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    Re: 3 Lop's
    From: Frank Reed CT
    Date: 2004 Nov 15, 01:22 EST
    Alex E wrote:
    "Where can I read more on George Huxtable's Anomalous Dip?"

    With all due respect to George, Fred's being a little idiosyncratic by refering to this as "George Huxtable's anomalous dip", though George appears to have been the first to bring it up on this list a couple of years ago (see the archives). This issue was widely discussed in the nineteenth century (less so in the 20th). For example, in Chauvenet's little 1868 article "Astronomy - comprising suggestions to U.S. naval officers", in item 5 under General Astronomy (p. 20) he suggests that careful records should be kept of dip observations and corresponding air and water temperatures in the hope that some corrected table of dip values might be created. A link to that article for those who didn't see it last month:

    If you read any account regarding the creation of a dip table, you will find that it is not based on simple "geometric" dip. That is, if you draw a triangle with a straight line running out to the geometric horizon and calculate dip values based on that triangle, you will not get the tabulated values, and more to the point you will not get values that match the apparent, observed dip. The actual dip is different because light rays are refracted by passing through air of variable density on its way from the horizon to the observer's eye. That shifts the real dip from the geometric value of dip by about 10% (roughly). IF refraction were fixed in value, this would be the end of the story, but the variations in temperature between the horizon and the observer can be quite complex. As a result the horizon moves around in ways that are not predictable. It turns out that Chauvenet's hope that observations might reveal a pattern were not realized. The dip bounces around by about 1 minute of arc in common cases and by 5 or even 10 minutes of arc in unusual cases. This is a real,practical limit on the accuracy of celestial navigation using a real sea horizon.

    Regarding the three LOP fix, clearly if all altitudes are displaced by 3 minutes of arc, the vessel's most likely position would be the center of the triangle rather than one of the vertices. How you would determine this in practice is probably a matter of navigational skill rather than clear science. Naturally, one can imagine theoretical circumstances that would decide the case (e.g. observe ten stars at ten azimuths... if they make a clean decagon, it's probably a constant error in dip and not observational error...) but in practice it's a matter of judgement.

    Regarding lunars for a moment, that business of altitude accuracy raises its ugly head in connection with the possibility of dip variations. For short-distance lunars, an error in the observed altitude of 1 minute or more could be trouble. But as I noted in my earliest message on that topic, it turns out that the lunar clearing process is not terribly sensitive to a simultaneous error in BOTH altitudes. So if the dip is wrong, it's not a big deal for clearing a lunar.

    Frank R
    [X] Mystic, Connecticut
    [ ] Chicago, Illinois (the X has shifted again)
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