of those into fiue if you can and so is eche quadrant diuided into 90. degrées Moreouer it were necessary if your Instrument were large inough to parte ech degrée into 60. minutes or at the least into 3. whereof ech parte may conteine 20. minutes This done fasten a thread wel wared in the centre E. with a plommet of leade on the end so that it may moue at frée libertie You may also if you will vpon this side of the quadrant between E. D. draw the diall whose delineation is taught in the 28. Chapter It were necessary to have here a little hole with a couer to put in your plâ—â—â—…et thread The â—omer â—â—â— of â—â—â—â— Instrument thus finished let the other be altogether liâ—e vnto it except that in stead of the the thread with the plâ—â—â—â—…t you must haue a plombrule made in this maner Prepare a péece of very good wood try it perfectly on both sides to an equal thicknes let it be about half an inch thick and twise so broad as the space betwéene the line C. D. of your instrument and the edge A. B. in the midst therof draw the right line G. H. and placing one foote of your compasses in the point G. with the other make a halfe circle according to the breadth of the ruler whereby you may cut the end round make the other end with a sharp point right in the end of the line G. H. as you sée in this figure Let the distance betwéen the point G. and the end H. be so much as is the semidiameter of the quadrant make by G. an hole so great that a ploÌ„met of lead hanging by a thread from the sharpe end may moue therein at libertie Make also an other round or square hole wherein you may place a néedle touched with the Loadstone as in the compasses or dyals you sée Finally make a little hole in the point or centre G. and with a broad headed naâ—e of brasse fasten it vpon the centre E. of your Instrument so as it may moue turne which way you wil and then your Instrument is finished Note that you may make your Instrument in forme of a quadrangle rightangled as Witekindê° teacheth cutting a round furrow without the circle and degrées made for the ploÌ„met to hang at libertie in so shall you néede but one side of your instrument to vse with a compasse or needle touched with the Loadstone for declinations But the form of the other whose making we haue taught seemeth more commnodious beholde the Figure The vse of this instruement CAP. 2. The vse of this instrument is in examining and placing the plat or dial In immoueble plats to know how they stand as if you would make a Diall vpon a wall first you must vnderstand whether the wall be erect or els recline or incline then whether it be direct East West North or South or els decline which you cannot know without the helpe of this Instrument Againe in moueable plats for the placing of them as if you haue made a South diall or any other kinde by this Instrument you shall easily and perfectly place them The triall of a plat for a Horizontall Diall IF your plat séeme to lye plaine making no angle with the horizon set the side or diameter A. B. of your Instrument vpon it and erect the plombrule right vp betwéene the two quadrants precisely ouer the lyne E. F. then if the thread with the plommet hanging at liberty fall directly vpon his line G. H. which way soeuer you turne your Instrument such a plat is saide to make no angle with the horizon and therefore the diall which is made vpon it is called a Horizontall diall In like maner may you place this kinde of dial being ready made parallele to the horizon and by the help of the néedle direct the stile towards the North pole The trying of plats for Erect Direct South North East and West Dials WHen the plat standeth vpright it maketh a right angle with the Horizon and is called Erect whereof some beholde one priucipall part of the world directly as the South North East or West other decline as the South and North toward the East or West of which kindes hereafter To examine an Erect plat apply the side or diameter A. B. of your Instrument vnto it the thread with the plommet on the foreside hanging at liberty If the thread fal vppon the line E. C. or E. D. the plat is Erect This done apply the said line or diameter A. B. to y â— plat your Instrument being placed equally distant to the Horizon and the plombrule vpon the line E. I. then if the néedle stand directly ouer his caracter the end touched with the Loadstone being next to the plat that plat is called a South Erect Direct In the North all the foresaid things are to be considered except onely that the end of the néedle touched with y â— loadstone is farthest from the plat These things knowen you may easily finde out the East and West Erect Direct if either you haue a line drawen squire wise to the caracter of the néedle or els if you place the plombrule ouer the line E. C. or E. D. And here note that the East and West are not saide to decline because the declination is accounted from the south and North to the direct East and West pointes The examining of plats for Declining Dials ALl such plats as beholde not some principall part of the world directly are called Declining The quantity of their declination is found out thus Apply the diameter A. B. of your Instrument to the plat remembring to hold it equally distant from the Horizon Then moue the plombrule vntill the néedle standeth right ouer the caracter and the point of the ruler which toucheth the degrées in the limb shall shew how many degrées and minutes it doth decline either toward the East if y â— plumb-rule lye in the quadrant C. E. F. or toward the west if in the quadrant D. E. F. The trying of such plats as recline IF the plat standeth not vpright but maketh an obtuse or blunt angle with the Horizon it is saide to recline The degrées of reclination are found out thus Apply the diameter A. B. of your Instrument to the plat the one end placed vpward the other downward theÌ„ moue the plomrule the thread with the ploÌ„met hauing frée course vntill the thread hang precisely ouer the line G. H. then the point of the ruler shall shew the degrées of reclination How Inclining plats are tried BUt if the angle which the plat maketh with the Horizon be acute or sharpe then it doth incline The quantity of inclination is thus knowen Apply the diameter A. B. of your instrument to the plat the thread with the ploÌ„met of the former side hanging at liberty and mark what degrée and minute the thrad shal cut for so much is the inclination The manner of trying those plats which recline and decline
or incline and decline IF your plat shall both recline and decline or incline and decline First séeke out the reclination as hath béen shewed and then the declination as in Erect declining The making of a Horizontall or plaine lying Sunne Dial. CAP. 3. YOur plat being prepared smoothe and plaine drawe vpon it two lines as in the figure following the one A. B. the other C. D. cutting themselues squirewise that is making right angles in the point E. vpon which make the quadrant of any circle from the line E. C. to the line E. A. or E B and write at C. the North at D. the South at A. the East at B. the West And the line C. A. which here is the quadrant being deuided into 90. degrées or parts the eleuation of the Pole shalbe accounted in it which in our example is 52. d. from C. to A. and at the ende of this number drawe a line from the centre E. which shalbe E F representing the stile and artrée of the world Then draw an other line K. L. by C. or by some other point of the line D. C. squire wise so long as you can which shalbe called the touch line or line of Contingence Then measuring with your compasses the least distance of the point O. and the line E. F. or the Stile the one foot placed in O. which is the point of intersection and the other extended toward E. where it shal chaunce to diuide or be placed in the line E. C. marke that point or centre with the letter G. and draw with your coÌ„passes a halfe circle vpon this centre for the equinoctial circle from H. by C. to I. whose diameter must be equally distant to the line L. K. Then diuide this halfe circle into 12. equall parts this done lay a ruler vpon the centre G. and vpon euery marke or diuision made in the halfe Equator and where the ruler shal touch y â— line of contingence there make marks or pricks by which pricks draw lines from E. for the houres E. C. is the 12. houre E. B. the 6. in the morning E. A. the 6. at euening the rest you may sée in y â— figure And whereas in Sommer the 4. and 5. in the morning and also the 7. and 8. at euening shalbe necessary in this kinde of Diall prolong or draw the lines of 4. and 5. at euening beyond the centre E. which shall shew the houres of 4. and 5. in the morning And likewise the 7. and 8. in the morning for the 7. and 8. at euening You may obserue an order both in these and in all other erect direct dials by diuiding the one halfe of the Equator drawing houre lines for the forenone and obseruing the same distance from the meridian line on the other side for the afternoone for the line of the 11. houre in the forenoone is of like distance from the Meridian that the 1. is in the afternoone and the 10. as 2. and so of the rest When you would draw or make the halfe houres you must diuide euery parte of the Equator into 2. equall parts 〈◊〉 the ruler and the line of contingence as you find in the drawing of the houre lines And this remember for the drawing of the halfe houre-lines not onely in this kinde but also in all other kindes of dials which afterward shall follow The Stile must be fixed in the centre E. hanging directly ouer the Meridian line E. C. with so great an angle as the lines C. E. F. make declining from that on neither sides The Equinoctiall circle the Quadrant the line of the Stile and of Contingence must be lightly drawen because they ought to be put out againe in that they serue to no vse but for the drawing of the Diall And this likewise remeÌ„ber in all other kindes of Dials that the preparatiue or pricked lines must after the making of the Dial be omitted and extinguished as altogither vnprofitable This and all other kindes of Dials may most fitly be drawen vpon a clean paper and then with the help of your compasses placed on the plat The making of a South Erect direct Diall CAP. 4. THe making of this is almost altogether like vnto other before Draw here also a line A. B. parallel to the Horizon out of the middest wherof let the line C. D. perpendiculer to that be extended and let the Quadrant be drawen from A. to D. or B. to D. parted into 90. degrées as before Aboue C. let Zenith be written beneath D. Nadir nigh vnto B. the East and by A. the West In y â— Quadrant number the Eleuation of the Pole which in our example is 52. degrées from A. toward D. And at the end hereof draw from the centre C. the line C. E. representing the Stile and by D. draw the line of Contingence I. K. squirewise as before Then the least distance of the point or intersection D. and the Stile being taken with your Compasses extend thâ—n in the line D. C. the one foote placed in D. set the other in F. toward C. and draw by F. the Diameter of the halfe circle of the Equator equally distant to the line K. L. which must be made vpon the centre F. from G. by D. to H. and diuide it into 12. equall partes vpon euery one of which and the centre F. the ruler being placed whersoeuer it shal happen to touch the line of contingence there make markes Then from the centre C. by these marks the houre lines must be drawen The line C. A. shall shew the 6. in the morning C. B. the 6. at euening C. D. the 12. c. The Stile must be placed or fixed in the centre C. hanging precisely ouer the line of the 12. houre with so great a distance as the angle D. C. E is This kinde of Dial doth receiue and shew onely but 12. houres at the most The making of a North Erect Direct Diall CAP. 5. HEre as in the South make a line Parallele to y â— Horizon A. B. cut it squire wise with the Perpendicular C. D. let C. be the centre At C. write Zenith at D. Nadir â—c From C. draw the Quadrant of a circle to D. or B. deuide this into 90. Degrées account the Eleuation of the pole which in our example is 52. d from A. toward C. Draw at the end of of this number the line E. F for y â— Stile Afterward draw the line of Contingence by C. squire-wise and take the shortest distance with your compasses betwéene the poynt C. and the Stile placing the one foote in the point C. extend the other toward E. in the line C. D making a poynt or pricke G wherupon as a centre the same widenesse of the compasses remaining describe the halfe Equator by C. ended with the Diameter H. I. equidistant to the line of Contingence When you haue deuided thus halfe circle of the Equator into twelue equall partes lay the ruler vpon the centre G. and
