Problem III.
To determine the Place and Altitude of the Style.
NOt only the Center of the Hours in these sorts of Dyals, but also the place of the [ 50] Style is in the Meridian Line
Note, First, That this Style is commonly Tri∣angular, and its Basis lyeth upon the Meridian Line, and terminates in the Center of the Hours, but it rises in Altitude towards the Aequinoctial Line, as is observed in the Scheme of the first Problem.
Note, Secondly, That this Style hath no de∣term••••ed Altitude, except in respect of the place in which it is fixt; for one part of the Basis of that [ 60] Triangle being Plac't in the Center of Hours that is in 〈◊〉〈◊〉, by how much this Basis shall be, whence consequently the other part of this side will be more distant from the Center; so much the more is the Altitude of the Style to be, and so much the bigger will the whole Triangle be. Thus the Triangle o, n, f, or m, l, f, or g, e, f, will be bigger than k, h, f. Moreover such ought to be the Altitude of the Style that the side f, o, which is subtended to the right Angle n, or l, or h, may agree with the Axis of the World, and tend directly to the Pole. And it is therefore called the Axis, because it agrees with the Axis of the World; and that side only, or shadow projected from it designs the Hours. There∣fore that a fit Altitude of this nature may be had.
Note, Thirdly, That the Degrees of the Poles Altitude ought to be numbred, and recourse had to the Instrument, by fixing the Foot of the Com∣pass in the Center thereof, and then extending the other to that part of the Aequinoctial Line where∣in the Radius cuts that Degree, which answers to the number of Degrees of the Poles Elevation; For Example; Supposing that in this Countrey the Pole is Elevated 49 Degrees, the Foot of the Compass ought to be extended to that part where∣in the 49th Degree is cut by the Radius, numbring from the Line of the 12th Hour. This extension of the Compass being made, is to be transferred to the Dyal in this manner; fix one Foot of the Compass thus opened in the Concourse of the Aequi∣noctial, and Meridian Lines, that is, in e; then with the other Foot mark in the Aequinoctial Line the Point g. Lastly, from f, the Center of the Hours draw through the said Point g, the f, k, g, m, o, without stint: This will give the sought Altitude of the Style; for if the Base be only f, h, the whole Style and its Altitude will be f, h, k: O∣therwise if the said Base be extended to e, the Style will be f, e, g; if to l, the Syle, will be f, l, m; if to n, the Style will be f, n, o, and so ad infi∣nitum.
Note, Fourthly, That the Angle which the said Axis makes at the Center of the Hours, in the Horizontal Dyal hath always the Degrees of of the Poles Elevation; and consequently that in our Hypothesis this Angle is in 49 Degrees.
Note, Fifthly, If in place of a Triangular Style there should be only a right Style erected, such as would be b, k, or e, g, or l, m, or n, o, the extremity of it only would shew the Hours by the Shadow projected from it. But observe that the Horizontal Dyal thus finish'd ought to be so ordered and disposed in its proper place; first that it be Parallel to the Horizon, which is tryed by the use of a Plum-Line, or Level; and some try it by casting in Quicksilver; for if the Plane incline never so little, the Quicksilver will slide into that part. Secondly, the Line of the Hour XII is exactly to be plac'd within the Meridian of the said place, which Meridian, how it is to be found, hath been already declared.