A SHORT TREATISE OF DIALLING: SHOWING, THE MAKING OF ALL sorts of Sun-dials, Horizontal, Erect, Direct, Declining, Jnclining, Reclining; upon any flat or plain superficies, how soever placed, with ruler and compass only, without any arithmetical calculation. By EDWARD WRIGHT. LONDON, Printed by john Beale for WILLIAM WELEY. 1614 The Contents of this Book. Chap. 1. The making of the Clinatory. Chap. 2. The first division of dials into horizontal, erect inclining, and reclining. Chap. 3. The second division of Dial's into direct & declining. Chap. 4. The third division of Dial's, either agreeing with the plain of the Meridian, or disagreeing from the same. Chap. 5. To find the elevation of the meridian line above the Horizon. Chap. 6. The describing of the figure of the dial first on paper, pasteboard. Chap. 7. The making of equinoctial Dial's. Chap. 8. The finding of the substylar line, and style, in grounds not Equinoctial direct, and Polar. Chap. 9 The finding of the distance of the style from the Meridian line in dials, that be neither equinoctial nor polar. Chap. 10. The finding of the substylar line & the distance of the style from it, when the style maketh a right angle with the merid▪ line. Chap. 11. From which end of the Meridian line the elevation of the style is to be counted. Chap. 12. The finding of the substylar line & style in dials that be not Polar nor Equinoctial the style making oblique angles with the Meridian line. Chap. 13. The drawing of the line of contingence, and of the Equinoctial circle, and how it must be divided. Chap. 14. The drawing of the hour lines in all dials that be not equinoctial. Chap. 15. What number must be set to the hour lines. Chap. 16. What hour lines are to be expressed in all sorts of dials. Chap. 17. How to translate the dial drawn on paper, or paste-board unto the dial ground. line. Errat. Correct. B2 b 28 neither neither B3 b 2 cliniatorie clinatory B3 b 2 live line B3 b 10 made make B4 a 12 alother all other Also in the Diagramme placed there, and in the leaf following, let K & ● be changed each into others place. B4 b 14 horozontal horizontal C1 b 21 leaveth leaneth C3 a 25 ground grounds C3 a 29 draw drew D1 a 25 neither neither D3 a 20 contingency contingence D4 b 2 gen●y gence E1 a 8 u●ust must E1 b 23 night from thence: night: from thence E2 a 17 zersection tersection E2 b 4 continued contain E3 a 8 as the in the E3 a 9 in the as the E3 a 15 unto into E3 b 12 on the one on the E3 b 14 bastbord pastborde. IT is also to be remembered that there should have been numbers set to every one of the figures, or pictures of the dials, adjoined to the end of this treatise, beginning at E4 b, as there is to the three last, viz. the 16. 17. and 18. figure. As in the 7. Chap. where I show the making of equinoctial dials sect 4. when I refer you to the first and second figure, I mean the figues or pictures of the equinoctial dials in E4 b. To the first of these therefore there should be set [1. Figure, to the next [2. Figure, and to the first of the polar dials in F1 b, there should be set [3. Figure, and to the next in F2 a [4 Figure etc. Also in the 18. figure the line F. E. should have been continued upwards so much longer, and it is between R. and E, and at the end thereof being so continued the letter▪ should be set. A TREATISE OF DIALLING CAP. I. The making of the Clinatory. 1 Dial's are diversly made according as they are diversly placed. Therefore their situation must first be known: which may be done by an instrument not unfitly called a Clinatory. 2 Let this instrument be made just four square, and let the thickness be about half a quarter of the breadth of it, upon one side thereof describe a quadrant, whose two semidiameters or sides must be parallel to the side of the quadrate. 3 The quadrant must be divided into 90. degrees, with figures set to every fifth or tenth degree (as the manner is) both forward and backward, and without the periphery thereof, a groofe or furrow must be made so deep that a plummet hanging by a third from the Centre of the quadrant may fall into it, in such sort that the third 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 magnetical needle within the same, whose true Meridian line must be perpendicular to one of the sides of the quadrant, which shall be called the North side, and the other side of the quadrant shall be 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 magnetical Meridian, must be drawn in the bottom of the box according to the variation of the place where you are. The figure of the Clinatory. CAP. II. The first division of Dial's into horizontal, erect inclining, and reclining. EVery flat whereupon a Dial is to be The Dial ground. made (which is also called the Dial ground) either lieth level with the horizon, or else is elevated the one side higher than the other. 