m. Distance of the Substile and the Meridian 6. d. 35. m. Distance of the Stile and Substile 4. d. 15. m. Eleuation of the Pole 52. d. Hetherto we haue taught the delineation of all kindes of Dials which are to be made vpon any plaine plat or superficies now followeth the garnishing of them with the 12. Signes and the howres vnequall How to draw the 12. Signes in all kindes of Dials before mentioned CAP. 22. FOr somuch as sometime the 12 signes of the Zodiake are placed in Sunne Dialls know in what signe y ◠Sunne is at any time which albeit any kinde will receiue yet most commonly the verticall directly opposite to y ◠South are garnished therewith Therefore in drawing the 12. Signes in these South and all other kindes of Dialls before mentioned doe thus Prepare a little Table of Iron Brasse or close grained wood in breadth 3. or 4. in length 5. or 6. inches Chose for the Diameter one of the shortest sides wherein draw vpon the centre A. halfe a circle to be deuided into two quadrants distinguished with a line drawen from the centre A. to the arke B. parte ech quadrant into 90. degrées The line A. B. is héere in place of the Equator shewing in the arke the beginning of Aries and Libra Moreouer how to finde the other Signes on both sides séeke in the Table of the declination of the Sunne from the Equinoctial circle which is afterward expressed First finde out the degrées of the distance in this Table of the beginning of Taurus from the Equator being 11. degrées 30. minutes Account this distance in the quadrant from the letter B. towards the left hand and at the end of this number draw a line from the centre A. which shall shew the beginning of Taurus and Virgo Account like wise the same distance on the other side from the line A. B. and make a line for the beginning of Pisces and Scorpius Againe in the 20. d. 12. m. from the line A. B. you shal haue the beginning of Gemeni Leo and so many degrées and minutes on the other side the beginning of Aquarius and Sagittarius To conclude on both sides in the 23 degrées 30 minutes there must bée on the one part Cancer and on the other Capricorne Afterward draw lines from the centre A by euery marke so long as your Table will receiue and at the end of these lines let the caracters of the 12 signes of the Zodiake bée fixed as in the figure following you may sée The vse of this Trigonall instrument in writing the 12 signes in Dialls YOur Diall being made and the Stile placed therein take your Trigonall instrument and set it vpon the Stile so that the whole Diameter thereof may stand plaine vpon the edge or vpper part the centre A. of your instrument alwaies remaining in one place of the Stile Let the line of ♋ bend vpward to the centre of your diall and the line of ♑ downe ward Then fasten a thred at the vppermost end of your trigonal in euery line of the signes so that you may direct it downward by the centre A. to the plat of your Diall and where the ende of the thred shall touch the Diall make a marke Then mouing the Trigonal on the right hand so that the thred may bée stretched on the left hand make there likewise a prick vpon the plat When you haue thus done 4 or 5 times vpon the one side of the diall that is on the left hand doe so likewise on the other side on the right hand These markes being thus made draw with your compasses or rather with a crooked ruler made according to those markes a line by them Doe thus with each one of the 7 lines of your Trigonal When you haue drawne al these lines being crooked except the middle line which is right and representeth the Equator then at the ends of them write the caracters of the 12 signes on this wise First on the right hand toward the East at the ende of the vpper line write or place ♑ At the second line downward ♒ At the third ♓ At the fourth ♈ At the fift ♉ at the sixt ♊ at the seuenth ♋ Then on the other side on the left hand toward the West at the ende of the nethermost line place ♋ At the second ♌ at the third ♠at the fourth ♎ at the fift ♠at the sixt ♠And finally againe at the vppermost set ♑ This done remember that in what place of the Stile the centre A. of your Trigonall was placed there fasten a small péece of yron or any such like thing which may shewe with the shadowe thereof the Signe which the Sunne shall be in at any time vnlesse the houre lines bée so short that where the small péece of yron should be placed you may cut the Stile that the ende thereof shall shew it But the first is the most conuenient way for the vse thereof You may in like manner with this Instrument drawe or place the 12 signes in Horizontal East West and all other kindes of Dials which before are recited because the difference is nothing but in placing the 12 signes at the ends of the lines the true doing where of you may easily perceiue by the course of the Sunne For in the South Erect when the Sunne occupieth Cancer then is the line of ♋ furthest distant from the centre of the Diall But in the Horizontall Diall the line of ♋ is next to the centre Few words shall suffice for this matter experience shall easilie teach you herein How to place the vnequall houres in a Horizontall Diall CAP. 23. FIrst you shall vnderstand that by an vnequall hower is ment the 12 part of the day whether it be short or long For when the Sunne is in the Equinoctiall circle the day hath 12 equall and like wise 12 vnequall houres But in winter solstice when the dayes be at the shortest and containeth with vs where the Pole is eleuated aboue the Horizon 52 degrées onely 7 houres 36 minutes then the vnequall houres be lesse For if you diuide these 7 houres 36 minutes by fractions into 12 you shall finde onely 38 minutes of an equall houre to make one vnequall houre But in the sommer solstice when the dayes bée at the longest and hath 16 houres 24 minutes then one houre with 24 minutes maketh one houre vnequall These bée like wise called the houres of the Planets and are placed in Dialls on this maner Your Diall being made and prepared draw vpon it the 12 signes of the Zodiake as you were taught before so large as your plat will giue leaue c. Note that alwaies the Meridian line or 12 equall houre is the 6 vnequall houre Marke likewise that when the Sunne entreth into the beginning of ♈ and ♎ both the equall and the vnequall houres be of like quantitie For the 7 equall houre in the morning is the first vnequall and the
