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    Re: Thomas Jefferson and Lunar Obs.
    From: George Huxtable
    Date: 2005 Mar 26, 22:56 +0000

    Frank Reed's quotation (below) of a letter from Jefferson to Dunbar is of
    considerable interest.
    
    Jefferson was right, in that when measuring on land, rather than at sea, it
    is possible to establish a precise North-South meridian line from the
    observer, and then observations can be made of the Moon with respect to
    that line. This method is discussed at length by Chauvenet, in "Spherical
    and Practical Astronomy", as "Longitude by Moon Culminations", writing half
    a century after Jefferson did. It's an alternative to lunar distances, but
    usable only from land.
    
    Jefferson attempted to persuade the Lewis and Clark expedition to carry
    with them, instead of the sextant, octant and chronometer, a theodolite or
    a "universal equatorial instrument". This latter was a telescope on an
    equatorial mounting with good scales for declination and hour-angle.
    Jefferson was familiar with these "surveying" or "astronomical"
    instruments, but not with the mariner's techniques that were in the end
    adopted. Lewis, and Ellicott and Patterson, politely ignored Jefferson's
    proposals, one of which was that in measuring time intervals between
    transit of the Moon and a star, "A portable pendulum for counting, by an
    assistant, would fully answer the purpose". This shows how out-of-touch
    Jefferson was.
    
    These matters are discussed in "The scientific instruments of the Lewis and
    Clark expedition", by Sylvio A Bedini, a contribution to "Mapping the North
    American Plains", ed. Luebke et al, Center for Great Plains Studies,
    Nebraska 1987. There's some interesting stuff in it, though Bedini gets a
    bit confused about lunar distances.
    
    How would such a measurement of longitude be made, using a theodolite? With
    Chauvenet's help, I see it like this.
    
    The theodolite is carefully levelled in a spot with a clear view of the
    Southern sky, and then one or more stars would be observed during their
    rise toward culmination, and later during their fall. Measuring their
    paired azimuths when at equal altitudes, and then splitting the difference,
    would give a precise value of azimuth reading that corresponded with due
    South. This is an important preliminary setup operation, that would
    probably take place on the night before the moon observation. It's
    essential that the theodolite doesn't get disturbed in the interim.
    
    Then (next night?) the Moon is observed as the centre of its disc passes
    that same Southern azimuth. An allowance has to be made, of course, for
    semidiameter, to get its centre from its illuminated limb. It's the timing
    of that moment that's needed. The Moon altitude is irrelevant, so there are
    no corrections for refraction or parallax. What is the time measurement
    referred to? To one or more known stars which transit near to the same time
    that the Moon does; Chauvenet suggests using 4 stars, two preceding the
    Moon and two following it.
    
    It's the difference between the Hour Angle of such a star and that of the
    Moon, deduced from that time difference, that is compared with the Almanac
    predictions for Greenwich, and interpolation then gives a value for
    Greenwich time at the moment of local Moon transit. So in some ways it's
    similar to observing a lunar distance, and places the same reliance on
    exact position of the Moon with respect to the star background. Local time
    is known, from the moment of transit of a known star, so Longitude can be
    calculated.
    
    This method presumes that Moon GHA was tabulated with sufficient accuracy
    and at small enough time intervals. This wasn't really true for the early
    Nautical Almanacs; mine, for 1767, provides Moon GHA only to an accuracy of
    one arc-minute, and at 12 hour intervals. Contrast this with lunar
    distances, which were tabulated to the arc-second (even if such precision
    was largely illusory), and at 3-hour intervals. I don't have easy access to
    the almanacs from 1803, which are relevant to Lewis and Clark's expedition,
    but expect that some Nav-L reader can kindly advise me how precise the
    predictions for Moon GHA were then.
    
    Judging by the hash that Lewis and Clark made, even of simple Sun
    altitudes, I greatly doubt whether they could have handled such a procedure
    as described above. Perhaps it's a good thing that Jefferson failed to get
    his way.
    
    I must confess that I find Jefferson's description (below) of three
    possible methods hard to follow, but it seems to me that his second method
    comes closest to Chauvenet's workable procedure.
    
    George.
    
    ================
    
    >One more  "longitudinal" quotation from the Lib o' Congress web site...
    >
    >From the  President of the United States, Thomas Jefferson, to William Dunbar
    >in a  letter dated May 25, 1805:
    >"While Capt. Lewis's mission was  preparing, as it was understood that his
    >reliance for his longitudes must be on  the Lunar observations taken, as
    >at sea,
    >with the aid of a timekeeper, and I  knew that a thousand accidents might
    >happen to that in such a journey as this,  & thus deprive us of the principal
    >object of the expedition, to wit, the  ascertaining the geography of that
    >river,
    >I sat myself to consider whether in  making observations at land, that
    >furnishes no resource which may dispense with  the time keeper, so
    >necessary at sea.
    >It occured to me that as we can always  have a meridian at land, that would
    >furnish what the want of it at sea obliges  us to supply by the timekeeper.
    >Supposing Capt. Lewis then furnished with a  meridian, & having the requisite
    >tables & Nautical Almanac with him, 1.  he might find the right ascension
    >of the
    >moon when on the meridian of Greenwich  on any given day. Then find by
    >observation when the moon should attain that  right ascension (by the aid
    >of a know
    >star) & measure her distance in that  moment from his meridian. This distance
    >would be the diference of longitude  between Greenwich & the place of
    >observation. Or 2dly. Observe the moon's  passage over his meridian & her right
    >ascension at that moment. See by the  tables the time at Greenwich when
    >she was on his
    >meridian. Or 3dly. observe the  moon's distance from his meridian at any
    >moment, & her right ascension at  that moment, & find from the tables her
    >distance
    >from the meridian of  Greenwich when she had that right ascension, which will
    >give the distance of the  two meridians. This last process will be simplified
    >by taking for the moment of  observation that of an appulse of the moon and a
    >known star, or when the moon  & a known star are in the same vertical.
    >
    >I suggested  this to Mr. Briggs, who considered it as correct & practicable
    >and proposed  communicating it to the Phil. society; but I observed that it was
    >too obvious  not to have been thought of before, and suppose had not been
    >adopted in practice  because of no use at sea where a meridian cannot be hand,
    >and where alone the  nations of Europe had occasion for it. Before his
    >confirmation of the idea  however, Capt. Lewis was gone. In conversation
    >afterwards
    >with Baron Humboldt,  he observed that the idea was correct, but not new &
    >that I
    >would find it in  the 3d vol. of Delalande. I recieved two days ago the 3d &
    >4th vols. of  Montuda's his of Mathematics, finished & edited by Delalande;
    >and find in  fact that Morin Y Vanlangren in the 17th century proposed
    >observations of the  moon on the meridian, but it does not appear whether
    >they meant to
    >dispense with  the timekeeper: but a meridian at sea being too impracticable,
    >their idea was  not pursued. The purpose of troubling you with these details
    >is to submit to  your consideration and decition whether any use can be made
    >of them  advantageously in our future expeditions, & particularly that up the
    >Red  river.
    
    ================================================================
    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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