vpon each diuision of the Equator and where it shall touch the Contingent line make markes This done draw the lines for the houres by those markes from the centre E. but those very fewe that is two nigh vnto A. and two by B. but prolong and extend them beyond the centre E. so that their contraries may bée made for in this kinde of Dials there bée but onely ten houres profitable that is 4 5 6 7 8 before noone and 4 5 6 7 8 after noone which shew but only in Sommer from the entring of the Sunne into ♈ vntill such tâ—ne as it entreth ♎ The Stile must bée fixed in the centre E. placed vpward directly ouer the lint E. C. with so great an angle as I. E. C. is Let the line C. D. bée placed vpward perpendicularly but so that it may not bée almost séene as afterward seruing to no vse because it is onely a line preparatiue Beholde the Figure A North Diall erect direct The making of the East and West Erect Dials CHAP. 6. IF you know the making of one of these you may easily make them both for they be very like differing onely in the naming of the houres for the one containeth houres for the forenoone and the other for the afternoone You must therefore on your plat make the quadrant of a circle A. B. C. which may afterward easilie bée put out as all the other lines must bée except the houre lines let the side A. B. be Perpendiculare B. C. Parallele to the horizon and let the arke beholde the South which being diuided into 90. degrées nomber therin the elenation of the Pole dounward from A. toward C. by the end of this number and by the Centre B draw a line so long as your plat will giue you leaue whose South ende shall behold precisely the Equinoctiall circle At which end draw a circle whose diameter shall bee almost the third part of the line Then draw another diameter or line in the centre squire wise to the other which shall shew the axtrée of the world and be the line for the 6. hour After ward at the cutward sides of the circle draw two contingent lines one beneath the other aboue so that they may be Parallele to the middle line Deuide each quarter of the circle into sixe equal partes Then place the ruler vpon the centre and eache of those markes or partes and where it toucheth the lines of contingence there make markes in them Afterward draw a line by those two markes which be next to the 6. houre in the lines of contingence which may be equallie distant from the line of the 6. houre In like maner doe with the rest so that you may haue in the East Diall two aboue the 6. houre the 4. and 5. in the morning and vnder it 7 8 9 10 11. In the West Diall like wise 7. and 8. in the euening aboue the 6. houre and vnder it 6 5 4 3 2 1. Neither of them doe shew the 12. houre because at that time the Sunne beames be Parallele to the plat Fixe the Stile in the centre of the circle right vp from the Plat so long as the Semidiameter of the circle is only shewing the houre with the very top or end thereof Yet it were more conuenient to haue it placed along ouer the line of the 6. houre being a plate of yron or some other metall being so broad as the Semidiamer of the circle is Behold the figures folowing The East diall Erect The West Diall erect Note that these fiue kinds of Dials before taught may be made vpon a stone cut square in forme of a die The making of a South Erect declining Diall which may be placed on any vpright wall whatsoeuer CAP. 7. IN all Declining Dials because the Stile doth not hang directly ouer the meridianline therefore you must first finde out and place the Substile which is the line ouer which the Stile directly hangeth and lik wise the line of the Stile which may bée both eastly and spéedily performed in this maner First by your instrument séeke out the Declination of the wall or plat whereupon you would make a diall which for example suppose I had found to be 50. degrées â— Therefore drawe the Horizontall line A. B. let the Meridian C. D. cut it squire wise in the point E. which may be in any place of the line A. B. and let the line F. G. cut the meridian squire-wise in the point C. which you may like wise take in what parte of the Meridian you thinke most conuenient Upon the center E. describe the quadrant of a circle from C. to A. if the declinatioÌ„ of your plat be West-ward or from C. toward B. if East-ward as in this example it is diuide it into 90. degrées and number in it from C. toward B. the Eleuation of the Equator 38. degrées and laying your ruler vpon the center E. and vpon the end of this number draw the line E. H. Againe account in the quadrant from C. toward B. the declination of the plat being 50. degrées and draw the line of Declination E. I. from E. to the end of this number Then take your compasses set one foote in the point C. extend the other vnto H. which is the intersection point of the line E. H. with the line C. G. and that same widnesse remayning place one foote in the centre E. and with the other marke the point 1. in the line E I. and from the point I. draw the line I. K. squire-wise to the Meridian E. C. placing K. at the intersection it maketh with E. C. Moreouer take with your compasses the iust length of the line I. K. and placing one foote in C. turne the other toward F. and make the point L. in the line C. F. drawe the Substile from E. by L. Let the line of Contingence bée drawne squire-wise to the Substile in the point L. This done take the distance betwéene the centre E. and the point K. and place it in this line of Contingence from the point L. vnto M. and make the point M. that the line E. M. may be made from E. vnto M. for the stile Measure with your compasses the least distance betwéene the point L. and the Stile and with the same widenes one foote remaining in L. turne the other toward E. and make the centre O. in the Substile vpon which describe the Equinoctiall circle Then placing your ruler vpon O. being the centre of the Equinoctiall circle and N. which is the point of intersection of the Meridian and Contingent marking where it cutteth the circumference for there you must begin to diuide it into 24. equall partes not withstanding those 12. are onely in vse which are next the contingent Finally place your ruler vpon the centre O. and vpon the seuerall diuision points of the Equator and where it toucheth the line of Contingence make markes by which from the center E. draw the
from the Meridian is fouÌ„d out altogether like to the South Erect declining Therefore you may resort thither for the working hereof I will onely drawe the Figure Let the line A. B. being parallele to the Horizon cut C. D. squire wise placing E. at the intersection Draw the quadrant from C. to B. diuide it into 90. d. accounting therein from C. toward B. the distance of the Substile from y e line which is as it were the Meridian which distance is 28. d. 55 m. At the end of this number draw the line E. F. for the Substile Then number from that line the distance of the Substile and the Stile which is 25. degrées 48 minutes toward B. Draw likewise at the end of this number the line for the Stile E. G. This done let the line of Contingence be drawen squire wise by the point F. and then taking the least distance betwéene the point F. and the Stile extend the compasses in the line F. E. the one foote being placed in F. where the other shall deuide the line place the letter H. With the same widenes of the compasses draw vpon the centre H. the Equator and where the ruler shall touch the same being laid vpon the centre H. and the intersection of the Contingent line and y t which is as it were the Meridian begin to deuide it into 24. equall partes Finish all things remaining as in y e South erect declining onely this excepted the Stile being fixed in the centre E. must be placed vpward beholding the substile with so great a distance or angle as the letters F. E. G. do shew The line C. D. being applyed to the plat perpendicularly sheweth as it were the 12. houre at midnight therefore account from that the houre lines as they follow in order 1 2 3. which houres haue no vse in this kinde of Diall for our Eleuation but from 4. c. Let the line A. B. be parallel to the Horizon being lightly drawen as the other preparatiue lines be seruing afterward to no vse Note if the plat decline towards the East as this figure doth it is for the forenoone and you must account the houre lines from that which is as it were the Meridian forward 4 5 6. c. If it decline toward the West account them backward 11 10 9. as we shewed before A North erect declining Diall The making of a Meridionall or South Reclining direct Diall CAP. 11. IF the Reclination of the plat be lesse then the complement of the Eleuation of the Pole adde this complement and the Reclination of the plat together and with this number as if it were the Eleuation of the Pole make a South erect direct diall and it will be perfect and fit for your plat Example and delineation of a South Diall reclining 25. d. MAke the first line A. B. drawe also an other C. D. cutting the other with right angles Then adde the Complement of the eleuation of the Pole which is 25. d to the reclination of the plat which is 38. d. and the totall summe shalbe 63. d. which number being in place of the Eleuation of the Pole account it in the Quadrant from A. towards D. and at the end hereof draw the line F. for the Stile Then make the line of Contingence K L. squire wise to the line C. D. Afterward take the least distance with your compasses betwéen the point G. and y â— Stile with y â— widenes the one foote extended toward C. make a point or prick E. by which point draw the line H. I. equidistant from A. B. or K. L. vpon E. make a halfe circle from H. by G. to I. which being diuided into 12. parts finish the rest as the South Erect direct A South Direct reclining 25. d. BUt if the Reclination be equall to the complement of the Pole make your Diall