Sundials and waterclocks

Marcia J. DeGonda

Presented 4/17/95
Received  4/20/95

by Marcia DeGonda
The most ancient sundials known to be recorded are simple stone dials from the time of Thutmosis III (1501 to 1448 B.C.) The dial was a horizontal stone bar approximately 30cm long. It had a short stem on one end which supported a second stone of the same length, but flat and sitting perpendicular to it as in a T-shape. The perpendicular piece sets toward the sun throwing a shadow on the bar behind where divisions were sketched to indicate the time. It is also believed gnomons in the form of obelisks were used in Egypt as well as China for the measurement of time. As early as 1000 B.C. the Chinese had succeeded in locating the astronomical meridian, had fixed the dates of the solstices and had even calculated the inclination of the ecliptic on the plane of the equator (Rohr, 5-6).

One of the most interesting sundials was the dial of King Ahaz, who reigned in Judea from 740 to 728 B.C. Reference to the king's dial can be found in the Bible: Kings 20:9-11; Isaiah 38:8; and Ecclus. 48:24. The story maintains that the Lord retracted the shadow ten steps on the stone steps of the dial of King Ahaz, thereby lengthening the king's life. It is the most celebrated dial because no older dial had such good coverage in old documents and because the nature of this sundial with its retracting shadow remains a mystery (Rohr, 8-9).

Clepsydras or "water clocks" were used to measure time after dark and on cloudy days. Duke Chan, alleged inventor of the compass, is said to have used a clepsydra as a timepiece in 1130 B.C. (Earle, 54). The general principal behind the water clock was the idea that a given amount of water always takes the same amount of time to drain from one bowl to another. That is unless it has been sullied by an attorney in a Roman court or its flow stopped altogether by the pearl from a bride's dress (Burns, 34-36).

In the 3rd century B.C., a Chaldean priest named Berossos designed a dial in Egypt shaped like the hemisphere and hollowed out of stone with a gnomon set upright in the center of the hollow. The shadow cast by the gnomon would trace an arc of a circle each day. To each arc there corresponded an arc of a circle in the hemisphere which was its exact image. This dial indicated hours which varied in length of the day for the various seasons (Dolan, 34-35).

The Arabs are credited for simplifying the processes of design and construction of sundials by using trigonometry. In the 13th century A.D., a Moroccan scientist named Abul Hassan wrote on the construction of hour lines on cylindrical, conical and other surfaces. He was also credited with designing a dial where the style was oriented towards the pole, and the introduction of equal hours, much like we use today.

The most common sundial found today is the horizontal dial. They are most popular in that they can tell time whenever the sun is shining (where some dials are restricted to certain hours) and they are relatively easy to make. In order for the sundial to operate properly it must be designed specifically for the latitude where it will be used. The typical horizontal dial consists of a flat, horizontal piece called the "dial plate" and a protruding gnomon, perpendicular to the dial plate and roughly triangular in shape. The gnomon throws a shadow on the hour lines inscribed on the dial plate. The hour lines can be computed using an elementary trig formula: tan D = (tan t)(sin y) where "t" is the time measured from noon in degrees and minutes of arc; i.e. the hour angle of the sun; "y" is the local latitude; and "D" is the angle the desired hour line makes with the 12 O'clock line (Waugh, 43-46).

For example: A sundial designed in latitude 36 degrees 10' would have the following hour lines:

Time Angle D
11:30 or 12:30 4 degrees 27'
11:00 or 1:00 8 degrees 59'
10:30 or 12:30 13 degrees 44'
Note: 15 degrees of arc = 1 hour of time
1 degree of arc = 4 minutes = 60'
1' of arc = 4 seconds

Solar time as it is read on the face of a sundial must be adjusted for both longitude and the "equation of time" to coordinate with the mean time our clocks keep. The equation of time is the difference between mean and apparent solar time which varies from day to day. The sundial agrees with the clock only four times a year. A brief explanation for this irregularity involves two factors: the earth's orbit is elliptical and the its axis is tilted about 23-1/2 degrees with respect to the orbit. Each have an affect on the length of the apparent solar day at different seasons. Some dials are designed to account for the equation of time.

A sundial of superb design and construction can be found at the public library in Riverside, California. It is a cylindrical equatorial type with a shadow-casting axis that contains a circular sphere which may be turned toward the sun. While the shadow of the axis indicates the hour, the sphere allows the viewer to read the date as the sun's declination changes with the seasons. There are also correcting devices built into the design so that local apparent, local mean, and Pacific Standard time may be read (Dolan, 22-33, 136).

Burns, Marilyn "This Book is about Time" Canada: Little, Brown & Co., 1978.
Cousins, Frank W. "Sundials" New York: PICA Press, 1969.
Dolan, Winthrop W. "A Choice of Sundials" Brattleboro, Vermont: The Stephen Greene Press, 1975.
Earle, Alice Morse "Sundials and Roses of Yesterday" New York: The MacMillan Co., 1902.
Rohr, Rene J. "Sundials: History, Theory and Practice" Great Britain: University of Toronto Press, 1965.
Waugh, Albert E. "Sundials: Their Theory and Construction" New York: Dover Publications, 1973.

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