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
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
the Instrument being a part of the Horizon the Parallels Meridians Verticall Circles that are contained or may be described in our Latitude sufficiently necessary induceth any one in the understanding of the uses of it that is but indifferently versed in the linaments and principles of the Globe what to speake and what to answere in a Proposition without farther direction And having had this Horizontall Quadrant for many yeares past as a Pocket Instrument diverse about this Kingdome being importunate with me for to have it or to publish the use of it seeing its great facilitie and expedition in comparison of such Pocket Instruments as are now used here or in forraigne parts I was willing at last after I had given order for the making of fower of these Instruments in Silver for severall Noble Personages to disburthen my selfe of Transcribing the uses of the Instrument and Tables for the making of it to satisfie those which were importunate and to let others that are studious in Mathematicall Practices also participate of it Now what I have delivered vpon the accommodating of the Instrument thus the making thereof with the uses that I have delivered in this Tractat upon it following I acknowledge due to none Inferiour assistant but to mine owne Industry search and labour and that 64. 65. and 66. Pages of the Booke of the Sector before specified in which is onely shewne the 2. 3. 19. 22. 25. and 30. Propositions of the Index or Table following as uses of the said Projection But I have extended them to many more and abundantly and plentifully supplied the obscuritie of that Scheme or Diagramme there drawne as for a generall good in the use of this Horizantal Quadrant I deliver therfore first the making of it first by the Sector somewhat different from that of Master Gunters secondly by Geometrie and lastly I shew a third way how it may be Proiected and made by my Mathematicall Ring and by Numbers which I have Calculated and accommodated to that end in Tables for more exactnesse Part of the generall scope and use of which Instrument I deliuer in the Index or Table following An Index or Table of the vses of the Horizontall Quadrant Viz of the Horizon Line of Shadowes Kalender Parallels Aequator Eclipticke Houre-lines Index 1 By the Horizon to shew 1. The Sunne or Starres Altitude at any time Pag. 53. 2. At any Day of the yeare how farre the Sun riseth or setteth from the true East or West Pag. 28. 3. The Suns Azimuth and Altitude at any houre for any day Pag. 62. 4. The Meridian line upon any appearance of the Sunne Pag. 55. 5. The vncertaintie of time by noting the Shadow of things Pag. 63. 6. The Site of a Building or Costing of a Place Pag. 57. 7. The Variation of the Needle Pag. 59. 8. The Declination of a Wall or Plaine the Sunne shining thereon Pag. 71. 9. The Inclination of a Plaine and to place a Plaine Horizontall Pag. 89. 2. By the line of shadowes is had 10. At what houre in any Day of the yeare the shadow of an Altitude is equall double triple c. unto it Pag. 35. 11. Instantly the houre of the day the Azimuth and Altitude of the Sun with the Meridian line without observation or sight of the Sun by knowing the Proportion betweene the length of a shadow upon a Horizontall Plaine that which casts the shadow Pag. 67. 12. At any houre an Altitude of the Sun or Azimuth what Proportion shadowes have to their Bodies Pag. 37. 13. Whether and Altitude be above or below the Iewell of the eye how much 14. The hight of an Altitude accessible or in accessible Pag. 100. 101. 15. The measure of any Part of Altitude not approchable Pag. 102. 3. By the Kalender is knowne 16. The inequality of Time in equall Months or equall number of Dayes Pag. 44. 17. What number of dayes wil make the day and houre longer or shorter at any time Pag. 43. 18. The houre of the Sun rising setting with the length of the day at any time Pag. 23. 19. What dayes are alike in length what day the Sun rising in the one shall be the Sun setting in the other Pag. 24. 20. The inequality of Time between day breake and Sun rising Pag. 41. 4. By the Parallels to search out 21. At any day the Suns declination Pag. 24 22. The Latitude of a Place or hight of the Pole above the Horizon Pag. 60. 