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    Re: Maskelyne's "British Mariner's Guide"
    From: Frank Reed CT
    Date: 2007 Jun 7, 21:06 EDT
    Sorry to take a while getting back to this topic. I've been working on generating sales for the new version of my historical atlas software.
    George, you wrote:
    "That's a remarkable work, containing all sorts of interesting stuff. Very advanced for its early date of 1763."
    Yes, it sure is. The lesson I take away from it's "very advanced" state is that everything that was needed to do lunars was readily available right from the beginning. They had it all worked out. There is a tendency to see a gradual evolution in the tools for lunars since the authors of later navigation manuals inevitably refer to their own works as "significantly better, easier, more accurate than any that have been published before" but it's really not the case. There were some incremental improvements, absolutely, but the plan as laid out by Maskelyne way back then was very complete.
    And you wrote:
    "Maskelyne impresses me by the clarity and precision of his careful explanations about a complex matter."
    Yes, it's very nice prose. There are some 18th century authors who wrote just miserable prose, John Harrison himself being a good example.
    "But the procedures for making those calculations, given in chap IV, (particularly in
    part 2 for the Moon) are mind-bogglingly complex. They were based on Mayer's
    observations and analysis. It would be an exceptional navigator who could
    meet the challenge of making those calculations at sea, though some managed
    to do so. "
    I don't find them particularly complex myself (on the second reading!), but the instructions sure are painfully dull to read if you don't have a compelling need. Working this calculation was harder than anything else a navigator would ever have done in that era, and it's the best case I've seen where a classroom experience would have been very helpful. Once you've plodded through a couple of examples, it's not difficult, but certainly time-consuming.
    And you wrote:
    "There's some unexpected stuff in the Mariner's Guide, including advice to
    mariners about the correct spacing of the knots in a log-line, and the
    timing of a sand-glass to go with it; a matter about which much confusion
    existed in 1763."
    Yes, it's a real measure of the primitive level of at least some navigation in this period that there was significant doubt over the length of a nautical mile. Maskelyne indicates that a reasonably correct value was known, but tradition-bound navigators were too stubborn or pig-headed to use it.
    A couple of interesting points from here and there in the book:
    Maskelyne mentions "error of adjustment" and says that this must be carefully assessed. This was the name for "index error" at that date. This gets back to a discussion we were having (where's Alex?) about Cook and co's sextant observations a decade later in the Pacific. The normal practice in this period was to "adjust" the sextant or octant before each use to line up the mirrors (and zero out what we would call "index error"). Maskelyne specifically suggests that this may not be desirable and proposes that it's better to leave the instrument alone and measure the residual "error of adjustment" by using the Sun's limbs, or multiple observations of the horizon, since that uses two or more observations that can be averaged instead of the common (active) adjustment procedure which involves only one single observation. Good point.
    In the preface, Maskelyne outlines the calculation of the quadratic correction [the "Q" in my "Easy Lunars" outline --google the archive at fer3.com/arc] and indicates that it was news to him at that time. This correction was later tabulated by Lyons so that it didn't have to be calculated with logs each time. It was in all of the navigation manuals (Moore, Bowditch, Norie) and was usually known as the "third" correction in later years. He clearly understands the conditions where this correction is small and indicates that they would have been minimal when the two objects were roughly in a vertical arc relative to each other (since it's proportional to the sine of the "corner angle" at the Moon in the Zenith-Moon-Star triangle).
    In his section on the instrument that should be used for measuring lunar distances, he mentions just about all of the features of a typical sextant from a century later. The way he describes it, it seems as if an instrument would have been custom made (and that seems likely).
    Maskelyne notes that an error in the altitudes of the objects is not important since an error of a degree would produce an error in the clearing process of only one minute of arc, which is about right for many typical lunar distance observations. For a 19th century observer, it would have been stated as "six minutes error in altitude" would produce no more than "a tenth of a minute error" in the clearing process (same thing, of course, just expressed differently). That distinction in the level of error that he's worried about clearly distinguishes Maskelyne's book from account of lunars written fifty years later. He was very happy to have errors of a minute of arc or so since he was only hoping for a longitude accurate to a degree or so. Expectations grew in later years.
    Anyway, there are lots of interesting bits of lunars trivia in the book. Since others may want to read it --Dan Allen mentioned he looked for it, I've made the pdfs available online:
    Later parts are numbered in sequence -2, -3, -4.
    42.0N 87.7W, or 41.4N 72.1W.

    See what's free at AOL.com.

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