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I wrote-

| > Halving an
| > angle with the compass is easy,

and Alex replied-

| Really??
| Would you explain me just how to halve a given angle
| with a compass? (No ruler/straightedge!!  The same
| famous Bird who said: there is NO WAY to draw a straight line
| between two given points. And this is true.)
| Is this taught in the British schools?

All right. Lets assume we have a precisely-drawn arc, struck from a centre,
more than 60 degrees long, with some arbitrary radius, defined by the
setting of a beam compass.

Mark an arbitrary starting point near one end of that arc. Without changing
the setting of the beam compass, strike a short arc, centred at that
starting point. Where it crosses the main arc is at exactly 60 degrees along
that arc. That wasn't specified in Alex's challenge, but it gives us an arc
we are going to halve, by a method we can use to halve any arc, not just one
of 60 degrees.

Set the beam compass to be, by eye, slightly more than the half-arc we plan
to mark off, and with it, strike a trial arc from both the start point and
the 60-degree end point. Those arcs should intersect at two points. Joining
those points by a straight line, that line crosses our 60-degree arc exactly
at its mid point. That's the way it would have been taught in British
schools, 60 years ago.

What the supposed problem is, in joining two points by a straight line, that
Alex quotes from Bird, I don't understand. But if he objects to that
straight line for some reason, then let the radius of the beam compass be
reduced a bit, and a new pair of arcs drawn from the start and end points,
to cross closer together than before. Adjust the radius still further, by a
trial-and-error process, until the two arcs just cross where they cross the
60-degree arc, at the one point. That marks the exact half-angle, in this
case 30 degrees from either end. In practice, the trial arcs would be drawn
so lightly as to be almost invisible, and only the final mid point would be
shown in bold.

Will that do, Alex?

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

In Navlist 2634, Alex wrote-

"So I study the question myself using the information available
to me: I examine certificates of the sextants sold on e-bay:-)
Unfortunately, they did not supply certificates in the first
half of the XIX century, so I can only study recent history of
division.

Interestingly, many mid XX century sextants have quite large
corrections in their certificates (30" to 45").
Which means of course that the manufactures simply DO NOT CARE
to make a perfect arc."

Well, I don't regard non-zero errors on the calibration certificate as
anything much to worry about, as long as there was a smooth variation
between them (though it would be hard to know for sure that that was the
case). It's an easy matter to guess an adjustment to apply, based on the
certificate that's pasted into the box.

But it's an interesting question as to how precise the test instrument (at
Kew, say) really was. Imagine that it got known, say, that the collimator to
test for a nominal  60 degrees happened to positioned 20 seconds high. Might
a sextant maker be tempted, then,  to make all the instruments he sent to
Kew to read, correspondingly, 20 seconds high at 60 degrees, so that their
certificates came out spot-on? Just a thought....

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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