Mechanick Dyalling TEACHING Any Man though of an Ordinary Capacity and unlearned in the Mathematicks to draw a True SUN-DYAL On any Given Plane However scituated Only with the help of a straight RVLER and a pair of COMPASSES And without any Arithmetical Calculation By Joseph Moxon Hydrographer to the Kings most Excellent Majesty LONDON Printed for Joseph Moxon on Ludgate-hill at the Sign of Atlas MDCLXVIII MECHANICK DYALLING Description of Dyalling DYalling originally is a Mathematical Science attained by the Philosophical contemplation of the motion of the Sun the motion of the Shaddow the Constitution of the Sphere the Scituation of Planes and the consideration of Lines Explanation THE motion of the Sun is regular it moving equal Space in equal Time But the motion of the Shaddow irregular in all parts of the Earth unless under the two Poles and that more or less according to the Constitution of the Sphere and scituation of the Plane And therefore Scientifick Dyalists by the Geometrick considerations of Lines have found out Rules to mark out the irregular motion of the Shaddow in all Latitudes and on all Planes to comply with the regular motion of the Sun And these Rules of adjusting the motion of the Shaddow to the motion of the Sun may be called Scientifick Dyalling But though we may justly account Dyalling originally a Science yet such hath been the Generosity of many of its studious Contemplators that they have communicated their acquired Rules whereby it is now become to many of the Ingenious no more difficult than an Art and by many late Authors so intituled Nay more by this small Treatise it will scarce be accounted more than a Manual Operation for though hitherto all the Authors I have met with seem to presuppose their Reader to understand Geometry and the projecting of the Sphere already or else endeavour in their Works to make him understand them as if they were absolutely necessary to be known by every one that would make a Dyal when as in truth the contemplative pains of others aforesaid considered they are not but indeed are only useful to those that would know the reason of Dyalling Thus they do not only discourage young beginners but also disappoint many Gentlemen and others that would willingly either make them themselves or set their Workmen about them if they knew how to make them This little Piece I have therefore composed for the help of those who understand neither the Projection of the Sphere or Geometrical Operations Only if they know how to draw a straight Line between two Points by the side of a Ruler describe a Circle with a pair of Compasses erect a Perpendicular and draw one Line parallel to another they may know how to draw a Dyal for any given Plane however scituated in any Latitude But perhaps these two last little Tricks are not known to all new beginners therefore I shall shew them First How to erect a Perpendicular For Example in Fig. 1. Upon the Line AB you would erect a Perpendicular to the Point C Place one Foot of your Compasses upon the point C and open the other to what distance you please For Example to the point A make there a mark then keeping the first Foot still in C turn the other Foot toward B and make there another mark then open your Compasses wider suppose to the length AB and placing one Foot in the point A with the other Foot describe a small Arch over the point C and removing the Foot of your Compasses to the point B with the other Foot describe another small Arch to cut the first Arch as at D. Then lay your straight Ruler to the point where the two small Arches cut each other and upon the point C and by the side of the Ruler draw the Line CD which shall be a Perpendicular to the Line AB Another way with once opening the Compasses as by Fig. 2. Draw the Line AB and place one Foot of your Compasses upon the point you would have the Perpendicular erected as at the point C and with the other foot describe the Semi-Circle A ab B then placing one Foot in B extend the other Foot to b in the Semi-Circle and keeping that Foot in b extend the other Foot to D and make there a small Arch Then remove one Foot of your Compasses to A and extend the other Foot to a in the Semi-Circle and keeping that Foot in a extend the other to D and make there another small Arch to cut the first small Arch and laying a straight Ruler to the point where these two small Arches cut each other and upon the point C draw by the side of the Ruler the Line CD which shall be Perpendicular to the Line AB To erect a Perpendicular upon the end of a Line as by Fig. 3. On the point B at one end of