8 equall the 2 planetare houre c. But in the Tropike of ♋ it is otherwise for then the vnequall houres be greater then the equal Therefore account how many houres and minutes is in the longest day for your Eleuation changing all the minutes of those houres into one totall summe Then diuide this number by 12 and the quotient shall shew how many minutes of an equall maketh one vnequall houre Example hereof with vs the longest day is 16 houres 24 minutes Wherefore I multiplie 60 which is the minutes of an equal houre by 16 which is the summe of houres of the longest day and the product ariseth to 960 whereunto I adde 24 the minutes remayning then the number shall be 984 which being diuided by 12 the quotient is 82. Wherefore I conclude that 82 minutes of an equall maketh one vnequall or planetare houre Then to draw them in Dialls worke thus First in the Tropike of ♋ diuide the space betwéene each houre into 60 equall partes but because those distances bée so small for the most part that this cannot be done therefore it shall suffice to diuide euery one of them into thrée equall partes Then shall euery parte conteine 20 m. and thrée of them 60 m. which is one equall houre When as therefore you will place the 7 vnequall houre account from the Meridian line or 12 houre 4 parts and 2 minutes which is 82 minutes and make there a marke Then place your ruler by this point or marke and the intersection of the line of ♈ and ♎ and the first houre after noone drawe a line from one Tropike to another that is from ♋ to ♑ Then for the placing of the 8 vnequall houre account from the 7 last made 4 of the foresaid parts and two minutes make there a marke by which and the intersection of the line of ♈ and ♎ and the line of the second houre after noone the ruler being placed draw a line as before For the 9 account from the 8 last made likewise 4 parts and two minutes drawing a line as before Doe in like maner for the drawing of all the other remaining that is for the 10 and 11. The 12 being the Sunne sitting shall néede no line As you haue finished the vnequall houres on this side for the afternoone doe in like maner for those in the forenoone accounting from the Meridian 4 parts and 2 m. of an equall houre to each vnequall drawing as before lines from one Tropike to another You may place the figures for the vnequall or planetare houres at the ende of the lines vnder the Tropike of Capricorne or aboue the line of Cancer as you will Note that the same part of the Stile which sheweth the 12 signes shall like wise shew the vnequall houres For better vnderstanding hereof Behold the Figure following An Horizontall Diall How to place the houres vnequall in a South erect direct Diall CAP. 24. THere is almost the same maner of placing the vnequall houres in this kind as in the Horizontall differing onely herein that whereas you diuided the spaces betwéene the houre lines in the Tropike of ♋ which is next to the centre of your Diall and accounted 4 partes 2 minutes of an equall to one vnequall houre in this you must diuide the Tropike of ♑ which is likewise next to the centre of the Diall taking onely 2 partes wanting 2 minutes that is 38 m. of an equall houre to ech vnequall Therefore your Diall being prepared and the 12 signes of the Zodiake placed therein c. account how many houres and minutes be in the shortest day in your country changing all the houres into minutes giuing to each houre 60 minutes Diuide the product by 12 and the quotient shall shew how many minutes of an equall will be answerable to each vnequall houre Example the shortest day with vs is 7 houres 36 minutes which being multiplied into one grosse number of minutes the product is 456 which I diuide by 12 and the quotient is 38. Therefore I affirme that 38 minutes of a vulgar or equall maketh one planetare or vnequall houre Then diuide the Tropike of ♑ here as in the Horizontall you did the Tropike of ♋ Afterward account from the Meridian line 38 m. or 2 parts wanting 2 m. of an equall houre to each vnequall c. Finish all thinges else in this Meridionall erect direct as you were taught in the Horizontal The figure ensueth A South Diall The placing of the howres vnequall in East and West Dials CAP. 25. FIrst draw your Diall true then place the 12 Signes of the Zodiake in it which you may doe on this wise The Stile of your Dial being fixed therin as before hath béen taught take your Trigonall before prescribed and place it vpon the edge of the Stile then according to the direction of the thread as in y â— South Diall before make marks vpon the plat as in the Figure following you may sée Afterward by these markes draw lines as before you did placing at the ends of them the Caracters of the 12 Signes Moreouer note that where the centre A. of your Trigonall doth touch the edge of the Stile there fasten a small péece of Iron or such like thing which may shew she place of the Sunne in euery Signe and likewise the planetare or vnequall howres When as therfore you would place the howres vnequal in those kindes of Dialls account the mâ—mber of howres and minutes which the halfe of the longest day in your Country doth conteine Example With vs the longest day conteineth 16 howres 24. m. the halfe thereof is 8 howres 12. m. wherefore numbring in the circumference of the circle from A. to D. 6 howres for that quadrant conteineth 6 equall howres and from D. toward C. the other 2. howres and 12 minutes so that you may haue from A. by D. toward C. the iust halfe of the longest day at the end thereof make a point X. Then diuide the arke A. X. into 6. equall partes Afterward placing the ruler vpon the centre E. and eche one of these partes where it shall touch the Contingent line D. F. make marks Likewise in the other line of Contingence G. B. make these markes being of equall distance in this line from the point B. as the other be from the point D. Then place the ruler vpon two of these marks being equidistant from the points B. D. in both the Contingent lines and where it shal touch the Tropike of ♋ make markes This done lay the ruler vpon the first marke in the Tropick of ♋ next vnto X and the intersection of the line of the 6 hower with the line of the beginning of ♈ and ♎ drawing a manifest line from one Tropike to another which if you haue wrought all things true will be parallele to the Horizon and it shall be the 12. vnequall hower line in the West Diall and the Horizon or Sunne rising in the East Diall Againe place your ruler vpon
