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George H, you wrote:
"But it's news to me that Dunthorne's procedure (one of the very earliest for
clearing the lunar distance, and included in Maskelyne's first "Tables
requisite" in 1766) is defective in that way."

Well, of course, it is not defective in this way. Dunthorne's formula is 
identical (in the mathematical sense) to any of the direct triangle solutions 
of the problem of clearing a lunar distance. 

I have now found a copy of this 1906 Lehrbuch der Navigation on Google Books 
(and therefore, everyone, please ignore my previous request for scanned 
pages). This link should take you right to the page in question:
http://books.google.com/books?pg=PA385&id=cjtLAAAAMAAJ
My German is mediocre, but I cannot find any explanation at all for this 
supposed limitation in Dunthorne's formula in the text. I think the author of 
this passage may simply have been mistaken. The only other possibility that I 
can think of is that the alternative formula proposed works better with 
five-figure log tables. Anyone care to try that out?

-FER


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