24 gr of ♉ his longitude shall be PI his right ascension PH his declination HI And if the place giuen be 19 gr of ♌ his longitude shal be PK his right ascension PN his declination NK Againe the declination brought to the horizon of the place shall there shew the ascentionall difference amplitude of ascension and the like conclusions of the globe But I intend not here to shew the vse of the Astrolabe but the vse of the Sector in proiection And after this maner may a nocturnall be proiected to shew the houre of the night whereof I will set downe a type for the vse of Sea-men It consists as you see of two parts the one is a plane diuided equally according to the 24 houres of the day and each houre into quarters or minutes as the plane will beare the line from the center to XII stands for the meridian and XII stands for the houre of 12 at midnight The other part is a rundle for such starres as are neare the North pole together with the twelue moneths and the dayes of each moneth fitted to the right ascension of the starres Those that haue occasion to see the South pole may do the like for the Southerne constellations and put them in a rundle on the back of this plane and so it may serue for all the world The vse of this nocturnall is easie and ready For looke vp to the pole and see what starres are neare the meridian then place the rundle to the like situation so the day of the moneth will shew the houre of the night 3 The Sphere may be proiected in plano by circular lines as in the particular Astrolabe of Ioh. Stophlerin by help of the tangent as before For let the circle giuen represent the tropique of ♑ let it be diuided into foure parts and crossed at right angles with AC the equinoctiall colure and MB the solstitiall colure and generall meridian the center P representing the pole of the world Let each quarter be diuided into 90 gr and so the whole into 360 beginning from A towards B. The meridian PM or PB may be diuided according to the tangent of halfe his arke So as the arke from the North pole to the tropique of ♑ being 90 gr and 23 gr 30 m. that is 113 gr 80 m. and the halfe arke 56 gr 45 m. the meridian shall be diuided into 90 gr and 23 gr 30 m. in such sort as the tangent of 56 gr 45 m. on the side of the Sector is diuided into degrees and halfe degrees of which PAE the arke of the equator 90 gr from the pole shall be giuē by the tangent of 45 gr And P 69 the arke of the Summer tropique 66 gr 30 m. from the pole shall be giuen by the tangent of 33 gr 15 m. And the circles drawne vpon the center P through AE and ♋ shall be the equator and the Summer tropique Hauing the equator and both the tropiques the ecliptique ♈ ♋ ♎ ♑ shall be drawne from the one tropique to the other through the intersection of the equator and the equinoctiall colure And it may be diuided first into the twelue Signes after this maner PE the arke of the pole of the ecliptique 23 gr 30 m. from the pole of the world shall be giuen by the tangent of 11 gr 45 m. The center of the circle of longitude passing through this pole E ♈ and ♎ shal be found at D somewhat below B by the tangent of 66 gr 30 m. Then through D draw an occult line parallell to AC and diuide it on each side from D in such sort as the tangent is diuided on the side of the Sector allowing 45 gr to be equall to DE. So the thirtith degree from D toward the right hand shall be the center of the circle of longitude passing through E ♉ and ♠The sixtith degree the center of ♊ E ♠The thirtith degree from D toward the left hand the center of ♓ E ♠The sixtith the center of ♒ E ♌ And the other intermediate degrees shal be the centers to diuide each Signe into 30 gr If farther we haue respect vnto the latitude we may the meridian being before diuided number it from P Northward vnto H and there place the North intersection of the meridian and horizon then the complement of the latitude being numbred from P Southward vnto Z shall there giue the zenith and 90 gr from Z Southward vnto F shall there giue the South intersection of the meridian and horizon The middle betweene F and H shall be G the center of the horizon ♈ H ♎ F passing through the beginning of ♈ and ♎ vnlesse there be some former error All parallels to the horizon may be found in like sort by their intersections with the meridian and the middle betweene those intersections is alwayes the center For example of this proiection let ☉ the place of the Sun giuen be 10 gr of ♉ a right line drawne from P through this place vnto the equator shall there shew his right ascension ♈ K and his declination K ☉ Then may we on the center P and semidiameter ☉ P draw an occult parallell of declinatiō crossing the horizon in L and M the meridian in G and N. So the right lines PL and PM produced shall shew the time of the Sunnes rising and setting ♈ Q the difference of ascension ♎ R the difference of descension ♈ L the amplitude of his rising and ♎ M the amplitude of his setting LGM sheweth the length of the day LN M the length of the night ZG sheweth his distance from the zenith at noone HN his depression below the horizon at midnight And then hauing the altitude of the Sunne at any time of the day the intersection of the parallell of altitude with the parallell of declination sheweth the azimuth and a right line drawne from P through this intersectiō giueth the houre of the day 4 The Sphere may be proiected in plano by circular lines after the maner of the old concaue hemisphere by the help of the tangent on the side of the Sector For let the circle giuen represent the plane of the horizon let it be diuided into foure parts and crossed at right angles with SN the meridian and EV the verticall so as S may stand for the South N for the North E the East V the West part of the horizon and the center Z representeth the zenith Let each quarter of the horizon be diuided into 90 gr and so the whole into 360 gr beginning from N and setting to the numbers of 10. 