The Description of a plain Instrument, that with much ease and exactness will discover the situation of any vertical plane howsoever inclining, reclining, or declining; and how to draw a Dyal upon any such plane, or upon the face of any vertical body how irregular soever, together with several other things requisite to the Art of Dyalling.
THe Instrument consists of two main parts, a Basis and a Dyal.
The Basis may be a plate of Brass, or a piece of wood smooth wrought, and of one thickness throughout, perfectly square, and divided into 4 little squares, by 2 right lines, cutting each other [Page 2]at right Angles in the precise middle, one being marked with W. E. for West and East, and the other with N. S. for the North and South; which latter line representeth the Meridian when the Dyal stands in its most natural position; but its more ordinary use will be to represent the Axis of the plane.
Upon the intersection of these two lines, as upon a Centre, must be described one circle or more; two quadrants whereof from N. both ways are to be divided into degrees (if not smaller parts) and distinguished by Figures, as the degrees of quadrants usually are.
The edge of the Basis noted with N. I shall for distinctions sake, call the fiducial edge.
So much for the Basis: The Dyal is a perfect horizontal one, fitted to the latitude of the place where 'tis presumed it will be most used, The Plate of the Dyal exactly circular, and having the same common Centre with the Hour circle, and the utmost edge of the Dyal-plate almost touching the circle of the Basis, whereof 2 quadrants were divided, as aforesaid.
Through the Centre of the Dyal is a smal Pin driven, or screwed into the Basis at the Centre, fastning the Dyal to the Basis, yet so as it may turn about somewhat straitly; and another Pin so contrived as to fix the Dyal at pleasure in any position; from the former of which Pins a threed of of strong silk issueth at the Centre of the Dyal.
Upon some convenient place of the Gnomon is a line drawn perpendicular to the Dyal-plate, with a thred and plummet fitted to it, and falling upon a large Arch of a Circle, divided both ways from the said line into degrees and parts, for shewing the inclination and reclination of Planes: And at the lower edge of the Gnomon, the North end hath a sharp point or Index, and another at the opposite end of the Meridian line I shall call the Counter-Index, serving to point out declinations.
It is convenient to have the uppe edge of the Gnomon long, and when the instrument must be placed far from the plane (as in some cases it will fall out) it is good to lengthen out the Gnomon and hour-lines in the operation, by applying thereunto a fine streight rule; and the same course will be convenient when the Instrument is a very little one.
There is besides belonging to it a plate and a needle: The plate may be of fine thin brass, or tin-plate smooth and purely flat, cut at right Angles, of the form of an Octavo leaf, but somewhat longer, with a long notch towards the middle cut out, about the length of the third part of the Diameter of the Dyal, or scarce so much, and of what depth you please, provided it be deep enough to give way, that the notched edge may touch the line of VI without disturbance from the Pin in the Centre of the Dyal.
The needle must be hafted and framed much after the fashion of a Shoemakers small Awl, but longer and more bowed, with a little streight point, having an eye in it like a Sadlexs bodkin.
The use of the aforesaid Instrument.
1. To draw an horizontal line,
Fix the Diall on the Basis with the Index upon either of the cross lines, then turning the Instrument with the graduated side of the Gnomon towards you, set the opposite edge to the plane, and holding it so as the thred playing at liberty, fal directly on the perpendicular line: you may by the edge of the Instrunent touching the plane, draw an horizontal, or level line.
2. To draw a perpendicular line
Draw first an Horizontal line, and laying the back side of the Instrument or the plate close to the plane till the upper edge touch that line, all along you shall have 2 edges to guide you at your choice, to draw a perpendicular line.
3. To draw a meridian line.
Fix the Instrument Horizontally, and set the Diall to the true hour of the day, then will the thred laid upon the meridian line of the Diall, and extended at pleasure, give you a meridian line upon any Horizontal plane that it can touch, and by the help of a thred and plummet upon any plane above or below the extended thred.
4. To find the Suns Azimuth.
Fix the Diall upon the Basis, with the Index standing over the line N. S. at N. Then turning about the whole Instrument, till standing Horizontally, it give you the true time of the day, (which you must first know by some good double ring-diall or otherwise) fix the Basis also to some stable thing by nailes driven through holes made in the Angles thereof to that purpose, and drawing up perpendicularly so much of your thred at the centre of the Diall, as will suffice to cast the shadow upon the circle of the Basis: the degree or part cut by that shadow, is the Azimuth from the South, and its complement to a quadrant the Azimuth from East or West: but if the shadow of the thred, fall not upon either of the divided quadrants, but nearer towards the letter S. then turn about the Diall (the basis remaining fixed till the Index stand upon the line W. E. at E. or W. as occasion is: that is at E. in the morning, at W. in the evening, then will the shadow give you the Sun's Azimuth from the East or West point, and that added to 90 degrees is his Azimuth from the South, and subducted from 90 degrees, it gives his Azimuth from the North.