2 The first kind is thus known: Take the Horizontal flats: and how they are known. Clinatorie and hold it so that the plummet fall upon on of the Semidiameters, or sides of the Quadrant: then if the neither side of the Clinatory, which way so ever you turn the instrument, will touch the flat, it lieth level with the Horizon, and Dial's made upon such flats, are called Horizontal Dial's. 3 Those flats which are elevated the one Elevated flats; Erect, Inclining Reclining: and how they are to be known side higher than the other, stand either upright (which are called erect) or else, they stand leaning: if they lean to you ward, when you stand right against them, they are called inclining: otherwise reclining, if they lean from you ward. 4 All these flats are thus known: 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 only touch it, it is reclining: if either of the upper corners only 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 the To know how much the reclination or inclination is. flat, in such sort, that the plumbline hanging at liberty, may fall upon the circumference of the quadrant: for then the ark of the quadrant, betwixt the plumbline and that side of the quadrant that is parallel, or aequidistant to the slatte, is the reclination thereof, if the centre of the quadrant be from the flat, or else the inclination, if it be towards the same. CAP. III. The second division of Dial's into direct and declining. ALl flats are either direct, or declining. 2 All flats lying level with the Horizon are direct. 3 But if the flat lie not level 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: hold the Clinatory to the flat in such sort, that the plumbline may fall upon one of the sides of the quadrant; then draw a line by the neither side of the Clinatory in recliners; or by the upper 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 be called the horizontal line. Set the North side of the Cliniatorie to this live, if the North end of the needle look towards the flat: then if the Magnetical Meridian be right under 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 look towards the flat, made your account contrary wise. CHAP. IU. The third division of Dial's, either agreeing with the plain of the Meridian, or disagreeing from the same. ALl flats do either agree with the plain of the Meridian circle (which may therefore be called meridian flats) or else they disagree from the same. 2 They are known thus: If the flat be erect and declining 90. degrees, it is a Meridian flat, otherwise it is no Meridian flat; and than you must first draw therein the meridian line, after this manner. 3 If the flat be Horizontal, take the clinatory How to draw the Meridian line, in horizontal flats. and lay it flat down thereupon; and turning it about till the needle hang precisely over the Magnetical meridian, by that side thereof that is parallel to the true Meridian line of the Clinatory, draw a right line, for that shall be the Meridian line desired. 4 In erect flats the Meridian line is perpendicular, and therefore laying the Clinatory close to such a flat in such sort that the plumbline hang precisely In erect flats. on either side of the quadrant, a line drawn 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 line In direct flats. aequidistant from the Horizon, is the Meridian line we seek for. 6 In flats reclining or inclining, declining also In 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 alother In inclining or reclining flats declining less than 90. degrees. inclining or reclining, & withal declining flats, draw a line upon some pasteboard or paper which shall be called the horizontal meridian AB. wherein settingone foot of your compasses, with the other draw an arch of a circle; & therein reckon the complement of the declination FC. drawing a right line BC. by the end thereof out of the centre B. This right line you shall cross squirewise with another as AC. which may be called the base of inclination or reclination, and must also meet with the horizontal meridian at A. and setting one foot of your compasses in the crossing at C. with the other foot draw an ark, counting therein the complement of the reclination or inclination AG. drawing a right line by the end thereof, out of the centre 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 thereof draw a line to (the centre of the ark of declination) B. Then continuing forth AC. to N. (that CN. be equal to CD) from N. you shall draw a line to B. which (if you have wrought truly) must be equal to BE. Now the angle contained between the lines NB. and BC. showeth how much the Meridian line in your Dial ground should be distant from the line which you drew aequidistant to the Horizon here represented by BC. In this line therefore (in the Dial ground) set one foot of your compasses, and extending the other that way which the Dial declineth, draw an ark of a circle, upwards in recliners, but downwards in incliners: and therein count the said angle from the line parallel to the Horizon, and draw by the end thereof a line, which shall be the true Meridian in the Dial ground. 8 From To find the angle which the dial ground (or flat) maketh with the plain of the meridian. A draw AH perpendicular to EBB. make BY. equal to BH. from I. let IK be drawn perpendicular to BN. make CL. equal to CK and draw 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. CHAP. V. To find the elevation of the Meridian line above the Horizon. THe Meridian line is either parallel to the Horizon, or else elevated the one end How to find the elevation of the meridian line. higher than the other. 