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 XIV.

Shewing the drawing of the Seeling Diall.

IT is an Axiom pronounced long since, by those who have writ of Opticall conceipts of Light and Shadow, that Omnis reflectio Luminis est secundum li∣neas sensibiles, latitudinem habentes. And it hath with as great reason bin pro∣nounced by Geometricians, that the Angles of Inci∣dence and Reflection is all one; as appeareth to us by Euclides Catoptriques; and on this foundation is this conceipt of which we are now speaking.

Wherefore because the direct beams cannot fall on the face of this plane, we must by help of a piece of glasse apt to receive and reflect the light, placed somwhere horizon∣tally in a window, proceed to the work, which indeed is no other then a Horizontall Diall reversed, to which required a Meridian line, which you must endeavour to draw and finde according as you are before taught, or by the helpe of the Meridian altitude of the Sun, your glasse being fixed marke the spot that reflects upon the seeling just at 12 a clock, make that one point, and for the other point through which you must draw your meridian line, you may finde by holding up a threed and plummet till the plummet fall perpendicular on the glasse, and at the other end of the line held on the seeling make another mark, through both which draw the Meridian line. Now for so much as the center of the Diall is a point without, and the distance be∣tween the glasse and the seeling is to be considered as the height of the style, the glasse it selfe representing the cen∣ter of the world, or the very apex of the style, wee must finde out those two Tangents at right angles with the Me∣ridian, the one neere the window, the other farther in, through severall points whereof we must draw the houre∣lines. Let AB be the Meridian line found on the seeling, now suppose the Sun being in the highest degree of Cancer should shine into the Glasse that is fixed in C, it shall again reflect unto D, where I make a mark, then letting a plum∣met fall from the top of the seeling till it fall just on C the glasse, from the point E, from which draw the line A B through D and E, which shall be the Meridian required, if you do this just at noon: Now if you would finde out the places where the hour-lines shall crosse the Meridian, the Center lying without the window EC, you may work thus

Divide the line EC into 12 parts, then may you en∣ter the Table of right & versed shadow, seeking the degrees and minutes of Elevation of the Equator, viz. 38 deg. 30′, to which answereth 15 parts 5 minutes of the parts of the Style, which prick down from E to F, and at that point draw the line FG, at right angles to the Meridian A

[illustration]

B, which shall represent the Equator. Now to know the center of the hour-lines, if you look again in the Table of shadows 51 deg. 30 min. the elevation of the Pole, you shall finde 9 parts 33 min. of shadow, which added to FE, 15 parts 5 m. shall give the center at B, making the whole line from F to B to be 24 parts 38 primes, and at 6 shall the center of the hour-lines meet. Lastly, supposing the former work to be done upon the floare, for the more ea∣sie working, and having drawn a line representing the Me∣ridian AB if from B you prick down 9 parts 33 min. of the radius EC, and at E draw it perpendicular to AB, & 15 parts 5 min. from E to F, where if you draw the line FG perpendicular to AB, also, if from the Center B you shall

proceed to make a horizontal Dial as is above taught: it shall divide the lines EC and FG in such parts by draw∣ing the hour-lines from the Center through those lines, which if they are transferred from thence to the seeling on each side the Meridian, upon the same line EC and FG, you have finished, for FB shal be the same as in the funda∣mental Diagram I call the Semidiameter of the Horizon; and FC shal be the semidiameter of the Equator: by the same meanes also may be made hour-lines, on a Wall re∣ceiving it's light only through some hole in a glasse win∣dow: as also very recreative Dials on the sides of Build∣ings, having water or glasse so placed, as that it may reflect the Beames according to several Azimuths: but the best way for the placing the glasse is, by preparing the hour∣lines first, and by a known altitude of the Sun at some known houre of the day, to mark out on that hour-line where the reflection ought to fal, and expect that houre precisely, and depresse or elevate the glasse til it fal on that spot or mark assigned.