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    Re: Star-star distances for arc error
    From: Frank Reed
    Date: 2009 Jun 25, 21:15 -0700

    Douglas, you wrote:
    "The point which seems to have been missed entirely in my quoting those 
    figures is that one sextant reads to 10 seconds, but has a tangent thread 
    worse by eight times that"
    This isn't relevant. The error from the calibration certificate (which you 
    quoted in a previous message) is a correctable error. It doesn't mean that 
    the instrument is incapable of measuring angles at that 10 second precision 
    that you see on the micrometer drum (of course, other factors might make it 
    worse than that anyway).
    And you wrote:
    "No doubt someone given the two sextants as if new to consider buying (but 
    without looking at the certificates) most would choose the former thinking it 
    had "better accuracy"  by reading to 10 seconds of arc; whereas in fact it is 
    a quarter less or worse in absolute terms."
    You cannot, in fact, judge which is the better instrument from these bits of 
    information (though my money is on the Freiberger). The reading precision of 
    the micrometer does not limit the accuracy for someone with a "good eye" for 
    visual reading of the micrometer without a vernier. And the collimation 
    certificate provides information on correctable errors. These corrections 
    MUST be applied for accuracy, which is why many sextant-users look for "home" 
    methods for checking arc error.
    And you wrote:
    "Is this why they put the small vernier there when a single fiducial mark 
    would suffice or am I being too cynical?"
    No, I don't think you're being too cynical. It's quite natural for people to 
    think that the vernier on the micrometer is important for their observations 
    even if they're mostly imagining things. And I know from personal 
    communication with a sextant dealer that high-end Plath sextants which 
    sometimes lack a vernier on the micrometer can be a hard sell because of that 
    despite the tremendous reputation of the brand. Sextants are bought by 
    navigators and by navigation enthusiasts. The appeal of apparent accuracy, 
    beautiful design, and available options are just as relevant as in any other 
    technology purchase. Putting fins on cars doesn't make them more aerodynamic, 
    but in the right market, it sells.
    Douglas, you added:
    "I was accused of not trying star separations.   "A sure indication that you 
    have never tried it!"   was thrown my way."
    An accusation? Come now, Douglas, you're in politics. You've run for office 
    and had real accusations thrown your way --real, nasty accusations (unless 
    there are two optometrists from Bosham named Douglas Denny!), and you know 
    quite well that a comment like mine was no "accusation". 
    You added:
    "Well having tried it I am quite sure it is not a practical method of 
    obtaining accurate enough information about the state of a sextant tangent 
    screw accuracy. That is my opinion."
    Ok. How many times have you tried it? How did you correct for refraction?? 
    Your previous comments make it quite clear that you do not really understand 
    the refraction correction for star-star distances. Now if you got that 
    correction wrong when you once tried star-star distances, your results would 
    have been disappointing.
    And you wrote:
    "Reading the vernier is not where the accuracy is impaired"
    So your earlier comments on the vernier... were saying what then??
    "making the co-incidence of the stars is.  Even with a clamped sextant (which 
    is what I did) one can only get a resolution of co-incident stars to about 
    one minute of arc"
    See my earlier post for some simple tricks to improve your results by a factor of five or so. 
    And you wrote:
    "In fact the resolution of the eye itself varies for different acuity tasks."
    It does indeed. The type of resolution here is closer to what you call "letter 
    acuity". I don't think it's a case of "grating acuity" since you're bringing 
    two bright objects together.
    George wrote previously:
    "One difficulty is in identifying the correct star-pair, as one star looks much like another."
    Just as a quick sidenote here, this is a case where the old lunarian trick of 
    pre-setting the sextant makes a huge difference. Prep a table of star-star 
    distances accurate to, let's say, 0.1 degrees, pre-set the instrument to that 
    angle, then aim straight at one star and slowly rotate the instrument about 
    the axis pointing to that star until the second appears. There are very few 
    cases where you would mistake one star for another.
    Douglas you wrote: 
    "I do not think you have a correct appraisal of the accuracy of 'Lunars'.   
    Lunar distances were very poor indeed.
    Sir  Frank Dyson,  Astronomer Royal, in the forward of Gould's 'Marine Chronometer':-
    ".... in spite of the attention devoted to the lunar theory by some of the 
    world's greatest mathematicians, .......even with perfect tables, it is found 
    that the most skilful navigator cannot obtain a very accurate postion in this 
    manner. With great pains and sometimes elaborate calculation he cannot be 
    correct to within 20 miles"
    I have noted many times on NavList that you have to be very careful with 
    sources from the early twentieth century discussing lunars. Lunars had fallen 
    into obsolescence decades earlier. While they were still an onerous part of 
    the navigator's classroom experience even in the very early years of the 20th 
    century, they had become exceptionally rare observations since about 1850 
    even in the less wealthy merchant fleets of the world. You might think that 
    an Astronomer Royal would be an impeccable source. But what did he know of 
    lunars? Probably no more than he had picked up from casual discussions. You 
    can be nearly certain that he had never taken a lunar distance observation 
    himself. As for me, I have taken hundreds of lunars, and I have studied 
    dozens and dozens of logbooks from the 19th century which include real lunar 
    distance observation and calculation data on regular basis (typically several 
    lunars over a few days taken every two weeks when the Moon was near First or 
    Last Quarter)
    And you speculated:
    "And this means with use of the reflecting circle too - more accurate than a 
    sextant - eliminating some of the inherent errors of the sextant."
