Dialling universal: performed by an easie and most speedy way. Shewing how to describe the hour lines on all sorts of planes whatsoever, and in any latitude. Performed by certaine scales set on a small portable ruler. By G.S. practicioner in the mathematicks. Serle, George. 1657 Approx. 52 KB of XML-encoded text transcribed from 20 1-bit group-IV TIFF page images. Text Creation Partnership, Ann Arbor, MI ; Oxford (UK) : 2012-10 (EEBO-TCP Phase 2). A92942 Wing S2622 Thomason E956_3 ESTC R207641 99866680 99866680 168529

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 Early English books online. (EEBO-TCP ; phase 2, no. A92942) Transcribed from: (Early English Books Online ; image set 168529) Images scanned from microfilm: (Thomason Tracts ; 143:E956[3]) Dialling universal: performed by an easie and most speedy way. Shewing how to describe the hour lines on all sorts of planes whatsoever, and in any latitude. Performed by certaine scales set on a small portable ruler. By G.S. practicioner in the mathematicks. Serle, George. [8], 31, [1] p. : ill. (woodcuts) printed by R. and W. Leybourn for Thomas Pierrepont at the signe of the Sun in Pauls Church-yard, London : 1657. G.S = George Serle cf. Wing. Apparently also issued with S5689. Diagrams throughout the work. Reproduction of the original in the British Library.

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DIALLING UNIVERSAL: Performed by an eaſie and moſt ſpeedy way.

SHEWING How to deſcribe the hour lines on all ſorts of Planes whatſoever, and in any Latitude.

Performed by certaine Scales ſet on a ſmall Portable Ruler.

By G. S. Practicioner in the Mathematicks.

LONDON Printed by R. and W. Leybourn for Thomas Pierrepont at the Signe of the Sun in Pauls Church-yard. 1657.

TO THE READER.

COurteous Reader, I here preſent to thy view a ſhort Tract containing the deſcription and uſes of certaine Scales to be put on a ſmall Ruler, ſerving for the eaſie and ſpeedy drawing of the Hour lines on all ſorts of Planes, in what Latitude ſoever, and howſoever ſcituated.

The firſt Scale of Hours and the Scale of Latitudes, I acknowledge to be the Invention of that famous Mathematician Mr. Samuel Foſter, laid down in his book of the uſes of a Quadrant publiſhed Anno 1638. His Scale of Hours on the Quadrant, being really divided onely into Hours and halfe hours. But by applying of the Thread and Bead, (by which means the hours are there found) the Scale is divided into any other parts requiſite. Now having peruſed the labours of divers Authours that have written on this Subiect and finding none (in my judgement) ſo eaſie, pleaſant, and of ſo quick diſpatch, for all Dialls with Centers; I cauſed that Scale to be put on a Ruler for my own uſe, ſubdivided into as many parts as the length of the Ruler would afford, which being exactly done. I found that the ſeveral hours and parts might be taken off with the Compaſſes from the Scale on the Ruler, with more eaſe and exactneſſe then could be done from the Quadrant, by the application of the Thread and Bead; which whoſoever ſhall carefully try both, will find to be true.

The other Scales on the Ruler, (by which are made all ſorts of Polar Dialls direct or declining, as alſo direct Meridian Dialls, together with farre Decliners, and generally all ſuch as fall neer the Pole, to be drawn without a Center) are of my own framing; which although I eſteem not worth publiſhing, yet I am confident will yield ſome contentment, and give ſome ſatisfaction to the ingenious; who will accept of my good will. Note that whereas in divers of the Chapters, I have ſet down ſhort Tables, it was done onely to ſhew the manner of the worke, not that there is any need at all thereof, for having the Inclination of the Meridians converted into time, you have ſufficient directions for ſetting off all the hours of any Diall; Note alſo that if your Ruler ſhall be a foot in length, the firſt hour Scale may have every ſeveral minute expreſſed on it, and the Polar Scales every fifth minute, and any Diall may be drawn in halfe a ſheet of ordinary paper. But if it be of the length in the Book, any Diall may then he drawn in a quarter of a ſheet of paper. I conclude referring thee to the Book it ſelfe, which if it ſhall find acceptance with thee in yielding thee in any kind the ſatisfctation expected I have my ends and deſires.

