phi-latitude

O. S. Open Source API trial

2011-11-08T10:05:00.002Z

I have just now registered for the OS Open Source facility and hope that it works as my initial trial was very good, in that not only is it a full map of the UK or Britain, but it gives universal grid references instead of the 'coded' form for the map sections i.e. with the two letter suffix followed by six figure references. This new facility gives twelve figure references, which is what I had been doing manually for many years now. It appears to be a new thing, to me at least, and is what I have been dreaming of for yonks now!

What spurred me into action was a recent request asking for any leads into the Glasgow area geometry. I found an interesting site based on the work of Harry Bell, who I knew of, but never met, and he was deceased before I tried to contact him. That was back in 2002/3, but a google search found many sites connecting with his work.

I have started to plot his points and see how it develops alongside my own findings, and the techniques I have developed over the years. This new resource is ideal, if I can get it working.

Here's hoping!

Roman altar stones at Inveresk, Musselburgh

2011-03-17T17:11:00.003Z

The B.B.C. reports the discovery of two Roman altar stones at Inverek, Musselburgh:

Two rare, carved altar stones found in East Lothian could shed new light about the Roman period in Scotland, it has been claimed.

The Roman stones were found during the redevelopment of a cricket pavilion in Lewisvale Park, Musselburgh.

Experts said they may help re-write the history books on the Roman occupation of Inveresk.

Although they were found in March 2010, it has only now become safe to fully inspect them.

Archaeologists said the stones were of "exceptional quality".

The experts from East Lothian Council, Historic Scotland and AOC Archaeology Group have been carefully removing the stones for the past year.

Only the backs and sides were visible until this month, when it was finally safe to make a full inspection.

The first stone has side panels showing a lyre and griffon as well as pictures of a jug and bowl, objects which would be used for pouring offerings on the altar.

The front face bears a carved inscription dedicating the altar to the god Mithras - the furthest north that such dedications have been discovered.

Mithraism was a religion in the Roman Empire from the 1st to 4th Centuries and the worshippers had a complex system of initiation grades.

Mithras is often shown slaying a bull with Sol looking on and there is often an association between both deities.

Face of God
The front face of the second stone shows female heads which represent the four seasons.

All are wearing headdresses, spring flowers, summer foliage, autumn grapes and a shawl for winter.

The centre of the stone contains a carving of the face of a God, probably Sol, wearing a solar crown.

Continue reading the main story
“
Start Quote

This is the first evidence for the god Mithras in Scotland, and changes our view of Roman religion on the northern frontier”

Dr Fraser Hunter
National Museums Scotland
The eyes, mouth and solar rays are all pierced and the hollowed rear shaft would probably have held a lantern or candle letting the light shine through, similar to a Halloween pumpkin or turnip lantern.

An inscription on a panel beneath the four seasons is currently partially obscured, but experts said it was likely to bear the name of the dedicator - who is believed to be a Roman centurion - and the God to whom the altar is dedicated.

Traces of red and white paint are still visible beneath the inscription panel, which experts said suggested it was originally brightly painted.

Ruth Currie, East Lothian Council's cabinet member for community wellbeing, said: "This is enormously exciting and its significance could be huge.

"These beautiful artefacts could reveal a whole new strand of East Lothian's history and possibly even shed light on the way the Romans lived on an international scale."

Dr Fraser Hunter, Iron Age and Roman curator at National Museums Scotland, said: "The quality of these sculptures is remarkable, and they will tell us an enormous amount.

"This is the first evidence for the god Mithras in Scotland, and changes our view of Roman religion on the northern frontier."

Dr James Bruhn of Historic Scotland said: "The discovery of altar stones to the eastern God Mithras adds a fascinating new chapter to the story of Inveresk's Roman past."

Inveresk is an interesting place, with prominent old church, a boundary point visited during the Common Ridng of Musselburgh, and some interesting old houses. I had thought Inveresk would have been more involved in the geometry than it has till present. I only have one alignment for it, and can't even remember what it is at present. I'll give another look.

A few years back a carved stone was found in the River Almond at Cramond, in which a lioness has a man in her mouth, which Bill Buehler found of interest.

Also, the headquarters of Scottish Widows Insurance Company between Melville and King's Gate, the riders neck/shoulder area, are built on the foundations of a Roman fort or villa with attached bathhouse. So, the Romans had a substantial presence in the area, and of course Dere Street runs up into the Lothians and there is also the Signal Station on the Eildon Hills.

Back to the future, or forward to the past !?

2011-03-03T02:19:00.003Z

It has been many months, eight or so, since I last posted, due to various factors, a new computer allowing greater access to the temptations of the internet, allied to my own lethargy and sheer laziness, and perhaps just life getting in the way.

Anyway, here I am back with the intention of carrying the work further.

My previous post was of the (near) summer solstice photo over the Forth Road Bridge from Hawes pier at South Queensferry. This year I intend to develop this further, and if possible be at Hillend fort for the summer solstice setting. This may not be practical given my lack of transport, but hopefully things will work out!

The photo was taken a few nights after the solstice so I am unsure exactly how the suns setting point had changed, but it would not have been by much. Also the photo was taken a bit after sunset from sea-level. Hillend is the logical point to get an accurate fix from at the point of sunset.

Dalmeny to Eildon solstice confirmation

2010-07-13T16:39:00.003+01:00

horse'n'rider slideshow

2010-03-17T15:58:00.005Z

just a basic slideshow, with the three images superimposed:

To get a full screen view, click on 'hnrslide3' button in bottom left corner, and chose 'slideshow'!

horse'n'ridercollection

2010-03-17T15:39:00.000Z

O.S. Pathfinder 420 NT26/36 Penicuik Dalkeith 1:25,000

2010-03-08T16:19:00.004Z

I came across this relatively clean copy, but showing some wear and tear, with added coffee or wine stain at the bottom.

Click on the image to open full screen in new window. The image size can then be increased or decreased using 'Ctrl and + or - keys'. Use back arrow to return to this page.

The same with a few labels:

G Galachlaw
M Mavisbank earthmound
MoW The Meeting of the Waters/Lady's Seat
NA Newbattle Abbey
NC Newtongrange Church
RC Rosslyn Chapel
Sh Shewington

horse and rider map: O.S. 1:25,000

2010-03-05T06:26:00.007Z

Well, a week ago I couldn't get a connection between my digital camera and the computer. I checked the USB lead at both ends, but it didn't connect with the computer. Tonight nothing different, but the usual window appeared with Picasa as an option for downloading with!? I put in the main pentagonal lines which cover this map, and the blue line from Allermuir Hill to Camp Ridge, which includes both Mavisbank earthmound and Newtongrange Church. I'll cover the unfolding geometry on this line with Mavisbank as centre later!

This is the original map which I had pasted onto a board with the surrounding maps, giving me the main area of my work. A closer look will show my working lines, with many highlighted spots. It was whilst gazing at this one dispirited night, back in 1999 and asking despairingly what it was all about that it appeared to my minds eye, it was like in bas relief, the image came out of the flat surface and was so obvious, how come I had never seen it previously. Well, my best guess is, the act of sitting back gave me a detached view, and at a suitable scale, and the frame of mind was probably a contributing factor. Stunned and shocked as I was, on inspection it was astonishing, but not entirely surprising that the features were actual landscape structures, made up of estate boundary walls, with specific points of the feature marked by farms, churches, castles and even housing developments, which in effect follow the lines of the fields upon which they are situated. For example, the horses ears, are delineated by the estate of Woodburn, with the space between them taken up by a school, the playing field/playground left white, with buildings/houses in black.

I eventually coloured the feature in, mostly green for outline and any woodland incorporated. I also sketchily filled in with yellow highlighter which I think can be seen. The whole looks a bit unnaturally coloured, due to me having put a coat of clear varnish onto it when I first mounted it, to keep it clean. In retrospect that was a mistake, but not major.

Labels:

Al - Allermuir Hill
Au - Auchendinny
Car - Carberry; Tower and Hill(Queen Mary's Mount, and ancient fort)
CR - Camp Ridge(earthworks)
DHC - Dalkeith House, site of old Castle. The boundary wall forms the helmeted rider's head. Originally Douglas land, then the Buccleughs. One of whom as Earl of Dalkeith was first Grandmaster of Grand Lodge back in the 18th century.
Ea - Easthouses, village where I spent my childhood
G - Galachlaw, centre of pentagonal system.
Gl - Glencorse Old Kirk
L(SH) - The Sun Hotel, at Lothianburn. At horses chin, part of the Newbattle Boundary. The Sun was a Kerr Family symbol.
LD(SF) - Langhill Farm, Dryden Tower, and Shinbanes Field, supposedly where bones are unearthed from the Battle of Roslin. The Researh Centre responsible for Dolly The Sheep is also here. The rider's knee, along with Nivensknowe.
LK - Lasswade Kirk.
KC - Kirkton Cottage, at corner of small inner pentagon.
KG - Kings Gate, near Sherrifhall, part of Dalkeith estate wall, rider's neck.
MC - Melville Castle.
ME - Mavisbank earthmound, at back of Mavisbank House, built by Sir John Clerk of Penicuik.
MoW - The Meeting of the Waters, the riders brow, where the two Esk rivers meet. The area inside the confluence is called Lady's Seat.
NA - Newbattle Abbey, the eye of the Horse. Cistercian Abbey originally, at Reformation became the personal property of the last Abbot, a Kerr, who became Earl of Lothian. Newtongrange village including the Church was part of Lothian Estates. The Sauniere Society hold their Scottish Symposia there, and is now an Adult Residential College, where I spent an academic year back in 1995/6.
NC - Newtongrange Church.
NK - Nivensknowe, where the rider's knee bends.
P - Penicuik, Sir John Clerk's estate is just to the south, but off this map section.
RC - Rosslyn Chapel, at rider's calf, and among other things a corner of the small inner pentagon.
Sh - Shewington, farm on a ridge, a corner of original pentagon.
ST - Shank Tongue. In Shank estate, where John Reid, the gardener who wrote the first book for Scottish Gardener's in 1683, who was insistent that in Scotland, land is measured by the Ell, 37 inches. His employer at Shank was Sir George Mackenzie(known as 'the bluidy', due to his treatment of the Covenanter's).
StMF - St Margaret's Farm, where the rider's elbow bends.
Td - Todhills Farm near Danderhall, a corner of small inner pentagon.
W - Woodburn, the horses ears/mane.

horse and rider grid additional graphic

2010-02-26T16:24:00.003Z

Trawling through my Picasa images, I found this:

A sketch of the landscape showing the river Esk continuing to the Forth at Musselburgh.

There is a lot of established geometry, and also some speculative stuff, which I haven't verified yet.

The horse and rider are shaded green, and I have left an area clear, as at the time I was unsure whether there was an additional feature still to be recognized. There was discussion about what else might be there, different people were asking if I could see this or that. One suggestion was two riders, a Templar symbol, and the area I have left perhaps owes something to this idea, but I am not convinced and it was a few years back. Just one of those threads which got laid aside, one of many!

Yesterday I took a photo of a map I have with the feature drawn in. Unfortunately, I can't get the camera to connect to the computer to download, for some reason. I'll get bak to it soon!

ps: If your eyes start to spin, welcome to the club!

horse and rider grid 'enhanced' graphic

2010-02-12T06:17:00.004Z

So, this is a photoshop enhanced graphic, on the hand-drawn original as shown in the previous post. The penta system is in purple, the grid in green. There is one yellow line representing the orientation of the Mavisbank hexagonal system, with Newtongrange Church defining the radius. The rest of the hexagon is omitted, for now.

There are a few light blue lines, which link some features and points of interest, including line of sight points, which would have aided in setting out and surveying.

The horse and rider feature is sketched in on the original, and I have left this be, as that is as artistic as I wish to get, for now.

This has labels attached, and constitute the main points, necessary for defining the geometry and notable features of the figure.

Key points:

A; Allermuir Hill
AS; Arthurs Seat
B; Borthwick Churh
BH; Black Hill
C; Carberry Tower/Queen Margaret's Mount
CK; Currie Kirk
CR; Camp Ridge
G; Galachlaw
L; Leith
M; Mavisbank Earthmound
May; Maybury/Gogar
MH; Mauldslie Hill
MOW; Meeting of the Waters in Dalkeith Park
NA; Newbattle Abbey
NC; Newtongrange Church
P; Penicuik, Sir John Clerk's Estate and House touches this point, and lies to the south.
PUC; Preston Cross(with unicorn on top)
RC; Roslin Chapel
S; Shewington Farm
St.MC; St. Mary's Chapel/Mount Lothian
St.MF; St. Margaret's Toll Farm
TH; Todhills Farm
T; Temple Kirk

First. The sale of the figure is defined by the side of the pentagon(MOW - S) plus an 18 degree segment which is 1.30902 times 6.0678 miles which equals 7.943 miles, which is just short of 8 miles.

Second. The central axis of the figure is defined by this same penta side, and is 31+/- degrees to O.S.grid, the Roseline shown, and true north.

horse and rider contd

2010-02-03T19:12:00.005Z

I found a graphic in my pictures which is the best I have at present. Hand drawn, and not labelled yet. In fact, a set of three and I will work on them soon.

Original penta system.

The grid for the system, but the Mavisbank hex system not included.

A rough drawing of the horse and rider in its grid, with the two rivers Esk shown.

Horse and Rider grid

2009-10-23T09:17:00.011+01:00

It is time , actually way beyond time, that I turn again to this topic. It is ten years since it made itself known, one night when I was at a low ebb, wondering what it was I had found with all the geometry. It has certainly defined my life situation, and instigated my contact with Bill Buehler which certainly has defined my work since.

Introducing this topic, I wish to emphasize the geometric grid which defines the 'possible' 'plausible' 'quite convincing' construct of the feature which 'appeared' back in 1999.

This grid system follows naturally from the original penta-system centred on Galachlaw and the hexa-system centred on Mavisbank earthmound which has the same radius as that found by Henry Lincoln round Rennes Le Chateau, and which equates to 5000 Scottish ells as defined by John Reid, a gardener, and author of The Scots Gardner, 1683. The main features of the construct, The heads of both horse and rider are defined by the boundary walls of Newbattle Abbey and Dalkeith estate respectively.

21st January, 2010

Well, A guid new year to all, if somewhat belated. I do believe, have been led to assume, some sort of process is 'directing' me at times, and have come to accept that sometimes trying to do this stuff is akin to knocking one's head against a brick wall, it just ain't going to happen till its 'ok' /'time'!

This topic is one instance, the image/feature appeared in a flash of 'revelation' over ten years ago, September 1999, as mentioned previously. I worked on the feature and its defining geometry, explored the landscape, and so on, till in March 2003, when I took advantage of the opportunity to drive Bill Buehler and his wife Joan around the area on a beautiful sunny spring day.

I took Bill to 'The Meeting Of The Waters, where the two Rivers Esk meet in Dalkeith Estate, which is the brow of the riders head, and the first corner found of the original pentagon. (Joan had hurt her ankle and stayed behind in the restaurant as it involved a walk of a good mile and back)

I also showed them the stretch of wall which is part of the horses head, and which was part of my childhood world at Easthouses, then I drove round to Newbattle Abbey itself, which is the eye of the horse, and where I spent a year as a student at the Residential College there in 1995/6. The Sauniere Society have held their Scottish Symposia there since the late nineties.

I was particularly kean to show these points to Bill as he had picked up on my referencing this feature in a discussion group back in late 1999, and had stressed its significance in the unfolding drama, namely the Assencion, the appearance/revelation/development of the Earth grids over the whole planet being an integral part. Mind blowing, it all certainly was!

Soon after, May 2003, I was attempting to write it all up, my own personal life associations with the area, and nostalgic meanderings, when reports of a particularly gruesome murder came over the radio, in an area of the Newbattle boundary wall, which I knew well. I stopped writing at that instant with the comment, with full irony intended, 'Nostalgia ain't what it used to be!' I felt more than a trifle spooked!

Also, my intention was not to let the horse and rider feature become something sensationalised and ridiculed like the Glastonbury zodiac. I wanted to emphasize the geometry that defines it, and be able to show how simple it would in fact have been to create, given a degree of coordination between the main players, the land owners, at a particular time in the past.

So I intentionally showed first all the main geometric systems, their extent, complexity, and even more astonishing, their degree of accuracy, and links to the other two main areas of proven geometry, Rennes Le Chateau and Bornholm, even the units involved are common.

So, some 1.5 years later, I am slowly getting round to it again. Even the graphic above has been a story of stupid oversight on my part. The image wouldn't upload, and I couldn't think what had changed. I gave up, and only returned to it today, when again it wouldn't upload. Till, that is, I noticed a check box, for the query, 'do I accept these new terms?' Doh! Weeks lost again! But, then again, who or what is in charge of this process? Cos, it sure don't feel like I am! And, why make me feel like a goddam fool, so often!? Eh?

