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    Re: The Nautical Mile and the arc minute
    From: Frank Reed
    Date: 2015 Jun 5, 13:25 -0700

    Bob, you wrote:
    "For instance, there was an "aha" regarding the Sumner line in the first half of the 19th century, and the St. Hilaire method in the second half."

    Beware the histories of navigation published in navigation textbooks! While Sumner first discovered his method in 1837, it was a relatively minor footnote in navigation for decades. Even Bowditch's Navigator provided only a very brief paragraph on Sumner's method, and that did not happen until 1855. The real evidence for the history of navigation is not found in navigation manuals or math books. It's in logbooks and navigator's notebooks (and occasionally scribbled in the margins of some of those other books). You will not find a sudden "aha" shift in navigation with a transition to Sumner lines in the mid-19th century, nor will you find a sudden shift to the intercept method at the end of the 19th century. The critical fact here, which many modern navigators don't understand, is that the traditional "Old Navigation" methods yielded latitude and longitude with the same exactness as those more refined line of position methods. For a small boat navigator, sailing at the same rather leisurely speeds of 19th century sailing vessels, the old methods are every bit as good as modern line of position techniques.

    You also wrote:
    "At what point did people realize that the observed height of a celestial object equated, at the rate of 60 nm per degree, to the distance to the geographic point?"

    For latitude at least, this was understood from the dawn of the concept of astronomical position-finding which goes back to ancient classical astronomy in the Mediterranean region. When Eratosthenes measured the diameter of the Earth using the changing altitude of the Sun on the same date separated by a large distance on the globe, fundamentally he was determining the linear length of one degree on the surface of the Earth (equivalently the length of the nautical mile). The key measurement was not the change in the Sun's angular position, but rather the linear distance measured on the ground that corresponded to that angular shift. In later centuries, the concept that one degree of altitude change corresponds to one degree of position change on the sphere of the Earth was plain enough. The only tricky part was locking that down more accurately in terms of linear distance. The nautical mile or "sea mile" was a means of admitting that remaining ignorance and effectively defining it away. How far south have we travelled since noon yesterday? By answering, for example, 120 "nautical miles", we know exactly what that means as an angle across the Earth (120 minutes of arc) but we don't have to specify how far that is in feet or meters. The nautical mile is "however long it needs to be" to match one minute of arc motion across the Earth's surface as measured from the center of the Earth.

    You also wrote:
    "I find that in talking to novice navigators today, the relation between height-of-celestial-object and distance-to-GP-in-nautical-miles seems to come as a bit of an eyebrow-raiser...it seems to produce an "aha" moment when it is first introduced to them. "

    I agree. This should be a big "aha" moment for a novice navigator because it's the key to the whole problem. We're talking here about the fundamental principle of celestial navigation. And that is something about the teaching of navigation that certainly improved in the 19th century. You can credit Lecky, author of Wrinkles in Practical Navigation and also the man behind the Wrinkles, Lord Kelvin (William Thompson). Kelvin in particular was convinced that navigators should learn the circle of position concept as a primary principle in every aspect of celestial navigation, and he wrote to Lecky encouraging him to emphasize it in Wrinkles. You won't find this emphasis in many earlier works on celestial navigation. Lecky didn't have much patience for drawing and crossing lines of position, but he understood the importance of the idea conceptually.

    You also wondered whether the concept of great circle navigation might have helped navigators understand the idea that the distance in degrees from the sub-stellar point was equal to the observed zenith distance in degrees (again, the fundamental principle in celestial navigation). I really don't think that's the case, though obviously any navigator who has understood one concept will have an easier time understanding the other.

    You wrote:
    "I read Lecky's "Wrinkles..." and it seems that in the late 1800s, there were still sailors who were skeptical about great circle routes being the shortest distance between two points. Lecky had a section where he seemed to be engaging in a sort of "great-circle evangelism"."

    I would say that Lecky still needed to spread the gospel of the great circle because of a problem that haunts navigators even today: the damned Mercator projection. Navigators worship the Mercator chart like medieval pilgrims worshiping bits of "the true cross". Even map-makers make the excuse for the Mercator projection that "of course... it's useful in navigation". When you can see, right before your eyes, that a straight line from Japan to California heads east, as it does on a Mercator chart, you would have to be crazy to sail northeast. But of course a moment's reflection with a common globe, and the recognition that every flat map projection is misleading, should convince any would-be transpacific voyager that the shortest route is the great circle route across the ocean.

    Frank Reed

    PS: I wrote that the "nautical mile is 'however long it needs to be' to match one minute of arc motion across the Earth's surface as measured from the center of the Earth." This definition was so "slick" that it also became the basis for linear measurement in the metric system. One kilometer was defined originally as 'however long it needs to be' such that 100 of them make up one grad of arc as measured from the center of the Earth (with 100 grads to a right angle). The metric system "borrowed" the concept of the sea mile for the original definition of the meter. And from that origin, we're still left with the 'fun fact' today that 54 nautical miles is almost exactly equal to 100 km (the very small difference arising from later re-definitions).

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