1 DIals are diuersly made according as they are diuersly placed. Therefore their situation must first be knowne: which may be done by an instrument not vn­fitly called a Clinatory.

2 Let this instrument be made iust foure square, and let the thicknesse bee about halfe a quarter of the breadth of it, vpon one side ther­of describe a quadrant, whose two semidiame­ters or sides must be paralel to the side of the quadrate.

3 The quadrant must bee diuided into 90. degrees, with figures set to euery fifth or tenth degree (as the manner is) both forward and backward, and without the peripherie thereof, a groofe or furrowe must be made so deepe that [Page] a plummet hanging by a thrid from the Cen­ter of the quadrant may fall into it, in such sort that the thrid may come close to the degrees of the quadiant.

4 Close within the limb of this quadrant make a great round hole or box, for the pla­cing of a magneticall needle within the same, whose true Meridian line must bee perpendicu­lar to one of the sides of the quadrant, which shall be called the North side, and the other side of the quadrant shall bee called the East­side, to the which the Westside of the Clina­tory is opposite, as the South side of the Cli­natorie is opposite to the Northside of the quadrant: and the magneticall Meridian, must bee drawne in the bottome of the box according to the variation of the place where you are.

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EVery flat whereupon a Diall is to beeThe Dial ground. made (which is also called the Diall ground) either lieth leuel with the horizon, or els is eleuated the one side higher then the other.

2 The first kinde is thus known: Take theHorizontal flats: and how they are known. Clinatorie and hold it so that the plummet fall vpon on of the Semidiameters, or sides of the Quadrant: then if the nether side of the Cli­natory, which way so euer you turne the instru­ment, will touch the flat, it lieth leuel with the Horizon, and Dials made vpon such flats, are called Horizontal Dials.

3 Those flats which are eleuated the oneEleuated flats; Erect, Inclining Reclining: and how they are to be known side higher then the other, stand either vpright (which are called erect) or else, they stand lea­ning: if they leane to you ward, when you stand right against them, they are called incli­ning: otherwise reclining, if they leane from you ward.

4 All these flats are thus knowne: Holding the Clinatory as before; if either the right, or the left side thereof (whereto the plumbline is aequidistant) will touch and lie close to the flat, it is erect: but if either of the neither cor­ners onely touch it, it is reclining: if either of [Page] the vpper corners onely touch it, it is inclining.

5 And how much the reclination or inclination is, you shall know after this manner.

6 Set one of the sides of the Clinatory to theTo know how much the re­clination or inclination is. flat, in such sort, that the plumbline hanging at li­berty, may fall vpon the circumference of the qua­drant: for then the arke of the quadrant, be­twixt the plumbline and that side of the quadrant that is parallell, or aequidistant to the slatte, is the reclination thereof, if the center of the quadrant be from the flat, or else the inclination, if it bee to­wards the same.

ALl flats are either direct, or declining.

2 All flats lying leuel with the Hori­zon are direct.

3 But if the flat lie not leuel with the Horizon: you shall thus know whether it be direct or declining. First, draw therein a line parallel to the Horizon, after this manner: holde the Clina­tory to the flat in such sort, that the plumbline may fall vpon one of the sides of the quadrant; then draw a line by the nether side of the Clinatory in recliners; or by the vpper side in incliners, or by either of those sides in erect flats, for that line shall be parallel or aequidistant to the Horizon, and may [Page] be called the Horizontall line. Set the North side of the Cliniatorie to this liue, if the North end of the needle looke towards the flat: then if the Mag­netical Meridian be right vnder the needle, it is a di­rect flat: but if it differ from it, it is declining, and that so much as that difference is, and that way which the North end of the needle declineth from the Northend of the Meridian line in the clinatory.

4 If the Southend of the needle looke towards the flat, made your account contrary wise.

ALl flats doe either agree with the plaine of the Meridian circle (which may therefore bee called meridian flats) or else they disa­gree from the same.

2 They are knowne thus: If the flat bee erect and declining 90. degrees, it is a Meridian flat, o­therwise it is no Meridian flat; and then you must first draw therin the meridian line, after this maner.

3 If the flat be Horizontal, take the clinatoryHow to drawe the Meridian line, in Hori­zontall flats. and lay it flat downe thereupon; and turning it a­bout till the needle hang precisely ouer the Magne­ticall meridian, by that side thereof that is parallel to the true Meridian line of the Clinatory, drawe a right line, for that shal be the Meridian line desired.

