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 latitude is 50 gr For the meridian altitude of the Sunne is 30 gr by the last Prop. and the Sun hauing 10 gr of South declination the meridian altitude of the equator would be 40 gr and therefore the obseruation was made in 50 gr of North latitude By the same reason if the lower side had stayed at 51 gr 30 m. the latitude must haue been 51 gr 30 m. and so in the rest 5 To find any North latitude by the meridian altitude of the starres to the Southward Let the vpper sight be set to the starre which you intend to obserue here placed in the fore side of the Bow Then hold the North end of the Bow vpward and turning your face to the South obserue the meridian altitude as before so the lower sight shall shew the latitude of the place in the fore side of the Bow Thus if in obseruing the meridian altitude of the great Dog-starre the lower sight shall stay at 50 gr it would shew the latitude to be 50 gr For this starre being here placed at 73 gr 48 m. if we take thence 50 gr his meridian altitude would be 23 gr 48 m. to this if we adde 16 gr 12 m. for the South declination of this starre it would shew the meridian altitude of the equator to be 40 gr and therefore the latitude to be 50 gr 6 To find any North latitude by the meridian altitude of the starres to the Northward Let the vpper sight be set to the starre which you intend to obserue here placed on the backe side of the Bow Then hold the North end of the Bow vpward and turning your face to the North obserue the altitude of the starre when he cometh to be in the meridian and vnder the pole so the lower sight shall shew the altitude of the pole in the back side of the Bow Thus the former guard coming to be in the meridian vnder the pole if you obserue and find the lower sight to stay at 50 gr such is the eleuation of the pole and the latitude of the place to the Northward For the distance betweene the two sights will shew the altitude to be 35 gr 45 m. the star is 14 gr 15 m. distant from the North pole These two doe make vp 50 gr for the eleuation of the North-pole and therefore such is the North latitude 7 To find any South latitude by knowing either the day of the moneth or the declination of the Sunne When you are come into South latitude turne both your sights to the backside of the Bow the vpper sight to the declination of the Sun or the day of the moneth at the South end and the lower sight toward the North end of the Bow Then the Sunne coming to the meridian turne your face to the North and holding the South end of the Bow vpward obserue the meridian altitude as before so the lower sight shall shew the latitude of the place in the backe side of the Bow Thus being in South latitude vpon the tenth of May if you obserue and finde the lower sight to stay at 30 gr on the backe side of the Bow such is the latitude For the declination is 20 gr Northward the altitude of the Sunne betweene the two sights 40 gr the altitude of the equator 60 gr and therefore the latitude 30 gr 8 To find any South latitude by the meridian altitude of the starres to the Northward Let the vpper sight be set to the starre which you intend to obserue here placed on the backe side of the Bow Then hold the South end of the Bow vpward and turning your face to the North obserue the meridian altitude as before so the lower sight shall shew the latitude of the place in the back side of the Bow Thus being in South latitude and the former guard comming to be in the meridian ouer the pole If you obserue and finde the lower sight to stay at 5 gr such is the latitude For this starre is 14 gr 15 m. from the North pole the altitude of the starre betweene the two sights 9 gr 15 m. the North pole depressed 5 gr and therefore the latitude 5 gr to the Southward 9 To obserue the altitude of the Sunne backward Set the vpper sight either to 60 or 70 or 80 gr as you shall find it to be most conuenient the lower sight on any place betweene the middle and the other end of the Bow and haue an horizontall sight to be set to the center Then may you turne your backe to the Sunne and the back of the Bow toward your selfe looking by the lower sight through the horizontall sight and mouing the lower sight vp downe vntill the vpper sight doe cast a shadow vpon the middle of the horizontall sight so the degrees contained betweene the two sights on the Bow shall giue the altitude required Thus if the vpper sight shall be at 80 gr and the lower sight at 50 gr the altitude required is 30 gr as in the third Prop. 10 To find any North latitude by a backe obseruation knowing either the day of the moneth or the declination of the Sunne When you obserue in North latitude place your three sights on the fore side of the Bow the vpper sight to the declination of the Sun or the day of the moneth at the North end the lower sight toward the South end of the Bow and the horizontall sight to the center Then the Sunne coming to the meridian turne your face to the North holding the North end of the Bow vpward the South end downeward with the back of it toward your selfe obsâ—rue the shadow of the vpper sight as in the former Prop. so 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 you obserue and find the lower sight to stay at 50 gr on the fore side of the Bow such is the latitude For the declination is 10 â—r Southward and the altitude of the Sunne betweene the two sights 30 gr the altitude of the equator 40 gr and â—herefore the latitude 50 gr as in the fourth Prop. 11 To find any South latitude by a back obseruation knowing either the day of the moneth or the declination of the Sunne When you obserue in South latitude place your three sights on the backe side of the Bow the vpper sight to the declination of the Sunne or the day of the moneth at the South end the lower sight towarâ— the North end of the Bow and the horizontall sight to the câ—nter Then the Sun coming to the meridian turne your face to the South and holding the South end of the Bow vpward with the backe of it toward your selfe obserue the shadow of the vpper sight as before so the lower sight shal shew the latitude of the place in the back side of the Bow Thus being in the South latitude vpon the tenth