23. At what houre in any day the Suns Azimuth and Altitude will be equall and how much the Altitude Azimuth wil be Pag. 42. 5. By the Aequator is seene 24. The Suns equall motion right Ascention and oblique Ascention Pag. 26. 6. By the Eclipticke to give 25. The Sunnes Place at any time of the yeare Pag. 25. 26. The Degree of the Aequator in the Horizon by supposing the degree of the Ecliptick in the Horizon Pag 46. 27. The Degree of the Eclipticke in the Horizon by supposing the degree of the Aequator in the Horizon Pag. 47. 28. The degree of Medium Coeli or the degree of the Eclipticke in the Meridian by supposing the degree of the Eclipticke in the Horizon Vel contra Pag. 47. 29. The Horoscope or the degree ascendant ' or descendant and the Nonagessima degree at any houre Pag. 49. 30. What Angle the Eclipticke makes with the Horizon or the Altitude of the Nonagessima degree and what Azimuth it is in at any houre Pag. 50. 7. By the hour lines to find 31. The houre of the Day and Azimuth of the Sunne Pag. 54. 32. The houre of the day agreeable to any Altitude or Azimuth Pag. 39. 33. The Sunnes Difference of Ascention for any day Pag. 23. 34. The Quarter of the yeare and day of the moneth houre of the day Meridian-line and Azimuth of the Sunne if it were forgotten Pag. 64. 8. By the Index adioyned with other lines you have 35. At what houre Altitude the Sun wil be due East at any day of the yeare Pag. 27. 36. The Suns Azimuth houre without observation Pag. 58. 37. The time of day-breake or end of Twi-light for any day in the yeare Pag. 30. 38. The hight or Depression of the Sun in the Meridian for any day in the yeare here or for any Latitude Pag. 29. 39. The Suns depression Azimuth at any houre of the Night assigned Pag. 40. 40. The houre of the day to our Antipodes by supposing the suns depression under the Horizon Pag. 42. 41. What houre Altitude the sunne commeth upon a declining wall any day in the yeare how long the sun shineth thereon Pag. 32. 42. At what houre and Altitude the Sun must have to be opposite or Perpendicular to a Declination Plaine Pag. 33. 43 The declinatiō of a wall by seing the sun beginning to shine thereon or going from it Pag. 69. 44. The houre Altitude of a stars coming to the Meridian at
the Colume M. 5294. which I take from the scale B. and protract it from T. to 30. in the line 2. 10. Now placing one foote of the Compasses in 30. next 10. and extending the other foote to P. the Eclipticke may be intersected in the points of ♉ and ♓ and placed in 30. towards 2. the same extent will Intersect the Eclipticke in ♠and ♠In like manner may the Centers of the rest of the degrees of the Eclipticke be protracted in the line 2. 10. from T. out of the Columes M. and P. and so all the Eclipticke divided from degree to degree but this may be otherwise done Besides that which is delivered touching the drawing of the Parallels Eclipticke and Houre lines there remaines yet how to put on the Callender to graduate the Index and to draw and divide the line of Shadowes This may be easily done from the Table R. Calculated and accommodated to that purpose for the yeare 1640 and may sufficiently serve for many yeares after without any sensible error Having divided the Quadrants Constru ∣ ction E.S. and E.N. as before into the usuall degrees of a Quadrant lay a ruler upon the Center Z. and account the degrees from the point E. in the Quadrant towards N. and S. out of the Table R. according to the severall Columes of the Table R. and Intersect the Quadrants How to inscribe the Callender with small short lines so shall the Arke of the Horizon of the Instrument from E. be divided into the usuall dayes of the Month which is the Callender and the beginning of these divisions may be at the 10. of March and so going on to the 11. of Iune and then againe to begin from the 10. of March and go on unto the 10. of December and these dayes may bee noted upon the inside of the Horizontall Arke with short lines from E. as before and at every Month may bee placed a representative letter for that Month and every 10. and 5. day of every Month may bee noted with a small stroke somewhat longer then the rest to helpe the memory the readier to number In like manner may the rest of the dayes of the Calender be intersected in the out side of the Horizontall Arke towards the Limbe beginning at the 13. of September and