Apian Card Dial

Uhrentäfelchen

All latitudes version

This instrument is a portable sundial for a single latitude, 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).

See instructions for interactive use below

Quadratum Horarium Generale (Regiomontan Dial)

Capuchin Dial (single latitude)

Gunter's quadrant

Visit my Applet Collection


Details for interactive use:

year
Enter the year into text field and hit "Apply input".
(Gregorian Calendar only, later than 1582)
latitude

latitude
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.
elevation angle
                altitude Sun
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.
date scale

- Click into the light gray date scale to set the thread.


The checkbox "Fix Lat." is an option to keep the latitude when clicking into the date/latitude scale.
declination
                sunrise sunset
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

Regiomontanus, Apian and Capuchin Sundials

Time system conversion


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

Das Allgemeine Uhrentäfelchen von Regiomontan

Tragbare Sonnenuhren in Europa ab 1400

Uhrentäfelchen von P. Aegid Everard

Pourquoi le cadran de Regiompntanus fonctionne-t-il ?

Horoscopion Apiani Generale Dignoscendis Horis cuiuscumque generis aptissimum

Peter Apian (Wikipedia, de)

Petrus Apianus (Wikipedia, en)

Petrus Apianus (Mac Tutor)

© 2009-2013 J. Giesen

Last modified: 2010, Aug 01