the length of the ruler from thâ—â—â—ntre to the end be of such quantitie as is from the centre of the great plat to the outward edge and an inch or more if y 〈◊〉 〈◊〉 〈◊〉 The foreside of your instrument being finished the backside must haue two small holes and a handle which may turne and moue about Prepare them thus Vpon your great plat on the backside right against the fourth degrée of â™ nigh the edge make a small hole wherein the little pinne of the handle may bée plaâ—ed when néede requireth and write by this the greater Beare Againe right against the 28 d. 1 m. of ♎ on the backside make another hole likewise so that the handle being remoued to it the pinne may enter as in the other And by this write the lesser Beare c. Prepare for your handle a thin plate of yron brasse or woode about sixe inches in length or more if you wil. Draw in the middest of it a line at the one ende thereof make a hole in the middest of the line of such bignesse as the hole in the greater plat is Vpon this handle you must fasten a litle short pinne right in the line so that the handle being fastened with the pinne toward the backside of the great plat and being moued the pinne may fall directly into the hole Beholde the Figure following Prepare a hollow pinne of yron or brasse according to this figure aboue so great as it may easilie enter into the hole of the handle so that it may turne vpon it but let it goe close into the great plat that it may remaine immoueable Let the Tothed whéele and the ruler moue likewise vpon it Then place the Tothed whéele and the ruler on the former side of the plat vpon the pinne and on the backside the handle with the little pinne towards the back of the plat fasten them so together that the handle the Tothed whéele and the ruler may turne vpon the plat seuerally or each by themselues at your pleasure and as néede shall require Notwithstanding you must bée carefull that the hole in your pinne may bée so great as you may perfectly sée the North Starre in the night thorow it Then your instrument shall bée finished whose vse followeth afterward For better instruction beholde the figure The vse of this instrument FIrst it shall bée expedient to finde out the Starres seruing to this purpose which you may doe by the figure following You sée in this figure the starres which serue to our vse The Polare Starre is a bright Starre in the North placed in the tayle of the lesser beare and mooueth but a small course as in the figure the letter A. sheweth There is also another Starre of the lesser beare greater and brighter then the other and is noted with the letter B. and serueth to this purpose also There is likewise in the greater beare called also Charles waine and of countrie men the plough two great bright starres and are placed almost in a right line with the Polare Starre are noted with the letters C. D. And these two Starres haue 5 other bright Starres by them but not so great as the other be These Starres which you sée in the figure as al other mooue equally aboue the Pole and finish their course in 24 houres Therefore when you would know the houre of the night by this instrument do thus Place the right line of the long tooth of the 12 houre directly ouer the day of the moneth and turne the handle on the backside to the hole of the greater beare and your instrument shall be prepared Then lift vp your instrument by the handle perpendicularly so that it declineth on neither sides and beholding the Polare Starre thorow the hole in the centre moue the ruler aboue vntill the right line there of be directly against or séemeth to touch the two Starres of the greater beare and vnder the line you shall haue the iust houre of the night which you may finde out by the number of the téeth with your finger in the night But if you cannot sée the two Starres of the greater beare because of clouds and yet you may sée the Polare Starre and the Starre of the lesser beare noted with the letter B. remoue the handle on the backside to the hole of the lesser beare Then lift vp your instrument as before and beholde the Polare Starre at the hole and turne the ruler to the foresaid Starre of the lesser beare and you shall finde the true houre of the night as before is taught The making of a Diall to knowe the houre by the Moone CAP. 30. PRepare a square péece of wood or metall 3 or 4 inches ouer draw thereon a circle so great as you can draw also another within that Now because the Moone finisheth her course in 29 dayes 12 houres and 44 minutes part the inward into 30 parts in this maner let 29 be equally diuided and the 30 which is the last must not be so great by a third part wherefore diuide one of those 29 equall parts into thrée parts and take two of them for the 30 and last part Cut out that which is within the inward limb and prepare another of the same or like wood or metall somewhat thicker and worke it so that it may goe into the former so much of the thicknes as it may be equal on the backside and that which remaineth of the thicknes let it hang ouer the foreside of the first plate to kéepe it from falling through draw a circle vpon it and diuide it into 24 equall parts draw from these parts houre lines so many as shall suffice for the longest night cut that which ouerhangeth with téeth at euery houre but especially at the 12 houre make a long tooth fixe a wier in the centre for the Stile equally distant from the circle on each side Let the Stile hang so much beneath the plat as it is aboue because you shall haue as much vse on the backside as before Cut out all that which is within the inward circle except a little portion to support the Stile so that this shall bée but as a hoope Drawe the houre lines on the backside of this plat as on the foreside so that the one may be right against another then drawe lines on the inside from euery one of these lines on the foreside to the lines on the backside This plat or whéele must be moueable and turne within the former The vse of this Diall PLace this Diall that each side may beholde one quarter of the world precisely the South side the South the North side the North c. Moreouer it must recline according to the eleuation of the Equinoctiall so that the Moone being in the Equinoctiall circle shall giue light both aboue and beneath this Diall You may place it perfectly with your instrument Your Diall being thus placed when you would knowe the houre of the night first
