Apian Card Dial

Uhrentäfelchen

Single latitude version

 This instrument is a portable sundial for all latitudes, developed by Peter Apian (Petrus Apianus, 1495-1552). 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).

Details for interactive use:

 Enter the year into text field and hit "Apply input". (Gregorian Calendar only, later than 1582) Enter the latitude (decimal degrees) into the text field and hit "Apply input". 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 date and latitude scale to set the thread. - To bead is set to the latitude automatically (scale at right, continuing the declination scale). The checkbox "Fix Lat." is an option to keep the latitude when clicking into the date/latitude scale. 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.

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. Web Links Petrus Apian: Instrument-Buch (1533, SLUB, digital images)