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    Re: Coordinates on Cook's maps
    From: George Huxtable
    Date: 2007 Apr 17, 23:39 +0100

    Alex has made a useful study of the precision of Cook's navigation, in
    latitude and longitude. Rather important work, in my view.
    
    Here's a suggestion. It may be worthwhile to both, if he exchanges
    information with "Jeremy Spencer" . Jeremy is a
    researcher at the Australian National Museum, in Canberra, and has been
    working on Cook's surveying techniques. I heard a talk from him on that
    topic at a Greenwich symposium last November. I suspect he might welcome
    collaboration with Alex.
    
    Alex wrote-
    |
    | I used photocopies of the original maps of
    | Cook's expedition published by Hakluyt Soc.
    | by Cambridge University Press
    | in 1955 (Available at Purdue library).
    | There are 68 maps and shore views,
    | and the collection is claimed to be complete.
    
    That set of maps and views was edited by Skelton, who was in charge of the
    map room at the British Museum. It was issued as a companion to the 4-volume
    magnum opus Hakluyt Society edition by J C Beaglehole, of Cook's Journals,
    covering his three voyages. The map set was indeed pretty complete for its
    time, but more recently (1988 to 1997) a 3-volume set has appeared, "The
    charts and coastal views of Captain Cook's voyages", again by the Hakluyt
    Society, edited by Andrew David. It contains a lot of additional material,
    though I don't know whether that includes any further stuff that meets
    Alex's search criteria, as described below. It's just worth drawing to his
    attention, in case it does. No doubt Purdue will have a copy.
    
    | Only the following maps have the right scale and
    | coordinates on the sides, with longitude from Greenwitch,
    | to determine positions
    | of certain points with 1' accuracy.
    |
    | I choose a conspicious point on a map,
    | usually a cape, take its coordinates from the map,
    | and then try to identify the same point on
    | Terraserver photos.
    
    I wonder if that's the most direct way to compare. How had Cook drawn that
    point on the map? At some time (on his first voyage, with no chronometer) he
    will have found longitude, from a lunar, and latitude. If that was actually
    at the conspicuous point or cape, well and good. Otherwise, there will have
    been mapping errors, in the placing of that point with respect to a lat and
    long, measured elsewhere.
    
    Take his first map, No 9, as an example. When traversing that part of the
    Society Isles that the map shows, Cook's journal refers to only one
    determination of longitude, at Huaheine Island (spellings differ), which is
    shown on map 9. The entry for 19th July 1767 states "... the Island, which
    is situated in the latitude of 16 d 43' S and longitude 150d 52'W ...". It
    isn't clear to me whether Cook intended it to be a central position of that
    small island, or of his anchorage near its NW corner; from the numbers, I
    suspect the former. Cook's map shows only two lines of longitude, and Alex
    has chosen one of them, at 151d 29', and its intersection with a marked
    latitude line at 16d 40'S, as his point of reference, to compare with a
    Terraserver position. Not a cape or landmark, just an anonymous spot in the
    sea, outside the reef of another island, Otaha. According to the map in
    Beaglehole (fig.36) showing Cook's presumed track, he hadn't actually
    visited that spot, but had that coast in view from about 4 to 6 miles off,
    beating for many hours against a headwind.
    
    It so happens that on map 9, if we extrapolate the longitude scale from the
    two spot values given, and assume that the given position was intended to be
    the centre of Huaheine I., then everything is consistent, lat and long.
    
    The point that I'm rather labouring here, is that by fitting a Terraserver
    fix to the outlines of Otaha, which I presume Alex has done, he is relying
    on two bits of navigation. First, on Cook's celestial position of Huaheine.
    Second, on his fixing, by coastal survey techniques, of the position of
    Otaha with respect to Huaheine, and his accurate drawing, from offshore, of
    the outline of Otaha, to compare with Terraserver.
    
    How much more direct, then, to compare Cook's stated position for Huaheine,
    with a Terraserver position for that same island, and leave Otaha out of it?
    Indeed, because Cook's chart is so self consistent, I doubt if the result
    would differ significantly, but it's the principle that matters.
    
    In respect of Chart 14, Cook's Journal quotes two astronomical positions,
    directly, for the two capes that Alex has considered, so I have no quibbles
    there about his analysis.
    
    Cook's journal scatters references to position determinations, many of lat.,
    much fewer for long. However, fuller information can be found in William
    Wales, "Astronomical observations ..." of 1788. Wales was astronomer on
    Cook's later voyages, but wasn't on the first, in which the astronomer was
    Green. Green died on the return voyage (of drink?) and left has papers in
    something of a mess, but years later, Wales extracted a lot of useful stuff
    from them, including many position determinations that are not to be found
    in Cook's Journal. I wonder if it's available in digitised form.
    
