DIA
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DIA
»ferting the Line GH, in the Point a BC A H. From E upon the right Line EG fet off the Intervals E a, Eb, iSc. fe E a from E to e, E b from E to f, E c from E to g, iSc. From the Centre A defcribe a little Circle, and applying a little Ruler to A, and the feveral Points ofDivifion a, b,c,d, H and e, f, a h G draw the Lines A 1 1, A 10, A 9, A 8, A 7, and Si, As, A3, A 4, A 5- Through A draw i. right Line 6,6 perpendicular to AB. Continue the tight Line A 7, beyond the little Circle to 7, A 8 to 8, A 5 to"? and A 4 to 4. Round the whole Scheme draw a Square, Circle, crOval Figure. And laflly in A fix an In- dex making an Angle DAC with the Meridian AB equal to the Elevation of the Pole : Or in C ereft a perpendicu- lar Style equal to CD; or at AE fix a Triangular Plate APE perpendicular to the Plane of the Dial.
Now, the Lines A 11, A 10, A 9, iSc. are the Hour- Lines of the Fore-noon; and A i, A2, A ;, (Sc. thofe of the After-noon : and the Shadow of any of the Gnomon's, or Styles above mention'd, at the feveral Hours, will fall on the refpeftivc Hour-Lines.
A Horizontal Dial, Trigonometricalty.
In large Dials, where the utmoft Accuracy is required, Geometrical Lines are bell fet a-fide ; and in lieu thereof, the Lines of the DM to be determin'd by Trigonometrical Calculation. Monfr. Clafies, in the Meraoires de I'Atade- KiihRoyste des Sciences, An. 1707, has done us good Service herein ; having render'd the Calculation of the Hour-Lines, which before had been operofe enough, exceeding eafy and expeditious : His Canons, or Analogies we fhall lay down under the refpeflive Kinds of Dials.
A r.d, firft, For a Horizontal, Dial ; The Elevation of the Pole of the Place being given, to find the Angles, which the Hour-Lines make with" the Meridian, in the Centre of the Dial.
Analogy, or Canon.
As the whole Sine is to the Sine of the Elevation of the Pole of the Place; fo is the Tangent of the Sun's Diftance from the Meridian, for the Hour required ; to the Tan- went of the Angle requir'd. That is, As the Side FC '(F/g.7.) is to DC : So is the Tangent of FDC ; to the Tangent FC of the Angle FAC. See Tangent, tSc.
Vertical Dim., is that drawn on the Plane of a Vertical Circle. See Vertical.
Of thefe there are feveral Varieties, according to the Ver- tical pitcht upon. The Verticals chiefly ufed are the Prime Vertical, and' the Meridian ; from which refpeflively arife South, North, Eajt, and Weft Dials.
Dials, which refpecf the Cardinal Points of the Ho- rizon, are particularly call'd DireB Dials. See Direct.
If any other Vertical be chofe, the Dial is faid to De- cline. See Decline?..
Further, If the Circle, whofe Plane is ufed, be perpendi- cular to the Horizon, as is fuppofed to be the Cafe in all thofe now mention'd, the Dials are particular denominated EreB. E. gr. Erea South ; DireB North, &c. See Ep.ect, ££c.
Otherwifc, the Plane being oblique to the Florizon, they are faid either to Incline, or Recline. See Incliner, Recliner, &c.
South Dial, or more particular an EreB DireS South Dial, is that defcribed on the Surface of the Prime Vertical Circle, looking to the South. See South.
Since .the Sun then 'illumines the Plane of the Prime Ver- tical, looking to the South, when, in its Progrefs he paffes from the Prime Vertical to the Meridian, or returns back from this to that ; in which he is employ'd fix Hours before, and fix after Noon ; A South Dial ihews the Hours from fix in the Morning to fix at Night.
To draw a Vertical South Dial. On the Plane of the Prime Vertical looking Southwards, draw a Meridian Line AB (F/g.8.) and taking the Inter- val AC at Pleafure for the Magnitude of the future Dial ; In C erect a Perpendicular of an indefinite Length CD, and making an Angle CAD equal to thcElevation of theEqua- tor, draw a right Line AD meeting the Perpendicular CD in D. Then in the Point D make the Angle CDE like- wife equal to the Elevation of the Equator, and draw the right Line DE cutting theMeridian in E. Through E draw the right Line GH, cutting the Meridian AB at right An- gles. Take EB equal to ED, and with this Radius de- scribe a Quadrant j*f. The reft is perform'd as in a Hori- Kontal Dial ; except that the Hours of the After-noon are to be wrote on the right Hand, and thofe of the Fore- noon on the left, as in the Figure. Laflly, in the Point A fo an oblique Style in an Angle equal to the Elevation of the Equator : Or in C erefl: a perpendicular Style equal to CD : Or, laflly, a Triangular Plate ADE uponAE, fo as to be perpendicular to the Plane of the Dial.
