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Re: Megalithic Measurements
by Dominic Search at 14:34 27/01/06 (Blogs::Simon)

Curious indeed, although I found the style a bit confusing at times. For completeness, here's a summary of a discussion we had a few years ago on Cix...


Calculating The Megalithic Yard

In The Book of Hiram, authors Christopher Knight and Robert Lomas propose a method by which ancient engineers may have calculated the Megalithic Yard. Here is a full description of the empirical method. It is based on the use of a pendulum to count 366 beats (half cycles) within a time frame defined as 1/366th of the length of a day (366 supposedly being the number of sunrises from one spring equinox to the next, as perceived by the megalithic builders). The length of pendulum cord that produces this period is then doubled to give one Megalithic Yard.

But Lomas/Knight omit a mathematical formula. It is based on the classic pendulum period (note the addition of 2 doublings - one to turn cycles into beats, and one to turn the pendulum length into a Megalithic Yard). Thus:

MY = 2(g(2T/2Pi)^2)  

where: 
   g = acceleration of gravity (approx 9.81 m/s^2)
   T = 1/366 of 1/366 of 1 day in seconds (86400/133956 = 0.644988 secs)

This produces 1 MY as 0.82699 meters, very close to the 0.82966 meters (2.72 feet) that Thom discovered. In fact it deviates by only 0.32%.

LITL.W/L
Dominic.


Hang on, I've got to do this for myself :-)

366 beats in 1/366 of a day is 366/2 = 183 periods (T) in 1/366 of a day, so the period for this pendulum is therefore:

183T = 86400/366 seconds
T = 86400/(366*183) s
T = 1.2899758 s

(I think you've used T for beats, which is why I was confused when I first read your post)

Now: T = 2 . PI . sqrt(L/g), where L is the pendulum length

So: L = g . (T / 2 . PI)^2

And: 1MY = 2L = 2 . (g . (T / 2 . PI)^2) - which is different to your formula in the coefficient of T because your T (beats) = half of my T (period)

Rearranging:
               2
          g . T       9.81 * 1.6640376
1MY =   ---------  =  ----------------  =  0.826994 m
               2         19.739209
         2 . PI

For no reason at all other than pleasing coincidence, the numerical value of 1MY in feet is only 5 parts in a thousand smaller than e :-)

86400/66978 = 4800/(61^2), which would seem to indicate that we'd be looking at a pendulum period T of 1 and 1/3 seconds if they did a Babylonia 1/360 of 1/360 division of the sky instead of a 1/366 of 1/366.

Nicely, that gives a beat of 2/3 of a second which is the only fraction the Egyptians used that didn't have a unit numerator, and had its own glyph (which evidently had associations of being sacred, for reasons now unknown).

S.


> I think you've used T for beats, which is why I was confused when I first read

Ah yes, I seemed to have confused myself in writing it up :)

> if they did a Babylonia 1/360 of 1/360 division of the sky instead of a 1/366

Since a Megalithic circle has 366 equal parts, Lomas/Knight suggest that "when mathematics came into use in the Middle East they simply discarded 6 units to make the circle divisible by as many numbers as possible". Plausible, but I've yet to encounter a decent study on the measurement origins of arc and time.

> Nicely, that gives a beat of 2/3 of a second which is the only fraction the Egyptians used that didn't have a unit numerator, and had its own glyph (which evidently had associations of being sacred, for reasons now unknown).

The two earthly pillars (of upper & lower Egypt) that when linked (as an arch) with divine ma'at, ensured the physical and spiritual well being of the nation? Or perhaps the two deities (Osiris & Isis), in who's man-god offspring (Horus) the pharaoh's divine power is rooted?

LITL.W/L
Dominic.


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