Horizon of the world But this may be more accurately done if you place the backe of the Instrument downe upon an Horizontall plaine and the edge of the Index being at the degree of the suns Azimuth observed and the perpendicular erected at the end of the Index as before then moving the Instrument as it so lyeth untill the shadow of the perpendicular fall by the side of the Index so the Meridian of the Instrument shall be in the Meridian of the World and every point and degree in the Limbe of the Instrument shall point out and be opposite and represent his like degree in the Horizon of the world Constru ¦ ctio 39 But here note that this Construction serves only but for the forenoone observation for if the practice be in the afternone the way to finde the Meridian line may be thus Having found the suns Azimuth as before lay the Index upon the houre line of 12. and erect the perpendicular at the end thereof and move the Instrument about Circular untill the shadow of the said perpendicular fall by the side of the Index for then if the edge of the Index be moved unto the suns Azimuth before known the edge of the Index shall represent the Meridian line 90. gr farther shall be the point of East and the Center of the Instrument the point of West therefore if upon the plaine that the Instrument lies upon you make a marke at the edge of the Index which is in the Meridian as before and another marke right under the Center and so place the North and South edge of the Instrument unto these two points then every degree in the Horizon or Limbe of the Instrument shall point out as before his opposite or â—ike degree in the Horizon of the world Fourthly how to finde the sit Pro. 30 of a Building or Costing of a place By the last Pro. finde out or draw the Meridian Constru ¦ ctio 40 line and place the North and South edge of the Instrument unto it if the Building or Place ly in the Easterne semicircle of the world but if it ly in the Westerne semicircle then let the East West edge of the Instrument be placed upon the Meridian line so the eye being over the Center of the Instrument and behoulding the place let the Index be moved untill it be also with the visual line observed by the eye that is opposite to the place so the edge of the Index from the Cardinall points of the Instrument in the Limbe viz. from the East or West North or South shall shew the bearing of that place from you in respect of the Cardinall points of the world in the Horizon but if two sights be placed at the Index which is according to the description thereof then may you observe the place through the sights of the Index by leting the Instrument rest and moving the Index to and fro untill you see the obiect so the edge of the Index in the limbe shall point out the bearing or Position of the place from you in degrees from the East West North or South accounting 11. gr and ¼ as often as you can in those degrees observed you have the point of the Compasse which the place or obiect beares from you Pro. 31 Fiftly to finde the suns Azimuth and houre without observation The Meridian line being drawne first upon a Constru ¦ ctio 41 plaine according to the former directions consider if it be in the forenoone or afternoone if in the forenoone then let the North and South edge of the Instrument be placed unto the Meridian line but if it be in the afternoone then set the edge of East West of the Instrument unto the Meridian line and let the Instrument rest there then erect the perpendicular at the end of the Index move the Index about untill the shadow of the perpendicular fall by the side of the Index so the edge of the Index will amongst the degrees in the Limbe shew the Suns Azimuth at that time and where the edge of the Index meeteth with the parallel of the day of the Month that is the houre of the day at that time But if the Axis be rectified then there is no neede of a Meridian line to be drawne for this Instrument will with great facilitie finde out his owne Meridian by moving it to and fro untill the shadow of the perpendicular which is ouer the Center of the Instrument intersect the same houre in the Parallel of the day of the Moneth that the Axis doth amongst the Common houres so that houre shall be the houre of the day for that instant and the shadow of the said perpendicular cutting the Limbe or extended unto it doth there shew the Suns Azimuth and so the Meridian of the Instrument at that position shal be in the Meridian of the world required Sixtly to finde the variation Pro. 32 of the needle By the twentie nineth Pro. vpon an even Plaine parallel to the Horizon draw the Meridian line Constru ¦ ctio 42 