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Hi Steve & All,
With respect to all the points you make, no contest. The remnants that
have survived to the present seem quite haphazard. Which portion of this is
wear and tear of ages, vandalism, faulty repair or features of the original
construction (keeping up with the Johnses without really knowing what they
did) is not subject to certain analysis.
My intent was simply to show that laying out an evenly spaced ring of 60
Brodgar stones would have been within their technical grasp had they chosen
to build it this way.
Dave
----- Original Message -----
From: "Stephen Shaw" <srshaw@Dal.Ca>
To: <naturens@chebucto.ns.ca>
Sent: Sunday, August 24, 2014 1:29 PM
Subject: RE: [NatureNS] Fw: 60 post Neolithic ring; very long/now even
longer
> Hi Dave,
> Very detailed, and could be how a Neolithic builder might plan a 60 post
> ring, but is that what they were actually aiming to do?
>
> Your basic idea ‘divide circle into 60 segments’ came from the Ring of
> Brodgar in the Orkneys (diameter 104 metres, m), which ‘originally
> comprised up to 60 stones’ (Wikipedia; that doesn’t sound all that
> definite as to number though). Each segment of the henge circle then
> would subtend 360/60 = 6° each. Not clear why the builders would be set
> on 60 segments, or 6°. What about other Neolithic circles – do they
> conform to this general construction pattern?
> Following this up, the answer seems to be 'no':
> The Stones of Stenness, nearby, elliptical ‘diameter’ ~32 m, had 12
> stones originally, as you say.
>
> I checked the same source under Avebury Ring, ~2600 BC, in Wiltshire
> UK, 332m diameter, huge, impressive, that I once visited as a teenager.
> The current reconstruction indicates that there were 98 Sarsen stones in
> the outer ring. The North Inner Circle inside this had 27 holes; the
> non-concentric South Inner Circle had 29.
>
> For Stonehenge, the outermost, oldest Aubrey circle (decayed wooden
> posts, ~100 m diameter ring) had 56 holes. A second concentric ring
> inside this had 30, and a third one inside that had 29. The huge intact
> part of the main currently visible ring has ~16 huge stones per half
> circle, projecting to 32 per complete circle, diameter ~36m; the ‘computer
> reconstructed model’ illustrated counts 36 of these uprights.
>
> The Stonehenge entry has links to similar Neolithic sites, but most don't
> have info on the number of stones that I could see, except
> Bluestonehenge (10 m diameter) had ~27 stones.
> Almendres-Cromlech, Spain: the earliest ring is Almendres I (6000BC, much
> older, early Neolithic) 23 holes outer ring; 20, inner ring.
>
> Many of these rings do not have perfectly equally spaced stones or
> postholes, though some of this could represent later subsidence, or later
> reconstruction (Stonehenge). The number of stones/segments in these
> examples then is 60, 12, 98, 27, 29, 56, 30, 29, ~36, 27, 23, 20. It
> doesn’t look as if there is an obvious common factor, a Neolithic cultural
> tradition to subdivide the circle carefully into some fixed number of
> segments. The circles have widely different diameters though, so perhaps
> the stone’s spacing might instead represent a constant distance between
> posts, some multiple of the Thoms’ megalithic yard, if that is real? That
> doesn’t pan out either. If ring diameter is D, step length L is L =
> Pi*D/N. Ring of Brodgar then gives L = 5.44 m; Stenness, 8.38 m; main
> Avebury ring, 10.6 m; Stonehenge (Aubrey), 5.61 m; Stonehenge (big ring),
> 3.14 m; Bluestonehenge, 1.16 m. The Thom megalithic yard supposedly is
> 2.72 feet (0.829 m, “accurate to 1 mm”). None of the intervals L above is
> close to a simple multiple of this 0.829m value.
>
> Perhaps the Neolithic builders simply laid out a rough circle to match the
> local terrain available, then stepped out the perimeter according to their
> personal whimsy, pegged it out provisionally then finally adjusted a few
> intervals to account for last step inaccuracy? That wouldn’t take much
> skill or insight. Neither the segment number nor the post spacing then
> would have any deep significance across these Neolithic henges.
