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    The Bygrave Slide rule
    From: UNK
    Date: 2009 May 29, 02:46 -0700

    Brad's point is interesting - he points out that the reversed 90-180 degree 
    markings on both scales show that the scales are logs of abs(tan) and 
    abs(cos) respectively. Maybe this is just a 'kludge' for the annoying fact 
    that logs of negative numbers don't exist. It's left to the user to sort out 
    the signs when using logs to work with mixed-sign numbers.
    
    However, I don't think Brad's point does impact on my postings, since it 
    applies whether or not the scales are 'thought of' as cotan/cos or 
    tan/secant. 
    
    In effect all I am saying is that I found the references to cotangent scales 
    in the papers by Ron and Gary were counter-intuitive, and the alternative 
    tangent/secant interpretation was easier to grasp, so I thought it worth a 
    posting. If no-one else agrees with me then I will go back into my cave.
    
    I can't contribute an answer to Gary's puzzle about the apparent impossibility 
    of using the tangent/cosine method at the equinoxes (this puzzle is not 
    limited to the Bygrave solution). A quick look at the celestial triangle 
    tells me that if the sun is near the equator then the perpendicular from the 
    sun to the observers meridian is also near the equator, so the equation for 
    azimuth simplifies to tan(A)=tan(H)/cos(c), but this may already be what Gary 
    has rejected as not being very pretty. I wondered whether the discarded 
    azimuth in the alternative calculation might be a clue, but this is just 
    equivalent to swapping the observer with the sun. The altitude comes out the 
    same of course, but the discarded 'false' azimuth is then seen to be the 
    azimuth of the observer as seen from the sub-solar point, which isn't very 
    useful, even on March 21st.
    
    regards
    Peter M
     
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