place the North South line of the Card directly over the said Meridian line so the Number of degrees that the Needle cutteth in the Card from the North and South line of the Card that shall be the variation of the Needle required otherwise it may be found thus Neere unto the Center of the Index upon the Index may a small Brosse pinne be so placed that it may be erected perpendicular to the Center of the Instrument and halfe an inch above it Let a Needle by placed upon this pinne then lay the East and West edge of the Instrument to the Meridian line when the Needle resteth move the Index untill the edge of it be directly under the Needle so the edge of the Index in the Limbe of the Instrument shall point out or shew the Needles variation required Pro. 33 Seventhly to finde the Latitude of a place or the Poles hight above the Horizon Constru ¦ ctio 43 First draw the Meridian line upon some plaine by helpe of the 38. Construction then erect the prependicular at the end of the Index and place the North and South edge of the Instrument to the Meridian line so drawne upon the plaine and move also the Index untill the edge thereof touch the houre of 12. let the Instrument rest at this position then marke diligently about noone or 12. of the Clocke when the shadow of the perpendicular doth fall by the edge of the Index for then the sun is in the Meridian at which time according to the 27. Pro. obserue or take the suns height which is his Meridian Altitude for that day and by the 3. Pro. finde the Suns declination agreeable to that day and adde it to the Suns Meridionall Altitude observe if it be South declination otherwise subtract it from the former Meridionall Altitude so have you the height of the Aequinoctial above the Horizon that taken from 90. gives the depression of
the South Pole under the Horizon which is alwayes equall to the elevation of the North Pole above the Horizon So if upon the tenth of Aprill Exam. the Meridian Altitude should be found to be 50. gr the Declination belonging to that day by the 3. Pro. is 11. gr and a halfe North which being subtracted according to the former directions leaves 38. gr 30. m the height of the Aequinoctiall above the Horizon that taken from 90. leaves 51. gr 30. m the depression of the South Pole under the Horizon or the elevation of the North Pole above the Horizon for the height of the Aequinoctiall knowne the Complement thereof is alwayes the Latitude of the place or height of the Pole and here note generally that the height of the Pole and Aequinoctiall together doe alwayes make a Quadrant or 90. gr therefore the height of one of them being knowne the height of the other is also knowne and further here note that if the sun have North Declination the sun is so much higher then the Aequinoctiall at none that day by so much as his Declination cometh to but if the Sun have South Declination then the Sun is lower then the Aequinoctiall that day at noone by so much as his Declination cometh to by which you may easily gether when to adde or subtract the suns Declination to or from the suns Meridianall Altitude to get the height of Aequator which knowne the Poles height cannot be unknowne Pro. 34 Eightly to finde the suns Azimuth and Altitude for any houre Constru ¦ ctio 44 Marke where the parallel for the day of the Month meeteth with the given houre and bring the edge of the Index thereto so the degree that the edge of the Index cutteth in the Limbe of the Instrument that shal be the Suns Azimuth and the degree that the houre cutteth in the Index that shall be the Suns Altitude required So if upon the tenth of December at nine of the Clocke in the Morning Exam. the Suns Azimuth and Altitude were required marke first where the Tropick of Capricorne which is the parallel for that day given meeteth with the given houre of nine and bring the Index thereto so the edge of it in the Limbe pointeth out neere 40. gr and a halfe so much is the Suns Azimuth from the South at nine of the Clocke in the forenoone the said tenth of December and the houre line meeting with the Index sheweth neere 5. gr 25. m. so much is the suns Altitude at that time now if you move the Index softly along as the edge of it passeth by any houre for any day of the yeare so the edge of the Index in the Limbe of the Instrument sheweth the suns Azimuth and the intersection of the parallel with the Index shall shew the Suns Altitude belonging to that houre Ninthly to shew the uncertaintie Pro. 35 of time by noting the shadow of things It is usually noted by some that when the shadow of the edge of a Window Dore Wall or such like shall touch such or such