DIA
[ 202 ]
DIA
Hand fet "off towards trie Left, and contrary wife • Omit- ting all Hour-Lines; which in fuch a Plane cannot be fhewn. For the Practice the beft Way is, after drawing a South Decliner upon Paper, to prick the feveral Points thereof through with a Pin ; Then applying the Face of the Paper to the Wall, the Back-fide thereof will fhew you all the Points neceifary for the North 'Declining 'Dial,
Inclined Dials are thofe drawn on Planes not EreB, but Inclining, or 'leaning forward towards the South, or Southern Side of the Horizon, in an Angle, either greater or lefs than the Equinoctial Plane. See Inclination.
Such an Inclined Plane is conceived by fuppofing one Part of the Plane of the Equator lifted up toward the Zenith, and the other deprefs'd toward the Nadir ; and thus to re- volve upon a Line drawn from the Ealt to the Weil Points cf the Horizon.
'To draw an Inclined Dial.
i. The Inclination of the Plane, as DC (Fig.iy.) being found by a Decline); as taught under Inclination $ If it fall between the Equinoctial Plane CE, and the Verti- cal one CB, in fuch manner, as that the Angle o'i Inclina- tion DCA is greater than the Elevation of the Equator EGA : On the Upper Side draw a North Dial ; and on the Lower a South Dial to the Elevation of the Equator, which is equal to the Aggregate of the Elevation of the Equator of the given Place, and the Complement of the In- clination to a Quadrant.
2. If the F/clincdVhne CF fall between the Horizontal one CA, and the Equinoctial CE, fo that as the Angle of Inclination TCA is lefs than the Elevation of the Equator EC A : defcribe an Horizontal Dial to an Elevation of the Pole, equal to the Aggregate of the Elevation of the Pole "of the given Place, and the Inclination of the Plane.
Dials thus inclined^ are drawn after the fame manner as tpYiraary Dials^ except, that the Index in the former Cafe mull be fitted under the Angle ADC, and in the latter un- der the Angle DFC : And that the Diltance of the Centre of the Dial from the Line of Contingency in the former Cafe is DC, and in the latter FC.
Reclining Di als, are thofe drawn on Planes not Erect, but Reclined, or leaning backwards from the Zenith to- wards the North, in an Angle greater, or lefs than the Polar Plane.
A Reclined Plane is conceived by fuppofing one Part of the Polar Plane raifed toward the Zenith, and the other depreffed towards the Nadir : And thus revolving about a Line drawn from Eaft to Weil:. To find the Reclination of a Plane. See Reclination.
7o dram a Reclining Dial.
I-. If the Reclined Plane HC fall between the Vertical Plane BC, and the Polar Plane IC ; fo as that the Angle of Reclination BCH is lefs than theDHiance of the Pole from the Zenith BCI : Defcribe two Vertical South and North Dials to an Elevation of the Equator, equal to the Diffe- rence between the Elevation ot the Equator or the given Place, and the Angle of Reclination.
z. If the Reclined Plane, as KG fall between the Polar Plane IC, and the Horizontal one CL j fo as that the An- gle of Reclination BCK is greater than the Diltance of the Pole from the Zenith ICB : Defcribe a Horizontal Dial thereon to the Elevation of the Pole, equal to the Diffe- rence between the Angle of 'Reclination ', and the Elevation of the Equator in the given Piace.
Inclining, and Reclining Dials, 'Trigono- metrically.
The Inclination, or Reclination of the Plane, and the Elevation of the Pole being known ; to find the Angles made in the Centre of an Inclining-, or Reclining Dial, by the Meridian, and Hour-Lines.
Such Dial is properly a Horizontal Dial, for a Latitude equal to the particular Elevation of the Pole on the Plane ot the Dial. Its Angles, therefore, are found by the Ana- logy laid down for Horizontal Dials.
'As to the Elevation of the Pole, on the Dial Plane, 'tis thus found : The Plane being inclined ; Either its Inclination is greater than the Elevation of the Pole of the Place 5 or lefs 5 or equal thereto. In the two firit. Cafes, for Upper South, or Lower North Dials, the particular Elevation of the Pole on the Plane, is had by taking the Difference between the Elevation of the Pole of the Place, and the Inclination of the Plane : And in the latter Cafe, the Dial is a 'Po- lar Dial, wherein the Hour-Lines will be parallel, by reafon the Plane being inclined on the Axis of the World, neither of the Poles can be reprcfented theteon.
For Upper North, and Lower South Dials : 1. If the Inclination be greater than the Elevation, the Comple- ment of the Inclination mull be added to the Complement of the Elevation. 2. If it be lefs, the Inclination mull be added- to the EJe/ation. 3- If it be equal, the Dial will be an I-'.quinotlial Dial, wherein the Angles at the Cen- tre will be equal to the Sun's Dilhnce from the Meridian,
Deinclined Dial's, are thofe which hoth decline, and incline, or recline. See Deinclined.
