Dialling, plain, concave, convex, projective, reflective, refractive. Shewing, how to make all such dials, and to adorn them with all useful furniture relating to the course of the sun; performed arithmetically, geometrically, instrumentally and mechanically: and illustrated with sculptures, engraven in copper, comprised in XIV distinct tractates... / [William Leybourn].

William Leybourn

Date:: 1700

Credit: Dialling, plain, concave, convex, projective, reflective, refractive. Shewing, how to make all such dials, and to adorn them with all useful furniture relating to the course of the sun; performed arithmetically, geometrically, instrumentally and mechanically: and illustrated with sculptures, engraven in copper, comprised in XIV distinct tractates... / [William Leybourn]. Source: Wellcome Collection.

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$3. Upon all Dii'e^l EaH or Weft Plains^ Reclmwg (how far foever) the 'North Pole is Elevated; and upon the Eaft and Weft hclimrs, oppofite to them, the South Pole, 4. Over all North Reclining Plains^ (whether Direct or Declining) the North Pole is Elevated; and over the Inclining Plains^ oppofite to them, the South Pole, Laftly, Over all South Reclining Plains, wliether Direa or Declining [If the plain pafs between the Zenith and the Pole] the Axis of th^Stue mufl: have refpefl to the South Pole; and on the Inclining Plains, oppo¬ fite to them, th& North Pole,--But, [If the Plain pafs between the Ho¬ rizon and the Pole] the North Pole ; and on the Incliners oppofite to them, the South Pole, Figure I. F CHAP. IX. To Bravo the Hour Lines u^on a Vertical {commonly called Horizontal) Plain. _ • 1. From the Projeftion. llrfi:, Draw a right Line NS, for the Meridian, and Hour-Line of 12, and crofs it with another E W, for the Hour-Line of Six, at right Angles in Z; And upon Z, as a Center defcribe a Circle E N W S, reprefenting tht Horiz,on of London, ivhofe Latitude is 51 d.- 32 m. and alfo this Dial-Plain, Within this Circle Project the Sphere according to your Latitude, as is before taught, then fhall the feveral Hour-Circles touching the Plain of the Horizon, give you Points to draw the Hour-Lines upon your Dial-Plain by: So that a Ruler laid to Z, and every of the Points i, 2,3, &c, 11. 10. 9, &c. Where thtHour Circles touch the Horizon, if you draW ftraight Lines thereby, they fhall be the true Hour-Lines for your Vertical (or Horizontal) Dial, For the making of an Horizontal Dial, there is nothing required to be known, but the Latitude of the Place, equal to which mufi: the height of the Stile be; wherefore take 51 deg. 3 2 min. out of your Scale of Chords, and fet them upon the Horizon from S to A, and draw a Line Z A for the Stile, The Subfile (upon which t\it^Stile ftandeth) in all Horizontal Dials is the Meridian or Hour Line of 12 ; and fo is the Dial finifhed. II. By Trigonometrical Calculation, There is nothing required to be found in this Dial by Calculation, ex¬ cepting the Hour-Diftances from the Meridian-, for which this is the Proportion. - • • As the Sine of 90 deo-. Is to the Sine of the Latitude. SoistheT^gent of each Hour’s Equinoftial Diftance from the Merid. To the Tangent of that Hour’s Diftance upon the Plain. Where$

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