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> -----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
> To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> 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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