markes that it shall be then such or such an houre of the day and so constantly to hould for all the yeare this obseruation is farre from truth and the principalls of Astronomie and may be easily contradicted by such which have but indifferent judgement in the Nature of shadowes and the Suns passages by the Meridians and verticall Circles of the Heavens for by how much greater the propinquitie of the Suns approchment is unto the Zenith or verticall point by so much the more shall the houre or time be various in one and the same Azimuth So in the last Pro. the Azimuth of the Sun the tenth of December at nine of the Clocke in the forenoone was found to be 40. gr and a halfe Exam and the Suns distance from the Zenith at that time was neere 84. gr 35. m Now admitte the Suns distance from the Zenith the tenth of Iune were but 32. gr 35. m the Sunne being in the same Azimuth the houre would be halfe an houre past 10. For the Index being layed to the houre of 9. in the Tropicke of ♑ which is the Suns parallel for the said tenth of December and it cutteth the Constru ¦ ctio 45 parallels of the Suns Motion in the inequalitie of time and so the complement of the former 32. gr 35. m in the Index meeteth with the Tropicke of ♋ which is the Suns parallel for the tenth of Iune in halfe an houre past 10. so that it evidently appeares that the shadow of a perpendicular thing on the tenth of December denoting the houre of the day to be 9. of the Clocke the same shadow the tenth of Iune shall represent halfe an houre past 10. so the error shall be an houre and a halfe but if you move the Index unto the houre of 9. belonging to the tenth of Iune the Index shall point you out in the Limbe neere 68. gr of Azimuth for that houre which at 9. of the Clocke the tenth of December was but 40. gr an halfe so the difference of Azimuth in one and the same houre shall be 27. gr and a halfe the time as before an houre and a halfe which differences are sufficient to confirme the point Tenthly to finde the Quarter of Pro. 36 the yeare and day of the month if it were forgotten Constru ¦ ctio 46 At any appearance of the Sun by the 27. Pro. take the Suns Altitude then place the North and South edge of the Instrument unto the Meridian line formerly drawne if in the forenoone otherwise place the East and West edge of Instrument to the meridian-Meridian-line and erect the prependicular at the end of the Index then moove the Index to and fro untill the shadow of the prependicular fall by the side of the Index so the parallel that meeteth with the degree of the Suns obserued Altitude in the edge of the Index parallel in the Kalender that shall shew the day of the Month required So if Exam. upon a certaine day in the yeare the suns Altitude were observed and found to be 36. gr having placed the edge of the Instrument to the Meridian line and rectified the Index then move the Index untill the shadow of the prependicular fall by the edge of the Instrument let the Instrument rest at this position and account the former 36. gr upon the Index which degree meeteth with the houre in the Aequator and also that intersecteth the Kalender in the tenth of March the thirteenth of September but which of these dayes is the day of the Month the next dayes obseruation of the Sun upon the same houre will helpe you for if the suns Altitude besound to be greater then the day of the month inquired after it was the tenth of March because the sun from the tenth of December unto the eleventh of Iune doth every day at one the same houre ascend but if the Suns Altitude be found to be
This instrument or any other for the Mathematicall arts are made in siluer or brasse by Elias Allen or Iohn Allen neare the Sauoy in the strand The making description and vse of a small portable Instrument for the Pocket or according to any Magnitude in forme of a mixt Trapezia thus Called a Horizontall Quadrant Composed and prodused soly for the benefit and vse of such which are studious of Mathematicall Practice Written and delivered by Delamain student and Teacher of the Mathematickes Attribuit nullo praescripto tempore vitae vsuram nobis ingenijque Deus London printed for Richard Hawkins and are to be sold at his shop in Chancery lane neere Sarjants Inne 1632. TO The right Honorable and his much honoured Lo. Thomas Lo. Brudenel Baron of Stauton Right honourable and my very good Lo. YOur singular knowledge in all excellent and solid Literature and your ever Heroicke and Noble disposition to the best kinds of Learning are not unknowne unto the world And amongst other studies in your Lo. minoritie at the Vniversitie you tooke no little affection