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I've changed the threadname from "the repeating circle" to "the repeating
reflecting circle". This is because there were other repeating circles, not
intended for use on shipboard, that therefore didn't require the familiar
two-mirror arrangement, but instead were fitted with two telescopes. They
were used mainly for surveying.

Alex Eremenko wrote-
>
>I checked the Chauvenet volume again from
>my library and I am ready to discuss your question.
>I agree with what you say, there is indeed
>some prohibited range of angles for "cross observations",
>like in Fig. 28.

Thank you, Alex. That increases my confidence, about that prohibited range
of angles, when making "cross observations", of depression rather than
elevation, relative to the direction of the telescope.
>
>I also looked at the paper
>"On an improved Reflecting Circle" by Mendoza Rios
>(Phil. Trans, June 4, 1801) which has much better
>pictures than Chauvenet. (Besides schematic diagrams,
>he has "real life" pictures of his instrument,
>they are of better quality than photos:-)
>Mendoza's
>description
>coincides with that of Chauvenet. In particular
>he has an exact counterpart of Fig 28.
>
>The pictures in Mendoza suggest however, that the range
>of prohibited angles conststs of rather small angles.
>(The line corresponding to EB in Fig 28 is much closer
>to the center in Mendoza pictures, and the mirror m is
>very small).
>
>Now I conjecture that the prohibited range is somewhere
>between 5 to 10 degrees, and such angles are rarely used
>both in altutudes and in lunar distances, for well known reasons.
>
>If nevertheless it is necessary to measure such angles,
>this also can be done by using Meyer's original procedure,
>where only configurations like Fig 29 are involved.
>
>This should not create much inconvenience in practice.
>Mendoza calls the method described on p 120 of Chauvenet
>the "Borda method".


Today I've had a look, in the library, at Borda's booklet, "Description et
Usage d'une Cercle ..." in the library. My French is very halting, but it
wasn't possible to pick out, in a quick scan, any mention of a range of
angles-of-depression, in which the Borda method couldn't apply because the
light path was blocked by the index mirror.

Borda's own diagrams seem exactly the same as those in Chauvenet, which
have probably been copied from Borda.

I haven't yet read the Mendoza paper (but will soon). In that geometry,
Alex reports that the angle at which light is blocked is from 5 to 10
degrees. In the Borda case, however, it looks more like 20 to 25 degrees or
a bit more (at a guess; I didn't take a protractor). Alex correctly states
that these are not angles that are commomly used for lunar distances: also,
at angles where observations by the Borda method are blocked, it's always
possible to revert to the original Mayer procedure. This requires twice as
many observations for a similar result, but otherwise is equally valid..

>On another subject we discussed last fall:
>notice that Chauvenet mentions the possibility of
>using a reflecting circle as a dipmeter, and also mentions
>some specially constructed dipmeters by Troughton and Daussy
>(see p. 127).

Yes, that is interesting. Chauvenet refers to a paper by Simms, "Treatise
on Mathematical Instruments", whick is likely to be in the Bodleian.
Daussy's instrument, described by Chauvenet as a dipmeter, seems to go way
over-the-top (for that purpose) in offering a complete circle for
measurement, when dip anhedral angles are always very nearly 180 degrees.

I have managed to get my hands on a repeating reflecting circle, at the
Museum of the History of Science in Oxford. This was a tiny device, not
much more than 6 inches diameter at a guess, by Lenoir. Unfortunately, it
was missing its eyepiece, and the mirrors had of course lost their shine,
so it wasn't possible to get a decent through-view to check on the light
blockage problem. But by now, with Alex's endorsement, it's fairly clear
that the light blockage must occur at some angles, although it's not a
serious problem (being easy to get round).

George

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