the Line AB place one Foot of your Compasses in the point B and extend the other on the Line towards A as to b and with it describe the Arch ba C then placing one Foot in b extend the other to a in the Arch and make there a mark Divide with your Compasses the Arch ba into two equal parts and keeping the Feet of your Compasses at that distance measure in the Arch from a to C then draw a straight Line from the point C to the end of the Line B and that straight Line shall be Perpendicular to the end of the Line AB To draw a Line Parallel to another Line as by Fig. 4. Example If you would draw a Line Parallel to the Line AB open your Compasses to the distance you intend the Lines shall stand off each other and placing one Foot successively near each end describe with the other Foot the small Arches CD lay a straight Ruler to the top of these Arches and draw a Line by the side of it and that Line shall be Parallel to the Line AB Definitions A Dyal Plane is that Flat whereon a Dyal is intended to be projected Of Dyal Planes some be Direct other Decliners others Oblique Of Direct Planes there are five sorts 1. The Horizontal whose Plane lies flat and is parallel to the Horizon beholding the Zenith 2. The South Erect whose Plane stands upright and directly beholds the South 3. The North Erect whose Plane stands upright and directly beholds the North. 4. The East Erect whose Plane stands upright and directly beholds the East 5. The West Erect whose Plane stands upright and directly beholds the West Of Decliners there are infinite and yet may be reduced into these two Kinds 1. The South Erect Plane declining more or less towards the East or West 2. The North Erect Plane declining more or less towards the East or West Of Oblique Planes some are Direct others Declining and are of four sorts 1. Direct Inclining Planes which lean towards you and lie directly in the East West North or South quarters of Heaven 2. Direct Reclining Planes which
is 38 ½ or which is all one the Complement of the Poles Elevation Therefore in a Quadrant of the same Radius with the occult Arch measure 38 ½ Degrees and set them off in the Plane from E to D Then from D to the Center C in the Perpendicular draw the prick't Line DC this prick't Line shall represent the Axis of the World Then cross this Line at right Angles with the Line CF and draw it from C to F so long as possibly you can This Line shall be the Contingent Line Then chuse a point in this Contingent Line as at VI draw a Line through that point at right Angles for the Substilar Line as G VI H for the Substilar Line then open your Compasses to a convenient width as to VIG and pitching one Foot in the point G with the other Foot describe a Semi-Circle of the Equinoctial against the Line of Contingence which Semi-Circle devide from VI both wayes into six equal parts as you were taught by the Example in the Horizontal Dyal and laying a straight Ruler on the Center of this Semi-Circle of the Equinoctial and to each of those equal parts mark on the Contingent Line where the Ruler cuts it for those marks shall be the several points from whence Lines drawn parallel to the Line CD shall be the respective Hour Lines The reason why the Contingent Line is drawn from VI. to F so much longer than from VI to C is because the Hour Lines from VI towards XII are more in number towards Noon than they are from VI backward towards IIII for this Dyal will only shew the Hours from a little before IV in the Morning to almost Noon For just at Noon the Shaddow goes off the Plane as you may see if you apply a straight Ruler to the Center of the Equinoctial Semi-Circle G and lay it to the point 12 in the Semi-Circle for the straight Ruler will then never cut the Line of Contingence because the Line of Contingence is parallel to the Line G XII on the Equinoctial Circle and Lines parallel though continued to never so great a length never meet To these Hour Lines set Figures as may be seen in the Scheme The Stile IK of this Dyal as well as of all others must stand parallel to the Axis of the World and also parallel to the Face of the Plane and parallel to all the Hour Lines and stand directly over the Substilar or VI a Clock Hour-Line and that so high as is the distance of the Center of the Equinoctial Semi-Circle from the Contingent Line OPERAT. VI. To describe a Dyal on an Erect Direct West Plane AN Erect Direct West Dyal is the same in all respects with an Erect Direct East Dyal Only as the East Dyal shews the Forenoon Hours so the West shews the Afternoon Hours Thus if you should draw the East Dyal on any transparent