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    Re: Sun Moon Lunars to 155 degrees
    From: Frank Reed
    Date: 2010 Apr 5, 04:38 -0700

    Antoine wrote:
    "However, they are just a reminder - maybe a true discovery for some of us - about the EXTRAORDINARY DIFFICULTY to carry out all such computations at sea on a moving vessel. There were so many opportunities for blunders, that it is ABSOLUTELY AMAZING that they so consistently kept performing their Lunars and Longitude computations almost to such "perfection" given the tools they had at hand ! They were certainly close to perfection"

    Extraordinary difficulty? No. You're judging this from trying to reverse-engineer published sights, and in this recent case, you're reverse-engineering sights that were absolutely unique, extreme cases in the history of navigation. This is an entirely different task from taking and working normal navigational sights at sea. First of all, the observations by Wales and Bayley have been cleaned up for publication (please note: before anyone panics, I'm NOT saying they've been "doctored" or anything like that --I'm simply saying that they've been cleaned up in the same way that any scientific observations are prepared for publication). You don't see any of the intermediate steps. Second, there are aspects to this that are much easier when you're working from day to day on observations. You never have to stop and ask whether you should add an extra 12 hours at some point, as we do today, because you go to your present location on the opposite side of the globe one day at a time. Third, with the very singular exception of calculating the lunar distances directly from the tables, none of this was any more difficult than the ordinary process of a time sight. It took longer --15 or 20 minutes-- to clear a lunar, while a time sight took 5 minutes or less, but the principles, the tools, the mental and calculational skills required, etc. were all the same.

    If you want to judge the calculational difficulty of lunars THEN YOU NEED TO TRY OUT SOME OF THE POPULAR HISTORICAL METHODS. I strongly encourage you to download an edition of Bowditch's Navigator from the early 19th century if you haven't already. There are links for this under "Resources" right at the top of the main NavList page here: http://fer3.com/NavList. Specifically, I recommend that you download the 1837 edition. Then pick any set of lunar data and try the clearing process. Good choices would be Methods I and II (respectively, Bowditch's Revised/Preferred Method first published in 1804 and Thomson's method first published in 1825 --both fundamentally similar as series methods but rather different in terms of the calculational steps). Begin reading on page 228. The methods themselves are outlined on pages 231 and 239. Also, in order to make a valid comparison, you should work some time sights by Method I of Bowditch --see pages 208-209 of the 1837 edition. Unfortunately, the language is archaic and there are editing errors, and of course, it's English. If those older sources don't appeal to you, then try the appendix on clearing lunars published in the "Abridged Nautical Almanac" early in the 20th century c. 1915. The math was not difficult AT ALL but it was a little time-consuming and definitely dull.


    And you wrote:
    "It brings my reflexion to another point now. It has always stunned me that the Marcq Saint Hilaire method was discovered so late in CelNav History. For us it is so simple, so much easier than Lunars."

    Many commentators have argued, and I think it's at least worth considering, that the advantages of methods involving celestial LOPs became dominant fundamentally because vessel speeds increased significantly in the late 19th century. You can decide for yourself whether that makes sense.

    But you're making a comparison here that doesn't fit: it wasn't the "Marcq St Hilaire" intercept method versus "lunars". Lunars died out much earlier. It was the "Old Navigation" (lat by Noon Sun, lon by Time Sight, usually of the Sun) versus the "New Navigation" (the various versions of the intercept method, usually involving stars during twilight in addition to daytime sun lines).

    And you wrote:
    "A possible explanation might be this one :
    For decades, if not centuries before MSH, Positions computations were and HAD TO BE carried out separately for each coordinate :
    - an (easy) computation for Latitude, and
    - a dreadfully difficult one for Longitude."

    You're right about the separation of lat and lon, but no way was the calculation for longitude "dreadfully difficult" --EVEN when lunars were in their 75-year-long heyday c.1770-1825 (British vessels), c.1790-1845 (American vessels). And even after lunars were dropped, navigators continued to use the methods known as the "Old Navigation" (separate sights for latitude and longitude) for many decades. Aboard a large percentage of merchant vessels, they were still using Noon Sun for latitude and time sights for longitude even in the 1940s. The reason for this is simply that the "Old Navigation" worked and worked well. The "New Navigation" of LOPs and especially the intercept method was more versatile but not enough to change minds for nearly a century.