HOROLOGIOGRAPHIA The Art of Dialling teaching an easie and perfect way to make all kinds of Dials vpon any plaine plat howsoeuer placed VVith the drawing of the twelue Signes and houres vnequall in them all Whereunto is annexed the making and vse of other Dials and Instruments whereby the houre of the day and night is knowne Of speciall vse and delight not onely for Students of the Arts Mathematicall but also for diuers Artificers Architects Surueyours of buildings free-Masons and others By T. Fale AT LONDON Printed by Thomas Orwin dwelling in Pater noster-Row ouâ—… against the signe of the Checker 1593. SINGVLIS ARTIVM MATHEMATICARVM STVDIOSIS IN CELEBERRIMA CANTABRIGIENSI ACADEMIA THOMAS FALVS EIVSDEM ALVMNVS ET VERAE MATHESEOS STVDIOSVS EXIGVVM HOC GRATI ANIMI MONVMENTVM DD. ANNO. 1593. Simonis Muri ad lectorem carmen Scire cupis certa cur machina tangitur vmbra Et breuis aethereum line a fignat iter Haec licet euoluas facili praecepta libello Tradita sed voto non leuiora tuo To the friendly Readers and namely to such as be welwillers to the Mathematiks THe Arts Mathematicall gentle Reader in regard of their antiquitie and excellencie may be compared with any other of the liberall Sciences whatsoeuer For Seth who liued in the first age of the world is commeÌ„ded of Iosephus and Abraham of Berosus to haue been skilfull masters in these mysteries And the very name importeth that in olde time these of all other were esteemed worthie to be taught being called for their excellencie Mathemata that is Sciences meete to be learned These be Arithmeticke Geemetrie and Astronomie from which this Art of Dialling taketh his beginning a knowledge also ancient and necessarie and therefore practised by Princes and famous men of former ages The first Diall that histories remember is Lib. 2. cap. 20. of the Kings in the holie scripture where the Lord turned the Sunne backe 10. degrees for Hezechias sake whereby it had gone downe in the Diall of Ahaz This Ahaz was King of Ierusalem and reigned in the 3200. yeare after the creation of the world and in the first Olympiade of the Grecians Afterward as Plâ—â—e writeth Anaximenes Milesius the scholler of Anaximander first found out the reason and proportion of shadowes amongst the Lacedemonians and there taught the Art of Dialling who liued 200. yeare after the raigne of Ahaz and was a famous Philosopher in Greece before Platoes time as Diogenes Laertius reporteth But some affirme that it was Anaximander himselfe that found out this Art and set forth the first Mappe of the earth Herodotus saith that the Grecians learned this art and the diuision of the day into twelue houres of the Chaldeans Diodorus writeth that one Hyperion first obserued the houres But if we may beleeue Macrobius it seemeth that this Science came from the Egyptians for they called the Sunne Horus which by his motion limitteth to each houre his appoynted time Vitruuius rehearseth sundrie inuentors of this Art of Dialling as Berosus the Chaldean Aristarchus Samius Eudoxus Theodosius with others who were renowmed and liued many yeares before the birth of Christ I need not here remember Architas Tarentinus who by art made a Doue of wood to flie in the ayre neither Archimedes who defended Syracusa against Marcellus and affirmed that if he had a place to stand on he would moue the earth with his engins both of them no doubt skilfull in this Science It was long after the inuention that this Art was knowne in Rome for in the twelue tables was onely mentioned the rising and setting of the Sunne and after certaine yeares the midday was added Then in the first Punike warre the Romanes obtayning victorie there was a Diall brought amongst other spoyles out of Sicilie But in processe of time they began to bee more common in Rome for 100. yeares before Cicero his time the parasite in a Comedie being hungrie spake against the multitude of Clockes and Dials which were then in the citie Optans vt suus cuique venter sit horologium Plinie also telleth of a Diall placed in the field of Flora at Rome which by the space of thirtie yeares had not agreed with the Sunne and the reason was as he thought because that either the Sunne had taken a new course or els the earth was slipped from his Centre wherein at the first it stood or the stile was put awry by the shaking of the citie Since which times learning spreading it selfe into diuers parts of the world this Art hath been amongst the rest in great account Concerning the profite of this Art daily experience teacheth how needful it is in a well ordered Common-wealth seeing nothing can be done in due and conuenient season where this Science is neglected for the diuision of the day into certaine parts or houres which this Art teacheth doth limit and allot to each action his due time This Art being then so ancient and the vse so necessarie I trust none will thinke this labour superfluous vnlesse they be rude without ciuilitie or such as haue alwaies at hand a Diall of natures framing of whom this verse seemeth to be made * Si tuus ad solem statuatur nasus hianti Ore bene ostendas dentibus hora quota est Many haue promised but none as yet performed to write of this Science in our English tongue which hath bin published in other languages as D. Recorde long since M. Digges M. Blagraue with other who if they would take the paines I knowe could doe it with great commendation Diuers haue written hereof in the Latin tongue as Munster Schonerus Orontius Witekindus Clauius and others yet euery one differing from other in precept Some teach the making of Dials by the helpe of the Globe as Gemma Frisius some by the Astrolabe as the same Gemma Frisius and M. Blagr which Instruments euery man haue not Some vse the table of Sines and Arithmetike as Witekindus which way as most plaine and easie is obserued in this booke though in some kinds for want of triall Witekindus deceiued himselfe Munster vseth a Rectificatorie with a circle which is vnfit for small plats and faileth in greater without great heed Schoner wandreth in a wildernes of lines that a man know not where to begin or when to end Vlmer hath not the Delineation of all kinds Othersome obserue the rules of Geometricall proportion which order also we thought to haue obserued in all kinds as we haue done in the South and North erect declining but that sundrie precepts of the same thing would haue bred tediousnes and trouble to the learner and the cutting of the Figures would haue been very chargeable By meanes whereof we contented our selues with this one way here set downe not doubting but that euery one with small paines may attaine to the making of all kinds of Dials in this booke expressed As for a great part of them euery Artificer may easily
