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Fig. LII.

III. By Trigonometrical Calculation.
In these Horizontal Dials, there is nothing to be found by Cal-
culation Trigonometrical, but the Hour-distances 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 Æquinoctial Distance 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 1.- 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 shall be the true Hour-lines : And so is your Dial finished.

The Stile must stand upright at 12 of the clock, not inclining on either side.

And in this manner may you describe Hour-lines upon an Horizontal Plain in



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CHA P. v.
How to describe Hour-Lines upon an Ere& direct South

Plain, in the Latitude of London, 51 deg. 30 m.


N-Ere& 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 Ere& Direct South Dial : So that an Ere&t Direet South Dial in the Latitude of si d. 30 m. will be the same as an Horizontal Dial in the Latitude of 38 de.' 30 m. which is the Coinplement of 51 de. 30

So that the making of such a Dial, both by the Globe and by Tri. Calculation is the same with the other,

only instead of 51 de. 30 m. Latitude you set your Globe to 28 d. 30 m. and fo in the Calculation also : But in these 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 these Dials must stand upon the Hour-Line of 12, and must point downwards towards the South Pole. As in Fi


gure LIII.


To make an Erect Direct North Dial, in the Latitude of

London 51 de. 30 m.

HE North Ere& Dire& Dial, is the fame with the South, on Fig.

ly the Stile must 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 inust 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 finished, as in Fig. LIV.


To make an Ered Direct East or Welt Dial in the Latitude
of London, si de. 30 m.

1. By the Globe.
HE Globe rectified to the Latitude, the Index to 12, the

Quadrant of Altitude in the Zenith : If you turn the 21.2. LV. drant of Altitude fo about till the graduated edge thereof do bė. hold the direct East or West-points of the Horizon, you shall find that it will lie in the very Plain of the Meridian-Circle, and so 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 lame time, wherefore the Hour-lines of these Plains will make no

; Angles at the Pole, and therefore must be parallel one to the other, which the Globe evidently demonstrates, but will not conveniently give the parallel distance of each from other, they being



upon which




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

For the Reasons aforesaid, there is no Trigonometrical Calculation required in the making of these Dials; and therefore, I shall pro

cecd to

II. The Geometrical Construction of these Dials.
Let the Plain

would make an East or Weft Dia al, be ABCD.

1. Upon D. (or any where towards the lower part of the Line BD, for an East Dial, or of A C for a Well ) with 60 degrees of your Chord, describe an Arch F G, upon which set the Complement of the Latitude of the place, viz. 38 deg. 30 min. from F to G, and draw. the Line D G E for the Equino&tial..

2. Towards the upper part of this Line, as at P, assume any point, and through it draw the Line 6 P 6 perpendicular to the Equinoctial, for the Hour-line of Six.- -Atro, towards the lower

of the same Line, assume another point. as L, and through it draw the Line 1 L 11. perpendicular also to the Æquinoctial for the Hour-line of Eleven.

3. With 60 degrees of your Chords, upon the point L, describe a sínall Arch of a Circle, as H K, and upon it (always) set 15 degrees (or one hours distance) from H to K, and draw the Line LKM, cutting the Hour-line of Six in M.

4. Upon Mas. a Centre, with 60 degrees of your Chord, dea seribe an Arch of a Circle N O, which divide into five equal parts in the

points O O O O. 5. Lay a Ruler upon M, and each of these points o OOO and the Ruler will cut the Equinoctial-line E D in the points **** through which paints, if you draw,Right Lines parallel to tine Hour-line of 6, they shall 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,

5 they retain the fame distance from 6, as do the hours of 7 and 8; and thus is your Dial finished.

The Stile must stand upon the Hour-line of 6, and be eJevated so high as is the length of the Line MP, and be a Pin of Wyre, or a Plate of Brass or Iron.

The West Dial is the faine with the East, only changing the names of the Hairs.

may either


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