on this maner like to the East and West Draw a line Parallele to the Horizon A. B. so long as the plat will giue you leaue diuide it into 7. equall parts and with the same widenes of the compasses in the midst of the line make a circle representing the Equator Then drawe two lines of Contingence by the circumference of the circle equidistant from the first A. B. Diuide the Equator into 24. equall parts Finish the rest like the East or West diall except in naming the houres for that which is in them the 6. houre line is here the 12. c. A South Direct reclining 38. d. BUt if the reclination of the plat be greater then the complement of the Eleuation of the Pole substract the complement of this Eleuation out of the reclination and that which remaineth shall serue in stead of the Eleuation of the Pole with which Eleuation make your diall altogether like a Horizontall which you shall finde fit for your plat Example of a South Diall reclining 55. d. FIrst I take the complement of the Eleuation which is 38. d. out of the Reclination of the plat which is 55. d. and there remaineth 17. d. which number kéep for the Eleuation of the Pole In Delineation of this Diall drawe a line Parallele to the horizon A. B. draw another C. D. making right angles with the line A. B. Then make the quadrant from A. to D. which being diuided into 90. degrées number in it that which is as it were the Eleuation of the Pole namely 17. degrées from D. towards A. Then draw the line of Contingence K. L. in any point of the line C. D. squire wise Take with your compasses the least distance of the point G. and of the Stile extend them forth in the line C. D. I meane from G. toward C. make there a point marked with E. vppon which point or centre with the same widenesse of the compasses drawe the Equator from H. by G. to I. diuide it into 12. equall partes c. Finish that which remaineth in all respects like to the Horizontall Diall in naming the houres drawing of the lines fixing of the Stile c. for in this kinde of Diall the Stile must bée fixed in the centre C. standing vpward with so great an angle as C. D. F. is Beholde the Figure folowing A South Reclining Erect The making of a North Diall Reclining Direct CAP. 12. IN these kindes if the Reclination bée lesse then the Eleuation of the Pole subtract that from this kéep the remainder for the Eleuation of the Pole according to which Eleuation make a North Diall Erect Direct and it will be fit for your plat In which the houres about Noone are placed being profitable onely in sommer and not then vnlesse the Reclination be greater then the distance of y â— Tropâ—k of S from y â— Zenith And the more your Diall Reclineth the longer time it will shew in Sommer Example of a North Diall Reclining 45. degrees FIrst I take the Eleuation of the Pole which wée account 52. d. 〈◊〉 the Reclination of the plat
the second marke in the Tropike of Cancer and the intersection of the line of the 5. hower with the Equator or line of Aries and Libra drawing like wise a line which shall shew the first howre in the East and the 11. howre in the West Diall make on this wise all the other vnequall howres namely the 10 9 8 and 7 in the West Diall And the 2 3 4 5 in the East Diall The making of an Horizontall Sphericall or hollow Diall CAP. 26. FIrst prepare your Sphere or plat perfectly hollow of what quantity you wil. Then with your compasses diuide the vpper brimme thereof into 4 equall partes marking it with the letters A. B. C. D. Afterward open your Compasses to the widenes of one Quadrant either A. C. or A. D. and with that widenesse one foote being placed in the point D. draw an obscure or light line from A. to B. This done set one foote of your Compasses in the point C and with the other you shall try whether the plat be perfectly Sphericall or not for if it be your Compasses will fall in the same line which you made before but if it be not perfect you may amend it And then draw this line manifest so that it may continue For it shall be the Meridian line shewing the 12 howre Againe place one foote in the point A. drawing with the other a light line from C. to D. then one foote being set in B. you may try with the other as before the truth of the line last made Now where these two lines cut eche other in the bottome of the plat place the letter E. Then diuiding the quadrant A. E. into 90. d. and accounting therein the Eleuation of the Pole from E. toward A. make y â— point F. by which the arke line of ♈ and ♎ representing the equinoctiall circle shall be drawen Afterward séeke out the greatest declination of the Sun from the Equator which you shall finde in the table of the declination of the Sunne which is 23. d. 30. m. Then account 23. d. 30. m. from F. toward E. making there a mark for the arke of Cancer Likewise from F. toward A. number the same distance for the arke line of Capricorne This done account from F. toward E. 20. d. 12. m. make there also a marke for the line of ♊ and ♌ And the like space from F. towards A. for the arke of â™’ and â™ To conclude number from F. towards E. 11. d. 30. m. making there also a marke for the â—ine of ♉ and â™ and so much from F. toward A. for ♓ and â™ When you haue thus made marks for al y â— arkes of the 12 Signes open your compasses to the Quadrant of the Spheare that is from A. to C. which widenes of the compasses remaining place one foote in the point F. in the arke of ♈ and ♎ in the Meridian and where the other foot shall touch the same Meridian towards B make the point G. which shall represent the Pole antarticâ— by which as it were from a centre draw a line from the point D. by F. to C. which shall be the line of Aries and Libra Then one foote of your compasses remaining in the point G. with the other draw lines from one side of the plat to the other by euery marke before made for the 12. Signes of the Zodiake The 12. Signes being thus finished procéede to the diuision of the equall howres on this manner Diuide y â— arke of the Equator into 12. equall partes beginning at D. by F. ending in C. Then open your Compasses to the quadraÌ„t of the plat and the same widenesse of them remaining place one foote on the first point of the diuision next C. in the Equator and if you haue diuided the Equator equally the other foote will touch the first part beyond F. towards D. by which from the centre G to the edge of the plat draw a line which shall shew the first howre afternoone This done remoue your compasses that widenesse remaining placing one foote in the second part from C. towards F. and the other foote touching the second part from F towards D. make a line as before from the centre G. to the brimme of the plat to shew the 2. howre afternoone In like manner finish all the other howre lines namely the 3 4 5 6 7 8 for the afternoone Then doe likewise on the other side for the howres in the forenoone namely the 11 10 9 8 7 6 5 and 4 drawing lines from the centre G. by euery diuision to the brimme of the plat c. The placing of the vnequall howres in this Diall When you will place the howres vnequal in this Sphericall Dial diuide the Tropick of Cancer and of Capricorne ech of them into 12. equall parts as before you did the Equator for the equall howres Then with the compasses ioyne eche thrée points of these thrée arkes answerable into one line or arke vntill you haue made 12. lines to shewe the 12. vnequall howres as in the figure following you may sée Whereof the Meridian or 12. vnequall howre shall alwaies be the 6. vnequall howre In placing the figures to the equall vnequall howres and the Caracters to the 12. Signes of the Zodiake the figure may sufficiently shewe notwithstanding you may place them where you will giuing to ech signe his proper Caracter and euery howre equall and vnequall their proper figures or names Fire the Stile in the centre G. standing vp so high as the brimme of the plat so that the vpper end may appeare as the centre of the circumference which you may try by placing a ruler vpon the points A. B. And againe vpon C. D. In like manner you may examine it with your Compasses but the former as practise wil teach you is the more conuenient way You may if you wil haue the Stile stand aboue the plat so that it may shew the equall howres aboue the edge of the Sphere and then fasten a knot of equall height with the plat which shall shew the motion of the Sunne in the 12. Signes and y â— vnequall houres which otherwise the end of the Stile should doo as in the figure following you may perceiue The Figure of an hollowe Horizontall Diall The making of a South Spherical erect direct Diall CAP. 27. YOu shall vnderstand that the making of this kind differeth almost nothing from the Horizontall except onely in the accounting the beginning of the Eleuation of the Pole drawing the houres vnequall First your Sphear or plat being prepared and parted into foure Quadrants as before in the Horizontall you were taught diuide the quadrant E. A. into 90 degrees Then number in it the Eleuation of the Pole from A. toward E. marking the ende of the number with F. Afterward open your compasses to the quadrant of the plat and the one foote placed in F. extend the other in the Meridian line towards B. making the
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
houre lines Place the Meridian perpendicularly vpon the wall the centre E. vpward the Stile pointing downeward Let the Stile hang directly ouer the Substile making an angle equall to E. M. L. The making of a North Erect Declining Diall CAP. 8. THe North Erect declining Dial differeth from the South onely herein that the centre is to be placed downeward the Stile pointing vpward to the North Pole and that the Meridian representeth the 12. houre at midnight and not at noone Therefore if the declination bée toward the East you must account the houre lines from that which is as it were the Meridian forthward 1 2 3 4 5 6 c. But if it decline toward the West number them backeward 11 10 9 8 c. omitting the first 3. which are before Sunne rising and after Sunne setting in our eleuation Let the line E. D. bée placed perpendicularly vpon the plat and the Stile point vpward to the North Pole Compare this figure with the former Another way to make the South Erect Declining Diall CAP. 9. ALbeit we haue plainely and perfectly shewed the making of the South and North erect Declining Dials in the two former Chapters yet to satisfie them that delight in variety here is also declared another way whereby you may make them namely by the helpe of Arithmetick and the Table of Sines which is placed in the end of this booke for this intent Therefore the Eleuation of the Pole being knowen and the Declination of your plat by your Instrument found out Multiply the Sine of the complement of the Eleuation by the Sine of the complement of the Declination diuide the product by the whole Sine which is 100000 and you shall haue a quotient Sine whose arke is the distance of the Stile from the Substile which distance kéep Then take the complement of this distance and the Elenation of the Pole and multiply the Sine of the lesser by the whole Sine parting the product by the Sine of the greater the quotient Sine which shall come of this diuision shall giue you an Arke whose complement is the distance of the line of the Substile from the Meridian which