SAILING DOWN THE WEST KENNET AVENUE.
At the southern gate of Avebury Henge there is a huge obelisk standing off to the side. This marks the beginning of the West Kennet Avenue, which runs to the Sanctuary Circle 1.4-miles to the southeast. The Avenue is marked by 2 rows of stones and there were, originally, about 100 of them. Unfortunately, in an effort to exorcise the devil from Avebury, zealous Christians of the 14th century AD and thereafter destroyed many of these markers. Thankfully, English Heritage archaeologists and other dedicated antiquarians have erected plinths to mark the precise spots where many of the plundered stones once stood, so sufficient evidence still exists to painstakingly determine mathematically what the purpose of the stone rows was.
A white line runs for 583.33333-feet from the obelisk within Avebury Henge to the centre of the eastern face of a large obelisk standing outside the southern gate at the beginning of West Kennet Avenue. The azimuth angle to this position is 166.6666-degrees (166 & 2/3rds). This gets students of navigation from the henge's main obelisk position to the giant obelisk where the comprehensive navigational tutorials begin. The values of distance and angle to this point are highly significant to ancient positional plotting methodology and this will become very apparent as we proceed.
The distance coding from the obelisk means five things simultaneously, depending upon what calculating function one is undertaking from this beginning position.
From this beginning position at the southern gate of Avebury, students of navigation learned how to do accurate positional plotting at sea, using two separate systems. These were:
In the above picture less than half of the West Kennet Avenue is seen. Meandering lines in different colours are shown to be running, side by side and from stone to stone down each side of the Avenue.
The yellow & green lines mark a route that was set out in increments that related to the "11" series mile of 5280-feet.
The cyan & red lines mark a route that was set out in increments that related to the "6&7" series mile of 5250-feet.
The students would navigate from stone to stone down the particular lines under study, stopping at each station to calculate the distance covered and the degree angles back to the point of departure and onwards to the destination. The distances between standing stones represented sea-legs of travel using specific increments of distance and angle relative to the system under study. At the end of a "sea-leg", the linear distance covered had to be converted to a scaled circumference (drawn, undoubtedly, on a large slate with a sharpened chalk pencil, aided by a compass drawing tool), then the precise degree angles worked-out with the aid of scaled rules and abacus calculators.
LET'S GO SAILING
From the designated launching position on the giant stone at the southern gateway, the students and their master traveled 247.5-feet due south to a small stone marker. The distance is symbolically representative of the 24750-mile (of 5280-feet) circumference of the Earth and all increments of lengths and angles encountered on this voyage to the Sanctuary Circle will relate to the "11" system of measurement (league @ 16500-feet, mile @ 5280-feet, furlong or furrowlong @ 660-feet, chain @ 66-feet, rod or perch @ 16.5-feet, fathom @ 5.5-feet, link @ 7.92-inches).
The distance covered (247.5-feet) is converted to a circle using PI @ 3.141818182 (essentially 314 & 2/11ths ÷ 100). This renders the "11" series diameter into a circumference that is perfectly divisible within a 360-degree environment. Therefore: 247.5-feet X 3.141818182 = 777.6-feet. Under this reading each 2.16-feet (2 &4/25ths ...25.92-inches) of circumference represented 1-degree of arc. Using a scaled rule and calipers the students could draw a scaled circle onto their (slate ?) chart and plot their first position away from the point of departure. Having established the position of true North, they could now use their scaled circle to accurately mark any point of the compass by calculation., They could work out the degree angle back to the obelisk position within the henge or, say, to the crown of Silbury Hill, etc. Their final destination was to be the Sanctuary Circle, 7920-feet from the obelisk at Avebury Henge, sitting at an azimuth angle of 140.8 -degrees from the henge obelisk.
The 7920-feet of distance from the obelisk within the henge to the Sanctuary, if read as miles, would represent the true diameter of the Earth. The angle of 140.8-degrees from the obelisk to the Sanctuary Circle is coding under the mile of 5280-feet and 14080-feet would be 2 & 2/3rds miles. A mathematical progression based upon 704 (1/2 of 1408) is very important to the 5280-feet mile and 70.4-feet is 1/75th of a mile.