>
> There doesn’t seem to be current enthusiasm for viewing these circles as
> general astronomical observatories, excepting that several do seem to have
> been aligned to observe sunrise or sunset at one or other solstice. This
> may have been only one of their cultural uses, though.
> Steve
> _____________________________________________________________________
> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on
> behalf of David & Alison Webster [dwebster@glinx.com]
> Sent: Saturday, August 23, 2014 4:33 PM
> To: NatureNS@chebucto.ns.ca
> Subject: [NatureNS] Fw: 60 post Neolithic ring; very long
>
> Sent by accident to DW hence forwarded.
> ----- Original Message -----
> From: "David & Alison Webster" <dwebster@glinx.com>
> To: "David and Alison Webster" <dwebster@glinx.com>
> Sent: Saturday, August 23, 2014 4:31 PM
> Subject: 60 post Neolithic ring; very long
>
>
>> ----- Original Message -----
>> From: "Stephen Shaw" <srshaw@Dal.Ca>
>> To: <naturens@chebucto.ns.ca>
>> Sent: Monday, August 18, 2014 2:25 AM
>> Subject: RE: [NatureNS] Neolithic stone rings etd.
>>
>> But subunits of 60 segments are not part of this series, so that remains
>> rawhide-unexplained too.
>>> Steve (Hfx)
>>
>> Hi Steve & All, Aug 23, 2014
>> Before launching into the 60 post circle I wish to make clear that I
>> am
>> in no position to say that these circles were installed as observatories
>> nor divine how they located the positions for these posts.
>>
>> But I think it is fair to say that such circles could have been used
>> to
>> record the apparent motion of the sun back and forth along the horizon
>> in
>> the course of the year and if they were astute enough to build this
>> circle
>> around a NS baseline then their records would be symmetrical, easier
>> therefore to grasp and less vulnerable to recording errors (West & East
>> readings should agree within measurement error).
>> In addition, if your survival depends upon crops grown then a calendar
>> (or some persons dedicated to keeping track of the seasons) is vital. And
>> in case those persons forget to carve a notch for a given day or two then
>> the observatory plus records would jog their memory. In a crude way such
>> circles could also be used to tell time with reference to sunrise (after
>> sunrise) or sunset (before sunset).
>> But most of all, there was not much leisure time back then so why
>> would
>> they have put so much time and effort into building these rings if they
>> were of no practical use ? If not for analog calendar and perhaps trying
>> to understand the pattern or sun movement (& perhaps moon movement) then
>> why do it ?
>>
>> Getting back to the 60 post circle one would as before lay out a NS
>> baseline and then, taking a new tack, install two posts at right angles
>> to
>> this baseline. Each of these quarters would eventually have 15 spaces
>> between posts on the circumference. The distance between all four posts
>> (N-E-S-W-N) should be equal and the astute ring designer would check
>> these
>> distances and make necessary adjustments before proceeding.
>>
>> The number 15 can not be divided by halving so, assuming that formal
>> math was unknown, other ways must be used that require only a crude
>> counting system and a bit of logic from first principles. I soon realized
>> that a stone age method to divide a hypothetical 6' diameter marble disk
>> into 360 degrees would be impractical for dividing a large ring into 60
>> parts so took a different tack. This became too involved to follow
>> without
>> a figure so I filed an image on Flickr at---
>> https://www.flickr.com/photos/91817127@N08/15011112022/in/photostream/
>>
>> First of all what is being divided ? Initially only the arc of the
>> radius running between two of the posts (e.g. North and East) is known so
>> that is the problem: how to divide this arc of unknown length into 15
>> equal lengths. And to do this readily one must derive a unit of measure
>> that is equal to unit edge of a 60 sided regular polygon that just fits
>> within the circle (these terms are for communication by e-mail not for
>> doing the practical job).
>>
>> Materials for measuring the arc between two corner posts e.g. North and
>> East:
>> 1) Four boat shaped measuring sticks about a foot long with a pointed
>> prow
>> and a notched stern to receive the point of boat behind it; call these
>> boatlets. The working length (prow tip to notch point) should be the same
>> for all four.
>> 2) The radius strand that was used to locate the North & South posts.
>> 3) A leather shoulder bag with pebbles for use as counting and recording
>> aids (pacing along the arc would indicate roughly the number required).