Calculations for Eildon - Forth Road Bridge line

2009-08-05T08:26:00.019+01:00

The O.S. grid references for the chosen points:

NT 550 325 Eildon(point midway between two largest hills)
NT 315 587 Temple Kirk
NT 275 630 Rosslyn Chapel
NT 245 662 Hillend Fort
NT 239 668 Cross 'T'- Wood
NT 144 775 Dalmeny Kirk
NT 125 796 Forth Road Bridge(mid-point)

Transposed form, and fine-tuned to the metre:

3550.32 6325.24 Eildon
3315.24 6587.30 Temple Kirk
3275.05 6630.66 Rosslyn Chapel
3245.24 6662.06 Hillend Fort
3239.84 6668.10 T-Wood
3144.44 6775.08 Dalmeny Kirk
3125.40 6796.35 Forth Road Bridge

The Eildon from the south-east

Calculation of orientation and distance:

1) Dalmeny - Eildon

3144.44 6775.08 Dalmeny
3550.32 6325.24 Eildon
---------- ----------
0405.88(x) 0449.84(y)
---------- ----------

By Pythagoras' Theorem(sq.rt(x^2 + y^2)):

605.88 km*100 = 60,588 metres

(60,588*3.2808)/5280 = 37.65 miles(E); times (16.5/18.5)= 33.58 miles(S)

angle of orientation:

(x/y); tangent-1;

405.88/449.84 = 0.9022764= tangent 42.06 degrees.

2) Forth Road Bridge - Eildon

3125.40 6796.35 Forth Road Bridge
3550.32 6325.24 Eildon
---------- ----------
0424.92 0471.11
---------- ----------

By Pyhtag;

63,443 metres = 39.42 miles(E); 35.16 miles(S)

angle;

42.05 degrees

3) Rosslyn Chapel - Eildon

Rosslyn Chapel, circa 1995, pre-canopy

3275.05 6630.66 Rosslyn Chapel
3550.32 6325.24 Eildon
---------- ----------
0275.27 0305.42
---------- ----------

By Pythagoras;

41,116 metres = 25.55 miles(E); 22.79 miles(S)

angle;

42.03 degrees

For the moment, what needs to be seen is that using the mid-point of the two main Eildon summits, Rosslyn Chapel, Dalmeny Kirk and the exact mid-point of the Forth Road Bridge are in a direct line line, to within 0.03 degrees, over a distance of 39.42 miles(E). Excluding the Forth Road Bridge, which is 'surely' coincidental, Dalmeny Kirk and Rosslyn Chapel are within 0.01 degrees, over 37.65 miles(E). 0.01 degrees is, using the visual reference of a clock-face-minute(cfm)(6 degrees), 1/600th of one c.f.m., or 35 feet.

If the two main summits of Eildon are used as a 'gate', then the other points listed are contained within using Dalmeny Kirk as reference:

3144.44 6775.08 Dalmeny Kirk
3554.33 6329.10 Eildon (Ring Fort)
---------- ----------
0409.89 0445.98
---------- ----------

By Pythag. theorem: 60,573 metres = 37.64 miles(E); 33.57 miles(S)

angle of orientation: 42.59 degrees

Dalmeny Kirk

3144.44 6775.08 Dalmeny Kirk
3548.19 6323.03 Eildon (O.S. trig. cairn)
---------- -----------
0403.75 0452.05
---------- -----------

By Pythag. theorem: 60,610 metres = 37.66 miles(E); 33.59 miles(S)

angle of orientation: 41.77 degrees

So, the two summits give a spread between 42.59 - 41.77 degrees = 0.82 degrees.

This spread, or 'gate' of 0.82degrees, less than 1/7th of one clock-face-minute, though small in itself, is a large enough 'unit point area' to contain all the chosen points with Dalmeny Kirk as focal point at the other end.

Just for completion, the remaining three points listed, Temple Kirk, Hillend Fort and the plantation known as T-Wood, with reference to Dalmeny Kirk:

Temple Kirk

3144.44 6775.08 Dalmeny Kirk
3315.24 6587.30 Temple Kirk
---------- ----------
0170.80 0187.78
---------- ----------

By Pythag. theorem: 25,384 metres = 15.77 miles(E); 14.07 miles(S)

angle of orientation: 42.29 degrees

Hillend Fort from Roslin Main Street

3144.44 6775.08 Dalmeny Kirk
3245.24 6662.06 Hillend Fort
---------- ----------
0100.80 0113.02
---------- ----------

By Pythag. theorem: 9.41 miles(E); 8.39 miles(S)

angle of orientation: 41.73 degrees

T-Wood from below at Swanston

3144.44 6775.08 Dalmeny Kirk
3239.84 6668.10 T-Wood
---------- ----------
0095.40 0106.98
---------- ----------

By Pythag. theorem: 14,334 metres = 8.91 miles(E); 7.94 miles(S)

angle of orientation: 41.73 degrees

n.b. The T-Wood is centred on a high point with a cairn on top, but unmarked on the map. This was noted on a visit a few years back.

Now, the Eildon has been found in previous sections to be an important point, and is a recognized major, mystical, magical feature of the Borders landscape. From Iron Age Ring Fort, Roman Signal Station, on the banks of the Tweed, on the Phi latitude, a fairy mountain with Thomas The Rhymer associations, with Melrose and its Abbey at its feet. The geometric links are many, and with the special spots on this particular line, it is no doubt worthy of further study, in this instance how this line fits with other systems already considered.

A additional thought, perhaps worthy of consideration, is that the three hills of The Eildon are reminiscent of the three Pyramids of the Giza plateau, even the alignment of the three are similar, in that the two biggest are to the east of the third smallest, and the smallest is also offset from the two largest, just like at Giza, and the configuration is reminiscent of the belt stars of Orion, just like the Giza Pyramids have been equated with, by Bauval and Gilbert, and Hancock. Jeff Nisbet, a few years back, presented a convincing Orion system, using the three islands near North Berwick as the belt stars, and found the other stars, and Sirius quite convincingly marked in the landscape of the area on both sides of the Firth of Forth. We had a discussion going on this, but due to my loss of computer and internet access, tailed off back in 2003. A link on Jeff's website to Gary A. David's site concerns another Orion in the landscape of Arizona, which I had not known of previously: http://azorion.tripod.com/ which is very interesting and worthy of study.

I shall return to this eventually, but for now I wish to return to a system covered early on but was left unfinished. I feel I have now covered the main geometric systems found over the fifteen years now, and cleared the decks, so to speak.

A special line in the landscape!

2009-06-09T16:46:00.011+01:00

Hillend Fort on skyline, with the T-wood just below, and Dalmeny Kirk mid photo, and Hawes Pier area, taken from the midpoint of the Forth Road Bridge, May, 2009.

When I started to investigate the landscape of Lothian for geometry similar to what Henry Lincoln had described around Rennes Le Chateau some 15 years back, I came across a bare system in Andrew Sinclair's: Sword and the Grail, but which I no longer have to hand. One line I did find intriguing, as I had found the same line, but with somewhat different marker points!

Where-as Sinclair had noted the points: Hawes Pier, at South Queensferry, the T-Wood, or Cross Wood, above Swanston Village, Rosslyn Chapel, and Temple Kirk; I had: Dalmeny Kirk, T-Wood, Hillend Fort, Rosslyn Chapel and Temple Kirk.

Those who have followed this blog will be aware, Hillend Fort is one of the main points in the landscape, not least as the G.P apex point in the (3 by 1) diagonal Reshel system, and one of the best vantage points for the whole of the Lothian landscape, and can be seen from Roslin village, looking along Main Street.

I eventually noted that this line extended to the exact mid-point of the Forth Road Bridge, surely coincidence, but intriguing none-the-less!(?)

While living in Selkirk(1999-2001) I would quite often drive up to Edinburgh via Innerleithen, quite deliberately to the point where the road came out of the Moorfoot Hills to a superb vantage point on the other side of the Esk Valley from Hillend, before turning sharply right, (north-east), and try to see the points Temple and Rosslyn in the direct line that the map showed them to be. The exact point is about 200 yards down this road. Rosslyn Chapel is identifiable, now with the white coloured canopy, but Temple is not visible as it sits by the river in the steep sided valley.

I also extended this line on the map not so surprisingly came to the Eildon Hills, by way of Carcant Hill, the slope of which this vantage point is on.

Three years ago when I moved to Inverkeithing came the opportunity to check this line often from the midpoint of the Road Bridge. I managed to identify Dalmeny Kirk, and tried whilst a passenger in a friends car to take a decent photo. This proved awkward in that the main cable at the centre obscures the view, and being on the move was a bit troublesome also. I knew I would have to walk to the middle of the Bridge sometime, but it took me till May this year to get round to it!

This is a recent shot taken from South Queensferry at Hawes Pier to the mid-point of the Forth Road Bridge. The hills below allow a visual guide for the extended line to the north-west. A rough check in Google Earth leads across Loch Tay, just west of Ben Lawers, and directly in line is Maggernie Castle in Glen Lyon. This shall be checked later.

The Eildon Hills, from the north-west. The two used in this report are left and centre.

The Great and second Great Pyramid Geometry

2009-03-19T19:51:00.014Z

This figure as found in Tompkins, pages 260-261, basically a four square with (1 by 1) and (2 by 1) diagonals, contains the necessary information to construct both of the great pyramids at Giza.

I've been a bit pre-occupied for the past few weeks, re-reading 'Secrets Of The Great Pyramid, by Peter Tompkins, and the appendix on Ancient Measure by Livio Stecchini. Slowly it dawned on me that the basic geometry the Great Pyramid is based upon is so simple, yet I have not seen it explained previously. I also came to realize that the Second 'Great' Pyramid is also derived as simply from a (2 by 1) rectangle, or double square.

Tompkins in a discussion about the above figure describes the idea of Tons Brunes who in The Secrets of Ancient Geometry
who 'shows that the Great Pyramid, like most of the great temples of antiquity, was designed on the basis of an advanced but hermetic geometry known only to initiates. only fragments o which percolated to the classic and Alexandrine Greeks.'

Tompkins states: Brunes shows how the ancient Egyptians used the basic design of a circle inscribed in a square to divide both circle and square geometrically into equal parts from 2 to 10, and all their possible multiples, without recourse to measuring or arithmetical calculations, with the aid of nothing but a straightedge and a compass - common emblems, along with the Pyramid, of the Masonic orders of yesterday and today.

He continues: In Brunes' reconstruction o the secret geometry, the cross emerges as the first geometric addition to the circle and square, and is the key not only to the solution of geometric problems but to the development of numerals and the alphabet.
By including the diagonals, every number both Latin and Arabic and all the letters of several alphabets may be obtained.
According to Brunes, both mathematics and the alphabet sprang from geometry, not the reverse. He says that nowadays we use numbers as the primary factor in our calculations, and geometry only as a subsidiary, whereas he believes the Egyptians reversed the order. He uses a detailed analysis of the Rhind Mathematical Papyrus to demonstrate that the ancient Egyptian system of counting was directly governed by geometric factors and that their ideas and theories were bound in geometric rules.
Brunes found that the circle was indeed considered sacred by the Egyptians, as were the square and the cross and the triangle, all of which are intimately incorporated into the Great Pyramid with its square base and triangular faces designed to represent the ''sacred'' circle.
Brunes demonstrates how the circle inscribed in a square and quartered by a cross enabled the ancient Egyptian geometer to inscribe in a circle the basic figures of pentagon, hexagon, octagon and decagon.

end quote.

Tompkins points out that the golden section is formed automatically between the sides and chords of the pentagon. This is so!

What is also true though is that very simply the golden section can be deirved directly from the (2 by 1) rectangle, as the diagonal is square root five, and if the unit side is added and the whole length halved, this is Phi in relation to the side. (1.618034 : 1)

It was musing on this and that the apothem of the Great Pyramid is Phi in relation to half of the base that the geometric construct of the Great Pyramid became apparent, as described below.

Right click on images, and 'Open in New Window' to see at full size:

figure 1: The basic (2 by 1) rectangle a circle is drawn centred on the common side with radius half the base. The points on the diagonals cut by this circle are 1.618034 units, with square side being 1 unit. Aa = Bb = Cc = Dd = 1.618034, Phi.

Diagonal = Square root five, 2.236068.

2.236068 / 2 = 1.118034

1.118034 + 0.5 = 1.618034.

figure 2.

figure 3.

Figure 2 is the construct of the Great Pyramid geometry. Figure 3 is labelled.

From points A and B with length Aa and Bb, or Phi, arcs are scribed to cut the axis, at P. The figure so formed is a cross section of the Great Pyramid, with base 2, apothem or slant height, Phi, and height square root Phi.

The angles PAQ and PBQ equals 51.8273 degrees.

figure 4.

figure 5.

Figures 4 and 5 show how the Second Pyramid geometry is found.

Stecchini, pages 378/379, gives Petrie's figures for the Second Pyramid at Giza, which he reckons best. He shows that the cross sectional triangle, half base, height and apothem are in the relationship, 3,4,5, which gives a base angle of 53.13 degrees.

In figure 4 the angle formed by the intersection of the two diagonals at O, is 53.13 degrees, so a construct of the Second Pyramid is possible from this fact alone. Angle BOM is 53.13. An arc is scribed from point B with length BO, to the intersection with the diagonal extended to M.

Figuire 5 shows a variation using the length Phi, Bb, to construct a triangle with the same apothem as the Great Pyramid, namely Phi.

Triangle BKL is a 3,4,5 triangle. KL is 3 units, BK is 4 units, BL is 5 units.

As the two pyramids are constructed I can't find any convincing correlation in dimensions, the second Pyramid being some 97% roughly smaller in base and height. Apparently, the Second Pyramid is on a higher level than the Great Pyramid so appears to be somewhat higher.

I find it fascinating that both can be found so simply from the same basic figure, namely figure 1 above.

Finally, the (2 by 1) rectangle diagonals form angles of 26.5650512 degrees, and 63.43495 degrees. The angle 26.5650512 degrees is very close to the angles given for the Ascending and descending passages of the Great Pyramid, adding further, perhaps, to the links shown here.

March 10, 2009, full moon

2009-03-11T09:56:00.005Z

Tuesday night shift, I went a bit Lunar, it was a stunning full moon rise in the evening. I took photos all through the night and even got the sunrise in the morning.

I'll get round to adding some text some time soon! I even took some of the Grassmarket as it is now after renovation.

The last one is in Inverkeithing walking home and I have incorporated phi into the composition.

Web album

full moon, March10, 2009

Grid Reshel Basic summary

2008-12-16T10:18:00.006Z

As the whole set of posts covering this whole topic is difficult to follow in sequence due to the nature of the blog format, and as it all involves many calculations, a brief summary post may help!

1. The Reshel system as defined by William S. Buehler, which came to my awareness in the late nineties. This was based on a 20 mile radius centred on St. Mary's Chapel Mount Lothian in Scotland, NT 275 570.

This radius I have since amended to 19.596 miles, being the side of a square with diagonal the same as that of the grid identified on the island of Bornholm which Haagensen and Lincoln show (and prove) to be a Secret Teaching Island of the Knights Templar. This grid in Imperial measure is (16 times the square root of 3) which equals 27.712813 miles (E).

This measure was found to be the exact distance between St. Mary's Chapel and St. Baldred's Chapel on The Bass Rock, NT 602 873.

This as diagonal of a square is in (square root two) relationship with the side, hence the 19.596 miles(E) radius mentioned above, which is the distance approximately to Seafield Tower, NT 279 885, to the north and Dryhope Tower, NT 267 247, to the south. (The double distance between the two Towers giving the diameter of the circle, which is 39.192 miles(E).)

Using the simple geometry of circles and squares, an inner square grid can be constructed naturally, with side half that of the original, 13.8564 miles (E).

2. Using this smaller grid with St. Mary's Chapel as centre, Blackness Castle defines the diagonal approximately, as example, NT 055 802.

It was then found from this grid that a point near Kelso, NT 716 340, and a point near Ericstane, NT 051 116, are both (2 by 1) diagonal points from St. Mary's Chapel, and are naturally a (3 by 1) diagonal distance apart from each other.

Using this as a baseline a line at 90 degrees from the mid-point through St. Mary's Chapel and extended north west is also naturally on a (3 by 1) diagonal, and it is on this line that a system is found corresponding nicely to the basic Reshel format as described by William Buehler.

N.b.: it needs to pointed out here that the orientation of the Bass Rock is some 2.4 degrees clockwise to that of the Rose-line/Tavhara line as commonly understood, and that there is a third in between using Berwick Law NT 556 842, which is used for the following excercise.

This spread of 2.4 degrees could be considered as a 'Selah' spoke, and as the geometry which gives the points below is accurate to the metre, an area of fudge could be considered at all points corresponding to this 2,4 degree spread but centred at St. Mary's Chapel.

3. A) The first point of note on this axis is St. Mary's Chapel itself, as it is naturally the point defining a square with the base-line as diagonal. From Pythagoras' theorem, a triangle with two sides equal to (square root five),which the diagonal of a (2 by 1) rectangle naturally is, with the third side (square root ten), that is the diagonal of a (3 by 1) rectangle, is a right angled triangle, with angles of 45 degrees. The other half of the square is to the south of the base-line, of course! This will be discussed later!

B) The second point on the axis, (and the clincher for me!) is Hillend Fort NT 245 662 which is at the point corresponding to the apex of the Great Pyramid, or Glory Pole in WSB's terminology for the system, 51.86416667 degrees, or 51 degrees, 51 minutes, 51 seconds. I have made many references to the significance of Hillend Fort in the landscape of Lothian, prior even to discovering this fact.

C) The point which defines an equilateral triangle with the base-line is in the Firth of Forth, with Inchmickery and Inchcolm NT 191 826, the nearest islands.

D) There is a pentagon super-imposed with side defined by the tangent from St. Mary's Chapel intersecting the circle with Hillend Fort as radius from the centre of the base-line, and dropping a perpendicular to the base-line, either side of the mid-point of the base-line. The two base line points are NT 116 150, Craigy Middens at Ask Law, and NT 646 318, near Rutherford Lodge, a 67 metre spotheight by a boathouse on the River Tweed at Dalcove.

