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    Re: longitude by lunar distance
    From: Frank Reed
    Date: 2012 May 10, 11:03 -0700

    Hello Paul,

    You wrote:
    "I always thought that lunar distance measurement gives accurate GMT and then one uses the GMT to calculate longitude by using sun/moon line-of-position (LOP)."

    Well, for the most part lines of position were not used in the nineteenth century, certainly not in the first of half of the century. Lunars were essentially over and done with at sea by 1850. But in modern "LOP terms", you would observe an altitude of the Sun nearly simultaneously with the lunar observation and keep count of the time until the lunar is taken, with a watch or by counting seconds. Then you clear the lunar observation to get GMT. Then you subtract out the seconds that passed between the Sun observation and the lunar. That gives you the GMT at the time of the Sun observation. Then you would use that GMT to work up the Sun LOP.

    You added:
    "In Joshua Slocum's book Sailing Alone Around The World, he states that the longitude is the difference between GMT (obtained by lunar distance) and Local Mean Time - LMT ("finding it is a simpler matter" p.104)."

    Right. Finding local time is a simple matter, which would have seemed superfluous to explain for any navigator in the 19th century. Today it's called a time sight. We worked some traditional time sights in the class I taught this past weekend at Mystic Seaport. As I describe it, "a time sight turns your sextant into a sundial". The local time we're looking for really is just "sundial time" (that's actually LAT, we convert it to LMT by adding or subtracting the equation of time). Any altitude of the Sun, so long as it's not too close to the meridian, is a measurement of local time. Then of course, we compare local time with GMT (from the lunar or from a chronometer) and the difference is longitude at the rate of 15 degrees of longitude per hour difference in time.

    "My confusion rises from the fact that the LMT has to be accurate, since an error of four minutes equals one degree. Slocum's alarm clock did not even have a minute hand, so how did he accurately calculate LMT? He claims longitude accuracy of a few miles."

    Slocum informs us that the minute hand was gone during his passage through the Indian Ocean. But in any case, he wasn't using it for celestial navigation. He was, almost certainly, using for it for dead reckoning navigation. He would record how long he had traveled on a particular course at some speed and then do the math to figure out his new DR lat and lon. When Slocum refers to that little clock as his "chro", he is just being cute. Back then, it was probably obvious to anyone who understood even the rudiments of navigation, but today it's a bit confusing. He wasn't using it as a chronometer in any way.

    But suppose Slocum had in fact brought his chronometer with him. You recall he owned one but decided against paying up to have it fixed since he seemed to have decided that traditional, non-mechanical navigation would be more suited to his goal in this leisurely circum-navigation. If he had brought his chronometer, he STILL would have faced the problem of finding LMT. The chronometer yields GMT and we have to compare that with the local time. So every single navigator at sea who used the stars for longitude necessarily had to learn how to work a time sight. It was the second most common sight in the nineteenth century, after latitude by Noon Sun.

    Back to lunars, note that you have to measure the altitudes of the Sun and Moon to clear the lunar anyway, so it was common to use the Sun's altitude as measured during this process to get the local time to compare against GMT. This wasn't strictly required though. If a navigator had a good common watch, an observation for local time hours earlier was just fine. As I noted above, you simply correct for the time difference (though if the interval is long enough and the vessel's course is not north/south, you also have to make some allowance for the change in longitude between the local time observation and the lunar).

    -FER

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