distance you shall likewise kéepe For better instruction herein consider the example Example of a South Diall declining 45. d. Eleuation of the Pole 52. d. FIrst I enter the Table of Sines for the Sine of the complement of the Eleuation which is 38. d. and I finde it to be 61566. Then I looke for the Sine of the complement of the Declination which is 45. d. and I finde that to be 70710. This done I multiply the one by the other and the product is 435333 1860. which I diuide by the whole Sine being 100000 wherof commeth a quotient 43533. With this quotient Sine I enter the Table and because I finde not the iust number I take that which is next either greater or lesse vnto it which you must alwaies remember to doe for so small a difference maketh no alteration and therfore I take in stead thereof 43523. whose Arke is 25 d. 48. m. which is the distance of the Stile from the substile Then I take the complement of this distance which is 64. d. 12. m. whose Sine is 90031. and the Eleuation of the Pole 52. d. whose Sine is 78801. and multiplying y e Sine of the lesser which is the Eleuation of the Pole by the whole 100000. the product is 7880100000. which I diuide by the Sine of the greater to wit the Sine of the complement of the distance of the Stile from y e Substile whose Sine is 90031 whereof commeth this quotient 87526 whose Arke is 61. d. 5. m. The complement of which arke is 28. d. 55. m. being the distance of the substile from the Meridian These distances being thus found out the drawing of the diall foloweth First draw a line Parallele to the Horizon A. B. out of whose middle point C. draw the Meridian line squire wise C. D. vpon the centre C. make the quadrant of a circle betwéene A. and D. Here vnderstand that generally in all kindes of declining Dials if the declination be towards the East you must draw the quadrant towards the West except in the South reclining declining and the North inclining Declining where the contrary is prescribed But if the declination be Westward the quadrant must be drawen Eastward Hereby you shall easily know on which side you ought alwaies to draw the quadrant and which way the figures following doe decline Your quadrant being made diuide it into 90. degrées number therein from D. the distance of the Substile from the Meridian which is 28. d. 55. m. Draw at the end of this number the line C. E. for the Substile Then from E. towards A. account the distance of the Stile from the Substile which is 25. d 48. m. and at the end hereof draw the line C. F. for the Stile Afterward by the point E. or in any place of the Substile draw the Contingent line G. H. so long as you can squirewise to the Substile Then take with your compasses the least distance betwéene E. and the Stile the one foote remaining in E. and the other extended in the Substile toward C. place at the pricke there made with the compasses I. vpon which pricke as a centre the same widenes of your compasses remaining draw a circle by E. which shall represent the equinoctiall or Equator Then lay the ruler vpon the point I. and the intersection whose marke is K. of the line of Contingence and the line C. D. which is alwaies drawen so that it may cut the other and where the ruler so placed shall touch the circle there make a marke and there begin to diuide it into 24. equall partes notwithstanding those 12. onely are to be vsed which doe beholde the contingent line Then lay the ruler vpon the centre I. and the Contingent line by euery diuision of the Equator and where it shall touch the line of Contingence there make markes by the which from the centre C. draw lines for the houres so many as shalbe necessary The line C. D. shall alwaies shew the 12. houre which must hang perpendicularly Number the residue of the lines in their place as they follow in order The line A. B. in such as doe decline is vnprofitable except it so chance that some houre line falleth in it Let the Stile be fixed in C. hanging directly ouer the Substile with so great an angle as E. C. F. is declining on neither side Note diligently the making of this declining Diall because in those which follow we meane not to repeate those things which héere haue béen taught And this one kinde well knowen all the other will séeme most easie For better vnderstanding hereof beholde the figure A South Erect declining Diall The making of a North Erect declining Diall another way CAP. 10. THe distance of the Stile from the Substile and of the Substile
which is 45. d. and there remaineth 7. d. which shall bée in place of the Eleuation of the Pole Then for the drawing of it resort to the North Erect Direct because their Delineation is like remembring alwaies to call that which remaineth the Eleuation of the Pole which in this example is but 7. degrées In the figure following you sée that most part of the houre lines bée drawne opposit from the Contingent beyond the centre E. as you must doe in any of this kinde if you will haue the houres about noone Example of a North Diall Reclining 52. degrees BUt if the Reclination be equal with the Eleuation of the Pole then describe a circle vpoÌ„ the centre E. and diuide it into 24. equall partes beginning the diuision at the 12. houre Draw by those points lines for the houres from the centre E. so many as shall be necessarie erecting the Stile being some small wier in the centre E. right vp This kinde of Diall serueth only when the Sunne is in the north signes which be ♈ ♉ ♊ ♋ ♌ â™ A North Reclining Direct You may with the help of a smale brasse quadrant and a néedle placed conueniently make this a portable and fit Diall for any Eleuation of the Pole Againe if the Reclination shall excéede the Eleuation of the Pole adde the complement of the reclination to the Eleuation and with that number as if it were the Eleuation of the Pole make your Diall altogether like a Horizontall and it shall be fit for your plat In which notwithstanding in winter very fewe houres will shew and those about noone and yet not these vnlesse the Reclination shall bée greater then the â—â—…hest bending of the Tropâ—ke of ♑ from the Zenith Example of a North Diall reclining 80. d. FIrst adde the complement of â—he reclination of the plat which is 10. d. to the Eleuation of the Pole 52. d. and with the totall number 62. d. â—â—â—f it were the Eleuation of the Pole make a Horizontall Diall as is shewed cap. 3. Alwaies remember to call the two numbers added together the Eleuation of the Pole A North reclining Direct The making of an East and West Diall reclining CAP. 13. FIrst multiplie the Sine of the Eleuation of the Pole by the Sine of the Reclination of the plat and diuide the product by the whole Sine whereof shall come a quotient whose arke is the distance of the Stile from the Substile Compare the Complement of this distance with the Complement of the Eleuation of the Pole and which you shall find least multiply the Sine thereof by the whole Sine parting the Product by the Sine of the greater The quotient shall yéelde an arke whose Complement shall be the distance of the Substile from the Meridian Example of an East or West Diall reclining 45. degrees FIrst I multiplie the Sine of the Eleuation of the Pole 52. degrées being 78801. by the Sine of the ReclinatioÌ„ of the plat which is 70710. the product 5572018710 I diuide by 100000 the whole Sine and the quotient is 55720. the arke whereof is 33. d. 52. m. which is the distance of the Substile from the Stile Then I compare the Complement of this distance which is 56. d. 8. m. with the Complement of the Eleuation of the Pole which is 38. d. and finding the Complement of the Eleuation to be least I multiply 61566 the Sine thereof by the whole Sine and the Product arising thereof is 6156600000 which I diuide by the Sine of the greater which is the Complement of the distance whose Sine is 83033. And the quotient 74141 yéeldeth an arke 47. d. 51. m. whose Complement is 42. d. 9. m. which is the distance of the Substile from the Meridian First draw a line Parallele to the Horizon A. B. drawe another squier wise C. D. Then make the quadrant from A. to D. Number therein the distance of the Substile from the Meridian which wée found to bée in our example 42. d. 9. m. from A. toward D. At the end of this number from the centre C. draw the line for the Substile C. E. Account from this line the distance betwéene the Stile and the Substile which is 33. d. 52. m. draw likewise at the end of this number from C. the line C. G. for the Stile Let the line of Contingence bée squire wise to the Substile in any point where you will Then take with your compasses the least distance betwéen the point E. and the line of the Stile with that widnesse the one foote remaining in E. extend the other in the line of the Substile toward C. make there the point F. vpon which draw the Equator from H. by E. to I. Diuide it into 12. equall partes beginning your diuision where the ruler being placed vpon the centre F. and the intersection of the Meridian with the Contingent shall touch the equator Lay the ruler from F. by each of those markes and where it shall touch the line of Contingence there make markes by which from the centre C. drawe the houre lines so many as shall be necessary The line A. B. is the Meridian and sheweth the 12. houre Finish all other thinges as in the rest before you were taught Note that if it be an East diall you must make the quadrant from A. to D. If a West from B. to D. Finish the residue as before c. An East or West reclining The making of a South reclining declining Diall CAP. 14. FIrst in this kinde as in other which follow you must finde out and place the Meridian the Substile and the Stile which being done that which remaineth is finished as in those before Therefore the Declination and the Reclination of the plat being known by your instrument multiplie the Sine of the Declination by the Sine of the complement of the Reclination diuiding the product by the whole Sine The quotient Sine shall yéeld an Arke whose complement shall be named the Complement to be repeated Afterward augment the Sine of the Complement of the Declination by the whole Sine diuide the Product by the Sine of the Complement to be repeated where of shall come a Sine whose arke shalbe the distance of the Meridian from the Horizon Againe multiply the Sine of this distance by the Sine of the Complement of the Reclination parte the Product by the whole Sine the arke of whose quotient shalbe called the Eleuation of the Meridian Then compare this Eleuation of the Meridian with the Eleuation of the Pole and which you shall finde least subtract that from the greater and that which remaineth kéep for it shall be called the difference kept being mindefull which of them was the greatest This done multiply the Sine of the Complement to be repeated by the Sine of the difference kept diuiding the Product by the whole Sine whereof shall come a Sine whose arke shalbe the distance of the Stile from y â—
