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    Re: How Many Chronometers?
    From: Frank Reed
    Date: 2009 May 11, 00:34 -0700

    Geoffrey Kolbe, you wrote:
    "The essence of the method is the LOPs from a number of star fixes will cross 
    neatly at a given point on the chart, but that point will in error in 
    longitude due to the error in the chronometer. The longitude error in a lunar 
    LOP will be slightly different due to the faster motion of the moon across 
    the sky. The trick then is to adjust the time so that all LOPs - including 
    the lunar LOP - cross at the same point. The amount of adjustment required 
    gives the error in the chronometer.
    I had not seen this described before and thought it quite neat."
    I have a hunch that we are seeing the influence of John Karl's advisor on this 
    book, namely Ken Gebhart. I've seen and heard Ken describe this technique in 
    just those terms more than once (including between sessions at Mystic last 
    June). He didn't invent it, of course. It's been around in one shape or form 
    for centuries. But Ken does like to sell the method that way.
    This method of getting longitude by lunar altitudes has two problems, but 
    they're not necessarily more problematic than standard "lunar distance" 
    First, this method only works if the motion of the Moon on the celestial 
    sphere (in SHA and Dec). is more or less vertical at the time its altitude is 
    observed. Since the Moon's "horns" are nearly perpendicular to its motion 
    among the stars, there is a simple observational test. If the line through 
    the horns is within thirty degrees of horizontal, then you can safely use 
    this method with minimal error. Even at 45 degrees tilt, the accuracy is 
    reduced from 1.00 to 0.707. Since it was considered acceptable, though not 
    desirable, to use stars which were as much as 45 degrees out of line for 
    lunar distances, we should probably apply that same standard to longitude by 
    lunar altitudes. By contrast, if the horns are nearly vertical (consider the 
    Moon while it's rising, even right at due East, at the time of the "harvest 
    moon" in high latitudes), then the motion from a change in GMT will not much 
    affect the observed altitude.
    Second, the horizon at sea probably shouldn't be trusted to more than half a 
    minute of arc. This applies mostly to sights taken at different times. If we 
    can observe the Moon's altitude and almost simultaneously observe altitudes 
    of other bodies, the lower limit on the horizon error probably can be dropped 
    to 0.25 minutes of arc. Measuring lunar distances, by contrast, does not have 
    this difficulty. On land, you can measure lunar altitudes with an artificial 
    horizon, and the problem of the horizon vanishes. In that case, and when the 
    above geometric condition for the orientation of the Moon is satisfied, lunar 
    altitudes are an excellent means of determining GMT using that method of 
    adjusting the LOPs to match as described in John Karl's book. 
    So we have a puzzle: why weren't lunar altitudes for longitude ever used or 
    recommended in practice (historically)?
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