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Babylonian Hours, Italian Hours, and Unequal Hours Sundial Applet

 Enter latitude in decimal degrees (southern negative), enter longitude in decimal degrees (western negative), then hit the button "Apply input". Key commands: you may use the keys "h", "d", "m" to increase the hour, date, or month, or Shift key and "h", "d", "m" to decrease the hour, date, or month ! Click the applet first !

The gnomon (length L) of this sundial is vertical. The shadow of it's top on the horizontal plane indicates the babylonian hour (and the standard time).

Sundials usually show hours starting at midnight. When the Sun culminates (local noon), these dials show 12 p.m.

The Babylonian system divides the day into 24 equally long hours beginning at sunrise and ending with the following sunrise.
Italian hours begin counting at sunset and ends 24 hours later with the following sunset.

The option "Italian Hours 24..0" is counting the hours til sunset.

An unequal (seasonal) hour is ne twelfth of the time from sunrise to sunset. As a consequence, hours on summer days are longer than on winter days

In this applet the times of sunrise and sunset are for 0°
altitude (discarding atmospheric refraction) instead of -0.83°. For low and mid latitudes the difference is only a few minutes.
sin h = sin(lat) sin(dec) + cos(lat) cos(dec) cos(H)
Setting the altitude h=0:
H = arc cos[-tan(lat) tan(dec)]

The (horizontal) declination lines are drawn for 0° (black), +/- 4°,
+/- 8°, +/- 12°, +/- 16°, +/- 20° (gray), and +/- 23.44° (red/blue).

Click into the applet area to shift the drawing up or down, and use the "Details" options for scaling.

Example:
Berlin (52.52°N, 13.41°E), on Jan 18 at 10:44 Standard Time, which is 2:30 hours after sunrise (8:14), declination -20.5°.

 Declination (°) Dates -23.44 Dec 21 -20 Nov 21, Jan 20 -16 Nov 06, Feb 05 -12 Oct 25, Feb 17 -8 Oct 13, Feb 28 -4 Oct 03, Mar 10 0 Sep 23, Mar 21 4 Sep 12, Mar 30 8 Sep 02, Apr 10 12 Aug 21, Apr 21 16 Aug 08, May 04 20 Jul 23, May 20 23.44 Jun 21

Sunset dial (Italien hours) in a CD box:
Mar 27 at 10:20 CET, about 8.5 hours before sunset.

Select "Zodiac Signs" from the "Details" menu:

Planetary (Unequal) Hours Clock

More of my sundial applets ...

Santuari de Lluc (Majorca),
2011 Sep 08, 14:08 CEST

The Traditional Roman Breviary:
(Benedict of Nursia, c.480–547)

 1. Matutinum Midnight (Matins, Vigils, Nocturns) 2. Laudes Dawn Prayer (Lauds), 3 a.m. 3. Prima Early Morning Prayer (Prime), 6 a.m. 4. Tertia Midmorning Prayer (Terce), 9 a.m. 5. Sexta Midday Prayer (Sext), Noon 6. Nona Midafternoon Prayer (None), 3 p.m. 7. Vesperae Evening Prayer (Vespers), 6 p.m. 8. Completae Night Prayer (Compline), 9 p.m.

Santuari de Lluc (Majorca), 39.823° N, 2.884° E,
on 2011 Sep 08 at 14:07 CEST

 Sundial: the Babylonian Hour is 6:40 Applet: the Babylonian Hour is 6:40

The sundial date is September 6 (instead of Sep 8)

true solar time 12:29

mean local time = true solar time (local apparent time) + 4*(15-
λ)m - EoT
EoT=2m 13s, longitude λ =2.884° E

mean local time (CEST) = 12:29 + 4*(15.0-2.884)m - 2.2m + 1h =
12:29 + 48.5m - 2.2m + 1h = 14:15 CEST

my clock was 14:08 CEST

 Books Savoie, Denis: La Gnomonique, Les Belles Lettres, Paris 2007 Web Links

Updated: 2013, Jul 28

© 2010-2013 J. Giesen