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    Re: My first Lunar
    From: George Huxtable
    Date: 2008 Jul 25, 00:09 +0100

    Kent Norstrom quoted me as saying-
    
    "George Huxtable wrote [5897]: Actually, Kent and I agree about that
    correction, when working a lunar with maximum rigour. My edition of Raper
    dates from 1864, and in that, it's table 53, "Correction of the lunar
    distance for the contraction of the vertical
    semidiameter". Perhaps Kent will confirm that's what he is referring to.
    That's used, just as it says, to correct the measured distance for the
    apparent vertical shrinkage of the Moon, and that certainly does depend on
    the difference in refraction between the Moon's centre and limb. Indeed, I
    took a look at that table, and noted that for all Moon altitudes above 30�,
    it would be less that 1", so disregarded it. So in this case, (unlike for
    the corrections to altitude, above) that correction really was a matter of
    being right in principle but numerically trivial. But it isn't to be used
    when correcting for altitudes above the horizon."
    
    
    
    I enclose a scanned copy of the tables, for which I have used the
    corresponding algorithms in my LD model. Hopefully at least one of them is
    exactly or near exactly to table 53 in Raper 1864, that George uses. These
    are Swedish tables so I take the liberty to try to translate into English.
    
    ......Tabell XXVI: Decrease of the SD for the sun and the moon due to 
    refraction
    (here George and I disagree). Arguments are apparent altitude and the angle
    between the distance and the object's vertical.
    
    I don't understand Kent's claim that "Here George and I disagree". In what 
    respect do we disagree? I agree that the Swedish table XXVI that Kent 
    provides corresponds in its purpose, and in its arguments, with table 53 in 
    my 1864 Raper, even though the actual tabulated numbers may differ somewhat. 
    Both tables predict change in the apparent vertical semidiameter of Moon or 
    Sun, depending on altitude, and the resulting component of that change in 
    the direction of the measured lunar distance. And indeed, that's a 
    correction that may be worth making, when working to utmost rigour with 
    low-altitude observervations. He and I appear to agree fully about all of 
    that.
    
    ===================
    
    Where we have disagreed is about a different matter altogether; the 
    correction for apparent altitude of the Sun and Moon as a result of 
    refraction. That will be taken completely and precisely into account by 
    making a refraction correction appropriate to the apparent altitude of the 
    limb that was observed; then adjusting the result by allowing for the true 
    semidiameter of Sun or Moon. Kent's proposed method, which he put forward in 
    [5775], is irrational. He wrote-
    
    "I am still of the opinion that the refraction correction used in altitude
    reduction must be referred to the geocentre of the moon. I find this
    correction  by calculating the refraction both on the UL/LL and the
    geocentre, which means as in Jeremy's case that I add a small value due
    measurement of the UL. George means that this approach is unnecessary
    because the correction (in Jeremy's case) is so small. Even if George has
    tried to convince me I still keep my opinion."
    
    Kent, here, mis-stated my argument which was NOT that the resulting was in 
    that case negligibly small; but that in principle no such additional 
    correction should ever be made at all. In support of his method he called in 
    that correction table, XXVI in his Swedish textbook, equivalent to 53 in 
    Raper. And presumably, that is where he perceives there to be a disagreement 
    between us.
    
    That Table XXVI has no relevance to the question of correcting observed 
    altitudes for refraction, being intended, instead, for the correction of 
    observed lunar distance due to the effect of refraction on apparent 
    semidiameter.
    
    Kent is welcome to "keep his opinion", and indeed, the differences that he 
    will find in doing so will usually be undetectably small; but there's a 
    right way and a wrong way of doing this job; and what's more, the right way 
    is far simpler.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
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