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    Re: How did Sumner navigate in 1837?
    From: Jim Thompson
    Date: 2003 May 14, 07:53 -0300

    > -----Original Message-----
    > From: Navigation Mailing List
    > [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Herbert Prinz
    > Sent: Wednesday, May 14, 2003 8:37 AM
    > Subject: Re: How did Sumner navigate in 1837?
    > 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?
    > Herbert Prinz replied:
    > 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?
    Herbert, thank you for confirming all this for me.  Very informative.
    Is your question, "How common was it to do a time sight at all?" rhetorical?
    Do you have the impression that Sumner was unusual in doing his mid-morning
    time sight?
    > > 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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