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.
Monday, 24 March 2008
Friday, 7 March 2008
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.
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.
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.
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:
2713.833 7547.736 Schiehallion
3275.280 6729.430 Arthurs Seat
By Pythagoras theory;
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
2713.833 7547.736 Schiehallion
3554.330 6329.100 Eildon North(ring-fort)
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:
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
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:
34.38900 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!
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.
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).
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)