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    Re: The Bygrave Slide Rule
    From: Brad Morris
    Date: 2009 May 28, 17:20 -0700

    Gentlemen
    
    On my MHR-1, the outer scale increases from left to right, from 0 deg to 89 
    deg 40 min and then REVERSES direction and increases from right to left from 
    90 deg 20 min to 180 deg.
    
    On my MHR-1, the inner scale increases from left to right, from 0 deg 20 min 
    to 89 deg 40 min and then REVERSES direction and increases from right to left 
    from 90 deg 20 min to 179 deg 40 min.
    
    This permits large LHA or T angles.  In fact, the Cylindrical Bygrave can 
    compute to lower meridian crossings!  At high latitudes, a celestial object 
    can move with the earths rotation and still be visible throughout the 24 hour 
    period.  The Cylindrical Bygrave can compute that circuit.  I am not sure if 
    the Flat Bygrave has continued the high angle labeling, although there is no 
    inherent limitation as it can always be added.
    
    Sample
    Declination S 75 deg 32 min
    t            145 deg 16 min
    Lat         S 67 deg 33 min
    Colat         22 deg 27 min
    X            101 deg 58 min
    Y            124 deg 25 min because same name, we added!
    Az           165 deg 44 min
    h             54 deg 44 min
    
    This may have impact on the formulation of the scales discussion.  For the 
    outer scale: Log(abs(cos)) is symmetric about 90 degrees, as is the secant, 
    log(abs(1/cos)).  For the inner scale, log(abs(tan)) is symmetric about 90 
    degrees, as is the cotangent, log(abs(1/tan)).  If the absolute value is not 
    obtained, then the symmetry is lost, as many of the trig values become 
    negative.
    
    Best Regards
    Brad 
    
      
    
    
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