G. S.
The Contents. The Deſcription of the Scales on the Ruler. Pag. 1 How to draw a Meridian line. Pag. 2 How to find the Inclination of a Plane. Pag. 3 How to find the Declination of a Plane. Pag. 4 How to draw a direct Polar Diall. Pag. 5 How to draw an Erect Meridian Diall. Pag. 6 How to draw an Horizontal Diall. Pag. 8 How to draw an Erect direct verticall. Pag. 10 How to make a verticall inclining Diall. Pag. 11 How to make an Aequinoctiall Diall. Pag. 12 How to find the height of the Pole above the Plane, &c. for Decliners and Declining Inclining Planes, Geometrically, onely by a line of Chords. Pag. 13 How to make a verticall declining Diall. Pag. 17 How to make a vertical declining Diall, where the Evation is ſmall. Pag. 19 How to make a Meridian Inclining Diall. Pag. 22 How to make a Declining Inclining Diall. Pag. 24 How to make a Polar Declining Diall. Pag. 27
diagram
An Advertiſement to the Reader.

NOte that the Diagrams are all contracted, otherwiſe they would have taken up a great deal of room to little purpoſe, for as they are, they give as much light to the ingenious practicioner as if they had been drawn by the Scale annexed, and every Diagram have filled a whole page or neer upon, whereas now it takes up but a ſmall portion of a page.

And note that theſe Scales and all other Mathematical Inſtruments whatſoever, are made and ſold by Mr. Anthony Thompſon, dwelling in Hoſier lane neer Smithfield.

DIALLING:
CHAP. I. The Deſcription of the Scales on the Ruler.

THe firſt Scale is a Scale of ſix hours, each hour divided into halves and quarters of hours, being proper for Dials that have no declination: as the Horizontal, the direct North or South, whether upright or inclining.

Moreover each hour is ſubdivided into as many unequal parts, as the length of the Scale will permit, this Scale is of ſpecial uſe in deſcribing all other Dials that have Centers; where the Altitude of the Stile above the Plain is not leſſe then 10 degrees; when that happens there are other Scales to performe it with ſpeed and exactneſſe enough.

This Scale hath the letters, (Hour,) at the beginning.

The ſecond is a Scale of 90 degrees, anſwerable to the Scale of Hours, every degree being alſo ſubdivided into as many parts as quantity will give leave. This Scale is known by the letters (Incl.) at the beginning; Note that the firſt and ſecond Scales together ſhew how many degrees and minutes of time are contained in any number of degrees and minutes of the Equinoctial under 90 & contra.

Example. Againſt 20 degrees on the ſecond Scale; you ſhall find on the firſt Scale 1 hour 20 minutes, and againſt 50 degrees on the ſecond Scale, you ſhall find 3 hours 20 minutes on the firſt Scale, and ſo of any other number what ever, if carefully computed.

The third Scale is a Scale of Latitudes, known by the letters (Lat.) at the beginning.

The fourth and fifth Scales are 2 Scales of hours of different lengths, either of which ſerve to make all direct Meridian or Polar Dialls, alſo all Polar Dialls that decline.

Both theſe Scales together ſerve for the ſpeedy drawing the hour-lines on all ſorts of Planes, where the height of the Stile is but ſmall, and the Center of the Diall left out, theſe Scales are known by the letters Pol. at the beginning.

Theſe are the chief Scales, there is alſo a Scale of Chords, whoſe uſe is common.

CHAP. II. To draw a Meridian line on an Horizontal Plane.

diagram

WIth your line of chords deſcribe the Circle ABCD, then holding up a thred and plummet, ſo as the ſhadow of the thred may paſs through the Center E, draw the line of ſhadow DEB: Take then the Altitude of the Sun (or rather let another take it at the ſame inſtant,) which done get the Suns Azimuth, which in this Example ſhall be 50 degrees from South towards Eaſt, which 50 deg. I take out of the line of Chords, and ſet it from the point D, Southward to A, drawing the line AEC for the Meridian line.

CHAP. III. To find the Inclination of a Plane.

