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.
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