With regards to the first plotting circle mentioned, with a circumference of 777.6-feet, if this was read as miles then it would be 1/32nd of the 24883.2-mile circumference of the Earth. In this same plotting circle, the increment representing 1-degree of arc is 2.16-feet. The Sun spends 2160-years in each house of the zodiac during the 25920-year cycle of precession, etc.
It is very important at this point to realise what's going on mathematically and to realise that the two systems of navigation were interrelated by two very close renditions of PI.
When using the "11" system, as we are doing now, the rendition of PI is 3.141818182. This converts an "11" diameter to (what is exploitable as) a sexagesimal circumference. In other words, the diameter immediately becomes the "6&7" system on the circumference divisible by 360-degrees.
Alternatively, when using the "6&7" system for linear travel as a straight-leg diameter, the rendition of PI used is 22/7ths. This converts the circumference to an "11" series reading. For example: One Greek mile of travel (5250-feet) X 22/7ths (3.1428571) = 16500-feet (an ancient British league of 3.125-miles) or 550-inches per degree of arc.
These two navigational systems seem to have been built into the base diameter of Silbury Hill. In one cross measure through the hill the distance is 525-feet, which indicates a circumference of 1650-feet (divisible by "11" within a 360-degree environment) using PI @ 22/7ths. In the other cross measure the diameter is 550-feet, which gives a circumference of 1728-feet (divisible by "6&7" within a 360-degree environment) using PI @ 3.141818182.
The students now "sail" away on the second leg of their journey, but this time it's on a heading of 120-degrees and a distance of 66-feet (1 chain) is covered. This segment of the voyage is now converted to a plotting circle on the slate. Therefore: 66 X 3.141818182 = 207.36-feet or 2488.32-inches. This means that 1-degree of arc is 6.912-inches or .576 (72/125ths) of a foot.
Remember: The Earth was considered to be 12 X 12 X 12 X 12 X 1.2-miles in circumference (24883.2-miles) under the literal system built into the Great Pyramid. In that calibration the miles were 5250-feet each. Yet another system used the same value, but in conjunction with a mile of 5280-feet. That "true" size value is only 18.8-miles short of the figure we use today.
The longest of the Egyptian Royal Cubits was 1.728-feet or 20.736-inches. This Egyptian Royal Cubit's length X 1200 = 24883.2. A cubic foot (12 X 12 X 12 -inches) = 1728 cubic inches, etc.
The student navigators, with their master at the helm set out on the next leg. This time the trainee-navigators veer 6-degrees further towards the South on a heading of 125.55555-degrees (the opposite of 305.5555 or 1/18th of 5500) and cover 88-feet during the leg. Again, the distance is converted to a plotting circle, therefore: 88-feet X 3.141818182 = 276.48-feet. This means that each degree of arc = 9.216-inches or .768 (96/125ths) of a foot. The sum of 921.6-miles would be 1/27th of the 24883.2-mile circumference.
Again the intrepid voyagers set out, but change their heading to 122.5-degrees (the opposite of 302.5-degrees). Under the "11" system perimeter value of the Great Pyramid @ 756.25-feet per side, one circumnavigation was 3025-feet. This leg of the journey covers 77-feet, which is later converted to a plotting circle. Therefore: 77 X 3.141818182 = 241.92-feet or 8.064-inches or .672 (84/125ths) of a foot per degree of arc.
The above picture shows an overlay of surveying information provided by English Heritage & AutoCAD lines superimposed upon the Google Earth image of West Kennet Avenue. Small white dots, which came with the English Heritage digital file, indicate the approximate positions of the marker stones on the Avenue. It seems probable that these slightly askew marks were done some years ago with a handheld GPS unit, which would account for the few feet of error in some instances. The white dots are, however, very helpful in locating the true positions of the markers in Google Earth. The bold white lines are from the English Heritage digital file and seem to very accurately mark the sides of the original Avenue of 5000-years ago. This overlaid Avenue drawing ends perfectly at the edge of the Sanctuary Circle. The thin, yellow AutoCAD line at the right side of the picture runs for 7920-feet from the obelisk in Avebury Henge to the Inner circle of the Sanctuary.
