7. Make A R equal to B C, and draw the Line Z R for the Subfilar Line of the Declining Dial.

8. From R erect a Perpendicular to Z R, making RQ equal to A B, and draw the Line R Q for the Stile of the Declining

Dial.

9. From the Center of the Declining Plain Z, draw right Lines from the Center T to the feveral Points 9, 10, 11. and I, 2, 3, 4, 5, &c. (where the Hour-Lines of the Horizontal Dial did cut the Line K T;) thofe Lines fhall be the true Hour-Lines belonging to the Declining Plain, and the Dial is finished, which you may bring into what form you please, Round, Square, &c.

And here, for the ease of the Practitioner, in making of Horizontal, and fuch other Dials as are hereafter mentioned, I have inferted this folowing Table, and its Ufe,

A Table

A Table (hewing the Degrees of each Hour-Line from 12, upon all
Horizontal Dials, from 30 to 60 deg. of Latitude, and for al!
Direct North or South Reclining or Inclining Dials, where the
Heighth of the Stile of fuch Dials is between 30 and 60 deg. of

Altitude.

Hours Distances from 12.

Degrees of Latitude, or of the Stiles (or Cocks) Heighth.

30

31

37116 726 34 40 54 61 49

77

8

5116 34 27
17 I 27
19 17 27 28
3117 54 29

154 44 5542

62 30

32163 II

37 43

20 63

49

13 44

5 64

24

Suppofe you were to make an Horizontal Dial for the Latitude of 35 Degrees, and a Direct South Dial for the Latitude of 55 deg. Or (which is all one) for any Direct South or North Dial, Reclining where the heighth of the Stile is 35 deg.

First

1

First draw a downright Line for the Hour-Line of 12, and upon any part thereof (towards the upper end) affume a Point for the Center of your Dial; and upon that Point with your Compaffes opened to 60 deg. of your Scale of Chords, defcribe a Semicircle; Then take 90 deg. of your Scale of Chords, and set that distance from the Hour-Line of 12, upon the Semicircle both ways; and through thofe Two Points draw another Right Line, which will pass alfo through the Center, and be the Hour-Line of 6 in the Morning and 6 in the Evening.

Then go to this Table, and look in the firft Column thereof for the Latitude 35 deg. and in the Line against 35, towards the Right Hand,you fhall find,

Which Degrees and Minutes taken out of your Scale of Chords, and fet upon the Semicircle on both fides of the Line of 12, Lines drawn from the Center, through thofe Points, fhall be the true HourLines proper for an Horizontal Dial for the Latitude of 35 deg. or of a South or North Dial in the Latitude of 55 deg. and of any Direct North or South Reclining Dial, where the Stile's Heighth is 35 deg.

1

CHAP. IV.

How, Mechanically, by help of an Horizontal Dial for any Latitude, to defcribe the Meridian, Subftile, Stile, and the other Hour-Lines upon any other Plain in that Latitude, Regular or Irregular.

I.

UN

Nder the Plain upon which you intend to make your Dial, let there be erected a Scaffold of one or more Boards broad (according to the bignefs of the New Dial you intend to make,) which Scaffold must be exactly Level, or parallel to the Horizon.

2. Being provided of an Horizontal Dial with Hours, Halves and Quarters (the larger the better) fet it upon the Scaffold, the Center towards the South, and the Stile pointing up towards the North Pole; then

3. Having attained the true Hour of the Day, either by fome true Sun-Dial, a Solar Obfervation by Quadrant, Ring, or other Instrument, or by a good Minute-Watch well rectified;

4. Bring

4. Bring the Horizontal Dial upon the Scaffold to the True Hour and Minute of the Day, at fuch convenient diftance from the Plain as your Judgment will direct you; and there with fmall Tacks, or Cement, fix your Dia! upon the Scaffold, for that it move not, there being a small ftring fixed in the Center of the Dial. Then,

5. Extend the Thread, which is in the Center of the Dial, along, justly, to touch the Top of the Stile of the Dial till it doth touch the New Dial Plain, and note that Point; for that fhall be the Center of the New Dial: The Thread it felf is the Stile or Axis, and the Line under_it (which may be found by help of a Carpenter's Square applied to the Plain and the String) is the Subfilar Line upon the Plain, by help of which the Stile may be made and fastned.

