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    Re: More on Lunars
    From: Frank Reed
    Date: 2008 Jul 12, 22:46 -0400

    Henry H, you quoted an old message of mine in which I wrote:
    "Here's an article published in 1847 discussing the uses of lunars and
    chronometers. The principal lunar story actually refers to events in 1825.
    Apparently, this navigator had good success taking lunar observations with a
    "quadrant" which in that era would have meant an ordinary wooden octant."
    You do understand, I hope, that the very reason this story was published was
    because it was such a novelty. Their sextant was useless so they were FORCED
    to use a wooden quadrant. It certainly was not something that was commonly
    done, and that's why it made such a good 'sea story'.
    And you wrote:
    "I now respond further ... It was not my intent to imply that octants were
    employed in Lunar observations to the exclusion of any other instrument
    type, and merely cited their construction as an example of the potential for
    Yes, of course. I did not take you to be implying that wooden instruments
    were used EXCLUSIVELY. But you did imply that they were used at least often
    enough to have decreased the quality of lunar observations historically. And
    I do consider that to be a historically inaccurate statement. Only a
    desperate navigator, like the one who wrote the 1847 article which I brought
    to everyone's attention, would have considered using a wooden instrument for
    And you wrote:
    "there were also wooden sextants manufactured . how many I don't know, but
    enough have wound up in collections and museums to give us a good sample."
    There are all sorts of instruments in museums including works of art never
    intended for use at sea, training instruments, family heirlooms with
    uncertain backgrounds donated by wealthy museum patrons, and also prototypes
    of instruments which never went into production (e.g. the "centerless
    sextant" which was recently discussed). Museums today often have a "one of
    everything" philosophy which gives undue weight to instruments with no
    historical importance.
    And you wrote:
    "Certainly, it is possible to reference log books containing worked up
    Lunars, but unless that logbook also specifies and describes the instrument
    used in some detail you really don't know what was used, do you now.
    Assumptions not based on hard evidence do not make historical fact."
    The problem with that logic here, Henry, is that you could just as easily
    claim USING THIS SAME LOGIC that lunars were shot using cross-staffs and
    kamals. I mean, you really don't know, do you now? But in fact, we DO have
    evidence. That article from 1847 is very good evidence that lunars using
    wooden instruments were considered extraordinary. The author of that article
    is telling us of his amazement that he was able to use a wooden instrument
    for something so demanding as lunars. Is there still a possibility that
    there was some mysterious group of navigators who avoided metal instruments?
    Sure. But until there's actual evidence for them, it's an unnecessary
    And you wrote:
    "Also, what degree of accuracy can be ascribed to such records of Lunar
    calculations at sea as have come down to us by way logbooks; unless
    associated with a landfall, or comparable navigational event, you again
    simply don't know."
    Frequently, lunars WERE taken near a landfall, so we do have that strong
    evidence. In the later period (c.1835-1850 on American commercial vessels),
    we also have chronometer longitudes that accompany most lunar longitudes so
    we can get some rough idea of the accuracy of the lunar observations, at
    least statistically. But of course, beyond that, there's no way to be sure.
    And you wrote:
    "My dictionary defines approximate: 1) as an adjective = . nearly exact, not
    perfectly accurate or correct., and 2) as a verb = .to come near to;
    approachclosely to.. So really what is the discussion about."
    Good question. But I have no idea why you think the dictionary definition of
    approximate is relevant. Henry, if I told you that you could calculate the
    height of a rock thrown from the top of a three-story building using the
    would you object? Would you complain, "that's only approximate; it's not
    rigorous." And in fact, it's not rigorous. The rigorous solution (ignoring
    relativistic corrections) is a Keplerian elliptical orbit about the Earth's
    center with significant air drag proportional to velocity squared and other
    factors. But here's the thing: if you do a "series expansion" of that
    Keplerian ellipse with drag term, you get the simple equation I quoted above
    and, of course, it will do all that is required in nearly every practical
    case. And you can even add terms to it as small corrections if conditions
    require it. In an analogouse fashion, the direct triangle solution (a.k.a.
    "rigorous") to the clearing process in lunar distances was subjected to a
    series expansion which offered (and still offers) considerable benefits. You
    complain that you could teach all of spherical trigonometry in a shorter
    time than it would take to teach these series methods. That's a modern
    perspective, but it has little to do with history. The series methods were
    exceedingly popular historically.
    "Is it now claimed that the methods mentioned in 3272, including the
    .straight triangle methods. are perfectly accurate or correct . if not, they
    are and have been properly called "approximate"."
    Well, you can call them whatever makes you happy! And certainly there were
    some methods that were MUCH worse than others. But this usually had nothing
    to do with whether the methods were series solutions or direct triangle
    solutions. Your contention that this was the root of the problem or even one
    contributing root is simply wrong.
    And you proposed:
    "I have long felt that Lunars should be perhaps categorized as 'Scientific'
    or 'Commercial', as well as by period."
    Yes, that might be a useful distinction.
    And you wrote:
    "Accuracy in the clearing of a Lunar Distance requires, in addition to other
    factors normally considered, attention to the Moon's parallax in azimuth,
    the spheroidal shape of the earth"
    This is a very small correction. A modern lunarian can easily apply it, if
    desired. And certainly some of those "scientific" lunarians felt the need to
    do it, but the idea that you MUST include this is just plain wrong. On
    average it will change a fix by little more than one nautical mile, in rare
    cases five nautical miles.