Then will the Shadow of any of the'e Indexes touch the feveral Hour-Lines at their refpeflive Hours,
North DrAt, or EreB DireB North Dial, is that de-- fcribed on the Surface of the Prime Vertical, looking North- ward. See North.
Since the Sun only illumines this Surface, while he ad- vances from the Eaft to the Prime Vertical, and proceeds from the fame Vertical to the Weft ; and fince he is in the Prime Vertical at fix a-Clock in the Morning, and fix in the Evening ; a North Dial fhews the Hours before fix in the Morning, and thofe after fix in the Evening. And hence, as in Autumn, and Winter Time, the Sun does not rife before fix, and yet fets before fix in the Evening ; a North Dial is of no Ufe all that Time. But being joyn'd with a South Dial, it fupplies theDefefls thereof. To defcribe a Vertical North Di al.
Draw a Meridian Line EB (Fig.'j.) and from A de- fcribe a little Circle at Pleafure. At A make the Angle DAC equal to the Elevation of the Equator, and from the. Point C taken at Pleafure, erect a Perpendicular CD meet- ing AD in D. Make another Angle CDE likewife equal to the Elevation of the Equator, and draw likewife a Line DE meeting AE in E. Then take IB equal to ED. And through 1 draw GH, cutting SB at right Angles. And from the Centre B with the Radius IB defcribe a Quadrant ; which divide into fix equal Parts. Through the two ex- tream Divifions draw Lines from the Centre B, viz. B d, and BH, meeting GH in little d, and H, and make I h equal to I d, and IG equal to IH. Then applying a Ruler to A and d, and H ; and again to A and h, and G, draw the right Lines A 5, A 4, A 7, and A 8. Laflly, in A fix an oblique Index AD, making an Anglo DAE with the Meridian Line in the Plane of the Meridian, equal to the Elevation of the Equator : Or a perpendicular Index in C equal to CD : Or, inftead of an Index, a Triangular Plate EDA on the Meridian Line EA, perpendicular to the Plane of the Dial.
Then will A 4, A 5, A 6, be the Hours of the Fore-noon ; and A 6, A 7, A 8, thofe of the After-noon ; and accord- ingly will be pointed out by the Shadow of the feveral In- dexes.
Or thus: In & South Dial (Fig. 10.) If the Hour-Lines 4 and 5, as alfo 7 and 8, be continued beyond the Line 6 A 6 5 and the Triangle ADE turned about its Pole A till AE fall directly again! A 12 ; it is evident, a North Dial is here- by had : only obferving what has been faid about writing the Hours.
AVertkalNorth, or»fl&Dr*t Trigonometrically.
Thefe only differ ftom the Horizontal Dial, in that the Anple CAB is equal to the Complement of the Elevation of the Pole of the Place ; fo that the fame Analogy ferves as for the Horizontal one : Only making the fecond Term the Complement of the Elevation of the Pole of the Place.
Eaft Dial, or EreB DireB EafrDikr., is that drawn on the Plane of theMeridian, looking to the Eaft. See East.
Since the Sun only illumines the Plane of the Meridian, looking Eaftward before Noon ; an Eaft Dial can only fhew the Hours till Noon.
To defcribe an EaftDikz.
On the Eaftern Side of the Plane of the Meridian draur a right Line AB (Fig.li.) parallel to the Horizon, and to this joyn AK, making with it an Angle KAB, equal to the Elevation of the Equator. Then with the Radius DE de- fcribe a Circle, and through the Centre D draw AC per- pendicular to AK ; by which means the Circle will be di- vided into 4 Quadrants. Each of thefe Quadrants fub- divide into fix equal Parts. And from the Centre D thro' the feveral Divifions draw right Lines, D 4, D 5, D 6, D 7, D 8, D 9, D 10, D 11. Laflly, in D erea a Style equal to the Radius DE, perpendicular to the Plane; or, on two little Pieces perpendicular fix'd in EC, and equal to the fame Radius DE, fit an Iron Rod parallel to AC.
Thus will each Index at the feveral Hours projea a Shadow to the refpeftive Hour-Lines 4,4 5,5 6,6 Vc.
Weft Dial, or EreB DireB Weft-Dikr., is that de- fcribed on the Weftern Side of the Meridian. See West.
As the Sun only illumines that Side of the Plane of the Meridian, looking to the Weft after Noon, a Weft-Dial can only fhew the Hours from Noon to Night.
This, therefore, joyn'd with an Eajl-Dial fhews all Hours of the Day.
To draw a Weft Dial.
The Conftruaion is perfeBly the fame as that : of an^ Eaft Dial : Only that its Situation is inverted, and the Hours wrote accordingly. „, , .
VolarDiAL, is that defcribed on a Plane paffing through the Poles of the World, and the Eaft, and Weft Points of the Horizon. It is of two Kinds : The firft, looking up to- wards the Zenith, and call'd V&er 5 the latter down to the Nadir, call'd Lower. ..,.,, , „
The 'Polar Dial, therefore, is inclin d to the Horizon in an Angle equal to the Elevation of the Pole.