THe Inclination of a Plane is the angle which it maketh with the Horizon: Draw firſt an Horizontal line as AB,

diagram
and croſſe it with the perpendicular CD, then apply a Quadrant to the vertical line CD, on a Ruler as the Figure directeth you, and holding up a thred and plummet, ſo as that the plummet may by means of the Ruler, play under the Center of the Quadrant, the thred paſſing through the Center, obſerve the degrees cut in the limb, and count them from that ſide of the Quadrant which is perpendicular to the plane, that ſhall be the Inclination of the Plane, as the angle HFE: the Complement whereof EFG, is the angle of Reclination of the Plane from the Zenith.

CHAP. IV. To find the Declination of a Plane.

THe Declination is alwayes reckoned in the Horizon, and is the angle contained between the line of Eaſt and Weſt and the Horizontal line upon the Plane: Now to get the Declination two obſervations are required, Firſt, the Horizontal diſtance of the Sun from the Pole of the Plane; Secondly, the Suns Altitude.

Draw firſt an Horizontal line, as the line I K in the figure of the laſt Chapter, then apply thereto the ſide of a Quadran, holding it parallel to the Horizon, then hold up a Threed and Plummet, ſo as the ſhadow of the Threed may paſs through the Center of the Quadrant, then obſerve the degrees cut off by the Threeds ſhadow on the limbe, and reckon them from that ſide of the Quadrant, that is perpendicular to the Plane, as the angle L M N, that is the Horizontal diſtance.

diagram

2 Secondly, take the Suns altitude, and finde his Azimuth, theſe compared together will help you to the declination, as may be plainly demōſtrated by this figure: deſcribe the Circle A B C D: repreſenting the Horizontal circle, draw A E C for the Horizontal line of the Plane, then ſet off the Horizontal diſtance L M N, which in this Example ſhall be 35 degrees: theſe I place from A to F, then having taken the Suns altitude, I find the Azimuth from Eaſt towards South to be 50 degrees, theſe I place from F the Suns place, to G Northward, and draw the line G H through the Center, ſo ſhal G H be the true points of Eaſt and Weſt, and I K drawn at right angles to G H ſhall be the points of North and South: Now the angle of declination is A E G, or K E M, which in this Example is 16 degrees.

CHAP. V. To draw a direct Polar Dial.

A Direct Polar Plane is that which is parallel to the hour circle of 6. Firſt, draw the Horizontal line A B, with its parallel C D, then draw the perpendicular E F, which ſhall ſerve for the ſubſtile and hour of 12, then repair to either of your Scales known by the letters Pol. and fixing one foot of your Compaſſes at the beginning of the ſaid Scale, extend the other foot to the hour of 1, ſet off that extent from E to 11, and from E to 1, as alſo from

diagram
G both wayes, on the line A B, and draw the hours of 11 and 1, parallel to the ſubſtile E G F: then again extend your Compaſſes from the beginning of the Scale to two hours, ſet off that extent from E to 10, and from E to 2, alſo from G both wayes, and draw the hours of 10 and 2: Then extend the Compaſſes from the beginning of the Scale to 3, and ſet off that from E to 9, and from E to 3, and draw the hours 9 and 3 parallel to the former: then extend the Compaſſes from the beginning of the Scale to 4, and ſet off that from E to 8, and from E to 4, alſo from G both wayes, and draw the hours of 8 and 4. Laſtly, extend the Compaſſes from the beginning of the Scale to 5, and ſet it off from E to 7, and from E to 5, alſo from G both wayes, and draw the hours of 7 and 5. So have you all the hours proper for this Plane.

The ſtile may be a thin Plate of braſs or Iron that muſt ſtand directly perpendicular to the Plane, and in the ſubſtilar line or hour line of 12. The length whereof muſt be the diſtance from the beginning of the Scale to the hour of 3. This done, the Dial is finiſhed.

CHAP. VI. To draw an erect Meridian Dial.

A Meridian Plane is that which is parallel to the circle of the houre of ſix, having one face to the Eaſt, the other to the Weſt, in each of them the ſtile and ſubſtile will be parallel to the Plane, and the hour-lines parallel one to the other, as in the direct Polar of the laſt Chapter, our example ſhall be of a Meridian Dial, with the face to the Eaſt, in the Latitude of 51 d. 30 min. and is thus deſcribed.

diagram

The diſtance from the beginning of the Scale to the hour of 3, gives the height of the Stile which muſt ſtand directly over the Subſtile, making right angles therewith, and may be made of a thin plate of Iron or Braſſe, or a pin of either ſharpned; whoſe extremity muſt give the ſhadow to the hour lines on the Diall; Note that the making of the Weſt Diall differeth from this only in its ſcituation and changing the hours, this Diall looking to the Eaſt and the other to the Weſt, this ſerving from Sun riſing to paſt 11, the other from before 1 to Sun-ſet.