20. 30. c. 90 at E 180 at S 270 at V 360 at N. The semidiameters ZN ZS may be diuided according to the tangent of halfe their arkes So as the arke from the zenith to the horizon being 90 gr and the halfe arke 45 gr the semidiameters are to be diuided in such sort as the tangent of 45 gr as
in the generall vse of the Sector concerning laterall and parallell entrance it may suffice onely to set downe the proportion of the three parts giuen to the fourth required and so I shew first by the sines alone In a rectangle triangle 1 To finde a side by knowing the base and the angle opposite to the required side As the Radius is to the sine of the base So the sine of the opposite angle to the sine of the side required As in the rectangle ACB hauing the base AB the place of the Sunne 30 gr from the equinoctiall point and the angle BAC of 23 gr 30 m. the greatest declination if it were required to find the side BC the declination of the Sunne Take either the laterall sine of 23 gr 30 m. and make it a parallell Radius so the parallell sine of 30 gr taken and measured in the side of the Sector shall giue the side required 11 gr 30 m. Or take the sine of 30 gr and make it a parallell Radius so the parallell sine of 23 gr 30 m. taken and measured in the laterall sines shall be 11 gr 30 m. as before So in the triangle ZPS hauing ZP 38 gr 30 m. and the angle P 31 gr 34 m. giuen we shall find the perpendicular Z R to be 19 gr 1 m or hauing PS 70 gr and the said angle P 31 gr 34 m. giuen we may finde the perpendicular SM to be 29 gr 28 m. 2 To finde a side by knowing the base and the other side As the sine of the complement of the side giuen is to the Radius So the sine of the complement of the base to the sine of the complement of the side required So in the rectangle ACB hauing AB 30 gr and BC 11 gr 30 m. giuen the side AC will be found 27 gr 54 m. Or in the rectangle ZRP hauing ZP 38 gr 30 m. and Z R 29 gr 1 m. giuen the side RP will be found 34 gr 7 m. 3 To find a side by knowing the two oblique angles As the sine of either angle to the sine of the complement of the other angle So is the Radius to the sine of the complement of the side opposite to the second angle So in the rectangle ACB hauing CAB for the first angle 23 gr 30 m. and ABC for the second 69 gr 21 m. the side AC will be found 27 gr 54 m. Or making ABC the first angle and CAB the second the side BC will be found 11 gr 30 m. 4 To finde the base by knowing both the sides As the Radius to the sine of the complement of the one side So the sine of the complement of the other side to the sine of the complement of the base required So in the rectangle ACB hauing AC 27 gr 54 m. and BC 11 gr 30 m. the base AB will be found 30 gr 5 To finde the base by knowing the one side and the angle opposite to that side As the sine of the angle giuen to the sine of the side giuen So is the Radius to the sine of the base required So in the rectangle BCD knowing the latitude and the declination we may find the amplitude as hauing BC the side of the declination 11 gr 30 m. and BDC the angle of the complement of the latitude 38 gr 15 m. the base BD which is the amplitude will be found to be 18 gr 47 m. 6 To find an angle by the other oblique angle and the side opposite to the inquired angle As the Radius to the sine of the complement of the side So the sine of the angle giuen to the sine of the complement of the angle required So in the rectangle ACB hauing the angle BAC 23 gr 30 m. and the side AC 27 gr 54 m. the angle ABC will be found 69 gr 21 m. 7 To finde an angle by the other oblique angle and the side opposite to the angle giuen As the sine of the complement of the side to the side of the complement of the angle giuen So is the Radius to the sine of the angle required So in the rectangle ACB hauing BAC 23 gr 30 m. and BC 11 gr 30 m. the angle ABC will be found 69 gr 21 m. 8 To finde an angle by the base and the side opposite to the inquired angle As the sine of the base is to the Radius So the sine of the side to the sine of the angle required So in the rectangle BCD hauing BD 18 gr 47 m. and BC 11 gr 30 m. the angle BDC will be found 38 gr 15 m. These eight Propositions haue been wrought by the sines alone those which follow require ioynt help of the tangent And forasmuch as the tangent could not well be extended beyond 63 gr 30 m. I shall set downe two wayes for the resolution of each Proposition if the one will not hold the other may 9 To finde a side by hauing the other side and the angle opposite to the inquired sine 1 As the Radius to the sine of the side giuen So the tangent of the angle to the tangent of the side required 2 As the sine of the side giuen is to the Radius So the tangent of the complement of the angle to the tangent of the complement