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    Re: Longitude via lunar altitudes, simplified
    From: Frank Reed CT
    Date: 2007 Mar 12, 01:20 EDT
    Peter, you wrote:
    "Lunar distances, I would contend, have NEVER
    really caught on, in the sense of becoming an accepted and widely used
    method of establishing what was so sorely needed by navigators: their
    Not so. They were widely used. I have posted numerous examples from ship's logbooks. You cannot open a logbook from an ocean voyage, on American vessels at least, without finding examples of longitude by lunars in the period from about 1800-1850 (I haven't studied earlier logbooks). They were *not*, however, used "just like a chronometer", which is what many modern commentators on celestial navigation are expecting. In other words, one did not shoot lunars every day the same way that navigators fifty years later looked at the chronometer every day. There are a variety of reasons for this which I've discussed before. I won't get into it again right now.

    And you wrote:
    "Yes, dedicated navigators from Cook onwards used them (Cook thought
    they solved the longitude problem). But those who did use them
    successfully on a regular basis tended to be professional navigators
    such as were found on naval vessels and similarly well organized
    Nope. That's wrong. Lunars were widely used by navigators with humble backgrounds. Anyone who could do the math required to use a chronometer to get longitude could also do the math required to clear a lunar distance.
    "If lunar distances never really caught on its not because chronometers
    appeared at much the same time, as these contraptions had their own
    problems. The main limiting factor here was their great cost, compared
    even to the cost of a ship. It wasn't until the cost came down due to
    (relative) mass production techniques that chronometers became
    widespread and most mariners could move across oceans with a
    reasonably good idea of longitude."
    That's right. The part that most people miss is that it took as much as 75 years for chronometers to become sufficiently inexpensive that they were used almost everywhere.

    "This seems to me to miss the point. If so many of those who needed
    longitude were unable to derive it because of their perception of the
    difficulties of calculation, then that was a very real drawback. They
    were not, typically, men of much training in astronomy or mathematics."
    From this statement, I have no doubt, Peter, that you have never studied the methods that were available. Now please don't get your feathers ruffled, but you are repeating an old MYTH. The mathematical techniques and skills required to clear a lunar distance by the methods commonly available were EXACTLY the same as those required to clear a time sight (which was an essential aspect of using a chronometer). There were, of course, many "fancy" methods for clearing lunars, which entertained the mathematically inclined, but they were not necessary to daily navigation. The total time required to work a lunar was longer --about fifteen minutes, compared to about five for a time sight (longitude by chronometer), but the mathematical skills and steps were almost identical. I've posted on this topic many times including documentary evidence of actual worked lunars from logbooks where it is clear that the steps are the same as for a time sight. I guess it's time to start repeating myself. :-)
    "Specifically; they did not have Bruce Stark's tables or Frank Reed's
    web site to help them with the mathematical challenges of clearing
    lunar distances."
    There were *numerous* easy methods for clearing lunars as far back as 1780. By 1800, there were twice as many. By c.1835, when chronometers were rapidly becoming common, even aboard vessels commanded by frugal Yankees, methods for clearing lunars, easily and rapidly, were widely known and commonly taught. The legend of mathematical difficulty arose later in the 19th century from two sources: First, lunars had become an instrument of torture for navigation students. They were certainly no longer used after about 1850, but by forcing students to learn several different clearing methods, navigation instructors could find new ways to make their art look more difficult and to "separate the wheat from the chaff" in their classrooms. Second, armchair navigators, who generally were (and are) more impressed by lunars needed a theory to explain why sea-going navigators were no longer using such wonderful techniques of nautical astronomy. The most commonly developed armchair theory was that it was all a problem of mathematical difficulty. There's simply no truth to this. When you look at the documents from the era, it is clear that navigators stopped using them simply because they were no longer necessary. They didn't complain about the math ever --not until those late 19th century classes.
    And you wrote:
    "Joshua Slocum WAS a master navigator; a clever and resourceful
    professional ship's captain who, when his ship washed up on a sandbank
    off the coast of Brazil, was quite capable of building a smaller boat
    from the remains and sailing it home to New York. Yet the one time (at
    the end of the nineteenth century) that he reports having made a
    successful lunar distance observation and calculation while sailing
    around the world alone in a yacht he makes such a song and dance about
    it, and congratulates himself so thoroughly on eventually achieving
    what he clearly saw as a difficult feat (including, according to him,
    needing to correct his log tables as part of the process) that we are
    left in little doubt that it was an operation rarely performed."
    Slocum's single lunar distance observation on his circum-navigation was taken when he was BORED. He did it, not because he needed it, but because he wanted to exercise his mind. It had been fifty years since lunars were a normal part of navigation (and even back then, c.1850, only as an occasional check on the chronometers). Slocum's comments on lunars are an epitaph for a dead art, not evidence of common practice.
    "Pity the poor navigator then, largely still without longitude."
    An alternate lesson to be taken from Slocum's description of his navigation is that it is not hard at all to sail without longitude --just as long as you're able to pick the time of your sailing and your destination. Of course, by the 1890s when Slocum was working his way around the globe, chronometers were ubiquitous and unremarkable. Even ordinary clocks, not designed to be chronometers, were often good enough by this date that they could serve to keep the longitude (more accurately than dead reckoning) for as much as a week.
    "This is the context in which an easier alternative; that of deriving
    longitude via measurement of lunar altitudes, should be considered.
    Put most simply, it is a much easier ask. "
    I agree with you that for a MODERN student of navigation, it is certainly easier to work up altitudes because the techniques have been perfectly honed and put into tabular form during the past century. But any modern navigator could learn to use something like Thompson's Tables for lunar distances (republished as the "third method" in Bowditch from 1837 to 1880) if they were updated a bit to reflect modern taste in terminology and style. The mathematical difficulty is minimal.
    But this all gets us back to the main question facing anyone who's thinking about lunar distances: why bother?? There are as many answers to this question as there are students of navigation but "practicality" ranks very low on the list.
    "And the price of that, it
    seems, is its relative lack of accuracy (although bear in mind
    that the results of lunar distances are also limited in accuracy)."
    Longitude by lunar altitudes is typically TEN TIMES less accurate than longitude by lunar distances. That's the intrinsic error. On top of that you have to add the usual errors of observation and sextant adjustment. Those folks in the 18th and 19th century that invented all of this weren't blind, and they weren't stupid. They knew all about getting longitude by lunar altitudes. They studied it and analyzed it. And they rejected it with good reason.
    And you wrote:
    "As the idea keeps getting reinvented I can only conclude that
    it never became well known."
    That doesn't follow. It is re-invented every few decades today because lunars and all the discussions and arguments that went with them are simply buried in history --and they were already buried 150 years ago. This was all discussed ad nauseam 200-250 years ago. They were smart guys, and they got it right. But we on this list can do a little something to correct the mis-conceptions. And one of those mis-conceptions is the idea that longitude by lunar altitudes would somehow have made things better, made lunars more practical, if it had been discovered earlier. That just ain't so.
    42.0N 87.7W, or 41.4N 72.1W.

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