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Cross Staff and Plumbline and
the Great Pyramid
Revealing the discovery of a
geometrical, spherical measuring instrument in the Pyramid of
Khufu
By Crichton E M Miller
This advanced protractor, similar to the cross and plumb line,
is an advanced mathematical device, capable of astronomy,
navigation and surveying. It is proposed, that the ancient
Egyptian architects and astronomers used this hybrid Celtic cross,
for the purposes of stellar alignment and timekeeping.
The proposal and thesis is based upon the discoveries and
calculations of the author, whilst working on the proposal that
the Celtic cross was an instrument derived from the astrolabe and
quadrant. That the Celtic cross was used as a spherical measuring
instrument for the purposes of navigation, astronomy, surveying,
cartography and time keeping is known. Since there is, and has
been, much debate amongst groups of academics over the ancient
methods of surveying the pyramids at Giza, we will attempt to
address the following questions.
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How did the ancient architects
survey and lay out the constructions?
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How did the architects achieve
alignment?
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Were the alignments achieved by
solar or stellar observation?
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How did the architects achieve
such accuracy?
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What instrument did they use?
It is known that the ancient Egyptians used plumb line
technology in several different areas, particularly in weights and
measures. This is depicted in many friezes and was used in
surveying, with the instruments known as the Bay and Merkhet. What
has not been found to date, is an instrument capable of acting as
an inclinometer or modern theodolite / sextant. Not only that, but
one that is accurate to degrees and fractions of degrees, which
would be necessary for the ancients’ calculations.
Degrees are broken down into minutes and seconds of arc. One
minute of arc is equal to one nautical mile on the meridian.
1. The proposal is that the pyramid of Khufu was surveyed with
an instrument capable of accuracy to 3 minutes of arc.
2. That the evidence of the use of this instrument, is not only
in the constructions, but that the author has found evidence of
the actual artifact.
The Evidence
I believe that the relics shown in Figure 1, which were
discovered in the North shaft of the Queens chamber in the Great
Pyramid of Khufu by Waynman Dixon and DR Grant in 1872, may have
been one of the greatest Egyptian treasures revealed to date.
Understanding them will open all kinds of avenues of new research
into the ancient past. It was Charles Piazzi Smyth in his 1878
book "The Great Pyramid" who recorded the relics found
in the north shaft of the Queens chamber by Dixon and Grant. These
items were found in the hermetically sealed north shaft broken
into by a Bill Grundy under the direction of W Dixon. The relics
were sent to Piazzi Smyth in a cigar box where they were recorded
in his diary with accompanying drawings and sketches. The loss of
these relics was the subject of an extensive investigation in
1993 conducted by Robert Bauval with the assistance of Dr. Mary
Bruck and the late Professor I.E.S. Edwards.
These events are documented in the epilogue of his book, The
Orion Mystery. In Mr. Bauval's book he mentions several times
that one of these relics, the bronze hook, was probably a form of
Pesh-en-kef and "also a sighting device for stellar
alignments", and that this was a view that was supported by
Professor I.E.S. Edwards. Bauvel also suggests in the book that,
like the Czech astronomer Zaba before him, "that the
Pesh-en-Kef instrument, fixed on a wooden piece and in conjunction
with a plumb-bob, was used to align the pyramid to the pole
stars."
Furthermore, he suggested, "it seemed very likely that a
priest placed the ritualistic tools inside the northern shaft from
the other side
of the wall of the Queen's Chamber." This prompted him to
state further in The Orion Mystery that "we cannot
help wondering if these ancient relics (were) indeed, perhaps the
very sighting instruments that were used to align the Great
Pyramid to the stars." (1)
Two of the objects can now be found in the British Museum.
The 1872 items consisted of a slat or rod of cedar wood about
13 centimeters long (part of a measuring rod), a granite ball
weighing 1lb 3 ounces and a bronze/copper hook type of instrument,
5 centimeters long, with a part of a wooden handle still attached.
