In a message dated 27/08/2014 11:10:39 GMT Daylight Time, writes:

Dear Dr Evans

I have been reading with interest a number of documents that mention the smallholding Pen y Foel at Penwyllt.

This is a spot I am quite familiar with, as I frequently stay in the caving hostel which was once the Penwyllt Inn.

Several references I have found mention that almost nothing remains of Pen y Foel. I can assure you that the walls of the cottage are very much still in place, albeit in poor condition, as are the various walls to the small holding enclosures. There is a “midden” from which rabbits occasionally turn up the day to detritus of life from when the cottage was occupied. Behind the cottage at the location of the “well”, I have sunk a small pit to a depth of about 2 ft, to find a hard bed of shale, over which there is a permanent seepage of water. The small hole I dug in July was filled to the brim a month later – it probably filled within 24-48 hours. I suspect that the “well” was probably a cistern filled from this spring. Without a huge amount of clearance of rocks and soil from the gritstone crag that overlooks the spot, is in impossible to know for certain.

There is a curious chance connection between the Potters and myself, in that I live in the ancient parish of Worth in Sussex, where the Penwyllt Potters originated.

I hope you find this information of interest. I have a number of photographs of the various features at Pen y Foel if they are of interest to you.

Kind regards

Peter Burgess

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To: EMyrone@aol.com

CC: mail@horst-eckardt.de

Sent: 28/08/2014 01:45:21 GMT Daylight Time

Subj: Proton structureSee Fig3 http://orbit.dtu.dk/fedora/objects/orbit:120960/datastreams/file_b168733e-b69a-40bf-b0e9-48a68cc3ffbd/content

Can similar mass ratios be derived from your current work? Regards Norman PageSent from Windows Mail

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** Summary Period: August 2014 – URL
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In a message dated 27/08/2014 16:47:08 GMT Daylight Time, writes:

This work gets better and better!

Best Wishes

Kerry

—-Original message—-

From : EMyrone@aol.com

Date : 27/08/2014 – 16:42 (GMTST)

.

Subject : Comment on 269(8)Thank you very much! This is the complete solution that we have been seeking for about a month, and finally found it. Agreed that Eqs. (3), (21) and (22) together will give additional information. These ellipses are a new type that have not been seen before. The 3 D curve will be very interesting and r as a function of theta and phi is the orbit.

To: EMyrone@aol.com

Sent: 27/08/2014 15:03:30 GMT Daylight Time

Subj: Re: 269(8): Complete Solution of the Beta EllipseThis is a very elegant solution for beta, congratulations! For consistency reasons eq.(3) should follow from (21) and (22). Time derivatives seem to give additional terms.

The beta ellipse can be graphed by using theta as the independent variable and settingphi = theta / sin(theta)

which follows from (21,22). I will see how this can be done, it is a curve in 3D.

Horst

EMyrone@aol.com hat am 27. August 2014 um 14:09 geschrieben:

This is the complete solution as requested by Horst yesterday using a lagrangian analysis. The beta ellipse is analyzed in terms of two precessing ellipses (23), one in theta and one in phi, whos half right latitude and ellipticity are defined in Eqs. (24) and (25). The trajectories are given in Eqs. (7) and (29). The problem is worked out in terms of two angular momenta L sub theta and L sub phi where

L squared = L sub theta squared + L sub phi squared

is the total angular momentum. These can be used as input parameters for graphics and animations. This solution is complete and fully self consistent. The lagrangian result is checked from fundamental first principles in Eq. (12). It gives an amazing result, the static beta ellipse can be expressed as two equivalent precessing ellipses, one in theta, one in phi. These are fully equivalent to the static beta ellipse. Eq. (23) gives Eckardt ellipses if L / L sub theta and L sin theta / L sub phi are integral. This solution is fully three dimensional and is a fully self consistent analysis which is entirely original.

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To: EMyrone@aol.com

Sent: 27/08/2014 15:03:30 GMT Daylight Time

Subj: Re: 269(8): Complete Solution of the Beta EllipseThis is a very elegant solution for beta, congratulations! For consistency reasons eq.(3) should follow from (21) and (22). Time derivatives seem to give additional terms.

The beta ellipse can be graphed by using theta as the independent variable and settingphi = theta / sin(theta)

which follows from (21,22). I will see how this can be done, it is a curve in 3D.

Horst

EMyrone@aol.com hat am 27. August 2014 um 14:09 geschrieben:

This is the complete solution as requested by Horst yesterday using a lagrangian analysis. The beta ellipse is analyzed in terms of two precessing ellipses (23), one in theta and one in phi, whos half right latitude and ellipticity are defined in Eqs. (24) and (25). The trajectories are given in Eqs. (7) and (29). The problem is worked out in terms of two angular momenta L sub theta and L sub phi where

L squared = L sub theta squared + L sub phi squared

is the total angular momentum. These can be used as input parameters for graphics and animations. This solution is complete and fully self consistent. The lagrangian result is checked from fundamental first principles in Eq. (12). It gives an amazing result, the static beta ellipse can be expressed as two equivalent precessing ellipses, one in theta, one in phi. These are fully equivalent to the static beta ellipse. Eq. (23) gives Eckardt ellipses if L / L sub theta and L sin theta / L sub phi are integral. This solution is fully three dimensional and is a fully self consistent analysis which is entirely original.

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To: EMyrone@aol.com

Sent: 27/08/2014 14:03:05 GMT Daylight Time

Subj: Re: 269(7): Animation of a Planar Precessing EllipseMaxima gives a more complicated expression for the integral, but maybe it is equal with yours.

My internet access at home is currently out of order, cannot read/send emails in the evening.

Horst

EMyrone@aol.com hat am 27. August 2014 um 10:26 geschrieben:

To give a detailed answer to the question by Sean MacLachlan received this morning GMT, the required equation from a lagrangian analysis is Eq. (14), which is conveniently analytical. So no numerical integration is needed and it is straightforward to make an animation using contemporary desktop animation packages. As x gets larger very intricate trajectories will result from the fractal conical sections, and very interesting motions of m around M or classical electron around proton in 2 – D. The Eckardt trajectory is obtained with integral x:

x = 1, 2, 3, …….

giving the motion of m in de Broglie waves around M, or electron around a proton. Note that the effective potential for a precessing ellipse is Eq. (2) from the Binet equation, and NOT the Einstein potential. Einsteinian general relativity does not in fact give a precessing ellipse. This fact is well known by now. The three dimensional analysis of precession must be developed carefully from first principles and after analyzing the beta ellipse for its trajectory, I will address that problem from first geometrical principles.

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L squared = L sub theta squared + L sub phi squared

is the total angular momentum. These can be used as input parameters for graphics and animations. This solution is complete and fully self consistent. The lagrangian result is checked from fundamental first principles in Eq. (12). It gives an amazing result, the static beta ellipse can be expressed as two equivalent precessing ellipses, one in theta, one in phi. These are fully equivalent to the static beta ellipse. Eq. (23) gives Eckardt ellipses if L / L sub theta and L sin theta / L sub phi are integral. This solution is fully three dimensional and is a fully self consistent analysis which is entirely original.

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