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As detailed questions about bacstaffs are now arising, I've tried changing
the threadname.

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).

Bennett is Director of the Oxford Museum for the History of Science, and
author of "The Divided Circle", and knows his subject rather well.

=====================

Attached is a picture of a backstaff, fig. 1 in the article.

Backstaff, signed "E. BLOW / LONDON Fecit / in Plow Alley at Vnion Staires /
Wapping. Mayye 10. 1736". Unusually, all the original vanes have survived,
as has the 'Flamsteed glass', shown detached. Whipple Museum of the History
of Science, Cambridge.

======================

Here is a longish extract, about the backstaff, from Bennett's article..

The basic function of the backstaff was to measure the noon altitude of the
sun on board ship, and from this reading, adjusting for the solar
declination for the date in question (usually discovered from a table), the
seaman could fi nd his latitude. To judge from surviving numbers, it is
clear that the instruments were widely used in the eighteenth century,
particularly among English seamen, and elsewhere the backstaff was sometimes
referred to as 'the English quadrant'.  Perhaps because of its familiarity,
it is rather taken for granted today, an attitude that may be reinforced by
examples being almost always made of wood - indicative of a relatively
inexpensive instrument - and having a robust character suited to shipboard
life. 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.

Essentially it is an altitude quadrant, held vertically and measuring
between the horizon and the zenith, but since the upper target is the sun,
it uses a shadow rather than a direct sight. The observer aligns two vanes
(the 'sight vane', where he places his eye, and the more distant 'horizon
vane') with the horizon and arranges for the shadow of a third (the 'shadow
vane') to fall on the horizon vane, when the angle subtended at the horizon
vane is the solar altitude. One ingenious feature is that the quadrant arc
is divided into two sections, one of which spans a smaller angle but is
constructed to a much larger radius. The 60-degree arc, as it is often
called (in fact it usually covers 65 degrees), is used only for setting the
shadow vane to an angle perhaps 10 to 20 degrees less that the expected
altitude measurement. Since it is used only for setting and not for
measuring, it need be divided only to single degrees, or even only to 5
degrees. The horizon vane is at the common centre of the two arcs and the
sight vane moves on the 30-degree arc (usually actually covering 25
degrees). This arc has a much larger radius, so the length of the arc is
much longer and it can be divided much more finely than the 60-degree arc.
Through the separation of the arcs, a magnification of the scale has been
achieved without making the instrument impossibly large.

Having set the shadow vane on the 60-degree arc, and keeping his back to the
sun, the backstaff user sights the horizon as noon approaches and keeps the
shadow cast by the shadow vane on the horizon vane. He will have to keep
moving the sight vane down the 30-degree arc until, once noon has passed, he
needs to move it back to continue. However, leaving the sight vane at its
maximum position, he adds together the set angle on the 60-degree arc and
the measured angle on the 30-degree arc to fi nd the meridian altitude of
the sun.

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. 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. This level of accuracy could scarcely be achieved in
practice, given the nature of the observation, involving shadows and a
moving ship, but it does indicate the ambition of the makers and their
concern to demonstrate their specialist knowledge and skill.

This is indicated also by a common feature of the scales on the 60-degree
arcs of backstaves. Graduations on the face of the wooden arc are to single
degrees, while a scale on the rim is marked to 5 degrees. A 5-degree
interval is suffi cient, since the shadow vane is merely set to a reading on
this scale. 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.

One final sophistication is the possible replacement of the shadow vane by a
lens whose focal length is the radius of the 60-degree arc. This accessory,
known as a 'Flamsteed glass', was useful in hazy conditions, when sunlight
was weak, and of course its use avoided any concern about correcting for the
semi-diameter of the sun. We do not tend to see this lens as a very
noteworthy example of the additional of an optical component to a
mathematical instrument, and perhaps we are right in that respect, but
Robert Hooke thought it important enough to feel aggrieved at not receiving
credit for what he regarded as his invention.2 Of course, Hooke was central
to the much more extensive project of the application of telescopic sights
to astronomical measuring instruments.

=================== end of quote

You well see, from his next-to-last paragraph, that at least some (perhaps
all according to Bennett) makers were concious of the necessity to make an
offset for the semidiameter of the Sun.

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.

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.

Nicolas de Hilster's observations, based on his own experience in
constructing and using such an instrument (and many other early instruments)
are most relevant.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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