2 If the flat be 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 plain of the Meridian circle, the Meridian line is elevated the one end higher than the other. 4 This elevation is either upright, as in all erect The elevation of the meridian line in erect dials. In reclining or inclining direct flats; in reclining or inclining declining flats. Dial's not declining 90. degrees, or else leaning, as in all inclining, and reclining flats not declining 90 degrees, which if they be direct, is equal to the complement of reclination, or inclination. 5 But if they decline, than the angle ABE. in the former figure, is the elevation of the Meridian line. 6 If the meridian line be not erect, it leaveth either Northwards, when the elevated end thereof The elevation of the meridian whether North or South. looketh towards the North, or else Southwards when the elevated end looketh towards the South. 7 All flats are either Polar (which being continued▪ would go by the poles of the world) as all Flats polar. leaning flats, wherein the elevation of the meridian line is Northwards, and equal to the poles elevation▪ and all erect decliners 90. degrees. Otherwise they are no polar flats. Not polar. CHAP. VI The describing of the figure of the Dial first on paper or pasteboard. NOw it shall be 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 Dial itself upon his ground: that is, upon the Trunk, Stone, wall, etc. 2 This paper, or pasteboord therefore, you shall place, or understand 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, upper part, neither part, etc. which you may do by help of the magnetical needle: for the North end thereof (hanging at liberty) showeth the North, whereto the South is diametrally opposite; and your face being turned towards the North, your right hand showeth the East, your left hand the West, the Zenith, or vertical point is above your head, the Nadir under your feet. Note also, which end of the Meridian line must be higher, and which lower; if the Meridian be not parallel to the Horizon. CHAP. VII. The making of equinoctial Dial's. ALl Dial grounds are equinoctial, or not equinoctial. 2 An equinoctial ground is that which agreeth even with the plain of the equinoctial Circle: which is thus known. If the Dial ground be direct, and the Meridian line elevated Southwards, equally to the complement of the poles elevation, it is an Equinoctial Dial ground, otherwise not. 3 In an Equinoctial Dial you shall describe the hour lines after this manner. 4 Set one foot of your Compasses in the Meridian How to make Equinoctial Dial's. line AB. and with the other, draw a circle DBC. and divide it into 24. equal parts, as D. E. F. G. etc. beginning at B. the crossing thereof, with the Meridian line; for then right lines, as AD. A AF. AG. etc. in the 1. and 2. figure drawn out of the Centre, by those divisions shall be the hour lines. 5 The style must stand upright out of the centre Placing of the style. of the Dial. 6 Of Equinoctial Dial's there be two sorts, the upper and the neither. 7 The upper Equinoctial Dial looketh upwards Upper Equinoctial dial. to the elevated Pole of the world: And it showeth the hour of the day, only in the Spring and Summer time, as in the first figure. 8 The neither, or lower Equinoctial dial, is that Nether Equinoctial dial. which looketh downwards to that Pole of the world which is beneath the Orisons and showeth the hours only in Autumn, and Winter, as in the second figure. CHAP. VIII. The finding of the substylar line, and style, in grounds not Equinoctial direct, and Polar. IN all Dial grounds that are not Equinoctial, the substylar line, and the distance of the style from the substylar must be found. 2 The substylar line is that right over which the Substilar line. style must be set. 3 The distance of the style from the substylar, is Distance of the style from the substylar. the angle, or space contained between the style, and the substylar line. 4 The finding out of these is divers, in divers The finding of the substylar line. kinds, and therefore must be specially showed in each kind. 5 In direct Dial grounds not Equinoctial, and In direct flats not aquinoctial In Polars not Meridian. Polars not Meridian, the substylar line is the same with the Meridian line, or else parallel thereto, in declining polars. 6 In Polar ground▪ agreeing with the plain of In Meridian Polars. the Meridian, the substylar line may thus be found. 7 Set one foot of the compasses in the South-end of the line that you draw equidistant from the Horizon and extending the other foot towards the North end of the same line, draw an ark of a circle: therein reckon the elevation of the Pole beginning at the foresaid line: for a right line drawn thereby out of the centre, shall be the substylar line AB. figure. 3. 8 In all Polar grounds draw a parallel CD. (figu. The stilar line in all Polar Dial's. 3. 4. 5. 6. 7. 8.) to the substylar line at a convenient distance from the same; for that shall be the line representing the style. CHAP. IX. The finding of the distance of the style from the Meridian line in Dial's that be neither equinoctial nor polar. IN all Dial grounds that be not equinoctial nor polar, before the substylar line, and distance of the style from it can be found, first the distance of the style from the Meridian line must be found after this manner. 