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Herbert, you wrote:
"Dunthorne makes the simplifying assumption that the effect of parallaxe is in 
the vertical towards the geographical zenith. Strictly, it is the geocentric 
zenith that is at play. Of course, he is not the only one amongst his 
contemporaries to take this practical approach"

That's a good thought, but it still wouldn't explain the angular limitation. 
The oblateness correction (which can be applied to any lunar clearing method) 
does not have the dependence on angle that would lead to the limits mentioned 
in the textbook (70 to 110 degrees).

And you wrote:
"I am only guessing here, because I don't have the text of the 1906 edition. 
The 1854 edition, which is online, goes at great length into the 
corresponding error analysis, but it does not mention the 70d to 110d rule. I 
don't see where it comes from."

The 1906 is online, too. This should take you to the page:
http://books.google.com/books?pg=PA385&id=cjtLAAAAMAAJ

You wrote:
"To understand the criticism we would need to see the proposed alternatives, i.e. no. 21 or 23."

It's mathematically identical to any of the standard direct triangle 
solutions. That is, Dunthorne (eq.18 in the textbook) and the recommended 
formulae (21+23) yield identical results in all cases. But the latter has 
practical calculational advantages. The whole calculation is done in logs. 
You don't have to work partly in logs and partly in natural functions. Also, 
the Dunthorne formula becomes less sensitive for very short lunar distances 
which means one needs more extensive logarithm tables in those cases, but of 
course those were never used historically in any case.

-FER
By the way, HP, nice to see you posting on NavList again. :-) Speaking of 
people I haven't seen online in a while, Marijke turned up on SciMath 
yesterday (I think you remember that particular math whiz).




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