The Ufe of Inclined, Reclined, and efpecially Dein- clined Dials, is very rare : The Geometrical, and Trigo- nometrical Conitruction of thefe lalt, therefore, as being fomewhat intricate withal, we here chufe to omit, and re- fer fuch as may have a Fancy for fuch a Dial, to' an Uni- verfal Mechanical Method of drawing all Kinds of Dials here fubjoyn'd.
Aii eafy Method-, to defcribe a DiAtj onahyKhid
of 'Plane, by means of an Equinoctial Dial,
or Circle.
Suppofe, e.gr. A Dial rcquir'd on a Horizontal Plane - If the Plane be immoveable, as ABDC (Fig.iB.) find a Meridian Line GF ; Or if moveable, affume the Meri- dian at Pleafure. Then by means of the Triangle EKF whofe Bafe is applied on the Meridian Line raife°hc Equi- noctial Dial H, till fuch Time as the Index Gl becomes pa- rallel to the Axis of the World, (which is had, if the An- gle KEF be equal to the Elevation of the Pole) and the ra Clock Line on the Dial hang over the Meridian Line of the Plane, or the Bafe of the Triangle. If then in the Night- time a lighted Candle being fuccefli vely applied to Axis GI fo as the Shadow of the Index, or Style GI fall upon one Hour-Line after another } 'The fame Shadow will mark out the feveral Hour-Lines on the Plane ABCD.
Noting the Points, therefore, on the Shadow, draw Lines through them to G : Then an Index being fix'd in G, according to the Angle IGF, its Shadow will point out the feveral Hours by the Light of the Sun.
If a Dial were requir'd on a Vertical Plane $ having raifed the Equinoctial Circle, as above directed, pufh for- ward the Index GI, till the Tip thereof I, touch the Plane.
If the Plane be Inclined to the Horizon, the Elevation of the Pole mould be found on the fame j and the Angle of the Triangle KEF made equal thereto.
Note, Befide the feveral Species of Dials, abovemen- tion'd, which are faid to be with Centres, there are others, call'd Dials --without Centres.
Dials without Centres, are thofe whofe Hour-Lines dd really converge, but fo ilowly that the Centre they converge towards, cannot be exprefs'd on the given Plane.
Horizontal D 1 a ls without Centres are to be made for Places the Elevation of whofe Pole is very fmallj or very great.
Vertical Dials without Centres for Places the Eleva- tion of whofe Pole is very grear.
For the Furniture of Dials. See Furniture.
Ring-DiM,
KWg-JJlA-I,. ~\
Portable Dial. ( <
JPiiadrantalDi&L. C k KefleBinzDiAu 3
-Ring Dial. ) Ring Dial. )Horodiclic Quadrant, ^Reflecting Dial.
that which ihews the
efleBing i
Notlumal, or Night-DiAL Hours of the Night.
Of this there are two Kinds, Lunar, an&SideriaL
Afoon-DiAL, or Lunar Dial, is that which mews the? Hour of the Night, by means of the Light, or Shadow of the Moon projected, thereon from an Index. %p defcribe a Moon-DiK-L.
Suppofe, e.gr. A Horizontal Moon-Dial required: Draw firit a Horizontal Sun-Dial : Then erect two Perpendiculars AB, and CD, (Fig.19.) to the Line of 12 a Clock, and divi- ding the Interval GF into 12 equal Parts $ Through the feve- ral Points of Divifion draw Lines parallel thereto. Now, ap- propriating the firflLine CD to the Day of the New Moon and the fecond to the L>ay, when the Moon comes an Hour later to the Meridian than the Sun, their Interferons with the Hour-Lines will give Points, through "which to draw a Curve Line 12, 12, for the Meridian Line of the Moon. After the like manner determine the other Hour-Lines n, 22, 33, &c. which the Shadow of the Moon projected from the Style of the Dial interfects at the refpective Hours. Blot out the Hour-Lines of the Sun-Dial, together with the Perpendiculars, whereby the Lunar-Hours were drawn, and divide the Interval GF, by other Parallel Lines into 15 equal Parts, anfwering to the 15 Days between New and Full Moon. Laftly, to thefe Lines write the feveral Days of the Moon's Ages.
Now, the Moon's Age being learnt from a Calendar; the Imerfection of the Lines of the Moon's Age, with the Lunar Hour-Lines, will give the Hour of the Night.
After the fame manner may any other Sun-Dial be con- verted into a Moon-Dial.
Lo draw a Portable Moon-Dikr..
On a Plane that may be raifed according to the Eleva- tion of the Equator defcribe a Circle AB (Fig. 20.) and di- vide its Circumference into 29 equal Parts. From the fame Centre C defcribe another moveable Circle DE, which di- vide into 24 equal Parts, or Hours. In the Centre C erect an Index, as for an Equinoctial Dial,-
