NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
What were the Lunar Distances for?
From: Jan Kalivoda
Date: 2002 Dec 26, 17:16 +0100
From: Jan Kalivoda
Date: 2002 Dec 26, 17:16 +0100
I am sorry that I touch this topic again. I had thoroughly studied your discussion of the past months about the matter and, thanks to George Huxtable, Cotter and some older German-written literature, I am informed about this navigational method and its background. Thank you very much, Mr. Huxtable, for your effort, enthusiasm and above all for your wit and knowledge. But I should repeat the question: What were the L.D. useful for? Let us consider the limit of their inherent errors. We can put pure personal errors of observation aside in a forlorn hope that they will be averaged in greater sets of shots. But take the instrument error. When measuring lunar distance, we must guess its value at 1 minute of arc for sextants from the year 1800 and at half a minute of arc for the year 1860 and for our times. The second important error was the one of the Moon tables. Up to 1810 the original table of Tobias Mayer (edited by Maskelyne as "Tabulae motuum Solis et Lunae" in 1770) was being used for computing the lunar distances in almanacs. Its internal accuracy for Moon's positions in ecliptical coordinates was 1 minute of arc, as Mayer himself stated. (This was the cause or pretence for the fact, that Mayer's widow obtained "only" 3000 pounds from the Board of Longitude, in comparison to 24000 pounds for Harrison.) Between 1810 and 1860, Laplace, B�rg, Burckhart, Pierce and Hansed improved this accuracy to 25 seconds of arc. Only after 1883, when all great almanacs adopted Newcomb's corrections for calculations, the accuracy of Moon's tables rised to 1 (one) second of arc. But it was too late then, "lunars" were as dead as Julius Caesar already (as Lecky in his "Wrinkles" said. Today, the accuracy of Almanac is not an issue, but this is compensated for by difficulties of observing distances from small boats and related errors.) Combining these two factors together, we must cope with the maximum error (not along the Gauss curve, but with the quadrate distribution, thus much more frequent) of 2 minutes of arc in the lunar distance for the year 1800 and 1 minute for 1860. This error created an error of 4/2 minutes in the GMT obtained and 60/30 minutes of longitude, respectively. (Sometimes twice more, according to the effect of the change of paralax near the zenith, as George Huxtable very cleverly emphasizes.) What could a sailor achieve on the basis of this piece of information? He could not rate his chronometer by lunars regularly, as the rate acquired would be too irregular (if intervals had been short) or not reliable (if intervals had been long, according to the varying temperature influence on the chronometer rate) or both (between). And he could not check his D.R. navigation continuously, as the inaccuracy of lunars (30 - 60 minutes of longitude) equals 10 - 30 % of daily run with sailing ships and the first steamers (we should omit the best runs of the best clippers). I can imagine only two modes of using lunars for navigation in the past - firstly, the check of D.R. position before a landfall when finishing a long deep-see passage. But even then, owing to inaccuracy of lunars, so called "easting/westing" from the target and the final latitude sailing would be necessary, only the initial amount of this deliberate longitude deflection could be smaller. And secondly, one could roughly check his lone chronometr by lunars - when the chronometer time fell within four (two) minutes of time found by lunars, the chronometer could perhaps be relied upon. Otherwise, it was to be neglected and latitude sailing (see above) took place. Even so, I wonder if many captains in the merchant sailing fleet used the lunars regularly. Maybe, I will be advised differently by you. I hope so and thank you in advance. Jan Kalivoda