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Megalithic Mathematics 10.

Avebury- alternative designs.

3.10.1  The 200 MY ring and point Z. Thom's Avebury design may not be the only approach to resolving this complex figure. If the 200 MY construction circle on which Thom based his approach is moved a few yards to the north west it picks up on the three most definitive features still remaining of the great ring, points G, F, M. These are clearly 'corners' of this unique shape.

Further it can be seen that positions F and M are the tri-section points of the semi-circle GFML as the three chords GF, FM and ML are all 200 MY in length and equal to the radius of the circle. The stones of the arcs GF and ML run close to the perimeter of the 200 MY circle. Note how the centre of the construction circle, point Z, rests perfectly on the perimeter of the older, northern stone circle.

3.10.2  The chosen dimensions for the Avebury design may be, as with Kerry Pole egg ring, a reflection of the units of measurement employed in the original devising. Thom remarks that this design must have been laid out time and time again before arriving at such a satisfactory solution. This may be so but not, perhaps, at Avebury or at least not to the large scale we now see. If the basic unit of measurement was the Megalithic Rod of 100 Megalithic Inches then a 1:10th scale would have made an appropriate initial model. This 1:10 model may itself be a larger version of an initial 1:100th plan worked out in sand or on flat rock by a process of trial-and-error which could furnish a variety of designs with acceptable dimensions. See also Kerry Pole egg ring Megalithic Mathematics7. para. 3.7.3. And Woodhenge. Also Mensuration 3 3.10.3  A method of drawing large arcs without rope scribing. Following is a construction algorithm with which large arcs may be drawn on a 200 MY radius without the use of long ropes. Essentially this approach requires the setting out of a small scale version of the intended design from which the larger ring's construction points may be located by sighting through ranging poles erected at the salient construction points on the model.

3.10.4  The 1:10 model.

At this scale, 1:10 of the great ring, a peg and rope-scribing method should be accurate enough, with care, but alternatively, if high precision is to be assured, base line survey could be used. That is each construction point is located by careful laying of accurate measuring rods end-to-end over level, prepared ground. This design would be particularly appropriate for such an approach being basically three equilateral triangles side-by-side.

3.10.5  Finding F and M by ranging.

Find G and L by base- line measurement from Z. Construct two further equilateral triangles at G and L each 200 MY from Z. Erect ranging poles at all points including the bisectors of the chords. By careful ranging through pole a to pole G and through f to Z point F may be located. Similarly point M may be found. G, F, M and L all lie on the perimeter of the nominal 200 MY ring. GF, FM and ML are all 200 MY chords.

	With a little experience ranging in locations by sighting through poles set at these distances can be achieved with an accuracy of plus and minus a few inches.

3.10.6  Setting the sagittae.

It would be known from prior investigation that the sagitta of a 200 unit chord set across a 200 unit radius circle will be exactly 27 units in length. When this length, 27 MY, is set as the perpendicular bisectors of the first and third chords, GF and ML, then the midpoints of these two arcs have been located on the nominal perimeter as at W, and V. If arc FM, which is much flatter, has a theoretical radius of 500 MY then it's sagitta would be 9.8 MY, perhaps accepted as a nominal 10, and used as the locator for point Y the bisector of arc FM on the perimeter.

3.10.7  Finding subsequent sagittae by subdividing chords

The next generation of chords are drawn from the last located perimeter point to the ends of the previous chord. Perpendicular bisectors of these new chords may be ranged in again from the 1:10 scale as sagittae. These second generation sagittae measure 1/4 the length of previous sagittae. This will give good approximations for locating further points on the chosen arcs.

3.10.8  Completing the arcs.

With this procedure there is no requirement to draw large arcs with the rope and pegs method. In the initial ranging through sighting poles any object tall enough to obscure the line could be ranged around by taking off-sets at right-angles.

3.10.9  There would be no necessity to draw the very large arc FYM's radii with either rope or base-line surveying. Although the nominal center of this arc is many yards outside the bank and ditch it is an entirely theoretical position as the arc is located by the tri-section of the initial 200 MY semi-circle and the known relationship between it's sagitta on a 200 MY chord.

3.10.10   Avebury plan with 200 MY ring and point Z. The above construction set applies only to half of the stones of the outer ring. Perhaps a case may be made for an arc GJ at the northern quadrant. The dimensions of this arc, if centred on point v1 are very acceptable as integers; radius = 360 MY, chord = 265 MY, sagitta = 29 MY and arc = 274.18, perhaps a nominal 275. Note that the bi-sector axis of this arc passes along the line of one side of the rectangular cove- a very early structure here. Also this arc axis runs through the centre of the northern 125 MY circle.

When the above construction set is laid over a plan of Avebury stones and earthworks we may see how it coheres with the remains we have today. Until further confident stone positions are recovered there will be difficulty identifying more arcs.

3.10.11  Astronomical setting of the 200 MY ring. The principal axis of the 200 MY ring, GZL lies at about 311.5 degrees azimuth. This is a few degrees short of the direction of summer solstice sunset. The bisector of the large arc FYM running through Z has an azimuth of 41.5 degrees also a few degrees short of indicating the Moon on the horizon when at a northern Major Lunar Standstill.

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