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THIS Plane (as passing from the Zenith to the Nadir) is still Vertical, and should (you may suppose) be by right the primary Vertical, but by its tendency towards the East or West Points, its Dial takes the Appellation of a Declining one,
that is to say, of a Dial, whose Plane declines so many degrees from facing directly the North and South, as is its tendency to∣wards the said East or West points.
As for the way of making this Dial it differs little from the first Direct Erect one, already treated of; for supposing your present given Plane declines 40 Degrees from full South towards the East, you must draw your String (which ever represents the Edges, as we have said, of your Plane) not throu' the East Point of the Horizon of your Globe, as before, but throu' 40 Degrees further towards the North, for this makes the String to represent part of a Plane that comes nearer (by so many De∣grees) the facing of the East than it did. Then opening your Compasses at 60 Degrees in any of the great Circles, and descri∣bing (as in Sch. 17th.) the blind one PZW, prick in it from its Meridian Line OZ, the distance between the Zenith of your Globe and the intersection of your String with the first Hour-Circle (to wit between Z and b in Sch. 15.) and it will give you a mark for the 11 a Clock line on your Dial; and the di∣stance between the Zenith and the Intersection of your String with the next Hour-Circle (to wit between Z and c) will give you the mark of the 10 a Clock line, and thus you must proceed to e∣very Hour-Circle cut thus by your String, till it falls on the Ho∣rizon, that is to say from z to d, e, f, g, h, letters marking (as you see in the said Scheme) the 9, 8, 7, 6, 5 and 4 a Clock Hour Circles▪ and consequently giving you those Hour-lines on your Dial.
Now for the Afternoon hour lines (which are no longer equal in distance to the Morning ones,) you have nothing to do but to draw your String, on the West-side of your Globe, throu' 40 De∣grees in the Horizon the contrary way (viz. from the West to∣wards the South) and the distance between the Zenith and the Point in the first Hour-Circle cut by your String (to wit from Z to k in Sch. 16.) will give you the mark for 1 a Clock, and the distance from thence to the next Point or Intersection gives you that of 2, to wit, from Z to l, and in this Order you are to pro∣ceed to n, the▪ 4 a Clock Hour Circle, that is to say, till you come to the intersection of the String with the Horizon on the West∣side of your Globe.
As for your Stile and Substilar they differ also from those of direct North and South Dials; for the said Stile or Cock is to be no longer plac'd on the 12 à Clock Line, nor will its height now
be equal to the Complement of your Elevation, therefore having drawn your String throu' the Degrees of Declension in the Ho∣rizon as before, and putting one foot of your Compasses in the North Pole, find with the other the nearest Point on your String, to wit S (as in Sch. 15.) and the distance between S the said nearest Point and the Zenith of your Globe will be ZS in the blind Circle of Scheme the 17th, to wit the distance between the Meridian Line of your Dial and your Substilar, which in this our Example lyes from the Moridian towards your left hand or Morning hours, and the distance from the said Point in the String to the Pole (being from S to P) will in the said blind Circle be the height of your Stile; so that if you erect and place your said Stile from the Center all along the Substilar OS it will continually show you the Hour.
But if you fancy that the Extension of your Compasses from the Pole to the String will not give you precisely this Point, since your said Compasses may seem to touch it in several Points; I say, if you doubt or fancy this, fasten a Thred on the Pole, and drawing it streight over the Horizon at 40 Degrees from the Meridian of your Globe Eastwardly (i. e. till it passes thron' the Pole of the Plane) see where the said Thred crosses your String (or edge of the Plane) and there the true requir'd Point will be. The Demonstration of this Dial is in the follow∣ing Operation.
What a De∣clining Plane is.
The Constru∣ction.
pag. 80. To describe the Morning hours of a Declining Dial.
To describe the Afternoon Hours.
How to make the Stile and Substilar of a Declining Dial.
A Memoran∣dum.