Recently, the author (A.C. Sparavigna) proposed that an item found in the Kha's tomb and kept at the Egyptian Museum of Torino is a protractor, able to measure angles. Here the author shows that it is suitable for surveying the stair angle of building

Sparavigna, Amelia Carolina

English

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An Egyptian surveying instrument - by
Amelia Carolina Sparavigna
Redazione Archaeogate, 14-10-2011   
In 1906, an Italian archaeological mission lead by Ernesto Schiaparelli,
found a tomb of the New Kingdom, which had survived intact until the
discovery. In this tomb, Kha and his wife Merit were buried. Kha was
an architect and an important supervisor at Deir El-Medina, during the
18th Dynasty [1]. Nowadays, coffins and items of the tomb are kept at
the Egyptian Museum of Turin [2], with a small wooden statue of the
architect (Fig.1). Kha had for his afterlife, some tools that he used for
his job as supervisor. Among them we can see a wooden cubit that
can be folded by hinges. Since wood was the preferred material for
the cubit rods of architects [3], quite probably this cubit was the one
that Kha handled during his job. Besides the rulers, Egyptians had
several other tools for masonry, such as plumbs, levels and squares
[1,3]. As ours, the Egyptian plumbs consisted of a suspended plumb
bob [3].
Among the items of the Kha's tomb, one is unique (see Fig.2). The
label tells that it is supposed to be the case of a balance scale, or the
scale itself. Due to its form and related moment of inertia, it is better
to reject the hypothesis that this object can be a sort of balance. The
complex decoration of the case suggested me that this is a protractor,
able then to determine directions and measure angles [1]. The
decoration (Fig.3) has a 16-fold symmetry of a compass rose with 16
leaves. Outside this rose there is a polygonal line with 36 sides. As
discussed in [1], the fraction 1/16, corresponding to one leaf of the
decoration, is a component of the Eye Of Horus, a symbol defined
during the Old Kingdom to represent the number one. The number of
the sides of the polygonal line corresponds to the number of Decans,
the 36 groups of stars which rise in succession from the horizon due to
the Earth revolution. Considering the case as a protractor, this is a
quite interesting gauge having two scales, one based on Egyptian
fractions, the other based on Decans.
To show how to use the Kha's protractor, we can consider the
measurement of the angle of an inclined plane. Note that the case has
a lid (Fig.2). Let us remove the lid; the case has a perfectly straight
side that can be put on a smooth surface, as shown in Fig.4. When the
surface is horizontal, using a plumb to have the vertical direction, one
of the directions of the rose of Fig.3 coincides with the direction of the
plumb. If the surface is inclined, the direction of the rose is inclined
forming an angle with respect to the vertical. This angle is equal to the
angle of the inclined plane. Therefore, architect Kha could have used
his tool, with the contemporary use of a plumb, for a practical
measurement of inclination.
Let us be even more specific and concrete: we can use the Kha's
protractor to measure the stair angle of buildings, as, nowadays, the
universal protractor - a tool available at most hardware stores - is
used to determine this angle. The procedure is the following; a
straightedge is laid across a minimum of three steps (see Fig.5). The
universal protractor is put on the straightedge and the angle
determined with a plumb. In the case that the flight of stairs is very
long, it is necessary to measure the stair angle at two or three
different places along the run to check that the angle remains constant
on all the flight of stairs. A modern universal protractor for masonry is
shown in Fig.6. Note that the modern tool has the same shape as the
object found in the Kha's tomb. In fact, during his job as supervisor,
Kha had surely the need of surveying the constant inclination of stairs.
To conclude this discussion, let me propose a comparison of the
decoration of this Egyptian item with that of a compass rose of
directions. The rose I use is that we can see in a table of Surveying
from the 1728 Cyclopaedia [4,5]. This rose has two scales. As shown
in Fig.7, we can go back from the compass rose to the Kha's rose, with
small adjustments. May be, the origin of the design of the compass
rose is in the ancient Egyptian tools.
References
1. The architect Kha's protractor, Amelia Carolina Sparavigna,
Archaeogate, July 28, 2011.
2. Turin Egyptian Museum: the tomb of Kha.
3. Building in Egypt; Pharaonic Stone Masonry, Dieter Arnold, Chapter
6, Tools and their applications, New York and Oxford, 1991.
4. http://en.wikipedia.org/wiki/Surveying
5.
http://en.wikipedia.org/wiki/File:Table_of_Surveying,_Cyclopaedia,_Volume_2.jpg
Amelia Carolina Sparavigna
Dipartimento di Fisica
Politecnico di Torino, Torino, Italy
Cliccare sull'immagine per
l'ingrandimento
Fig.1: The architect Kha.
Fig.2: The label is  telling that the
object is  the case of a balance scale
(Egyptian Museum, Torino)
Fig.3 The decoration of this  object
has  a 16-fold symmetry, as  a
compass  rose with 16 leaves .
Outs ide this  rose, there is  a
polygonal line with 36 s ides . One of
the directions  of the rose is
perpendicular to the base of the
object.
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Fig.4: Cons idering the object of the
Kha’s  tomb as  a protractor, we can
measure the angle of an inclined
plane. We can put it on a smooth
surface. In the case that the surface
is  horizontal, us ing a plumb to have
the vertical direction, one of the
directions  of the rose in Fig.2 is
coincident with the plumb. In the
case that the surface is  inclined, the
direction of the rose is  inclined with
respect to the vertical. The angle
with the vertical direction has  the
same value of the angle of the
inclined plane.
Fig.5: We can use the Kha’s
protractor to measure the s tair angle
of buildings . Nowadays , a universal
protractor, available at most
hardware s tores , measures  this
angle in the following way. A
s traightedge is  laid across  a
minimum of three s teps . The
protractor is  put on the s traightedge
and the angle determined with a
plumb.
Fig.6: A modern universal protractor
for masonry. Note that the modern
tool has  the same shape of the
object found in the Kha’s  tomb.
Fig.7: Starting from a compass  rose
of directions  (up-left, from a table of
Surveying in the 1728 Cyclopaedia
[4,5]), we can go back to the Kha’s
rose (down-right) with small
adjus tments .
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Fig.7: Starting from a compass rose of directions (up-left, from a table of Surveying in the 1728 Cyclopaedia [4,5]), we can go back to the Kha’s rose (down-right) with small adjustments.