of May if you obserue and find the lower sight to stay at 30 gr on the â—ledgeâ—acke of the Bow such is the altitude For the declination â—ledgeâ— 20 gr Northward the altitude of the Sunne betweene the â—ledgeâ—wo sights 40 gr the altitude of the equator 60 gr and thereâ—ledgeâ—re the latitude 30 gr as in the seuenth Prop. 12 To find the day of the moneth by knowing the latitude of the place and obseruing the meridian altitude of the Sunne Place your three sights according to your latitude the hoâ—ledgeâ—zontall sight to the center the lower sight to the latitude â—ledgeâ—d the vpper sight among the moneths Then when the â—ledgeâ—nne cometh to the meridian obserue the altitude looking â—ledgeâ— the lower sight through the horizontall and keeping the â—ledgeâ—wer sight still at the latitude but mouing the vpper sight â—ledgeâ—til it giue shadow vpon the middle of the horizontal sight â—ledgeâ— the vpper sight shall shew the day of the moneth requiâ—ledgeâ—d Thus in our latitude if you set the lower sight to 51 gr 30 â—ledgeâ— and obseruing finde the altitude of the Sunne betweene â—ledgeâ—at and the vpper sight to be 28 gr 30 m. this vpper sight â—ledgeâ—ll â—all vpon the ninth of October and the twelfth of Feâ—ledgeâ—uarâ—e And if yet you doubt which oâ— them two is the day â—ledgeâ—u may expect another meridian altitude and then if you â—ledgeâ—d the vpper sight vpon the tenth of October and the eleâ—ledgeâ—nth of Februarie the question will be soone resolued 13 To find the declination of any vnknowne starre and so to place it on the Bow by knowing the latitude of the place and obseruing the Meridian altitude of the Starre When you find a starre in the Meridian that is fit for obâ—ledgeâ—uation Set the center of the Bow to your eye the lower â—ledgeâ—ht to the latitude and moue the vpper sight vp or downe â—ledgeâ—till you see the horizon by the lower sight and the starre by the vpper sight then will the vpper sight stay at the declination and place of the starre Thus being in 20 gr of North latitude if you obserue anâ—redgeâ— find the meridian altitude of the head of the Crosier to bâ—redgeâ— 14 gr 50 m. The vpper sight will stay at 34 gr 50 m. and therâ—redgeâ— may you place this starre For by this obseruatioÌ„ the distance oâ—redgeâ— this starre from the South pole should be 34 gr 50 m. and thâ—redgeâ— declination from the equator 55 gr 10 m. And so for the resâ—redgeâ— The starres which I mâ—ntioneâ— beâ—â—re do come to the meridian in this order after the first point of Aries  Ho. Mi. The pole starre at 0 29 The rams head 1 46 The head of Medusa 2 44 The sidâ— of Perseus 2 58 The Buls eye 4 15 The goate 4 49 Orions left shoulder 5 5 Orions girdle the first the second the third 5 13 5 17 5 22 Orions right shoulder 5 35 The great dog 6 29 Castor 7 10 The little dog 7 20 Pollux 7 22 The Hydra's hart 9 9 The lions hart 9 48 The great beares backe 10 40 First in gr beares taile 12 37 The Virgins spike 13 5 Second in gr beaâ— taile 13 9 Third in gr beares taile 13 33 Arcturus 13 58 The formost gu rd 14 52 The North crowne 15 19 Thâ— hâ— dmost guard 15 25 Scorpions hart 16 7 The harpe 18 24 Vulturs hart 19 33 Swans taile 20 29 Fomahant 22 36 The end of the second Booke THE THIRD BOOKE Of the vse of the lines of Numbers Sines and Tangents for the drawing of Houre-lines on all sorts of Planes THere are ten seuerall sorts of Planes which take their denomination froÌ„ those great circles to which they are parallels and may sufficiently for our vse be represented in this one fundamentall Diagram described before in the vse of the Sector and be knowne by their horizontall and perpendicular lines of such as know the latitude of the place and the circles of the sphere 1 An horizontall plane parallell to the horizon here represented by the outward circle ESWN 2 A verticall plane parallell to the prime verticall circle which passeth through the zenith and the points of East and West in the horizon and is right to the horizon and the meridian that is maketh right angles with them both This is represented by EZW 3 A polar plane parallell to the circle of the houre of 6 which passeth through the pole and the points of East and West being right to the Equinoctiall and the Meridian but inclining to the horizon with an angle equall to the latitude This is here represented by EPW 4 An equinoctiall plane parallell to the Equinoctiall which passeth through the points of East and West being right to the Meridian but inclining to the Horizon with an angle equall to the complement of the latitude This is here represented by EAW 6 A meridian plane parallell to the meridian the circle of the houre of 12 which passeth through the zenith the pole and the points of South and North being right to the horizon and the prime verticall This is here represented by SZN 7 A meridian plane inclining to the horizon parallell to any great circle which passeth through the points of South and North being right to the prime verticall but inclining to the horizon This is here represented by SGN 8 A verticall declining plane parallell to any great circle which passeth through the zenith being right to the horizon but inclining to the meridian This is represented by BZD. 9 A polar declining plane parallell to any great circle which passeth through the pole being right to the equinoctiall but inclining to the meridian This is here represented by HPQ 10 A declining inclining plane parallell to any great circle which is right to none of the former circles but declining from the prime verticall and inclining both to the horizon and the meridian and all the houre circles This may be here represented either by BMD or BFD or BKD or any such great circle which passeth neither through the South and North nor East and West points nor through the zenith nor the pole Each of these planes except the horizontall hath two faces whereon houre-lines may be drawne and so there are 19 planes in all The meridian plane hath one face to the East and another to the West the other verticall planes haue one to the South and another to the North and the rest one to the zenith and another to the nadir but what is said of the one may be vnderstood of the other To find the inclination of any Plane For the distinguishing of these Planes we may finde whethâ—r they be horizontall or verticall or inclining to the horizon and how much they incline either by the vsuall inclinatorie quadrant or by fitting a thread and plummet vnto the Sector For let the Sector be opened to a right angle the lines of Sines to an angle of 92 gr the inward edges of the Sector to 90