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Dear Herbert,

Yes, I am listening, but I reply with delay, sorry. One should to divert his 
mind from navigational problems sometimes and devote oneself to his job and 
family for a while.

If I understand you, the method for clearing the lunar distance that deserves 
to be called "rigorous" by you should proceed on Earth's ellipsoid without 
any simplification from the beginning to the end. From this point of view, no 
such method does exist, you are right.

But you must accept that the differentiation between "rigorous" and 
"approximative" methods was accepted in the 19th century to the intent that 
rigorous methods worked with equations for both apparent and true lunar 
triangles coinciding at zenith, while approximative methods used calculus for 
obtaining the small differences between the apparent and true lunar distance 
while omitting higher members of polynoms gained. By no means is Cotter the 
author of this classification, you can find it in full blossom in Weyer's 
"Vorlesungen ?ber die nautische Astronomie" from 1871, which was the pillar 
for the navigational training in Germany up to the end of the 19th century. 
And as Weyer lays no claim to invent this classification (which is more 
detailed, but I omit it), he had to find it in English or French sources. 
Cotter doesn't know Weyer or any German titles, therefore he found this 
classification independently in the older English literature that could be 
indentified by someone !
spending a time in a greater scientific library in English speaking countries.

The question, if a method uses correction for Earth's ellipsoid, is not 
important in these sources for the classification of a method as "rigorous" 
or "approximative".

Accordingly, you probably should respect the language of the sources and give 
up your rigorous resistance to the use of the phrase "rigorous method for 
clearing LD's". Or is the Dunthorne's method approximative in your eyes up to 
now? If so, why, please?

Chauvenet isn't the first which uses the correction for oblateness of the 
Earth, although he probably allows for it very neatly. Herbert refers to 
Borda in 1778, R?mker explains it in his "Handbuch der Schifffahrtskunde" 
from 1844 and so on. This correction can be applied at the end of any 
"rigorous" or "approximative" method, but as its maximum value was 13 
arc-seconds theoretically and 8 arc-seconds practically, it was duly 
neglected at sea.


Jan Kalivoda

   

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