The arke 11. d. 47. m. of the quotient Sine 23184 is the distance of the Stile from the Substile Now the Complement of this distance being 76. d. 36. m. compared with 74. d. 47. m. the Complement of the difference kept I encrease 96494 the Sine of the lesser by the whole sine and y ◠product therof 9649400000 I distribute by 97277 the Sine of the greater And the quotient is 99191. whose arke is 82. d. 43. m. The complement wherof being 7. d. 17. m. is the distance of the Substile from the Meridian The delineation of the Diall If the Equator of the Meridian be greater then the Elenation of the Pole draw a line A. B. parallele to the Horizen make another C. D. squire-wise to the former describe the quadrant on the left hand from A. to C. because the Declination is on the right hand numbring therin from A. vpward 76. d. 32. m. the distance of the Meridian from the Horizon draw at the end thereof from D. the line G. representing the Meridian From this backward toward A accoūt the distance of the Substile from the Meridian which is 7. d. 41. m. making likewise at y ◠end of this number from D. the line E. for the Substile From hence account 11. d. 47. m. being the distance of the Stile from the Substile drawing in like maner from D. the line F. for the Stile Let the line of contingence cut the Substile squirewise as before make the Equator in this as in the other before Place the ruler vpon the centre H. and the intersection of the Contingent line and the Meridian beginning the diuision thereof into 24. equall parts where the ruler shall touch the Equator Finish all things remaining as before Remember that in this kinde of North inclining declining Diall the Meridian line rather representeth the 12. houre at midnight then in the day wherefore in accounting the houre lines let the meridian be alwaies for the 12. hower in the night And then if your plat decline Westward account backward as it were 11. 10. 9. which howers with the 12. you may omit in the delineation of your diall because they haue no vse in our Eleuation But account forward 8 7 6 5 4. c. so many as you think shall be necessary for some declination will receiue more then other will the greater the more the lesser the sewer howers But if the declination of your plat be Eastward then account from the Meridian line forward 1 2 3 4. c. so many as shall be néedfull omitting likewise y ◠first thrée c. A North inclining declining The second kinde But if the Eleuation of the Meridian and the Eleuation of the Pole be equall the making of the Diall differeth from the other before For an example hereof and y ◠drawing of the Figure resorte to y ◠South reclining 33 d. 30. m. declining 32. d. for these are both alike only remember here that if this decline Eastward make the quadrant likewise on the East side c. But if the plat decline toward the West make the quadrant Westward as in the figure following finishing all things els as here you sée done Obserue the same order in naming the howre lines which I taught you before A North inclining declining The third Example of a North Diall Inclining 45. d. Declining 45. d. If the Eleuation of the Meridian be lesser then the Eleuation of the Pole make your Diall thus For the working of the example and the delineation of the figure resorte to the South reclining 45. d. declining 45. d. for that agréeeth with this except only that in this the Stile is placed downward and sheweth but fewe howres and those likewise are drawen downward but in the other y ◠Stile standeth vpward shewing many houres and those likewise for the most part are drawen vpward Marke also in this kinde if your plat decline westward draw the Quadraut on the West side but if the declination be Eastward make the Quadrant on the East side c. The making of these are more pleasant to know then profitable to vse vnlesse the declination be the greater for so it may shew the more howres For the naming of the howres doe as you were taught before in the first of these thrée kindes A North Declining Inclining The delineation of those Dials whose plat lyeth nigh to the Eleuation of the Pole CAP. 21. WHen as the declination and reclination or declination and inclination shall cause the plat of your Diall to lye nigh to the Eleuation of the Pole then the hower lines must be drawen very long to make the distances somwhat large so that they may be discerned one from another And commonly these folowing be such as here we meane A South Reclining direct Declining erect Declining reclining An Eastor West Reclining Inclining A North Inclining direct Declining erect Declining inclining In all these kindes oftentimes the distance betwéen the Stile and the Substile is so small that it is not possible to draw your Diall except the plat be very large which at al times you shall not haue Therefore the best way is this First drawe your Diall very true as before hath béen taught vpon a large paper making your quadrant so great as may be Draw likewise the howre lines very long which will cause the greater distance betwéen the Stile and the Substile and in like maner betwéen the howre lines It will also procure y ◠greater Equator which wil be a great help in the drawing of your Dial as by the figure following you may perceiue When you haue thus drawen your Diall then at y ◠end of the paper wher the lines be of greatest distance draw the line I. K. parallel to the Horizontall line make likewise the other line L M. according to the greatnes of your plat of equall distance from y ◠other This done finde out or rather draw a line vpon your plat which may represent the true Horizon of the plat cutting the paper in sunder by the line I. K. and the line L. M. placing it vpon your plat very plain so that one of the edges may be parallel to y ◠Horizon Then make markes vpon the plat at both ends of all the howre lines drawing by those marks y ◠lines for y ◠howers Draw likewise light lines vpon the plat for the Stile the Substile easily to be extinguished as you did vpon the paper Let the Stile N. be fastened ouer y ◠Substile as you haue béen taught in the East West or Equinoctiall Dialls But here note that the Stile must not be of equal height at both ends But let it be so high as the distance betwéene the Stile the Substile is in the place where it standeth as in the examples folowing you may plainely perceiue A North Diall Declining Westward 65. d. Inclining 22. d. 20. m. Distance of the Meridian from the horizon 50. d. 50.
