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    Halley's lunars, back in 1698-1700
    From: George Huxtable
    Date: 2004 May 5, 17:46 +0100

    I've been in touch with a correspondent in Scotland who has been doing some
    serious work on Edmond Halley (1656-1742), and look forward to its eventual
    publication. He kindly reminded me of Halley's "lunar" observations, that
    were made on his two voyages around the Atlantic, in the British Navy
    89-ton pink "Paramore", as early as 1698-69 and 1699-70.
    Although I had a copy on my shelves of Norman J W Thrower's account "The
    three voyages of Edmond Halley in the Paramore 1698-1701", (Hakluyt Society
    1981), I had only glanced through it, and had not appreciated the
    significance of the navigational details. Now, I have, and it seems to be a
    remarkable story. I recommend anyone interested in the history of
    navigation to give it a read.
    Halley, of course, was famous for predicting the reappearance, long after
    his death, of the comet that bears his name. Astronmers know him as the
    author of the first catalogue of Southern stars, observed from the South
    Atlantic island of St Helena in his 20s. But his real hobby-horse was in
    proposing, long before the days of the famous longitude prize, that if
    magnetic variation could be accurately mapped worldwide, it could provide a
    tool for determining longitude. In the end, of course, that goal was
    To that end, he persuaded the Admiralty to fit out and man a small vessel
    under his command, for surveying magnetic variation over the Atlantic
    Ocean. It was, I think, the first time (and probably the last) that such a
    command was given to someone who was not  a Navy Officer, but a scientist.
    He sufferd from disciplinary troubles with his officers and crew; perhaps
    they resented being commanded by an outsider, throughout his three voyages.
    The third was to study the tides of the English Channel.
    Because his Atlantic voyages were magnetic surveys, rather than a simple
    passage from A to B, Halley had to estimate his positions, along his path,
    as best he could. Latitudes were no problem, of course. For longitudes, his
    main tool was dead reckoning, by log, line, and sandglass, compass and
    traverse table. On the rare occasions of a Moon eclipse, he timed that. He
    carried some sort of timekeeper, better than an hourglass, on board,
    because he occasionally refers to "at 3h 15m in the morning". Balance-wheel
    watches existed then, but were in no way chronometers, though they would do
    for maintaining apparent time from one day to the next. When he arrived on
    land, he observed Jupiter satellites with a telescope to get Greenwich
    What interested me, though, and what may interest Nav-l members, was his
    use of lunars, for determining time at sea. Remember, Hadley's (or
    Godfrey's) quadrant (= octant) was 30 years away yet. The only instrument
    Halley had for measuring angles across the sky, for a lunar, was the
    cross-staff, good to a degree or so. So how did Halley measure his lunar
    distances with sufficient accuracy?
    He didn't measure his lunars. He timed them instead, directly. For that,
    all he needed was his telescope. Here's how the trick was done.
    Remember, Halley had spent two years observing and cataloging Southern
    stars at St Helena, and had done the same at his observatory in Britain. He
    knew just what star was where, and no doubt had with him a good catalogue
    of their precise (for that date) positions, especially the zodiacal stars.
    When the Moon follows its wandering path across the sky, it never departs
    from the ecliptic by more than 5 degrees or so. Thoere's no shortage of
    stars in the sky. Sometimes the Moon will pass right over one, blotting it
    out. That an occultation, but it wasn't what Halley was looking for.
    What he was looking for was a star that the Moon passed really close to,
    grazing it if possible: a close conjunction, with the Moon passing above or
    below it. Then he drew a line in the sky (either in his mind, or using a
    cross-wire in his telescope) that passed through the two "horns" of the
    Moon, and therefore passed through the Moon's centre also. That line swept
    through the sky slowly, as the Moon moved through the stars. Halley would
    note the time when that line swept past a star he could identify, with a
    position that he knew. And that was all there was to it. The job was done!
    If the Moon followed the ecliptic exactly, then the line between the horns
    would be exactly at right-angles to its path. Being off, by up to 5
    degrees, the line between the horns could be skewed around by a few
    degrees. That's why a close conjunction was called for. He wouldn't want to
    extrapolate that line far, if a star was away from the Moon.