Note if you turne the Eaſt Dyall drawn in paper from you, and look on the backſide, you ſhall there ſee the perfect form of the Weſt Diall, onely inſtead of the hours 11, 10, 9, 8, 7, 6, 5, 4, you muſt write 1, 2, 3, 4, 5, 6, 7, 8.

CHAP. VII. To draw an Horizontal Diall for the Latitude of 51 deg. 30 min.

AN Horizontal Plane is that which is parallel to the Horizontal Circle of the Sphere, to draw the hours proceed thus.

diagram

With your line of Chords make an angle of 51 deg. 30 min. for the ſtile or cock of your dial, and ſet it over the ſubſtile A D, at right angles as the angle E A D, in the Diagram, and the Dial is finiſhed.

CHAP. VIII. To draw a Dial on an erect direct vertical Plane.
diagram

The Stile E A D muſt containe an angle of 38 deg. 30 min. and muſt ſtand directly over the Subſtile A D.

For the North face, the Center muſt be below and the Stile point upward. The hours fit for that Plane are the hours of 4, 5, 6, 7, in the morning, and 5, 6, 7, 8, in the evening.

CHAP. IX. How to draw a vertical Inclining Dial.

IF the Inclination be towards the North part of the Horizon, you are to ſubtract the Inclination out of the complement of the elevation, and the remainer is the new Latitude.

Example. Of a South Diall in the Latitude of 51 deg. 30 min. inclining Northward 25 deg. I deduct 25 out of 51.30, and there remaineth 13.30. the elevation of the Pole above the Plane, having found the elevation of the Pole above the Plane I proceed to make the Dial, as if it were an upright South Dial, for the Latitude of 13 deg. 30 min making A B and A C equal to 13.30 taken out of the line of Latitudes, following the rules of the laſt Chapter for the reſt of the work.

The Stile muſt contain an Angle of 13.30 and muſt be ſet directly over the Subſtile A D, and the Diall is finiſhed.

But if the Inclination be towards the South part of the Horizon, then adde the Inclination to the Latitude and the ſumme is the elevation of the Pole above the Plane, if the ſumme exceed 90, take it out of 180, and the remainer is the elevation of the Pole above the Plane.

Example. In the Latitude of 51 d. 30. a Plane found to incline Southwards 15 degrees, I add 15 d. to 51. 30 the ſumme is 66.30 that is the elevation of the Pole above the Plane, ſo obſerving the former directions you may proceed to make the Diall as is before taught.

CHAP. X. How to draw an Equinoctial Diall.

AN Equinoctial Plane is that which is parallel to the Equinoctial Circle of the Sphere: Make AB and AC of the former Diagrams, equal to the whole line of Latitudes, and proceed as if you were to make an Horizontal Diall, and ſet up a ſharpned point in the Center of any convenient length.

But the beſt way to draw this Diall, being the houres are equidiſtant, is to divide 360 by 24, the quotient is 15, ſo having with the Radius of your line of Chords deſcribed a Circle and drawn the Diameter for the 2 hours of ſix, and the perpendicular for the hour of 12, take 15 degrees out of your line of Chords, and ſet it off from hour to hour, let this Diall containe as many houres as the Horizontal and ſo numbred.

CHAP. XI. How to find the height of the Pole above the Plane, the diſtance of the Subſtile from the Meridian, and the Inclination of Meridians, for upright declining and Meridian inclining Dialls; as alſo what ever elſe is neceſſary to be found for all other Dialls, hereafter treated of before the hour lines can be drawn.

THe beſt and exacteſt way to find theſe, is by the Tables, or Canons of Logarithms; but of that I will not touch in this ſmall Treatiſe, but make uſe of ſome Geometrical way whereof there are divers, but the beſt and eaſieſt in my judgement (it requiring onely a line of Chords,) is that of Mr. Stirrup, which I here make uſe of (I hope without offence.

