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Thanks to Frank for his further explanation of the Mendoza proposal for
calibrating sextant angles, in such a way that even I can follow it (this
time). Though I am still of the opinion that it would be a difficult matter
to find a suitable location for putting it into practice.

I wonder if, at last, we might have stumbled on the true purpose behind
Stonehenge; as a National Calibration Facility for megalithic sextants...

Frank referred to Mendoza's "Tables for Facilitating the Calculations of
Nautical Astronomy" published in 1801. I have a copy of another Mendoza
paper, from that same year, "On an improved Reflecting Circle", page 363 of
Phil. Trans., read June 4 1801.

In that paper, the English language is quite flawless, so Mendoza had picked
it up well, or benefitted from a good editor. By that date, he was well into
the scientific Establishment, having been elected FRS.

Clive Sutherland has kindly provided me with a transcribed copy of that
paper, with its beautiful engravings of his repeating circle. In my view,
such engravings are art-objects in their own right, in addition to their
techical content. I recommend that paper as well worth reading.

I have long had an interest in repeating circles, which were intended to
overcome the deficiencies in hand-division of arcs, by allowing the same arc
to be remeasured again and again, and summed automatically, each time using
a new segment of the scale, adjacent to the previous one. That allowed any
irregularity in the division to be averaged out, though by Mendoza's date,
engine-division had minimised those irregularities. Mendoza reviews the
principle of Mayer's original invention, of Borda's adaptation, which
doubled the rate at which angles were accumulated, and his own development,
which doubled it again.

One innovation was a new type of Vernier scale, for reading out the angle
against a circular ring, which was divided all around in whole degrees, 0 to
360. The Vernier, instead of being a short segment a few degrees wide, as
normal, was instead another complete circle, placed within the main circle
and in contact, uniformly divided in a rather similar way to the first one,
but this time into 361 divisions rather than 360, and marked as 0 to 59
minutes, split into sixths of a minute, with one extra sixth of a minute
thrown in, where its head met its tail. I haven't seen an arrangement like
that elsewhere.

As I see it, that spread-out Vernier didn't offer any advantage in reading
accuracy, over the ordinary short Vernier segment. You were still restricted
to the precision with which you could estimate that two marks were aligned,
or were not. Unlikely though it may seem, it was a labour-saving device, in
the dividing of the main scale. For the same accuracy, if the Vernier had
been restricted to a segment subtending only 10 "true" degrees, and
therefore its sixth-minute markings being far closer together, the markings
all around the main scale would also have to be correspondingly closer
together. That would add enormously to the labour of dividing such a long
arc, especially if hand-division was contemplated, and would have added to
the clutter. Mendoza's alternative Vernier seems particularly clear and easy
to read. The difficulty must have been in precisely dividing that Vernier
ring into 361 parts rather than 360, and I wonder how that job was done.

By the way, I refer above to "true" degrees, because Mendoza's circle was
divided into 360 degrees, as was Borda's, and also Bird's brass version of
Mayer's. Not like Mayer's original prototype, which went 0 to 720 around the
circle; with two marked degrees for the price of one real one. That, just as
in the conventional sextant, allowed for the doubling of the reflection
angle as the index mirror tilted.

Oh dear, I seem to have strayed way off the original topic. But Mendoza was
certainly an interesting character.

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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