4 In erect flats the Meridian line is perpendicu­lar, and therefore laying the Clinatory close to [Page] such a flat in such sort that the plumbline hang pre­ciselyIn erect flats. on either side of the quadrant, a line drawne by the side of the clinatory, parallel to that side of the quadrant, shall be the meridian line.

5 In direct flats, a line perpendicular to the lineIn direct flats. aequidistant from the Horizon, is the Meridian line we seeke for.

6 In flats reclining or inclining, declining alsoIn reclining or inclining flats, declining 90. degrees. 90. degrees (which are commonly called, East, or West reclining or inclining) the meridian line is parallel to the horizon.

7 For alotherIn incl [...]ning or reclining flats declining lesse then 90. de­grees. inclining or reclining, & withall de­clining flats, drawe a line vpon some pastbord or paper which shall bee cal­led the hori­zontal me­ridian AB. wherein set­tingone foot of your cō ­passes, with the other draw an arch of a circle; & therin reckon the complement of the [Page] declination FC. drawing a right line BC. by the end thereof out of the center B. This right line you shall crosse squire-wise with another as AC. which may be called the base of inclination or re­clination, and must also meet with the horizontall meridian at A. and setting one foot of your com­passes in the crossing at C. with the other foote draw an arke, counting therein the complement of the reclination or inclination AG. drawing a right line by the end therof, out of the center of the fore­said ark CGD. & from A erect AD. perpendicular to AC. which may meet with CGD. the line of re­clination or inclination at D. Also from A. draw the line AF. perpendicular to the horozontal meridian, AB. in the point A. and equal to the former perpen­dicular AD. and from the end therof draw a line to (the center of the arke of declination) B. Then con­tinuing foorth AC. to N. (that CN. be equall to CD) from N. you shall draw a line to B. which (if you haue wrought truely) must be equall to BE. Now the angle contained betweene the lines NB. and BC. sheweth how much the Meridian line in your Diall ground should be distant from the line which you drew aequidistant to the Horizon heere represented by BC. In this line therefore (in the Dial ground) set one foote of your compasses, and extending the other that way which the Diall de­clineth, drawe an arke of a circle, vpwards in recli­ners, but downewards in incliners: and therein count the said angle from the line parallel to the Horizon, and drawe by the end thereof a line, [Page] which shall bee the true Meridian in the Dial ground.

8 FromTo finde the angle which the dial ground (or flat) maketh with the plaine of the meridi­an. A draw AH perpendicu­lar to EB. make BI. e­qual to BH. from I. let IK be drawn perpendicu­lar to BN. make CL. equal to CK and drawe a line from L to A. of these three lines AH. IK. and LA. make the triangle AHM. for then the angle AHM. is the angle which the dial ground maketh with the plain of the meridian.

THe Meridian line is either parallel to the Horizon, or else eleuated the one endHow to finde the eleuation of the meridian line. higher then the other.

2 If the flat bee either horizontal, or East, or West, and inclining, or reclining, the meridi­an is parallel to the Horizon.

3 In all other flats that disagree from the plaine of the Meridian circle, the Meridian line is eleuated the one end higher then the other.

4 This eleuation is either vpright, as in all erectThe eleuation of the meridian line in erect dials. In recli­ning or incli­ning direct flats; in recli­ning or incli­ning declining flats. Dials not declining 90. degrees, or else leaning, as in all inclining, and reclining flats not declining 90 degrees, which if they be direct, is equall to the complement of reclination, or inclination.

5 But if they decline, then the angle ABE. in the former figure, is the eleuation of the Meridian line.

6 If the meridian line bee not erect, it leaueth either Northwards, when the eleuated end there­ofThe eleuation of the meridian whether North or South. looketh towards the North, or else Southwards when the eleuated end looketh towards the South.

7 All flats are either Polar (which being conti­nued▪ would goe by the poles of the world) as allFlats polar. leaning flats, wherein the eleuation of the meridi­an line is Northwards, and equall to the poles ele­uation▪ and all erect decliners 90. degrees. Other­wise they are no polar flats.Not polar.

NOw it shall bee best to take a sheet of pa­per, or rather a pastebord, that you may therein describe the figure of your Dial, before you draw the Diall it selfe vpon his ground: that is, vpon the Truncke, Stone, wall, &c.