The firſt Example ſhall be of a Plane declining from South 28 degrees towards the Eaſt: as by the firſt Diagram of this Chapter is Demonſtrated as followeth.

diagram

Then from the point L, draw LT cutting the arch GR in O; draw AOI: ſo ſhall CI be the Inclination of Meridians 34 deg. 12 minutes.

diagram
diagram
CHAP. XII. How to draw the hours on an erect vertical declining Plane.

HAving by the laſt Chapter obtained thoſe neceſſary requiſites there mentioned I now proceed to draw the hour-lines on all thoſes Planes treated of in that Chapter, by our firſt Scale of Hours, as alſo all Polar declining Dials, and all far declining vertical, by the Polar Scales. And firſt for the vertical Decliner mentioned in the laſt Chapter declining from South towards Eaſt 28 degrees in the Latitude of 51 deg. 30 min. Proceed thus: firſt, draw a line at length as BAC, then conſidering that the height of the Pole above the Plane was 33 deg. 20 min. I take 33 deg. 20 min. out of the Scale of Latitudes, and ſet it off from A to B, and from A to C, chuſing A for the Center of the Dial. Then take in your Compaſſes the whole firſt Scale, or Scale of Hours, and with one foot fixed in B with the other make an arch at D, and with the ſame extent, one foot fixed in C, with the other croſs the arch at D, and draw the lines BD and CD, as alſo the line AD for the Subſtile: Then having found the Inclination of the Meridians to be 34 deg. 12 min. I ſeek that in the ſecond Scale known by the Letters Ind. and juſt againſt it on the firſt Scale, I find two hours 17 min. then take off two hours 17 min. from that Scale, and ſet it from D to 12, and from B to 6, then extend your Compaſſes from the beginning of the ſame Scale too hours 17′ and ſet that from D to 10,

diagram
and from B to 4, then open your Compaſſes to 1 hour 17′ of the ſame Scale and ſet it from D to 11, and from B to 5, then open the Compaſſes to 3 houres, 17 min. and ſet it from D to 1, and from B to 7, then open the Compaſſes to 4 ho. 17′, and ſet it from D to 2, and from B to 8, then laſtly, open your Compaſſes to 5 houres 17 min. and ſet it from D to 3, and from B to 9. So lines drawn from A to thoſe points ſhall be the hours proper for this Plane: if you pleaſe you may ſet off the largeſt extents firſt, as 5 hours 17 min. and ſo go on cloſing of the Compaſſes till you come to o hours 17 min. for D 10, and B 4. Note that the firſt Columne of the Table contains the hours and minutes that are to be taken in your Compaſſes off of the firſt Scale, and ſet from D or B to their Ho. M. from D toward C, from B towards D. 5. 17 D — 3 And B—9 4. 17 D — 2 And B—8 3. 17 D — 1 And B—7 2. 17 D — 12 And B—6 1. 17 D — 11 And B—5 0. 17 D — 10 And B—4
reſpective hours on the Plane, contained in the ſecond and third Columns of the Table: conſider alſo that the Inclination of Meridians; being 34 d. 12′ or 2 ho. 17′ of time and the declination towards Eaſt, the Subſtile falls between the hours of 9 and 10 in the morning, whereas if the declination had been Weſt the Subſtile would have fain betwixt the hours of 2 and 3 in the afternoon, and the hour of 12 would have been towards the left hand of the Subſtile, whereas the declination being Eaſt, it ſtands on the right hand of the Subſtile.

The ſtile muſt have elevation 33.20. as the angle EAD, and muſt ſtand directly over the Subſtile AD, and the Diall is finiſhed. I have been more large in this Chapter then I ſhall be in what ſhall follow, touching all other Dials with Centers, by reaſon the drawing and ſetting off the hours is the ſame with the work of this Chapter.

CHAP. XIII. To draw the hours on a farre declining vertical Plane, by the 2 Polor Scales on the Ruler.

