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    Celestaire Bubble Horizon
    From: Bill B
    Date: 2005 Feb 28, 00:32 -0500

    > on 2/11/05 7:22 AM, Jim Thompson at jim2@JIMTHOMPSON.NET wrote:
    > -----Original Message-----
    > From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On
    > Behalf Of Frank Reed
    > Sent: Friday, February 11, 2005 12:20 AM
    > Subject: Re: More on Thomas Hubbard Sumner
    > George H wrote:
    > "What surprises me, is that it took until 1837 for navigators to realise
    > that a useful position line could be drawn from a single observation of the
    > altitude of a body, even if it wasn't at meridian passage."
    > ... Plotting a celestial line of position would have seemed alien and
    > inexact when first proposed.
    > And yet Sumner's pamphlet was ordered onto all US Navy ships the year it
    > came out, although by then Sumner had spent 6 years verifying, refining and
    > writing up his manuscript.  His pamphlet is still very convincing to read,
    > partly because it was written so logically, and partly because it was
    > verified with so many real examples by a practising ship's captain who used
    > the method at sea himself.  At publication it had the endorsement of a
    > highly regarded Harvard mathematics Professor, who had written to Bowdtich,
    > so those clear-thinking experts, might have promptly focussed the navigation
    > community on Sumner's discovery.  From Vanvaerenbergh and Ifland, we know
    > that he had been talking about his ideas prior to publication.  It was
    > rapidlly adopted in the UK, but only slowly in France, which explains
    > perhaps why it was still there for Saint Hilaire, 40 years later.
    > He opens his Introduction with this glorious single-sentence paragraph:
    > "It is not so much the object of this work to present the navigator with a
    > new method of 'Double Latitudes', as to afford him an accurate method of
    > finding, by one Altitude of the Sun taken at at any hour of the day, wiht
    > the Chronometer time, the True Bearing of the Land, the Latitude, &c.,
    > being, from any cause, uncertain; and to place him on his guard, when near a
    > dangerous coast (and all coasts are dangerous when the Latitude is not
    > accurately known) against those errors of Longitude by Chronometer, which
    > arise from an erroneous Latitude used in finding the apparent time at the
    > ship; directing, particularly, his attention to the fact, as shown in these
    > pages, that when the Latitude is uncertain, a single altitude of the sun, at
    > any time of day, whne not less than say 7 degrees high, is, with a good
    > Chronometer, as useful as a Meridian Observation for Latitude ;  and the
    > errors above alluded to are rendered apparent."
    > In the Introduction, he also hints at extant navigators' thinking:
    > "...the fact, that ship-masters universally understand, and daily practice
    > the numerical calculation, namely, that of finding the apparent time at the
    > ship, which is the only one used."
    > "Many navigators, having taken morning sights for the Chronometer, supposing
    > the observation useless without 'the Latitude', wait for the meridian
    > observation, in order to deduce the Longitude by Chronometer; or, if the sun
    > be obscured till afternoon, think a single altitude under such circumstances
    > is of small value ; and, by the common methods, with good reason ; for then
    > the Latitude by dead reckoning form the preceding noon, must, in general, be
    > used to find the apparent time of the ship ; and here is the source of error
    > ; because, 26 to 30 hours having probably elsapsed, in such time the ship
    > may have sailed 250 to 300 miles ... cause an error in the Latitude by dead
    > reckoning, and consequently in the Longitude by Chronometer.'  {Jim: we
    > always talk about the "quest for longitude", but forget that in the early
    > 1800's there was a less advertised and perhaps less understood "quest for
    > accurate latitude".]
    > "None of the works on Navigation, within the writer's knowledge, exemplify,
    > or even hint at this important source of error" [Jim: he was referring to
    > error in estimating longitude owing to error in dead reckoning the latitude,
    > which was a necessary ingredient for calculating longitude] "but merely
    > direct the observations be taken when the sun bears nearly 'East or West as
    > possible', but it is impossible, for nearly 7 months in the year, to observe
    > the sun in the East or West points."
    > "It is hoped, that the 'Method by Projection', which explains these errors,
    > and renders a single altitude, taken at any bearing of the sun, available,
    > in a similar manner as a Meridian Observation, will supply a want which
    > every practical navigator must have frequently experienced." [Jim: he was
    > referring to accurate latitude.]
    > I think his most convincing evidence is the last plate, which he mentions in
    > the last sentence of his Introduction, almost as an afterthought.  It shows
    > their trip from the Mississippi, through the Gulf of Mexico, around Florida
    > and then north up the coast.  He was out of sight of land the whole time,
    > and in waters plaqued with strong currents, which made dead reckoning
    > treacherous.  His plate shows 3 tracks: (1) if done by dead reckoning alone
    > (they would have thought that they had sailed past the tip of Florida and
    > could turn north safely, if they had not grounded on Cuban beaches on the
    > way, but in fact they were still in the Gulf and would have grounded at
    > Tallahassee), (2) if done by dead reckoning modified by noon sights alone
    > (miles out compared to #3), and (3) their true track made good, determined
    > by using his procedures (tacked precisely between the Florida keys and
    > Cuba).  Studying that chart, I imagine that any navigator of the day could
    > see the advantages of studying the rest of the book.  I can imagine rushing
    > into a tavern to show that plate to buddies, if only for the obviously
    > interesting sea tale it told.
    > Sumner was pleased with this plate because it proved how his method made it
    > possible to more accurately calculate the various currents in the Gulf.  His
    > mind really did soar -- he had found a better way not only to navigate, but
    > also do to oceanography.
    > On re-reading his pamphlet this morning, I was stunned to finally understand
    > that he also clearly discovered the Celestial Fix!!  Page 11: "And likewise
    > if two altitudes be observed, the times being noted by Chronometer, and the
    > two lines, corresponding to the two altitudes, be projected as before, then
    > both the true Latitude and the true Longitude is found at the intersection
    > of the two projected lines."  Wow -- I had not heard that before about
    > Sumner, but it only seems logical.  (I should have read Vanvaerenbergh and
    > Ifland more carefully).  The term "line of position" did not surface until
    > about 1866.  I don't know about the term "fix".
    > He took brilliant advantage of special cases during his voyages.  In another
    > example, his ship was becalmed at 25W, 44N.  Because he was basically not
    > moving (about 1 knot, he wrote), his two sights varied primarily in time,
    > about one hour.  The mid-morning sun's altitude climbed from 14 to 19
    > degrees.  He worked out the lat/longs of the two sights each twice, using
    > latitude 43d and 44d.  That produced two LOPs subtended by a small angle.
    > "It is seen that these two lines intersect each other in Latitude ... which
    > is the true Latitude, and the true Longitude is ...".  He had plotted a
    > celestial fix, in January 1939.
    > It seems to me as though the world then was ripe for the idea, hot tinder
    > waiting for the match, as if everyone had it on the tips of their minds, but
    > could not put it into practice.  Richardson suggests that another feature
    > distinguishing Sumner was that, for some reason, he took the time out to
    > nail his ideas down and finish a 25,000 word manuscript.  Perhaps other
    > navigators had the same idea over years prior, but procrastinated, perhaps
    > attending to ship's business, a snooze after lunch or a good novel, rather
    > than hauling out old notes and going over them yet again.  So they lost the
    > opportunity to beat Sumner to his well-deserved place in history.
    For optimal results with Celestaire's Johnson practice-bubble horizon for
    Sun and Moon observations (and acknowledging corrections to Hs/Ha differ in
    each case), would you recommend:
    1.  Centering the Sun/Moon on the hairline?
    2.  Observing the body's limb tangent to the hairline?
    Thank you

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