The fragment of measuring rod is currently reported as missing.
No further examination of the shafts in the Queens chamber had
been carried out until 1993, when Rudolf Gantenbrink developed a
remarkable robot known as Uphaut 2 to explore the shafts and to
install a ventilation system in the Pyramid of Khufu designed to
reduce humidity within the pyramid. He was subsequently to make
the most accurate internal survey of the shafts to date. This work
was undertaken on behalf of the Egyptian Government with the
approval of Dr. Zahi Hawass. The operation was a success and a
credit to Rudolf Gantenbrink. The discoveries made were remarkable
and increased our understanding of the construction of the
pyramid. The robot is now in the British museum and the story of
this work is public knowledge.
How is this relevant to my theory? It appears that in
1872,Waynman Dixon explored the northern shaft with an extendible
iron rod.
It seems that Dixon’s crude rod had damaged the original
artifact, from which the relics originated. This blind probing may
have caused the items to become damaged and dislodged from higher
in the shaft, enabling Dixon to recover them easily. On the video
footage of the shaft, taken by Uphaut 2 in 1993, there can be seen
the remainder of a long wooden rod from which the 13-centimeter
piece had broken. What can also be seen is an object that appears
to look like a rectangle of wood or metal, with two corresponding
holes to match the rivets on the metal instrument. Unfortunately,
Rudolf Gantenbrink was unable to explore the shaft further for
technical reasons.
Having collated the information available from the relics found
in 1872 and those seen in the shaft in 1993, theoretical
reconstruction of the instrument can be achieved.
The items are as follows:
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Recovered collection
of parts |
Parts recorded but missing |
Parts not yet discovered |
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Figure 3
1872 objects:
1993 objects:
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A piece of wood with holes that match the
rivets on the bronze item.
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A 2-meter plus length of wood resembling a
staff with a portion missing.
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Various pieces of unidentified material,
located in two areas of the shaft.
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A large rectangular object can be seen at the
upper end of the shaft attached to the 2-meter length of wood.
With this component list, it is possible to assemble the known
parts in a logical format.
Exploded View of the Instrument
Figure 5
Method of assembling the instrument from the component list.
1. The metal fork appears to be designed to attach to one
end of the long staff by a half housed joint held by the two
rivets on one side of the hook.
2. The plumb line is looped over the fork, on the top of
the staff, by way of a slipknot. The working end returning
over the side of the fork opposite to the scale, this allows
the line to cut the apex of the joint between the cross arm
and the staff precisely.
3. A pouch or net is fixed to the opposite end of the plumb
line, to hold the plumb bob.
4. A cross bar is mounted on the fork, at right angles to
the staff and fixed with the remaining two rivets at the front
of the instrument.
(I believe that this is the purpose of the object with two
corresponding holes still in the shaft)
5. One end of a measuring rod is fixed at 45o to one arm of
the cross bar.
6. The other end of the measuring rod is fixed at 45o to
the upright of the staff.
Assembled view of the Instrument
Figure 6
Having completed the initial assembly and understanding the
principles of the instrument earlier outlined, it can be
established what components are missing to complete the instrument
and turn it into a working model, proving the hypothesis.
Measuring Rods
Proof that the Egyptians had sufficient knowledge of decimals
and degrees to allow construction of the measuring rod has already
been proved and published by Sir William Flanders Petrie when he
surveyed the Pyramid of Khufu, where he stated that the Royal
Cubit measured 523.95 millimeters or 20.6 inches. It was
established that Fourth Dynasty builders divided the cubit into
decimals. Sir William also named a unit of measurement used at
Giza as a digit, which is constantly accurate to one tenth of a
millimeter:
1.75752 cubits = 9180 digits = 918 millimeters = 90 centimeters
approximately.
This is sufficiently close enough for centimeters and
millimeters to represent degrees and minutes for the purposes of
this experiment.
