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Re: Mendoza's method for clearing lunars.
From: Frank Reed CT
Date: 2004 Aug 3, 20:45 EDT
From: Frank Reed CT
Date: 2004 Aug 3, 20:45 EDT
George H wrote:
"I have to apologise to Frank Reed here (not for the first time). Almost
everything I need to know about Mendoza's method is covered in his various
postings on lunars over recent months. I should have scanned those postings
first."
No apology necessary at all. Lists like this are ephemeral, and posts from two or three months ago might as well be ancient history. Did you verify for yourself that those entries in Table XXXV can be calculated from the simple equation (1/2)*cot(d)*x^2? If you would like to derive this equation, take the standard cosine formula for the lunar distance (d as a function of two zenith distances and the difference in azimuth) and then do a two-dimensional Taylor series expansion for small changes in the two zenith distances. If you drop any term which is always smaller than 0.1 minutes of arc, you will be left with three terms, two linear and one quadratic, and after a little crunching through the trig identities, you'll find that the quadratic term is that "Q" I've written about, proportional to cot(d) as above. And notice that if you read the instructions for Witchell's Method in Norie, you will be directed to Table XXXV, too. This table, and the quadratic term from which it is derived, are not limited to the method of Jose de Mendoza y Rios (*), but are part of most of the series methods for clearing lunars.
* In Spain, his name is usually written "Jose de Mendoza y Rios" and that seems to be the prefered form. But he worked for most of his life in England and there he was usually known as "Josef Mendoza Rios" or just "Mendoza Rios". There are a few other variants floating around, but I think they're mostly mistakes and/or misprints.
A little trivia: it seems that Thomas Jefferson may have learned his lunars from Mendoza Rios. Jefferson owned a copy of a navigational manual written by Jose.
And:
"probably related to the antiquity of my Mac, which runs Internet Explorer 4.0 (and isn't upgradeable)."
That's a tough predicament. I'm annoyed by sites like Mystic Seaport's which rely on scripting unnecessarily and end up making much of their content inaccessible to non-standard browsers. I understand the problems web designers face, but I'm not sympathetic when the mistakes are merely careless.
As pointed out by "cfuhb-acdgw@earthlink.net" (sorry, I don't remember a real name to go with that e-mail), you can go directly to the URL for the GIFs of the pages. You might also be able to go directly to the chapters via this URL:
www.mysticseaport.org/library/initiative/ImPage.cfm?BibID=13617&ChapterID=31
The link as written will take you to the lunars chapter in Norie, but you can edit the URL to go to any chapter. For example, the preface, which you'ce already seen, has ChapterID=1.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
"I have to apologise to Frank Reed here (not for the first time). Almost
everything I need to know about Mendoza's method is covered in his various
postings on lunars over recent months. I should have scanned those postings
first."
No apology necessary at all. Lists like this are ephemeral, and posts from two or three months ago might as well be ancient history. Did you verify for yourself that those entries in Table XXXV can be calculated from the simple equation (1/2)*cot(d)*x^2? If you would like to derive this equation, take the standard cosine formula for the lunar distance (d as a function of two zenith distances and the difference in azimuth) and then do a two-dimensional Taylor series expansion for small changes in the two zenith distances. If you drop any term which is always smaller than 0.1 minutes of arc, you will be left with three terms, two linear and one quadratic, and after a little crunching through the trig identities, you'll find that the quadratic term is that "Q" I've written about, proportional to cot(d) as above. And notice that if you read the instructions for Witchell's Method in Norie, you will be directed to Table XXXV, too. This table, and the quadratic term from which it is derived, are not limited to the method of Jose de Mendoza y Rios (*), but are part of most of the series methods for clearing lunars.
* In Spain, his name is usually written "Jose de Mendoza y Rios" and that seems to be the prefered form. But he worked for most of his life in England and there he was usually known as "Josef Mendoza Rios" or just "Mendoza Rios". There are a few other variants floating around, but I think they're mostly mistakes and/or misprints.
A little trivia: it seems that Thomas Jefferson may have learned his lunars from Mendoza Rios. Jefferson owned a copy of a navigational manual written by Jose.
And:
"probably related to the antiquity of my Mac, which runs Internet Explorer 4.0 (and isn't upgradeable)."
That's a tough predicament. I'm annoyed by sites like Mystic Seaport's which rely on scripting unnecessarily and end up making much of their content inaccessible to non-standard browsers. I understand the problems web designers face, but I'm not sympathetic when the mistakes are merely careless.
As pointed out by "cfuhb-acdgw@earthlink.net" (sorry, I don't remember a real name to go with that e-mail), you can go directly to the URL for the GIFs of the pages. You might also be able to go directly to the chapters via this URL:
www.mysticseaport.org/library/initiative/ImPage.cfm?BibID=13617&ChapterID=31
The link as written will take you to the lunars chapter in Norie, but you can edit the URL to go to any chapter. For example, the preface, which you'ce already seen, has ChapterID=1.
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