2 This paper, or pasteboord therefore, you shall place, or vnderstand to be placed so as your Dial ground is or must be placed, and therein write the names of the parts of the world, as they lie in respect of your Dial ground, as East, West, North, South, Zenith, Nadir, vpper part, nether part, &c. which you may do by helpe of the magnetical nee­dle: for the North end thereof (hanging at liberty) sheweth the North, whereto the South is diame­trally opposite; and your face being turned to­wards the North, your right hand sheweth the East, your left hand the West, the Zenith, or ver­ticall point is aboue your head, the Nadir vnder your feete. Note also, which end of the Meridian line must be higher, and which lower; if the Me­ridian be not parallel to the Horizon.

ALl Diall grounds are aequinoctiall, or not ae­quinoctiall.

2 An aequinoctiall ground is that which agreeth euen with the plaine of the aequinoctiall Circle: which is thus knowne. If the Diall ground be direct, and the Meridian line eleuated South­wards, equally to the complement of the poles ele­uation, it is an Equinoctiall Diall ground, other­wise not.

3 In an Equinoctial Dial you shall describe the houre lines after this manner.

4 Set one foot of your Compasses in the Meri­dianHow to make Equinoctial Dials. line AB. and with the other, drawe a circle DBC. and deuide it into 24. equall parts, as D. E. F. G. &c. beginning at B. the crossing therof, with the Meridian line; for then right lines, as AD. AE. AF. AG. &c. in the 1. and 2. figure drawne out of the Center, by those diuisions shall bee the houre lines.

5 The stile must stand vpright out of the centerPlacing of the stile. of the Diall.

6 Of Equinoctiall Dials there be two sorts, the vpper and the nether.

7 The vpper Equinoctial Diall looketh vpwardsVpper Equi­noctial dial. to the eleuated Pole of the world: And it shew­eth the houre of the day, onely in the Spring and Summer time, as in the first figure.

[Page]8 The nether, or lower Equinoctial dial, is thatNeather Equi­noctial dial. which looketh downewards to that Pole of the world which is beneath the Horizons and sheweth the houres onely in Autumne, and Winter, as in the second figure.

IN all Dial grounds that are not Equino­ctiall, the substilar line, and the distance of the stile from the substilar must bee found.

2 The substilar line is that right ouer which theSubstilar line. stile must be set.

3 The distance of the stile from the substilar, isDistance of the stile from the substilar. the angle, or space contained betweene the stile, and the substilar line.

4 The finding out of these is diuers, in diuersThe finding of the substilar line. kinds, and therefore must bee specially shewed in each kinde.

5 In direct Dial grounds not Equinoctiall, andIn direct flats not aquinoctial In Polars not Meridian. Polars not Meridian, the substilar line is the same with the Meridian line, or else parallel thereto, in declining polars.

6 In Polar ground▪ agreeing with the plaine ofIn Meridian Polars. the Meridian, the substilar line may thus be found.

7 Set one foot of the compasses in the South­end of the line that you drawe equidistant from the Horizon and extending the other foot towards the [Page] North end of the same line, draw an arke of a circle: therein reckon the eleuation of the Pole beginning at the foresaid line: for a right line drawne there­by out of the center, shall be the substilar line AB. figure. 3.

8 In al Polar grounds draw a parallel CD. (figu.The stilar line in all Polar Dials. 3. 4. 5. 6. 7. 8.) to the substilar line at a conuenient di­stance from the same; for that shall be the line re­presenting the stile.

IN all Dial grounds that be not aequinocti­all nor polar, before the substilar line, and distance of the stile from it can be found, first the distance of the stile from the Me­ridian line must be found after this maner.

2 If the Meridian line be parallel to the Hori­zon, as BC. the distance of the stile from the Meri­dian line, is equal to the height of the Pole, as BR.

3 But if the eleuation of the Meridian be either vpright, as AG. or leaning towards the North, and withall greater then the Poles eleuation, as AH. the height of the Pole BR. taken out of the height of the Meridian line BH. or BG. shal leaue the di­stance of the stile from the Meridian line RH. or RG.

4 If the eleuation of the meridian line be North­wards, and lesse then the height of the Pole, as BI. [Page] take the eleuation of the meridian line BI. out of the height of the pole BR. and there shall remaine the distance of the stile from the Meridian line RI.

