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applied to the Plain, and held Level (as near as you can conje- Fig. LI
cture) hold up a Thrid and Plummet at full Liberty, near the Eimb
of the Quadrant; fo that the Shadow of the Thrid may país.
through the Centre and Limb of the Quadrant: And then.
obferve the Degrees cut by the Shadow of the Thrid in the
Limb of the Quadrant; and number them from that fide of
the Quadrant, that ftandeth Square or Perpendicular to the
Plain For thofe Degrees are the Horizontal Distance fought

II. To find the Sun's Altitude.

Hold up a Quadrant with both your Hands, turning the Leftfide of your Body to the Sun; then raife up, or deprefs the Quadrant, fo held, till the Sun fhining through the Hole in that Sight which is neareft the Centre, do caft its Beam of Light upon: the Hole in the other Sight fartheft from the Centre: And at fuch time mark exactly what Degrees of the Quadrant are cut by the Thrid, for thofe Degrees are the Sun's Altitude at that time. The Horizontal Distance, and the Sun's Altitude thus Obferved, at the fame inftant (as near may be) will help you to the Plain's Declination; by the Rules following. For,

1. By having the Sun's Altitude; you may find the Sun's Azimuth,
as in PROBL. IX. of the Ufe of the Calestial Globe in Aftro-
nomy And by CASE_XI. cfO. A. S. T.. Then,

II. When you make your Obfervation of the Horizontal Distance
Mark whither the Shadow of the Thrid did fall between the
South, and that Side of the Quadrant which was Perpendicu--
lar to the Plain:

Firft. If the Shadow fall between them: Then the Sun's-
Azimuth from the South, and the Horizontal Diftance added
together, do give the Declination of the Plain And (in this
Cafe) the Declination is unto the fame Coaft with the Sun's Azi--
muth; that is, Eastward, if the Obfervation were made in the
Forenoon; or Weftward, if in the Afternoon.

Secondly. If the Shadow fall Not between them::

Then, The Difference between the Sun's Azimuth and Horizontal Distance is the Declination of the Plain: And in this Cafe)If the Azimuth be the Greater of the two, then the Plain Declines to the fame Coaft whereon the Sun is; But if the H. Diftance be the Greater; then the Plain Declines the contrary Coafti

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Fig. LI.

And here Note] That the Declination thus found, is always accounted from the South; and that all Declinations are counted from either North or South, towards either Eaft

or Weft: And muft never exceed 90 Degrees.

I. If therefore, The Degrees of Declination do exceed 90 deg. you must take the refidue of that Number to 180 deg. and that fhall be the Plain's Declination from the North.

II. If the Degrees of Declination exceed 180; then the Excefs above 180, gives the Plain's Declination from the North, towards that Coaft, which is Contrary to the Coast whereon the Sun was, at the time of Obfervation.



How Hour-Lines may be defcribed upon an Horizontal
Plain in any Latitude-; viz. of London, 51 d. 30 m.


I. By the Globe.

Levate the Globe to the Latitude of the place for which you would make your Dial, (fuppofe for London, in the Latitude of 51 deg. 30 min.). Then bring the Vernal Equinoctial Colure (which is the firft point of Aries alfo) to the Meridian, and (if you will) the Index of the Hour-Circle to 12. This done,

1. Turn the Globe about Weftward, till the Hour-Index points at I a Clock, or rather [till 15 degrees of the Equinoctial come te be juft under the Meridian] and there keeping the Globe, look upon the Horizon how many degrees thereof are cut by the Equinoctial Colure; which you fhall find to be 11 deg. 30 min. which fet down in a little Table, as you fee here is done; for this 11 deg. 50 min. is the distance that the Hour-lines of 11 and 1 a clock are di ftant from the Meridian upon the Dial Plain.

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24.20 38. 3 53.35



2. Turn the Globe more Weftward, till 30 degrees of the Equinoctial comes to the Meridian, and then fee what degrees of the Horizon are cut by the Equinoctial Colure; which you will find to be 24 deg. 20 min. which note down in a Table as before, for that is the Hourdiftance of 10 and 2 a clock from the Meridian.

3. Turn

3. Turn the Globe ftill more Weftward, till 45 degrees of the Equinoctial come to the Meridian; and then fhall the Equinoctial Colure cut 38 deg. 3 min. of the Horizon counted from the Acridian, which is the diftance of 9 and 3 a clock.

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Do thus with the other hours of 8 and 4, of 7 and 5, and fo fhall the Colure cut 90 degrees at 6 a clock, or when 90 degrees - of the Equinoctial comes to the Meridian. And this being done, your Dial is fo far made as the Globe can affift


II. The Geometrical Conftruction of this Dial, in order to the Tigometrical Calculation.

1. With 60 Degrees of a Scale of Chords, defcribe a Circle re- Fig. prefenting your Dial-plain, and Horizon of the Place, (viz. Lon- LII. don.) Crofs it with 2 Diameters S N, reprefenting the Meridian of the Globe, and Hour-line of XII; and the Line EW, for the Hour-line of VI: then will Z reprefent the Zexith of the Place, and be the Centre of the Dial.

