Figure 1 and 2
by
Fer J. de Vries
Mac Oglesby
William S. Maddux
In recent issues of Compendium some vertical card dials based on the measurement of the altitude of the sun were described. In this article we describe two horizontal dials which are also based on the measurement of the sun's altitude.
These dials are examples of Islamic sundials and descriptions may be found in the book "Gnomonik der Araber," Karl Schoy, 1923. As Schoy mentions, such dials should have been in existence in the Middle Ages and the time system used is therefore antique, or unequal time, with the day between sunrise and sunset divided into 12 hours. Islamic prayer lines are also present on the dials. In addition, we will calculate these dials for local suntime. The names for these two types of horizontal dials, spelled as Schoy did, are HĀFIR and HALAZŪN.
HāfirIf a vertical gnomon is placed on a horizontal plane, the length of the gnomon's shadow is determined by the sun's altitude. When we have drawn a scale for the dates, the time is read after the dial, which remains horizontal, is rotated to place the gnomon's shadow along the proper date line.
For altitude sundials, the configurations of the dates may vary, but in the case of a HĀFIR the date scale is equiangular and divided into 12 segments of 30° each, for the signs of the zodiac. See Figure 1. Of course, this may be subdivided in degrees, but for clarity no subdivisions are shown. Also, the dates may be shown as months and days, but in older times the zodiacal signs were more common.
Figure 1 shows the pattern of a HĀFIR with antique hour lines for latitude 40° N. The hours are counted from outside to inside from 1 to 6, with 6 as the noon line, then outward from 6 to 11. Of course, lines for sunrise and sunset don't appear on this type of sundial.
Figure 1 and 2
Because between sunrise and sunset every antique hour line will always be present, all of the antique hour lines are closed curves. For local suntime this is different. At any latitude other than 0° fewer hour lines will be present in winter than in summer. Therefore, if we draw such a dial for local suntime for latitude 40° N, some hour lines are open, as shown in Figure 2. Since this is a more modern design, we wouldn't use the name HĀFIR for this dial.
Figure 3
Figure 3 shows the three most common Islamic prayer lines, called ZUHR, ASR-AWWAL and ASR-TĀNĪ, from inside to outside, drawn for the same latitude of 40° N. Normally, these prayer lines would be combined with the antique hour lines shown in Figure 1. We have separated the hour and prayer lines only for clarity. An explanation of the prayer lines is given below.
HalazūnInstead of a circular zodiacal calendar with 12 segments of 30° each, a circular calendar with segments of 60° is drawn, and each segment is used for two signs. This is possible because of the symmetry of the calendar. The resulting sundial is called a HALAZŪN. For latitude 40° N the patterns for antique hours, local suntime, and Islamic prayer lines are given in Figures 4, 5, and 6, respectively.
Figure 4 and 5
Figure 6
Since the figures in this article are calculated using a computer program, it is easy to design such dials for any latitude and to see how the patterns change with the latitude. The shape of the noonline is especially interesting between the tropics, for at such latitudes the sun can, on some dates, reach the maximum value of 90° and the sun is at the zenith. This means the noonline will cross the footpoint of the gnomon. Figure 7 shows the noonline of a HĀFIR for a latitude of 15° N. The shape of the noonline suggests an apple.
Figure 7
Qbasic programs HAFIR.BAS and HALAZUN.BAS, which can be downloaded from the start page, calculate these dials and print out their delineations. These programs draw directly onto the screen, but also save calculated points in a text file, xxxx.txt. With the conversion program, CNVXXXX.EXE, the text file can be converted into xxxx.rlt and also into xxxx.dxf files. These converted files may be used as input for Zonwvlak or a CAD program such as Deltacad.
Literature1) Die Geschichte der Zeitmessung und der Uhren, Band I, Lieferung F, GNOMONIK DER ARABER, Karl Schoy, 1923, pages 54 - 58.
2) Bulletin of De Zonnewijzerkring, nr. 3, 1994, Hāfir en Halazūn, Fer J. de Vries, pages 24 - 28
3) APPUNTI PER UNO STUDIO DELLE MERIDIANE ISLAMICHE, Gianni Ferrari and Nicola Severino, 1997, pages 68 - 70. ( Private publication ).
Islamic Prayer LinesThe most common Islamic prayer lines on sundials and astrolabes are zuhr, asr-awwal and asr-tānī, spelled as in the book of Karl Schoy. There are several definitions for these lines but most of the time the following are used.
Measure at noon on an horizontal plane the length of the shadow ( nsl ) of a vertical gnomon with length g. Add to the length of the noon shadow a factor n times g in which:
for zuhr, n = 0.25
for asr-awwal, n = 1
for asr-tānī, n = 2
Calculate the time that the length of the shadow on an horizontal plane of the same gnomon reaches the length nsl + n times g. This is the time for the appropriate prayer.
By repeating this process for many dates the prayer lines can be calculated and constructed. In the case of the horizontal hāfir and halazūn, the points of the prayer lines on each radial can easily be found for the distances of 0.25g, g, and 2g from the noonline.
EndnotesThe figures we have presented for the hāfir are cut off in a rectangle while the drawings for the halazūn are circular. This is a free choice but we think that for a real dial with antique time and prayer lines a circular shape will fit best. The center of such a circle can be the footpoint of the gnomon but this isn't necessary.
The shape of the halazūn resembles the shell of a snail. Schoy also writes that the word halazūn should mean snail.
At a latitude of 0° there is no difference between antique time and local suntime, so the calculation of one set will do for both the time systems.
We don't know of any historical sundials which would qualify as hāfir or halazūn. Perhaps one of our readers knows of such.
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