    And you wrote:
    "On top of that, just add that - until the 1830's or so - they kept playing with a "non uniform" time variable, i.e. the Apparent Time which had for effect of providing them with so many additionnal opportunities for blunders ..."


    What blunders?? This was no issue. Antoine, I fear that your very intense and detailed focus on delta-T, the oblateness/flattening of the Earth, and other such calculational minutiae has led you astray. There was no difficulty working with a "non-uniform" time variable, at least no more so than our modern difficulties with things like "Daylight Saving Time". Even as chronometers became dominant, there was only a very minor inconvenience during the transitional period. Apparent Time was quite normal to them and indeed it was known as "true time" in distinction from the 'mechanical' time provided by clocks. Of course, just as today, any navigator contemplating these methods must go through a brief learning period, getting used to the difference between "Apparent Time" and "Mean Time". But we get over that soon enough.

    And you wrote:
    "I think that any kind of MSH method could not have emerged until the Lunar calculations definitely belonged to History. Navigators must have been fed up then with their extraordinary complex Navigation computations until they could definitely do without Lunars thanks to reliable Chronometers, and also until thay were given the opportunity of using Greenwich Mean Time instead of Local Apparent Time. Only by that period could they and did they have enough time to "relax" and think of "inventing" new ways of tackling Celestial Navigation."

    For the actual navigators themselves, that theory doesn't seem to fit the historical evidence. You can easily find examples of British navigators, for example, noticing that no one has used lunars in vessels that they have served on in decades --and they were writing in the 1840s and 50s. Lunars were apparently gone from (better-equipped) British vessels at least 20 years before they faded away on American vessels, so that means by 1825 or so. It was 60 years before celestial LOPs began to make a regular appearance. But you have a good point here when it comes to shore-bound nautical astronomers and mathematicians and lunarian enthusiasts, like H. Wilberforce Clarke. Many of them continued to "beat the dead horse" of lunars mathematics even as the intercept method was beginning to make its appearance. Lunars were just too appealling as a mathematical game. There were so many ways to transform the problem and re-arrange the mathematical terms and tables. Even Chauvenet, a brilliant mathematician, wasted a couple of years developing a new method of clearing lunars when excellent methods were available already and well-known. His time might have been far more productively spent on the consequences and implications of Sumner's method, which gets minimal treatment in his great two-volume work on "Spherical and Practical Astronomy". But there's no use worrying about histories that "might have been"... There's only one history of navigation.

    Back to this myth of the painfully difficult math of lunars... It dates from the two extreme ends of the historical timeline of lunars. At the very beginning of that timeline, c.1765, lunars were exceedingly difficult, requiring some four hours of calculation, because the navigator had to generate his own lunar almanac data, calculating the actual position of the Moon from Mayer's tables. This was real labor, and yet even here, if you read Maskelyne's "British Mariner's Guide" from 1763 you will find nothing beyond ordinary means. After the publication of the Nautical Almanac, which was specifically designed to eliminate most of that horrible chore, there was a great variety of methods for clearing lunars, some easy, some torturous, and this variety kept things confusing for a while. But by about 1800, that confusion had all settled out, and there were several easy, well-organized methods for clearing lunars not significantly different from methods for working common time sights. You'll find these methods published in most any of the navigation manuals of that era. And lunars are found in the logbooks regularly when they are needed throughout this period in the first-half of the 19th century. Then at the opposite end of the timeline, the myth of the difficulty of lunars math re-appears in the late 19th century when navigation students were being forced to clear lunars by rote for the purposes of certain licenses and certifications, working every calculation to the last second of arc when they all knew that the instruments of the day would only read reliably to the nearest 30 seconds or so. This was an onerous and unfortunate system that guaranteed lunars would be remembered as "painfully difficult". And finally, after the lunar distances ceased to be published in the almanacs, some would-be lunarians had to calculate the geocentric lunar distances themselves, roughly doubling the amount of work in the calculations.

    We have to be careful not to confuse our own efforts to calculate very fine astronomical details of lunar distance observations in modern computer code, at precisions far beyond any necessity, with the reality of lunars as actually practiced in the period when they were practical tools. Again, the proof is in the logbooks. If you want to understand the history of navigation, look to the papers and notes of navigators.

    -FER


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