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Dear George,

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.

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".

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).

Alex.

   

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