Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	east_n	north_n	west_n	5,069	5	9.1516	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A51544	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 ruler and a pair of compasses, and without any arithmetical calculation / by Joseph Moxon ...	Moxon, Joseph, 1627-1691.	1668 (1668)	Wing M3009; ESTC R20066	27,959	54

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

a Clock and IV a Clock Hour Lines If you will have the half Hours and quarter Hours or any other devision of hours you must devide each six devisions of the Equinoctial into so many parts as you intend and by a straight Ruler laid to the Center of the Equinoctial and those devisions in the Equinoctial Circle make marks in the Line of Contingence as you did before for the whole Hour Lines and Lines drawn from the Center of the Plane through those marks shall be the sub-devisions of the Hours But you must remember to make all sub-devisions short Lines and near the verge of the Dyal Plane that you may the easier distinguish between the whole Hours and the parts of Hours as you may see in the Figure Having drawn the Hour Lines set the number of each Hour Line under it as you see in the Figure Last of all sit a Triangular Iron whose angular point being laid to the Center of the Dyal Plane one side must agree with the Substilar Line and its other side with the Stilar Line so is the Stile made And this Stile you must erect perpendicularly over the Substilar Line on the Dyal Plane and there fix it Then is your Dyal finished OPERAT. III. To describe an Erect Direct South Dyal YOU may know an Erect Direct South Plane by applying the North side of the Declinatory to it For then if the North end of the Needle hang directly over the North point of the Card in the bottom of the Box it is a South Plane but if it hang not directly over the North point of the Card it is not a Direct South Plane but Declines either East or West and that contrary to the pointing of the Needle Easterly or Westerly from the North point of the Card for if the North point of the Needle points Easterly the Plane Declines from the South towards the West if it point Westerly the Plane Declines from the South towards the East You may know if the Plane be truly Erect or upright by applying one of the sides AB or AD to it for then by holding the Center A upwards so as the Plumb-line play free in the Grove if the Line falls upon 0 or 90 the Plane is upright but if it hang upon any of the intermediate Degrees it is not upright but Inclines or Reclines If you find it Incline apply the side AB to it and see what number of Degrees the Plumb-line falls on for that number of Degrees counted from the side AB is the number of Degrees of Inclination If you find the Plane Reclines apply the side AD to it and see what number of Degrees the Plumb-line falls on for that number of Degrees counted from the side AD is the number of Degrees of Reclination These Rules being well understood may serve you to find the scituation of all other sorts of Planes But for the making a Dyal on this Plane you must first draw a Meridian Line through the middle of the Plane by applying a Plumb-line to the middle of it till the Plumbet hang quietly before it for then if the Plumb-line be black't for a white Ground or chalked for a dark Ground and strained as Carpenters do their Lines you may with one stroak of the string on the Plane describe the Meridian Line as A XII This Meridian is also the Substilar Line Then on the top of this Meridian Line as at A draw another Line athwart it to cut it at right Angles as VI VI for an East and West Line At the meeting of these two Lines on the top make your Center whereon describe a Semi-Circle on your Plane as large as you can which by the Meridian Line and the East and West Line will be devided into two Quadrants One of these Quadrants devide into 90 Degrees as you were taught Fol. 12. and from the Substilar Line count the Complement of the Poles Elevation which here at London where the Pole is elevated 51 ½ Degrees its Complement to 90 is 38 ½ Degrees and make there a mark as at E. Then on the Substilar Line chuse a point where you please as at F for the Line of Contingence to pass through which Line of Contingence draw as long as you can so as it may cut the Substilar Line at right Angles and from the point F in the Substilar Line measure the shortest distance between it and the Stilar Line and keeping one Foot of your Compasses still in the point F transfer that distance into the Substilar Line as at G then on the point G describe a Semi-Circle of the Equinoctial against the Line of Contingence which Semi-Circle devide into twelve equal parts as you were taught by the Example in the Horizontal Dyal Fol. 13. and by a straight Ruler laid to each of these Devisions and to the Center of the Semi-Circle make marks in the Line of Contingence by the side of the Ruler For straight Lines drawn from the Center of the Dyal Plane through these marks in the Contingent Line shall be the 12 Hour Lines before and after Noon Then mark your Hour Lines with their respective Numbers The Substilar or Meridian Line is XII from thence towards the right hand with I II III c. and from thence towards the left hand with XI X IX c. The Stile must be erected perpendicularly over the Substilar Line so as to make an Angle with the Dyal Plane equal to the Complement of the Poles Elevation viz. 38 ½ Degrees OPERAT. IV. To make an Erect Direct North Dyal THE Erect Direct North Dyal Stile and all is made by the same Rules changing upwards for downwards and the left side for the right the Erect Direct South Dyal is made for if the Erect Direct South Dyal be drawn on any transparent Plane as on Glass Horn or an oyled Paper and the Horizontal Line VI VI turned downwards and the Line VII mark't with V the Line VIII with IIII the Line V with VII and the Line IIII with VIII then have you of it a North Erect Direct Dyal All the other Hour Lines in this Dyal are useless because the Sun in our Latitude shines on a North Face the longest Day only before VI in the Morning and after VI at Night OPERAT. V. To describe an Erect direct East Dyal HAng a Plumb-line a little above the place on the Wall where you intend to make your Dyal and wait till it hang quietly before the Wall Then if the Line be rubbed with Chalk like a Carpenters Line you may by holding the Plumbet end close to the Wall and straining it pretty stiff strike with it a straight Line as Carpenters do This Line shall be a perpendicular as AB Then chuse a convenient point in this Perpendicular as at C for a Center whereon describe an occult Arch as DE This Arch must contain the number of Degrees of the Elevation of the Equinoctial counted between D and E which in our Latitude

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