of the side required So in the rectangle ACB hauing the right side AC 27 gr 54 m and the angle BAC 23 gr 30 m. the side BC will be sound to be 11 gr 30 m. 10 To find a side by hauing the other side and the angle adiacent next to the inquired side 1 As the tangent of the angle to the tangent of the side giuen So is the Radius to the sine of the side required 2 As the tangent of the complement of the side to the tangent of the complement of the angle So is the Radius to the sine of the side required This and the like where the tangent standeth in the first place are best wrought by parallell entrance And so in the rectangle BCD hauing BC the side of declination 11 gr 30 m. and BDC the angle of the complement of the latitude 38 gr 15 m. the side DC which is the ascensionall difference will be found 14 gr 57 m. By the ascensionall difference is giuen the time of the Sunnes rising and setting and length of the day allowing an houre for each 15 gr and 4 minutes of time for each seuerall degree As in the example the difference betweene the Sunnes ascension in a right sphere which is alwayes at 6 of the clocke and his ascension in our latitude being 14 gr 57 m. it sheweth that the Sunne riseth very neare an houre before 6 because of the Northerne declination or after 6 if the Sunne be declining to the Southward 11 To finde a side by knowing the base and the angle adiacent next to the inquired side 1 As the Radius to
and Azimuth CHAP. I. Of the description of the Quadrant HAuing described these standing planes I will now shew the most of these conclusions by a small Quadrant This might be done generally for all latitudes by a quarter of the generall Astrolabe described before in the vse of the Sector pag. 58 and particularly for any one latitude by a quarter of the particular Astrolabe there also described pag. 63. which if it be a foote semidiameter may shew the azimuth vnto a degree and the time of the day vnto a minute but for ordinary vse this smaller Quadrant may suffice which may be made portable in this maner 1 Vpon the center A and semidiameter AB describe the arke BC the same semidiameter will set of 60 gr and the halfe of that will be 30 gr which being added to the former 60 gr will make the arke BC to be 90 gr the fourth part of the whole circle and thence comes the name of a Quadrant 2 Leauing some little space for the inscription of the moneths and dayes on the same center A and semidiameter AT describe the arke TD which shall serue for either tropique 3 Diuide the line AT in the point E in such proportion as that AT being 10000 AE may be 6556 and there draw another arke EF which shall serue for the Equator 5 This part of the ecliptique may be diuided into three Signes and each Signe into 30 A Table of right Ascensions Gr. ♈ ♉ ♊ Gr. M. Gr. M. Gr. M. 0 0 0 27 54 57 48 5 4 35 32 42 63 3 10 9 11 37 35 68 21 15 13 48 42 31 73 43 20 18 27 47 33 79 7 25 23 9 52 38 84 32 30 27 54 57 48 90 0 gr by a table of right ascensions made as before pag. 60. As the right ascension of the first point of ♉ being 27 gr 54 m. you may lay a ruler to the center A 27 gr 54 m. in the Quadrant BC the point where the ruler crosseth the Ecliptique shall be the first point of ♉ In like maner the right ascension of the first point of ♊ being 57 gr 48 m. if you lay a ruler to the Gr. Parts 1 176 2 355 3 537 4 723 5 913 6 1106 7 1302 8 1503 9 1708 10 1917 11 2130 12 2348 13 2571 14 2799 15 3032 16 3270 17 3514 18 3763 19 4019 20 4281 21 4550 22 4825 23 5108 Tro 5252 center A and 57 gr 48 m. in the quadrant the point where the ruler crosseth the ecliptique shal be the first point of ♊ And so for the rest but the lines of distinction between Signe Signe may be best drawne from the center G. 6 The line ET betweene the equator and the tropique which I call the line of declination may be diuided into 23 gr ½ out of this Table For let AE the semidiameter of the equator be 10000 the distance betweene the equator and 10 gr of declination may be 1917 more between the equator and 20 gr 4281 the distance of the tropique from the equator 5252. 7 You may put in the most of the principall starres betweene the equator and the tropique of ♋ by their declination from the equator and right ascention from the next equinoctial point As the declination of the wing of Pegasus being 13 gr 7 m. the right ascension 358 gr 34 m. from the first point of ♈ or 1 gr 26 m. short of it If you draw an occult parallell through 13 gr 7 m. of declination and then lay the ruler to the center A and 1 gr 26 m. in the quadrant BC the point where the ruler crosseth the parallell shall be the place for the wing of Pegasus to which you may set the name and the time when he cometh to the South in this maner W. Peg. * 23 Ho. 54 M. and so for the rest of these fiue or any other starres  Ho. M. R. Ascen Decl. M Pegasus wing * 23 54 1 26 13 7 Arcturus * 13 58 29 37 21 10 Lions heart * 9 48 32 58 13 45 Buls eye * 4 15 63 33 15 42 Vultures heart * 19 33 66 56 7 58 8 There being space sufficient between the equator and the center you may there describe the quadrat and diuide each of the two sides farthest frō the center A into 100 parts so shall the Quadrant be prepared generally for any latitude But before you draw the particular lines you are to fit foure tables vnto your latitude First a table of meridian altitudes for diuision