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    Re: How did Sumner navigate in 1837?
    From: Herbert Prinz
    Date: 2003 May 14, 11:37 +0000

    Jim Thompson wrote:
    
    > 2. Was the celestial LOP completely unknown in 1837, or were academicians
    > aware of the concept, but nobody had been able to operationalize it at sea?
    
    Globes had been used since the 16th century for the graphical solution of
    astronomical problems. They had to be rather large to be useful and were
    impractical at sea.
    
    > 3. Exactly how would he [Sumner] have determined his longitude in 1837?
    
    By chronometer and time sight, using one of the methods given in a contemporary
    Bowditch (preferring No.3 over No.1, passing over No.2).
    
    > 4. How aware were navigators in his day that their longitude calculation was
    > dependant on latitude?  They must have been.  It must have been part of the
    > sight reduction?
    
    Not every longitude calculation is dependent on latitude. For example, the
    "method by equal altitude" isn't - well, at least not to an extend where an
    error of 1 deg of latitude would matter. But with most commonly practised
    methods there was indeed such a dependency and navigators were well aware of it.
    
    The problem was by no means new or unique to celestial navigation. Already
    before the chronometer, dead reckoning was based on Traverse Tables that kept
    track of changes in latitude as well as meridian departures and thus, longitude.
    If possible, the Sun was observed at noon. This observation overruled the DR
    latitude. Now the the Traverse Table had to be adjusted so as to reflect the new
    latitude, thereby yielding a new DR longitude. J. H. Moore, for instance,
    (Practical Navigator, 1800) has a whole chapter on this. Although he claimed to
    present to this end "the most rational methods", I can't help the feeling that
    this was an area where navigation had more to do with art (or magic) then with
    science. Some of the worked examples in Moore are charmingly naive and quite
    amusing to read.
    
    > Putting together some information on 18th century celestial navigation from
    > www.lunardistances.com, I assume that he [Sumner] probably had done this:
    >
    > 1. Determined latitude by DR from his last fix, 900 NM to the west, at 21
    > deg W longitude (he was now at 6 deg W).  Is there no way he could have
    > determined latitude from the sextant altitude of the sun and his chronometer
    > time?
    
    Only if he would have had his longitude in addition to Greenwich Time, or local
    apparent time instead of it. Neither is a realistic assumption.
    
    As Sumner himself stated convincingly, from one observation you get exactly one
    position line, no more, no less. If this position line happens to be
    perpendicular to your meridian (it will be, if, and only if the celestial body
    is on it), then you happen to have got your latitude.
    
    >
    > 2. Determined longtitude by using these known variables: DR latitude, his
    > chronometer GMT time, the altitude of the sun from his 1000 shot, and tables
    > showing declination of the sun.  From those he could determine local time,
    > from which he could determine the difference in time between his local
    > meridian and Greenwich.  I still don't understand the steps he used, but I
    > think that's the basic process he would have used.  Am I right?
    
    Yes, you are.
    
    > The critical point is that his longitude estimate was dependant on his
    > latitude.  He seemed to understand that, which is why he reworked the 10 AM
    > sight with two presumed latitudes.  How common was that practice in 1837?
    
    How common was it to do a time sight at all? And would not the first person to
    plot three lat/lon pairs have made Sumner's discovery?
    
    
    > If that old DR latitude was way off, then his longtitude was too -- which
    > was one of the points that navigators in those days might not have
    > appreciated, because they did not commonly understand the concept of a
    > celestial LOP.latitude.
    
    As I said before, I do think that navigators were aware that wrong input lead to
    wrong results. But before Sumner, an observation was either good or bad, the
    result right or wrong. By contrast, Sumner adopts a quantitative approach to the
    problem. He asks how much error one may expect under certain given conditions.
    In the treatise where he presents his new "Method by projection on Mercator's
    chart", he spends over 13 pages out of 90 on error analysis. He even has it in
    the title:
    
    "[...] First, The True Bearing of the Land; secondly, The Errors of Longitude by
    Chronometer, Consequent to Any Error in the Latitude; thirdly, The Suns True
    Azimuth.[...]"
    
    I believe he is the first one to undertake any serious attempt at error analysis
    in a work of navigation and is perhaps not sufficiently appreciated for this by
    historians. Later in the century this would become a big topic, specially in
    France.
    
    Herbert Prinz
    
    
    

       
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