5 If the eleuation of the Meridian line be South­wards, and either greater, or equal to the comple­ment of the Poles eleuation, as AF. and AE. then the complement of the Meridian lines eleuation, FG. or EG. added to the complement of the Poles eleuation GR. shall make the distance of the stile from the meridian line.

6 If the eleuation of the meridian line be South­ward and lesse then the complement of the poles eleuati­on [Page] as CD. the eleuation of the meridian line CD and the height of the Pole C [...]. put together shall make the distance of the stile from the meridian line.

SEcondly, in a ground not Equinoctial nor Polar we must consider whether the stile make a right angle, or an oblique angle with the meridian line.

2 The stile shall make a right angle with the me­ridian line, if the eleuation of the meridian line be Southwards and equall to the complement of the Poles eleuation, as in the 9. 10. 11. and 12. figure Herein a right line drawne squirewise ouerthwart the meridian line, towards that part of the world, which is opposite to that whereto the dial ground declineth, shall be the substilar line, as BA. in the 9. 10. 11. and 12. figu. and the distance of the stile from the substilar line shal bee equall to the angle which the dial ground maketh with the plaine of the meridian circle as the angle BAD. fig. 9. 10. 11. 12. which angle is found by the third Chap.

IF the stile make an oblique angle with the meridian line, we must first finde out from whether end of the meridian line, the e­leuation of the stile must be reckoned, thus:

2 If the meridian line be parallel to the horizon as in the 13. figure, the eleuation of the stile shal be reckoned from the North end of the meridian line in reclining, and horizontal flats looking vpwards, as BR. from B in the former figure, but contrari­wise in incliners as PC. from C. in the same figure.

3 If the meridian line be eleuated the one end higher then the other from the horizon, and the dial ground looke towards the South, the eleuati­on of the meridian being also Northwards, and lesse then the eleuation of the pole: the eleuation of the stile shal be counted from the vpper end of the meridian line: as IR. from I.

4 But if the eleuation of the meridian be greater then the eleuation of the pole, or vpright, or south­wards and greater then the complement of the poles eleuation; the eleuation of the stile shall bee counted from the neather end of the meridian line, as PM, PN, PO, from MNO.

5 If the eleuation of the meridian line be South­wards and lesse then the complement of the poles eleuation, the eleuation of the stile shal be counted [Page] from the vpper ende of the meridian line as DP. from D.

6 If the Dial ground looke toward the North, the eleuation of the stile from the meridian line shal be reckoned contrariwise in euery kinde.

HAuing thus found out from whether end of the meridian line the eleuation of the stile is to be reckoned, set one foot of your compasses in the meridian line as in A. and stretching foorth the other foot towards that end of the meridian line, from which the ele­uation of the stile is to bee reckned as towards L. draw an arch of a circle MDLN. and (beginning at the Merîdian line) reckon and marke therein the eleuation of the stile from the Meridian line, LD. figure 13. 14. 15. in the rest LO. either East­wards or Westwards in direct Dials, as in the 13. 14. 15. fig. but in decliners towards that part of the world which is opposite to the part whereunto the Dial declineth, as in the 16. 17. 18. fig.

2 Then in direct Dials, a right line ACD. fig. 13. 14. 15. drawne out of the center of the said arke by the marke of the stiles eleuation from the me­ridian line shall be the line representing the stile, and [Page] therefore the distance of the stile from the substilar line shall be the distance of the stile, from the me­ridian line.

3 But in decliners you shall thus finde the substi­lar line: From O the point of the stiles eleuation from the meridian line in the foresaid arke drawe OP. a perpendicular to the meridian line AL. and taking the length of this perpendicular with your compasses, leaue one foote in P. the concurse ther­of with the meridian line, and with the other des­cribe a quadrant of a circle QRO. beginning from the Meridian line, and so proceeding vnto O the other end of the perpendicular line: and in that quadrant beginning at the meridian ALQ. reckon and marke QR. the complement of the angle conteined betweene the plaines of the diall ground and of the meridian circle, and take with your compasses RS. the distance of that marke from the meridian line, and setting one foote of the compasses in P. the meeting of that perpendicular with the meridian line, with the other make a prick T, in the same perpendicular line: for then AB. a right line drawn by this prick T. out of the center of the foresaid arke MDLN. shall bee the substilar line.

