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    Re: How good were chronometers?
    From: Frank Reed CT
    Date: 2006 Mar 15, 19:21 EST

    I wrote earlier:
    "Stars, including Polaris,  were  rarely used in celestial navigation before
    the 20th century except  occasionally  for lunar distance sights."
    Greg, you replied:
    "I  seem to recall reading in a number of places that they were especialy on
    land.  Hard to say what is right when you hear so many different things!"
    Land  "navigation" and marine navigation are parallel universes. Everything I
    said  previously in this thread applied to marine navigation. For exploration
    and  mapping work on land, there are a number of differences. Stars were more
    popular  (they're easier to shoot from a stable platform, night is the
    prefered time for  this sort of work, and more), and lunars lingered longer
    (chronometers don't  like riding horseback and they don't like being dunked in
    Also,  I should add that there is no intrinsic reason why stars were not used
    in 19th  century marine navigation (the extra work required is minimal). They
    just  weren't popular.
    In another post, you wrote down one equation which can  be used to clear a
    time sight:
    "cos t = (sin h - sin L sin d) / (cos L cos  d)"
    and asked:
    " (1) I thought you had to use co-latitude ,  co-declination, &  co-Ho? (If
    this was already done I must have  missed it)."
    Yes, that step is already done. It just swaps sines for  cosines and cosines
    for sines. The equation you've quoted above is a direct  application of the
    fundamental spherical trig cosine law (try deriving it  yourself). Note that
    there are a number of other equations that will allow you  to calculate the
    corner angle of a spherical triangle from the three sides.  They're mathematically
    equivalent so the results are always the same. Using one  instead of another
    is a question of calculational convenience, and that can be a  big deal when
    you're working with logarithms.
    And you asked:
    " (2)  This looks suspiciously like every other spherical / navigational
    triangle so  why do you say stars were not used except for lunars?"
    Because that's  what's in the logbooks! Celestial navigation (the maritime
    flavor) was very much  a daytime activity in the late 18th and 19th centuries
    --something like 98% of  all sights. So why didn't they use stars more often?
    Any ideas?
    And you  asked:
    " (3) Are you saying you can't get a good longitude from just the  noon
    I can answer 'yes' to that as you've qualified it: you  can't get a "good"
    longitude from "just" the noon sight. Noon sights (alone)  were not generally
    used for longitude. But a series of sights around noon can be  used to get a
    fairly good estimate of local time. For example you could do an  altitude roughly
    half an hour before noon and record it and the time on your  watch. Let's say
    your watch shows 11:35:00. Then shoot the noon sight and record  the maximum
    altitude. Perhaps you record the time on your watch and find that  it's
    12:06:10. Finally you wait until the Sun returns to exactly the same  altitude after
    noon that you observed half an hour before noon (and maybe you're  even smart
    enough to adjust the altitude for the change in the declination in an  hour).
    At that moment, you look at your watch and it shows 12:34:30. The average  of
    the times before and after noon is 12:04:45 so that means that your watch is
    4m45s fast on Local Apparent Time. After adjusting for the equation of time,
    you  can then compare the corrected time with GMT from a chronometer and
    you're done.  Notice that the time I suggested for the maximum altitude does not
    match the  time half-way between the equal altitudes. This happens because the
    Sun appears  to "hang" at its maximum altitude for a rather extended period of
    time --the  exact time of noon is very hard to estimate from the single
    observation used for  noon latitude. Also note that the equal altitudes on either
    side of noon are  extremel sensitive to small changes in altitude so you need a
    good observer with  a good instrument and a stable platform to make this work
    "My  reason for asking is that I do a lot of rev-war & pre-1840  re-enacting
    and I'm trying to understand exactly what was done
    on land  & sea."
    Aha. Very interesting. I suppose I would just re-iterate that  practice on
    land could be, and usually was, quite different from maritime  practice. Partly,
    this is because the problem is very different. At sea,  navigation is a
    little simpler, from one point of view, because you can sail in  a straight line
    for an extended period of time. From a different point of view,  it's much more
    difficult at sea because, of course, there are no landmarks. The  reasons for
    recording exact latitude and longitude are really very different in  the two
    And you wrote:
    "I know for example that on land  both David Thompson & Lewis & Clark took
    Lat via  Polaris."
    Another difference between land-based celestial navigation and  ocean
    navigation in the 19th century: the ocean navigators were vastly greater  in their
    numbers, guiding thousands of vessels across the world's oceans every  year, but
    can you name any three of them ? They're an anonymous horde.  By contrast,
    the land explorers, though few in number and frequently only  marginally
    competent in the art (Lewis & Clark), they are often names that  we all know
    today. The navigation practiced by Lewis & Clark is justly  famous because of the
    historical significance of the expedition, but their  navigational technique is
    idiosyncratic, singular, and theirs  alone.
    42.0N 87.7W, or 41.4N  72.1W.

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