5. To find the Suns altitude or Almicantar.
Let the Index be placed over one of the great cross lines of the Basis, and a line drawn upon the Gnomon, meeting the perpendicular at right angles in the Centre or hole for the thred. Then [Page 6]holding that edge to which the Index looketh, horizontally, and erecting a pin perpendicularly in the said hole, hold up or depress the opposite edge till the shadow of the said pin run along the line, then will the thred, playing at liberty, fall upon the degrees and parts of the Suns height above the horizon.
6. To find the unknown latitude of a place, the hour being given.
Draw a Meridian line by the rules of Art, as Mathematicians teach (which are too long to be here recited) Then placing the Meridian of the Dyal upon the Meridian so drawn, and lifting up the South or North end of the Dyal (Basis and all, except you have taken the Dyal off from the Basis) till the shadow give you the true time of the day, the thred will shew how many degrees, and parts the latitude of the place where your work is to be performed, is more or less than the known latitude of that place for which the Dyal was projected; but for this purpose the Dyal should be large, and the time of the day a great space from noon.
7. To find the inclination or reclination of a plane.
Apply the plate to the plain flat side of the Gnomon, or stile, so as the long edge may rest upon the Dyal-plate, and the short edge reach just to the edge of the Basis, towards which the Index pointeth, standing upon one of the cross lines of the Basis; Then having drawn an horizontal line [Page 7]upon the plane, apply thereunto the edge of the Basis, with the plate so plac'd upon it in such sort, as that the short edge of the plate may rest all along upon the plane. Then will the thred playing at liberty, shew upon the other side of the Style the degrees and parts of Inclination or reclination, viz. of inclination when the thred falleth between the perpendicular line and centre of the Dyal; of reclination when the said thred falleth between the perpendicular line and the Index, The quantity of the Angle being ever reckoned from the perpendicular to the place cut by the thred.
8, To find the declination of a Plane.
Apply the fiducial edge of the Basis, with the Index set towards it, upon the line N. S. to an horizontal line drawn upon the plane, so as the Plummet hanging at liberty, the thred will fall upon the perpendicular line (the Dyal being fitted to the latitude of the place where it is to be used) then turning about the Dyal, till (by the Sun shining upon it) it shew the right time of the day: and upon one of the divided quadrants you shall find either the Index pointing out the declination of the Axis of the plane, from the South towards the East or West; or the counter-Index shewing the declination from North, towards the East or West: always reckoning the degrees and parts from N. where the degrees begin.
A caution.
If your Diall be for another latitude, considerably [Page 8]differing: you must both in this, and the following cases, so hold your Instrument, that upon the Arch on the Gnomon, so many degrees and parts may be cut by the threed, from the perpendicular line towards the index, as the latitude of the place for which the Diall was made, is greater then that where it is used: or contrarily so many degrees and parts from the perpendicular line towards the centre of the Diall, as the latitude for which the Diall was drawn is less then of the place where you make use of it; This caution is ever to be understood when I speak of placing the Instrument Horizontally.
9. To draw a true Dial speedily, without skill in the Mathematicks, upon any erect plain, or irregular face of a body, being situate more Southerly, than the East or West points, viz. when the Index shewes the declination.
Place the Instrument Horizontally upon a Table, or some other stable thing: and having fixed the Basis, turn about the Diall to the true time of the day, and fix it also by the pin made for that purpose; then drawing out the thred at the centre of the Dyall streight along the upper edge of the Gnomon, till it touch the place where the dyall must be made: the point so touched by the thred, shall be the centre of your Dyall, and the thred drawn out straight shews the Angle and forme of the Gnomon: then lay the thred upon all the hours, half-hours and quarters, which the plane [Page 9]or other face, will receive, and drawing the thred out streight, and perfectly even with the Dyall-plate, till it touch the plain or other face, make points where it toucheth, by which and the centre of the Dyall, you may draw all the hour lines, and mark out the half-hours and quarters.
Here once for all note these 3 things
1. That i'ts good to try, before you fix the Instrument, where the centre of the Dyall will be, removing the Instrument backward, and forward, till the thred hir where you would have it; and if by this means the Instrument stand far off from your work, you may by a ruler or plate laid even, (so far as you can apply it) with the edg of the style guide the thred more perfectly; The same course is to be held, when the Instrment is very small.
2. If you draw out the thred at the centre of the Dyall, along the meridian line, straight over the Index till it touch the plane, it will give you a point, by which and the centre of the Dyall, you may draw a line which shall be your substyle, where the foot of your style or Gnomon must stand.
3 If you apply the long edge of the plate to the substyle, and lay the flat side to the thred drawn out straight from the centre of the Dyall, along the upper edge of the Gnomon, till it touch the plane in the centre for the new Dyall as aforesaid, [Page 10]you may by your pen, pencil, or the like, make 2 or more points where the thred toucheth, and by the help thereof draw a line, which, together with the edge applyed to the substyle, giveth you the perfect Angle and form of the Gnomon upon a fixed thing, which will guide a Workman far better than the thred to make the Gnomon; and by this means the pattern may be sent any whither.
