Ben Lawers pentagon extensions




The north/south line from Ben Lawers to Snowdon just grazing the pentagonal system.  The purple north/south lines with Lochnagar shown is from the Ness of Brodgar on Orkney runs through the centre of the penta systemand as can be seen would almost define the Welsh/English border if extended.

 

With Ben Lawers found by extension of the pentagonal system and very near tangent due south to the western most corner of the pentagon, it was then found that by extension Snowdon was found to be on this line(second image).  On the way south, Windy Standard and St John's Town of Dalry were found also(third image)

Snowdon

the Ben Lawers-Snowdon line nearly tangential to the circle and penta corner!

the connections to Ben Lawers from the penta extended lines the connection to the western penta corner should be exact but cumulative error has perhaps been highlighted at this point.  The question of how much play can be allowed is open to debate!

the Ben Lawers perfect parallel to penta side virtually the same discrepancy as the western north/south line to Snowdon. 

Newbridge Tumulus and Abercorn Church and the inner penta chord which extends to Ben Lawers.

Penicuik House/Estate

St. Mary's grid (full) penta development.

Development of the penta system introduced in previous post.

The penta elements are coloured yellow in this set of images.

Developing the pentagonal system based on the 3by1 diagonal of the North Berwick Law orientation(in red) with St Mary's chapel as centre of the two inner circles.  The outer circle is centred on the centre of the calculated pentagon with the 3by1 diagonal from Kelso to Ericstane just north of Moffat as base side length.

The first thing of note is that the penta-chord is tangential to the inner grid circle with St.Mary's chapel at centre.  Of note also is that the northeast running radius crosses the Isle of May which is nice as I have wondered what part this island played in the geometry.

the completed penta-star.

Surprisingly the two sides of the outer pentafgon are seen to be tangential to the Bass Rock circle centred on St Mary's chapel.  The Bass Rock is not marked but is just above the 'r' in North on the crossing point of the chord on the circle circumference, but Markinch is marked on this circumference.

completion of the pentagon.

the same figure as above but with the grid system changed to green perhaps clearer.

St.Mary's grid part2 - North Berwick Law grid development

This section covers the pentagonal system using the full 3 by 1 diagonal as base, a variation to the basic system described by Bill Buehler.

The grid is not shown here, apologies, but the fundamentals are for the development of the 3by1 grid.  The base-line(3by1) runs obliquely south - north-east at the bottom of the image with the mid-point axis running NNWest through St Mary's chapel also a 3by 1 diagonal. 

somewhat simplified.  The two lines from St Mary's to the 3by1 points are themselves 2by 1 diagonals with a 90degree angle between them suggesting a square extended south, not done yet!  The other two lines are the Great Pyramid angles which meet at Hillend Fort, not marked but mentioned often in the past.The other two lines meeting west of Perth are five units long.and a natural 3,4,5, triangle is found with the horizontal one unit north of the Ericstane point on the 3by1 diagonal.  This also gives a close approximation to the pentagon to be shown later.

here I have added the equilatral triangle which gives an apex just off the Inchcolm shore.  These are the main components of WSBuehler's Basic Reshel system, with an amendment of the pentagon using the full base-line.  The original used a shorter side.

the penta centre established and the five arms drawn.

