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    Re: The backstaff. was: Re: The Shovell disaster
    From: Michael Daly
    Date: 2007 Nov 03, 14:13 -0400

    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 
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