Plane as on Glass Horn or oyled Paper on the one side will appear an East Dyal on the other side a West Only the numbers to the Hour Lines as was said before in the North Dyal must be changed for that which in the East Dyal is XI in the West must be I that which in the East Dyal is X in the West must be II that which in the East Dyal is IX in the West must be III c. The Stile is the same OPERAT. VII To describe a Dyal on an Erect North or Erect South Plane Declining Eastwards or Westwards THese four Dyals viz. the Erect North Declining Eastwards the Erect North Declining Westwards the Erect South Declining Eastwards and the Erect South Declining Westwards are all projected by the same Rules and therefore are in effect but one Dyal differently placed as you shall see hereafter First draw on your Plane a straight Line to represent the Horizon of your place and mark one end of it W for West and the other end E for East Chuse a point in this Horizontal Line for a Center as at A whereon you may describe a Circle to comprehend all these four Dyals Draw a Line as MAM perpendicular to the Horizontal Line WE through the Center A for a Meridian Line and on that Center describe a Circle which by the two Lines WAE and MAM will be devided into four Quadrants which will comprehend the four Dyals aforesaid for if it be a North declining West you are to draw the upper Quadrant to the left hand serves your purpose If a South Declining West the same Lines continued through the Center A into the lower Quadrant to the right Hand serves your turn if a North Declining East the upper Quadrant to the right Hand serves your turn or if a South Declining East the same Lines continued through the Center A into the lower Quadrant to the left hand serves your turn and you must draw the Declination Complement of the Poles Altitude Substile Stile and Hour Lines in it but the Hour Lines must be differently marked as you shall see hereafter I shall onely give you an Example of one of these Dyals viz. A South Declining East We will suppose you are to draw a Dyal that declines from the South 50 Degrees towards the East here being but one Dyal you need describe but one Quadrant of a Circle Set off in the lower Quadrant WAM 50 degrees from the Meridian Line M towards W and from the Center A draw a straight Line through that mark in the Quadrant as DA which may be called the Line of Declination then set off from the Meridian Line the Complement of the Poles Elevation which in our Latitude is 38 ½ degrees and there draw another Line from the Center as AP which we will call the Polar Line Then take in the Horizontal Line a convenient portion of the Quadrant as AB and from the point B draw a Line parallel to the Meridian Line AM and continue that Line till it intersect the Polar Line as at P from which Point P draw a Line parallel to WA as PC Then measure the distance of AB in the Horizontal Line and set off that distance in the Line of Declination as from A to D and from that point of distance draw a Line parallel to the Meridian AM through the Horizontal Line at R and through the Point D and continue it through the Line PC as at S then laying a straight Ruler to the Center A and the Intersection of the Line PC at S draw the Line AS for the Substile Then upon the Point S erect a Line perpendicularly as ST Then measure the distance between R and D and set that distance off from S to T and from the Center to the point T draw the Line AT for the Stile or Gnomon and the Triangle SAT made of Iron or Brass and erected perpendicularly over the Substile SA shall by its upper side TA cast a shaddow upon the Hour of the day But you will say the Hour Lines must be drawn first It is
lean from you and lie directly in the East West North or South quarters of Heaven 3. Inclining Declining Planes which lean towards you but lie not directly in the East West North or South quarters of Heaven But decline more or less from the North or South towards the East or West 4. Reclining Declining Planes which lean from you but lie not directly in the East West North or South quarters of Heaven But Decline more or less from the North or South towards the East or West If the Scituation of the Plane be not given you must seek it For there are several wayes how to know these several kinds of Planes used among Artists But the readiest and easiest is by an Instrument called a Declinatory fitted to the variation of your Place And if it be truly made you may as safely rely upon it as any other OPERATION I. The Description of the Clinatory THE Clinatory is made of a square Board as