>> and an empty basket to record each time a boatlet is placed along the arc
>> by moving a pebble from the bag to the basket.
>> 4) a wedge shaped slab of wood or rock coming to a point at one end and
>> not less than a boatlet wide at the other end.
>> 5) Four staff:
>> one to walk from the East post to the North post, just ahead of the
>> other three, with the radius strand pulled tight,
>> one to place boatlets along the arc defined by the radius strand
>> (stern notch to prow),
>> one to move a pebble from the bag to the basket whenever a boatlet is
>> placed and
>> one to hold the string of three or four boatlets and pass the rear
>> one forward to the placer.
>>
>> Unless by some fluke the arc length were exactly equal to some whole
>> number of boatlets there will be gap between the prow of the last boatlet
>> and the near side of the North post. Insert the wedge into this gap so
>> one
>> edge touches the prow and the other touches the post and mark these two
>> points on the wedge so this length can be measured. On a scrap of flat
>> stone record the approximate radius of the North and East posts (This is
>> needed because the arc has been measured between proximal sides of the
>> posts.)
>>
>> Now the full length of the arc is known as the recorded number of
>> boatlets (the number of pebbles in the basket) + the wedge line + the two
>> post radii. The next task is division of this total length into 15 equal
>> parts.
>>
>> Materials for division of arc:
>> 1) a straight edge about 5' long.
>> 2) a flat rock about 14" x 14" squared on one corner for drawing right
>> angles.
>> 3) a flat slab of rock not less than 3 boatlets long and one boatlet wide
>> on one end or both ends.
>> 4) a scrap of hard rock (flint or quartzite) that is flat near a sharp
>> tip
>> for inscribing lines on #3.
>> 5) Fifteen isolated compartments (bowls, areas of hide segregated by flat
>> rocks, hollows in sandy soil etc.) into which pebbles from the basket can
>> be transferred after the full arc has been measured.
>>
>> Methods for division of arc:
>> Using the above straight edge, chose the longest side of large flat
>> slab (#3) that has a surface most free of humps and hollows, chose this
>> to
>> be the lower edge of the slab and inscribe a straight line near this edge
>> (slab baseline). Using the square (#2), draw a line that is perpendicular
>> to the baseline, of length equal to or greater than a boatlet and near
>> the
>> end of greatest slab width [for ease of description assume this to be
>> near
>> the right end of the baseline]. Call this corner B and mark on the
>> perpendicular the exact working length of a boatlet measuring from corner
>> B to upper point A.
>> Take a linen thread that is slightly longer than the baseline and fold
>> it back on itself four times, mark this length (1/16 of the thread
>> length)
>> on a scrap of flat rock and check that there is room along the baseline
>> for 15 intervals of this length (16 tic marks counting the perpendicular
>> at the right end). Measuring carefully from the long perpendicular,(point
>> B) and then from subsequent tic marks, inscribe 15 additional marks along
>> the baseline to obtain a total or 15 tic marks not including the long
>> perpendicular. Call the final tic mark O and, using the straight edge,
>> inscribe a line joining points O and A.
>> Using the square, inscribe lines perpendicular to line OB from each of
>> the 14 tic marks between O and B and long enough to reach line OA. Call
>> these perpendicular lines, from shortest to longest, 1*, 2*, 3*...14*.
>> Notice that the length of 1* is 1/15 of a boatlet, 2* is 2/15 of a
>> boatlet etc.
>>
>> This structure makes it possible to divide the combined length of one
>> to fourteen boatlets into 15 parts of equal length. And also makes it
>> possible to divide a length of less than one boatlet into 15 equal parts.
>>
>> Move pebbles from the basket to each of the 15 compartments in turn
>> until less than 15 pebbles remain to draw from (most readily done by
>> setting aside 15 reserve pebbles for final use). Continue transfer of
>> pebbles to compartments until the basket is empty and some of the reserve
>> pebbles have been drawn. Count and record the number of pebbles in each
>> of
>> the 15 compartments to ensure freedom from error. If there has been error
>> then move pebbles as necessary so all compartments have the same count,
>> drawing from or adding to reserve as necessary. Call this number of
>> pebbles in each of the compartments Compartment count (C). Count and
>> record the number of remaining reserve pebbles (R)..
