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    Re: Haversines with Logarithms
    From: Brian Walton
    Date: 2020 Oct 17, 02:01 -0700

    Water is rushing by my ear, the forecast for my projected route is ominous, and Corvid19 restrictions loom worldwide. The smoke alarm just went off. (Bacon and eggs.)

    The all-haversine formula quoted by Matthew Gianelloni is identical to the ones advocated and demonstrated by Rev. Hall in 1910, and also used by d’Ocagne for his nomogram, and later by Doniol.

    The log-haversine tables I have in hand return Right Ascension or Hour Angle by having both scales printed along the top and bottom, and both edges. The logs are to base 10, and the exponent has 10 added to help simple sailors like me, rather than “bar 1” as taught once at school.

    Copyright infringement and plagearism are rife in old textbooks, but civil or international law seem to override them. (David.C.) The British Reed’s Almanac, which favoured versines, and which I used for 20 years, fell foul of these rules 20 years ago.  I expect to be sued shortly by the European Court of Justice for using a Bygrave whilst flying solo.

    I am trying to replicate reduction systems used by my forefather in around 1890. Reversed sines ( versines) existed in antiquity. Not haversines, introduced in 1905. When did log-sin or log versine tables appear?

    Brian Walton

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