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    Re: The backstaff. was: Re: The Shovell disaster
    From: Nicolàs de Hilster
    Date: 2007 Nov 03, 14:42 +0100

    George Huxtable wrote:
    > Relevant to Nicolas'well-informed views about the backstaff is a recent 
    > article by Jim Bennett, "Catadioptrics and commerce in eighteenth-century 
    > London", in History of Science, vol xliv, 2006, pages 247-277. I have it as 
    > a .pdf file of about a megabyte, and can post it to the list, or send it 
    > backstage, as requested. "Catadioptrics" is just a complicated term for 
    > mirror-instruments (a category that excludes the backstaff, to be pedantic).
    This is indeed a must-have-read-article for those interested in these 
    early developments, even though I do not share the same opinion 
    throughout the text.
    Then George gave us a longish extract about the backstaff, from 
    Bennett's article:
    > It is often presented as a development of the cross-staff, simply 
    > adapted to avoid looking directly at the sun, but that is an inadequate 
    > account of quite a sophisticated instrument that is ingeniously tailored to 
    > its very singular purpose.
    Well, I wonder if Bennet took a look at the full development, from 
    Master Hood (1590, first shadow casting staff), to Thomas Harriot (1594, 
    first backstaffs, three of them to be precise), John Davis (1595, two 
    different backstaffs) and Dutch backstaff instruments like the hoekboog 
    (1623, also known in English as the 'double triangle') and the 
    demi-cross (1625). These instruments (their dates are first publications 
    on them) do tell the story all together and show that the Davis Quadrant 
    was a development originating from the cross-staff. Somewhere next year 
    I expect to publish an article on this development.
    > In all cases the 30-degree arc carries a transversal scale of the type used 
    > by Tycho Brahe, adapted to the backstaff from the fi rst 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.
    > The basic scale is generally divided to 5 minutes, and 
    > transversals across the 10-minute divisions mean that the fi nal reading is 
    > to a minute of arc. 
    Early textbooks show a wide variety of possible divisions of the 
    diagonal scale with six, ten or twelve concentric circles and 10 or 20 
    minute intervals. The oldest surviving Davis Quadrant (1661) has 20 
    minute divisions and 10 concentric circle, so a 2 minute division.
    > What at fi rst seems curious is that these 5-degree divisions do 
    > not quite coincide with the corresponding divisions on the face of the arc, 
    > but are slightly offset. What might at fi rst glance look like carelessness 
    > is clearly deliberate, since it occurs on all instruments. It is, in fact, 
    > an attempt to correct for the fact that the altitude required is that of the 
    > centre of the sun, while the limit of the shadow depends on the edge of the 
    > solar disc. The offsetting of the scale is an attempt to correct for the 
    > semi-diameter of the sun - an inadequate attempt, because of the shading in 
    > the penumbra, but again an indication of the concerns and ambitions of the 
    > makers.
    There are also examples that have either both lines on them or only the 
    'real' 5 or 10 degree divisions rather than the offsetted ones.
    > =================== end of quote
    Then George continued:
    > I differ from the conclusion in his last paragraph, however, that inclusion 
    > of the Flamsteed glass, to throw a focussed image of the Sun on the horizon 
    > vane, made such a correction unnecessary. The lens would image a Sun disc 
    > with sharp edges, instead of the shadow, with penumbra, that occurred 
    > before. But that would be a disc, not a point, still having the angular 
    > diameter of the Sun, 30 minutes or so, and an offset for semidiameter would 
    > be just as necessary as before.
    Depending on the brightness of the sun that disc shows with varying 
    diameters on the horizon vane, or at least this is how the human eye 
    experiences it. The projection of a fully bright sun is that bright that 
    it still hurts the eye and makes you see 'elephants' for at least 15 
    minutes afterwards (and there is no clear edge to be seen as a result of 
    it). So taking an upper or lower limb would only be accurate when the 
    sun was almost completely dimmed by the clouds. It is however more easy 
    to get the centre of the sun using the Flamsteed lens in both conditions.
    Another thing is that in those days it was quite hard to get the focal 
    length 100% right. The W. Garner Davis Quadrant at the NMM has a focal 
    length of 185-190 mm, while the lens sits at a distance of at least 
    195mm from the horizon vane. Even the US$1.50 lenses I use today have 
    this problem by which my replica has a focal length almost 10mm too 
    long, but it does its job properly when aiming for the centre of the sun.
    Although the image of the sun is not projected perpendicular to the 
    horizon vane, but at an angle that depends on the lens vane setting by 
    which it appeares as an ellipse, the ellipsoidal shape of the image does 
    not influence the reading as the lower or upper limb is projected on the 
    line which is at the centre of the arc. The horizon vane has an angle of 
    15 degrees with the main beam of the Davis Quadrant, so any lens vane 
    setting smaller or greater than 50 degrees will make the sun appear as 
    an ellipse.
    > And I wonder about the logic behind making one part of the arc (the 60 
    > degree section) to have a much smaller radius than the other, seeing that 
    > the overall reading was the addition of the two arcs, and both therefore 
    > needed to be set, or read, to similar accuracy.
    The logic was to have a smaller instrument that was less susceptible to 
    the wind. Leaving both arcs with the same radius was an instrument known 
    as the Gunters Bow (I do not recall seeing that one with a lens though). 
    I had that one in my hands in Sweden and it is quite large. The large 
    diameter is necessary to get a large interval on the scale.
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