the morning and 5 in the euening at both 6. and the 5. houre in the morning and 7. at night Also at 5. in the morning and 7. in the euening the Sunne being in the beginning of ♊ But because the working of this to finde out these altitudes requireth much time and labour we will set downe these distances ready found out calculated for the Eleuation of the Pole 50. d. and 52 d. which you may likewise vse without any notable difference where the Pole is Eleuated 49. d. 51 d. and 53 d. The first table calculated for 50 degrees Hour Hour ♋ ♈ ♎ ♑ 10 deg ♉ 10 deg ♊   D. M. D. M. D M. D. M. D. M.  12 63 30 40 0 16 30     11 1 61 2 38 23 15 19     10 2 54 42 33 50 11 51     9 3 46 15 27 2 6 24     8 4 36 53 18 45   30 23   7 5 27 15 9 35   20 55   6 6 17 47 0 0   11 19   5 7 8 48     2 3 7 14 4 8 0 36       0 0 The second table calculated for 52 degrees of latitude Hour Hour ♋ ♈ ♎ ♑ 10 deg ♉ 10 deg ♊   D. M. D. M. D M. D. M. D. M.  12 61 30 38 0 14 30     11 1 59 13 36 28 13 21     10 2 53 15 32 7 10 0     9 3 45 12 25 33 4 45     8 4 36 12 17 32   29 36   7 5 26 53 8 46   19 22   6 6 17 42 0 0   11 4   5 7 8 58     2 4 7 46 4 8 1 1       0 0 If therefore you will make your Quadrant Horologicall for the Eleuation of the Pole 50. d. extend a thread or lay a ruler from the centre E. by the 63. d. 30. m. of the limbe of the quadrant beginning at F and where the thread so placed shall touch the Tropike of ♋ there make a point or marke Againe let the thread be placed vpon the 40. d. of the limbe and where it shall touch the Equator there also make a marke Thirdly let y â— thread be drawen by the 16. d. 30. m. of the quadrant and where it shall touch the Tropike of ♑ there make likewise a marke This done search out the centre by the 5. Proposstion 4. Euclid and ioyne these thrée markes into one arke which shall be the line for the 12 hower Afterward place the thread vpon the 61. d. 2. m. of the limbe and where it shall cut the Tropike of ♋ note it Draw likewise the thread vpon the 38. d. 23. m. of the limbe marke where it cutteth the Equator Then by the 15 d. 19. m. of the limbe extend the thread making a marke in the section therof and the Tropike of ♑ Drawe into one arke these thrée markes as you did before finding out the common centre so shall you haue the line of the 11. hower before noone and 1. after noone In like maner are the rest of the hower lines drawen by 3. points accounted and found out by the altitude of the sunne But because before 9. and after 3. in this Eleuation of the Pole it will not serue for this delineation there must another be made by the table of the 12. Signes or Quadrangles Therfore draw that from the 10. d. of ♉ so shall you haue a line or place wherein the third points may be marked Then to prepare the points of the arke for the howers of 8. and 4. of 7. and 5. and both the 6. besides the two markes made in the Tropike of ♋ and the Equator let the third be noted in the arke drawen from the 10. degrée of ♉ 〈◊〉 draw the line of the 5. and 7. howers vse besides the Tropike of Cancer and this drawen from the 10. degrée of ♉ the third which shall come from the beginning of ♊ The line of 4. in the morning and 8. in the euening is very short included in y â— angle next vnto I. Thus you haue finished 9 arkes or lines for the houres of which each one of them doth shew two houres except one which is onely for the â—2 houre And to the intent that there should be no space left voyd and vnprofitable betwéene the Tropike of ♑ and the centre E. you may drawe in that place the vnequall houres which you shall very easily doe on this maner Describe vpon the centre E. an arke very little distant from the Tropike of ♑ to be diuided into 6 equall parts and take the middle point betwéene the beginning of that arke at S. and betwéene E. Then vpon this point as it were a centre make a halfe circle from S. to E. which shall be the line of the 6. vnequall hower that is of midday Afterward one foote of the compasses being placed in the same Semidiameter E. D. and remoued eche way as occasion shall require and the other extended in the meane time so far that it may touch the second point of the arke diuided into 6. partes and the centre E. draw an arke or line from the centre to that point which shal shew the 5. and 7. howers Inlike maner are the other 4. drawen one foote of the compasses being remoued as necessity shal require in the Semidiameter E. D which may be prolonged if it shall be too short the compasses so opened that the other foot may touch the point of the diuided arke and the centre E. and ioyne them all into one arke line then fixe a thread in the centre E. well waxed hauing two small beades vpon it to moue with a plummet of iron or lead Last of all prepare two sights of brasse or other metall with ioynts which you must place in one right line vpon the side or edge A. B. so that you may direct them and againe turne them downe vpon that side A. B. at your pleasure that if you make this Dial vpon the Table or instrument prescribed in the beginning of this book they be no hinderance to you in trying or examining of your plats Thus is your diall prepared but for further instruction beholde the Figure The vse of this Diall or quadrant Horologicall TO know the hower of the day when the Sun shineth worke thus First séeke out in some Calender in what Signe and degrée the Sun is at that day then extend the thread with the beades vpon the Semidiameter E. D. and place the neathermost beade vpon that degrée in the Table of the 12. Signes which the Sunne then occupieth Afterward lifting vp your quadrant the thread with the plummet hanging at liberty let the Sun beams
