276 Fig. nearer or farther off each other according as the Stile is proporLV. tioned to the Plain, which I fhall now come to fhew.

For the Reafons aforefaid, there is no Trigonometrical Calculation required in the making of thefe Dials; and therefore, I fhall proceed to

II. The Geometrical Conftruction of thefe Dials..

Let the Plain upon which you would make an Eaft or Weft Dial, be ABCD.

1. Upon D (or any where towards the lower part of the Line BD, for an Eaft Dial, or of A C for a Weft) with 60 degrees of your Chord, defcribe an Arch F G, upon which fet the Complement of the Latitude of the place, viz. 38 deg. 30 min. from F to G, and draw the Line DGE for the Equinoctial..

2. Towards the upper part of this Line, as at P,. affume any point, and through it draw the Line 6 P 6 perpendicular to the Equinoctial, for the Hour-line of Six. Alfo, towards the lower part of the fame Line, affume another point. as L, and. through it draw the Line II L II perpendicular alfo to the Equinoctial for the Hour-line of Eleven.

3. With 60 degrees of your Chords, upon the point L, defcribe a finall Arch of a Circle, as H K, and upon it (always) fet 15 degrees (or one hours diftance) from H to K, and draw the LineLKM, cutting the Hour-line of Six in M.

4. Upon Mas a Centre, with 60 degrees of your Chord, de feribe an Arch of a Circle NO, which divide into five equal parts. in the points 0 0 0.

5. Lay a Ruler upon M, and each of thefe points o and the Ruler will cut the Equinoctial-line ED in the points ****, through which points, if you draw Right Lines parallel to the Hour-line of 6, they fhall be the Hour-lines of 7, 8, 9, and 10 of the Clock, the Hour-lines of 6 and 11 being drawn before.

6. For the Hour-lines of 4 and 5 in the Morning, before 6, they retain the fame diftance from 6, as, do the hours of 7 and 8; and thus is your Dial finished...

The Stile muft ftand upon the Hour-line of 6, and be elevated fo high as is the length of the Line M P, and may either be a Pin of Wyre, or a Plate of Brafs or Iron.

The West Dial is the fame with the East, only changing the names of the Hours

For

To make an Erect Dial, declining from the South, Eaftward, or Weft-ward; 30 degrees in the Latitude of 51 deg. 30 min.

I. By the Globe.

HE Globe being Rectified to the Latitude of the place, the Fig. Quadrant of Altitude in the Zenith, the Index of the Hour-Cir- LVL cle at 12, and the Equino&ial Colure brought under the Meridian;

1. Count the Declination of the Plain upon the Horizon, from the Eaft or Weft-points thereof (according as the Plain declines) towards the South namely, 30 degrees, and to that point of the Horizon bring the Quadrant of Altitude, and there keep it.

2. Turn the Globe about till the Index of the Hour-wheel cuts 11 of the Clock, or rather (as I faid before) till 15 degrees of the Equinoctial have paffed the Meridian, and then shall you find the Equinoctial Colure to cut the Quadrant of Altitude at 9 deg. 50 min. if you count the degrees from the Zenith point downwards.

3. Turn the Globe farther about, till 30 degrees of the Equinoctial be paft the Meridian, and then fhall yon find the Colure to cut the Quadrant of Altitude at 18 deg. 14 min. counted from the Zenith downwards as before.

you

4. Do the like with all the reft of the Hours, and fhall find that at the feveral 15 degrees of the Equinoctial, the Equinoctial Colure will cut fuch degrees of the Quadrant of Altitude as are expreffed in this Table, if you count them from the Zenith downwards,as is before directed. This done

5. Bring the Quadrant of Altitude to the other fide of the Meridian, and fet it to 30 degrees, the Plains declination, counted from the Eaft or Weft-points Northward, as you did Bbb 2

Fig.LVI before towards the South, which will be in the juft oppofite point of the Horizon to which it was before; and alfo, bring the Equinoctial Colure under the Meridian. Then,

1

6. Turn the Globe about (the contrary way to what you did before) till 15 degrees of the Equinoctial be paft the Meridian, and then fhall you find the Equinoctial Colure to cut at 12 deg. 23. min of the Quadrant of Altitude counted from the Zenith.

Hours
from

Noon.

12

I

2 10

Hour-di

ftances on the Plain.

d. m.

00 00

12 23

29 19

13

9 8

52 42

80 07

And fo continuing turning the Globe about till 10, 45, and 60 degrees of the Equinoctial have paffed the Meridian, you fhall find the Equinoctial Colure to cut the Quadrant of Altitude at fuch degrees as are expreffed in this

Table.

The Hour-distances upon the Plain being thus attained, there are two other requifites in all upright declining Dials alfo to be found by the Globe, before the Dial can be finished. Namely,

1. The diftance of the Sub-file from the Meridian.

2. The height of the Pole above the Plain, or the height of the Stile above the Sub-file.

To find both which,

Bring the Equinoctial Colure to the Plains declination 30 degrees counted upon the Horizon from the South-Eaward; and the Quadrant of Altitude to 30 degrees counted in the Horizon from the Eaft-Northward: So fhall the Quadrant cut the Colume at Right Angles. And

The number of degrees of the Quadrant contained between this Interfection and the Zenith (which here is 21 deg. 41 min.) is the diftance of the Sub-file from the Meridian. And the degrees of the Colure contained between this Interfection and the Pole (which here is 32 deg. 37 min.) is the height of the Pole above the Plain.

II. The Geometrical projection of this Dial, in order to the Trigonometrical Calculation of the Hour diftances and other Requifites belonging to fuch an Erect Declining Plains.

I. Upon the Point Q, as a Centre, with 60 de. of a Scale of Chords, defcribe a Circle, reprefenting your Dial Plain And crofs it with two Diameters ZQN for the Vertical; and H QO for the Horizontal Line of the Plain

2. Set