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:
73,240.92 ............31,071.52 .........Point Christianso
39,444.21 ............60,223.48 .........Point C
distance, by Pythagoras = 44632.44 metres
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:
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