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    Re: Coordinates on Cook's maps
    From: George Huxtable
    Date: 2007 Apr 18, 13:32 +0100

    Alex's latest posting contains much interesting stuff, including-
    
    | I used Cook's Astronomical observation logs.
    | Available on the web.
    | There they list all observations.
    | Most of them cannot be tied to certain places
    | whose position I can verify.
    
    Where did those come from, on the web? Please give us the address. I, for 
    one, would like to get access.
    
    Were they derived from William Wales' "Astronomical Observations ...", that 
    I suggested Alex might consult, I wonder?
    
    Many observations, of course, will have been made in the open ocean, and 
    therefore useless for Alex's purpose. It's only those taken near a definable 
    landmark that can be tied to Alex's Terraserver positions.
    
    Please, Alex, tell us a bit more about Terraserver, and give the address at 
    which it can be found.
    
    | But some of these observations have very specific
    | places on the shore attached. Like "Point Venus".
    | I find this "point Venus" on a Cook map.
    | I suppose that this is the place whose position he
    | (they) determined with the most care
    | (Hundreds of observations are listed under "point Venus"
    | in the astronomical obs. log.
    | They had an observatory there. I suppose
    | that co-ordinates on the map were
    | all measured FROM this point
    | Venus, whose position they determined with such care.
    | Then I find this point Venus on the Terraserver.
    
    Yes, Point Venus was the main spot from which the Transit of Venus was 
    observed, which was one main purpose of the whole expedition., It's exact 
    location was very important. Taken together with reports from other 
    observers in various parts of the World, the transit was used to determine 
    the size of the Solar System. So Cook was surveying much more than just 
    Earthly geography!
    
    | On other maps, I used suspicious capes,
    | anchor stations etc.
    
    I pointed out with reference to map 9, that in the
    | > Society Isles that the map shows,
    | > Cook's journal refers to only one
    | > determination of longitude, at Huaheine Island
    |
    | I was not using Cook's journal.
    | I was using the "Original astronomical Observations..."
    | by his associates like Bayly, and Wales and other officers
    | (available on the web)
    | to determine the points where
    | they made really carefull observations.
    
    Ah. Where, on map 9, had such observations been noted?
    |
    | Like 50-100 Lunars with 4 sextants and 4
    | or 5 different people
    | from land.
    
    Yes, indeed. The Navy was by no means short-staffed on such expeditions, and 
    there were also many young midshipmen under training. Green used all the 
    talent he had, and took his training duties seriously. Many expert 
    navigators emerged from their voyages with Cook; for example Bligh and 
    Vancouver.
    |
    | Comparable with what I made from my balcony:-)
    
    Indeed, they were comparable with Alex's work. And like Alex, their 
    measurements, when on land, extended over many weeks, in which case some of 
    the monthly variation in the almanac predictions would cancel out.
    |
    | I used THESE points on THEIR maps.
    
    =====================
    
    About possible errors in the Almanac predictions of lunar distance, I had 
    written-
    
    | > 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,
    
    Alex asked-
    | American or British?
    
    The Journal of Navigation is the British publication; 3 per year, soon 
    increasing to 4, from the RIN (Royal Institute of Navigation).
    
    The American complement, from the Institute of Navigation, is named 
    "Navigation".
    
    ============Digression starts here-
    
    | I renently bought a CD from the American one,
    | and was very much disappointed. I mean I payed $50
    | (including delivery)
    | for a piece of crap. I mean there are 4-5, maximum 10
    | papers worth reading (from my point of view) on the whole
    | disc, and 3 or 4 of these
    | papers are available on the web for free
    | anyway.
    
    I agree with Alex here in one respect only. The CD cost $25, and "shipping" 
    to the UK cost another $25! I thought that overseas buyers were being 
    ripped-off over that delivery charge, when the stamp cost no more than $5, 
    but am appalled to learn that the same charge was made to buyers within the 
    US. That all leaves a sour taste.
    