The apex of this pentagon is to the north of Loch Leven in the village of Milnathort, on Pace Hill NO 123 051. Burleigh Castle is close by at NO 129 047, some half kilometer east.

The 'wings' of the pentagon have points at; i)in the west at NS 793 603, the junction of Biggar and Motherwell Roads, and; ii)in the east at sea NT 651 874, off St. Baldred's Boat in the vicinity of the Bass Rock and Tantallon Castle. St. Baldred's Chapel on the Bass Rock is of course one of the points where this grid originated.

The mid-point of this penta-chord is at Craigleith Avenue, NT 222 738, in Edinburgh near Mary Erskine's school at Ravelston.
The centre of the pentagon is found to be just south of Rosslynlee Hospital at NT 266 599, near a claypit.

Reshel basic google map

2008-11-28T08:39:00.001Z

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View Larger Map">

St. Mary's Chapel grid 3 by 1 diagonal pentagon

2008-11-07T10:43:00.006Z

In the Reshel basic system shown by William Buehler is a pentagon constructed within the base-line, and this drawing shows my geometric interpretation, based on Bill's drawings.A tangent drawn horizontally from St. Mary's Chapel intersects a circle of radius C - H, centre of base-line to Hillend Fort or G.P apex point. Then a perpendicular is dropped to the base-line defining point P1.

Using the theorem of Pythagoras C-P1 = sq.root[{CG^2) - (CS^2)], where CG is the same as the radius CH, and CS equals the half-base EC;

Using figures calculated in previous post this gives a distance of 17,283343miles(E), or 278.15 O.S. units.

This line extended the same distance towards Kelso through C, gives point P2.

These two points can be determined by calculating the x and y coordinates as before, and subtracting from C for P1 and adding to C for P2:

x: cos17.4742 * 278.15 = 265.32

y: sin17.4742 * 278.15 = 83.52

P1:
x: C-265.32 = 3380.88 - 265.32 = 3115.56

y: C- 83.52 = 6233.87 - 83.52 = 6150.35

P2:
x: C+265.32 = 3380.88 + 265.32 = 3646.20

y: C+ 83.52 = 6233.87 + 83.52 = 6317.39

P1 proves to be Craigy Middens on Ask Law (NT 115 150).

P2 proves to be near a 67 metre spot height at Rutherford Lodge on a bend in the river Tweed at Dalcove (NT 646 317).

Now that the base points are established, the altitude of the pentagon can be calculated.
This is most easily done by using the tangent of 72 degrees multiplied by the half base measure, and oriented to the 17.4742 degree angle. Reminder; The 3 by 1 angle adjusted for the North Berwick Law orientation!

So, MC = tan72 * 278.15 = 856.07 O.S. units

x: C - sin17.4742 * 856.07 = 3380.88 - 257.06 = 3123.82

y: C + cos17.4742 * 856.07 = 6233.87 + 816.56 = 7050.43

This point is Pace Hill(NO124 050), in Milnathort, on the north shore of Loch Leven. Of interest perhaps is Burleigh Castle(NO129 047) some 0.5 KM east.

The line from C to M crosses Loch Leven between Kinross House and Loch Leven Castle Island. Loch Leven also contains St Serf's Island. The line also crosses Benarty Hill to the south, near to the fort there. This latter high point is visible from Hillend Fort, south of the Firth of Forth, and of course the G.P. angle point and much more!

Next, the 'wings' of the pentagon can be calculated using the same methods as before, but the workings are omitted here. The two points are given here labelled W(west) and E(east):

W: 2792.71 6603.40, which is at a crossroad of the Biggar Road, Motherwell Road near Pickerston, (NS793 603).

E: 3651.31 6873.68, in the North Sea, near to St.Baldred's Boat(NT611 849), marked rocks near Seacliff, with St. Baldred's Cave at (NT604 845), with Tantallon Castle close by. St. Baldred's Chapel on The Bass Rock is of course the origin of the grid with St. Mary's Chapel.

The chord of the pentagon between W and E cuts the altitude line at Ravelston in Edinburgh near to Mary Erskine's School(NY218 740) at 3222.01 6738.54.

One other point of the pentagon to be considered is the centre O which is at 3265.92 6599.05, near clay pits just south of Rosslynlee Hospital(NT265 608).

Coincidentally, or otherwise, the distance from O to St. Mary's Chapel calculates to 1.88 miles(E). The distance of 188 miles(E) and (S) was found to be the measure of the sides of the triangle described in previous post from Preston Cross to Flodagh and Callanish respectively.

There are other points or poles that can be determined but for now the main geometrics have been established for one half of the basic Reshel system as defined by William Buehler, and other points on the altitude which may be of interest. And, this is only one half of the system, a mirror system on the other side of the base line should be considered, and that can be done later. For me this system based on the grid found on Bornholm and then in Scotland using the 3 by 1 diagonals and the simple way of determining especially the Great Pyramid point, Hillend Fort, is the clincher. As previously mentioned Hillend Fort is a most important geometric point in the landscape. Inchcolm island being close to the equilateral triangle point is also good. And, that the altitude passes through the gap between Kinross House and Loch Leven castle island, with Benarty Hill giving a good line of sight point is also very impressive. Bearing in mind that the orientation used is that to Berwick Law, with a spread of a degree or so either side, the gap between Kinross House and Loch Leven Castle could be considered as a 'gate' through which the three options pass is interesting. Kinross House is designed looking out to the Castle island with the path leading from the House to the shore points directly towards the island.

The Kelso area is also interesting, with the Abbey, Roxburgh Castle and Floors Castle forming a triangle containing the three options. The Ericstane/Devils Beef Tub area at the other end of the base line is also intriguing, not least because the Rivers Tweed and Annan have their sources there. Kelso also has the Tweed passing through it and where the Teviot joins the Tweed. The Tweed also runs along the Phi-latitude roughly, the title of this blog.

With this exercise I have reached a stage which has taken me so long, due to my personal need to prove to myself that the method I employ is mathematically OK, and just getting the photos and graphics together has also taken time.

I have a few things I need to do yet, and as mentioned above there is still more to do on this system, but for now I can draw relax a bit, go over what I have already done here and improve things a bit. There are also some things to consider as a result of this exercise which I also need to look at. There is one issue I left unfinished way back, that I can now return to also. Another grid, quite specific in the Esk Valley, which contains a feature I have known about for some nine years now, but have not shown here yet, as I needed to establish the full set of geometric systems I have found over the 15 years now I have been researching this subject before speculating further on the who, when and why questions, although a few people have been aware of some of this work. Some have grown impatient with my lack of progress, I guess, but I needed to do this stuff in a way that I felt was necessary.

For me this goes beyond 'mere' ley-lines as commonly perceived. The geometry, IMHO is too accurate, too specific, beyond that considered by some other researchers to be necessary. The work of Henry Lincoln at Rennes Le Chateau is questioned by some, but the work he and Erling Haagensen did on Bornholm shows that there would appear to have been some kind of 'school' system unbeknown to most, working to the same accuracy as I have adopted in Scotland. Then there is the work of William Buehler and the explanations he gives, which I have been aware of for nine years now also, which is still beyond my understanding. Also, as complex and accurate as these systems are, the use of line of sight points, high points in the landscape show how simply it could all be surveyed. Simple, perhaps, but the overall design so complex, covering all of Scotland and incorporating Scottish and English/Imperial measure, and even the metric to some extent, allowing for the slight inaccuracy of the metre as originally calculated. The fact that the foot is such an accurate measure relating to the equatorial circumference of the earth is still an issue to be resolved: (360 * 365.242 * 1000)/ 5280 = 24,902.864 miles(E) which is accurate to within a mile of most authoritative estimates. Who calculated this, when and how???

St. Mary's Chapel grid - 3 by 1 diagonal

2008-10-31T10:45:00.004Z

In this post I shall describe the first two elements of the 'Reshel' basic grid, which is the work of William S. Buehler, previously mentioned, constructed by me on the 3 by 1 diagonal system shown in the previous post.

The first element is the Great Pyramid triangle from the two base points, Kelso and Ericstane:

This point proves to be Hillend Fort(HF), a very significant point in the landscape mentioned previously.

The simplest way to calculate this point is to use trig. function tangent of the Great Pyramid angle, 51d 51m 51s, or 51.86416667 degrees, multiplied by the distance Ericstane(E) to base centre(C), to obtain the point on the axis through St. Mary's Chapel(SM):

For this exercise I have used the St. Mary's Chapel(SM) - North Berwick Law(NBL) orientation which gives a 3 by 1 diagonal to O.S grid of 17.4742 degrees, for now, as it is between the other two options, the Bass Rock, and the Roseline through Arthur's Seat.

The distance from E - C is [{16*sq.rt.3}/2]*(sq.rt.10)/2, which is 21.909miles(E), or 352.59 O.S units, (hundred metres)

tan 51.86416667 * 352.59 = 449.10 O.S.units.

The x and y components can be calculated using the 17.4742 deg. offset angle.

x: sin 17.4742 * 449.10 = 134.85 O.S.grid units

y: cos 17.4742 * 449.10 = 428.38 O.S.grid units.

The calculated base mid - point(C) at this orientation was calculated as 3380.88 6233.87; approximately NT 381 234.

Due to the north west north slant the x component will be subtracted, the y component added:

x: 3380.88 - 134.85 = 3246.03

y: 6233.87 + 428.38 = 6662.25

I have Hillend Fort(NT 245 662) as 3245.50 6662.25 universal O.S. grid coordinates, a mere 50 metres west on the x-axis, and exact on the y-axis. The Roseline orientation would take this towards the west a tad. I will get back to this later, to check!

This second graphic shows two grid connections for this point to within fractions of a degree, which could be used for any practical purpose, for this awkward point.

The line from KA(Kelso approx.)through Hillend coincides with the 2 by 3 diagonal to Blackness Castle, and as can be seen the 2 by 1 diagonal connects at the same point.

I have just noticed the 2 by 1 connection, which only reinforces my opinion of the importance of Hillend Fort, and even more convinced of the practicality of using the 3 by 1 grid diagonal, and indeed this particular grid. Found on Bornholm, applied to Scotland, and defining a specific, and very special point in the construct provided by William Buehler. Wow!

This third drawing is simple in comparison. It is the point which forms an equilateral triangle with the two base points.

Again using the half base length, 352.59 O.S units and the tangent of 60 degrees, defines the point on the axis:

Tan 60 * 352.59 = 610.70 O.S. units
x and y components found using the offset angle of 17.4742 degrees:

x: sin 17.4742 * 610.70 = 183.38 O.S. units

y: cos 17.4742 * 610.70 = 582.52 O.S. units

and again using base centre:

x: 3380.88 - 183.38 = 3197.50

y: 6233.87 + 582.52 = 6816.39

Oxcars (NT 202 817) a tiny island in the Forth is the nearest land, about 0.5 km, but the line clips Inchcolm at the eastern end, a distance of approx 0.75 km.

St.Mary's Chapel grid, continued!

2008-10-17T09:42:00.009+01:00

The set of graphics below show first what has been established previously, the first two, and then the extension of the inner smaller derived grid, in (1/sq.root two) relationship, using Blackness Castle, and the simple use of grid diagonals, (2 by 1) and (3 by 1) to find a remarkable system linked to the work of William S. Buehler, whose original work, the ''20 mile radius'' system centred on St. Mary's Chapel. The square on this circle, with The Bass Rock as north-east corner, and the subsidiary system oriented on North Berwick Law, and indeed another with Arther's' Seat summit as main North axis at the half-radius point, (which incidentally has Rosslyn Chapel on it, discussed previously) with a spread of approximately 2.5 degrees is shown in the first sketch.

Sketch One

This shows the original circle and square grid derived from it, with a few points marked, St. Marys Chapel(NT275 570) in the centre, The Bass Rock(NT602 873) at the north-east corner, with North Berwick Law(NT556 842) indicated, Seafield(NT279 885) and Dryhope Towers(NT267 247) marking the north and south points respectively. The Arther's' Seat area is marked, and is at the half-radius point, but not indicated as such, but may be considered further, but later! The derived inner grid is found naturally in the geometry!

Sketch Two

This shows the smaller, inner grid, in (1/sq.root two) relationship, with Blackness Castle indicated at the north-west corner.

The length of side of this grid is where the Scot's measure system reveals the phi connection, discussed in previous post. Namely, (16* sq.root 3* 33) / (2* 37) equals 12.35842 miles(S), (half of which is 6.17921).
Incidentally, the discrepancy from phi exact is 6.5 feet, which is lost in the practical margins of error in my method. I work at all times with the limit in practice suggested as the optimum that medieval surveyors could achieve by known methods, by Professor Lind, in connection with the Bornholm work of Erling Haagensen and Henry Lincoln, in The Templar's Secret Island. This limit is 1 in 2000, or 99.95%, as discussed previously. 6.17921 mile(S) is 99.982% of 6.18034 miles(S).

The Scot's measure system I use is that defined by John Reid, 1683, in The Scot's Gard'ner, with the Scot's mile being in the ratio of 37 : 33 with the English/Imperial system. Inches and feet are common. Which raises many questions, not considered here!

Also, extreme accuracy that can be expected from O.S. maps is one metre, as explained to me by a professional cartographer friend, so any coordinates used here will be less than this. I would allow myself a discrepancy of up to ten metres. 6.5 feet is less than two metres (1.98 metres, to be precise)!

The issue of what accuracy the designers/surveyors worked to is not known, but the number of sites/points that are 'spot-on' indicates they got lucky very often.

I have been encouraged to allow for 'telluric'* off-set, and/or geographic/landscape practicalities in the past. I have allowed myself some leeway as at Blackness Castle(NT055 792), or Seafield Tower(NT280 885), where the exact geometric point is off the coast. I have also allowed the consideration of the 2.5 degree spread, and that these two points sit within this spread, as marker points. And, as at Arther's' Seat, the natural area of Holyrood Park, to be a 'unit-point-area', when considering such distances as the 200 mile plus spanning most of Scotland, and previously discussed.

* related to earth forces in some way! No further comment, for now!

These diagrams are simple representations of the geometry found so far.

Sketch Three

In late 1999 I moved to Selkirk to write up my findings till then. As previously mentioned I got connected to the Internet, made contact with William S. Buehler, and the geometry expanded, commensurate with my growing awareness of the landscape of the Tweed Valley and the countryside between Selkirk and Edinburgh. I was a member of the Sauniere Society at the time, and was privileged to hear Alistair Moffat discussing his book, Arthur And The Lost Kingdom, where my attention was drawn to Kelso, and the Roxburghe Castle area, east of Selkirk, where the Tweed and Teviot rivers meet.

On investigation I found that Kelso Abbey(NT727 339) was at the corner of the (2 by 1) grid point, south-east of St. Mary's Chapel:

A quick calculation here, to establish the accuracy of this. I am doing this from memory, and only using a list of O.S. coordinates, and re-doing the calculations as I go. And, I am aware that Kelso Abbey is not the exact point, as it is in the Schiehallion system described previously, but that a point closer to Roxburghe Castle(NT713 337) is the exact point. I shall first consider Kelso Abbey, to establish that we are in the right area:

3275.00 6570.19 St. Mary's Chapel
3728.87 6337.92 Kelso Abbey
--------- ----------
-453.87 232.27

Us usual using Pythagoras' Theorem, a grid unit distance of 509.85 hundreds of metres; which converts to 31.681 miles(E). Converting to Scots measure; using (33/37) gives 28.2557 miles(S).

What needs to be established is the approximation to the ( 2 by 1) diagonal which this distance represents, and the angle to O.S. grid:

We know that the side of the grid square is 12.38542 miles(S), (6.17921 * 2), and that the ( 2 by 1 ) diagonal is side times square root five, and the angle has a tangent of (1/2), or its complementary angle with a tangent of (2/1), which are 26.565 degrees, and 63.435 degrees respectively!

(6.17921 * 2) * square root five = 27.6343 miles(S). This is 0.6214 miles(S) short of Kelso Abbey!

The angle to O.S. grid has as tangent: (453.87/232.27) = 62.8987 degrees. or its complement to 90 degrees of 27.1013 degrees. This latter figure can be added to 90 to allow comparison with the north axis of orientation of the O.S. grid; 90 + 27.1013 = 117.1013. The exact angle for this vector should be (90 + 26.56505) 116.56505 degrees. The difference is 0.53625 degrees, well within the 2.5 degree spread discussed above!

Kelso Abbey could well be considered a marker point, for this grid!

I am content to leave this for now. Should anyone care to do some calculations for themselves I give a few more points around Roxburgh Castle, and also Floors Castle just to the north of Roxburgh Castle:

3716.82 6339.96 'hillock' east of Roxburgh Castle
3710.00 6335.22 'hillock' south of Roxburgh Castle
3713.04 6337.38 mean of two previous

3711.12 6346.62 Floors Castle

Sketch Four

In this part Ericstane Hill(NT059 122) shall be considered in relation to Kelso Abbey as marking the (3 by 1) diagonal south- west, and St. Mary's Chapel, as the (2 by 1) point south and west.

Ericstane Hill is north of Moffat between the A701, and the A74(M), with the 'Devil's Beef Tub' where stolen cattle were apparently penned in seclusion, in the valley to the north-east. It is the area where the Annan river rises, and close to the source of the Tweed. There is a Roman fortlet on its flank, with also the Eric Stane and monument.

3728.87 6337.92 Kelso Abbey
3059.81 6121.89 EricStane Hill(summit)
---------- ----------
669.06 216.03

By Pythagoras' theorem; 703.072 O.S.units(hundred metres); 43.68687 miles(E); 38.964 miles(S).