2 If the Meridian line be parallel to the Horizon, as BC. the distance of the style from the Meridian line, is equal to the height of the Pole, as BR. 3 But if the elevation of the Meridian be either upright, as AG. or leaning towards the North, and withal greater than the Poles elevation, as AH. the height of the Pole BR. taken out of the height of the Meridian line BH. or BG. shall leave the distance of the style from the Meridian line RH. or RG. 4 If the elevation of the meridian line be Northwards, and less than the height of the Pole, as BY. take the elevation of the meridian line BY. out of the height of the pole BR. and there shall remain the distance of the style from the Meridian line RI. 5 If the elevation of the Meridian line be Southwards, and either greater, or equal to the complement of the Poles elevation, as AF. and A than the complement of the Meridian lines elevation, FG. or EGLANTINE. added to the complement of the Poles elevation GR. shall make the distance of the style from the meridian line. 6 If the elevation of the meridian line be Southward and less than the complement of the poles elevation as CD. the elevation of the meridian line CD and the height of the Pole C●. put together shall make the distance of the style from the meridian line. CHAP. X. The finding of the substylar line and the distance of the style from it, when the style maketh a right angle with the meridian line. SEcondly, in a ground not Equinoctial nor Polar we must consider whether the style make a right angle, or an oblique angle with the meridian line. 2 The style shall make a right angle with the meridian line, if the elevation of the meridian line be Southwards and equal to the complement of the Poles elevation, as in the 9 10. 11. and 12. figure Herein a right line drawn squirewise overthwart the meridian line, towards that part of the world, which is opposite to that whereto the dial ground declineth, shall be the substylar line, as BASILIUS. in the 9 10. 11. and 12. figu. and the distance of the style from the substylar line shall be equal to the angle which the dial ground maketh with the plain of the meridian circle as the angle BAD. fig. 9 10. 11. 12. which angle is found by the third Chap. CHAP. XI. From which end of the Meridian line, the elevation of the style is to be counted. IF the style make an oblique angle with the meridian line, we must first find out from whether end of the meridian line, the elevation of the style must be reckoned, thus: 2 If the meridian line be parallel to the horizon as in the 13. figure, the elevation of the style shall be reckoned from the North end of the meridian line in reclining, and horizontal flats looking upwards, as BR. from B in the former figure, but chose in incliners as PC. from C. in the same figure. 3 If the meridian line be elevated the one end higher than the other from the horizon, and the dial ground look towards the South, the elevation of the meridian being also Northwards, and less than the elevation of the pole: the elevation of the style shall be counted from the upper end of the meridian line: as IR. from I. 4 But if the elevation of the meridian be greater than the elevation of the pole, or upright, or southwards and greater than the complement of the poles elevation; the elevation of the style shall be counted from the neither end of the meridian line, as PM, PN, PO, from MNO. 5 If the elevation of the meridian line be Southwards and less than the complement of the poles elevation, the elevation of the style shall be counted from the upper end of the meridian line as DP. from D. 6 If the Dial ground look toward the North, the elevation of the style from the meridian line shall be reckoned chose in every kind. CHAP. XII. The finding of the substylar line and style in Dial's that be not Polar nor Equinoctial, The style making oblique angles with the Meridian line. Having thus found out from whether end of the meridian line the elevation of the style is to be reckoned, set one foot of your compasses in the meridian line as in A. and stretching forth the other foot towards that end of the meridian line, from which the elevation of the style is to be reckoned as towards L. draw an arch of a circle MDLN. and (beginning at the Merîdian line) reckon and mark therein the elevation of the style from the Meridian line, LD. figure 13. 14. 15. in the rest LO. either Eastwards or Westwards in direct Dial's, 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 Dial's, a right line ACD. fig. 13. 14. 