Tuesday, 18 September 2007

Some Lothian geometry, Borthwick as focus, leading to The Eagles'Nest - consider as Part two

The first diagram shows the first hint of geometry I found way back in 1993/4. I wont comment further yet, as it is the set of four after I wish to concentrate on. Just that this first highlighted the Meeting of the Waters in Dalkeith Estate, which led eventually to the pentagonal system shown, which is central to the whole complex, as found by me. It is relevant also in that Carberry Tower or Queen Margarets Mount in the Carberry Estate is identified by Bill Buehler as being the radius of the circle centred on Borthwick, which is the topic here.

This diagram shows the Borthwick axis in relation to the pentagonal system. This axis is that identified by Bill Buehler, whose work I have been studying for some 8 years now, with emphasis on his geometrical systems as applied to the Lothian area. Just when I seem to be getting on top of things geometric, along comes Bill with another stunning system which leads me off on another trail for weeks/months, years even. This system is one such. I had been offline for a while, working on whatever, and when I got back online, there's this system centred on Borthwick, using the David Wood's pentagram based on a 15 division circle. These diagrams show what I found, the basic geometry. My previous post shows the development of this system to a perfect pentagon based on the circle mentioned above. Part two gets complex, later. The angle of the axis is emphasised by Bill as being indicative of a Parhelion effect of the sun, the 'Sun-Dogs' phenomenon, at 23(+/-) either side of east. The Sun-Dogs effect is created by the hexagonal ice crystals if the upper atmosphere.

This is the circle centred on Borthwick, with Queen Margaret's Mount as radius. The 15 divisions are shown.

This shows the completed perfect pentagon extended to Craigleith Island, off North Berwick. This line extended south, off the page, leads to Eagles Nest near teh Gordon Arms, on the Yarrow, at Mountbenger, some two miles east of St. Mary's Loch, just off the Innerleithen Road. This point proved to be of great significance in the whole scheme. see Part two, after this.

I have included a circle either side of the Borthwick one, and these also play a part in the developing whole.

A lot of dots can be seen on some of these diagrams. They are all specific points in the geometry, and a list shall be provided with Grid References later, as the chance occurs!

Part Two

Ok! Part two, which is actually the third part, with the David Wood penta excercise being the first. I'll get round to changing things to suit to avoid confusion.

I've spent the past week re-reading The Ascent Of Man, by Prof. Bronowski, the book of the early seventies BBC TV series, some may remember. Still fascinating!

I've also been watching the night/morning sky. Mars is up near the Gemini twins, Orion AND Sirius have appeared again just below Mars, with Venus stunningly bright in the morning eatsern sky. I note that Saturn is around there too, but I havent spied it due to dawn light and Venus dominates. Wednesday night the sky was clear and the full moon was brilliant. Jupiter is west of south in the evening.

Anyway, part two of the Borthwick excercise:
This first image shows three lines converging towards the bottm. These all meet at Eagles Nest, unfortunately the scaling didn't allow this point to be included. This series of drawings was done when I had a clapped out, limited computer last year. They were all done in Paint, accurate to the pixel, which is as good as I could manage. This is insufficient to show the actual accuracy. Most of the points were calculated and plotted individually, and checked prior to plotting. This took a long time, as did the drawings in fact. Many months hard slog, if I may add! The first drawing shows what in effect was the stunning finding when it all panned out. Namely finding that Eagles Nest point confirmed the interrelatedness of the original pentagonal, the Borthwick complex, and the Preston Cross(unicorn atop) which I have been working on for a few years now. I took Bill Buehler there in 2003, as it had already become a very important point. It is also why I took the unicorn as a symbol! There are three lines coloured green in the drawing. The left hand one, projects from the chord of the original pentagon, which includes Arturs Seat(AS), and includes two corners, Leith(L) and Shewington(Sh). The central line runs from Preston(unicorn) Cross(PuC), through Borthwick Church, the centre of afore mentioned system, and the right hand line is the chord of the found perfect pentagon, running from Craigleith Island(CI), through Pilmuir House(Pil,H,).

The second drawing again shows these three lines with a few interesting findings. For instance the original pentagon has two sides projected to the Craigleith chord line were it cuts the Borthwick Church axis. I have included the three circles cnetred on Borthwick as a guide.

The third drawing has the Mavisbank hexagon included and it may be seen that it too converges with the axis at a significant point. The colours are inverted giving the black background, and the three lines under discussion are in the primary colours.

This fourth drawing is rotated so that the Borthwick axis is horizontal, which allowed me more space to work in the Eagles' Nest point(EN at the very bottom) at long last. That was an effort in itself. As I mantioned previously, it all gets a bit complex, and this ain't it all. Again the accuracy is to one pixel, and I have circled certain areas, as they are multiple point areas. For instance, BWM is the Black and the White Meldon, just outside Peebles. ETM, is the Eildon Hills, Trimontium to the Romans and Melrose. AS is Arthurs Seat and surrounding area.

The light green grid is the Borthwick hexagon projected, just to see what happened. A few points of inteest but I won't bother with that just now.

I haven't put in the Arthurs Seat line to Eagles Nest in this drawing, an omission, partly due to the complexity already there. There is an additional line from Eagles Nest to the Eildon. I first found this when working on that area, when I lived in Selkirk, and there were indicatiuons of another sytem at the time, and should be followed up when time allows. I shall finish here for now. I shall do a follow up soon, concentraing on the Preston Cross point and the astonishing trinagle found to have its apex there. I have made the last two larger which may help, if they are clicked on they should open in a new window. If anyone wants them even larger, let me know!


Anonymous said...

Thanks for the helpful post! I would not have gotten this otherwise!.

Tom Graham - Landscape Geometry said...

Thankyou, It is all very complex, I'm glad to know someone at least got something from it all.
I hope to return to this blog soon, there is still a lot of work to do to take it all forward.