In the preceding commentary the mathematical method has been described to convert each leg of the journey into an calibrated circle from which accurate degree angles back to the point of departure and onwards to the destination or to any landmark could be calculated. Under this system the "foot" value of the outer circumference was divided up into 125 parts per foot. This meant that navigators using the "11" system of increments could, potentially, work to a refined tolerance of 45000 calibrations per 360-degrees if they so desired or had the visual capacity to do so.
The point is that the mathematical accuracy and capacity to work to finite refinements was achievable under their very sophisticated system. When the skeleton of an ancient dignitary of obvious importance was found buried at Bush Barrow tumulus mound beside Stonehenge, a plane table and alidade sighting rule were found to be buried with him. This find should give us some clues as to how the angle calculations were being expedited, as well as refinements or tolerances achieved.
The ancient navigator-mathematicians of 5000-years ago not only had a very accurate concept of the true size of the Earth, but they also had a very versatile, factorable and precise method for doing positional plotting. The mathematical sophistication is more than sufficient to do very good relative computations of Longitude, as well as Latitude. An experienced navigator, keeping a very good record of boat speed, distance covered and heading angle in each leg, had at his disposal, an accumulation of known-length and angles to calculate from. As the voyage proceeded, angles of heading could be added to or subtracted from with each new leg. Accuracy in determining angles could be easily calculated by converting the leg length of travel into a calibrated circle of very precise incremental values. Any of the points of the compass could be easily determined using this mathematical method. As long as the experienced navigator was adept at calculating distances covered, then calculating longitude was achievable.
Other navigational aids would have included:
The length of this leg is 82.5-feet and the azimuth angle remains 123.75-degrees (half of 247.5-degrees).
This length is 5 rods or 15 ancient fathoms of 5.5-feet each. When converted to a circle, this length achieves a circumference of 259.2-feet or .72 of a foot per degree of arc or 18/25ths of a foot.
The length is 77-feet and the azimuth angle is 123.75-degrees (half of 247.5).
Again, .672 (84/125ths) of a foot = 1-degree of arc.
This is an exact repeat of the last leg in distance and angle.
The length is 82.5-feet and the azimuth angle remains 123.75-degrees.
The voyage continues down the avenue to the Sanctuary Circle. The precisely drawn and angled lines shown fall accurately onto the stone positions at each leg of the journey and there can be no doubt that what is being described mathematically herein was the design intention of the original architects 5000-years ago.
Having now sailed for a considerable distance on a lay-line of 123.75-degrees, the intrepid sailors need to adjust their course. They veer slightly more to the south and hold a new course of 129.375-degrees (180-degrees opposed to 309.375-degrees). The sum of 309.375-miles would be 1/80th of the 24750-mile equatorial circumference of the Earth under this "11" series navigational system.
The distance covered during this leg is 73.33333-feet (73 & 1/3rd). At the end of the run the plotting circle is again created to calculate the angles back to the port of departure and onwards to the destination. Therefore: 73.3333333-feet X 3.141818182 = 230.4-feet or .64 (80/125ths) of a foot per degree of arc. The sum of 73.333333-feet would be 1/72nd of a mile.
The course shifts back eastwards to 129.375-degrees (180-degrees opposed to 309.375-degrees). The sum of 309.375-miles (309 & 3/8ths) would be 1/80th of the equatorial circumference of the Earth under the 24750-mile assignment.
The distance traveled in this leg is 88-feet. This is converted to a circle and produces 276.48-feet (276 & 12/25ths) of circumference or .768 (96/125ths) of a foot per degree of arc.
The distance is 77-feet and the angle is 120-degrees (180-degrees opposed to 300-degrees).
Again, .672 (84/125ths) of a foot = 1-degree of arc.
The angle was possibly meant to convey 121-degrees in a second reading (11 X 11).