of the circle of dayes and moneths which may be thus made Consider the latitude of the place and the declination of the Sun for each day of the yeare If the latitude and declination be alike both North or both South ad the declinatiō to the complement of the latitude if they be vnlike one North and the other South substract the declination from the complement of the latitude the remainder will be the meridian altitude belonging vnto the day Thus in our latitude of 51 gr 30 m. Northward whose complement is 38 gr 30 m. the declination vpon the tenth day of Iune will be 23 gr 30 m. Northward wherefore I adde 23 gr 30 m. vnto 38 gr 30 m. the summe of both is 62 gr for the meridian altitude at the tenth of Iune The declination vpon the tenth of December will be 23 gr 30 m. Southward wherefore I take these 23 gr 30 m. out of 38 gr 30 m. there wil remain 15 gr for the meridian altitude at the tenth of December and in this maner you may find the meridian altitude for each day of the yeare and set them downe in a table Dies 0 5 10 15 20 25 30 Mo Gr. M Gr. M. Gr. M Gr. M. Gr. M. Gr. M Gr. M. Ianuary 16 31 17 24 18 26 19 37 20 57 22 24 23 58 February 24 17 25 59 27 45 29 35 31 29 33 25  March 34 35 36 33 38 32 40 30 42 27 44 22 46 15 April 46 37 48 26 50 11 51 50 53 25 54 53 56 15 May 56 15 57 29 58 35 59 33 60 22 61 2 61 31 Iune 61 36 61 54 62 0 61 58 61 45 61 22 60 49 Iuly 60 49 60 6 59 14 58 13 57 4 55 48 54 24 August 54 7 52 36 50 59 49 17 47 31 45 41 43 49 September 43 26 41 30 39 33 37 36 35 38 33 41 31 46 October 31 46 29 53 28 3 26 16 24 35 22 59 21 29 Nouember 21 12 19 51 18 39 17 36 16 43 16 0 15 28 December 15 28 15 7 15 0 15 2 15 17 15 44 16 22 The Table being made you may inscribe the moneths and dayes of each moneth into your quadrant in the space left below the tropique For lay the ruler vnto the center A and 16 gr 31 m. in the quadrant BC there may you draw a line for the end of December and beginning of
is here represented by the arke figured with these letters I F M A M c. signifying the moneths Ianuary February March April c. each moneth being diuided vnequally according to the number of the dayes that are therein 1 The day of the moneth being giuen to find the altitude of the Sunne at noone Let the thread be laid to the day of the moneth and the degrees which it cutteth in the Quadrant shall be the meridian altitude required As if the day giuen be the 15 of May the thread laid on this day shall cut 59 gr 30 m. in the quadrant which is the meridian altitude required 2 The meridian altitude being giuen to finde the day of the moneth The thread being set to the meridian altitude doth also fall on the day of the moneth As if the altitude at noone be 59 gr 30 m. the thread being set to this altitude doth fal on the 15 day of May and the 9 of Iuly and which of these two is the true day may be knowne by the quarter of the yeare or by another dayes obseruation For if the altitude proue greater the thread wil fall on the 16 day of May and the 8 of Iuly or if it proue lesser the thread will fall on the 14 of May and the 10 of Iuly whereby the question is fully answered CHAP. VI. Of the Houre-lines THat arke which is drawne vpon the center of the quadrant by the beginning of declination doth here represent the equator that arke which is drawne by 23 gr 30 m. of declination and is next aboue the circle of moneths and dayes representeth the tropiques those lines which are betweene the equator and the tropiques being vndiuided and numbred at the equator by 6. 7. 8. 9. 10. 11. 12. at the tropique by 1. 2. 3. 4. c. do represent the houre-circles that which is drawne from 12 in the equator to the middle of Iune representeth the houre of 12 at noone in the Summer and those which are drawn with it to the right hand are for the houres of the day in the Summer and the houres of the night in the Winter That which is drawne from 12 in the equator to the middle of December representeth the houre of 12 in the Winter and those which are drawne with it to the left hand are for the houres of the day in the Winter and the houres of the night in the Summer and of both these that which is drawne from 11 to 1 serues for 11 in the forenoone and 1 in the afternoon That which is drawne frō 10 to 2 serues for 10 in the forenoon 2 in the afternoon for the Sun on the same day is about the same height two houres before noon as two houres after noone The like reason holdeth for the rest of the houres 1 The day of the moneth or the height at noone being knowne to finde the place of the Sunne in the Ecliptique The thread being laid to the day of the moneth or the height at noone for one giues the other by the former proposition marke where it crosseth the houre of 12 and set the bead to that intersection then moue the thread till the bead fall on the ecliptique and it shall fall on the place of the Sun As if the day giuen be the 15 of May or the meridian altitude 59 gr 30 m. lay the thread accordingly and put the bead to the intersection of the thread with the houre of 12 then moue the thread till the bead fall on the ecliptique and it shall there shew the fourth of ♊ the fourth of ♠the 26 of ♋ and the 26 of ♑ and which of these is the place of the Sunne may appeare by the quarter of the yeare or another dayes obseruation 2 The place of the Sun in the Ecliptique being knowne to finde the