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    Re: "Time Sights" and Lines of Position
    From: Frank Reed
    Date: 2016 May 15, 12:30 -0700

    Doug MacPherson, you wrote:
    "a LOP can be easily obtained from the "time sight" information at hand by computing the Azimuth"

    Or you can do it by working the time sight twice with two slightly different latitudes (e.g. latitudes of 35.0 and 35.1). This is only slightly more work than determining the azimuth, and if you have a calculator it's an insignificant difference. For a modern navigator, a really substantial advantage of avoiding azimuths is that you can plot your lines of position on common graph paper instead of requiring conformal plotting sheets. But the key point here is that, once you realize you can get the LOP by working the time sight twice, the so-called "time sight" becomes a generic method for computing any LOP (with only a small adjustment and special procedure for sights very close to the meridian).

    You asked:
    "Did those navigators commonly obtain an LOP after the "time sight" calculation by computing an azimuth?"

    No, they did not commonly (either by azimuth or by second time sight). Lines of position were considered "fancy navigation" until late in the century. Plotting was for "college boys" and stuffy mathematicians. In the English-speaking world, the growth in the use of lines of position can be attributed in large measure to one of those stuffy mathematicians (actually we call him a physicist today) -- William Thomson, also known as Lord Kelvin, and his influence over T. S. Lecky who wrote about lines of position in his 'Wrinkles'. In earlier decades, navigators understood that they could simply advance their latitude by the usual dead reckoning. The computation then picks off a single point on the line of position (which always exists as the outcome of each celestial altitude, regardless of whether we calculate the whole thing or not) for that latitude. This was only problematic when no recent latitude was available, as in the prototypical case that Sumner outlined in his original book. For normal "good weather" navigation, you get the latitude at noon, advance it three hours based on course and speed, and then use that to work the 3pm time sight. This is generally sufficiently accurate, and you can easily work out the error by thinking about it in line of position terms.

    You may recall some scrap paper time sight examples that I posted three years ago. In fact, you yourself posted a message wondering if the anonymous navigator behind those calculators had independently discovered the Sumner method. Lars Bergman had discovered after analyzing those calculations that there were cases where the navigator had worked the same sight for two different latitudes. But there's no evidence that any line of position was plotted. The calculation result by itself provides all the information that we really require: it puts bounds on the possible longitude. Navigators back then had no concept of "error ellipses" and "error boxes" but I suspect that many of them would have thought of this in terms like that. That is, rather than seeing the result of the calculation as implying that the vessel was narrowly along a line running from one lat/lon pair to the other (and extending more or less linearly from there), they may have envisioned the vessel's position as falling in some "hazy" range with some general uncertainty with the calculations providing the bounds on that range.

    Frank Reed
    Conanicut Island USA

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