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    Re: Bygrave formula
    From: Hanno Ix
    Date: 2014 Jun 9, 11:43 -0700

    Cannot wait to see the missed attachments!
    After I have seen them I will give you more details on the cursor/pointer rolls
    as I imagine them.

    However, please hold off on the sin(x) version for now. I am working on a study that
    compares scale lengths with a "1 mm for 1 arcmin" scale of different trig functions.
    And so far, sin(), cos(), sec() and csec() don't come out too good, tan(0) and cot(0)
    are OK: tan() / cot() require  30 meters - sin() etc require 64 meters!
    Next will be the haversine. My guess: very long scale as well.

    That may not be the end for sin() / cos(), though.

    Sight seeing reduction formulas can be expresses in sin() / cos() alone. So one scale is sufficient.
    They cannot be expressed by tan() / cot() alone. ( At least I have not seen such a formulation yet.
    If anyone did PLEASE send them to me! ) So we will need combinations of tan() / cot()
    and sin() / cos() i.e. at least two scales as for instance on the Bygrave.

    Consequently, even if we do not need "1mm for 1 arcmin"  on the sin() / cos() in such a
    combination for an accurate end result the total lengths of two scales might come
    close to the length of a single hi-res sin() / cos() scale.

    As I mentioned before, though, a Fuller version with 1 or 2 scales and with
    "1mm for 1 arcmin" scales will be quite a bit larger than the Bygrave as is we know it.
    But only a Bygrave with a "1mm for 1 arcmin" resolution  would be a truly fair comparison.

    I am attracted to the inherent simplicity of the Fuller, both in concept and construction.
    My wish is to find a method of construction of it that fits the mechanical capabilities
    of a lot of CelNav aficionados even if it would be bigger than the Bygrave.
    The Bygrave will always have its own fans.



    PS: Your attachments just arrived - thx!

    On Sun, Jun 8, 2014 at 11:11 PM, Francis Upchurch <NoReply_Upchurch@fer3.com> wrote:


    not sure if attachments got through?

    Am I doing something wrong?


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