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    Bissaker Sliderule
    From: Nicolàs de Hilster
    Date: 2008 Mar 31, 16:05 +0200

    Dear Group,
    
    I cross-post this message to Rete and NavList, so some of you will get 
    this message twice.
    
    Last January I was contacted by Werner Rudowski with questions about the 
    Bissaker sliderule. Rudowski is currently writing an article about the 
    Bissaker sliderule. Robert Bissaker was a Mathematical Instrument Maker 
    who worked between 1642 and 1664 and created this sliderule, which is on 
    display at the Science Museum in London, in 1654.
    
    Rudowski contacted me with several questions, one of which concerned one 
    of the scales: This scale, the so called 'm-scale' (after a description 
    by Baxandall from 1914), has a, yet unknown, purpose. The divisions have 
    been measured using a modern metric ruler (which I post here with his 
    permission):
    
    degrees on m-scale
        90  85  80  75  70  65  60  55  50  45  40  35  30  28  26  24  22
    mm  0   10  20  32.5    46  61.5    80  99  124     154     189.5   -
        -
        331     366     406     454
    
    
    The origin (90 degree mark) is located at 111mm from the start of the 
    sliderule.
    
     From these values I was able to reconstruct the following two formulae:
    
    1) 154/(TAN(degrees)^1.2)
    2) 154/SQRT(2) * ((1/TAN(degrees/2))-1)
    
    I attached an image with both formulae in a more clearer notation. The 
    constant 154 was taken from the 45 degree measurement and might be 
    slightly different.
    
    Although the first formula gives a better fit, it seems to me that the 
    second is more likely as I am not sure whether or not they were able to 
    solve the power 1.2 in those days.
    
    Would any of you be able to explain the purpose of this scale based on 
    the figures and formulae given? The part 1/TAN(degrees/2) of the second 
    formula is known from stereographic projections, so perhaps there is a 
    link?
    
    on behalf of Werner Rudowski
    best regards,
    
    Nicolàs de Hilster
    
    
    
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