But if such Erect Plains do not behold the Direct East, w'eff North or South Points of the Horizon, they then will behold either South-East South-Wef And then they are called "? North-West SEaft >Ere&t Plains ; Declining or South West. A or III. Of Plains that lie Obliquely to the Horizon : (such as the Roofs of Houses, the Cooping of Walls, &c.) are called Reclining Plains. And if such Plins do behold the direct East. West North Points of the Horizon: They are then South called Direct Edft, West, North or South Plains : Reclining from the Zenith of the place in which such Plain stands. But if such Reclining Plain doth not respect the true Eaft, West, North, or South Points, then they will lie open either to the South-Ealt 1 North-West Seaft Reclining Plains : Declining or North Weft. And these are all the Varieties of Plains, upon which Haur-Lines, may be described. Only note,] That all Reclining Plains whatsoever ; whether Direct or Declining, have Two Faces; the Upper-Face, which beholds the Zenith of the Place, is called the Reclining Plain : And the Under-Face, which beholds the Horizon of the Place, is called the-Incliner : And one and the fame Dial serves for both Places. South 2 or CH A P. III. How to find the Situation of any Plain, in respect of De clination and Reclination, in any Latitude. I. To find the Reclination. Fig. LI. Difrition. T the Arch of that Vertical or Azimuth Circle which HE Quantity of the Reclination of a Plain, is: is perpendicular to the Reclining Plain, comprehended between the Zenith of the Place and the Plain. To find which, let A B C D represent such a Reclining Plain : Draw, first, thereon, by, help of a Ruler and Quadrant, a Right a Line G H, parallel to the Horizon of the place ; which thall be the Horizontal Line of the Plain. . Crofs this Line G H, with another Right Line K S at Right-Angles to it ; which Line K S shall be the Vertical Line of the Plain. - To this Line K S, apply a streight Ruler K L : And to that end of it which lyeth clear of the Plain, as at L; apply a Quadrant O E P, having a Thrid and Plummet hanging from the Centre. Then see what number of Degrees of the Quadrant are contained between 0 and E; for so much doth that Plain Res cline from the Zenith of the Place; and is the Reclination of the Plain. Defnition: T II. To find the Declination. *HE Declination of a Plain, Is an Arch of the Hoa rizon comprehended between the Pole of the Plain, and the Meridian of the Place. - Or, It is the distance of the Plain it felf, from the Prime Vertical Circle, or Azimuth of East or West. To find out the Declination of any Plain, there are required two Observations to be made by the Sun, both at the same Time, as near as may be. The First, Of the Horizontal Distance of the Sun, from the Pole of the Plain.----And the Second, Of the Sam's. Altitude. I: 'To find the Horizontal Distance:. applied 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 Limb of the Quadrant ; so that the Shadow of the Thrid may pass. through the Centre and Limb of the Quadrant : And then observe the Degrees cut by the Shadow of the Thrid in the Limb of the Quadrant; and number them from that side of ; the Quadrant, that_standeth Squire or Perpendicular to the Plair : For those Degrees are the Horizontal Distance fought for. 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 raise up, or depress the Quadrant, fo held, till the Sun shining through the Hole in that Sigbt which is nearest the Centre, do caft its Beam of Light upon the Hole in the other Sight farthest from the Centre : And at such time mark exactly what Degrees of the Quadrant are cut by the Thrid , for those Degrees are the Sun's Altitude at that time. The Horizontal Distance, and the Sun's Altitude thus Obferved, at the same instant (as near may be) will help you to the Plain's Declination ; by the Rules following: For, as in PROBL. IX. of the Use of the Coleftial Globe in Afro nomy :- And by CASE XI. of O. A. S. T. Then, Mark whither the Shadow of the Thrid did fall between the First. If the Shadow fall between them: Then the Sun's Azimuth from the South, and the Horizontal Distance added together, do give the Declination of the Plain : And (in this Case) the Declination is unto the same Coast with the Sun's Azien · mutb; that is, Eastrard, if the Observation were made in the Forenoon ; or Westward; if in the Afternoon. Secondly. If the Shadow fall Not between them :: . . Coats And! Pig. LI. And here Note] That the Declination thus found, is always accounted from the South; and that all Declinations are must never exceed 90 Degrees. you must take the residue of that Number to 180 deg. and that shall be the Plain's Declination from the North. above 180, gives the Plain's Declination from the North, to- CHA P IV. ; I. By the Globe. would make your Dial, (suppose for London, in the Latitude 1. Turn the Globe about Westward, till the Hour-Index points at I a Clock, or rather (till 15 degrees of the Equino&tial come to be just under the Meridian] and there keeping the Globe, look upon the Horizon how many degrees thereof are cut by the Equino&tial Colure ; which you shall find to be 11 deg. 30 min. which set down in a little Table, as you fee here is d. m. done ; for this 11 deg. 50 min. is the distance Latitude 51. 3d that the Hour-lines of 11 and 1 a clock are di d. 2 stant from the Meridian upon the Dial Plain. 12 2. Turn the Globe more Westward, till 30 11.50 degrees of the Equino&tial comes to the Meri 24.20 dian, and then see what degrees of the Hori- zon are cut by the Equino&tial Colure ; which 90. d distance of 10 and 2 a clock from the Meridian. il I 8 6 a 3. Turn j 3. Turn the Globe still more Westward, till 45 degrees of the 8 trical Calculation. 1. With 60 Degrees of a Scale of Chords, defcribe a Circle re- Fig.. 2. The Latitude of the Place being 51 d. 30 m. Set them froin Divide the Semicirle W N E, into 12 equal parts, at the ***, & 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 ***, Bc. it will cut the Circle of your Plain in the points 1, 2, 3, &c. on the East-side of N, and 11, 10, 9, &c. on: the West-side of N. Lasily. If you lay a Ruler to the Centre Z, and the respea ētive points 1, 2, 3, 8c. and 11, 10, 9, &c. they shall be the : true Hour-lincs belonging to an Horizontal Dial for the Latitude -of 5ı de. 30 m. And their respective distances from N will be the fame as in the Table they were found to be by the Globe, III. By points *** |