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Equinoctial makes with the Horizontal-line: because in [[strikethrough]] this [[/strikethrough]] erect Dials declining from the South these [[strikethrough]]Tow[[/strikethrough]] Two are perpendicular to one another, since the represent Circles which are perpendicular to one another; and One of those Circles is perpendicular to the Plane of the Dial, [[underline]] viz [[/underline]] the Meridian of the Plane.
4. To find the Angle which the Six a Clock makes with the Meridian, or Arch ZL. In the Right Angled [[strikethrough]] Triangle [[/strikethrough]] Spherical Triangle NPLZ, Rectangular at NP say
As. Rad.: Cos. < LZNP (or S. of Plane's Declin^n) :: [[strikethrough]] Tang^t [[/strikethrough]] Cot. ZNP (or t. of the height of the Pole) : Cot. of ZL, the arch, required.
5. To find the Angles of other Hour-lines with the Meridian or Substylar.
Suppose it were required to find the angle of 10 a Clock-line with the Substylar; let the 10 o'clock-circle be NPRS, then will the Horary-distance or Spherical-angle ZNPR be 30. [[degree symbol]], which subtract from the Angle ZNPI, the Plane's difference of Longitude, there will remain INPR, and in the Spherical Triangle RNPI, Rectangular at I, there may be found the Side RI, the Angle which the 10 a clock-line makes with the Substylar by this proportion
As rad.: Tang.^t RNPI::S. INP (before found): Tang.^t RI, the Angular distance of the 10 a clock-line from the Substylar, required.

Ozinam's Course of Mathm.^s upon Gnomonics. Vol. 5. p.93.

This last proportion for obtaining the Hour-lines from the Substylar, being the very same as for an Horizontal Dial in the Place I, the Complement of whose Latitude is NPI and difference of Longitude ZNPI. therefore every Erect (at least) Decliner may be Geometrically constructed, like an Horizontal one, (shewn & demonstrated on the page facing the [[?5A or 54]] of My M.S. of Spherical Trigonometry) by reckoning each hour circle's or ^the Time's distance [[strikethrough]] forom [[/strikethrough]] from the Meridian of the Plane SKNP, upon the Equinoctial AEQ, instead of the Time from Noon, in the said M.S. that is, in short, Every Erect Dial [[strike through]] is an [[/strike through]] in any [[strike through]] Horizontal one [[/strike through]] Latitude, whether Direct or Declining, is an Horizontal one in the place I, And therefore may be calculated or constructed as such. ___ The Principles of Dialling are very well laid down in Gregory's Astronomy Vol. I. Book 2. [[section symbol]] 6. Prop^s 42, 43,& 44. p. 331, to 336. He also has a method of making an Horizontal Dial. Book 2. Prop. 15. p. 274. 
If a dial be made according to the strict rules of calculation, and truly set at the instant when the sun is on the meridian; it will be a minute too fast in the [[strike through]] after [[/strike through]] ^[[fore]]noon, and a minute too slow in the afternoon, by the shadow of the style; for the edge of the shadow that shews the time is even with the sun's foremost edge all the time before noon, and even with his hindmost edge all the afternoon, on the dial. But it is the sun's center that determines the time in the (supposed) hour circles of the heavens. And as the sun is half a degree in breadth, he takes two minutes to move through a space equal to his breadth; so that there will be two minutes at noon in which the shadow will have no motion at all on the dial. Consequently, if the dial be set true by the sun in the forenoon, it will be two minutes too slow in the afternoon; and if it be set true in the Afternoon, it will be two minutes too fast in the forenoon. The only way that I know of to remedy this, is to set every hour and Minute division on the dial one minute nearer XII. than the calculation makes it to be. Gents. Mag. for May 1767 & that from Ferguson's Tables & Tracts, &c.