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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
at:
http://www.archive.org/stream/newnavaltazitabl00aquirich#page/n37/mode/1up

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:

http://www.fer3.com/arc/m2.aspx?i=108462&y=200905

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?

gl




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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