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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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