NavList:

   

Reply

Wolfgang and Nicolas have provided authoritative answers to some of Brad's
questions about the cross-staff, but there's a bit more to add.

Brad wrote- "From the recommendations of "A Regiment for the Sea", Bourne;
the mariner was advised to align the upper limb of the sun with the upper
edge of the cross staff, but only when above 60 degrees.  Below 60 degrees,
and the mariner is informed to align the center of the sun with the upper
edge."

Not the way I read his tract. Though that text may run without paragraph
separations, there are section-headings in the margins. The previous section
had been headed ""The astrolobe is best to take the heigth of the Sunne at
.60. 70. or .80 degrees in heigth". But then he goes on to discuss what to
do when your staff is not provided with dark glasses, marginal note "How to
preserve your eyes when you touch the Sunne with your crosse staffe and have
no glasses. The diameter of the Sunne is 30. or .31. minuts". No longer,
there, is he referring to the 60-degrees-and-over situation, as I read it.
He is providing a general rule for observing the Sun at any altitude, if you
have no dark glass at the tip of the transom. He recommends that then you
should protect your eyes by covering the complete Sun disc with the top of
the transom, and subtract 15 minutes from the result. Not much chance of
doing that in a rolling vessel!

However, I don't see any great instrumental difficulty about the procedure,
using a dark glass, of putting the Sun's mid-point at the tip of the
transom, by eye estimation. To my mind, anyone should be able to bisect the
Sun disc, by eye, to put its centre within a couple of minutes of the truth;
an error that's small in comparison with the imprecision of a any
cross-staff.

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

Brad and Wolfgang referred to the illustration Brad gave from Apian, at
http://www.fer3.com/arc/imgx/COSMOGRAPHIA-PETRI-APIANI-1574.doc

Unfortunately, the top of that picture was cut off, but as it's rather
interesting. I attach a complete, slightly-different engraving from another
edition.
The picture on the left shows the geometrical construction required to
divide the stick of a cross-staff. The bottom picture shows a portly
observer measuring a lunar distance. He is aligning the centre of the Moon
with the end of the transom; more difficult to estimate than for the Sun,
especially with a crescent Moon.

But look at the top picture, which Wolfgang points out is intended to show
parallax. Or is it?

It shows two observers, 30 degrees apart on the Earth's surface, seeing the
Moon at two different positions in the sky, against the star background,
that are also 30 degrees apart! But that's not how parallax works: if it
was, lunar distance navigation would be simple. Moon parallax can never be
more than a degree-or-so. It's only because the distances of Moon and sky
are so grotesquely distorted that the engraving has come out as it has. Such
a picture would mislead any reader's understanding, and indeed raises the
question as to whether the designer of the engraving, or the author of the
text, really understood the nature of parallax. Of course, at that date Moon
and star distances were not precisely known, but even Ptolemy and Hipparchus
knew much better than that, as did Kepler.

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

Anyway, the whole notion of lunar distance measurement of longitude was then
nonsense, for two reasons. First, the precision of a cross-staff was nowhere
near good enough for a lunar. Second, the predictions of the Moon's motion
were nowhere near good enough either. It was an interesting idea, that could
not be fulfilled until two centuries later.

But no question about it, the cross-staff (or Jacob's staff, ot Balestilla)
was a worthwhile and useful instrument for measuring latitude, widely used
by mariners over several centuries.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

--~--~---------~--~----~------------~-------~--~----~
NavList message boards: www.fer3.com/arc
Or post by email to: NavList@fer3.com
To , email NavList+@fer3.com
-~----------~----~----~----~------~----~------~--~---

File:

   

Reply