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The modern Moon culmination hobbyist at least has the advantage of
accurate ephemerides. In the 19th century, culminations of the Moon were
one of the principal longitude methods on land. But the complexity of
the lunar orbit gave much trouble. The 1854 annual report of the US
Coast Survey has a "Report on Moon Culminations" by Prof Benjamin Pierce
of Harvard U:

"The most serious difficulty in the reduction of moon culminations
arises from the acknowledged errors of the lunar ephemerides, which
often exceed twenty seconds of arc. The empirical method sometimes
adopted of correcting the lunar ephemeris by assuming the mean of all
the observed errors of any period as the constant error for that period,
cannot be safely employed for a longer period than two or three days,
for the variations of the error are so great, that in a week they often
change by twenty of thirty seconds of arc.

Furthermore, he says, "If the law of error embodied in the method of
least squares were the sole law to which human error is subject, it
would happen that by a sufficient accumulation of observations any
imagined degree of accuracy would be attainable. I believe that the
careful examination of observations reveals another law of error. The
small errors which are beyond the limits of human perception, are not
distributed according to the mode recognized by the method of least
squares. On this account there is in every species of observation an
ultimate limit of accuracy beyond which no mass of accumulated
observations can ever penetrate. A wise observer, when he perceives that
he is approaching this limit, will apply his powers to improving the
methods, rather than to increasing the number of observations.

"The ultimate limit of accuracy of the longitude of a place derived from
moon culminations, can be so nearly attained by the observations of a
few years, that a longer continuance must be censured as a waste of
time. With its great liability to error, the method of moon culminations
cannot come into competition with other methods of determining
longitude, which are susceptible of ten times greater accuracy. Such a
degree of accuracy seems to be quite possible of attainment between
Europe and America by means of chronometric expeditions."

(from the 1854 annual report, p. 213 of the PDF)

https://libguides.library.noaa.gov/coast-geodetic-survey/annual-reports

The report of 1867 (p 70 of the PDF) includes a longitude determination
with the new cable across the Atlantic and compares the results of moon
culminations and chronometer expeditions.

Taking the mean of each method, and applying the 0.06 s correction
mentioned in the document, and omitting the hours and minutes, I get
these values (seconds of time) for the Greenwich to Washington longitude
difference:

10.1 culminations
12.3 chronometers
12.4 telegraph

A more refined telegraphic value is in the report of 1874 (p 201): 12.1 s.

I was amazed by the number of chronometers in the expeditions mentioned
in the 1854 report. Did they really transport 175 chronometers at a
time? I did a quick search for some details but found nothing. Today I
doubt that in the whole world there are 175 mechanical chronometers
suitable for such a project, i.e., in good condition with rate records.

My unsuccessful search did find some interesting hits:

https://www.usni.org/magazines/proceedings/1881/december/coefficient-safety-navigation-concluded


https://www.boatinternational.com/luxury-yacht-life/lifestyle/beautiful-marine-chronometers-for-your-superyacht--26013

I didn't realize anyone was still manufacturing mechanical chronometers.
However, the Wempe web page was astounding in its lack of information.
Maybe people willing to pay $40,000 for a chronometer are looking for a
status symbol and don't care about "gearhead" stuff.

--
Paul Hirose
sofajpl.com

   

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