The English globe being a stabil and immobil one, performing what the ordinary globes do, and much more / invented and described by the Right Honorable, the Earl of Castlemaine ; and now publish't by Joseph Moxon ...

OPERATION XXXII. How to describe Geometrically a Cieling Dial.

SEeing the Glass (which reflects the Suns Rayes to show us the Hour) is commonly fixt in the corners and by-places of Windows, the Globe can seldom be so well order'd (by reason of its Bulk) as to help us in the Construction of this Dial, there∣fore I shall only give you the Geometrical way, which is (as I take it) both short and new; and because these Dials have commonly the Windows (or inlets for the Sun) Southerly, for otherwise they will show but very few hours, we'l suppose ours also in the following Example to stand thus, and afterwards you shall see the difference between such a Dial, and those whose Windows have another Aspect.

First make on any Past-board, Trencher, &c. an Horizontal* 1.1 Dial, as in Scheme 38. and fix in O its Center a Thred of a good Length, to wit OP; then fasten the said Dial so with a Nail to a Long Masons Ruler, that its Fiducial edge (KL) may lye upon the Meridian or 12 a Clock Line, and having cemented and plac't Level a piece of Looking Glass (of the bigness of a Three pence) in the Window, or what convenient place else you please of your Chamber, (which we'l suppose to be G) find by the Plumet AE the Poynt A in the Cieling (WXYZ) being the poynt (in Scheme 39.) directly over the said G, and draw throu' it a Meridian line, viz. the Line AL.

In the next place, fix one end of a piece of Packthred on G

the Center of the Glass, and the other on some point of your Meridian line in such manner that it make an Angle with it of 51. 30′. i. e. the Angle of the Elevation, which may be easily perform'd by the application of the side of a Quadrant to the said extended Packthread, and when 'tis right, let the Point thus found in your Meridian line be called B. Lastly, take the distance between the aforesaid Points A and B, and marking it, suppose at C, on the edge of your Ruler from O, the Center, (or fastning of the Horizontal) place so the said Rulers Fiducial edge (KCL) along the Meridian line on the Cieling, that the point C may lye just on A, and all is done; for then if you draw but the Thred OP streight over each Hour-line of the Horizontal, it shows you where you are to draw all the fair Lines of the required Dial.

[illustration]

Sch. 40.

As for the truth of this* 1.2 Dial, it appears (in Scheme 40.) by the right Angle Triangles OGH and GHF, where HF is part of HM, a suppos'd Meridian line on the Floor, under that in the Cieling, G the Station of the Glass in the Window, H the Point under the said Station, as formerly A was the Point over it, and to facilitate the Demonstration, let us imagine GH equal to GA, i. e. that the Glass lyes in the middle, between the Floor and Cieling; This being so, suppose that GH (instead of representing a Perpendicular Line in the Wall (as here we conceive it) had been a Perpendicular Stick, and that you were to describe an Horizontal Dial on the Floor, whose Stile was to be the said Stick; I say supposing this, you must (you know) to perform the Operation, produce the Meridian Line MH to suppose N, and fastning a String on G, find in it the Point (v. g.) O for the Center of the Dial, (I mean a Point, to which a String being extended from G, makes with the Meridian (OH) the Angle of the Elevation) and so draw the several Hour-lines from the said O according to their respective An∣gles and Distances; all which is exprest at large in the third * 1.3 Scheme or first Horizontal Dial; for there (you see) GH is a Perpendicular Stile, showing the Hour with its top, and that O

is the Center of the Dial, having a Line drawn to it from G ma∣king the Angle of the Elevation with the Meridian OH: Now since O in our present case is a point without the Chamber and consequently the Line MH cannot be produc'd to it, you must draw your Thred from G to the said Meridian Line (HM) within the Chamber, and find in it the Point F, to wit the Point where the said Thred GF makes with it an Angle equal to that of the Elevation, for thereby you will have the distance of O, your true Center from H, as being the distance of F from H, seeing the side GH is common, and the Angles in both Triangles equal: This being so, if you put out of the Chamber an Hori∣zontal Dial whose Center shall lye on O, and its Meridian Line concurr with HF, 'tis but producing all its Hour-Lines on the Floor, and it must necessarily follow that G the Top of the Perpendicular Stile, will show you truly the time of the Day; But by Construction all the hour-lines are thus drawn on the Cieling, and consequently are exactly over the supposed ones on the Floor, Ergo, the Reflext Ray from G must as truly show you the Hour above, as the Direct Ray below; for both Rayes are ever in the same Plane.

Nor is there to be any real Difference in the Operation tho'* 1.4 the Chamber-window should look another way; for you are only to remember, that whilst it enjoys the least Point of South, the Center of your Dial is without the Chamber, when it looks full East or West 'tis in the side or edges of it, and when it ver∣ges Northward, 'tis altogether within; so that in a full Southern Aspect, the said Center will be most abroad, and in a full Northern one the Contrary; all which plainly appears to any one, that will consider an Horizontal Dial truly plac'd (having a Perpendicular for its Stile) if he draws over the Hour-lines, a Line that shall represent the aforesaid side of your Chamber according to its Position and Site.

Notes

• * 1.1

  The Constru∣ction.
• * 1.2

  The Demon∣stration.
• * 1.3

  pag. 73.
• * 1.4

  How this Di∣al is to be made when the windows lye not South∣ward.