15. drawn out of the centre of the said ark by the mark of the styles elevation from the meridian line shall be the line representing the style, and therefore the distance of the style from the substylar line shall be the distance of the style, from the meridian line. 3 But in decliners you shall thus find the substylar line: From O the point of the styles elevation from the meridian line in the foresaid ark draw OPEN. a perpendicular to the meridian line AL. and taking the length of this perpendicular with your compasses, leave one foot in P. the concourse thereof with the meridian line, and with the other describe a quadrant of a circle QRO. beginning from the Meridian line, and so proceeding unto O the other end of the perpendicular line: and in that quadrant beginning at the meridian ALQ. reckon and mark QR. the complement of the angle contained between the plains of the dial ground and of the meridian circle, and take with your compasses RS. the distance of that mark from the meridian line, and setting one foot 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 than AB. a right line drawn by this prick T. out of the centre of the foresaid ark MDLN. shall be the substylar line. 4 Then take with your compasses TR. the distance of the foresaid mark in the quadrant, QRO. and this prick, and leaving one foot of your compasses in the same prick T. with the other make another prick V. in the ark you first described; for then a right line AU. drawn thereby out of the arch you first described shall be the stilar line, or line representing the style. 5 In Dial's not polar nor equinoctial, if the distance of the style from the substylar line be but small as in the fig. 10. 12. 17. it may be increased by drawing a parallel CD. to the style already found, The style augmented. which for distinctions sake may be called, the style augmented. CHAP. XIII. The drawing of the line of Contingence, and of the Equinoctial circle, and how it must be divided. NOw in all Dial's that be not equinoctial, draw a right line, EHF. so long as you can, making right angles with the substylar line, which is called the line of contingence, or touchline. 2 Then describe the Equinoctial circle GHI. after this manner: Take with your compasses the shortest distance between H. the intersection of the line of contingence with the substylar line, and the stilar line, and leaving one foot in that intersection, with the other make a prick B. in the substylar line, whereupon describe a circle GHI. which shall be called the equinoctial circle. 3 If the distance of the style from the substylar be augmented, you must draw two touch lines and two equinoctial circles: as in 10. 12. 17. figures. 4 The half of the equinoctial circle next the line of contingence must be divided into 12. equal parts, beginning at H, the intersection thereof with the substylar 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 plain of the meridian) be numbered and marked in the equinoctial circle, beginning at the substylar line, and proceeding that way which the dial ground declineth as from H. to K. for at that mark K you must begin to divide. 6 In decliners not polars, if the style make a right angle with the meridian line, as in the 9 10. 11. 12. figu. a parallel to the line of contingence, drawn by the centre of the equinoctial, shall show the beginning of the division, as BK in figu. 9 10. 11. 12. 7 But if the style make an oblique angle with the meridian line, and the line of contingency, cut the meridian line, as in the 16. figu. your ruler laid to that cutting at X and the centre of the Equinoctial B. shall show in the periphery thereof, the beginning of the division K if the distance of the style from the substylar be not augmented. 8 But if it be augmented (as in the 17. figure) the shortest distance HX between H the intersection of the touch line, with the substylar line, and the style not augmented AV must be taken with the compasses, and resting one foot in that intersection H, with the other make a prick Y in the substylar line, towards B the centre of the Equinoctial; by which prick Y & Z the mutual intersection of the next touch line with the meridian line, let a right line YZ be drawn, for BK. and BK. parallels to it drawn out of the cenrers of both the Equinoctials, towards the meridian line, at their cross with the Equinoctials K & K shall show the beginnings of their divisions. 9 But if the touch line cut not the meridian line as in the figure 18. let a parallel thereto XY be drawn, which may cut the meridian line in Y and take with the compasses the shortest distance ZA betwixt the intersection thereof with the substylar line and the style not augmented; and leaving one foot in that intersection Z, with the other make a prick B in the substylar line towards the centre of the Equinoctial; from this prick draw a right line BY from B to Y the intersection of the said parallel with the meridian line; for BKA parallel to this line drawn out of the centre of the Equinoctial B. shall show the beginning of the division K. CHAP. XIIII. The drawing of the hour lines in all Dial's that be not Equinoctial. Having thus, divided the Equinoctial circle, lay your ruler to the centre thereof B. and to every one of those pricks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 by which it is divided, and make marks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 etc. in every place where it crosseth the line of contingence for then 2 In all polar Dial's parallels to the substylar line, drawn by those marks, shall be the hour lines, as in the 3. 4. 6. 7. 8. figu. 3 In Dial's not polar, in which the height of the style is not augmented, right lines drawn out of the centre of the dial by those marks shall be the hour lines as in the 9 11. 13. 14. 15. 16. 18. figu. And if any of the divisions of the equinoctial circle do fall in to the substylar line, a parallel to the line of contingence drawn by the centre of the said dial, shall show two opposite hours, distant by the space of six hours from the substylar line; as for example in direct Dial's, six in the forenoon and six in the afternoon, as in the 13. 