to the Mathematicall Arts as by your Lo. owne Manu-scripts and excellent Bookes in your Lo. great Librarie I have often seene Besides not onely by mine owne sundry conferences with your Lo. but also by the relation of others of more mature judgement I have bin amply informed in these your L. more aged yeares not onely of your continued love to these Arts but also that your knowledge in them far exceedes many of the Nobilitie of this kingdome Now my L. when I caused the subject of this Tractat to be made for your Lo. last Summer I meane your Lo. Horizontall Quadrant I had not then any intention so soone to have written publikely upon it But having then but declared unto your Lo. the excellent and abundant use of the Instrument by the heads of the propositions then slightly compiled farre exceeding the Instrumentall way in this nature that eyther Nobilitie Gentrie or others are now acquainted with in this kingdome for a recreative Instrument as well for the copious use thereof as its great facilitie and expedition in operation your Lo. then incouraging me to the publishing of it for a generall end many Moneths after I considered thereon and drew it up into a Body and thus accommodated it as I here present it now unto your Lo. favourable censure and Patronage to be sheltred under the wings of your Lo. clemency against all calumniators and malevolents as belonging especially to your Lo. sith you were the sole motive to this worke and had both the use of the Instrument before it came thus to a publicke view and the first Quadrant that ever was made common in this kind accept therefore favourably I beseech your Lo. this small mite of my labours as from the hands of one of your poorest servants yet true affectionate who shall alwayes acknowledge your Lo. Noblenesse towards him and ever rest Your Lo. most humbly devoted to Honour and serve you De la main To the Reader BEfore I shew the Projection describe the particulars and deliver the uses of this Horizontall Quadrant it will not bee impertinent for the satisfaction of some to give the Reader to understand what moved me unto it how it exceeds other Instruments and whence it might be drawne and projected Now the ingenious aptnesse for Inuention and accomodating of things in a faire and expedite course for Mathematicall Practices of that late professor of Astronomy Mr. Gunter is not unknowne unto many about this kingdome satisfying many of his friends according to his free and noble affection by Transcripts in that of more solid matter but such of vulgar Practices he hath publikely made manifest for the use of all such as affect those Studies In which worke many yeares past I tooke occasion to consider the Scheme or Diagramme of the fourth Projection in his Booke of the Sector Page the 64. 65. which according as he saies is after the manner of the old Concaue hemisphere but being in truth a naturall Projection of the visible Hemisphere that is one Moytie of the Globe projected on a Plaine which Diagram and Projection is now chalenged by my Reverend good friend Master Oughtred and it should seeme that Master Gunter had the Original of it from his labours invention who composed and made the same so for more then thirty yeares past as appeares by his owne Writings Manuscripts upon that Protection shewen me in the time of the Printing of this Tractat upon my Horizontall Quadrant whose excellent knowledge in Mathematicall Learning may evidently confirme it which Projection the said Master Oughtred gave to the late Bishop of Winchester Doctor Bilson for more then 20. yeares past and to some others of very good quality And it may also by a Letter from that most famous and admired Geometer Master Henry Brigges unto Master Oughtred dated from Gresham College Iune the 2. Anno. 1618. be collected that the said Master Gunter had the first overture of that fourth Projection from the said Master Oughtred in which letter are these words Master Gunter doth here send you the Print of an Horizontall Diall of his drawing after your Instrument And afterwards the said Projection was also presented by Master Gunter to many Noble Personages and in particular to the Right Honourable the Earle of Bridgewater causing it to be cut in Brasse in such a forme aâ— I have placed at the end of this Tractat some uses of which Diall are extant viz. the 2. 18. 