substile To conclude compare the Complement of this distance with the complement of the difference kept and which you shall finde least multiply the Sine thereof by the whole Sine part the Product by the Sine of y â— greater and thereof shall come a Sine the Complement of whose arke shalbe the distance of the Substile from the Meridian Example of a South Dial Declining 18. d. Reclining 25. d. First looke out in the Table the Sine of the Declination which is 30901. Then the Complement of the Reclination being 65. d. the Sine hereof is 90630. Afterward multiply 90630 by 30901. and the product 2800557630 diuide by the whole Sine which is 100900. the quotient shalbe 28005. whose arke is 16. d. 16. m. The complement whereof being 73. d. 44. m. is the complement to be repeated This done multiply 95105 the Sine of the Complement of the Declination 72. d. by the whole Sine 100000. the product shalbe 9510500000. which being diuided by 95996 the Sine of the complement to be repeated the quotient shalbe 99071 whose arke is 82. d. 11. m. which is the distance of the Meridian from the Horizon Afterward augment the Sine of this distance 99071. by the Sine of the complement of the Reclination which is 90630. and the product 8978804730 part by the whole Sine and the quotient 89788 shall yéeld an arke 63. d. 53. m. which is the Eleuation of the Meridian Then compare the Eleuation of the Meridian with the Eleuation of the Pole which in this example is 52. d. and finding the Eleuation of the Pole to be least substract this namely 52. degrées from 63. d. 53. m. the Eleuation of the Meridian and there remaineth 11. d. 53. m. which is the difference kept Now multiply 95996 being the Sine of the Complement to be repeated which is 20591. the product is 1976653636. which diuided by the whole Sine the quotient shalbe 19766 whose arke 11. d. 24. m. is the distance of the Stile from the Substile Then to conclude y â— Complement of this distance which is 78. d. 36. m. being compared with the Complement of the difference kept which is 78. d. 7. m. you shall finde the Complement of this difference kept to be least wherefore multiply 97856 the Sine thereof by the whole Sine and the product 9785600000. part by the Sine of the greater to wit of the Complement of the distance of the Stile from the Substile which is 98027. the quotient shalbe 99825. whose arke is 86. d. 37. m. The Complement whereof is 3. d. 23 m. which is the distance of the Substile from the Meridian There be thrée sundry kindes of these Dials the one differing from the other The first kinde Marke therefore if the Eleuation of the Meridian be greater then the Eleuation of the Pole drawe a line parallele to the Horizon A. B. out of the middest whereof extend an other C. D. squire wise to the line A. B. make the quadrant from A. to D. number therin from A. towards D. the distaÌ„ce of the Meridian from the Horizon which is 82. d. 11. m. at the end hereof from y â— centre C. draw the line C. E. for the Meridian From which account backward towards A. the distance of the Substile from the Meridian which is 3. d. 23. m. draw at the end of this number the line C. F. for the Substile Then from the Substile toward A. number the distance of the Substile from the Stile 11. d. 24 m. and at the end therof extend the line C. G. which shall represent the Stile This done in the line of the Substile in the point F. which you may take where you wil in y â— Substile draw the line of Contingence squirewise to the Substile Then take the least distance of the point F. from the Stile Afterward extend your compasses the one foote being placed in F. in the line of the Substile toward C. vnto H. Describe vpon the centre H. the Equinoctiall circle by F. Diuide it into 24. equall partes beginning where the ruler shall touch the Equator being placed vpon the centre H and vpon euery marke of the Equator and where the ruler shall touch the line of Contingence there make markes by which from the centre C. draw the houre lines somany as shall be necessary C E. alwaies she wing the 12. hower Let the Stile hang directly ouer the Substile with so great an angle as F C. G. is fixing it in the centre C. pointing downward to the Pole Antartick Place the line A. B. parallele to the Horizon hauing afterward as other preparatiue lines no vse A South Declining Reclining The second kinde But if the Eleuation of the Pole and the Eleuation of the Meridian be found equall the making of your Diall differeth from the former yet y â— finding out of the Meridian and the Substile c. is wrought as in the other before whither you may resorte It shal be sufficient here to shew an example of this kinde Example of a South Diall whose Declination is 32 d. Reclination is 33. d. 30. m. Eleuation of the Pole is 52. d. 2. m. First I multiply 52991 the Sine of the declination by 83388 the Sine of the Complement of the Reclination and the product 4418813508 arising thereof I diuide by the whole Sine the quotient Sine 44188 yéeldeth an ark 26. d. 14. m. whose complement being 63. d. 46. m. is y e complement to be repeated Then I increase the Sine of the Complement of the declination which is 84804 by the whole Sine and the product is 8480400000 which I parte by 89700 being the Sine of the complement to be repeated The arke of whose quotient Sine 94541 being 70. d. 59. m. is the distance of the Meridian from the Horizon This done I multiply this Sine 94541 by the Sine of the complement of the reclination which is 83388 and the product arising hereof being 7883584908 I diuide by the whole Sine the quotient therof is 78835 whose ark 52. d 2. m. is the Eleuation of the Meridian which I compare with the Eleuation of the Pole and finding them equall I end my worke héere For this shalbe sufficient in this kinde of Diall as you may more plainely perceiue by the delineation of the Figure Wherefore if the Eleuation of the Pole and of the Meridian be found equall as in this example it is make a line parallel to the Horizon A. B. Draw another C. D. making right angles with the line A. B. Draw the quadrant from A. to D. number therein the distance of the Meridian from the Horizon from A. toward D. which is 70. d. 59. m. being here in place of the Substile Then draw the line of Contingence squire wise to the Meridian C. E. which is also the Substile C E. in any point thereof as before Place one foot of your Compasses in the intersection E. then set the other foote in y â—
Meridian or Substile being of any widenes make there the point or centre F. vpon which centre drawe the halfe Equator from G. by E. to H. Diuide the one half therof from E. to H. into 90. d. Account therein from the Meridian E. towards H. the declination of the plat 32. d. place the ruler vpon the centre F. and the end of this number and where it shall touch the Contingent line there make a marke by this marke you must draw a line squire wise to the Contingent line which shall be for the 12 hower And where the ruler shall touch the Equator there begin to diuide it into 12. equall partes by which lay the ruler from the centre F. making in the line of Contingence markes for the other hower lines all which shall cut the Contingent line squire-wise Note that sometime in diuiding of the Equator the two parts at both ends next to the Semidiameter G. H shall both of them make but one whole parte vnlesse you will make a whole circle for the Equator and diuide it into 24. partes Let the Stile be a small wyer standing right vp in the point E. being so long as the semidiameter of the Equator It may be also a plate of iron or brasse fastened in the Substile so broad as the Semidiameter is as in the East and West erect dialls c. Let the line A. B. be parallele to the Horizon Finish all other things as before A South reclining declining The third kinde If the Eleuation of the Meridian be lesse then the Eleuation of the Pole the making of this Diall i◠vnlike to both the other mentioned before yet the finding out of the distance of the Stile from the Substile is done like to the first kinde as by the example following may appeare Example of a South Diall Declining 45. d. Reclining 45. d. Eleuation of the Pole 52. d. First I multiply the Sine of the declination being 7071 by the Sine of the complement of the reclination which is likewise 70710 and the product 4999904100 I part by the whole Sine The quotient is 49999 whose arke is 30. d. The Complement of this arke is 60. d. which is the Complement to be repeated Then I increase the Sine of the Complement of the declination which is likewise 70710 by the whole Sine and the product thereof 7071000000 I diuide by the Sine of the Complement to be repeated 86602 the quotient Sine 81649 yéeldeth an arke 54. d. 44. m. which is the distance of the Meridian from the Horizon Afterward I multiply this Sine 81649 by the Sine of the Complement of the Reclination which is 70710 the product arising 5773400790 I part by the whole Sine the quotient is 57734. The arke whereof is 35. d. 16. m. the Eleuation of the Meridian which I compare with the Eleuation of the Pole being in our example 52. d. and finding the Meridian Eleuation to be least I substract it out of the Eleuation of the Pole there remaineth 16. d. 44. m. which is the difference kept This done I augment 86602 the Sine of the Complement to be repeated by 28791 the Sine of the difference kept and the product 2493358182 comming hereof I diuide by the whole Sine the quotient Sine 24933 yéeldeth an arke 14. d. 26. m. the distance of the Stile from the Substile Now comparing the Complement of this distance being 75. d. 34. m. with the Complement of the difference kept which is 73. d. 16. m. and séeing the Complement of the difference kept to be least I multiply 95765 the Sine thereof by the whole Sine and the product 9576500000 I diuide by 96843 the Sine of the complement of the distance and 98886 shalbe the quotient therof whose arke is 81. d. 27. m. The Complement of this arke is 8. d. 33. m. which is the distance of the Substile from the Meridian In the Delineation of this diall drawe first as before a line Parallele to the Horizon A B. extend another C. D. making right angles with the line A. B. Draw the Quadrant from A. to D. diuide it into 90. degrées In which account the distance of the Meridian from the Horizon from A. towards D. which is 54. d. 44. m. drawe at the ende of this number the Meridian line from the centre C. which shall shew the 12. hower Account from this toward D. the distance of the Substile from the Meridian which is 8. d. 33. m. at the end hereof extend from C. the line E. for the Substile From this number the distance of the Stile being 14. d. 26. m. toward D. if there be so much space if not account it from the Substile toward A. make at the end of this number the line C. F. for the Stile Let the line of Contingence cut the Substile squire-wise in what poynt you will Finish all other things as in the first of these thrée kindes of South reclining declining Dials In this kinde of reclining Dials whose Stile must bée placed from the centre C. vpward toward the Pole Artick if at any time you cannot draw to both ends of the Contingent line so many howre lines as shall be necessarie then prolong beyond the centre C. the lines opposite on the other side As if you would make the 8. houre line for the morning draw the 8. for the euening beyond the centre C. and you shall haue your desire Note that moreouer in this kinde contrarie to the other before if the plat decline toward the West as in this example it doth thē draw the quadrant towards the West c. But if the Declination be towards the East make the quadrant towards the East A South reclining declining The making of a North reclining declining Diall CAP. 15. The first kinde IN this kinde as in the South before first multiply the Sine of the Declination by the Sine of the Complement of the Reclination parting the product by the whole Sine The quotient Sine thereof shall yéelde an arke whose Complement shall be called the Complement repeated Then increase the Sine of the Complement of the Declination by the whole Sine diuide the product by the Sine of the Complement repeated the quotient Sine thereof will giue an arke which shall be the distance of the Meridian from the Horizon The same quotient Sine multiply by the Sine of the Complement of the reclination and the number arising part by the whole Sine the arke of this quotient is the Eleuation of the Meridian Now adde the Eleuation of the Pole to the Eleuation of the Meridian and the totall number or arke hereof wée will call the compounded arke And if the compounded arke be lesse then 90. degrées then multiply the Sine therof by the Sine of the Complement repeated diuiding the product by the whole Sine and hereof shall arise a quotient Sine whose arke shalbe the distance of the Stile frō the Substile Now compare