14. 15. figure. Also if the ruler laid to B. the centre of the Equinoctial circle, and some division thereof, as V in the 16. and 18. figu. cannot cross the line of contingence, and yet draweth nearer to it,: draw BY. a right line from the centre of the Equinoctial by that division, and draw OF a parallel to that line, which may cross the substylar and line of contingency in F. then let HA. the other part of the substylar that is between the line of contingence and the centre of the dial A. be cut in such sort that the segments, of the substylar line concurring at the line of contingence AH and HB. may keep the same proportion which the greater segments BH. and HA. have, which are contained between the centre of the Dial and line of contingence, and betwixt the centre of the Equinoctial and the line of contingence. And let aright line BF. be drawn by that section B and the section of the line of contingence F. For AI a parallel to this right line drawn out of the centre of the Dial shall be the hour line that we seek for. 4 In those dials wherein the distance of the style from the substylar is augmented, right lines drawn by those marks in both lines of contingence which are proportionately distant from the substylar line shall be the hour lines. CHAP. XV. What number must be set to the hour lines. IN meridian Dial's, the substylar line is the line of the sixth hour: 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 forenoon hours only must be set in this Dial, and therefore the substylar line showeth six of the clock in the morning; from which towards the South are the morning hours before six, viz. 5. 4. 3. etc. but towards the North after six, 7. 8. 9 10. 11. as in the 3 figure. 3 An occidental Dial looketh directly Westwards: and only the hours after noon can be set into this dial. Therefore the substylar line showeth the sixth hour after noon: from which toward the North are the hours before six in this order. 5. 4. 3. 2. 1. but towards the South after six thus. 7. 8. 9 etc. as in the 4. figure. 4 In Dial's not Meridian, if a ruler laid to the centre of the equinoctial and the beginning of the division thereof do cross the touchline; then the hour line drawn by that crossing is the line of twelve a clock. But if it cannot cross the touch line, imagine notwithstanding, that crossing and the twelve a clock line, drawn thereby without the bounds of your Dial, whereabouts you think it would be, if the ruler and touch line were continued forth long enough. 5 Then in all Dial's not meridian, imagine the style to be fastened in his place, in equinoctial Dial's perpendicularly erected out of the Centre. In Dial's that be not Equinoctial, conceive it to be placed exactly over the substylar line, so much raised from the same as the stilar line in your paper or pasteboard, is distant from the substylar line. 6 After this, place your paper or pastebord (whereon 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 than if the 12. a clock line be towards the North, from the style it is the line of the 12. hour of the day. From hence therefore towards the West are the forenoon hours, 11. 10. 9 8. 7. etc. and toward the East, the afternoon hours, 1. 2. 3. 4. 5. 6. etc. 7 But if the 12. a clock line be Southward from the style, it is the line of the twelfth hour in the night from thence: therefore on both sides are the night hours: toward the West, after midnight, 1. 2. 3. 4. etc. towards the East before midnight, 11. 10. 9 8. etc. CHAP. XVI. What hour lines are to be expressed in all sorts of Dial's. IN all Dial's, those hour lines only are to be expressed, upon which the shadow of the style shall fall. Therefore the hours of the day only are to be expressed. 2 In Dial's not Polar, wherein the height of the style is not augmented, if the style point upwards, and the elevation thereof from the substylar line, be not less than the complement of the suns greatest declination, all the hour lines serving for the longest day, are to be expressed therein. 3 But if the clevation of the style from the substylar be less than the complement of the suns greatest declination, draw a right line out of the intersection of the line of contingence, and substylar perpendicularly overthwart the stilar line: and setting one foot of your compasses in the centre of the dial, and extending the other towards the other end of the stilar line, draw an ark there from equal to the complement of the suns greatest declination: and thereby draw a line out of the centre 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 foot of your compasses in the centre of the equinoctial circle and with the other cross the line of contingence on both sides the substylar: now if you lay your ruler to these crosses and the centre of the Dial: right lines drawn thereby beyond the centre of the Dial shall continue between them the space wherein no hour lines are to be expressed. 4 This rule holdeth also in meridional Dial's inclining, when the elevation of the style is counted from the upper end of the Meridian line, and the elevation of the style from the substylar is less than the complement of the suns greatest declination. 