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    Re: Lunars in 1766
    From: George Huxtable
    Date: 2004 Oct 1, 23:56 +0100

    Alex Eremenko quotes from the Russian translation of Bougainville, about
    his position for Cape Virgins, at the North point of the entry to Magellan
    Strait from the Atlantic.
    
    >"This fix, combined with bearings gives the following
    >coordinates for the cape of Vierges:
    >Lat. S 52d23' and Long. 71d25'20" West of Paris.
    >Because the cape of Vierges is an interesting point
    >for geography, I have to explain what made me believe
    >that its position was fixed by me with almost
    >absolute precision.
    >
    >"On November 27, afternoon, Chevalier du Bouchage measured
    >eight Lunar distances whose averaging gave the
    >longitude of 65d0'30'' (West of Paris) at 1h43m26s of
    >real time; M. Verron on his side measured 5 lunar distances,
    >whose average gave our longitude at the same time as
    >64d57'. The weather was good and favorable for observations.
    >On 29-th at 3h57m35s of true time, M. Verron, by 5-fold
    >measurement of Lunar distances found the longitude as 67d49'30"
    >(West of Paris).
    >
    >"Now, having found the place of the ship in view of cape Vierge,
    >and taking as a basis [for dead reckoning - A. E.]
    >the longitude determined
    >on November 27,
    >by averaging the results of observations of
    >Chevalier du Bouchage, and M. Verron, we will obtain that
    >the cape of Vierge is placed on the longitude 71d29'42" W of Paris.
    >Obserevations at the moment of determination by bearings
    >of position of cape Vierge would give the result of 38'47" more
    >to the West. However, I suppose that one has rather to take as a base
    >the observations of Nov. 27, because they were made several times,
    >by two observers who did not communicate with each other,
    >while their results differ only by 3'30", and seem so plausible
    >that it is hard to reject them.
    >
    >"These observations were made using an English octant.
    >The method of determining longitude in sea
    >by way of Lunar distances to the Sun
    >or to Zodiac stars is known for many years.
    >Mr. de la Caille and  d'Apres, used this method in the sea,
    >also with the Hadley octant."
    
    ============
    
    The latitude is simple: Bougainville gives S 52d 23', and a table of lats
    and longs in a 1914 Norie's  gives S 52d 20' 10", a discrepancy of 3 miles.
    More-or-less what one would expect for a latitude.
    
    Longitude seems somewhat more confused. Norie gives W 68d 21' 42" (from
    Greenwich), to which we have to add 2d 20' 15", the Easterly long of the
    Paris observatory, to give W 70d 41' 57" from Paris. I make the longitude
    referred to in the first paragraph, of W71d 25' 20", to be 43' 23" too far
    West.
    
    But other numbers for longitude occur in the passage above. Bougainville
    appears to set great store by the lunars of Nov.27, and from that it seems
    that DR gives him a long for the Cape of 71d 20' 42", so  38' 45" too far
    West, from Norie's position.
    
    Those longitude discrepanies are not surprising. They are the sort of
    errors one might expect from a lunar at sea, even if they confute
    Bougainville's own verdict that "its position was fixed by me with almost
    absolute precision."
    
    Lunars taken on 29th Nov gave a long of 67d49'30" West. Presumably, that's
    the ship's position, which may well have been some way off when the Cape
    came into view, and an allowance has to be made to arrive at the long. of
    the Cape itself. Bougainville is quoted
    as follows- "Obserevations at the moment of determination by bearings of
    position of cape Vierge would give the result of 38'47" more to the West."
    More West than his quoted 71d25'20" West, presumably, which would take him
    to W 72d 04' 07". But that's further West than the ship's position (on the
    29th) of 67d49'30", by as much as 4d 14' 37". That would imply that Cape
    Virgins was more than 150 miles from his ship. All in all, I don't
    understand this passage explaining how the observations of 29th were
    treated, and I wonder if Alex finds any greater clarity in the Russian
    version.
    
    ============
    
    But now compare that Russian version with Dunmore's modern translation.
    From this we see that Cape Virgins was not sighted until 2.30pm on 2
    December! He states that it was then bearing south, 7 leagues [21 miles]
    away. He goes on- "We were then in latitude 52d 3' 30" and longitude 71d
    12' 20" according to Verron, which taking our bearings into account would
    place the Cape of Virgins in latitude 52d 23' and longitude 71d 25' 20"  "
    
    To me, this is rather puzzling. If Cape Virgins was indeed bearing South
    from the ship, then I would expect the Cape and the ship to have the same
    longitude, not a 13' difference.
    
    But leaving that aside, this passage from Bougainville is clearly the
    source of the position of Virgins, which was quoted at the very start of
    this mailing.
    
    How did he determine his ship's position at that time? At midday on 2 Dec
    he gives as observed latitude of 52d.
    
    He gives "Calculated longitude 71d 12'. Bellin 70d 17'"
    
    The reference to "Bellin" is to a chart of the area, of doubtful accuracy,
    which was on board. Bellin's chart had shown Montevideo in 58d longitude,
    whereas V?ron had made it to be 58d 55' 30" (presumably by lunars or
    Jupiter's moons). So when they computed their longitude by DR, from a
    departure from Montevideo, there were two alternatives, depending on which
    value was adopted for Montevideo's long. It's clear, then, that the
    "calculated longitude" values for the ship, shown above, are based on DR
    since Montevideo, and not on a lunar-distance measurement.
    
    As for those quotations in the Russian version, about the lunar distances
    measured on 27 and 29 November, with his statement "its position was fixed
    by me with almost absolute precision.", I can find no trace in the Dunmore
    account, and no note in the journal of any lunar observations at all on 27
    and 29 Nov.
    
    So the basis for Bougainville's stated position for Cape Virgins is by no
    means clear (to me).
    
    ==============
    
    Magellan passed this cape on the feast-day of the 11,000 virgins; hence its
    name. It commemmorates a dark-age massacre which took place in the city of
    Cologne. To me, the surprise is that there were 11,000 virgins to be had. I
    doubt if it could happen in Cologne today.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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