the Complement of this distance with the Complement of the compounded arke and increase the Sine of the lesser by the whole Sine part the product by the Sine of the greater and thereof shall come a Sine the Complement of whose arke shal be the distance of the Substile from the Meridian But marke here the diuersitie which doth arise by reason of the compounded arke for hereby you shall haue thrée sundry waies both in finding out the distances betwéene the Meridian and the Horizon the Stile and Substile c. And likewise in the delineation of the figure Whereof ariseth thrée sundry kinds of Dialls the first of them being already taught The second kinde If the compounded arke be iust 90. degrées then the distance of the Stile from the Substile shall be the Complement repeated and the distance of the Substile from the Meridian shall be also 90. degrées Note that in the working hereof there is no difference from the first kinde For here as in the other before you shall first â—inde out the complement repeated then the distance of the Meridian from the Horizon Afterward the Eleuation of the Meridian which being added to the Eleuation of the Pole if the totall number bée iust 90. d. you shall not néede to procéede forward for this as before I made mention shall bée the distance of the Meridian from the Substile In this kinde you shall haue no intersection of the Meridian and the Contingent line therefore you shall begin the diuision of the Equator at the line of the Substile which shall shew the 6. houre either in the morning or euening according as the plat doth decline The third kinde But if the compounded arke be greater then 90 degrées substract it from 180 and that which remayneth shalbe called the difference kept Then multiplie the Sine of the Complement repeated by the Sine of the difference kept diuiding the product by the whole Sine hereof shall come a Sine whose arke shall be the distance of the Stile from the Substile Then compare the Complement of this distance with the ComplemeÌ„t of the difference kept increasing the Sine of the lesser by the whole Sine and parting the product by the Sine of the greater whereof shall come a Sine the ComplemeÌ„t of whose arke being taken from 180 degrées the remaynder shal shew how much the line of the Substile must be distant vpward by the Horizon from the Meridian For the better vnderstanding of these thrée kinds mark these thrée examples following with the delineatioÌ„ of their figures Example of a North Diall whose Declination is 45. d. Reclination 45. d. EleuatioÌ„ of the Pole 52. d. First I worke this altogether like to the South reclining 45. d. declining 45. d. vntill I haue found out the Eleuation of the Meridian Then I adde the Eleuation of the Meridian which is 35. d. 16. m. to the Eleuation of the Pole 52. d. the totall number is 87. d. 16. m. which is the compounded arke and being lesse then 90. d. I procéede with this arke c. Now therefore I multiplie the Sine of this compounded arke which is 99884 by the Sine of the complement to be repeated being 86602 and the product 8650154168 I part by the whole Sine The quotient thereof is 86501 whose arke 59. d. 54. m. is the distance betwéene the Stile and the Substile Then I compare 30. d. 6. m. being the Complement of this distance with the Complement of the compounded arke which is 2. d. 44. m. and finding this least I increase 4768 the Sine thereof by the whole Sine diuiding the product which is 476800000 by 50151 the Sine of the greater the quotient Sine yéeldeth an arke 5. d. 27. m. the Complement hereof 84. d. 33. m. is the distance of the Substile from the Meridian In drawing of this Diall first as before make a line Parallele to the Horizon A B. Then extend the line C. D. cutting the other squire-wise Marke the intersection or centre with E. draw thereupon a circle A. B. C. D. whose two quadrants at the least toward A. if the plat decline Westward or else toward B. if it decline Eastward being diuided into 90. d. each of them number therein from A. towards D. the distance of the Meridian from the Horizon which is 54. d. 44. m. and at the end hereof from the centre â— draw the line F. for the Meridian or 12. houre Account from this vpward toward C. the distance of the Substile from the Meridian bring 84. d. 33. m. make likewise at the end of this number from E. the line for the Substile Againe number from hence vpward if there be so much space or else downward 59. d. 54. m. which is the distance betwéen the Stile and the Substile and at the ende hereof drawe the line H. for the Stile Let the Contingent line cut the Substile squire-wise in the point G. which you may take in any place of the Substile Then with your compasses the least distance of this point G. and the Stile being taken with that widenesse extend them forth in the line of the Substile toward E. making there the point I. vpon which draw the Equator or Equinoctiall circle This done place the ruler vpon the centre I. and the intersection of the Meridian and the Contingent line and where it shall touch the Equator there begin to diuide it into 24. equall partes Finish all other things as in those which went before A North reclining declining The second kinde of North Diall reclining 45. degrees 14. minuts declining 38. degrees IT shall not bée necessarie to shewe an example of this second kinde because the Complement repeated the distance of the Meridian from the Substile and betwéene the Stile and Substile c. is found out altogether like to the other before and that which foloweth Therefore it sufficeth to set downe the number of these distances First the Complement repeated is 64. d. 18. m. The distance of the Meridian from the Horizon is 60. d. 59. m. The Eleuation of the Meridian is 38. d. which I adde to the Eleuation of the Pole being 52. d. and the totall 90. d. is the compounded arke Draw therefore in this kinde as before a line Parallel to the Horizon A B. make another squire-wise C. D. Draw the two quadrants from C. by A. to D. diuiding each of them into 90. d. Then number herein the distance of the Meridian from the Horizon which is 60. d. 59. m. drawing from E. at the end here of the line F. for the Meridian From this account 90. d. being here the distance of the Substile from the Meridian and like wise at the end of this number from E. drawe the line for the Substile Againe from this line downward because there is no space vpward account the Complement repeated 64. d. 18. m. which here we take for the distance of the Stile from the Substile make likewise by this
number the line E. H. for the Stile Let the Contingent line cut the Substile squire-wise in any place Then taking the least distance with the compasses of the point G and of the Stile with that widensse in the Substile make the poynt I. vpon which draw the Equinoctiall circle by G And because here as in all other Dials where the compounded arke is iust 90. d. there is no intersection of the Meridian and the Contingent line therefore begin the diuision of the Equator into 24 equal parts at the Substile which in this kinde shall shew the sixt houre either in the euening or morning according to the declination of the plat Place the ruler vpon the centre I. and so many of these parts as you can making markes in the line of Contingence as before draw the houre lines by them c. finish the rest as in the other A North Declining Reclining Example of the third kinde of North Diall before mentioned Reclining 21. d. 30. m. Declining 30. d. Héere first as before I multiply the Sine of the Declination being 50000 by 93041 which is y ◠Sine of the complement of the Reclination and the product 4652070000 I part by the whole Sine the quotient 46520 yéeldeth an arke 27. d. 43. m. The complement whereof is 62. d. 17. m. being the Complement to be repeated Then I encrease 86602 the Sine of the complement of the Declination by the whole Sine diuiding the product by 88525 the Sine of the Complement repeated The arke of the quotient Sine 97827 is 78. d. 2. m which is the distance of the Meridian from the Horizon This done I augment this quotient Sine 97827 by the Sine of the Complement of the reclination which is 93041 the product 9101921907 I distribute by the whole Sine and the quotient 91019 giueth an arke 65. d. 32. m. the Eleuation of the Meridian Now I adde 65. d. 32. m. being the Eleuation of the Meridian to 52. d. the Eleuation af the Pole and the totall number 117. d. 32. m. being the compounded arke because it is greater then 90. d. I substract it from 180 and there remaineth 62. d. 28. m. which is the Difference kept Afterward I multiply 88525 the Sine of the Complement repeated by 88674 the Sine of the difference kept parting the product 7849865850 by the whole Sine The quotient is 78498 whose arke is 51. d. 43. m. which is the distance betwéen the Stile and the Substile Then comparing the Complement of this distance being 38. d. 17. m. with the complement of y ◠difference kept which is 27. d. 32. m. and finding this to be least I amplifie 46226 the Sine thereof by the whole Sine diuiding the product 4622500000 by the Sine of the greater which is 61955 and 74612 the quotient comming hereof yéeldeth an arke 48. d. 15. m. whose Complement being 41. d. 45. m. I take out of 180 and the remainder is 138. d. 15. m. the distance of the Substile from the Meridian The delineation of the Figure First as before draw a line A. B. parallele to the Horizon Make another C. D. squire-wise to the former Draw two quadrants at the least C. A. D. diuiding ech of them into 90. degrées number therein from A. toward D. the distance of the Meridian from the Horizon which in our example is found to be 78. d. 2. m. draw at the end hereof from E. the line F. for the Meridian Then account from this vpward 138. d. 15. m. being the distance of the Substile from the Meridian drawing likewise at the end of this number from E. the line for the Substile Afterward account from this line on which side you will 51. d 43. m. the distance betwéen the Stile and the Substile extending the line E H. by the end of this number for the Stile