>>
>> Note that the desired result, length of the arc between the North
>> post and the first new post is equal to C boatlets + R boatlets/15 + (
>> the
>> wedge line + the two post radii)/15.
>>
>> The length of R boatlets/15 will be equal to the perpendicular R*,
>> e.g.
>> if R=5 then R/15 will be the length of line 5*.
>>
>> Combine the length of the wedge line and two post radii into one
>> length
>> (by end to end addition) and inscribe a tic mark on line BA this height
>> above B. Call this point Wr. Using the straight edge join points O and
>> Wr.
>> Call the point where line OWr intersects perpendicular 1* 1**. The length
>> from 1** to the baseline is equal to [( the wedge line + the two post
>> radii)/15].
>>
>> Now the measures necessary to position that first post east of north
>> are available as C boatlets + R* + the height of 1** above the baseline.
>> Because the full arc was measured between post centers this first short
>> arc will have to be measured in the same way. To prepare for field work,
>> add R* to the length of the 1** line by end to end addition and subtract
>> the two radii (north post and first new post) by end to end subtraction.
>> Call this length Gap. Find the position on the field wedge that is Gap
>> distance between edges and mark it for field use.
>>
>> Starting with the North post place the prow of a boatlet against the
>> post, and with the radius strand pulled tightly as before, lay boatlets a
>> total of C times using the same procedures as previously. Place the wedge
>> with the Gap line just at the last stern notch and install the first post
>> on the circumference and against the wedge.
>>
>> The linear distance between these two posts (North and first) is the
>> unit of measure that can now be used to install the remaining 55 posts
>> (unit edge of a 60 sided regular polygon that just fits the circle).
>> Fabricate a light rawhide strand (length adjustable if necessary) with a
>> loop at one end to fit over the previous post and a yoke at the other to
>> fit against the next post. To confirm that this length will work well one
>> could leapfrog using two mobile posts to see if in fact the East post was
>> just reached in 15 unit edges.
>>
>> yt, Dave Webster, Kentville
>>
>>
>>
>> ________________________________________
>>> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on
>>> behalf of David & Alison Webster [dwebster@glinx.com]
>>> Sent: Sunday, August 17, 2014 7:34 PM
>>> To: NatureNS@chebucto.ns.ca
>>> Subject: [NatureNS] Neolithic stone rings etd.
>>>
>>> Dear All, Aug 17, 2014
>>> The August issue of National Geographic has an article that features
>>> the
>>> stone rings and other old (~5000 yrs.) structures of the Orkney Islands.
>>>>From this article & Wikipedia; the circular Ring of Brodgar; spaced for
>>>>60
>>> stones of which 27 remain and the slightly nearly circular but elliptic
>>> (so
>>> they say) ring of the Stones of Stenness; spaced for 12 megaliths with
>>> perhaps 1 or 2 never erected.
>>>
>>> Is it now so widely recognized that such structures served as
>>> observatories (an analog calendar and crude sundial) that it is too
>>> obvious
>>> to mention ? Alignment to the winter solstice at sunset (which would
>>> also
>>> fit the summer solstice at sunrise I think) is mentioned but surely
>>> these
>>> could have been used to keep track of time throughout the year.
>>>
>>> Even short stones would cast a long shadow at sunrise and sunset and
>>> the
>>> changes in direction with time would be consistent from year to year. A
>>> circular structure with 12 stones is a snap to lay out if you have
>>> enough
>>> rawhide and this natural and practicable number likely accounts for our
>>> 12
>>> signs of the zodiac, 12 months of the year and 24 hours in the day. But
>>> a
>>> ring with 60 markers is slightly more tricky to lay out, using Neolithic
>>> hardware, then say a ring of 48 or 96. The number 60 has the advantage
>>> of
>>> being divisible by 2,3,4,5&6 so the designer of this ring was just a
>>> step
>>> away from a 360o circle; dividing a circle into 60 or 360 parts is
>>> essentially the same problem and both have similar advantages if
>>> fractions
>>> are difficult to deal with.
>>>
>>> Yt, Dave Wwbster, Kentville
>
>
>
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