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    Re: The Bygrave
    From: Gary LaPook
    Date: 2009 Jul 23, 01:27 +0100

    I'm not so sure.
    According to Bowditch Aquino published in 1909 using the formulas
    previously published by Fuss.(see attached article 2111.) None of these
    formulas look like Bygrave's.
    I looked at Aquino's tables published in 1918 available for download
    His procedures, formulas, explanations, and sample computations also
    bear no resemblance to Bygrave's method. (But, I will admit, I am not
    the world's greatest mathematician's, so I might be missing something.)
    The Aquino "Log tangent +/- Log secant" method that you posted at:
    is very similar to Bygrave's procedure but Aquino's second formula is
    not used by Bygrave. His first, third and forth formulas appear to
    produce the same results as Bygrave's even though they are slightly
    different they appear to be equivalent. This method also appears to bear
    no resemblance to the method that Aquino had previously published in
    1909 and 1918.
    So I wonder, were there two very different Aquino methods, one which he
    published at the turn of the century and the other one much later after
    the invention of the Bygrave?
    douglas.denny@btopenworld.com wrote:
    > Eight Bygraves.
    > Six HR1s
    > Twelve MHR1s.
    > Three HR2s.
    > What a pitiful number of survivors.  It is even worse than I thought.
    > I wonder how many were made?
    > -----------
    > I made an error again which should be corrected:-
    > I wrote:
    > "The explanation of Aquino's short-method of logTan / logCosecant  sight
    > reduction (I sent in a copy of the explanation recently from 'Spherical
    > Trigonometry' by J.H. Clough-Smith) makes the argument conclusive for me.
    > Aquino published his method a couple of decades later than Bygrave. In fact,
    > Aquino's method should perhaps really be called Bygrave's method,  as the
    > latter invented the principle of perpendicular from the observer's meridian
    > to the star meridian  firstly,  in 1921 (using a mechanical implementation)."
    > ----------
    > This is quite wrong. I was assuming Clough-Smith was correct in his book 
    (published 1966) which states "Aquino's Tabular Method ... first published in 
    Rio de Janeiro in 1943".
    > I only learned from a posting here that Aquino first published the details 
    of his method in 1908; and the tables were published by Potter in London in 
    1918.  Thank you Mr. Waldendand for post 8770 with these details.
    > ----------
    > This puts a completely different complexion on the development of the Bygrave slide rule.
    > It is not unreasonable to expect that Captain Bygrave was fully familiar 
    with all contemporaneous developments in navigation.
    > The publishing of tables by Aquino in 1918 in London makes it as close a 
    certainty as is possible, that he would have known of them and the principles 
    of the method.
    > It is not unreasonable to extrapolate slightly further and suggest perhaps 
    he started thinking about the mechanical implimentation of the method, which 
    led to the development of the instrument.
    > This tends to add favour the logtan/logcosecant combination of scales 
    arrangement for Bygrave... as in Aquino's log tan/logcosecant method.
    > Douglas Denny.
    > Chichester.  England.
    > >
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