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    Re: Lunar distance accuracy
    From: Frank Reed
    Date: 2007 Oct 27, 21:29 -0400

    Alex,
    
    One little request first: You listed the URL for the article in your reply.
    Although it resolves to an address under "clockwk.com", it's in everybody's
    best interest if you use the address I originally gave, which is
      www.HistoricalAtlas.com/lunars/ejwhite/
    One of these days, clockwk.com is going to disappear, while
    HistoricalAtlas.com is here to stay, so if you can remember to do so, please
    use that domain when referring to files on my site(s). Thanks!
    
    You wrote:
    "1. George discusses at length the question, what is "pillar sextant". I
    think it is reasonable to assume that this was a "pillar-frame" sextant,
    typical for this manufacturer (Troughton), rather than a column-mounted
    sextant. White emphasises all the time that his experiments are relevant for
    the sea use. It would be stupid or dishonest to use a mounted sextant in
    such experiments:-)"
    
    Yep. And in addition, the expression "pillar sextant" did NOT refer to
    sextants mounted on stands back then. The terminology is bound to be in flux
    in the year 2007 since sextants like this have not been manufactured in
    almost a hundred years, but certainly when White was writing, there would
    have been no question.
    
    Next, you wrote:
    "2. Several things in White's article look very suspect to me. First of all,
    what his "observations" really mean. Are these individual shots or averages
    of series? Notice: he records at most ONE "observation" per day.
    (In fact, one per week, in the average). While the normal practice at that
    time (and in our time!) is to take series of several observations."
    
    I agree that there is no way to be certain on this point. However he says
    nothing about averaging multiple sights (except at the end when he averages
    the whole lot). Considering how carefully he has spelled out other details,
    I think it's unlikely that he took multiple sights. Also notice his comment
    about the possibility that he mis-read the clock on one of his observations.
    Would that comment make sense if he had taken multiple observations? As for
    "normal practice at that time"... there was no normal practice. Lunar
    observations were long dead by 1887 when White was experimenting with them.
    I see him as one of the earliest lunarian hobbyists. He would have loved the
    Navigation List. :-)
    
    And:
    "Taking a single lunar shot PER WEEK seems ridiculous to me
    and contrary to the common practice."
    
    See above. He was doing this for relaxation and his own amusement.
    
    "3. On page 90, White writes that the "greatest excentric error of his
    sextant was 20 seconds." Of arc, of course. Which is the maximum arc
    correction from the certificate, I suppose. And then on page 91, line 1 he
    says "The correction for excentricity have NOT BEEN APPLIED (!!!)" and then
    states a ridiculous reason for this. Which means he NEGLECTED a known
    instrumental correction of up to 20"=0.3' for his sextant!"
    
    In a follow-up post, you decided that this wasn't so ridiculous after all,
    and I agree with your logic there.
    
    And you wrote:
    "This correction is LARGER than the supposed typical accuracy
    of his shots..."
    
    Ah, but that correction is the maximum correction at only one point along
    his sextant's arc. I propose that his arc error table would have read
    something like this: 30d: 0", 60d: +10", 90d: 0", 120d: -20". It should
    actually be possible to tease out the arc error from the sights that he has
    listed. But assuming that the table has a form at least "somewhat" like the
    one I've proposed, you can see that the error from ignoring arc error would
    tend to cancel out if observations are taken over a wide range of angles, as
    they are, and in many cases would be insignificant.
    
    "4. Now about his results, as recorded. He obtains the "most probable error"
    of his "single observation" 21 seconds of time which is roughly equivalent
    to 10.5" in distance or 0'.2 in distance. I confirm this calculation from
    the data of his table. But again as I wrote above, I have very strong doubts
    that his "single observation" recorded in the table is indeed a "single
    shot" rather than the average of a series (which would be a normal
    practice)."
    
    The standard deviation is equivalent to about 0.25 minutes of arc in the
    measured distance. As I said, I agree that there is at least the possibility
    that these are averaged sights, but without evidence that this is ACTUALLY
    the case, you're only speculating.
    
    And you wrote:
    "5. How Frank comes with the "mean error" of 0'.1, I don't know."
    
    Take them in sets of four and average. Yes, this is a legitimate procedure
    when each sight is individually cleared to yield a longitude.
    
    I found your point "6" amusing. You seem to be saying that you don't trust
    him because he writes plainly and without pseudo-academic pretense. Oddly
    enough, I like him for that.
    
    "7. And finally I want to bring the following passage from White to your
    attention:
    "As observations can be taken at sea with nearly
    the same ease as on shore,..."
    Well, I am also mostly an armchair sailor, but I would never say such
    thing:-) My very limited sea experience completely contradicts
    this opinion." "
    
    You know, they do have calm days on the oceans, Alex. :-) I have no sea
    experience at all. But to your point, we have only one list member who has
    been both a professional navigator and a lunarian. That's Henry Halboth.
    After getting a longitude accurate to within 6 miles from a lunar distance
    observation, he recently wrote, "I am not of the opinion that sea state has
    a significant effect on the observer, unless a vibratory effect is present,
    such as when a vessel be laboring or pounding, or when vibration is enduced
    by operating machinery. It does seem usual for a vessel to have been eased
    off or hove-to so as to provide more favorable conditions for observation."
    ...So that's ONE data point.
    
    Finally, I would emphasize that lunars were widely used in the early
    nineteenth century --so they MUST have been accurate "enough", whatever
    "enough" means. There is ample evidence for them in the logbooks. For those
    of you who haven't looked at them, there are dozens of scanned logbooks from
    the era available on the web site of Mystic Seaport:
    http://www.mysticseaport.org/library/initiative/MsList.cfm
    For fun, here is an example of a worked lunar from one of those logbooks:
    http://www.mysticseaport.org/library/initiative/PageImage.cfm?PageNum=48&Bib
    ID=35388
    Scroll down the page to see the scan. The calculation of the lunar
    observation occupies the top third of the page. The rest of the page is an
    unrelated tabulation of chronometer error.
    
     -FER
    
    
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