so going on to the 11. of Iune then againe from the 13. of September and going on unto the 10. of December and these Months may bee also noted with significant letters appropriate to each Month and each 10. and 15. day of the Month may be also denoted as before with a stroke somewhat longer than the rest according to the Scheme against Page the 1. How to graduate the Index for the Instrument Let the Index be equall to the semidiameter Z. E. and then may it bee divided out of the Table Q. by the helpe of the scale A. beginning at the Center the Index being diuided and placed on the Center of the Instrument at Z. it shall helpe to put on and divide the line of shadowes as followeth Lay the edge of the Index to A. in the Limbe which is neere the 10. of December and move it to any degree in the Table S. and account the like degree in the Index and then make a marke upon the plaine of the Instrument where that degree toucheth and so goe on from point to point untill the whole line bee described and divided according to the Table S. This line might bee placed betweene the Calender and the Limbe or in a Quadrant c. But I have caused it to bee described as is seene upon the Scheme against Page the 1. for expedition and conveniency ☞ Let A. B. C. D. be a plaine divide the length A. B. within halfe an Inch of the higher end and an Inch of the lower end in to 3. equall parts which suppose the line M.N. then divide each part into halfe so the line M. N. shall bee divided into 6. equall parts the middle of which will bee at Z. Then take 4. of these parts for Radius and on Z. describe the obscure Arke A. E. B. and upon Z. erect a perpendicular to the line M. N. to cut the Arke A. B. in E. now from E. to A. protract 40. gr and from E. to B. protract 50. gr so the Angle E. Z. M. shall be 90. and also A.Z.B. shall be 90. Now having made a scale of Z.E. like to the scale A. according to the former directions then out of the Colume C. and by helpe of the said scale A. from Z. you may protract Z. ♋ 2493. Z.Q. 4823. and Z. ♑ 7673. and from the Colume F. y u may protract the distances of the Centers of those intersections from Z. viz. Z. 1.5269 Z. 2.7949 and Z. 3.16217 and so placing the Compasse in these Centers you may describe the Equator and both Tropicks But if Z. M and Z. N. be divided according to the scale A. then from Z. you may account the intersections of the parallels and distances of the Centers and so describe the parallels with greater expedition and so shall you have the Scheme or Trapeziall forme of the Instrument B. A. ♑ ♋ and may bee finished according to that against Page the 1. by the Tables and directions here calculated and delivered to that end Now to augment the Instrument to any proportion assigned as if betweene the Tropickes were supposed to bee 10. Inches the Radius might be found out or if the Radius were 4. foote which is according to mine owne Instrument what distance might there bee betweene the Tropickes the proportion would be as 516. to 1000. so the breadth to the scale or as 1000. to 516. so the scale to the breadth therefore by the Ring bring 516. in the moveable to 1000. in the fixed so right against any Radius in the fixed is the distance betweene the Tropickes in the Moveable or against the distance assigned for the Tropickes in the Moveable is the measure of the Radius or Scale in the fixed So if ♑ ♋ be allotted to be 10. Inches for the distance betweene the Tropickes the Scale or Radius of the Instrument should be 19 4 10. fere but if the scale or Radius were 4. foote or 48. Inches then the distance betweene the Tropickes of ♑ and ♋ will be neere 24 77 100. Inches Thus for the making of the Instrument the description of which followeth The Description of the Horizontall Quadrant THe forme of this Instrument is like a mixt Trapezia as appeares against Page 1. where of two sides are right and the other two sides are Circular which falleth out to bee so from the nature of the Projection and that part which I have thought most convenient for use and is fully sufficient for that which I have deliuered upon it and may be made of any plaine Materiall but fittest in Brasse or Silver the severall parts of which Instrument are five viz. the Backe the Face the
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-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