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