The distance is 70.4-feet and the opposed and angle back towards the henge is 314.1818182-degrees.
This distance, when converted to a plotting circle equals 768/1250ths of a foot per degree of arc.The sum of 70.4-feet equals 1/75th of a mile.
It would appear that the tutors used this position to teach the varied expressions of PI, including the more rounded renditions of 3.15 & 3.125.
The distance is 77-feet and the return angle of travel is 312.5-degrees.
There were 3.125-miles in the ancient British league of 16500-feet.
The distance is 79.2-feet and the angle is 148.5-degrees.
The smallest increment in the "11" series of lengths was the link @ 7.92-inches, so this leg-length would be 120 links. The diameter of the Earth is 7920-miles. The length of this leg of travel X 3.141818182 = 248.832-feet or 864/1250ths of a foot per degree of arc for a circumference based upon this diameter. Under the other navigational system seen to be running side-by side to this one being discussed, the equatorial circumference was 24883.2-Greek miles. That navigational method, as taught on the West Kennet Avenue, will be discussed in depth as we proceed.
The value of 148.5 = 6 X 24.75. It will be remembered that the equatorial circumference of the Earth coded by this line of increments on the West Kennet Avenue is 24750-miles of 5280-feet each. The "Y"-Holes Circle at Stonehenge, measuring 178.2-feet diameter = 2.475-feet X 72. Similarly, the "Z"-Holes Circle at Stonehenge, measuring 132-feet (1584-inches) diameter = 24.75-inches X 64.
An increment of length that was coded into landscapes from Britain to Nazca Peru is based upon the value 891 (2.475 X 360) and it's very apparent that an increment based upon 2475 was much used in navigational calculations 5000-years ago. The angle value of 148.5 X 3.141818182 = 466.56. At Stonehenge, a marker in the Avenue indicates the rim of a circle that was intended to convey 466.56-feet of design diameter.
A circle with a circumference of 466.56-feet would be 1.296-feet (15.552-inches) per degree of arc. There would be 53 & 1/3rd increments of 466.56-miles in the 24883.2-mile circumference. Alternatively, there would be 192 increments of 129.6-miles in the 24883.2-mile circumference. The sum of 1555.2-miles would represent 1/16th of the 24883.2-mile circumference. The sum of 1296-years would be half the duration of the Precession of the Equinoxes (25920-years).
The distance is 88-feet and the angle is 146.66666-degrees towards the Sanctuary.
The distance, of course, converts to a circumference of 88-feet X 3.141818182 = 276.48-feet. This means that each degree of arc = 9.216-inches or .768 (96/125ths) of a foot. The sum of 921.6-miles would be 1/27th of the 24883.2-mile circumference.
The angle of 146.6666666 (146 & 2/3rds) X 3.141818182 = 460.8 or (÷ 360) 1.28 per degree of arc.
The distance is 68.75-feet and the angle remains 146.666666-degrees.
Under the 24750-mile assignment for the equatorial circumference, the sum of 68.75-miles would be 1-degree of arc. This length at West Kennet Avenue converts to a circle of 216-feet using PI @ 3.141818182 or .6 of a foot per degree of arc. There would be 115.2 increments of 216-miles in the 24883.2-mile equatorial circumference.
The sun spends 2160-years in each house of the zodiac during the 25920-year cycle of Precession. The ancient British Bushel volume was 2160 cubic inches. Here is one example of the recurring 216 value in ancient mathematical progressions, this time in a Babylonian volume standard.
6 Homer @ 21600 cubic inches, or
36 Artaba .. @ 3600 cubic inches, or
216 Sutu @ 600 cubic inches, or
2160 Qa . @ 60 cubic inches.
Having ventured 16 legs down the West Kennet Avenue, we'll take a little breather, then recommence. The Avenue markers are very complete for 32 legs for the "11" series and somewhat more for the "6&7" series. In time we should be able to calculate the exact positions where the missing markers once sat, sufficient for English Heritage archaeologists and other researchers to relocate the former positions with ground-penetrating radar.