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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).

Mike


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