Now, the diagonal of a (3 by 1) rectangle is square root ten, so dividing we get 12.32132 miles(S), against the square unit side of 12.3584 miles(S), a difference of 0.03708 m(S), a discrepancy of 71.2 ells, or 73 yards, too short.

In real terms it is a discrepancy of 230 yards over the full distance, not great, not bad, good enough for immediate purposes.

The angle to O.S. grid is tangent (669.06/216.03), which gives an angle of 72.1055, and complement to 90 degrees of 17.8945.

The angle of the line from St. Mary's Chapel to Kelso Abbey, from above was found to be 27.1013 degrees.
Now, interestingly, the adjacent angles of a (2 by 1) and (3 by 1) is 45 degrees exactly; so 27.1013 plus 17.8945 equals 44.9958, 45 - 0.0042 degrees
As a check, Ericstane Hill can be compared to St. Mary's Chapel:

3275.00 6570.19 St. Mary's Chapel
3059.81 6121.89 EricStane Hill(summit)
---------- ----------
215.19 448.30

By Pythagoras' theorem 497.2722 O.S. grid units(hundred metres); or 30.899miles(E); or 27.5586 miles(S).

Dividing by square root five(the length of a (2 by 1) diagonal) gives 12.3246 miles(S), a discrepancy of 0.03381 miles(S) from grid square length, 12.3584 miles(S), some 65 ells, or 67 yards, short, similar in scale to the Kelso Abbey measure.

The angle to O.S grid is tangent (215.19/448.3) = 25.64163 degrees, which added to the St. Mary's Chapel - Kelso Abbey angle of 62.8987 degrees is 88.54 degrees, against the 90 degrees it should be. a shortfall of 1.46 degrees, well within the spread of 2.5 degrees, disussed above.

I could 'tweak' things a bit, and get the exact spots at both Kelso and Ericstane, and have done so previously, it's all in my notes somewhere, but for now I shall leave this, content in having established these two areas as containing the corners of the grid centred on St. Mary's Chapel discussed above.

Sketch Five

This sketch shows the next task, establishing the (3 by 1) axis through St. Mary's Chapel, from the mid-point of the Kelso - Ericstane line shown here:

St. Mary's Chapel, Mount Lothian grid contd.

2008-10-10T03:43:00.009+01:00

So, having established That there is a grid in Lothian, based on the the exact same dimensions as that found at Bornholm, with St. Mary's Chapel and St. Baldred's Chapel on The Bass Rock forming the diagonal, which links with the side of a square through Dunsappie hill-fort and extends to Seafield Tower between Kinghorn and Kirkcaldy, I shall now show the other diagonal, north-west of St. Mary's Chapel. This diagonal can be fixed by Blackness Castle, and a natural sub-division is found, namely the side of the square fixed by Seafield Tower, becomes the diagonal of a smaller nested square, which shall then be used in the next quite astonishing development. For this exercise though, I shall use the North Berwick Law orientation, confirming that in the landscape, both are relevant. See below!

3275.00 6570.19 St. Mary's Chapel
3055.66 6792.48 Blackness Castle
---------- ----------
219.34 -222.29

Using Pythagoras' Theorem: 312.29 O.S grid units(100 metre), which converts to:
19.4046 miles(E), which is some 337 yards short of the exact figure of 19.596 miles(E)! Now as Blackness juts out into the Firth of Forth, the exact point is in fact off-shore, just like at Seafield Tower.

Through calculation the exact grid reference is found to be :

3275.00 6570.19 St. Mary's Chapel
3055.71 6796.88 Blackness(calculated point)
---------- ----------
319.29 -226.69

again, using Pythagoras' theorem: 315.40 grid units of 100 metres, which converts to: 19.598 miles(E), and allowing for the small rounding off in the calculations is good to 0.002 miles! (I have restricted the figures to two decimal places for convenience here, and to 3 decimal places in the final miles calculation! A discrepancy of some 10 feet. I trust this is acceptable! I normally work to 10 figures on the calculator!)

And the angle to grid north is 44.05 degrees west of grid north, which corresponds to ninety degrees difference to the North Berwick line, 45.95 degrees east of grid north.

The grid squares having diagonal St.Mary's Chapel to Blackness are shown below, with sides equal to 19.598 miles(E)/square root 2 = 13.858 miles(E):

The next section uses this smaller square as the grid unit for the next stage, which extends this grid in all directions.

Now, a final point for now, as I have just realized:

This grid square side length of 13.858 miles(E) is equal to 12.36 miles(S)(33/37 is the onversion factor, see explanation in previous posts, and why I here, always distinguish between the two systems by the (E) and (S).

Now, half of 12.36 miles(S) is 6.18, a harmonic of phi, or little phi, or 1/Phi!!!

This is a new finding, although I may have it in my notes, but I don't recall having found this previously in relation to this system, and has to be of significance, to my mind! Quite astonishing, but then again, that's nothing new in this whole research!

I shall work on this, and see what else is to be found!

Good grief, the time on my computer at this exact moment is 6.19am, BST!!!

I had just done some calculations, one of the dogs barked, and I checked the clock!!!!

This is what I found:

The Bornholm grid axis is 16*square root three miles(E). This equates to 24.71683315miles(S). This divided by 40 gives 0.617920828. The reciprocal is 1.6183303, which squared is 2.61899296. Now that is an approximation of Phisquared, or Phi^2. This multiplied by 6/5; or 1.2 is 3.142791552, which multiplied by 7 = 21.99954086, which is 99.998% of 22. 22/7 is a rough, and often used form of Pi.

So, this grid, and hence the Bornholm grid, in Scottish measure is based on a common form of Pi, and Phi! I had found some correlation with Scottish measure when I was working on the Bornholm grid, but nothing so convincing!

So the full factors involved must all resolve in some way:

[(16*sq.rt3*33/37*40)^2]*5/6 = 7/22; so; (16^2,*3,*33^2,*5,*22)/(37^2,*40^2,*7) = 1;

which resolves to (2^2,*3^2,*11^3)/(5,*37^2) = 47916/47915; which equals 1.00002087, the reciprocal of which is 0.99997913, equivalent to 99.9979% of 1.

Interesting exercise! Or perhaps I should get a life!?

Then again, astonishing find!

St.Mary's Chapel Bass Rock system further consideration

2008-10-02T15:48:00.008+01:00

Having established the Bass Rock line, and considering this to be the diagonal of a square, the vertical will be 45 degrees anti-clockwise, a line which proves to run through the Arthurs' Seat area, and in fact a special rock on Dunsappie Fort, which I call pulpit Rock, whih intrigued me when first found back in the mid-nineties. The line extended north finishes just east of Seafield Tower, just offshore.

A lot of calculations were done using both the Bass Rock and North Berwick Law alignments, but the easiest way here is to just show the Dunsappie calculations first then the Seafield Tower point, just to keep things simple:

3275.00 6570.19 St. Mary's Chapel
3281.32 6731.72 Dunsappie 'notch' or Pulpit Rock
---------- ----------
-6.32 -161.53

Using Pythagoras again the distance is 161.6536, in One hundred metre units which converts to 10.0447 miles(E). This may be of interest but for now it is the angle this line makes to the O.S grid for comparison to the Bass Rock line:

6.32/161.53 = 0.039126, which is the tangent of 2.2406 degrees.

Comparing to the Bass Rock angle of 47.1803 - 2.2406 = 44.94 degrees, which is 0.06 degrees, or 1/100th of one clock-face-minute!

As the diagonal of a square is in square root two relationship with the side, this line extended north to a distance of 19.59592 miles(E), (16*sq.rt.3/sq.rt.2), the point indicated on the map just off-shore at Seafield Tower, which lies between Kinghorn and Kirkcaldy, is found.

Now that the St.Mary's -Bass Rock-Seafield Tower 45 degree right-angled triangle has been established, the full square can be projected, to complete the square on the circle of Bill Buehler's original circular system. And also, some of the sub-divisions also show points of interest.

click on image to see larger version!

This schematic was drawn prior to the calculations, and was what I needed to verify. It is good enough for now, as it shows the extended square and circle and some natural sub-divisions.

AS stand for Arthurs' Seat, and can be seen to be halfway between St. Mary's Chapel and Seafield Tower. It should be pointed out that the exact halfway point is some 440 yards south of Dunsappie, or one quarter mile, which is Duddingston loch, a beautiful spot famed in Scottish art for the painting by Raeburn of the Reverend Walker skating on Duddingston loch. And on the north-east shore lies Duddingston Kirk, the minister at the time was the Reverend John Thomson, who was also an amateur painter and had a studio down by the shore, still extant, an octagonal building which was also the home of the first curling club in the world.

Intriguingly, on the north wall of the kirk is a carved symbol, the same as is shown in 'The Templars' Secret Island', the book of the geometry of Bornholm, by Erling Haaagensen and Henry Lincoln, page 13, where there are examples of stones from Bodilsker, Nylars, Osterlars and Vestermarie, which 'echo the Cross of the Knights Templar'.

It should also be pointed out that there is also the Line from St. Mary's Chapel through Rosslyn Chapel and Arthurs' Seat summit which is the Roseline commonly or as Bill Buehler calls it the Tavhara Line, which passes just to the west of Seafield Tower, previously mentioned. This may constitute a more generous Selah Spoke, with the North Berwick Law line running between Arthurs' Seat and Dunsappie, and we can in passing check this:

3275.00 6570.19 St. Mary's Chapel
3275.28 6729.43 Arthurs' Seat summit
---------- ----------
-0.28 -159.24

and using Pythagoras' theorem: 159.24 O.S.units of 100 meters, which equates to 9.895 miles(E), and the angle to O.S. grid north being: 0.28/159.24 = 0.00176, which is the tangent of 0.1 degrees.

So the gap between this line and the Dunsappie line being 2.24 - 0.1 = 2.14 degrees, which may be considered as a 'Selah spoke'!

I consider the Arthurs' Seat area to be a 'unit point area' at large landscape scale.

So this gap being contained within the Arthurs' Seat area at a landscape scale this may be considered valid!

Also, and more pertinent to the next section is the Blackness Castle/Drem line. This can be seen to be between the diagonals at a distance the same as Seafield Tower, taken as radius. The squares on these sections of diagonals prove to be the unit squares of the next sub-system to be described! See next section!

Bornholm Grid Part Two - Lothian Scotland

2008-08-29T05:36:00.011+01:00

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.

2008-07-22T07:16:00.020+01:00

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

2008-07-10T05:47:00.003+01:00

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

2008-06-17T03:41:00.004+01:00

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

2008-05-01T04:54:00.003+01:00

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

2008-04-29T09:17:00.003+01:00

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

2008-04-11T10:13:00.002+01:00

View Larger Map

Schiehallion - Galachlaw - Rubers Law

2008-04-11T06:28:00.010+01:00

Back in the year 2000, I was driving south to England from Selkirk, early morning, to be in Lichfield for 9.30am.

From Hawick I took the A6088 towards Bonchester Bridge, and as the road took a turn east just after Kirkton, I was stunned by the hill silhouetted by the early dawn light:

On the way back later that day, I took another photo of the same hill:

I confirmed this hill to be Rubers Law, O.S grid reference: NT 579 155.

I had been working on some geometry, see previous Schiehallion - Eildon line post, and was discovering the landscape of the Borders as I went. Rubers Law was part of the discovery process. I can't quite describe the feeling of shocked awe when I turned east that morning to see the hill in the dawn light, dark and brooding in silhouette. I had to check the maps to see if and where it fitted in. With great amazement I found it to be in a direct line with Schiehallion and Galachlaw, the entre of the original pentagonal system previously described. Especially so since I had already confirmed the Schiehallion -Arthurs Seat - Eildon line.

When I got round to doing the detailed calculations, I was even more amazed to find that Galachlaw was indeed very close to the Phi-point.

A few calculations to show this:

Grid References (full, and normal forms)):

2713.83 7547.74 Schiehallion summit NN 714 547
3253.65 6683.21 Galachlaw cairn NT 253 683
3249.37 6687.44 Water Works mast( exact Phi-point) NT 249 686
3580.35 6155.75 Rubers Law summit NT 579 155

Schiehallion:

first calculation; Schiehallion - Rubers Law:

2713.83 7547.74 Schiehallion
3580.35 6155.75 Rubers Law
--------- ----------
0866.52 1391.99

By Pythagoras' theorem; 1639.66

which converts to 101.88 miles(E), and 90.87 miles(S)

The angle to grid north is 31.9024 degrees, using the tangent of the two calculated values above.

Second Calculation; Schiehallion - Galachlaw cairn:

2713.83 7547.74 Schiehallion
3253.65 6683.21 Galachlaw cairn
--------- ----------
0539.82 0864.53

By Pythag. 1018.22

which converts to 63.33miles(E)and 56.48miles(S)

angle to grid; 31.98075 deg.

using the English miles distances of both we ind the relationship to be 99.424% of Phi:

101.88/63.33 = 1.60872, which is 99.424% of 1.618034.

Galahlaw Cairn:

The exact Phi-point proves to be some 660 yards to the north west of the cairn, at point (3249.37 6687.44), which is in the Water works where a Mast is erected, normal grid reference NT 249 686.

view of gap between Hillend fort on right and Galachlaw with Water Works Mast to the left:

This mast can be seen to the left of this photo, with Hillend Fort to the right.

Comment:
All I can say about this is that it was around this time that I came to strongly accept a 'sense of process' involving time and place, and which I for sure am not in control of. It is not just an excuse for me to be lazy in presenting all this material, it has taken years to get to, and I have learned to accept patience as an essential. All the geometry and correlations have in a sense been presented as and when 'this process' deems necessary. I no longer question this, it just happens when it does.

supplementary

When plotting this line on Google Maps, I checked Fordell Castle which I had noted originally was on this line, and on calculation was found to be at the centre, Fordell Hill precisely, within the estate. Fordell was the home/seat of Nicholas 'Nicky' Fairbairn, a Tory MP, government Minister and somewhat extrovert.

As Galachlaw is at the phi-point of the line, there is another equivalent on the other side of the centre-point. On examination and confirmed by calculation, it was found to be White, or Hood Hill, NO 042 018, near Tullibole Castle, by Crook of Devon.
There is also a radio/electronics mast on Hood Hill!? (Once is chance, twice is coincidence...!)

(There was reported that a sign-post in Crook Of Devon had neatly printed under it: 'Twinned with Thief Of Baghdad'! - btw! lol)

In addition it was noted that Lauriston Castle is on this line, and Cramond Island. Lauriston Castle came to my attention in connection with John Napier of Merchiston, an Alexander Napier having owned it. Lauriston Castle proved subsequently to be a geometric node, and still to be described.

Cramond has been highlighted recently by Bill Buehler, in connection with the Roman lion staue with man in its mouth, which I also linked with John Napier, or the double lion-gate at Merchiston, in an e-mail exchange!

Google Maps trial

2008-04-07T15:04:00.008+01:00

First attempt at drawing lines on Google Maps. This is the Schiehallion to Eildon Hills North line:

View Larger Map

It seems to be slightly off at Arthurs Seat in comparison to calculations and Google Earth. Needs to be considered further!?

I have also marked Newtongrange and Borthwick on this line now.

sense of place - photo-album

2008-03-24T19:40:00.005Z

After all that math of the previous posts, I have spent the day 'playing' with photos, and have managed to upload some as a web-album in Picasa.

Here's some photos of Lothian and the Borders of Scotland, un-captioned as of yet, and pretty much random.

Schiehallion alignments part one - Arthurs Seat to Eildon

2008-03-07T07:30:00.024Z

The grid references to be used in this section are:

2713.833 7547.736 Schiehallion summit(S)

3275.280 6729.430 Arthurs Seat(AS)
3554.330 6329.100 Eildon north Ring Fort(E)
3333.750 6642.000 Newtongrange Church(N)

3580.350 6155.750 Rubers Law(RL)
3253.645 6683.210 Galachlaw Cairn(G)
3249.370 6687.440 Water Works, calculated exact golden-section point near Galachlaw

3189.702 6826.692 Inchcolm Abbey(I)

The calculations to follow on the three lines on the drawing. What I shall show is: 1) that Schiehallion, Arthurs Seat and Eildon Ring Fort, and Newtongrange Church are all on a straight line, within very tight margins.

2) That Galachlaw Cairn, the center of the original penta-system, is very close to the EXACT phi-point(golden section/mean) between Schiehallion summit and Rubers Law summit. The exact point is in fact in the local water-works, where a radio mast stands(!?).

3) That Inchcolm Abbey is at one degree, very lose, to the Arthurs Seat line, at Schiehallion, which may be relevant.

On the diagram, it can be seen that the Inchcolm line extends to a point labelled (FC), this is Fatlips Castle near Minto in the Borders. The calculations to Fatlips have not been included here.

The axis of the original penta-system is shown, from Roslin(R) through Galahlaw(G) to Inchcolm(I).

There is a vertical line, indicating what has been called the 'Roseline', or in Bill Buehler's terminology, the Tavhara, with Dryhope Tower(DT) at the bottom, and Seafield Tower(ST) at the top, both on the circle circumference, centre St Mary's chapel(St M), radius 20 miles. This is still to be explained in detail.

Part 2

The line highlighted in the diagram, between Schiehallion(S) and The Eildon Hills(E), runs through the Arthurs Seat(AS) area, with a ratio of 2:1, and also includes Newtongrange Church(N), which is one of the determining points of the Rennes Le Chateau radius as determined by Henry Lincoln, with Mavisbank as centre.

