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    Re: Bygrave to clear lunars.
    From: Frank Reed
    Date: 2013 Dec 6, 10:46 -0800

    Geoffrey, you wrote:
    "The Bygrave is set up to solve equations involving the division or multiplication of Cosines and Cotangents, and so I am not sure that the Bygrave slide rule can be used to solve the equations given in Frank's "Easy Lunars"."

    Hey, it's all trig identities from here to there! :) Of course, forcing an obsolete device to perform even more obsolete calculations which that obsolete device was never designed to do is a form of insanity --but one with a long pedigree on NavList. :) And who can resist its siren call??

    Here's the deal: Francis informs us that can solve the standard great circle problem with his Bygrave: given two latitudes and a difference in longitude he can solve, by some set of twisting and turnings, for the true great circle distance between the points. He has then mapped this onto the second half of the "standard triangle" process of clearing lunars. The latitudes are replaced by the corrected altitudes, and the difference in longitude is replaced by the difference in azimuth. And when solved, by the same set of twistings and turnings, this yield the corrected distance. Now to continue the game, Francis requires the inverse process. Is that impossible with the Bygrave?? Can we not simply replace "twist right" with "twist left" and "turn clockwise" with "turn counterclockwise"? All he needs is the procedure to solve the great circle problem for longitude difference given a pair of latitudes and the great circle distance between two locations. I suppose it's possible that this inverse problem requires radically different procedures, but that would surprise me.

    -FER

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