Time and Time Intervals 4111 Sundials

We have already mentioned the gnomon, essentially a rod, the permanent placement of which permits calibration of its shadow direction to time of day. A gnomon placed perpendicular in level ground must have constituted the first sundial, and there is indeed a very early "shadow-clock" from Egypt, which seems to be precisely this. It measures in projection the hour angle of the Sun. Many examples exist of horizontal sundials, although, according to Gibbs (1976, pp. 4, 78), Greek and Roman sundial makers preferred rounded surfaces. Of 256 sundials from the Greco-Roman world, of the 3rd century b.c. to the 4th century a.d., described by Gibbs, only 15 are flat and horizontal and only 25 vertical. There are conical, cylindrical, and spherical shapes in abundance. Among the most ingenious (op. cit., p. 23) are the "roofed" sundials, which had a notch or a small carefully drilled hole on the midline of the roof that would act as a tip of a gnomon. Other sundials used the tip of a small pyramid-shaped metal gnomon, and not the side of the gnomon shadow, as in most modern sundials, to mark the hours (see Figure 4.1).

3 18;7° = 18 + 7/60 = 18.11667°. Multiplied by 51/2, this yields 99.64167°, and divided by 15 degrees/hour, the result is 6.64278 hrs. = 6h + (60 x

0.64278 = 38.57) mins. = 6;38,34 or about 6;38. Apparently, Ptolemy is rounding off. The rate, 15°/hour, is from the equivalence between 360°

and 24h.

Figure 4.1. A modern cyclindrical sundial with a pyramidal stylus, from a private home in Calgary. Photo by Dr. T.A. Clark.

Much of the description of these sundials comes from Vitruvius's De architectura, which dates from about 80 b.c. The largest in this collection are the vertical sundials on the eight facings of the "Tower of the Winds" in the Plaka district, of Athens, below the Acropolis. This structure, still visible today (see Figure 4.2), was known in the first century b.c. as the Horologium of Andronikos (from Kyrrhos in Macedonia) or Andronicus Cyrrestes in Latin sources; we discuss this structure and its place in the culture of its time in §7 and report the informed speculation concerning a water clock in the structure in §

Figure 4.3 shows a 15th-century horizontal sundial now located in the courtyard of the "Old Beijing Observatory" in Beijing, China. A modern vertical sundial in Lucerne, Switzerland can be seen in Figure 4.4. A small vertical sundial dating from the Greco-Roman period was found in Luxor (Figure 4.5).

A stone sundial in a courtyard in the Forbidden City in Beijing, China is shown in Figure 4.6. In the latter case, the distortion due to the projection of the hour angle is avoided, because the dial is set in the plane of the equator, and the cursor is a narrow rod projecting through the center onto both faces. This type of sundial has an added advantage: Between the equinoxes, the Sun will illuminate only one of the two faces. At an equinox, the cursor shadow will appear on both faces equally, and thereafter, only one of the surfaces will be fully illuminated.

Sundials were among the elaborate reconstructions of astronomical instruments at Delhi and Jaipur (Figures 3.24 and 9.10) by the Maharajah of Jaipur in the 18th century (see Figure 4.7). Sundials came in an array of geometric styles, including the cylindrical (see Figure 4.1).

The sundial was widely used in the ancient Mediterranean world. Properly used,4 it could be read to a few minutes or better, perhaps to one minute. Precision is ultimately limited by the lack of sharpness of the shadow because of the finite size of the solar disk, a shortcoming of which Ptolemy was well aware (Almagest, Book II, §5; Toomer 1984, p. 80).

The use of the shadow of a gnomon as an indicator of time requires in principle at least empirical knowledge of the altitudes of the Sun at particular times of day and seasons of the year. Where projections are involved, as in flat sundials, the effect at the latitude of the intended site must be known. Finally, the markings should be long enough to extend over the annual range of shadow length at each hour. As we noted in the previous section, the Greco-Roman world did not use mean solar time, and their hours were usually not of uniform length but literally varied over time scales of days. Seasonal hours divided the daylight interval into 12 hours, regardless of the season. This meant that a winter day had shorter seasonal hours than did a summer day. Moreover, at the same time of year, the seasonal hour had a different length as one traveled to a location with a different latitude. Table 4.1 lists the lengths of daylight (2H0rise/set) and length of the seasonal hour for seasonal extremes at selected sites. Note that the ratio of the lengths of the longest to shortest days is a strong indication of the latitude of the site. The accuracy of a sundial reading depended on the time of year, and the suitability of the sundial for the latitude and maybe longitude of a particular place (the noon meridian of the sundial should have agreed with the celestial meridian of the site). In the ancient Mediterranean world, the establishment of the length of daylight was an important function of astronomy. Neugebauer (1957/1969, pp. 158ff.) shows that this was carried out by studying the "ascensions" of the zodiacal signs during the course of the night. For Alexandria, the night lasted about 10 hours in the summer (thus the day lasted 14 hours), and in the winter, the night lasted 14 hours (and thus the day, 10 hours). This ratio, 7:5, was determined in antiquity.

Table 4.1 contains no correction for atmospheric refraction, which lifts the Sun by slightly more than its diameter, on average (see §3 for a discussion of both the mean refraction and its variation from the mean value). Because the Sun

4 Gibbs (1976) relates that a case is known of a sundial that was designed for use in Catania in Sicily but used quite happily in Rome for a considerable interval of time, although the markings were no longer quite right for the site.

Figure 4.2. Views of the Horologion designed by Andronicus Cyrrestes, in Athens: The upper parts of the eight external sides of this structure were vertical sundial faces from which projecting rods provided the gnomons. (a)-(b) six of the eight faces; (c) Notos, the South wind; (d) Lips, the SW wind; (e) the interior, showing evidence of water works. Photo (a) by Andrew Kyrgousious for E.F. Milone. Photos (b)-(e) taken on an early August afternoon in 1982 by E.F. Milone.

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