Working projection of possible plan

A very dear friend, who took it upon herself to leave no manuscript unturned in Dublin, to find for me illusive information on the Grianán, brought home from her last visit a plan, drawn in January 1835, signed by Robert Kearsley Dawson, containing some additional measurements.
Having watched a programme about the pyramids in Giza, it occurred to me that some measurement unit would be required to built any structure worth their stones. And a plan of its layout, contents, as well as the principles applied throughout the construction, based on the meaning and function of the build.
With the outside diameter now at hand (106 ft. or 32.3088m) I could establish the circumference of the monument: π = circumference divided by diameter, therefore diameter = c x π = 333 ft. or 101.50m.
Having a circular structure as subject, I had already divided it into 12 sections a couple of years ago, based on measurements for time and distance by observations of the stars. The Ordnance Survey plan had to be rotated with east and the gate facing upwards, for that is the way the ancient builders saw their world. The plan below also contains additionally the locations of artefacts found by Dr. Walter Bernard during his restoration fifty years later and the midden at the ‘drain’, neither of which was discovered during the Ordnance Survey.

Dawson's plan with additions

Dawson’s plan with additions

1/12 of the circumference = 28’1” or 8.4583m.
Playing around with lines of alignments of known points within the monument, particular in the upper right quarter, I got my 12 sections. Only they were not equal. But neither are the passages of the different stars or the moon. The three sections of this quarter also seem to increase by an equal, or at least, similar percentage. For the purpose of simplifying the matter for me, I named the three section a – for the upper, b – for the middle and c- for the lower one. B, as being in the centre, was given the value of 1/12 of the circumference of 28’1” or 8.4583m, a = b – 25% = 20’10” or 6.3437 m and c = b + 25% = 67’6” or 10.573m. A + b + c = 83’3”  or 25.375m = 1/4 of the circumference.
It does not seem very likely that a variation of a rather complex number like 25.375 would have been used as measurement unit. But 0.25375m = 0’11” and 0.025375 = 0’01” – 1 inch, making it a more practical number to work with and a reasonable contender for the unit which may have been applied during the construction of the Grianán.
The layout of the monument appears to be mainly based on quarters. At the entrance the width at the bottom is 4’ or 1.2192m. The width at the top is 3’ or 0.9144m = bottom width – 25%. Strangely enough, the same could not be established at the entrance to the southern passage with a width at the bottom at 2’1” or 0.635m and at the top at 1’11” or 0.5842m, only that their combined number equals the bottom width of the main entrance. Staying with entrances, on this plan and a second, in great excitement delivered by my good friend, and dated 14 August 1834, signed ‘Drawn by James Mc Gann’, the northern passage remains entrance-less, confirming William Blacker’s observation of there being no such thing.
My estimation of the height of the monument, which would be an average, for the southern section of the wall lies deeper, at the beginning of the slope, and as noticed and executed accordingly by Walter Bernard, had to be built higher in effort to give it a more uniform appearance, is 1/4 of the circumference divide by 4 = nearly 20’10’ or 6.34375m, which also equals section a of the quarter above.  The only number I could come up with for the approximate height of the entrance gate, which should be in proportion to the rest of the building is 6’11” or 2.1146m, arising from the fascinating possibility of being the same figure when a is divided by 3, b by 4 and c by 5, reflecting the percentage which occurred before of b being 1/12 of the circumference, a = b – 25% and c = b + 25%.
Theoretically the layout of the interior, where goes what, may have been based on this or a similar principle. Missing measurements could be calculated, like the original position of stairways, their height and their amount of steps, as well as the extent of each platform amongst other unanswered questions. Walter Bernard only based his restoration and reconstruction on known examples of other monuments like Staigue Fort in Kerry. It has been some time since. But this, I gladly leave to someone, who can guide his way more educated through the jungle of mathematics and geometry.

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