THoſe Planes whoſe declination, or declination and Inclination ſhal cauſe them to fall neer the Pole, ſo as that the hours can hardly be diſtinguiſhed they falling ſo neer together, muſt have the Center left out and the Stile increaſed, and then the hours may be eaſily and ſpeedily drawn by the directions following.

diagram

Now for the other line DIBF, you muſt ſet off the hours thereon taken out of the leſſer Polar Scale from B, according to the Table in all reſpects changing only A for B: this done draw lines through the reſpective points in the lines CAE and DBF, which ſhall be the hour lines of the Diall.

Note that a Diall of this kind is neer as ſocn made as ſpoken of, The Stile muſt be a thin plate to ſtand directly over the Subſtile, as in the figure is demonſtrated by AB and CD.

CHAP. XIV. To draw the Hours on a Meridian Inclining Plane.

THoſe Planes whoſe Horizontal line is the ſame with the Meridian line, are called Meridian Planes, as the direct Eaſt and Weſt. But if they lean to the Horizon they are called Incliners.

Thoſe Planes may incline either to the Eaſt or Weſt part of the Horizon, and each of them hath two faces, the upper towards the Zenith, the lower towards the Nadir.

diagram

Take notice that when you are to draw any of the Dialls with Centers, let the line BAC ſtand towards you, as if it were the Horizontal line, and the line AD a Plumb line, and ſo you will ſet off the hours with more eaſe as the direct vertical. Note that this Example is of a Meridian Plane inclining Eaſt, and therefore the Subſtile muſt ſtand to the left hand of the Meridian or hour of 12.

CHAP. XV. To draw the Hour lines on a Declining, Inclining Plane.

A Plane that declines from the prime Vertical and Inclines to the Horizon, and yet lyeth not even with the Poles of the World, is called a Declining Inclining Plane.

Of theſe there are ſeveral ſorts, for the Inclination being Northward, the Plane may fall between the Horizon and the Pole, or between the Zenith and the Pole.

Or the Inclination may be Southward, and may fall either below the interſection of the Meridian, and the Aequator, or above it: and each of theſe have two faces, the upper towards the Zenith, and the lower towards the Naidir.

diagram

Then conſidering the Inclination of Meridians was 15 deg. 17 min. I find it on the ſecond Scale, and againſt it on the firſt Scale, I find 1 hour 1 min. ſo I ſet off the hours as hath been formerly ſhewn and this Table demonſtrateth.

from D towards B from C towards D. Ho. Min. Hours on the Plane. 0. 1 D — 11 And C — 5 1. 1 D — 12 And C — 6 2. 1 D — 1 And C — 7 3. 1 D — 2 And C — 8 4. 1 D — 3 And C — 9 5. 1 D — 4 And C — 10

The Stile muſt containe an angle of 30 deg. 20 min. as IAK in the Diagram to ſtand directly over the Subſtile AD, and ſo the Diall is finiſhed.

Now when you meet with Declining Inclining Planes you muſt conſider which Pole is elevated above your Plane and how to place the Meridian from the Horizontal line, for upon the upper faces of all North Incliners, whoſe Meridians Elevation is leſſe then the Latitude of the Place, on the under faces of all North Incliners, whoſe Meridians Elevation is greater then the Latitude of the place, and on the upper faces of all South Incliners the North Pole is elevated. And upon the under faces of all North Incliners, whoſe Meridians Elevation is leſſe then the Latitude of the place, on the upper faces of all North Incliners, whoſe Meridians Elevation is greater then the Latitude of the place, and on the under faces of all South Incliners the South Pole is elevated.

Now for placing the Meridian from the Horizontal line, upon the upper faces of all South Incliners whoſe Meridians Elevation is greater than the complement of Latitude, on the under faces of all South Incliners, whoſe Meridians Elevation is leſſe than the Latitudes, complement, on the under faces of all North Incliners, whoſe Meridian Elevation is greater then the Latitudes of the place, and on the upper faces of all North Incliners, whoſe Meridians Elevation is leſſe than the Latitude of the place the Meridian muſt be placed above the Horizontal line as in our Example. Again, contrariwiſe for the upper faces of all South Incliners, whoſe Meridians Elevation is leſſe than the Latitudes complement. On the under faces of all South Incliners, whoſe Meridans Elevation is greater than the complement of Latitudes, on the under faces of all North Incliners, whoſe Meridians Elevation is leſſe than the Latitude of the place, and on the upper faces of all North Incliners, whoſe Meridians Elevation is greater then the Latitude of the place, the Meridian muſt be placed below the Horizontal line. But if it be either the upper or under faces of a South Inclining Plane, whoſe Meridians Elevation is greater than the Latitudes complement, or either the upper or under faces of a North Inclining Plane, whoſe Meridians Elevation is leſſe than the Latitude of the place, that then the Meridian muſt be placed from that end of the Horizontal line with the Declination of the Plane but on all the other faces of theſe kinds of Planes, the Meridian muſt be placed from that end of the Horizontal line, which is contrary to the Declination of the Plane.