passe thorow both the sights and then the neathermost bead shall shew the hower of the day either before or after noone for eche line as you see hath two howers but you may easily discern what hower of the day it is The vnequall hower of the day is thus found out The neather bead being placed vpon his iust degrée in the Zodiake lay it vpon the arke of the 12. hower the thread being extended thus holding this immoueable place the vppermost bead vpon y ◠line of the 6. hower vnequal This done the Sun beames entring both y ◠sights the highest bead shal shew the vnequall and the neathermost the equall hower The rising and sitting of the Sunne whereby the length of the day and night is knowen you shall finde out on this maner Place the neather bead vpon the iust degrée of the Sunne in the Zodiake then extend the thread vpon the semidiameter E. F. of the quadrant and the bead shall shew at or betwéen what howers the Sunne riseth and falleth The height of the Sunne aboue the Horizon at any time of the day is thus taken Receiue the Sunne beames by the holes in your sights and the thread with the plunmet hauing liberty to moue shall cut in the limbe of the Quadrant the iust degrée of the altitude of the Sunne aboue the Horizon In like maner is the Eleuation of the Starres aboue the Horizon searched out You shall finde out the eleuation of the Pole by the help of your Quadrant thus Take the height of the Sunne at 12 of the clock when the dayes and nights bée of equall length which being subtracted from 90 d. the eleuation remaineth But if you assay that vpon any other day then the Equinoct you must consider whether the Sunne occupieth the North or the South signes and then vse the table of the Declination of the Sunne on this wise When the Sunne is in the North signes substract his declination from the Meridian height thereof But if it be in the South signes adde the declination to his Meridian altitude The remainder or totall summe being taken from 90. d. the Eleuation of the Pole shall remaine How to make an instrument whereby you may know the iust howre of the night by the Starres CAP. 27. FIrst prepare a plat or Table of brasse or firme and solide wood which will not change or bend somwhat thinne let the forme of it be round thrée inches broad or more or lesse as you will Draw a circle nigh vnto the edg and diuide it into 12. equal parts wherein shal be placed the 12. Signes of the Zodiake then diuide ech of these parts into 30. equal partes which shall shew the number of the daies that the Sunne moueth in euery Sign Make a second circle wherin you may number the daies and a third circle wherein write the Caracters of the 12. Signes as you sée in the Figure following Draw likewise another circle wherein you may write the daies of euery moneth in the yéere which you may doe by any Calender but for more easines beholde the Table following whereby you may likewise doe it Month. Daies Deg. M. Caracters of the 12. Signes Signes Ianuary 1 20 13 ♑ Capricorne  15 5 33 ♒ Aquarius  31 21 44 ♒  February 14 5 52 ♓ Pisces  28 19 48 ♓  March 15 4 36 ♈ Aries  31 20 18 ♈  Aprill 15 4 51 ♉ Taurus  30 19 13 ♉  May 15 4 38 ♊ Gemini  31 18 50 ♊  Iune 15 3 3 ♋ Cancer  30 17 22 ♋  Iuly 15 1 40 ♌ Leo.  31 16 58 ♌  August 15 1 24 ♠Virgo  31 16 58 ♠ September 15 1 40 ♎ Libra  30 16 30 ♎  October 15 1 30 ♠Scorpius  31 17 43 ♠ Nouember 15 2 30 ♠Sagittarius  30 18 13 ♠ December 15 3 38 ♑ Capricorne Enter this Table and you shal finde that the first day of January must be placed against the 20. d. 13. m of Capricorne and the 15. day against the 5. d. 33. m. of Aquarius c. Therfore lay your ruler vpon the centre A. of your plat and vpon the 20. d. 13. m. of ♑ and where it shall touch the circle which you made for the daies of euery moneth there make a marke which shall shew the first day of January Then lay it vpon the 5. d. 33. m. of ♒ and the centre A. and where it shall touch the circle make a marke for the 15. day of January Then lay your ruler vpon A. and the 21. d. 44. m. of ♒ and make likewise a marke for the 31. day of January Again place the ruler vpon the centre A. and the 5. d. 52. m. of ♓ for the 14. day of Februarie worke thus with all the rest vntil you haue set down the beginning and middest of euery month as the Table doth direct you then hauing found out the beginning middest of euery month you may at ease diuide euery space into so many partes as there be daies in the month which it serueth for according as you sée in this figure following It shall be also necessary to make one circle to write the number of the daies of the moneth and another for the names of the monthes you must make also a hole in the centre of this plat of such bignesse as you may sée a Starre thorow it as in the figure you may perceiue Hauing prepared this plat with the circles vpon it for the 12. Signes and months you must prepare an other whéele full of téeth which you shall make on this maner Take a thime Table or platte of the same matter your other was draw a circle vpon it so great as the inward circle of the first plat and diuide it into 24. equall parts Then draw lines from the centre to euery one of those parts vntill you haue so many as there be howers in the longest night in your Country Then cut téeth by these lines for the howres and write the number of them vpon the téeth as you sée in this figure Let the tooth for the 12. howre be so long from the centre to the end as is betwéen the centre A. of the other plat and the circle of the 12. Signes You must likewise make a hole in the centre of this whéele of the same bignes of that in the other plat The thothed wheele This done you must prepare a ruler which shalbe placed vpon this whéele Take therefore a thin péece of wood or brasse and draw vpon it a light line at y ◠one end therof in the middest of the line make a hole of the same bignesse which that is in the great plat and tothed whéele Then draw a circle halfe an inch wide or more if you will afterward cut the ruler round at the end cutting off likewise the one halfe of the breadth of the ruler by the line Let
