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Hi Steve, Jane & All,
The logical way to lay out a 12 post observatory is as follows.
1) Find a relatively level area of open land with unobstructed horizons =
from ~NE through S to ~NW.=20
2) Prepare 7 relativey slim and untapered, smooth rossed posts; say 2" =
in diameter =20
3) Select the center point and mark it with one of these posts.
4) Select a radius for the circle, braid a loop in one end of the =
rawhide length that is large enough to just slip down over the posts as =
this will be used numerous times. A wooden yoke at the other end would =
increase precision.
5) Sight from the center post to the Pole Star and mark the position of =
the North and then the South posts using the radius strand. These act as =
a baseline and enable checking the length of the rawhide radius strand =
which if not well oiled and protected can shrink or stretch.=20
DIGRESSION:=20
The hexagon must have been noticed even before the first crude tools =
were made; Bee & wasp hives/nests, snowflakes, drying silty mud =
deposits, Thallose Liverworts, some large celled Mosses... And if the 6 =
points of a hexagon are joined by drawing lines between opposite points =
you have a cluster of six equilateral triangles. Therefore the radius of =
a circle is exactly equal to the distance between the six points of a =
hexagon that fall on that circle.=20
END OF DIGRESSION
6) Using the above one can proceed to fix the location of the remaining =
4 points of the hexagon. If the ground is readily marked (weak sod or =
cultivated) one could simply inscribe an arc from the center post at the =
approximate location of the next post and then measure this exactly by =
moving the radius strand to the previously fixed post (initially the =
North or South post). If the ground is not readily marked then use of =
two strands of equal length would be indicated.
7) If one proceeded to locate post positions, starting at the North =
post, then the distance from the 4th post should be one radius strand =
from the South post provided no errors have been made.=20
8) Having installed the 6 posts of a hexagon one need only bisect the =
arc between adjacent posts (as before, most readily done if the soil is =
easily inscribed); bisect the line between posts, mark with temporary =
post flush with ground then swing the radius strand around the center =
post until it lies over the flush post. Repeat five more times and you =
have 12 posts equally spaced around a circle.
After this has been digested I will describe how to mark a 60 post =
circle. Some decades ago, for amusement, I went back in time mentally =
and worked out a way to divide a disk edge into 360 equal parts using =
stone-age hardware and the 60 post layout would use the same stone-age =
"math".=20
Yt, Dave Webster, Kentville
----- Original Message -----=20
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.
> Hi Dave: You need an astronomer with an interest in history for this, =
so stand by, hopefully, for input.
>=20
> Meanwhile, this astronomical observatory idea originated I think with =
Alexander Thom, based on his idea of a a common unit of length, the =
megalithic yard (MY) of 2.72 feet. This unit supposedly had been used =
with precision to lay out British and French neolithic stone circles. =
While this seems not to have been entirely discredited, later critics =
doubted that there was a unit with this precision in universal use, and =
that distances could have been measured adequately instead simply by =
pacing-out, not necessarily by using a common physical yard-stick. I =
can't remember the connection, but the MY supposedly was somehow related =
to an astronomical cycle, indicating that you must have had active =
neolithic astronomers to make the connection. Perhaps someone else can =
remember the connection, or if I've got this wrong.
>=20
> Not sure about the universal '12' ideas. The main units of time that =
we and presumably earlier populations used were based on 3 quite =
different astronomical cycles that are unrelated. Days are/were =
measured based on Earth's daily rotation on its axis, easily counted =
though not precisely constant. Months depended on the Moon's rotation =
about Earth, easily observed as recurring phases of the Moon. Years =
are/were measured in time units based on the Earth's orbiting around the =
Sun -- much more difficult to calibrate accurately, probably accounting =
for the need to calibrate by building fancy sunrise-observing =
structures, accurate to the day at solstices. Very important for =
correct crop planting. Unsurprisingly, neither of the smaller units in =
use at present divide exactly into the largest unit, the year, or into =
each other, hence yearly movement of Easter, calendar day regression and =
the need for leap years. Not clear how you would use a megalith with =
one annually precise alignment axis to tell the time (for instance the =
day, month) at other times of the year.
>=20
> I've forgotten most Euclid, but how do you subdivide a circle easily =
('a snap') into 12 subunits? I can see how you draw the first line and =
find its centre (will become the centre of the circle) with a rawhide =
compass-divider, and how you can draw the second diameter at right =
angles to this with the same gear, and then complete the circle. You =
are then left with a circle with 4 equal quadrants, each of which has to =
be subdivided finally into 3 segments to make a total of 12, like the =
hours on a clock. Isn't this the difficult problem of trisecting the =
angle (bisecting is a snap with a simple compass, but I thought =
trisection was not)? Please advise.=20
> Once you've somehow accomplished the trisection of 4 segments into 12 =
sub-segments with 30=B0 central angles, then 24, 48, 96... segments are =
easy (bisection), as you imply. But subunits of 60 segments are not =
part of this series, so that remains rawhide-unexplained too.
> Steve (Hfx) =20
> ________________________________________
> 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.
>=20
> 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