St. Mary's Chapel - North Berwick Law/Bass Rock grid Part 1

The next series of posts details and investigates further the grid I worked on starting some 13/14 years ago, round the turn of the millenium when I had moved to Selkirk from Edinburgh and not only did I become better aquainted with the countryside of the Borders but the geometry kind of 'followed' me!  Around that time I was attending a few of the symposia held by the Sauniere Society, which had as honorary president Henry Lincoln, whose geometric findings around Rennes Le Chateau as described in 'The Holy Place' had intrigued me and led to my initial interest in the lanscape of Lothian.  At one symposium at Newbattle Abbey, Henry and Erling Haagensen were presenting their work on Bornholm Island in the Baltic, and the associated book, 'The Templar's Secret Island' which I bought there and had it signed by both. I spent many months studying their geometry which was basedon the Danish Kort en Matrikelstyrelsen survey accurate to the milimetre as KenM had used the centre points of the four round churches on the Island as datum points.  I had established to my own satisfaction that the basic unit of the hexagonal grid was the modern English mile and that the main axis was (16 times the square of three miles(E)).  The square root of three is the altidude of an equilateral triangle of side 2.  One half of two is one, so an equilateral triangle can be considered as two right angled triangles with sides (1;sq.rt 3; and 2) with the sq.rt 3 side common.
I had previously found the basis of a grid in the landscape of Lothian and the Borders, centred on St Mary's Chapel, Mount Lothian which is point that was found early in my research, as others had also found and a significant alignment almost due north through Roslin Chapel and the summit of Arthurs Seat and south to a hill top in the Moorfoots, Dundreich.  Using maps I had noted that the Bass Rock was at roughly 45 degrees to this line which suggested  the diagonal of a square.  It was also noted that the line from St Mary's chapel through North Berwick Law was also roughly 45degrees to the said line.  I worked away on these two possible grid alignments, completing the square and extending in all directions from St Mary's and incorporating the natural subdivisions of (one and square root of two) squares and circles a quite convincing grid system was found.  This extended  system also brought the geometry the full distance south to include the area I was now investigating, Selkirk and the Borders.

The move to Selkirk, ostensibly to write up into book form the stuff I had already found, also coincided with my getting an internet connection and contact with William S Buehler and the introduction to his work on grid systems which also included the landscape I was looking at.  Indeed, he had the same St Mary's Chapel line but he had it extended to Seafield tower between Kirkcaldy and Kinghorn in Fife, and Dryhope tower near St Mary's Loch at the head of the Yarrow Valley just a few miles west of where I was now staying, but both these points were outwith the scope of my maps at that time.  In the next post I will describe the specific format used by WSB, the basic Reshel system which later on in this process I found using a (3by1)diagonal of the grid which was developing.

When I had done enough work on the Bornholm geometry which honed my skills with a calculator I returned to the St.Mary's Chapel/Bass Rock system and to my astonishment the distance from St Mary's Chapel to St Baldricks Chapel on the Bass Rock was the exact, to the metre, same distance as the axis on Bornholm!!!!

This excercise is an attempt to reconstruct this grid in Google Earth, employing a neat application I found where I could draw accuate circles in Google Earth:


So, first I created the circle using 'radius round a point' a very handy tool, with St Mary's Chapel as centre and radius (168square root of three)miles which coincides with St Baldred's Church on The Bass Rock.  Markinch is found to be on this circumference at 45degrees to The Bass, as its often called.I then drew in western half diagonal and the horizontal square side.



extension of the axes.

completion of the intial square.

I then began on the North Berwick Law orientation.  Now, NBL is 13/16ths of the full distance, exactly, but is extended the full distance so the circle is common.  The vertical and corresponding western half diagonal are also shown.  All in red.

The blue line is the 'roseline' or Tavhara in WSBuehler's terminology.  This line is through Rosslyn Chapel and the summit of Arthurs Seat with Seafield Tower, between Kinghorn and Kirkcaldy where the horizontal from The Bass crosses.

Right! Back to work!

A quick update.  2012 has been and gone, and so has a third of 2013!  My son kindly passed his old laptop to me in January and allowed me to indulge in longer youtube videos and stuff which I couldn't do on my old compromised computer(shockwave flash was a real pain in the backside, and AVG was too!!) and it finally gave up the ghost so I now only have the laptop.  I guess I've lost all my google earth stuff, and so will have to re-do the essentials but at least I can perhaps be a bit more methodical as I investigate the Edinburgh grid I was working on, and some other related stuff.

I've watched all the Ancient Aliens series on youtube, and listened to Coast to Coast AM radio a lot, and also watched a whole lot of stuff to do with alternative energy, zero-point, wind turbines, magnets and rocket stoves and a lot more besides.  Also found some interesting geometric links which are very interesting, but can't recall off-hand..

I find it hard to believe that four months have passed, though!

and finally a photo of yours truly:

a self-portrait taken on a walk around Salisbury Crags on my home one Sunday morning last September with Arthurs Seat in background.


best wishes all

tom

original penta-system in Google Earth

In earlier posts I covered the geometry I had found in detail with full calculations prior to having Google Earth to play with, using full Ordnance Survey coordinates which I think left some totally confused.

