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George-
 I have come back to your question of the 9th, "Is that clearer, Jared? And if 
so, please suggest how you would express it."

And my first step was to simply remove the word "Parallax" from the statement 
before that question, and replace it with a definition of parallax. If the 
definition is reasonably correct, the resulting new paragraph will seem 
logical and correct, so let's take a look at it. I've set the definition of 
parallax in [square braces].

"[An apparent change in the direction of an object, caused by a change in 
observational position that provides a new line of sight] displaces the 
apparent position from the true position (of the Moon). [An apparent change 
in the direction of an object, caused by a change in observational position 
that provides a new line of sight] changes throughout the day, as a result of 
the observer riding round the Earth's surface."

It sounds a lot like someone refering to speed in tems of "knots per hour". 
Simply badly put, if not to say wrong, when one says "I was moving at five 
knots per hour." Or per hour.

Parallax does not change as a result of your position, rather, parallax is 
FROM your relative position, so that when your position changes, the parallax 
shifts relative to the change in your position. "Parallax" itself is not a 
fungible object, nor does it change. The amount of parallax that you have 
measured will change.

That may seem trivial and I may not be making it clear enough, but when I'm 
trying to grasp an obtruse concept in debated spherical trigonometry, hearing 
someone refer to "knots per hour" does not help to make any point. Those of 
us who are not mathematicians by training are easily lost by things that 
professionals would gloss by, and that in turn is one reason why historically 
"navigation" has glazed so many eyes and lost so many students.

I'm quite sure that I do not grasp the overall picture of the trigonometry 
involved in lunars despite having looked at the Arthur Pearson's fine 
diagrams in lunars1.pdf (linked from www.ld-DEADLINK-com). The "discovery" 
that there are in fact two parallax corrections rather than one needed to 
clear a lunar would indicate that all prior lunars taken have been wrong, and 
that the diagrams in Arthur's PDF file must also therefore be wrong, since 
they only mention one parallax correction. The alternative is to ask whether 
the second compensation is of any real value, and if so, whether anything 
else has been masking it. Or, does the one general adjustment made (to 
correct readings taken on the earth's surface rather than from its core) also 
conveniently null out the problem of earth-lunar parallax? (What you call 
"parallactic retardataion".)

Have I missed something while my eyes were glazing over, or has there been any 
correction made for the low altitude refraction that must also be affecting 
the parallax correction for a low-altitude moon? And wouldn't that then need 
to be made based on air temperature and density, the same way that a 
conventional sun sight takes these factors into account?

On the bright side, if this can be diagrammed and explained so simply that I 
understand it, then anyone will be able to grasp it. And to grasp why the 
past 300(?) years of lunars have simply been inaccurate. And Arthur's 
diagrams redrawn, and so on.

   

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