Schiehallion:

The Eildon Hills, known to the Romans as Trimontium, has Melrose Abbey nestled in the low ground near the river Tweed. The example given here uses Eildon North, with a large ring-fort on its summit, and was used as a signal station by the Romans.

Eildon Hills:

I shall later also use Eildon Mid-hill, which has an O.S. trig-point on its summit.

Arthurs' Seat also has a trig-point on its summit, and it is the summit which really defines the 'Roseline', through Rosslyn Chapel(R), and is shown on the diagram, with centre at St. Mary's Chapel(St.M), and a 20mile radius circle, with Seafield Tower(ST) on the 'Roseline' to the north, and Dryhope Tower(DT) to the south. The Arthurs Seat complex covers quite a lage area, from Holyrood Abbey/Palace/Parliament Building, St. Anthony's chapel, Dunsappie Fort, Duddingston Church, Crow Hill and Whinny Hill, and Salisbury Crags. There is a lot to consider and this post has been somewhat delayed due to my need to compare a whole set of calculations between Arthurs' Seat and the Eildon Hills, with some interesting correspondences and ratios of distances and angles.

Arthurs Seat, from Hillend Fort,(very important geometric point, to be discussed), over Galachlaw, (centre of original pentagon, and to be discussed in the Schiehallion to Rubers Law line, Galachlaw at Phi-point):

Schiehallion summit is taken as a constant. It has already been seen to lie on the hypotenuse of the Preston Cross triangle.

All three sites are special, with their associated myths and legends, in a sense they are all considered 'magic' mountains.

Using the Grid references listed in the previous post, and using the same procedure as before:

Calculation (1)

2713.833 7547.736 Schiehallion
3275.280 6729.430 Arthurs Seat
------------ ------------
0561.447 0840.167

By Pythagoras theory;
0992.395

which converts to;
61.664556 miles(E); or 54.998 miles(S)

The angle to the O.S. grid, again using the tangent of the ratio of the two derived grid components is 34.4544 degrees

Calculation(2)

2713.833 7547.736 Schiehallion
3554.330 6329.100 Eildon North(ring-fort)
------------ ------------
0840.497 1218.636

By Pythag; 1480.375

which converts to;
91.9862 miles(E); or 82.042 miles(S)

Angle to O.S.grid; 34.59415 degrees

First of all the angles to grid are:

34.45440deg.
34.59415deg.
------------
0.13975deg. difference

This is 1/43rd of one clock-face-minute(cfm), (reminder that one cfm is six degrees).
This discrepancy at Arthurs' Seat summit is some 265 yards.

The exact line runs to the north east, between the summit and Dunsappie fort. If the Arthurs' Seat line is used and projected to the Eildon, it passes through the gap between Eildon North and Mid-hills.

The Schiehallion/Eildon North line runs through the gap between Arthurs Seat summit and this stone, convenient marker(!), on Whinny Hill:

So, Schiehallion, Arthurs' Seat and the Eildon Hills are in a straight line!

The distance ratio is 61.664556:91.9862 = 2:2.98344(99.45% of 3)

The exact distance of Arthurs Seat to Schiehallion should be 61.324 miles(E) for a 3:2 ratio. A discrepancy of 600 yards, or 0.34 miles(E), north towards St. Anthony's Chapel and Holyrood Abbey.

Holyrood Abbey/Palace, lower foreground and St. Anthony's Chapel, the ruin left centre:

This is relevant perhaps to geometrical grid work, the 3:1 ratio having shown up elsewhere. More needs to be done on this aspect at a later date. Just to note in passing that the diagonal of a 3 by 1 grid is the square root of ten!

William Buehler(Bill) has recently described a temple format using this ratio, and I have found it to be in use in a grid based on the twenty mile radius in the diagram, which was first defined, to my knowledge, by Bill.

Enough on that topic for now!

Next to consider the position of Newtongrange church:

2713.833 7547.736 Schiehallion
3333.750 6642.000 Newtongrange Church
----------- ------------
0619.917 905.736

By Pythag. 1097.568

converts to; 68.1997 miles(E); or 60.827 miles(S)

Angle to O.S. grid: 34.389 degrees.

Comparing this angle to that of Schiehallion/Eildon North:

34.59415 Schiehallion/Eildon(N)
34.38900 Newtongrange churh
-------------
0.20515 deg. (1/29th cfm, or some 430yards at Newtongrange) A quarter of a mile may seem a lot, but at this scale it is in reality not much, and later I shall show that Newtongrange is more accurately in line with Eildon Mid-hill and Arthurs Seat.

Keeping this in bite-sized chunks I shall leave this here for now!

Supplementary one

The exact 3 by 1 ratio mentioned in the previous post, existing between Schiehallion, Arthurs Seat and Eildon North can be shown to be just over 60 yards from St Anthony's Chapel, O.S.grid reference (3275.755 6737.100).

I'm not bothering with full calculation sets here, but shall give O.S.grid references used, so can be verified by anyone with a calculator, and an interest!

St. Anthony's chapel is also 323606 feet, (61.289 miles(E)) from Schiehallion, a 2*Phi relationship.

2*Phi is 2 * 1.618034 = 3.236068, hence correspondence is 99.9997%, ignoring decimal points.

The calculated distance from St. Anthony's Chapel and Eildon North is 30.698 miles(E), or 162084 feet, a discrepancy of 93.5 yards from perfect of 161803.4 feet

As calculated in previous post, the exact 2:3 point at Arthurs Seat is 61.324 miles(E) from Schiehallion, and St.Anthony's Chapel is 61.289 miles(E), the difference being 61.6 yards.

The angle to O.S.grid is found to be 34.7292 degrees, and Duddingston Church (O.S. grid ref. used 3283.113 6726.172), an angle of 34.72 degrees, at a distance of 62.1075 miles(E).

These two angles are nearly identical, (a difference of 0.0092 deg, at a distance of 0.8185 miles(E), or 4321 feet, or 1440 yards (!?) is 0.7 feet, exact given the limit of practicality in my method. Anything within ten yards is too close to differentiate!)

So, Duddingston Church and St. Anthony's Chapel are in direct line with Schiehallion summit!

Also, St. Anthony's Chapel is also remarkably at the exact Phi harmonic distance in feet, from Schiehallion, and also marks the 2:3 point!!

And a final point of note concerning Duddingston Church and St. Anthony's Chapel:

the ratio of their distances from Schiehallion is: 62.1075 : 61.289, which is 1.013355 : 1! This ratio is greater than 99.97% of the Comma of Pythagoras as found in the work of Robert Temple, The Sirius Mystery, for example (page 24); the ratio of 3^12 : 2^19, or 531,441 : 524,288, or 1.0136433.

Duddingston Church and loch:

So, the area between both can be considered as the area of harmonic fluctuation between the ideal and the real in geometric terms, in accordance with the theories of the Pythagoreans. This area contains most of the Arthurs Seat area, including the summit. I consider this to be a perfect example of what I term a 'unit point area', which varies in size with distance, especially at special sites like Arthurs Seat and the Eildon.

Also, St. Anthony's Chapel is situated very close to the projection of the Tavhara line mentioned previously, to the north of Arthurs Seat summit.

Thus St. Anthony's Chapel can be considered a very special geometric marker.

Duddingston, too, is also a special point, including the area of the loch which it sits by. The exact line from Schiehallion to Eildon North passes by the western end.

added 20/03/08. Taking the tangent of the difference in angles between Duddingston and St.Anthony's to Schiehallion:

34.792 - 34.72 = 0.0092, the tangent of which is 0.00016057, times the distance from Schiehallion to St. Anthony's Chapel, 61.289 miles(E), equals 0.0098412 miles(E), which equals 51.9615eet, or 17.32049908 yards, which is an incredible 99.99995% harmonic of the square root of three!

I have difficulty coming to terms with a finding like this. It implies, an intent in the positioning of St.Anthony's and Duddingston, with an accuracy so great to beggar belief. Root three is of course an integral component of an equilateral triangle, namely the altitude in relation to the side.

The correspondences between St. Anthony's chapel and Duddingston and Schiehallion are astonishing, and leave much room for thought.

Supplementary two

As mentioned in main post, Newtongrange Church is more exactly in line with Arthurs Seat summit and Eildon Mid-Hill summit (O.S.grid reference used: 3548.19 6323.03)

Arthurs Seat to Eildon Mid-Hill, the distance is 30.418 miles(E), and the angle to O.S. grid is; 33.8826 degrees.

Newtongrange Church to Eildon Mid-Hill, the distance is 23.88252 miles(E), and the angle to O.S. grid; 33.9125 degrees.

The distance from Arthurs Seat and Newtongrange Church is some 6.5355 miles(E), and the difference in angle, 0.03 degrees; and using the tangent of this angle a discrepancy of 18 feet, near enough to be considered exact! (0.03degrees is 1/200th of one clock-face-minute!)

Finally, worthy of note, perhaps, is that there is found to be a 'near' pi, (99.97%) relationship between the two distances:
A.S. to E.M.-H.; 30.418 miles(E)
N.C. to E.M.-H.; 23.88252 miles(E)

23.88252/30.418 = 0.785144322, multiplied by four gives; 3.1406, (99.97% calculator pi, or 99.93% of 22/7, a commonly used version).

Supplementary three

Consideration of a significant geometric centre, already discussed in the Borthwick series of posts, namely Borthwick Church and Castle.

The references in the form used here are:

Borthwick Church 3368.785 6596.075

Borthwick Castle 3370.00 6597.597

I do not intend giving the full calculations here, just to point out that the exact line from Schiehallion to Eildon North, is at an angle to the O.S. grid of 34.594 degrees.

The angles to Borthwick Church, 34.5365 degrees, and to Borthwick Castle, 34.62 degrees.

From this it can be seen that the line passes between the two Borthwick points. It passes some 58 yards from the castle, and 126 yards from the church.

The distances are 71.7844 miles(E), or 64.024 miles(S) for Borthwick Church, and 71.765 miles(E), or 64.0067 miles(S). for Borthwick Castle.

The distance in Scottish miles, of 64 miles(S), is worthy of note, being 8 squared!

So, the line from Schiehallion to Eildon North passes through Borthwick.

Borthwick Castle, left, Church, right, looking south-east towards The Eildon, way beyond horizon:

This is looking north-west over Arthurs Seat, summit just visible, towards Schiehallion, faintly discernible on horizon, (click on image for larger version). Borthwick is on other side of foreground rise, not visible. This is taken from the point on the A7 south o Middleton, where the line crosses:

Finally, there are several points on this line, from a scan of Google Earth, but not calculated:

Drum estate, and the corner at The Wisp, near Danderhall, and Edmonstone House, just south of Arthurs Seat. North, Starbank Park on the coast, and Aberdour harbour on the Fife coast.

Extending south to the North Sea, the line passes through Lincolnshire and The Wash. A crop circle was found in Lincolnshire in Google Earth, very close the line. This is an area which a fellow researcher is looking at.

Main Finding from investigation, (so far)

The main finding rom this investigation, so far, is that Arthurs Seat/Holyrood Park sits at the 2/3rds distance between Schiehallion and The Eildon Hills. St.Anthony's Chapel in Holyrood Park can be assumed as the marker point. Not only that, but St. Anthony's Chapel is 'exactly' 323,606 feet from Schiehallion, and approximately 161,804 feet from Eildon North. Phi, (golden section) is 1.618034, so both distances are an exact harmonic of Phi!

This is a simple representation of the three by one rectangle, using the diagonal as the Schiehallion - Eildon line. I could have done it as the side of the rectangle, but chose the diagonal, as later I shall be discussing the 3 by 1 rectangle in connection with a grid, which has a 3 by 1 diagonal as a baseline for a very special geometric system. The diagonal of a 3 by 1 rectangle is in fact, square-root ten.(By Pythagoras, (3^2 plus 1 equals 10. The diagonal is thus square-root 10)

PuC triangle - a very special triangle!

2008-01-24T16:20:00.026Z

After far too long a gap I can at least start to cover the astonishing geometry found incorporating this Market Cross, at Preston, East Lothian.

This photo is of the Market Cross, with the unicorn on top. Bill Buehler is on the right, with his black cowboy hat. Preston Tower can be seen in the background! This was taken in March 2003, after the Sacred Geometry Conference at the Templar Lodge Hotel in Gullane. The weather was lovely spring sunshine for about six weeks. It was in fact the week the Iraq War was started!

In the geometry I will show, I have used the best grid references I can get, using printed off sections of Ordnance Survey 1:25,000, and measuring the fractions as best I could, and calculating to the metre, which in theory is the best achievable! I think that an allowance to ten metres would be reasonable.
Especially in the case of the triangle of which this point is the apex, which covers distances of over two hundred miles, and extends a further 50 miles or so, with astonishing accuracy, the hypotenuse including Schiehallion, summit tip, to a mound at Calanais/Callanish, and the adjacent includes the summit of Ben Cruachan, and extends to Flodagh a small island south of Barra. The short right-angle return side from Flodagh to Calanais runs through the Outer Hebridean land mass.

What is astonishing is that the hypotenuse and adjacent are in the precise ratio of Scots Mile to Imperial/English Mile: 1:1.1212121212, or 37:33, as described by John Reid, in his book of Gardening in 1683, the first book to deal specifically with Scottish conditions. I shall describe this later.

The two lines extend to the south and east, the hypotenuse to Kelso Abbey, and the adjacent to the highest point on Lindisfarne/Holy Island, namely Bible Law.

It is mainly because of this unicorn that I use the name, it signifies so much to me about this whole subject. Its now a kind of side hobby, collecting photos of unicorns, and I have some I will also show later.

This is just a wee intro to this topic. The geometry and calculations will be next.

Preston (Unicorn) Cross triangle sketch

It has taken ages for me to get this stuff together, from notes and re-calcs just to check. (A strange lethargy/inertia came over me over the 'festive' season, part laziness, and part something else I've learned to accept, and patience is needed till 'the time is right' kind of thing!)

These calculations were originally done in 2003/4, as a series over many months, using as detailed Ordnance Survey grid references I could muster.

Explanation of method:

Originally my search area was confined to the Lothians area of Scotland, centered on Midlothian, the area of my youth, which includes Roslin, Arthurs Seat and the Pentland and Moorfoot Hill Ranges, with the Esk River Valley system, and the City of Edinburgh.

This area was available on one map at a scale of 1:50,000, which is ok for Hillwalking and such. The best though is 1:25,000, and for my chosen area three needed to be joined on top of each other. To extend to East and West Lothian, to include Cairnpapple in the west and Traprain Law in the east two wing sections had to be attached. This took up a lot of wall space, and the Firth of Forth with its islands, and Fife would have been on the ceiling, so limits were defined by wall height. As the geometry developed the map became a mess, and distortions in jointing and stretching became inevitable. A number of maps were destroyed in this way, but it was a necessary process. I always knew verification would be necessary and it took many years to get to the stage were I felt confident enough and had access to the on-line Ordnance Survey, 'Get-A-Map', and after practice with the accurate references available for the island of Bornholm, as described by Erling Haagensen and Henry Lincoln in their book, 'The Templar's Secret Island'. That is another topic, which shall be covered eventually.

The geometry in Scotland had expanded to the extremities of Scotland, and further south, and a system had to be found to check it all out.

A concern was how much curvature would there be on this scale, and so what deviation would result. Rough calculations indicated that or Scotland as a whole, if a stretched table cloth was brought down on Scotland, to a height of some 2000feet, there would be sufficient mountain/hill tops over the whole area to allow flat geometry to be done.

What remained to be settled was the accuracy of the Ordnance Survey Grid over such a large area.

Speaking to a Cartographer friend, I was advised that the OS grid was accurate to a meter, but not to expect any better. A meter was/is good enough for me. Subsequently Dr. Nicolas Crane, of the Open University, best known from the series 'Coast', did a TV programme on this very topic. He checked the OS grid in Caithness, as far from the origin of the grid, (Reading, I believe) as practical on the mainland as possible. The discrepancy he found was minuscule, thus verifying the accuracy further.

Being in a phase were I had no computer I used the local library to print out sections of the OS map, 1:25,000 for all the selected points I wanted to check. I then carefully calculated as best I could, the fractions of kilometer squares of the said points, and using the absolute number prefix* in place of the 'usual' letter components obtained twelve figure references, to the meter, and did comparative calculations to verify angle and measures, converted to Miles(Imperial, or English, and also Scottish). The angle was of course vital, to determine orientation, and to confirm a straight line between three or more points. The distance measures were also examined for any whole number correlations with the postulated grid, and the common square root diagonals, namely, sq.rt. two, three and five, and the transcendent numbers, 'phi', 'pi' and natural log. base number 'e'. The latter being so close to the Megalithic Yard determined by Professor Alexander Thom, as to be remarkable that no-one I know, other than Bruce Cathie, makes the connection. These correlations prove to be so numerous, and involved that this present post shall be restricted to confirmation of the triangle with Preston Cross as apex, shown previously.

*Normal Grid references consist of a two letter prefix, and two sets of three numbers, for example: NT 348 765.

For work which crosses map boundaries, a universal grid number can be prefixed to the two number sets, giving eight figure references: NT 348 765, then becomes 3348 6765.

These two sets are called 'eastings' and 'northings', that is, the first set denotes the horizontal component, the second, the vertical component.

These sets are approximately to the hundred meter scale. The last number in each set is a fraction of the kilometer square which is denoted by the first two.