6. To draw the Hour Lines: Extend the Thread fixed in the Center of the Horizontal Dial, over every Hour (Half and Quarter, if you will) till the Thread do touch the Plain upon the Horizontal Line thereof, (which will always be in the fame Level with the upper part of the Scaffold,) and where they interfect this Lire (or the Plain,) make Marks, noting them with the fame Figures as the Thread paffed over in the Horizontal Dial: So Lines drawn from the Center of the New Dial, through thefe Points, fhall be the true Hour Lines of the New Dial.

But fome Hour Lines may run beyond the Limits of the Plain, or the paffage of the Thread may be obftructed by fome Objects, or Irregula rities in the pay, that it cannot come to touch the Plain; Then to help thefe, or the like Impediments,

7. Upon the Horizontal Scaffold, draw as large a Square, or Parallelogram as you can (or you may extend the Hour-Lines of the Horizontal Dial upon the Scaffold it felf) and transfer (by help of the CenterThread) all the hours of the Horizontal Dial into the fides of the Square or Parallelogram: And then,

8. Bring a Thread from the Center of the New Dial, and rest it upon the Hour-Point marked in the fide of the Square or Parallelogram: Then the Thread in the Center of the Horizontal Dial carried along, fo as only to touch the other Thread from the Center, will defcribe the HourLine desired, whether upon an Even or Uneven Plain, from the Center of the New Dial.

Thus far for Dials whofe Centers will fall within their Plains ; but for Juch as decline much from the South towards the Eaft or West, in fuch the Thread which paffeth from the Center of the Horizontal Dial, by the fide of the Stile thereof, the Thread will not meet with the Plain at all, or (at least) not in a great distance, so that no Center can be found upon the Plain it felf. In fuch Cafes you must,

9. Set up a Board or other Object, over, or on that fide of the Plain towards which the Axis tendeth, to receive the Center; and then, fixing a Thread there, by that, and the other Thread you may describe all the Hour-Lines, as was before thewed in Irregular Plains: And the Thread from the Center will be the true Axis or Gnomon of the Dial, and muft be fixed to the Wall by two Stays.

BY

CHAP. V.

Of Projective Dials.

Y this Artifice Hour-Lines may be Projected upon all kinds of Superficies, without any regard had to their standing; either in respect of Declination, Reclination, or both; Or whether the Plains be Flat or Curved; One or more: For if a Point be affigned, wherein the HourLines and Axis thall concur, Hour-Lines may be Projected upon fuch Plains, and an Axis set up after the usual manner, by the directions following.

First, To the Point affigned (upon any fide of it) by help of a Semicircle, or other Level, ftretch out an Horizontal Thread, ferving for the Horizontal Line, which Line (or Thread) need not be one fingle Line, but may be returned by Two, Three, or more Angles, provided that all the parts of it do lie in the fame Superficies, and parallel to the

Horizon..

Secondly, With a Perpendicular Thread held up, project the Sun into the affigned Point, and into the Horizontal Thread alfo, and there ftick in a Pin, or make a Mark upon the Horizontal Line, through which the Shadow cutteth, and at the fame Inftant also take the Sun's Altitude.

Thirdly, By the Altitude taken, find out the Sun's Azimuth for that time. This Azimuth, whatever it be, is reprefented by the Mark before made in the Horizontal Line or Thread.

Fourthly, Apply a Paiftboard to the affigned Point, holding it flat, that it may lie in the fame Plain with the Horizontal Thread ; and upon this Paiftboard protract your Azimuth, by a Thread extended from the Point affigned for the Center, to the Mark made upon the Horizontal Thread. This done,

Fifthly, By help of that Azimuth upon the Paiftboard, protract the Meridian Line, obferving the true Coaft; and to the Meridian thus found, describe an Horizontal Dial for the place.

Sixthly, Apply the Paiftboard to its place again, all things ftanding right as before, project all the Hour-Lines into the Horizontal Thread from the Paifboard, and make Marks upon the Horizontal Line from the Points of each feveral Hour.

Seventhly, Project the Meridian Point by a Perpendicular Thread upon fome Object, into that place whereabouts you imagine the Axis of the World would pais, whether it be above or below, from the Point affigned for the Center.

Eighthly, By help of a Semicircle (ora Quadrant applied to a String) elevated, or depreffed (as occafion offers) from the Point affigned for the Center, according to your Latitude, project the Pole of the World.

Ninthly, Extend a Thread from the Point affigned for the Center to the Pole of the World, which Thread will reprefent the Axis.

Tenthly