4 Then take with your compasses TR. the di­stance of the foresaid marke in the quadrant, QRO. and this pricke, and leauing one foote of your com­passes in the same pricke T. with the other make another pricke V. in the arke you first described; for then a right line AV. drawne thereby out of the [Page] arch you first described shall bee the stilar line, or line representing the stile.

5 In Dials not polar nor aequinoctiall, if the di­stance of the stile from the substilar line be but smal as in the fig. 10. 12. 17. it may bee increased by drawing a paralel CD. to the stile already found,The stile aug­mented. which for distinctions sake may bee called, the stile augmented.

NOw in all Dials that be not aequinoctiall, draw a right line, EHF. so long as you can, making right angles with the substi­lar line, which is called the line of contin­gence, or touchline.

2 Then describe the Equinoctiall circle GHI. after this manner: Take with your compasses the shortest distance betweene H. the intersection of the line of contingence with the substilar line, and the stilar line, and leauing one foot in that interse­ction, with the other make a pricke B. in the sub­stilar line, whereupon describe a circle GHI. which shall be called the equinoctiall circle.

3 If the distance of the stile from the substilar be augmented, you must draw two touch lines and two aequinoctial circles: as in 10. 12. 17. figures.

4 The halfe of the aequinoctiall circle next the [Page] line of contingence must be deuided into 12. equal parts, beginning at H, the intersection thereof with the substilar line in all direct dials, and erect or me­ridian polars which are commonly called East or West dials erect, as in the 3. 4. 5. 6. 13. 14. 15. figures.

5 In polars not meridian nor direct, let HK, in fig. 7. & 8. (the complement of the angle which the dial ground maketh with the plaine of the me­ridian) be numbred and marked in the aequinoctial circle, beginning at the substilar line, and procee­ding that way which the diall ground declineth as from H. to K. for at that marke K you must begin to diuide.

6 In decliners not polars, if the stile make a right angle with the meridian line, as in the 9. 10. 11. 12. figu. a paralel to the line of contingence, drawne by the center of the aequinoctiall, shall shew the be­ginning of the diuision, as BK in figu. 9. 10. 11. 12.

7 But if the stile make an oblique angle with the meridian line, and the line of contingencye, cut the meridian line, as in the 16. figu. your ruler laid to that cutting at X and the center of the Equinoctial B. shal shew in the peripherie thereof, the begin­ning of the diuision K if the distance of the stile from the substilar be not augmented.

8 But if it be augmented (as in the 17. figure) the shortest distance HX betweene H the inter­section of the touch line, with the substilar line, and the stile not augmented AV must bee taken with the compasses, and resting one foot in that interse­ction H, with the other make a pricke Y in the [Page] substilar line, towards B the center of the Equino­ctiall; by which pricke Y & Z the mutuall inter­sectiō of the next touch line with the meridian line, let a right line YZ be drawne, for BK. and BK. pa­ralels to it drawne out of the cenrers of both the E­quinoctials, towards the meridian line, at their cros­sings with the Equinoctials K & K shall shew the beginnings of their diuisions.

9 But if the touch line cut not the meridian line as in the figure 18. let a paralel thereto XY bee drawne, which may cut the meridian line in Y and take with the compasses the shortest distance ZA betwixt the intersection thereof with the sub­stilar line and the stile not augmented; and leauing one foote in that intersection Z, with the other make a pricke B in the substilar line towards the center of the Equinoctiall; from this pricke drawe a right line BY from B to Y the intersection of the said paralel with the meridian line; for BKA pa­ralel to this line drawne out of the center of the E­quinoctiall B. shall shew the beginning of the diui­sion K.

HAuing thus, deuided the Equinoctial cir­cle, lay your ruler to the center thereof B. and to euery one of those prickes [...] by which it is deuided, and make marks [...] &c. in euery place where it crosseth the line of contingence for then

2 In all polar Dials paralels to the substilar line, drawne by those markes, shall bee the houre lines, as in the 3. 4. 6. 7. 8. figu.