5 If the style point downwards, no hour lines are to be expressed above a line parallel to the horizon drawn by the centre of the Dial. 6 And if the cross in the line of contingence (made as before was showed) be above the line aequidistant to the horizon, drawn by the centre of the Dial; no hour lines are to be expressed above a right line drawn from the cross and continued beyond the centre of the Dial. 7 If any part of the Dial whereupon the shadow of the style may fall, be void of hour lines: let the hour lines before described be continued forth into that part of the Dial, as in the 13 and 15 figure. CHAP. XVII. How to translate the Dial drawn on paper or paste-board unto the Dial ground. 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 lie in respect of the Dial ground. 3 Then as the hour lines and substylar line are described in your pastebord, so in like manner, and in like position, let them be inscribed unto your Dial ground that so little part of the ground as may be, be left void of hour lines serving for use, and that the spaces on both sides from the substylar line drawn on the Dial ground be proportionable to the number of hour lines that are to be expressed in the Dial. 4 In Polar dials draw a right line squirewise overthwart the substylar in the Dial ground; then take with your compasses the distances of the hour lines from the substylar in the pastebord, and set them into that line drawn squirewise in the Dial ground, setting always on foot in the intersection thereof with the substylar line, and with the other foot making pricks in the said line drawn squirewise: And let parallels to the substiar line be drawn by those pricks, for they shall be the hour lines we seek for, set into the dial ground. 5 The style must be parallel to the substylar line, and must be placed directly over it, so much distant from the same, as the stilar line is distant from the substylar in the figure of your Dial drawn on the pasteboard or paper. 6 In Dial's that be not polars, wherein the elevation of the style from the substylar is not augmented, describe two peripheries of equal bigness on the Dial ground, the centre thereof being placed in the meridian line, the other upon the centre of the Dial in the bastbord: then in this periphery take the distances of the substylar and the hour lines from the Meridian with your compasses, out of the figure of your Dial in the paper or pasteboard, & set those distances likewise into the dial grounds, and by them draw the hour lines and the substylar from the centre of the dial. 7 The style must be fastened in the centre, and must hang directly over the substylar, elevated so much from the same, as the stilar line in the figure of your dial is distant from the substylar. 8 But in Dial's that be not polars, wherein the elevation of the style from the substylar is augmented, let the substylar line be described in the Dial ground so much distant from the Meridian, which you first described therein, as the substylar is distant from the Meridian in the figure of your dial. And let two lines of contingence be drawn squirewise overth wart that substylar 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 hour lines from the substylar line be 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 Dial ground, setting one foot of your compasses always in the substylar line, which is in the Dial ground, and with the other making marks in the lines of contingence drawn therein: for then right lines drawn by those marks, differing alike from the substylar line, shall be the hour lines. The style must hang perpendicularly over the substylar line, so much distant from the same, and from the sections thereof with the lines of contingence, as the style augmented in the figure of your Dial is distant from the substylar. Equinoctial Dial's. North direct reclining 51. degrees, ●0. minutes, or the upper Equinoctial Dial. South direct, inclining 51. degrees, 30. minutes. The manner of finding the substylar line in Meridian Polar Dial's. This example serveth for the Oriental dial. Meridian Polar dials. A South direct dial reclining 38 degrees 30. minutes, or a South direct polar dial. A North direct dial inclining 38 degrees 30. minutes, or a North direct polar dial. South declining Eastward 27. degrees, reclining 34. degrees 40. minutes. North declining Westward 36 degrees inclining 32. degrees 15 minutes. North declining Eastward 43. degrees reclining 42. degrees 20. minutes wherein the style and meridian line make right angles. North declining 84. degrees westward, reclining 7 degrees 20 minutes, the style pendicular to the Meridian line. South declining Eastward 31 degrees, inclining 48 degrees. ●0 min. the style perpendicular to the meridian. South declining Westward 86▪ degrees 40. min. inclining 4. degrees style perpendicular to the meridian. In all the figures following, the style maketh a sharp angle with the meridian: a direct dial lying level with the Horizon, commonly called an Horizontal dial. A South dial erect direct. A North Dial erect, direct. A South dial erect declining Eastward 30. degr. A South erect dial declining westward 80. degr. North declining westward 41. de. 40. min. reclin. 4●. de. 30. min.