Gunter's Quadrant Applet

Edmund Gunter (1581-1626), a mathematician and astronomer, first described his quadrant, a simplified version of the Arabic astrolabe, in  the 1623 publication "De Sectore et Radio".  The quadrant presented here was produced by the eminent instrument maker Henry Sutton in 1657. It was used to tell the time of day and to simplify astronomical calculations for the Sun (altitude, azimuth, declination, right ascension, position of the Sun in the zodiac).
The instrument is equipped with a simple Sun sight on one edge. A weighted thread with a sliding bead is hanging from the apex.

See instructions for interactive use below

Quadratum Horarium Generale (Regiomontanus Dial)

Apian Dial

Capuchin Dial

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 lower left.

The interactive regions (light gray scales) are changing the cursor to cross hair.
declination
Click into the light gray part of the declination scale to set the bead (set the date first).

Click into the degree scale (light gray) on the limb to rotate the thread.

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,  inner part for winter and spring, or outer part for summer and autumn) to set the thread to the date.


- To set the bead to the declination then click within the region of the hour curves on the point where the thread crosses the 12 hours curve.

- Then click into the degree scale (light gray) to rotate the thread and the bead.
declination
                right ascension ecliptic longitude zdiac sunrise sunset
Read the angle, and the date within the shadow square. The values (for 0 UT) of the declination, the ecliptic longitude (and position in the zodiac), the right ascension, and the times of rise and set (local apparent time) are computed and shown within the shadow square.
display
                options menu
Select from the "Display Options" menu.


table
Setting a date will enable the button "Table", which opens a list of the Local Apparent Time, the Standard Time, the altitude of the Sun, and the azimuth angle (East of North, and West of South).

Thanks to James E. Morrison (Janus) for the instructions making the Quadrant.

The zodiac and the ecliptic longitude:

aries
taurus tau
gemini gem
cancer can
Leo
virgo vir
Libra Lib Scoorpio sco
sagittarius sag
capricorn cap
Aquarius Aqu
Pisces Pis
Aries Taurus Gemini Cancer Leo Virgo Libra Scorpio Sagittarius Capricornus Aquarius Pisces
0° - 30°
30° - 60° 60° - 90° 90° - 120° 120° - 150° 150° - 180° 180° - 210° 210° - 240° 240° - 270° 270° -
300°
300° - 330° 330° - 360°

The zodiac symbols are from the MarVoSym font, used by the applet.

J2000
RA Declin. mag
Arcturus Arcturus
213.92° 19.18° -0.05
Aldebaran Aldebaran
69.98° 16.56° +0.853


Examples for use of the digital Gunter Quadrant on 2009, Aug. 10

More Sample Problems in the PDF of James E. Morrison
1. Find the declination of the Sun:

Set the date and the thread by clicking into the outer date scale.
Click on the intersection point of the 12 Hours line and the thread to set the
bead.









Turn the thread to the declination scale by clicking at lower left end of
degree scale, and read the declination at the bead: 15.7°
(computed: 10.58°)



declination

declination of the sun
2. Find the altitude of the Sun at local noon:

Set the date by clicking into the outer date scale.
Read the altitude on the degree scale (limb): 54.0°
(computed: 53.9°)
sun altitude
3. Find the ecliptic longitude (position in the zodiac) of the Sun:

Set the date and the thread by clicking into the outer date scale.
Click on the intersection point of the 12 Hours line and the thread, setting the bead.
Turn the bead to the Ecliptic scale by clicking into the degree scale, and read the longitude angle: 137.0°, Leo 17°
(computed: 137.5°, Leo 17.5°)

ecliptic
                longitude zodiac position sector
4. Find the Right Ascension of the Sun:

Set the thread to the longitude of the sun on the ecliptic (see ex. 3, 137°).
Read the angle on the degree scale (limb): 40.5°
The Right Ascension is 180°-40.5°= 139.5°
(computed: 140.0°)

ecliptic
                longitude zodiac position sector
5. Find the time of sunrise:

Set the thread to the date. Click on the intersection point of the 12 Hours line and the thread to set the bead. Rotate the bead to the horizon line, and read the angle on the degee scale (limb): 20.6°
This angle corresponds to 4*20.6 min = 82.4 min. Subtract (as the date is in summer) this time from 6:00 hours to get 4:38
(computed: 4:32)
sunrise
                sunset
6.1 Find the altitude at 3 PM:

Set the thread to the date. Click on the intersection point of the 12 Hours line and the thread to set the bead. Rotate the bead to 3 Hours line, and read the altitude angle on the degee scale (limb): 39.4°
(computed: 39.2°)
altitude
                elevation Sun
6.2 Find the azimuth at 3 PM:




Now turn the thread to the co-altitude 90°-39.4°=50.6°, and read the azimuth angle from the azimuth curves using the bead between the 60° and 70° curve: 62° (North of South).

(computed: 61.6°)
azimuth

My prototype of Gunter's quadrant, set to Aug.10:

Gunter Quadrant


Under construction!

Books
Morrison, James E.: The Astrolabe, Janus. Softcover edition, 2007,
Rehobot Beach, DE USA,
ISBN-10: 0939320304, ISBN-13: 978-0939320301.
Details...

D'Hollander, Raymond: L'Astrolabe. Histoire, theorie et pratique. Institut océanographique, Paris, 1999. ISBN 2-903581-19-3.

Hügin, Johannes: Das Astrolabium und die Uhr, Ulm, 1978,
ISBN 3-921348-23-4.

Stautz, Burkhard: Die Astrolabiensammlung des Deutschen Museums und des Bayerischen Nationalmuseums, Oldenbourg, München 1999.

Rohr, Ren
é R. J.: Die Sonnenuhr. Geschichte, Theorie, Funktion.
Callwey, München 1982.

Meyer, Jörg: Die Sonnenuhr und ihre Theorie.
Harry Deutsch, Frankfurt 2008.

Web Links

The Astrolabe (James E. Morrison)

Gunter's Quadrant (J. E. Morrison, PDF)

Edmund Gunter biography (MacTutor History of Mathematics archive)

Gunter's quadrant (Navigation Museum)

Gunter quadrant (The Whipple Museum)

A Gunter quadrant and practical knowledge (The Whipple Museum)

Gunter quadrant (National Maritime Museum)

The Electric Astrolabe (J. E. Morrison)
executable file and documentation

Astrolabium (Deutsches Museum)

Der Gunter-Quadrant (Gunter W.)

Das Astrolab (Informatik Uni Erlangen)

Keith's Asterolabe (Java applet)

Literature on astrolabes (M. Brunold)

R. Doerfler: The Analemmas of Vitruvius and Ptolemy (PDF)

J. G. Freeman: A Latitude-Independent Sundial (PDF)

F. A. Stebbins: A Mediaeval Portable Sundial (PDF)



© 2009-2013 J. Giesen

Last modified: 2013, Jun 10