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George: further to my previous posting, I have further referred to
Norie's 1839 edition, and find Method 4 credited to Joseph de Medoza
Rios, as noted by Bruce, with instructions on working together with Table
XXXV and its appendant explanation. Should it be of assistance to you, I
would be glad to copy off the instructions, although I quite frankly see
little in these so called approximate methods that exceeds the simplicity
of the rigorous trigonometrical solution previously posted, especially
when one makes use of the haversine tables.

On Mon, 2 Aug 2004 13:55:28 EDT Bruce Stark  writes:
> George,
>
> You are right. That particular method of Captain Mendoza del Rios'
> (sometimes
> called "Norie's fourth method") is an approximate one. It's similar
> to
> Bowditch's original method, before that was improved by special
> tables, and looks to
> me to be a simplification and improvement of it. A special feature
> of both is
> that, unlike other approximate methods, the rules don't depend on
> which body
> is highest or whether or not the distance is over 90 degrees.
>
> Norie's old Table XXXV was three pages long. The title, "To correct
> the
> Apparent Distance of the Moon from the Sun, a Star, &c, for the
> Effects of Parallax
> and Refraction," isn't exactly a fit. What it does is adjust for the
> error
> caused by treating the moon's corner as if it were a plane right
> triangle, with
> the moon's altitude correction as the hypotenuse.
>
> Two sides of this little triangle are always straight lines. That
> is, they
> are sections of great circles. The side opposite the angle at the
> moon is seldom
> part of a great circle, so is curved. Table XXXV adjusts for the
> error caused
> by the curve.
>
> Bruce

   

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