Next message: Peter Fogg: "Re: 7/8 SCALE SEXTANTS"
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