    =====================
    
    A comment about the table below. Alex lists the error as positive if Cook's
    value is numerically greater that that from Terrafix, and vice versa. But
    some longs are measured Easterly, and some Westerly, from Greenwich, so at
    180, the sign of the quoted error suddenly reverses. It would be more useful
    to quote the divergence always as an error, + or -, in the same sense.
    
    | The results are rounded to 1 minute.
    | First error is in latitude, second in longitude.
    |
    | First voyage (no chronometers were available):
    |
    | Chart 9.  Cook's coords:      16d40'S 151d29'W
    |          Terraserver:        16d41'S 151d32'W Er:-1', -3'
    | Chart 13. East Cape: 37d43'S 179d0'E,
    |          Terraserver:        37d41'  178d33'  Er:+2', +27'
    |          Table Cape:         39d07'  178d25'
    |          Terraserver:        39d12'  178d00'  Er:-5', +25'
    | Chart 18. Cape Teerawitte:    42d21'S 175d35'E
    |          Terraserver:        41d18'  174d42'  Er:+3', +53'
    |          Cape Campbel:       41d41'  175d13'
    |          Terraserver:        41d47'  174d20'  Er:-6', +53'
    | Chart 24. Cape York:          10d42'S 141d42'E
    |          Terraserver:        10d43'  142d36'  Er:-1', -54'
    |
    |
    | Second and third voyages (both chronometers and Lunars used):
    |
    | Chart 35. Friendly Islands:   21d16'S 174d44'E
    |          Terraserver:        21d17'  174d55'  Er:-1', -11'
    | Chart 55. N point Hawaii isl: 20d17'N 156d00'W
    |          Terraserver:        20d16'  155d52'  Er:+1',  +8'
    |          Karakakooa bay:     19d28'N 156d00'
    |          Terraserver:        19d28'N 155d56'  Er:-0',  +4'
    | Chart 57. Aivatcvhka bay:     52d54'N 157d33'E
    |          Terraserver:        52d56'  158d28'  Er:-2',  -45'
    |          Another point there:52d51'  157d48'
    |
    | Second and third voyages (both chronometers and Lunars used):
    |
    | Chart 35. Friendly Islands:   21d16'S 174d44'E
    |          Terraserver:        21d17'  174d55'  Er:-1', -11'
    | Chart 55. N point Hawaii isl: 20d17'N 156d00'W
    |          Terraserver:        20d16'  155d52'  Er:+1',  +8'
    |          Karakakooa bay:     19d28'N 156d00'
    |          Terraserver:        19d28'N 155d56'  Er:-0',  +4'
    | Chart 57. Aivatcvhka bay:     52d54'N 157d33'E
    |          Terraserver:        52d56'  158d28'  Er:-2',  -45'
    |          Another point there:52d51'  157d48'
    |          Terraserver:        52d53'  158d42'  Er:-2',  -54'
    |
    | The average absolute error in latitude is 2.3'.
    | The average absolute error in longitude is 33' (36' in
    | the first voyage).
    | This corresponds to a Lunar distance measurement
    | accuracy of about 1', approximately.
    |
    | I may conclude that the measurement accuracy was
    | about 1', and extra 1' in latitudes comes from
    | the horizon (or perhaps they used wood quadrants
    | instead of metal sextants for
    | altitudes, as Norrie advises:-)
    
    Cook had metal sextants, with large radius, and Vernier scales, so their
    scales could be read rather precisely. But they were divided by hand,
    machine division being a decade or two into the future, so systematic errors
    in the scale calibration were the big problem. I suppose they could have
    been corrected by a programme of measuring star-to-star distances, but I
    have no idea whether that was ever done.
    
    | The log of astronomical observations shows that enormous
    | number of measurements was made for each Lunar,
    | with 3 or 4 sextants and different observers.
    | It seems that to determine longitudes of important points
    | on the shore they made around 100 measurements altogether
    | for each such point.
    
    Certainly, at places like Cape Venus, Tahiti, and Ship Cove, Queen Charlotte
    Sound, New Zealand (where Cook returned many times on his travels)  many
    observations were made, and a precise North-South transit set up, with a
    precise pendulum clock, to get the position with great precision.
    
    | It is interesting to find out how much of these
    | errors is due to the almanac errors.
    
    That's a really important question, well worth asking, and answering. The
    best study of such matters that I know of was made by Nicholas Doe, "Captain
    Vancouver's longitudes - 1792", in Journal of Navigation, vol 48, 3, pages
    374-388, September 95. This looked at errors in predictions of Moon's
    ecliptic longitude, in the Nautical almanac (from which lunar distances were
    calculated) a couple of decades after Cook's time.
    
    Doe compared predictions in that almanac with modern calculations from the
    JPL ephemeris, and with actual Moon observations made from Greenwich around
    that time. Over the month in question, predicted Moon longitudes were
    consistently too great, by varying amounts between about 5 and 45
    arc-seconds over the monthly cycle. That, by itself, could give rise to
    systematic errors in longitude of 2 to 22 arc-minutes, or thereabouts.
    
    It would be no surprise if corresponding errors occurred in the almanacs
    used by Cook, and it would be a valuable and simple exercise to discover if
    they did.
    
    ==========================
    
    As Alex correctly notes, Cook carried a chronometer on his second and third
    voyage, but not on the first.
    
    A voyage away from civilisation for several years, such as Cook made, in hot
    weather and cold, was really far beyond the timekeeping powers of any
    chronometer. Although Cook said many nice things about the usefulness of his
    "watch", it was only so useful because it had been checked against lunars
    (or Jupiter satellites) at each shore-station, whenever the opportunity
    occurred. Even the best watch showed a rate of going that varied by up to 10
    seconds a day. Over a 3-year voyage, that could integrate up to over 3 hours
    of error, or 45 degrees of long! Only by resetting the time error, and
    rechecking the rate, at every opportunity, could the chronometer perform its
    valuable service. This is documented in Derek Howse's paper on "Navigation
    and Astronomy", pages 160-184 of "Background to Discovery", ed. Howse,
    University of California Press, 1990.
    
    So really, Cook's basic longitudes still depended on his lunars, even when a
    watch was aboard. The main use of the watch was in allowing short-term
    assessment of longitude, from a simple time-sight, without the necessity of
    a lunar observation, and this was invaluable when surveying.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
    
    
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