In this post I now want to cover the original pentagonal system I found back in 1995 and to see what connections turn up with the other systems I have discussed, the Mavisbank hexagonal, for instance and perhaps also the grid of the city of Edinburgh which I discovered lately.  Well there is quite a lot and it will take some time to cover what I have found already.

The pentagonal system I found came after months of drawing lines on maps quite a few of which ended up a right mess till I was finally convinced that what I had found was in fact real.  A final version was established when the Eagle's Nest spot was discovered linking at least three separate systems, the pentagonal, the Borthwick system and a direct link to the Preston unicorn Cross, with an accuracy somewhat beyond belief, all described previously in this blog.

I have done this present exercise without reference back to the relevant posts and this first pass throws up some of the queries I struggled with before, but I chose to work this way as some interesting stuff has come up which I want to explore further.

One advantage of using Google Earth is that true north can be established from any given point whereas the Ordnance Survey grid has only its own specific orientation and a rough guide to magnetic north.  True bearings thus difficult to establish!  I shall be investigating this aspect later, some intriguing stuff already showing up.

This first image shows the penta-system in conjunction with the hex-system previously covered.  At this stage I have drawn in a double pentagon, which allows for the slack in the system which I struggled with originally and is still possibly pertinent.  The line to the left running from bottom slightly west of north to the top, (pale blue then continues pale yellow), was in fact one of the most impressive early lines to be found.  Braidwood is a ringed earthwork just west of Penicuik, and the line includes the summits of both Scald Law and Black Hill, through Currie Kirk, and a hillock with a walled circle of trees on its top in a field at Cammo.  It was when I took a right-angle from Currie Kirk that Galachlaw was found and the confluence of the two Esk rivers at Dalkeith mentioned in my recent post(First Geometry) which defined the altitude of the original pentagon.  The Braidwood - Curriekirk - Cammo line extends both north and south and shall be discussed later.

In addition, it can be seen that the exact line from Mavisbank through the galachlaw point through the intersection of the initial circle to a 'flower of life' format intersects this Braidwood line at Cammo!

The initial Mavisbank circle in yellow can be seen to pass through the marker circles of both Galachlaw, the centre of the pentagon and Shewington, a farm house on a ridge to the south of Mavisbank.  The line from Shewington connects with Rosslyn Chapel then through Galachlaw to the highest point at the east end of the island of Inchcolm.

Newbattle Abbey is also on this circle circumference and shall be considered in the next post  which shows even more astonishing stuff than all that has been covered previously.  (As does the Leith corner in next paragraph.) More new revelations!  (TG-15/1/13.)

The chord from the Leith corner, top-most (unmarked in this image) through the exact summit of Arthurs Seat through Shewington is the orientation which hits the Eagles Nest point exactly.

click on image for full-screen version!

This second image has the secondary hex-circles stripped away and some of the points mentioned above marked.  The first point to note is that Rosslyn Chapel can be seen to lie on the line joining the mip-points of two of the pentagon sides and this line extends to/from Braidwood.  Rosslyn could be defining an inner system which almost includes the earthwork at Mavisbank.  This shall be examined later!  I have left the yellow line from Mavisbank to the Scott Monument in as The Scott Monument can be seen to be on the penta-chord from Black Hill to Leith.  I have also noticed and confirmed that The Scott Monument is at the midpoint of the upper section of the chord.  Again to be looked at later!

The penta-side from Gyle to Leith crosses Corstorphine Hill , the two lines shown straddling Clermiston Tower, dedicated to Sir Walter Scott!  Also, I have included one of the Edinburgh grid lines(orange) which extends to the Gyle/Gogar penta-corner!  Also the chord from Shewington to Gyle/Gogar includes Caerketton Hill, and the radius from Galachlaw to Black Hill includes Allermuir, both seen as green mountain symbols!

This image is a close-up of the Galachlaw, Shewington, Mavisbank, Rosslyn Chapel configuration!

