Bornholm Grid Part Two - Lothian Scotland

In this section, The grid, based on 16*sq.root three miles(E), found on Bornholm is confirmed with the very first calculation applied to Scotland. In 1999, I first made contact with Bill Buehler, an Earth-Grid researcher of some 30 plus years, and promoter of what is known as Reshel grid dynamics, and much more, (of which more later!). I had known of his Rosslyn Chapel geometric analysis, from two A4 photocopies that were lying in the shop at the Chapel, a couple of years previously. I don't know why there were two piles of these on a shelf opposite the counter, and the assistant/volunteer gave the ok to take a copy of each, presumably there for use by a tour party. One was a plan of the Chapel, and the other an elevation, both with complex geometric constructs, and labeled with terms totally foreign to me, with explanations mostly beyond my comprehension, seeming to hint at a life spirit/force based on principles of geometric design, which the Chapel Design seemed to follow perfectly. It was the first hint that the geometry I had been finding, was somehow more precisely purposed than a mere cartographic exercise. I had ound of course precise pentagonal geometry, which did in fact incorporate Rosslyn Chapel, and related in measure to what Henry Lincoln had described in the south of France. More on this later!

When I had joined a discussion forum there was a topic in which this same mysterious terminology was referred to, so I posted my interest, and described something of what I had found. Biil Buehler answered, explaining that what I had obtained in the Chapel Tea-Room was his work. He congratulated me on my work, very pleased with the pentagonal system I had found, and even more so when I described a feature in the landscape, which I still have to describe, which for him was a sure sign of activation of a Reshel Grid system in the Edinburgh/Rosslyn area. I have been receiving posts from Bill for some Nine years now, and there have been many fascinating developments in that time.

One of the first systems he described in the landscape was based on the Roseline, or in Bill's terminology the Tavhara line, which passed through Arthurs' Seat Summit, Rosslyn Chapel, and St. Mary's Chapel to the south at Mount Lothian. This line I knew of, it's the one everyone finds. Bill described though a Reshel system, centred on St. Mary's Chapel, and a 20 mile radius circle, from Seafield Tower in the north, between Kinghorn and Kirkcaldy, in Fife, and Dryhope Tower in the Yarrow valley, near St. Mary's Loch to the south.



copyright William S. Buehler

It is the recti-linear grid derived from this graphic that I had been working on for a few years, finding The Bass Rock to be at the north east corner of the square constructed on the 40 mile diameter outer circle. This was one of the main systems that had developed when I had moved to Selkirk in the Scottish Borders, and the geometry kind of opened up or expanded with my investigations of the landscape, as I commuted back and forth to Edinburgh. I shall expand on this later.

After my Bornholm exercise, it was the diagonal from St. Mary's to The Bass Rock, I wanted to try first. I obtained the two relevant sections of 1:25,000 O.S. maps from the 'Get-A-Map' feature on their website, from the local library. And the obvious place to try on The Bass, was St. Baldred's Chapel. I worked out the grid references to the metre for both points, and did the calculations. To my total amazement, it was to within a few feet 16*Square root three miles (E), the exact same as the grid found on Bornholm.

Deleted google map, for now, see top of page!

The three main lines for now are the St.M's to The Bass Rock, St. M's to N. Berwick Law, and the St.M's to Dunsappie extended line.

Monday 22 Sept, 2998, equinox!
OK, after a few weeks break, I should get back to work!

Calculations

1. St. Mary's Chapel, Mount Lothian, (NT 275 570) to St. Baldred's Chapel, The Bass Rock. (NT 602 873).

3275.00 6570.19 St Mary's Chapel
3602.26 6873.26 St. Baldred's Chapel
---------- ----------
-327.26 -303.07

Using Pythagoras Theorem: 446.04 0.S.grid units of 100metres

which converts to 27.71556 miles (E)

divided by sq.root three = 16.0016, which is a 99.99% correlation with 16!

I am redoing the calculations as I go, with my hand-held calculator, as a check, and this still amazes me, how close it is to the Bornholm grid size. It is 8.4 feet and the references are calculated to the metre, 3.28084 feet, in theory only, in practice my calculations involve small areas of map, and pencil and ruler, so there is an added discrepancy inherent.

The angle of this line to the O.S map can be compared to the others and the angles to each other compared!

Using the two calculated figures above to give the tangent ratio the angle can be obtained.

(-327.06)/(-303.07) = 1.07915663, this gives the angle as 47.1802838.

