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    Re: Precision of lunars
    From: George Huxtable
    Date: 2007 Apr 22, 18:10 +0100

    Frank has just ridden out, once again, on one of his favourite hobby-horses.
    Not that anyone should mind that; we all have our own pet topics.
    
    | Although he was a great authority on late 19th century navigation,
    | Lord Kelvin was absolutely NOT an authority on lunars.
    
    Well, how is Frank able to state that, with such certainty? Has he found
    some error, in Kelvin's text about lunars, that the rest of us have missed?
    It's likely, being a rich man, with a rich man's yacht, that Kelvin had the
    very best equipment of the day on board, which in those days would have
    included multiple chronometers. But he had experience of practical
    navigation at sea that far outweighs mine, or Frank's, or that of most of us
    on this list. He was a man with boundless intellectual curiosity, and a
    thoroughly logical mind, and must have been shipmate with many seamen who
    had been brought up on lunars. So I reckon that Frank does him wrong to
    belittle his authority in that way, unless he can offer hard evidence to
    back it.
    
    The lecture
    | you're quoting from was delivered in 1875. This is forty or fifty
    | years after lunars ceased being used even as a backup measure aboard
    | British ships and twenty to thirty years after they ceased that role
    | aboard American vessels.
    
    That's another "sweeping statement" from Frank. I wonder what firm evidence
    he can provide. I can quote Victor Slocum's biography of his father Joshua,
    as master of the "Constitution" (not THE "Constitution"!), a passenger
    vessel plying between Honolulu and San Francisco.
    
    On one passage, which cannot have been earlier than 1872, his chronometer
    broke down but his vessel made port on schedule. "But as it had always been
    rated by lunars, the mishap made no difference as far as the navigation of
    the vessel was concerned." Victor Slocum, himself a ship master, adds -
    
    "In the hands of skillful observers and patient computers the Lunar Method
    is reliable to within a quarter of a degree longitude, which would be the
    distance of a high landfall."
    
    That's an estimate that most of us would go along with, I suggest.
    
    And he continues-
    
    "I have before me the log of the ship Clive which in 1859 made a six months'
    passage, from the English Channel to Madras, and sighted the landfall within
    an hour of the expected time. That could not be beaten at this day.  Captain
    Shaw reported that he checked his chronometers, which had altered their
    rates considerably, by lunars. He said he could by this means keep to the
    sea four years, the period of time that Lunar Tables in the Nautical
    Almanacs were published in advance."
    
    So, those are two examples to contradict Frank's opinion about the early
    demise of lunars, as a backup to chronometers.
    
     It's clear from the lecture that Kelvin was
    | trying to warn young navigators not to be seduced by the stuffy old
    | advocates of lunars who still enforced their teaching in navigation
    | schools.
    
    Kelvin may have thought that; I just don't know. But that isn't what he says
    in his lecture, as I read it. I ask Frank to recount what Kelvin said, to
    back up that view. True, Kelvin pointed to the big disadvantage of lunars,
    their imprecision; and so he should, and so did every other commentator.
    
    Frank's comments about the Sumner method, however, are to the point.
    
    In fact, his principal astronomical suggestion to navigators
    | has nothing to do with lunars: his suggestion is that they should all
    | be using Sumner's method instead of the methods that are usually used
    | aboard ship in 1875. As we've discussed previously on the list, even
    | decades after Sumner's method was published, the great majority of
    | navigators were still shooting separate sights for latitude and
    | longitude --they just didn't see the merit of Sumner's method over the
    | common meridian sights for latitude and time sights for longitude.
    | There's a moment in the lecture where you can almost see him standing
    | there: Kelvin announces that he is publishing some tables (indeed he
    | did) to help facilitate Sumner's method and he says "I hold in my hand
    | copies of these tables which are soon to be published" (or words to
    | that effect).
    |
    | Kelvin is dismissive of lunars for the same reason that Lecky was
    | dismissive of them at about the same time. Everybody with common sense
    | knew very well that the best backup for the chronometer was another
    | chronometer. It was rather silly that all those poor students were
    | still studying lunar distance calculations so many decades after they
    | had fallen out of use. Kelvin is simply repeating the "common
    | perception" of the accuracy of lunars decades after they were commonly
    | used. He is not describing his own research or saying anything about
    | the fundamental accuracy of sextants.
    
