Horometrical.

CHAP. I.

How to make an Horizontal Dial for any Latitude,
by help of a Line of Chords.

Orizontal Dials are fuch as are ufually made on Brass Plates,
and fet upon the tops of Pofts in Yards, Gardens, Windows,
and other places.

H

A Line or Scale of Chords (by which this and other Dials are made) is fuch a Line or Scale as is defcribed in Geometrical Recreations, Chap.V. Section II.

How to make an Horizontal Dial in any Latitude, by help of this Scale of Chords...

I

1. With 60 deg. of the Chords, upon the Center C, defcribe a Cir. cle, and divide it into Four equal parts, by the Lines, B C. A for the Meridian, or Hour-Line of XII, and DE for the Prime Vertical Cırcle, or Hour Line of VI.

2. If you would make your Dial for the Latitude of 50 degrees; take 50 deg. out of your Scale of Chords, and fet that distance upon the Circle from A to N, and draw the Line C N, for the Stile or Cock of your Dial.

3. Divide the Two Quarters of your Circle, A E and AD, each of them, into fix equal parts, fo fhall you have in each Quadrant five Points, by which you may draw five Chord-Lines, all Parallel to DE, the Line of fix, which will crofs the Line of Twelve C A, in the Points I, F, G, H and A.

4. Take one half of the Line A, and fet it in the Line of the Stile CN, from C to O: From which Point O, take the nearest Extent unto the Line C A. This Distance fet from A upon the fame Chord-Line A, on both fides thereof, at a and a, through which Points a and a draw the Lines C a and Ca for the Hour Lines of XI and I of the Clock. In like manner,

b b

Take half the Sand fet it Stand Stake the near- $6

L

(H Left diftance to G Chord Line, FfromC to M from MCA, and fet F

(N)it from

to

C C

d d

e e

Which done (which may very fpeedily, and exactly be performed) draw Lines from the Center C through the refpective Points b b, c c, dd, and e e, on both fides C A, and they fhall be the true Hour Lines belonging to an Horizontal Dial, for the Latitude of 50 Deg. that is, the the Hour-Lines from fix in the Morning till fix at Night.

5. For the other Hours before and after fix, as four and five in the Morning, and feven and eight at Night, they may be put in, by drawing the Hour Lines of four and five in the Afternoon, and feven and eight in the Forenoon, through the Center C, above the Line D E, as is evident by the Figure.

6. If you would infert the Halves and Quarters of Hours, you must then divide the Two Quadrants into 12 or 24 Equal Parts, and draw Chord-Lines through the Meridian- Line CA, and deal with them as you did with thofe for the whole Hours.

7. For the Cock or Stile of your Dial, it may be either a Plate of Brafs cut into a Triangular Form, the Pattern whereof is the Triangle CSA, which muft ftand Square (or Perpendicular) upon the Meridian-Line CA. Or it may be a Rod of Iron bended to that form.

In Horizontal Dials obferve thefe following NOTES.

I. An Horizontal Dial in any Latitude, is an upright South Dial in that Latitude, which is equal to the Complement of that Latitude for which the Horizontal Dial was made--So the foregoing Horizontal Dial being made for the Latitude of 50 Deg. take 50 from 90, and there will remain 40; fo that the former Dial will be a Direct South Dial in

the

the Latitude of 40 Deg. And the Cock, or Stile, muft point downwards towards the South Pole,

II. From an Erect Direct South Dial, an Erect Dire& North Dial is deduced-For, if you draw the Hour- Lines (Stile and all) of a South Dial through the Center, then will 12 at Noon on the South be 12 at Midnight in the North; and the Cock, or Stile of the North Dial must point upwards towards the North Pole; And the Hour Lines about 12 at Night (viz. 9, 10, 11, 12, 13, 1,2,3.) must be omitted; As in Fig. i. all Three Dials are diftinguifhed. So that a North Dial is no other than a South Dial inverted.

CHA P. II.

To make an Erect Direct Eaft or West Dial.