Exponential Scale
Extreme accuracy for the time of three arc minutes would be
achieved by the development of an exponential scale. This is
achieved by drawing lines from the center point of a circle
outward, through the rule. This can be seen in figure 7, kindly
provided by Jim Bowles.
Figure 7
Evidence of Tools
Sir William Petrie also established that no tools would be
discovered and described the reasons why. The tools were sacred
and belonged to the Royal Family; losing one was a serious crime
and could have resulted in the loss of life for the unfortunate
individual at fault. The use of the types of tools employed in the
construction was through analysis of the marks on the stone,
therefore it was possible to deduce that there was metal in the
tools used, as indicated by the evidence left in the cuts.
According to Sir William Flanders Petrie, bronze and copper saws
and drills of various designs were employed. Some used precious
stones for tips and accordingly would have been very valuable.
Secrecy
I believe that these tools were owned by Master Craftsmen,
practicing in Guilds and that their tools and skills were precious
to them, much as they were by later generations of craftsmen
employed during the Great Cathedral building age in Europe. I
further believe that this instrument is tangible proof of the
Ancient Egyptians’ depth of knowledge in the disciplines of
astronomy, surveying and navigation, hitherto underestimated. And
I believe that this knowledge may have been practiced by members
of craft guilds, in secret, right up to the age of Cathedral
building in Europe. The knowledge may have been kept secret for
two reasons.
- That the Trade Guild or Society members were sworn to
secrecy after or during their apprenticeship, so as to protect
their knowledge from the uninitiated.
- That there was persecution, even to death, by the religious
powers during certain historical periods, who would allow no
dealing with astronomy or other "occult practices".
Finally, I believe that the Christian Cross originated from an
instrument used by the craftsmen in ancient Egypt and possibly
other more ancient civilizations such as the Neolithic Peoples.
Figure 8
This photograph is provided with the kind permission of Maureen
Palmer and shows the parts of the instruments in the Temple of
Horus at Edfu. These hieroglyphs probably are Ptolemaic in origin.
I think that the relics discovered by Dixon in the Queens
chamber, were part of an originally complete instrument that had
been sealed into the pyramid by the architects, in the same manner
that masons and craftsmen made their mark on their stone
masterpieces. This tradition is carried forward to this day and is
usually found in foundation and corner stones of buildings.
Applications
I intend to show that in the hands of a skilled and
knowledgeable operator, this simple instrument can be used for the
following purposes:
Figure 9
This illustration demonstrates the ability of the Instrument to
measure angles accurately.
1. The Instrument can be used to take remarkably accurate
astronomical measurements.
2. Measuring distances for chart and map making including
measuring the circumference of the Earth, to an accuracy of 3
arc minutes.
3. The Instrument can be used for Civil engineering
projects such as surveying and construction.
4. Timekeeping and the calendar upkeep are possible with
this instrument.
5. Navigation including latitude to an accuracy of 3
nautical miles on a handheld version.
Figure 10
This diagram shows the unique ability of the instrument to take
sidereal angular measurements of the movement of astronomical
bodies.
With the knowledge of local time coupled with a rudimentary
knowledge of astronomy, it is possible to find both latitude and
longitude with this instrument.
Figure 11
This example shows the use of the bronze fork. If an
observer uses the cleft in the fork to sight the star at night, it
would be difficult to see without a polished and reflective
surface.
Figure 12
This example of a cross type of instrument shows how linear
angles can be found with the addition of an effective scale set at
45 degrees to the upright and cross bars. The tripod at the foot
of the assembly, adds stability. This particular instrument at
this size would have an accuracy of 3 arc minutes. The
illustration was taken from UK Patent No. GB 2 344 654 A
The following example is a tutorial for finding latitude with
the instrument using the current pole star of Polaris.