ABCD of a good thickness and the larger the better between two of the side is described on the Center Aa Quadrant as EF devided into 90 equal parts or degrees which are figured with 10 20 30 to 90 and then back again with the Complements of the same numbers to 90 between the Limb and the two Semi-diameters is made a round Box into which a Magnetical Needle is fitted and a Card of the Nautical Compass devided into four Nineties beginning their numbers at the East West North and South points of the Compass from which points the opposite sides of the Clinatory receives their Names of East West North and South But Note that the North point of the Card must be placed so many degrees towards the East or West sides of the Clinatory as the Needle varies from the true North point of the world in the place where you make your Dyal which your Workman that makes your Clinatory will know how to fit Upon the Center A whereon the Quadrant was described is fastened a Plumb-line having a Plumbet of Lead or Brass fastned to the end of it which Plumb-line is of such length that the Plumbet may fall just into the Grove GH below the Quadrant which is for that purpose made of such a depth that the Plumbet may ride freely within it without stopping at the sides of it See the Figure annexed With this Clinatory you may examine the scituation of Planes As if your Plane be Horizontal it is direct and then for the true scituating your Dyal you have only the true North and South Line to find which is done only by setting the Clinatory flat down upon the Plane and turning it towards the right or left hand till you can bring the North point of the Needle to hang just over the Flower-de-luce for then if you draw a Line by either of the sides parallel to the Needle that Line shall be a North and South Line If Your Plane either Recline or Incline Apply one of the sides of your Clinatory parallel to one of the Semi-diameters of the Quadrant to the Plane in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant for then the number of degrees of the Quadrant comprehended between the side of the Quadrant parallel to the Plane and the Plumb-line shall be the number of degrees for Reclination if the Center of the Quadrant points upwards or Inclination if the Center points downwards If your Reclining or Inclining Plane Decline Draw upon it a Line parallel to the Horizon which you may do by applying the back-side of the Clinatory and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Semi-diameters for then you may by the upper side of the Clinatory draw an Horizontal Line if the Plane Incline or by the under side if it Recline If it neither Incline or Recline you may draw a Horizontal Line both by the upper and under sides of the Clinatory Having drawn the Horizontal Line apply the North side of the Clinatory to it and if the North end of the Needle points directly towards the Plane it is then a South Plane If the North point of the Needle points directly from the Plane it is a North Plane but if it points towards the East it is an East Plane if towards the West a West Plane If it do not point directly either East West North or South then so many degrees as the Needle declines from any of these four points to any of the other of these four points so many degrees is the Declination of the Plane You may find a Meridian Line another way thus If the Sun shine just at Noon hold up a Plumb-line so as the shaddow of it may fall upon your Plane and that shaddow shall be a Meridian Line OPERAT. II. To describe a Dyal upon a Horizontal Plane FIrst draw a North and South Line which is called a Meridian Line through the middle of the Plane Thus Set your Declinatory flat upon the Plane and turn it to and fro till the Needle hang precisely over the Meridian Line of the Declinatory then by the side of the Declinatory parallel to its Meridian Line draw a straight Line on the Plane and if that straight Line be in the middle of the Plane it shall be the Meridian Line without more ado But if it be not in the middle of the Plane you must draw a Line parallel to it through the middle of the Plane for the Meridian Line or twelve a Clock line And it shall be the Meridian Line and also be the Substilar Line then draw another straight Line through the middle of this Line to cut it at right Angles for the VI. a Clock Lines and where these two Lines cut one another make your Centre whereon describe a Circle on your Plane as large as you can which by the Meridian Line and the Line drawn at right Angles with it will be devided into four Quadrants one of the Quadrants devide into 