NavList:

Hi George,

Thanks for bringing a most interesting viewpoint on Lunars to our attention. Although again probably past the prime era of the method, it reinforces my often stated opinion that, given more time, innovation, and practice, it would have been significantly perfected in its accuracy and consistency.

I too have some difficulty in deciphering the E/W and W/E notation, but assume that it may refer to sextant position in observing, i.e., with the instrument right side up and then upside down so as to measure the distance from both directions, which was contrary to generally accepted practice at the time.

We are also not advised as to whether or not the Captain had access to the newly calculated Lunar Tables which came out about the time of the published observations – I know only that the American Almanac first contained the new tables in 1855, but that does not necessarily mean that they might not have been available elsewhere before that date. Unfortunately, both officers allow to having discarded sights; the question here obtains to why they were considered poor, as opposed to there just not agreeing with the premises proposed in the article, which latter circumstance would go directly to the matter of consistency. The chronometer error had been established at Madras and, but for apparent heavy weather experienced in rounding the Cape of Good Hope, could have again been established via the Lloyd’s Signal Station then there maintained.  I certainly suspect that they had a pretty good idea of both the CE and its reliability – sufficiently so to reject any error completely out of the ballpark, especially as they had other chronometers for comparison. Chauvenet, at about this time, as I recall had some rather earthy remarks regarding Lunars and CE determined therefrom which, as I recall, basically advised that if the determined error agrees with that carried forward, fin, if not, forget it.

I do not question your often stated accuracy of LD observations to only within 1’ of arc when using the instruments available at inception of the method, i.e. the late 1700’s, however, by the 1850’s much improved instruments were available and accuracies to within 10” of arc have been opined by writers of that era. In my opinion, for what it may be worth, an LD error of 1” of arc, by an experienced observer using a well-calibrated modern instrument would be enormous – no so, however, to quickly state, in an altitude measured on a questionable sea horizon. My last full, single observer, LD, worked up on July 27, 2007 (Greenwich date), in a known Longitude, cleared by Borda’s Method, using 6-place Logarithms, with careful attention to the 2^nd Correction, produced results to within 3-seconds of the true GMT; this result was posted on this List at the time.

Regards,

Henry

From: George Huxtable <george@hux.me.uk>
Subject: [NavList 8192] Re: How Many Chronometers?
To: NavList@fer3.com
Date: Friday, May 8, 2009, 9:40 AM

Paul Hirose pointed us to an  interesting paper in the monthly notices of
the royal astronomical society, 1853, at

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?journal=MNRAS&year=%3f%3f%3f%3f&volume=..14&letter=.&db_key=PRE&page_ind=19&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES&high=4899d32e1929742

This was "On rating chronometers by lunars", by H Toynbee, commander of the
Gloriana, East Indiaman.. It had a few surprises, for me.

It argued (contrary to an opinion I had recentltly expressed in a posting,
that lunars were insufficiently accurate to use for rating chronometers)
that lunars, taken at regular fortnightly intervals, provided useful
chronometer information. Anyone interested in this matter will find his
figures worth examining.

The paper referred only to a single chronometer on board, made by Dent.
There seem to have been others, though, because he writes, at the end of the
voyage, "the chronometers were taken by the maker", but for some reason
other chronometers were not discussed. East India Company vessels were
usually regarded as being lavishly fitted-out, and as late as 1853, I would
expect a set-of-three, as we've discussed before.

She was making a return passage from Melbourne, via Madras and St Helena.
She had taken all of two months from Madras to St Helena, which I would have
thought to be slow, even by East India Company standards. Their ships had a
reputation of being safe and reliable, but ponderous and slow.

The approach to St Helena is of interest. "We hove-to at 4am, July 12th, and
at daybreak found the island bearing north-west 10 miles, as expected.".
Shows some confidence in their astro navigation, doesn't it? That they press
on in the dark towards a rocky steep-to island until they reckon to be
within 10 miles, and only then do they heave-to. Would we be as bold, I
wonder?

It's interesting that St Helena had its own time-ball, in 1853, which ships
would use to check their times. That would depend on knowing a precise
longitude for the island. I wonder how that had been ascertained? Jupiter
satellites, perhaps, or Moon occultations? Might it have come from Halley's
observations there, 170 years before?

But I'm puzzled by their tables of numbers, and I wonder if Paul Hirose, or
anyone else, can throw light on it. The observations appear to have been
taken at dates in 1853 of May 14, May 30, June 12, and so on, at fortnightly
intervals when the Sun was in quadrature with the Moon; the best times for
Sun Lunars, at first or last quarter. And yet, for each of these dates, two
values of deduced clock error are shown, each against one or other of the
following labels-
either
1. (Sun symbol) E. (Moon symbol) or else
2. (Sun symbol) W. (Moon symbol)

where what I take to be the Sun symbol is a circle with a dot in the centre,
and the Moon symbol is a crescent. In alternate fortnights, as at May 14th,
line 1 is above line 2, and vice versa on May 30th etc.

However, over a particular quadrature, the Sun can be only East or West of
the Moon, not both. On May 14th, it was East. On the 30th, West. So what are
those two lines of data? What am I misunderstanding?

Of course, if star lunars were being observed, they could be either East or
West of the Moon, but that's not what those symbols indicate, as I see it.
And Toynbee's words "In several instances lunars were obtained on only one
day of the sun and moon's continuing in distance" imply to me that he was
taking Sun, not star, lunars: otherwise, those words "in distance" wouldn't
apply.

I'm also puzzled about his numbers for "maker's error" near the foot of his
table, and somewhat suspicious about his comment that "the chronometers were
taken by the maker on the 14th, and the daily rate gradually decreased to
6.5s during the first five days."

If anyone else takes a look at this interesting paper, I would be pleased to
see any comments.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.




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