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FIrst draw the Horizontal Line AB, and on the Center at C describe the Semi∣circle AEB, with the Chord of 60 deg. and from A and B lay down 90 deg. unto E; so shall you draw CE the Meridian Line or Hour of 12; then in
the former Diagram take the Substile distance DM 23 deg. and lay the same in the Dial following from E unto F, and from the Center C through F you shall draw CFK the Substiler Line. Next take the Chord of 90 deg. and lay it from F both ways upon the Arch, so shall you draw the Gnomon Line GH, whereon from C, with the Stiles Altitude before found, 31 deg. 40 min. taken from the Gnomon Line, you shall make CG and CH. Then take the whole Line of 6 hours, and with the same distance from G describe an Arch at K, and with the like from •• cross the same Arch, and draw the Lines GK and HK, which last Line cuts the Meridian at N. Now if you measure KN on the Hour-lines, you shall find it neer 2 ho. 36 m. ½ as you found in the last Diagram. Then take one Hour more, which is 3 ho. 36 min. and lay the same from K unto M; and so increasing one Hour more, you shall have the Hour points l and i; also diminishing one Hour less than 2 ho. 36 min. which is 1 ho. 36 min. the same will reach from K to O, and so 38 min. from K to P. Now as you have divided KH, the very same distance as is from K towards H, must be from G towards K; so drawing the Lines from the Center C through those Points, you shall have the Hour-lines, as you see in the Dial following.
By Calculation,
| As the Radius 90 deg. | 10 |
| Is to the Sine of the Stiles or Gnomons Height. 31 d. 40 m. | 972013 |
| So is the Tangent of the Dist. of an Hour from the Subst. 9 d. 9 m. | 920701 |
| To the Tangent of the Hour-Arch from the Substile 4 d. 50 m. betwixt the 10 a clock Line, and the Subst. Line on the Arch | 892714 |
By this Rule was this Table made;
| Hours. | Equal. Dist. | Hour Arches. |
| D. M. | D. M. | |
| 4 | 80 51 | 72 57 |
| 5 | 65 51 | 49 30 |
| 6 | 50 51 | 32 from 49 |
| 7 | 35 51 | 20 46 |
| 8 | 20 51 | 11 18 |
| 9 | 5 51 | 3 5 |
| Meridian. | Substile. | |
| 10 | 9 9 | 04 50 |
| 11 | 24 9 | 13 15 |
| 12 | 39 9 | 23 8 |
| 1 | 54 9 | 36 0 |
| 2 | 69 9 | 54 2 |
| 3 | 84 9 | 78 57 |
and by the same you may make one for any Latitude, and for any Declining Dial; and you may by it prove your former Work: for if you prick from the Substiler Line F the Chord of 4 deg. 50 m. and draw a Line from the Center, it will be the Hour-line of 10; and prick the Chord of 3 deg. 5 min. from the Substile, and draw a Line through that Point to the Center, and it will be the Hour-line of 9 a clock; and so of the rest, as you find them in the last Column.
Note, That the Height of the Stile FS being equal unto MN in the former Dia∣gram, which is the Chord of 31 d. 40 m. now because the Plane declines East, there∣fore the Gnomon shall decline West: for the Dial being such a Projection of the Sphere, wherein all the usual Lines cross in the Nodus of the Gnomon, and thence disperse themselves again towards the Plane; therefore that which is East in the Sphere, will be expressed West on the Plane, and contrarily, as was said Chap. 2. Theorem 2. Also I consider, that howsoever the Plane be turned East or West, the Gnomon place is fixed, because it is a part of the Axis of the World, or a Line Parallel to it. Now therefore I turn a South Dial, and make him decline East, and hold the Gnomon unmovable, the West side of the Dial will approach neerer to the Gnomon, as reason and sense will require. Likewise the Hours which are found on the same side of the Meridian or Noon-line with the Substile, must be set the same way with it from the Noon-line in the Dial.
And if you would draw the North Dial of this Plane, do but prolong those Hour lines, and the Substile upwards beyond the Center, and you have the North Dial beyond C, or above the Horizontal Line AB, as the South Dial below it. And note, Because the Sun sets after 8 a Clock in Summer, therefore the three hours next before and after midnight, may be left out in this Dial, and all others which must serve in our Latitude.
This is the most ready way to delineate the opposite face of any Dial. Note, That if a Wall decline from the South Eastwards 32 deg. 30 min. therefore the Plane which lieth 90 deg. from his Pole, is in the 32½ Azimuth from the East Northward.
Note this well: Extend the Compasses as before from K to N, the Intersection of the Meridian with the Line KH at N, before found to be 2 ho. 36 min. which converted into Degrees, by allowing 15 Degrees to an Hour, and 4 Minutes to a Degree, it makes 39 deg. 9 min. which 39 deg. 9 min. shew me the Difference of Longitude between our Country and the Country of this Dial.
You may apply this Distance to the Line of Inclination of Meridians, and it will give you the Distance before 39 deg. 9 min.
Note, I allow this Countries Longitude to be 27 deg. 44 min. at Bristol, to the Eastward of the Grand Meridian Flowers and Calfs one of the Isles of Azores, which added to 39 deg. 9 min. shews the Longitude of the Country of the Dial to be 66 d. 53 min. Eastward, and Latitude 31 deg. 40 min. which I find by my Globe is in the Desarts of Arabia at Asichia neer Soar.