2. The Latitude of the Place being 51 d. 30 m. Set them from S to a, and from W to b: Then a Ruler laid from W to a, will crofs the Meridian S N in P, the Pole of the World: And laid from E to b, it will cross the Meridian N S in Æ, the interfecti-on of the Meridian and Equinoctial. And now. you have three Points, viz. W, E, E, through which you may defcribe the Equinoctial Circle WA E, whofe Centre will be at c, always in fome part of the Line NS, extended, if need be.

3. Divide the Semicirle W N E, into 12 equal parts, at the points, &c. And laying a Ruler to Z, and every of thofe points oo, it will crofs the Equinoctial Circle WEE, in the points ***, &c. dividing that Semicircle into 12 unequal parts.

4. A Ruler laid to P, the Pole of the World, and to the feve- ral points ***, &c. it will cut the Circle of your Plain in the points 1, 2, 3, &c. on the Eaft-fide of N, and 11, 10, 9, &c. on: the Weft-fide of N.

Laftly. If you lay a Ruler to the Centre Z, and the refpeEtive points 1, 2, 3, &c. and 11, 10, 9, &c. they fhall be the true Hour-lines belonging to an Horizontal Dial for the Latitude of 51 de. 30 m. And their refpective diftances from N will be the fame as in the Table they were found to be by the Globe.

III.: By

Fig. LII.

III. By Trigonometrical Calculation.

In thefe Horizontal Dials, there is nothing to be found by Calculation Trigonometrical, but the Hour-diftances upon the Plain from the Meridian, for which, This is

The Canon for Calculation.

As the Sine of 90 de.

Is to the Sine of the Latitude P N, 51 de. 30 m.

So is the Tangent of 15 d. (the Equinoctial Diftance of One hour;
of 30 d. for Two hours; of 45 d. for Three hours, &c.)
To the Tangent of 11 d. 50 m. for II and I---- of 24 d. 20 m.
for 10 and 2---- for 38 d. 3 min. for 9 and 3, &c. as in the
Table, before found by the Globe.

So have you all the Hour-lines between 6 in the morning and 6 at night; and for the Hour-lines of 4 and 5 in the morning, and of 7 and 8 at night, draw the fame Lines before and after 6, through the Centre, as in the Figure, and they fhall be the true Hour-lines And fo is your Dial finished.

The Stile muft ftand upright at 12 of the clock, not inclining on either fide.

And in this manner may you defcribe Hour-lines upon an Horizontal Plain in any Latitude.


How to defcribe Hour-Lines upon an Ere& dire& South
Plain, in the Latitude of London, 51 deg. 30 m.


N-Ered Direct South Dial, in any Latitude, is no other than an Horizontal Dial in that Latitude, which is equal to the Complement of that Latitude in which it is an Ered Direc South Dial: So that an Erect Direct South Dial in the Latitude of 51 d. 30 m. will be the fame as an Horizontal Dial in the Latitude of 38 de. 30 m. which is the Complement of 51 de. 30 So that the making of fuch a Dial, both by the Globe and by Tri. Calculation is the fame with the other, only inftead of 51 de. 30 m. Latitude you fet your Globe to 38 d. 30 m. and fo in the Calculation alfo But in thefe Dials there needs no Hour


Lines to be drawn through the Centre, for that the Sun never Shines upon them before 6 in the Morning, nor after 6 at Night. The Stile of thefe Dials muft ftand upon the Hour-Line of 12, and muft point downwards towards the South Pole. As in Figure LIII.




To make an Ered Direct North Dial, in the Latitude of
London 51 de. 30 m.

HE North Ere Dired Dial, is the fame with the South, on Fig. Tly ly the Stile muft point upwards towards the North-Pole, and LIV. the hours about Midnight, as 9, 10, 11, 12, at Night, and I, 2 and 3 in the Morning must be left out, and 4 and 5 in the Morning; and 7 and 8 at Night muft be drawn through the Centre: So is your North-Dial also finifhed, as in Fig. LIV.


To make an Erect Direct East or West Dial in the Latitude of London, 51 de. 30 m.

I. By the Globe.


TH HE Globe rectified to the Latitude, the Index to 12, the Fig. Quadrant of Altitude in the Zenith: If you turn the Qurdrant of Altitude fo about till the graduated edge thereof do behold the direct Eaft or West-points of the Horizon, you fhall find that it will lie in the very Plain of the Meridian-Circle, and fo the Pole will have no elevation over it; for turning the Globe about, the Equinoctial Colure will not cut the Quadrant of Altitude in any particular degree, but it will cut all the degrees thereof at the fame time; wherefore the Hour-lines of thefe Plains will make no Angles at the Pole, and therefore must be parallel one to the other, which the Globe evidently demonftrates, but will not conveniently give the parallel diftance of each from other, they being



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