Quadratum Horarium Generale (Regiomontanus Dial)
Uhrentäfelchen
| This
instrument
is a portable sundial for all latitudes, developed by Regiomontanus
(1436-1476). It also indicates the time of
sunrise and sunset. It is equipped with a simple Sun sight on the upper edge. A thread with a sliding bead is hanging from the point of suspension (at the end of a brachiolus) which is adjustable in two dimensions (declination, latitude). |
See
instructions for interactive use below
Capuchin Dial (single
latitude)
 |
Enter the year into text field and hit Return key. (Gregorian Calendar only, later than 1582) |
  |
Enter the latitude (decimal degrees) into the
text field and hit Return key. The latitude is indicated in the text field. |
 |
The interactive
regions (light gray scales) are changing the cursor to cross hair. |
 |
Click into the
degree scale (light gray) on the lower and left limb to direct the
quadrant to the Sun. The thread will follow the elevation angle. |
 |
Use the
"Today"
button to set the thread to the current date. The bead is set to the
current Sun's declination. |
 |
- Click into
the light gray
calendar (date scale, upper part for
winter and spring, or lower
part for summer and autumn) to set the thread to the date. - To bead is set to the declination (by the declination scale at right) automatically. |
 |
Read the date,
the declination, and the time of sunrise and sunset (neglecting
refraction on the horizon), the equation of time, the current time, and
elevation as computed by
astronomical algorithms. |
| Select from the
"Display Options" menu. |
|
| The red frame
of the applet area is a square (753 x 753 pix, same size as for
Gunter's quadrant). |
|
| The dial is
obeying the equation of the nautic spherical triangle (h = elevation
angle, φ = latitude,
AH = hour angle):
sin h = sin φ
sin δ + cos φ cos δ cos AH
A very short proof can be found in the book of Rohr.The formula is symmetric with respect to φ and δ, thus the dials of Regiomontanus and Apian are equivalent. A very short proof (by E. Guyot) can be found in the book of Rohr:  φ = Latitude, h = Altitude, δ = Declination, τ = Local Hour Angle The thread is suspended at P and the bead is set to R. The radius r = MO = OS = 1 is set to unity. OQ = tan φ SR = tan δ PQ = tan φ tan δ The angles POQ and ROS are equal to the declination δ. The triangle ∆POR is rectangular: PR2 = OR2 + OP2 = OS2 + SR2 + OQ2 + PQ2 = 1 + tan2 δ + tan2 φ + tan2 φ tan2 δ PR2 = (1 + tan2 φ) (1 + tan2 δ) = 1 / (cos2 φ cos2 δ) PR = 1 / (cos φ cos δ) Directing the dial to the Sun the bead is at C and the altitude angle is h. The hour angle is τ and BC = sin (90°-τ) = cos τ AC = PR sin h = sin h / (cos φ cos δ) = AB + BC = tan φ tan δ + cos τ sin h / (cos φ cos δ) = tan φ tan δ + cos τ sin h = sin φ sin δ + cos φ cos δ cos τ
|
Under
construction!
| Books |
| Rohr, René R. J.: Die
Sonnenuhr. Geschichte, Theorie, Funktion. Callwey, München 1982. Meyer, Jörg: Die Sonnenuhr und ihre Theorie. Harry Deutsch, Frankfurt 2008. |
|
|
|
Regiomontanus,
Apian and Capuchin Sundials Das
Allgemeine
Uhrentäfelchen
von
Regiomontan Tragbare
Sonnenuhren in Europa ab 1400 (PDF) Uhrentäfelchen von P. Aegid Everard Pourquoi le
cadran de Regiompntanus fonctionne-t-il ? Horoscopion
Apiani Generale Dignoscendis Horis cuiuscumque generis aptissimum Quadratum
Horarium Generale Georgius Hartman |
©
2009 J. Giesen
