from the Equinoctial line toward the North South This for the most part is not true in the ordinary Sea-chart These days mentioned in this example are to be understood according to the new Roman Gregorian Kalender which goeth always ten days before ours used in England The use of this Table Equinoctal Equinoctial
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
of the Ruler in the midst standing upright the very midst of both Vanes being placed upon the line HI Through the centers of which two Vanes shall be made two little holes both which must stand directly over the line HI and in equal distance from the upper face of the Ruler This Ruler by a hole bored thorow the midst thereof shall be fastened upon the said Astrolabe through another hole of the bignesse of that in the Ruler at the very center A with a nail which may be made fast with a little pin as is to be seen in the figure CHAP. II. Of the heighth of the Sun TO take the heighth of the Sun you must hold the Astrolabe by the ring or knot D in your left hand and turning your right side to the Sun lift up the Ruler with your right hand till the beam of the Sun entring by the hole of the uppermost Vane doth also pierce thorow the hole of the nethermost Vane And then note the degree and part of the degree which the line HI doth touch for that is the heighth of the Sun above the Horizon which if it be the greatest heighth that the Sun hath that day it will teach us how far we are distant from the Equinoctial This greatest heighth is to be taken at mid-day lifting up the uppermost Vane till we be assured that the Sun ceaseth to rise any higher but beginneth to fall again Then note that greatest heighth and keep it for the making of your account of the Latitude by the Sun CHAP. III. Of the Shadows THe shadowes being compared with the Sun may be of three sorts for at high noon the shadow falleth either towards that part of the World â—o which the Sun declineth or towards the contrary part or else we make no shadow at all The first and second sort are when the heighth of the Sun is lesse then 90 degrees and the third is when it is just 90 degrees high The first is when the Sun keepeth his course on the North side of the Equinoctial which is from the 1â— of March to the 13 of September and likewise when the shadows fall towards the North of the Compasse or when the Sun runneth on the South side of the Equinoctial which is from the 14 of September to the 10 of March and the shadows likewise fall towards the South of the Compasse and this is when the Sun and the shadows go both one way The second is when the Sun coming towards the North the shadows are cast towards the South of the Compasse or when the Sun is on the South side of the Equinoctial the shadows fall towards the North and this is when the Sun and the shadows are differing The rule of the shadowes is that we look well to the lower Vane of the Astrolabe when we are taking the height of the Sun at noon For if the line HI fall directly upon the line of the Astrolabe DE then we have no shadow because the Sun is in our Zenith 90 degrees high But if the line HI fall not upon the line DE you must mark towards what part of the World the lower part of the Ruler doth decline from the point E which if it decline towards the North of the Compasse then the shadowes fall Northwards But if it decline towards the South of the Compasse then the shadows fall Southwards CHAP. IIII. Of the Regiment and Rules of the Sun WHen you know the part or parts of the Sun and shadows and desire by the Sun to know how far you are distant from the Equinoctial you have five rules The first whereof sheweth in what part of the Heavens the Sun is that is whether he be North or South from the Equinoctial at the time of your observation The second teacheth what account we are to take of the Sun when he casteth no shadow because he is in our Zenith and is found in the Astrolabe to be just 90 deg high The third is of the account to be made by the Sun when taking the heighth thereof in lesse then 90 degr it maketh a shadow at high noon and hath no Declination because it is under the Equinoctâ—al The fourth is of the account that is to be made when the Sun and the shadows are both one way from the line The fifth is when the Sun and the shadows are different onâ— being towards the North and the other towards the South The first Rule of the Sun From the 11 of Mâ—rch to the 13 of September the Sun runneth on the North side of the Equinoctial And from the 14 of September to the 10 of March he goeth on the South side thereof The second Rule of the Sun When we observe the Sun in 00 degrees of heighth we must see what degrees and minutes of Decâ—ination the Sun hath the same day And then we may say that we are so much distant from the Equinoctial towards that part of the world to which the Sun declineth The third Rule of the Sun When the Sun is less then 90 degrees high if there be no Declination the same day then so much as it wanteth in heigth of 90 degrees so much are we distant from the Equinoctial towards that part of the world towards which the shadow falleth The fourth Rule of the Sun· When the Sun and the shadowes are both towards the same part of the world we must note how much the Sun wanteth of 90 degrees in heighth And that which it wanteth being added to the Declination of the Sun the same day is our just distance from the Equinoctial towards that part of the world to which the Sun and shadowes decline The fifth Rule of the Sun When the Declination of the Sun and the shadowes be different we must add the height of the Sun unto the Declination which it hath the same day And if the Sun amount to 90 degr just then are we under the Equinoctial line but if it exceed 90 degrees we are so much distant from the Equinoctial towards that part of the world wherein the Sun is as that excesse or overpluss commeth to And if the heigth and Declination added together come to lesse then 90 look how many degrees and minutes you want of 90 so many are you distant from the Equinoctial towards that part to which the shadowes fall And here is to be noted that we must likewise make account of the minutes because they may be both in Declination and in heigth and so alwaies in that Declination where we shall find 60 minutes we must make of them one degree And if in taking the heighth we find half a degree besides all the whole degrees it is as much as 30 minutes and one third part of a degree is 20 minutes one fourth 15 minutes one fifth part 12 minutes and one sixth part 10 minutes CHAP. V. Of the Declination of the Sun and of his Tables THat wee may know what use to make of the five foresaid