    Certainly, Lecky was dismissive of lunars, but I do not see Kelvin as being
    dismissive. He simply treated lunar distance as a way of obtaining
    longitude, with its defects.. What Frank has provided above is the Frank
    Reed view of lunars, rather than the Kelvin view of lunars.
    
    By the way, the "best backup for a chronometer" was two extra chronometers,
    not just one. If you only had two, and they disagreed, you were hardly any
    better off, as you didn't know which to trust.
    
    | Somewhere along this thread you speculated that Lord Kelvin had access
    | to better ephemerides for the Moon than those available in the
    | official almanacs. No way... Exceedingly unlikely. There were very few
    | people on Earth who dealt with modelling the Moon's motion, and Kelvin
    | would have had no reason to hunt down that research since it was
    | irrelevant to his practical advice to navigators. I would add that the
    | nautical almanacs were improved just a few short years after Kelvin's
    | lecture and the inaccuracy due to the almanac data went away. Lecky
    | notes this improvement in his book, but of course, it was too little,
    | too late.
    
    I agree with most of that. But experienced astronomers were still applying
    their minds to improving the predictions of the Moon's motion, for several
    reasons beside navigation, around that period (as they are still). Hansen
    had made great improvements in 1857, which were applied in the Nautical
    Almanac from 1862, but the great American astronomer, Simon Newcomb, made
    further corrections, which were applied from 1883 onward. These are what
    Lecky refers to in a footnote, added after his first edition. The main text
    had said that there was a small longitude error of 6' to 8' due to
    uncertainty in the position of the Moon as given in the tables, which must
    correspond to positional error of the Moon of about 15 arc-seconds. The
    footnote adds that by 1891, this had been reduced to a "mean error" of just
    over 1". He doesn't state any scatter, however.
    
    Newcomb published two papers in 1878 on the Moon's motion, as follows-
    
    "Researches on the motion of the Moon", in Washington Observations for 1875,
    Appendix 2, page 1 to 280.
    
    "Corrections to Hansen's tables of the Moon, prepared and printed for the
    use of The American Ephemeris and Nautical Almanac." Washington.
    
    If anyone has easy access to a Nautical Almanac from 1883 to 1922, it
    contains an appendix of 2 to 4 pages of Newcomb's corrections to Hansen's
    tables, which I would greatly like to see.
    
    Earlier, there were published (1853, 2nd ed. 1865) by B. Pierce (a name
    that's appeared recently in these columns) "Tables of the Moon", under
    "Tables prepared for The American Ephemeris and Nautical Almanac".
    
    I haven't seen any of those, and they may be hard to find, but I expect
    Newcomb's, at least, would be valuable. He wrote very clearly.
    
    ================
    
    Kelvin had quite a lot of stuff in his lecture about chronometers, and one
    example is instructive. Two chronometers were put aboard the ship
    Tenasserim, which left Liverpool in Jan 1874, and arrived in Calcutta 4
    months later. On arrival, they differed by 4 minutes 35 seconds, after
    correction by "the ordinary method". Kelvin was advocating a new method of
    correction for temperature variation, based on a daily temperature reading,
    and a quadratic temperature law, with its two constants determined in
    advance, for each chronometer. With the corrections made that way, one
    differed from Greenwich by only 3.5 seconds, the other by 8.5 seconds.
    
    It's clear, then, that on long slow sailing-vessel voyages, the chronometer
    was not necessarily the answer to the maiden's prayer, when adjusting for
    temperatere by a different technique can have such a large effect on the
    result. At least, with lunar distances, the error didn't grow with time;
    with a chronometer, it certainly did. So I suggest that a large influence on
    the replacement of lunars by chronometers was the introduction of steam.
    Voyages were then got over in a shorter time, and the long voyages between
    Europe and the East would be broken by a passage through Suez. As a result,
    there was less time for big errors to accumulate.
    
    George.
    
    contact George Huxtable at george---.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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