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    "Sumner" before Sumner
    From: Frank Reed CT
    Date: 2006 Mar 30, 19:06 EST

    Some history fun.
    In 1826, an appendix by  W. Lax was published in the Nautical Almanac for the
    year 1829. It's a method  for using altitudes of two different objects taken
    simultaneously (more or less)  to get a complete fix of a ship's position. It
    yields latitude and local  apparent time (and hence longitude if we can get
    GMT) with one calculation based  on those measured altitudes. It's long and not
    particularly practical. The  emphasis is on observations taken for a lunar
    distance observation which  complicates the analysis. If Lax had instead focused
    on altitude observations  with Greenwich Time "given" by some abstract method,
    the whole process might  have appeared much more relevant to practical
    navigation, and he might have  "scooped" Sumner who published his graphical method
    almost 20 years later. Lax  got close, but he didn't see the big picture.
    Lax even talks about error  analysis (which I mentioned in an earlier
    message) and notes that this method of  fixing the position is prone to error when
    the relative azimuth between the two  bodies is low and is least prone to error
    when the relative azimuth is close to  90 degrees --which of course is very
    familiar to 20th century navigators as the  result of the crossing angle between
    two celestial lines of  position.
    42.0N 87.7W, or 41.4N  72.1W.

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