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    Newton and Halley: was Re: the Shovell Disaster
    From: George Huxtable
    Date: 2007 Nov 15, 00:22 -0000

    As this discussion has taken a different turn, I have relabelled the thread
    Mike Daly has jumped to some conclusions.
    I had written-
    | > And his octant didn't appear until over 20 years later, at its one-and 
    | > public mention, noted in the Royal Society's Journal Book for 1699, when
    | > Newton referred to it as having been used at sea by Halley.
    Mike commented-
    | It was also published in the Phil.Trans. N. 465 in 1742, described as:
    | "A true Copy of a Paper found, in the Hand Writing of Sir Isaac Newton,
    | among the Papers of the late Dr. Halley, containing a Description of an
    | Instrument for observing the Moon's Distance from the Fixt Stars as Sea."
    True. What was published in 1742 was was presumably written well before the 
    Royal Society gathering in 1699, being a private note sent to Halley  That 
    note is interesting, in that its wording suggests that it predated any 
    attempt to divide the arc of such an instrument, by Newton or by his 
    craftsmen at the Royal Mint, of which he was then Warden. His words 
    described it as being divided "by a diagonal scale, and the half-degrees, 
    half minutes, and one-twelfth minutes, counted for degrees, minutes, and 
    one-sixth minutes." At that point he had obviously not appreciated the sheer 
    impossibility of dividing to 10 arc-seconds by a diagonal scale. No doubt, 
    he would find that out the hard way.
    I continued-
    | > For
    | > example, Halley never even mentioned what instrument he used to obtain 
    | > precise latitudes, in his three voyages, though it must have been 
    | > special, to achieve the results he did.
    And Mike asked-
    | Latitude or longitude?
    I was referring to Halley's latitude observations, which have been collected 
    by Ted Gerrard for the three voyages in "Astronomical Minds", and can be 
    referred to in more detail in Thrower's 2-volume "The three voyages of 
    Edmond Halley in the Paramore 1698-1701", Hakluyt Society 1981.
    In particular, in his English Channel  survey of 1701, out of 12 
    identifiable latitudes, Gerrard quotes two as being in error by 4 miles, 2 
    by 3 miles, 3 by 2 miles, 2 by 1 mile, and 3 were spot-on to modern values. 
    I suggest that many of us would have been rather proud of such results 
    today, with a modern instrument. Could such results have been obtained with 
    a cross-staff, or a backstaff? But Halley doesn't say a word about what 
    instrument he used.
    | Halley published his technique in an appendix to the second edition of
    | "Mr. Street's Caroline Tables" around 1684.  He used the time of an
    | observation of an occultation of a star by the moon (instead of lunar
    | distances) and the instrument was simply a telescope.  What isn't clear
    | is whether he used this technique on only one or on all three voyages.
    Not on his third voyage, within the English Channel, when it would be 
    imprecise enough not to improve on the rough longitudes which were already 
    known for headlands. But on the other two, out in the Atlantic. And not, 
    usually, an "occultation", but an "appulse" or near-miss, of the Moon as it 
    passed a star. As near as I could tell, he timed (relative to a star 
    time-sight) the moment when he judged the star to be aligned with an 
    extended line which joined the horns of the Moon. How he allowed for 
    parallax, I do not know. I've seen no mention, in Thrower, of any 
    measurement of lunar-distance that could be identified as such. That does 
    not imply that it didn't happen, however. Halley's method avoided the need 
    for a measure of lunar distance
    This is the way Halley described his procedure, as referred to in Thrower 
    and in Gerrard.. At the time he was off the coast of Brazil, 7 deg 6' S, 35 
    deg 00' W, the (converted to Gregorian) date being 7th March 1699. "I 
    observed the Moon to apply to the Bull's Eye [= Aldebaran], and that the 
    star was in a right line with the Moons horns when it was 10 deg 26' high in 
    the West, or at 10h 11' 44" [pm estimated local time] from both which 
    observations I conclude that the Longitude of this coast is a full 36 deg to 
    the Westward of London...". From which he concuded that a previously unknown 
    current had set Paramore Westward 200 leagues. He had discovered the Brazil 
    Current. The star altitude provided his local time, the passing of the star 
    through the line of the Moon's horns provided his Greenwich Time. Other 
    observations were described in similar terms, though usually in less detail.
    | If he did use lunar distances, it is often suggested that he used
    | Newton's, which E.G.R. Taylor says was constructed by Thomas Heath and
    | may have been shown in his shop window.
    Mike has that quite wrong. Where does Eva Taylor say that? In "The 
    Mathematical Practitioners of Tudor and Stuart England", her entry for Heath 
    says "He exhibited in his shop ... a quadrant on the principle of Hadley's 
    sextant which had been designed by Isaac Newton c. 1677 for finding lunar 
    distances". As Thomas Heath flourished in the period 1714-65, he was of 
    quite a different generation from Newton.
    He added-
    | However, I can't find much to
    | support the claim that Halley used Newton's.
    Well, what I referred to were Newton's words, as recorded in the Royal 
    Society's Journal Book for 1699, when Newton referred to his instrument, in 
    Halley's presence, as having been used at sea by Halley. Halley was in 
    London, in the short interval between his two Atlantic voyages to survey 
    magnetic variation. Here is what the record states, on 16th August 1699-
    "Mr Newton showed a new instrument contrived by him for observing the moon & 
    Starrs, the Longitude at Sea, being the old Instrument mended of some 
    faults, with which notwithstanding Mr Hally had found the Longitude better 
    than the Seamen by other means".
    Mike concludes-
    It is also possible he
    | used one of his own design, the "folding-telescope on a radio latino
    | with a screw adjustment" described in Cotter's "The Mariner's Sextant
    | and the Royal Society".
    I don't know that work of Cotter's, and would welcome a more detailed 
    citation, if it's in a journal. But I have Cotter's "History of the 
    Navigator's Sextant", 1983, which shows Halley's "Instrument of Observing at 
    Sea" on page 109, and states that it was described to the Royal Society in 
    1692. From Cotter's diagram, showing an instrument with a screw adjustment, 
    then if that's the same instrument, I can't see how it could possibly have 
    worked (but that doesn't prove that it couldn't). However, Cotter himself 
    concludes "There is no evidence that Halley's instrument was ever tested at 
    PS. If Ted Gerrard's book is of interest, you can order it direct from 
    www.samosbooks.org at �13.95 (about $29) and free worldwide (surface) 
    shipping is included.
    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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