The North Berwick Law line from St.Mary's Chapel, Mount Lothian

OK, time again to do some more. It is now Obtober first, another month of distraction and laziness.

Having established the Bass Rock line to St. Baldred's Chapel as being the exact same as the Bornholm grid, I need to show another possibility, on a slightly diferent orientation. This time using North Berwick Law:

3275.00 6570.19 St Mary's Chapel
3556.32 6842.23 N. Berwick Law
---------- ----------
-281.32 -272.04

again using Pythagoras' theorem: 391.34 O.S.grid units of 100 metres
which converts to 24.31672 miles(E)

which divided by square root three, gives 14.0393, which is a 99.72% correlation with 14. This discrepancy is some 69 yards, so not to the same 'exactness' as I normally allow, but North Berwick Law and The Bass Rock do seem to interact in the landscape from the area of Midlothian in the landscape.

The angle to O.S. grid again is found rom the tangent ratio of the two calculated components.

281.32/272.04 = 1.034113, which gives the angle 45.96 degrees.

I note this alignment due to the fact that Nylars Church on Bornholm marks the 13/16 point on the grid axis.

Compared to the Bass Rock line of 47.18 - 45.96 = 1.22 degrees, or 'roughly' one fifth of one clock-face-minute!(one c.f.m. is six degrees, there being 60 minutes in one hour, or 360 degrees!)

This could be considered as a 'Selah-spoke' in Bill Buehler's terminology, which he normally expects in a 'spinner' system. In discussion he would actually want it a bit greater, up to 3 degrees. I shall from here on consider only the Bass Rock alignment, but it should be kept in mind that this second alignment is there.

Bornholm Island, Baltic Sea, grid findings. Part One.

Introduction

This section summarizes the main results of many months of calculations on the data supplied by the Danish Government mapping office, Kort & Matrikelstyrelsen System 45 Bornholm, as provided by Erling Haagensen and Henry Lincoln in 'The Templars' Secret Island', page 177, published in the year 2000.

I restrict the findings to what is most relevant to the landscape geometry of the Lothians and Border regions of Scotland.

For this purpose I require only to use three site coordinates, those of Point Christianso*, where it is believed that a compass rose was carved in the bedrock of the small island, some 12 miles north-east of Bornholm, and two of the four round churches on the actual island of Bornholm, Osterlars* and Nylars. A fourth found/calculated point, at sea, is also used, and labeled by the authors Point C.

(* there should be a diagonal stroke through the 'O' of Osterlars, and the small case 'o' at the end of Christianso. Apologies if the omission offends, I don't have the correct characters to hand.)

The coordinates given here are the theoretical coordinates calculated by Haagensen and Lincoln, based on the altars to the east of both churches and the calculated position of the compass rose, which was blown up for building material at the end of the 17th century, and is mentioned in an extant letter by the officer in charge of the defensive construction at the time.

The actual Kort & Matrikelstyrelsen coordinates are for the tips of the conical roofs of the two circular churches. to the west of the altars, and for the Store Tarn on Christianso.

Haagensen's calculations were 'checked' by Distinguished Professor Emeritus Niels C. Lind at the University of Waterloo, Victoria, BC. His letter of reply is on page 144.

His first point of consideration was the accuracy of Haagensen's calculations:

(1) I calculated the coordinates of 12 churches and four auxiliary points according to the layout you specify in your Appendix, using a double precision computer spreadsheet. I have not discovered any errors in your calculations.**

(Neither did I, and took that as in some way verifying my methods, and workings. TG)

**My italics and bold. Lind merely has the final statement in italics!

This is in essence all that is necessary for the main point under discussion here. His fourth point I quote as it also gives a rule of thumb margin I use for accuracy of all the geometry I show in this blog. Namely 1:2000, or 99.95% accuracy:

(4)It is interesting to consider how medieval surveyors could have laid out a design such as ''the map'' in the field and positioned the churches. I have several years experience with similar field work, albeit using mid-20th century technology. I have no knowledge of what instruments and procedures they can have used, but they probably laid out open traverses in the terrain, sighting by eye and chaining distances with metal chains without correcting for temperature, sag and slope. I believe they could not achieve accuracies better than 1:2000 in the measured lengths over 10-20 km distances in fairly wooded and hilly terrain and 0.01 degree in directions. This would give RMS* errors of at least 7 m, roughly. Again, my italics - TG!

* RMS I take to mean Root Mean Square, of which I am not accustomed to using, and take his word on this final statement which he gives in italics which I also em-bold-en:

An RMS error of about 24.8 m, as found in (2) above** is not incompatible with the belief that the churches were located according to a plan such as ''the map''.