Let the Contingent line cut the Substile squire-wise in any point where you will Afterward taking with your compasses the least distance betwéene the point G. and the Stile with that widenesse in the Substile toward E. make the point I. vpon which draw the Equinoctiall circle by G. And because in this kinde where the Compounded arke is greater then 90. d. there is none intersection of the Meridian and the contingent line beneath the ceutre E. therefore draw forth the Meridian beyond the centre then place your ruler on the intersection of the. Meridian and Contingent line aboue the centre and the point ◠and where it cutteth the Equator there begin to diuide it into 24. equall partes Finish that which remaineth as before A North reclining declining The making of a South Inclining direct Diall CAP. 16. IF the inclination of the plat be lesse then the Eleuation of the pole take that from this accoūting the remainder for the Eleuation of the Pole And with this number as if it were the Eleuafion of the Pole make a Diall like to the South erect direct and it shall be fit for your plat But if the Inclination of the plat be equal with the Eleuation of the Pole make your Diall altogether like to the North reclining direct whose reclination likewise is equall to the Eleuation of the Pole They differ onely herein that this is placed downward to the earth and that vpward But if the Inclination of the plat be greater then the Eleuation of the Pole substract this from that and with the number remaining as if it were the Eleuation of the Pole make your Dial like to the North erect direct Example of this kinde incling 65. d. Substract 52. d. the Eleuation of the Pole out of 65. d. being the Inclination of the plat and the remainder 13. d. account the Eleuation of the Pole For y ◠delineation hereof resort to the North erect Diall Cap. 5. A South inclining direct You sée in this Figure that all the lines for the howers are drawen opposite from the Contingent line beyond the centre E. In like maner must you doe in the delineation of all such which incline more then the eleuation of the Pole Let the Stile in this kinde be placed directly ouer the Meridian with so great an angle as D. E. F. is c. The making of a North inclining direct Diall CAP. 17. IF the Inclination of the plat be lesse then the complement of the Eleuation of the pole adde the inclination to the Eleuation and with that number as if it were the Eleuation of the Pole make a North crect direct diall for your plat But if the inclination be equall with the complement of the Eleuation of the Pole then make a Diall as you were taught in the second kinde of South reclining direct for as that plat so reclining in the South is placed vpward so is this placed down ward Note that this North diall sheweth but onely 4. howers the two first in the morning and the two last in the euening and that only in the middest of Sommer But if
the inclination be greater then the Complement of the Eleuation of the Pole substract this lesser out of the other being greater and with the number remaining as if it were the Eleuation of the Pole make your diall like to an Horizontall This kinde likewise sheweth very few howers Example of this last kinde inclining 45. d. First I take 38. d. being the complement of the Eleuation of the Pale out of 45. d. the inclination of the plat and there remaineth 7. d. which I kéep for the Eleuation of the Pole For the delineation of this diall resort to the Horizontall Cap. 3. A North inclining Direct The making of the East and West inclining Dials CAP. 18. MUltiply the Sine of the Eleuation of the Pole by the Sine of the Inclination of the plat diuiding the product by the whole Sine the quotient arke shall be the distance of the Stile from the Substile Then compare the complement of this distance with the complement of the Eleuation of the Pole increasing the Sine of the lesser by the whole Sine part the product by the Sine of the greater where of shall come a Sine the Complement of whose arke shalbe the distance of the Substile from the Meridian It shall not be necessarie to shew any example hereof because the East and West reclining bée altogether like to this Wherefore resort thither for the working of your example for those distances in drawing this figure shall bée here obserued The delineation of an East Diall inclining 45. d. First drawe a line Parallele to the Horizon A. B. make the perpendiculare line C. D. squire-wise to the other Describe the quadrant from A. to D. number from A. toward D. 33. d. 52. m. the distance of the Substile from the Meridian and at the end hereof from C. draw the line E. for the Substile account from this 42. d. 9. m. drawing likewise at the end of this number the line G. for the Stile Let the Contingent line cut the Substile squire-wise Finish all things els as in the East reclining An East and West inclining The making of a South inclining declining Diall CAP. 19. FIrst multiplie the Sine of the Declination by the Sine of the complement of the inclination parting the product by the whole Sine The quotient Sine shall yéeld an arke whose complement shall bée named the complement repeated Then increase the Sine of the Complement of the Declination by the whole Sine and the product diuide by the Sine of the Complement repeated whereof shall come a Sine whose arke is the distance of the Meridian from the Horizon Afterward this Sine being multiplied by the Sine of the Complement of the inclination and the product parted by the whole Sine the arke of the quotient Sine shall bée the Eleuation of the Meridian Which arke you must adde to the Eleuation of the Pole And if the totall number bée lesse then 90. d. it shall bée named the Doubtfull arke But if it be greater then 90. d. take it from 180 and let the remainder be called the Doutfull arke This done augment the Sine of the Complement repeated by the Sine of the Doutfull arke the product arising thereof being diuided by the whole Sine the quotient arke shall be the distance of the Stile from the Substile Now compare the Complement of this distance with the Complement of the Doutful arke multiplying the Sine of the lesser by the whole Sine diuiding the product by the Sine of the greater the arke of the quotient Sine comming thereof shall bée the distance of the Substile from the Meridian But note if the doubtfull arke be found without subtraction from 180 which is if it bée lesse then 90 d. then you must subtract the distance of the Substile from the Meridian out of 180 and the number remaining shall be the true distance of the Meridian from the Substile Marke this likewise if the doubtfull arke be equall 90 degrées let the Complement repeated be the distance of the Stile from the Substile then shall there bée iust 90 d. for the space betwéene the Substile and the Meridian as before is taught in the North declining reclining whither you may resort for the working hereof Here it shall bée sufficient to shew two examples with the delineation of their figures the one where the doubtfull arke is subtracted from 180 d. and the other where there is no subtraction hereof because it is lesse then 90 degrées Example of a South Diall Inclining 45 degrees Declining 45 degrees Forasmuch as this is altogether like to the North reclining 45 d. declining 45 d. whither you may resort I wil omit the working of the former part of this exāple vntil I come to the finding out of the distance of the Substile from the Meridian The former part of this example you may finde to bée thus wrought in the North reclining declining 1 First the complement repeated 60 d. 2 Then the distance of the Meridian from the Horizon 54 d. 44 d. 3 Next the Eleuation of the Meridian 35 d. 16 m. 4 The compounded arke there which we call the doubtfull arke here 87 d. 16 m. 5 The distance of the Stile frō the Substile 59 d. 54 m. 6 Last the distance of the Substile from the Meridian 84 d. 33 m. But here as before is taught you must subtract this distance from 180 d. because the doubtfull arke was lesse then 90 d. and then the remainder 95 d. 27 m. shall bée the true distance of the Substile from the Meridian In the delineation of this diall first as before make a line paralele to the Horizon A. B. Draw another perpendicular C. D. cutting the former squire-wise Make two quadrants from A. by D to B. If the plat decline westward number the distance of the Meridian from the Horizon from A. toward D. c. But if the declination be Eastward as in this example it is then account this distance of the Meridian from the Horizon which is 54 d. 44 m. from B. toward D. drawing at the ende hereof from the centre C. the Meridian line which shall shew the 12 houre Account likewise from that toward A. 95 d. 27 m. the distance of the Substile from the Meridian making in like maner the line E. C. for the Substile From this line on which side you will number the distance of the Stile from the Substile being 59 d. 54 m. drawe by this the line G. representing the Stile Let the line of Contingence cut the Substile squire-wise in any point where you will Make the Equator begin the diuision thereof and draw the houre lines in all respects as in the North reclining 21 degrées 30 minutes declining 30 degrées Cap. 15. A South declining inclining Diall The secōd example of a South Diall Inclining 33. d. 40. m. Where the doutfull arke is subtracted frō 180. Declining 31. d. Where the doutfull arke is subtracted frō 180. First 51503
the Sine of the Declination being multiplied by 83227 the Sine of the Complement of the inclination and the product 4286440181 diuided by the whole Sine the arke of the quotient is 25 d. 23. m. The complement whereof being 64 d. 37 m. is the complement repeated Then I increase the Sine of the Complement of the declination which is 85716 by the whole Sine and I part the product 8571600000 by 90346 the Sine of the Complement repeated The quotient 94875 yeeldeth an arke 71 d. 35 m. which is the distance of y ◠Meridian frō y ◠Horizō Agayne I multiply this Sine 94875 by the Sine of the Complement of the Inclination being 83227 and the product 7895961425 arising thereof I diuide by the whole Sine The arke of the quotient is 52 d. 9 m. which is the Eleuation of the Meridian Now this being added to the Eleuation of the Pole 52 d. and the total number 104 d. 9 m. taken from 180 there remayneth 75 d. 51 m. which is the doubtful arke Therefore I augment 90346 the Sine of the Complement repeated by 96930 the Sine of the doubtful arke and the product 8760399890 I parte by the whole Sine The arke of the quotient 61 d. 10 m. is the distance of the Substile from the Stile This done I compare 28. d. 50. m. the Complement of this distance with 14. d. 9. m. the Complement of the doutfull arke multiplying y ◠Sine of the lesser which is 24446 by the whole Sine diuiding the product 2444600000 by 48226 the Sine of the greater The quotient Sine 50741 yéeldeth an arke 30 d. 30. m. whose Complement 59 d. 30 m. is the distance of the Substile from the Meridian First draw a line A. B. Parallele to the Horizon drawe another C. D. squire-wise to the line A. B. make the two quadrants from A. by D. to B. And because this Declination is on the left hand number from A. towards D. 7 d. 35 m. the distance of the Meridian from the Horizon drawing by this