Horlogiographia optica. Dialling universall and particular: speculative and practicall. In a threefold præcognita, viz. geometricall, philosophicall, and astronomicall: and a threefold practise, viz. arithmeticall, geometricall, and instrumentall. With diverse propositions of the use and benefit of shadows, serving to prick down the signes, declination, and azimuths, on sun-dials, and diverse other benefits. Illustrated by diverse opticall conceits, taken out of Augilonius, Kercherius, Clavius, and others. Lastly, topothesia, or, a feigned description of the court of art. Full of benefit for the making of dials, use of the globes, difference of meridians, and most propositions of astronomie. Together with many usefull instruments and dials in brasse, made by Walter Hayes, at the Crosse Daggers in More Fields. / Written by Silvanus Morgan.

CHAP III.

Shewing the making of a direct North Verticall Diall for an Oblique Sphear, as also a more easie way of drawing the South or Horizontall Planes.

THe North Diall is but the back side of the South Diall; and differeth little from it, but in naming of the houres, for account∣ing the sixth houre from the Meridian in the direct South verticall, to be the same in the direct North Verticall, and account∣ing the first houres on the East side of the South, on the West side of the North plane, and so vice versa, the first houres on the West side of the South, on the East side of the North plane, as by the figure appeareth.

And because the North Pole is elevated, the Style must point up toward it the visible Pole.

It must have but the first and last houres of the South plane, because the Sun never shines but at evening or morning on a North wall in an oblique Sphear, and but in Somer, because then the Sun hath North Declination, but in a right Sphear, it may shew all the houres as a South Di∣all, but for a season of the yeare.

But if you will make the Verticall plane or Horizontall in a long angled Parallelogram, you shall take the Secant of the elevation of the Pole, which is the same with AC in the fundamentall Diagram, and make that your Meridi∣an line, and shall take the Sine of the elevation of the Pole above the Meridian, which in a direct South or North is equall to the elevation of the Aequinoctiall, and in the Fun∣damentall

Diagram is the line DE, and prick it down from A and C at right angles with the line AC, and so inclose the long square BADBCD, it shall be the boūds of a direct North or South Diall; lastly, if from the fundamental di∣agram you prick down the several tangents of 15, 30 45, from Band D on the lines BB and DD, & the same distances from C toward B and D, & lastly if from the cen∣ter A, you draw lines to every one of those marks, they shall be the houre-lines of an erect direct South Diall.

[illustration]

To make an Horizontall Diall by the same projection you shall take the Secant of 38 deg. 30 min. the elevation of the Equator, which in the fundamentall Scheme is the line AF, for the Meridian, and the Sine of the elevation of the Pole, which in the fundamentall diagram is the same with DA, and

prick that down from the Meridian at right angles both wayes, as in the former planes, and so proceed as before from the six of clock houre and the Meridian, with the se∣verall Tangents of 15, 30, 45, you shall have constituted a Horizontall plane.

I have caused the pricked line that goes crosse, and the other pricked lines which are above the houre line of six, to be drawn only to save the making of a figure for the North direct Diall, which is presented to you if you turn the Book upside down, by this figure, contained between the figures of 4, 5, 6, the morning houres, and 6, 7, 8, the evening. And because the North pole is elevated a∣bove this plane 38 deg. 30 min. the Axis must be from the center according to that elevation, pointing upward as the South doth downward, so as A is the Zenith of the South, C must be in the North.

The Arithmeticall calculation is the same with the for∣mer, also a North plane may shew all the houres of the South by consideration of reflection: For by Opticall de∣monstration it is proved, that the angles of incidence is all one to that of reflection: if any be ignorant thereof, I pur∣posely remit to teach it, to whet the ingenious Reader in labouring to finde it.

The Figure of a direct East and West Diall for the Latitude of London, ▪51 deg. 30 min.

[illustration]

East Diall. West Diall.