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    Re: The backstaff. was: Re: The Shovell disaster
    From: Nicol�s de Hilster
    Date: 2007 Nov 03, 22:49 +0100

    Michael Daly wrote:
    > Nicol�s de Hilster wrote:
    >> George Huxtable wrote:
    >>> In all cases the 30-degree arc carries a transversal scale of the type used 
    >>> by Tycho Brahe, adapted to the backstaff from the first half of the 
    >>> seventeenth century. 
    >  >
    >> 'In all cases' means in 'all surviving instruments with 30 degree arcs'. 
    >> Not only are there two types of surviving Davis Quadrants, those with 25 
    >> degree arcs and those with 30 degree arcs, but through my research I 
    >> found proof that there was a time that the Davis Quadrant (if we may 
    >> call it that way already) did not have diagonal scales at all. The 
    >> earlier instruments were divided in a similar way as the hoekboog in 
    >> half or quarter degrees. The introduction of the diagonal scales was 
    >> most probably not before 1650.
    > I'd be interested in knowing whether the transversals were always linear 
    > or whether they (in later instruments) used circular transversals.  The 
    > former could be used on a circular arc with some error (error decreasing 
    > with increasing arc radius).  Circular arcs require circular 
    > transversals to be accurate.  However, it was difficult to figure out 
    > how to construct them (one technique was determined by Philippe de La 
    > Hire and used by Nicolas Bion) and very tedious to construct (I have 
    > created a diagram of linear transversals on Wikipedia but have yet to 
    > tackle the effort of making a circular transversal diagram - yet I have 
    > the advantage of a CAD program, not a sheet of brass with dividers and 
    > compasses).
    Hmmmm, I'm not sure what you mean with the difference between linear 
    transversals and circular transversals regarding the Davis Quadrant. I 
    guess that you mean that the diagonals should be arcs instead of 
    straight lines to be more accurate. The earlier Davis Quadrants did not 
    have any transversals at all, just plain straight forward scales, evenly 
    divided in half or quarter degrees. From about 1650 that changed to the 
    diagonal scales as we know them today. As far as I know these diagonal 
    scales were all made using straight diagonals. I once made a comparison 
    in AutoCAD to see what difference there would be between both methods, 
    but can't remember what the difference was. I'll try to see were I left 
    that and post the results here.
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