90 degrees thus Keeping your Compasses at the same width they were at when you described the Quadrant place one Foot in the twelve a Clock Line and extend the other in the Quadrant and make in the Quadrant a mark with it so shall you have the sixtieth degree marked out then place one Foot of your Compasses in the six a Clock Line and extend the other in the Quadrant and make in the Quadrant another mark with it so shall that Quadrant be divided into three equal parts each of these three equal parts contains 30 degrees Then with your Compasses devide one of these three equal parts into three parts and transfer that distance to the other two third parts of the Quadrant so shall the whole Quadrant be devided into nine equal parts Then devide one of these nine equal parts into two equal parts and transfer that distance to the other eight equal parts so shall the Quadrant be devided into eighteen equal parts
perpendicular Line So now set that distance from F to m in the Horizontal Intersection on the left hand in the Perpendicular Line and draw the Line A m for the Meridian Line Then as before you were directed to add AL to AK So now substract the distance of AL from AK and the remainder will be LK Set therefore the distance of IK from A to q in the same Line of Obliquity and from the point q draw the Line qr parallel to the perpendicular Measure then the distance of A r and set off that distance in the Line HN from H to s for the Substilar Line Then erect on the point s a Perpendicular and on that Perpendicular set off from s to t the distance of qr And lastly from A draw the Line A t for the Stilar Line If K falls upon L the Plane is parallel to the Axis of the World and the Dyal drawn upon it will have no Center But s will fall upon H and AH or A s will be the Substile I shall give you two Examples of these Rules One of a Dyal with a Center and the other of a Dyal without a Center And first OPERAT. X. How to draw a Dyal with a Center Declining 20 Degrees and Inclining 30 Degrees HAving by the foregoing Precepts of the last Operat found the Substile Stile and Meridian you must as you have often been directed chuse a point in the Substilar Line through which at right Angles to the Substilar Line draw the Line of Contingence as long as you can Then measure the shortest distance between the point of Intersection and the Stilar Line and transfer that distance on one side the Line of Contingence upon the Substilar Line and so describe the Equinoctial Semi-Circle against the Line of Contingence Then lay a straight Ruler to the Center of the Equinoctial Circle as at Ae and to the point where the Line of Contingence cuts the Meridian Line as at Z and mark where the straight Ruler cuts the Equinoctial Circle and from that mark begin to devide the Semi-Circle into twelve equal parts and by a straight Ruler laid to those devisions and the Center of the Equinoctial make marks in the Line of Contingence Then shall straight Lines drawn from the Center A of the Dyal through every one of those marks in the Contingent Line be the Hour Lines of the Dyal and must be numbred from the XII a Clock Line towards the right Hand with I II III IV c. And the other way with XI X IX c. OPERAT. XI How to draw a Dyal without a Center on a South Plane Declining East 30 Degrees Reclining 34 Degrees 32 Minutes HAving by the Precepts of Operat IX found the Substile you must find the Meridian Line otherwise than you were there taught For having drawn the Lines of Latitude Declination and Reclination and found the Substile measure the distance of BP and set it off on the Line of Declination from A to K and draw from the Perpendicular AF the Line KQ parallel to AB Then measure the length of KQ and set it off on the Polar Line AP from A to V then take the nearest distance between the point V and the Line AB and set it off on the Line QK from Q to M through which point M draw a Line from the Center A Then measure with your Compasses in the Semi-Circle WNE which in this Dyal may represent the Equinoctial the distance of the Arch N m and set off that distance from the Intersection of the Substile with the Semi-Circle at S to T in the Semi-Circle which point T shall be the point in the Equinoctial that you must begin to devide the Hours at for the finding their distances on the Line of Contingence Then consider according to the bigness of your Plane what heighth your Stile shall stand above the Substile and there make a mark in the Substile For the distance between the Center A and that mark must be the heighth of the Stile perpendicularly erected over the