3 In Dials not polar, in which the height of the stile is not augmented, right lines drawne out of the center of the dial by those markes shal be the houre lines as in the 9. 11. 13. 14. 15. 16. 18. figu. And if any of the diuisions of the aequinoctiall circle doe fall in to the substilar line, a paralel to the line of contingence drawne by the center of the said diall, shall shew two opposit houres, distant by the space of six houres from the substilar line; as for exam­ple in direct Dials, six in the forenoone and six in the afternoone, as in the 13. 14. 15. figure. Also if the ruler laid to B. the center of the Equino­ctial circle, and some diuision thereof, as V in the 16. and 18. figu. cannot crosse the line of contin­gence, and yet draweth neerer to it,: draw BY. a right line from the center of the Equinoctial by that diuision, and draw AF a paralel to that line, [Page] which may crosse the substilar and line of contin­gency in F. then let HA. the other part of the sub­stilar that is betweene the line of contingence and the center of the dial A. be cut in such sort that the segments, of the substilar line concurring at the line of contingence AH and HB. may keepe the same proportion which the greater segments BH. and HA. haue, which are contained betweene the cen­ter of the Dial and line of contingence, and betwixt the center of the Equinoctiall and the line of con­tingence. And let aright line BF. bee drawne by that section B and the section of the line of contin­gence F. For AI a paralel to this right line drawne out of the center of the Diall shall be the houre line that wee seeke for.

4 In those dials wherein the distance of the stile from the substilar is augmented, right lines drawne by those markes in both lines of contingence which are proportionately distant from the substilar line shall be the houre lines.

IN meridian Dials, the substilar line is the line of the sixth houre: but for the rest, we must consider whether it be an oriental or an occidental dial.

2 An oriental Dial looketh to the East, and the forenoone houres onely must bee set in this Dial, and therefore the substilar line sheweth six of the clocke in the morning; from which towards the South are the morning houres before sixe, viz. 5. 4. 3. &c. but towards the North after six, 7. 8. 9. 10. 11. as in the 3 figure.

3 An occidental Dial looketh directly West­wards: and onely the houres after noone can bee set into this dial. Therfore the substilar line sheweth the sixt houre after noone: from which toward the North are the houres before six in this order. 5. 4. 3. 2. 1. but towards the South after six thus. 7. 8. 9. &c. as in the 4. figure.

4 In Dials not Meridian, if a ruler laid to the center of the aequinoctial and the beginning of the diuision thereof doe crosse the touchline; then the houre line drawne by that crossing is the line of twelue a clocke. But if it cannot crosse the touch line, imagine notwithstanding, that crossing and the twelue a clocke line, drawne thereby without the bounds of your Dial, whereabouts you thinke it would bee, if the ruler and touch line were [Page] continued foorth long inough.

5 Then in al Dials not meridian, imagine the stile to be fastned in his place, in aequinoctial Dials perpendicularly erected out of the Center. In Di­als that be not Equinoctial, conceiue it to be placed exactly ouer the substilar line, so much raised from the same as the stilar line in your paper or pastbord, is distant from the substilar line.

6 After this, place your paper or pastebord (wheron the figure of your Dial is described) in the same site or position that the dial ground is, or must be placed▪ so that the quarters of the world writ­ten thereupon, may answer in like position to the quarters of the world as they lie in respect of your dial ground: for then if the 12. a clocke line be to­wards the North, from the stile it is the line of the 12. houre of the day. From hence therefore to­wards the West are the forenoone houres, 11. 10. 9. 8. 7. &c. and toward the East, the afternoone houres, 1. 2. 3. 4. 5. 6. &c.

7 But if the 12. a clocke line bee Southward from the stile, it is the line of the twelfth houre in the night from thence: therefore on both sides are the night houres: toward the West, after midnight, 1. 2. 3. 4. &c. towards the East before midnight, 11. 10. 9. 8. &c.

IN al Dials, those houre lines onely are to be expressed, vpon which the shadow of the stile shal fall. Therefore the houres of the day onely are to bee expressed.

2 In Dials not Polar, wherein the height of the stile is not augmented, if the stile point vpwards, and the eleuation thereof from the substilar line, bee not lesse then the complement of the sunnes greatest declination, all the houre lines seruing for the longest day, are to be expressed therein.