    What Halley had measured, to reasonable accuracy, was the moment when the
    Moon's centre had the same ecliptic longitude as the star did. All that he
    needed to do was to compare his observation with the predicted motion of
    the Moon, to discover the Greenwich time of the event. Because the Moon and
    star were so close, correction for refraction didn't arise. If the
    measurement could be made at a time when the line between the horns was
    vertical (somewhere near the Moon's meridian passage) then not even Moon
    parallax was important, as parallax moves it only in altitude, and so
    wouldn't affect the timing of such an event.
    Halley was making these lunar observations as a matter of scientific
    interest, to test out the method. Also he was using the results for
    navigational purposes, to discover (for example) how near he had got to the
    coast of Brazil. In that case he showed that his dead reckoning was many
    degrees short of where he found he had got to. But the real purpose was to
    help him to plot the positions for his magnetic surveying. Presumably, for
    that purpose (unlike for navigation) there was no need for a result to be
    available in real-time. Remember, at that date lunar orbit theory was very
    much in its infancy. Moon position predictions could not be relied on to
    any great accuracy. But obtaining his survey positions was a job that could
    wait until he returned to Greenwich., when he could discover what Moon
    positions had actually been recorded there, on the same night as his own
    observation was made. If that day had happened to be cloudy at Greenwich,
    no doubt he could interpolate between others, or ask of another
    observatory. If he used that technique (which was the way land-surveyors of
    the period would obtain their longitudes from Jupiter satellites) he would
    then become quite independent of the inadequacy of predictions
    Please note: in the description of Halley's measurement technique above,
    there's a lot of surmising, from me, about the details. Halley's own
    descriptions are tantalisingly terse. I will quote an example, of the log
    entry for that observation off Brazil, on (nautical day) 4 Dec 1699, which
    is about as full as Halley ever gets.
    "Latitude by observation 20deg 58' Wind and Weather as before
    we Stear away S W b S p Compass which makes a S 43 W Course correct
    Distance 79 Miles Diff: of Long 57 minutes Long a' London 31deg 13'West
    Last night the Amplitude was 34 1/2 and this Morning 15 1/2 very good
    observation, theSea being verySmooth and the Ship quiet True Variation
    Stated from both is 9deg 30'West in 20deg 30' This Morning the Moon aplyed
    to a Starr in Virgo of the 4 Mag: whose Longitude is [approx. equal to]
    0deg 39' Laty 1deg 25' The Moon did exactly Touch this Starr with her
    Southern Limb at 3h 15' in the Morning, and at 3h 20' 20" the Southern horn
    was just 2 Minutes past the Starr haveing carefully examin'd this
    observation and Compared with former observations made in England I
    conclude I am in True Longitude from London at the time of this observation
    36deg 15' and at this Noon 36deg 35'. That is according to the Account I
    have of it, about 5 Degrees East of Cape Frio."
    Note that Halley makes a step-change in his presumed long. at noon, from
    his DR value of W 31deg 13' to a new value, based on his lunar, of W 36deg
    35', a change of 5deg 20' or nearly 500 miles! He used that longitude for
    further dead-reckoning, from then on. Halley didn't sight land until
    several days later, so unfortunately we have no good confirmation of the
    accuracy (or otherwise) of his lunar longitude.
    Cotter in "History of Nautical Astronomy", notes that as early as 1615
    Baffin measured a Sun-Moon distance using a cross-staff for altitudes
    combined with azimuth observations. The ship was beset in ice at the time,
    so its stability may have helped. Being far North, both Sun and Moon were
    presumably very low in the sky, which may have made azimuth measurement
    more feasible. However, it seems unlikely that such a crude technique could
    possibly provide a useful measurement of lunar distance.
    However, it's something of a surprise to me, that neither in Cotter nor in
    Andrewes (ed.) "The Quest for Longitude", does there seem to be any mention
    of the 1698-1700 lunar observations made by Halley, although his many
    other contributions to navigation are fully credited. He appears to qualify
    as the first navigator to use lunars at sea in a practical way. This note
    is an attempt to redress the balance.
    contact George Huxtable by email at george@huxtable.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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