    But I think that Alex's dismissal of its contents as "a piece of crap" is 
    quite unjustified. It depends, I suppose, on the breadth of your 
    navigational interests. Over recent years, Alex has concentrated, very hard, 
    on a single (important) question, that of observational precision. I am 
    delighted to note that he is now expanding his interests into navigational 
    history, and I hope that will grip him as hard as it has gripped me. Having 
    my own small boat, I've been tinkering into various aspects of navigation 
    for forty-odd years, so I have found a MUCH greater fraction of the papers 
    on that disc to be of interest, than Alex has. I suspect that many other 
    listmembers are likely to find the same.
    
    | My general philosophical opinion is that
    | "REAL science is available for free",
    | on the web or otherwise, is strongly confirmed
    | by this CD.
    
    Well, though I agree that in a perfect World that might be the case, we have 
    to take it like it is, make the best of it, and do what we can to change it. 
    Things are changing, in the right direction. I wonder if any of Alex's 
    mathematical publications have ever appeared in a journal which charges a 
    cover price?
    
    I compare the IoS disc with a corresponding offer from RIN, in which they 
    offer the digitised run of fifty-odd years of Journal of Navigation, on CD 
    (the whole thing, not a distillation of celestial papers only) for about �70 
    (=$140) to members, a bit more to non-members. So far, that cost has put me 
    off, though I know there's a wealth of stuff out there I would enjoy 
    reading. Perhaps I'll drop some hints, nearer my birthday.
    
    =================end of digression.
    
    There's too much in that Doe paper to transmit to Alex over the ether, but 
    if he sends me his postal address I will be pleased to post a scanned copy.
    
    | > 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.
    |
    | I wolud like to do this.
    | (I am mostly interested in sextant performance,
    | so I would like to seratate the sextant errors from
    | the almanac errors).
    | The hardest thing (for me) is to discover
    | what almanacs precisely did they use, and to find
    | these almanacs on the web or elsewhere.
    |
    | The "true almanac" with exact positions is supposedly
    | available on the Frank web site.
    
    There's no problem about the Almanac that was used by navigators of those 
    days, starting with Cook. It was "The Nautical Almanac and Astronomical 
    Ephemeris", first published by order of the Commissioners of Longitude for 
    the year 1767, and continuing, with some changes of title and publisher, 
    every year to this day. Some voyagers, mostly French, would have the older 
    "Connaissance du Temps"  on board as well.
    
    Pirated versions emerged, which were generally copies of the original.
    
    I understand that early years of the Nautical Almanac are available in 
    scanned form from various websites, for most years at least, perhaps by now 
    for all years. Some reader, more familiar with the web than I am, will I 
    hope point Alex to where they can be found.
    
    The early almanacs carried predictions for lunar distance, mostly to two 
    celestial objects, one East and one West of the Moon, for most days. These 
    were stated to an arc-second, though the errors in prediction were far 
    greater than that, at three-hour intervals.
    
    The (human) computers deduced those figures by quadratic interpolation 
    between Moon predictions, the ecliptic latitude and longitude of the Moon 
    being given, on another page of the almanac, to the nearest arc-second for 
    noon and midnight of each day. Longitudes were quoted in signs (there were 
    12 signs, each of 30 degrees), degrees (up to 30), minutes, and seconds, so 
    degrees (to 360) are found by multiplying the sign-number by 30, then adding 
    degrees.
    
    Discrepancies between the old almanac and modern calculations are best 
    studied in terms of those twice-a-day Moon ecliptic lats and longs, rather 
    than in the 3-hourly lunar distances themselves.  This assumes that the 
    computers did a precise job of interpolating, and then calculating the 
    angular separation to the body; which indeed they did. Precise positions of 
    those few reference-stars had by then been well enough established, by 
    Halley and others.
    
    It's easy to convert between those ecliptic coordinates and the RA / dec of 
    a modern prediction, for which you need an accurate value of the Earth's 
    tilt of axis, at that date. And you need to be aware that the time scale of 
    the old almanacs (up to 1834) was in terms of apparent time not GMT, so the 
    Sun really was exactly on the Greenwich meridian at noon. For comparison, 
    modern Moon predictions have to be taken, not for noon and midnight UT, but 
    offset from that by the equation of time.
    
    Once the errors in the lunar positions have been uncovered for the dates of 
    Cook's voyages, that shows the unavoidable errors that were imposed on 
    Cook's longitudes, but also the same errors applying to all other 
    navigators, using that almanac, anywhere in the World at those same dates. 
    So it would be useful evidence for maritime history generally. A worthwhile 
    bit of study.
    
    George.
    
    contact George Huxtable at george@huxtable.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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