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In NavList 3743 I wrote:

> If you check my graph you will see that depending on whether you observe 
> the upper or lower limb you will have constant errors. The problem with 
> observing the sun using shadows on a Davis' Quadrant is that the shadow 
> is not a sharp line, but a transition zone from bright sunlight to dark 
> shadow with the same angular width as the sun (about 32 arc minutes). 
> Now it is up to the observer to make his pick prim there. So when 
> observing the lower limb one has to observe that part of the transition 
> zone where the shadow begins (so where there is still full sun light), 
> otherwise it is where the shadow ends (so where one has full shadow).
>
> Both spots are difficult to estimate as you can see on attached picture. 
> The horizontal shadow is difficult to see due to the line on the horizon 
> vane, but the shadow of the arc is well visible on the right, giving a 
> good indication of the width of the shadow transition. The lines on the 
> shadow vane are almost half a sun diameter wide and will therefore add 
> to the confusion.
>
> The the intensity of the light on the horizon vane will influence the 
> reading as well. I doubt if the human eye is able to distinguish the 
> first 5% or even 10% of shadow (or sunlight) on that vane. 10% of the 
> total sunlight/shadow is an error of already five arc minutes (see 
> graph). This coincides with the remark in the Philosphical Transactions 
> of the instrument being not better than 6 arc minutes. It also means 
> that using this instrument one cannot but take false readings, unless 
> one knows how to correct for the human factor.
>   

Yesterday I have been out in the field testing several instruments: A 
demi-cross, Master Hood's cross-staff, a cross-staff (used in the Dutch 
fashion) and a Davis Quadrant. Main goal of that exercise was testing 
the demi-cross and Master Hood's cross-staff, but on the go we compared 
the Davis Quadrant with the demi-cross as these two must have been 
competitive instruments in the 17th century. The cross-staff had proven 
itself in previous tests and was also used to compare the other data.

Attached you will find the results of this test. No data is added of 
Master Hood's cross-staff as it would render the graph useless (random 
errors of up to 8 degrees!). During this test we all tried to measure 
the centre of the sun. Again the Davis Quadrant is giving us a much 
higher altitude. When skipping the data from the trial stage (up to 
12:17) an average error is calculated of 10.5 minutes (sd = 5.1 
minutes), but overall the average error was 13.7 minutes (sd = 8.5 
minutes). The largest observed error was no less than 37 minutes, but 
this was due to misalignment in the horizontal plane. After the test I 
checked the instrument for fixed errors, but none was found. Apart from 
that the errors seem to be consistent with a test performed two years 
ago with a different Davis Quadrant.

 From this test it also became clear that the cross-staff and demi-cross 
perform similarly, but giving excellent results (average error 2 arc 
minutes over all data). The Davis Quadrant remains the winner when 
comparing handling, something that can be seen from the amount of data 
collected from it. None of the period instruments tested so far gives a 
better feel and quicker observations. This also explains the popularity 
of the instrument.

Nicolàs







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