21. and 34. Pro. of the Index or Table following Now having considered diverse Pocket Instruments that many men are practised in looked into sundry Projections amongst which that of Gemmafrisius there drawne in the Booke of the Sector is of admirable use yet making a more serious quaere contemplating more intensively upon that Diagram drawne and specified in that 64. and 65. Pages of the Sector aforesaid I found it farre to exceede all others in the Multiplicity and excellencie of performance If I should adde unto it a Kalender of time and an Index graduated with an Axis and Perpendiculars to be erected vpon it at pleasure referring only the Trapeziall forme it should be fitted farre to exceede any portable Instrument for the Pocket ever yet produced in respect of the general uses of it in resolving such ordinary Propositions which are practiced in Astronomie upon the Globe Spheare Hemispheare Quadrants of all sorts Astrolabe of Frisius Blagraue and others for facility expedition or certaintie like Magnitudes considered for in these Instruments for severall times and severall Propositions there must be diverse rectifications of the parts belonging to these Instruments and that diversly by reason of their diversity By this Horizontall Quadrant the former redifications are avoided Contemplation the eye being only the Index the aptnesse fitnesse of the parts and lines so naturally projected or described as they are upon the plaine of
21. 19. 25. 24. 35. 2. 38. 37. 20. 41. and 42. as followeth The day of the Month knowne to finde 1. The houre of Sunne rising setting and length of the day 2. The Sunnes difference of Ascention 3. The Sunnes Declination 4. What dayes are alike in length and what day the Sunne rising in the one shall be the Sunne setting in the other 5. The Sunnes place or degree in the Eclipticke 6. The Sunnes right Ascention and oblique Ascention 7. The houre and Altitude of the Sunnes comming East or West 8. The distance of the Sunnes rising or setting from the East or West 9. The height or depression of the Sunne in the Meridian here or for any Latitude 10. The time of day breake and end of twylight 11. The inequality of time betweene day breake and Sunne rising 12. The houre and Altitude of the Sunnes comming upon any declining wall 13. At what houre and Altitude the Sun must have to be opposite or perpendicular to a declining wall First to finde the time of Sunne Pro. 1 rising or setting and length of the day for any day of the yeere Seeke the day of the Month in the Kalender Constru ¦ ctio 1 and the houre line that meeteth therewith sheweth the time of Sunne rising or setting So if the day of the Month were the 13. Exam. of October the parallell that meeteth therewith is the houre viz. 7. of the clocke at which time the Sun riseth the same houre is noted also with 5. which is the time of Sun setting that day this doubled makes 10. the length of the day required Secondly to finde the difference Pro. 2 of Ascention for any day of the yeere Marke what Meridian meeteth with the day Constru ¦ ctio 2 of the Month in the Kalender as suppose the day to be the former 13. of October which is the houre line of 7. and 5. as before and account the Numbers of Meridians to the houre of 6. so have you 15. gr or an houre which is the difference of Ascention for the 13. day of October required Pro. 3 Thirdly to finde the Sunnes declination for any day Constru ¦ ctio 3 Marke what parallell of Declination meeteth with the day of the Month in the Kalender and account how many degrees it is from the Equinoctiall so have you the Sunnes Declination for that day Exam. So if the day were the last of August the parallell that meeteth therewith is the 5th from the Equator and somuch is the Sunnes declination that day viz. 5. gr North declination Pro. 4 Fourthly to finde what dayes in the yeare are alike in length and what day the Sunne rising in the one shall be the Sunne setting in the other Constru ¦ ctio 4 For the first note that the dayes betweene the 10th of December and the 11th of Iune are dayes of Increase and the rest are dayes of Decrease Now right against any day of decrease in the Kalender is the day of increase which dayes are equall one to the other Exam. So the 19. day of May is against the 4. of Iuly at which time the Sunne riseth and setteth alike without sensible error viz. 4. of the clocke and therefore those dayes are of equall length and so of others For the second to finde what day the sunne rising in the one shall be the sunne setting in the other Admit the day to be the 18th of February and according to the first pro. finde the time of Sunne rising which is at 40. m. after 6. Exam. of the clocke Constru ¦ ctio 5 for that day and the setting 20. m after 5. then marke what day of the Month the houre line of 20 m after 5. in the forenoone meeteth with the Kalender which will be the 23. of August so the 18th day of February the Sun did