learne the age of the Moone by an almanack and especially the houre of the change then turne the great ouer-hanging tooth to the day of the Moone on the first limb and to the houre of the change accounting from 12 of the clock The shadow of the Stile shall shew the howre of the night either beneath your Diall or els aboue This Diall will serue also for the Sunne if you turne the great tooth of the moueable whéele to the little strick A. which is right opposite to the beginning of the first and end of the last day of the Moone nere the 15. day and then it is fit for the Sunne For it differeth nothing from y â— North reclining direct where the Reclination is equal to the Eleuation of the Pole The vse of the Table of the declination of the Sunne TAke what degrée you wil of any signe and by this table you may know his declination from the Equinoctiall circle The Signes are written partely on the head of the Table and partely on the foote of the same The Degrées in the first columne doe serue for the Signes that be on the head of the Table and the Degrées in the last columne doe serue for the Signes in the foote of the Table And the common Area or angle against the Signe and the Degrée which you séeke for doth containe the Degrées and Minutes of the Declination due to the same Example I would know how much the tenth degrée of Leo doth decline from the Equinoctiall I must looke in the columne ouer Leo right against the number of 10. in the last columne where I finde 17. d. 46. m. the declination therof c. The table of the declination of the Sunne from the Equinoctial circle  Aries Libra Taurus Scorpius Geminâ— Sagittarius  Deg. Deg. M. Deg. M. Deg. M. Deg. 1 0 24 11 30 20 12 29 2 0 48 12 11 20 35 28 3 1 12 12 32 20 47 27 4 1 36 12 52 20 58 26 5 1 59 13 12 21 9 25 6 2 23 13 32 21 20 24 7 2 47 13 52 21 30 23 8 3 11 14 12 21 40 22 9 3 34 14 31 21 49 21 10 3 58 14 50 21 58 20 11 4 21 15 9 22 7 19 12 4 45 15 27 22 15 18 13 5 8 15 55 22 23 17 14 5 32 16 3 22 30 16 15 5 55 16 21 22 37 15 16 6 18 16 39 22 44 14 17 6 41 16 56 22 50 13 18 7 4 17 13 22 55 12 19 7 27 17 29 23 1 11 20 7 50 17 46 23 5 10 21 8 12 18 2 23 10 9 22 8 35 18 17 23 13 8 23 8 57 18 33 23 17 7 24 9 19 18 48 23 20 6 25 9 41 19 2 23 22 5 26 10 3 19 17 23 24 4 27 10 25 19 31 23 26 3 28 10 47 19 44 23 28 2 29 11 8 19 58 23 29 1 30 11 29 20 12 23 30 0 Deg. Deg. M. Deg. M. Deg. M. Deg.  Virgo Pisces  Leo. Aquarius  Cancer Capricorne   The Table of Sines The whole Sine conteineth 100000. partes The vse of the Table of Sines WHereas the making of some Dials and this Table of Sines may séeme obscure and hard to them who are not acquainted with Sinicall computation it shalbe expedient to declare the vse hereof so much as perteineth to the vnderstanding of this booke omitting all other vses as impertinent to our present purpose Wherfore know that the Grades or Degrées are found in the vpper head of this Table and the Minutes pertaining to the Degrées on the left side in the Area or common méeting of them both a number which is called the Sine answerable to ech Degrée and Minute offereth it selfe Againe the Sine being found out you may easily know the arke that is the Degrée and Minutes thereof these being on the left hand the other on the head or vpper part Vnderstand by the Complement that which remaineth of any number being taken or substracted from 90. Degrées If at any time you enter the Table with iust Degrées without any Minutes resolue one Degrée into 60. Minutes and then séeke out his Sine And whereas you shall finde some numbers imperfect you must remember to supply their want with those which be perfect immediatly going before Example The Eleuation of the Pole at Cambr. is 52. Degrées whose Sine I desire to know therefore resoluing one of the Degrées into Minutes I enter the Table with 51. degrées 60. Minutes and in the common Area I finde the Sine to be 78801. If then you desire to know the complement of this Eleuation substract 52. out of 90. and the remainder shalbe 38. the complement thereof and entring the Table with 37. d. 60. m. you shall finde in the Area 66. which number because it is imperfect you must supply the want thereof by adding the 3. former figures in that which is next before perfect to wit 615. and theÌ„ the whole number shalbe 61566. the Sine of 38. d. which is the Complement of 52. d. the Eleuation of the Pole These thinges well considered there is nothing in the booke so obscure but it shall séeme plaine and easie 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 FINIS Note that some of the letters in the Instrument page 2. are omitted in the printing place A. at the vppermost corner towards the left hand B. at the neathermost C. by 90. beneath and D. at 90. aboue D 0 1 2 3 4 5 M Partes Partes Partes Partes Partes Partes  1 29 1774 3519 5262 7004 8744  2 58 1803 48 91 33 73  3 87 32 77 5320 62 8803  4 116 61 3606 49 91 31  5 45 90 35 78 7120 60  6 74 1919 64 5407 49 89  7 203 48 93 36 78 8918  8 32 77 3722 65 7207 47  9 61 2007 51 95 36 76  10 90 36 80 5524 65 9005  11 319 65 3809 53 94 34  12 49 94 38 82 7323 63  13 78 2123 67 5611 52 â—92  14 407 52 96 40 81 9121  15 36 81 3925 69 7410 50  16 65 2210 55 98 39 79  17 94 39 84 5727 68 9208  18 523 68 4013 56 97 37  19 52 97 42 85 7526 66  20 81 2326 71 5814 55 94  21 610 55 4100 43 84 9323  22 39 85 29 72 7613 52  23 69 2414 58 5901 42 81  24 98 43 87 30 71 9410  25 727 72 4216 59 7700 39  26 56 2501 45 88 29 68  27 85 30 74 6017 58 97  28 814 59 4303 46 87 9526  29 43 88 32 75 7816 55  30 73 2617 61 6104 45 84 D 0 1 2 3 4 5 M Partes Partes Partes Partes Partes Partes  31 901 2646 4391 6133 7874 9613  32 30 75 4420 62 7903 42  33 59 2704 49 91 32 71  34 89 34