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Andres Ruiz wrote:
>
> I am interested in the use of the Circles of reflection _at sea_.
>
> Any information would be welcoming
>

And Nicolas de Hilster replied-
"You might want to check the following works:
P. Ifland "Taking the stars" contains a whole chapter (pp. 135-139) and
many 'loose entries' on circles
W.E. May "A History of Marine Navigation" (p. 145)
C.H. Cotter "A History of the Navigator�s Sextant" (p. 147)

They all credit Johann Tobias Mayer for the reflective circle although
they mention varying dates (1752 - 1758). According to May, Mayer made
his circle to support his tables for lunar observations which he had
made in 1752."

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

Comments from George-

I've taken a particular interest in Mayer and his reflacting circle (and in 
his surveying circle also). A translation of Mayer's contribution, in Latin, 
to Maskelyne's "Tables of the Sun and Moon..." has kindly been made for me. 
To that, I have added copious explanatory notes for a modern reader. That 
was, rather half-heartedly, intended for publication, some years ago, but I 
haven't got round to submitting it, as yet. Andres is welcome to a copy, if 
he asks. And if he happens to be a Latin scholar, comments about the 
translation would be appreciated.

Mayer's lunar tables had already been sent to the Board of Longitude, and 
were to be improved later. In the winter of 1754-5, Mayer sent the board 
this account in Latin, with an engraving of how his proposed instrument 
should be constructed, together with a rough wooden model of it. The 
proposal was that the Board would get the real thing constructrd in London, 
and this was indeed done, by Bird, sparing no expense. It was tested at sea 
by Campbell, who seems to have acted as the Admiralty's guru in such 
matters, and who found it too clumsy in use. He recommended, instead, that 
the Hadley reflecting quadrant should be developed into the sextant.

This was the first of the circular instruments, and its principle was 
simple. Its aim was to achieve a higher accuracy in measuring angle than had 
ever been done before; better than an arc-minute, ideally half of that. 
Repeated measurements of lunar distance could do a lot to reduce scatter, 
but in the Hadley quadrant, each time, (nearly) the same bit of the arc was 
used. The big problem with the instruments of the day was hand-dividing the 
arc, and any error in the division of the arc would be the same for each 
such measurement, so wouldn't average out in multiple observations. The 
circle allowed a new bit of the arc to be used each time, and no matter how 
badly it was divided, 360� on the arc always had to correspond to a complete 
circle, so any such systematic errors could average out.

Maskelyne didn't publish this account until long after Mayer's early death. 
Mayer's widow benefited to the tune of �3,000, part of the longitude prize, 
which was presumably awarded more for Mayer's tables of lunar prediction 
than for his rather unsuccessful measuring instrument.

Mayer never saw the completed instrument that Bird had made. Indeed, in the 
whole of his 39-year life, he had never seen the sea; somewhat ironic for a 
man who made great contributions to navigation. He had many varied 
contributions to astronomy and to surveying, of which details can be found 
in the 1980 biography "Tobias Mayer", by astronomer Eric Forbes.

Reflecting circles were later improved by Borda and by Mendoza. They tended 
to be more popular in continental Europe than in England, because early on, 
the problem of uneven divisions had been solved in England, by the 
introduction of division by machine. I've read an account in English, by 
Mendoza about his improved circle, with a beautiful engravin, but can't now 
lay hands on it.

On the attachment that Anres provided (Borda, at a guess) the mirror angles 
and ray paths do not appear to make sence.

There's a paper "Angle measurements with the Borda repeating circle", by 
Suzanne Debarbat, in Bulletin no 94 of the Scientic Instrument Society, 
September 2007. I need hardly add that I don't agree with every word.

George.




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