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    Re: Fw: Letcher page 103
    From: Henry Halboth
    Date: 2010 Feb 18, 18:27 -0800

    I usually do not buy books on the subject of Navigation. My library is already overflowing and internet sources are prolific, so there appears little reason to invest in what generally turns out to be a reinvent of some old theme, or at best a different slant on the same. The recent exchange of posts on the subject of John Letcher’s  “Self Contained Navigation by HO 208” and the simple fact that I for many years used the original HO 208 in sight reduction, as well as the knowledge that John is a careful researcher, piqued my interest - so for the grandiose sum of $3.75 + a modest shipping charge (original 1977 jacket cost noted as $12.50) I have acquired a copy of this pub, used but in otherwise mint condition.


    John’s perspective on clearing a Lunar Distance is conventional to say the least; he does present a formula, without derivation, to clear the sextant distance, which is observed in the usual manner. He claims this formula to be a simplification which, including “neglected effects, such as oblateness of the earth, augmentation of the Moon’s semi-diameter, parallax of the Sun, and the elliptical figures of the Sun and Moon due to refraction might combine in some cases to cause an error as large as 0.3 minute in the clearing…”. He gives an example of a clearing whereby his methodology gives a cleared distance of 59-05-36 against the same clearing by Chauvenet’s method of 59-05-33. I am here acting solely as the “messenger” and have not sought to prove or disprove his claim.


    The real apparent novelty of his methodology is that he presents a method, using HO 208, whereby the true Lunar Distance may be calculated at hourly intervals to allow for interpolation in finding the GMT once the sextant distance is cleared. Given the fact that in 1977 tables of Lunar Distances were probably not published on a then non-existent Internet, as they are today, this convenience was certainly attractive – in the 1940s, when I first began doing Lunars, I found it necessary to calculate the true distances by spherical trig, as there were then no known (to me) distances published.


    John does devote a Chapter to “Time by Lunar Lines of Position”, which I assume to be the basis for many of the comments previously posted on this List. He here advances the theory that a Chronometer error will show in a disagreement between Sun or Stellar Sights and Moon Sights, i.e., “If the Chronometer is wrong, and you work the sights as if it were right, the moon lines will lie consistently to either the eastward or westward of the other lines, depending on whether the chronometer is fast of slow on GMT.” Thereafter, by a process of trial and error, a time may be found at which the lines come into coincidence and thus the CE determined at the time of sights. As a special circumstance of the method of Lunar Altitudes, John does deal with the matter of “Same or Opposite Azimuths” of the Moon and another body, stating here that the separation of LOPs here generated for any specific time by chronometer is an indicator of CE, depending again on eastward or westward displacement of the LOP based on the Moon sight. There are a number of caveats and case differentiations applicable to this methodology generally which are far too detailed for incorporation in this post – if interested, get the book, for $3.50 you can hardly go wrong. Again, please understand that I am only the “messenger” here and fully realize that any use of altitudes is fraught with error occasioned by the vagrancies of dip, refraction, and other variable horizon conditions too numerous to mention.


    Of particular interest is the preference to the reproduced HO 208 Tables, which states in part  “Prior to reproduction, a total of 203 errata were corrected by the publisher. The corrections were noted during machine recomputation of the tables at the Ladd Observatory …”. Unfortunately, these corrections are not identified of quantified. I now have in hand four copies of HO 208, one of which must be assumed more correct than the others.





    --- On Sat, 2/13/10, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList] Re: Fw: Letcher page 103
    To: NavList@fer3.com
    Date: Saturday, February 13, 2010, 6:15 AM

    Henry Halboth wrote-

    Frank and George are otherwise most correct in inviting attention to the
    affect of accumulated errors in sights taken above opposing sea horizons.
    Such methodology has often been advocated as providing the most accurate
    fix, in that the box-like configuration resulting tends to average out the
    errors of both instrument and observation - but that's another tale.


    Henry is right to point to what looks like a bit of a paradox here.

    In the context he is referring to, which I take to be a round of star-sights
    at dusk to obtain a position, it is indeed excellent practice to observe
    altitudes of a number of stars, over a wide range of azimuths. Indeed, if
    it's possible, each observation of a star in a particular direction
    (southeast, say) can be "balanced" with that of another star in a roughly
    opposite direction (northwest). And then, to get a decent "angle of cut"
    between position lines, to observe another pair of stars, roughly at
    right-angles to the first pair. Which ends up with the sort-of box-like
    plotted quadrilateral on the chart, just as Henry describes, rather than the
    triangular "cocked hat" that's so often spoken-of on this list.

    And there are sound reasons for that long-established practice. There could
    be common-errors, applying to all such altitude observations, all round the
    horizon: these can be a failure of the actual dip to observe textbook
    predictions, or an uncorrected index error in the sextant.  These errors
    will move all the resulting position-lines, all towards, or all away from,
    the direction of the bit-of-horizon above which they were measured. Then,
    when the navigator strikes some sort of middle-value for his estimated
    position, within that box, most of any bias due to dip or index error will
    be averaged out. This is the "another tale" that Henry refers to.


    But what we have recently been discussing is another matter altogether:
    determining the angle-across-the-sky between the Moon and another body, by
    measuring the two altitudes up from different bits of the horizon. And in
    that context, if those two horizons are in opposite directions, then the two
    dips (or index errors) combine, and add in such a way that the effect on the
    resulting angle between the bodies is doubled, not nulled.


    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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