|FIRST PAGE||SURVEY LIMBURG (Dutch)||SURVEY TYPES (Dutch)||WORTH KNOWING (Dutch)|
|The oldest surviving
sundial found in Egypt around 1500 BC
earliest surviving sundial is located in the Egyptian museum in Berlin,
with the catalog number 19744. Probably, it was found in Eschmunein. It
dates from the reign of Thutmosis
III (1479 - 1425 BC) during the New Kingdom. The name and
titles of the pharaoh are engraved on the side
It is made of stone (schist) and is shaped like the
letter L. The short piece is the gnomon (vertical rod giving a shadow). In the gnomon there is a hole for attaching a small plumb bob. Below is a vertical groove to align the thread of the plumb bob.
In the horizontal plane of the long bar there are five circles as marks of a time scale. The distances between the marks are proportional to the numbers1,2,3,4,5.
Photo: Website Verein zur Förderung des Agyptischen Museums Berlin
The hypothesis of Ludwig Borchardt and Evert Bruins
1910 the German Egyptologist Ludwig Borchardt formulated the hypothesis
that the shadow of the gnomon gives an indication of the so-called unequal
hours on the time scale.
Those divide the period between sunrise and sunset into twelve equal parts. Because in wintertime the period between sunrise and sunset is shorter than in summertime, the hours, so determined, are unequal in length depending on the season. Unequal hours were in use until the Middle Ages.
The height of the sun varies also with the seasons and hence the length of the shadow. To give a shadow to the correct mark in every season, the gnomon should be variable in height. Therefore Borchardt assumed that the sundial, as it was found, is incomplete.
Adapted to the season, a crossbar of a suitable height had to be added, in his hypothesis. In the course of history these crossbars were lost.
In the morning, the sundial was facing with the gnomon to the east and at noon it had to be turned with the gnomon to the west.
In 1965 the Dutch mathematician Evert Bruins calculated the shadow of a higher gnomon. He checked whether, given an exact indica¬tion at a certain mark, the reading at the other marks are also correct. His finding was that the time keeping, as assumed by Borchardt and tested with a graphical method, was a good approximation of the measurement of the unequal hours.
The L-shaped sundial fitted with a crossbar
as L. Borchardt drew him (a hypothesis rejected by Sarah Symons)
The hypothesis rejected by Sarah Symons
Symons received a doctorate after defending the thesis
"Ancient Egyptian Astronomy: Timekeeping and Cosmography in the New
In 25 out of 229 pages she examined the L-shaped sundials and rejected the theories of Borchardt and Bruins. For this she used her knowledge of Egyptian texts and culture and the mathematical background of gnomonics.
In passing, she pointed out that the obelisks at the temples were not intended as a sort of sundial. There was surely a connection with the sun and the cult of the sun. The high peak of an obelisk, covered with an alloy of gold and silver, reflects the sun before sunrise. The main function of an obelisk was, according to its engravings, to serve as a memorial in honour of the pharaoh to whom it was devoted.
Only when obelisks later were moved to Rome and Paris later on, they were used as a sundial.
Sarah Symons refutes Borchardt’s theory about the ancient Egyptian L-shaped sundial based on four arguments:
1. The text in the cenotaph named Osireon
the cenotaph, named Osireon,
near the temple of Seti I at Abydos there is a text on a ceiling that
describes the construction and usage of such L-shaped sundials.
In the text and on the accompanying drawing, there is no mention of a crossbar, only of the L-shape.
The simple ratios of the distances between the marks are indicated as corresponding to 3, 6, 9, 12. As in other ancient Egypt drawings, the distances are not drawn to scale. The text describes these relations as "an established procedure.”
The passage in the text on the orientation of the sundial can be interpreted in two ways: an east-west orientation with a rotation of 180 degrees at noon or a continuous turning towards the sun.
The figure in the Osireon text with the distances between the markings
indicated as ratio's 3, 6, 9, 12.
2. The sundial hieroglyph
other characters the Egyptian used logograms. These are characters
whose form refers to the concept it stands for. The sign for "sundial"
is such a logogram. It shows the L-shape with a small plumb bob,
but a crossbar cannot be seen.
Later developments in the shape of the sundial are always shown in logograms. There is never a crossbar image.
The hieroglyph for sundial: the shape refers to the concept it stands for,
the L-shaped instrument with the little plump bob.
3. The calculation of the indications of unequal hours
calculated the length of the
shadow for a given (unequal) hour – in this case
the 10th or the 2th hour - at the winter solstice, the equinoxes and
the summer solstice.
For each of these moments he calculated a crossbar of suitable height so that the shadows have the same length and reach the mark of the chosen unequal hour.
Then he calculated for those crossbars the length of the shadows of other (unequal) hours and compared them with the distances to the corresponding marks, determined by the ratios indicated in the Osireon figure.
He deduced from the differences that there was a 'good approximation' of the measurement of the unequal hours.
In the figure beside the results of the calculations, after recalculation (see below), are converted in a drawing.
Sarah Symons also recalculated the shadow lengths. It is clear, she concludes from the percentage errors, especially for the shortest and longest shadows, that the unequal hours are not measured with a degree of accuracy that merits the addition of a crossbar.
4. The usage of the sundial
According to the hypothesis of Borchardt the sundial should have an east-west alignment, in the morning with the gnomon to the east and rotated in the afternoon to the west. This requires an external reference for the cardinal directions, which is not always available for this ‘portable’ instrument.
The only tool to set up the sundial, is the plumb bob to level it. Directing the sundial with the gnomon towards the sun - the shadow coinciding with the long part of the L-shape over its full width - is the obvious method of use, to carry out without tools.
Moreover, it is consistent with the Osireon text: "Then the shadow of the sun will be aligned on this instrument”.
Sarah Symons' conclusion is: the simplest, most obvious and most easily supported
theory is that the sundial is an L-shaped instrument which is portable and can b
used in any place marking certain time periods. Alignment is provided by levellin
it using a 'built in' plumb bob and pointing the device towards the sun.
The simple relationship between the marks is a convenient 'rule' for making a sundial
rather than an accurate measure for unequal hours.
Adding a crossbar is a clever idea, but sprang from the need to impose modern
insights about equally divided time periods to the time keeping in antiquity.
Francis Maddison and Turner Anthony talk about "the over-sophisticated theory
of L. Borchardt and the wild fantasies of E. Bruins " versus “the most recent
- and correct - discussion of Sarah Symons”.
Eleven years ago Sarah Symons threw a new light on the oldest surviving sundial.
Isn’t it about time to correct the description of the sundial in numerous Internet
publications, especially in the catalog of the Egyptian Museum in Berlin.
|The formulas behind the calculations