NavList:

Tom,

I think the main reason that Cook mentioned that he could find the longitude within 30 minutes, specifically, was because this was the goal sought by the Longitude Act. He was affirming that this goal had finally been achieved by the modern tools and methods of lunars.

As for the statistical results mentioned in the student's video, we just don't know whether they're a correct representation of Cook's accuracy in finding longitude. We don't know the methodology that she used. It sounds like a reasonable method from the general description, and the numbers sound plausible, but until we know the details, that's all that anyone can say. One problem with Cook's lunars is that he describes locations and then gives their longitude by lunars. But we can't really be sure of the exact spot. His locations were rarely equivalent to stone markers and were often rather hazy topographic features like capes. Many can be identified today within a mile. In other cases, it's not that easy. Also, the longitude by lunar may have been extrapolated by DR from a previous or later observation. Those details have to be checked very carefully.

Cook's celestial navigation observations, including lunars, were performed by some of the most skilled observers of that period, so that's a plus. But their instruments were among the earliest attempts to produce high accuracy sextants (they weren't necessary before lunars came along), so that's at least an unknown and probably a negative. And of course, they cleared their lunars using some of the earliest tables available. The errors in the lunar distance tables were themselves rather high at those early Nautical Almanacs. The error cited for these lunar observations usually is the total system error, and I assume that's what the student calculated for the video. The actual error in the observations was certainly less.

For lunars today, using a well-adjusted sextant with a 7x scope (with good weather, on land), I get a typical standard deviation on individual lunars of about one-quarter of a minute of arc --roughly two-thirds of my individual lunars are as accurate as that. When sets of four are averaged, the error of the group is usually around half of that, as it should be when there's no systematic error. An eighth of a minute of arc error in a lunar corresponds to just about 15 seconds error in Greenwich Time which is just under four minutes of longitude or, in mid-latitudes, about three nautical miles error in position. I find that many, but not all, observers can get similar results under similar conditions. I have little doubt that Cook's observers would have gotten similar accuracy with better instruments and better lunar distance tables.

-FER

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