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.