My apologies for such late input to this thread, I have been a little behind in my e-mail!  I encountered many of these problems and the same questions when designing my Analemmic Equatorial sundial
( http://netnow.micron.net/~petes/sundial ).  I hope the following will help.
Luke Coletti wrote:

    I have found the best method of correcting for the periodic variability
of the EoT relative to the calendar is to take the EoT as a four year
average.
 
Tom Semadeni wrote:

How do you do that?  Do you pick a 12 month year which straddles the
mid point between two leap years, like Jun 30, 97 to Jun 30, 98?

The method I used to derive "average" date points for my analemmic gnomon, and a table of the resultant values, may be found at  http://netnow.micron.net/~petes/sundial/dialcalc.htm .  As others have stated, this does not affect the shape of the analemma, just the location of the date's position on the analemma.  This normally does not affect the time accuracy of the analemmic sundial, except near the solstices; a 1 day error near the winter solstice would affect the indication of time by 1/2 minute .

Luke Coletti wrote:

     The temporal variability, as has been discussed in earlier
threads, is chiefly due to the phase relation between obliquity and
eccentricity as caused by the precession of the equinoxes and the
shifting of perihelion. The magnitude of obliquity and eccentricity
changes too but on a slower time scale.

I prepared several graphs last year, prior to the NASS conference, using Luke Coletti's Solar Calculator program ( http://www.gcstudio.com/suncalc.html - Thanks Luke! ) and Excel to show how the effects of changing obliquity and eccentricity of the Earth's orbit may be expected to change the accuracy of my sundial long-term.  The graphs show the necessary shape of the analemmic gnomon for the years 2000 BC, 0000, 2000 AD, 4000 AD and 6000 AD.  I found them rather interesting, and so I hope you will forgive me for attaching them to this e-mail.

Thanks.  Pete S.  ( http://netnow.micron.net/~petes ) Attachment converted: MAC Hard Disk:Millen.gif (GIFf/JVWR) (000127E6)

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