** not included here!

This letter is dated March 22, 1999.

Their book was published in 2000, and I was lucky enough to be at the launch at the Sauniere Symposium at Newbattle, in Midlothian, Scotland. I knew then I would have to study the material. It is now 2008 and am only getting to the stage of presenting it all! Time, continuous new findings, reading, computer resources/skills and so on.

I did my work on this in 2003/4, and wrote a report dated 10th November 2004, and distributed to a few friends/associates, along with an additional report covering the follow-up investigation into the landscape geometry of Scotland on 16th December, 2004.

Calculations

Keeping this section as simple as possible, the first and most important point to show is the span of the grid which follows by implication, namely the distance between the two furthest points on the line, from the island of Christianso through Osterlars and Nylars on Bornholm to the Point C, found by Haagensen and Lincoln:

the theoretical coordinatesin metres:

Y-component..... X-component
73,240.92 ............31,071.52 .........Point Christianso
39,444.21 ............60,223.48 .........Point C
------------ ............------------
33796.71 ............-29151.96

distance, by Pythagoras = 44632.44 metres

=146431.88 feet;
=27.7333 miles(E)

This distance is very close to 16*sq.root3, or27.7128 miles(E), a correspondence of 99.926%, or 0.0205 miles, or 108.24 feet, or 36 yards, over a distance of 27.7+miles(E).

This is all that is necessary for the next section when this 16*sq.rt.3 miles(E) is applied to a specific system in Scotland, namely St. Mary's Chapel in Midlothian to St.Baldred's Chapel on the Bass Rock in the Firth of Forth, near North Berwick.

I first came upon the 16*square root three miles(E)unit whilst doing the Christianso - Nylars distance:

Y-component..... X-component
73,240.92 ............31,071.52 .........Point Christianso
45,803.24.............54,738.38...........Nylars
-------------.............-------------
27,437.68.............-23,666.86

By Pythagoras' theorem: 36,234.604 metres, which converts to; 118,888 feet, or; 22.51514 miles(E), which divided by 'square root three' is 12.999122, which is a 99.99325% correspondence to 13.

And this also correlates to the system in Scotland, and complicates things somewhat as it indicates a second grid a mere degree or so off the main one, St. Baldred's Chapel/Bass Rock version mentioned above, but the second version using North Berwick Law at 14/16ths units of grid measure, as I shall cover in part two! Both systems centred on St. Mary's Chapel, Mount Lothian.

[I would like to include a bit on the Osterlars - Nylars measurement, which is on the same axis, and identified as the controlling radius of the system described by Haagensen and Lincoln.

y - coordinate..... x - coordinate

56,658.79............45,374.73..........Osterlars
45,803.24............54,738.38..........Nylars
-------------............-------------
10,855.55............-9,363.65

which is, by Pythagoras' theorem; 14,336 metres precisely(to within 4/100ths of a millimetre)!

For now I just wish to note that this radius gives a circle circumference of 56 miles(E) to 99.9875%, using pi - 22/7, and 99.945% using calculator pi, as indeed pointed out by (H & L).

There are some points of note which are interesting in themselves regarding this measure and the full grid measure, but not necessary for the immediate concern, applying the '16*square root three' miles(E) to the landscape of Scotland, centred on St. Mary's Chapel, Mount Lothian.]

A Google Map of Bornholm and main points. Osterlars and Nylars define the orientation, and Olsker Nyker extended defines Point C and meets axis at 30 degrees, hinting at hexagonal geometry.

The axis from Point C to Christianso is divided into 16 sections, each of 1.732 miles(E), (or the square root three):


View Larger Map

Tinto Hill - Preston Cross - Isle of May

Having had a break of some weeks from the geometry, I was checking a sketch I had done a few years back, and noticed a line I had not checked by calculation. It passes again through the unicorn Cross at Preston(NT 391 740), and links two points not previously mentioned, Tinto Hill(NS 952 343) and the Isle of May, or May Isle(NT 658 990, which is the Grid Reference for St. Adrian's Chapel).

[When I started my investigation, I was working with 1:25,000 scale maps, and the Isle of May was too far north of Lothian, as was Fife, and so no casual links could be made. The same was true for Tinto Hill, but to the south. It was when I was living in Selkirk that Tinto came to my awareness, as the part of a grid I shall be describing soon.]

