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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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