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    Re: Patrick O'Brian characters discuss time and longitude
    From: Peter Monta
    Date: 2016 Jun 26, 11:49 -0700

    However, this discussion caught my eye and I wonder if O'Brian is just reflecting how the 18th (very early 19th) century navigator would generally calculate a lunar to the nearest second of arc. With our modern knowledge of statistics and instrument error, we would automatically round this down to a more realistic number to reflect the accuracy of the instrument, the tables and the mathematical methods. However, I suspect that this is a relatively modern attitude to experimental method and the statistical knowledge that underpins had yet to be developed when Aubrey sailed Surprise to the far ends of the Earth.

    I don't know if the majority of navigational practitioners would have been sophisticated about the statistics of the probable errors, but I think the upstream lunar modeling people (and table makers) must have known something.  The improvement made by Mayer and Euler, say, would have been directly visible in the data and, I guess, summarizable by a few statistics.

    Aubrey was said by the author to have become a good mathematician over the course of his career, which would conflict with any sort of confidence in longitude to a second.  Seems unlikely, too, that Aubrey would be crowing about just the precision of the reduction algorithm, especially if he did it that way every time.  Oh well.

    The almanac tables were given to seconds, but did the Nautical Almanac and the supplemental books and tables directly state the uncertainties, or was it merely folk knowledge among navigators as to what to expect?  The 1767 edition says only this:

    The Distances of the Moon from the Sun and fixed Stars, contained in the Four last Pages of the Month, ar set down to every Three Hours of Apparent Time by the Meridian of Greenwich, and are designed to relieve the Mariner from the Necessity of a Calculation, which he might think prolix and troublesome, and to enable him, when compared with the same Distances observed carefully at Sea, to infer his Longitude readily and with little Danger of a Mistake to a Degree of Exactness that may be thought sufficient for most nautical Purposes.  But useful and valuable as the Practice of this Method may be at present, it is a Remark not unworthy our Notice, that there is Room to hope, by future Improvements of the lunar Tables, and the Introduction of a more accurate Method of constructing Instruments, it may be carried to a much higher Degree of Perfection.

    Would it have killed the author to give a few numbers on just what the current Degree of Perfection was, based on the track record and known performance of the almanac?

    There is a scene in which bad weather has obscured the skies for days, preventing him from taking a lunar measurement.  He would have simply relied upon his chronometers for longitude, but they were acting up and he couldn't trust them.

    Ah, that's indeed a false note from the author.  Generally, though, I was charmed by all the references to nautical astronomy, and especially by Aubrey's being under the tutelage of Caroline Herschel for mirror-making.

    Additionally, Aubrey puts a great importance upon observing Jovian moons for triple-checking both his chronometers and lunars.  Presumably these take place while ashore on some island.  Perhaps I am mistaken, but I did not think that Jovian moons were anywhere near as accurate as lunars for determining Greenwich time in the early 19th century.

    From what I understand they were better than lunars by a fairly large factor (maybe a factor of 5):

    - no sextant error (the eclipse of the Jovian moon involves no angle measurement)
    - the inherent high precision of the eclipse event (lasts only 10 seconds or so)
    - here I'm guessing, but low perturbations of the Jovian-moon orbits, so the almanacs weren't so limited by orbital models on the theory side?  The NA gives data for these eclipses, so it would be possible to check how well they did.


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