Galachlaw cairn, roughly as it is impossible to see it through the trees but I can get the exact coordinates later!  The Mavisbank circle (yellow) can be seen to fall a little short, but its close enough for now! Incidentally, the wooded area is somewhat reminiscent of an elephant's head and trunk, don't ya think!?

A close-up of the chord from Leith to Shewington which includes the summit of Arthurs Seat.

(Incidentally, Google Earth's green mountain symbol for Arthurs Seat is not quite at the highest actual point as it usually is! )

A few points of interest:
Braidwood earthwork:

Currie Kirk:

The clump of trees at Cammo:

Clermiston tower dedicated to Sir Walter Scott on Corstorphine Hill:

The Gogar/Gyle penta-corner with Clermiston tower and Cammo clump indicated.  This orner is at Maybury, where the railway line cuts across the A8, where the old Redheughs Road met the A8 roughly.

The Leith corner which has led me a merry dance over the years!  The area shown here stretches from the Custom's House in the docks to Queen Charlotte Rooms near Leith Links and includes the King's Wark pub,  Lamb's House, Chapel Lane(but no chapel now, as far as I know!), Leith Police Station and the old Church in Constitution Street:

The confluence of the two Esk rivers in Dalkeith Estate Park, the forehead of the rider in the horse and rider landscape form, with Newton Old Kirk(ruined tower) the dark spot on the light coloured middle line between the bypass and the wooded area of the estate:

Rosslyn Chapel still with the canopy over it:

The Shewington penta-corner with the Mavisbank circle passing directly through the farmhouse.  There was no open-cast mining going on when I was last there!:

A section of the side from Leith to Gyle/Gogar between Clermiston Hill and Leith showing Fettest College to the left and Inverleith House on the pink line to the right(Botanic Gardens) and the almost perfect alignment of Inverleith Place and the near alignment of Inverleith Park path, and perpendicular East Fettes Avenue:

Black Hill and Scald Law summits and penta-corner with the light blue line from Braidwood to Curriekirk and Cammo clump of which I can now show the extensions both to the north and south with a truly astonishing finding:

To the south the line passes between the two Meldon hills, the black and the white, to the west of Peebles.  An interesting area of the Tweed valley, with iron age forts and settlements, a Roman Fort and Lyne kirk and so on.  This gap came up in another system many years ago(2000/1) related to a golden ratio rhombus described by William S. Buehler, mentioned many times preiously, involving the triangle defined by Inchcolm, Rosslyn Chapel and the Black Hill.  I can't recall off hand all the details but I guess the link between Inchcolm and the Meldon gap was an alternate system I had introduced, using Inchcolm - Rosslyn as phi^2(phi-squared or 2.618034), the hypotenuse, and the other two sides of sq.rt phi(1.27202) and one(1).  Mathematically that works but whether this gives the orientation to the Meldon gap, I would have to check!  This just came to mind as I typed so this task is added to the list: To Do!

I've got some photos of the Meldons which I shall include later, along with photos of other points mentioned in all the GE stuff!:

This is interesting but its when this line was extended north that my socks blew off!

Scone Penta-maze!  Exact to the 100th of one degree!

The Arthur Sear line, the one that extends to Rennes Le Chateau is in green.  The difference in orientation of the two is 10.02degrees, 1/36th of a circle!  Remembering also that these two lines were two of the first I found some 19 years ago!  I still have more to show, just discovered, but at least I publish this stuff on 20/12/12, one day prior to the 21/12/12 solstice date, we all await with interest!

Mavisbank, Sir John Clerk of Penicuik, Cammo and Edinburgh grid

After some further development of the Edinburgh grid found to be exactly(to two decimal degree points) perpendicular to the Scone - Holyrood Abbey/Arthurs Seat - Rennes Le Chateau line shown in the last post, I decided to get back on my original track and do in Google Earth the Mavisbank hexagonal system described a few years ago.  This was discovered, by me at any rate, way back in 1994/5, and calculated by hand using Ordnance Survey co-ordinates, with an earthmound at the back of Mavisbank House as centre,  and Newtongrange Church defining radius and orientation.  The radius was found to be some 5000 Scottish ells, as defined by John Reid in 1693 in the first book of gardening for Scottish conditions, The Scots Gardner.  Now 5000 Scottish ells is approximate(99.983%) to the radius of churches in the Rennes Le Chateau area, described by Henry Lincoln in The Holy Place.  He gives this radius as 2miles 1618yards, which equates to 4999.135135 ells, a discrepancy of some 2.6 feet.   (nb 1618 is Phi as commonly used, and used by Lincoln as a mnemonic!)