The full grid references I shall use:

2952.75 6343.79 Tinto Hill

2965.23 6345.47 Scout Hill, a hill a mile to the east of Tinto, which is found to be a more exact point in line with the southern point on The May Isle.

3391.27 6740.57 Preston Cross, {unicorn}

3658.68 6990.19 St. Adrian's Chapel, May Isle.

3662.83 6988.49 South Ness, May Isle.



3658.68 6990.19 May Isle, St. Adrian's Chapel. The May Isle is roughly at 45 degrees to grid, from North-west to south-east and is a bit more than the diagonal of a grid kilometre square, or a mile approximately. The range is from North Ness {NT 651 999} to South Ness (NT 662 988}.
Marked features on the Island include, between St.Adrian's Chapel and South Ness, Pilgrim's Haven, Pilgrim's Well, Maiden Hair, The Pillow and Kettle Ness. To the north-west of the central Lighthouse are features marked as The Bishop, St. Andrews Well, Altarstanes and Standing Head. Near the Lighthouse, on the western shore, is Mill Door, a natural arch. The island is a designated Nature Reserve with sea-bird colonies on the impressive cliffs. It is less than a half-mile wide.

What I found was that the line of Tinto Hill through Preston Cross extended just misses the southern tip of The May Isle. To the east of Tinto is Scout Hill(NS 965 345), which is a mere 1/32nd of a clock-face-minute(6 degrees) off the Preston Cross - St.Adrian's Chapel line(0.188 degrees).

The bunch of angles range from 46.6 to 47.6 degrees to O.S grid north, which could be taken as being approximately 43 degrees north of east. This is possibly a midsummer sunrise line, if looking north-east from Tinto, or from Preston to the May Isle, across the Firth of Forth. At latitude 55/56 north, midsummer sunrise is approximately 45 degrees dependent on altitude. There is also a minor allowance required for the O.S. grid being 'normal' to true-north at 2 degrees west(Berwick upon Tweed). As this line is roughly in the area of 3 degrees west the adjustment would be minimal, and too complex for me to account for. It would seem likely therefore that midsummer sunrise from Preston Cross, or nearby Tower, would occur over the May Isle. The May Isle I am sure could be seen from the Tower. It would be interesting to get photo/video of the midsummer sunrise from the Tower. Perhaps next year, but access would need to be arranged.

Mid-winter sunrise would be seen in the opposite direction.

Calculations:

Only two included here, Scout Hill to Preston Cross, and Preston Cross to St. Adrian's Chapel.

1. Scout Hill/Preston Cross:

2965.23 6345.47 Scout Hill
3391.27 6740.57 Preston Cross
---------- ----------
-426.04 -395.10

By Pyhtagoras' theorem:

58105 metres
or 36.1045 miles(E), or 32.2 Miles(S), (20 times phi !?)

angle to grid north, 47.16 degrees, (426.04/395.1 = 1.0783; which is tan 47.16deg.)

2. Preston Cross/St. Adrians Chapel, May Isle

3391.27 6740.57 Preston Cross
3658.68 6990.19 St. Adrian's Chapel
---------- ----------
-267.41 -249.62

By Pythag. theorem:

365812 metres (120017 feet)

or 22.73 miles(E), or 20.273 miles(S)(remarkably 20 times the Comma of Pythagoras, 1.0136433, to within 99.999%, or 9.5 inches!!!)

[5/08/08 - just noticed that 22.73 miles(E) is close to 13*'square-root three', 22.5167 miles(E), after doing the following post on Bornholm! This is found to be the distance from Christianso to Nylars! I shall come back to this! The discrepancy is 375 yards, so something may show! TG.]


angle to grid north; 46.97 degrees.

angles difference: 47.16 - 46.97 = 0.19 deg., (1/32nd of one c.f.m.)

[Although not included in these calculations, the distance from Tinto Hill to St. Adrian's Chapel is 314034 feet, a 99.96% correlation with calculator pi, or 99.92% of 22/7.

A circle of this radius would have a circumference of 373,7 miles(E), or 333.3 miles(S).]

Tinto shall be mentioned in following posts, as well may The May be.

I shall do a google map for this line, but I will, no doubt, play about with a bit to see what turns up, using Google Maps and G-Earth.

Salisbury Crags Face and general area

In July 2006 I moved to Inverkeithing, and I had to get the train into Edinburgh, then get to Portobello Road to pick up the taxi for my nightshift. During the Festival I sometimes walked, from the staion, if the weather was nce. One time when crossing the Forth Rail Bridge there was a cloud formation in the form of a head over Burntisland facing north-east, with a trail of cloud over the Forth.