from C. the Meridian line From that toward B. account 59 d. 30 m. the distance of the Substile from the Meridian making in like manner at the ende of this number from C. the Substile line E. Againe from this forward if you can or else backward number the distance of the Stile from the Substile which is 61 d. 10 m. Draw likewise by this frō C. the line G. for the Stile Let the Contingent cut the Substile squire-wise in any place where you will c. The making of the reclining declining Dials before shall teach you the finishing of this likewise A South declining inclining The making of a North inclining declining Diall CAP. 20. THe working of this kinde is altogether like the South reclining declining diall First therefore multiplie the Sine of the Declination by the Sine of the Complement of the inclination diuiding the product by the whole Sine The quotient shalt giue an arke whose Complement shall be named the Complement repeated Then augment the Sine of the Complement of the Declination by the whole Sine the product part by the Sine of the Complement repeated Whereof will come a quotient Sine whose arke shall be the distance of that which is as it were the Meridian from the Horizon For the finding out of the Eleuation of the Meridian because it may bée done two sundry waies I will set them downe both referring the choyse to your selfe Compare the Complement of the arke last found out with the Declination of the plat multiplying the Sine of the lesser by the whole Sine and diuiding the product by the Sine of the greater The quotient Sine shall yéeld an arke whose Complement shall be the Eleuation of the Meridian Or multiply y ◠Sine of the arke last found out by the Sine of the Complemēt of the inclination part the product by y ◠whole Sine and the arke of y ◠quotient Sine shalbe y ◠Eleuatiō of y ◠Meridian Now comparing the Eluation of the Pole with the Eleuation of the Meridian subtract the lesser from the greater retaining the number remaining which shall be called the difference kept Afterward increase the Sine of the difference kept by the Sine of the Complement repeated and diuide the product by the whole Sine The quotient arising of this diuision shall giue an arke which shall be the distance betwéene the Stile and the Substile To conclude the Complement of this distance being compared with the Complement of the difference kept multiplie the Sine of the lesser by the whole Sine and part the product by the Sine of the greater The Complement of the arke of the quotient Sine shall be the distance of the Substile from the Meridian But note if the Eleuation of the Meridian the Eleuation of the Pole be found equal make an Equinoctial dial as before you were taught in the Meridionall reclining declining for there is no difference but only that this is placed downward and the South vpward There be of this north as of the South reclining declining thrée sundrie kinds of Dials as by the examples and figures following you may perceiue Example of a North Diall Inclining 20 d. Declining 30 d. First I multiplie 50000 the Sine of the declination by 93969 the Sine of the Complement of the inclination and the product thereof 4698450000 I diuide by the whole Sine 100000 the quotient Sine 46984 yéeldeth an arke 28 d. 2 m. whose Complement 61 d. 58 m. is the Complement repeated Then I augment the Sine of the Complement of the declination which is 86602 by the whole Sine parting the product 8660200000 by 88267 the Sine of the Complement repeated the quotient is 98113. The arke therof being 78 d. 51 m. is y ◠distance of the Meridian frō the horizon Now in comparing the Complement of the arke last found out with the declination of the plat I find the Complement of the arke least Wherfore I multiply y ◠Sine therof being 19337 by the whole Sine and the product 1933700000 I diuide by 50000 the Sine of the greater The quotient 38673 giueth an arke 22 d. 46 m. whose Complement 67 d. 14 m. is the Eleuation of the Meridian Or multiplie 98112 the Sine of the arke last found out by the Sine of the Complement of the inclination which is 93969 and the product 9219566568 part by the whole Sine The quotient shall bée 92195 whose arke 67 degrées 14 minutes is the Eleuation of the Meridian This done I compare the Eleuation of the Meridian 67 d. 14 m. with the Eleuation of the Pole 52 d. subtracting the lesser from the greater and there remaineth 15 d. 14 m. which is the difference kept Then I multiply 26275 the Sine of the difference kept by 88267 the Sine of the Complement repeated parting the product 2318455682 by the whole Sine
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.
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
point G. where it shall touch the Meridian line from which point as a centre you shall draw the lines for the 12 signes as you were taught in the Horizontall Diuide likewise and draw the lines for the equall houres as before in the Horizontall The placing of the houres vnequall in this kinde is done as in the South Erect Direct vpon a plaine superficies except onely that whereas there you did draw them with a ruler here you shall doe it with compasses on this manner Open your compasses to the Quadrant of the plat that is from A. to C. accounsing from the Meridian in the Tropike of Capricorne two parts wanting two minutes of an equall houre making there a marke And that widenesse of your compasses remaining draw a line from that marke made in the Tropike ♑ by the intersection of the line of Aries and Libra the line of the first houre in the afternoone vnto the Tropike of Cancer Draw all the other lines for the vnequall houres in like maner as in the figure you may plainely sée Fixe the Stile in the centre G. as you did in the Horizontall placing the figures for the equall and vnequall houres and the caracters to the 12 signes as in the example following or otherwise as you will The making of a Diall vpon a Quadrant or the Table described in the beginning of the Booke CAP. 28. IF you will make this Diall vppon a Quadrant alone prepare and diuide it altogether like one of the Quadrants of the table whose making is prescribed in the first Chapter or if you will make it vpon that instrument alreadie prepared worke thus Diuide the diameter E. D. into foure equall partes then leauing out the fourth part next E. describe vpon the middle point betwéene C. and S. an obscure halfe circle which diuide into sixe equall parts From each point of which diuision draw light lines vnto the Semidiameter D. E. touching it squire wise Then draw nigh to the line D. E. two other lines parallele thereto which with the crosse lines drawne from the halfe circle may make 12 vnequall quadrangles wherein the 12 signes of the Zodiake may be figured the North towards D. the South toward S. And to the intent you may proportionally part these Quadrangles into fiue or ten degrées diuide those sixe parts of the halfe circle equally into so many degrées Then drawe againe from those diuisions right liues to the Dimetient D. E. squire-wise as before This done vpon the point E. from S. that is to say from the end of ♠and beginning of ♑ drawe an arke to the Semidiamer D. E. which shall be for the winter Tropike Againe vpon the same centre draw another from the beginning of ♈ and ♎ for the Equator To conclude make another from the angle D. that is from the end of ♊ and beginning of ♋ which shall bée for the Summer Tropike By the helpe of these arkes you shall draw the houre lines so that you first know the height of the Sunne aboue the Horizon at euery houre when it occupieth the beginning of ♑ ♈ and ♋ Whose altitude is thus found out Take the Eleuation of the Pole and the Complement thereof also the declination of the Sunne from the Equinoctiall and the distance of the Sunne from the Meridian accounting 15 degrées for euery houre with the Complement of this distance Then if you desire to knowe the altitude of the Sunne at sixe of the clock either in the morning or at euening at which houre onely in Sommer it is aboue the Horizon multiply the Sine of the Eleuation of the Pole by the Sine of the declaration of the Sunne diuiding the product by the whole Sine and you shall haue your desire But if the Sunne shall bée distant from the Meridian fewer howers then sixe multiply the Sine of this distance giuing to euery houre 15 degrées by the Sine of the Complement of the altitude of the Pole and the product hereof diuide by the whole Sine Then take the arke of the quotient from 90 degrées and the first number found out shall remaine which must be kept Then compare the Sine of this number found out with the Sine of the Eleuation of the Pole augment the lesser by the whole Sine diuiding the product by the greater Whereof shall come a quotient Sine to the complement of whose arke adde the declination of the Sunne if it shall be in the North signes or subtract it from that if it occupieth the South signes And if the number which commeth hereof shall bée greater then 90 take it from 180 and you shall haue the second number found out The Sine of this number found out being multiplied by the Sine of the first number found out shall yéelde a product which part by the whole Sine and the arke of the quotient Sine shall shew the desired altitude of the Sunne for the houre propounded But if the distance of the Sunne from the Meridian shall excéede sixe houres that is 90 degrées take the degrées of that distance from 180 multiplying the Sine of the remainder by the Sine of the Complemēt of the altitude of the Pole diuiding the product by the whole Sine and subtract the arke of the quotient from 90 the remainder shal be called the First number found out The Sine of which number found out compared with the Sine of the Eleuation of the Pole increase the lesser by the whole Sine and distribute the product by the greater Then take the Complement of the Declination of the Sunne from the arke of the quotient and you shall haue the second number found out Finally the Sine of the first number found out and the Sine of the second being multiplied by themselues and the product parted by the whole Sine the quotient Sine shall yéeld an arke which shall bée the altitude of the Sunne But when the Sunne occupieth the beginning of ♈ or ♎ you shall finde the altitude thereof euery houre onely by multiplying the Sine of the Complement of the distance of the Sunne from the Meridian by the Sine of the Complement of the Eleuation of the Pole diuiding the product by the whole Sine the quotient which commeth hereof shall yéeld the arke of your desire At both the sixe houres because the one sixe is the rising and the other the sitting there is then no altitude of the Sunne aboue the Horizon Moreouer to know how much the Meridian altitude is of the Sunne entring into ♋ adde the greatest Declination thereof to the Complement of the Eleuation of the Pole and by subtracting the greatest Declination of the Sunne from the complement of the Eleuation of the Pole you shall likewise haue the Meridian altitude of the Sunne entring into ♑ You shall likewise séeke the height of the Sunne being in the 10 degrée of ♉ aboue the Horizon at 8 of the clock before noone and at 4 after noone at 7 in
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
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