NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Makelyne et al
From: Ken Muldrew
Date: 2003 Jun 14, 12:02 -0600
From: Ken Muldrew
Date: 2003 Jun 14, 12:02 -0600
On 13 Jun 2003, at 21:06, Steven Wepster wrote: > The main reason for Mayer's > success is that he managed to fit over 20 parameters in his theory to > over 200 observations of eclipses and occultations made after the > invention of the telescope. In my dissertation I want to answer (a.o.) > the question how he did the fitting, before the invention of the least > squares method. According to an article by P.J.G. Teunissen published in De Hollandse Cirkel, 2 nr. 1/2, April 2000 (but reproduced at http://www.ncg.knaw.nl/uk-site/Teunissen.htm) Mayer invented the method of averages for fitting arbitrary parameters. Briefly, if you have more equations than unknowns, you divide up the equations into as many groups as there are unknowns (a subjective procedure that makes the technique a bit dodgy), sum (or average) the equations in each group to produce n equations in n unknowns, and then solve for the unknowns. This was the first technique to incorporate all observations but it replaced the subjective act of throwing out some observations with the subjective act of grouping the equations (and so left room for improvement). Ken Muldrew.
