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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: refraction
From: Alexandre Eremenko
Date: 2007 Jan 5, 02:05 -0500
From: Alexandre Eremenko
Date: 2007 Jan 5, 02:05 -0500
Lu and Guy, I hope you received the paper. I just read it, and I have to say that this is a truly outstanding example of popular scientific writing. It is long time since I read something so good. Maybe "Lectures on navigation" by Lord Kelvin can be compared. One has to write something like this about the history of refraction after Kepler. I knew that Snell (Snellius) discovered the "Snell law" which the ancients tried and failed to discover. (The paper says that it was really first discovered by an Arab whose name was Ibn Sahl). Actually I even have a conjecture why Ptolemy and his contemporaries failed to discover this law despite their efforts. The law says that the ratio of sines of the two angles is constant. The problem is that the Greeks did not have sines! Sines were invented by the Arabs some time in VIII century. The Greeks used chords instead: chd(t)=2sin(t/2) as their main trigonometric function. Stated in terms of chords, the law of refraction is too complicated to be discovered empirically as Ptolemy intended:-) And of course I did not know (and now know from the paper) that the "tables of refraction" were first developed by Tycho Brahe, which answers the original question of Guy. But I guessed correctly HOW he did this:-) The precise theoretical law of atmopspheric refraction is mathematically complicated. It could have been possibly discovered only in the late XVII century, not earlier. But there is no doubt that by that time very accurate empirical tables already existed (composed on the same principle Tycho used). Alex P.S. If anyone else is interested, go to http://www.math.purdue.edu/~eremenko/Refraction1.pdf I will keep it there for 2 days. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---