What I did was to measure as best I could and calculate to the meter, giving another two numbers in each section, making twelve figure references to work with: the above example becoming, say; 3348.63 6765.21! Ranging thus from hundreds of kilometers to meters. The decimal point retained as reminder to myself that to the right is my calculations!

The origin of the grid system is in the Atlantic south-west of the Lands End. It is a 'false' origin in that the Meridian 2degrees west is used for orientation, which happens to be the longitude of Berwick upon Tweed. Due to the curvature of the earth and the flat grid a discrepancy develops between the spheroid and the map, 2degrees west is roughly central of the area covered by the grid and the discrepancy kept symmetrical either side of 2dwest. (As explained by my Cartographer friend, from memory, and no fault of his if inaccurate!) Numbers thus increase from west to east, and south to north.

So, having two such attained numbers, calculations can be performed. A purely random pair can be used, for example:

The one already given, 3348.63 6765.21
and another, say,.........1234.56 9876.54
.......................................--------- ---------
subtracting both sets: 2114.07 -3111.33(the negative sign is important for orientation, this minus sign in the northing signifies that the second/bottom site is further north than the first/top, and should be borne in mind. It disappears from the square of the number, and can be ignored when calculating angle to grid, but is essential when drawing)

These numbers give us a horizontal and a vertical, at right angles to each other so the hypotenuse can be determined by using the Theorem of Pythagoras, (at least that's the name we use, although it is fairly certain it was known and used prior to him).

Theorem: the square on the hypotenuse is equal to the sum of the squares on the other two sides. X^2 + Y^2 = hypot^2

in our case: (2114.07)^2 + (-3111.33)^2 = 4469291.965 + 9680374.369 = 14149666.33

The square root of this number is 3761.604223.

This is in units of hundred meters. The conversion factor to change meters to feet is 3.28084; thus 3761.604223*100*3.28084 = 1234122.16 feet.

Convert to miles using the factor 5280: 233.7352576 miles(English)

Convert to miles(Scottish) using ratio 33:37, or 0.891891891repeat = 208.4665811 m(S)

These two measures are then analyzed for correlations with whole numbers and the important square roots, irrationals and transcendental numbers mentioned above, but not considered here.

What is now required is the angle this hypotenuse actually makes with the OS grid, for comparison purposes with other alignments, either for straightness or angle between. This achieved using the tangent ratio, from trigonometry, of opposite to adjacent, for sake of consistency the 'eastings' over 'northings', that is, first over second:

2114.07/3111.33 = 0.679474694, (using calculator tan function)=34.195116 degrees.

[I apologize for giving so many decimals after the point, just copying what the calculator gives. In terms of distance measures, in the Imperial/English system it should be 233 miles 1294 yards; and in Scottish measure 208 miles 896 ells. The yard(36 inches) and the ell(37 inches) being the equivalent to the meter, and thus the level of accuracy achievable. The same with degrees, 34d 11m 42.42s is the transposed number above into minutes and seconds. I could limit the decimals to 3 or 4 places but my calculator gives 10 figures so I have by habit just used that format, but aware of the 'nonsense' in practical terms, the final few figures actually are.]

So, with angle and measures comparisons can be made between any two points and any others.

PUC triangle calculations part 1

The first line to be considered is the line from Sandragh to Lindisfarne, through Ben Cruachan, Inchcolm and the apex of the triangle at Preston Cross.

The grid references to be used are, blue circles from left to right;
Sandragh/Carn Ghaltair--: 0640.79 7915.49
Ben Cruachan/summit----: 2069.62 7304.60
Inchcolm/Abbey------------: 3189.70 6826.69
Preston(unicorn)Cross---: 3391.27 6740.57
Lindisfarne/Bible Law-----: 4136.54 6422.64

The hypotenuse of the triangle, from Calanais/Callanish, Schiehallion, Preston Cross apex, and Kelso Abbey:

Grid references, again from left to right:

Calanais/stone circle and cairn--: 1221.50 9325.33
Schiehallion/summit---------------: 2713.83 7547.74
Preston Cross----------------------: 3391.27 6740.57
Kelso Abbey------------------------: 3727.85 6338.90

PUC triangle calculations part 2

First I shall do the Sandragh/Carn Ghaltair point and Preston Cross. Sandragh is not the end of this line, a point very near the island of Flodagh a mile or so further west is the corresponding point at right angles to the Callanish point. This is less important than establishing the two lines, adjacent and hypotenuse, and their angle and relationship to the English/Imperial mile system, and the hypotenuse the Scottish mile system, more on this later:

0640.79 7915.49 Sandragh/Carn Ghaltair
3391.27 6740.57 Preston Cross
------- -------
2750.48 1174.92

Using these two numbers, and the Theorem of Pythagoras, that is adding the squares of these numbers and finding the square root of the result:

(2750.48^2) + (1174.92^2) of which the square root is 2990.916. Now, this is in units of hundreds of metres, so 2990.916 *100 = 299091.6 metres.

Metric is no use to us, so converting to feet using 3.28084 feet/metre, we get

299091.6 * 3.28084 = 981271.685 feet.

There are 5280 feet per English/Imperial miles s;

981271.685 / 5280 = 185.8469 miles(E)-(my way of differentiating between English and Scottish miles.

To convert to Scottish miles the factor is 33:37, so;

185.8469 * (33/37) = 165.75534 miles(S)

So we have the distance between Sandragh and Preston Cross, and I found no neat correspondences with any of the common roots, so next and for now more important is the angle to the O.S. grid.

Using the two obtained numbers again, the tangent of the angle is 'opposite' over 'adjacent', in this case:

2750.48 / 1174.92 = 66.869 degrees

So, that is the method, in words and format, from now on I shall omit most of the explanations.

Next, Preston Cross and Bible Law, the highest point on Lindisfarne:

3391.27 6740.57 PUC
4136.54 6422.64 B.L./Lindisfarne
------- -------
0745.27 0317.93

By Pythag, times 100:

81025.11 metres = 50.34667 miles(E), 44.904 miles(S)

Angle to O.S. grid:

0745.27 / 0317.93 = 66.897 degrees

The difference between these two angles is thus; 66.897 - 66.869 = 0.028 degrees.

As a visual aid, a clock-face has sixty minutes marked, hence each clock-face minute is 6(six) degrees. 6 / 0.028 = 214. Try dividing a clock-face minute visually into 214 parts. This gives an indication of the accuracy here. Over the whole length, 185.85 + 50.35 = 236.2 miles, but using the midpoint as fulcrum the discrepancy either side would be: (236.2/2)* tangent 0.028 = 100 yards at both Lindisfarne and Sandragh. In other words a circle of 100yards radius at either end would contain this discrepancy, with ease.

To finish this first line, for now, the points Ben Cruachan(summit) and Inchcolm Abbey shall be compared to Preston Cross:

2069.62 7304.60 Cruachan summit
3391.27 6740.57 PUC
------- -------
1321.65 0564.03
which Pythagoras times 100 is 143697.20 metres or; 89.2893 miles(E), 79.6364 miles(S)

angle to grid:

tangent (1321.65 / 564.03) = 66.889 degrees.

3189.70 6826.69 Inchcolm Abbey
3391,27 6740.57 PUC
------- -------
0201.57 0086.12

By Pythag( times 100):

21919.653 metres, 13.62 miles(E), 12.148 miles(S).

angle to O.S. grid:

tangent(201.57/86.12) = 66.866 degrees.

Just to compare angles obtained:

066.869
066.897
066.889
066.866
------
267.521 / 4; mean = 66.88025 d.

The greatest discrepancy from mean is that between PUC and Inchcolm, 0.01425 degrees, representing some 18 feet at a distance of some 14 miles(E), or a 420th division of a clock-face minute.

Carn Ghaltair is the high point of the island of Sandragh south of Barra, Cruachan summit, and Bible Law, the highest point on Lindisfarne, and Inchcolm Abbey and the apex of the triangle, Preston Cross, with its unicorn on top, form a straight-line!

PUC triangle calculations part 3

There are four points on the hypotenuse line now to be considered, from top left to bottom right, Calanais/Callanish, stone circle and cairn, Schiehallion summit, Preston Cross, apex, and Kelso Abbey on the line extended through PC.

The line from Callanish through Schiehallion to Preston Cross proves to be straight to an astonishing degree, to 1/177th of one degree, or less than 1/1000th of one clock-face minute.

1221.50 9325.33 Calanais stone circle and cairn
3391.27 6740.57 Preston (Unicorn) Cross
------- -------
2169.77 2584.76

By Pythag.

337475metres, or 209.7miles(E), or 187.03miles(S)

angle to O.S. grid:

40.0117degrees.

2713.83 7547.74 Schiehallion summit
3391.27 6740.57 Preston Cross
------- -------
0677.44 0807.17

By Pythag.

105377.66metres, or 65.48miles(E), or 58.4miles(S)

angle to O.S. grid:

40.0061degrees

The two angles obtained; 40.0117 and 40.0061degrees are as mentioned above, in such close correlation as to be dead straight, 0.0056degrees, taking the reciprocal, 1/178th of one degree, or 1/1070th of one clock-face minute.

At Callanish, from Preston Cross, this is a discrepancy of 108 feet:

tan 0.0056 * 209.7 * 5280 = 108.22feet, at a distance of 209.7 miles(E). An average step or pace being of the order 2.5 feet, this is 43 paces from the centre of the stone circle used in this exercise. The Callanish site is large enough to accomodate this with ease. When I first did this I used a 45 meter spot height on the O.S. map, as being the highest point in the immediate vicinity which gave a distance o just over 188miles(S), and which gave the extended point of Flodagh on the previous line, the adjacent, forming a right angled triangle, and a distance of just over 188miles(E). More on this 188 measure later, the main interest here for now being the fact that the two sides are in 37:33 ratio, the ratio of miles(E) to miles(S).

The proof being that the difference in angle to the O.S. grid of Hypotenuse to Adjacent is 26.888degrees within limits of 1:2000, as given by Professor Lind as being that achievable by 'medieval' surveyors, and then he was talking of a very localized area, I do not think he intended to imply they could achieve the same accuracy at distances in excess of 200miles(E):

Preston Cross to the summit of Ben Cruachan: 66.866d
Preston Cross to the summit if Schiehallion: 40.001d

difference: 26.865d, cosine = 0.892073739; the reciprocal being 1.120983564.

37/33 = 1.121212121repeating:

a correspondence of 99.98%, or better than 1:4000.

I have spent a long time on this relationship and the use of the 37 inch ell, in Scotland, and the six ell fall, as opposed to the 36 inch yard and 5.5 yard pole in the English or Imperial system. Notably, the inch and foot are common, as is the number of falls and poles in the respective miles, namely 320.

It is the (37*6:36*5.5)ratio, or (222:198) which reduces to 37:33!

37 is an interesting prime number. All the triple numbers are multiples of 37; 111, 222, 333, 444, 555, 666, 777, 888, 999. (111 being 37*3)

A friend, Richard Heath, whose work is fascinating, see link to the right)has pointed out that there are 37 lunations in three years, or 36 months! So it may be related to the lunar cycles, this triangle giving the number of lunations on the hypotenuse, in the corresponding number of months on the adjacent. But, why at such a scale?

It was John Reid, in 1683 who insisted that in Scotland, land was measured in falls and ells, in the first book of gardening with focus on the climatic conditions of Scotland.(Chapter 8, see list of books at bottom of page, intro. by Annette Hope). I shall discuss Reid more, later.

The 37 system also shows up in my work on the geometry of Bornholm, whih is a big topic, to covered later, also!

All I intend to do here is establish this triangle, and highlight the positioning of Preston (unicorn) Cross, in relationship to two special mountains, Cruachan and Schiehallion, with the Iona of the east, Inchcolm Abbey, within the triangle, and with the Holy island of Lindisfarne on the adjacent extended, and with Callanish on the hypotenuse, with great accuracy and in this special relationship.

To finish, the hypotenuse extended south-east finds Kelso Abbey, to a fair degree of accuracy, slightly less, but well within the boundary of the Abbey.

3391.27 6740.57 Preston Cross
3727.85 6338.90 Kelso Abbey
------- -------
0336.58 0401.67

By Pythag:

52404.3metres, or 32.5625 miles(E), or 29.04 miles(S)

angle to O.S. grid:

39.9613 degrees.

The difference in angle is 0.0497, at a distance of some 32.5miles(E):

tan0.0497 * 32.5625 * 5280 = 149feet, or say, 50 yards.

The relative distances both show the 188 harmonic to within limits of 1:2000.

32.5625m(E) divided by sq.root 3 = 18.799968 (99.9998% of 18.8)

29.04226m(S)* phi(1.618034) = 46.99136412(99.9816% 47) * 4 = 187.9654565(same 99.98% of 188)(188 being 47 * 4).

There is a lot here still to ponder. I am content though for now, to have laid this down.

I still have to consider the relationships of most of these points to one another, and there are many possible correspondences already noted, but a fuller report later.

PUC triangle calculations part 4

I am not going to spend much time on the third side of the triangle, at present. Should the need arise I can always return to it.

I have in fact spent a lot of time trying to get a best fit, and looked at various measures around the 188 mile, English and Scots measure on the adjacent and hypotenuse respectively. There are just too many options, and most fit in some way or other. The line in fact runs up the spine of the Outer Hebrides, and various landmarks could be used from Mingulay through Vatersay, Barra(personal wish, Caisteal Chiosmuil, or Kishmul's Castle) in Castlebay, is in very good alignment with Roineabhal at the southern end of Harris, at 23.167 degrees to O.S. grid, which is within 0.1 degrees of required angle.

At Callanish/Calanais I used the stone circle with cairn, and mentioned the local high spot to the north west of the Callanish site. Using the gap between the two points gives a band some half-mile wide. At the Barra end this is from a calculated point just off the small island of Flodagh, includes Castlebay, and some of the other islands a bit further south, such as Mingulay/Muighlaigh.

The observant will have noticed other systems and lines drawn on the graphic. There is still a lot to cover and it is to some of these issues I shall turn to next.

Final comments for now!

It is enough for now to have shown this triangle and that Preston Cross is the very accurate apex, and that PC is also a pointer for Eagles Nest, through Borthwick Church, though I did not show the calculations for that system. I shall get back to that some time. The calculations though show the same level of accuracy!

A Google Map of the system:

View Larger Map

I have added temporarily another line. From Lindisfarne to Duart Castle, on Mull, including points such as Cramond Island, Tulliallan Castle, Stirling, Port Of Menteith, and Ben Vorlich.

I intend to try and cut down the number of Google Maps, as they are taking a while to load.

Happy New Year, to all!

2008-01-04T07:48:00.001Z

Belated, but it's still that season, so:

A guid New Year tae ane an aa!

Lots of ground still to cover this year, the calculations to show, and many more geometric systems to describe, and photos to add!

Newgrange: winter solstice, 2007

2007-12-24T03:43:00.001Z

A video of the winter solstice sunrise at Newgrange, Boyne Valley, Ireland.

Alistair Moffat - Arthur & The Lost Kingdoms

2007-11-23T15:01:00.001Z

I had the pleasure of reading this book a few years back, borrowed from a friend. At the time I was living in Selkirk, and finding that the geometry I was working on not only stretched into the Borders, but specifically on Kelso and Roxburghe Castle, identified by Moffat as being Arthur's main base.

Arthur & The Lost Kingdoms

When I get round to doing some more geometry, this will prove relevant!

Castlehill, Edinburgh

2007-11-19T20:37:00.001Z

It's not often that the street is empty of vehicles and people. Camera Obscura on left, Witchery and Whisky Heritage Centre on the right. The brooding spire in the background is of the Tollbooth Church, now The Hub, and the highest point in Edinburgh!

Just as an excercise in posting photos direct from Picasa! A bit confusing, as it tries to do it through Internet Explorer, and an error message comes up. Click all that away and it works, but a bit clumsy!

Bruce Cathie; a Phi correlation

2007-11-19T13:30:00.001Z

Bruce Cathie, an ex-airline pilot from New Zealand, started his grid research whilst plotting sitings of UFO's back in the fifties.

A link to his site is provided in the list to the right.

Going through his site recently, I came across his work on the magnetic fields of the Earth.

I hadn't noticed a Phi correlation previously, but did this time:

According to Cathie there are two magnetic fields which combine, or counter-act the other.

The two fields are given he gives the figures for combined field strength and their diffeence.

Field A 1850.900532 lines of force per square centimetre, or as he prefers, 12245.6998per square geographic inh.

Field B 1257.139035 per square cm, or 8317.32698 per square geo-inch.

Combined, that is (A+B) = 20574.234 per square geo-inch.
Difference, that is (A-B) = 3928.371 per square geo-inch.

(A+B)/(A-B) = 5.237344945.

which; divided by 2 = 2.618672493, which is close to Phi-squared.

The square root is 1.618231279, of which Phi (1.618034) is 99.9878%.

One in ten thousand is a very good correlation! At this point I do not know what this could signify, just noting in the passing!

Afternoon excursion to Dunsappie and Duddingston

2007-10-19T09:53:00.002+01:00

Thursday afternoon I went on an excursion with a group of six Americans, including Laura Dunham, whom I had met two years earlier. They wanted to visit some interesting spots that I might know. After lunch I suggested a drive round Arthurs Seat, stopping at Dunsappie which is a place I had spent a lot of time at when I first started investigating the landscape. I felt drawn to it many times, photographing a midsummer sunrise from there back in 1994. Laura and her group felt a strong earth energy, which is not surprising as Dunsappie is a volcanic vent. The views are impressive, to the north, east and south. A lot more to be said about Dunsappie, and this is a good spur.
The weather was sunny and bright, with a slight chill in the Mid-October breeze.

