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Only several words, I should do something quite different now.

Frank R is right that the terminology of the "approximate" and "rigorous" 
methods is archaic.  But Fred H is right that it is established. And as 
lunars are only of a historical interest, I don't understand, why not to use 
the terminology of their users. It is the matter of taste, of course. Herbert 
Prinz had objected to this terminology one year ago in this list, too. But he 
supposed that this terminology was contrived by Cotter, if I remember his 
thoughts correctly. This wasn't  the case, as I had maintained and proved by 
sources cited then and as Frank's historical remarks now prove, too.

The "rigorous" and "approximate" methods were two distinct classes of 
solutions, taken from the point of practice. The approximate (or serial) 
methods worked with small increments to the measured distance (the 1st, 2nd, 
3rd correction in most of them) and 4-place logs sufficed to them. The 
"rigorous" (triangle) methods required 6-place logs and a tedious 
interpolation in them, as they sought the cleared distance directly from 
other elements of the spherical triangle. Very substantial difference for 
practitioners, indeed.

In the theory, the approximate/serial methods can be so accurate as 
rigorous/triangle methods. But in the reality, most approximate solutions 
used simplifications so as to shorten their tables and to simplify their use. 
(George Huxtable's analysis of Arnold's tables showed this, two weeks ago. 
Chauvenet's and Bolte's methods make an exception, e.g.) It wasn't possible 
to push the accuracy to the last point working with those tables, as it was 
possible in ALL rigorous methods. But is wasn't necessary at sea, of course, 
and the accuracy of these approximate solutions had fully sufficed for 
sailors. If Frank R is attaining the accuracy of 0.2' in measuring LD's on 
land today, as he said some days ago, one must take into account the accuracy 
of 0.5' at sea in the early 19th century at least. (We had discussed this in 
the spring in a long thread.) And as George H cited from Chauvenet some days 
ago and as I had written during the previous year, Moon's positions in 
almanacs (and th!
erefore the precomputed LD's) were sometimes in error of another 0.5' up to, 
say, 1880. The effect of e.g. elliptical earth's  shape on the value of the 
cleared LD (some 11" at most and very rarely) was ridiculous against those 
factors. I cannot but refer to my article 
http://3web.dkm.cz/kalivoda/LunDistClass.htm for details once more.

Cotter's text on lunars is quite insufficient from the historical point of 
view today. George H (with my and Herbert P's little help - see Ringo Star) 
published the long list of his errors on Internet for the list members and 
others - see http://www.huxtable.u-net.com/cotter01.htm. And I strived to 
fill up some his gaps in the article cited above.

But Cotter's text, although a rare book now, is definitely more available than 
Mendoza's paper, which is published for the interested persons only 20 days 
ago, (many) thanks to Frank Reed. Previously it was buried in several 
specialized libraries (but maybe I am wrong in Prague). Cotter can be used 
for 40 years today. He cannot be blamed too much. In the sixties, there 
wasn't much interest in the HISTORY of CelNav, some ten specialists 
throughout the world excepted - and they weren't more informed in details 
than Cotter, I guess. Cotter was a real beginner, as Frank R defines them.


Jan Kalivoda

   

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