Tuesday, 22 July 2008

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


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.


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

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


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

Thursday, 10 July 2008

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.


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.