On the way from Waverley station to Holyrood.

Arthurs Seat from Dunsappie.

A rock feature on Dunsappie that has intrigued for many years! Laura said a prayer here which I felt appropriate.

I then suggested driving down and round to Duddingston, which lies directly below Dunsappie, and is an interesting place, the church, loch, and village being very picturesque. Sometimes I wonder what is going on! The road to Duddingston at the Pollock Halls entrance was just being closed by workmen, so it was down round past where we started and all the way round in a clockwise direction to Duddingston. Only to find that the church gate was locked. A local lady advised us that we could never-the-less gain entry to Dr O'Neil's garden through the Manse entrance. Everyone loved the garden, and the view of the loch. We sat down by the waterside for a while, chatting and just taking in the view and appreciating the stillness and the quiet.

A couple of photos in Dr O'Neil's garden at Duddingston.

Time was becoming an issue as they wanted to be back at their Roslin hotel before dark. Cal, the driver didn't want to be navigating in the dark, which is understandable in a strange place. My original plan of heading down the coast didn't happen, but it was a nice afternoon anyway.

We parted in the High Street as they were off to St Giles cathedral and I down Cockburn Street for my train home.

Venus distance 0.618034 A.U.

2007-10-19T07:31:00.001+01:00

Keeping an eye on Venus, and Mars, in the morning sky at present, I checked Stellarium to find out when Venus, and Mars, was at its closest. It seems to have just passed this point, but on Wednesday it was approximately 0.609 AU (Astronomical Units. 1AU being the distance from Earth to the Sun.) At 20.03 GMT, 21.03 BST on Thursday, that is last night, the distance had increased to 0.618(034) AU, the exact phi number. This distance would also have been true a couple of days previous, which I missed. It is perhaps more coincidence than of any significance, but as Venus is a Phi object in relation to the Earth, forming a pentagon every eight years, I note it anyway.

This set planetary patterns is from Bronowskis's The Ascent Of Man, page 190. The caption is:

A sense of the heavens moving round their hub and the hub was the round earth. The diagram shows the paths traced out by the planets as seen from the Earth. The Ptolemaic theory tried to explain these. The photograph shows the movements of Mercury, Venus, Mars, Jupiter and Saturn, (right to left) recorded by long exposure in the Munich Planetarium.

Venus and Mars enlarged.

Emphasizing the importance of astronomy to navigation making the point that the 'New' World did not use the stars for navigation purposes, whereas the 'Old' World did, attributing the seafarers of the Meditteranean in the Greek era with combining adventure with logic, 'the empirical with the rational - into a single mode of inquiry'. He makes the point that although Astronomy is 'not the apex of science or of invention. But it is a test of the cast of temperament and mind that underlies a culture.'

Whether the geometry in the landscape of Britain and the Baltic can ultimately be attributed to Meditteranean seafarers is a debate I don't consider vital for now!

Mars is increasing in luminosity as the Earth swings round towards its nearest point, Mars being in its apparent retrograde loop.

One observation I was not aware of till noticing in Stellarium that a good pointer to north, other than the two stars in Ursa Major, is a line through the gap between Rigel and Bellatrix in Orion through Capella in Auriga. At the oblique angle through the gap in the two Orion stars, it is a more accurate indicator than that of the two UM stars. Once seen Orion is easily identified, and Capella is bright. And if the point at which Orion is at its zenith, nightly in the winter sky at least, a very accurate North south line can be determined.

Solar Eclipses - N.A.S.A.

2007-10-11T05:36:00.001+01:00

Watching the Moon pass Venus, Saturn and Regulus, and realising Regulus sits on the ecliptic, it seemed possible that there might be a solar eclipse about to happen. I checked in Stellarium, and it seems that this time round, close but no coconut. In Stellarium, the Moon passes just below the Sun, later today(11th Oct 2007), and becomes a new moon.

I decided to check to see what astronomers made of it. This site by N.A.S.A. predicts the next total solar eclipse to be August 2008.

This site has tables giving eclipses, both solar and lunar, from as far back as 2000BC, to 3000AD:

http://sunearth.gsfc.nasa.gov/eclipse/solar.html

A couple of handy astronomy sites

2007-10-09T04:25:00.001+01:00

A couple of sites I've found which are both good but both limited, but together allow a good grasp of the sky and its objects, and Stellarium shows the sky as seen. Mine is set to a Paris viewpoint, am still playing and haven't adjusted for Edinburgh. Celestia is not Earth-based. Space travel is possible!

The First
Stellarium

The second:
Celestia:

some images from Celestia:
1.

2.

3.

4.

5.

Druid School - Tara na Ri

2007-10-09T03:33:00.001+01:00

interesting site, become a Druid, Save Tara: Tara na Ri

Moon and Venus weekend 5/6Oct 2007

2007-10-09T03:02:00.002+01:00

The Moon rising over East Lothian, across the water, photo taken at Seafield:

Two photos of the Moon and Venus, taken from Canonmills Service Station, around 5.30 GMT, 6.30 BST:

1.

2.

two again, some twenty minutes later:

1.

2.

Astrology/Astronomy plug-ins

2007-10-09T01:30:00.001+01:00

From this site: Widgets Astrology World

Moon phase:

Moon position:

Planetary interaspects, whatever they may be:

These should update regularly!

Moon and Venus

2007-10-05T09:19:00.002+01:00

This shows Venus and the Moon in the eastern sky on the morning of October 4th, approximately 5.30am GMT, 6.30am BST. Saturn is to the left of Venus, both straddling Regulus in Leo, neither recorded on this image. Mars is also not shown, but is between the Gemini twins, and Sirius is also rising, again not seen in this photo. Procyon, Canis Minor, is the other star seen forming a near right angle with the Moon and Venus.

Around 5.55 am GMT, dawns light increasing.

These photos don't do the sky justice. The Moon is now very near Venus and Regulus. A thought here, is that Regulus is on the ecliptic, and so the Moon's position can be judged accurately from its relation to Regulus, as it passes! The Moon varies by some 5+ degrees either side of the Sun's path! Something else to watch for over the coming winter months. On checking my Planisphere, I note Virgo is also on the ecliptic. Sky-watching is a bit of a hobby when I'm working nights.

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

2007-09-18T06:32:00.004+01:00

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!

Back to some geometry

2007-09-18T06:08:00.001+01:00

After a three week break, unplanned, but due to getting into something of a reading frenzy, or re-reading I should say, with a lot of calculator work, I need to get back to what I was intending to do. I was sitting at the computer waiting for something to happen one slow system day, and I just thought to look at Robert Temple's The Sirius Mystery again, for the umpteenth time. This led to Tompkin's The Secrets Of The Great Pyramid, especially the Livio Stechini section at the back, Haagensen and Lincoln's Bornholm book, The Templar's Secret Island, Thom's Megalithic Lunar Observatories, and lastly, but in way least, Richard Heath's The Matrix of Creation, and a few others not so relevant for now.

The sky, too, is fascinating at present. Jupiter west of south after dark, but the morning sky is stunning. Mars is near the Gemini Twins, with Orion showing after its summer lost in the sun's light. Sirus has again appeared, and Venus is stunning as a Morning Star. 4.50am British Summer Time, both Sirius and Venus have risen. This is my usual time for going home, and crossing the Forth Bridge, the view to the east is spectacular, Venus especially. No decent photos though!

Lots to report later, after I get a load of geometry done.

Football/Soccer has been good. Scotland took 6 points recently in two European Championship qualifiers. Lithuania 3-0 was good, but going to Paris and holding out for a 0-1 win was fantastic. McFaddens goal in Paris, outdoen his Hampden strike, and in my opinion is better than Gemmill's in 1978 in Argentina. Oh what a night!

Then on Saturday Hearts beat Rangers 4-2, to cap a great week's footie.

Full Moon Agust 28, 2007, Edinburgh

2007-08-31T14:57:00.001+01:00

A special pentagonal figure, after David Woods in GENESET - consider this Part One

2007-08-24T05:47:00.004+01:00

This is the penta-shape discovered by David Woods in the Rennes Le Chateau area, with a controlling circle of 15 divisions, of 24 degrees each, or 4 clock-face-minutes(cfms). I only have GENESET of his works, and this figure is presented there but with subtle alterations which do not concern us here. This is a symmetrical firgure with all angles equal to 36 degrees.
This little session is vital for the next stage, describing it in the landscape of Lothian and its implications for the development of the geometry in total. It was described first by W.S.Buehler, and I did some follow up work on it with interesting developments. A special point of intersection was found which allowed a tightening up of the original pent system as it was found that it and this interlinked.

The hexagon in the circle.

The penta and the hexagon, with common horizontal chord.

The perfect pentagon is found by extending the short chord, and drawing a horizontal at 42degrees, or 7 minutes on a clock-face. I believe this to be correct but shouldn't get upset if it was slightly off. My geometry ain't fool-proof, and I am the living proof!

The centre of the pentagon is found by drawing in of axes.

An interesting construct on the pentagon gives a golden ratio rhombus, using a half penta side as unit. The golden ratio rhombus is a figure I first heard about from the postings of W.S.Buehler, who I have mentioned previously, and shall be covering common geometric topics.
It has axes of phi(FC&CG), and phi-squared(HC&CI), with the half penta-side as unit, equal to BC&CO.
This post explains the geometry that is based on Bill's centering this figure on Borthwick church. To follow.

Next, I will describe this system as it is in the landscape of Lothian and the Borders. It gets very complex, and this and the original penta system need to be understood seperately to keep track!

strange lights - msytery solved, I guess!!

2007-08-24T05:22:00.001+01:00

On the probability that the lights where a 'ghost' lense reflection I went back and took another set of five, from the same positions, with the same camera.

The same lights appeared in some of them to convince me that was the explanation. Lower in the photograph, due to less light more camera shake.(The flash function is 'lost' on my digi-camera). Although I took this around the same time of night, the light has gone from the north at midnight. The nights are fair drawing in, are they no!? Sin be christmas!

Thanks to 'anonymous' for pointing it out!

why Phi-latitude!?

2007-08-24T02:32:00.001+01:00

Geoff Simmons asked the question. A fuller answer is given here.

I've been a bit distracted for the past couple of weeks, re-reading Robert Temples' The Sirius Mystery for the first time in a few years, especially the Oracle Centres octaves, with their omphalos stones, and carrier pigeons/swallows. This led me to ploughing my way through Peter Tompkins' The Great Pyramid, and even more so through Livio Stecchini's material at the end on ancient measure. I came up with some interesting stuff, related to the general topic of geodetics and ancient Man's knowledge and abilities. Fascinating but time consuming.
One tantalising snippet is that Thebes/Karnak is at latitude 27.5degrees north. Hadrian's Wall is at 55degrees north, twice the number. The Antonine Wall straddles the 56 degree latitude.

The area between is the main focus of my investigations.

Phi, the Golden Section, is well known to those who dabble in pentagonal geometry. It is inherent in the perfect pentagon, being the ratio of side to chord. It is considered the perfect proportion, in words, the ratio whereby a line is divided such that the short is to the long as the long is to the whole. Numerically, it is 1.618(034). The reciprocal is 0.618(034). The square is 2.618(034).

The square, 2.618(034) times 6/5 is within 99.9985% of pi, 3.1416408, against calculator pi, 3.141592654. Using the short version, 2.618, 6/5ths gives 3.1416, a version of pi used by engineers as it is a neat number, even closer at 99.999766%.

It is astonishingly easy to construct phi, phi-squared, and pi, as a straight line, without having to know the numbers at all.

Draw a two by one rectangle, draw in a diagonal, extend the diagonal by one unit, (the short rectangle side is one unit), by use of compasses, half this length is phi in relation to initial unit. (sq.rt 5 plus one, divide by 2). Add one unit to this constructed phi, gives phi squared. (phi + 1 = phi-squared). Divide the phi-squared length into five parts, extend the line by one of these parts, gives pi.

So, a very practical proportion. Very Pythagorean too, in that only straight edge, compasses, and pencil, (and a sheet of paper, or even sand) are necessary.

So when I went to stay in Selkirk, in 1999, I soon became aware that I was living very near to the phi-latitude. In that, 90/Phi is 55.62306degrees. This latitude is straddled by the River Tweed. It runs east to west, from Ross on the Northumberland coast, just to the south of Lindisfarne, very close by Smailholm, the Eildon, Innerleithen/Walkerburn, Cademuir, Stobo, Broughton, Biggar, Thankerton, Lesmahagow, Ardeer on the west coast of the mainland, Goat Fell on Arran, between Carradale and Grogport on the Kintyre peninsula, and between Port Ellen and Risabus on Islay. I did this in Google Earth.

Now this assumes a perfect spheroid for the northern hemisphere. I have been aware that this latitude would have to be corrected, and Livio Stecchini provides a table of the lengths of all latitudes in his section in Tompkins. Pages 329 and 330.

So today I calculated the total of these 90 degrees, and the phi of that total came out at 55.75799 degrees. Again in Google Earth, I plotted this across the breadth of Scotland. From east to west, The very mouth of the Tweed, actually just on land at Tweedmouth, Fishwick, Sinclair's Hill, Westruther, Corsehope Rings Fort, near Borthwick Hall near Heriot, Northshields Ring Fort, Lamancha and West Linton, Auchengray, East Kilbride, and Fairlie on the coast. Millport, Kilchattan Bay, Claonaig on Kintyre, and Bowmore on Islay.

So in a 10 mile band the two versions of phi are contained. To check Google Earth I measured from the equator to the north pole, with the intention of taking the phi value and comparing with what I had just done. A bit disconcerting to find that the distance was only 9900740 metres. Compared to 10,001,987 metres for the Heimert figures given in Stecchini, and other sources where the length is slightly more than the ideal distance of 10,000,000 metres assumed for the French metre. The calculated phi distance is equivalent in Google Earth to 55.7547degrees, agreeing with the figure derived from Stecchini. The discrepancy is some 365.7 metres or 1200 feet.

On a planetary scale I see this as meaningless, and am happy enough to consider the phi-latitude as that lying between 55 and 56 degrees, that is between the two Roman Walls. As stated above, the core of the geometry I have been investigating is included there-in.

And that was the domain name I secured, so used it here as a title on advice from someone who knows more than I do about the internet.

So, that hopefully covers why the name is used!

Song For Tara

2007-07-31T08:12:00.001+01:00

An issue of great importance is the construction of a motorway through the gap between Tara and Skreen in the Boyne Valley, County Meath, Ireland.

A landscape of such importance should not be tampered with lightly, never mind a gigantic scar, an open sore, with noise, pollution, and a flood-lit roundabout destroying an area which for untold centuries has been sacred to Ireland and its people.

There is an on-line petition which I urge everyone to sign.

This is quoted from a speech given by Dr Brian Lacey, Chief Executive Officer for the Discovery Programme researching the Archaeology and literature of Ireland:

(quote)
Tara

Since our inception we have had a Tara Project, investigating both the archaeological remains as well as the literary and historical sources. Three of our books and many of our research reports have dealt specifically with Tara, and a major study dealing with the kingship of Tara in the period AD 400 to 800 will be published later this year. I think we can claim that we have done more research on Tara than everyone else put together. Our work on Tara has included all forms of survey, excavation, and study of the ancient and modern historical sources for the site and its hinterland. One example of the results of this work is that, before we started, only about thirty individual monuments were known on the Hill and there was, effectively, no understanding of their chronological relationship. The number of known sites on the Hill now stands at about one hundred and twenty and we have an overall model of their development through time, which can be tested by excavation in the years to come. In addition, there has been a growing appreciation that the Hill of Tara itself is just the dominant element of a wider surrounding landscape of related ritual and settlement sites, which seems to extend from Ringlestown Rath to the west, along the Riverstown linear earthwork to Rathmiles to the north, and onwards to Rath Lugh and Skreen to the east.

The M3

The Discovery Programme is a research institution and has no function in planning or development matters; it is certainly not a campaigning body. Nevertheless, given our major involvement with Tara, we felt that it was appropriate for us to make our views known at the motorway planning stage. The Discovery Programme involves individuals who, in their separate capacities, have taken differing positions and roles in relation to the M3 debate but, as a corporate body, we said, both in written objections and at the oral hearing, that we were against the route subsequently approved. However, once the decision on that matter had been made with due process, we believed that we had no further role and that it would be beyond our powers to engage in the controversy that subsequently emerged. Although both sides in that debate have frequently referred to us, we have scrupulously avoided any further public comment on the matter.

We would, however, wish to reiterate the following points:

1. It would be hard to overstate the national and international importance of Tara.

2. The Hill of Tara is only one element of a wider related archaeological landscape, the additional richness of which is continually being further revealed.

3. The Discovery Programme, of course, welcomes the development of our national infrastructure but is occasionally disappointed when, even in good faith, a major cultural asset is depleted by such development.

4. We would assert that, in the event of any impingement on such an extremely important asset, the very least that can be expected is that the highest possible standard of archaeological investigation and mitigation be deployed.

Dr Brian Lacey

Chief Executive Officer

The Discovery Programme
(end quote)

A song has been recorded in support of the campaign against the road going through Tara-Skreen: by Teamhair!

A map of the Tara area with the planned motorway drawn in.

five zoomed images of Edinburgh lights

2007-07-27T08:06:00.001+01:00

These five images are cropped from the originals of previous post. These are the images which make up the video on YouTube, two posts back.

They can be examined in greater detail by clicking on them individually!

The timespan was of the order of two/three minutes.