3 But if the cleuation of the stile from the sub­stilar be lesse then the complement of the Sunnes greatest declination, draw a right line out of the in­tersection of the line of contingence, and substilar perpendicularly ouerthwart the stilar line: and set­ting one foot of your compasses in the center of the dial, and extending the other towards the other end of the stilar line, draw an arke there from equal to the complement of the Sunnes greatest declina­tion: and thereby draw a line out of the center of the Dial, and setting one foot of your compasses in­the intersection of this line with the foresaid per­pendicular, extend the other foot to the stilar line: Then keeping this distance, set one foote of your compasses in the center of the aequinoctial cir­cle and with the other crosse the line of contin­gence [Page] on both sides the substilar: now if you lay your ruler to these crosses and the center of the Dial: right lines drawne thereby beyond the center of the Dial shal continue betweene them the space wherein no houre lines are to be expressed.

4 This rule holdeth also in meridional Dials in­clining, when the eleuation of the stile is counted from the vpper end of the Meridian line, and the eleuation of the stile from the substilar is lesse then the complement of the Sunnes greatest declina­tion.

5 If the stile point downwards, no houre lines are to be expressed aboue a line parallel to the hori­zon drawne by the center of the Dial.

6 And if the crosse in the line of contingence (made as before was shewed) be aboue the line ae­quidistant to the horizon, drawne by the center of the Dial; no houre lines are to be expressed aboue a right line drawne from the crosse and continued beyond the center of the Dial.

7 If any part of the Dial whereupon the sha­dow of the stile may fal, bee void of houre lines: let the houre lines before described bee continued foorth into that part of the Dial, as in the 13 and 15 figure.

THe figure of your Dial being thus descri­bed, you shall translate the same into the Dial ground, after this manner.

2 Place the paper or pastebord where­as the figure of your dial is described in such sort, in the Dial ground is placed, so as the quarters of the world written on the paper or pastebord may answer in like position to the quarters of the world as they lye in respect of the Dial ground.

3 Then as the houre lines and substilar line are described in your pastebord, so in like manner, and in like position, let them be inscribed nto your Dial ground that so little part of the ground as may be, be left voide of houre lines seruing for vse, and that the spaces on both sides from the substilar line drawne on the Dial ground bee proportionable to the number of houre lines that are to bee expressed in the Dial.

4 In Polar dials draw a right line squire-wise o­uerthwart the substilar in the Dial ground; then take with your compasses the distances of the houre lines from the substilar in the pastebord, and set them into that line drawne squire-wise in the Dial ground, setting alwaies on foot in the intersection thereof with the substilar line, and with the other foote making pricks in the said line drawne squire­wise: [Page] And let paralels to the substiar line be drawn by those prickes, for they shall bee the houre lines we seeke for, set into the dial ground.

5 The stile must be paralel to the substilar line, and must be placed directly ouer it, so much distant from the same, as the stilar line is distant from the substilar in the figure of your Dial drawne on the pastbord or paper.

6 In Dials that be not polars, wherein the eleua­tion of the stile from the substilar is not augmen­ted, describe two peripheries of equal bignesse on the Dial ground, the center thereof being placed in the meridian line, the other vpon the center of the Dial in the bastbord: then in this peripherie take the distances of the substilar and the houre lines from the Meridian with your compasses, out of the figure of your Dial in the paper or pastbord, & set those distāces likewise into the dial grounds, and by them draw the houre lines and the substilar from the center of the dial.

7 The stile must bee fastned in the center, and must hang directly ouer the substilar, eleuated so much from the same, as the stilar line in the figure of your dial is distant from the substilar.

8 But in Dials that be not polars, wherein the eleuation of the stile from the substilar is aug­mented, let the substilar line bee described in the Dial ground so much distant from the Meridian, which you first described therein, as the substilar is distāt from the Meridian in the figure of your dial. And let two lines of contingence be drawne squire­wise [Page] ouerth wart that substilar in the Dial ground, so much distant each from other, as the lines of contingence in the paper are. And let the distan­ces of the houre lines from the substilar line bee ta­ken in both lines of contingence in the figure of the dial, and be set in like manner in to the lines of contingence, answering to them in the Diall ground, setting one foot of your compasses alwaies in the substilar line, which is in the Diall ground, and with the other making markes in the lines of contingence drawne therein: for then right lines drawne by those markes, differing alike from the substilar line, shall bee the houre lines. The stile must hang perpendicularly ouer the substilar line, so much distant from the same, and from the secti­ons thereof with the lines of contingence, as the stile augmented in the figure of your Diall is distant from the substilar.