day of the moneth c. Let the thread and beade be first laid on the place of the Sunne in the Ecliptique and then moued to the line of 12. As if the place of the Sunne giuen be the fourth of ♊ the bead being laid to this degree and then moued to the houre of 12 in the Summer the thread will fall on the 15 day of May and the 9 of Iuly or if it be moued to the houre of 12 in the Winter the thread wil sall on the 6 of Ianuary and the 16 of Nouember which of these is the day of the moneth required may appeare by the quarter of the yeare In this and the former propositions you haue two wayes to rectifie the bead by the place of the Sunne and by the day of the moneth the better way is by the place of the Sunne for in the other the Leap-yeare may breed some small difference There is yet a third way For the Sea-men hauing a table for the declination on each day of the yeare may set the bead thereto in the line of declination 3 The houre of the day being giuen to find the altitude of the Sunne aboue the horizon The bead being set for the time by either of the three ways let the thread be moued from the houre of 12 toward the line of declination till the bead fall on the houre giuen and the degrees which it cuts in the Quadrant shall shew the altitude of the Sunne at that time As if the time giuen be the tenth of April the Sunne being then in the beginning of ♉ the bead being rectified you shall finde the height at noone 50 gr 0 m. at 11 in the morning 48 gr 12 m. at 10 but 43 gr 12 m. at 9 but 36 gr at 8 but 27 gr 30 m. at 7 but 18 gr 18 m. at 6 but 9 gr at 5 it meeteth with the line of declination and hath no altitude at all and therefore you may think it did rise much about that houre Then if you moue the thread again from the line of declination toward the houre of 12 you shal find that the Sun is 8 gr 33 m. below the horizon at 4 in the morning neare 16 gr at 3 and 21 gr 51 m. at 2 and 25 gr 40 m. at 1 and 27 gr at midnight 4 The altitude of the Sunne being giuen to finde the houre of the day The altitude being obserued as before let the bead be set for the time then bring the thread to the altitude so the bead shall shew the houre of the day As if the 10 of April hauing set the bead for the time you shall finde by the quadrant the altitude to be 36 gr the bead at the same time will fall vpon the houre-line of 9 and 3 wherefore the houre is 9 in the forenoone or 3 in the afternoone If the altitude be neare 40 gr you shall find the bead at the same time to fall halfe way betweene the houre-line of 9 and 3 and the houre-line of 10 and 2 wherefore it must be either halfe an houre past 9 in the morning or halfe an
houre past 2 in the afternoone and which of these is the true time of the day may be soone knowne by a second obseruation for if the Sunne rise higher it is the forenoone if it become lower it is the afternoone 5 The houre of the night being giuen to find how much the Sunne is below the horizon The Sunne is alwayes so much below the horizon at any houre of the night as his opposite point is aboue the horizon at the like houre of the day and therefore the beade being set if the question be made of any houre of the night in the Summer then moue it to the like houre of the day in the Winter if of any houre of the night in Winter then moue it to the like houre of the day in Summer so the degrees which the thread cutteth in the Quadrant shall shew how much the Sunne is below the horizon at that time As if it be required to know how much the Sunne is below the horizon the 10 of April at 4 of the clock in the morning the bead being set to his place according to the time in the Summer houres bring it to 4 of the clocke in the afternoone in the Winter houres and so shall you finde the thread to cut 8 gr and about 30 m. in the quadrant and so much is the Sunne below the horizon at that time 6 The depression of the Sunne supposed to giue the houre of the night with vs or the houre of the day to our Antipodes Here also because the Sun is so much aboue the horizon at all houres of the day as his opposite point is below the horizon at the like houre of the night therefore first set the bead according to the time then bring the thread to the degree of the Suns depression below the horizon so shall the bead fall on the contrary houre-lines and there shew the houre of the night in regard of vs which is the like houre of the day to our Antipodes As if the 10 of April the Sunne being then in the beginning of ♉ and by supposition 8 gr 30 m. below the horizon in the East it be required to know what time of the night it is first set the bead according to the day in the Summer houres then bring the thread to 8 gr 30 m. in the quadrant so shall the bead fall among the Winter houres on the line of 4 of the clocke in the afternoone wherefore to our Antipodes it is 4 of the clocke in their afternoone and to vs it is then 4 of the clocke in the morning 7 The time of the yeare or the place of the Sunne being giuen to find the beginning of day-breake and end of twi-light This proposition differeth little from the former for the day is said to begin to breake when the Sun cometh to be but 18 gr below our horizon in the East and twi-light to end when it is gotten 18 gr below the horizon in the West wherefore let the bead be set for the time and then bring the thread to 18 gr in the quadrant so shall the bead fall on the contrary houre-lines and there shew the houre of twilight as before So if it be required to know at what time the day begins to breake on the tenth of April the Sun being then in the beginning of ♉ first set the bead according to the time in the Summer houres and then bring the thread to 18 gr in the quadrant so shall the bead fall among the Winter houres a little more then a quarter before 3 in the morning and that is the time when the day begins to break vpon the tenth of April CHAP. VII Of the Horizon THe Horizon is here represented by the arke drawne from the beginning of declination towards the end of February diuided vnequally and numbred by 10. 