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We should thank both Henry Halboth and George Huxtable for the impressive 
presentation and analysis of very interesting Arnold's tables.


Allow me two short remarks:

1) As for Arnold's originality - I don't doubt that Arnold knew Mendoza's 
method. Norie's publication from 1816, cited by George,  was probably only a 
late repetition of Mendoza's original text, as the time of Mendoza's 
professional life belonged to the turn of centuries. He published the paper 
"Recherches sur les principaux problemes de l'Astronomie Nautique" in the 
Philosophical Transactions of the Royal Society for 1797, where he summed up 
40 direct methods of lunars and investigated many indirect methods. And in 
the year 1801, he published giant "Tables for facilitating the calculations 
of nautical astronomy" (some 400 pages) in London. Both works weren't much 
known at sea, of course, but they were used by teachers of navigation and 
cited in the literature. I cannot consult them in Prague, but I bet that the 
method cited as Mendoza's one by Norie in 1816 was published in one of these 
works or in both ones.

Of course, Arnold improved Mendoza's method essentially. George's recent 
posting explains this fact thoroughly.


2) As for the distances between the Moon and planets in the Nautical Almanac 
(George's question) - their use was firstly illustrated in the Dutch 
publication from the year 1781 with a long Dutch title I won't repeat here, 
but for your possible request. Here the distance of Jupiter was used and 
evaluated by the pre-Almanac method comparing Moon's ecliptical longitude 
calculated from the measured (and cleared) distance to her longitude gained 
from Mayer's Moon tables. But it was only a "shot in the dark", concerning 
the use of planets for lunars, as Almanac method for the Sun and stars was 
tenfold easier and available from 1767 and almanacs didn't give lunar 
distances for planets then.

The Danish astronomer Schumacher changed this situation in 1821, when he began 
editing the special ephemeris (in English) of lunar distances for four 
navigational planets in Copenhagen. He continued the edition up to 1838 and 
this publication was known to some seamen - Thomson mentioned and recommended 
it in the commentary to his famous tables. When this ephemeris stopped to be 
published (I don't know the reason, but I am afraid that Schumacher's death 
was the cause), national almanacs started to publish the lunar distances for 
planets shortly after this year. If you have old volumes of the Nautical 
Almanac in a neighbouring library, you can accurately nail down the year by 
briefly consulting the volumes 1838 - 1842 or so.


3) Allow me the private question to George Huxtable now - George, did you 
receive my personal e-mail to you, sent twice?



Jan Kalivoda

   

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