The architect Kha's protractor,

An Egyptian surveying instrument

SPARAVIGNA, Amelia Carolina

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEAn Egyptian surveying instrument / A.C. Sparavigna. - In: ARCHAEOGATE. - ISSN 1973-2953. - ELETTRONICO. - :14-10-2011(2011).OriginalAn Egyptian surveying instrumentPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2450375 since:I.I.C.E. - Istituto Italiano per la Civiltà Egiziahttp://www.archaeogate.org/egittologia/article.php?id=1481An Egyptian surveying instrument - by Amelia CarolinaSparavignaRedazione Archaeogate, 14-10-2011In 1906, an Italian archaeological mission lead by Ernesto Schiaparelli, found a tomb of the NewKingdom, which had survived intact until the discovery. In this tomb, Kha and his wife Merit were buried.Kha was an architect and an important supervisor at Deir El-Medina, during the 18th Dynasty [1].Nowadays, coffins and items of the tomb are kept at the Egyptian Museum of Turin [2], with a smallwooden statue of the architect (Fig.1). Kha had for his afterlife, some tools that he used for his job assupervisor. Among them we can see a wooden cubit that can be folded by hinges. Since wood was thepreferred material for the cubit rods of architects [3], quite probably this cubit was the one that Khahandled during his job. Besides the rulers, Egyptians had several other tools for masonry, such asplumbs, levels and squares [1,3]. As ours, the Egyptian plumbs consisted of a suspended plumb bob[3].Among the items of the Kha's tomb, one is unique (see Fig.2). The label tells that it is supposed to bethe case of a balance scale, or the scale itself. Due to its form and related moment of inertia, it is betterto reject the hypothesis that this object can be a sort of balance. The complex decoration of the casesuggested me that this is a protractor, able then to determine directions and measure angles [1]. Thedecoration (Fig.3) has a 16-fold symmetry of a compass rose with 16 leaves. Outside this rose there isa polygonal line with 36 sides. As discussed in [1], the fraction 1/16, corresponding to one leaf of thedecoration, is a component of the Eye Of Horus, a symbol defined during the Old Kingdom to representthe number one. The number of the sides of the polygonal line corresponds to the number of Decans,the 36 groups of stars which rise in succession from the horizon due to the Earth revolution.Considering the case as a protractor, this is a quite interesting gauge having two scales, one based onEgyptian fractions, the other based on Decans.To show how to use the Kha's protractor, we can consider the measurement of the angle of an inclinedplane. Note that the case has a lid (Fig.2). Let us remove the lid; the case has a perfectly straight sidethat can be put on a smooth surface, as shown in Fig.4. When the surface is horizontal, using a plumbto have the vertical direction, one of the directions of the rose of Fig.3 coincides with the direction of theplumb. If the surface is inclined, the direction of the rose is inclined forming an angle with respect to thevertical. This angle is equal to the angle of the inclined plane. Therefore, architect Kha could have usedhis tool, with the contemporary use of a plumb, for a practical measurement of inclination.Let us be even more specific and concrete: we can use the Kha's protractor to measure the stair angleof buildings, as, nowadays, the universal protractor - a tool available at most hardware stores - is usedto determine this angle. The procedure is the following; a straightedge is laid across a minimum of threesteps (see Fig.5). The universal protractor is put on the straightedge and the angle determined with aplumb. In the case that the flight of stairs is very long, it is necessary to measure the stair angle at twoor three different places along the run to check that the angle remains constant on all the flight ofstairs. A modern universal protractor for masonry is shown in Fig.6. Note that the modern tool has thesame shape as the object found in the Kha's tomb. In fact, during his job as supervisor, Kha had surelythe need of surveying the constant inclination of stairs.To conclude this discussion, let me propose a comparison of the decoration of this Egyptian item withthat of a compass rose of directions. The rose I use is that we can see in a table of Surveying from the1728 Cyclopaedia [4,5]. This rose has two scales. As shown in Fig.7, we can go back from the compassrose to the Kha's rose, with small adjustments. May be, the origin of the design of the compass rose isin the ancient Egyptian tools.References1. The architect Kha's protractor, Amelia Carolina Sparavigna, Archaeogate, July 28, 2011.2. Turin Egyptian Museum: the tomb of Kha.3. Building in Egypt; Pharaonic Stone Masonry, Dieter Arnold, Chapter 6, Tools and their applications,New York and Oxford, 1991.4. http://en.wikipedia.org/wiki/Surveying5. http://en.wikipedia.org/wiki/File:Table_of_Surveying,_Cyclopaedia,_Volume_2.jpgAmelia Carolina SparavignaDipartimento di FisicaPolitecnico di Torino, Torino, Italy Pagina stampata da Archaeogate: http://www.archaeogate.org/Vietata la copia e la distribuzione (anche parziale) senza la previa autorizzazione di Archaeogate.itCopyright © 2004-2011 ARCHAEOGATE  - Tutti i diritti riservati   

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An Egyptian surveying instrument

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