Note alſo that if the Inclination be Southward and the Elevation of the Meridian, equal to the complement of your Latitude, then ſhall the Subſtile lie ſquare to the Meridian.

CHAP. XVI. To make a Dial on a Polar declining Plane.

THeſe Planes if the Inclination be Northward and the Elevation of the Meridian equal to the Latitude of the Place then neither Pole is elevated above the Plane, and therefore its a declining Polar.

diagram

Example. A Plane declining Eaſt from South 30 deg. and inclining North 34 deg. 30 min by the rules of the eleventh Chap. I find the diſtance of the Horizon and Meridian to be 71 deg. 53 min. which I ſet off from A to B in the arch AB, and draw BD for the Subſtile. Then at right angles to the Subſtile, I draw the lines FG and CE: Then conſidering the Inclination of Meridians to be 24 deg. 19 min. I find it on the ſecond Scale, and againſt it on the firſt Scale I find 1 ho. 37 min. Then having recourſe to the Table, I ſet off the hours from K and H, according to the directions of the 13 Chapter, for the farre Decliner, taking the ſeveral diſtances with my Compaſſes out of either of the Polar Scales, and ſetting them off from K towards C or E, as the Table plainly ſheweth.

from K toward E, from K towards C. Ho. M. Ho. Plane Ho. M. Hours Plane. 0. 37 K 11 0. 23 K 10 1. 37 K 12 1. 23 K 9 2. 37 K 1 2. 23 K 8 3. 37 K 2 3. 23 K 7 4. 37 K 3 4. 23 K 6

The extent of the Compaſſes from the beginning of the Scale to the hour of 3 gives the height of the Stile, which muſt be a plate of Iron or Braſſe, ſet up juſt over the Subſtile HK, and the Diall is finiſhed.

Some obſervations relating chiefly to the Diall of the 12 Chap. being a vertical Decliner.

WHereas in the Diagram of the 12th Chapter the Subſtile ſtands ſquare to the Horizon, you ſee here how it ought to ſtand, that is to ſay the 12 of clock hour muſt in this and all other vertical Decliners be the Plumb line as the Diagram here ſheweth.

diagram

Note that no hour lines are to be drawn beyond the line BC.

Note alſo that if you oil the Pattern of this Diall drawn in paper, it will ſerve for 3 other Dialls that have the ſame Declination.

Firſt, a Dial for the Southweſt face of the Plane if you change the ſide, and the numbers ſet to the hours, the Center of the Diall upwards and the Stile and Subſtile pointing downwards.

Secondly, a Dial for the Northweſt face, if you turn the pattern upſide down, and changing the ſide taking the backſide for the foreſide, not altering the hours the Stile and Subſtile pointing upward.

Laſtly, a Diall for the Northeaſt face, if you take the foreſide onely turning it upſide down, and altering the numbers ſet to the hours, the Stile and Subſtile pointing upward.

A Table ſhewing the Latitude of the moſt principal Cities and Towns in England. Name of the places. Latitude   d. m. St. Albans 51 55 Barwick 55 49 Bedford 52 18 Briſtol 51 32 Boſton 53 2 Cambridge 52 17 Cheſter 53 20 Coventry 52 30 Chicheſter 50 56 Colcheſter 52 4 Darby 53 6 Exon 50 40 Grantham 52 58 Halifax 53 49 Hereford 52 14 Hull 53 50 Launſton 50 41 London 51 32 Lancaſter 54 8 Leiceſter 52 40 Lincolne 53 15 Newcaſtle 54 58 Northampton 52 18 Oxford 51 54 Shrewsbury 52 48 Warwick 52 25 Wincheſter 51 10 Worceſter 52 20 Yarmouth 52 45 York 54 0

FINIS.