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
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
right side 41 38 2 56 2 The goat or wagoners left shoulder 44 30 4 49 1 The wagoners right shoulder 45 11 5 30 2 The first in the great bears fore-foot 40 30 8 24 3 The second in the same foot 41 28 8 32 3 In her former left knee 36 37 8 58 3 The great bears side 31 26 10 58 2 The great bears back 26 05 10 40 2 The end of the Dragons tail 18 26 11 08 3 The great bears thigh 34 03 11 32 2 The great bears rump 30 41 11 54 2 The next to the end of the Dragons tail 17 57 12 14 3 The first in the great bears tail next her rump 31 49 12 32 2 The middlemost in her tail 32 55 13 06 2 In the end of her tail 38 37 13 32 2 The next before the turning of the Dragons tail 23 40 13 53 3 The formost guard 14 11 14 54 2 In the turning of the Dragons tail 29 37 15 14 3 The hindmost guard 16 42 15 26 2 Next after the turning of the Dragons tail 30 20 15 54 3 The Dragons eye 37 18 17 22 3 The Dragons head 38 22 17 44 3 In the Swans right wing 45 44 19 34 3 In her tail 46 06 20 30 2 Cepheus his right shoulder 29 00 21 10 3 The back of Cassiopeia's chair 33 02 23 48 3 CHAP. XXXII To know at what time any of the foresaid fixed stars come to the Meridian for any day of the year NOw because the fixed stars are then onely meet to be observed for finding the latitude when they are in the meridian it is therefore good for him that meaneth to observe them to know at what time they come to the meridian To this end there are tables published and almost in every mariners hands pretending to shew at what hour and minute every star in the first of these two former tables commeth to the meridian for the beginning and midst of every moneth in the year agreeing likewise in every errour one with another but because these errours breed not at any time greater danger or damage to the Mariner that is ware of them then to make him watch for their coming to the meridian a quarter or half an hour longer then otherwise he needed this inconvenience onely provided for those tables may serve the turn well enough for them that list not trouble themselves to learn a better way But for them that are desirous of a more true and generall way I have also made the table following of the Suns right ascensions reduced into hours and minutes for every day of this present year 1599 according to the Ephemerides of the Sun before set down with help of which table it may easily be known for any day of any year in our age at what time not onely any of the foresaid fixed stars about the Equinoctial but those also about the Pole or any other whose right ascensions are known in hours and minutes come to the meridian and that after this manner Finde out in the table following the moneth and day wherein you observe the moneth in the upper margine of the table the day in the first column thereof next the left hand the common meeting of the column descending from the moneth and of the line proceeding from that day towards the right hand shall give you the Suns right ascension in hours and minutes for the same day This right ascension of the Sun subtract alwayes out of the right ascension of the star adding 24 hours to the stars right ascension if it be lesse then the right ascension of the Sun the remainder sheweth how many hours and minutes after noon the star cometh to the upper part of the meridian which if they be more then 12 hours subtract 12 from them and the remainder shall shew you how many hours and minutes after midnight the star cometh to the upper part of the meridian The upper part of the meridian I call that which passeth from the Pole by the Zenith to the Horizon southwards But it shall be needful also many times when you would observe the stars about the Pole which never set to know the time of their coming to the nether part of the meridian which may easily be done onely by adding 12 hours to the time of their coming to the upper part of the meridian if it be lesse then 12 hours or by subtracting as much if it be more Suppose for example the 25 of February 1599 I would know the time of the great dogs coming to the meridian First therefore in the next table following the column descending from February downwards and the line proceeding from the 25 day towards the right hand in the common meeting of them both I finde 23 hours 10 min. the Suns right ascension that day at noon Then in the first table of fixed stars I finde the great dogs right ascension to be 6 degr 27 min. to which because it is lesse then the Suns right ascension I adde 24 hours and the sum of both cometh to 30 hours 27 min. out of this I subtract the Suns right ascension 23 hours 10. min. and there remais 7 hours 17 min. the time of the great dogs coming to the upper part of the meridian in the afternoon Take one example also of a star that never setteth and admit the 20 of December the same year you would know what time the formost Guard cometh to the Meridian beneath the Pole First therefore you shall finde as before the Suns right ascension that day to be 18 hours 36 min. and the right ascension of that star in the second table of fixed stars 14 hours 54 min. to which being lesse then the Suns right ascension adde 24 hours and from the sum 38 hours 24 min. subtract the Suns right ascension 18 hours 36 min so there shall remain 20 hours 18 min. the time of the formost Guards coming to the upper part of the meridian from which subtract 12 so you have the time when it cometh to the nether part of the meridian 8 hours 18 min. after noon A Table of the Suns Right Ascension in hours and minutes for every day of the year  January February March April May June D. H. M. H. M. H. M. H. M. H. M. H. M. 1 19 30 21 39 23 25 1 18 3 11 5 15 2 19 34 21 43 23 28 1 22 3 15 5 19 3 19 39 21 47 23 32 1 26 3 19 5 25 4 19 43 21 50 23 36 1 29 3 23 5 27 5 19 47 21 54 23 40 1 33 3 27 5 31 6 19 52 21 58 23 44 1 36 3 30 5 36 7 19 56 22 02 23 47 1 40 3 34 5 40 8 20 00 22 06 23 51 1 43 3 38 5 45 9 20 04 22 09 23 55 1 47 3 42 5 49 10 20 08 22 14 23 58 1 51 3 46 5 53 11 20 13 22 18 0 02 1 55 3 50 5 57 12 20 17
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