NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: S Tables Question
From: Herbert Prinz
Date: 2002 Oct 23, 03:54 +0000
From: Herbert Prinz
Date: 2002 Oct 23, 03:54 +0000
Arthur, If Sin and Cos do not work, try Secans for S, and Cosecans for C. I have not seen the particular tables that you are referring to and I am shooting from the hip. Apologies, if this leads into the wrong direction, but I would be surprised if this were the case. There is an uncounted number of tables out there that are all variants based on the Ageton method. The basic idea behind this method is to split the navigational triangle into two rectangular triangles. Each of them can be solved with a formula that contains just multiplicative terms (as opposed to the cosine theorem that involves the addition of two such terms), the advantage being that they can be solved with logarithms without having to find the anti-logarithm of intermediate results. For details look up Bowditch for formulas of the rectangular spherical triangle. One can always use sin instead of cosec, and cos instead of secans, as they are reciprocal. Instead of adding the logarithms, you would subtract. I don't know why one function is given preference over the other; I am sure there are procedural advantages. Obviously, one tries to device a method that can use either sin/cos functions, or sec/cosec only, as in each pair each function is the co-function of the other (as their names suggest) and therefore, space for tabulation is cut in half. You can check this out in your tables: If it folds at 45 deg and S(x) = C(90-x) and vice versa, we are on the right track. Herbert Prinz