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I've been looking at Chauvenet a bit further, and it looks as though he
deals, fully, with the terms for correcting Moon parallax that depend on
Moon azimuth; terms that I have ignored, but which, under some circumstances
Kent Nordstrom considers worth correcting for. Indeed, he may be right.

In section 94 he shows an example for correcting the Moon's true
(geocentric) altitude and azimuth for parallax, to produce apparent altitude
and azimuth, and in section 95, the converse (which is what's needed in for
correcting a lunar). And to my surprise, in that example (in no way
extreme), those corrections appear to differ by as much as 15" (in altitude)
and 10" (in azimuth) from those for a spherical Earth. In section 95 he
shows a different way to arrive at the same result. I haven't tried to get
to the bottom of the reasoning involved, which is rather heavy going, but
Kent may find it instructive, in his quest for ultimate precision.

That may have interesting implications. In the normal clearing process for
lunar distances, which uses the formula; see [5530]

D = arc cos[(cos d - sin s sin m) cos S cos M /(cos s cos m) +sin S sin M]

or some variant of it, the assumption is made that correction for parallax,
as for refraction, is only in the vertical plane, and has no component that
alters the Moon's azimuth. So when Earth oblateness affects not only the
altitude, but also the azimuth, that assumption fails; or at least, further
correction is called for.

Chauvenet deals with that by two alternative methods for clearing lunars, in
sections 248 and 249, which I have made no attempt to follow in any detail.
Like everything else that he touches, it's all treated with the utmost
rigour.

It should be appreciated that although Chauvenet is to some extent
addressing mariners (and had previously been in charge of teaching
navigation to US Navy students) he was an astronomer, and mainly writing for
astronomers and surveyors. He wrote in an era when many of them remained out
of reach of the electric telegraph, needed to obtain time to a much higher
precision than mariners did, and had available more precise instruments,
which could be firmly planted on the ground. So much of the detailed stuff
is over-elaborate for marine navigators, but may be just the sort of
material that appeals to Kent Nordstrom. For me, Chauvenet comes over best
in small doses.

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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