Edinburgh lights originals

2007-07-27T07:39:00.001+01:00

This is the series of five photos I took mentioned in previous post. No lights in the first but in these originals they can just be seen in the fourth best! Click on images for an enlarged version!

Next post will have the cropped enlarged images!

Strange lights over Fettes College, Edinburgh, summer 2007

2007-07-27T06:36:00.001+01:00

One night just after midsummer, five or six days after the solstice, I decided to take some photos of the residual light in the northern sky at Midnight GMT, so 1 am BST. At the latitude of Edinburgh for a few weeks either side of solstice the sky does not get completely dark, and I have wanted to get a photo record of this for a few years now.

I figured the view from Learmonth Terrace north over Fettes College would be good.

I used my basic digital camera, hand-held, no flash, and mediocre resolution, but I wanted the sky-light and wasn't too bothered about a bit of camera shake!

I took five, two landscape and three portrait style. When downloaded onto computer I became aware of lights in the sky on some of them, all bar the first. Strange, shouldn't be planes at that time of night, certainly not in formation. If military, jet planes, or helicopters, at least four, would have made a bit of a din. There was no noise at any time!

Also I was unaware of any lights in the sky, at the time of taking the photos!

I considered birds, swans or gulls perhaps, as these lights were white, but too brilliant to be birds I reasoned, and they should be in silhouette against the light to the north.

I considered particles of whatever on the lens, but as stated above the camera was rotated 90 degrees between landscape and portrait, any surface particles should also have been rotated.

They are not stars, they move and are too bright, and appear against or below the cloud in the second and third photos.

A friend made a video of them and posted them on YouTube, the link being here!

Then an e-mail arrived with a link to the Daily Mail report of a formation of lights over Stoke-On-Trent recently!

Seems similar to what I had found in my photos!

The five photos shall be posted, (next post above) and a series of five zoomed images of the lights above Fettes College. The video above at least shows the movement of the formation of three/four lights, arcing over the College and dropping down to the west.

The Arthurs' Seat Roseline and Roslin/Rosslyn Chapel and Glen

2007-06-11T15:24:00.022+01:00

There is a major alignment which all researchers find with ease, in the Lothian area. It runs a few degrees from west of north and includes the summit of Arthurs' Seat Roslin Chapel, St. Mary's Chapel at Mount Lothian, and the summit of Dundreich, a hill at the western end of the Moorfoot Ridge/escarpment. It extends both to the north and south. The area between Arthurs' Seat and Dundreich is the area I lived in during my childhood and a good part of my youth and adult life. It is the area which contains the Esk River system, and a lot of the geometry already described. When I began this investigation I was frustrated that at Roslin Chapel, Arthurs' Seat could not be seen. It was in 1997 when the canopy was installed over the Chapel, that allowed me to confirm by eyesight and photos that the map did not lie, as both Arthurs' Seat and Dundreich are to be seen in dead straight lines looking along the handrail of the gantry, north and south, at the east end of the Chapel.

This is the view along the handrail to Arthurs'Seat, looking north, seen faintly in this photo.

Dundreich to the south, looking across Roslin Castle, hidden in the trees below. (I'm having a bit of difficulty getting the images neat on the page, but that's ok for now!)

St.Mary's Chapel is a ruin in this clump of trees, between Roslin and Dundreich, and a major geometric point. A great deal of interest has focussed on this site over the years I have been active.

This line extends both north and south and for now I shall conclude with a graphic from an American friend, William S Buehler, whose work has taken mine to greater lengths and depths over the past seven years than I ever contemplated possible. That his and my geometry kind of fused together as it has done continues to astonish me. That is a long story, I still have difficulty telling. A lot more to do on that whole issue. This graphic shows the system Bill developed based on the Roseline, or Tavhara line in his terminology:

Roslin/Rosslyn Chapel

The Chapel is situated on the flat ground at the top of the valley slope, above the castle. I am concerned here with its setting in the landscape, and this is again a very short introduction and this shall be developed as time goes on. The photos below are all pre. 1997, when the canopy was installed in an effort to dry out the stone of the chapel. These are old photos and not very good quality and are scanned from worn prints.

This is a view from the opposite side of the glen, from the south-east, on the Rosewell road, on a fine summers day, through a gap in the trees.

This is a view of the east side showing the window with the engrailled cross of the Sinclair's, and some of the pyramidian pinnacles.

In May the bluebells down the glen cover large parts either side of the path. The east wall of the chapel can be seen through the trees, quite faint. Not a very good photo, but I am fond of the view from this spot.

This is from a print given to me by an American friend, Ward Ginn. It would appear that there is no glass in the windows at the time of drawing:

Roslin Glen part one

There is a rock on the path down the glen, known as 'lovers leap' which is covered in graffiti, and is a convenient spot to pause, and enjoy the view upstream towards the castle.

some friends resting and gazing upstream.

This little head is reckoned by some to be ancient, and there are marks to the right of it reckoned to Ogham script. The head shown previously is some hundred metres down stream, and may be some indication or way-marker for it. It has lately been identified as a power point of some potency by an American friend who has been working on earth-grids for over thirty years now, William S. Buehler, and I shall be mentioning him often when the story develops.

This black and white was taken in December 1994, when attempting to gain an image of the face described previously. It matched my mood then as I was starting out on this investigation, dark, sombre, lifeless. It was a life-changing period. The ruined castle can be seen at the top.

Same approximate view from the rock upstream, a few years later in spring, and life and colour returning.

Roslin Glen - spirals and rings

Mark Oxbrow, co-author of a recent well received book, Rosslyn & the Grail, showed me this spot a few years back, circa 1999. There are many concentric spirals and ring features covering the walls of the shallow cave/recess. See images below:

Roslin Glen part three - Wallaces Cave

On the opposite bank from the chapel, there is a cave, called
Wallace's Cave, obviously man made, with an 'L' shaped door as seen in this photo. I have been inside only once and from memory it has three round chambers. Unfortunately I didn't have my camera with me that day, and I have not managed to get back to it. At that time there was a fallen beech tree which allowed access to the other bank. It could still be accessed via Gorton House, but I don't know what the owners or occupants think of folks just tramping through. The onus would be on those wishing to visit to check first.

Roslin Glen part four - Castle

A copy of a print given to me by an American friend, Ward Ginn. What the castle is thought to have looked like in its heyday.

Down from the Chapel is Roslin Castle. In a mostly ruinous state after the bombardment by General Monck and his troops, in the mid 17th century. A road leads down to the castle, which ends in a right angled bend at the bridge into the castle. This is formed by an arch across a gap, which seems to have been worked somewhat from the bedrock, as can be seen in these views, with sharp clear angles, especially on the castle side of the arch.

Roslin Glen part five - Hawthornden

Hawthornden Castle is a writers retreat, one time home of Henry Drummond. I seem to have mis-layed my photos of the castle itself so here are some from The Gazetteer of Scotland
These two photos were taken when I took a walk from further downstream, back in 1994, one is of a queer set of steps, the only thing on the other side is a fifty foot(+/-) drop to the river. The other is of 'Hanging Rock' marked on the OS map, 1:25,000.

Roslin Glen part six - The Green Man!?

In 1994 after reading The Temple And The Lodge, I decided to look for the enigmatic face carved in a 'cave' gazing out on passers-by in Roslin Glen, mentioned by the authors Baigent and Leigh.

This was just prior to starting the search for geometry in the Lothian landscape, after finding The Holy Place by Henry Lincoln in Waterstones in Princes Street in Edinburgh one day I went out for a pair of trousers, and came home with 3 books instead. (The other two were Noam Chomsky's 'The 500 Year Conquest Continues', and a book called 'The History Of The Future', concerning R. Sheldrakes theories of morphological resonance, but don't hold me to that, both have gone west a while back.)

Anyway, a group of us cycled to Roslin and spent a few hours down the glen. I ended up making my way down the river bank, slowly, whilst the others kept to the path. I got a shout to come look as they had found it a bit further down.

It was on the other side of the river, some 100 yards downstream from the rock known as 'lovers leap', a flat rock some 50 feet directly above a bend in the river, with names and initials carved over the whole surface. The ruined castle can be seen directly upstream, and the first photos I took were in black and white, on my next few visits whilst attempting to get an image of the 'face'. This took a couple of tries , as I was using too slow a film and the camera was mal-functioning a bit, and I was out of practice.

I eventually got a colour image the one included here.

The river is not always crossable, and care needs to be taken at all times, the bedrock is slippery even at low water when the stream is contained in a channel some 4/5 feet in width which has to be jumped. A small leap of faith for most, but any slip could be disastrous. Extreme caution is advised, at all times.

Once across it is possible to climb up to the feature, which has a pool where a stream splashes onto the beard of the 'face' before settling into the pool at the base. The moss/algae on the face changes colour and shape over the seasons and I came to consider this as The Green Man, larger and more 'alive' than the many representations within the chapel.

To the right is a dry spot, sandstone overhung by rock, with a ledge which later I was to notice comprised a reclining figure with long hair and a beard covered in drapes, perhaps intended to be the figure of the person depicted in the cave.

This second feature was only perceived when on another visit with some other friends, a few years later. I checked back on my photos and it was there all the time. It was a perception thing, I just didn't see it previously.

Two of the reclining figure:

Roslin Glen part seven - end of tour for now!

Just to complete this wee tour of Roslin Glen, two photos I like, one of the bluebells in May and one from the Castle Bridge in autumn:

From the castle bridge, looking downstream, that is north-east, early autumn sunshine.

Mavisbank Earthwork circle centre

2007-06-11T11:31:00.001+01:00

This earthmound is just behind Mavisbank House, a Palladian villa, destroyed by fire back in the 1970's. It was built by Sir John Clerk of Penicuik. The architect was William Adam, father of Robert, who is perhaps better known.

The earthwork was found to lie on the side of the inner pentagon, which has Roslin Chapel in the south-east corner, some 1.5 miles south of Mavisbank, upstream on the steep slope of the River North Esk. Restore Mavisbank link:

The history of the earthmound is unknown, to me, at present, but I recall a mention of some discussion between Clerk and Adam concerning some ancient feature behind the house, and this circular mound is directly behind the house. Clerk was an 'Antiquarian', and there is an extant letter of his addressed to the London Society of Antiquarians concerning a Roman Temple which was destroyed to make way for the building of the Carron Ironworks near Falkirk.

A photo of mine of the derelict house from the west:

Geometrically it is the Earthmound which is of particular interest at this time. It was found that a radius very close to the radius of churches at Rennes Le chateau described by Henry Lincoln. In Scottish measure it was found to be 5000 ells, one Scottish ell being 37 inches. A section on the Scottish Measure system shall be included later.

This drawing was done by hand, pencil on paper, but is inverted here cause I like it like that. I shall be describing this all more fully later, but already it can be seen how comnplex it all quickly becomes. There are a few specific points which allow the systems to be inferred. The line which defines the orientation is from Allermuir Hill in the Pentland Hills to the west, to the Camp Ridge, above Mayfield to the east. Newtongrange Church, defines the radius of 5000 ells. Henry Lincoln defines the radius he found as 2miles 1618 yards, which is equivalent to 4999.135 ells, a correlation of 99.983%. There is a lot to discuss about different measure systems, which gets very involved, and an attempt will be made to cover this topic at a later date. Just for starters the work of Professor A Thom, and more recent works by Knight, Lomas, and Butler. See the list of books for further info, for now.

What I want to do is to take this one stage further and show the rectilinear grid which results from the two systems already mentioned. The Pentagonal system centred on Galachlaw, and the hexagonal centred on the Mavisbank Earthwork.

This drawing was constructed in Paint, the best I had on my old clapped out computer when I was doing the calculations. It should be pointed out that the accuracy of the drawing is not as good as the calculations. I shall describe the method I developed using O.S. grid references, and simple trigonometry. The references were read accurately to ten metres, and then refined to one metre by calculation from print-outs of the relevant O.S. grid squares.

There are a few other lines and extensions on the drawing, that shall be discussed later. It all gets a lot more complex, but there are are other points to make prior to showing this.

Introduction

2007-05-11T09:03:00.027+01:00

A life-long fascination with the landscape of Lothian and Edinburgh, and a long time ere!interest in photography, contributed to an investigation of the possible geometry to be found there, after reading Henry Lincoln's; The Holy Place. This little book described the geometry he had found in the landscape of Southern France, centred on the now famous/infamous village of Rennes Le Chateau. Having previously read the two books he co-authored with Michael Baigent and Richard Leigh; The Holy Blood And The Holy Grail and The Messianic Legacy. Just prior to reading THP I also read The Temple And The Lodge by the latter two authors, a continuation of their previous works, and focussed on Scotland and its connections to the main story of the previous two.
I was thus suitably primed to respond to THP by having a 'look-see' at the landscape of Lothian and Edinburgh for the possible presence of something similar.

Geometric patterns eventually appeared from the myriad of single line alignments of natural landscape features and human artefacts, churches, castles, standing stones, stone circles and so on.

A regular pentagon was eventually found, stunning in its incorporation of many interesting points, and including Arthurs Seat summit, Roslin Chapel, Caerketton Hill cairn, an earthworks at Braidwood settlement on an extension of one of the pentagon's sides, the confluence of the two rivers Esk in Dalkeith Estate, the centre Galachlaw cairn mound, and Currie Kirk. The latter three points formed an axis, with the Braidwood line perpendicular to it. From this the pentagon was found. This is an incomplete list of points of interest and more shall be listed as this site progresses.

The graphic included here was hand drawn in 2006, but is not labelled completely. It is a negative image with high contrast for effect, and is in reality black pencil on white paper. I shall describe the points better as I progress with this project.

Photos of penta-points

Arthurs Seat

Arthurs Seat dominates the city of Edinburgh. It contains a whole set of geometry within the boundary of Holyrood Park. It is on a chord of the pentagonal system and has a major long distance line running north-south. Both running through the summit, to the left in this summer morning silhouette.

A section will be devoted to Arthurs Seat, in all its moods and as seen from various places.

Galahlaw - penta centre

Galachlaw cairn is the centre of the pentagonal system. In a mixed woodland plantation on a high point between Buckstone and what used to be the Princess Margaret Rose hospital, and Mount Hooly Loan.

There isn't much to see really, just bracken and a bit of dug ground on the top. Whether just kids or someone looking for something I dont know.

Black Hill penta-corner

Nothing is marked on the map for the penta-corner which lies on the south-east flank of the Black Hill in the Pentlands. On an exploratory excursion there mounds and circles, ditches and stones were indication of activity sometime in the past.

Leith penta-corner

this archaeological dig next to Lamb's House in Leith fascinated me back in 1994(ish) when first setting out on the trail of exploration. Oyster shells by the ton were found in the foundations of these medieval buildings. Activity traced back 5000 years. This is not the exact fixed corner, that comes later.

Meeting of the Waters - Dalkeith

The two Esk rivers converge in Dalkeith Estate. This photo from my first visit in 1994 shows an exposed coal seam there.

Maybury penta-corner

This is an obviously built up area, but the exact corner turns out to be where the railway line crosses the old A8 at Maybury. This shot is from the road bridge, looking towards Corstorphine Hill and Clermiston Tower, which marks the line to the Leith corner.

Shewington penta-corner

It may not seem much but the farmhouse on the left sits at the highest point of a ridge with an old drove road passing by. It is the south east corner with Roslin Chapel being the inner corner on line to the centre Galachlaw. The exact corner is in the trees to the left of the house.

Clermiston Tower on Maybury Leith line

Dedicated to Sir Walter Scott, a superb panorama is seen from the top. Open Sunday afternoons I believe, still, the viewing platform is above tree height. A section shall be devoted to Clermiston Hill.

Rosslyn/Roslin Chapel inner penta-corner

The east window of Roslin Chapel, in the morning sunshine.

At first Roslin did not seem to be a major point in the system, but when the inner nested pentagon was found, Roslin was found to be at the south-east corner of the inner penta.

The Roseline, or Tavhara line runs direcly through this eastern end, north-south, and can be shown in photographs, using the handrail of the gantry of the canopy at present erected over the Chapel to aid in the drying out process. Arthurs' Seat summit to the north and Dundreich to the south in the Moorfoots are seen to be in direct line. This merely confirms what was found to be so on the map.

Inchcolm island and Abbey penta extended plus

Inchcolm being an island in the Firth of Forth, it is on the main axis of the penta system but an extended penta corner falls just short. A compensatory factor was found involving Crichton Castle and Church. More on later.

Mavisbank earthmound - on inner penta and centre of 5000ell circle

This circular earthmound and a snaking path to it, is at the back of Mavisbank House, built by Sir John Clerk of Penicuik, who features in the overall story. Mavisbank House was a finalist in the renovation money competition on television a few years ago.
The hexagonal system centred here gave the first indication of a possible link to the geometry of Henry Lincoln, around Rennes Le Chateau. It also shows the use of the Scots Measure the ell, 37 inches. 5000 ells being equivalent to the radius identified by Lincoln. Lots more to say on Mavisbank and the hex system.

That's a start at least, and amended somewhat 17/03/08
A list of web-links, is to the right, and a list of books appears at the bottom of each page.

Any positive feed-back would be appreciated. Presentation or ideas for improvement generally!

I shall now work on linking web albums through Picasa, and develop links to each page with perhaps more photos.

I shall also introduce some basic geometry and maths and units of measure found to be intrinsic to the overall systems. A demonstration of the accuracy of the geometry will be approached, which will entail a look at the geometry of Bornholm and my findings there.

There is also the hexagonal system centred on Mavisbank to describe.