20. 30. 40. 1 The day of the moneth or the place of the Sunne being knowne to finde the amplitude of the Sunnes rising and setting Let the bead rectified for the time be brought to the horizon and there it shall shew the amplitude required As if the day giuen be the 15 of May the Sunne being in the fourth degree of ♊ the bead rectified and brought to the horizon shall there fall on 35 gr 8 m. such is the amplitude of the Sunnes rising from the East and of his setting from the West which amplitude is alwayes Northward when the Sunne is in the Northerne Signes and when he is in the Southward Signes alwayes Southward 2 The day of the moneth or the place of the Sunne being giuen to finde the ascensionall difference Let the bead rectified for the time be brought to the horizon so the degrees cut by the thread in the quadrant shall shew the difference of ascensions As if the day giuen be the 15 of May the Sunne being in the fourth degree of ♊ let the bead be rectified and brought to the horizon so shall the thread in the quadrant shew the ascensionall difference to be 28 gr and about 50 m. Vpon the ascensionall difference depends this Corollarie To find the houre of the rising and setting of the Sun and thereby the length of the day and night The time of the Sunnes rising may be guessed at by the 3 of the last Cap. but here by the ascensionall difference it may be better found and that to a minute of time For if the ascensionall difference be conuerted into time allowing an houre for 15 gr and 4 minutes of an houre for each degree it sheweth how long the Sunne riseth before six of the clock in the Summer and after six in the Winter As if the day giuen be the 15 of May the Sunne being in the fourth of ♊ and his ascensionall difference found as before 28 gr 50 m this conuerted into time maketh 1 ho. and somewhat more then 55 m. of an houre wherefore the Sun at that time in regard it was Summer rose 1 ho. and full 55 m. before 6 of the clocke and so hauing the quantitie of the semidiurnall arke the length of the day and night need not be vnknowne CHAP. VIII Of the fiue Starres I Might haue put in more Starres but these may suffice for the finding of the houre of the night at all times of the yeare and first I make choice of Ala Pegasi a starre in the extremitie of the wing of Pegasus in regard it wants but 6 minutes of time of the beginning of ♈ but because it is but of the second magnitude and not alwayes to be seene I made choice of foure more one for each quarter of the Ecliptique as of Oculus ♉ the Buls eye whose right ascension conuerted into time is 4 ho. 15 m then of Cor ♌ the Lions heart whose right ascension is 9 ho. 48 m next of Arcturus whose right ascension is 13 H. 58 m and lastly of Aquila or the Vultures heart whose right ascension is 19 H. 33 m. These fiue starres haue all of
L These questions well considered and either resolued by the Staffe or pricked downe on the chart and compared with the globe and the common Sea-chart will giue some light to the direction of a course and reduction of places to their due longitude which are now fouly distorted in the common Sea-charts An Appendix concerning The description and vse of an instrument made in forme of a Crosse-bow for the more easie finding of the latitude at Sea THe former Prop. suppose the latitude to be knowne I will here shew how it may be easily obserued Vpon the center A and semidiameter AB describe an ark of a circle SBN. The same semidiameter will set of 60 gr from B vnto S for the South end and other 60 gr from B vnto N for the North end of the Bow so the whole Bow will containe 120 gr the third part of a circle Let it therefore be diuided into so many degrees and each degree subdiuided into six parts that each part may be ten minutes but let the numbers set to it be 5. 10. 15. vnto 90 gr and then againe 5. 10. 15. vnto 25. that 55 may fall in the middle as in this figure The Bow being thus diuided and numbred you may seâ— the moneths and dayes of each moneth vpon the backe and such starres as are fit for obseruation vpon the side of the Bow If you desire to make vse of it in North latitude you may number 23 gr 30 m. from 90 towards the end of the Bowe at N and there place the tenth day of Iune And 23 gr 30 m. from 90 toward S and there at 66 gr 30 m. place the tenth day of December And so the rest of the dayes of the yeare according to the declination of the Sunne at the same dayes The starres may be placed in like maner according to their declinations Arcturus at 21 gr 10 m. The Buls eye 15 42 The Lions heart 13 45 The Vultures heart 7 58 The little dog 6 9 from 90 toward the North end of the Bow at