    "and the true shape of the Sun/Moon disks as affected by refraction."
    Only when the Sun or Moon are quite low in the sky. Tables for doing this
    were easy to use and were included in one of the most famoous series methods
    (Thomson's tables) as well as many other collections of tables. It's an
    unimportant correction except at very low altitudes.
    You wrote:
    "William Chauvenet, in his 1868 paper entitled .Navy Scientific Papers No. 1
    . Astronomy: Comprising Suggestions to US Naval  Officers., details a more
    modern and balanced view of Lunars. This paper, once discussed on this List
    extensively, details and quantifies the errors to which Lunars were subject
    previously by reason of tabular inaccuracies prior to 1855, neglect of
    certain corrections, instrumental error, and observational error. "
    You're reading an article by a land-bound professor written years after
    lunars were commonly practiced at sea. This is NOT a paper about navigation.
    It's about a textbook MODEL of navigation.
    And you wrote:
    "I will not extend this writing by further quoting from this paper, but will
    strongly recommend it to budding Lunarians and for review by the pundits of
    this List for it lays bare the inadequacies, at least in the authors
    opinion, of the older methods."
    Yes, it's well worth reading. But Chauvenet suffered from the same disease
    that afflicted many other mathematical astronomers of his era. He wrongly
    and IGNORANTLY attributed the decline of lunars to mathematical problems. Of
    course, he was proud of his method. He put a lot of work into it. But his
    claims of superiority were expressions of his pride, not his science. And
    his belief that he could dust off the defunct technique of taking lunars at
    sea by cleaning up the math were naive in the extreme.
    And you wrote:
    "Chauvenet's method seems to have impressed the US Hydrographic Office, as
    the 1888 edition of HO 9 (Bowditch) includes its use, to the exclusion of
    others. "
    Chauvenet was the 'great old man' of nautical astronomy of his era (in the
    US). His method was included in the revised Bowditch because he wanted it
    included, and he would not have been turned down. However if you consult the
    Congressional record from about this same period, you can read testimony
    from the commandant of the US Naval Academy (which Chauvenet helped found).
    When questioned about lunars, he replies that they are not taught AT ALL,
    but the interested student can consult the textbook. The inclusion of
    Chauvenet's method (starting in 1881, not 1888) was in deference to
    Chauvenet personally and to the weight of his reputation.
    It is also worth noting, while we're discussing Bowditch editions, that not
    one single change was made to the section on lunars from 1838 to 1880.
    That's how insignificant lunar observations had become. Not even the
    examples were updated. Obvious typos were left in place for those long four
    And you wrote:
    "In a paper presented before the Royal Society of Victoria in 1889, E. V.
    White, FRAS, reported a mean of 42 Sun/Moon Lunars, observed by him at a
    place of known Longitude"
    I like that paper very much. You do realize, I hope, that I am the one who
    brought it to the group's attention --twice, in fact, in the past three
    "between August 27 and October 2, 1887 and cleared by Chauvenet's method, to
    have exceeded the true Longitude by 4.8 seconds in time; the probable error
    of a single observation is said to have been +/- 21 seconds in time."
    If you think that any of this accuracy is due to his use of Chauvenet's
    method, in opposition to some other method, I am sorry to say that you are
    mistaken. Chauvenet's method offered no significant improvement for the vast
    majority of lunars analysis. And if I recall, White himself recommends using
    Thomson's tables, doesn't he?
    And I think it's important to remember what White was doing. He was not a
    scientist doing lunars to find a precise longitude. He was not a navigator
    at sea trying to get his vessel to port. He was, at the time of writing, a
    semi-retired astronomer enjoying himself as a sextant enthusiast with his
    fine old instrument. The year 1887 was long after the end of real practical
    use of lunars. Nevertheless, it's an interesting article and well-worth
    And you wrote:
    "Mr. White also has a number of less than favorable remarks to make
    regarding the accuracy of sextants encountered over his some 40 years prior
    experience in their use."
    Indeed. In the decades immediately preceding White's article the quality of
    sextants seems to have declined quite a bit. Lecky also talks about this. Of
    course, for noon latitudes and time sights, which were the bread and butter
    of navigation in the latter half of the 19th century (and well into the
    20th), less accuracy was required than for lunars and there were presumably
    fewer commercial pressures to make accurate instruments.
    And you wrote:
    "I certainly agree with George's philosophy regarding Lunars, as set forth
    in 5647"
    Well, I re-read that message, and I can't see any connection with your
    latest comments. Maybe you would elaborate.
    And you wrote:
    "and perhaps carry it a step further. Lunars have evolved, from a rather
    crude beginning to an ever more scientific approach."
    That statement is sufficiently broad that it can't help but be true. Yet if
    you read the article by Mendoza Rios from 1797, you will find that
    practically everything that is claimed to be "new" about lunars in the
    latter half of the 19th century was already well understood back then. There
    are indeed incremental improvements in the tables during the early 19th
    century. This was due to straight-forward commercial competition. But most
    of the stuff published in the latter half of the century was comparable to
    're-inventing the wheel'.
    Regrettably, many modern fans of lunars have read late 19th century books on
    lunars, filled with juicy math and claims of greatly improved accuracy, and
    they have erroneously concluded that this was still an active field. It was
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