set at the same houre that it did rise the 23. day of August Fiftly to finde the sunnes place or Pro. 5 degree for any day of the yeere Note where the parallel of the day of the Month crosseth the Eclipticke that is the Sunnes Constru ¦ ctio 6 place So the former parallell of the 13th of October meeteth with the Eclipticke in the beginning of ♠and ♓ but which of these is the Sunnes place the quarter of the yeare may easily tell you viz. ♠which is the Sunnes place or the degree in the Eclipticke for that day Pro. 6 Sixtly to finde the Sunnes right ascention and oblique ascention at any time Constru ¦ ctio 7 Consider what Meridean meeteth with the Sunnes place in the Eclipticke for the day given and marke the number of Meridians in the Equator for the Meridians are numbred in the Equator as is sayd before in the description so have you the Sunnes right Ascention but here note that the degrees in the Eclipticke are numbred forward and backeward in the Eclipticke unto 360. gr upon this Instrument so are the right Ascentions of those degrees also numbred forward and backward in the Aequator for the right ascention of any degree in the Eclipticke is that degree of the Aequator which is opposite unto it the succession of the signes considered so if the Sun were in the beginning of ♠the right Ascention is neere 208. degrees for the Meridian that passeth by the beginning of ♠is accounted in the Equator from ♈ and is within 6. m of 28. gr Now the right Ascention of ♋ is 90. gr and the beginning the of ♎ is 180. gr and from the beginning of ♎ to the beginning ♠is within 6. m of 28. gr as before all is which put together makes neere 208. gr the right Ascention of the Sun the 13th day of October To find the Sunnes Oblique Ascention at any time Note that the difference of Ascention is the Constru ¦ ctio 8 difference alwayes betweene the right Ascention of the Sun and the oblique Ascention thereof therfore the right Ascention known by the last directiō the difference of Ascention by the second direction the oblique Ascention is easily had by Addition or substraction thus If the Sun be in a Southerne signe then the oblique Ascention is greater then the right Ascention by so much as the difference of Ascention comes to but if the Sun be in a Northerne signe the oblique Ascention is so much lesse which difference of Ascention as before by the 2 Pro for the said 13th of October was 15. gr this ad unto the right Ascention of the beginning of ♠viz. 208. gr makes 223. gr the Suns oblique Ascention for the beginning of ♠on the 13th day of October but if the Sun had beene in the beginning of ♉ the oblique ascention would have beene onely neere 13. gr viz. 12. gr 54. m. Seventhly to find the suns Altitude Pro. 7 and houre of the suns comming East or West any day of the yeare above the Horizon Here note that this Proposition holds in use Constru ¦ ctio 9 onely for that time of the Suns being
which conuerted into measure and accounted Eastward or Westward according to the houre given from the former points of the Aequator in the Horizon at 12. will give the degree of the Aequator in the Horizon at the houre proposed then by the 23. Pro. I seeke out the degree of the Eclipticke in the Horizō answerable to the degree of the Aequator so have you the degree Ascendant from which account 90. gr or 3 signes so have you the degree of the Nonagessima point in the Horizon but if you reckon 6. signes from the Ascendant you have the desendant degree of the Eclipticke in the West of the Horizon Pro. 26 Thirteenthly to finde what Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree of the Eclipticke above the Horizon and what Azimuth it is in at any houre According to the last Pro. sinde the degree Constru ¦ ctio 34 Ascendant and the Nonagessima degree then by the 24. Pro. finde what degree of the Eclipticke is in the Meridian Answerable to the degree of the Eclipticke in the Horizon so shall you know on which side of the Meridian the Nonagessima degree is how far from the Meridian then if that Index be layed upon the houre of 12 where the parallel of the Nonagessima degree crosseth it that should be the height of it if it were in the Meridian account therfore from the Meridian or houre of 12. in the Aequator the number of degrees betweene the Nonagessima degree and the degree of the Eclipticke in the Meridian marke where that Meridian meeteth with the parallel of the of the Nonagessima degree lay the Index thereto so have you the Altitude of the Nonagessima degree in the Index and the Azimuth in the Horizon or Limbe of the Instrument There are yet the 48. 49. 50. 9. 13. 