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    Re: Trombone Kamal Prototype
    From: Frank Reed
    Date: 2009 Jun 5, 15:28 -0700

    Greg, George H. wrote:
    "Greg hasn't (yet) told us at what angle his plastic plate should be held. It 
    doesn't matter (much) for his present small angles, but it will become more 
    important as angles increase. Should it be held vertical, at right angles to 
    the observer's sight-line to the horizon?"
    This is a good point. I have assumed that you're holding the plate 
    perpendicular to the tape measure. Is there some way to guarantee that? In a 
    traditional cross-staff, the design ensured that the cross-piece was very 
    close to perpendicular to the staff.
    And he wrote:
    "So, the dimension that needs to be measured, if the tan formula is going to 
    work, is between the cross-piece (or plastic plate) and the centre of the 
    eyeball. Not a practical proposition, obviously, but what is the best that 
    can be done? There's a notch in the edge of the skull-bone, just close to the 
    side of the eye, which isn't far from a plane drawn through the centre of the 
    eyeball. Just the spot where the user of a cross-staff would press the end of 
    the staff. There was much argument, then, about whether different individuals 
    should shave off a suitable amount from the staff, appropriate to their own 
    eye-socket dimensions."
    This is what I was getting at about not knowing the exact length of the 
    baseline. But rather than try to figure it out theoretically, we today, with 
    our experience with sextants, can treat this as a calibration question 
    comparable to checking index error, or maybe arc error, in a sextant. You 
    measure a series of known angles, possibly with the plate clamped onto a 
    fixed mounting, and then find whatever additional length added to the 
    observed baseline yields minimal error in the observations. You can then hold 
    the end of the tape (or the end of the staff in a cross-staff) wherever you 
    find comfortable, as long as it's repeatable, and then add in that "index 
    correction" distance to every observed baseline.
    And George wrote:
    "in this aspect, the cross-staff wins, hands-down, on convenience, being 
    direct-reading. You read the angle straight off, marked on one of a number of 
    scales, each dependent on the chice made from a range of transoms of varying 
    Once it's calibrated, the angle conversions could be printed up in a small 
    table, one for each of the three horizontal lines. The slide rule would save 
    you an interpolation step if the printed table isn't fine enough.
    Crossing the threads and tangling them up a little, why didn't those 
    Polynesian navigators a thousand years ago ever invent the cross-staff? Is it 
    possible that the "dead reckoning" cues in the tropical Pacific, things like 
    bio-luminescence, are so much better there than in the Atlantic that 
    Polynesian navigators simply never had any practical reason to go beyond the 
    tools of dead reckoning (and possibly basic zenith stars)?
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