Looking at the photo now, at this scale the cloud face is none too clear!

Whatever the processes going on in my brain, walking into Holyrood Park between the Parliament Building and the Palace, taking a few photos of the crags and the lion carving near the car-park, gazing towards the crags at their eastern end, I took a shot of the interesting rock formations. Later when I downloaded the photos I was looking at this photo and saw a face formed by the crags rock. I could also see another two faces to the left.

I have been drawn back there many times since, examining the crags and verifying to myself that these are real stone formations and are identifiable in all light conditions. One in particular is very impressive, and is about 30 feet in scale.

Below is a link to a web-album with more photos of this and the other faces, and some of broom, and gorse in bloom this May, and some of St. Margaret's Loch and St. Anthony's Chapel ruin. This area covers the extent of spread of all the lines considered in the section on Schiehallion through Arthurs' Seat to The Eildon Hills:

gorse/whins/broom Arthurs Seat crags face May 2008

Lindisfarne to Duart Castle, Mull

The work of William S. Buehler has been mentioned previously, and Bill has been highlighting a grid possibility incorporating the River Almond and Cramond at its mouth. He has also in the past described a system using the Lindisfarne (NT 136 422) - Duart Castle (NM 748 353), on the island of Mull, extending from there to both Iona and Staffa.

Whilst in Google Maps I decided to plot this line and see where it crossed the entral area of my focus, and what else was included.

Using several points I calculated their relationships with both Lindisfarne and Duart Castle. Omitting detailed calculations for now, I found that the line from Lindisfarne to Duart Castle passed between Arthurs Seat and Inchcolm, and precisely the northern tip of Cramond Island (NT 197 787), some 68 yards offshore, at a distance from Lindisfarne of 63.5 miles(E).

(As I did this exercise I saw the line as a guitar string being plucked and vibrating between Arthurs Seat and Inchcolm, like a gate mechanism, limiting the pitch of the string.)

Other points of interest on this line Yester Castle, Musselburgh, Devilla Forest/Tulliallan Castle, Port Of Menteith, Ben Vorlich.

The line is on the Google Map on the Preston Cross triangle page. I need to limit the number of G-Maps I include as they slow loading down too much!

This is just a brief note on this topic, for now!

Schiehallion - Inchcolm

To complete this exercise I shall now compare the Inchcolm line with the Arthurs Seat line and perhaps some others. I am interested to see if there is some sort of system evident centered on Schiehallion.

2713.833 7547.736 Schiehallion
3189.700 6826.690 Inchcolm Abbey
--------- ----------
-475.867 0721.946

By Pythagoras theorem: 0863.92, which converts to 53.6815 miles(E), and 47.878 miles(S)

The angle to O.S Grid: 33.42352 degrees

The initial impulse for this exercise was noticing that the the lines from Schiehallion to Arthurs Seat and Inchcolm were separated by a very close approximation of one degree.

One of the findings of Haagensen and Lincoln, on Bornholm was a one degree construct, which was pointed out as having potential relevance as an example of a Medieval solution to a fact of geometric drawing that it is impossible to divide an angle into three, using the classic instruments of pen, compass and straight-edge. This is a purely technical problem, in that we use 360 degrees in a circle, which has a base of three, so that an angle of one degree is impossible under Pythagorean/Sacred geometry principles. I shall be discussing Bornholm later.

The angles from Schiehallion to:

34.4544 degrees: Arthurs Seat
33.4235 degrees: Inchcolm Abbey
---------
01.0309 degrees

0.0309 derees is 1/194th of one-clock-face minute, the tangent of this angle being, 0.00054, which at 54 miles(E) is 154 feet, or 50 yards approximately. Certainly on the island.

I then checked the Preston Cross line and the Galachlaw phi-point line

Schiehallion to:
40.0061 degrees: Preston Cross
31.9024 degrees: Galachlaw phi-point
---------
08.1037 degrees

Now, 8 degrees is easily divide three times to give one degree; and 8.1037 divide three times gives: 1.0129625 deg.

0.0129625 deg (1/463rd of one c.f.m.) has a tangent of 0.00022624, and at 63 miles(E) is 75 feet, or 25 yards.

So, some intriguing results but not a major concern at this moment.

8 degrees is 1/45th of a circle, so may be related to the circle divided into 15, 45 being three times fifteen. Perhaps relevant!

Google Maps line; Schiehallion - Galachlaw - Rubers Law

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