14. and 15th uses of the said Index or Table which haue no relation to the suns sight or observation in there operation and resolutions and should have followed these 26. uses that have beene delivered but I referre them to the end of this Tractat as for these uses of the Instrument which depend upon the Suns sight or observation they are these 13. following viz. the 1. 31. 4. 6. 36. 7. 22. 3. 5. 34. 11. 43. and 8th viz. to shew 1. The Sun or starres Altitude above the Horizon at any time 2. The houre of the day and Azimuth of the sun 3. The Meridian Line upon any appearance of the Sun 4. The sit of a building or costing of a place 5. The Suns Azimuth and houre without Observation 6. The variation of the Needle 7. The Latitude of a place or height of the Pole above the Horizon 8. The Suns Azimuth and Altitude at any houre 9. The vncertainetie of time by noting the shadow of things 10. The Quarter of the yeare and day of the Month with the houre Azimuth and the Meridian line 11. Instantly the houre of the day the Azimuth and Altitude of the Sun with the Meridionall line without observation or sight of the Sun by knowing the Proportion betweene the length of a shadow upon a Horizontal Plaine and that which did cast the shadow 12. The Declination of a Wall by seeing the Sun beginning to shine thereon or going from it 13. The Declination of a Wall the Sun shining thereon First how to obserue the Sun or Pro. 27 starres Altitude above the Horizon at any time Lift up the edge of the Instrument to the eye Constru ¦ ctio 35 so that the sight which is at the Limbe or Circumference of the Quadrant be next the eye and the Index to hang perpendicular and to play easily by the side therof then move the Quadrant up and downe untill you may through both sights see the Center or midle of the Sun or starre so the Index in the Limbe shall fall upon the degrees of the Sun or starres Altitude above the Horizon at that time Or without looking at the sun the Altitude thereof may be thus found hould the Quadrant Constru ¦ ctio 36 that the Index may hang perpēdicular or be verticall as before then move about the Instrument untill the edge of it be opposite to the body of the Sun Now supposing the Instrument to hang thus upon his Center softly lift up the edge thereof which is towards the Sun untill you see the beames of the sun passe through both sights then the Index in the Limbe shall give the suns Altitude as before Pro. 28 Secondly how to finde the houre of the day and Azimuth of the Sun upon any appearance of the Sunne Constru ¦ ctio 37 By the last Pro. obserue or take the suns Altitude and account it on the Index then seeke for the parallel of the day of the Month for the day present move the Index untill that degree of Altitude in the edge of the Index meete with the parallel of the day so the Meridian that meeteth with that degree of Altitude in the Index shall be the houre of the day required the edge of the Index in the Limbe of the Instrument shall likewise shew the Suns Azimuth belonging to that houre So if upon the last of August the Suns Altitude in the forenoone should be obserued and found to be 30. Exam. gr a halfe seeke this Altitude out upon the Index move the Index untill the degree of Altitude meete with the parallel for the day of the Month given viz. the fift parallel from the Aequator Northward so the houreline that meeteth also with the 30. gr a halfe in the Index is the houre viz. neere 9. that shall be the houre of the day at that instant the edge of the Index in the Limbe cutteth neere 35. gr and 30. m from the point of East towards the South and so much is the Suns Azimuth at that time Thirdly how to finde the Meridian Pro. 29 line and the true points of North South East and West upon any appearance of the Sunne According to the 27. Pro. first obserue the Constru ¦ ctio 38 Suns Altitude above the Horizon and by the last Construction finde the Suns Azimuth agreeable to that Altitude let the Index and rest at that degree and erect the prependicular at the end of the Index then houlding the plaine or face of the Quadrant parallel to the Horizon move the Instrument Circular untill the shadow of the said perpendicular fall by the side of the Index and so the houerline of 12 or the edge of the Instrument which is parallel unto it which is the North and south edge of the Instrument shall represent the Meridian line and pointeth out the North and South in the Horizon of the world by the termes thereof and the other straight edge of the Instrument which is perpendicular unto that edge is the East and West edge of the Instrument and denoteth or sheweth the line of East and West in the