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The Numbers in the third Column of the Table being set off from the Chords from T to the Righthand will give the Points 3, 4, 5, 6, 7; and on the Lefthand, the Points 2, I, 12, 11, 10, &c. on the Circle, from which the HourLines are
to be drawn ;
and thus ( the Stile
being fixed ) the Dial is finished.
12. 57 08 16 14
53 5138 423 3613 3) 8 36 4
Substile 2 6
241 3 I 21 24/11 36 24121
24134 2451 24174
I2 I 2
In making this one Dial, you have in effect made four, viz.
I. Al Direct S Declining W 30° co'. 2. A Direct S Declining E 30° oo!. 3. A Direct N Declining Ę 3000'. 4. A Direct N Declining W 300 oo'.
The Distance of the Hour Lines being the fame in each, only in different Positions, and differently figured; the Hour Lines also of the South being drawn through the Center do make those of the North Dials.
All which is plain and evident from the Schemes themselves ; and may easily be understood by any one who knoweth any thing of this excellent Art, without any farther Explanation.
To draw Hour-Lines on any Direct South Reclining Planes.
Practice. The best way to make Dials on those Planes is by reducing them to the new Latitude, wherein they will become Horizontal Planes, as taught in Prob. 5, of this Chapter
Example. Suppose in the Latitude 51° 32' a Plane reclines from the Zenith 20 Degrees.
Then the Difference of the Co-Latitude 382 28', and the Reclination 20° 00', viz. 18° 28' is the new Latitude ; for which let an Horizontal Diał be made by Pröb. 14, and this shall be the Dial adapted to that Reclining Plane, as required. See thë Figure thereof following.
Note, The Stile of the Dial must point to the South Pole by Prob. 10, of this.
A South Direct Plane Reclining equal to the Pole is an Equinoctial Dial; the making of which is taught
Again, suppose a Plane recline from the Zenith 70° 00' in the Latitude 51° 32'.
This Dial may be made as the last preceeding, by reducing it to its new Latitude 31° 32' ; but for the sake of Variety for the young Learner, I have shewn how it is made by a Projection on the Horizon of London.
For let the Reclination be set from Z to H, then WH E is the reclined Plane, which the Hour-Lines interfect in the Points 5, 4, 3, 2, I, H, 11, 10, 9, 8, 7 ; the Point Q is the Pole of this Plane, from which if a Ruler be laid to the aforesaid Points of Intersection, it will cut the Horizon in the Points XXXXXX, &c. from which, by a Ruler laid on the Center Z, the Hour-Lines are all to be drawn as in the Figure. VOL. II.
Z z 2
From this Projection 'tis evident also how this Dial may be made by Calculation only, that is, by finding the Quantity of the several Arches of the Planes H 1, H 2, #3, &c. For in the Spherical Triangle 11 HP, Right-angled at H, there's given P H = 31° 32', and the Angle HPI = 15° 00'; to find H11, by the fame Analogy as in Prob. 16, 17. These Arches thus found being taken from the Chords and fet each way from the North Point of the Meridian N, give the Marks X X X X X, &c. as before.
PROBLEM XIX. To describe Hour-Lines on Direct North Reclining Planes.
Pratice. 1. Suppose a North Plane in the Latitude 519 32! recline from the Zenith 30° oo'.
The new Latitude found for this plane is 689 28! (by Prob. 6,) therefore an Horizontal Dial in that Latitude shall be proper to this plane, and such is that following