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 III. To describe an Horizontal Dial Geometrically, for the Elevation of London.

Describe a fair Circle as ABCD, and if you would have your Dial of another Shape, you may afterwards de∣scribe about it what Figure you please; I say, describe the fair Circle ABCD, and draw throu' its Center O the Line AOC for your Meridian or 12 a Clock hour line, and cros∣sing it at right angles with BD for the Morning and Even∣ing 6 a Clock hour lines, mark in it (by the help of your Line of Sines or any way else) from A the value of 51. 30. or Latitude of your dwelling, which happening to reach, (for example sake) to K, draw the blind line OK; then throu' any point of AO (suppose A) draw GH, another blind line, paral∣lel to BD, or at right Angles with the said AO, and taking with your Compasses the nearest distance between A and OK, which being (suppose) the point L, let AL, by the help of your Sector (according to our former directions,) be the Ra∣dius to the Tangent Line GH, so that marking in it on both sides of A, the Tangents of 15, 30, 45, 60, and 75 Degrees, the said Center O and the point 15 will give you the Hour-lines of 1 and 11, the Center O and 30, those of 2 and 10, and in this manner proceed to 75, which will give you the Hour∣lines of 5 and 7; and as for those beyond the 6 a Clock lines, do but produce 8 in the Morning, and 'twill give you 8 at Night, and 7 in the Morning 7 at Night, as will 4 and 5 in the Evening, the like forenoon Hours.

Thus then you have not only an Horizontal Dial Geo∣metrically described, almost as soon as the former, (and this without embroyling the Plane with multiplicity of blind Circles and Lines) but a way also (in case you have no Sector) how to make any Tangent Line serve your turn; for, 'tis but ta∣king between the Compasses 45 Degrees of it (i. e. a distance equal to its Radius) and finding out (by a trial or two) the Point

(suppose) R in the line OA, where one foot of your Compasses being placed, the other just touches M (the suppos'd nearest point or distance in OK from the said R) draw throu' R a line at right Angles with the Meridian, and noting in it, as we show'd you before, the Degrees of each hour (according to this new Tangent line) the Center O and these Degrees will give you the points of each hour line; for as the former Radius AL was to the several Degrees in its Tangent Line, so will the now Ra∣dius RM be to the several Degrees in its Tangent Line.

As for the Demonstration or Reason of this Dial, every body that understands Gnomonics comprehends it, I doubt not, at the first sight; for the Angle O in the Triangle KOA, being by con∣struction equal to the Elevation, do but place the Base AO on a Meridian Line, and if you consider the Side KO as the Indica∣ting Side of the Stile or Cock, it necessarily follows, that it will re∣present the Axis of the World; for it is evident that its Top K will point directly to the Pole, and touch it, if produc'd, whilst O its other extremity passes throu' the Center of the Horizontal Plane; therefore if a Circle (whose Radius is AL) were so plac't on this Stile or Axis, that its Diameter crost it at right Angles at L, the said Circle would represent Circulum maximum sem∣per apparentium, for that Circle in the Heavens ever touches the Horizon, as this would do at A. This Circle then being parallel to the Aequator, is divided by the Hour Circles into twenty four equal parts, and consequently each fifteen Degrees in its Tan∣gent Line GH, will correspond with its said equal parts or Divi∣sions. Now GH is also the Tangent Line of the Horizon, as touching it in the Point A, but where the Hour Circles cut the Horizon, or its Tangent line, there the Points will be, to which (from the Center) the Hour Lines in an Horizontal Dial are to be drawn; ergo O the Center of your Horizontal Plane, and the several fifteen Degrees in the common Tangent GH are the true points of the Hour Lines. Besides as the distance▪ between each Hour Line (if AL, be the Radius) is 15 Degrees, so if AO be Radius (I mean OA the Radius of the Horizon∣tal Plane) the said Hour Lines will be distant as many Degrees asunder, as they are in the Horizon of the World, or as you found them in the Fabrick of the second Horizontal Dial by the Globe. Here also you may see, that the true place of this Dial is to be in the Center of the Earth, and

not on its superficies, but by reason of the Suns vast distance, the Error, which thereby happens) is not sensible; nay, because the Error is not sensible, we may safely conclude, that the Sun is vastly distant from us.

So much then for Horizontal Dials, since there now remains nothing necessary to be known, but how to find whether they stand Level or no (which is handled in the first Section) and how to draw a Meridian Line for their true placing, which is learnt by the following Operation. But before we go further let me advise you (whensoever you make a Dial of consequence, of what kind soever it be) to describe it first on Paper, and thence to mark out the Lines on your real Plane, for thereby you will not only keep your said Plane neat, and more judiciously chuse the best place for the Center of your Dial, but (besides the several conveniences which practice will show you) the Lines themselves will be more exactly drawn, by reason you can ma∣nage your Paper draught as you please.

Notes

• pag. 71.
• The Demon∣stration.
• pag. 4.
• A Memoran∣dum.