T

Hefe Dials are the fame in all Latitudes, and may be made Geometrically, after this manner.

Towards the bottom of your Plain, draw an Horizontal Line B A ; At the North end thereof (as at A,) with 60 deg. of your Scale of Chords, defcribe an Arch of a Circle, as SC V. Then out of your Scale of Chords take the Complement of the Latitude (in this Example 40 deg.) and fet them from S to C, and draw the Line A CD, quite through the Plain; which Line DA divide into five equal parts in the Points a, b, H, E; and with that distance of the Compaffes,upon the

A 2

Point

point E, deferibe the Circle D 6 H 6, and through the Center E, draw the Line 6 E 6, at right Angles to the Line AD, and that fhall be the Hour Line of fix; And by the Points 6 and 6 draw the Lines 6 11, and 61, both parallel to the Equinoctial Line A D Then divide one Quarter of the Circle into fix equal parts, and laying a Ruler upon the Center E,and each of thofe parts,it will cut the uppermoft parallel Line in the points 6, 7, 8, 9, 10 and 11. From which points, if you draw Lines parallel to the Line 6 E 6, they fhall be the Hour Lines of an Erect Direct East Plain. For the Hour-lines before 6 in the Morning and after 6 in the Evening, they are the fame with thofe before 6 in the Morning, and before 6 in the Evening: For the distance betwixt 6 and is the fame as is between 6 and 7, and the diftance between 6 and 4 the fame as between 6 and 8----For the Stile of thefe Dials, it may be a Plate of Brafs, fo broad as is the diftance between the Hour-lines of 6 and 9. and must be placed perpendicularly upon the Hour-line of fix. This Plain hath Two Faces, one open to the Eaft (as this in the Figure) the other to the Weft; and one being made the other is made alfo: For, if you prick (or draw) the Lines of the Eaft Dial through the Paper, thofe Lines on the back fide fhall be a Weft Dial, only the Eaft Dial Lines are thofe of the Morning from 4 till 11, and thofe of the Weft Dial are those of the Afternoon from 1 to 8 at Night.

5,

From an East or West Dial, a Polar Dial may be deduced.

Suppofe the Line A D in the East Dial to lie upon the Horizontal Line A B, in the fame Dial Plain, then will the Eaft Dial be a Polar Dial, and muft behold the South, and the Hour-Line of 6 must be the Hour Line of 12, upon which the Stile (or Cock) muft ftand. And the Hour-Line of II in the Eaft Dial must be the Hour-Line of 5 at Night in the Polar; and the Hour-Line of 1, the Hour-Line of 5 in the Morning,

in the Polar Dial.

CHAP.

By help of an Horizontal Dial, in any Latitude, to make a Declining Dial in that Latitude.

Uppofe an upright Plain in the Latitude of 51 deg. 32 min. to decline from the South Weftward. 30 deg.

Sup

1. Draw a right line K T, representing the Bafe or horizontal Line of your declining Plain.

2. In this line, affume any point (as A.) and from it draw another line A S, making an Angle S AT equal to 30 deg. the Plain's declination, (towards K, if the Plain decline Eastward) or towards T, if it decline Weft, as here it doth.

3. Upon this point A, erect a Perpendicular to K T. for the meridian line of the declining Plain; ----And from the fame point A, another perpendicular to the Line A S, for the Meridian (or 12 a Clock line) of the horizontal Dial, and in this line affume any point at pleasure (as X) for the Center of the horizontal Dial.

4. Upon X defcribe the Horizontal Dial KTDE, for the Latitude of 51 deg. 32 min. and draw the Stile thereof X B, continuing it, till it cut the Line AS in P, and all the Hour Lines till they cut the Line KT, in the Points 9, 10, 11, and 1, 2, 3, 4, 5.

5. Make AZ equal to A P; fo fhall Z be the Center of the Declining Dial.

6. Upon the Point B, (where the Line X P cutteth the Line KT) erect a Perpendicular, cutting the Line AS in C.

7. Make