Mavisbank House was built by Sir John Clerk of Penicuik, whose memoirs I have finally read finding it available for download recently:  Memoirs of the life of Sir John Clerk of Penicu..., and is well worth a read for those who are interested in the subject of The Treaty Of Union, 1707.  Clerk was one of the Commisioners who worked on the details of the Treaty, and gives a personal account of the whole process and describes the factions and characters involved and a running commentary on the main events of the early eighteenth century, up to and beyond the '45 rebellion.  I found this fascinating, but of interest also was his land dealings, he also owned Cammo estate near Cramond as well as the estates of Penicuik and Mavisbank.  In this excercise both Mavisbank and Cammo are featured, and Penicuik generally.

As mentioned above the centre of the circle is the earthmound to the rear of the House and in his memoirs is a note by the editor, page 249, and additional notes, note M, p. 115, giving a quote by a Professor James: ''Behind the house rises, in green abruptness, a trenched Roman Camp, which must have been dear to the Baron's reverently antiquarian soul.''

There is also quite a bit of coverage of the work he did in enclosing and developing the estate of Penicuik which is also of interest although not of relevant for now!

I have so much to cover and am way behind in this side of the work, so on to the presentation of this system of geometry.  Again some more astonishing findings, and I have to remind myself I am not making this up, but
are merely extending what I have had for years now, without the benefit of Google Earth!

So, the circle centred on Mavisbank, with radius that defined by Henry Lincoln at Rennes Le Chateau, and using Newtongrange Church as orientation, with Allermuir to the Camp Ridge as line of sight:

although neither are marked here Allermuir is indicated by the second mountain symbol, the most left of the two outside the circle to the left.

From here a 'flower of life' can be constructed by drawing in circles of the same radius round the circumference starting from Newtongrange where the circles intersect:

It is possible to draw in the hexagon using these found points, but what I want to do is extend the radial lines through these from Mavisbank:

There are two points of immediate interest.
First: The yellow radial in the first image running (NNW - SSE) can be seen to run into the centre of Edinburgh and in the second with some of the previous grid included shows a very intriguing link with Mavisbank.  This line extended to the circumference of the secondary turquoise circle cuts directly through the the spire of St. Giles Cathedral and meets the circumference, which cuts through the Scott Monument in Princes Street Gardens directly opposite South St. David's Street, named after David Hume the philosopher of the Enlightenment period(18th century), called 'Le Bonne David' by Voltaire(if memory serves right). In the second image below St. Giles and the Scott Monument are marked(reminder: clik on the image for a full screen shot!).  Very intriguing! And in the next post I shall show another link with this point, only just discovered.
In the image below the square found from previous post defined by Heriot's School(originally hospital founded George Heriot in the 16th century) and the 'face' in the crags near Holyrood, and Pilrig with the exact 45d diagonals included, the line from the centre of this square parallel to the sides and cutting the Heriot's/ face line at the exact mid-point extended goes exactly to the Mavisbank earthmound, as can be seen in the above image.  Totally unexpected!

There are many interesting points found on the circumferences of the circles shown, but too many to investigate for now.  I am still too amazed by certain of the connections found to give them all sufficient attention!  This first interaction between the City grid defined by the Scone/Holyrood line and this hexgaonal system which I repeat I have known of for over 15 years is astonishing, but it gets even more so later.

The second radial extension I wish to show goes straight to Cammo House(ruin) to within a few feet actually!

Not only that but the grid line from Mavisbank intersects the right angled return from Cammo House at the corner of Starbank Park on the coast just west of Newhaven.

A one time nice ornamental garden, now neglected!

So, a lot to ponder and look at again, after I catch up on the other stuff I have found recently linking into all this and piling on the astonishment factor even more!