    Not so. Reflecting circles never became especially popular, and sextants were 
    THE instrument for shooting lunars. Sextants were created specifically for 
    shooting lunars and navigators in the early 19th century normally carried 
    both a sextant and a quadrant. The expensive sextant was reserved for those 
    observations requiring high accuracy --specifically, lunars.
    You wrote:
    "The Lunar method was too impractical on grounds of inadequate tables; great 
    difficulty in measuring and far too complex a method of calculation for 
    ordinary use by seamen. It took at least an hour for the astronomers on board 
    ship when the method was tested to 'clear the distance'  to find longitude,  
    and thus it was rejected for the longitude prize when Tobias Meyer put his 
    tables before the Longitude Board around 1759."
    You are repeating a certain mythology of lunars that is based on secondary 
    sources. 1) the inadequate tables were sufficiently "adequate" in enough 
    situations so that many mariners practiced lunars right through the first 
    half of the 19th century. They were not sufficient, however, to serve as a 
    primary means of determining longitude. Instead, they served as a check on 
    the primary means (DR before about 1835, chronometer after that year, for 
    American merchant vessels; up to 25 years earlier on well-equipped British 
    vessels). 2) Lunars took a little practice and there was certainly a learning 
    curve, but there's no documentary evidence from the era that there was "great 
    difficulty in measuring". 3) it is a HUGE myth that the calculations were too 
    complicated. They were in fact only slightly longer than the calculations for 
    an ordinary "time sight" which was a daily calculation through the 19th and 
    into the 20th centuries. There are numerous examples of fully-worked lunar 
    calculations in the logbooks which are still extant today from that period. 
    4) It did not take "an hour" (nor "four hours" which you'll also find in some 
    secondary sources) to clear the observations. It took twenty minutes with 
    some of the longer methods and as little as ten minutes for some brief 
    methods like Thomson's (also published in Bowditch). TEN minutes was no great 
    effort for any navigator, and the steps required were completely analogous to 
    a common time sight --there were no "astronomers" required except in the 
    earliest period (e.g. on Cook's voyages). So why do people think it took 
    "hours"? Because in the early 1760s, before the Nautical Almanac was first 
    published, Maskelyne's "British Mariner's Guide" provided all the tools 
    necessary to do lunars even though there were no published Moon positions. So 
    in that brief era the navigators had to calculate the Moon's ephemerides by 
    hand! That took hours. This datum of information was transferred into later 
    secondary histories mistakenly asserting that it applied to all lunars. 5) 
    While Mayer's tables did not win the Longitude Prize, Mayer's widow was 
    awarded the sum of 3000 pounds (then an enormous sum for a mathematical 
    achievement and a substantial percentage of the full prize), and his tables 
    were immediately put to use computing the Nautical Almanac. The Nautical 
    Almanac owes its very existence to those early lunar distance tables computed 
    via Mayer's tables of the Moon.
    Douglas, you added:
    "You are again bringing in red herrings into the argument.  The resolving 
    power of the telscope is not the issue here,  but the ability to superimpose 
    star images - accurately. In other words: eye acuity is the issue.  Already 
    dealt with as above."
    Nope. That's a simple mistake, as I am sure you will agree if you give it a 
    little thought. The telescope magnifies the angles. So if the unaided eye is 
    capable of resolving at 1' of arc, then using a 10x telescope, we can resolve 
    0.1' of arc (in the angle on the celestial sphere; the limit of angular 
    resolution in the visual field through the telescope is still 1'). This, 
    after all, is the principle that allows an amateur astronomer to resolve 
    double stars with separations of one second of arc. You magnify by 60 or more 
    and one second turns into one minute as seen through the telescope.
    And you wrote:
    "Once again: My point is:  that it is not good practice nor good science to 
    attempt to use a method for obtaining accurate measurements,  where the 
    errors involved in the measuring process are comparable with (and can in this 
    case exceed) the measurement accuracy itself."
    And that's a good general point. But it DOES NOT APPLY HERE. Your comment that 
    the refraction may exceed a minute of arc is simply irrelevant. There's no 
    problem correcting for refraction.
    And Douglas, you concluded:
    "I am beginning to detect there are many sacred cows here which are being 
    threatened with slaughter, causing distress to their owners"
    Well, that's an easy way out, Douglas. We all have to worry about our "sacred 
    cows" and continually question our assumptions and our analyses. It's 
    fundamental to good scientific skepticism. But you may well discover that 
    those sacred cows are YOUR pets and not ours. Hear any lowing from your 
    backyard...? :-)
    Finally, Douglas, I would like to add that I understand where you're coming 
    from (at least I think I do). You're a smart guy and confident and proud of 
    the things you understand, but my guess is that you haven't had the benefit 
    of a community of people to bounce ideas off of in the particular topic of 
    navigation, and so you've developed some mistaken notions. It's not the end 
    of the world. We all learn... And now you do have a community of people to 
    bounce ideas off of --if you can deal with that.
    Navigation List archive: www.fer3.com/arc
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