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    Re: Star-star distances for arc error
    From: Douglas Denny
    Date: 2009 Jun 29, 08:35 -0700

    Dear Brad,
    Many thanks  for the comments, which I agree with totally, as both versions 
    come to the same result with the same operations so it is a non sequitur - 
    either logically is correct.
    What is more interesting to query is why Bygrave did not specify in his patent 
    more accurately? that is the fascinating thing to ponder I think.
    It is clear he had a perfectly good working model of the 'system' all sorted 
    out in exquisite detail,  and even gives a diagram/picture of the device and 
    it's scales with numbers, and the operation sequence on the outer sliding 
    cursor sleeve.  
    So why did he say:-
    "... an inner cylinder of log tangents.......
    and an outer cylinder of log cosines ......"
    I think, for what it is worth, this is either a simple 'slip-up' when he wrote 
    the specification;  or more likely to my mind,  he was meaning the scale is 
    derived from the basic function of log cosines; and I think this was done 
    deliberately to link with the given formulae in the patent itself which only 
    uses cosines being mentioned.
    As one finds with the device itself though, he uses the slide-rule operation 
    of division when a multiply is needed, and vice versa to facilitate the 
    operations required for the sight reduction purpose. This therefore needs an 
    invesrse function for one of them. (Choose which you think - log Cotan or log 
    Cosecant - same thing when used in the operations of this device).
    I believe he was _fully_ aware of what he wrote, but did so with what is now, 
    to us, an apparent anomaly,   only to illustrate for the purposes of the 
    patent requirements the _principle_ of the device; and he just kept to 
    himself the detail of the actual nitty-gritty mechanics of it.  The patent 
    requirements had been fulfilled  in describing the principles and were 
    accepted. That was that.. but leaving us to now speculate as to his thought 
    processes in what amounts to historical archeology I suppose.
    Douglas Denny.
    Chichester.  England.
    Navigation List archive: www.fer3.com/arc
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