Substile as at I. Draw through this point I a Line of Contingence as long as you can to cut the Substile at right Angles and then laying a Ruler to the Center A and successively to each Devision of the Equinoctial make marks in the Line of Contingence and through those marks draw straight Lines parallel to the Substile which shall be the Hour Lines and must be numbred from the left hand towards the right beginning at the XII a Clock Line with I II III c. and from the right hand towards the left on the XII a Clock Line with XI X IX c. The Stile to this Dyal may be either a straight Pin of the length of AI or else a Square of the same heighth erected perpendicularly upon the point I in the Substile Line OPERAT. XII To make a Dyal on the Ceeling of a Room where the Direct Beams of the Sun never come FInd some convenient place in the Transum of a Window to place a small round piece of Looking-Glass about the bigness of a Groat or less so as it may lie exactly Horizontal The point in the middle of this Glass we will mark A and for distinction sake call it Nodus Through this Nodus you must draw a Meridian Line on the Floor Thus Hang a plumb-Plumb-line in the Window exactly over Nodus and the Shadow that the plumb-Plumb-line casts on the Floor just at Noon will be a Meridian Line or you may find a Meridian Line otherwise by the Clinatory Having drawn the Meridan Line on the Floor find a Meridian Line on the Ceeling thus Hold a plumb-Plumb-line to the Ceeling over that end of the Meridian Line next the Window If the Plumbet hang not exactly on the Meridian Line on the Floor remove your hand on the Ceeling one way or other as you see cause till it do hang quietly just over it and at the point where the Plumb-line touches the Ceeling make a mark as at B that mark B shall be directly over the Meridian Line on the Floor then remove your Plumb-line to the other end of the Meridian Line on the Floor and find a point on the Ceeling directly over it as you did the former point as at C and through these two points B and C on the Ceeling strain and strike a Line blackt with Smal-Coal or any other Colour as Carpenters do and that Line BC on the Ceeling shall be the Meridian Line as well as that on the Floor Then fasten a string just on the Nodus and remove that string forwards or backwards in the Meridian Line on the Ceeling till it have the same Elevation in the Quadrant on the Clinatory above the Horizon that the Equinoctial hath in your Habitation and through the point where the string touches the Meridian Line in the Ceeling shall a line be drawn at right Angles with the Meridian to represent the Equinoctial Line Thus in our
Latitude the Elevation of the Equator being 38 ½ degrees I remove the string fastned to the Nodus forwards or backwards in the Meridian Line of the Ceeling till the Plumb-line of the Quadrant on the Clinatory when one of the sides are applied to the string falls upon 38 ½ degrees and then I find it touch the Meridian Line at D in the Ceeling therefore at DI make a mark and through this mark strike the line DE as before I did in the Meridian Line to cut the Meridian Line at right Angles This Line shall be the Equinoctial Line and serve to denote the Hour Distances as the Contingent Line does on other Dyals as you have often seen· Then I place the Center of the Quadrant on the Clinatory upon Nodus so as the Arch of the Quadrant may be on the East side the Meridian Line and underprop it so that the flat side of the Quadrant may lie parallel to the string when it is strained between the Nodus and the Equinoctial and also so as the string may lie on the Semi-diameter of the Quadrant when it is held up to the Meridian Line on the Ceeling Then removing the string the space of 15 degrees in the Quadrant and extending it to the Equator on the Ceeling where the string touches the Equator there shall be a point through which the I a Clock Hour line shall be drawn and removing the string yet 15 degrees further to the Eastwards in the Semi-Circle of Position and extending it also to the Equator where it touches the Equator there shall be a point through which the II a Clock Hour Line shall be drawn Removing the string yet 15 degrees fâ—rther to the Eastwards in the Semi-Circle of Position and extending it to the Equator there shall be a point through which the III a Clock Hour Line shall be drawn The like for all the other After-noon Hour Lines So oft as the string is removed through 15 degrees on the Quadrant so oft shall it point out the After-Noon distances in the Meridian Line on the Ceeling Having thus found