To find latitude at night, clear skies permitting, one must
first find the pole star. the North pole star is currently
Polaris and is found by first locating the constellation known
as the Plough or Big Dipper. The Plough constantly revolves
around Polaris in an anti clockwise direction when viewed in
northern latitudes. The two stars at the outer edge of the Big
Dipper are known as the pointer stars. By following the
pointer stars as in the drawing, the next star that is seen in
line with the pointer stars is Polaris. By pointing the
instrument at Polaris and reading off the degrees from the
scale, one is able to find one's latitude directly. this is
because when pointing the cross bar at the pole star the view
is a parallax due to the great distance of the body being
observed.
The plumb line will always point to the earth's center can
be observed. The nature of the instrument being in the shape
of a cross and scale mounted on the opposite side allows the
opposite angle to that of the actual angle between star and
the earth's center to be measured. The smaller resulting angle
is equivalent to the 90 degrees of latitude from the equator
to the pole.
As the observer moves toward the pole following the
curvature of the earth, the instrument will tilt further back
increasing the angle. By moving toward the equator, the angle
will decrease. Therefore, the angle can be measured directly
from the scale and the latitudinal position obtained.
Figure 13
This figure shows how accurately a modern observer can find
latitude with this instrument. Polaris was not the pole star at
the time of the building of the Pyramid of Khufu. Because of the
effect of precession, the polar region has moved to its present
position. It is, however, possible to find a meridian with this
instrument, both day and night.
The system works by interpolating the declination of an
astronomical body with the use of equal altitude observations.
This is only possible with an instrument of this type.
Earth Circumference Measurements
It is possible to take complete spherical measurements in every
plane with the instrument. If one uses it as an inclinometer,
(sextant) a hand held variant with a scale of 900 millimeters can
be accurate to 3 arc minutes or 3 nautical miles as measured on
the meridian.
Any passage, land or sea, tracking true north for units of
this distance, will allow simple interpolation that shows the
approximate circumference of the Earth on meridians (not allowing
for the planet being an oblate spheroid). In other words, the
circumference of the earth can be fairly worked out by traveling
only 6 nautical miles, whilst taking regular observations.
The unique feature of the instrument, however, is that it is
capable of sidereal or horizontal measurements. This is beyond the
scope of a sextant and the reason why I was granted a patent on
the instrument. It means that one is able to take measurements of
ecliptic constellations as they track from east to west horizons.
One must find latitude first and be aware of the declination
of the ecliptic at the time of observation.
For instance:
In our epoch, at the winter solstice, at midnight at any
position on the globe, Orion is due south and the ecliptic
stars are directly overhead at 23.4o north latitude as
translated onto the planet. True North is found first by
sighting the pole star and correcting for local
latitude. True south is then calculated by
measurements on a single body of equal altitude,
interpolated, as it passes either side of the chosen
meridian.
Constellation Stars on the ecliptic are measured by
sidereal observation to equal minutes of arc adding up to
individual degrees. Each constellation Taurus to the east and
Gemini to the west is 30 degrees long or 1800 nautical miles
translated onto the Earth's surface. These two constellations
represent 3600 nautical miles. Twelve of these represent 21600
nautical miles. And there you have it, the Earth's
circumference.
Solar observations
The instrument is capable of taking solar observations and
measuring declination and Hour angles. This is achieved by
indirectly viewing the sun. The instrument is directed at the sun
and the shadow is projected onto a horizontal surface. By aligning
the cross bar toward the sun an accurate shadow image can be read,
and the degrees read from the scale.
(Update)
The instrument was granted a Patent by The United Kingdom
Patents Office under Patent No GB 2344887 after extensive
worldwide searches and publications. The Patent was granted in
November 2000 .
The patent was granted because the instrument was not
"obvious" in that it had two unique features not
available to any instrument in the world today.
- The ability to take sidereal (horizontal) angular
observations.
- The use of a fulcrum for steadiness and accuracy.
This work, to all intents and purposes, has been peer reviewed
and published accordingly. Please visit Crichton E. M. Miller's
home page at http://www.crichtonmiller.com
for information on this and other topics.
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