10. To draw a true Dyal speedily upon any erect plane situated more Northerly than the East or West point, viz. when the Counter-Index shews the declination.
Turn the Index to the place where the Counter-Index stood when you took the declination; then going to the other fide of the open wall or building, find a place where that declination fits, that is, where the Dyal standing as aforesaid, and the fiducial edge of the instrument applyed to the plane horizontally, the Gnomon shews the true time of the day, by the shadow; and if that prove difficult, you may by a door moved upon its hinges, or reared up in a due position, relieve your self: Upon the place found, pin a large sheet of Past-board, or Paper-Royal, streight and even, and thereon draw a Dyal, as was last directed, for a Southerly plane. Then take it down, and pricking it through, draw so many of the lines as the Sun in the longest dayes will shine on, upon the back-side, which being placed on your Northerly [Page]plane, with the Centre downwards, in a perpendicular line directly under the point, which on the other side would have stood for 12 of the clock, will be a perfect pattern to draw a Dyal on it, whose lines you may extend or shorten at your pleasure, as best fits your plane.
11. To draw a Meridian Dyal upon an East or West plane.
When you are taking the declination of a plane, if the Index and Counter-Index stand upon the line E. W. It is a meridian plane, whose Axis is true East or West, according to the letter pointed at by the Index. Now to draw a Dyal on such a plane, place the instrument horizontally, the fidncial edge touching the plane. Then laying the thred upon all the hour-lines and half-hours that the plane will receive, draw forth the thred streight to the plane, and mark the points where the thred toucheth (which may be best done if the Dyal stand close to the plane, by help of the needle before described) for if you put the thred through the eye thereof, and hold it streight, the streight end will help you to mark the points exactly, and the crooked part rising upward will give way to your eye, to see whether the thred lie right upon the hour-lines, &c. Then laying your plate flat upon the upper edge of the Gnomon, the long edge of the plate resting all along upon the line VI. the shorter touching the plane, will be your guide to draw the substyle, which by a ruler you may [Page 12]extend at pleasure; Then removing your instrument a little higher or lower (it matters not whether, so that it stand again horizontally close to the plane, and so as the plate will again fall into the substylar line) mark points for hours as aforesaid, by which points and the former, lines may be drawn parallel to the substyle, which must be marked with the same numbers with the hours on your Dyal-plate, that guided you to them.
But here also it is good to note diverse things.
1. Your style must be a pin with a sharp point, or else a parallel plate set up perpendicularly in the substyle, just so high as may reach the hour-line of 9 in an Eastern Dyal, and 3 in a Western.
2. If you have the Art of drawing parallel lines either Geometrically, or by help of the plate (which will supply the place of a square) you may spare the second application of the Instrument to the plane.
3. If the plane be high and inconvenient for the fixing of your Instrument close to it, you may pin a Past-board or paper upon any Wall, as if that were a true meridian Wall, and draw a Dyal upon it (having first observed in the fixing of your Instrument, that the Index stand as it did when you took the declination, and the fiducial edge be applyed to the plane) Then striking a perpendicular, or horizontal line quite through your paper, [Page 13]draw the like line upon the plane where the Dyal should be drawn, and placing the perpendicular or horizontal line, which is on the Past-board or paper, upon that which is drawn on the plane, you may prick two points through every line in the paper, and thereby draw them upon the plane.
4. If you would make a larger Dyal than the Instrument set close will give you, you may do it by setting the Instrument further off; but then if you know not how to draw parallel lines, without a second application of the Instrument, you must be sure to set it just at the same distance from the plane at both applications; to which purpose it will be convenient to interpose a parallel piece of wood truly wrought; but to make a less Dyal of this sort, you must have a less Instrument, or else by taking the Dyal off the Basis, you may apply it closer, or make use of a small horizontal Dyal, which indeed will do this work (and some of the other) as well as the Instrument.
5. The Line of VI. and the substyle are the same.
6. You may make the Dyal of what shape you please, as round, square, oval, or in the form of an heart, &c. but a long square is most usual: Nor doth it matter how long or short the hour-lines be, provided they run streight on so far as they go.
12. To draw an Horizontal Dyal upon its own plane.
This is so easie that I thought to have omitted [Page 14]it, for if you place the Instrument upon it, and turning the Dyal to the true hour of the day, there fix it, the thred laid upon the several hours, half hours, and quarters, will transfer them to the plane, and lines drawn from the opposite hours of the same number, will meet in the centre, and the Gnomon of the Dyal gives the pattern of the Gnomon of the other which must be placed in the meridian line (which I shewed before how to draw) to the centre of the new Dyal.
The Instrument may be made use of for drawing of reflecting Dyals, and many other curiosities, but the performance presupposeth more skill than I can presume to be in them for whom this contrivance is principally intended.