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    Re: The Shovell disaster
    From: Nicolàs de Hilster
    Date: 2007 Nov 02, 16:24 +0100

    In the meanwhile I was asked the following question off-list:
    > Do you have any idea as to why all 7 backstaffs  produced  
    > "under-readings" of the sun's altitude on 1st November 1707?  If this 
    > was a common fault, why no allowances?
    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.
    Nicolàs de Hilster wrote:
    > Ted Gerrard wrote:
    >> *
    >> What was surprising was that the spread across the fleet's 7 backstaff 
    >> noon sights was biased entirely to the south of the fleet's true 
    >> position, the best of the bunch being some 12 miles in error. Had the 
    >> spread straddled the true latitude the disaster just might have been 
    >> averted.
    >> *
    > Being 1707 we may assume that the backstaffs were Davis' Quadrants.
    > In Philosophical transactions, volume 37, num 423, page 277 (1731-32) we 
    > can find the following information on the accuracy of the Davis' 
    > quadrant, compared to the Elton's Quadrant (a Davis' Quadrant with 
    > artificial horizon):
    >> There was at the same time laid before the Society,
    >> " An Extract made by Mr. Elton of Observations of
    >> " the Latitude from the Journal of Capt. Walter
    >> " Hoxton, Commander of the Ship Baltimore from
    >> " the River of Thames to Maryland on the Conti-
    >> " nent of America, by Davis's (or the common)
    >> " Quadrant with the Horizon, and by Mr. Elton's
    >> " (a new invented Quadrant) without the Horizon,
    >> " Anno Dom. 1730."
    >> From this Extract it is observable, that in mode-
    >> rate Weather the Difference of the Observations, made
    >> by the two Sorts of Quadrants, was commonly no
    >> more than 1'; with strong Galse and large Sea 5';
    >> in fair Weather; in hard Squalls; the Sea running
    >> high, 6'; in easy Gales 9'; in fir Weather and a
    >> large Swell 16'; once in smooth Water 16'; and the
    >> greatest Difference of all was, with fresh Gales, 21':
    >> And this Difference was constantly found to give the
    >> Latitude more Northerly by Mr. Elton's Quadrant
    >> than by Davis's;...
    > Furthermorein his book 'A History of Marine Navigation' W.E. May states 
    > (page 23, 2nd paragraph) that 'It was generally considered that even the 
    > Davis back-staff was not accurate within six minutes.". In the 
    > accompanying footnote it can be read that "Walter Maitland, in 'An Essay 
    > towards the Improvement of Navigation' (c. 1750), says twelve minutes".
    > Finally tests done by me using a Davis Quadrant on shore showed that 
    > getting a proper altitude is far from easy. A graph is included in this 
    > mail showing that even on Terra Firma errors over 20' are easily 
    > achieved (the graph can also be found on my website: 
    > http://www.dehilster.info/instrumenten/spiegelboog/images/results.jpg). 
    > We took several lower limbs and one upper limb to see whether the error 
    > was due to instrument errors or due to observation errors. It is clear 
    > that the latter was the case.
    > As from 1731 it was no longer allowed to use the Davis Quadrant on board 
    > of the Dutch VOC vessels, simply because of its inaccuracy. The octant 
    > was not allowed on board of the VOC vessels until 1748, so they had to 
    > rely on the cross-staff and spiegelboog during that period (although it 
    > is known that octants have been in use during this period as well).
    > Nicolàs
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