N. Then for Southerne starres you may number their declination from 90 toward the South end of the Bow at S. As first the three starres in Orions girdle The first at 0 gr 37 m. The second 1 28 The third 2 11 The Hydra's heart 7 5 The virgins spike 9 10 The great dog 16 12 The Scorpions heart 25 30 Fomahant 31 30 And so the South crowne the triangle the clouds the crosiers or what other starres you think fit for obseruation This I call the fore side of the Bow If you desire to make vse of it in South latitude you may turne the Bow and diuide the backe side of it and number it in like maner and then put on the moneths and dayes of the yeare placing the tenth of December at the South end and the tenth of Iune toward the middle of the Bow and the rest of the dayes according to the Sunnes declination as before The chiefest of the Northâ—rne starres may here be placed in like maner according to their declination Anno 1625. The pole starre at 87 gr 20 m. The first guard 75 45 The second guard 73 25 The great Beares backe 63 45 In the great Beares taile first second third 58 2 57 55 51 15 The side of Perseus 48 28 The goate 45 33 The taile of the swan 44 0 The head of Medusa 39 30 The harp 38 30 Castor 32 38 Pollux 28 52 The North crowne 28 0 The Rams head 21 40 Arcturus 21 10 The Buls eye 15 42 The Lions heart 13 45 The Vultures heart 7 58 Orions right shoulder 7 17 Orions left shoulder 5 57 And so any other starre whose declination is knowne vnto you which being done The vse of this Bow may be 1 The day of the moneth being knowne to finde the declination of the Sunne 2 The declination being giuen to finde the day of the moneth These two Prop. depend on the making of the Bow If the day be knowne looke it out in the backe of the Bow so the declination will appeare in the side Or if the declination be knowne the day of the moneth is set ouer against it As if the day of the moneth were the 14 of Iuly looke for this day in the backe of the Bow and you shall find it ouer against 20 gr of North declination If the declination giuen be 20 gr to the Southward you shal find the day to be either the eleuenth of Nouember or the eleuenth of Ianuary 3 To find the altitude of the Sunne or starres Here it is fit to haue two running sights which may be easily moued on the backe of the Bow The vpper sight may be set either to 60 gr or to 70 gr or to 80 gr as you shall find to be most conuenient the other sight may be set on to any place betweene the middle and the other end of the Bow Then with the one hand hold the center of the Bow to your eye so as you may see the Sunne or starre by the vpper sight and with the other hand moue the lower sight vp or downe vntill you haue brought one of the edges of it to be euen with the horizon as when you obserue with the Crosse-staffe so the degrees contained betweene that edge and the vpper sight shall shew the altitude required Thus if the vpper sight shal be at 80 gr and the lower sight at 50 gr the altitude required is 30 gr 4 To find any North latitude by knowing either the day of the moneth or the declination of the Sunne As oft as you are to obserue in North latitude place both the sights on the foreside of the Bow the vpper sight to the declination of the Sunne or the day of the moneth at the North end and the lower sight toward the South end Then when the Sunne cometh to the meridian turne your face to the South and with the one hand hold the center of the Bow to your eye so as you may see the Sunne by the vpper sight with the other hand moue the lower sight vntill you haue brought one of the edges of it to be euen with the horizon so that edge of the lower sight shall shew the latitude of the place in the fore side of the Bow Thus being in North latitude vpon the ninth of October if I set the vpper sight to this day at the fore side and North end of the Bow I shall find it to fall to the Southward of 90 vpon 80 gr and therefore at 10 gr of South declination Then the Sunne coming to the meridian I may set the center of the Bow to mine eye as if I went to find the altitude of the Sunne holding the North end of the Bow vpward with the vpper sight betweene mine eye and the Sunne and mouing the lower sight vntill it come to be euen with the horizon If here the lower sight shall stay aâ— 50 gr I may well say that
the houre of 4 after noone was found before to be 51 gr 30 m if you would find the distance between the center and the equator extend the compasses frō the sine of 51 gr 30 m. vnto the sine of 90 gr the complement of the declination the same extent will reach in the line of numbers from 12 vnto 15.33 and such is the distance vpon the houre-line of 4 between the center and the equator If you would finde the distance vpon this houre-line between the center and the inner tropique whose declination is knowne to be 23 gr 30 m. adde the declination to the angle at the equator so the angle at the parallell wil be 75 gr wherefore extend the compasses from the sine of 75 gr vnto the sine of 66 gr 30 m. the complement of the declination the same extent will reach in the line of numbers from 12 vnto 11.40 and such is the length of the houre-line of 4 betweene the center and the tropique of ♑ If you would finde the distance vpon this houre-line between this center and the tropique of ♋ which is here the farthest from the center take the