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.
How did the ancient architects survey and lay out the constructions?
How did the architects achieve alignment?
Were the alignments achieved by solar or stellar observation?
How did the architects achieve such accuracy?
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.
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 investigationin 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 Dixons 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:
Recovered collection of parts
Parts recorded but missing
Parts not yet discovered
Fragment of scale rule (now missing but recorded by Piazzi Smyth)
Bronze or copper fork with fixing rivets attached.
A piece of wood with holes that match the rivets on the bronze item.
A 2-meter plus length of wood resembling a staff with a portion missing.
Various pieces of unidentified material, located in two areas of the shaft.
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
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
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.
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.
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.
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.
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.
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.
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.
I intend to show that in the hands of a skilled and knowledgeable operator, this simple instrument can be used for the following purposes:
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.
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.
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.
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.
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 thedeclination of the ecliptic at the time of observation.
In our epoch, at the winter solstice,at midnight at any position on the globe,Orion is due south and the ecliptic stars aredirectly overhead at 23.4o north latitude as translated onto the planet. True Northis found first by sighting the pole star and correcting for local latitude.True southis thencalculated by measurements on a single bodyof equal altitude, interpolated,as it passeseither side of the chosen meridian.
Constellation Stars on the eclipticare 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 1800nautical 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.
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.
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.
You may write Paul at PFG88@aol.com with any questions or comments.
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