out the points in the Equator through which the After-noon Hour Lines are to be drawn I may find the Fore-noon Hour distances also the same way viz. by removing the Arch of the Quadrant to the West side the Meridian as before it was placed on the East and bringing the string to the several 15 degrees on the West side the Quadrant or else I need only measure the distances of each Hours distance found in the Equator from the Meridian Line on the Ceeling for the same number of Hours from XII have the same distance in the Equinoctial Line on the other side the Meridian both before and after-noon The XI a Clock Hour distance is the same from the Meridian Line with the I a Clock distance on the other side the Meridian the X a Clock distance the same with the II a Clock distance the IX with the III c. And thus the distances of all the Hour lines are found out on the Equator Now if the Center of this Dyal lay within doors you might draw lines from the Center through these pricks in the Equator and those Lines should be the Hour lines as in other Dyals But the Center of this Dyal lies without doors in the Air and therefore not convenient for this purpose So that for drawing the Hour Lines you must consider what Angle every Hour Line in an Horizontal Dyal makes with the Meridian that is at what distance in Degrees and Minutes the Hour Lines of an Horizontal Dyal cut the Meridian which you may examine as by Operat II. For an Angle equal to the Complement of the same Angle must each respective Hour Line with the Equator on the Ceeling have Thus upon the point markt for each Hour distance in the Equinoctial Line on the Ceeling I describe the Arches I II III IV as in the Figure and finding the distance from the Meridian of the Hour Lines of an Horizontal Dyal to be according to the Operat II. Thus The 1 a clock Hour line 11.40 whose Complement to 90 is 78.20 The 2 a clock Hour line 24.15 whose Complement to 90 is 65.45 The 3 a clock Hour line 38.14 whose Complement to 90 is 51.56 The 4 a clock Hour line 53.36 whose Complement to 90 is 36.24 I measure in a Quadrant of the same Radius with those Arches already drawn from the Equinoctial Line for the 1 a Clock Hour 78.20 for the 2 a Clock Hour 65.45 for the 3 a Clock Hour 51.56 for the 4 a Clock Hour 36.24 and transfer these distances to the Arches drawn on the Ceeling For then straight Lines drawn through the mark in the Arch and through the mark in the Equator and prolonged both ways to a convenient length shall be the several Hour Lines aforesaid And when the Sun shines upon the Glass at Nodus its Beams shall reflect upon the Hour of the Day Some helps to a young Dyalist for his more orderly and quick making of Dyals IT may prove somewhat difficult to those that are unpractised in Mathematical Projections to devide a Circle into 360 Degrees or which is all one a Semi-Circle into 180 or a Quadrant into 90 degrees and though I have taught you in the projecting the Horizontal Dyal the original way of doing this yet you may do it a speedier way by a Line of Chords which if you will be curious in your Practise you may make your self or if you account it not worth your while you may buy it already made on Box or Brass of most Mathematical Instrument-Makers This Instrument is by them called a Plain Scale which does not only accommodate you with the devisions of a Quadrant but also serves for a Ruler to draw straight Lines with the manner of making it is as follows Describe upon a smooth flat even-grain'd Board a quarter of an whole Circle as BC whose Radius AB or AC may be four inches if you intend to make large Dyals or two inches if small but if you will you may have several Lines of Chords on your Scale or Rule Devide this Quadrant into 90 equal parts as you were taught in the making the Horizontal Dyal Then draw close by the edge of your straight Ruler a Line parallel to the edge and at about 1 20 part of an Inch a second Line parallel to that and at about â…› of an Inch a third Line parallel to both Then place one Foot of your Compasses at the beginning of the first degree on the Quadrant descibed on the Board as at B and open the other Foot to the end of the first degree and transfer that distance upon your Rule from B to the first mark or devision between the two first drawn Lines Then place one Foot of your Compasses again at the begining of the first degree on the Quadrant described on the Board as at B and open the other Foot to the end of the second Degree and transfer that distance upon your Rule from B to the second mark or devision between the two first drawn Lines And