declination out of the angle at the equator so the angle at the parallell will be 28 gr vnto wherefore extend the compasses from the sine of 28 gr vnto the sine of 66 gr 30 m. the same extent will reach in the line of numbers from 12 vnto 23.44 and such is the distance betweene the center and the tropique of ♋ vpon this houre-line of 4. The like reason holdeth for all the rest which may be gathered and set downe in a table That done and the equator drawne as before if you would draw the tropique of ♋ looke into the table and there finding vnder the title C ♋ the distance of the substylar between the center and the parallel of ♋ to be 20 inch 80 cent take 20 inch 80 cent out of the line of inches and prick them downe in the substylar of your plane from C vnto ♋ Or if either the center fall without your plane or the extent be too large for your compasses you may pricke downe the difference betweene C ♈ and C ♋ As here the distance C ♈ between the center the equator is 14.57 the distance C ♋ 20.80 the differēce 6.23 therfore taking 6 inch 23 cent pricke them downe on the substylar from ♈ vnto ♋ and you shall haue the same intersection of the tropique and the substylar as before the like reason holdeth for pricking down of the rest of these distances on their seuerall houre-lines Then hauing the points of intersection betweene the houre-lines and the parallell you may ioyne them all in a crooked line without making of any angles the line so drawne shall be the tropique required And after this maner may you draw any other parallell of declination whereof you haue examples in the most of the former Diagrams CHAP. XIIII To describe the parallels of the Signes in any of the former Planes THe equator and the tropiques before described do shew the Suns entrance into 4 of the Signes the equator into ♈ and ♎ the one tropique into ♋ and the other into ♑ the rest of the intermediate Signes will be described in the same maner as the tropiques if first we know their declination The maner of finding the declination not onely of the beginning of the Signes but of all other points of the ecliptique is before set downe in 2. Prop. Astronomicall pag. 52. by which you may finde the declination of the beginning of ♉ ♠♠and ♓ to be 11 gr 30 m. and of ♊ ♌ ♠and ♒ to be 20 gr 12 m. If then you inscribe the chords of 11 gr 30 m. and of 20 gr 12 m. into the former figure BDT Pag. 145. from D toward T the lines drawne from B through the termes of those chords shall be the Signes required And with these declinations the height of the style and the length of the axis you may finde the angles at the parallell and then the distances between the center and the parallell which being pricked downe vpon their seuerall houre-lines shall giue you the points of intersection by which you may draw the parallels of the Signes as in the figures belonging to the polar planes CHAP. XV. To describe the parallels of the length of the day in any of the former Planes THe length of the day will alwayes be 12 houres long when the Sunne cometh to be in the equator and this holdeth in all latitudes but at other times of the yeare the same place of the Sunne wil not giue the same length of the day in another latitude wherefore the latitude being known we are first To find the declination of the Sunne agreeing to the length of the day Consider the difference betweene the length of an equinoctiall day and the day proposed and turne the time into degrees and minutes As the sine of 90 gr is to the sine of halfe the difference So the cotangent of the latitude to the tangent of the declination If then you inscribe the chords of these arks into the former figure BDT the lines drawne from B through the termes of these arks shall be the lines belonging to the diurnall arkes and the seuerall distances betweene them and the point C giue the like distances betweene the center and the parallels of the length of the day vpon the houre-lines in your plane CHAP. XVI To draw the old vnequall houres in the former Planes IT was the maner of the Ancients to divide the day into twelue equall houres and the night into twelue other equal houres and so the whole day and night into 24 houres Of these 24 those which belonged vnto the day were either longer or shorter excepting the two equinoctial dayes then those which belonged vnto the night and the Summer houres alwayes longer then the houres in the Winter according to the lengthening of the dayes whereupon they are called the old vnequall and by some the Planetary houres To expresse these in the former Planes first draw the common houre-lines the equator and the tropiques as before then describe two occult parallels of the length of the day one for 9 houres the other for 15 houres for so you may draw a streight line for the first vnequall houre through 5 ho. 45 m. in the parallell of 15 and through 8 ho. 15 m. in the parallel of 9. This streight line shal passe directly through 7 ho. 0 m. in the equator and so cut off a twelfth part of the arks aboue the horizon both from these two parallels and the equator and being continued vnto the tropiques it shall also cut off about a twelfth part from them and all the rest of the parallels of declination without any sensible error In like maner may you draw the second vnequall houre through 7 ho. in the parallell of 15 through 8 ho. in the equator